THE UN I V E R S I T Y OF MICHIGAN COLLEGE OF ENGINEERING Department of Nuclear Engineering Final Report RADIATION EFFECTS STUDIES USING THE MOSSBAUER EFFECT D. H. Vincent J. F. Ullrich ORA Project 07921 supported by: NATIONAL SCIENCE FOUNDATION GRANT NO. GK-871 WASHINGTON, D.C. administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR June 1969

TABLE OF CONTENTS Page I. INTRODUCTION 1 II. SEARCH FOR RADIATION EFFECTS IN TELLURIUM COMPOUNDS 2 III. MAGNETIC PROPERTIES OF TELLURIUM COMPOUNDS 3 57 40 IV. NEUTRON BEAM EXPERIMENTS WITH Fe AND K 5 V. ANALYSIS OF QUADRUPOLE SPLITTING DATA 6 VI. FUTURE PLANS 6 REFERENCES 7 APPENDICES 125 A, "Te Mossbauer Effect Study of Neutron Capture Effects in PbTe, Te, and Te02" B. T25Te M'ossbauer Effect Study of Magnetic Hyperfine Structure in the Ferromagnetic Spinel CuCr2Te4" Co "Mossbauer Measurements with K 4 D. "A New Method for the Analysis of Temperature Dependent Quadrupole Splitting in M'ssbauer Spectra" ii

I. INTRODUCTION The NSF Grant GK-871 was extremely important for the initiation of a Mossbauer spectroscopy project within the frame work of the materials research program of the Department of Nuclear Engineering at The University of Michigan. Through it we were able to buy some of the necessary instruments, to support three students during part of their doctoral work, and to cover current costs for materials and supplies for two years. But beyond that the grant was also instrumental in helping us to obtain additional support from other sources: The College of Engineering of The University of Michigan supplied a Nuclear Data 512-channel multichannel analyzer; two grants from the Michigan Memorial Phoenix Project were obtained-one for student support, the other for the acquisition of a liquid helium cryostat; and finally, the Argonne National Laboratory gave financial support to the recipient of this grant in order to make possible his cooperation in that part of the research which was conducted at the Argonne Laboratory. The original proposal was to study neutron induced recoil defects in tellurium compounds. However, after this investigation was completed to the extent that seemed feasible (see Section II), other problems were attacked. The choice of these was influenced mainly by the general interest that the solution of these problems might have. As will be seen, these investigations did not always fall under the general topic of defect studies by the Mossbauer effect, which we consider as the guiding principle of our research effort. 1

II. SEARCH FOR RADIATION EFFECTS IN TELLURIUM COMPOUNDS The principle of our experiments is the following: The source nuclei for the Mossbauer spectroscopy are produced by neutron capture. The energetic gamma rays emitted following neutron capture impart a recoil momentum to the source nucleus. The recoil energy is just large enough to produce a few displacements in the lattice containing the source nucleus. It seems likely, therefore, that the source nucleus itself may end up in a defect position, or that a defect may be located in it's immediate neighborhood. In both cases, the Mossbauer spectrum may be modified in comparison to the undisturbed spectrum either in intensity or in its hyperfine structure, or both. To avoid possible chemical effects it seemed important to require, that the Mossbauer transition should occur in the same nucleus, which is produced by the neutron capture.* This can be achieved in two ways: 1. The Mossbauer transition is observed immediately following neutron capture as the final transition in the capture gamma ray cascade. This makes it necessary to conduct the experiment in the neutron beam at the reactor. 2. The neutron capture process may lead to a long-lived isomeric state. In this case the neutron irradiation of the source may be conducted in the reactor and the isomer produced may be used in a conventional Mossbauer spectrometer away from the reactor. We have chosen the second possibility. There are only very few isomers of convenient half-life which may be used 125m for Mossbauer experiments. Out of these we selected Te for our experiments. Usually, M'ssbauer sources are:-emitters, i.e. the gamma transition used for resonance absorption occurs in the nucleus which is chemically different from its long-lived radioactive parent. 2

125 Our work is described in detail in Appendix A, "Te Mossbauer Effect Study of Neutron Capture Effects in PbTe, Te and TeO2."* Our results indicate that the thermal neutron capture process does not affect the Mossbauer spectra of 125 Te in the compounds investigated. However, we feel that our results, though they are negative in the sense that we did not observe the effect which we had been looking for, have some importance, particularly in view of the fact that Stepanov and Aleksandrov did see an effect in PbTe following neutron irradiation with much higher total doses than ours. Details of the comparison of our measurements with those of the Russian authors are given in Appendix A. III. MAGNETIC PROPERTIES OF TELLURIUM COMPOUNDS After the conclusion of the work on defect properties in Te-compounds it was decided to look at the magnetic properties of some Te-compounds. Two facts led to this decision: On one hand we had developed the necessary skill to do 125 Mossbauer spectroscopy with Te and on the other hand we learned at that time of an interesting ferromagnetic spinel, CuCr2Te4, which had been the subject of (2,5,4) some recent investigations. This compound seemed to us to offer a unique opportunity to measure transferred hyperfine fields by Mossbauer spectroscopy since Te is the only chalcogenide with a known MOssbauer nuclide and CuCr2Te4 is the only ferromagnetic spinel which has been successfully prepared using Te as the anion. A description of the work on CuCr2Te4 is to be found in Appendix B, which This paper has been accepted for publication in the Journal of Chemistry and Physics of Solids. 5

is a reprint of our publication in the Physics Letters. The great interest which this paper aroused may be seen from the fact, that within 6 months of our publication, two other papers appeared in the Physics Letters, one being a 125 measurement of the transferred hyperfine field at the Te -nucleus in CuCr2Te4 (6) by NMR techniques, the other being an improvement on our measurement of the 125 (7) magnetic moment of the first excited state in Te o A recalculation of Hef using the new value for the excited state magnetic moment gives Heff = 164 kgauss; this value is in closer agreement with the NMR results than was our original determinationo Besides CuCr2Te4, we also remeasured the spectra of two other compounds: antiferromagnetic MnTe and ferromagnetic CrTeo The results of these measurements have not been published and are therefore given here in brief: The MnTe displayed no measurable line broadening, indicating that both the electric quadrupole and magnetic hyperfine interactions are very weako In conclusion, the antiferromagnetic "superexchange" coupling of the Mn transition metal ions apparently causes little unpairing of the Te spinso Line broadening was observed for CrTe, however it is difficult to ascertain whether the origin is the quadrupole or magnetic interaction. The magnetic interaction is a distinct possibility since the ferromagnetic Cr ions could cause spin unpairing of the Te s-electrons either by exchange polarization or covalent mixing. If the broadening in CrTe is solely magnetic in origin, the internal hyperfine field at the Te site is Heff 20 kgauss. eff'~~~

57 40 IVo NEUTRON BEAM EXPERIMENTS WITH Fe AND K Simultaneously with the work described in Section III, we began to look 57 56 for the Mossbauer effect in Fe following neutron capture in Fe ) In this case there is no long-lived isomeric state preceding the 14.4 kev transition in * 57 Fe so that the experiment must be conducted in the neutron beam at a reactor. This experiment is quite difficult to do because of the very high gamma background in and around a neutron beam, A carefully designed collimator was built and installed in a beam port at the Ford Nuclear Reactor (FNR) of The University of Michigano Many arrangements of gamma- and neutron shielding were tested until we were eventually able to see the 14.4 kev radiation as a 4.5o effect above background in a double-window xenon filled proportional counter. At this time we learned that the same experiment had already been done with much higher (8) neutron flux at the FR2-reactor in Karlsruhe, Germany ) Since the student engaged in the experiment, a citizen of the Republic of China, faced some problems concerning the extension of his visa, it was then decided, to abandon the experiment at the FNR for the time being and to accept an offer of the Argonne National Laboratory, to conduct similar experiments there. At ANL a number of Mossbauer nuclei were tested in the neutron beam at the CP-5 re40 actor and K was eventually chosen as the subject of our investigation. Financial support by the laboratory made it possible for me to actively take part in this investigation during part of the summer 1967, and during shorter trips throughout that year. The results of this work have been published in the (9) Physical Review and may be found as Appendix C to this reporto It is hoped, that Mossbauer experiments in the neutron beam at the FNR 5

will eventually be taken up again, since recent measurements at Karlsruhe show that this method is one of the most promising for the investigation of radiation effects by Mo'ssbauer spectroscopy. V. ANALYSIS OF QUADRUPOLE SPLITTING DATA Guided by the special interest of a graduate student in the Chemistry Department of The University of Michigan, a systematic investigation into the temperature dependence of the quadrupole splitting of some Fe-complex compounds was undertaken. The results of these measurements are appended as Appendix D. Publication of these results with an interpretation of their meaning is intended and reprints of the paper will be submitted when available. VI. FUTURE PLANS We are planning to continue our efforts to develop Mossbauer spectroscopy as a tool for the investigation of radiation effects. After a number of unsuccessful attempts in this direction by various authors, Czjzek and Berger have recently obtained very promising results by doing Mossbauer spectroscopy with FeAl-alloys in the neutron beam. Our own work will also concentrate on order-disorder alloys, as well as age-hardening alloys, as will be described in more detail in a new research proposal. 6

REFERENCES (1)o Eo P. Stepanov and A. Yu. Aleksandrov, Change in the Mossbauer Spectrum of Tel25m in the Semiconductor PbTe Following Irradiation in a Reactor, ZhETF Pis'ma 5, Noo 3, 101-103, 1 February 1967. (2). Fo K. Lotgering, in Proc. Intern. Conf. on Magnetism, Nottingham, England, 1964, 5335 (3)~ Po K. Baltzer, P. Jo Wojtowicz, M. Robbins, and E. Lopatin, Phys. Rev. 151, 367 (1966)O (4). C, Colominas, Phys. Rev, 153, 558 (1967)o (5). J. F. Ullrich and Do H. Vincent, Physo Letters 25A, 731. (1967)o (6). S, B. Berger, J. I. Budnick, and T. J. Burch, Phys. Letters 26A, 450 (1968). (7). R. Bo Frankel, J. Jo Huntzicker, D. A. Shirley, and N. J. Stone, Phys. Letters 26A, 452 (1968). (8)0 W. G. Berger, J. Fink, and F. E. Obenshain, Phys. Letters 25A, 466 (1967). (9). P. K. Tseng, S. L. Ruby, and D. H. Vincent, Phys. Rev. 172, 249 (1968). (10)o W. Go Berger and Gordon Czjzek, private communication (1968). 7

APPENDIX A 125 "Te Mossbauer Effect Study of Neutron Capture Effects in PbTe, Te, and TeO2" by J. F. Ullrich and D. H. Vincent Accepted for publication in the Journal of Physics and Chemistry of Solids

J. Phys. Chem. Solids Pergamon Press 1969. Vol. 30, pp. 1189-1195. Printed in Great Britain. Te125 MOSSBAUER EFFECT STUDY OF NEUTRON CAPTURE EFFECTS IN PbTe, Te AND TeO*2 J. F. ULLRICHt and D. H. VINCENT Department of Nuclear Engineering, University of Michigan, Ann Arbor, Mich. 48104, U.S.A. (Received 28 August 1968; in revisedform 4 November 1968) Abstract- The Mossbauer emission spectra of Te125 in PbTe, Te metal, and TeO2 have been measured following neutron capture in Te 24. Mossbauer data for each sample were taken after the source irradiation and following thermal annealing. The irradiation conditions were chosen so that only the thermal neutron capture induced defects should have a significant effect on the environment of the Mossbauer emitting nuclei. Comparison of the data taken before and after the source annealing showed no differences in linewidth, isomer shift, quadrupole splitting, or resonance intensity within the standard deviations of the parameters. The results show that the thermal neutron captuie process in Te124 does not affect the Te125 Mossbauer spectra. The possible reasons for this are discussed. The results also indicate that the anomalous isomer shift reported by Stepanov and Aleksandrov in a similar experiment on PbTe is probably caused by a high background of fast neutron induced displacements. 1. INTRODUCTION lems of low neutron intensity and high backCHANGES in the structure of Mossbauer emis- ground radiation associated with neutron sion spectra due to the presence of neutron beam experiments. There is one limitation, capture induced displacements have been however, in the use of in-pile irradiations studied in processes involving both neutron for investigating radiation effects; the measactivation of the first excited state of the urements are restricted to materials with Mossbauer nuclide[1-3] and neutron activa- defect annealing temperatures greater than tion of an isomeric state parent [4, 5]. Because the reactor irradiation temperature (generally of the short lifetime of the first excited state 50~C or higher). This severely limits the of Mossbauer nuclides (10-lO-10-5 sec), number of potential experiments. This, of the neutron activation of this state and the course, is not true if low temperature irradiMossbauer measurement must be done simul- ations are possible; however, low temperature taneously. Thus, the first type of experiment irradiation facilities are not available at most must be done in a neutron beam. However, reactors. if the Mossbauer nuclide has a long-lived iso- Sn119 and Te125 are two Mossbauer nuclides meric state, then the neutron activation and that offer favorable thermal neutron capture the Mossbauer measurement can be done at cross sections, isomeric state half-lives, and different times. In the second type of experi- resonant gamma ray energies for use in the ment the neutron irradiation can be done in- second type of experiment. Previous Mosspile and the Mossbauer measurement can be bauer investigations of the effect of neutron made at leisure after the irradiation. irradiation on the resonant emission spectra The principle advantage of the second type of these nuclides have given some evidence of of experiment is that it avoids the usual prob- recoil induced changes in the electronic configuration about the emitting nuclei. *Research supported by the National Science Founda- Hannaford et al.[4] found a small satellite tion, Grant No. Gk-871. tPresent address: Scientific Laboratory, Ford Motor peak in the emission spectrum of Sn19 in Company, Dearborn, Michigan. Mg2SnO4 following neutron activation. The 1189

