THE UNIVERSITY OF M I C H IGAN COLLEGE OF ENGINEERING Department of Nuclear Engineering 125 Te 5 MOSSBAUER EFFECT STUDY OF RADIATION EFFECTS AND MAGNETIC HYPERFINE STRUCTURE IN TELLURIUM COMPOUNDS John F. Ullrich Dietrich H. Vincent ORA Project 07921 supported by: NATIONAL SCIENCE FOUNDATION GRANT NO. GK-871 WASHINGTON, D.Co administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR July 1967

This report was also a dissertation submitted by the first author in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan, 1967.

ACKNOWLEDGEMENTS I am deeply grateful for the patient and helpful guidance and advice provided throughout my academic career, and most particularly through the course of this work, by Professor Dietrich Vincent o The advice and assistance on numerous aspects of the research by the other members of the doctoral committeeProfessor A. Ziya Akcasu, Professor Chihiro Kikuchi, and Professor Paul Go Rasmussen, are also deeply appreciated. I want to express particular thanks to Mro Poh-Kun Tseng for his kind help and many interesting discussions I am grateful to the entire staff of the Phoenix Memorial Laboratory for the technical and administrative help they providedo Particular thanks are due the personnel of the Ford Nuclear Reactor for their assistance in many sample irradiations, but morc-r particularly for their willing cooperation in monitoring experiments and filling with liquid nitrogen during overnight runs. Financial support of the research was provided by the National Science Foundation (Grant GK 871) o Support in the early stages of the research was provided by the National Aeronautics and Space Administration (Grant NsG-115-61) and the Michigan Memorial-Phcenix Project (Project 310) Financial assistance during my academic career was provided by three Atomic Energy Commission Special Fellowships in Nuclear Science -ii -

and Engineering and a University of Michigan Rackham Predoctoral Fellowship. I would like to thank Miss Helen Walker for the excellent job done in preparing the final manuscript under rather trying circumstances. The most heartfelt expression of gratitude is due my wife, Sue, for her untiring support and encouragement during the course of this thesis. Our children, Frederick, Kathryn, and Amy, also deserve recognition for the enjoyable respites they provided. -iii

CONTENTS Page ACKNOWLEDGEMENTS OO o o.. o o. o o o o o o o e o o.. o o. e 0. ii LIST OF TABLES.......................................... viii LIST OF FIGURES........... 0 0........................ i ABSTRACT o o o...................... o o o o o o o................... x Chapter Io INTRODUCTION.o,.................................. 1 Ao Motivation for Present Study.....o...o.. o.., 1 Bo Literature Survey....................... 4 1o Radiation Effect Measurements Using the MMssbauer Effect.......................... 4 2 Neutron Capture Effects................. 7 3. Radiation Effects in PbTe and Te Metal.... 8 a. PbTe. o............... o o o o 0.. e o. o o o o.. 8 b. Te,.oooooo...*.....o................oo 9 4, MIssbauer Effect Measurements Using Te 12 10 II. BACKGROUND o o.............o o o o o o o... o o o 0 o 13 Ao Selection of Suitable MOssbauer Nuclide for Studies of Neutron Capture Effects. 0.......... 13 Bo Thermal and Fast Neutron Effects in Tellurium Compounds.................................... 16 1. Thermal Neutrons................. o o o. 16 2. Fast Neutrons............................. 20 Co Characteristics of Mbssbauer Spectra in TeT25. 24 1. Decay Scheme of Te 25m 0 0 0... o.... 24 2 Msbar Rcoilsser Reco s Fraction oo.....o... 27 -iv

Page 3. MSssbauer Hyperfine Structure............ 29 a o Isomer Shift. o o....... o......o o 30 bo Quadrupole Splitting................ 32 Co Magnetic Hyperfine Splitting......... 36 4o Possible Effects of Neutron Capture Induced Displacements on Mbssbauer Spectra o.................................. 41 III. APPARATUS AND EXPERIMENTAL PROCEDURES............ 48 A. M6ssbauer Spectrometer....................... 48 1. Drive System............................. 48 2. Cryostat................................. o o o o o o 54 3. Detection System........00.................0000000 57 B. Source and Absorber Preparation.............. 60 1. Sources oo.................................. 60 a o PbTe.... o...................... o o o.. o o.... 61 b. Te Metal................ooo o oo o o............. 62 Co TeO2 o. o.. o e e o o o o o o o.............................. 62 2. Absorbers. o o oo................................oeo ooooooooooo oooooo 64 c. CuCr 2Te4o. o o........ o o o o o o o o o................... o 71 d o MnTe o................................. 71 e. CrTe................................. 71 fo H6TeO6................................ 72 Co Source Irradiations o o o. o o. o o o o o o o o o o o o............ o o 72 IVo EXPERIMENTAL RESULTS COF THE RADIATION EFFECTS MEASUREMENTS...............................o o oo o o o o o o o o o...... 75

Page 1o Results................................. o o o e o o o o. 76 2 Discussion of the Data................... 78 a Radiation Effects.................... 78 b. Line Width. o... o o o... o..... o o 79 Bo Te Metal................................ 81 1o Results.............................. 81 2. Discussion of the Data............. 84 a. Quadrupole Splitting o............., 84 b. Asymmetry........ oo...........oo.. 86 C o TeO o o o e o o o o o.......o o o o o o. 87 1. ResultS.o.oo....oo..ooco......c...oo.... 87 a. Radiation Effects..,,.,,............ 87 b. Absorber Measurement...........o.... 89 2. Discussion of the Data.................... 90 D. Discussion of the Radiation Effects Measureme RInste n tyo o, o, o............ o...... o o.. 92 1. Resonant Intensity....................... 92 2o Reasons for the Observed Results..... o o 95 a Recoil Energy....................... 95 b. Replacement Collisions..o............ 96 Co Defect Annealing O........o....o..... 98 do Hyperfine Interactions..ooo....o.. o 98 Vo EXPERIMENTAL RESULTS OF MOSSBAUER EFFECT MEASUREMENTS IN OTHER TELLURIUM COMPOUNDS...o o o......o. 100 A CuCr2Te4 o o.. o o.................. o.. o o. 100 1. Results.o......oo......ooooo.....o.......o. 101 a. Interpretation of Observed Spectrum.o 103 b. Hyperfine Interaction Parameters..... 104 -vi

Pae 2. Interpretation of the Data o............. 107 a. Crystal Structure and Spin Configuration......e.................... 107 bo Superexchange Interactions........... 110 c. Transferred Hyperfine Field......... 112 3. Magnetized Absorber Measurement.......... 114 B. MnTe......................................... 116 1. Results.................................. 117 2. Discussion of the Data................... 117 C. CrTe.....o..........O........o.............. 123 l. Results e o o o o o o o o o.............................o o o.....o o o 123 2. Discussion of the Data................... 125 Do H.Te6....................... o 128 1. Results..o...................o o.......... 128 2. Discussion of the Data.............o..... 130 E. Isomer Shifts in Tellurium Compounds......... 130 APPENDIX Ao SUMMARY OF RADIATION EFFECTS MEASUREMENTS USING THE M6SSBAUER EFFECTo.....0...,,,,.. 134 APPENDIX B. CIRCUIT DIAGRAMS OF MAGNET FIELD SUPPLY AND DRIVE AMPLIFIER o....o.............o.... 138 APPENDIX Co DESCRIPTION OF DATA ANALYSIS PROGRAMS....... 141 Ao Least Squares Curve Fitting............. 141 Bo Data Analysis Program................... 146 lo Main Program....................... 146 2 Theory Subroutine................... 148 C. Listing of Computer Programs............ 151 1o Main Program..................... 151 2. Theory Subroutine (Sample).......... 157 REBERENCES. 00.00000. ooo o oeooo oooooeo ocooooo aooooooooooooo e 159 -vii

TABLES II-1. RELEVANT PARAMETERS FOR MOSSBAUER NUCLIDES WITH ISOMERIC STATEP PAENTS POPULATED BY AN (n,W) REACTION.o.................................. 15 II-2. PARAMETERS RELATING TO FAST NEUTRON INDUCED DISPLACEMENTS IN TELLURIUM SOURCE MATERIALS o.... 23 III-io MEASURED THICKNESS AND ESTIMATED LINE WIDTH FOR TELLURIUM ABSORBERS.......................... 69 III-2. IRRADIATION CONDITIONS FOR Te125 SOURCE MATERIALS FOR RADIATION EFFECTS MEASUREMENTS..... 73 IV-1. PARAMETERS FROM PbTe RADIATION EFFECTS DATA..... 76 IV-2. PARAMETERS FROM Te RADIATION EFFECTS DATA...o.... 83 IV-3. PARAMETERS FROM TeO2 RADIATION EFFECTS DATA AND ABSORBER MEASUREMENT....................... 89 V-1. PARAMETERS OBTAINED FROM SIX LINE FIT TO RESONANCE ABSORPTION SPECTRA OF CuCr2Te4......... 105 V-2. PARAMETERS OBTAINED FROM SINGLE LORENTZIAN FITS TO M([SSBAUER SPECTRA OF H6TeO6, MnTe, AND CrTe..... o................... o o o..............o o o..o e o o o o.. 119 V-3. ISOMER SHIFTS FOR VARIOUS TELLURIUM COMPOUNDS WITH RESPECT TO A PbTe SOURCE................. o o o 131 A- o SUMMARY OF RADIATION EFFECTS MEASUREMENTS USING THE MOSSBAUER EFFECT....................... 135 -viii

FIGURES Page II-1. DIAGRAM OF Te124 (n,,) Te125 RECOIL MECHANISM..... 17 11-2. Te125m DECAY SCHEME............................. 25 II-3 RELATIVE LOCATION OF X-RAY AND GAMMA RAY ENERGIES IN DECAY OF Te125m. o............... 26 II-4. MAGNETIC HYPERFINE SPLITTING OF THE 3/2 + AND 1/2 + STATES OF Te125..................... 37 11-5 "g-FACTOR DIAGRAM" SHOWING THE RELATIVE LOCATION OF MAGNETIC HYPERFINE STRUCTURE LINES AS A FUNCTION OF THE RATIO OF THE EXCITED STATE TO GROUND STATE g VALUES.............. 38 II-6. (a) LEAD TELLURIDE CRYSTAL STRUCTURE........... 43 (b) FRENKEL DEFECT IN LEAD TELLURIDE LATTICE... 43 III-1 SCHEMATIC OF THE EXPERIMENTAL SYSTEM............. 49 I I -2. CRYOSTAT........................................ 55 III-3. Te125m GAMMA AND X-RAY SPECTRUM TAKEN WITH A XENON-NITROGEN PROPORTIONAL CObUNTER USING: (a) NO X-RAY FILTER, AND (b) 5 Mil Cu X-RAY FILTER oo.. o.........................................o 59 III-4. OPTIMUM EFFECTIVE ABSORBER THICKNESS FOR MAXIMUM INFORhMATION o o o................ 68 IV-lo RESONANCE ABSORPTION SPECTRUM FROM THE PbTe SOURCE AND PbTe ABSORBER BEFORE AND AFTER ANNEALING....................................... 77 IV-2. RESONANCE ABSORPTION SPECTRUM FROM THE Te SOURCE AND PbTe ABSORBER BEFORE AND AFTER ANNEALING...oo......o........oo....o o....... 82 IV-3. (a) PROJECTION OF TELLURIUM CRYSTAL STRUCTURE (DIFFERENTLY SHADED CIRCLES REPRESENT ATOMS AT DIFFERENT LEVELS.......oo............. 85 (b) TELLURIUM CRYSTAL STRUCTURE......o.... o 85 IV-4, RESONANCE ABSORPTION SPECTRUM FROM THE TeO2 SOURCE AND H TeO ABSORBER BEFORE AND AFTER THE SOURCE RECRYsTALLIZATIONo........ oo.......... 88 -ix

Page IV-5. RESONANCE ABSORPTION SPECTRUM FROM A PbTe SOURCE AND TeO2 ABSORBER.................... 91 V-I. RESONANCE ABSORPTION SPECTRUM FROM A PbTe SOURCE AND CuCr2Te4 ABSORBER (53o5 mg/cm2)...... 102 V-2. CRYSTAL STRUCTURE OF CuCr2Te4 SPINEL............. 108 V-3. PREDICTED MAGNETIC HYPERFINE SPECTRA IN CuCr2Te4 WITH ORIENTED INTERNAL FIELDS ( RANDOMLY ORIENTED (MEASURED SPECTRUM), - PERPENDICULAR TO GAMMA-RAY BEAM, - PARALLEL TO GAMMA-RAY BEAM)............................... 115 V-4. RESONANCE ABSORPTION SPECTRUM FROM A PbTe SOURCE AND MnTe ABSORBER......................... 118 V-5. CRYSTAL STRUCTURE OF MnTe AND CrTe (NiAs)........ 120 V-6. RESONANCE ABSORPTION SPECTRUM FROM A PbTe SOURCE AND CrTe ABSORBER........................ 124 V-7. RESONANCE ABSORPTION SPECTRUM FROM A PbTe SOURCE AND H6Te06 ABSORBER. e...................o 129 B-l. CIRCUIT DIAGRAM OF MAGNET FIELD SUPPLY.......... 139 B-2. CIRCUIT DIAGRAM OF DRIVE AMPLIFIER.............. 140

ABSTRACT The purpose of the first part of this study was to experimentally determine the effects of neutron capture induced defects on MOssbauer hyperfine spectra in Te125 Thermal neutron capture in Te124 is used to simultaneously produce the M6ssbauer isomeric state parent Te5m and to introduce the parent nucleus as a defect in the latticeo The displacement mechanism is the recoil of the nucleus due to the emission of 604 Mev of "prompt" gamma rays following the neutron capture. Since the Mbssbauer hyperfine spectrum is sensitive to the immediate electronic environment of the emitting nucleus, the Mbssbauer spectrum should provide information on characteristic defect environmentso The effects were experimentally investigated by irradiating tellurium compounds enriched in Tei24 with thermal neutrons. The M3fssbauer resonance absorption spectrum was then measured against a single line absorbero This spectrum should be characteristic of the lattice with the atoms displaced from the normal lattice sites. The spectrum characteristic of the "ideal" lattice was obtained using the same sources following heat treatment to restore the atoms to their normal Lattice environment. The measurements were performed using sources of PbTe, Te metal, and Te02o For all three compounds, there were no statistically significant differences in the pre-anneal and post-anneal Mb6ssbauer hyperfine spectra. Differences of -xi

several percent in the resonance intensity are within the experimental accuracy of the measuremento The lack of any significant changes in the hyperfine spectra may be due to eithero a) a recoil energy too low to produce displacements, b) replacement collisions. c) defect annealing; or d) insignificant changes in hyperfine interaction parameters. The purpose of the second part of this study was to experimentally investigate magnetic hyperfine spectra in magnetic compounds of tellurium. The diamagnetic Te2- ion with paired 5s and 5p electrons would not normally be expected to give rise to a magnetic hyperfine field at the Te nucleus. However, in compounds with the transition metals, the magnetically coupled transition metal ions can act to spin polarize the paired electron shells of the tellurium iono The unpaired tellurium 5s electron spins will have a net spin density at the tellurium nucleus and will give rise to a magnetic hyperfine field through the Fermi contact interaction. Mbssbauer resonance absorption measurements in the ferrcmagnetic spinel CuCr2Te4 show a partially resolved magnetic hyperfine pattern, From the least squares curve fitting to the data, the magnetic moment for the 3/2 + excited state of Te25 was determined to be s e = +,74 t o07 nm. The internal hyperfine field was measured as Heff = 148 + 5 kgauss The unpairing of the tellurium 5s electrons in the spinel probably arises throuagh either covalent mixing of the 5s electrons with the -xii

chromium 3d electrons or exchange polarization of the 5s electrons by the chromium 3d electrons. MOssbauer resonance absorption measurements in antiferromagnetic MnTe and ferromagnetic CrTe show only broadened lineso The broadening in MnTe is presumably due to unresolved quadrupole splitting, whereas the broadening in CrTe is probably unresolved magnetic hyperfine splitting. -xiiio9oo ~Xl 1 1g

CHAPTER I. INTRODUCTION A Motivation for Present Study Recoilless emission and absorption of nuclear gamma radiation (the Mbssbauer effect) was discovered in 1958. The hyperfine structure in Mbssbauer spectra has provided a very valuable tool for study of the solid state. From the spectra it is possible to gain information on lattice binding forces, internal magnetic fields and electric field gradients, and s-electron densities at the nucleus. This information can consequently provide an understanding of the electron environment of the Mbssbauer emitting or absorbing nucleus. In the past few years the use of the Mbssbauer effect as a solid state probe has been applied to the study of radiation effects. The interest has developed in part from the expanded use of new techniques for population of the MBssbauer level. Traditionally, the MBssbauer level has been populated by the beta decay of a parent nuclideo In many cases low lying nuclear levels which should be potential Mbssbauer levels are inaccessible by such decayso Many new techniques have been developed recently in an attempt to make Mbssbauer effect measurement in these nuclides possibleo These techniques include alpha decay, Coulomb excitation, nuclear reactions, and thermal neutron activation. The use of these techniques has caused concern for the effects of the method of production on the environment of the Mbssbauer emitting nucleus. -1

-2 Considerable interest has also developed in the use of the Mbssbauer effect as a tool for study of radiation induced defects in solids. The Mbssbauer effect is rather unique as a tool for study of the defect solid state in that the spectra are characteristic of only the immediate environment of the emitting nucleus. Such information is not obtainable by most techniques which are used for study of the defect solid state such as resistivity, Hall coefficient, thermal conductivity, specific heat, optical emission and absorption, etc., since these techniques essentially provide information on the transport properties of the material. The only technique providing comparable information on the defect environment is electron spin resonance. The fact that the characteristic structure of Mbssbauer spectra is only sensitive to the immediate environment of the emitting nucleus excludes observation of any radiation effects producing low defect concentrations unless the emitting nucleus itself is in the defect state. Thus, although the transport properties of materials may be drastically altered by charged particle, electron, gamma ray, or neutron irradiation, the characteristic Mbssbauer pattern would probably be little changed due to the relatively low defect concentrationso Since time and intensity limitations usually exclude the possibility of high defect concentrations, the alternative is to use low defect concentrations in which the MOssbauer nucleus itself is introduced as the defect.

-3 The neutron capture process offers such a possibility for simultaneously producing the Mbssbauer parent nuclide and introducing it as a defect in the lattice. The displacement mechanism is the recoil of the nucleus due to the emission of prompt gamma rays following the neutron capture. This displacement mechanism also has the advantage that recoil energies are relatively low, so the resultant displaced atom configurations remain rather simple. In studying neutron capture induced recoil effects, it is desirable to produce a parent nuclide which is an isomeric state. This eliminates any complicating effects caused by the chemical change associated with beta decay. In some cases, the Mbssbauer level itself is populated very shortly after the neutron capture so Mbssbauer experiments must be performed with a neutron beam (e.g., Fe56 (n,u)Fe57m). In other cases, a long-lived metastable state precedes the Mbssbauer level so that in-pile irradiation may be done first and the Mbssbauer experiment may be conducted away from the reactor (e.go, Te124(n,) Te125m(58d) ) The effects of neutron capture induced recoils have been studied most extensively in semiconducting materialso This is due to the expanding use of semiconducting devices (ioeo, transistors, diodes, thermoelectric elements, radiation detectors, etco) in radiation environments (i.e., reactors, weapons systems, space, etco) o As mentioned earlier, most techniques used in studying the radiation effects involve measurement of transport properties. It was hoped that Mbssbauer effect measurements would provide supplementary information on defect environmentso

-4 Te125 seemed to be one of the best Mfssbauer nuclides for studying neutron capture effects. Previous studies of radiation effects in tellurium compounds have principally involved PbTe. This compound has received considerable attention because it is a good thermoelectric material and has potential application for energy conversion in radiation environments. Mbssbauer effect measurements of Te125 have been rather limited. Thus a great deal of valuable information is yet to be obtained from isomer shift and quadrupole splitting data in tellurium compounds One of the most interesting and least explored areas of MWssbauer measurement in Te125 is in magnetic hyperfine structure. The magnetic compounds formed from tellurium and transition series metals offer an opportunity to measure transferred hyperfine fields at the nonmagnetic tellurium site. These measurements can provide information on both the excited state magnetic moment in Te125 and the internal magnetic field. B. Literature Survey 1o Radiation Effect Measurements Using the Mbssbauer Effect A considerable number of papers have appeared the past few years which are concerned with the effect of nuclear reaction induced recoils on the Mtssbauer spectrum. In one group of papers the impetus was the development of new techniques for populating Mbssbauer parent nuclides. The methods employed include alpha decay, (1 Coulomb excitation, (2-5) nuclear reactions, (-8) and thermal neutron activation. (9) The results

-5 indicate that all of these processes can be used for source production without destroying the recoilless emission. However, in most cases the recoil effects due to the source production did alter the line intensity or line width to some degree. A second group of papers, which we shall now discuss in more detail, is directly concerned with the use of the Mbssbauer effect for lattice defect studies. The feasibility of using Mbssbauer effect techniques for study of lattice defects was first proposed by Gonser and Wiedersich.(10) Dederichs, Lehmann, and Wegener(ll) theoretically investigated the replacement probabilities for displaced atoms and proposed a Mbssbauer experiment using Coulomb excitation in which the replacement probability could be measured. Belogurov, (12) in a comment to the paper by Dederichs, et al., proposed neutron capture gamma ray recoil as an alternative method for studying replacement collisions. Fink and Kienle(l3) have investigated the recoil effects following neutron capture in Gd155 and Gd157. In a "mirror experiment" in which the spectrum for a Gd metal target and Gd5803 absorber was compared to that for a Gdl570 target and Gd metal absorber, the corrected area under the transmission line for the oxide target was only.6 that for the metal target. The line for the oxide target was also about 10 percent broader. The Johns Hopkins group(14) has performed Coulomb excitation measurements in Fe203 and observed an f value a factor of two less than that for a normal Fe2C3 lattice. No changes were observed in the hyperfine splittingo The results can be

-6 qualitatively explained on the basis of a dynamical model in which individual displacements occur but do not seem to be explainable on the basis of a localized heating or thermal spike model. Effects of thermal neutron capture in Sn118 have been observed by Hannaford, Howard, and Wignall(15) in the Mbssbauer spectrum of Mg2SnO4. The irradiation of Sn118 to produce the isomeric state Mbssbauer parent Sn19m produced a weak secondary line in the Mbssbauer spectrum. The secondary line was removed by annealing in the temperature range 600-1000~Co The authors concluded that the secondary line was due to Sn atoms in the divalent state and that approximately 25 percent of the atoms have suffered the displacement induced valence change from four to two Neutron capture experiments in Fe56 by Obenshain and Berger(l6) have given evidence of changes in the effective hyperfine field due to recoil effects. Using both Fe metal and Fe203 targets, the effective hyperfine fields were seen to increase in Fe metal and decrease in Fe203 with respect to the fields obtained using the same materials as absorberso In a very recent letter, Stepanov and Aleksandrov(l7) report on the effects of neutron capture in Te124 on the Mbssbauer spectrum for PbTe125. After irradiating the PbTe124 with 2.3 x 1014 neutrons/cm2-sec for 45 days, the isomer shift was measured with respect to a PbTe absorbero Twenty days after the irradiation, the isomer shift was.2 cm/sec. The isomer shift then changed exponentially as a function of time with a

-7 characteristic lifetime T =10 + 3 days, eventually reaching the value 0. The results of all Mbssbauer measurements described above are summarized in Appendix A. 2. Neutron Capture Effects Possibilities of neutron capture induced defects in silicon and germanium were first pointed out by Schweinler(l8) in 1959. With average recoil energies of 780 ev in silicon and 180 ev in germanium, it was concluded that almost every neutron capture results in a displacement of the capturing nucleus. Walker(19) noted that in a number of elements neutron capture induced defects can form a significant fraction of the total defects produced upon reactor irradiation. Experimental evidence of the neutron capture induced defects in silicon and germanium has been shown by Crawford and Cleland(20) Hall coefficient and resistivity measurements in silicon and germanium indicated approximately two and one electron removed respectively per thermal neutron captured. Annealing at 450~C in the germanium restored the displaced atoms to the normal lattice sites. Neutron capture effects have been studied in the semiconductor CdS by Oswald and Kikuchi(21) and in CdS and CdTe by Barnes and Kikuchi. (22) The effects of the Cd114 recoil in CdS were studied using luminescence and conductivity measurementso Both properties changed drastically with thermal neutron irradiation and were restored with annealing at 500~Co

-8 The thermal neutron effects in CdS were monitored by use of the Hall effect, electrical conductivity, and luminescence. The Hall coefficient and resistivity measurements in CdTe indicated one Cd vacancy and one Cd interstitial are introduced per thermal neutron absorbed. Annealing occurred between 160 and 2000C. 3. Radiation Effects in PbTe and Te Metal ao PbTe Since considerable interest has been shown in the use of the thermoelectric properties of PbTe for direct energy conversion, many measurements have been made of the effect of reactor neutrons on this material. Danko, Kilp, and Mitchell(23) have investigated the changes in electrical resistivity and Seebeck coefficient in PbTe due to irradiation in a thermal neutron flux. The coefficients were first measured prior to the irradiation. The samples were then irradiated at reactor ambient temperature (500C) with a dose of 1.5 x 1020 thermal neutrons and a similar number of fast neutrons. The measurements following the irradiation showed an increase in both the electrical resistivity and Seebeck coefficient. After annealing above 200~C both parameters returned to the preirradiation values The group at Knolls Atomic Power Laboratory has performed numerous measurements of the Hall coefficient, electrical resistivity, and Seebeck coefficient in both n- and p-type PbTe. (24,25) Irradiating with doses up to 5 x 1019 fast

-9 (E > 1 Mev) neutrons/cm2 and 6 x 1020 thermal neutrons/cm2 at 60~C, both the Seebeck coefficient and resistivity showed an increase. From the Hall coefficient measurements, it was determined that the increase in Seebeck coefficient and resistivity could be attributed to a decrease in carrier concentration. Similar results obtained in comparison with cadmium shielded and unshielded specimens indicated most of the effect was due to the fast neutrons. Annealing experiments indicated recovery occurred in the range 100~C to 170~C and 140~C to 180~C for p- and n-type material respectivelyo b. Te Much less effort has been devoted to the study of radiation effects in tellurium. However, some measurements have been performed. Samples of p-type tellurium were irradiated at 780K with 25 Mev electrons by ran Lint, Wikner, and Miller. () The irradiation caused an initial increase in conductivity due to the introduction of carrierso Annealing measurements indicated the defects introduced were stable at 78~K but were completely annealed out when the specimen was left at room temperature for several hours. Similar increases in conductivity were obtained by irradiation of tellurium in neutron doses of 1013/cm2.(27) No annealing measurements were reported.

