T HE UN IV ER SIT Y OF MI CHI GAN COLLEGE OF ENGINEERING Department of Nuclear Engineering Final Report - Part 4 ESR OF VANADIUM IN CaO AND MgO G. H. Azarbayejani No Mahootian C. Kikuchi ORA Project. 0o4385 under contract with: NATIONAL SCIENCE FOUNDATION GRANT NO. G-15912 WASHINGTON, D. C. administered through: E OF RESEARCH ADMINISTRATION ANN ARBOR September 1963

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TABLE OF CONTENTS Page LIST OF TABLES v LIST OF FIGURES vii ABSTRACT ix I. INTRODUCTION 1 II. EXPERIMENTAL PROCEDURE 3 Ao General 3 Bo CaO:V 3 C. MgO:V (Crystal) 8 D. ZnS: Mn 12 E. MgO:V Powder Samples 12 III. DISCUSSION 21 Ao Line Position 21 B. Line Broadening 30 C. Irradiation Result s 30 IV. NEW RESULTS 33 ACKNOWLEDGMENTS 35 APPENDIX A 37 APPENDIX B 49 REFERENCES 51 iii

I ~

LIST OF TABLES Table Page I. Angular Variation of the Components., 3, and y of V++ in the (110) Plane of CaO: V 17 II. Angular Variation of the Components C, I, and y of V8 in the (100) Plane of MgO:V 18 III. AyU in the (100) Plane of MgO:V as a Function of m and G 18 IVo Angular Variation of V8 Component in the (110) Plane of MgO:V 19 V. Aya as a Function of m in Powder Samples (Ku-Band Spectrum) at Vo = 17.136 KMC/SEC 19 A-1. Matrix Elements of L+, L_, and Lz for L = 3 With Respect to F2, F4, and r5 Energy Levels 40

LIST OF FIGURES Figure Page 1. ESR spectra of V++ and Mn++ in CaO at different angles. 4 2. ESR spectra of V++ and Mn++ in CaO at different frequency bands and at 9=0 (HII[100]). 6 3. Angular variation of the spectrum of V++ (m=7/2) in CaO. 7 4. ESR spectra of V++, Mn++ and Fe3+ in MgO at different angles. 9 5. ESR spectra of V++, Mn++ and Fe3+ in MgO at different frequency bands and at 9=0 (HI [100]). 10 6. Angular variation of the spectrum of V+ (m=7/2) in MgO. 11 7. Angular variation of the spectrum Mn6+ (m=5/2) in CaO and ZnS. 13 8. Angular variation of the spectra of the V8 (m=7/2), Mn6 (m=5/2) and Fe3+ in MgO. 14 9. ESR spectra of vanadium in MgO powder. 16 10. The angular variation of the components a, P, and y in the plane (100) of MgO (S306). 24 11. Variation of the separation of the components a and y vs. m at X-band and at 0=0 of the (100) plane of MgO (S306). 25 12. A7y vs. m at Ku-band in the powder of MgO. 26 13. Zeeman splittings of V++ electronic and nuclear spin levels. 27 14. Designation of the components of the expected V++ ESR in a cubic field. 28 15. X-ray irradiation of MgO:Fe, V, Mn. 31 A-1. Orbital levels of V2+ in MgO. 39 A-2. Coupling channels. 41 vii

ABSTRACT Spin resonance measurements of CaO and MgO single crystals containing vanadium and other impurities of the 5d transition elements have been carried out. The usual spin Hamiltonian coefficients have been measured at room temperature. They are: g = 1.9678, A = -75.97 x 10-4 cm-l* in CaO and g = 1.980 and A = -74.19* in MgO respectively. An anisotropy due to both fine and hyperfine components has been observed and discussed. *Others5 have reported AO = 7.2x10-4 cm-1. Theproductof74.19 i-~~ 75.2x10 cm.The product of 74.19 by (gfree/gion) MgO gives AMg0 = -752x-4 cm1 also Ata = -75.97 x gfree -7730x1 cm gion ix

I. INTRODUCTION The electron spin resonance (ESR) of V++ ion in MgO has been reported by a number of earlier investigators.1-5 Low2 reports the presence of a very small rhombohedral distortion at V++ site in MgO being similar to that at the Mn++ site in this crystal. In addition it is observed6 that the positions of the fine-structure components of V++ ion do not agree with the predictions of the usual spin Hamiltonian* provided only corrections of up to second order are included. Ham and others7 have reported an improved spin Hamiltonian for S = 3/2 (Co++) system in a cubic field containing terms of the third power in electron spin components, Sx, Sy, and Sz. This Hamiltonian produces an angular dependence of the fine structure components and it can be applied in our case. (The ground state of Co++ in tetrahedral compounds is the same as the ground state of V++ in octahedral AIIBIV compounds.) The purpose of this report is to give a detailed investigation of the ESR of V++ in CaO and MgO crystals. Besides the ESR of V++ and V4+ ions in MgO powders is studied to augment the results in the crystals. Since the discrepancy in the position of the fine structure component of V++ ion6 caused by contributions from higher orders of approximation and these contributions depend on the microwave frequency band, we have performed our meas*v=gBS.H+AtS.I.

urements at X-, Ku- and K-band spectrometers. The experimental procedures and the results are given in Section II and a discussion of the anistropy, asymmetry and line broadening of the fine structure components is given in Section III.

