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Nuclear orientation experiments in paramagnetic, antiferromagnetic and ferromagnetic substances LeBlanc, Marcel Armand Rene Joseph 1959

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NUCLEAR ORIENTATION EXPERIMENTS IN PARAMAGNETIC, ANTIPERROMAGNETIC AND FERROMAGNETIC SUBSTANCES by MARCEL A.R. LeBLANC A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OP PHILOSOPHY i n the Department of Ph y s i c s We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OP BRITISH COLUMBIA January, 1959 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t permission f o r e xtensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood ; t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date P U B L I C A T I O N S Photoneutron Emission from T h 2 3 2 , U 2 3 3 , U 2 3 8 a n d P u 2 3 9 L. Katz, K . G . M c N e i l l , M . LeBlanc and F. Brown C anadian Journal of Physics 35 , 470 (1957) Nuclear Orientation of Mn^4 i n Antiferromagnetic Single Crystals -J . M . Daniels and M . A . R. LeBlanc, Canadian Journal of Physics 36, 638 (195 Nuclear Orientation Experiments with P r ^ 2 and Y b 1 ^ Nuclei J . M . Daniels, J . L . G . Lamarche and M . A . R . LeBlanc Canadian Journal of Physics 36, 997 (1958) Nuclear Orientation of C o 6 " in Antiferromagnetic Cobalt Ammonium Sulphate Single Crystal J . M . Daniels and M . A . R . LeBlanc, to be published in Canadian Journal of Physics G R A D U A T E S T U D I E S Field of Study: Physics Quantum Mechanics G . M . Volkoff Electromagnetic Theory J . H . R . Dempster Nuclear Physics K. C . Mann Low Temperature Physics J . M . Daniels Quantum Theory of Radiation.' F . A . Kaempffer Other Studies: Differential Equations T . E . Hul l Numerical Analysis F . M . C . Goodspeed Transients in Linear Systems E. V . Bohn Servomechanisms E . V . Bohn Faculty of Graduate Studies PROGRAMME OF THE F I N A L O R A L E X A M I N A T I O N FOR T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y of M A R C E L L E B L A N C B . A . Universite'd'Ottawa B . A . University of Sask. M . A . University of Sask. R O O M 3 0 1 , P H Y S I C S B U I L D I N G - M O N D A Y , F E B R U A R Y 9 t h , 1 9 5 9 , at 2 : 3 0 p. C O M M I T T E E ' I N C H A R G E D E A N G . M . S H R U M , Chairman J . M . DANIELS F A T H E R E . A L L E N M . B L O O M C . A . M c D O W E L L R . E . BURGESS F . M . C . GOODSPEED J . B . BROWN F . NOAK.ES External Examiner: J . C , W H E A T L E Y , University of Illinois N U C L E A R O R I E N T A T I O N E X P E R I M E N T S I N P A R A M A G N E T I C , A N T IF E R R O M A G N E T I C A N D F E R R O M A G N E T I C S U B S T A N C E S A B S T R A C T Through the technique of a'diabatic demagnetization of paramagnetic salts substances may be cooled to temperatures of the order of O . I ° K and 0 . 0 1 ° K . At these low temperatures the hyperfine structure interaction can produce an appreciable degree of nuclear orientation. The orientation of an assembly of radio-active nuclei may be detected by measuring the anisotropy in the emission of gamma radiation. By this method we have investiga-ted nuclear orientation in paramagnetic, antiferromagnetic and ferromagnetic substances. : 142 We have studied the nuclear orientation of Pr and 175 Y b introduced as impurities in paramagnetic single crystals of cerium magnesium nitrate. The anisotropy of the 1. 57 M e v -ray of Pr-*- 4 2 was measured as a function of temperature in the range 0. 0 0 3 ° K to 1. 0 ° K both in zero external magnetic f ield and in a f ie ld of 320 gauss parallel to the trigonal crystal axis. Values for the magnetic moment of P r 1 4 2 were assigned from our results for two assumed decay schemes; these are 0. 11 nuciear magnetrons for the spin assignments 2 — % 2 . . » 0 and 0. 15 nuciear magnet-1 2 ons for the spin assignments 2 » 2 s0. Similar experiments 175 were carried out on Y b . Measurements were made in a variety of external magnetic fields up to 700 gauss, and at temperatures as low as 0. 0 0 3 ° K . No anisotropy was observed for the 396 kev » - r a y , nor for the 282 kev JT-ray. T h e most iikely explanation for this result is that the lifetime of the s -emitt ing state is about 1 0 " ^ seconds. This conclusion has since received independent confirmation. vVe have established that nuclear orientation can be produced in antiferromagnetic single crystals. We have explored some of the possibilities and features of nuclear orientation in this class of substances by investigating salts of manganese and cobalt with transition temperatures differing by an order of magnitude. Single crystals of these antiferromagnetic salts were cooled in thermal contact with potassium chrome alum and the anisotropy of the gamma radiation emitted by C o 6 0 and M n 5 4 introduced in the lattice was observed. These measurements show that the hyperfine structure splittings in the antiferromagnetic state are comparable to those found in the paramagnetic state and give i n -dications that nuclear spin relaxation times may be of the order of minutes and hours in antiferromagnetic materials at temperatures beiow 1 ° K . We have attempted to detect nuclear orientation arising from a possible hyperfine structure interaction at the anion in anti-ferromagnetic M n B r 2 4 H 2 0 and M n C l 2 4 H 2 0 . T o detect the nuclear orientation we observed the anisotropy of the gamma rad-iation emitted by B r ^ 2 introduced into M n B r 2 4 H 2 0 and l 1 3 1 in both M n C l 2 4 H 2 0 and M n B r 2 4 H 2 0 . This attempt yielded negative results. The anisotropy of the gamma radiation of CaF® in a ferro-magnetic single crystal of cobalt metal was measured before and after heat treatment of the crystal. The results before heat treat-ment show a significant discrepancy with the data reported by other workers and differ from those found for the heat treated crystal. A qualitative explanation of these results in terms of crystalline stack-ing faults in cobalt metal is presented. vVork was initiated on nuclear orientation in binary ferro-magnetic alloys. The nuclear orientation may arise from the hyper-fine structure interactions which may exist in one or both components of a ferromagnetic binary alloy. The intermetallic compound chosen for special study was M n B i . Although only preliminary and inconclu-54 sive results on the orientation of M n nuclei in this substance were obtained the technique adopted is briefly described. i ABSTRACT Through the technique of a d i a b a t i c demagnetization of paramagnetic s a l t s substances may be cooled t o temperatures o ° of the order of 0 . 1 K and 0 . 0 1 K. At these low temperatures the h y p e r f i n e s t r u c t u r e i n t e r a c t i o n can produce an appreciable degree of nuclear o r i e n t a t i o n . The o r i e n t a t i o n of an assembly of r a d i o a c t i v e n u c l e i may be detected by measuring the aniso-tropy i n the emission of gamma r a d i a t i o n . By t h i s method we have i n v e s t i g a t e d n uclear o r i e n t a t i o n i n paramagnetic, a n t i -ferromagnetic and ferromagnetic substances. 142 We have stud i e d the nuc l e a r o r i e n t a t i o n of P r and 175 Yb 1^ introduced as i m p u r i t i e s i n paramagnetic s i n g l e c r y s t a l s of cerium magnesium n i t r a t e . The anisotropy of the 1 .57 Mev. y 142 « -ray of P r was measured as a f u n c t i o n of temperature i n the range of 0 . 0 0 3 ° K to 1 . 0 ° K both i n zero e x t e r n a l magnetic f i e l d and i n a f i e l d of 320 gauss p a r a l l e l to the t r i g o n a l 142 c r y s t a l a x i s . Values f o r the magnetic moment of P r were assigned from our r e s u l t s f o r two assumed decay schemes, these are 0.11 nuclear magnetons f o r the s p i n assignments 0 2 2 ^ 2 > 0 and 0 . 1 5 nuclear magnetons f o r the s p i n 1 2 assignments 2 —=-> 2 — 0 . S i m i l a r experiments were 175 c a r r i e d out on Yb . Measurements were made i n a v a r i e t y of e x t e r n a l magnetic f i e l d s up t o 700 gauss, and at tempera-o t u r e s as low as 0 . 0 0 3 K. No anisotropy was observed f o r the 396 kev /-ray , nor f o r the 282 kev / - r a y . The most l i k e l y e x p l a n a t i o n f o r t h i s r e s u l t i s t h a t the l i f e t i m e of the - e m i t t i n g s t a t e i s about 10 seconds. This c o n c l u s i o n has since r e c e i v e d Independent c o n f i r m a t i o n . We have e s t a b l i s h e d that nuclear o r i e n t a t i o n can be produced i n antiferromagnetic s i n g l e c r y s t a l s . We have explored some of the p o s s i b i l i t i e s and features of nuclear o r i e n t a t i o n i n t h i s c l a s s of substances by i n v e s t i g a t i n g s a l t s of manganese and coba l t w i t h t r a n s i t i o n temperatures d i f f e r i n g by an order of magnitude. S i n g l e c r y s t a l s of these a n t i f e r r o -magnetic s a l t s were cooled i n thermal contact w i t h potassium chrome alum and the anisotropy of the gamma r a d i a t i o n emitted 60 54 by Co and Mn introduced i n the l a t t i c e was observed. These measurements show t h a t the h y p e r f i n e s t r u c t u r e s p l i t t i n g s i n the a n t i f e r r o m a g n e t i c s t a t e are comparable to those found i n the paramagnetic s t a t e and give i n d i c a t i o n s t h a t nuclear s p i n r e l a x a t i o n times may be of the order of minutes and hours i n a n t i f e r r o m a g n e t i c m a t e r i a l s at temperatures below 1°K. We have attempted t o detect nuclear o r i e n t a t i o n a r i s i n g from a p o s s i b l e h y p e r f i n e s t r u c t u r e i n t e r a c t i o n at the anion i n antiferromagnetic MnBr 2 4 H 2 0 and MnCl 2 4 E^O. To detect the nuclear o r i e n t a t i o n we observed the anisotropy of the gamma r a d i a t i o n emitted by Br® 2 introduced i n t o MnBr 2 4 H 2 0 and I 1 3 1 i n both McCl 2 4 H 2 0 and MnBr 2 4 HgO. This attempt y i e l d e d negative r e s u l t s . fin The anisotropy of the gamma r a d i a t i o n of Co i n a ferromagnetic s i n g l e c r y s t a l of coba l t metal was measured before and a f t e r heat treatment of the c r y s t a l . The r e s u l t s before heat treatment show a s i g n i f i c a n t discrepancy w i t h the i i i data reported by other workers and d i f f e r from those found f o r the heat t r e a t e d c r y s t a l . A q u a l i t a t i v e explanation of these r e s u l t s i n terms of c r y s t a l l i n e s t a c k i n g f a u l t s i n c o b a l t metal i s presented. Work was i n i t i a t e d on nuclear o r i e n t a t i o n i n binary ferromagnetic a l l o y s . The n u c l e a r o r i e n t a t i o n may a r i s e from the h y p e r f i n e s t r u c t u r e i n t e r a c t i o n s which may e x i s t i n one or both components of a ferromagnetic b i n a r y a l l o y . The i n t e r -m e t a l l i c compound chosen f o r s p e c i a l study was MnBi. Although only p r e l i m i n a r y and i n c o n c l u s i v e r e s u l t s on the o r i e n t a t i o n 54 of Mn n u c l e i i