1190 J. F. ULLRICH and D. H. VINCENT intensity and isomer shift of the satellite ation conditions chosen so that the Mossbauer peak indicated that approximately 25 per cent spectra should only be affected by displaceof the Sn atoms had suffered a recoil induced ments caused by the thermal neutron capture valency change. The valency change was process. The results indicate that the thermal clearly shown to be attributable to neutron neutron capture process in Te124 does not have capture induced displacements. an effect on the Mossbauer spectra of the Stepanov and Aleksandrov[5] recently re- Te125. In conclusion, the anomaly observed by ported a Missbauer measurement on Te125 Stepanov and Aleksandrov in PbTe is probin PbTe following neutron activation. The ably the result of a high concentration of measurement showed an anomalous isomer displacements induced by mechanisms other shift. The PbTe source measured against a than thermal neutron capture. The most PbTe absorber had an isomer shift of 1-7 mm/ likely mechanism is fast neutron elastic sec (measured 20 days after the end of the scattering. irradiation) when, in fact, there should be no isomer shift if the source and absorber are 2. RADIATION EFFECTS chemically identical. The anomalous isomer The Missbauer isomeric state parent shift indicated that the s-electron configuration Te'25'"(58d) is produced by thermal neutron of the PbTe source had been altered by the capture in Te124 (i.e. Te'24 +nth -> Te125'm irradiation. The anomalous isomer shift was +y). The Te125'" nucleus can be introduced observed to decrease exponentially with time into the lattice as a defect if the recoil energy with a mean life of 10 3 days. This indicated from the (n, y)-reaction is greater than the that the defect structure was annealed at room minimum energy for displacement, Ed, temperature. which is typically of the order of 25 eV. The The measurements reported in this paper recoil energy arises from the emission of the were also done on Te'25 following neutron 6-4 MeV of excitation energy of Te125 by activation. In addition to a measurement on'prompt' gamma rays. By conservation of PbTe, measurements were also made on Te momentum the emitted gamma rays impart metal and TeO2. Mossbauer measurements kinetic energy to the emitting nucleus. were made on each of the three materials A calculation of the mean recoil energy refollowing the source irradiation and then quires knowledge of the gamma rays emitted following thermal annealing of the same in the de-excitation process, including their source. The two spectra were then compared energies, emission probabilities, and time to see if there were any changes in the hyper- and angular correlation. Unfortunatley the fine spectra caused by neutron capture in- capture gamma ray energy spectrum has not duced displacements. been measured for neutron capture in Te124; Contrary to the results of Stepanov and therefore the mean recoil energy cannot be Aleksandrov the Mossbauer spectrum for accurately estimated. PbTe reported in this paper showed no In general the mean recoil energy for capanomalous isomer shift after the neutron irra- ture gamma ray emission is low (of the order diation. In fact, no changes were observed of Ed). This means that the number of disin the hyperfine spectra of any of the three placed atoms produced per thermal neutron materials. captured is small; subsequently, the number of The difference between these results for possible defect configuration is small. This is PbTe and those of Stepanov and Aleksandrov a particularly nice feature for Mossbauer yields considerable insight into the defect measurements since the resultant Missbauer mechanisms involved. The measurements re- spectrum is a weighted sum of the spectra ported in this paper were made with irradi- characteristic of each defect configuration.

Te125 MOSSBAUER EFFECT STUDY 1191 The isolation of displacements which are the density of defects must be kept much less induced specifically by thermal neutrons is than the number density of atoms. Since the often very difficult when doing in-pile irradia- defect density is a linear function of the total tions. This is due to the'background' effects radiation dose (in the absence of self annealcaused by displacements due to other recoil ing), it is possible to minimize the effect of processes. All of the types of radiation present undesirable displacements by proper choice in a reactor (i.e. fast neutrons, gamma rays, of irradiation fluxes and times. etc.) can produce displacements through The measurements reported in this paper either scattering processes or nuclear reac- were carried out under conditions where the tions. For most elements the ratio of defects thermal neutron capture effects played a produced by thermal neutron capture to those dominant role. Fast neutron scattering was produced by fast neutron scattering is less the principal source of additional displacethan one[6]. Thus, fast neutrons are usually ments; however, the estimated density of responsible for most of the radiation effects these displacements was - 10-4-10-3 of the observed with in-pile irradiations. tellurium atom density. Thus, the fraction of Under some conditions the Mossbauer Mossbauer emitting nuclei which are in close effect measurement provides a means of proximity to a fast neutron displaced atom is separating displacements due to thermal very small. The fast neutron induced disneutron capture from those arising from fast placements then should have little effect on neutrons and other sources. This is possible the Mossbauer spectra. because the characteristic hyperfine interactions are, for the most part, only influenced EXPERIMENTAL PROCEDURE by the'local' electronic environment (atomic (A) Sources and absorbers electrons and first few near neighbour atoms). The PbTe, Te metal and TeO2 used in the The fraction of the resonant emissions measurements as sources were prepared from which have hyperfine structure character- Te enriched to 94 per cent in Te124. The PbTet istic of a defect environment is related to the and Te metal powders were pressed into thin probability that a defect is within the'local' discs and then sintered in a hydrogen atmosenvironment of an emitting nucleus. For phere at 550~C for 3 hr and 350~C for 6 hr, defects produced by thermal neutron capture respectively. The TeO2 was prepared from this probability should be nearly equal to 1 nitric acid solution following the procedure of since the emitting nucleus itself is in a defect Marshall[7]. This procedure results in TeO2 position. On the other hand, defects produced with the tetragonal crystal structure. The by other types of radiation are randomly structures of the materials were all verilocated with respect to the emitting nuclei. fled by X-ray diffraction measurement. Hence the probability that these defects The materials to be used as sources were are within the'local' environment of an emit- irradiated in the Ford Nuclear Reactor. ting nucleus is of the order of the ratio of the Samples were generally irradiated in fluxes defect density to the appropriate atomic of 1012-1013 neutrons/cm2-sec for periods density. * of 10-15 days. The total thermal neutron In order to minimize the effect of displace- doses for the PbTe, Te and TeO2 samples ments caused by other types of radiation, reported on in this paper were 8x1017, 9x1017 *The atomic density used here must take into account and 8x1018 neutron/cm2, respectively. The the range of the hyperfine interactions (referred to as the fast neutron doses were a factor of 12 lower.'local' environment). This density will be smaller than the number density of atoms for long range interactions and will approach the number density for short range interactions (hyperfine interactions affected only by the tPrepared by New England Nuclear Corp., Boston, atomic electrons). Mass.

1192 J. F. ULLRICH and D. H. VINCENT The sample temperatures during the irradi- The multichannel analyzer was calibrated ation were measured to be ~ 45~C. using the magnetic hyperfine spectrum After the Mossbauer measurement was of Fe57 in iron metal. Calibration runs were made following the source irradiation, the made before and after each Te run to check sources were all annealed to restore any dis- the constancy of the equipment. placed atoms to normal lattice sites. The PbTe The source and absorber were both cooled and Te sources were annealed in a hydrogen to liquid nitrogen temperature in a styrofoam atmosphere at 400~C for 11 hr and 350~C insulated dewar similar to the one described for 12 hr, respectively. The TeO2 was dis- by DeWaard et al.[9]. The source and solved in HNO3 and recrystallized following absorber temperatures were not externally the procedure in the initial preparation. controlled and were generally - 82~K. The M6ssbauer measurements for PbTe and Te were made using a single line absorber 4. RESULTS of PbTe (17-5mg/cm2) enriched to 95 per The results of the measurements on PbTe, cent in Te125. The measurements for TeO2 Te and TeO2 are shown in Fig. 1. The data were made using a single line absorber of points shown are those taken in the Mossbauer Te(OH)6 (39mg/cm2) with a natural abun- measurements immediately following the dance of Te125 (7 per cent). (B) Apparatus The Mossbauer measurements were made using the 356 keV gamma ray resonance in Te125. Details of the decay scheme and the relevant Mossbauer parameters have pre- 2 viously been reported [8]. The 356 keV gamma rays were detected _ \ using a xenon-nitrogen filled proportional Annealed counter. With this detector the 356 keV F.. gamma ray is only partially resolved from the - |'.' intense background due to the Te Ka and K, b. X-rays at 27-4 and 31-2keV. The gamma ray can best be discriminated by using the \ escape peak at 70 keV. All measurements f2 were made with the single channel analyzer set at the escape peak energy.' / Annealed The signal-to-noise ratio of the escape peak c. 3 was further improved by using a 5 mil copper - (113 mg/cm2) absorber to reduce the X-ray intensity. This increased the signal-to-noise ratio by a factor of 3-5 with only a factor of 2 0-33 reduction in the count rate. The 8-0 keV Annealed copper X-rays which are generated in this 3 absorber are almost completely absorbed in -2- 0 -10 - 10 2-0 the 20 mil aluminum window on the propor- VELOCITY (cm/sec) tional counter. Fig. 1. Resonance absorption spectra taken before and The resonant absorption spectra were taken after source annealing for: (a) PbTe; (b) Te metal; (c) using a time mode M6ssbauer spectrometer. TeO2.

Te125 MOSSBAUER EFFECT STUDY 1193 irradiations. The solid line is the least squares contribution due to variations in experimental fit to the data with an assumed spectral shape. conditions. Several experimental factors can A single line of Lorentzian shape was fit to have a significant effect on the measured the PbTe spectrum and two lines of Lorentzian resonance intensity. These include the detecshape (quadrupole split) were fit to the Te tor signal-to-noise ratio, the source and and TeO2 spectra. absorber temperature, and the experimental The spectra characteristic of the normal geometry. An accurate comparison of resonlattices were obtained after treating the ance intensities for two different runs requires sources to restore any displaced atoms to that these factors not only remain stable normal lattice sites. The results of the curve during the course of each run but be exactly fitting to the Mbssbauer spectra taken after reproducible for each run. In both respects annealing are shown in Fig. 1. by the dashed the conditions for our experiments were not lines. the most desirable. Runs were generally of The parameters obtained from the least the order of 4-5 days in duration; this, of squares fit to the spectra taken before and course, put a limitation on the temperature after annealing are listed in Table 1. The and electronic stability. In addition, the standard deviations of the parameters listed samples had to be removed between runs for in the table are calculated from the error annealing; this made exact reproducibility Table 1. Parameters obtainedfrom the least squaresfit to the data of Fig. I Quadrupole Source Linewidth Isomer shift* splitting Resonance (mm/sec) (mm/sec) (mm/sec) intensityt PbTe - Pre-anneal 9-69) 0-23 0.07 + 005 0 0-0324 0-0003 Post-anneal 9-58 + 0-22 0.03 0-04 0 0-0351 0-0003 Te -Pre-anneal 9-07~0-24 -0-44~0-08 7-51~ 0-14 0-0197+0-0004 Post-anneal 8-83 0-26 -0-41 ~0-09 7-35 0-15 0-0221 ~0-0005 TeO2 -Pre-anneal 6-42 0-12 - 1 98 0-04 6-72 0-11 0-0226+ 0-0002 Post-anneal 6-49 0-12 - 1 99 004 6-89 0-11 0-0219 0-0002 *Shift relative to PbTe for the PbTe and Te source and Te(OH)6 for the TeO2 source. tMaximum resonance intensity uncorrected for background. matrix generated in the final iteration of the of all conditions difficult. A careful analysis least squares fitting routine. It is apparent of the stability and reproducibility of all the from this tabulation that the linewidth, the previously mentioned factors for our measureisomer shift and the quadrupole splitting for ments indicates that the experimental unthe three materials are identical in the two certainty in the resonance intensity amounts runs within the standard deviations of the to about 10 per cent. parameters. As a result, the observed variations in the The only parameter which shows a signifi- resonance intensity are only of the order of cant variation between runs is the resonance the uncertainty in the measured intensity. intensity. In all cases the variation in resonance To see if the variations in resonance intensity intensity (3-11 per cent) is greater than the for each material were reproducible, the sets standard deviation in the intensity parameter of measurements were repeated using new (1-2 per cent). However, this standard sources. This second set of measurements deviation reflects only the statistical uncer- for each material (only the measurements with tainty in the fitting and does not include a the best statistics are reported in this paper)