II. EXPERIMENTAL PROCEDURE A. GENERAL Samples of these crystals have been placed in the cavity so that the d-c magnetic field could be rotated in one of its (110) and (100) planes. X-band measurements are made with both rectangular TE012 and cylindrical TE011 lavite cavities9 when at Ku- and K-band measurements only cylindrical TE011 cavities have been used. The magnetic field is produced with a rotating base 12 in. Varian magnet and the field modulation of 100 kcps has been used. The microwave frequency is determined by zero heating against the harmonics of a Beckman 7580 transfer oscillator whose frequency in turn is measured by a Beckman 7370 counter. Magnetic field measurements are made with a Varian F-8 fluxmeter. Calibration of the field as accomplished with the resonance of polycrystalline diphenyl picryl hydrazyl with g = 2.0036. B. CaO:V Single crystals of this material which are colorless and slightly hydroscopic are obtained from Semi-Elements, Inc. Pieces of the sizes of 1 x 4 x 4 mm are used for both X- and Ku-band measurements when at K-band a piece of the sizes 1 x 2 x 2 mm is used. All of these crystals contain manganese as a natural impurity and therefore the spectra of ESR of V++ ion in these crystals are mixed with those of Mn++ In Fig. I1 the spectra of V++ and Mn++ at Ku-band and at about 77~K is shown. The angle 0 in this figure and all others represents the angle between the d-c magnetic field H and one of the

F-7-Ir -—. 0..................-.. 8~. 1....:..... ]........... ~~~~~~~.......... ~~.-.-....'......................'..... e'~~~~~~~~~~~~~. i.'" —': -!...-~i. -~ -I_ -.,.-.j —-..- -;-r__-. -.ia —-— ~t-~ - I I-..-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...'............ - HI10]............,...............,!.....; —-..-'-L —F-~~'-, —— I —-— I~~~~~~~~~~~. —— L..-~ — ~.i............ ~-~.-r — -....._. -—:.............. — 1.~ ~ ~ ~ ~ ~ ~~~~i.___L.. —....''............~.:.L-....'_:.....:].: 1..-... V V V V V V ~V V If ar 9- 90' -- ~~. — ~ti:i ~~i-::......'...'__L.. —':.:-. —:.-I —-- -t''-!... i::: ~~ ~ ~ ~ I —' ——: —i — C- ~t_..,.. _::_:': —:?~'-J -:1 —::~ —:::'I.....:,-.. _,____-~-~_ i_<a: ~-~, _.-: -:_.i ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-"-I —--... ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-i" —-- _ —-......' 1. I: —.:... —f-..; ~...-., - ~ ~ --- -, — -: —-: —, —...:-~-:- -' ~~~~~~~~~~~~t —---- F —., —— es- -----— ff,~1:.... 1i'-,t —--- - qql —_. R-.....I_: ~..... —-:'...." -~ —'8~~~~~~~~~~~~~~~~~~~~~~. o._~ ~_. ".........1......:......... "... -[..~.'-' " _._-:.'.-:~3 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~.....::-' -:........... — " -.:':: —----.. V V V..........I_....-:.. V' V'" —.. —- ~~~g-~ —- ~ — ~-~~~~ —-— jb f ~1 ~~~.... i......'_._.....-. —::T -/'-~ —-'-! —~-' _ ~-:+-1.,.... -Fx-:....-:~.~ —-t~... T-?_' L —-:: ——:- -. —-—: —t —::- _~... _-:-~... _ Fig. -~- ~-. -.. ~1. E spectra of and in at different"angl"s................. r-' —:-....' ----—.... i...........::-',....i.. ~ —- ~_ i... ~~~ —1_:.L -:'-q- _L_.....L:: -........:...:......-.....:..............~~ -.-: — -: —t+~- tH-...'H~....'........' —, /,..............~'..... —::-::, " i'I_0__-: _. —.. ——,_,. "-' M V MaV MaV IiV.... ~...:[, t.-~- -',:4T:-r+~-~-~;-:: ~:,':~:-...I..........:..... -'~~~~~~~~~~~~~~-.....-..1._... _.... i......... i:L...-.-~.L__._~.::. -~-_ 1'~-~ —:HICIO ~ ~ g 1_. E S pct o~. ~++ I-d.._++.. ~n 0aO — a t- d~fee- n'ls

principal axes of the cube, [100]. The angle has been determined by comparing the spectra of Mn++ in these crystals with those in a standard sample of MgO. The standard sample has been examined by X-ray diffraction and the result indicates that the faces of these crystals are mostly in (100) planes. The assumption that the cleavage planes of the CaO samples are of the (100) type was confirmed by the symmetry of the ESR spectra of Mn++ in these samples. Since in all of the samples we have used, the manganese impurity is present, we have been able to determine G within 1.~o In Fig. 2 the spectra at G = 0 and at about 9, 18, and 24 G/sec are shown. The samples S102; S101 and S102R are of the same source and R in S102R indicates irradiation with X-rays. A comparison of these spectra shows that the second order effects are the major mechanisms responsible for the splitting of the lines of T++ ions. To determine these effects as a function of different parameters the measurements at X-band was investigated in more detail. In Fig. 3 the angular variation of the line in extreme left of Fig. 2a is shown. This line, V8, corresponds to the V++ ion for nuclear magnetic quantum number m = 7/2. The variation in the (110) plane of the crystal S101 (Fig. 3a) indicates that the fine structure components o and Z (see Fig. 14) are sharpest along the [100] directions where they are broadest along the [111] directions. In the (100) planes the general trend is the same but the components a and y (Fig. 3b) are not smeared off completely as in the (110) plane. To investigate the same phenomenon as a function of lattice constant a0 it was necessary to run crystals of MgO containing vanadium impurity. The results are as follows.

61 6 0 70~~~~~ ~~~~~~~~~~~~~~~~~~~~~0 6 7S 0'i -i'j 1.'jj~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.'& I' ~ ~ ~ ~ ~ i 01t,...... ii ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4. I rt I4. 60 I Nil Iild030d0 040 sii'i -T~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-,II 14''''ib''.'ILL 7) >~~~~~~~~~~~~~~~~~~~~~~~~~~e 10 0 00' 4000 700180601 tI~~~~~~~~~~~~~ 04t 1.:'',~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i +'I iL-I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~q it 4HO *~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~H 1' 20l 3Ait 607 08 0000C *. I'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~p.C''LI'' ~ ~ ~ 6~~~~~~~~~~l