n t h i s substance were obtained the technique adopted i s b r i e f l y described. ACKNOWLEDGMENTS I would l i k e i n the f i r s t p l a c e t o express my g r a t i -tude to Dr. J.M. Dan i e l s f o r suggesting the experiments of 142 17S Pr and Yb 1 J and the i n v e s t i g a t i o n of nuclear o r i e n t a t i o n i n ferromagnetic binary a l l o y s , and f o r having c a r r i e d out the 175 t h e o r e t i c a l c a l c u l a t i o n s i n v o l v e d i n the Yb experiment. I am a l s o t h a n k f u l to him f o r many d i s c u s s i o n s of the t h e o r e t i -c a l and experimental aspects of the research reported i n t h i s t h e s i s . Dr. J.L.G. Lamarche, who constructed the major p a r t 142 175 of the equipment, i n i t i a t e d the p r o j e c t on Pr and Yb , and guided me i n my f i r s t experiments, deserves s p e c i a l acknow-ledgment . The work could not have been c a r r i e d through w i t h -out the e x c e l l e n t cooperation of Mr. H. Zerbst i n making a v a i l -able a ready supply of l i q u i d helium, a s s i s t i n g i n the design, c o n s t r u c t i o n and maintenance of apparatus and drawing the f i g u r e s presented i n t h i s t h e s i s . I thank e s p e c i a l l y Mr. J . Lees, the g l a s s blower i n our department, f o r h i s generous cooperation during r e g u l a r working hours as w e l l as a f t e r hours and on week-ends. I wish t o express my a p p r e c i a t i o n t o Dr. W. L i t t l e f o r h i s continued i n t e r e s t i n t h i s research, f o r s t i m u l a t i n g d i s c u s s i o n s and valuable suggestions. I am indebted t o Dr. Myer Bloom e s p e c i a l l y f o r d i s -cussions and c a l c u l a t i o n s of nuc l e a r s p i n r e l a x a t i o n processes i n a n t i f e r r o m a g n e t i c m a t e r i a l s and advice on the p r e p a r a t i o n of t h i s t h e s i s . I am g r a t e f u l a l s o to Mr. H. Schneider f o r h i s help 82 i n the Br experiment as w e l l as f o r the loan of and a s s i s t a n c e i n the o p e r a t i o n of equipment. I wish a l s o t o thank Dr. R.E. Burgess and the Van de G r a f f group f o r the loan of e l e c t r o n i c equipment. I am indebted t o Dr. R. Wiles of the Department of M e t a l l u r g y f o r a l l o w i n g me t o use the f a c i l i t i e s of h i s r a d i o -a c t i v i t y l a b o r a t o r y and to Dr. V. G r i f f i t h s a l s o of the Department of Metallurgy f o r advice on the c r y s t a l s t r u c t u r e of c o b a l t metal. F i n a l l y , I wish t o acknowledge g r a t e f u l l y the f i n a n -c i a l a s s i s t a n c e of the N a t i o n a l Research C o u n c i l of Canada through the award of three Studentships ( 1 9 5 5 - 5 6 , 1 9 5 6 - 5 7 , 1 9 5 7 - 5 8 ) , three summer supplements ( 1 9 5 6 , 1957 , 1958) and a d d i t i o n a l a i d a f t e r the t e r m i n a t i o n of these grants. v i TABLE OF CONTENTS Page INTRODUCTION 1 CHAPTER I A General Remarks on Nuclear O r i e n t a t i o n 8 B General Remarks on the Angular D i s t r i b u t i o n of Gamma R a d i a t i o n 26 CHAPTER I I D e s c r i p t i o n of the Apparatus A The Apparatus f o r A d i a b a t i c Demagnetization . . 31 B Gamma Ray Detect i o n Equipment 35 CHAPTER I I I Nuclear O r i e n t a t i o n Experiments w i t h p rl42 and Y b l 7 5 N u c l e i i n Paramagnetic S i n g l e C r y s t a l s H i s t o r i c a l Remark 40 P a r t I Nuclear O r i e n t a t i o n of P r 1 ^ 2 I n t r o d u c t i o n 42 Experimental Procedure 42 Decay Scheme 44 R e s u l t s . . . . . . . . . 45 D i s c u s s i o n 47 175 P a r t I I Nuclear O r i e n t a t i o n Experiments w i t h Yb ' J I n t r o d u c t i o n 54 Experimental Procedure . . . 54 Decay Scheme 56 R e s u l t s 56 D i s c u s s i o n 57 v i i CHAPTER IV Nuclear Orientation Experiments i n Ant i f e r r o -magnetic Single Crystals <S4 Part I Nuclear Orientation Experiments with Mtr and Co" 0 i n Antiferromagnetic Single Crystals Introduction . . . . . . . . . . . . . . . . . . . 64 Experimental Procedure 67 Decay Scheme of Mn^ and Co^° . . . . . . . 74 MnClrt4 H 0 2 2 General Information 75 Mn52* i n MnCl24 HgO; Results and Discussion . . . . . . . . . . . . . 76 C o 6 0 i n MnCl04 HO; Results and Discussion f . t . . . . . . . . . . . . . 79 MnBr24 ^0 General Information 79 Mn-^ i n MnBrp4; Results and Discussion . . ....... ,. . . . . . .. 80 MnSiF 66 H20 General Information ,. ,. . . . . . . . . 80 Mn5^ i n MnSiFg6H 0; Results and ,. . Discussion . . ? 8l C o 6 0 i n MnSiF 66H 20; Results and Discussion ... . . . . . . . . . . . . . . 83 Co(NH4)2(S04).26 H20 , General Information . . . . 84 fin Co ; Results and Discussion . . . . 86 CoC1^ 6 HO 2 2 General information . 88 Co^° i n C0CI06 Ho0; Results and Discussion 7 t . . . . . ,. .. .. 89 Mn54 i n coCl 26 H20; Results and . Discussion *. . 90 v l i i Part II Nuclear Orientation Experiments with l l 3 1 and B r ° 2 i n Antiferromagnetic Single Crystals Introduction . . . . . 92 Procedure and Results I 1 3 1 i n MnCl_4Ho0 and MnBr 4Ho0 . . . 94 2 2 2 2 B r 8 2 i n MnBr24 H 20 96 Discussion 98 CHAPTER V Nuclear Orientation Experiments i n Ferro-magnetic Substances • Introduction 99 Part I Nuclear Orientation of Co^° i n a Cobalt Metal Single C r y s t a l Experimental Procedure and Results . . . 100 Discussion . . . . . . . . . 105 Part II Nuclear Orientation Experiments with Mn54 i n Ferromagnetic MnBi Introduction I l l Procedure 112 Results and Discussions 115 BIBLIOGRAPHY 118 LIST OF ILLUSTRATIONS i x F i gure T:o ^OMJOVK pa|e;e 1 Vacuum system 51 2 Mutual Inductance Bridge . . 55 3 Block Diagram of Counter Array . .' 55 4 Decay Scheme of P r 1 ^ 2 . 45 5 Anisotropy of the 1 . 5 7 Mev tf-ray of P r 1 ^ 2 . No e x t e r n a l magnetic f i e l d 44 6 Anisotropy of the 1 . 57 Mev / - r a y of P r 1 ^ 2 . An e x t e r n a l magnetic f i e l d of 320 gauss a p p l i e d along the t r i g o n a l a x i s 45 7 Decay scheme of Yb 1"^ 45 8 R e s u l t s w i t h the 396 kev /-ray of Y b 1 7 5 . . . 55 9 R e s u l t s w i t h the 282 kev / - r a y of Y b 1 7 5 . . . 56 10 Decay scheme of M n ^ 75 11 Decay scheme of Co^° 75 12 E x t e r n a l morphology of MnCl 2 4 HgO c r y s t a l . . 13 Anisotropy of Mn 5^ i n MnCl 24HpO, In c r e a s i n g to maximum 75 14 Anisotropy of Mn 5^ i n MnCl p 4 HpO decreasing from maximum . . . . . 7o 15 Anisotropy of Mn 5^ i n MnBr 2 4 HgO 78 16 Anisotropy of Mn 5^ i n MnSiFg6 H"20 79 17 Anisotropy of C o 6 0 i n MnSiF 6 6 H 20 8 2 18 E x t e r n a l morphology of Co(NH^) 2(S0i +) 26H 20 c r y s t a l ' 19 Anisotropy of C o 6 0 i n C o ( N H 4 ) 2 ( S 0 4 ) 2 6 H 2 0 . . 8 5 20 E x t e r n a l morphology of CoCl 0 6 H o0 y L c r y s t a l d . ' X 21 S u s c e p t i b i l i t y versus temperature of CoCl 2 6 HgO 88 22 Anisotropy of Co°° and Mn^ i n CoCl 6 H o 0 89 2 2 23 Decay scheme of B r 8 2 95 24 Decay scheme of I 1 3 1 95 Op 25 ^ -ray spectrum of Br 96 fin 26 Anisotropy of Co i n c o b a l t c r y s t a l (before heat treatment) cooled by one copper s t r i p of 6 cm 2 surface 1 0 0 27 Anisotropy of Co^° i n c o b a l t c r y s t a l (before heat treatment) at "high" temperatures 1 0 1 28 Anisotropy of Co^° i n c o b a l t c r y s t a l ( a f t e r heat treatment) cooled by one copper s t i p of 6 cm surface 1 fin 29 Anisotropy of Co i n c o b a l t c r y s t a l ( a f t e r heat treatment) cooled v i a copper wires w i t h 150 cm surface * 60 30 Anisotropy of Co i n c o b a l t c r y s t a l ( a f t e r heat treatment) cooled v i a a r copper sheet w i t h 200 cm 2 surface INTRODUCTION In t h i s t h e s i s we present the r e s u l t s of experiments i n n u c l e a r o r i e n t a t i o n i n paramagnetic, antiferromagnetic and ferromagnetic substances. S e v e r a l methods have been proposed to o b t a i n o r i e n t e d systems of n u c l e i and extensive experimental r e s u l t s have already been obtained from the a p p l i c a t i o n of these i d e a s . An e x c e l -l e n t review of the methods suggested and the experimental work done has been given by Steenland and Tolhoek (1957). The magnetic h y p e r f i n e s t r u c t u r e method of o r i e n t i n g n u c l e i i n paramagnetic s i n g l e c r y s t a l s has been e s t a b l i s h e d by Daniels et a l (1951) and Gorter et a l (1951) and has proved u s e f u l i n e s t a b l i s h i n g d e t a i l s of n u c l e a r decay schemes, and i n e v a l u a t -i n g n u c l e a r magnetic moments (e.g. Grace and Halban 1952). As p a r t of a program to e x p l o i t the p o t e n t i a l i t i e s of such experiments, we have a l s o made use of t h i s method to o r i e n t 142 17c; Pr and Yb l z > i n cerium magnesium n i t r a t e and i n v e s t i g a t e d the anisotropy i n the emission of the gamma r a d i a t i o n from these i s o t o p e s . 142 Since the decay scheme of Pr i s f a i r l y w e l l known our measurements enabled us to deduce a value f o r the magnetic 142 moment of P r . This p r o j e c t was undertaken c o n c u r r e n t l y at Oxford and the r e s u l t s are i n good agreement. No anisotropy was observed f o r the 396 kev tf-ray, nor f o r the 282 kev i f - r a y 175 which occur i n the decay of Yb . The o r i e n t a t i o n of t h i s 2 isotope was a l s o c o n c u r r e n t l y s t u d i e d by the Oxford group i n the e t h y l s u l p h a t e l a t t i c e and a n i s o t r o p i e s were measured f o r these two gamma ra y s . Our negative r e s u l t s can be explained and r e c o n c i l e d w i t h the p o s i t i v e r e s u l t s obtained by the Oxford -10 group by a s s i g n i n g a l i f e t i m e of the order of 10 seconds to the y'-emitting s t a t e . This c o n c l u s i o n has r e c e n t l y been confirmed by V a r t a p e t i a n (1957) who measured a l i f e t i m e of -9 3.4 x 10 seconds f o r t h i s s t a t e . I t had been suggested t h a t nuclear o r i e n t a t i o n could occur through the hy p e r f i n e s t r u c t u r e i n t e r a c t i o n i n a n t i -ferromagnetic c r y s t a l s (Daunt 1951> Gorter 1951). We undertook to t e s t t h i s suggestion u s i n g M c C l 2 4H20 which has an a n t i -ferromagnetic t r a n s i t i o n at a temperature r e l a t i v e l y h i g h w i t h respect to the temperature range g e n e r a l l y r e q u i r e d f o r nuclear o r i e n t a t i o n . 