1194 J. F. ULLRICH and D. H. VINCENT did not show the same variation in resonance spectra of Te125 which could be attributed to intensity as the first set. In all cases the neutron capture induced recoils. There are magnitude of the change was different and in several possible explanations for the lack of one case even the direction of the change any observable effects; however, it is difficult was different. Again, as in the first set of to establish any conclusive explanation due to measurements, the resonance intensity the lack of supplemental information. changes ranged up to about 10 per cent. First, the changes in the hyperfine structure From this evidence we conclude that if may be too small to be resolved. The broad there are any f value changes in any of the lines of the Te125 resonance, of course, make materials due to the source irradiation, the observation of small changes in the hyperchange is certainly less than 10 per cent of fine spectra very difficult. It is also very diffithe normal f value. To determine whether cult to theoretically predict the isomer shift or not there indeed is a real f value change and electric quadrupole splitting that might would require that the experimental con- occur for various possible defect configuraditions be much better controlled than in our tions. measurements. Second, there may be insufficient recoil The quadrupole splittings for Te and TeO2 energy on the average to displace the atoms obtained in our measurements are in agree- from their normal lattice sites. ment with previously reported values. All Third, defect annealing may occur at the previous results, except for a recent measure- reactor irradiation temperature of 45~C. ment by Pasternak and Bukshpan[10], are Previous measurements indicate that such summarized in a paper by Violet and Booth annealing probably does occur in Te metal, [11]. For comparison with previous results, but definitely not in PbTe. A study of electron the values obtained for the quadrupole splitting bombardment effects on Te metal showed that in our measurements are 0-75 ~0-01 cm/sec the defects anneal fairly rapidly even at room and 0-69 +001 cm/sec* for Te metal and temperature[13]. Rather extensive measureTeO2, respectively. ments of the Hall coefficient, the Seebeck To compare isomer shifts with the values coefficient, the electrical resistivity and the tabulated by Violet and Booth, our values thermal conductivity of PbTe both during and have all been referred to a Te source. With following thermal and fast neutron irradiation respect to a Te source, the isomer shifts are show little annealing below temperatures -0-04 + 001 cm/sec and +0-02 ~ 001 cm/sec - 150~C[14, 15]. There are no previous for PbTe and TeO2t, respectively. The isomer measurements of radiation effects in TeO2. shift for TeO2 agrees with the value obtained It is quite clear from our results that the by Violet and Booth; however the isomer shift thermal neutron capture process in Te124 for PbTe is less than the value reported by does not lead to any significant changes in Stepanov et al.[12]. the Mossbauer hyperfine spectra. The PbTe data, in particular, give evidence that the 5. DISCUSSION isomer shift anomaly observed by Stepanov Our measurements show no clearly and Aleksandrov is probably caused by disresolved changes in the Mossbauer hyperfine placements induced by other types of reactor radiation. All the measurements reported *The values quoted here are the average values obtained in this paper were made within approximately from several runs. three weeks after the end of the irradiation. tThe TeO2 isomer shift was obtained by combining the Using Stepanov and Aleksandrov' annealing results reported in this paper with an additional measurement with a PbTe source and Te(OH)6 absorber whichcurve, an lsomer shlft of at least 1 5 mm/sec showed an isomer shift of-0 13 + 0-01 cm/sec. should have been observed if the anomaly was

Te125 MOSSBAUER EFFECT STUDY 1195 caused by neutron capture induced recoils. 3. BERGER W. G., FINK J. and OBENSHAIN F. E., The most likely cause of the isomer Phys. Lett. 25A, 466 (1967). he most ikey case te some 4. HANNAFORD F., HOWARD C. J. and WIGshift anomaly observed by Stepanov and NALLJ. W.G.,Phys. Lett. 19,257(1965). Aleksandrov is fast neutron induced displace- 5. STEPANOV E. P. and ALEKSANDROV A. YU., ments. No information is given on the fast JETPLett. 5,83(1967). 6. WALKER R. M.,J. nucl. Mater. 2, 147 (1960). neutron flux used in their irradiation; how- 7. MARSHALL H., In Inorganic Syntheses (Edited ever, if it is assumed that the fast flux is by L. F. Audrieth), Vol. 3. McGraw-Hill, New York 1i the magnitude of the thermal flux quoted in (1950). 8. See Mossbauer Effect Data Index (Compiled by their paper and that there is no saturation A. H. Muir Jr., K. J. Ando and H. M. Coogan). of defects, the Te defect density could be as Interscience, New York (1966). large as A the Te atomic density. Thus the 9. DeWAARD H., DEPASQUALI G. and HAFEMEISTER D., Phys. Lett. 5, 217 (1963). Stepanov and Aleksandrov measurement 10. PASTERNAK M. and BUKSHPAN S., Phys. seems to have been carried out under Rev. 163,297 (1967). irradiation conditions where'background' 11. VIOLET C. E. and BOOTH R., Phys. Rev. 144, 225 (1966). displacements have a high enough density to 12. STEPANOV E. P., ALESHIN K. P., MANAPOV significantly affect the Mossbauer spectrum. R. A., SAMOILOV B. N., SKLYAREVSKY V. V. and STANKEVICH V. G., Phys. Lett. 6, 155 (1963). 13. VAN LINT V. A. J., WIKNER E. G. and MILLER REFERENCES P. H., Jr., Rep. No. GA-1513 (1960). 14. DANKO J. C., KILP G. R. and MITCHELL P. V., 1. HAFEMEISTER D. W. and SHERA E. B., Phys. Adv. Energy Conversion 2, 79 (1962). Rev. Lett. 14, 593(1965). 15. FROST R. T., CORELLI J. C. and BALICKI M., 2. FINK J. and KIENLE P.,Phys. Lett. 17,326 (1965). Adv. Energy Conversion 2, 77 (1962).

APPENDIX B 1 Te M'ossba,uer Effect Study of Magnetic Hyperfine Structure in the Ferromagnetic Spinel CuCr2Te4" by J. F. Ullrich and D. H. Vincent Physics Letters 25A, 731 (1967)

Volume 25A. number 10 PHYSICS LETTERS 20 November 1967 125Te MOSSBAUER EFFECT STUDY OF MAGNETIC HYPERFINE STRUCTURE IN THE FERROMAGNETIC SPINEL CuCr2Te4* J. F. ULLRICH ** and D. H. VINCENT Department of Nuclear Engineering, The University of Michigan, Ann Arbor, Michigan Received 3 October 1967 The Mossbauer hyperfine spectrum of 125Te has been measured in the ferromagnetic spinel CuCr2Te4. The hyperfine field was found to be 148 ~ 5 kOe. The nuclear magnetic moment of the 35.6 keV excited state of 125Te wvas determined to be + 0.74 ~ 0.07 nm. In this letter, we report on the measurement predominantly a magnetic dipole (M1) transition, of a transferred hyperfine field at the tellurium the M6ssbauer pattern will consist of six lines. anion site in the ferromagnetic spinel CuCr2Te4. The relative location of the six lines in the magThis compound represents a unique opportunity netic hyperfine pattern is completely determined for studying transferred hyperfine fields using by R = /1/Jo, the ratio of the excited state nucMbssbauer techniques since Te is the only lear magnetic moment to the ground state nuclear chalcogenide with a known M6ssbauer nuclide and magnetic moment. The ground state moment is CuCr2Te4 is the only ferromagnetic spinel which known from nuclear magnetic resonance measurehas been successfully prepared using tellurium ments (io = - 0.8872 nm) [6]. The excited state as an anion [1,2]. moment has not been determined although previous CuCr2Te4 is one of the interesting groups of Mdssbauer measurements [7,8] have definitely chromium spinels which have shown anomalous established the moment as positive. From theoferromagnetic behaviour [2-4]. CuCr2Te4 has a retical considerations, the excited state moment Curie temperature Tc = 3650K [1]. The spin con- has been estimated to be /q1 + 0.7 nm [8]. figuration of this particular spinel was recently The measurements were made using a source investigated by neutron diffraction techniques [5]. of 125Tem (58d). The 125Tem was obtained by From the results, it was concluded that CuCr2Te4 neutron irradiation of Te enriched to 94% in was a normal spinel with the magnetic Cr3+ ions 124Te. The Te was in the form of cubic PbTe occupying solely the B sites and diamagnetic Cu+ which provided a single resonance line source. occupying the A sites. A model proposed to des- The CuCr2Te4 powder was embedded in acrylic cribe the magnetic behaviour in the ferromag- plastic for use as an absorber. The powder abnetic spinels [2] involves a dominant exchange sorber thickness was 53.5 mg/cm2. interaction of the 90~ Cr-X-Cr superexchanges The 35.6 keV gamma rays were detected using type, where X is the anion. For the 3d3 cations, a xenon-nitrogen filled proportional counter. this exchange interaction is ferromagnetic. Selection of the escape peak provided separation In this study, the magnetic hyperfine inter- of the gamma ray from the intense X-ray (27.4 action at the Te anion site was investigated using keV and 31.2 keV) background. The resonant abthe 35.6 M6ssbauer gamma ray resonance in sorption spectrum was obtained using a time mode 125Te. The magnetic hyperfine interaction causes MBssbauer spectrometer. Both the source and abthe 35.6 keV + excited state to split into four sorber were cooled to liquid nitrogen temperature levels and causes the + ground state to split into for the measurements. two levels. Since the gamma ray transition is A typical resonant absorption spectrum is shown in fig. 1. In order to determine whether this spectrum was a partially resolved six-line spectrum * Research supported by the National Science Foun- r ri r dation, Grant No.GK 871. due to magnetic hyperfine splitting or whether it ** Present address: Scientific Laboratory, Ford Motor was a two-line spectrum due to quadrupole splitCompany, Dearborn, Michigan. ting, the data were analyzed assuming the follow731

Volume 25A. number 10 PHYSICS LETTERS 20 November 1967 observed splitting (eq = 4.3 x 1016esu) is 10 percent greater than that due to a single 5p electron o 1 [9]. Any reasonable bonding model for Te in A"^-^S-~..~~~~. j I ~CuCr2Te4 would yield less than the equivalent of.i5.s=.t- i. one unbalanced 5p electron. ^Vt\~:: ~ ~~/ ^>r^In the final six-line analysis, a small quadruIve \ He:+ 74 ~ 07 nm./pole interaction was taken into account since the z \ Heft =148 ~ 5 kgouss.'symmetry of the tellurium site is not cubic. The average quadrupole coupling constant obtained from the computer fit to several measurements m 1 <m \,.,/ is e e2qQ/ = - 0.08 ~ 0.08 mm/sec. 2 | The average value of R = l1//Xo obtained from i o \ / X\ t the data is R = - 0.84 ~ 0.09. Using the previous25. ly determined value of the ground state nuclear.>~ ~moment, we find the nuclear moment of the 35.6 keV excited state to be /il = + 0.74 ~ 0.07 nm, -20 -1.5 -1.0.5 0.5 1.0.5 2.0 in good agreement with the estimated value. The VELOCITY (cm/sec) average value of the effective hyperfine field is Fig. 1. Resonant absorption spectrum from a PbTe source Heff = 148 ~ 5kOe. and CuCr2Te4 obsorber (53.5 mg/cm2) at liquid nitro- The nonmagnetic Te2 ion would not normally gen temperature. The solid line is the "best fit" six- be expected to have a hyperfine field at its nucline spectrum. The bars denote the location and rela- leus. However, in a ferromagnetic compound tive intensity of the six lines. such as CuCr2Te4, the Te 5s electrons can be spin polarized through interaction with the magnetic cations, leading to a hyperfine field at the ing spectral shapes. First, it was assumed that Te nucleus through the Fermi contact interaction. the spectrum consisted of two Lorentzian-shaped The following two mechanisms are the most prolines with equal line widths, but different line in- bable source of the polarization. First, covalent tensities. The line locations, line intensities, mixing of the Te 5s orbitals with the Cr 3d orbiand line widths were used as variables in the fit- tals, and second, exchange polarization of the ting. Second, it was assumed that the spectrum Te 5s electrons by the Cr 3d electrons. A 5s consisted of six Lorentzian-shaped lines with electron polarization of a few percent would proequal line widths. The line intensities were con- vide a field of the right magnitude [10]. strained to the ideal intensity ratio for a powder absorber (3:2:1:1:2:3 for the locations determined The authors express sincere thanks to C.Coby 1 i + 0.7 nm). The variables used in deter- lominas for graciously providing the sample of mining the line locations were R and Heff, the CuCr2Te4. effective hyperfine field. Other variables were the line width and a line intensity parameter. The result of the least squares computer fit with the six-line spectrum is shown as the solid line References in fig. 1. The bars denote the location and rela- 1. F.K. Lotgering, in Proc. Intern. Conf. on Magnetism, Nottingham, England, 1964, 533. tive intensity of the six lines. Nottingham, England, 1964, 533. 2. P.K.Baltzer, P.J.Wojtowicz, M.Robbins and On the basis of the fittings with the assumed E.Lopatin, Phys.Rev. 151 (1966) 367. spectra, it was concluded that the splitting was 3. P.K. Baltzer, H.W. Lehmann and M.Robbins, Phys. due to a magnetic hyperfine interaction. The Rev. Letters 15 (1965) 493. reasons were as follows: 1) the X2 value for the 4. N.Menyuk, K.Dwight, R.J.Arnott and A.Wold, "best fit" six-line spectrum was 25 percent smal- J.Appl.Phys.37 (1966) 1387. 5. C.Colominas, Phys.Rev. 153 (1967) 558. ler than the value for the two-line spectrum; 6..E.Weaver Jr., Phys.Rev.89 (1953) 923. 2) the line width for the two-line spectrum was 7. R.B.Frankel, J.Huntzicker, E.Matthias, S.S. 36% broader than the expected line width cor- Rosenblum, D.A.Shirley and N.J. Stone, Phys. rected for finite absorber thickness, whereas Letters 15 (1965) 163. theline width for the six-line sp m ws in. 8. N.Shikazono, J. Phys. Soc.Japan 18 (1963) 925. the line width for the six-line spectrum was RG.Barnes and W.V.Smith, Phys.Rev.93 (1954) 9. R.G.Barnes and W. V. Smith, Phys.Rev.93 (1954) excellent agreement; and 3) the magnitude of the 95. electric field gradient needed to produce the 10. D.A.Shirley and G.A.Westenbarger, Phys.Rev. 138 (1965) 170. * **** 732