.-. —~~~~~~~~~~~~~~~~ —. —- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~?;..:-.-'- -......7'..-.-v' i...-' -1.............. ~...II {L —..........V-'~-'..-t-...';.......' —- ~..J-.....-.. -_..........................._......'..:...-4....7_........'..._.-...'.........'............ __-4.................I.......L....._...._;...1am........1.......-1: -17....~-............. 5...0..20...30..40. 90..........25...........i.....60 -... O....7___I.....:... ao(1,0) PLANE........ _....... ~ I -1~~, ~~~~~~~~~~~~~~ __-4 -4 —----.. i' -'-F.-07_10.....5..... 20.... 30. 45C0 60...-"" 70. " - Q_ 85 90'CI —-OO......____,,... —-+..........~.....~...............b. (100)~ PLANE'r Fig 5.Anula vaiaionof hespetru o ~ m=72)in aO

C. MgO: V (CRYSTAL) As in the case of CaO most of the samples available to us contain an appreciable amount of other impurities such as manganese, chromium and iron. The spectra of V++ can be, however, enhanced by irradiating the crystals with X-rays for a few hours. The spectra of V, Mn, and Fe+++ in Mg are given in Fig. 4. The fine structure components of V is very well resolved along [100 ] directions (Fig. 4a) whereas along [111 and [110 directions they are smeared off (Figs. 4c and 4d). The spectrum at = 0 in which the two components Ca and y (Fig. 4a) are sharpest is taken at X- and K-band (Figs. 5a and 5c) in the samples S306 and 306. At X-band the components are clearly resolved when it is difficult to find them at K-band. It is also very interesting to note that the separation of the components with m < 0 is larger than the corresponding lines with m > 0. The angular variation of the vanadium line V8 (m = 7/2), (Fig. 5a) in the planes (110) and (100) (Figs. 6a and 6b) is similar to Ca0, (Figs. 3a and j3b). Since one of the sources of the broadening in solid state paramagnetic resonance is the spin lattice relaxation the angular variation of V8 in the (100) plane was investigated at liquid nitrogen temperature (Fig. 6c). It was found that the effect of temperature was unobservable. Therefore, we conclude that, in Mg0:V, the spectra of V++ show the same dependence on the crystalline field as in Ca0:V. In both of these materials a variation of the separation of the two components a~ and y' is observed which could not be expressed by the usual spin

HIC1003 d. e90, V V V ~~ ~~ ~ ~~v V VP v V, Fig h ESR spectra of V~~~~~~~~~~~~~~~~~ Mri' and Fe5~~~~~~~~~~~ in MgO at different angles~~~~~~~~~~~~~~.a k