-10 4. Mbssbauer Effect Measurements Using Te125 Mbssbauer effect measurements using Te125 have been performed by several groups. Resonance scattering studies were performed in Te25m by Hien, Shapiro, and Shpinel(28) in 1962. Using a source of neutron irradiated Te2402 at both liquid nitrogen temperature and room temperature and an absorber of Te12502 at room temperature, values of the recoil-free fraction were obtained. At liquid nitrogen temperature f=.12 +.03 and at room temperature f=.067 +.008. No apparent quadrupole splitting was observed for the TeO2. No effect was observed for Te25 metal at room temperature. The most extensive study of the Te125 Mbssbauer resonance (29-31) has been done by the group at Lawrence Radiation Laboratory,(2 3 Measurements were performed using sources of I125 in NaIO3 which exhibited four resonance lines and 1125 in a Cu host lattice which had a single line emission spectrum. Absorbers studied include ZnTe, MnTe, -FeTe, TeF4, TeI4, TeO2, Na2TeO4, and Te metal. Measurements were made at liquid nitrogen temperature. The quadrupole splitting in Te metal was observed to be 7.6 +.2 mm/sec.* A calculation of the electric field gradient using a molecular orbital model(30) for Te yielded eq=-2.8 +3 x 1016 esu. The resultant quadrupole moment was then IQI=.20 +~03 barns. This was in good agreement with -~02 a configuration-mixing calculation which gave Q=-.23 barns(32) *For the 35,6 kev gamma ray resonance in Te'5 X mm/s/c = iol9 x 10-7 ev. (See Equation (III.1)o)

-11 Violet, et al, (31) did not observe quadrupole splitting in cubic ZnTe, in the Cu host lattice source, or in hexagonal NiTe. Quadrupole splittings reported for MnTe, B-FeTe, o-TeO2, TeF4, and TeI4 are respectively 3 + 1, 3 1, 7.3 +.1, 7 + 1, and 6 ~ 1 mm/seco Violet, et alo, attributed the existence of four lines in the emission spectrum of the NaI03 source to the presence of two charge states.(31) This may result from the K x-ray and Auger transitions following the 1125 decay. In the model proposed, the higher charge state decays to the lower charge state by electron capture with a half life of o1.6 x 10-9 sec. Shikazono(33) has reported observation of the Mbssbauer effect in several compounds of Te25. From the observed quadrupole splitting of 7 mm/sec in Te metal an electric field gradient calculation yielded an excited state quadrupole moment IQI=.17 barns. The o(-TeO2 spectrum had an identical quadrupole splitting of 7 mm/seco No quadrupole splitting was observed in MnTe- the lack of splitting was attributed to the ionic structure of this compoundo A broadened single line spectrum observed for CrTe was attributed to an unresolved magnetic hyperfine splitting. An estimate of the excited state nuclear moment e~-.7 nm led to an upper limit for the internal field at the Te nucleus in CrTe of 50 kgausso A source of Sb125 imbedded in an iron lattice produced a partially resolved magnetic hyperfine splitting with internal field ~600 kgauss.

-12 Using both a source and absorber of Te metal, the Debye temperature GD=125 + 50 has been determined for Te metal by Frankel, Barrett, and Shirley. (34,35) The measured quadrupole splitting was 7.7 mm/sec. Buyrn and Grodzins32) measured quadrupole splittings in Te, TeO2, Na2TeO4, and NiTe of 7.5 mm/sec, 7.0 mm/sec, 7.0 mm/sec, 0, and 0 respectively. The isomer shifts relative to Te for the latter three compounds were 0, -1.5, and -1.0 mm/sec with error + 1 mm/sec. Debye temperatures for Te, TeO2, and Na2TeO4 were estimated as 125~K, 1700K, and 190~K. Stepanov, et al.,(36) observed Te125 Mbssbauer resonances in PbTe, Te metal, "amorphous" Te, and Te02. The quadrupole splitting for Te metal was reported as 7.8 mm/sec. The TeO2 spectrum consisted of four lines with splittings 5.5 mm/sec and 10,1 mm/sec which were attributed to the presence of both the tetragonal and orthorhombic crystal modifications of TeO2o Magnetic hyperfine structure has been measured for Te2 by Frankel, et al 37 using an Sb25 source in both Fe and Ni hosts, The hyperfine pattern measured against a single line ZnTe absorber showed a partially resolved hyperfine structure with the pattern 3e:201.1~2.3. This established the excited state moment re as positive.

CHAPTER II, BACKGROUND Ao Selection of Suitable Mtssbauer Nuclide for Studies of Neutron Capture Effects Several factors were considered in selecting a suitable Mbssbauer nuclide for studies of neutron capture effects. The principal factor in the selection was the desire for a Mbssbauer parent which was an isomer of the Mbssbauer level. This is necessitated by the fact that any non-isomeric parent will be a chemical impurity in the host lattice (e g., Fe57 populated by the electron capture decay of Co57) Use of an isomeric state parent eliminates any effects the chemical impurity could have on the Mbssbauer spectrum. This includes changes in the recoil-free fraction attributable to localized lattice modes introduced by the impurity and changes in the isomer shift and guadrupole splitting arising from the electronic rearrangement associated with the decay. In all likelihood these effects are small. The mass difference between the impurity and host would be only 1 amuo Electronic relaxation times are usually fast (/1010 sec) compared to the lifetime of the Mbssbauer levels however, metastable charge states may be produced. Nevertheless, to avoid any possible effects, it appeared best to use an isomeric state parent. A second consideration was that the Mbssbauer effect should have been observed previously so that- 1) there was some guarantee of obtaining a spectrum, and 2) the relevant -13

-14 parameters were known. From the list of nuclides for which the Mbssbauer effect has been observed,(38) those listed in Table II-1 can be populated from an isomeric state. Also included in the table are the thermal neutron activation cross section, (39) the half life of the isomeric state, and the binding energy of the neutron in the product nucleus. (40) The relevant M6ssbauer parameters, including the lifetime and energy of the Mbssbauer level, (38) are also given. The criteria used in selection of the nuclide most suitable for radiation effect measurements are: 1) the Mbssbauer parent must have a reasonably long half life so that Mbssbauer measurement, annealing, and remeasurement can be performed; 2) the thermal neutron activation cross section must be sufficient so that sources can be activated within a reasonable length of time/ 3) the recoil-free fraction should be as large as possible (implies a low lying energy level, large mass number, and chemical compounds with a high Debye temperature) - and 4) the resonance line width should be sufficiently narrow to resolve hyperfine structure (implies a long lifetime for the M5ssbauer level) ) On the basis of these considerations, Te125 provides the best compromise of the conditionsO The only unsatisfactory parameter for Te125 is the rather short lifetime ( T = 1.4 x 10-9 sec) of the Mbssbauer level. The natural line width (F= 2.744 mm/sec) is quite broad and makes resolution of hyperfine structure somewhat difficulto

TABLE II-1 RELEVANT PARAMETERS FOR MOSSBAUER NUCLIDES WITH ISOMERIC STATE PARENTS POPULATED BY AN (n,l) REACTION Stable Isotope Ge72 K82 n118 Sn Te124 Xe128 130 Xe W182 Pt194 C (n, Y) Barns 94 t.09 45 + 15 10 + 6mb 40 + 25mb L 5 L5 z 5 19 + 2 1.2 ~.9 Birxding* Energy Mev6.4 7,5 6.54 6.48 7.1 6,60 6,29 6.09 Mbssbauer Parent Ge73m Kr83m 119m Sn1 Te125m Te Xe129m Xe131m W183m ptl95m T~ for Parent 53s 1.86h 245d 58d 8d 12d 5.5s 4. Id Mossbauer Level Eo T1i key Sec 13.5 4.0 x 10-6 9.3 1.47 x 10-7 23.8 1.85 x 10-8 35.6 1.4 x 10-9 40 9.6 x 10-10 80.2 5.0 x 10-10 46.5 1.5 x 10-10 99.1 5.2 x 10-10 98.9 1,7 x 10-10 129.7 5.5 x 10-10 I Ln I *Binding energy of the neutron in the product nucleus.

-16 119 In retrospect, the Sn probably would have been a better choice of nuclides. At the time of selection the Te124 activation cross section was listed as 5 t 3 barns rather than the more recently tabulated 40 t 25 millibarns.(39) The two orders of magnitude larger cross section for Te124 then seemed to outweight the order of magnitude decrease in line width for Sn119. Only after we had become seriously involved in Te125 measurements did we find that the Te124 activation cross section was in error and the broad lines of Te125 were a handicap in resolving hyperfine structure. B. Thermal and Fast Neutron Effects in Tellurium Compounds 1. Thermal Neutrons The Mossbauer isomeric state parent Tel25m is produced by thermal neutron capture in Te24, described by Tel24+n - Te125* - Te125m+ W-rays (Il1) Intrinsic defects can be introduced in the solid if the recoil energy of the Tel25m nucleus is greater than the minimum energy for displacement. The recoil energy arises from the conservation of momentum following the emission of the prompt gamma rays. The process is depicted in Figure II-1 for the emission of a single gamma rayo By conservation of momentum, the recoil energy ER is given by E =-EW ER 2McZ ) (II.2)

-17 nth Te / 0 / FIGURE II-1 DIAGRAM OF Te124(n,W) Te125 RECOIL MECHANISM

-18 where EX is the gamma ray energy, M the nuclear mass, and c the speed of light. Evaluating Equation (11.2) numerically for Te125 with a gamma ray energy of 6.37 Mev, ER- 174 eVo However, the decay of the highly excited state does not usually proceed by the emission of a single gamma ray, but rather a cascade of gamma rays emitted in transitions between various nuclear excited levels. If it is assumed that the gamma rays are emitted randomly and isotropically, Schweinler(41) has shown that the mean recoil energy <ER) is just equal to the sum of the recoil energies due to the individual gamma rays, or z E<R> = MC (11.3) Unfortunately, the spectrum of neutron capture gamma rays has not been experimentally measured for Te125o Thus the mean recoil energy for Te125 can only be estimated. In the study of neutron capture effects in germanium, Crawford and Cleland(20) estimated the recoil energy assuming that after neutron capture in the even-even isotopes two photons of equal energy were emitted and in the even-odd isotopes four photons of equal energy were emitted. Assuming that two photons of equal energy are emitted for neutron capture in Te124, the mean recoil energy obtained from Equation (II.3) is <ER) = 87 eVo This estimate may be somewhat high in consideration of data on neutron capture in other even-even nuclides.(4 Most exhibit maxima in the energy distribution curve of gamma rays emitted in the range 2-2~5 Mev. This would indicate that

-19 perhaps an assumption of three equal energy gamma rays would be more realistic. Based on this assumption, the resultant mean recoil energy is <ER> = 58 ev. In the measurement by Muehlhause(97) of the mean number of prompt gamma rays emitted for a series of elements, the number increased with increasing mass. Judging from his results, an estimate of three gamma rays does not appear unreasonable for Te125 An estimate of the average number of displacements produced per thermal neutron captured can be obtained using simple radiation damage theory. The average number of displacements, 7, is given by(42) 0 <ER)< Ed 1 Ea< <ER) < ZEa (I1i4) <ER) E; 2 2E'<ER><EL 2Ea E < <ER> where Ed is the threshold energy for displacement and Ei is the ionization cut-off energy, If it is assumed that the threshold energy for displacement in tellurium compounds Ed = 25 ev and <ER> = 58 ev, the average number of displacements y = 1.16. This means that on the average we can expect only one displacement per thermal neutron captured, the Te125 nucleus itself.

-20 2o Fast Neutrons Since all source irradiations were done in or near the core of the Ford Nuclear Reactor (FNR), it is necessary to consider the effects of the fairly significant fast neutron flux on the tellurium compoundso Since the cross section for thermal neutron capture in Te124 (40 millibarns(39)) is fairly small, the number of fast neutron induced displacements may be considerably larger than those produced by thermal neutron capture. However, as discussed in Chapter I, the fast neutron induced displacements may still have little effect on the M6ssbauer spectra due to the relatively low concentration of defects and the small probability of their being near the Mbssbauer emitting nucleus. We will consider the effects of the fast neutrons in PbTe, Te metal, and TeO2 The displacements are created by the scattering of a high energy neutron from a lattice atom. The primary recoiling atom creates additional displacements as it dissipates its energy in the latticeo The number of displacements produced by a fast neutron flux can be estimated using simple radiation damage theory. In an elastic collision, the maximum energy of the primary recoiling atom is 43) M + (II5)

-21 where M and m are the mass of the atom and neutron respectively, and En is the neutron energy. For target atoms where M>>m, Equation (II.5) can be approximated by 41En Ep (mh - A' (11.6) Where A is the ratio of the target atomic mass to the neutron mass. If the scattering is isotropic in the center of mass coordinate system, the mean energy of the primary recoiling atom is 42) - Ep (mac)^ P 0 *(I o 7) Combining Equations (IIo7) and (IIo5) together with a correction factor, f, E - F (MF - Et, (II.8) where f is a factor correcting for anisotropy and inelasticity (43) in fast neutron scattering (43) The average number of displacements produced per primary recoil atom can be determined using Equation (IIo4) where Ep replaces <ER>) However, it is first necessary to determine (44) whether E is less than the ionization energy Eio Seitz has shown that Ei can be estimated as Em - M E (II 9) t; 8 god 9 v

-22 where M and me are the mass of the primary recoiling atom and electron respectively and Eg is the lowest electronic excitation energy. The total number of fast neutron displacements produced per unit volume in the material is given by I -= ES s t, (II.10) where Vf is the mean number of displacements per fast neutron scattered, / is the macroscopic fast neutron scattering cross section, Tp is the fast neutron flux, and t is the irradiation time. The foregoing parameters were evaluated for the source materials PbTe, Te, and Te02 The results are shown in Table 11-2o E is calculated from Equation (IIo8) for each of the elements assuming an average fast neutron energy En 1 Mev and a omna value of 2/3(43)The band gap energies Mev and a nominal value of f'"2/3o The band gap energies in PbTe, Te, and TeO2 are respectively Eg=.31 ev, Eg=o34 ev, and E =1.5 ev. (45) The respective ionization energies are calculated from Equation (IIc9). Again assuming Ed=25 ev, the average number of displacements produced by each primary recoiling atom, 4p, can be determined from Equation (IIo4). (39) The macroscopic fast neutron scattering cross sections are also listed in Table II-2. Values of the integrated flux ( -t ) are obtained from Table III-2 for each of the sources. The total number of fast neutron displacements produced per unit volume is calculated for each element using Equation (II.10)

TABLE II-2 PARAMETERS RELATING TO FAST NEUTRON INDUCED DISPLACEMENTS IN TELLURIUM SOURCE MATERIALS Compound PbTe Element Pb Te (keyv) 6 11 E,31 Ei (key) Vf 14.6 120 8.8 176 Z 5 (cm-l).088.094 tPFt (n/cm2) 6.4 x 1016 I (defects/cm3) 6.8 x 1017 1.1 x 1018 Te Te 11.34 9.6 192.194 7.6 x 1016 2o8 x 1018 TeO2 Te 0 11 83 1.5 42.4 220.137 5.5 110.150 6.5 x 1017 2,0 x 1019 1.1 x 1019 I IO (Continued) Itot Compound (defects/cm3 ) PbTe 1 8 x 1018 2 8 x 1018 N (atoms Te/cm3) 1.5 x 1022 2.9 x 1022 1.2 x 10-4 9.7 x 10-5 Itot/N (defects/atom Te)...... -- Te TeO2 3. 1 x 1019 2.1 x 1022 1.5 x 10-3

The total number of defects per unit volume for each compound is compared to the density of tellurium atoms per unit volume, N=P No A0 For each of the source materials, the concentration of fast neutron induced displacements is only 10-4-10-3 of the concentration of tellurium atoms. Hence, on the average, the displaced atoms will be separated by approximately ten lattice spacings. The probability of such widely spread displaced atoms being in the immediate environment (nearest or nextnearest neighbor) of a Mbssbauer emitting nucleus is very small. Co Characteristics of Mdssbauer Spectra in Te125 1o Decay Scheme of Te125m The decay scheme for Tel25m is shown in Figure 11-2. The 145 key- isomeric state decays to the 3506 key level with the emission of a 109o4 kev gamma ray ( 1)o The 35.6 kev Mbssbauer level has a half life T- = 1.4 x 10-9s and decays to the ground state by the emission of a 35.6 kev gamma ray (EM) o The decay from the 58 d state is highly converted with internal conversion coefficient 0( = 160O (47) The ratio of conversion coefficients K is K~LoM~N = 54:36:8.3:1o7 and LIoLSILiiI = 0.66:0.30:1. The internal conversion coefficient for the decay from the 35.6 kev level is oK = 11.4.(47) The ratio of conversion coefficients is KLo.MoNN = 80o11 1o7~0o3.

-25 Te125m.r., 58d II/ YM Te'25 145 35.6 T1/2 1.4 x109s 0 3/2+ 1/2+ FIGURE II-2 Te125m DECAY SCHEME

-26 One of the difficulties in using the 35.6 kev gamma ray from Te125 for Mbssbauer measurements lies in the discrimination of the gamma ray from the x-ray background. The relative locations of the gamma ray and x-ray energies are shown in Figure II-3. The x-ray energies are K( = 27.47 kev, Ka = 27.20 kev, K - = 31.06 kev, and K = 31.71 kev. FIGURE II-3 RELATIVE LOCATION OF X-RAY AND GAMMA RAY ENERGIES IN DECAY OF Te125m K20 Ken` o0 o 20 30 40 E(Kev) Not only are the x-ray energies very close to the gamma ray energy, but the x-ray intensities are much greater. The relative intensity of the 35.6 kev gamma ray and the tellurium x-rays can be calculated using the internal conversion coefficientso The total internal conversion coefficient is just the sum of partial coefficients, so 0( = 296.2 and ok = 13.25 for transitions 61 and M respectively. The relative intensities of the K. and Kp components of the x-rays emitted can easily be calculated 48) and KIoK. =.823. o77 Using these values and the K-shell fluorescent yield 0K =.855, (48)

-27 the yield of Ka and K x-rays and 35.6 kev gamma rays per decay of the 145 kev excited state are KO-K~ = o942:S2030o070. The weighted average of the components of the KA and K x-ray lines yields x-ray energies EK =27.4 kev and EK =312 kev. 2o Mfssbauer Recoilless Fraction The Mbssbauer effect is the recoilless resonant emission and absorption of gamma rays by nuclei. Resonance occurs if a gamma ray emitted by a nucleus in decaying from an excited state to the ground state is then absorbed by an identical nucleus which is excited from the ground state to the excited state. For a free nucleus, the recoil energy loss will usually prevent the resonance process. For a nuclear transition energy E, the gamma ray energy E~ will be E=E -E,,E (II.11) where the recoil energy ER is given by the expression described earlier in Equation (IIo2), or Z Z E E-S- Ez 2 (II.12) M is the mass of the nucleus after emission and c is the speed of light. Since approximately the same recoil energy is given up to the absorbing nucleus, the gamma ray emission spectrum and absorption cross section will be separated in energy by 2ER R'

-28 Due to the finite lifetime of the nuclear excited state, the energy level has a Lorentzian distribution of energies described by a line width r = Ar (11.13) where' is the mean lifetime of the state. For Te25 E =' or Te, ER 5.44 x 10-3 ev and r= 3.27 x 10-7 ev so ER->P and negligible resonant absorption will occur for emission by the free nucleusO Mbssbauer discovered(98) that for nuclei bound in a solid, there are conditions for which a fraction, f, of the gamma rays are emitted or absorbed without recoil loss. In such a case, the recoil momentum is imparted to the entire crystal rather than an individual nucleus. The gamma ray then has the full transition energy or E = E o For such"recoilless" emission and absorption, the resonance process can occur. The recoilless fraction, which is variously referred to as the f value or recoil-free fraction, has been discussed in innumerable papers. Assuming a Debye model for the case of an infinite crystal lattice, the recoilless fraction can be (99) expressed as -2W -- e (II.14) where the Debye-Waller factor W is given by 3 ER 1 eT e x E)D GD e

-29 In this expression ER is the recoil energy for the free nucleus, T is the ambient temperature of the source or absorber, and eD is the Debye temperature. It is readily apparent from Equations (IIo14) and (11.15) that in order to obtain a significant recoilless fraction f, keD must be greater than ER and T must be less than GD. GD is of the order of 150~K in most tellurium compounds. In tellurium compounds, then, keD8 13 x 10-3 ev, which satisfies the first condition since kGD> ERo To satisfy the second condition requires temperatures T< 1500K —or temperature of the order of liquid nitrogen temperature or lower. It must be kept in mind that the Debye model is only an approximation to the real lattice frequency spectrum. In fact, for anything but a monatomic lattice the use of the Debye model is questionable. The use of an "effective" Debye temperature, however, has proven adequate in characterizing Mbssbauer recoilfree fractions. In general, though, Debye temperatures obtained from Mtssbauer effect measurements do not agree with Debye temperatures obtained from specific heat measurement, etc. The difference arises in the different sensitivity to the shape of the real lattice frequency spectrum. 3. Mbssbauer Hyperfine Structure The Mbssbauer spectrum can display either individually or in combination the isomer shift, electric quadrupole splitting, and magnetic hyperfine splitting. The following is a description of the interactions leading to these phenomena.

-30 a. Isomer Shift The isomer shift arises from the change in electrostatic interaction between the nuclear charge and the s-electron charge density caused by a difference in the nuclear radius between the excited and ground states. A non-relativistic perturbation calculation yields an energy difference between the source and absorber of(49) |TZ' < R - > <R [l( (II.16) where <R2> e and <R2> g are the mean square radii of the nucleus in the excited and ground state, respectively, and |Is~) | and | 9)(o are the s-electron densities at the nucleus in the absorber and source, respectively. Assuming the nuclear charge distribution has a constant value out to radius R, the isomer shift can be rewritten as 2 =47 e R W(~l |-sR) v(I( L17) where R= Re-R3 and R -- R (51) In heavier elements, relativistic effects become important. These relativistic effects can be accounted for by multiplying Equation (II.17) by a correction factor S'(Z), which for tellurium is S'=2.44.