APPENDIX C 40 "Mossbauer Measurements with K by P. Ko Tseng, S. L. Ruby, and D. H. Vincent Physics Rev. 172, 249 (1968)

Reprinted from THE PHYSICAL REVIEW, Vol. 172, No. 2,249-258, 10 August 196$ Printed in V. S. A. Mossbauer Measurements with K40t* P. K. TSENG AND S. L. RUBY Argonne National Laboratory, Argonne, Illinois AND D. H. VINCENT~ University of Michigan, Ann Arbor, Michigan (Received 1 April 1968) This paper describes an investigation in which the 29.4-keV y ray formed in the neutron capture reaction K" (n, y) K10 was studied by use of the M6ssbauer effect. Several potassium compounds were used as the neutron targets, i.e., as y-ray sources for M6ssbauer measurements. The results are: (a) All spectra show a single absorption line at v=0 whose width is no more than 1.3 times the minimum predicted from the lifetime; (b) the background and the recoilless fraction vary strongly from one case to another; and (c) the quadrupole splitting and isomer shifts are small if not zero. The recoilless fraction was measured as a function of temperature for a KF target. By fitting the results to curves based on a simple theory of diatomic solids, a value for the effective Debye temperature of potassium in these targets was obtained. In order to arrive at a value of (r )/ (r2) for the K40 nucleus, four careful center-shift measurements were carried out with K metal at 10~K and KF at 10, 55, and 80~K as targets, and KC1 at 80~K as absorber. Comparison of these results with calculations of the thermal shifts based on our determinations of the effective Debye temperatures of the different targets shows that the measured line shifts are mainly due to thermal shifts. The accuracy of the measurements is sufficient to place an upper limit of (r2 )/ (r' )<5 X 104- for K4~. I. INTRODUCTION investigated nuclear reactions, one by (n, 7) reactions1 OF all nuclides with suitable properties for the Moss- and the other by (d, p),2as a means of forming a suitbauer effect, the one with lowest Z is K40but it able number of excited K40 nuclei in an appropriate chemical or solid-state environment. The neutrondoes not have a radioactive parent. Two groups'2 have chemcal or sold-state environment. The neutroncapture method proved to be the more useful one, t Work performed under the auspices of the U. S. Atomic and provided quantitative results. In particular, within Energy Commission. * Based on a dissertation by P. K. Tseng in partial fulfillment the large experimental error, the result of Hafemeister of the requirements for the Ph.D. degree at the University of and Shera,l using the (n, 7) reaction, showed no Michigan. isomer shift between K and KF. This led to the conclut Permanent address: Physics Department, National Taiwan University, Taipei, Republic of China. sion that the fractional change of the expectation value ~ This work was partially supported by the U. S. National of the squared nuclear charge radius is 8(r2)/(r2)< Science Foundation (Grant No. NSF GK 871). 1 D. W. Hafemeister and E. B. Shera, Phys. Rev. Letters 14, 80X 10. 593 (1965). According to Goldstein and Talmi,3 the 7/2 neutron 2 S. L. Ruby and R. E. Holland, Phys. Rev. Letters 14, 591 - (1965). S. Goldstein and I. Talmi, Phys. Rev, 102, 589 (1956),

250 TSENG, RUBY, AND VINCENT 172 state and the d3/2 hole state can couple together to (108 neutrons/cm2/sec in our case); and, more imporform four levels whose angular momenta are 4-, 3-, tant (2) since most of the neutrons (-99% in our 5-, and 2-. This study is concerned with the first two experiment) do not interact with our necessarily thin of these. Calculations on the binding energy4 and the target and most of the reaction energy escapes from magnetic moment5 of this nucleus have been made and the target as high-energy y rays, the heat deposited fit the experimental results rather accurately. Since in the target is small. Thus the target can easily be the coupling of the states involves only the angular cooled. This is a big advantage over the techniques in parts of the wave function, this model leads to the which the Mossbauer level is populated by chargedconclusion that 6(r2)/(r2) for the K4~ nucleus will be particle reactions. zero-in agreement with the initial experiments. A schematic diagram of the experiment is shown in On the other hand, a simple calculation of the elec- Fig. 1. A thermal-neutron beam from the reactor core tric quadrupole moment of K4~ by coupling the Q of emerges through collimators in the reactor shielding K39 with that of the extra f7/2 neutron gives Qtheor= wall. The K39 target produces the signal y ray (29.4 -0.036 b, whereas the experimental value is Qept= keV) after the neutron-capture reaction. Those y rays -0.07 b. Similarly, Nathan and Nilson6 find that even are detected after passing through an absorber enriched in K39, Qtheor= +0.040 b, while Qept= +0.09 b. These in K4~. Either the target or the absorber is moved in together suggest that the polarization of the core by order to perform a conventional M6ssbauer transmisthe valence nucleons may be a noticeable effect, and sion experiment. The first beam used was at a through hence that 6(r2)/(r2) in K40 nuclei may have a nonzero hole provided with a graphite scatterer. This provided value. Moreover, nonzero values of 6(r2)/(r2) have been a moderate flux along with a low background. To get observed in the rotational levels of deformed nuclei7 more time than was available at this very popular for which comparably rough nuclear models would also facility, we moved the experiment to a temporarily predict 5(r2)=0. unused beam hole, which had been designed wide and The upper limit for (r2)/(r2) from the earlier experi- thin for a heutron-mirror experiment. For this hole we ment' is too large to be useful. That limit, in fact, is built a special tapered collimator consisting of alternate larger than the observed value for any known nucleus. layers of lead and plastic; and in its exit aperture we This means that the validity of the model leading to placed a plug of plaster containing lead and Li6 to ab5(r2)/(r2)=0 should be tested by more precise measure- sorb unwanted neutrons and to minimize high-energy ment-and this, in fact, was our major purpose. -y rays. Also it was hoped that measurements of the mag- In our effort to reduce the background count of our netic moment j and the electric quadrupole moment detector in the neighborhood of the 29.4-keV line of Q for the first excited level of K40 would be possible by K0, we found that a considerable fraction of this backusing appropriate compounds. For example, the anti- ground is due to scattered low-energy 7 rays; these ferromagnetic substances KNiF3 and KCoF3 might have were emerging from the reactor along with the neutrons. had a large transferred hyperfine magnetic field at the Figure 2 shows the striking reduction of the backK nucleus and the layered structure KC8 might have ground line when a j —in.-thick lead sheet was mounted generated a measurably large electric field gradient. before the collimator exit (as shown in Fig. 1). Finally, it was expected that measurements of the temperature dependence of the second-order Doppler shift A. Cryostats and of the resonant fraction f would lead to informa- Since the Debye temperature of potassium in most tion on the lattice-dynamical behavior of the potassium of its compounds is well below room temperature, it is compounds under study. NEUTRON II. TECHNIQUE tEAM CP-5 In our experiment, we chose the K39 (n, y) reaction \ / REACTOR TARGET; //M/// WALL to populate the Mossbauer level in K40. The reasonsTARGET \ // for choosing the (n, y) reaction rather than the (d, p) EACTOR reaction are: (1) The yield of the signal y rays can be. - CORE comparatively large for a high-intensity neutron beam i 4S. Goldstein and I. Talmi, Phys. Rev. 105, 995 (1957).ABSORBER [ Pb SHtET 6 I. Talmi and S. Unna, Ann. Rev. Nucl. Sci. 10, 353 (1960). -B E 16 6 0. Nathan and S. G. Nilson i, in a,, and e-Ray Spectroscopy, edited by K. Siegbahn (North-Holland Publishing Co., Amster- DETECTOR dam, 1965), Chap. X, p. 618.DETECTOR 7 S. Bernow, S. Devons, I. Duerdoth, D. Hutlin, J. W. Kast, E. R. Macagno, J. Rainwater, K. Runge, and C. S. Wu, Phys. Rev. Letters 18, 787 (1967); D. Yeboah-Amankwah, L. Grodzins, FIG. 1. Schematic diagram of the experimental setup. The douand R. B. Frankel, ibid. 18, 791 (1967); P. Steiner, E. Gerdau, P. ble arrow shows the direction of motion of the target or absorber Jienle, and H. T. Korner, Phys. Letters 24B, 515 (1967). in the Mossbauer experiment.

172 MOSSBAUER MEASUREMENTS WITH K4b 251 advantageous to cool both target and absorber. (Here ECLANICAL and in the following, "Debye temperature" is used to DRIVER B mean that characteristic temperature which gives the observed resonant fraction f when a monatomic Debye 7 7 model is assumed for the solid.) When both target and absorber were to be kept at liquid-nitrogen tempera- ture, the simple arrangement shown in Fig. 3 was used. The cryostat shown here consists of a cylindrical styrofoam container E and a cover F. The space inside the container is divided into an upper and a lower c part. The upper part is an aluminum can J with an ~ ~ annular hole; it serves as a liquid-nitrogen reservoir. 1E The lower part, refrigerated by the cold walls of J, E contains the source and the absorber. | j' 1 H The neutron target (source) is moved by an insu- TA lated rod C which connects through the annular hole-. l NEUTRON of the can J to the moving axis of an electromechanical / 1[ ABSORBER _ driver B. The thermal-neutron beam enters and leaves ~, K the cryostat directly through the styrofoam wall. The _ -, effect of the styrofoam on the neutron beam is merely L -- to increase the background at the detector to about 10% more than that without styrofoam. This disadvan- DETECTOR tage is a small price for avoiding the difficulty of designing and handling a metal cryostat. FIG. 3. Liquid-nitrogen cryostat for a Mossbauer-effect experisigni17e t a* n1.e g,.i, s t, ment with a beam of reactor neutrons. In the figure, B is the For some experiments the target (source) was kept electromechanical driver, C an insulating rod connecting the at liquid-He temperature. This is necessary, especially driver to the target, D the target holder, G the liquid-nitrogen for potassium metal, because of the very low Debye filling tube, H the sensing element of the automatic filling system, J the liquid-nitrogen reservoir, K the legs for J, L the neutron temperature of this material. For reasons of conven- shielding (borated polyethylene), and M the - shielding (lead ience, source and absorber were kept in different cryo- plate). _''' I''i I stats for these experiments, the absorber still being at liquid-nitrogen temperature. The target was mounted in the tail section of a regular liquid-helium cryostat which had been modified to allow passage of the neutron beam with minimal production of background 7 radiation. The entrance and exit windows for the neuwL 29.4 keV tron beam had to be made fairly large and, conse5~R-|:s~~ T4~ /^^ - quently, the heat shielding of the target was not too effective. We estimate that the target temperature was |~z~~~ \ / ~ ~\ ~(10i6)~K. Since our measurements are quite insensi_ | / \ _tive to temperature fluctuations in this range, no efforts o / \ were made to lower the temperature further or to imU 0- A \ prove the accuracy of its determination. The absorber'\ I \ \ ~ in these experiments was kept at liquid-nitrogen tem_' \~ ~I \, \. perature in a styrofoam cryostat similar to the one J v \xy X \ depicted in Fig. 3. Figure 4 shows both cryostats and v- -a:n ~ ~k \ - the detector in their proper relative positions. Since \ ^\ A the neutron beam is only slightly attenuated in passing.. " through one of our cryostats, we were able to use our. B limited reactor time efficiently by usually running both spectrometers simultaneously, the one behind the other,,X, i,, I IIo l I in the beam. 0 50 I 0 150 ENERGY (keV).. B. Mossbauer Spectrometer FIG. 2. fy-ray spectra detected by a 1/32-in. NaI detector. Curve A: the spectrum when thelreaction is induced by an un- When the styrofoam cryostat described in Sec. I A filtered beam of neutrons. Curve B: the spectrum when the reac- was used in measuring Mssbauer spectra at liquidtion is induced by a reactor neutron beam filtered through an measuring Mssbauer spectra at lqud1/16-in. lead sheet. nitrogen temperatures, we used a standard Kankeleit