OT i II Lnr — e T - - J... -Id I_ j 1Ii Ii12!lt~ ~~ti~ *10,.. -..i.::-''.2 5.. 41'' 0,:I0'0-: C+~~ 1 ~~.. l.T. T I-I +'':', IH!'...: iII 11 X.,,. 0 +:,;i O t s I 1 cl WS I I MitfienlA - I i Aq! l t. 1l, t'+' t-'_O P ii. C+.I Ii~,,' Q- WI I~!tW., HH,~: ffl~~l~i.0Uu lgunlmnulmlTIi-l-nmmn 11W s

~~~~~~~~~~~~~~~~........ -— i;, i,' I i l R I ---'11411-' PLAE NE e~ouoo' I' 0. e 3. 5 5:: I II o C I;',EIIi O'6; leW: 0)'l 2+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~- 11 ~ b.V2% —wU(IOO)-~~iPLANE Fig. ~~~~~~~~~~~~~~~~~~~~~~~. III Ag....r variation~t~ o' the spectrum'-?~,~! ofm V!!T! (m72 in Mg.,~' r a 0 - 0: 0-g ~: Is~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C- ( T/z). OO)PLANEE T- 77 K v-;.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~t,711:.......... 10, 20- 0 4 — -. - ~ —,. 0. 80 — 90. ~1 Fig. 6. Angular variation of the Spectrum of V: (M=7/2) in Mg0~ -I;~~~~~~~~...;.. ~_:lI. ~:~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~-.... F... ~ —.-:~-s-i-__ t~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 80 e-o, tO l 10 * 2o~ 30, 40.11 60 ~ 0- -... ~'' 90, [~~oo c'VI+IrT/2)'{JOOIPLA~~~~~m=72) NEMO T-77'Kig I' Anua.~,~....n.-]r_~ r....~-_Jr__..~_Ur ri

D. ZnS: Mn To obtain the origin of the broadening of the components of V8 as a function of crystalline structure we took a spectrum of manganese in cubic ZnS in the (110) plane (Fig. 7b). A similar spectrum of Mn++ in CaO in the (110) plane (Fig. 7a) is taken for comparison. It is evident that the line broadening of Mn++ fine structure components a, P, 6, and \ in ZnS are opposite to their broadening in Ca0. The angular variation of the broadening of the components a and y of V1 and a, i, 5, and A of Fe+++ and Mn++ in MgO are given in Fig. 8. A comparison among the spectra in Figs. 8a-8e indicates that the broadening of V++ components is opposite to the broadening of the components of Mn++ and Fe+++ in MgO but is similar to the broadening of the components of Mn in ZnS. The spectra of V++ in tetrahedral field10 shows a broadening which is apparently similar to the components of n++ in MgO. The numerical values of the splitting and separation of the components a and v from each other and from the central line (3) are given in Tables I-V. E. MgO:V POWDER SAMPLES Powder samples were prepared by wetting MgO powder with a few drops of aquous solution of vanadyl chloride to obtain a thick dough-like mixture with an atomic relative concentration V/Mg of about 0.05%. The samples were then dried at 100-150~C and "fired" subsequently at high temperatures for several hours. Firing was done in an electric conduction furnace that could be operated at a maximum temperature of 13000Co The fired samples were then x-irradiated at 50 KVP x 35 ma for about an hour. 12

T-4 -.. ____ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~;... (I101PLANE ~ r —-~ — ~ ~I I~ 1.~~~~~~~~~~~~~~~~~~~~~~~~~r ~.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0'~2 1 Li 11 K.." — =':: _ ili ~ 55-, [n 30 10.: — I _........ +t —'T —-~- -2......'[.~:-~ _:........ - +....................~~~~~~~~~~~~F I _....:; iL II:i._c~~~~ul ii... I- ii I I: - I ii i i~~~~~~~~~~~~~~1- J.1.- F-J~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~J b Z S (Td),, (110) RANE (.:-, [NO] 20, EFig.A..L"_i_ -::.'i.....; Fi.7 nua aito fte-spect'm M (m=/2 in CaG and ZnS. o............................ ~'' ~-~L.~-~: [;~>-~:t[- ~:~~~~ f tr'-"i~i i: ~'~- -- -'-[: -:'"=-''':t:l,.:l -E-''-.:t......F... i... t::'-:......~t —:~-f-.. I...['!... t-':~e'M-'~."!"'[:~ qIl~ iI'J:''-IJ[[;,T........................,-t+H:!?ti_,~., ~.i~~~i ~-'T?=p_..~-~-f-Y=I:: ~ ~ ~~~~~~~iI~i I I~ II:i, 1 i I i I7 ~ 1.... _ t, ~ jq ZnS(Td),:.L..:._..-:;...... -'; 4 —,' -:'~ I.:.! ~." —~t7.T~TItFir:- i~-' 4 (11o) PLNE._ -~~..tr1 I — e-90'UI I I, rio 5~;Y [I],:.. ~~-~-~~ — Fig. 7- Angu~lar variation of the spectrum (m=52 n a ndZS

T.3001K — 77 — f —~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ — 44-.4+i- T-i L. -(r, I 1003'[03 9w~~~~~~~~~~~~~~m anU 360W' SCO 4z- --— 4 -4-4 +~i —iFig.~Ya 8. Angular variation of the spectra of the Vt (m=7/2), (m=5/2) and Fe51 in MgOI ilj 1~~~~~~~~~~~~ ~~~9[1001 KT #r 00' tD~ #~~~~~~~~~~~~~~~~~~~~~~~~PD~00 e~~~or, #Kn to. to. Sb~ to: rrl to.~~~~~~~~~~~~~~~~~~or a Fi g. 8. Angular variation of the spectra of the M= 8 (m=5/2) and Fe3+ in MgO.

The spectra of the powder samples depend on the heat treatment as follows: (a) Samples fired at 700-1000~C in air do not show any vanadium spectra either at 300~ or at 77~K prior to x-irradiation. After the irradiation a set of eight sharp lines* (line width about 1.2 gauss) about g = 2. The lines are separated by 77-83 gauss and do not have any satellites (Fig. 9a). (b) Samples fired at about 10000C in a reducing atmosphere such as hydrogen show, after x-irradiation, an ESR spectrum which contains a set of eight lines, each flanked by two satellites (Fig. 9b). The line width and position of the central lines in the magnetic field are quite the same as in (a). The separation of the satellites from each other depends on location of the corresponding central line (Table V), similar to the case of the single crystal samples. (c) Samples fired at 1200-13000C in air show no spectra, before irradiation, either at 300~ or at 770K. Upon x-irradiation, an ESR spectrum, similar to (b), is obtained. (d) Finally, samples fired at 1200-1300~C in an oxidizing atmosphere and x-irradiated subsequently show an ESR spectrum similar to (a), i.e., a set of eight sharp lines without any accompanying satellites. The above observations lead us to believe that the set of lines in (a) and (d) can be associated with V4+ (I = 7/2, S = 1/2) ions. In (b) and (c) *These are in addition to the characteristic lines of Mn++, Fe++, and Cr+++ which are present as impurities in the magnesium oxide powder used in preparation of our samples. 15