-31 The isomer shift is measured by determining the shift of the centroid of the Mbssbauer spectrum with respect to zero velocity. It is difficult to obtain information on s-electron densities from a single isomer shift since both source and absorber s-electron densities are included. However, by measuring relative shifts for a series of compounds with respect to a standard source or absorber, the change in selectron density can be determined. Tellurium has a wide range of valence states in different compounds. These should provide measurable changes in the selectron density. Ionic tellurium configurations range from Te2- with the electronic configuration (KLM) 424p64d105s25p6 and filled 5s and 5p shells to Te6+ with a bare 5s and 5p shell, Metallic tellurium with configuration 5s25p4 and Te4+ with configuration 5s25p0 both have filled 5s shells, but differ in 5p shell filling. In purely ionic configurations, there should be an obvious difference in s-electron densities between the Te6+ with an empty 5s shell and the ions with a filled 5s shell. Different s-electron densities can also be expected between ions with filled 5s shellso Here the different selectron densities arise due to variations in shielding of the 5s electrons by the differing numbers of 5p electrons. In 6s electrons, it has been estimated that this shielding effect is 10 percent for 6p electrons shielding 6s electrons.(52) Covalent bonding can also provide intermediate conditions since both 5s and 5p electrons are involved in the bonding

-32 orbitals, Covalency results in the delocalization of the 5s and 5p electrons associated with the ionic configurations. Such effects can be directly reflected through variations of the 5s electron density or in variations in 5p shielding. Interpretation of isomer shifts in the covalent compounds is much more difficult than in ionic compounds, however, since rigorous theoretical treatment of the molecular orbitals has been done in only relatively few cases. Knowledge of the variation in isomer shift with variation in s-electron density can provide information on the change in nuclear radius between the excited and ground states. Shirley(51) has estimated 8R/R in Tei25 from the experiments which have been performed. Using the shift of -1.5 mm/sec obtained by Buyrn and Grodzins(32) for a tellurium source versus a tellurate absorber, the value R/R++0.7 x 10-4 was obtained assuming the environments differed by one 5s electrono This numerical value for ER/R should only be taken as a rough estimate since other calculations by Shirley yield values differing by an order of magnitude. The sign of SR/R definitely appears to be positive, however b, Quadrupole Splitting Electric quadrupole splitting arises from the interaction between the nuclear quadrupole moment and the electric field gradient created by the electronic environment of the nucleus. The Hamiltonian for the interaction can be written as(50)

-33 Q = 4 [3 -Iz - I(I+ (I + I ) (II 18) 4: (21-i) (11.18) where Q is the electric quadrupole moment, eq = Vzz is the z component of the electric field gradient in the crystal principal axis system, v = xxv - is the asymmetry parameter, and Iz, I+, Vzz and I_ are the spin projection and raising and lowering operators respectively. The ground state in Te125 has no quadrupole moment since Ig =. (53) The eigenvalues of HQ for the excited state with spin I = 3/2 are Em- D i[3m - (l + [(1+ q (II.19) Hence the electric quadrupole interaction partially removes the spin degeneracy of the excited state, splitting it into two levels (Iml = 1/2, 3/2). In this case, the transitions between the excited and the ground states give rise to a two-line Mbssbauer pattern with quadrupole splitting AE = - E3/ ( + f /3 (II,20) The quadrupole moment for the excited state obtained by Violet, Booth, and Wooten(30) from quadrupole splitting in Te metal is [QI =.20 +~02 barns. The configuration-mixing calculation r(32) lation result is Q = -~23 barns.

-34 Using the value IQI =.2 barns for the excited state moment, it is possible from measurements to determine the crystalline electric field gradient. The electric field gradient arises from two sources, eqc due to electrons inside the central cell surrounding the nucleus and eql due to all electrons and nuclei surrounding the cell in the rest of the lattice. The resultant field gradient is ecq= et (L- )+ e (- R) ) (II.21) where XA and R are Sternheimer polarization factors. The polarization factors account for the polarization of the closed electron shells by the lattice and cell electrons, respectively, and the resulting induced field gradient. In purely ionic configurations Te, Te4, and Te6+ there should be no contribution eqc since the 5p shell is either filled or empty. If the lattice structure has cubic symmetry, eql is also zero since = 0 and Vzz = 0 for cubic symmetry. For lower symmetry, there should be a contribution eq1 Evaluation of eq does not require precise knowledge of the electron wave functions and may be considered in a first approximation by assuming the lattice as an assembly of point chargeso For a crystal structure with axial symmetry, r = 0, and the field gradient tensor is reduced to eq1 = Vzz where(54) RQ J 3 -2 2 3 eq cYS 3 (II 22) L~t "-(/ 7-,r'

-35 eq = 2fjp(v,) P( r (II.23) Assuming a point charge distribution, the integral reduces to a lattice sum i ^- PR(urQe e = 2e-e 3 (II.24) 1 c In general, eq1 will be small compared to eqc due to the l/r3 dependence. However, the polarization factor &d may be very large for heavier ions,(55) providing a significant enhancement of eqlo In covalently bonded tellurium compounds, the dominant contribution to eq comes from eqc. Evaluation of eqc requires rather precise knowledge of the electron wave functions. eqc arises principally from the valence p-electrons and knowledge of these wave functions requires a molecular orbital calculation for the solid. Needless to say, such calculations have been done for only a limited number of cases. c. Magnetic Hyperfine Splitting Magnetic hyperfine splitting arises from the interaction of the nuclear magnetic moment with the magnetic field at the nucleus. In the absence of an applied magnetic field, the magnetic field is solely the internal magnetic field arising

-36 from the electronso The Hamiltonian for the interaction can be written as(50) 4 D - V Hj (II.25) where U is the nuclear magnetic moment and Heff is the effective internal magnetic field. Magnetic hyperfine splitting can occur in both the excited and ground states in Te125 as shown in Figure II-4. The energy eigenvalues of HD are _ -. (II.26) I The magnetic hyperfine interaction completely removes the spin degeneracy of each of the states. The 35.6 kev gamma ray transition is predominantly a magnetic dipole (Ml) transition with only a.035 percent(56) admixture of electric quadrupole (E2) radiation. The selection rule for magnetic dipole transitions is Am = 0, +1, implying that six transitions between the excited and ground states are allowed. These are shown in Figure II-4. The relative location of each of the six component lines is completely determined by the ratio ge/gg where ge and gg are the excited and ground state g factors (g = V/I). All the possible absorption patterns can be described by a "g-factor diagram" as shown in Figure II-5. For a given g-factor ratio, the magnetic hyperfine spectrum is obtained by drawing a horizontal

-37 3/2 —---— 3/2'-+ 123"-1/2 3/2+- 2L-eHeff 3 6 +1/2 Hef f +3/2 — 35.6 keV^,, +1/2 123 /2+ 2 ieff FIGURE II- -1/2 456 FIGURE II-4 MAGNETIC HYPERFINE SPLITTING OF THE 3/2 + AND 1/2 + STATES OF Te125

-38 -3/2 -— 1/2 -1/2 —1/2 +1/2 —-1/2 1.0.5 01 - 05 \ - A _ >,, =+.7nm -.5 -1.0 I I I I I I I I I I -5 -4 -3 -2 -I 0 1 2 3 4 5 RELATIVE ENERGY (ARBITRARY UNITS) FIGURE II-5 "q-FACTOR DIAGRAM" SHOWING THE RELATIVE LOCATION OF MAGNETIC HYPERFINE STRUCTURE LINES AS A FUNCTION OF THE RATIO OF THE EXCITED STATE TO GROUND STATE g VALUES

-39 line across the diagram. The intercept of this line with the transition lines then gives the relative splitting in the magnetic hyperfine spectrum. The value of 1 g determined by nuclear magnetic resonance techniques for Te125 is K g = -0.8872 nm.(57) The excited state moment f e has not been experimentally measured, although it is definitely observed to be positive.(3337) Shikazono(33) has estimated V e:_+.7 nm by comparing the single neutron d3/2 nuclear state of Te125 with the nuclides Sn119 and Xe131 which also have single neutron d3/2 excited states. Using the estimated value for P e, the g-factor ratio is ge/gg = -.26. The relative location of the lines in the magnetic hyperfine spectrum for this g-factor ratio is shown in Figure II-5. The theoretical angular dependence of the intensities of the six transitions numbered in Figure II-4 are(50) I,=I,= %(4 + Gc) I= — I5 -- S3 a (11.27) 33 4 —3/4(1+-9) where G is the angle between the axis of quantization and the direction of the gamma ray beam. If the internal fields (axis of quantization) are randomly oriented as in a nonmagnetized polycrystalline aggregate, then an average over angles in Equations (IIL27) leads to relative intensities 3:2:1:1:2:3 for the six lines. With the application of an external magnetic field, the

-40 internal fields can be aligned. If the internal field is aligned perpendicular to the direction of the gamma ray beam (e = 900), the relative intensities of the six lines are 3:401:014:30 If the internal field is aligned parallel to the direction of the gamma ray beam (e = 0~), the relative intensities are 3X0: 11:03o. The effective internal magnetic field arises from several different sources. For an independent electron model(58'59) Heff_ = Z(-Q<r)+( S-3(S,- dr)<r -3 S.<r>} (11.28) L where g is the electron g value and r is the Bohr magneton. The sum is taken over all electrons. 1. and s. are the orbital and spin angular momenta for the ith electron and Krli3> <r s >, and <rc 3> are appropriate radial averages of r sci ~ and rci the wave function of the ith electron for the orbital, spin dipolar, and Fermi contact contribution to the effective hyperfine field. The sum in Equation (II.28) is simplified considerably by the fact that for spherically symmetric states the orbital and spin dipolar contribution is zero. Hence only unfilled electron shells need be considered. The Fermi contact term is proportional to the s-electron spin density at the nucleus, or |I)Stl= | )2-b) |8)(o)| * (II.29) a z

-41 For a filled s-shell, the spin density should be zero since the spins are pairedo The sum in Equation (II.28) is then reduced simply to a sum over unpaired electrons. In magnetic compounds of tellurium, the Te2- ion itself is nonmagnetic. On the basis of an independent electron model, the electrons in the 5s25p6 electronic configuration for Te2 would be expected to be paired —consequently yielding an Heff=O. However, the experimental measurement of hyperfine fields for ions with paired electron orbitals in magnetic materials implies that unpairing of the electron orbitals can occur. Such may be the case for the normally nonmagnetic tellurium ion in magnetic compounds. This unpairing presumably arises from interelectron interactions unaccounted for in the independent electron model. (Such effects are not unexpected since the Sternheimer polarization factor is a manifestation of interelectron interactions for the quadrupole coupling.) Theoretical interpretations of core and conduction electron polarization have been performed for magnetic atoms in ferromagnetic materials. (58,59) However, this has not generally been applied to nonmagnetic atoms in ferromagnetic materials. Only the hyperfine field at the diamagnetic F- site in MnF2 has been studied in any detail. (60,61) A discussion of the hyperfine field at the tellurium site in magnetic compounds of tellurium will be presented in Chapter Vo 4. Possible Effects of Neutron Capture Induced Displacements on Mbssbauer Spectra Of the three compounds, PbTe, Te, and TeO2, used for the study of neutron capture induced displacements, PbTe offered

-42 the best possibility for observation of changes in the characteristic Mbssbauer spectrum. The previous neutron radiation effects measurements indicated that defects introduced into the PbTe lattice were stable at reactor ambient temperatures. (23-25) For the Te metal, recoil induced displacements are more than likely not stable at reactor temperatures. Measurements of the effects of electron bombardment on Te metal indicate that defects anneal fairly rapidly even at room temperature. ( No previous radiation effects measurements have been made using TeO2, so whether or not defects would be stable at reactor temperatures is a matter of conjecture. Based on the defect annealing characteristics then, PbTe is the only compound for which there is positive evidence that defects can be introduced which are stable at reactor irradiation temperatures. Since PbTe appears to be the most interesting possibility, the effects of defects on the Mbssbauer spectrum will be discussed in relation to PbTeo PbTe has the NaCl crystal structure with lattice constant a0 = 6,452o. The structure is shown in Figure II-6(a)o In the normal lattice, the tellurium atoms are in a cubic environment, so no quadrupole splitting is expectedo The lack of quadrupole splitting in the normal Mbssbauer pattern confirms this observation~ If the tellurium atom was displaced from a normal lattice site, many possible defect configurations could result. In most cases, however, the displaced tellurium atom would end up in a site which no longer had cubic symmetry. Such an environment should give rise to an electric field gradient at the

-43 (a) L- a = 6.452 A X (b) O - Te atom * - Pb atom FIGURE II-6 (a) LEAD TELLURIDE CRYSTAL STRUCTURE (b) FRENKEL DEFECT IN LEAD TELLURIDE LATTICE

-44 tellurium nucleus and subsequent electric quadrupole splitting in the Mbssbauer spectrum. One possible simple configuration is shown in Figure II-6(b). Here a Frenkel defect is formed consisting of a vacancy at the original tellurium site and an interstitial at the center of one octant of the unit cello This configuration was chosen for computational simplicity and does not necessarily represent an energetically stable configuration. (71) It is readily apparent from the figure that there will be an axially symmetric field gradient in the (111) direction. Each of the possible configurations would also be expected to have a somewhat different isomer shift than found at the normal lattice site due to the alterations in chemical bonding associated with the displacement of the atom from its normal site. The recoil-free fraction, or f value, would also be changed for atoms in defect configurations. Localized vibrational modes would be introduced at the impurity site due to the altered lattice binding forces at this location. These in turn would affect the f value for the impurity atomo The resultant Mbssbauer emission spectrum would be described by a sum over all possible normal and defect configurations of the emission line characteristic for each configuration times the fraction of sites with that configuration. The emission line characteristic of each site would be described by an isomer shift, quadrupole splitting, and f value dependent on the particular configuration.

-45 One of the reasons for using neutron capture induced displacements for the investigation was that the number of possible defect configurations was small. Since the recoil energy due to the prompt gamma ray emission is low, few displacements are produced per thermal neutron capturedo With a minimum of displacements, only a relatively small number of defect configurations can be formed. Even with a limited number of defect configurations, it is still highly probable that the resultant Mbssbauer spectrum would not display well-defined structure. A sum over several equally probable defect configurations with different isomer shifts and quadrupole splittings would only result in inhomogeneous broadening. The only conditions for which a well-defined structure might be expected is if one defect configuration was dominant and the quadrupole splitting for this configuration was large compared to the natural line width (AEQ-> f ) To make a quantitative evaluation of the Mbssbauer parameters for defect environments is extremely difficult. As discussed in the preceding section, the electric field gradient eq arises from both the valence electrons and the external lattice charges. The valence electron contribution eq is usually the larger due to the l/r3 dependence of eq. Evaluation of the valence electron contribution to eq for displaced atom environments would require knowledge of the defect atom chemical bonding. Detailed knowledge of the electron environment for displaced atoms is known for relatively few

-46 configurationso The only contribution to eq that can be estimated is eql due to the external lattice charges. If an ionic model is assumed, eql can be calculated by performing a lattice sum calculation as described in Equation (II.24)o For covalently bonded structures such as PbTe, a lattice sum calculation will certainly be in error. In doing the lattice sum calculation, it is assumed that the valence electrons are localized at the lattice site so the effective charge is that of the free ion. Covalency would result in delocalization of the valence electrons and a reduced effective chargeo Being aware of the inadequacy of a lattice sum calculation for a covalent crystal, any result obtained from such a calculation must be treated with some care. Nevertheless, a lattice sum calculation was performed for the configuration described in Figure II-6(b). The result is a field gradient eq1=49.3 e/ao in the (111) direction. Using a = 6.452A for PbTe and the measured quadrupole moment Q =.20 barns, the calculated quadrupole splitting isAEQ = 265 x 109 ev =.0223 mm/sec. This is very small compared to the line width 2r = 5.488 mm/sec. However, we have not taken into account the Sternheimer polarization factor (1 - o ) Although, has not been calculated for the Te125 2 ion, indications are that it is very large in heavier ions such as this (e.g.,, for the I127- ion is -179) (55) Such a large Sternheimer antishielding factor would make the quadrupole splitting of the same order of magnitude as the natural line width and perhaps measurable.

-47 Variations in isomer shift are expected to be very small compared to the line width 2r. The principal result of the defect production would most likely be in alternation of the 5p valence electron configuration. Such changes would only affect the isomer shift through variations in shielding of the 5s electrons The measured variation in isomer shift from an empty to a filled 5p shell is of the order of.5 mm/sec. These isomer shifts are quite small compared to the natural line width and not measurable with a high degree of accuracy. The effects of the defect environment on the Mbssbauer recoil-free fraction or f value are even more difficult to predict than hyperfine structure changes. As mentioned earlier, the altered binding forces for the defect atom will introduce localized modes into the lattice vibrational spectrum. These changes in the lattice vibrational spectrum will definitely affect the f value, but the effect is difficult to determine quantitatively. Only for very simple lattices with mass impurities and force constant impurities has quantitative analysis been made of the change in f value. (7273) The expected effect of displaced atoms on the Mbssbauer spectrum for Te and TeO2 cannot be predicted with any more certainty than for PbTeo The significant difference for Te and TeO2 is that the normal Mbssbauer spectrum contains a significant quadrupole splitting. Here displaced atom configurations may have significantly lower electric field gradients and may produce structure between the two normal lineso Again isomer shift variations would probably be small.

CHAPTER III. APPARATUS AND EXPERIMENTAL PROCEDURE A Mbssbauer Spectrometer 1. Drive System The Mbssbauer effect is observed by measuring the transmission of the resonant gamma ray through an absorber as a function of the relative velocity Ut between the source and absorber. For each velocity, the gamma ray is then given a Doppler shift in energy AE=- Es, (IIv) where E is the gamma ray energy and c is the speed of light. Relative velocities in the present experiments were obtained by moving the source with a velocity U- while the absorber was held stationary. By cyclically sweeping a range of velocities, the energy spectrum can be continuously scanned. To minimize data correction and optimize the counting time, equal times should be spent in each velocity interval. Imposing this condition on the cyclical motion, the velocity wave form should have a triangular shape as a function of timeo A schematic of the experimental system used is shown in Figure II-1. The source was mounted on the moving shaft of a commercially available electromechanical transducer* operated *Modei C31, Pickup Calibrator/Exciter, MB Electronics, New Haven, Connecticuto -48

-- LEAF SPRINGSPERMANENT FIELD MAGNET COI L IS I AWTr PROPORTIONAL I S r:1- DRIVE COIL MAGNET FIELD SUPPLY | TtME | | SINGLE |> T-IME SINGLE ~o BASE CHANNEL GENERATOR ANA LYZER MULTICHANNEL ANALYZER TELETYPE FIGURE III-1 SCHEMATIC OF THE EXPERIMENTAL SYSTEM

-50 in the horizontal positiono The moving shaft is supported at both ends with leaf springs. These allow free movement in the horizontal direction but suppress other motiono The original springs were changed to o010 inch phosphor bronze springs to reduce the natural frequency and the effect of transient oscillations and allow greater control of the vibrator with less current. Mounted on one end of the moving shaft is a drive coil which moves within an outer field coil. A magnetic field was produced within the field coil by applying a DC voltage to the magnet coil windingso The magnet field supply is shown in Appendix B, Figure B-l. With the magnetic field activated, the displacement of the moving shaft is proportional to the current through the drive coil. The velocity of the moving shaft is measured with a pickup coil mounted on the end opposite the drive coilo The pickup coil moves within a radial magnetic field created by a permanent magnet. The output voltage of the pickup coil is proportional to its velocity with a proportionality constant approximately equal to o065 volts/cm/sec. The electromechanical transducer was driven by a Nuclear Data* multichannel analyzer operating in the time mode. With a rather inexpensive modification by the manufacturer, the analyzer was adapted for operation as a forward-backward multiscaler. The multiscaler dwell time was controlled with a Nuclear Data time base unite* The analog address scaler signal'Model ND-180FM, Nuclear Data, Inco, Palatine, Illinoiso. *Model ND-180 ITB

-51 generated by the forward-backward multiscaler is a triangular wave form. Using a feedback amplifier, the velocity of the transducer can be forced to follow this triangular wave form. The linearly varying time scale of the multiscaler then corresponds to a digital representation of the linearly varying velocity of the transducer. With the forward-backward drive, only a single Mbssbauer spectrum was stored, corresponding to a reflection and overlap of the double spectrum stored in (62) other time mode spectrometers (62 The drive amplifier used was similar to that employed by Mo Bo Stearns.* It is a modified version of the amplifier originally designed by Rubin. (63) A schematic of the drive amplifier is shown in Appendix B, Figure B-2. The analog address scaler signal (.44 volts peak to peak for 256 channels) is amplified 50 times by an operational amplifier** and integrated and differentiated by subsequent operational amplifierso Since the displacement of the moving shaft is proportional to the current (voltage) through the drive coil, the velocity is proportional to the time derivative of the current. To produce a triangular velocity wave form requires a parabolic displacement wave formo Hence the principal driving voltage is the parabolic output of the integrating amplifier. Triangular and square wave (output of differentiating amplifier) voltage components are combined to provide corrections for the friction eScientific Laboratory, Ford Motor Company, Dearborn, MichiganO **All operational amplifiers are by George A, Philbrick Researches, Inc., Boston, Massachusetts.

-52 and inertia of the transducer. The combined signals are fed through two booster amplifiers to provide the driving current for the transducer. Without feedback, however, the output of the velocity pickup coil varies somewhat nonlinearly. Feedback is provided by amplifying the output of the pickup coil 55 times and comparing it to the triangular wave input signal. The difference signal is then also applied to the booster amplifier. The operating frequency of the transducer was normally about 10 cps. The frequency is determined by the multiscaler dwell time and the number of channels used (200 xsec and 256 channels, respectively, for the above). The operating velocity range for most of the Te125 measurements was - +2.5 cm/sec. This velocity range can easily be varied by changing the amplification factor of the signal from the velocity pickup coil, The observed velocity error signal was approximately 02 percent of the maximum velocity. The major portion of this error signal arises from 60 cycle pickup and noise due to the finite steps in the analog address scaler driving signal. The linearity of the drive system was checked using the magnetic hyperfine spectrum of Fe57 metal and plotting the measured peak locations versus the known peak locations. The deviation from linearity was less than o5 percent. Some difficulty was encountered with a phase shift of the analog address scaler signal in the first amplifier stage of the drive amplifier. Efforts to eliminate this were not completely successful and the phase shift had to be compensated electronically using

-53 the differentiated signal. The maximum line broadening due to both noise and phase shift was determined by evaluation of the excess broadening in the lines of the Fe57 calibration spectrum. Correcting only for absorber thickness, the unaccounted broadening amounted to.27 percent of the full velocity range of ~2.5 cm/sec. Live display of the multichannel analyzer memory was provided by a Tektronix oscilloscope.* Data was printed out using a teletype machineo** The teletype provides both a typewritten page printout and an ASCII coded punched paper tape output. The velocity scale of the analyzer was calibrated using the room temperature Mbssbauer hyperfine spectrum of Fe57 in a natural iron absorber. The six-line spectrum was fit using the excited and ground state splitting factors gl = 2.245 mm/sec (87) and go = 3.922 mm/sec determined by Preston, et al. Some care must be exercised, however, in the interpretation of such calibrations, using uncalibrated natural iron absorbers. The effective internal hyperfine fields can vary by ~ l5 percent between different natural iron foils, depending on the metallurgical history of the samples. This uncertainty was included in the error bars listed for all measurements. Velocity calibrations were performed after each tellurium run. The only difficulty encountered using the Fe5 hyperfine spectrum for calibration was the difference in velocity range *Type 503, Tektronix, Inc o, Beaverton, Oregon. **Model 33TC, Teletype Corporation, Skokie, Illinois.

-54 125 57 57 hyperfine of Te and Fe Mbssbauer spectra. The full Fe5 hyperfine spectrum occupied only one-fifth of the velocity span used 125 for the Te measurements. When using 128 channels, this provided limited resolution of the six-line spectrum. A room temperature calibration standard with larger splittings than 57 151 Fe would be desirable. Eu5 is currently being investigated as such a standard. 2o Cryostat The low Debye temperatures for most tellurium compounds (EDN150~K) necessitate Mbssbauer measurements with both the source and absorber at liquid nitrogen temperature or lower. The cryostat shown in Figure III-2 was designed for use with both the source and absorber at liquid nitrogen temperature and with the motion fed through from the outside to the sourceo The cryostat was similar to one originally described by DeWaard, DePasquali, and Hafemeister (64 65) The chief features of this cryostat were the low cost, simplicity in construction, and ease of operation. The cryostat consisted of a commercially available 8 liter stainless steel Dewaro* A 3" x 2~" x 15" block of aluminum acted as a cold finger for conduction cooling of the source and absorber. The source and absorber mounting was completely assembled prior to insertion in the cold finger and then was simply threaded into the aluminum block. The source and absorber mounting consisted of an outer aluminum holder fitted *Virtis Company, Inco, Gardner, New York.