252 TSENG, RUBY, AND VINCENT 172 - rays from K40; they contain elements which emit y rays or characteristic x rays of energy close to 30 keV, and/or they contain nuclei with high neutron absorpr-^ _ L-1 =tion cross section, in which case the K39 nuclei would,El-ectroal be shielded from neutrons while at the same time a - e aDriver very high y background would be produced. Lq. He DriveAfter selecting a target compound and determining C ryostat~... — ^B~~, lI lits optimum thickness, a disk 14 in. in diameter was: _Absorber obtained by pressing a fine powder of the compound Target L = k j _ cryostat into a mold. In some cases Lucite was used as a binder; Absorber-_ __- ^- > jin other cases the powder was pressed while enclosed Detector -.1i. in an aluminum foil. The latter method can give a moderately rigid disk even for noncompacting powders. D. Absorbers Ex p.. Stand llSince the natural abundance of K40 is only 0.0118%, it was necessary to use a sample enriched in this isotope. A KC1 sample enriched to 1.9% K40 was obtained &_____ -==cS~~~ ~from Oak Ridge National Laboratory and the absorber __ it ___ ___ ____was made by pressing the powder, with Lucite as a FIG. 4. Over-all experimental setup to measure the relative binder, just as in preparing the targets. The K4 thickM6ssbauer line shift between K and KF. ness of the KC1 absorber was 0.66 mg/cm2. This gives an effective thickness t=nafz2 at 80~K when the type8 spectrometer (i.e., the target moved with a con- effective Debye temperature is taken as 180~K. stant acceleration and the multichannel analyzer was in the time mode). III. RESULTS AND DISCUSSIONS In measurements with the liquid-helium cryostat (Fig. 4), the moving absorber is supported by a long A. Observations in Various Potassium Compounds horizontal arm and a vertical aluminum rod. They are Several potassium compounds were used as targets.,.,,,,,.,,.:.. *ySeveral potassium compounds were used as targets. driven by the electromechanical driver, which is cou- i i hh.,,*..;,~ ~., r,.,. ^ In particular, we selected compounds in which a magpled to the aluminum rod by a flexible junction Since * * 1 pled to the aluminum rod by a flexible junction. Since netic field, an electric field gradient, or a variation of this complexity makes the assembly somewhat flexible, the s-electron density at the site of the nucleus might it is unwise to drive this system in the constant-reasonably be expected. acceleration mode. Instead, we decided to drive the * * o'. Ie t dive All the spectra of the various potassium compounds moving system sinusiodally at its resonant frequency. moving system sinusiodally at its resonant frequency. used, either as targets or as absorbers, showed a single The reference signal for this sine wave is generated by absorption peak whose width is no more than 1.3 times a Hewlett-Packard model-202A function generator. In that of the one calculated from the half-life and the that of the one calculated from the half-life and the this case, the time mode of the multichannel analyzer effective thickness. These experimental results are sumis still used, but with a reset pulse for the address marized in Table I, which lists the target material, the scaler derived from the function generator. scaler derived from the function generator. absorber material, the shift v0 of the center of the MossC. Targets bauer line from v=0, the width 3 of the line, the observed amplitude a of the line, the true amplitude ao Since the yield of the interesting y rays and the (corrected for background), and an effective Debye background are both functions of the thickness of the temperature eD of the target material. The recoilless target, special consideration was given to the thickness fraction f was calculated for these sources from the of the target in order to obtain experimental results corrected dip ao along with the known properties of the efficiently. The target thickness was usually in the absorber. range of 100-300 mg/cm2. For some target materials, The fact that all the runs in Table I gave a single however, even optimized targets did not allow a useful unshifted line indicates that (a) 6(r2)/(r2) is small and experiment. For example, the compounds KI, KBr, (b) the electron configuration of the potassium atom K2W03, and K3Sb all were unusable. These difficult in various compounds retains its K+ ion structure and materials have one or more of the following properties: hence does not produce large electric field gradients They contain elements with high atomic number and, nor magnetic fields at the nucleus. consequently, have high self-absorption for the 29.4-keV It should be mentioned that little, if any, evidence 8 E. Kankeleit, in M6ssbauer IEffect Methology (Plenum Press, for radiation-damage effects is seen in these data. Since Inc., New York, 1965), Vol. II, p. 47. energies up to 800 eV can be given to the nucleus from

172 MtOSSBAUER MEASUREMENTS WITH K'0 253 TABLE I. Results of experiments at liquid-nitrogen temperature. Here vo is the shift of the M6ssbauer line from v=0, ib is its full width at half-maximum, a is the observed amplitude of the M6ssbauer line, ao is the true amplitude (corrected for background), and OD is the Debye temperature of the target [with ED(KCl) = 190~ taken as standard]. vso a ao OD Target Absorber (mm/sec) (mm/sec) (%) (%) (~K) KF KI 0.01540.012 2.5540.04 0.8840.01 2.4 KF KC1 -0.005~0.008 2.744-0.04 3.2140.04 6.4 230 KC1 KC1 -0.015~-0.033 3. 1 0.2 0.69=40.02 2.7 190 KCs KC1 0.00640.006 2.7~-0.03 1.303=-0.006 3.4 195 KNiFa KCI -0.00-0.02 2. 740.1 1.05i-0.02 5.1 215 KCoF3 KCI 0.0140.03 2.9=40.1 0.604-0.01 3.9 205 K02 KC1 0.02=40.01 2.82=40.06 0.044=40.006 1.4 170 KA1Si3O0 KC1 -0.13 40.09 3. 20.4 1.244-0.07 3.6 200 KNs KC1 0.0164-0.09 2.64-0.3 0.854-0.06 2.7 190 KOH KCI 0.01=40.04 3.04-0.2 1.8840.05 3.0 190 KCN KC1 -0.440.3 2.9=-0.9 0.514-0.09 1.0 160 KH KC1 0.054-0.04 3.240.3 1.42=40.05 2.7 190 KF-HF KC1 -0.034-0.02 3.34-0.1 1.0240.02 2.1 180 the y-ray emission following neutron capture, it is con- the errors of single runs (0.005-0.010 mm/sec). Comceivable that disruption of the lattice could affect the parison with similar data in the literature,' 2 also plotted Mossbauer emission; a small number in the last two in this figure, shows the great improvements in expericolumns of Table I might be explained by such a mech- mental techniques that have been obtained. anism. In cases in which the Debye temperatures are known approximately from other evidence (as described C. Measurements with a F Target and KI Absorber in Sec. III B), such radiation-damage effects are too According to Shirley,9 the isomer shift can be desmall to be observed. scribed by the equation B. Measurement with a KF Target and a KCI Absorber 6= rZe2S'(Z) (r2(A) ) | 1o(0) 12-| 4,(0) 21](r2)/(r2). The target material that gives rise to the largest (1) Mossbauer effect is potassium fluoride. With a KF... effectispotssiumluod. WHere Z is the atomic number and A the atomic weight target it was therefore possible to take a reasonably Here the atomic number and A the atomic weight accurate Mossbauer spectrum in a comparatively short he s uer n e r ss r, ) an of*(~) are the electron wave functions at the nucleus time (-6 h). Since the experimental equipment and techniques evolved steadily in the course of the experi- for absorber and source atom, respectively, S(Z) is a relativistic correction tabulated in Ref. 6, and the fracment, we reran the KF-KC1 measurements several tion (r2)/(r2) is the mean square fractional change in times-both to take advantage of improvements and tion )/() i the mean square fractional change in to assess their value T te K experimentthe nuclear radius as a result of the transition from the to assess their value. Thus the KF-KC1 experiment first excited state to the ground state. became the standard test to evaluate the latest changes he largest imer s between potassim in the neutron collimators, shielding, detectors, etc.; T e ser sht b potassium..i.'..'.'i ~.1- TVT" would probably be that for a KF target and KI abthe observed amplitude a of the Mossbauer line was w p b t a sorber, in analogy with the results of the Mossbauer squared and multiplied by the counting rate R to ob- er, i n ths the tsaue r.1,.,. rr experiments1~ on the Csm33 halides. In the latter, the tain the figure of merit Ra2. Moreover, the stability hali. In te l, isomer shift between a CsF source and a CsI absorber of the over-all experimental system could be tested by s fo t be 0.031 0.04 m/sec. If *.~ *.~,~ P~ r~ * ~ rwas found to be 0.031-0.004 mm/sec. If examining the results of several runs of the same experiment. If the results fluctuate only in the anticipated[ I (0) I- I a(0) ]2- ](0) (r')/(r2) statistical fashion, then the over-all experimental apparatus is functioning in a stable, reproducible manner. Eq. (1) were assumed to be the smee in potassium In order to estimate the reproducibility of the experi- as in cesium, the isomer shift 6 between KI and KF ment we plotteds the values of i for the repeated runswould be expected to be 0.0025 mm/sec. The decreased ment we plotted the values of v0 for the repeated runs shift in the potassium experiment results from the in chronological order, as shown in Fig. 5. Since the shift in the potassium experiment results from the scatter among the several oruns is no t muc h greater combination of several factors, including the relativistic scatter among the several runs is not much greater e o I /'(0) 1 than the uncertainty in each experiment, there seems enhancement of | 6(0) i2 the change in nuclear radi to be no appreciable drift. More quantitatively, this can (as discussed in Ref. 9), and the atomic number. On be shown by comparing the weighted standard devia- D. A. Shirley, Rev. Mod. Phys. 36, 339 (1964). tion of the experimental points (0.007 mm/sec) with o0 A. J. F. Boyle and G. J. Perlow, Phys. Rev. 149, 165 (1966).

254 TSENG, RUBY, AND VINCENT 172, X- E-r-^-T —-— T-^ — From the point of view of the M6ssbauer effect, one ~0.~T2~ ~ -i~ ~consequence of this is that I ((0) 12, the electron density at the K nucleus in KCs, may differ from that of the potassium ion. There has been a report'2 that a Knight shift has been observed in CsC8. It is reasonable o0 -T - to assume that the conduction electrons in KC8 have d~^ |i l r T 0some s character, in agreement with the above result. E - a i,, 1! L;A second consequence is that an electric field gradient E 3ot^ _ t (EFG) at the K nucleus may result from the layered'- - * * structure of the graphite. This argument is supported by the observation of a splitting in the M6ssbauer. - i Ispectrum in cesium graphite CsC8.'3 Unfortunately, the'~-~o'" ~'~I'idata on the Missbauer effect in CsCs are still tentative and we are not able to make very certain judgments from these data. -0.2_- -Nevertheless, we made a careful Mossbauer measurement oa KC8 (as target), but the result was disappoint1 2 3 4 5 6 7 8-9 ing. The Mossbauer spectrum of KC8 is a single line SERIAL NUMBER, N, OF RUN with = 2.70+0.03 mm/sec and Avo=0.006-+0.006 mm/see. This result shows that the quadrupole splitFiG. 5. Experimental values of the M6ssbauer line shifts found mm/se This result shows that the quadrupole slit in separate runs. The point marked (1) was taken from Ref. 1 ting is very small. The upper limit of the line broadenand (2) from Ref. 2. (There is some uncertainty concerning the ing due to possible quadrupole splitting is less than chemical form of the target in Ref. 2.) Other data are from the 0.13 mm/sec. If we assume Qe/Q01, then it follows present work and are plotted in chronological order. that e2qQ< 12 MHz. that e2qQ< 12 MHz. the other hand, the thermal shift due to the 40~K E. Measurement of Mossbauer Line Shift between difference between the Debye temperatures of the two and KF solids at 80~K is Vth= 0.01 mm/sec. [Here we have taken eD(KF) -240K and Dm(KI) = 2000K.] wThe ex- This experiment is the main part of the work. Its perimental result for this pair of halides (Table I) is purpose was to use the isomer shift of K40 between potassium metal and KF to evaluate the fractional vo=0.015+0.012 mm/sec. (2) difference 6(r2)/(r2) between the ground state and the c r t to.~~,..first excited state. This result indicates that the major contribution to * * s This result indicates that the major contribution to The same KC1 absorber, kept at liquid-nitrogen temthis shift in the Mossbauer line is due to the thermal perature in a separate cryostat, was used throughout effect. Of course 6 \ 1(0) 12 for these two ionic crystals these experiments. Two target materials and three temis expected to be small. peratures were used in the four experiments. In experiD. Potassium Gr e ( ) ment I, potassium metal was used as a target and D. Potassium Graphite (KCs) liquid helium was used as a coolant. The same KF Among the various chemical compounds used as tar- target was used for the other three experiments but gets, potassium graphite KC8 has the most interesting its temperature was changed. It was maintained at crystal structure. This is an intercalation compound" 10~K by liquid helium in experiment II, at 55~K by in which the carbon atoms form stable sheets of linked solid nitrogen in III, and at 78~K by liquid nitrogen in hexagons. The structure of each sheet is identical with IV. Experiments I and II afford a direct comparison that of graphite; but the atoms in successive carbon of the line shift between K and KF. planes in KC8 are in identical positions, whereas the Experiments II, III, and IV serve to check the tematoms in the successive carbon planes in graphite are perature behavior of the thermal shift, from which in displaced from each other in a sequence ABCABC or turn one can determine the Debye temperature for K ABABAB. The interplanar distance of KC8 is 5.41 A, in KF. On the other hand, we did not plan measurewhereas that of graphite is only 3.35 A. The potassium ments on potassium metal at temperatures other than atoms always occupy positions above or below the that of the liquid helium because of its extremely low middle of a hexagonal ring of atoms. Each K atom Debye temperature (about 90~K). Each of the four gives up its outermost s electron to a conduction band. measurements was divided into numerous equal time The result is that the thermal and electrical conductiv- intervals, and the set of data obtained from each subrun ity are much higher in KC5 than in graphite. 12 V. Jensen, D. E. O'Reilly, and Tung Tsang, J. Chem. Phys. n W. Rtidorff, in Advances in Inorganic Chemistry and Radio- (to be published). Chemistry (Academic Press Inc., New York, 1959), Vol. 1, p. 223. 13 G. J. Perlow (private communication).