-~....1 I-t —-~-......... i ~ ~, -'-i-....-' — t-.... i -i.N~1''...... -! —" i —:-.t-..:......_' i~~~~~~~~~ -....5..... —-.L, —— ~~ —~~~~~~~~~~~~~~~~~~~, -T...... I~~~~:e I ~ i~~~~~~~~~~~~~~~~... ~~~~~~~~~~~~~~~~~~~~~~.. b.-,.- -.._:_.;:.-.-'...........;!:...'c.... ~-~-'t- - ~~I,..__.. I,......,*-: ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ I........i.I c~~ ~~~~~~~~~~~~~~~~~~~~~~..._.._......_. I r~~~~~~~~~~~~~........:........ 1....,.. 5891.9 Gauss 6455.8' -t -.1..-....... /I —--...........,-:"i' i....I ",'~-~-...... — I iC ~ li____~....:.... — -: ~.... L.........t _, —i ~..! ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 - 0"-:'-:: -':"? __ ~~~~~u _,...__~._.. _; 0 _ ~~~~~~~~~~~~~~~~~~~~~~~-i —~4......... I~ -~c~ —--— ~~.....:_......~.::-~ —::.- —!- —!-.....!_:.......:_.- --— 7 _.~ _L_:_._.~. i._..........- -]........._... I, ~... i~~~~~~i..9 ~B1 sl-e-b' o~ a~t_~.. IO1orc.e'

however, the two satellites flanking each hfs principal line suggests that the electron spin of the paramagnetic center is 3/2, and thus vanadium must be in V2+ state. In fact, very good agreement between theory and experiment is obtained by assuming that the satellite splitting is due to second-order effects in the electron-nuclear interaction term, Our tentative conclusion receives further support from the fact that ESR spectrum of the single crystal MgO:V2+ samples in the [100] direction is quite similar to those of the powder samples in (b) and (c). Further investigations are being made to determine the mechanism of temperature and radiation effects in powder samples. TABLE I ANGULAR VARIATION OF THE COMPONENTS a, P, AND y OF V++ IN THE (110) PLANE OF CaO:V a Line e GY 53 ifP A YA o 0 1394961b 1398100b 1400931b 7o37c 6.65c 14.02C V- (m = 7/2) 150 1395029 o398103 1400931 7~22 6~64 13.86 V7 (m = 5/2) 0~ 1361935 1364162 1365970 5o23 4.25 9.48 aUnless specified the data are taken at X-band~ bIn arbitrary unit, CAij is the separation of the two components i and j in units of gauss. 17

TABLE II ANGULAR VARIATION OF THE COMPONENTS OC, I, AND y OF V8 IN THE (100) PLANE OF MgO: V G Add a Aya ya/2 0 o 6.72 6.0o8 12.80 6.40 15 6.62 6.43 13.05 6.52 300 6.41 6.87 13.28 6.64 45~ 6.64 7.02 13.67 6.83 60 ~ 6.41 6.78 13.20 6.60 750 6.64 6.27 12.91 6.45 900 6.77 6.0o8 12.85 6.42 TABLE III Aya IN THE (100) PLANE OF MgO:V AS A FUNCTION OF m AND G M+ -7/2 -5/2 -3/2 -1/2 5/2 7/2 0o [100oo] 14.09 11.o25 8.24 3.43 7.8 12.87 45 o [110] 13.35 12.06 9.55 - 18

TABLE IV ANGULAR VARIATION OF V8 COMPONENT IN THE (110) PLANE OF MgO:V O" 6o60a 5.84 12 44 15o 6.02 5.70 11.72 300 5o,62 5,82 11.44 550 5.73 6,54 12.27 900 5 40 6~33 11.73 aAll values are in gauss. TABLE V Aa AS A FUNCTION OF m IN POWDER SAMPLES (Ku-BAND SPECTRUM) AT v = 17.136 KMC/SEC m -7/2 -5/2 -3/2 -1/2 1/2 3/2 5/2 7/2 Central Line V1 V2 V3 V4 V5 V6 V7 V8 Gausses 7~2 5~6 4.6 - 19

I

III. DISCUSSION A. LINE POSITION The position of the 2+ lines can be expressed in terms of the magnetic field H as (see Appendix A, Section 1) H(M 3/2+M 1/2 = (1+1.2Up/g) 1 [Ho-A(l+l.2Up/A)m + -] - (m,) H(M=35/2-M=/2) =~(1+.2up/g (1) H(M=l/2+M=-1/2) = ( 1+1 8up/g) -1 [Ho-A(l-l.8Up/A) m ] H1 A.8up/g) (2) H(M=-l/2M=-3/2) = (1+1.2up/g) 1 [Ho-A(l+l.2Up/A) + - 2(m,) Ho (3) where Ho = hvo/gp, u and U are constant coefficients, and p is defined by p 1 5( n22 + n2 n + n2 n) (4) With nl, n2, and n3 being the direction cosines of the magnetic field with respect to the three cubic axes. Al(m,G) and A2(m,G) in (1) and (3) denote the discrepancies between the experimental values of line position and the calculated ones. Higher order perturbations caused by hyperfine interaction make substantial contribution to A1 and A20 The value of u and U, obtained from Eq. (2), are u~ 3 x 10-5, U 10-6 cm-l 21

A major contribution to u and U comes from the fourth order perturbation8 caused by the spin-orbit interaction term XL*S together with the Zeeman term P(L+2S)H, or with the hyperfine interaction term P(L.I). Denoting these contributions by ul and U1, they are found to be (see Appendix A, Section 2, Eqs. (A.22) and (A.23)) ul = 120 X3/(E52E2) (6) and U1 = Pul (7) where \ is the spin-orbit coupling constant, E52 - Er5-Er2, and 52 54E11,12 E42 - Er4-Er2. Substituting for %, E52, and E42 one obtains: ul = 120(90)53/(132002 x 19900) 2.8 x 1-5 and (8) U1 -. 10- cm Ham et al.,8 have used the first two terms of Eqs. (1) and (3). They have neglected the third term apparently because its effect on the line position of Co2 in CdTe is at most 0.14 gauss to be compared with U a 1 gauss. In our case, however, both the third and the fourth terrms of these equations are necessary to describe the position of V2+ lines in the octahedral field. To obtain the magnitude of A1 and A2 (Eqs. (1) and (3)) (we consider Fig. 10 and Eqs. (1)-(5). Equation (5) indicates that at G = 30~ and in (100) planes 22