To Transducer!W v I/ / //// / -— I /"nIw Counter Rubber / Iron- Constantan bsorberL Membrane / Thermocouple / Source / / / / Stainless / Steel Tubes Aluminum Block 0 1 2 in. l I I Stainless Steel Dewar Nitrogen FIGURE III-2 CRYOSTAT

-56 with a ~" diameter stainless steel tube. The sources were mounted in a small aluminum holder which was attached to a 1-1/8" diameter, 6 mil thick beryllium-copper flexure plate* and a ~" diameter stainless steel tubeo This tube acted as the source driving rod. The flexure plate was held in the holder with a cap on which was mounted the absorber holder. The cap and absorber holder were firmly clamped in place with a second screw cap. After mounting in the aluminum cold finger, the stainless steel driving rod was coupled to the moving shaft of the electromechanical transducer by a second piece of tubing. The source and absorber holder was sealed to the air with a rubber membrane mounted at the joint of the two driving rods and clamped between two pieces of aluminum attached to the outer stainless steel tube An iron-constantan thermocouple was sealed inside the aluminum source holder with epoxy. The leads pass out through the driving rod to a temperature recorder.** The aluminum cold finger and source and absorber holder were insulated with styrofoam. A single block of styrofoam was cut in the proper shape to fit over the aluminum cold finger and to seal on the rim of the stainless steel Dewaro The source and absorber holder was mounted through a hole in the side of the styrofoam block, which was sealed with a piece *The beryllium-copper flexure plates were prepared by etching the pattern in ferric chloride etching solution. **Fi sher Recordall, Fisher Scientific.

-57 of styrofoam after mounting. The styrofoam block was rigidly clamped to a work bench after the driving rod was coupled to the transducero The temperature of the source and absorber in the cryostat was 820K when the Dewar was completely full. The temperature increase during a cycle was approximately 9~K. The liquid nitrogen boil-off rate was about 1 liter/hour. 3. Detection System As discussed in Chapter II, one of the difficulties in the detection of the 35.6 kev gamma ray of Te125 is the intense background from the K and Kp x-rays at 27.4 kev and 31.2 kev. The number of x-rays and gamma rays emitted per decay from the 145 kev level was calculated in Chapter II as K. -:KO = 942s o203 o070. The three energy peaks cannot be resolved using a NaI scintillation crystal and can only be partially resolved with a proportional counter. The difficulty with resolution can be circumvented by detecting only the escape peak. Violet(29-31) originally used this method with a NaI scintillation detector; however, the method is equally applicable with a xenon-filled proportional counter. In both iodine and xenon, the energy of the K-absorption edge (33.17 kev and 34.51 kev, respectively) is between the Te125 x-ray and gamma ray energy. Thus, only the 3506 kev gamma ray absorption is capable of K-shell photoelectric absorption and subsequent excitation of iodine and

-58 xenon x-rayso The escape peak arises from the loss of the iodine or xenon x-rays from the detector. The technique was tried using both a thin NaI(Tl) scintillation crystal* and xenon-filled proportional counter.** The calculated optimum NaI crystal thickness for this technique is 9 mils; however, there is considerable difficulty in cleaving crystals this thin. The crystal provided by Harshaw was apparently much thicker, and consequently the escape peak efficiency was quite low. In addition, the resolution of the escape peak was considerably better with the proportional counter than with the scintillation detector. Subsequently, all measurements were made with the proportional counter rather than the scintillation detector. The pulse height spectrum taken with the xenon/nitrogenfilled proportional counter is shown in Figure III-3 (a) The x-ray and gamma ray photopeaks are not resolved. Escape peaks occur at both 3o0 kev and 7,0 kev energies corresponding respectively to the loss of the xenon Kp and Kc x-rays. The 3~0 kev peak occurs below the noise threshold, so only the 7o0 kev peak is selected for the Mbssbauer experiment. The signalto-noise ratio of the escape peak can be improved a factor of 3.5 with only a factor of lo5 reduction in the count rate by using a Cu absorber to selectively filter out the tellurium x-rayso With a 5 mil Cu absorber (113 mg/cm2), the intensities at the detector are reduced to Kc oKp o~ =,186e.066.o033. Less *Integral Line Assembly, Harshaw Chemical Company, Cleveland, Ohio **Model RSG-30A, Reuter-Stokes Electronic Components, Inco, Cleveland, Ohio.

(a):2) z 0 0 0 10 o I0.J I Ur I Escape Peak 7.0 KI. 41. 5I K27.4 31.2 35.6 27.4 31.2 35.6 102 I I I I I I I I I I I I I I I I 0 100 200 300 400 500 CHANNEL NUMBER FIGURE III-3 Te125m GAMMA AND X-RAY SPECTRUM TAKEN WITH A XENON-NITROGEN PROPORTIONAL COUNTER USING: (a) NO X-RAY FILTER, AND (b) 5 Mil Cu X-RAY FILTER

-60 than 1 percent of the 8o0 kev copper x-rays generated by the photoelectric absorption are transmitted through the 20 mil aluminum window on the proportional counter. The spectrum taken using the 5 mil Cu absorber is shown in Figure III-3(b)o The energy resolution of the escape peak is 26 percent and the signal-to-noise ratio is 3:1o The signal-to-noise ratio could be improved further by using a thicker copper selective absorbero However, the decreased count rate made this prohibitive. The output pulses from the proportional counter were fed through a preamplifier and double delay line linear amplifier into a single channel analyzer.* The proportional counter voltage was supplied by a regulated high voltage power supply,** The pulses in the escape peak were selected with the single channel analyzero Peak settings are easily accomplished using a multichannel analyzer by coincidence gating the total spectrum with the output pulses of the single channel analyzer, The single channel analyzer output pulses were stored in the multichannel analyzer operating in the multiscaler mode Bo Source and Absorber Preparation 1, Sources All of the sources used in the experiments described in this paper consisted of Tel25m in various compounds of telluriumo The Te125m was prepared by the reaction Te124(n,6)Tel25m as described in Chapter II. Irradiations must be done using *Models NB-19, NA-12D, and NC-14, Hamner Electronics Company, Inc, Princeton, New Jersey. *"Model N-4035o

-61 tellurium compounds enriched in Te124 This is made necessary by the presence of stable isotopes of tellurium (notably Te20, Te122 Te126 Te128 and Te130) which have abundances and cap124 ture cross sections comparable to Te and which produce reaction products with half lives comparable to Te125m. The gamma and x-rays produced in the decay of these reaction products would create a background intolerable for detection of 125m the Te 35.6 kev gamma ray. The source enrichments were all 93.9 percent in Te a. PbTe The PbTe24 was prepared by New England Nuclear Corporation (NEN)* by reacting stoichiometric amounts of Pb and Te in vacuum for 30 minutes at 900~C. The sample was in powder form and had a purity greater than 99 percent. The principal contaminant in the sample was sulfur, which was present in the enriched Te124 obtained by NENo For use as a source in the radiation effect measurements, the PbTe124 powder was pressed into the form of a thin platelet and sintered. The initial density of the powder was only 37.6 percent of that of the solid material. Densification was achieved by several compacting and grinding steps. The final platelet was formed by grinding the densified powder through a 100 mesh screen and pressing between two steel plates with approximately a 20,000 pound load. *New England Nuclear Corporation, Boston, Massachusetts.

-62 The ~" diameter platelet was sintered in a hydrogen atmosphere in an annealing furnace at 550~C for three hours. The annealing removes the stresses induced by the compacting and causes recrystallization and coalescence of the powder particles. Less than 10 percent of the mass was lost by sublimation during the sintering. The resultant platelet was quite brittle, but successfully withstood several handlings. The weight of the irradiated platelet was 57.7 mg. b, Te Metal 124 The Te metal was supplied by NENo The metal was electromagnetically enriched in Te24. The samples were of purity greater than 99 percent,with sulfur as the major contaminant. A sintered metal platelet was prepared using the same procedure as for the PbTe. The platelet was annealed at 350~C for six hours. The weight of the irradiated platelet was 30.3 mg. co TeO2 Te12402 was prepared from Te124 metal using a modification of the procedure described by Marshall. (66) Samples of Te2 weighing approximately 60 mg were placed in a 50 ml beaker and covered with 10 ml of water. 10 ml of HNO3 were slowly added to dissolve the Te metal. The clear liquid was then evaporated on a water bath in an open 20 ml beaker. Crystals of basic tellurium nitrate (2TeO2oHN03) were deposited during the evaporation. Evaporation was continued to dryness The beaker was

then covered with a watch glass and heated in an oven for two hours at 415~Co The decrepitation of the basic tellurium nitrate yielded TeO2 in the tetragonal crystal form. X-ray diffraction analysis of the powder confirmed the existence of only the tetragonal crystalline modification with lattice o 0 constants a = 4.810A and co = 7.613A (X-Ray Powder File, Card 11-693). Some other interesting observations were made during preliminary preparations of TeO2. X-ray diffraction measurements of the "basic tellurium nitrate" crystals deposited on evaporation indicated the structure was nearly identical to the tetragonal Te02o Only a slight trace of additional structure was discernible in the diffraction pattern. This observation was further confirmed by the catalogued diffraction pattern (X-Ray Powder File, Card 1-0862) for "basic tellurium nitrate," which is essentially the pattern for tetragonal TeO2 with only slight differences. The origin of the apparent similarity is the nearly identical Te-O structure for tetragonal TeO2 and 2Te02 HN03 (101) The possibility of introducing a phase change from the tetragonal to the orthorhombic structure on heating was indicated by Marshall. (66) The existence of a phase change was studied by heating the sample at various temperatures and taking the x-ray diffraction pattern after each heatingo Samples were heated in an annealing oven at 405~C, 6300C, and 7750~C The first two samples were heated for two hours. The

-64 latter sample was melted (MP = 733~C) and quickly cooled to room temperature. The diffraction pattern for each of the samples following heating showed only the tetragonal crystal structure. This indicates that over the temperature range from 405~C to the melting point TeO2 forms only a tetragonal lattice. No structure change from the tetragonal to the orthorhombic phase was observed. This result is confirmed by Zlomanov, et al.,(67) who observed the identical result over the range 457-704~Co Dutton and Cooper (68) have concluded that the tetragonal form is produced by any artificial method of preparation and the rhombic structure occurs only for the naturally occurring mineral "tellurite." For use as source material, the Te12402 was retained in powder form. Powder samples were sealed in aluminum foil packets for irradiations. 2o Absorbers All of the absorber material used were in powder form. Rigid absorbers were prepared by imbedding the powder in lucite. The procedures was as follows: The powdered tellurium compounds were ground through 100 mesh screen and thoroughly mixed with - 100 mg of 100 mesh lucite powder. The mixture was placed in a 5/8" diameter stainless steel mold between two heater plates in a mechanical press* Approximately 200 psi was applied and the mold was heated to 115~C and quenched. The powder appeared to be very homogeneously dispersed. The thin, rigid mounting proved very convenient to use. *Carver Laboratory Press, Fred So Carver, Inc., Summit, New Jersey.

-65 It was originally felt that absorbers enriched in Te125 would be necessary to provide significant f values. Assuming no resonant absorption occurs in the source, the maximum resonant intensity is given by (69) P(Mo)- P(o) 6(o)= - (III.2) fs ri-e Jo (T^t) (III.3) where f is the source f value and TA is the effective absorber thickness TA = hf A C+ tA (III.4) fA is the absorber f value, nA is the number of atoms per cubic centimeter, aA the fractional abundance of resonantly absorbing atoms, T0 the resonant cross section, and tA the absorber thickness. An increased abundance aA increases TA and C (0) approaches the source f value. However, the resolution of hyperfine structure in Te125 is inherently poor due to the broad natural line width. This necessitates the use of thin absorbers to minimize the line broadening. The experimentally measured line width is given as69) r.eet =(2a+.27T r +T27 T5. (Iiis5) 1 +heoy A''A0

-66 Here it is assumed that the effective source and absorber line widths are equal and equivalent to the natural line width, For values of TA less than one, the line width increase is less than 15 percent. With poor resolution, however, even a broadening of this magnitude can be significant. In the end, the need for better resolution exceeded the need for higher f values and natural abundance absorbers were used. The absorber thicknesses were chosen to maximize the information obtainable from a Mbssbauer experiment. The criterion for maximum information is that the ratio of the maximum resonant intensity in counts per channel to the standard deviation of the counts per channel be a maximum, or aQ^n,, - max (^ ) E(O)).(III.6) Using Equation (IIIo3) and the fact that - XA P()= Se, (IIo7) where S is an appropriate source strength per channel, r is the electronic absorption coefficient in cm2/mg, and XA = tA is the absorber thickness in mg/cm2 the maximum of Equation (III 6) can be determined. The ideal effective absorber thickness is given as the solution to (/cA jTA/a Liot^/- I, (T^/Z)] (IIIo8) (L/CA-TA!/2 -(TA

-67 where CA = TA/XA. The solution to Equation (III.8) is shown in Figure III-4 for various //CA ratios. The optimum effective absorber thickness is the intercept with the appropriate A/CA curve. Since the f values for most of the tellurium absorbers were not known, the I /CA ratio could only be estimated. This introduced considerable uncertainty in the optimum thickness. For 125 most natural abundance tellurium absorbers (aA25 = 699 percent), 2 the optimum thickness is of the order of 50 mg/cm2 The effective thicknesses of the prepared absorbers were determined by measuring the attenuation in the absorbers of the 14.4 kev Fe57 gamma ray from a Co57 source. These values are all tabulated in Table III-1. From Equations (II4) and (III.5), it is possible to calculate the expected line width for each absorber, correcting for the absorber broadening. For most of the absorber materials, the Debye temperature is unknown so the value cannot be calculated directly. The Debye temperature for TeO2 was measured previously as ED Cr 1700K. (32) A comparison of the measured resonance intensities and absorption areas of the other compounds with TeO2 indicated that an assumed Debye temperature of GD ~ 170~K for each of them would net be too unreasonable. The line widths listed in Table III-1 were calculated under this assumption. For the absorbers with a natural abundance of Te 25 the absorber corrections amounted to^10 to 20 percent of the natural line width. An extreme error

.5 1.0 1.5 20 25 3.0 3.5 4. 2.5 4 2.0 3.7 TA j00 06.5,4.3 o0 2 o.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 TA FIGURE III-4 OPTIMUM EFFECTIVE ABSORBER THICKNESS FOR MAXIMUM INFORMATION

TABLE III-1 MlF A.R TT'RI'T T T T'R.. T AN nTT PF.rPTMArP.'n T.TMT' WTT-nT'FrD rr1T T.T TTD TTThI A' rDC TD'T'D C L11J.;AL-1 uj % d Y ~j;A " Ll~-ql J ~ A &J JL - U I L J-:A " u -L LN J:j YV -L " I. " V % / V N. ILJ LfiJTJlUsl VI'L I-i 1-i.DOCnMF-An l Absorber PbTe-1 PbTe-2 TeO2 CuCr2Te4-1 CuCr2Te4-2 MnTe CrTe H6TeO6 Tota 1* Thickness (mq/cm2) 17.2 17.9 61.9 30.7 53.5 32.8 35.2 39.0 Te125 (%) 95 95 7 7 7 7 7 7 Te125 Thickness (mg/cm2) 6.2 6.4 3.5 1.6 2.8 1.6 1.4 1.5 (D (~K) 150 150 170 170 170 170 170 170 T 2.0 2.1 1.5.7 1.2.7.8.7 Itheor (mm/sec) 7.0 7.1 6.6 5.9 6.4 6.0 6.1 6.0 I C1I I *Thickness determined by gamma ray attenuation measurement. **Debye temperatures are estimated values except for PbTe and TeO2.

-70 of 100 percent in the estimated value of TA would amount to only ^ 10 to 20 percent error in the estimated line width. The M6ssbauer spectra for H6TeO6, CuCr2Te4, and TeO2 gave measured line widths which were only of the order of 5 percent greater than the calculated value. Broadening of this magnitude can be accounted for principally by the uncertainty in the estimated line width and the experimentally introduced broadening. Other small contributions include source broadening and absorber inhomogeneities. The MnTe and CrTe lines were broadened by unresolved hyperfine splittings, as will be discussed in Chapter Vo The PbTe absorbers enriched in Te25 displayed line widths approximately 36 percent greater than the expected value. This will be discussed in Chapter IV. Information on the procedures used for preparation of the tellurium compounds used as absorbers is given below. a o PbTe Lead telluride enriched to 95.0 percent in Te125 was prepared by NEN as described in the above section dealing with sources o b. TeO2 Tellurium dioxide with natural abundance tellurium was prepared using the procedures described in the above section dealing with sources. X-ray diffraction confirmed the existence of only the tetragonal crystalline form.

-71 c. CuCr2Te4 CuCr2Te4 powder was obtained from C. Colominas.* The procedure used in preparation of the material and the results of neutron and x-ray diffraction study of the material are reported in a recent paper.( d, MnTe A sample of manganese telluride powder was obtained from Tseng-Ying Tien,** The sample was selected from several which had been prepared as being the closest to a stoichiometric mixture. The sample was prepared using approximately 1 percent excess tellurium by weight. High purity Mn and Te powder were ground through 200 mesh screen, mixed, and pressed into pellet form. The powders were reacted in a graphite crucible in an evacuated Vycor tube. The graphite was used because of the high heat of reaction and because the MnTe reacts with Vycor. The powder was reacted for four hours at 500~Co X-ray diffraction patterns indicated no trace of the elements or other compositions. e. CrTe Chromium telluride was prepared by reacting high purity Cr and Te powder. Stoichiometric amounts of Cr and Te were mixed and ground together. The powder was sealed in an evacuated quartz tube and heated at 1000~C in a temperature controlled, *C.NRoSo, Grenoble, France. **Department of Chemical and Metallurgical Engineering, The University of Michigan, Ann Arbor, Michigan.

-72 rotating combustion furnace for 19 hours. The CrTe was removed from the quartz tube and the sample was reground and again sealed in an evacuated quartz tube. The powder was heated to 1000~C for 21 hours and then quenched to room temperature. The reheating was done to insure the homogeneity of the sample. X-ray diffraction patterns confirmed the presence of CrTe of hexagonal structure with lattice constant a = 3.96R and co = 6.17R (X-Ray Powder File, Card 2-0682). There was no trace of any additional structure in the diffraction pattern. f. H6TeO6 A sample of orthotelluric acid in powder form was obtained from the Department of Chemistry of The University of MichiganO The procedure used in preparation was not known. X-ray powder diffraction patterns agreed well with the data for the cubic phase with lattice constant a = 15.51 (X-Ray Powder File, Card 1-0329). Some monoclinic form may be present since it is somewhat difficult to distinguish between the two phases with the x-ray diffraction pattern (68) Co Source Irradiations The sources were all irradiated in the Ford Nuclear Reactor at The University of Michigan. The reactor is a swimming pooltype research reactor which operates at two megawattso The core consists of enriched U-235 fuel elements. The core is light water moderated, but a tank of D20 has been installed on one face to act as a reflecting element. Provision is made for

-73 irradiations in core, in the heavy water tank, or in the light water moderator away from the core. The highest thermal neutron flux is obtained in the D20 tank holes nearest the core. The flux here is approximately 2.5 x 1013 neutrons/cm2-sec; however, the cadmium ratio (thermal flux/fast flux) is only 4.5. Sources which were not used for radiation effects measurements were usually irradiated at this location or in the core (approximately 1-3 \2 1.5 x 1013 neutrons/cm2-sec maximum thermal flux). The sources used in the radiation effects measurements were irradiated at lower thermal neutron fluxes but with higher cadmium ratios to minimize fast neutron effects. The thermal and fast neutron fluxes used for each of these sources are listed in Table III-2. TABLE III-2 IRRADIATION CONDITIONS FOR Te125 SOURCE MATERIALS FOR RADIATION EFFECTS MEASUREMENTS Y+h Y + Y ^6t qf tf Source (n/cm2-sec) (n/cm2-sec (hrs) (n/cm2) (n/cm2) +h/ PbTe 6.4 x 1011 5.3 x 1010 336 77 x 1017 6.4x1016 12 Te 6.4 x 1011 5.3 x 1010 400.7 9.2 x1017 7.6x 106 12 TeO2 5.8 x 1012 4.5 x 1010 399o3 8.3 x l08 6.5x017 13 Both the PbTe and Te metal platelets were mounted in an aluminum holder for the irradiations. The TeO2 powder was sealed in an aluminum foil packet. The source holders were then sealed in a 3/4" diameter by 2' aluminum tube by welding

-74 caps on both ends of the tube. This was made necessary by the relatively long irradiation times. Sources were irradiated by inserting the tubes directly into the irradiation holes. Following irradiation, the samples were stored in the pool for a period of approximately one week. This reduced the 15hour Na24 activity produced by the reaction A127(n,o)Na24 to a tolerable level so that the irradiation tube could be safely handled. The Te125 sources were then removed from the aluminum holders and remounted to eliminate any background activity from the holders. All irradiations were done at reactor ambient temperature. Measurements were made of the sample temperatures during irradiation by inserting dummy source holders into the core with copper-constantan thermocouple wires attached. Equilibrium sample temperatures ranged from a maximum of 55~C at the incore irradiation hole to 41~C in the second irradation cup (C2) in the water away from the core.

CHAPTER IV. EXPERIMENTAL RESULTS OF THE RADIATION EFFECTS MEASUREMENTS The procedure used for investigating the effects of neutron capture on the M5ssbauer spectrum was as follows: The PbTe, Te, and TeO2 source materials were prepared and irradiated as described in Chapter III. After irradiation, the Mbssbauer spectrum was taken for each of the sources against a single line absorber. These spectra should be characteristic of the lattice with atoms displaced from normal lattice sites by the mechanism described in Chapter II. The spectra characteristic of the "ideal" lattice were obtained using the same sources following treatment to restore the displaced atoms to their normal lattice environment. In the case of the PbTe and Te metal, the defects were removed by annealing. The PbTe was heat treated in a hydrogen atmosphere for 11 hours at 400~C. The Te metal was also annealed in a hydrogen atmosphere at 350~C for 12 hours. The TeC2 powder was dissolved and recrystallized following the procedure described in Chapter III. The Mbssbauer spectrum was taken again for each of the sources under the same conditions as the initial spectrum. These data served as reference spectra characteristic of the "ideal" lattice. By comparison of the "defect" and "ideal" Mbssbauer spectra, the effects of the neutron capture induced displacements could be determinedo The following are the results and discussion of the measurements on PbTe, Te metal, and Te02. -75

-76 Ao PbTe 1. Results The Mbssbauer spectrum was taken using the PbTe125 source and a single line PbTe absorber enriched to 95 percent in 125 Te. The measurements were all made at liquid nitrogen temperature. The data taken in the Mbssbauer measurement before annealing are shown in Figure IV-1. The data, uncorrected for background, are presented as the resonance absorption normalized to the background counting rate. The solid line is the best fit with a single Lorentzian line shape.* The results of the fitting to the Mbssbauer spectrum after annealing are shown by the dashed line in Figure IV-1. The fitting parameters and the error limits** for each of the spectra are listed in Table IV-1. TABLE IV-1 PARAMETERS FROM PbTe RADIATION EFFECTS DATA F' *** f # ## ### PbTe ep Resonance Area Source (mm/sec) mm/sec) Intensity (mm/sec) /N Pre-annea 9.60 23.07+ ~.05.0324+ 0003 444 1.469 Post-anneal 9.58~.22.03.04.0351~.0003.471 1.142 *The least squares fitting program is described in Appendix Co **The error limits for line shifts and splittings include both statistical error and uncertainty in the velocity calibration. The error limits on the intensity are only statistical and do not include experimental uncertainty. ***Full width at half maximum of the resonance line. #The center shift relative to zero velocityo ##Maximum resonance intensity uncorrected for background. ###Area under the resonance spectrum obtained by numerical integration.

0 ~z ~. 0 I I I aa3 00 w z 3- \ / —Annealed -2.0 -1.0 0 1.0 2.0 VELOCITY (cm/sec) FIGURE IV-1 RESONANCE ABSORPTION SPECTRUM FROM THE PbTe SOURCE AND PbTe ABSORBER BEFORE AND AFTER ANNEALING

-78 The following observations can be made of the data. The line width remains constant in the two measurements. The isomer shift is slightly more positive* before annealing, but it is not statistically significant. A similar experiment performed earlier did not show this same trend. The line intensity, uncorrected for background, increases 7.7 percent upon annealing. The increase in area of 5.8 percent is approximately equal to the change in line intensity. 2. Discussion of the Data ao Radiation Effects In summary, the only apparent difference between the spectra is in the resonance intensity. This change in resonance intensity will be discussed following presentation of the results of the Te and TeO2 data. These results for reactor irradiation 1 ^2 of PbTe124 do not show the dramatic change in isomer shift reported by Stepanov and Aleksandrov. (17) The reported isomer shifts up to 2 mm/sec should easily be seen in the present measurement. The lack of such a shift in the present measurement is probably due to the lower concentration of fast neutron defects. The irradiation conditions for the Stepanov and Aleksandrov experiment were considerably different than ourso The integrated thermal flux for irradiations by Stepanov and Aleksandrov was 9.0 x 1020 neutrons/cm2 compared to the value 707 x 10 neutrons/cm2 listed in Table III-2 for the present *Positive velocities are defined by the motion of the source toward the absorber.