172 MOSSBAUER MEASUREMENTS WITH K40 255 TABLE II. Results on the K-KF relative line-shift measurements. Experiment T a t Vo No. Target (~K) (%) (mm/sec) (mm/sec) I K 1046 1.26+0.05 3.3240.13 -0.0654-0.006 II KF 10~6 7.37=i0.20 3.4240.11 -0.012~0.005 III KF 55 4.7440.47 3.3940.12 0.006~0.005 IV KF 78 4.4140.10 3.24~0.09 0.015~=0.004 was analyzed individually. The scattering of the data quently, of the relative change 8(r2)/(r2) in the nuclear obtained from those subruns was no greater than the radius will be discussed below. Obviously, to obtain 6 statistical error of a single subrun. These results show from our measurements of v0, a value for the thermal that the experiments were normal and reproducible. shift vth is needed. Table II lists the results of the computer analysis The relation between the data points obtained in of the sum of all the subruns. The values of a, /, and experiments I-IV and the Debye temperatures of K the relative shift vo to an arbitrarily selected channel in potassium metal and in KF may be seen in Fig. 6. are listed in the third, fourth, and fifth columns, re- This figure shows how the thermal shift Vth in K40 spectively. In each case, the quoted uncertainties reflect varies with temperature for various values of the Debye only the statistical errors. The Missbauer line shift temperature Ds, of the source. The relation between between a KF source at 10~K and a K metal absorber the thermal shift and the temperatures of both source at the same temperature is and absorber may be expressed'4 as vo= 0.0534-0.008 mm/sec, Vth= (1/2mc) [(9/8) kD8+3kT8D(X,) where a positive value of v0 means that the source and -(9/8) ko D- 3kTTD(Xa)] (4) absorber are approaching each other. This line shift where corresponds to the sum of the isomer shift 8 and the thermal shift Vth, i.e., D 3 fX =d Vo=6+vh. (3) X1, e0-1 The determination of the isomer shift and, conse- and OD, is the Debye temperature of the source crystal, oDa the Debye temperature of the absorber crystal, o4, - __j-0. —14 Xs=OeDs8/T, and Xa,=Da. The curves in Fig. 6 were computed from Eq. (4) by setting both Da, and Ta equal to zero. Inspection o.12 ~ of Eq. (4) shows that this merely suppresses an additive constant. O. 260 The data points obtained from experiments I-IV O.IC L24-0.-'- / ^ // ^ were superimposed on this graph by choosing OD = 90~K 1 - i220 ////////X^^'for potassium metal on the basis of the specific-heat E o - measurement.'5 After this choice, the position of the ts180 —-^ //j/ / - KF data points are automatically determined. They 1, 6 _j/p ^ /// _~ seem to group very nicely around the curve with the __ 0.06E - 8 4// / parameter OD,=240~K. The mean deviation of these r 2) -,H \^ ^// / 1' ~ ~ points is less than the experimental error. < 100 ~0.04 -~ / \ KF vs KCI - F. Measurement of the Recoilless Fraction as a Ir~~~~~ l'-'. 9~ / T -Function of the Source Temperature F / A K vs KCI o002 / It is impossible to determine the isomer shift between /- K and KF unless the thermal shift between K and KF / I.I. I _, 1_ 0is known. Therefore an experiment was planned to - 20 40 60 80 100 confirm our earlier measurements of the Debye temTEMPERATURE (~K) perature of KF. FIG. 6. Thermal shifts of KF at 10~, 55~, and 78~K and of K at 10~K. The curves were calculated relative to a fictitious absorber 14 R. V. Pound, in Proceedings of the International Conference on whose Debye temperature is 0~K and whose temperature is 0~K. the Mossbauer Effect, Saclay, France, 1961, edited by D. M. J. Here the Debye temperature of K is assumed to be 90~K. The Compton and A. H. Schoen (John Wiley & Sons, Inc., New points for K metal and KF sources and a KCl absorber are from York, 1962), p. 222. experiments I-IV. 15 L. M. Roberts, Proc. Phys. Soc. (London) B70, 744 (1957).

256 TSENG, RUBY, AND VINCENT 172 Fr-'' - X - - w X —T -r- - — r —- 1 ing the count nr(I) from the resonant 7 ray, the other - a- accumulating the count no(I) from a nonresonant part; o-.: ~- 5 i of the y-ray spectrum. Then yexpt(T) is obtained from, yexpt(T) = C[nr (I)/no(/)], os 0.99- q/ oC eaf/ KF(T) vs KCI(800~K) where C is a parameter to be adjusted to fit the propert, ^ A^X // y- ('+)[I-O.15f(T)] ties of Eq. (6), i.e., 4- X0 R+/0/ e,(KF) (230 20) K ba i~~ -b> lim yept(T)= 1, (8) 0.98 I'. I. I T- I00 ~K 150 K 200 K 250~K TARGET TEMPEPATI"RE. T y(To) =ypt(To) =1-cof(To) = -a (9) FIG. 7. The experimental results (points) on the recoilless fraction f(T) as a function of the target temperature. The target is Equation (8) means that the resonant absorption will KF. The curves give the calculated relative transmission y(T) h w the temperature of the source is considerthrough the M6ssbauer absorber with known effective thickness. v sh when the temperature of the source s consderIn addition, the background ratio is given by a separate measure- ably higher than the Debye temperature; and Eq. (9) ment. These calculated curves have then been shifted along the means that y is equal to one minus the amplitude a of y axis a small amount - to fit the experimental data. r r the resonance peak when a Mossbauer spectrum is taken at temperature To. The experiment is the measurement of the counting In practice, C is replaced by C'/(l+y), where C' is rate R,=o of the transmitted 7 ray as a function of the a constant obtained by a rough estimate from the relatemperature of the target. The rate R,=o depends on tions (8) and (9), and y is a parameter to be adjusted the temperature in accordance with the relation5 when the yexpt points are fitted to the value of y(T) calculated for each Debye temperature by use of Eq. (6). Ro(T) = RBG+Rse-tl 1-fe(T) [l —e-t'Jo(it,))]}, The fitting was done graphically, by making use of the strong variation of the curvature of y(T) with ED>. (5) The resultant best fit for the KF target is where RBG is the counting due to the background and ED= (230+ 20)~K. does not depend on the presence of the absorber, R, is the counting rate of the resonant y ray when the Figure 7 shows the experimental points and the fitting absorber is not present, t is the thickness of the ab- curves for the case of KF versus KC1. Each experimensorber,.u is the y-ray attenuation coefficient of the tal point is the average of ten analyzer channels. absorber material at 29.4 keV, fe(T) is the recoilless The importance of this result to the final accuracy fraction of the emitted 29.4-keV 7 ray from the target of the (r2)/(r2) measurement was not reflected in the at temperature T and Debye temperature OD, and t, duration of this experimental run. The quoted unceris the effective thickness of the absorber for the Mbss- tainty of ~420~K could have been reduced by a factor bauer 7 ray. After dividing R-=o by its temperature- of four by running for several days instead of several independent part, we find that the reduced function hours. At the time these data were taken, it was asy(T) is sumed that an accurate value of OD could be obtained from specific-heat data on KF. y(T)= Ro(T)/(RBG+Re-t) = l-cofe(T), (6) G. Estimation of the Debye Temperatures of K and KF where As was mentioned in the discussion of Eq. (3), a co=ne-It/(RBG+Re-Ot) 1-e-tJo(~ite)]. (7) value for the thermal shifts of both K and KF would permit us to obtain the isomer shift between these two In Eq. (6), co can be calculated from the information materials from our measured value of the relative Mosson the signal-to-background ratio and on the equivalent bauer line shift between K and KF. resonant thickness te of the absorber. Then y(T) can Equation (4) gives the relation between the thermal be calculated numerically for a particular Debye tem- shift and the Debye temperatures of both the source perature. To measure y(T) experimentally, the source and the absorber. In the following we discuss our and absorber were kept at rest with respect to each choices for OD for potassium metal and KF, which we other and each temperature interval (from T to T+ AT) used for the determination of the thermal shifts bewas associated with a particular channel I of the multi- tween these two substances. All relevant data are assemchannel analyzer. Counts were simultaneously accumu- bled in Table III. lated in two halves of the analyzer-one half accumulat- Our single determination of the Debye temperature

172 MOSSBAUER MEASUREMENTS WITH K40 257 of potassium metal was made by computing it from from Ref. 1 will not be used. In addition, we were the single observed amplitude of the Mossbauer reso- surprised to find no precise specific-heat data for KF. nance line. This value is Therefore the above-mentioned weighted mean of the four effective Debye temperatures from the present D (K) =(90~8)~K. work is used. For confirmation of this value we may look to OD H Estimate of the Isomer Shift between K and KF values extracted from specific-heat measurements.l1 In and of a (r2)/ (r2) for K40 the range from 0<T<20~K, these values drop from 90~ down to 83~ and return to 95~. We feel that our For the reasons explained in Sec. III G, the Debye experimental value for the Debye temperature should temperatures have been taken to be be compared with the specific-heat result16 at 0~K, namely (89.1~5)~K. O(K)=(90~8)~K for K, As seen in Table III, four different values for the E(KF)=(236-20)~K for KF Debye temperature of KF were obtained by different methods in the present work. The weighted mean of When these data are substituted in Eq. (4), the therthese four Debye temperatures is mal shift vth between KF and K is found to be OD (KF) = (236420) K. Vth= 0.055~-0.009 mm/sec. The Debye temperatures obtained from the previous Then by Eq. (3), the isomer shift 8 is Mossbauer experiment' differ moderately from our result. It seems that their results are strongly dependent 8=V0o-Vth= -0.002~0.012 mm/sec. (10) on the precise determination of the background in the pulses from the single-channel analyzer. In their experi- Equation (1) is a relation between 6 and (r2)/(r2). ment, this background was not measured, but only This relation becomes simple after substituting the estimated from the shape of the y-ray pulse-height numerical data. Then according to Shirley,9 the shift spectra. In our case, the y-ray spectra were studied in mm/sec is as a function of attenuation in lead absorbers with 6= (1/00214)A 1 ^i(O) 2(r2)/r2) () thicknesses ranging from zero to 120 mg/cm2. This provided a better criterion by which 29.4-keV pulses where A 1 ^ (0) 12 is the difference between the s-electron due to y rays emitted by the target could be distin- density in K and that in KF in atomic units (i.e., in guished from those created in the detector itself. In units of ao-3, where ao=0.52918X10-8 cm). Since our our further analysis, the effective Debye temperatures upper limit on the shift is 8<1.2X10-2 mm/sec, it follows that TABLE III. Estimate of the Debye temperatures of K and KF (r2/(r2< (2.66X10-4)/A |1 (0) 2, (12) from various methods. where A 1 ^I(0) 12 can be calculated theoretically. As a material measurement (~K) (~K) Ref. first approximation to the charge-density difference ~~~____~~________________.between the potassium ion and the metal, the charge density due to a 4s electron in a free potassium atom K ac (amplitude of the 1046 904-8 a will be used. This neglects the (probably small) effect K a 4 60i (?) b of the rearrangement of the inner electrons in the K+ K Speciic heat 0 89.10.5 ( ion. Shirley9 gives 1 P48(0) 12=1.11 per atomic volume for 4s electrons. This value agrees with the value KF a 78 235~-+b20 d [(| 1 48(0) 12=1.06 per atomic volume] calculated on KF a(10/ac(78) 10, 78 247~25 e the basis of the results of Skillman and Herman.16 KF f(T) (recoilless 100-200 230f20 a By using Hartree-Fock calculations with an improved f v (hrac lsition) 1557 0method for electron correlations, Wilson'7 obtained the KF th (thermal shift) 10, 55,78 205~55 a difference between the value of 1 ^(0) 12 for a free KF ac 4 145~ (?) b potassium atom and a free K+ ion. This result is 0.76 KF a 78 190~ (?) b per atomic volume. Since Wilson's method seems to - be a better approximation to physical reality, his value a Present work. b D. W. Hafemeister and E. B. Shera, Phys. Rev. Letters 14, 593 (1965). will be used for further calculation. o L. M. Roberts, Proc. Phys. Soc. (London) B70, 744 (1957). d Present work. See Table I. 16 S. Skillman and F. Herman, Atomic Structure Calculation e Present work. The data used for the calculation of the Debye tempera- (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1963). ture were taken from Table II, 17 M. Wilson (private communication).