p = 1 - 15/16 0 (9) and (up/g)H < 3 x lo-5 x 3 x 103 x 6 x 10-2 _ 0.005 gauss (10) and Up - 10-6 x 6 x 10-2 _ 0.0007 gauss (11) These quantities are certainly negligible compared to the deviations of the position of the components a and y as illustrated by Figs. 10-12o The Eqs. (1)-(3) can, therefore, be re-written neglecting the terms having up and Up" H(M = 3/2,m,300) = Ho - Am + mA2/Ho - Al(m,G) (12) H(M = 1/2,m,300) = Ho - Am (13) H(M = -1/2,m,30~) = Ho - Am - mA2/Ho - A2(m,G) (14) whence IH(M = 3/2,m,G=300) - H(M = -1/2,m,30~) I = 12mA2/Ho - (1-A2) | (15) Assuming A < 0, as is obtained from nuclear magnetic moment measurements, the Zeeman splittings of V++ nuclear and electronic spin levels is shown in Fig. 13. Therefore the components a and y of V1 and V8 in Fig. 7 can be designated as in Fig. 14. Here m is the nuclear magnetic quantum number and assignment of M to -1/2, 1/2, and 3/2 is according to Kikuchi's designa23

Fig. 10. The angular variation of the components o, 5, and y in the plane (100) of MgO (Sj06). 24~~~~~~~~~~~~~~~~A

g () r.D ~1o O I (t) Oci -p O HredO CO -P0 f I I I I~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~fC O o ii~ *Hl ci I L 4 H APP *-H O4 I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ IIII O I,rCF PCk 0~ — I I I I AP I IL I- I I~~~~~~~~~~~~~~~~~~~~~~~b~i I Al~~~~~~~~~~~~~~~~~

o aGpftod Gq,_ ui pueq-nX q:e ui'SA /"DV OFT'Old......................................... 111111111 Kill. III[ III milli I I lot.[ 61..6d IIII.J I IL....Al I 6 6" L. A KOMAR I A" I IA X Li AII lilt IL lilt I LA I A I I...... ji II I 10111111 lilt I ILI I IL I I I I I I I IV I IL I I F I XM'LI I I I unit I I I El I I IA I I -A I - - - II I II I I AV mm I 1ww`0IIFI I I -1-1 I I-Li z 7-T

ENERGY —-P' I I T ++_ CPQ 4+ (D IL CD: I I I I P I I I -T- -rT-rI t I. liv er I it I. till ( till,, J'I I i I Fd (limit C+ IL C+ 11 it it till ++ + rn F-b 1 I I L-L 14 1 _44+I (D LL TR Ft CD C) C-fF + Ali I I I it 11 + 1 1 1 1 1 i t 4-4 L -4+ 7-4 -T!+ L 4 (D tjt+j i-j_r: 7 HF I Till[ Tj F, —'-14+I4-'; 44- 4:1 7 ttt 7, 4. fill +H T4 CD I Hills Li I-L-.1 CD 44*1 t.4 P4 flown L 4-f T- Hlflii4 1

t mS~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~- me-1 i _._ i _tft -T < C C i ~ l X m m t,Lt|}t |H w w < | X X X X 5 S m XI T TI~~ ~ I ml — fT- 01 = 1 1 1 I 1 1 [-'~~~~7 H X0-11 I —H + W1. o-3l 1-01- tXE IX-tEX 04i~A I 1I 110 r!L I 07! i W aH rTX -|||i- -4-H~ttW-l — #-. A t3:.l.-0.-X~l-l-4 i il-!i: IlltHS 1S! —Ii 1WE1 Li0ir:Lt-=l —-X!-0 1 - I t 77-!: Iri~ 1t W ~; - - |-:!-S+ 1 ri~~t; gitri~~ti44l l i t!X1 -t4W!-lrl~~~tT1- F tt ill iM Fig 1. esinaio o th cmpnets f heexectd +4ES in4 a cuicfil

tion. Thus, for V8(m = 7/2), Eq. (15) gives: 2a = [H(M = 3/2,m = 7/2,G=300) - H(M = -1/2,m = 7/2,0=300)] = 17A2/Ho- (A1-A2) I (16) where: 2c = 13 30 (gauss) (17) and 7A2/Ho = 13.51 (gauss) (18) Equations (16) -(18) give (Al-A2) 0.21 (gauss) (19) Equations (12) and (13) give: A7y(G=300,m=7/2) -= A2/Ho - A1(7/2,300) + A1 = -0.13 gauss (20) and Ao,(G0=300,m=7/2) = 2 A2/Ho + A2(7/2,30)) + A2 = -0.35 gauss (21) Considering Eqs. (9)-(11) and (19)-(21) one finds that the parameters u and U at most would do a contribution smaller than 0,1 gauss when both A1 and A2 are larger than 0.10 gauss. The dependence of the parameters A on m is more pronounced for smaller m as shown in Figs. 11 and 12. 29

B. LINE BROADENING Our investigations concerning the line broadening suggest that charge transfer may account for this phenomenon provided we assume that in case of Mn++ and Fe+++ the transfer takes place, through a-bonding and e orbitals of t23e2 configurations of these ions. But in case of V2+ only through t23 orbitals. This mechanism explains why the Mn++ and Fe+++ ESR spectra in ZnS show similarity with that of V++ in MgO and CaO and the spectrum of V + in silicon shows similarity with Fe+++ and Mn++ in MgO and CaO. C. IRRADIATION RESULTS Irradiating MgO and CaO with X-rays we have been able to increase Fe+++ and V++ populations. These ions, however, anneal as is shown by Fig. 15. 3o

Fe (mm 5/2) t 7hrs. AFTER IRRAD....:o~~~~~~~~~ — - L... i i ~~~~~~~~~~~~~~~~~1 b. ~ 0 hrs. AFTE RA b. 3 0 hrs. AFTER IRRAD,~~: r~~L.. A-.!- -—''Kr~)- PP IT M

I

IV. NEW RESULTS In addition to the usual fine lines in each of the six groups of the Mn++ ESR spectrum in CaO (Fig. 3, G = 550) we observe two extra components in each group. These components are tentatively assigned to Mn4+ Further investigations are necessary to identify these lines. 33

ACKNOWLEDGMENTS The authors wish to thank Dr. H. Watanabe for his valuable discussions and helpful comments. 35