-79 measurement. No information was presented in their paper on the fast flux; however, with a reactor thermal flux of 2.3 x 1014 neutrons/cm2-sec, the cadmium ratio is probably no better than 5. With this assumption, the integrated fast flux would be 1.8 x 1020 neutrons/cm2 compared to our value of 6.4 x 1016 neutrons/cm2. Assuming no saturation behavior, the defect concentration produced by the fast flux in the Stepanov and Aleksandrov irradiation would be approximately.4 —meaning roughly one of every two tellurium atoms would be displaced by fast neutron scattering. In this case, the concentration of fast neutron induced defects is so large that these defects, in addition to the thermal neutron induced defects, may have a significant effect on the Mbssbauer emission spectrum. Stepanov and Aleksandrov interpret the origin of the isomer shift as a change in the band structure of PbTe which alters the probabilities of s- and p-electron transitions to the conduction band. The surprising fact is that the defects appear to anneal at room temperature, contrary to what had been (23-25) reported earlier on neutron effects in PbTe(2325) b. Line Width The apparent single line spectrum for PbTe confirms the absence of quadrupole splitting in cubic structures. The one disturbing feature of the spectrum is the unexpectedly large line width. The measured line widths are approximately 36 percent broader than the predicted line widths. The predicted line widths rheor may be as much as 10 percent in error, however, due to the

-80 estimate of the f value and the uncertainty in the measured thickness. In all likelihood the predicted line widths are low estimates. Part of the broadening arises due to the difference between the line width determined from a "best-fit" Lorentzian and the true width at half maximum of the absorption spectrum. For increasing values of TA, the Lorentzian line shape differs significantly from the true absorption spectrum. This was readily apparent in observation of the deviation of the "best-fit" Lorentzian from the true absorption spectrum for PbTeo The result showed identical behavior to that described by Bowman, et al.(102) A significant deviation is also confirmed by the relatively large t /N values for the PbTe spectra. The paper by Bowman, et al., indicates that this broadening may amount to several percent. A second contribution to the broadening is the effect of the granular absorbers. Bowman, et alo, have shown that the line widths are broadened by the finite grain size of the absorber powdero If it is assumed that the average powder size is 200 mesh (.074 mm diameter), the average resonant thickness of a grain of PbTe125 is approximately TA = 40 The total average resonant thickness of the PbTe125 absorber is TA 2.1. The results of Bowman, et al., indicate the relative A width for such an absorber is r C 3 r4 r = 9~35 mm/sec. theor This is in good agreement with r = 9.6 mm/sec. This exp estimated line width must be treated with some care since some of the factors are only crude estimates. The point of interest

-81 is the fact that the grain size can provide broadening factors of the order of 30 percent. It appears that this factor easily explains the observed broadening. Such a large broadening would not be expected in the absorbers with a natural abundance of Te125 Assuming the powders are of identical grain size, the average resonant absorption per grain will decrease approximately in proportion to the ratio of abundances (.07/.95 = o074); so for the natural abundance absorbers T.r ~3. With a total average resonant A thickness TA- 1, the broadening is now only about 3 percent. Other sources of broadening which were discussed in Chapter III include that due to resonant absorption in the source and instrument broadening. Both of these factors contribute relatively little broadening in the measurements reported herein. A final possible source of broadening may arise from inhomogeneous hyperfine structure in the Mbssbauer spectrum due to defects, nonstoichiometry, dislocations, grain boundaries, etc. These effects are also expected to be small. B. Te Metal 1. Results The Mbssbauer spectrum was taken using the Te125 source 125 and a single line PbTe absorber enriched to 95 percent in Te The measurements again were all taken at liquid nitrogen temperature. The Mbssbauer data taken before annealing are shown in Figure IV-2. The data are fit with two Lorentzian

O ~~ i^ * s, S ~A A a. 0 w z~s' B 00 C2- 2I f ~ / —— Anneoaed 3 -2.0 -1.0 0 1.0 2.0 VELOCITY (cm/sec) FIGURE IV-2 RESONANCE ABSORPTION SPECTRUM FROM THE Te SOURCE AND PbTe ABSORBER BEFORE AND AFTER ANNEALING

-83 line shapes with variable intensities for each of the lines. The results of the fitting and the subsequent fitting to the spectrum after annealing are shown as the solid and dashed lines, respectively, in Figure IV-2. The fitting parameters for each of the spectra are listed in Table IV-2. Te Source Pre-ar Post-a PARAMETERS FROt (mm/sec)? (mm/sec) neal 9.07~.24 inneal 8.83~.2E TABLE IV-2 4 Te RADIATION EFFECTS DATA g AEgQ Resonance* (mm/sec) (mm/sec) Intensity [ -.44~.08 7.51~.14.0197~.0004 -.41~.09 7.35~.15.0221~.0005 *Average resonance intensity for the two lines, uncorrected for background. Te Source Pre-annea Post-anneal Area (mm/sec).528.573 L2/N.894 1.065 The line width, isomer shift, and quadrupole splitting parameters remain constant within the statistical accuracy of the fitting. The resonance intensity increases 10.1 percent upon annealing and the area increases7.9 percent. Again, for Te metal there appear to be no hyperfine effects attributable to displacements. This is not unexpected in Te though due to the probable self-annealing during irradiation. With rapid annealing

-84 prior to measurement, the initial spectrum should also be characteristic of the "ideal" lattice. In consideration of the annealing, resonance intensity changes are unexpected. This would lead one to suspect that the observed changes in resonance intensity are not real effects but due to uncertainty in the experimental measurement. This will be discussed in detail in this chapter. 2. Discussion of the Data ao Quadrupole Splitting The quadrupole splitting in tellurium metal has been analyzed in considerable detail by both Violet, et al.,(30) and Shikazono. (33) The structure of tellurium metal is shown in Figure IV-3(a) and (b)o The crystal consists of infinite spiral chains of tellurium atoms. The atoms are covalently bonded in the chains but only weakly bound between chains by electronic and van der Waals forces. The electric field gradient arises principally from bonding between adjacent atoms on the same chain. The covalent bending scheme results in unbalanced px, py, and Pz orbitals, which provide a field gradient ____ 1M u..ir(Iv.1) eq = eq L X2 - Nz = eO Up N, N, and N are the electron populations in the pX, py, and x y z pz orbitaist eqo is the electric field gradient due to a single unbalanced p-electron; and f is the fractional importance of such

-85 0 0 — O 0 0 0 0* (a) g a I I I I %...j a = 5.927 c= 5.927R (b) pi ^ J a=4.457 A FIGURE IV-3 (a) PROJECTION OF TELLURIUM CRYSTAL STRUCTURE (DIFFERENTLY SHADED CIRCLES REPRESENT ATOMS AT DIFFERENT LEVELS) (b) TELLURIUM CRYSTAL STRUCTURE

-86 bondingo The electric field gradient for a single unbalanced p-electron in atomic tellurium calculated by Barnes and Smith(74) is eq = 3.9 +.4 x 1016 esu. Violet, et al.,(30) used such a 0 formulation and obtained a value eq = -2.8 + x 1016 esu for tellurium metal. The quadrupole splitting, as described in Equation (IIo20), is determined by the separation of the two lines in the Mbssbauer spectrum shown in Figure IV-2. The average value of the quadrupole splitting obtained from our measurements is AEQ = 7.50 +.10 mm/seco It is in excellent agreement with previous measrements(30,32-34,36) measurements. b. Asymmetry In all measurements with tellurium metal, the two lines in the spectrum were slightly asymmetric. The results consistently showed that the intensity of the negative velocity component was a few percent greater than the positive velocity component. However, the difference was of the order of the standard deviation of the fitted intensities. The asymmetry arises from the anisotropy of the f value. The origin of the effect was first discussed by Nicholson and Burns (75) and is known as the Goldanskii effect. (76) For a polycrystalline source such as the tellurium metal used here, the relative intensities of the components of the Mbssbauer spectrum are obtained by averaging the angularly dependent emission probabilities over all angles. This is identical to the procedure described earlier for the intensities in the magnetic hyperfine

-87 spectrumo With an isotropic f value, the average over angles involves only the emission probabilities and the ratio of intensities is 1. However, with an anisotropic f value, f is also angularly dependent and the angular average may provide a ratio unequal to 1. An angularly dependent f value would be expected for tellurium metal which has a highly anisotropic crystal structure. The asymmetry is clearly not in agreement with the result reported by Stepanov, et al.(36) The asymmetry is opposite to and much smaller than their reported values. Violet, et al.,( reported no apparent asymmetry within the statistical accuracy of the fitting. C. TeO2 lo Results a. Radiation Effects The Mdssbauer spectrum was taken using the Te12502 source and a single line H6TeO6 absorber with a natural abundance of 125 Te 25 The measurements were all made at liquid nitrogen temperature. The Mbssbauer data taken before annealing are shown in Figure IV-4. The data are fit with two Lorentzian line shapes with variable line intensities. The results of the fitting and the subsequent fitting to the spectrum taken with the recrystallized source are shown as the solid and dashed lines in Figure IV-4. The fitting parameters for each of the spectra are listed in Table IV-3.

0o e. 0 \ S. * -. | O~~~~~~~~~~g' ~ e z 0 0 I_ I a. 0 (f) m 00 02 Annealed g~ S 3 -2.0 -1.0 0 1.0 2.0 VELOCITY (cm/sec) FIGURE IV-4 RESONANCE ABSORPTION SPECTRUM FROM THE TeO2 SOURCE AND H6TeO6 ABSORBER BEFORE AND AFTER THE SOURCE RECRYSTALLIZATION

-89 TABLE IV-3 PARAMETERS FROM TeO2 RADIATION EFFECTS DATA AND ABSORBER MEASUREMENT TeO2 rexp' EQ Resonance Area Source (mm/sec) (mm/sec) (mm/sec) Intensity (mm/sec) 2k/N Pre-anneal 6.42+.12 -1.98~.04 6.72+.11 0226.0002.514.902 Post-anneal 6.49+.12 -1.99-.04 6.89+.11.0219!.0002.505.791 TeO2 Absorber 6.79+-. 28.62+.16 6.96~.16,027 5.0009.540.967 As in the previous measurement with tellurium metal, the line width, isomer shift, and quadrupole splitting parameters remain constant within the statistical accuracy of the fitting. The line intensity was 3.2 percent less for the recrystallized source spectrum r with the area decreased by 1.8 percent. These results again indicate that no significant hyperfine changes occur which could be attributed to radiation induced displacements. The variation in resonance intensity is opposite to the change seen in both PbTe and Te metal. b. Absorber Measurement For an additional measurement of the quadrupole splitting in TeO2 and to obtain the isomer shift with respect to PbTe, the Mossbauer spectrum was taken using a source of PbTe125 and a TeO2 absorber with a natural abundance of Te125 The measurements were made at liquid nitrogen temperature. The experimental

-90 data are shown in Figure IV-5. The data are fit with a spectrum consisting of two Lorentzian line shapes. The results of the fitting are also shown in Figure IV-5, and the parameters are listed in Table IV-3. 2. Discussion of the Data The value obtained for the quadrupole splitting is EQ = 700 +.2 mm/sec. This result is in good agreement with the value obtained by several authors.(31-33) However, the value AEQ f 5.6 mm/sec has been quoted by two other authors. (35,36) The difference in the two ranges of AEQ values is much greater than the quoted errors so the difficulty apparently arises from improper characterization of the material. Since there are three presumed structures for TeO2,( some care must be exercised. The origin of the apparent differences has not yet been fully explained. The crystal structure used in the preceding Mbssbauer measurements is that of tetragonal o -TeO2o The lattice is a distorted variant of the rutile structure. The structure appears to consist of a distorted trigonal bipyramid of oxygen atoms around each tellurium. One equatorial position is occupied by a lone pair of electrons. The average of the four Te-O distances is 2.003R. There are also two oxygens at an intermediate Te-O distance of 2.89ko Unfortunately, the complexity of the structure precludes any simplified analysis of the bonding scheme. Swink and

oh * 0 a. I o 0 o) 0 <2 0 (n LLI Q: K I I 3 -2.0 -1.0 0 1.0 2.0 VELOCITY (cm/sec) FIGURE IV-5 RESONANCE ABSORPTION SPECTRUM FROM A PbTe SOURCE AND TeO2 ABSORBER

-92 Carpenter(101) have indicated that the nearest neighbor axial and equatorial bonds probably involve different hybridizationso The origin of the intermediate length Te-O bonding is uncertain, and Te-Te bonds have also been postulated for the structure.(68) The possible existence of an electric field gradient at the tellurium site is obvious. Until the bonding scheme is clarified, though, an estimate of the field gradient is not possible. D. Discussion of the Radiation Effects Measurements 1. Resonant Intensity Summarizing the results of the radiation effects measurements, there appear to be no measurable changes in the Mbssbauer hyperfine spectra in either PbTe, Te metal, or TeO2. The only change observed in the measurements was a variation in the resonant intensity. However, after careful analysis, the variation does not appear to be due to a real change in the recoil-free fraction; rather, the variations may be considered as deviations within the experimental accuracy of the measuremento The measured changes in resonant intensity (3 to 10 percent) were certainly greater than the statistical error in the computer fit intensity (% 1 percent); however, other experimentally introduced errors are considerably larger than the statistical error. The deviations in the experimental measurement of the resonant intensity arise from both the lack of stability in the detection system during the course of a run and variations

-93 in the reproducibility of experimental conditions between runso To examine the lack of stability in the electronics during a run, the data were periodically analyzed during the course of the run. In the preceding PbTe measurement, the intensities, uncorrected for background, were observed to have a considerable variation over the course of the run. On the basis of these observed variations, the error bars on the measured resonant intensity are +2.2 percent for the unannealed run and +4.1 percent for the annealed run. These variations arise principally from changes in the gamma ray detection system. Since the runs were usually of one-week duration, this is not wholly unexpected. Any part of the system which would cause gain drifts, gain changes, or noise variations would vary the signal-to-noise ratio in the escape peak and consequently affect the measured resonant intensity. Although changes in high voltage, amplification, and discriminator setting would affect the signal-to-noise ratio, no noticeable changes were encountered. The most likely source appeared to be the proportional counter and preamplifier. During the course of the measurements, difficulties were encountered with both noise from the preamplifier and gain variations and count rate fluctuations in the proportional counter. The signal gain and count rate fluctuations do not appear to be a unique problem with our proportional counters since the same effects have been encountered by other experimenterso* This appears to severely limit the use of *Ro Do Taylor, private communication.

-94 gas-filled proportional counters for accurate measurement of Mbssbauer resonant intensitieso Careful attempts were made to exactly reproduce the experimental conditions between the pre-anneal and post-anneal Mbssbauer runs. Some differences were unavoidable, howevero Variations in the signal-to-noise ratio no doubt occurred in resetting the single channel analyzer window. Analysis of the total gamma ray spectrum and escape peak spectrum taken before each PbTe run indicated a variation of approximately 1 percent in the signal-to-noise ratio. Since the determination of the signal-to-noise ratio is not extremely accurate, the reasonably close agreement may be fortuitous, and the error may even be larger. The source temperature was continuously monitored and recorded during the course of an experiment. However, it is not possible to determine the actual temperature better than to within a few degrees from the recorder trace. In addition, the temperature was not controlled, so variations of the order of 9~K occurred during a filling cycle. A variation in the average temperature would affect the measured f value. An average temperature variation of 10K would change the resonant intensity by 1.4 percent. From the foregoing analysis, the experimental uncertainty in the measured resonant intensity could be of the same order as the measured differences. This is further confirmed by the fact that the effect is seen in Te metal where it is not expected, and variations of the same magnitude occur in other non-radiation effects measurements.

-95 2. Reasons for the Observed Results The presence of radiation induced changes of the order of a few percent in the Mbssbauer recoil-free fraction cannot be excluded on the basis of the present measurements. There are a number of reasons, however, why the effects on the recoilfree fraction and the hyperfine spectra may be very small. Unfortunately, the data currently available is not satisfactory to fully confirm or eliminate any of the explanations. The explanations are the following. a. Recoil Energy The mean recoil energy of the atom after prompt gamma ray emission may not be sufficient to displace the atom from the normal lattice site. The value obtained in Chapter II was based on several assumptions regarding the prompt gamma ray spectrum, time and angular correlation of the gamma rays, and the displacement energy. In reality, the capture gamma ray spectrum may be much more complex than is assumed in the estimate of the recoil energy. Since the mean recoil energy estimated in Chapter II was only of the order of 2Ed, a more complex capture gamma ray spectrum may yield a mean recoil energy less than the displacement energy Ed. Then only a small fraction of atoms would be displaced from the normal lattice site. The resultant Mbssbauer pattern would then be characteristic of the "ideal" lattice, with only a small "background" contribution due to displaced atom sites. Since the statistics of the accummulated

-96 Mbssbauer data were usually of the order of ~.l percent, any fraction of sites less than about 5 percent of the total would not provide a Mbssbauer line distinguishable from the statistical backgroundo In fact, even a fraction greater than 5 percent might not provide a distinguishable line if the defect sites are characterized by widely differing hyperfine interactions. This uncertainty in recoil energy cannot be resolved without a measurement of the Te125 prompt gamma ray spectrum. A measurement of the Te125 capture gamma ray spectrum was (91) attempted by Clifton, but the effort was fruitless. The fact that thermal neutron effects are observed in PbTe using other measurement techniques may be due to displacements produced by neutron capture in other isotopes of tellurium. The probability of displacements being produced due to neutron capture in the stable odd-n isotopes of tellurium (Te123 and Te 25) is certainly greater due to the approximately 2 Mev pairing energy increase in the binding energy. More favorable capture gamma ray spectra may also occur in the other tellurium isotopes. b. Replacement Collisions The final environment of the displaced atom may be a normal lattice site. Dederichs, Lehmann, and Wegener(ll) have calculated the replacement probability for a primary recoiling atom, Assuming hard-core interactions, the probability P(E)

-97 that a primary atom of energy E replaces a lattice atom during slowing down is given as (vi E/Ea E E Z2Ed P(E) = (IV.2) vr a ZEAL E Assuming the values E = 58 ev and Ed = 25 ev used in Chapter II, the probability of replacement for the recoiling tellurium atom is P = In 2 -.7. Thus, a large fraction of the recoiling atoms arrive at a normal lattice site. However, even though these atoms are in a normal lattice site, the characteristic environment may not be that of the "ideal" lattice. First, since the recoil energies are low, the replaced atom probably remains very near the replacement site. Likewise, the initial site of the recoiling atom (now a vacancy) is probably also near the replacement site. Thus, although the primary tellurium atom may not be in the defect state, it is probably a near-neighbor to a defect. Second, the recoiling atom may replace the lead or oxygen in PbTe and TeO2 rather than the tellurium. The replaced atom would then act as a substitutional impurity. This site would also be different from the normal tellurium site. In both of these cases, the characteristic environment should be different than that in the "ideal" lattice. So even though the replacement probability is large, the characteristic Mbssbauer spectrum should still be alteredo

-98 c. Defect Annealing Defect annealing may occur to restore the defects to normal lattice environments. This has been discussed in some detail in Chapter II so it will not be repeated here. The gist of the discussion was that defects are probably stable in PbTe, unstable in Te, and uncertain in TeO2. d. Hyperfine Interactions The hyperfine interactions characteristic of the defect environment may be too small to produce resolvable changes in the Mbssbauer spectrum. As discussed in Chapter II, isomer shift changes are expected to be very small compared to the experimental line width. Since the s-electron density could both increase and decrease in different defect environments, the sum over different defect configurations could easily produce an averaged spectrum which is apparently unshifted. The rough calculation of the electric field gradient in Chapter II indicates that it should be possible to see quadrupole splitting in the Mbssbauer spectrum for atoms in a defect environment. This cannot be further substantiated, however, without a more rigorous calculation of the electric field gradient involving the defect atom bonding. Evidence would indicate that defect atoms in noncubic environments (such as expected in PbTe) should produce quadrupole splitting which would at least broaden the characteristic spectrum.

-99It is unfortunate that more specific conclusions cannot be drawn from the present measurements. However, the present state of knowledge makes it impossible to conclusively confirm or deny any of the preceding observations.

CHA PTER V, EXPERIMENTAL RESULTS OF MOSSBAUER EFFECT MEASUREMENTS IN OTHER TELLURIUM COMPOUNDS Mbssbauer effect measurements were made of several additional compounds of tellurium. The interest here was solely in the information obtainable from the Mbssbauer hyperfine structure. The measurements were all made with a single line source of PbTe125. Both the source and absorber were at liquid nitrogen temperature in all of the measurements. The results for the various materials are described below. A. CuCr2Te4 The ferromagnetic spinel CuCr2Te4 appeared to be an excellent candidate for the detection of magnetic hyperfine structure in the Te125 Mtssbauer spectrum. This spinel is one of the group of chromium chalcogenide spinels which have shown an anomalous ferromagnetic coupling of the Cr spins. (80-82) The magnetic hyperfine field which would be measured in our experiment is not the field at the magnetic Cr cation site, but rather the field at the nonmagnetic Te anion site. The Te2- ion would not normally be expected to have a magnetic hyperfine field at the nucleus due to the completely filled 5s and 5p electron shells. However, the ferromagnetically coupled Cr spins can act to spin polarize or unpair the filled tellurium electron shells. This unpairing leads to a net spin density at the nucleus and a subsequent magnetic -100

-101 hyperfine field through Equation (11.28). This is often referred to as a transferred hyperfine field. Most spinels which have been studied have had magnetic properties dominated by antiferromagnetic interactions. The Cr spinels have been prepared with all of the chalcogenides 0, S, Se, and Te and the metallic cations Cu, Ag, Zn, Cd, and Hg. A group of these chromium chalcogenide spinels, including CuCr2Te4, have magnetic properties dominated by strong ferromagnetic interactions. (80-82) For all metallic cations except Cu, the attempts to produce the Te anion spinel have been unsuccessful.(79,80) Since none of the other chalcogenides are amenable to Mbssbauer study, this compound represents a rather unique opportunity for studying transferred hyperfine fields in the ferromagnetic spinels. (78) The compound was first prepared by Hahn, et al.,(78) in 1956. The magnetic properties were studied by Lotgering and reported at the 1964 Magnetism Conference.(79) Colominas(70) very recently performed x-ray and neutron diffraction measurements on the material to ascertain the spin configuration. 1. Results Mbssbauer measurements were taken using a single line PbTe125 source and a CuCr2Te4 absorber with a natural abundance of Te125. Measurements were made with two different absorber thicknesses. The spectra for both absorbers consisted of two rather broad lines. The experimental data for the thicker absorber is shown in Figure V-lo

0 *. -.5 *% 0 z 0 a0 I) LJ wr,Le = +.74.07 nm I Heff = 148 + 5 kgauss 1.5H I 0 2.5H 3 -2.0 -1.5 -I.0 -.5 0.5 1.0 1.5 2.0 VELOCITY (cm/sec) FIGURE V-1 RESONANCE ABSORPTION SPECTRUM FROM A PbTe SOURCE AND CuCr2Te4 ABSORBER (53.5 mg/cm2)

-103 a. Interpretation of Observed Spectrum At first appearance, the spectrum seems to display two lines characteristic of a large quadrupole splitting. However, closer analysis indicates that the structure is due to a partially resolved magnetic hyperfine splitting rather than electric quadrupole splitting. The spectrum was fit with the following theoretical curves: First, a spectrum consisting of two Lorentzian line shapes with identical widths and varying intensities; and second, six Lorentzian line shapes with intensities constrained to the ideal intensity ratio for a powder absorber. Both the ratio of the excited state to ground state g value and the effective internal hyperfine field were used as variables for the six line fit. The smooth curve shown in Figure V-l is the best fit with a six line spectrum. The bars denote the location and intensity of the six lines. On the basis of the curve fitting, the two line spectrum was ruled out for two reasons: First, the 7C2/N value for the fitting with two lines is greater than that for the six line fit; and second, the line width obtained with the two line fit is broader than the predicted line width. As mentioned in Appendix C, )C2/N is a measure of the "goodness of fit." The smaller %2/N, the better the fit. The values obtained in the fitting were Y/N) 2 = 1.32 and N)l = 1.01. The line width obtained in the two line fit was exp = 8068 mm/sec. This is 36 percent broader than the predicted line width theor = 6.4 mm/sec corrected for absorber broadening. The line width

-104 for the six line fit is e = 6.83 mm/sec, which is in agreeexp ment with the predicted line width. The third consideration ruling out electric quadrupole splitting as the origin of the hyperfine structure is the magnitude of the splitting. For a two line fit, the quadrupole splitting is EQ = 10.75 mm/sec. Using the quadrupole moment Q =.20 barns, the field gradient needed to give such a splitting is eq = 4.3 x 1016 esu. This is even greater than the field gradient from a single unbalanced p-electron, which as mentioned earlier is eqo = 3.9 x 1016 esu.(74) If the tellurium occurred as purely ionic Te2- the electronic structure would be (5s)2(5p)6 with no unbalanced p-electrons. For any intermediate covalently bonded structure, such as (5s)2(5p)4, the number of unbalanced p-electrons, as defined in Equation (IVol), is at most one. For the reasons described earlier, lattice field gradients would certainly be much less than this valueo On the basis of these arguments, no possible bonding mechanism would contribute a field gradient as large as that determined above. The conclusion is that the origin of the hyperfine structure must be in the magnetic interaction. b. Hyperfine Interaction Parameters The fitting parameters obtained from the six line fit are listed in Table V-l for both of the absorbers. In the final fitting, a quadrupole splitting parameter was also included in the analysis. The combined effect of the magnetic field

TABLE V-1 PARAMETERS OBTAINED FROM SIX LINE FIT TO RESONANCE ABSORPTION SPECTRA OF CuCr2Te4 \ exp (mm/sec) tg Heff (mm/sec) AEQ (mm/sec) Resonance* Intensity Absorber (mm/sec) CuCr2Te4-l 6.75~.19 -.05~.05 CuCr2Te4-2 6.83+.21 -.01+.03 3.45~.20 3.55+~.11 -.261~.046 -.293+~021 -.00+.30 -.77+.33.00282~.00010.00437~.00007 I J-J 0 Un I I Continued Absorber CuCr2Te4-1 CuCr2Te4-2 Area (mm/sec).298.580.966.991 *Actual resonance intensity for each line is obtained by multiplying by the appropriate relative intensity factor (3, 2, or 1).