54 S i n g l e c r y s t a l s of MnCl 24H 20 c o n t a i n i n g some Mn were cooled i n thermal contact w i t h potassium chrome alum. The i n t e n s i t y of the 835 kev gamma ray from Mn^ n u c l e i was observed p a r a l l e l and pe r p e n d i c u l a r to the p r e f e r r e d a x i s of antif e r r o m a g n e t i c alignment. The measurements showed th a t the manganese n u c l e i were i n f a c t a l i g n e d along the p r e f e r r e d a x i s . To f u r t h e r confirm t h i s method of o r i e n t i n g n u c l e i a s i m i l a r experiment was c a r r i e d out usi n g antiferromagnetic MnBr^HgO a l s o c o n t a i n i n g some Mn^. Although an anisotropy 54 i n the emission of the gamma r a d i a t i o n from Mn was observed, the long time r e q u i r e d f o r the anisotropy t o reach a maximum 3 i n these experiments, about 1 0 0 minutes i n the f i r s t case and some 8 hours i n the second, cast some doubt on the value of t h i s method. The slow increase of the anis o t r o p y , hence of the nuclear o r i e n t a t i o n may be a t t r i b u t e d to long nuclear s p i n r e l a x a t i o n times and to slow heat conduction from the c r y s t a l s . Since n u c l e i of d i f f e r e n t ions incorporated i n the l a t t i c e s of the same c r y s t a l may have d i f f e r e n t r e l a x a t i o n times t h i s could provide a method of d i s t i n g u i s h i n g between these pro-go cii cesses. Some Co and Mn-^  was introduced i n a s i n g l e c r y s t a l of MnClg^HgO and the anisotropy of the gamma r a d i a t i o n was observed simultaneously i n separate counting equipment. The 60 measurements showed only a n e g l i g i b l e anisotropy f o r the Co gamma r a d i a t i o n hence no co n c l u s i v e i n f o r m a t i o n on t h i s p o i n t was derived from t h i s experiment. The theory of Van Kranendonk and Bloom (1956) pre-d i c t e d t h a t the nuclear s p i n r e l a x a t i o n time i n a n t i f e r r o -magnetic substances should be s t r o n g l y dependent on the t r a n s i -t i o n temperature. In order to i n v e s t i g a t e t h i s p r e d i c t i o n and to o b t a i n f u r t h e r i n f o r m a t i o n on the general features of nucle a r o r i e n t a t i o n i n antiferromagnetic s i n g l e c r y s t a l s we undertook the f o l l o w i n g s e r i e s of experiment. We studied the o r i e n t a t i o n of Mn^ i n MnSiF ,-6H 0 w i t h a low t r a n s i t i o n temperature of 0 . 1°K, Co i n C o C l 2 6 H 2 0 and Co(NH4) 2 ( S 0 4 ) 2 6 H g 0 w i t h t r a n s i t i o n temperatures at 3 ° K and 0 . 0 8 4 ° K r e s p e c t i v e l y . S i g n i f i c a n t a n i s o t r o p i e s , hence nuclear o r i e n t a t i o n , was observed i n a l l these c r y s t a l s , but the 4 experiments did not provide unambiguous evidence of long nuclear relaxation times. The magnitude of the anisotropics was generally comparable to those observed f o r the same nuclei i n paramagnetic single c r y s t a l s at corresponding . temperatures. This indicates that the hyperfine structure interactions are not appreciably altered i n the a n t i f e r r o -magnetic state. We resumed the attempt to distinguish between the ef f e c t of long nuclear relaxation times and gradual cooling i n these c r y s t a l s . In t h i s second attempt we prepared a 60 single c r y s t a l of MnSiF^6H20 containing some Co as an impurity. The measurements i n t h i s case showed a r e l a t i v e l y large anisotropy and a comparison with the r e s u l t s of the 54 experiment with Mn i n t h i s l a t t i c e indicated a more rapid 60 r i s e of the anisotropy i n the case of Go . Consequently a 54 60 single c r y s t a l of t h i s s a l t containing both Mn and Co was grown. Preliminary measurements with t h i s c r y s t a l seem to indicate that the anisotropies increase at the same rate. The difference In r i s e times observed with each isotope i n the c r y s t a l s separately mounted must then be ascribed to d i f f e r e n t rates of cooling and the contribution of relaxation 60 processes remains obscure. In a s i m i l a r experiment both Co and Mn^ were introduced i n a single c r y s t a l of CoCl 6H 0 . 54 2 2 Measurements showed a large anisotropy for the Mn gamma 60 r a d i a t i o n . However the e f f e c t observed f o r the Co was too small to provide any r e l i a b l e comparison i n the rate of cool-ing of the d i f f e r e n t n u c l e i . r 5 Nuclear magnetic resonance experiments i n para-magnetic and antiferromagnetic substances have shown that i n some cases a hyperfine structure coupling exists i n the cation. This free ion i s expected to be diamagnetic and nor-mally would not give r i s e to a hyperfine structure i n t e r -action. However i n the s o l i d state the electron configuration may be modified i n such a way that the amplitude of the wave function of the unpaired electrons does not vanish at the pos i t i o n of the cation and a hyperfine i n t e r a c t i o n occurs i f the nucleus has non-zero spin. This phenomenon provides a p o s s i b i l i t y of greatly extending the number of nuc l e i that may be oriented by s t a t i c methods. Experiments were undertaken to attempt to detect nuclear orientation a r i s i n g from t h i s i n t e r a c t i o n by measur-ing the gamma ray d i s t r i b u t i o n of radioactive nuclei at these c r y s t a l s i t e s . A single c r y s t a l of MnBrg^H^O contain-82 ing Br was prepared and cooled and the anisotropy of some of the gamma rays occurring i n the decay of t h i s isotope was 131 measured. In si m i l a r experiments I was incorporated as an impurity i n the l a t t i c e of MhBr^H 0 and MnCl 4H g0 single c r y s t a l s and the anisotropy of the 396 kev gamma ray from t h i s nucleus was investigated. No anisotropies were observed i n any of these experiments. . This may be due to long nuclear relaxation times and inadequate cooling. This work i s d i s -cussed i n Chapter IV, Part I I . 6 Measurements on m e t a l l i c c o b a l t c o n t a i n i n g some Co have shown the p o s s i b i l i t y of nuclear o r i e n t a t i o n i n a ferromagnetic m a t e r i a l by the h y p e r f i n e s t r u c t u r e i n t e r a c t i o n (Grace et a l 1955* K h u t s i s h v i l i 1955). We undertook to extend t h i s method and determine whether a hyperfine s t r u c t u r e coupling occurred i n both components of a ferromagnetic binary a l l o y and could produce nuclear o r i e n t a t i o n of both types of n u c l e i . The m a t e r i a l s e l e c t e d f o r t h i s study was the i n t e r -m e t a l l i c compound MnBi. Only the i n i t i a l phases of t h i s p r o j e c t have been completed and no s i g n i f i c a n t e f f e c t s have been observed to date w i t h Mn-^ i n t h i s l a t t i c e . Measure-207 ments on B i ' i n t h i s l a t t i c e have not yet been c a r r i e d out. The experimental approach i s described i n Chapter V, P a r t I I . In p r e p a r a t i o n f o r the above experiment the author sought to acquaint h i m s e l f w i t h v a r i o u s techniques of c o o l i n g m e t a l l i c specimens to temperatures below 0.05°K. To t e s t these d i f f e r e n t techniques the author used a s i n g l e c r y s t a l of co b a l t metal c o n t a i n i n g some Co . The anisotropy of the Co gamma r a d i a t i o n when r e f e r r e d to the reported data served as a thermometric parameter and a measure of the e f f e c t i v e n e s s of the method of c o o l i n g . In the course of t h i s work a s i g n i -f i c a n t discrepancy was observed between the a n i s o t r o p i e s measured at various temperatures of the c o o l i n g agent and the r e s u l t s reported by the Oxford group. Subsequently the c r y s t a l was heat t r e a t e d f o r some 10 minutes at about 1000°C and the measurements repeated. I t was found that the aniso-t r o p i e s corresponding t o v a r i o u s temperatures of the coolant 7 s a l t were ap p r e c i a b l y reduced and now showed much b e t t e r agreement wi t h the Oxford r e s u l t s . These experiments and a t e n t a t i v e e xplanation are presented i n Chapter V, P a r t I. The general method of o r i e n t i n g n u c l e i by the magnetic hy p e r f i n e s t r u c t u r e i n t e r a c t i o n i n paramagnetic, ferromagnetic and antiferromagnetic c r y s t a l s i s reviewed b r i e f l y i n Chapter I. The apparatus used i n our experiments was set up by previous workers i n t h i s l a b o r a t o r y and i s a l s o described b r i e f l y i n t h i s t h e s i s . CHAPTER I GENERAL REMARKS ON NUCLEAR ORIENTATION In nuclear o r i e n t a t i o n experiments we wish to pro-duce a p r e f e r e n t i a l p o p u l a t i o n of c e r t a i n d i r e c t i o n s i n space i n an assembly of n u c l e i . An i s o l a t e d nucleus wi t h s p i n I can be considered t o be i n a (21+1)-fold degenerate s t a t e . I f a weak magnetic f i e l d i s a p p l i e d , say i n the z - d i r e c t l o n so that the degeneracy i s re s o l v e d we have (21+1) independent s t a t e s and we may regard each d i f f e r e n t s t a t e as corresponding . to a d i f f e r e n t o r i e n t a t i o n of the nu c l e a r s p i n w i t h respect to t h i s a x i s . The d i f f e r e n t o r i e n t a t i o n s or magnetic substates are such that the z-component of the s p i n I has a value m c a l l e d the magnetic quantum number which v a r i e s from - I to +1 i n u n i t steps. For an assembly of n u c l e i w i t h random o r i e n t a t i o n the p r o b a b i l i t y Wm of f i n d i n g a nucleus i n a substate m w i l l be — — and w i l l be independent of m. To produce an o r i e n t -21+1 a t i o n of the n u c l e i along a d i r e c t i o n f i x e d i n the l a b o r a t o r y system, we must a l t e r the r e l a t i v e populations of the magnetic substates of the n u c l e i from t h i s normal e q u i l i b r i u m value. Then f o r the assembly of n u c l e i the p r o b a b i l i t y of the va r i o u s substates m w i l l vary w i t h m. When i n an assembly of n u c l e i the p opulations of the v a r i o u s m s t a t e s are no longer equal but equal numbers of nuclear spins are d i s t r i b u t e d among the +m and -m s t a t e s , the nuclear spins are o r i e n t e d i n d i r e c t i o n 8 9 only and not i n sense and we speak of an alignment. However when the p l u s and minus m substates are no longer e q u a l l y populated, there occurs a preponderance of spins i n one d i r e c t i o n over those i n the opposite d i r e c t i o n , the n u c l e i are o r i e n t e d i n both sense and d i r e c t i o n and a net magnetic moment a r i s e s due to the n u c l e a r magnets. The s i t u a t i o n i s then r e f e r r e d to as a nuclear p o l a r i z a t i o n . The word o r i e n t -a t i o n i s used when no d i s t i n c t i o n i s made between p o l a r i z a t i o n and alignment. The methods of producing nuclear o r i e n t a t i o n may be d i v i d e d i n t o s t a t i c ( s t a t i o n a r y ) and dynamic (non-stationary) methods. In the dynamic methods d i f f e r e n c e s i n the p o p u l a t i o n of the various m s t a t e s are e f f e c t e d by causing t r a n s i t i o n s e i t h e r between the v a r i o u s l e v e l s of the n u c l e i or of another system which i n t e r a c t s w i t h the nuclear s p i n system by means of resonance r a d i a t i o n . We are not concerned w i t h t h i s approach to nuclear o r i e n t a t i o n i n t h i s t h e s i s . The general aspects of the subject are reviewed i n the paper by Steenland and Tolhoek ( 1 9 5 7 ) . In the s t a t i c methods the temperature i s lowered u n t i l a considerable d i f f e r e n c e i n the e q u i l i b r i u m populations of the v a r i o u s m s t a t e s occurs. Except f o r some very s p e c i a l cases the energy d i f f e r e n c e s between the d i f f e r e n t m s t a t e s are so small t h a t temperatures obtainable only by a d i a b a t i c demagnetization must be used i n order to produce any appreciable nuclear o r i e n t a t i o n by s t a t i c methods. The energy d i f f e r e n c e s between the v a r i o u s m s t a t e s can r e s u l t from i n t e r a c t i o n between the magnetic moment of 10 n u c l e i and a magnetic f i e l d , and i n t e r a c t i o n of the e l e c t r i c quadrupole moment of n u c l e i and an inhomogeneous e l e c t r i c f i e l d . Thus nuclear o r i e n t a t i o n w i l l depend on the magnetic f i e l d s and inhomogeneous e l e c t r i c f i e l d s present at the nucleus. In order t o use the i n t e r a c t i o n of the nuclear e l e c t r i c quadrupole moment with an inhomogeneous e l e c t r i c 14 / • f i e l d to o r i e n t n u c l e i , g r a d i e n t s of the order of 10 Volts/cm' are r e q u i r e d at a temperature of 0 . 