APPENDIX A 1. DERIVATION OF V2+ LINE POSITION The spin Hamiltonian for S < 2 ions in a crystalline field of cubic or tetragonal symmetry is usually written as ( (o) = gpS~H + A'S*I - gNPI. H (A-1) However, this simple spin Hamiltonian cannot explain the angular variation of ESR spectra that we have observed. Similar observations have been reported by othersol4,8 As Bleaney15 and Koster and Statzl6 have suggested, there are cases where some of the observed anomalies can be accounted for by addition of a correction term to (o) This correction term is given by A s -- A (=S3HX + S3Hy + S3HZ -1 (S.H) [3S(S+1)-l1 (A-2) + U{SxIx + SyIy + S3Iz - (s I) [3S(S+1)-1-) where x, y, and z are the cubic axes of the crystal and u and U are constants depending on g. Using above additive terms and neglecting the last term of (A-1) which is very small and causes a constant shift in all energy levels, the new spin Hamiltonian can be written as 37

s - gPS.H + A'S.I + upTSsHX + S3H + S3HZ - (S-H) [3S(S+l)-i]) (A-3) + U(SXI, + + sIz - 1(S.I) [3S(S+l) -1]I Using the corrected spin Hamiltonian 0, the energy levels to second order in A and to first order in u and U are found to be EM = gPHM + A'mM M,m +A [I(I+l)-m2+m(2M-l) ] (A-4) 2gPH0 + (uPH+Um) (M3 - 1 [3S(S+1)-l]MpP 5 where, M and m are eigenvalues of S and I along the magnetic field H, Ho stands for hv/gp, and p-~ 2 2 2 2 a 2 np ln + n n + nsn+ ) with nj, n2, and n3 denoting direction cosines of the magnetic field H with respect to the three cubic axes. The position of the V2+ lines in gauss is found from Eq. (A-4) to be H(M=3/2+M= 1/2) = (1+1.2up/g) - [HO-A(1+1.2Up/A)m + A] (A-5) H(M=1/2+M=-l/2) = ( 1+18up/g) -l [ H-A( l-18Up/A) m] (A-6) 1/ /u 1 [+A2 H (M=_/2+M=_3/2) = (l+l.2up/g)-1 [Ho-A(l+l.2Up/A) +-in] (A-7) (M=-l/2+=-5/2) H

where A stands for (A'/gp), and A' is the usual hyperfine coupling coefficient 2. DERIVATION OF ul AND U1 The octahedral crystalline field of MgO and CaO splits the orbital level of V2+ to give a singlet F2, lowest lying, and two triplets F4 and F5 as shown in Fig. A-1. 3) (T) 4/. 8Dq 3/2 " ~4 > = (3) (8l2 (T2/) 10Dq x, ~ (1) r2 (A2g) Figo A-io Orbital levels of V2 in MgOo Assuming weak bonding, eigenfunctions of F2, F4, and F5 energy levels are as following Jr > = (2)=/2[ 1.2 > - -2 >] Ir41 > = lo > Ir42> = (8)-1/2[ 41-3 > + 4 I+l> ] J43 > = (8)-1/2[ 4 13 > + 4 - I- > 1 Jr51 > = (2)-l/2[12 > + 1-2 > ] I!52 = (8)-~/2[-4 I-3'> + 47 I > i Ir53 > = (8)-1/2[- 4 13 > *+ I- - > ] 39

The matrix elements of L+, L_, and Lz for L=5 with respect to these states are given in Table A-1. TABLE A- 1 MATRIX ELEMENTS OF L+, L_, AND Lz FOR L = 3 WITH RESPECT TO F2, F4, AND rF ENERGY LEVELS 1r2 > 51 >. Ir52 > r53 > 41 > r42 > r43 > Lz L. LL L. L z L L L L L L L Lz L+ L_ L L+ L_ Lz L+ L_ < r2t o o 0 2 0 0 o 242 0 O O -242 O O O O O O O O O < r 0 0 2 0 0 O 0 2 0 /2 0 0 0 /2 0 O O 0 0O O 3 0 2 < r521 0 0 2 4 0 0 2/2 -1/20 0 0 0 0 O 3/2 0 /12 0 0 0 0 0 /< r53 | O -2 o o 1'/2 O O O O 1/2 0 0 O O 1'/2 O O O -J4/2 0 0 < r411 o o 0 0 0 0 0 0/ 41/2 O 305/2 0 O O O O 0 3 4/2 0 3 2/2 0 <r421 0 0 0 0 ~ J~0/2 1J/2 0 0 0 0 0 0 3 2/2 0 -3/2 0 0 0 0 0 < r431 0~ o o 30/2 0o o o o 0 1/2 0 0 0O o0./2 O O o 3/2 0 0 For instance, according to this Table < F53 |L+ |2 > = -2 J. Figure A-2 shows all possible coupling channels among F2, F4, and F5 levels. Several possible mechanisms contribute to the coefficients u and U in Eq. (A-2). It can be seen that one of the major contributions to u, which lends itself to theoretical calculations, is made by the Zeeman term, BL.H+2pS.H and the spin-orbit coupling term XL5S. We denote this contribution by ul. Similarly, a major contribution to U comes from the Zeeman term and the hyperfine interaction term PL'I and is denoted by U1. Using 4th order perturbation theory, the interaction between these terms and the energy levels of V2+ can be calculated. a. Calculation of ul The factor ul can be obtained by computing the numerical coefficient 40

rL ~,L rs L QA < L L L IL 41 L r S r5 41+

of either pS3HXfS3yHy,'or 5S3H3 in Eq. (A-2). In order to do this, we use the 4-th order perturbation calculations to determine the interactions between the perturbation Hamiltonian V1 = P(L+2S) H + \L.S (A-8) and the orbital triplets.* The coefficient ul can be found by collecting terms of first order in H and 3rd order in S. The term 2S- H in Eq. (A-8) does not contribute anything to ul and hence it can be excluded from V1. The simplified perturbation Hamiltonian can be then written as, vl = PL.H + LD'S (A-9) The 4th order perturbation formula for non-degenerate ground state is X= - V' < rrlVIrj,k > < rjklVlrfm > < r,mlV1rpq > < FpqIlVlr > W4. k,m,q j.p (Ej-Er)(Ej-Er)Er) (EpEr) + ) 1< T'FrrlIVI2,m >12 1< f'j,klVlrr >12 B1m El-Er j,k (Ej-Er)2 2- < JrIVIIr >2, < rrlVI lrjk > < rklV rr(A-l - 1< rrlVi r (A-10) j,k (Ej-Er)3 *It may seem that another source of contribution to u1 arises from 2BS H in first order along with XL-S in second order. However, the result of third order calculation for these perturbation operators is zero.

where Irr > and Er denote the ground level wave function and energy respectively and the prime on Z denotes the omission of the terms with index r from the summation. The last two terms of Eqo (A-10) have vanishing result in our case because < rrlvilrr > = 0 Hence, the 4th order perturbation formula, Eq. (A-10), reduces to W4 = W4 + W4 (A-ll) where W = - X t < rrIVIFj k > < rj,klVIIrm > <Pq,mlVIrpq > <rpqlVIf r> k,m,q j,e,p (Ej-Er)(Er-Er) (Ep-Er) ( A,12) and, TI 7 < rrlVlr,m >12 < rklVlr 2 (A-1 ~,m El-Er jk (Ej-Er)2 Furthermore, we can show that components SXHx, etco, can not be obtained from W" and therefore this part of the perturbation formula is not needed for calculation of ulo To prove this, first we notice that W4 can. mix P2 and P5 levels only because matrix elements of v1 with respect to F2 and all r4 levels are zero. Now, using shift operators 43