-106 and electric field gradient on the nuclear levels can be quite complicated. However, with some simplifying assumptions, the level scheme can be easily interpreted. It was assumed that the magnetic field and electric field gradient principal axes coincided and that there was axial symmetry for the electric field gradient ( V = 0). It was also assumed that Heff>> e2qQ so that the electric quadrupole interaction merely acted as a perturbation to the magnetic substates. For the small quadrupole splitting obtained in the actual fitting, these assumptions are not unreasonable. Averaging the results obtained from the two measurements, the g factor ratio and effective internal hyperfine field were determined to be ge/gg = -o28 ~+ 03 (V.1) and Heff = 148 ~ 5 kgauss. (V,2) Using the ground state nuclear moment.g = -.8872 nm determined by nuclear magnetic resonance measurement(57) and the measured g factor ratio, the excited state nuclear moment is e = +.74 ~.07 nm. (V.3)

-107 This result is in good agreement with the value of le 0 +.7 nm estimated by Shikazono. (33) 2. Interpretation of the Data a. Crystal Structure and Spin Configuration An understanding of the origin of the effective field (Equation (V.2)) requires a more detailed study of the magnetic properties of CuCr2Te4. The spinels have the crystal structure shown in Figure V-2. The structure can be visualized as a close-packed array of Te atoms, into the interstices of which the metal ions are packed. There are two types of voids: the tetrahedral, or A sites, of which there are two per Te atom; and the octahedral, or B sites, of which there is one per Te atom. Since there are only three metal ions per molecule, only one-quarter of the sites are occupied. One of the points of interest is how the metal ions occupy the A and B sites. This can be partially understood from the magnetic data. Lotgering(79) determined that the material showed spontaneous magnetization with Curie temperature TC = 365~K. At high temperature, the susceptibility followed a Curie-Weiss law with paramagnetic Curie temperature G = 400~K and molar Curie constant Cm = 2.90. The saturated moment at 40K is 4.93 rBThe Cr3+ ions have the electronic configuration 3d3. When a transition metal ion is subjected to an octahedral crystalline field, the d energy levels lose their degeneracy and are split

-108 ^ K = 11.137 ao= 11.137 A 0 0 C) Tetrohedrally Coordinated Cu+ (A site) Octahedrally Coordinated Cr 3+(Bsite) Tellurium ion FIGURE V-2 CRYSTAL STRUCTURE OF CuCr2Te4 SPINEL

-109 into a lower energy triplet, denoted by t2g, and an upper energy doublet, denoted by eg. The t2g triplet contains the orbitals of the type dy, dyz, and dzx. The eg doublet contains the orbitals of the type d2 2 and d 2 The Cr3+ ion has a strong x -y z preference for octahedral sites since the three 3d electrons are stabilized in the t2 orbitals. The Cu2+ ions have the 2g electronic configuration 3d9. Hence Cu2+ has a single hole in the 3d shell. Assuming that the Cr ions occupy the octahedral B sites in CuCr2Te4, the following spin configurations were proposed to explain the measured saturated moment (^ 5 kB) 5 I. Cu2+ Cr23 Te with ferrimagnetic spin ordering. II. Cu+ | Cr3+ Cr4+ Te4 with ferromagnetic ordering on the B sites. The fact that T CG eliminates the possibility of ferrimagnetic ordering as in configuration I. The Curie constant Cm = 2.88 calculated for II is also in better agreement with the experimental value. Colominas(70) recently reported neutron diffraction studies of CuCr2Te4 which indicated that neither configuration I nor II was correct. To fit the neutron diffraction data, the B sites were divided into two distinct sublatticeso The moments on each of the B sublattices and the A sites were allowed to vary independently. The data were best fit with equal Cr moments on each of the B sublattices and zero moment at the A site. The magnitude of the moments indicates that all Cr is present

-110 as Cr3 and the Cu as Cu+t However, the predicted saturated moment for this model is 6 rB. This does not agree with the measured value of 4.93 B'. This anomalous moment can be explained by assuming a nonlocalized moment of 1 rB antiparallel to the Cr moments. A cause for this deviation from the theoretical value may be a spiral magnetic configuration.(80) b. Superexchange Interactions Since the origin of the hyperfine field may be intimately related to the ferromagnetic coupling of the Cr3 spins, it is of importance to investigate the exchange interactions. The exchange interactions in ferromagnetic spinels were investigated by Baltzer, et al.(80) These authors assumed a Heisenberg spin Hamiltonian of the form H=- 2J[St St-2KES- S o.s:. (vo4) S.S (VA) Z Z The sum over ij includes the six nearest-neighbor pairs, and the sum over ik includes the 30 next-nearest-neighbor interactions. The interaction between nearest-neighbor pairs was assumed to be a 90~ superexchange of the type Cr3 - Te - Cr3+ This interaction is referred to as a superexchange interaction since the coupling does not involve direct exchange between the cations. The cations are instead coupled through the intermediary anion. The 900 refers to the Cr - Te - Cr bonding angle. For octahedrally coordinated Cr3+ this exchange interaction is ferromagnetic, (83) so J is positive. Direct Cr - Cr

-111 exchange is excluded due to the large separation of the ions. This is consistent with the lack of metallic conductivity in the ferromagnetic spinels. The next-nearest-neighbor interaction is assumed to be of the type Cr3+ - Te - Cu - Te - Cr3+ Baltzer, et al.,(80) correlated the high temperature susceptibility with the Curie temperature and determined that the long range exchange interaction is antiferromagnetic, or K is negative. In a paper by Kanamori(83) various mechanisms are discussed to explain the superexchange interaction. As mentioned earlier, in octahedral symmetry the three t2g orbitals lie lower in energy than the two eg orbitals and are singly occupied. The 900 ferromagnetic exchange interaction between Cr3+ ions can be explained by the symmetry relationships between the Cr3+ 3d orbitals and the Te2- 5p orbitals. The bonding and exchange interactions can most easily be understood on the basis of the mechanism proposed by Anderson(84) Anderson's proposal involves a virtual transfer of an electron from the 5p1- orbitals to the neighboring Cr3+. The unpaired spin left on the Te2 couples with the spin of the other neighboring Cr3+ through exchange interaction. For the 90~ Cr3+ - Te - Cr3+ interaction, an electron is transferred from the 5p6- orbital of Te2- to the nonorthogonal unoccupied eg orbital of Cr3+0 On the basis of Hund's rule, the spin of the 5p0- electron transferred is parallel to the t2 spins of the cation. The 5p0- spin remaining is antiparallel to the t2g spns of the Cr ion on the Te2- is antiparallel to the tg spins of the Cr ion.

-112 This antiparallel 5p- spin is exchange coupled to the t2 spins of the Cr3 ion at 900. Since the 5pc orbital is nonorthogonal to the t2 orbital, the exchange interaction 2g is negative. The t2g spins are then coupled antiferromagnetically to the unpaired 5p6- spin. This results in parallel or ferromagnetic coupling of the t2g and t2g spins. The spins are identically coupled through the interaction involving 5pG and t2g orbitals. The bonding and exchange interactions involving the 5p- - eg orbitals and the 5p~- - e orbitals also predict ferromagnetic coupling of the cation spins.(83) Co Transferred Hyperfine Field As discussed in Chapter II, a purely ionic Te2 configuration would not be expected to give rise to an effective hyperfine field. The spin paired 5s and 5p electrons would yield no contribution to Heff through Equation (II.28)o In the ferromagnetic spinel CuCr2Te4 both covalency and the exchange interaction could lead to an unpairing of the 5s electrons. Like the 5p0orbital, the Te 5s orbital can mix with the Cr eg orbitals. In this case a partial covalent bond can be formed between the Te 5s and Cr eg orbitals. Due to the ferromagnetic exchange between orthogonal orbitals (Hund's rule), the 5s spin transferred must be parallel to the t2g spins. The net 5s spin density left at the tellurium nucleus must then be negative (antiparallel to the Cr t2g spin).

-113 The tellurium 5s electron spin polarization can also arise through the ferromagnetic exchange interaction of the 5s spins with the t2g spins. Due to the different exchange interaction for the parallel and antiparallel 5s spins, the radial wave functions are no longer the same. For ferromagnetic exchange coupling, the parallel 5s spin has a lower potential energy in the vicinity of the t2g spins. The parallel 5s spin is then "attracted" outward by the ferromagnetically coupled Cr3 ions. With the radial expansion of the parallel 5s spin, a region of negative (antiparallel) spin density is left at the nucleus. The hyperfine field due to covalency and exchange effects (59) has been discussed by Watson and Freeman for MnF2. As described above, the covalency and exchange effects provide an unpairing of the tellurium 5s electrons (presumably 5s, although other orbitals may provide a small contribution). The unpaired tellurium 5s electrons provide an effective hyperfine field through the Fermi contact interaction in Equation (II.28)o Both of the mechanisms described above provide a negative (antiparallel to Cr spins) spin density at the Te nucleus. This would lead to a positive contact hyperfine field.* The spin polarization need not be large to provide an effective field of Heff = 148 gauss as in CuCr2Te4o Although the effective field has not been calculated for a single unpaired 5s electron in tellurium, indications are that it is of the order of 2.0 Mgauss.(86) A polarization of only 7.5 percent would then produce a field of the right magnitude.,..., *Internal fields are defined as positive if parallel to an external magnetizing field. The magnetic moment of the 3d electrns orients parallel to an external magnetic field which orients the 3d spins antiparallel to the external field.

-114 3. Magnetized Absorber Measurement The fact that the hyperfine structure in CuCr2Te4 is magnetic in origin can be convincingly demonstrated by observing the hyperfine spectrum with oriented absorberso As discussed in Chapter II, the relative intensities of the hyperfine components can be varied by orienting the spin axis with respect to the gamma ray beam. Several attempts were made to magnetize the absorber both parallel and perpendicular to the gamma ray beam. The absorber magnetization was done using either small permanent magnets or a solenoid coil with magnetic fields which varied from 300-1300 oersteds. Unfortunately, the magnetic fields were not sufficient to saturate the absorber magnetic moment. The result is a Mbssbauer hyperfine pattern with intensities which are averaged with an angular distribution of domain orientations characteristic of a partially magnetized absorber. The angular distribution function will be intermediate to the constant distribution characteristic of a random, nonmagnetized sample and the delta function characteristic of a fully magnetized sample. The magnetization of CuCr2Te4 at liquid nitrogen temperature has not been measured as a function of the applied field, so the degree of magnetization in these experiments is not know. As shown in Figure V-3, the difference in shape of the spectra is not considerable even in the limit of complete alignment perpendicular or parallel to the gamma ray beam. The best possibility appears to be in using magnetization parallel to

0 acr 0 LLI U) z z 0 Un LU U ILU I i-J n l CHANNEL NUMBER FIGURE V-3 PREDICTED MAGNETIC HYPERFINE SPECTRA IN CuCr2Te4 WITH ORIENTED INTERNAL FIELDS ( - RANDOMLY ORIENTED (MEASURED SPECTRUM) - - PERPENDICULAR TO GAMMA-RAY BEAM, PARALLEL TO GAMMA-RAY BEAM)

-116 the gamma ray beam. The spectrum measurements with partially magnetized absorbers showed only slight changes with respect to the nonmagnetized absorber. This would indicate that the absorbers were only partially magnetized. B. MnTe Other interesting magnetic compounds of tellurium are formed with the transition metals. These include MnTe and CrTe, both of which have the NiAs crystal structure. The coupling of the transition metals in these compounds is antiferromagnetic and ferromagnetic, respectively. The MnTe results are discussed in this section and the CrTe results follow. Some disagreement has arisen over the presence or lack of hyperfine splitting in the Mbssbauer spectrum of MnTe. Shikazono(33) originally reported that the spectrum of MnTe taken at liquid nitrogen temperature consisted of a single line with no apparent broadening due to hyperfine interactions. In similar measurements at liquid nitrogen temperature, Violet and Booth ( observed a quadrupole split spectrum with A EQ = 3 + 1 mm/sec. Shikazono attributed the lack of quadrupole 2+ 2splitting to a nearly ionic Mn2 - Te crystal with a filled 5p shell on the tellurium and a negligibly small lattice field gradient. Violet contends on the basis of the observed splitting that either the lattice field gradient is not negligibly small or there is covalent bonding in MnTe. It was hoped that measurements with good stoichiometric MnTe would help to clarify the disagreement.

-117 1. Results The Mbssbauer spectrum was taken using a single line source of PbTe125 and an absorber of MnTe with a natural abundance of Te125. The experimental results are shown in Figure V-4. The Mbssbauer spectrum was fit with a single Lorentzian, which is also shown in Figure V-4. The fitting parameters are listed in Table V-2. It is apparent from the large difference between the theoretical and experimental line widths ( theor = 5.9 mm/sec and r = 7.66 mm/sec) that there is hyperfine splitting in exp MnTe. No resolved quadrupole splitting is observed, however. If it is assumed that the broadening is due solely to quadrupole splitting, the resultant splitting is approximately AEQ C 1.7 mm/sec. This is smaller than the value quoted by Violet and Booth, but the difference is still within the maximum error limits. The thickness of the absorbers used in this experiment and Violet and Booth's experiments were nearly identicalo Since the line widths are nearly identical, the resolution should be nearly the same.* In such event, the hyperfine splitting in the present measurement would indeed appear to be smaller. 2. Discussion of the Data MnTe has the NiAs crystal structure. As shown in Figure V-5, this structure consists of a hexagonal close-packed Te anion sublattice with Mn cations in the octahedral interstices. *This is valid only if source broadening and experimental broadening are assumed negligible.

. 0H *0.0 * *.. *O * 0 0l< z 0 To an UJ 0 0 UJ Q: IL 21 I I-' 00 I 3H -2.0 -1.0 0 VELOCITY (cm/sec) 1.0 2.0 FIGURE V-4 RESONANCE ABSORPTION SPECTRUM FROM A PbTe SOURCE AND MnTe ABSORBER

TABLE V-2 PARAMETERS OBTAINED FROM SINGLE LORENTZIAN FITS TO MOSSBAUER SPECTRA OF H6TeO6, MnTe, AND CrTe Source PbTe25 PbTe125 PbTe125 Absorber H6TeO6 MnTe CrTe fexp (mm/sec) 6.17~.15 7.66~.21 9.59~ 22 (mm/sec) -1.34. 04 -.17+~05.05. 05 Resonance Intensity.0377~.0004.0331+.0004.0324+~.0003 Area (mm/sec),339.362.376 X2/N.948.795.746 theor * (mm/sec) 6.0 5.9 6.1 I I *Values of rtheor are obtained from Table III-1.

-120 * Cation O Tellurium Anion * Cation Interstitial FIGURE V-5 CRYSTAL STRUCTURE OF MnTe AND CrTe (NiAs)

-121 The cations form a simple hexagonal structure. Both the cations and anions have a six-fold coordination. The Mn sites are precisely octahedral only if the axial ratio c/a = 1.63. For MnTe the c/a ratio is c/a = 1.624. The origin of the variations in hyperfine structure measurements with MnTe may arise from variations in composition of the material. As will be discussed in the next section for CrTe, it is difficult to characterize materials with NiAs structure due to the ease with which interstitial cations may be formed. The presence of interstitial cations can drastically alter physical, chemical, and magnetic properties. It is not at all unlikely that the Mbssbauer hyperfine pattern would also be altered. MnTe is antiferromagnetic with Neel temperature TN = 3230Ko The saturated magnetic moment is 5.0 LB, which is the expected value for a purely ionic Mn2+ 3d5 electronic configuration. The measured effective paramagnetic moment is eff = 6.1 This agrees with the spin only value 5.92 B~o It was on the basis of the magnetic structure that Shikazono(33) concluded that the crystal must be ionic. However, as will be discussed shortly, this does not appear to be the case. The exchange coupling of the Mn spins again involves the superexchange process. The Mn-Mn bond distance (3o34R) is much greater than the sum of atomic radii (2o80R), (92) so direct exchange is not probable. (84) This is confirmed by the lack of metallic conductivity. The predominant cation-anioncation superexchange interaction is between basal-plane layers.

-122 The cation-anion-cation angle is' 135~, and the magnetic interaction is assumed to have the sign of the 1800 superexchange interaction,(89) which is antiferromagnetic for the 3d5 electron configuration. The spin structure then consists of planes of ferromagnetically coupled Mn spins coupled antiferromagnetically. MnTe has intrinsic semiconducting properties, high resistivity, and high thermoelectric power. This evidence seems to indicate that the bonding in MnTe is predominantly covalent. One model proposed for the MnTe bonding consists of resonating p3 bonds.(90) This bonding mechanism does not involve the d-electrons, so the magnetic measurements still remain consistent. This bonding also fulfills the intrinsic semiconducting properties. The superexchange mechanism in MnTe could presumably be the exchange polarization described by Slater(85) involving the Te 5s electrons. This superexchange mechanism does not involve a radial polarization of the 5s electrons, but rather an asymmetric angular polarization. The exchange interaction tends 2+ to "attract" the parallel 5s spin toward one Mn2+ and the antiparallel 5s spin toward the other Mn2+. This polarization would affect the 5s electron charge density at the Te nucleus, but due to the equivalent exchange effects for parallel and antiparallel spin the 5s spin density should still remain paired at the Te nucleus. Then for antiferromagnetic coupling of the Mn2+ spins, no transferred hyperfine field is expected at the Te nucleus o

-123 The tellurium sites in the NiAs structure are characterized as trigonal-prismatic. On the basis of covalent bonding, the structural symmetry would tend to indicate that the p orbitals are not equivalent. This would lead to an electric field gradient at the tellurium nucleus and quadrupole splitting in the Mbssbauer spectrum. The previous arguments support the claim that the measured hyperfine broadening has its origin in electric quadrupole splitting and not in magnetic hyperfine splitting. The variation in results observed in different measurements cannot yet be fully explained. C. CrTe Mbssbauer measurements in CrTe were first reported by Shikazono.(33) A broadened single line was observed which was attributed to unresolved magnetic hyperfine splitting. Under the assumption that the width of the broadening was equal to the ground state magnetic splitting, the resultant internal field was estimated as Heff = 50 kgauss. Due to the apparent disagreement between MnTe results, it was felt that the CrTe measurements were worth repeating. 1. Results The Mtssbauer spectrum was taken using a single line source of PbTe125 and a CrTe absorber with a natural abundance of Te125o The data are shown in Figure V-6. The data were fit

*. 0 * I 00* a. cr rn 0 m <[ z z 0 U) nLIJ a: 1 I N) I 3 -2.0 -1.0 0 VELOCITY (cm/sec) 1.0 2.0 FIGURE V-6 RESONANCE ABSORPTION SPECTRUM FROM A PbTe SOURCE AND CrTe ABSORBER

-125 with a single Lorentzian as shown in Figure V-6. The fitting parameters are listed in Table V-2. It is readily apparent from a comparison of p and theor exp theor that there is considerable broadening in the Mbssbauer spectrum. A quadrupole splitting equivalent to the observed broadening AEQ 3.5 mm/sec should be partially resolved since A EQ'.6 eor' The fact that there is no resolved structure strongly suggests that the origin of the broadening is more likely magnetic hyperfine splitting. Assuming that the broadening is due solely to magnetic hyperfine splitting, the measured effective hyperfine field is Heff = 58 kgauss.* The apparent agreement with Shikazono's result is somewhat fortuitous since the values were arrived at using different numbers and a different interpretation. 2. Discussion of the Data CrTe, like MnTe, has the NiAs structure (Figure V-5) The composition of CrTe is even more difficult to characterize than MnTe due to the formation of interstitial ions. The tetrahedral interstices of the anion sublattice form a single trigonal-bipyramidal hole with a coordination of five. These holes easily accommodate cations as interstitials. An interstitial site is shown in Figure V-5. The presence of the interstitial sites makes it difficult to obtain stoichiometric CrTe and also allows the NiAs phase to extend over a considerable *Heff is calculated by assuming the broadening is equivalent to the spacing between peaks 2 and 5 in the hyperfine spectrum. (By observing the CuCr2Te4 spectrum in Figure V-l, it will be noted that the centers of the two unresolved peaks are approximately at the locations of peaks 2 and 5.) The measured value e = +o74 nm (5.3) is used in the calculation.