0 1 ° K. Pound (19^9) pointed out that inhomogeneous f i e l d s of t h i s magnitude may be set up by the asymmetric e l e c t r o n cloud which occurs i n c e r t a i n chemical bonds as i s shown by the e l e c t r i c h y perfine s t r u c t u r e s p l i t t i n g s observed. This method has been s u c c e s s f u l l y a p p l i e d (Dabbs et a l 1 9 5 6 ) . The d i r e c t i n t e r a c t i o n between the nuc l e a r magnetic moment and a strong e x t e r n a l magnetic f i e l d (when no stronger f o r c e s act on the n u c l e i ) can i n p r i n c i p l e b r i n g about the re q u i r e d energy d i f f e r e n c e s so t h a t at s u f f i c i e n t l y low temperatures an appreciable d i f f e r e n c e i n e q u i l i b r i u m popul-a t i o n s of the var i o u s m s t a t e s a r i s e s and leads t o nuclear p o l a r i z a t i o n . This approach t o the problem commonly r e f e r r e d t o as the Brute Force Method (Gorter 1 9 3 4 ) , ( K u r t i and Simon 1933) has been a p p l i e d w i t h success (Dabbs 1 9 5 5 ) . I t was not used i n our work and we w i l l not discuss i t f u r t h e r . I t was pointed out tha t magnetic f i e l d s much more powerful than those g e n e r a l l y a v a i l a b l e i n the l a b o r a t o r y are already present at the nucleus of c e r t a i n atomic systems. These magnetic f i e l d s may be of the order of 10^ to 10 gauss and a r i s e from the magnetic moment of the unpaired e l e c t r o n s surrounding the nucleus. The coupling or i n t e r a c t i o n of the nucl e a r magnetic moment wit h i t s surrounding e l e c t r o n s gives r i s e to hyp e r f i n e s t r u c t u r e s i n o p t i c a l and paramagnetic resonance s p e c t r a , and Is r e f e r r e d to as the magnetic hyper-f i n e s t r u c t u r e i n t e r a c t i o n . -It has been suggested t h a t the hype r f i n e s t r u c t u r e i n t e r a c t i o n may cause the de s i r e d d i f f -erences i n the energy l e v e l s corresponding to the various m s t a t e s of the n u c l e i so tha t at temperatures of some hundredths of a degree the lowest energy l e v e l s w i l l be pre-f e r e n t i a l l y populated and an appreciable nuclear o r i e n t a t i o n may be achieved. To o b t a i n n u c l e a r o r i e n t a t i o n however i t i s f i r s t necessary that the magnetic f i e l d of the e l e c t r o n i c moments be i t s e l f o r i e n t e d w i t h respect t o some d i r e c t i o n f i x e d In the l a b o r a t o r y system. The d i r e c t i o n of t h i s f i e l d w i l l depend on the o r i e n t a t i o n of the e l e c t r o n spins and o r b i t s . S e v e r a l mechanisms may determine the o r i e n t a t i o n of the e l e c t r o n i c moments. Among these are the c r y s t a l l i n e e l e c t r i c f i e l d s , e x t e r n a l magnetic f i e l d s and exchange i n t e r a c t i o n (ferromagnetic and a n t i f e r r o m a g n e t i c ) . We di s c u s s each sep a r a t e l y although a l l these f a c t o r s may be present i n an a c t u a l s i t u a t i o n . 12 A C r y s t a l l i n e f i e l d s . The strength and symmetry of the powerful magnetic f i e l d at the p o s i t i o n of the nucleus w i l l depend on the e l e c t r o n i c c o n f i g u r a t i o n . .In an assembly of i s o l a t e d atoms (or ions) t h i s magnetic f i e l d w i l l have random o r i e n t a t i o n . In the s o l i d s t a t e however the neighbouring atoms set up an e l e c t r i c f i e l d c a l l e d the c r y s t a l l i n e f i e l d which may a l t e r the e l e c t r o n i c c o n f i g u r a t i o n and a l s o i n f l u e n c e the o r i e n t -a t i o n of the e l e c t r o n i c spins and o r b i t s . Due to the r e g u l a r arrangement of the atoms i n c r y s t a l s t h i s c r y s t a l l i n e f i e l d may have d i r e c t i o n a l p r o p e r t i e s . Hence not only w i l l the d i f f e r e n t r e l a t i v e o r i e n t a t i o n s of the nucleus and atomic moment have d i f f e r e n t energies b u t . d i f f e r e n t o r i e n t a t i o n s of the nucleus and e l e c t r o n i c system as a whole wi t h respect to some c r y s t a l l i n e d i r e c t i o n w i l l have d i f f e r e n t energies. The behaviour of a paramagnetic i o n under the i n f l u e n c e of a c r y s t a l l i n e inhomogeneous e l e c t r i c f i e l d has been t r e a t e d by s e v e r a l authors and i t has been shown that the energy l e v e l s of a paramagnetic i o n i n a c r y s t a l possess-i n g a x i a l symmetry about the z - a x l s may be represented by the f o l l o w i n g Hamiltonian. (Abragam and Pryce 1 9 5 1 , Bleaney and Stevens 1 9 5 3 ) . = D [ s z 2 - I S (S+ljj + A S Z I Z + B ( S X I X + S y I y ) .... (1) T h i s Hamiltonian i s formulated i n terms of an e f f e c t i v e e l e c t r o n s p i n S defined by s e t t i n g the m u l t i p l i c i t y of the e l e c t r o n i c l e v e l s equal to 2S + 1. I i s the n u c l e a r s p i n and the A and B terms represent the hype r f i n e s t r u c t u r e s p l i t t i n g due t o the i n t e r a c t i o n between the nuclear mag-n e t i c moment and the magnetic f i e l d of the u n f i l l e d e l e c t r o n s h e l l s . The term i n D represents the s p l i t t i n g of the e l e c t r o n i c l e v e l s by the c r y s t a l l i n e e l e c t r i c f i e l d . We assume tha t no e x t e r n a l magnetic f i e l d i s present and we neglect terms due t o the nucl e a r quadrupole i n the c r y s t a l l i n e e l e c t r i c f i e l d g r a d i e n t . To i l l u s t r a t e the i n f l u e n c e of the c r y s t a l l i n e environment i n terms of t h i s Hamiltonian we consider two s p e c i a l s i t u a t i o n s . In the f i r s t the c r y s t a l l i n e f i e l d s lead d i r e c t l y to nuclear o r i e n t a t i o n by causing a p r e f e r r e d d i r e c t i o n of the e l e c t r o n i c angular momentum. In the second the c r y s t a l l i n e f i e l d s lead i n d i r e c t l y t o nuc l e a r o r i e n t a t i o n through an a n i s o t r o p i c h y p e r f i n e s t r u c t u r e I n t e r a c t i o n . i.J The manganous i o n Mn + + i n the f r e e s t a t e accord-i n g t o Hund's r u l e i s i n a 85/2 s t a t e a n d should show no hyper f i n e s t r u c t u r e . According to Abragam and Pryce (1951) the h y p e r f i n e s t r u c t u r e may be due to an admixture of the ground s t a t e and higher s t a t e s w i t h unpaired s - e l e c t r o n s . The hyper f i n e s t r u c t u r e i s t h e r e f o r e i s o t r o p i c and A = B i n the Hamiltonian given above. I f the e l e c t r o n i c angular momentum behaves l i k e a f r e e s p i n no p r e f e r r e d d i r e c t i o n f o r the nu c l e a r s p i n w i l l e x i s t . In such a case no nucl e a r o r i e n t a t i o n could be expected at any temperature. 14 Although the hyperfine structure coupling i s p r a c t i -c a l l y unconnected with o r b i t a l electronic motion, and hence independent of the p a r t i c u l a r c r y s t a l l i n e surrounding, i t has been found that the c r y s t a l l i n e environment may s t i l l lead to a preferred d i r e c t i o n for the elec t r o n i c angular momentum and thus to nuclear orientation along t h i s preferred d i r e c t i o n . This s i t u a t i o n may be v i s u a l i z e d i n the following way. The asymmetric c r y s t a l l i n e f i e l d w i l l cause a d i s t o r t i o n of the in d i v i d u a l electron o r b i t s so that the charge cloud instead of being s p h e r i c a l l y symmetric may become s l i g h t l y elongated or contracted along a c r y s t a l axis. The dipole-dipole energy of the spins varies with t h e i r orientation with respect to the axis of t h i s d i s t o r t i o n , and the orientation of the r e s u l t -ant spin of the ion with respect to t h i s c r y s t a l axis w i l l have d i f f e r e n t energies. The 2S + 1 spin states w i l l no longer be equally probable. This i s referred to as the f i n e structure or Stark s p l i t t i n g and i s represented by the D term i n the Hamiltonian given above. This Stark e f f e c t causes a s p l i t t i n g of the 6-fold degenerate electronic ground state of Mn + + into 3 doublets. I t has been found that i n three Mn + + s a l t s investigated by paramagnetic resonance.: manganese f l u o s i l i c a t e , manganese ammonium sulphate and manganese bismuth n i t r a t e (Bleaney and Ingram 1951), (Trenam 1953), the o v e r a l l Stark s p l i t t i n g i s of the order of 0.3°K. This means that below o about 0.05 K even i n the absence of an external magnetic f i e l d , only the lowest l e v e l w i l l be appreciably populated. This lowest state i s S z = + 5/2 fo r the f l u o s i l i c a t e and the double n i t r a t e ( < 0) and predominantly S z = + 1/2 for the Tutton s a l t (D>0). The i s o t r o p i c magnetic hyperfine coupling i s of the same order as the Stark s p l i t t i n g so that alignment of the electron spins i s accompanied by alignment of the nuclear spins. i i ) In the case where S = 1/2 the term i n D vanishes. This means that the c r y s t a l l i n e f i e l d has no direc t effect on the spin. There Is however another mechanism which can al i g n the electronic moment and lead to nuclear alignment. For ions i n the iro n group the 3d electrons are i n the outer s h e l l and consequently they are strongly exposed to the e l e c t r i c f i e l d of the neighbouring water dipoles. The influence of the e l e c t r i c f i e l d on the or b i t s of the 3d electrons may be larger than the spin-orbit coupling. The c r y s t a l f i e l d i n a large number of these s a l t s arises from an octahedron of water molecules surrounding the magnetic ion and i t w i l l have a symmetry dictated by the c r y s t a l structure. The o r b i t s of the electrons