L+ = Lx iL S+ = Sx + iSy the perturbation operator vl can be written as v1 = [LzHZ + (L+H_+L_H+) ] + X[LzSz + (L+S_+LS+) ] (A-14),T Using (A-14) in W4 we obtain T! W4 = [I(PHZ+Sz) < r2ILzIrS1 >12 + 1 I H +xS 12 < F2 1LIF52 > < 52L IF2 > 4 - - + 1 I H++XS+l2 < P21LI55 > < Fj1IL+IF2 >]2 (A-15) Replacing the matrix elements in (A-15) by their values from Table A-1 we have W4 = 4[2(HZ+Sz)2+ IH-++S_|2 + I H++S+2 2 (A-16) Expanding (A-16) and making use of relationships SzHz + 1 (S-H++S+H_) S~H and SS + S+S = 2S(S+1) - 2S[ we find, W = 6.4.. [S H(S+l) S] + w (A-17) 44

where w denotes the terms of second 4th power in s and in H, and E52 stands for E5-E2. We notice that W4 does not contain explicitly terms such as S3HX, S3Hy, etco It has rather the form of the 4th term in Eqo (A-2). Therefore, to calculate ul we must apply W4 to the perturbation Hamiltonian v1. But first we consider that S3HX = 1 (s++s_)3( H++H_) S3Hy = 1 (S+-S_)3( H+-_) y 16 Hence, S3Hx+S3Hy+SRHz = i [( S+S+S2+S_S+S_+S2S+)H+' y 8 + (S3+SS_++S SS++S_S)H_ ] + S3Hz (A-18) Replacing S_ in the first parenthesis by S+-2iSy, and S+ in'the second parenthesis by S_+2iSy (A-18) can be written as, SxHx+SHy+SHz = 1 (S3H++S3H_) + S3zH+lR (A-19) 2 + + ( 3 3 3 where R represents the terms not reducible to either S+H+, SH_, or SHz Comparing (A-19) with (A-2) it is easily seen that ul can be found by applying the 4th order perturbation calculations (W4 part) to v1 and determining the coefficient of any term of the right side of Eq. (A-19). However, the first two terms are much easier than the others to deal with and tahus we will do the calculations for SxxHo The perturbation Hamiltonian reveals 45

that this term can only come from operators such as (XLS+) (3) (B LH+) According to Fig. 2-A the only chain through which operator L(4) can interact with the energy levels is < 21L Irg53 > < r531L_lr41 > < rF411L- Ir52 > < r521L-_lrF2 > (A-20) However, since L.H~ can occupy any of the four channels in the chain (A-20), there are effectively four chains similar to (A-20). Using the scheme (A-20) in W4 and taking the factor of 4 into account we obtain 2 S+H+ < r2L_ lr53 > < r531_-ir41 > < r411L-lr52 > < r521L lr2 > E52E42 (A-21) Table A-1 gives the values of the matrix elements r2lLlr53 > = -22 < r531Lr941 > = 3o/2 < r4lLlr 52 > = V30/2 < r521L I2 > = 2 Hence, the coefficient of PS+H+ is obtained from (A-21) to be 240X3/E52E42 and so, 1 240X3 U1 =2X 22 E52E42 or, 12022 u1 = (A-22) E52E142 46

b Calculation of U1 If in the perturbation calculations PLo H is replaced by PLU I we obtain the coefficient U1. However, since as far as operation on the orbital levels is concerned I can be regarded as a constant similar to H the two coefficients u1 and U1 are equal within a constant factor P. That is, U1 = Pul (A-23) 47

I.

APPENDIX B THE SHIFT IN THE g-FACTOR Since in an octahedral field g is isotropic, gx = gy = gz The Zeeman term and spin-orbit coupling term may be written as (with Hl z-axis) H[ = (LzHz+2SzHz) + %L~S As we have seen before since all matrix elements of L with respect to r2 and F4 levels are zero, we have only to deal with F2 and F5 interactions. To the first order W1 = < r2IHlr2 > = 2PSzHz To the second order approximation we have two possible chains, rLzHz~ LzSz and'LzSz PLzHz Thus, W2 = -2 - < 21T LzHzIl > < r51 ILzSzlr2 > E52 w2 = _ 8_ Sz~z E52

Neglecting the higher order approximations we have W1 + W2 = 2SzHz 8~A SzHz= - 8A SzHz E52 E52 Comparing this expression with the Zeeman term in spin Hamiltonian Hs = gPSzHz +.. we find g = (2P 8 \ E52 or g-2 = (B-l) E52 Now from Eq. (A-22), 2 3 = U1E2E42 (B-2) 120 Eliminating \ between (B-l) and (B-2) and use E52/E42 = 5/9 we get, Ui 25 (g-2)3 (B-3) 192 50

REFERENCES 1. J. Eo Wertz, J. L. Vivo and B. Musulin, Phys. Rev, 100, 1810A (1955). 2, Wo Low, Phys. Rev. 101, 1827 (1956). 3. J. E. Wertz, P. Auzins, JOH.E. Griffith and J. W. Orton, Farad Soc, Disc. 26, 66 (1958). 4. WO Low, The New York Acado of Sci. 72, 69 (1958). 5o J. E. Wertz, JO W. Orton and P. Auzins, J. Applo. Physo 33, Suppl. 1, 322 (1962) o 6. G. H. Azarbayejani and C. Kikuchi, Bullo Amn Phys. Soc., Seri II, 8, 344 (1963). 7. A. J. Shuskus, Phys, Rev. 127, 1529 (1962). 8. F. S. Ham, Go Wo Ludwig, G. D. Watkins and H. H. Woodbury, Phys, Rev. Letters 5, 468 (1960) o. 9o J. Lambe and Ro Ager, Rev, Sci. Inst. 30, 599 (1959) o 10. H. H. Woodbury and G. WO Ludwig, Physo Rev. 117, 102 (1960) o 11, M. D. Sturge, Physo Rev. 130, 639 (1963). 12. C. E. Moore, Atomic Energy Levels, Nat. Bur. Stands.,, Circo 467~ 135 Mattarese and C. Kikuchi, J. Physo and Chemo Solids, 1, 117 (1956). 14. M. Dvir and WO Low, Proc. Phys. Soc. (London) 75, 136 (1960). 15o B. Bleaney, Proc, Physo Soc. (London) A73, 939 (1959). 16. F. Koster and H. Statz, Physo Rev, 113, 445 (1959). 51

UNIVERSITY OF MICHIGAN 3III II 02Il227 069Illllllll 3 9015 02227 0691