-126 range of composition. (93) Cation-rich compositions form interstitials and cation-poor compositions form vacancies. The formation of interstitials in CrTe lowers the c/a ratio to c/a = 1.56. The smaller c/a ratio reduces the Cr-Cr bond distance to 3.10R compared to the sum of atomic radii which is 2.80Ao The interstitial cations can interact through cation-cation exchange with the six neighboring octahedral cationso This introduces collective electrons as is evidenced by the metallic conductivity of CrTe. CrTe is ferromagnetic with Curie temperature Tc = 350-360~Ko The saturated magnetic moment is 2.45 3B, and the effective paramagnetic moment is K eff = 4.00 rB. Both of these values are lower than the expected values 4 rB and 4.90 jB' respectively, for a spin only Cr2+ 3d electronic configuration. The principal coupling of the Cr is again through the ^ 1350 cationanion-cation superexchange interaction. For 3d4 cations, the interaction is ferromagnetic.(89) There are three possible explanations for the reduced moments: First, the presence of interstitials would reduce the saturated ferromagnetic moment since the cation-cation coupling is antiferromagnetic. The interstitial cations would then couple antiparallel to the principal cation lattice. Nevertheless, the paramagnetic moment should still approach the spin-only value 4.9 AB at high temperatures. Second, covalent bonding of the Cr 3d electrons with the Te would reduce the moment. Evidence from K absorption spectra in the

-127 Cr indicates, however, that there is only a small participation of the d-electrons in the bonding.(94) Third, the competition between the antiferromagnetic cation-cation interactions and the ferromagnetic superexchange interaction may lead to spiral magnetic configurations and a reduced saturated moment. The mechanism producing the hyperfine field is again the spin polarization of the Te 5s electrons by exchange coupling with the Cr 3d electrons. For ferromagnetic coupling of the Cr2+ spins (as opposed to the antiferromagnetic coupling of Mn2+), the tellurium 5s electrons can be spin polarizedo Since the exchange interactions with the parallel and antiparallel 5s spins are not equivalent, a radial polarization can occur resulting in unpaired 5s spin density (antiparallel to the Cr2+ spin) at the Te nucleus. This would yield a positive contact hyperfine field. The bonding in CrTe may also be described by the resonating p bonds.(44) As in MnTe, an unbalancing of the p-electrons may give rise to a field gradient at the Te site and subsequent quadrupole splitting. On this basis, the quadrupole interaction cannot be excluded as a source of the hyperfine broadening in CrTe. Hyperfine measurements at anion sites in other ferromagnetic NiAs structures indicate the presence of both magnetic and electric quadrupole hyperfine effects. NMR measurements of the As75 resonance in MnAs95 and the Sb123 resonance in MnSb96 indicate internal hyperfine fields Heff of 283.2 kgauss and 35206 kgauss, respectively, and quadrupole coupling constants

-128 e2qQ of 16.1 Mc/sec and 93 Mc/sec, respectively. These quadrupole coupling constants correspond to splittings \EQ.28 mm/sec and AEQ = 1.63 mm/sec. The measured broadening in CrTe was definitely larger than these values, but quadrupole splitting cannot be ignored as a possible contributor to the broadening. D. H6TeO6 1. Results Mtssbauer measurements were taken using a single line source of PbTe125 and an orthotelluric acid (H6TeO6) absorber with a natural abundance of Te125 The experimentally measured spectrum, shown in Figure V-7, consisted of a very narrow single line. The parameters obtained from the fit with a single Lorentzian are listed in Table V-2. The fitting curve is also shown in Figure V-7. These are the first reported Mbssbauer measurements for this compoundo The experimentally measured line width r = 6o17 mm/sec exp is in excellent agreement with the theoretical line width r = 6.0 mm/sec corrected for absorber thickness. This theor would indicate that there is no additional broadening caused by unresolved quadrupole splitting. This would confirm the existence of only the cubic crystalline modification of orthotelluric acid. The octahedrally coordinated tellurium sites in this structure would not be expected to have a quadrupole splitting. On the other hand, a monoclinic structure would

0 Fz o a. vn m ul < 2 bJ z z 0 LU - 3 * *0 ~ 0 *0 * 0 - " " 0 0 a~. * * 0. * -, I I,I 4 -2.0 - 1.0 0 VELOCITY (cm/sec) 1.0 2.0 FIGURE V-7 RESONANCE ABSORPTION SPECTRUM FROM A PbTe SOURCE AND H6TeO6 ABSORBER

-130 presumably contribute an electric field gradient at the tellurium sites and subsequent quadrupole splitting. 2. Discussion of the Data The large negative isomer shift for H6TeO6 indicates a change in the 5s electron density compared to PbTe, Due to the strong electronegativity of the OH ligand, the compound presumably has considerable ionic character. In the limit of a complete ionic character, tellurium would be present as Te6+ with a bare 5s and 5p electron shell. Since an ion with this large a positive charge is highly unlikely, there is undoubtedly some covalent character. As an extreme limit, the bonding could be described as completely covalent. For octahedrally coordinated tellurium, the bonding can be represented by sp3d2 (77) hybridization. Since one electron occupies each orbital and the s character of each orbital is 1/6, there is the equivalent of one 5s electron at the tellurium site. On the basis of this simple treatment, the 5s density could vary from the equivalent of one 5s electron to zero 5s electrons depending on the percent ionic character. The effect of this change will be treated in more detail in the following section. E Isomer Shifts in Tellurium Compounds The details of the isomer shift interaction were described earlier in Chapter II. Since nearly all of the preceding measurements were made using either a PbTe source or absorber, it is convenient to give the isomer shifts with respect to

-131 this standard compound. In Table V-3, the measured values of the isomer shift are listed in order of increasing velocity. All of the values except that for the Te metal were obtained using the PbTe as a source.* TABLE V-3 ISOMER SHIFT FOR VARIOUS TELLURIUM COMPOUNDS WITH RESPECT TO A PbTe SOURCE Isomer Shift Absorber (mm/sec) H6TeO6 -1.34 ~.04 MnTe -.17 +.05 CuCr2Te4 -.03 ~.03 PbTe + o03 t.03 CrTe +.05 +.05 Te +.41 +.09 TeO2 +.62 ~ o16 If the change in s-electron density at the nucleus is known for the compounds, the measured isomer shifts can be used to determine R/R from Equation (II.17). Such an interpretation is simplified if we first make the assumption that only the outer 5s valence electron shell produces a change in the selectron density at the nucleus. To make an accurate prediction of the change in s-electron density requires precise knowledge of the molecular wave functions. However, in some cases, it is possible to estimate the sign and perhaps the magnitude of the change in s-electron density without complete knowledge of the electron wave functions.** From this it is then possible to determine the sign and magnitude of &R/Ro *The sign of the isomer shift is reversed when the PbTe is used as the absorber rather than the source. **These simplified interpretations can sometimes lead to erroneous results, though, as exemplified by the Sn119 controversy.

-132 The isomer shift measurements for Te metal and H6TeO6 can easily be interpreted on the basis of a rather simplified description of the electronic structure for the compounds. Violet, et al,(30) have estimated the 5s electron density for Te metal from their molecular orbital bonding scheme. The 5s electron density is calculated to be the equivalent of 1.6 5s electrons. In the models proposed earlier for H6TeO6, the density is the equivalent of 1 5s electron in the covalent bonding limit and 0 5s electrons in the ionic bonding limit. In using either bonding scheme for H6TeO6, the 5s electron density in Te is definitely greater than that for H6TeO6o As described in Chapter II, the isomer shift for H6TeO6 and Te can be written as 4 - e.e RS's|^p, (' ) (Vo5) S = eR S() - t c)( t) (V.6) Combining Equations (Vo5) and (VO6) to eliminate the s-electron density for PbTe yields 4 2v RS (F s(O1)So (V 7) ^-^ 41r eo( L-6Te-S I.T. OT N o From the measured isomer shifts - 6 =+1.75 mm/sec Te H6TeO6 Since the 5s electron density at the nucleus is greater for Te than for H6TeO6, the sign of the term in brackets is positive.

-133 Since both the isomer shift and s-electron density terms are positive, i R/R must be positive. This implies that the nuclear excited state radius must be greater than that for the ground state. This confirms the identical conclusions reached by other authors. (31,51) If it is assumed that H6TeO6 has completely ionic character, the difference in s-electron density in Equation (V.7) is the equivalent of 1.6 5s electrons. Equation (V,7) can then be evaluated numerically using S' (52) = 2.44 and nuclear radius R C lo5 A1/3 x 10-13 cm. The 5s electron density in tellurium can be estimated from the results of Shirley. (51) The value is approximately S (0) =.18 x 1026 cm3. Evaluating Equation (V.7) numerically yields a value of SR/R = +2.8 x 10-4. In the limit of completely covalent character, the value would be reduced to ER/R = +1.1 x 10-4 This range of values is in reasonable agreement with the values estimated by Shirley for 125 Te

APPENDIX A SUMMARY OF RADIATION EFFECTS MEASUREMENTS USING THE MOSSBAUER EFFECT -134

TABLE A-1 SUMMARY OF RADIATION EFFECTS MEASUREMENTS USING THE MOSSBAUER EFFECT Preparation of Mbssbauer Chemical Form ReferM6ssbauer Level Nucleus Source Absorber Radiation Effects ence AlDha Decav Mbssbauer fraction f following Am41-Np7+ ( Np237 NpO2 NpO2 o-decay approximately ~ f following -decay. 1 Nuclear Reaction Observed f=l,19% compared to K (d,p)K40 K40 K metal KC1 expected f=.03%. Suspect oxi3.5 Mev deuterons dation in the source. 6 Nuclear Reaction No reduction in f value. Less Fe56(d,p)Fe57 Fe57 Fe Fe than 10% change in hyperfine 2.8 Mev deuterons metal metal interaction. 7 Nuclear Reaction Stain- StainFe56(d,p)Fe57 Fe57 less less No reduction in f value. 8 4.8 Mev deuterons steel steel Coulomb Exci- f value only 75% of that obser tation Ni61 Ni Ni ved for F -decay parent. Absorp metal metal tion areas identical. No change in f as a function of irradiation time. 2 Coulomb Exci- Fe Na Fe(CN)6 Essentially no change in f tation Fe57 metal o10H20 value. Fe2O3 Fe2O3 f value reduced by a factor of, 2. No change in hyperfine splitting. I n I

Coulomb -Excitation Thick Ge metal Ge metal Source f value at 78~K=,8%o Ge showed conversion from crystalline to amorphous state after i rradi +i on Ge73 Thin Ge Ge Source f value at 78~K=5.8%. metal metal Absorber f value at 78~K=6.0%. on Cr... I, 4,5 Thin Ge metal on Cr GeO2 Thin targets used to implant Coulomb excited Ge atoms in Cr metal. Neutron Capture KF Observed f values are smaller in Thermal Neu- K40 KC1 KC1 than computed in all cases. tron Beam K 9 Neutron Capture Gd "Mirror experiment" in Gd158 in Thermal Neu- Gd 56 Gd203 metal shows the following effect: tron Beam 1 Gd f oxide target x f metal Gd8 metal Gd203 absorber =.6 x f metal target x f oxide absorber. Gd23O Gd metal Line for Gd203 target approx. 10% greater than for Gd metal target. 13 Neutron Capture Fe Stainless Splitting of outer lines in in Thermal Neu- metal steel |yperfine spectrum greater than tron Beam Fe57 if used as absorber with Co57 ______ source. 16 Fe203 Stainless Splitting of outer lines in steel hyperfine spectrum less than absorber valueo Reduction in f value still uncertain... h >.. ~.... J... _ *..... I I-J

Isomer Production S 9 SnO2 SnO2 No evidence of radiation ffects. by Neutron Cap- Sn |Mg2SnQO SnO2 Satellite peak which anneals 15 ture out at 600-1000~C. Postulate peak due to Sn2+ produced by (n,f) recoil. Approx. 25% of Sn atoms in defect environment. Isomer Production 12 Isomer shift of 2 mm/sec after by Neutron Cap- Te125 PbTe PbTe irradiation. Decayed to 0 ture with exponential lifetime r= 10 days. 17 Isomer Production PbTe by Neutron Cap- Te25 Te PbTe No evidence of radiation ture metal effects. Present TeO2 Work - I

APPENDIX B CIRCUIT DIAGRAMS OF MAGNET FIELD SUPPLY AND DRIVE AMPLIFIER -138

115v — L P6161 P3138 ISOLATION LINE REG. r+T IT0 r1 70 7vI + +1 700 + + 700 190 v I0 -3 300 30300 ~300.7a -FIGURE BFIGURE B-1 CIRCUIT DIAGRAM OF MAGNET FIELD SUPPLY

IOOK 450n ANALOG ADDRESS SCALER INPUT SIGNAL TO DRIVE COIL "INPUT AMPLIFIER" 2.21K PIC KUP --- COIL INPUT, -,.., r^ -. 7 He-.7 11 Q |^- ~' r~ I "BOOSTER AMPLIFIER' ~~~~~OO>.5K01 IOK 2.2 K I VELOCITY ER 135 ANALOG ER" BF IGURA E B-2 CIRCUIT DIAGRAM OF DRIVE AMPLIFIER "FEEDBACK AMPLIFII

APPENDIX C DESCRIPTION OF DATA ANALYSIS PROGRAMS The following is a description of the data analysis programs used for least squares fitting of Mbssbauer effect data. In writing such a program to analyze data, it would be desirable to have a "universal program" which could be used to analyze all of the types of M6ssbauer data that can be acquired. Experience has indicated that new situations arise so frequently that such a program is never up-to-date. For greater efficiency, a "main program" has been written which performs the basic data operations for all types of Mbssbauer spectra. The details of the particular spectrum being analyzed are included in a "theory" subroutine. This subroutine can easily be modified to analyze any type of MBssbauer spectrum.* The programs are all written in the MAD (Michigan Algorithmic Decoder) language for use on the IBM 7090 computer.** Ao Least Squares Curve Fitting The problem to be solved in a curve fitting routine is the following: For each channel in the analyzer, i, an experimentally measured number of counts, Yi, are stored. One wishes to construct a curve of a known shape (Lorentzian shape for the resonance lines of Mbssbauer spectra) so that it most closely approximates the data. *This technique was suggested by W. Henning, Technische Hochschule, Mtnchen. **The translation from the MAD to FORTRAN language can be made rather easily. -141

-142 In using the least squares procedure, we assume the measured values Yi have a Gaussian distribution about the true value Fi with a standard deviation' i. The probability that for an experimentally determined Yi the true value lies between F. and Fi + dF. is 1Zit L ~ ea Z (c.1) The best (most probable) guess of the fitting function F occurs when the product of the probabilities is a maximum. (F~-~t' Fp==7T-7== & -;2^ (c.2) P- ) F-. -Tr, = e' Ad2' Tr - (Co3) j ((F -yY Equation (C.3) is a maximum when - i9 is a minimum. A reasonable estimate for the standard deviation t i is -i' the experimental standard deviation of Yi. Two general approaches can be used for minimizing q. The first is a brute force "variation of parameters." The independent variable parameters in F are incremented in preset steps and the function q is calculated for each set of parameterso The combination resulting in the smallest value of q is taken as the "best" set of fitting parameters. Due to the fact that the parameters are varied in finite increments, there is no assurance that the true minimum is reached nor that

-143 there is not another set of parameters giving an equally good minimum. This particular technique was in use for some time for Mbssbauer effect data analysis.* The main disadvantage was that it proved to be very time consuming when high accuracy in the parameters was desired. This method may be necessary, however, in analyzing complex spectra where other methods may fail. The second approach used in minimizing q is the use of Gauss' method. The function Fi depends on i and the independent variable parameters Pi''PM or Fi = F(i,P1-~~PM) To minimize q, the partial derivatives of q with respect to the variable parameters are taken and set equal to zero, or A, X (F'i:( Y.) o (C.4) This forms a set of M simultaneous equations. Suppose an initial estimate is made of the parameters (Plo0''-P0) and the function Fi is expanded in a truncated Taylor series about this point in parameter space, so F.-F; o a 9)4 (C.5) t y ( I.o -Y ^ XP *);i,. AP %) )F ) (c.6) ^% P; S)P,.L O * *The program was similar to one used by M. B. Stearns, Scientific Laboratory, Ford Motor Company, Dearborn, Michigan.

-144 Equation (C.6) can be rewritten as _l_' Pp.F a - -- (C.7) 1. L i O D This forms a set of M simultaneous equations of the form D A = B (c.8) This set of equations is known as the normal equations, where -Do= ~r^, (c.9) ^- 1 ^F\ aF(\ - ) F p. ),p.) (c.lo) l X- ^i ~ /to 8 "'^X/^o *'Jo t. Since Akj and Bj are obtained from the initial estimates of the parameters, the normal equations can be solved for Dk, or D- B (C.12) The solutions Dk are then used as corrections to the initial estimates of the parameters giving a new set of parameters P PS+ +Ap. (C.13)

-145 Using the corrected parameters of Equation (Co13), the entire procedure can be repeated to obtain the next increment t Pko After each iteration, the value of A2/N is computed where / = t (IM- M (C.14) In this expression IM is the number of data points and M is the number of fitting parameters. Equation (C.14) is related quite simply to the earlier expression referred to as q. The function'% 2/N is a measure of the deviation of the measured spectrum and the fitted spectrum —the smaller the value, the better the agreement. The iteration procedure described earlier is continued until ) 2/N reaches a minimum value. This method of solution has the added advantage that the statistical error in the parameters is immediately available. It can be shown 103) that -1 t r=o (A i */) v (C.15) where Akk1 is the kth diagonal element of the inverse matrix of Akj. Gauss' method has proved very satisfactory in analyzing most MWssbauer datao Fully and partially resolved spectra were handled with no difficulty. Unresolved spectra could not be properly fit, however. In addition, the initial parameter

-146 estimates need not be extremely precise to achieve rapid convergence. Most parameter estimates were made by just a quick visual check of the spectrum. B. Data Analysis Program 1. Main Program As mentioned earlier, the basic mechanics of the least squares fitting and routine data corrections are performed by a "main program." The following is a general outline of the operations the "main program" will perform- Several sets of input data can be added together with the appropriate number of overflow counts for each set. The data is then printed out along with the various input parameters. The input parameters are checked to see if: a) the number of fitting parameters M is less than 25, b) the number of data points IM is less than 512; and c) there are more data points than fitting parameters. The solution is terminated if any of these checks fail. The infinite velocity background count rate and slope are determined approximately from the average count rates at large negative and positive velocities. The end points of the spectrum are determined so that 5 percent of the channels at each end of the spectrum are eliminated from the analysiso This is done because of the large error signal in this region of the spectrum. The first and last data points are used to check the "theory" subroutine. The partial derivatives in the "theory"

-147 subroutine are all evaluated using the first and last data points and the initial parameter estimates. These results are then printed out. This provides a very convenient check for errors in the subroutine if later analysis proves unsuccessful. The program initially uses Gauss' method to provide an iterative solution for the "best" fit to the data. The solution is obtained as described in the first part of this appendix. The normal equations are evaluated for the fitting function described in the "theory" subroutine. The function is evaluated using the initial estimates of the parameters which are included as input to the program. The normal equations are then solved to give the increments in each parameter. The fitting parameters and 2 /N value are printed out after each iteration. The iteration is continued at least three times and is terminated either when the number of iterations exceeds twenty or when the value of 1 2/N reaches a minimum. In the event the normal equations are unsolvable or the error in the fitting is greater than a preset value, the method of steepest descent is used rather than Gauss' method to provide the interative solution for the "best" fit. In practice, this method was rarely needed so the details will not be discussed. After the iteration is terminated, the data are normalized so the results are expressed as percent resonance intensity. In addition, the standard deviation of the data points and the

-148 difference between the measured spectrum and the fitted spectrum are calculated. The area under the spectrum is obtained by numerical integration, The error in the fitting parameters is calculated using the method described in the first part of the appendix (see Equation (C,15)). The distribution in standard deviation units of the error between the measured and fitted spectrum is also calculated. The final results which are printed out include the "best" fitting parameters and their statistical fitting error, the area under the spectrum, and the error distribution for the fitting curve. The data printed out include the normalized measured spectrum, the fitted spectrum, the difference in spectra, and the standard deviation of the data. The data are also plotted using an internal subroutine. The measured spectrum and the fitted spectrum are plotted on the same graph. The difference between the spectra is plotted on a separate graph. This provides a very quick visual check of the success in fitting the data. The complete "main program" is included in section C of this appendix. 2. Theory Subroutine The "theory" subroutine includes all of the details of the function which is to be fitted to the data. A typical subroutine is included in section C of this appendix. The

-149 function which is fitted to the data consists of a superposition of Lorentzian line shapes and has the form F ) J) z +(C) 16) FT(I) r= 1:()- Y c) where LUo = infinity counting rate I(J) = intensity of the Jth line X(J) = position of the Jth line /2(J) = half width at half maximum of the Jth line SL = normalized linear slope of the background counting rate. The parameters 1/2(J) and X(J) are expressed in channel units so I can be used in channel units. The line location X(J) can be expressed as a function of the isomer shift, quadrupole splitting parameter, and magnetic hyperfine interaction parameters. All of these are expressed with respect to the zero velocity channel. In addition to the function itself, the subroutine must include the partial derivatives DFT of the function FT with respect to each of the variable parameters. For the example include in section C of this appendix, several simplifying assumptions have been made. The subroutine describes a six-line spectrum with equal line widths for each line. The intensities of the lines are constrained to the ratio 3:2:1. The variable parameters include r/2, rgHeff, T, b C, C, R = ge/gg, and SL. r/2, the half width at half

-150maximum of the resonance line; lgHeff, the magnetic hyperfine interaction constant; and i, the isomer shift, are expressed in channel units. C is the fractional multiplying factor for the line intensities, so the resultant line intensity ratio is 3C: 2ColC. This subroutine can easily be changed to provide any possible variations in the fitting function.

-151 C. Listing of Computer Programs 1. Main Program DIMENSION Y(512),SETUP(24),YS(512,P(25),X(512),DF1(25),DF2(2 1 5),UY(512), BV(25) 5,M 625,AVV),PM(625,AVVZ(25),LR(25),DP(25) 2,FI T(512),YNRM(512),DYNRM(512),DIFF(512),SIG(25),INVDI(25),XX 3 (512),ZP(512),IMAGE(10000),DF(25 VECTOR VALUES AVV=2,1,O INTEGER SETUPIM,M,NDECKSI,ID,ILC,IUC,K,ILP,IUP,J,L,SP,MDIF, 1 P3S,P2S,P1S,POS,NOS,NS,N2S,N3S READ AND PRINT INPUT DATA START EXECUTE ZERO.(Y(O)...Y(511), YS(O)...YS( 511 ) EXECUTE SPRAY.($$,SETUP ()... SETUP(24 ) READ FORMAT INPUT,SETUP(1)...SETUP(24),IM,M,VCAL,NDECKSINCR VECTOR VALUES INPUT=$12C6/12C6/213,F8.5,13,F8.0*$ PRINT FORMAT INITAL,SETUP(1)...SETUP(24) VECTOR VALUES INITAL=$1H1,S10,12C6/Sll,12C6*$ PRINT COMMENT $0 1 INPUT DATAS PRINT FORMAT INPR,IM,M,VCALNDECKS,INCR VECTOR VALUES INPR=$S20,4HIM= I3,S43HM=,I3,S4,6HVCAL=,F8. 1 5,10H MM/SEC/CHS4,8HNDECKS= 1I3,S4,6HINCR= tF8.0*S THROUGH FI,FOR ID=1,1lID.G.NDECKS READ FORMAT ADDIN,ADDC VECTOR VALUES ADDIN=$F8.0*$ PRINT FORMAT ADDPRADDC VECTOR VALUES ADDPR=$//S20,20HADDITIVE CONSTANT =,F8.0*$ READ FORMAT IPUTY(O)...Y(IM) VECTOR VALUES IPUT=$18F8.0)*$ PRINT FORMAT DAT,Y(O)...Y(IM) VECTOR VALUES DAT=$//(S19,8F8.0)*$ THROUGH F1,FOR I=O,1,I.G.IM Fl YS(I)=YS(I) Y(I)+ADDC PRINT COMMENT $0 SUMMA 1 TION OF INPUT DATA$ PRINT FORMAT YSUMYS(O)...YS(IM) VECTOR VALUES YSUM=$//(S19,8F8.0)*$ READ FORMAT PARINP(1)...P(Mf VECTOR VALUES PARIN=$(8F8.0)*$ PRINT FORMAT INITAL SETUP(1)..SETUP(24) CHECK FOR PROPER CONDITIONS FOR ANALYSIS WHENEVER M.LE.O OR WHENEVER M-25.GE.O PRINT FORMAT MVALtM

-152 VECTOR VALUES MVAL=$1HO,S20,48HONLY 1 TO 25 FITTING PARAMETER 1 S ARE ALLOWED, NOTI3*$ TRANSFER TO START OTHERWISE CONTINUE END OF CONDITIONAL WHENEVER IM.GE.512 PRINT FORMAT IMVAL,IM VECTOR VALUES IMVAL=$1HOS20,42HONLY 1 TO 512 DATA POINTS ARE I ALLOWED, NOT,I3*$ TRANSFER TO START OTHER I SE CONTINUE END OF CONDITIONAL MDIF=IM-M WHENEVER MDIF.LE.O PRINT FORMAT DIFVAL,IM,M VECTOR VALUES DIFVAL=$1HO,S20,17HMORE PARAMETERS (,I3,20H) TH 1 AN DATA POINTS (,I3,1H)*$ TRANSFER TO START OTHERWISE CONTINUE END OF CONDITIONAL APPROXIMATE SLOPE AND BACKGROUND ILC=I IUC=IM-1 YMAX=O. THROUGH F2,FOR I=ILC1,II.G.IUC F2 WHENEVER YS(I).G.YMAX,YMAX=YS(I) BK=.7*YMAX SLP=O. THROUGH F5,FOR K=l,1,K.G.2 XBKL=O. XBKU=O. BKL=O. BKU=O. THROUGH F3,FOR I=ILC,1,I.G.IUC/2 WHENEVER YS(I).L.BK+SLP*I TRANSFER TO F3 OTHERWISE XBKL=XBKL+1. BKL=BKL+YS(I) F3 END OF CONDITIONAL THROUGH F4,FOR I=IUC,-1,I.L.IUC/2+1 WHENEVER YS(I).L.BK+SLP*I TRANSFER TO F4 OTHERWISE XBKU=XBKU+1 BKU=BKU+YS( I) F4 END OF CONDITIONAL BKL=BKL/XBKL BKU=BKU/XBKU