may then be more strongly d i s -torted i n certa i n planes than i n others. This "locking into" the f i e l d of the neighbours of the o r b i t a l motion may greatly reduce the o r b i t a l moment. It i s then said that the o r b i t a l angular momentum i s "quenched", i . e . the expectation value of the components of the o r b i t a l angular momentum L z , Ly, L x i s zero. However the spin-orbit coupling cannot be completely neglected. When It i s taken into account and combined with the influence of the c r y s t a l l i n e f i e l d on the o r b i t a l angular 16 momentum In p e r t u r b a t i o n c a l c u l a t i o n s two general consequences u s u a l l y f o l l o w . F i r s t the lowest l e v e l of the i o n may be c h a r a c t e r i z e d by an e f f e c t i v e s p i n S 1 = 1/2 and a two-fold degeneracy remains. Second, the quenching of the o r b i t a l angular momentum i s p a r t i a l l y removed and the expectation values of L z , Ly, L x are no longer zero. Indeed the expect-a t i o n value f o r L z i s g e n e r a l l y d i f f e r e n t from t h a t of L x and Ly. Further the magnitude of the f i e l d which the unpaired e l e c t r o n s produce at the nucleus v a r i e s w i t h the o r i e n t a t i o n of the e l e c t r o n s p i n S z. The e l e c t r o n which produces t h i s f i e l d at the nucleus i s to be considered as d i s t r i b u t e d i n space according to some wavefunction. I t i s the nature of t h i s wavefunction, i . e . the shape of the " e l e c t r o n c l o u d " , which i s r e s p o n s i b l e f o r the v a r i a t i o n with o r i e n t a t i o n of the f i e l d at the nucleus, and the shape and o r i e n t a t i o n of t h i s e l e c t r o n cloud i s determined by the c r y s t a l l i n e p o t e n t i a l . This means tha t the magnitude of the magnetic f i e l d at the p o s i t i o n of the nucleus w i l l be stronger i n the d i r e c t i o n of some c r y s t a l a x i s than i n any other d i r e c t i o n . The hyperfine s t r u c t u r e i n t e r a c t i o n i s then a n i s o t r o p i c , i . e . A B i n the Hamiltonian given above and the d i r e c t i o n and magnitude of the anisotropy i s l i n k e d to the c r y s t a l s t r u c t u r e . In f a c t i t has been found i n a number of s a l t s i n v e s t i g a t e d by paramagnetic resonance that the hy p e r f i n e s t r u c t u r e i s exceedingly a n i s o t r o p i c (Bleaney 1950). 17 Although we have r e s t r i c t e d our d i s c u s s i o n t o two s p e c i a l cases i n some a c t u a l instances both a Stark s p l i t t i n g and an a n i s o t r o p i c h y p e r f i n e s t r u c t u r e may be present. In such cases these two mechanisms w i l l determine the o r i e n t -a t i o n of the e l e c t r o n i c moment and hence of the nuclear s p i n . In p r i n c i p l e when the e f f e c t i v e e l e c t r o n i c s p i n S, the nuclear s p i n I , and the values of the constants D, A, and B are known, the energy d i f f e r e n c e s of the various l e v e l s may be c a l c u l -ated. Such c a l c u l a t i o n s may be extremely complicated and a d e t a i l e d d i s c u s s i o n has been given by Bleaney ( 1 9 5 1 b ) . The method of nuc l e a r alignment through the i n f l u e n c e of the c r y s t a l l i n e f i e l d i s known as Bleaney's Method (Bleaney 1 9 5 1 a ) . B E x t e r n a l Magnetic F i e l d At temperatures of a few hundredths of a degree a small magnetic f i e l d of a few hundred gauss should completely p o l a r i z e the e l e c t r o n i c magnetic moments since kT i s much smaller than the s p l i t t i n g of the e l e c t r o n i c s p i n s t a t e s i n the magnetic f i e l d . I f a hype r f i n e s t r u c t u r e coupling i s present and the temperature i s low enough so that the thermal energy kT i s of the order of the energy d i f f e r e n c e s c o r r e s -ponding t o d i f f e r e n t o r i e n t a t i o n s of the n u c l e i i n the magnetic f i e l d of the e l e c t r o n s , the lower l e v e l s w i l l be p r e f e r e n t i a l l y occupied and an appreciable n u c l e a r p o l a r i z a t i o n w i l l occur. This method was suggested independently by Gorter and Rose and i s known as the magnetic hyp e r f i n e s t r u c t u r e p o l a r i z a t i o n method (Gorter 1 9 4 8 , Rose 1 9 4 9 ) . 18 In the i d e a l case the e l e c t r o n i c moments to be p o l a r i z e d by the e x t e r n a l magnetic f i e l d should behave l i k e f r e e s p i n s . In p r a c t i c e however a p r e f e r r e d d i r e c t i o n f o r the e l e c t r o n i c moments already e x i s t s . This as we have pointed out above may be due to a Stark s p l i t t i n g i n the c r y s t a l l i n e f i e l d and may a r i s e from the anisotropy of the i n t e r a c t i o n of the e l e c t r o n i c s p i n and nucleus system w i t h the c r y s t a l l i n e f i e l d . The method w i l l then be most e f f e c t i v e when the magnetic f i e l d can be a p p l i e d p a r a l l e l to the a x i s of p r e f e r r e d d i r e c t i o n already present i n the c r y s t a l . The Hamiltonian f o r the energy l e v e l s of the ions now has the form: W = 9nPH«V J i W x + V y > + D[ S 2 " f ( S + 1] + A S* ^ V x + S y V .... (2) where g / ; and g^ are the values of g, the spectroscopic s p l i t t i n g f a c t o r p a r a l l e l and per p e n d i c u l a r to the z - a x i s , f3 i s the Bohr magneton, H zHyH x are the components of the e x t e r n a l magnetic f i e l d i n the z,y,x d i r e c t i o n s r e s p e c t i v e l y . The terms i n D, A and B have the same meaning as i n equation ( I ) . We again assume tha t c o n t r i b u t i o n s from the i n t e r a c t i o n of the e l e c t r i c quadrupole moment w i t h the e l e c t r i c f i e l d g r adient are n e g l i g i b l e . To i l l u s t r a t e v a rious aspects of t h i s method we d i s -60 cuss b r i e f l y the p o l a r i z a t i o n of Co n u c l e i i n cerium magnesium n i t r a t e (Ambler et a l 1 9 5 3 , Wheatley et a l 1 9 5 5 ) . Trenam (1953) i n v e s t i g a t e d the paramagnetic resonance of C o + + i n the isomorphous c r y s t a l s of bismuth magnesium n i t r a t e . For the Co"M" i o n i n t h i s l a t t i c e the e f f e c t i v e s p i n i s S' = \ hence the D term vanishes i n the Hamiltonian given i n equation ( 2 ) . There are two C o + + ions i n the u n i t c e l l . fin Assuming t h a t the nuclear magnetic moment of Co i s 3 - 5 nuclear magnetons and 1=5 Wheatley et a l (1955) have c a l c u l -ated the constants i n the Hamiltonian from Trenam's data f o r C o 5 9 (Trenam 1 9 5 3 ) . For 3/8 of the ions g j j = 7 . 2 9 , gj_= 2 . 3 4 A/k = 0 . 0 2 l 6°K, B/k = 0 .00008°K whi l e f o r 5/8 of the ions the constants are g = 4 . 1 1 , g = 4 . 3 8 , A/k = 0 .0065°K, B/k = 0 .00786°K The r a t i o 3^5 f o r the two types of ions was found to f i t the nuclear o r i e n t a t i o n data b e t t e r than the r a t i o of l . : 2 given by Trenam ( 1 9 5 3 ) • We note that f o r 3/8 of the ions the h y p e r f i n e s t r u c t u r e i s extremely a n i s o t r o p i c , hence some nuclear a l i g n -ment would be expected i n the absence of an e x t e r n a l f i e l d as i n Bleaney's Method. This was observed by Ambler et a l ( 1 9 5 3 ) . For these ions the h y p e r f i n e I n t e r a c t i o n i s aniso-t r o p i c w i t h i t s maximum i n the z - d i r e c t i o n . Due t o t h i s f a c t o r and the r e l a t e d l a r g e value of g along t h i s a x i s , when a small e x t e r n a l f i e l d i s a p p l i e d i n t h i s d i r e c t i o n we should expect a considerable degree of nuclear p o l a r i z a t i o n i n t h i s set of ions at low temperatures. However f o r 5/8 of the ions the h y p e r f i n e s t r u c t u r e i s almost i s o t r o p i c and i n zero f i e l d no nuclear alignment 20 would then occur i n these ions at any temperature. More a c c u r a t e l y , since B i s s l i g h t l y g r e a t e r than A, the h y p e r f i n e i n t e r a c t i o n i s somewhat a n i s o t r o p i c w i t h the maximum i n the x-y plane. This means tha t i n zero f i e l d these n u c l e i w i l l show a small degree of alignment i n t h i s plane; hence w i l l a l i g n p e r p e n d i c u l a r l y t o the other set of n u c l e i . The o v e r a l l s i t u a t i o n consequently does not commend i t s e l f f o r an a p p l i -c a t i o n of Bleaney's Method. But the l a r g e g ^ value f o r t h i s set of ions make them very s u i t a b l e f o r p o l a r i z a t i o n by a r e l a t i v e l y s m a ll magnetic f i e l d . With a small f i e l d , say 100 gauss, i n the z - d i r e c t i o n the presence of the B term i n the h y p e r f i n e i n t e r a c t i o n w i l l tend to mix the nuclear magnetic substates and reduce the nuclear p o l a r i z a t i o n . This e f f e c t w i l l become n e g l i g i b l e as l a r g e r f i e l d s are a p p l i e d . Never-t h e l e s s the h y p e r f i n e s t r u c t u r e i n t e r a c t i o n of t h i s set of ions w i l l not as r e a d i l y lead to n u c l e a r p o l a r i z a t i o n as the other group since the A term (and hence the magnetic f i e l d at the nucleus) i s a p p r e c i a b l y s m a l l e r . The energy l e v e l s f o r the two types of Co ions i n cerium magnesium n i t r a t e w i t h a p o l a r i z i n g f i e l d of 280 gauss i n the z - d i r e c t i o n have been c a l -c u l a t e d by Wheatley et a l and are depicted i n t h e i r paper (Wheatley et a l 1955). This group observed a maximum aniso-tropy of the emitted gamma r a d i a t i o n of 0.45 at the lowest temperatures u s i n g a p o l a r i z i n g f i e l d of 200 gauss. I n c o r p o r a t i n g the C o + + ions i n magnesium s i t e s i n the l a t t i c e of cerium magnesium n i t r a t e i n s u r e s that very 21 i n t i m a t e thermal contact w i t h a c o l d r e s e r v o i r i s e s t a b l i s h e d . C r y s t a l s of t h i s s a l t are p a r t i c u l a r l y s u i t a b l e as a r e f r i g e r -a t o r f o r the C o + + ions f o r two reasons. F i r s t , s ince the nuclear moment of s t a b l e cerium i s zero no hyp e r f i n e s t r u c t u r e i n t e r a c t i o n i s present and d i p o l e - d i p o l e i n t e r a c t i o n s are very weak due to the l a r g e distances between the cerium ions i n t h i s very d i l u t e d s a l t . Thus very low temperatures can be a t t a i n e d by a d i a b a t i c demagnetization from moderate values of H/T. Indeed these c r y s t a l s have been cooled t o temperature of 0 .00308°K (Daniels and Robinson 1 9 5 3 ) . Secondly, the g-values of the Co i o n are h i g h l y a n i s o t r o p i c . The g-value i n the d i r e c t i o n of the c r y s t a l l i n e t r i g o n a l a x i s i s gjj= 0 . 