258 TSENG, RUBY, AND VINCENT 172 For a second approximation, the difference between Note especially that the usefulness of increasing the the free atom and the metal must be considered. The accuracy of measurement a is severely limited by the density I 6(0) 12 of 4s electrons in pure K metal is present uncertainty in assumptions b and c. No precise complicated to calculate. Most of the band-theory cal- Debye temperature of KF is available. In any case, culations are done with no particular interest in the a Debye solid is only a first-order approximation to a behavior near the nucleus, and the pseudopotential real crystal. Moreover, even if one could get precise calculations are completely useless for the present pur- data on the internal energy of K and KF, the lack pose. Shirley9 has presented reasons for believing that of a precise and practical theory to deduce useful vala better approximation might be obtained by taking ues from these data would still render the Debye tem1 4I(0) 12=0.7 1 /a(0) ]2, the electron densities at the perature uncertain. (For example, the Debye temperanucleus being I (0) 12 for the s electrons of the conduc- ture computed from the specific-heat data on KF needs tion band and Ij a(0) 12 for the 4s electrons in a free to be modified'1 before it can be used as the eD in the atom. M6ssbauer effect.) In addition, the induced radiation In the light of this discussion, the most reliable value damage due to the preceding high-energy y-ray emisfor A I f(0) 12 would be 0.7 times the value calculated sions of the target nuclei may limit the direct applicaby Wilson.l8 Then the upper limit of 6(r2)/(r2) is tion of the reduced internal energy to the target crystal. 6 r2(r2) < 5 X 14 For these reasons, we conclude that our measurement S(r2)/(r2)< <5.0X1-' is the best that can be justified so far, and that more accurate measurements on a will have no physical sigIV. CONCLUSION nificance unless the uncertainty in the thermal shift The conclusion at the end of Sec. III H was that can be overcome by both theoretical and experimental 6(r2)/(r2) for the K40 nucleus must be quite small and efforts. that, with some confidence, its upper limit can be It should be pointed out that the measurements regiven as ported here forf(T) are by no means at their limits of 6 r2)/ (r2)<5.o 1-4. accuracy. Therefore, although it does seem clear that little useful chemical or magnetic information can be This result indicates that the simple vector-coupling found by use of the M6ssbauer effect in K40, lattice calculation of b(r2)/(r2) for the K40 nucleus, which dynamical measurements utilizing potassium do seem gives exactly zero, is still true within the uncertainty to be practical. For example, it may be profitable to 5X10-4. study the ferroelectrics KH2PO4 or K2Fe(CN)6.3H20 In using this result, one should keep in mind the with this technique. various measurements, parameters, and assumptions on which we have based our estimate of 6(r2)/(r2).ACKNOWLEDGMENTS These are: (a) The over-all Mossbauer line shift be- We would like to thank G. J. Perlow, R. S. Preston, tween K and KF at liquid-helium temperature was and G. M. Kalvius for their constant advice and enmeasured to be 0.053~t0.008 mm/sec. (b) Potassium couragement. We also wish to thank the neutron measmetal is assumed to be a Debye solid with an effective urements group for use of the H- beam hole and G. R. Debye temperature equal to 90~8~K at liquid-helium Ring and V. rohn for use of the H-13 hole. temperature. (c) Similarly, KF has an effective Debye Special thanks go to B. J. Zabransky for his clever temperature equal to 236~420~K at liquid-helium tem- help in the construction and maintenance of some of perature. (d) The value for the difference A 1| (0) 12 the apparatus and for his diligent help with the combetween the electron densities at the nuclei of K and puter program. We also appreciate the kind help of the KF was based on (1) Wilson's calculationl8 of the dif- operating staff of the CP-5 reactor at Argonne and of ference A |,(0) 12 between a free potassium atom and the Ford Nuclear Reactor at the University of Michigan a free K+ ion and (2) a correction factor defined as during the neutron-beam experiments. the ratio 4' of the wave function for the 4s electrons For their help in the special arrangements to make in the conduction band of potassium metal to the wave possible their research at Argonne National Laborafunction for the 4s electrons in a free potassium atom, tory, one of the authors (P. K. T) is grateful to L. M. both wave functions being evaluated at the nucleus- Bollinger of Argonne and to W. Kerr of the University (We used'= 0.7 as suggested by Shirley.9) of Michigan. In addition, he wishes to thank K. H. Sun 18 Y.nisatnik, D. Fainstein, and H. J. Lipkin, Phys. Rev. 139, for suggesting this combined program of study at MichiA292 (1965). gan and research at Argonne.

APPENDIX D "A New Method for the Analysis of Temperature Dependent Quadrupole Splitting in M9dssbauer Spectra" by P. Bo Merrithew, P. G. Rasmussen, and D. H. Vincent Submitted for publication

A New Method for the Analysis of Temperature Dependent Quadrupole Splitting in Mossbauer SpectraP. B. Merrithew, P. G. Rasmussen Chemistry Department, The University of Michigan and D. H. Vincent Nuclear Engineering Department, The University of Michigan

Abstract A new method for the analysis of temperature dependent quadrupole splitting in Mossbauer spectra has teen developed. Accurate quadrupole splitting data has been obtained for the compounds Fe(py)4C12 (py = pyridine), Fe(py)412, Fe(py)4I2 2py Fe(py)4(SCN)2, Fe(NH4SO4)2 6H20, Fe(phen)3(C104)3 (phen = 1,10 phenanthroline), and K3Fe(CN)6 in the region 100~ to 300~K. A plot of ln(IQ.S.~-Q.S.I) vs 1/T (Q. S. = quadrupole splitting, Q.S.~ = low temperature maximum quadrupole splitting) is found to be linear in most of the cases studied. This implies that these compounds can be well described as a two state system over this temperature range. The high temperature intercept (IQ.S.el) is the quadrupole splitting expected from the totally populated excited state and is independent of the so called lattice contribution to the quadrupole splitting. It is concluded from the results that spin orbit coupling effects have previously been overestimated and covalency effects underestimated.

I. Introduction 2+ In Mossbauer spectroscopy experiments high spin Fe and low spin Fe3+ compounds normally show relatively large, temperature dependent, electric quadrupole splittings. These large splittings and their temperature dependence are due to the presence of an uncompensated 3d electron. For Fe57m the quadrupole splitting is given by Q.S. = 1/2 e2 qQ[ + 1/3 27)1/2 where Q is the quadrupole moment of Fe57m and q and r7 are expressed in terms of the components of the electric field gradient tensor (e.f.g.) at the nucleus. When the principal axes have been chosen so that Vzz IVyyl 1 Vxx, q = Vzz/e and n7q = (Vxx-Vyy)/. Assuming an ionic model these quantities can be written q = (l-R) qal + (l-y) qlat iq = (-R) 77val qval + (1-7o) 7lat qla where the subscript val refers to the charge distribution of the uncompensated 3d electrors of the metal ion and the subscript lat refers to the charge distribution of the neighboring ions. The 1,2 Sternheimer factors,l2 (l-R) and (1-y ) are included to account for the polarization of the electron core. In octahedral symmetry the appropriate metal ion eigenfunctions are t2g~ = 1/2 (d2-d_2 ) 2g = dl t + dl t2g -.

-2The contribution to the e.f.g. from a single electron occupying these orbitals can be obtained by calculating the appro4 priate expectation values: for t2g Vz/e= 4/7<r3> for t2g Vzz/e = -2/7<r3 > and for t2g+, Vz/e = -2/7<r3>. val is zero for these wave functions. If the lattice contribuvals tions to the e.f.g. can be considered not to effect the orientation of the major axes of the e.f.g. tensor then, because all of these wave functions have the same major axis, the quadrupole splitting may be treated as a scalar. For example, the temperature dependence of the quadrupole splitting for a Fe2+ high spin, purely ionic, compound with a small axial distortion can be approximated by: 0 (t2g ground orbital) Q.S. = Q.S.lat K/7<r- > + 2K(-2/7)<r3>exp -AE/kT and ln(Q.S.~ - Q.S.) = ln(K4/7<r-3>) -AE/kT where Q.S. = Q.S.lat + K4/7<r 3> and K = 1/2 e2Q A plot of ln(Q.S.~ - Q.S.) vs 1/T will be linear with intercept of K4/7<r 3. In a real case covalency effects must be considered. These effects can be thought to produce an expansion in the radial part of the wave function and hence will reduce the Q.S. contribution from each state. Since in general this effect will

-3not be the same for each state we will designate the Q. S; produced by the totally populated ground and excited state as Q.S. and Q.S. respectively. In addition to Q.S.lat another temperature independent contribution must be included due to anisotropy in bonding to the orbitals occupied by the compensated 3d electrons. We will call the sum of these effects Q.S.lg. With the additional assumption that the covalency effects do not alter the major axes of the e.f.g., then, we can write for the above case: ln(Q.S0~ - Q.S.) - ln(-Q.S.e ) -A/kT where Q.S Q S +. Q.S.. Q.s~ <_ Slig @.~g g For the experimental cas-e when only the mag)nitude of the Q.S. is known we write ln( Q.S.~ - Q.S.) = ln((IQS.e) -AE/kT. This expression is a phenomenological description of the parameters, wjhose validity will be demonstrated empirically by the data below. A good straight line fit to a plot of ln (IQ.S.0 - Q.S. ) vs 1/T will also imply a two state system. II. Experimental Details The compounds Fe(py)4C12, Fe(py)4I2, Fe(py)4I2 2py and Fe(py)4(SCN)2 (py = pyridine) were prepared according to the methods of Golding, Mok and Duncan.5 The room temperature Q.S.

-4results for Fe(py)4C12 and Fe(py)4(SCN)2 agreed with those of the above authors. The room temperature Q.S. values for Fe(py)1I2 and Fe(py)4I 2 py were about 0.3 mm/sec smaller. The absence of third peaks confirm the purity. The compound Fe(phen)3(ClO)3 (phen = 1,10 phenanthroline) was prepared by the slow addition of nitric acid to a Fe(phen)32 solution until the solution turned blue. Excess NaC104 was added and the solution allowed to stand for twelve hours. The crystals which formed were filtered and dried. The room temperature Q.S. obtained agrees with that of Erickson.6 The Fe(NHlSO4)2 6H20 was Merck reagent. The K3Fe(CN)6 was Mallinckrodt reagent. The Mossbauer drive is described elsewhere.' The spectra were analyzed with a Fortran IV translation of a Michigan Algorithm Decoder (MAD) program described elsewhere. The errors are determined statistically by the computer program. The results are found to be normally reproducible within the stated error. The accuracy is 1. The dewar consisted of an aluminum sample holder fastened beneath a liquid nitrogen reservoir with a thermal resistor. Heating wire was wound above the sample holder. The whole apparatus was insulated with styrofoam. Variation of the thermal resistors and the heating current allowed temperature control in the range of 100~ - 300~ K. The temperature was measured with a Cu - Constantan thermocouple. The temperatures are accurate to + 0.5~.

-5III. Results and Discussion The data is shown in Table I. A typical spectrum is shown in Figure 1. Since our data was confined to the region above IOOK, Q.S.0 could not be directly determined. Estimation of Q.S.~ was simple for the compounds Fe(py)4(SCN)2, Fe(py)412, Fe(py)4I22py, Fe(py)4C12 and Fe(phen)3(ClO0)2 since by 100~K the Q.S. has become nearly independent of temperature. Choice of Q.S.0 for K3Fe(CN)6 and Fe(NH4S04)2 6H20 is more difficult. These values were chosen to give a linear plot. Our predicted value for lQ.S. ~ for K 3Fe(CN)6 of 0.535 mm/sec agrees quite well with the value of 0.524 mm/sec obtained by Oosterhuis, Lang and de Bendetti.8 Their Q.S. value at 77~K fits on the linear plot. The plots are shown in Figures 2 to 8. The data on all these compounds, except Fe(py)jI2 and Fe(NH4SO )2. 6H20, is described by equation 2. The plot for Fe(py)4I2 definitely is not linear. Because of the uncertainty in Q.S.0 for Fe(NHILS04)2o 6H 20 it is possible that this compound exhibits non-linear behavior at low temperatures. From the rate of change of the Q.S. at 100~K we estimate that Q.S.0~ 2.76 to 2.96 mm/sec and IQ.S. I = 3.40 to 3.64 mm/sec. The AE value obtained from the slope of the linear plot for this compound thus represents an upper limit. A. Spin Orbit Coupling An axial field splits the 5T2 ground term of high spin Fe2+ into a 52 and a degenerate 5E sta;te. The combined effect of an

-6axial field and of spin orbit interaction on a cubic 5T2 term 2 produces nine levels.9 The free ion value of the spin orbit 10 coupling constant X is 148~. Because three of the five high spin Fe2+ compounds considered here can be described well as two state systems in the region below room temperature, it appears that the effects of spin orbit coupling are relatively minor. Eibschutz, Ganiel and Shtrikmanll fit their data obtained for the compound, FeNb206, and conclude that X = 90~. This value of' results in a splitting of the excited level of about 300~. Since our compounds show crystal field splittings of 500~ to 6000, a value of \ as large as 90~ is inconsistent with the simple two state analysis of these systems. Their conclusion of a large spin orbit coupling constant probably results from their assumptions of axial symmetry and zero Q.S.lig. Spin orbit coupling mixes the t2g wave functions and therefore should reduce the values oflQ.S.e andIQ.S.1. Consider the results obtained for the compound Fe(NH4SO4)2'6H20. On the 12 basis of Ingalls' treatment of spin orbit mixing, a compound with free ion spin orbit coupling and an axial splitting of 380~, should have!Q.S.e andIQ.S.~ values at least 50% reduced from those values observed in a compound with very large AE. Fe(NH4S04)2'6H20, however, has the largest value forlQ.S.e!of the compounds studied but has the smallest axial splitting. IQ.S.elfor this compound (3.44 - 3.64 mm/sec) is nearly as large as the Q.S. observed for the compound FeSiF6-6H20 (3.67 mm/sec)13l4 which has a AE of about 1200 cm1 15,16 This compound has the largest Q.S. known. It is likely that the large Q.S., compared

-72+ to other Fe(H20)62 salts, arises because the Q.S. ig contribution happens to augment the Q.S.. Spin orbit mixing in the g compound Fe(NH4SO1)2 61020 must then be considered negligible. For spin orbit coupling effects to be negligible, (reduction in Q.S. less than about 10l) the effective spin orbit coupling constant must be less than 4-0~ The combination of an axial field and spin orbit coupling removes the degeneracy of the ground cubic 2T state of low spin Fe3+.17 Since the data on K3Fe(CN)6 indicates that to a good approximation the cubic 2T state has been split into only two states, it must be concluded that either the axial field or spin orbit effects are minor. The values of IQ.S. 0 and Q.S.e are not equal indicating that the CN bonding is not isotropic. The splitting AE observed here is therefore due to ligand asymmetry. An exact value for the spin orbit coupling constant in this compound cannot be obtained without accurate low temperature data. The spin orbit coupling constant is related to the splitting of the 2E state and is therefore related to the deviation from linear behavior at low temperatures. We estimate that the spin orbit coupling constant must be less than 60~ since a splitting of this magnitude would be easily detected in the temperature range we have studied. This value is at considerable variance with the value of 575~ derived from susceptibility data. 7