-153SLP=2.*(BKU-BKL) / (IUC-ILC) F5 BK=(BKL+BKU)/2.-SLP*(IUC-ILC)/2. BKND=BK SLOPE=SLP/BK*( IM+1)*100 PRINT FORMAT APPSB,BKND,SLOPE VECTOR VALUES APPSB=$1HOSI9,25HAPPROXIMATE BACKGROUND = F14. 1 4//S20,20HAPPROXIMATE SLOPE = F14.4,8H PERCENT*$ END POINTS OF SPECTRUM ILP=ILC+.05*IM IUP=IUC-.05*IM PRINT FORMAT ENPT,ILP,IUP VECTOR VALUES ENPT=$1HO,S19,18HLOWER END POINT = 15//S20,18HU I PPER END POINT = I5*$ CHECK OF FIRST AND LAST DATA POINTS WITH THEORY THROUGH F6,FOR I=O,1,I.G.511 DY( I )=SQRT. (YS( I)) F6 X(I)=I J=0 I=ILP EXECUTE THEORY.(J,X(I),P,A1,B1,FlDF1) I=IUP EXECUTE THEORY.(J,X(I),PA2,B2,F2,OF2) PRINT FORMAT CK,ILP,IUP,X(ILP),X(IUP),YS(ILP),YS(IUP),DY(ILP) 1,DY(IUP),F1,F2 VECTOR VALUES CK=$////S1O,20HCHECK OF DATA POINTS,I5952,3HAND 1,I5,S2,11HWITTH EORY//S20,2HX,2E18.4/S20,2HY,2E18.4/S20,2H 2 DY,2E18.4//S20,2HF,2E18.4/*$ THROUGH F7,FOR K=I,l,K.G.M F7 PRINT FORMAT PARCK,K,OF1(K),DF2(K) VECTOR VALUES PARCK=$/S20,5HDF/DPI3,E12.4,E18.4*$ SETTING UP NURMAL EQUATIONS PRINT FORMAT INITALSETUP(I)...SETUP(24) PRINT COMMENT $0 1 NTERMEDIATE RESULTS$ PRINT COMMENT $0 ITERATION CHISQ/N PA 1 RAMETERS$ AVV(2)=M CHISQ=1. F8 WVAR=O. EXECUTE ZERO. (BV( )...BV 25), AM (...AM(625) ) THROUGH F9,FOR I=ILP,1 I.G.IUP EXECUTE THEORY.(J,X(I),P,A,B,FDF) WT=DY(I).P.-2 DIF=YS( )-F WVAR=WVAR+WT*DIF.P.2 THROUGH F9,FOR K=l,1,K.G.M BV(K)=BV(K)-WT*DIF*DF(K) THROUGH F9,FOR L=1,l,L.G.M F9 AM K,L)=AM( KL)+WT*DF(K)*DF(L)

-154 CHI SQ=WVAR/MDIF PRINT FORMAT INTRE,J,CHISQ,P( 1)...PM) VECTOR VALUES INTRE=SlHO,1S3,I3,S3,E15.6,S5,4E15.6/(S39,4E15. 1 6)*$ TERMINATION OF ITERATION WHENEVER J-3.L.O TRANSFER TO FIO OR WHENEVER WVAR-WVPRE.GE.O TRANSFER TO F20 OR WHENEVER J-20.GE.0 TRANSFER TO F19 OTHERWISE CONTINUE END OF CONDITIONAL SOLUTION OF EQUATIONS F10 Fil THROUGH F11,FOR K=l,l,K.G.M Z(K)=-BV(K) THROUGH Fll,FOR L=1l,,L.G.M PM(K,L)=AM(K,L) R=SLE.(M,M,PM(1),DP(l),Z(1),LR(1),O0 WHENEVER R.LE.O PRINT COMMENT $0 NORMAL EQUATIONS UNSOLVABLE 1, USE METHOD OF STEEPEST DESCENTS TRANSFER TO F13 OTHERWISE CONTINUE END OF CONDITIONAL H1=0. THROUGH F12,FOR K=1,l1K.G.M HL=H+DP(K).P.2*AM(K,K) WHENEVER SQRT.(H),.LE.INCR,TRANSFER TO F17 F12 METHOD OF STEEPEST DESCENT F13 F14 PRINT COMMENT $0 1 USEDS Hl=O. H2=0. THROUGH F14,FOR K=1,1,K.G.M H1=BV(K).P.2 THROUGH F15,FOR K=1,1,K.G.M THROUGH F15,FOR L=1,1,L.G.M H2=H2+BV(K) *AM(K, L*BV( V(L THROUGH F16,FOR K=1,1,K.G.M DP( K)=-H*BVt K)/H2 METHOD OF STEEPEST DESCENT F15 F16 F17 F18 WVPRE=WVAR THROUGH F18,FOR K=1,1,K.G.M P(K)=P(K)+DP(K) J=J+1 TRANSFER TO F8

-155 TERMINATION OF ITERATION F19 PRINT COMMENT $0 L RATIONS$ PRINT COMMENT $0 NO CONVERGENCE AFTER 20 ITE FINAL RESULTSS F20 NORMALIZATION OF DATA AREA=O. THROUGH F21,FOR I=ILP,1,I.G.IUP EXECUTE THEORY.(J,X(I),P,A,B,F,DF) FIT( )=- I. YNRM(I)=(YS(I)-A)/A DYNRM(I)=DY(I)/A DIFF(I)=YNRM(I)-FIT(I) AREA=AREA-FIT(I) CALCULATION OF ERRORS F21 F22 PRINT FORMAT INITALtSETUP(1)...SETUP(24) PRINT COMMENT $0 1 FINAL RESULTSS THROUGH F22,FOR K=t1,lK.G.M THROUGH F22,FOR L=l,1,L.G.M PM(K,L)=AM(KL) RS=GJR. (M,M,PM(1),DETER) WHENEVER RS.NE.1 PRINT COMMENT $0 MATRIX INVERSION UNSUCCESSF 1 UL$ THROUGH F23,FOR K=l1,1K.G.M SIG(K)=0. TRANSFER TO F25 OTHERWISE CONTINUE END OF CONDITIONAL THROUGH F24,FOR K=lIK.G.M INVOI(K)=PM(K,K) SIG(K)=SQRT.(CHISQ*.ABS.INVDI(K)) F23 F24 F25 ERROR DISTRIBUTION SD=SQRT. (A) /A EXECUTE ZERO.(P3S,P2S,PIS,POS,NOS,N1S,N2SN3S) THROUGH F26,FOR I=ILPl,I,.G.IUP WHENEVER DIFF(I.G.SD*3.,P3S=P3S+1 WHENEVER DIFF().G.SD*2..ANO.DIFF(II).L.SD*3.,P2S=P2S+I WHENEVER DIFF(I).G.SD*I..AND.DIFF(I).L.SD*2.,PIS=PlS+l WHENEVER DIFF(I).G.O.AND.DIFF(I).L.SD*I.,POS=POS+ WHENEVER DIFF( I.G.-SD*1..AND.DIFF(I).L.0,NOS=NOS+1 WHENEVER DIFF(I).G.-SD*2..AND.DIFF(I).L.-SD*I.,N1S=NlS+l WHENEVER DIFF(I).G.-SD*3..AND.DIFF(I).L.-SD*2.,N2S=N2S+l WHENEVER DIFF (I.L.-SD*3.,N3S=N3S+1 F26

-156 DATA PRINT OUT F27 F28 PRINT COMMENT $0 FITTING PARAMETER 1 S$ THROUGH F27,FOR K=I,i,K.G.M PRINT FORMAT PAROUT,KP(K),SIG(K) VECTOR VALUES PAROUT=$S20,I3,10H PARAMETER,S5,E15.6,4H +-,El 1 5.6*$ PRINT FORMAT AROUT,AREA,P3SP2S,PIS,POS,NOS,NlS,N2S,N3S VECTOR VALUES AROUT=$SHO,S19,6HAREA= F12.4//S20,18HERROR DIST 1 RI8UTION,815*$ PRINT FORMAT INITAL,SETUP(1)...SETUP(24) PRINT COMMENT $0 CHANNEL MEASURE 1 D FITTED DIFFERENCE MEASUREDS PRINT COMMENT $ NUMBER SPECTRU 1 M SPECTRUM IN SPECTRA ERRORS THROUGH F28,FOR I=ILP,1,I.G.IUP PRINT FORMAT DATOUT,I,YNRM(I),FIT(I),DIFF(I),DYNRM(I) VECTOR VALUES DATOUT=$S25,I5,46E8.8*$ DATA PLOT F29 PRINT FORMAT INITAL,SETUP(1)...SETUP24) PRINT COMMENT $0 1 SSBAUER SPECTRUM VS CHANNEL NUMBERS EXECUTE ZERO.(ZP( 1)...ZP(IM)) YMAX=O. YMIN=O. DMAX=O. DMIN=O. THROUGH F29,FOR I=ILP,I,I.G.I UP XX( I)=-I WHENEVER YNRM(I).G.YMAXYMAX=YNRM(I) WHENEVER YNRM (I).L.YMINYMIN=YNRM(I) WHENEVER DIFFI).G. DMAX,DMAX=DIFF(I) WHENEVER DIFF(I).L.DMIN,DMIN=DIFF(I) DELY=YMAX-YMI N DELD=DMAX-DMI N YMAX=YMAX+. 1*ELY YMIN=YMI N-. 1*DELY DMAX=DMAX+. 1*DELD DMIN=DMIN-.1*DELD SP=IUP-ILP FILP=ILP F IUP=IUP EXECUTE PLOT1.(0,1,SP,1,100) EXECUTE PLOT2. IMAGE,YMAX,YMIN,-FILP,-FIUP) EXECUTE PLOT3. $-$, ZP( ILP),XX(ILP), SP+1) EXECUTE PLOT3.($*$,FIT(ILP),XX(ILP),SP+i) EXECUTE PLOT3.($+$,YNRM(ILP),XX(ILP),SP+1) EXECUTE PLOT4.(1,S $) PLOT OF MO

-157 PRINT FORMAT INITAL,SETUP(1)...SETUP(24) PRINT COMMENT $0 I ROR VS CHANNEL NUMBERS EXECUTE PLOT1.(O1,,SP,1,100) EXECUTE PLOT2.(IMAGE,DMAX,DMIN,-FILP,-FIUP) EXECUTE PLOT3. $-$,ZP( LP),XX(ILP), SP+) EXECUTE PLOT3.($*$,OIFF(ILP),XX(ILP),SP+1) EXECUTE PLOT4.(1,$ S) TRANSFER TO START END OF PROGRAM PLOT OF ER T1 2. Theory Subroutine (Sample) EXTERNAL FUNCTIUN(JT,XT,PT,AT,BT,FT,DFT) DIMENSION PPT(25) INTEGER JTI ENTRY TU THEORY. THEORY FUR CUCR2TE4 SPECTRUM, SIX LINES, R LESS THAN 0, CONST RAINED INTENSITIES, SAME WIDTHS, P2, 256,SLOPE CODE 6L,3INT-CONSTR,1LWR.L.OISP2,256,SL THROUGH TILFOR I=1,1,I.G.25 PPT(I)=PT(I) XI=127.5+PPT(3)+PPT(2)PPT(2( PT(6)-1) X2=127.5+PPT(3)+PPT(2 )*(PPT(6)-1) X3=127.5+PPT(3)+PPT(2)*(-PPT(6)-1) X4= 127.5+PPT( 3)-PPT(2)*(-PPT(6)- ) X5=127.5+PPT(3)-PPT( 2)*(PPT(6) —) X6=127.5+PPT(3)-PPT(2)*(3*PPT(6)-1) I1=PPT(5)*PPT({).P.2 I2=2*PPT(5)*PPT( 1).P.2 I3=3PPT( 5)*PPT(1).P.2 D1=PPT( 1).P.2+(XT-X1).P.2 D2=PPT(1 ).P.2+(XT-X2).P.2 D3=PPT( ).P.2+(XT-X3).P.2 D4=PPT(1 ).P.2+(XT-X4).P.2 D5=PPT(1).P.2+(XT-X5).P.2 D6=PPT(1).P.2+(XT-X6).P.2 C =2.0*I3( XT-X1)/D1.P.2 C2=2.0*I2:*(XT-X2)/D2.P.2 C3=2.0*I L*( XT-X3)/D3. P.2 C4=2.0*I 1*(XT-X4)/D4.P.2 C5=2.012*( TXT-X5)/D5.P.2 C6=2.0*I3*( XT-X6 /D6. P.2

-158br= 1.0-I3/) 1- I2/D2-I1 /D3-I 1/D4-I 2/05-13/D6-PPT(7 )*XT AT=PPT(4) E=2.0*PPT (1) FT=AT*BT G=-A i-PPT (1) P. 2 H=(13-3.0*PPT(5)*01)/D1.P.2+(12-2.0*PPT(5)*D2)/D2.P.2+(I1-PPT 1 (5)*D$3) /03.P.2+(I1-PPT( 5) D4)/04.P.2+(I2-2.0*PPT(5)*D5)/05.P. 2 2+( I3-3.0*PPT(5)*D6)/06.P.2 OFT (1 )=AT*E*H OFT(2)=AT*( (3.0*PPT(6)-1.O)* (C6-C) +( PPT(6)-1)*(C5-C2)+(-PPT( 1 6)-1)*(C4-C3)) OFT (3)=-AI* (C1+C2+C3+C4+C5+C6) DFT (4) =T DFT () = * (3.0/0 1+2. 0/2+1. 0/D3+1.0/D4+2. /05+3. 0/6) OFT(6)=AT*PPT (2 *(-3.0'C1-C2+C3-C4+C5+3.0*C6) DFT(7)=-AT*XT FUINCTIUl RETURN END OF FUNCTION

REFERENCE S 1. J A. Stone and W. L. Pillinger, Phys. Rev. Letters, 13, 200 (1964). 2. D. Seyboth, F. E. Obenshain, and G. Czjzek, Phys. Rev. Letters, 14, 954 (1965). 3. Y. K. Lee, P. W. Keaton, Jr., Eo T. Ritter, and J C. Walker, Phys. Revo Letters, 14, 957 (1965). 4. G. Czjzek, J. L. C. Ford, Jr., F. E. Obenshain, and D. Seyboth, Phys. Letters, 19, 673 (1966). 5. G. Czjzek, J. L. C. Ford, Jr., J. Co Love, F. E. Obenshain, and Ho H. F. Wegener, Phys. Rev. Letters, 18, 529 (1967). 6. So L. Ruby and Ro E. Holland, Phys. Rev. Letters, 14, 591 (1965)o 7. D. A. Goldberg, P. W. Keaton, Jr., Y. K. Lee, L. Madansky, and J. C. Walker, Phys. Rev. Letters, 15, 418 (1965). 8. J. Christiansen, E. Recknagel, and G. Weyer, Phys. Letters, 20, 46 (1966)o 9. D. W. Hafemeister and E. Bo Shera, Phys. Rev. Letters, 14, 593 (1965) 10. U. Gonser and H. Wiedersich, J. Phys. Soc. Japan, 18, Suppl. II, 47 (1963). 11. Po H. Dederichs, Co Lehmann, and H. Wegener, Phys. Stat. Sol., 8, 213 (1965). 12. V. N. Belogurov, Phys. Stato Sol., 10, K41 (1965). 13. J. Fink and P. Kienle, Phys. Letters, 17, 326 (1965). 14o D. A Goldberg, Yo K. Lee, E. To Ritter, Ro Ro Stevens, Jr., and J. C. Walker, Phys. Letters, 20, 571 (1966)o 15. P. Hannaford, C. J, Howard, and J. W, Wignall, Phys. Letters, 19, 257 (1965) 16. Fo E. Obenshain and Wo Berger, Bullo Amo Phys. Soc.o, II, 12, 24 (1967). 17. Eo Po Stepanov and A Yu Aleksandrov, JETP Letters, 5, 83 (1967) -159

-160 18. Ho C. Schweinler, J. Appl. Phys., 30, 1125 (1959). 19. R. M. Walker, Jo Nucl. Mat., 2, 147 (1960) 20. J. H. Crawford and J. W. Cleland, Radioisotopes in the Physical Sciences and Industry, IAEA, Vienna, 269 (1962). 21. R. Oswald and C. Kikuchi, Nuclear Sci. Enq., 23, 354 (1965). 22. Co Barnes and C. Kikuchi, ORA Technical Report, University of Michigan, Ann Arbor (1967). 23. J. C. Danko, G. R. Kilp, and P. V. Mitchell, Advanced Energy Conversion, 2, 79(1962). 24. R. T. Frost, J. C. Corelli, and M. Balicki, Advanced Energy Conversion, 2, 77 (1962). 25. J. C. Corelli, Ro T. Frost, and D. M, Amorosi, IRE Trans. on Nuclear Science, NS-9, 303 (1962) o 26. V. A. J. van Lint, E. G. Wikner, and P, Ho Miller, Jr., GA-1513 (1960). 27. E. G. Wikner, GACD-2699 (1961). 28. P. Zo Hien, V. G. Shapiro, and V. So Shpinel, Soviet Physics JETP, 15, 489 (1962)o 29. Co Eo Violet, D. Lo Davis, and R. Booth, UCRL-7045 (1962). 30. C. E, Violet, R. Booth, and F. Wooten, Phys. Letters, 5, 230 (1963). 31. C. E. Violet and R. Booth, UCRL-12438 (1965); Phys. Rev., 144, 225 (1966). 32. Ao B. Buyrn and L. Grodzins, Bull. Am. Phys. Soc., 8, 43 (1963) 33. N. Shikazono, J. Phy. Soc. Japan, 18, 925 (1963). 34. R, Bo Frankel, Po H. Barrett, and Do A. Shirley, Bull. Am. Phys. Soc., 7, 600 (1962). 35. P. H. Barrett, R. Bo Frankel, and D. A. Shirley, UCRL-10624 (1962) 36. E. P Stepanov, K. P. Aleshin, R. A. Manapov, B. No Samoilov, V. Vo Sklyarevsky, and Vo G. Stankevich, Physo Letters, 6, 155 (1963).

-161 37 Ro B. Frankel, J. Huntzicker, E. Matthias, S. S. Rosenblum, Do A. Shirley, and N. J. Stone, UCRL-11882 (1965); Physo Letters, 15, 163 (1965). 38. A. H. Muir, Jr., K. J. Ando, and H, Mo Coogan, Mbssbauer Effect Data Index, Issue 3 (1965) 39. Do Jo Hughes and R. B, Schwartz, BNL-325, Second Edition, Supplement No. 2 (1965). 40. L. V. Groshev, A. M. Demidov, VO N. Lutsenko, and V. I, Pelekhov, translated by J. B. Sykes, Atlas of -Ray Spectra from Radiative Capture of Thermal Neutrons, Pergamon Press (1959). 41. Ho C. Schweinler, Chemical Effects of Nuclear Transformations, IAEA, Vienna, 1, 63 (1963). 42. D. S. Billington and Jo Ho Crawford, Jr., Radiation Damage in Solids, Princeton University Press, Princeton, New Jersey (1961)o 43. G. J. Dienes and G. H. Vineyard, Radiation Effects in Solids, Interscience Publishers, Inc., New York (1957). 44. Fo Seitz, Dis. Faraday Soc., 5, 271 (1949) 45. R. Ho Bube, Photoconductivity of Solids, John Wiley and Sons, Inc. (1960) 46. I. N. Rozantsev, IzVo Akad. NaukO SSSR, Ser. Fiz. 28, 88 (1964). 47. Ro S, Narcisi, Tech. Report No. 2-9, Department of Physics, Harvard University (1959)o 48. Ao Ho Wapstra, G, J. Nijgh, and R. Van Lieshout, Nuclear Spectroscopy Tables, Interscience Publishers, Inc., New York (1959)o 49. H. Frauenfelder, The Mbssbauer Effect, W. A. Benjamin, Inc., New York (1962). 50. G. Ko Wertheim, MOssbauer Effect: Principles and Applications, Academic Press (1964) 51. Do Ao Shirley, Rev. Mod. Phys., 36, 339 (1964). 52. P. Brix and H, Kopfermann, Rev. Mod. Phys., 30, 517 (1958). 53. Mo H. Cohen and F. Reif, Solid State Physics, Vol. 5, Academic Press (1957).

-162 54. F, W. deWette, Phys. Rev., 123, 103 (1961). 55. Ro Bersohn, J. Chemo Phys., 29, 326 (1958). 56. Jo S. Geiger, R. L. Graham, I. Bergstroem, Nucl. Phys., 68, 352 (1965). 57. H, Eo Weaver, Jr., Phys Rev., 89, 923 (1953). 58. R. E. Watson and Ao J. Freeman, Phys. Rev., 123, 2027 (1961)o 59. A. J. Freeman and R. E. Watson, in Magnetism (G. T. Rado and H. Suhl, editors), Vol. II, Part A, Academic Press, New York (1965). 60. R. Go Shulman and V. Jaccarino, Physo Rev., 108, 1219 (1957). 61. A. Jo Freeman and R. E Watson, PhysO Rev. Letters, 6, 343 (1961). 62. E. Kankeleit, Rev. Sci_. Inst., 35, 194 (1964). 63. D. Rubin, Rev. Sci. Inst., 33, 1358 (1962). 64. Ho DeWaard, G. DePasquali, and D. Hafemeister, Phys. Letters, 5, 217 (1963) 65. Mo Kalvius, in Mbssbauer Effect Methodology (I. J. Gruverman, editor), Vol. 1, Plenum Press, New York (1965) 66. H. Marshall, in Inorganic Syntheses (Ludwig F. Audrieth, editor-in-chief), Vol. 3, McGraw-Hill (1950)o 67. Vo P. Zlomanov, Ao V. Novoselova, Ao S. Pashinkin, Yu P. Simanov, Ko N. Semenenko, Zhuro Neorg, Khim., 3, 1473 (1958) 68. W. A. Dutton and Wo Charles Cooper, Chemical Reviews, 66, 657 (1966)o 69. So Margulies and J. R. Ehrman, Nucl. Inst. and Methods, 12, 131 (1961). 70. C. Colominas, Phys. Rev., 153, 558 (1967). 71. J. Bo Gibson, A. N. Goland, M. Milgram, and Go H. Vineyard, Physo Revo, 120, 1229 (1960) 72. Wo M. Visscher, Phys. Rev., 129, 28 (1963) 73O A. Ao Maradudin and P. A. Flinn, Phys. ReVo, 126, 2059 (1962)o

-163 74. Ro G, Barnes and W. V. Smith, Phys. Rev., 93, 95 (1954). 75O Wo Jo Nicholson and Go Burns, Phys. Rev., 129, 2490 (1963). 76. V. I. Goldanskii, E. F. Makarov, and Vo V. Kharapov, Soviet Physics JETP, 17, 508 (1963) 77. Lo Pauling, The Nature of the Chemical Bond, Cornell University Press, Second Edition (1948) 78. Ho Hahn, C. de Lorent, and B. Harder, Zo anorg. Chem., 283, 138 (1956)o 79. F. K. Lotgering, Proc. Int. Conf. on Maqnetism, Nottingham, 533 (1964). 80. P. Ko Baltzer, P. Jo Wojtowicz, Mo Robbins, and Eo Lopatin, Phys. Rev., 151, 367 (1966)o 81. Po Ko Baltzer, H. Wo Lehmann, and Mo Robbins, Phys. Rev. Letters, 15, 493 (1965) 82. No Menyuk, K. Dwight, and R. J. Arnott, J. Appl. Phys., 37, 1387 (1966) 83. J. Kanamori, Jo Phys. Chem. Solids, 10, 87 (1959). 84. P. W. Anderson, Phys. Rev., 79, 350 (1950)o 85. Jo C. Slater, Quarto Proqr. Rep. MoIoT., July 15 and Oct. 15 (1953) 86. Do Ao Shirley and Go A. Westenbarger, Physo Rev., 138, 170 (1965)o 87. Ro SO Preston, So So Hanna, Jo Heberle, Physo Rev,o 128, 2207 (1962)o 88. Fo Ko Lotgering and E. Wo Gorter, Jo Phys. Chem. Solids, 3, 238 (1957)o 89. Jo Bo Goodenough, Magnetism and the Chemical Bond, Interscience Publishers (1963)o 90. W, Bo Pearson, CanoJ. Phys., 35, 886 (1957) 91. Do Clifton, Master's Thesis, Department of Nuclear Engineering, The University of Michigan, Ann Arbor (1966) 92o J. Co Slater, Quantum Theory of Molecules and Solids, Volo 2, McGraw-Hill (1965)

-164 93. Ho Haraldsen and A. Neuber, Z. anorq. Chem., 234, 353 (1937). 94 L G. Gaidukov, N. P. Grazhdakina, I. G. Fakidov, Soviet Physics JETP, 12, 636 (1961). A. 95. T. Hihara, Y. Koi, and Ao Tsujimura, Jo Phys. Soc. Japan, 17, 1320 (1962). Ai, 96. Ao Tsujimura, T. Hihara, and Y. Koi, Jo Phys. Soc. Japan, 17, 1078 (1962). 97. C. 0, Muehlhause, Phys. Rev., 79, 277 (1950) 98. R. L. M6ssbauer, Z. Physik, 151, 124 (1958). 99. K, So Singwi and A. Sjblander, Phys. Rev., 120, 1093 (1960). 100. R. Wo Go Wycoff, Crystal Structures, Second Edition, Interscience Publishers (1966). 101. Lo N. Swink and G. Bo Carpenter, Acta Cryst., 21, 278 (1966). 102. J. D. Bowman, E. Kankeleit, E, N. Kaufmann, and B. Persson, Nucl. Inst. Methods, 50, 13 (1967). 103. Po Cziffra and M. J. Moravscik, UCRL-8523 (1958).