2 5 and the g-value i n the plane perp e n d i c u l a r t o the t r i g o n a l a x i s i s i s o t r o p i c and equal to g j _ = 1.84 (Cooke et a l 1 9 5 3 ) . This means that w i t h a p o l a r i z i n g f i e l d a p p l i e d along g no appreciable temperature r i s e w i l l r e s u l t . This d i r e c t i o n a l s o corresponds t o th a t most e f f e c t i v e f o r p o l a r i z i n g ++ the Co ions and n u c l e i . C) Exchange Interactions.: I t i s w e l l known t h a t exchange i n t e r a c t i o n s may lead t o p a r a l l e l and a n t i p a r a l l e l alignment of the e l e c t r o n i c magnetic moments. When the exchange i n t e r a c t i o n i s p o s i t i v e i t r e s u l t s i n a p a r a l l e l o r i e n t a t i o n of spins and we speak of ferromagnetism, i n the case of an a n t i p a r a l l e l alignment the i n t e r a c t i o n i s negative and we speak of antiferromagnetism. These exchange f o r c e s may be a n i s o t r o p i c i n which case the p r e f e r r e d d i r e c t i o n of the e l e c t r o n i c moments w i l l not be 22 determined s o l e l y by the c r y s t a l l i n e e l e c t r i c f i e l d , i ) Antiferromagnetism.: In a number of c r y s t a l s there i s a c e r t a i n c r i t i c a l temperature c a l l e d the Neel temperature below which the atomic magnetic moments are arranged a l t e r n a t e l y p a r a l l e l and a n t i -p a r a l l e l due t o a negative exchange i n t e r a c t i o n between near-est neighbours. I t i s thus p o s s i b l e t o d i v i d e the magnetic ions i n t o two equivalent i n t e r l o c k i n g s u b - l a t t i c e s (or more) i n such a way tha t ions of one s u b l a t t i c e a l l p o i n t i n a given d i r e c t i o n and are immediately surrounded by ions of the other s u b l a t t i c e which p o i n t i n the opposite d i r e c t i o n . For each such s u b l a t t i c e the magnetization approaches s a t u r -a t i o n as T-> 0, but since the s u b l a t t i e e s are magnetized i n opposite d i r e c t i o n s the r e s u l t a n t magnetization of the system vanishes. Thus below the Neel temperature a c e r t a i n degree of alignment of e l e c t r o n i c moments w i l l e x i s t which may lead to a nuclear alignment through magnetic hy p e r f i n e coupling when the substance i s s u f f i c i e n t l y cooled, as suggested independ-e n t l y by Gorter (1951) and Daunt (1951). In the i d e a l case only two s u b - l a t t i c e s w i t h a p r e f e r r e d d i r e c t i o n of alignment i s d e s i r e d , however i t has been found th a t i n c e r t a i n sub-stances s e v e r a l sets of s u b l a t t i e e s are present w i t h t h e i r p r e f e r r e d a x i s of alignment i n d i f f e r e n t d i r e c t i o n s . E x c e l -l e n t review a r t i c l e s on antiferromagnetism have been pre-sented r e c e n t l y ( L i d i a r d 1954, Nagamiya et a l 1955). Above the Neel temperature the moments may be d i s -ordered but more g e n e r a l l y anisotropy f o r c e s i n the c r y s t a l s 23 w i l l c o n s t r a i n the moments to p o i n t along c e r t a i n c r y s t a l l o -graphic d i r e c t i o n s . These d i r e c t i o n s may c o i n c i d e w i t h the p r e f e r r e d a x i s or axes of antiferromagnetic alignment as i n cob a l t ammonium sulphate and manganese f l u o s i l i c a t e . This i s p a r t i c u l a r l y evident i n the alignment of Mn-' i n manganese f l u o s i l i c a t e reported i n t h i s t h e s i s , i i ) Ferromagnetism.: In a ferromagnetic substance i f the unpaired e l e c t r o n s can be considered as s u f f i c i e n t l y l o c a l i z e d so that an appre-c i a b l e h y p e r f i n e s t r u c t u r e s p l i t t i n g can be expected then the s i t u a t i o n i s again analogous t o the paramagnetic and a n t i f e r r o -magnetic cases. In a ferromagnetic substance below a c r i t i c a l temperature c a l l e d the Curie temperature the p o s i t i v e exchange i n t e r a c t i o n w i l l cause a p a r a l l e l o r i e n t a t i o n of the e l e c t r o -n i c moments i n a domain. I f a p r e f e r r e d o r i e n t a t i o n of the domains e x i s t s an alignment of the n u c l e i w i t h respect to t h i s a x i s can be expected at temperatures of the order of 0.1° K and 0.01° K. In an e x t e r n a l magnetic f i e l d which i s high enough to cause s a t u r a t i o n , the domains w i l l p o i n t i n the same d i r e c t i o n and a p o l a r i z a t i o n of the n u c l e i may occur at s u i t a b l e temperatures. In the absence of an e x t e r n a l magnetic f i e l d the anisotropy energy of the domains In a s i n g l e c r y s t a l may be of such a nature t h a t s e v e r a l p r e f e r r e d d i r e c t i o n s f o r the o r i e n t a t i o n of the domains e x i s t along d i f f e r e n t axes i n the c r y s t a l . Such substances are not very s u i t a b l e f o r nuclear 24 o r i e n t a t i o n . Nevertheless r e c e n t l y nuclear o r i e n t a t i o n experiments have been s u c c e s s f u l l y performed i n such m a t e r i a l s u s i n g an e x t e r n a l magnetic f i e l d to saturate the ferromagnetic moments (Scurlock 1 9 5 8 ) . In cases where the exchange i n t e r a c t i o n i s large (e.g. when an antiferromagnetic of ferromagnetic ordering occurs) the nuc l e a r o r i e n t a t i o n can no longer be discussed s o l e l y i n terms of the energy l e v e l s of an i s o l a t e d atom or io n as represented by the s p i n Hamiltonian given above. We must then introduce terms of the form J S^, where J i s a parameter p r o p o r t i o n a l t o the magnitude of the i n t e r a c t i o n s , and S"1" and are the s p i n v e c t o r s of the i t h and j t h i o n . When J ) ) A , the e l e c t r o n s p i n performs many t r a n s i -t i o n s between d i f f e r e n t m s t a t e s i n a time and the e f f e c t i v e magnetic f i e l d at the nucleus may be s i g n i f i c a n t l y m o dified. Since i n t h i s t h e s i s we only present some e x p e r i -mental data on nuclear o r i e n t a t i o n i n such environments we w i l l not attempt to di s c u s s t h i s d i f f i c u l t t o p i c i n gre a t e r d e t a i l . In the above d i s c u s s i o n we have considered separately three f a c t o r s which may a l i g n the e l e c t r o n i c moments and through the hy p e r f i n e s t r u c t u r e i n t e r a c t i o n or through an e f f e c t i v e magnetic f i e l d at the nucleus b r i n g about a nuclear o r i e n t a t i o n . In an a c t u a l instance some combination of these mechanisms may be o p e r a t i v e . An example mentioned was the 60 experiment w i t h Co i n cerium magnesium n i t r a t e where nuclear o r i e n t a t i o n occurred i n zero f i e l d by Bleaney's Method. The 25 o r i e n t a t i o n was enhanced and nuclear p o l a r i z a t i o n produced by the a p p l i c a t i o n of an e x t e r n a l magnetic f i e l d . This i s 142 a l s o the case i n the o r i e n t a t i o n of P r reported i n t h i s t h e s i s . We have a l s o r e f e r r e d to our experiment w i t h manganese f l u o s i l i c a t e where the nu c l e a r alignment by Bleaney's method merges i n t o n uclear alignment by antiferromagnetic ordering as proposed by Daunt and Gorter. 2 6 General Remarks on the Angular D i s t r i b u t i o n of Gamma Radiation.: The o r i e n t a t i o n of an assembly of n u c l e i may be detected i n s e v e r a l ways.: f o r example, by measuring the aniso-tropy of emission of <^  , | 3 and ^ rays or by measuring the d i f f e r e n t i a l absorption cross s e c t i o n of p o l a r i z e d neutrons. By f a r the e a s i e s t technique and the one we have used i n our research i s the d e t e c t i o n of the gamma rays emitted by some r a d i o a c t i v e i s o t o p e s . We r e s t r i c t our remarks to t h i s method. Since gamma r a d i a t i o n c a r r i e s i n t e g r a l u n i t s of angular momentum the wave f u n c t i o n of the r a d i a t i o n w i l l not be s p h e r i c a l l y symmetric w i t h respect to the nucleus. When a nucleus makes a r a d i a t i v e t r a n s i t i o n i n which the angular momentum I and i t s component m along an a x i s of alignment change by A 1 and A m r e s p e c t i v e l y , the p o l a r diagram of the r a d i a t i o n w i l l depend on the values of I , m, A I and ftm, For an assembly of n u c l e i w i t h random o r i e n t a t i o n the r a d i a t i o n w i l l be i s o t r o p i c . I f , however, some o r i e n t a t i o n s are pre-f e r e n t i a l l y populated the r e s u l t i n g r a d i a t i o n may no longer be i s o t r o p i c and the p o l a r diagram w i l l depend on the r e l a t i v e p opulations of the v a r i o u s m s t a t e s and the m u l t i p o l e order of the t r a n s i t i o n . The r a d i a t i o n emitted by e x c i t e d n u c l e i can be c l a s s i f i e d according to the angular momentum c a r r i e d away by the photon, and the p a r i t y changes i n v o l v e d i n the t r a n s i -t i o n . I f the angular momentum c a r r i e d away from the nucleus i s Ji then the r a d i a t i o n i s s a i d t o be of m u l t i p o l e order 2 The p o l a r i z a t i o n of the electromagnetic wave depends on the 27 nature of the r a d i a t i o n which can be e i t h e r e l e c t r i c or mag-n e t i c . The nature of the r a d i a t i o n depends on both the m u l t i -p o l a r i t y and the p a r i t y change i n v o l v e d i n the t r a n s i t i o n . Since no attempt was made In t h i s research t o study the p o l a r i -z a t i o n of the r a d i a t i o n , we w i l l not di s c u s s t h i s t o p i c f u r -t h e r . The angular d i s t r i b u t i o n of the r a d i a t i o n depends only on the m u l t i p o l e order and not on the p a r i t y . The necessary formulae may be developed s t a r t i n g from the wave f u n c t i o n f o r the photon and u s i n g the r u l e s of a d d i t i o n of angular moments (Daniels 1957). the gamma e m i t t i n g s t a t e w i l l be determined by the i n i t i a l r e l a t i v e p o p u l a t i o n of the m-states of the parent nucleus and a l l the t r a n s i t i o n s by which the parent nucleus transforms to the gamma e m i t t i n g s t a t e . To i l l u s t r a t e the approach we con-s i d e r one of the simplest cases where there i s emission of a beta ray t o an e x c i t e d s t a t e of the daughter nucleus followed by a gamma ray d e - e x c i t a t i o n t o the ground s t a t e as shown sc h e m a t i c a l l y i n the diagram. The r e l a t i v e p o pulations of the v a r i o u s m-states of We assume t h a t the sp i n of the various l e v e l s and the angular momentum c a r r i e d away i n the beta and gamma t r a n s i t i o n s are a l l known and proceed as f o l l o w s : F i r s t l y , we determine the p o l a r diagram f o r the l i m i t i n g case where a l l r a d i o a c t i v e parent n u c l e i are e f f e c t -i v e l y a l i g n e d ; i . e are In a d e f i n i t e J . n u c l e a r substate M. We can w r i t e at once.: 28 where 1 J - j , 1 < j < r \ J + j J . The cf„ Jl J 2 are the Wigner or Clebsch-Jordan c o e f f i c i e n t s that can be evaluated from the t a b l e s given i n Condon and Sh o r t l e y ( 1 9 5 3 ) . Now we can evaluate f o r a l l m th a t appear i n t h i s summation. J J J , M - F N O 3 ' (2) where the ^  . are the components of the normalized wave func-t i o n s f o r the photons of m u l t i p o l e order 2 J . Should the t r a n s i -t i o n i n v o l v e a mixture of r a d i a t i o n s , a l l t h e i r wave f u n c t i o n s are considered and the r e l a t i v e importance of the r a d i a t i o n s of d i f f e r e n t orders i s taken i n t o account by i n t r o d u c i n g weigh-a a a i n g f a c t o r s <=<, (3 and V where o<+^+"Jf+...