-8B. Discussion of the Results for Individual Compounds Table II shows the expected values for Q.S.0 and Q.S. in the absence of covalency factors and lattice contributions for Fe2F high spin and Fe3+ low spin compounds. In the absence of anisotropic covalency factors the ground and excited levels can 2~t be easily identified. Consider a Fe2 high spin compound with axial symmetry and a ground t2 orbital (case 1, Table II) In the approximation thatiQ.S.gt =Q.S.el then Q.S. + Q.S.e = Q.S.!ig and Q.S.li is of the same order of magnitude as (or smaller than) the splittings observed for Fe3+ high spin compounds. Consider a Fe3+ low spin compound with t - ground orbital t 0 excited and t + much higher in energy (case 7). Here Q.S.0 4- 1/2 Q.S. = Q.S.li and Q.S. should be the e> Q.S. + /.... lig same order of magnitude as the Q.S. observed for similar Fe low spin compounds. The quadrupole splittings for high spin Fe3+ and low spin Fe2+ seldom exceed 0.6 mm/sec. Consider the compound Fe(NH4S04)2-6H20. The ground orbital is t2g~ and the first excited level a (to the first approximation) degenerate (t2g+, t ) pair. The predicted positive sign for 2g' 2g Vzz of the ground state agrees with that Which has been previously determined.18 Q.S.ig is negative and its magnitude is between 0.6 and 0.9 mm/sec. A Q.S.lig as large as 0.9 mm/sec is unlikely. Thus the symmetry for this compound is not precisely axial and the Q.S.0 assumed to give the plot shown is somewhat small. The compound Fe(phen)3(C104)3 is described by case 7. Q.S.lig for this compound ism2 mm/sec, of the same magnitude as the Q.S.'s

-9observed for Fe 2 low spin compounds with similar ligands.619 The sign of V for the ground state of this compound is predicted to be positive. The relatively small Q.S.0 here is seen to be primarily due to the nature of the electronic structure and not due to covalency effects as has been previously suggested.20 Fe(py)+(Cl)2 is described by case 1. Q.S.li here is + 0.5 mm/sec. The positive sign indicates that the compound is probably cis. The reduction in the Q.S.el value for this compound is expected since pyridine and chloride ion are stronger w bonding ligands than H20. Assignment of the energy levels in K3Fe(CN)6 is clouded by uncertainty in the strength of the strong w bonding ligand CN Comparison of the results for this compound with the results 21 obtained for similarly coordinated iron in other compounds2 indicates that this compound has a E ground state. Q.S.0 and IQ.S.e have been reduced by at least 70% by w bonding. This reduction is substantially greater than that estimated by Goldig.20 The orbital level system cannot be unambiguously defined for the compounds Fe(py)lI2'2py, Fe(py)412 and Fe(py)4(SCN)2 because the possibility exists for substantial anisotropic w bonding. For example, for case 1 the difference Q.S.~ - Q.S.e may be larger than in previous cases because Q.S.g is reduced by v bonding more than!Q.S.eI. nTe compound Fe(py),l(SCN)2 is known to be trans.2 Because the molecular and orbital major axes would be expected to be colinear in such a case, Q.S.lig is negative. A likely level arrangement is as case 4 and a negative Q.S.lig of 0.5 mm/sec augments the Q.S. contribution to give the larger (Q.S. ~. It is g

-10possible, however, that the level system is described by case 1 and that the combination of a negative Q.S.lat and relatively delocalized ground state produce the reduced Q.S.~. The temperature dependence for the compound Fe(py)4I2 is particularly interesting. The small room temperature quadrupole splitting observed for this compound is not due to a small AE as concluded by other authors5 but must be due to a large w interaction with I. The non-linearity of the plot for this compound prevents explicit determination oflQ.S.el. Q.S.e, however, has about the same absolute magnitude as Q.S., indicating that the three tg orbitals show approximately equal ligand interactions. 02g Evidently the strong w donating interaction of the I ions promotes stronger 7 acception by the pyridine. This indicates that the various bonding properties of a ligand cannot be considered independent of the compound. The compound Fe(py)4I2 2py might be described by case 4 and a positive Q.S.i or case 1 with the small Q.S.~ being due to a lig oD strong T interaction. In either case the results do not appear consistent with the results for Fe(py)4I2 and suggest that the I ions might not be in the first coordination sphere. These ambiguities could be resolved with knowledge of the crystal structure and the sign of the low temperature quadrupole splitting.

-11IV. Conclusion The results of this work indicate that, in general, covalency effects in iron compounds have been greatly underestimated. In particular, treatments that assume that the Fe-H20 bond is 100 ionic 1,' 23 24 are unjustified. The reduction of the spin orbit coupling constant from 1480 to 40~ or less reflects a great degree of ligand interaction. Q.S.a values calculated on the pla basis of a point charge model for Fe2 six-fold coordinated with water are small (<.l mm/sec). 4 Although a Q.S lat value has never been explicitly determined for Fe(NH4S0)2 6H20 it seems highly unlikely that the Q.S. ig value found for this compound (0.6 to 0.9 mm/sec) could be explained without allowing for some ligand to metal charge transfer. The differences in thelQ.S.el values for Fe coordinated with H20, 1,10 phenanthbloline, pyridine, and CN indicate a substantial degree of d orbital-ligand interaction. 2+ Since even Fe high spin compounds cannot be treated satisfactorily with an ionic model several conclusions based on this model must be treated with skepticism. If the spin orbit coupling constant for the compound Fe(NHS S04)2 6H20 is as small as we believe then the value for Q, the quadrupole moment for the 57 14 Fe57 excited state, calculated on the basis of an ionic model14 24must be consideraby u. If te cannot be considered as ionic then the Felikel - Hih20 bond is surely covalent and the Mossbauer isomer shift model based on the ionicity of these compounds24 is incorrect. In all likelihood Fe3+

-12high spin compounds show smaller isomer shift values than Fe2+ high spin compounds simply because the 4s density is much greater in the more covalent Fe3+ compounds.25

-13Table I. Com-oound Temperature Quadrupole Splitting ( K) (mm/sec) Fe(py)4(SCN)2 294.2 1.538 +.003 261.7 1.625 +.005 227.7 1.730 +.003 196.7 1.829 +.003 140.2 1.987 +.003 120.2 2.011 +.003 98.7 2.033 +.003 Fe(py)4I2 2py 293.5.548 +.013 248.2.689.008 216.2.775 +.008 187.4.853 +.006 172.2.901 +.005 149.2.957 +.004 128.2 1.000 +.004 116.2 1.005 +.003 103.2 1.015.003 Fe(py)4I2 295.0.317 +.007 255.6.337 +.006 228.5.368 +.006 201.5.388 -.006 171.5.434 +.005 142.5.462 +.004 126.1.480 +.004 110.5.498 +.004 99.4.503 ~.004 Fe(py)4C12 294.0 3.144 +.006 248.2 3.275 +.006 225.2 3.323 +.006 197.4 3.392 -.006 172.8 3.430 T-.004 150.8 3.458 +.004 149.4 3.460 T.004

-14Table I. (Cont'd.) Compound Temperature Quadrupole Splitting Compound (OK) (mm/sec) Fe (NH 4SO )2'6H 60 295.0 1.721 +.002 4 42 20 246.9 1.968 -.003 204.2 2.185 ~.003 167.4 2.368 +.003 162.2 2.418 +.003 137.1 2.519 +.003 114.8 2. 618 +.003 102.2 2.673 +.003 K3Fe(CN)6 294.2.282 -.003 249.7.308 +.003 200.5.341 +.004 172.2.359 +.004 149.2.377 +.003 137.1.385 +.003 125.0.403 +.003 110.7.428 +.003 99.7.439 +.003 Fe(phen)3(C104)3 295.0 1.578 +.003 257.0 1.649 +.005 236.0 1.679 +.003 218.4 1.705 -.004 196.1 1.736 +.004 170.2 1.756 ~.003 149.6 1.767 ~.003

Table TI ground 1st level nt populated Q.S.0 Q.S. 1, t 2 (t2g+'t2g) " K 4/?7<r-3> K-4/7Kr3 2+ +t 3 Fe2 2. (t2ggt2g t --- K-2/7<r 3> K 2/7<r3> 2g 2g 2E ~~~~~~~~~~~~~~~~- / high spin 3. t2g t2g(t2g) t2g(t2g) K 7<r3> K-2/7<r-3> 4. tg g(t g) t0 t2g+(t,-) K-2/7<r-3> K 4/7<r-3> ground 1st level 2nd level Q.S.0 Q.S. e t? Fe34 5. t (t2-t +) --- K 2/7<r-3 K-2/7r3> 2g ~ ~ 2g' 2g > K-/ low spin 6. (t2gg g t2go ~~ K-4/<r-3> K+4/7<r3> ^E(t2g" 2^g 2g+) 7. t2g(t2g+) tg0 t2g+(t2g) K 2/7<r-3> K-4/7<r3> K = 1/2 e2Q Table II. The values of Q.S.0 and Q.S. expected for various orbital arrangements in the ionic case with no lattice effect. The cases where t2g or tpg4 might be degenerate with t 0 are not included. 2g

-16-* This work was partially supported by the National Science Foundation, Grant GK871. 1. R. M. Sternheimer, Phys. Rev. 130, 1423 (1963) 2. A. J. Freeman and R. E. Watson, Phys. Rev. 131, 2566 (1963) 3. C. J. Ballhausen, Introduction to Ligand Field Theory (McGraw-Hill, New York, 1962) 4. M. Weissbluth, Structure and Bonding, 2, 1 (1967) 5. R. M. Golding, K. F. Mok and J. F. Duncan, Inorg. Chem. 5, 774 (1966) 6. N. E. Erickson, Ph.D. Thesis, University of Washington (1964) 7. J. Ullrich, Ph.D. Thesis, University of Michigan (1967) 8. W. T. Oosterhuis, G. Lang and S. de Bendetti, Phys. Letters 24A, 346 (1967) 9. E. Konig and A. S. Chakravarty, Theoret. Chim. Acta (Berl.) i, 151 (1967) 10. R. E. Trees, Phys. Rev. 82, 683 (1951) 11. M. Eibschutz, U. Ganiel and S. Shtrikman, Phys. Rev. 156, 259 (1967) 12. R. Ingalls, Phys. Rev. 133, A787 (1964) 13. C. E. Johnson, W. Marshall, and G. E. Perlow, Phys. Rev. 126, 1503 (1962) 14. A. J. Nozik and M. Kaplan, Phys. Rev. 159, 273 (1967) 15. M. H. L. Pryce, Nuovo Cimento Suppl. 6, 817 (1957) 16. D. Palumbo, Nuovo Cimento 37, 271 (1958) 17. B. N. Figgis, Trans. Faraday Soc. 57, 198 (1961)

-1718. R. L. Collins and J. C. Travis, Mossbauer Effect Methodology 3, 123 (1967) 19. R. L. Collins, R. Pettit and W. A. Baker, J. Inorg. Nucl. Chem. 28, 1001 (1966) 20. R. M. Golding, Molecular Physics 12, 13 (1967) 21. P. B. Merrithew and P. G. Rasmussen (unpublished data) 22. I. Sotofte and S. E. Rasmussen, Acta Chem. Scand. 21, 2028 (1967) 23. L. Pauling, The Nature of the Chemical Bond (Cornell University Press, Ithaca, New York, 1960) 24. L. R. Walker, G. K. Wertheim, and V. Jaccarino, Phys. Rev. Letter 6, 98 (1961) 25. P. B. Merrithew (to be published)

Caption Page Fig. 1. A typical spectrum. Fe(py)4(SCN)2 at 98;7~K. Velocity given vs Na 2FeCN NO -2H20 (0I3S standard No. 725)

0 Q C) 0 CeD nagcf~ ~ ~ ~ ~~~c f) CDJ >1 eS| t — t — --— ^ r 0 000' 1 OL6' 0I6' 0 1i 6' 1 I o A_ k | -1 1 v I T _ s v | | I _ _ | |

0.0X F4h (p/2 (SCAN -1.0 \ QS~ = 2.050mmn/sec Q.S.= 3.04 mm/sec AE = 511~ U \ t -2.0E CA ~ -4.0 2 4 6 10

In (Q.s. - Q.S) (mm/sec) fI) i - i iw.. 0 0 00 0 D t iD 0I 0 00 0 0 X ^3 J ^Or XOJ~ ~ o~~? 0-o: 3j ^ oCJ% C) ^

-1.0O 6 -1.5- \ Q.S. =- 0.535 mm/sec E \Q.S 0.404. mm/sec AE = 146~ 0f'-I a -2.0;c -2.5........_ I I I. - 2 4 6 8 10 1/T x 103 (K')

L 9g 9 1? 0 - I- X3 o9L9 3V ~es/Luu i1O5'= =S'' 01Deo/wuu oi'c ='SI)

Fe (phen (C/QI -l.0o Q.S~ = 1.780 mm/sec QSe = 316 mm/sec 0s| \ L AE = 826~ a) -2.0 E (ii C -3.0 9\ 0 5 -c -4.0- 5.03 4 56 7 1/Tx103 (~K)

F(/VCH SQ) 6H 0 44 2I0.0 \. Q.s~ 2.760 mm/5ec U a< |) A^ Q.S. - 3.64 mr/sec E AE = 379~ E-1.0 I co \ -2.0\ - ______6 8 10 2 4 6 8 10 1/Tx103 (0K')

In (Q.S. - Q.S) (mm/sec) (Jn -i 6) r,s i D I o70) 0 0. I... It -~0')~ ~0 U, O Or l/f30 @ / D~~~~~~~