=l. Returning now to the case of a pure m u l t i p o l e t r a n s i -t i o n the p r o b a b i l i t y of emission along the angle 6 between the c r y s t a l a x i s and the d i r e c t i o n of emission i s obtained by <\TJ M * \U M forming the product j _ ± -x a n d i n t e g r a t i n g t h i s l a t t e r expression over a l l space but not over the angle 6 . Thus we f i n d : IM .... IIT,"^,"!"' SI Kt+ir>x m i t n , Mmm, ' " ^ ^ o J ^ . . (3) 3 The eigenfunctions (3- and Cp • form othonormal sets orthogonal to each other so th a t f i n a l l y . : .... (4) This i s an expression of the form.: IM ( 8 ) = 1 + a Mcos 20 + b^rcos^e + + ,5 c o s 2 0 8 where 2 i s the m u l t i p o l e order i n v o l v e d . M . . . . (5) When the r a d i a t i o n i s not a pure m u l t i p o l e , t h i s expression contains the parameters«=>< , (3 , V , ... mentioned e a r l i e r . I t should be remarked that when the p r o b a b i l i t y i s formed from ( ^  -y ^ J I t n e r e a r e non-zero cross terms w i t h f a c t o r s 3 °< Y, ... which appear. I t turns out that they modify c o n s i d e r a b l y the angular dependence. I f there i s a cascade of two or more gamma rays to the ground s t a t e , then the formulae become somewhat more in v o l v e d since repeated use of the r u l e s f o r summation of angular momentum has to be p r a c t i c e d . Steenberg (1953) has obtained formulae f o r the angular d i s t r i b u t i o n of the r a d i a t i o n as a f u n c t i o n of temperature f o r d i f f e r e n t methods of nuclear alignment and p o l a r i z a t i o n . Using h i s n o t a t i o n we have f o r any temperature.: i wM i M o) ••••(6) where the are the temperature dependent r e l a t i v e p o p u l a t i o n of the substates M. The complete a n a l y t i c a l expressions f o r Wjyj are r a t h e r complicated. Steenberg gives f o r each method of nuclear o r i e n t a t i o n a p e r t u r b a t i o n c a l c u l a t i o n c a r r i e d to the second order. A u s e f u l measure of the p o l a r diagram and th e r e f o r e of the nuclear o r i e n t a t i o n i s the anisotropy f a c t o r E which may be defined w i t h respect to an a x i s of alignment as f o l l o w s £ = z P l a n e " x A x i s (7) ^ l a n e which i n terms of the i n t e n s i t y d i s t r i b u t i o n 1 ( 0 ) discussed above can be w r i t t e n : £ = i C 7 a ) - i (o) • • • • ( 8 ) where the I are the normalized I n t e n s i t i e s of the r a d i a t i o n w i t h respect to an a x i s of alignment. To measure t h i s parameter i t i s s u f f i c i e n t to use simultaneously two counters, one along the a x i s of alignment and the other p e r p e n d i c u l a r to i t . The v a r i a t i o n of the anisotropy as a f u n c t i o n of temperature i s r e a d i l y obtained as the sample cools and warms up wit h time. In general the co r r e c t decay schemes can be deduced from the measurement of t h i s anisotropy f a c t o r , or a l t e r n a t i v e l y i f the decay scheme i s known, a value can be assigned t o the nuclear magnetic moment of the parent nucleus. CHAPTER I I DESCRIPTION OF THE APPARATUS A The apparatus f o r a d i a b a t i c demagnetization The c r y o s t a t and s u s c e p t i b i l i t y bridge used i n our experiments were constructed by previous workers i n t h i s l a b o r a t o r y and have been described i n d e t a i l elsewhere (Lamarche 1 9 5 6 ). Some a d d i t i o n s were made to the equip-ment. For the sake of completeness we describe b r i e f l y the apparatus, as we have used i t , i n t h i s chapter. The paramagnetic specimen t o be cooled by a d i a b a t i c demagnetization i s suspended i n s i d e a g l a s s c o n t a i n e r or "sample tube" which i s connected to a high vacuum system. The "sample tube" f i t s snugly i n s i d e a mutual inductance c o i l which i s p a r t of a b a l l i s t i c galvanometer c i r c u i t used i n reading the s u s c e p t i b i l i t y of the sample and hence i n determining i t s temper-ature. The sample tube and the c o i l are immersed i n a l i q u i d helium bath contained i n the u s u a l set of dewars. The pressure on t h i s helium bath may be reduced by pumping w i t h a la r g e c a p a c i t y Kinney mechanical pump. The High Vacuum System A schematic diagram of the high vacuum system, whose main f u n c t i o n i s t o i n s u l a t e the s a l t t h e r m a l l y before demagneti-z a t i o n , i s given i n Figure 1. The pumping equipment c o n s i s t s of a mercury d i f f u s i o n pump preceded by a r o t a r y pump and followed by a l i q u i d a i r 31 CZD D TO SIPHON JACKET M °0 OUT RESERVOIR MERCURY DIFFUSION PUMP ROTARY PUMP D: DISCHARGE TUBE M: MANOMETER TO SAMPLE TUBE PHILLIPS GAUGE M HELIUM BATH M M Hg OIL 2 0 cm 1 0 0 cm FIGURE I V A C U U M S Y S T E M t r a p . I t produces a vacuum of the order of 10 mm. of mer-cury. A 5 l i t r e r e s e r v o i r w i t h i t s own mercury manometer can be evacuated from the high vacuum side and serves as a back vacuum f o r the d i f f u s i o n pump should i t be r e q u i r e d to stop the r o t a r y pump t e m p o r a r i l y . The sample tube can be evacuated through two paths, a narrow and a broad one. P r o v i s i o n s are made to evacuate the syphon used i n the t r a n s f e r of l i q u i d helium and the high vacuum s i d e of the mercury and of the o i l manometers. The exchange gas can be obtained from the 300 cm3 r e s e r v o i r which a l s o has i t s own mercury manometer, or a l t e r -n a t i v e l y by t a k i n g f r e s h helium gas from the helium bath through the pressure l i n e l e a d i n g t o the manometers. To read the pressure and help i n d e t e c t i n g leaks i n the system, one gauge, two manometers and three discharge tubes have been attached. The P h i l l i p s gauge wi t h a range of 25 microns down t o 0 . 0 0 1 microns of mercury i s used t o i n d i c a t e the pressure i n the sample tube as w e l l as other p a r t s of the system when d e s i r e d . The three discharge tubes are conveniently l o c a t e d to help i n leak d e t e c t i o n and to show the nature and the approxi-mate pressure of the gas at d i f f e r e n t p o i n t s . The high ten-s i o n f o r the discharge tubes i s obtained from an automobile spark c o i l . To pump over the l i q u i d helium bath, a l a r g e c a p a c i t y Kinney mechanical pump has been i n s t a l l e d i n a room adjacent to the l a b o r a t o r y and i s l i n k e d to the apparatus by a 5 i n c h p i p e . The pressure over the helium bath i s read on a mercury manometer from atmospheric pressure down t o about 40 mm. of mercury. For lower pressures an o i l manometer i s used. The de n s i t y of t h i s o i l (Apiezon B) i s 15.85 times s m a l l e r than t h a t of mercury. At maximum pumping speed, a temperature of 1.3° K can be obtained; t o help i n a t t a i n i n g t h i s temperature some l i q u i d a i r i s kept i n the cap which s e a l s the l i q u i d h e l -ium dewar. The Sample Tube The sample c o n t a i n e r s used throughout our experiments had e s s e n t i a l l y the same design. They were made of pyrex g l a s s , w i t h an outer diameter of 18 mm. which g i v e s a good f i t w i t h the s u s c e p t i b i l i t y c o i l , an i n n e r diameter of 15 mm. and an o v e r a l l length of 25 cm. The specimens used were f i x e d to a s t r i p of mica, or placed i n s i d e a l u c i t e c y l i n d e r which was suspended by nylon threads between g l a s s hooks at top and bottom of the sample holde r . To allo w f o r some leeway i n sus-pending the specimen and to enable the g l a s s tube t o be sealed without burning the thread, the bottom thread i s attached to the g l a s s hook by a tungsten c o i l s p r i n g . The Magnet An i r o n core, water cooled electromagnet w i t h a d j u s t -able gap and interchangeable pole pieces was used i n these experiments. With a 2 i n c h gap and pole pieces 4 inches i n diameter t h i s magnet produces a maximum f i e l d of 22 k i l o g a u s s w i t h a power output of 75 k i l o w a t t . Since the water pressure a v a i l a b l e i n the l a b o r a t o r y i s below that r e q u i r e d f o r maximum c G P S, T AMMETER WITH 0.050 TO 5.00 AMP. SHUNTS EXTERNAL COMPENSATOR TINSLEY GALVANOMETER WITH TELESCOPE AND SCALE PARAMAGNETIC SAMPLE SECONDARY SURROUNDING THE SAMPLE IN THE HELIUM BATH SECONDARY COMPENSATING PARTIALLY S7 IN HELIUM BATH REVERSING SWITCH 5.6 I A / W W W v A y 4 6 { WWWVvV— 7 5 { VyAA/VvWv 710 I -VWVWWv— LIQUID HELIUM BATH FIGURE 2 MUTUAL INDUCTANCE BRIDGE 34 power d i s s i p a t i o n the magnet was g e n e r a l l y operated at 160 v o l t s and 200 amperes, i . e . , 21 k i l o g a u s s . This l\ ton magnet i s mounted on a t u r n t a b l e c a r r i a g e r o l l i n g on a r a i l w a y and can be moved e a s i l y to and from the c r y o s t a t by one person. The S u s c e p t i b i l i t y Bridge The bridge t o measure the s u s c e p t i b i l i t y i s a d.c. mutual inductance bridge whose c i r c u i t i s given i n Figure 2 . The mutual inductance c o i l around the paramagnetic sample i s wound on a b a k e l i t e former and c o n s i s t s of two secondaries i n o p p o s i t i o n separated by a gap of 1", and a primary extending a t o t a l length of 5 " . One secondary i s 1" i n l e n g t h , while the other i s 1^". The sample i s placed i n s i d e the s h o r t e r secondary at the centre of the former. The longer secondary, near the end of the former serves as a compensator. Another compensator, at room temperature, can be v a r i e d continuously from 0 to 4 m i l l i h e n r i e s . Hence the d e f l e c t i o n before c a l i -b r a t i o n can be adjusted e a s i l y . In the course of our e x p e r i -ments s e v e r a l s u s c e p t i b i l i t y c o i l s were wound w i t h approximately the same number of t u r n s . Reference to F i g u r e d can be supple-mented by the f o l l o w i n g data on the s u s c e p t i b i l i t y c o i l s . S had about 3000 turns and S g about 3600 turns of No. 40 B & S S.S.C. copper wire which at room temperature had a t o t a l d.c. r e s i s t a n c e of a 1 , 6 0 0 ohms. The primary had about 600 turns of No. 36 B & S D.S.C. copper wire w i t h a room temperature r e s i s -tance of 75 ohms. 35 B Gamma Ray Detection Equipment S c i n t i l l a t i o n counters were used f o r the d e t e c t i o n of the gamma r a d i a t i o n . The necessary equipment c o n s i s t s of Nal c r y s t a l s , p h o t o m u l t i p l i e r s , cathode f o l l o w e r s , l i n e a r ampli-f i e r s , amplitude d i s c r i m i n a t o r s , pulse height analysers and s c a l e r s . The r a d i a t i o n i s recorded simultaneously i n two d i r e c t i o n s as the temperature of the r a d i o a c t i v e specimen v a r i e s ; hence two separate channels are used as shown i n the block diagram given i n Figure I I I . The Nal ( T i ) s c i n t i l l a t i o n c r y s t a l , the p h o t o m u l t i p l i e r w i t h i t s p o t e n t i a l d i v i d e r , and the cathode f o l l o w e r form a po r t a b l e u n i t . The c r y s t a l i s 1^ i n c h i n diameter, 1" long, and was obtained ready mounted from Harshaw Co. I t i s h e l d i n o p t i c a l contact on a RCA 6342 p h o t o m u l t i p l i e r by Dow Corning F l u i d 2 0 0 . The phototubes were m a g n e t i c a l l y s h i e l d e d against s t r a y f i e l d s by a Mu metal tubing and l a t e r by Conetic-Fermetic t u b i n g . The high voltage supply was a commercially a v a i l a b l e type manufactured by Te c h n i c a l Measurements Corporation (HV 4 A ) . The p o t e n t i a l i s a p p l i e d to the cathode, the dynodes and the anode through a chain of r e s i s t o r s . Cathode f o l l o w e r s designed f o r negative pulses were used. The pulses from the cathode f o l l o w e r were fed i n t o a l i n e a r pulse a m p l i f i e r through low impedance cabl e s . The a m p l i f i e r s have been b u i l t f o l l o w i n g c l o s e l y the c i r c u i t and the layout of the commercially a v a i l a b l e L i n e r a A m p l i f i e r Model 218 of Atomic Instrument Co. I t c o n s i s t s of two separate three stage a m p l i f i e r s w i t h negative feedback loops. The gain i s L I Q U I D H E L I U M A N D N I T R O G E N D E W A R S C A L O R I M E T E R A N D S U S C E P T I B I L I T Y C O I L S S O U R C E C A T H O D E F O L L O W E R L I N E A R A M P L I F I E R C A T H F O L L C O D E ) W E R i L INE A M P L : A R I F I ER A M P L I T U D E D I S C R I M I N A T O R P U L S E H E I G H T A N A L Y Z E R A M P L I T U D E D I S C R I M I N A T O R P U L S E H E I G H T A N A L Y Z E R S C A L E R S C A L E R S C A L E R S C A L E R F I G U R E 3 BLOCK DIAGRAM OF THE COUNTER ARRAY 36 c o n t r o l l e d at the Input by a potentiometer p r o v i d i n g an a d j u s t -ment of the s i g n a l between 50$ and 100$ of i t s maximum value. A coarse g a i n c o n t r o l f o l l o w s which g i v e s roughly steps of 2 . The gain of the a m p l i f i e r i s 6,000 f o r a r i s e time of some 0.7 microsecond and a pulse d u r a t i o n of 5 microsecond. Some modi-f i c a t i o n s of the o r i g i n a l c i r c u i t have been made and d e t a i n e d c i r c u i t diagrams are given i n the t h e s i s of G.L.J. Lamarche ( 1 9 5 6 ) . The f i l a m e n t s on a l l tubes have been set at a D.C. p o t e n t i a l of 40 v o l t s w i t h respect to the c h a s s i s . The s i g n a l at the output i s a p o s i t i v e pulse w i t h amplitude between 0 and 100 v o l t s . This s i g n a l i s fed t o an amplitude d i s c r i m i n a t o r and/or to a pulse height analyzer. The amplitude d i s c r i m i n a t o r i s the u s u a l Schmidt t r i g g e r c i r c u i t . The output from the d i s -c r i m i n a t o r i s a l s o a p o s i t i v e pulse w i t h constant amplitude of 40 v o l t s . Since i n general Berkeley s c a l e r s were used and these w i l l accept only negative p u l s e s , the pulses are d i f f e r e n -t i a t e d before being fed t o the s c a l e r . The s i n g l e channel pulse height analyzers were the commercially a v a i l a b l e Model 510 manufactured by Atomic Instrument Company. The s c a l e r s were Berkeley Decimal S c a l e r s (Models 1 0 0 , 2 1 0 5 , and 2001) but Atomic Instrument Co. Model 101A Scale of 64 s c a l e r s were a l s o used. The simultaneous use of a d i s c r i m i n a t o r and pulse height analyzer w i t h a t o t a l of 4 s c a l e r s enable us t o observe the anisotropy of two d i f f e r e n t gamma rays i n a s i n g l e run. In some experiments the e n t i r e e l e c t r o n i c equipment was d u p l i c a t e d by borrowing various components from other groups 37 i n our department. This enabled us t o accumulate more data and b e t t e r s t a t i s t i c s i n each run. A permanent d u p l i c a t e e l e c t r o n i c set up I s being assembled. The e l e c t r o n i c equipment operates on a standard reg u l a t e d 1 k i l o w a t t power supply ( S t a b i l i s e Voltage Regulator made by Superior E l e c t r i c Corp.). The s c a l e r s were turned on and o f f manually. Since counting p e r i o d s of minute up t o s e v e r a l minutes were used, the s l i g h t e r r o r i n t u r n i n g two s c a l e r s on and o f f simultan-eously t h a t t h i s procedure may introduce i s n e g l i g i b l e . A p a i r of water cooled, a i r - c o r e Helmholtz c o i l s was constructed. These c o i l s are operated i n p a r a l l e l and produce a maximum magnetic f i e l d of 1 , 0 0 0 gauss at the center of a 3 Inch gap w i t h a current of 15 amperes f l o w i n g through each. The dimensions of each c o i l are the f o l l o w i n g : Inner Diameter 4 1/2" , Outer Diameter 8 1/2" , Width 3 " . They c o n s i s t of approximately 1 , 100 turns of No. 16 B & S enamelled copper w i r e , each l a y e r separated by s t r i p s of 1 mm. t h i c k b a k e l i t e and the whole i s encased i n a water t i g h t brass case. The c o i l s f i t c l o s e l y around the t a i l of the outer dewar 2 1/2" i n diameter. P r i o r t o and during a run the current was passed through the c o i l s c o n t i n u o u s l y so t h a t the system was i n thermal equi-l i b r i u m and the current constant. The s t r a y magnetic f i e l d produced by the c o i l s at the p h o t o m u l t i p l i e r s w i l l completely d i s t u r b t h e i r o p e ration. This d i f f i c u l t y i s solved by (a) removing the phototubes from the strong magnetic f i e l d r e g i o n , (b) by magnetic s h i e l d i n g , 38 and (c) by the use of a bucking c o i l . The p h o t o m u l t i p l i e r s were placed about 8 inches from the s c i n t i l l a t i o n c r y s t a l s and a l u c i t e pipe provides a path f o r the l i g h t . The l u c i t e rods, 1 1/2" i n diameter, are w e l l p o l i s h e d arid i n good o p t i c a l contact w i t h the p h o t o m u l t i p l i e r s and the c r y s t a l s . The l u c i t e ro.ds are r i g i d l y mounted w i t h a minimum of contact at the p o i n t s of support. Besides the Mu metal or F e r n e t i c - C o n e t i c tubing a d d i t i o n a l magnetic s h i e l d i n g was obtained by p l a c i n g two c o n c e n t r i c c y l i n d e r s of m i l d s t e e l around each phototube. The c y l i n d e r s extend about two inches beyond the f r o n t of the phototube, they are 1/4 and 1/8 i n c h t h i c k each,, and are separated by a t h i n brass sheet. The above arrangement s t i l l does not provide adequate s h i e l d i n g f o r the phototube i n the d i r e c t i o n of the f i e l d . In t h i s case a bucking c o i l c o n s i s t i n g of one l a y e r of enamelled copper wire was wound around the outer s t e e l c y l i n d e r and the current adjusted u n t i l the e f f e c t of the s t r a y f i e l d on the counting r a t e was approximately c o r r e c t e d . Due t o the presence of the s t e e l c y l i n d e r s i n s i d e the bucking c o i l the adjustment of the current through the bucking c o i l i s l e s s c r i t i c a l . A change of about 10$ i n t h i s current does not a f f e c t the counting r a t e by more than 1$ once the current has been adjusted. The c i r c u i t s of the bucking c o i l and the Helmholts c o i l s are placed i n p a r a l l e l ; hence a change i n the D.C. generator voltage w i l l cause both to vary p r o p o r t i o n a t e l y . The d e t e c t o r units.and the Helmholtz p a i r are mounted on a t u r n t a b l e which i s placed on a c a r r i a g e r o l l i n g on r a i l s ; hence the assembly can be moved e a s i l y and q u i c k l y around the dewar, a l l o w i n g the counting t o s t a r t not l a t e r than 30 seconds a f t e r the end of the demagnetization. A l i g n -ment of the detectors w i t h respect t o the sample was done v i s u a l l y p r i o r to the experiment u s i n g some d i s t a n t o b j e c t s as reference p o i n t s . The alignment i s estimated to be accur-ate w i t h i n some 5°» CHAPTER I I I NUCLEAR ORIENTATION EXPERIMENTS WITH Pr AND Y b 1 7 5 NUCLEI IN PARAMAGNETIC SINGLE CRYSTALS H i s t o r i c a l Remark: The research described i n t h i s chapter was i n i t i a t e d by Dr. J.L.G. Lamarche while working as a graduate student i n t h i s l a b o r a t o r y at the suggestion of Dr. J.M. D a n i e l s . At th a t time a l i q u i d a i r c o o l e d : s o l e n o i d capable of producing a maximum f i e l d of 14 to 15 k i l o g a u s s was used i n t h i s l a b o r a t o r y f o r a d i a b a t i c demagnetization. This cumbersome set up not only l i m i t e d the temperature range f o r i n v e s t i g a t i o n s but rendered the accumulation of s t a t i s t i c a l data a most l a b o r i o u s procedure. 142 Nevertheless p r e l i m i n a r y measurements on Pr i n zero e x t e r n a l f i e l d had been c a r r i e d out down t o a temperature of 0 . 0 0 5 ° K. These f a i l e d t o show any r e l i a b l e anisotropy g r e a t e r than 1 $ . Further extensive measurements of the 396 and 282 kev /- r a y s of Y b 1 7 ^ were performed down to a temperature of 0 . 0 0 5 ° K i n zero e x t e r n a l f i e l d , and p r e l i m i n a r y observations of both j'-rays w i t h an e x t e r n a l f i e l d of 180 gauss p a r a l l e l to the t r i g o n a l a x i s were c a r r i e d out down t o a temperature of 0 .009° K. These measurements i n d i c a t e d no a n i s o t r o p i e s g r e a t e r than 1 $ . When the l a r g e water-cooled electromagnet mentioned i n Chapter I I became a v a i l a b l e the c o l l e c t i o n of more accurate s t a t i s t i c a l data became much e a s i e r and the attainment of lower temperatures became p o s s i b l e . I t was decided t o repeat o t h i s work and extend the range of i n v e s t i g a t i o n to 0 . 0 0 3 K. 40 41 The r e s u l t s reported i n t h i s chapter are based e n t i r e l y on t h i s new s e r i e s of measurements c a r r i e d out by the author. Part I 42 Nuclear Orientation of Pr  Introduction.; The magnetic hyperfine structure method of orienting n u c l e i has been established by Bleaney et a l (1954) and has already proved usef u l i n establishing d e t a i l s of nuclear decay schemes and i n evaluating nuclear magnetic moments (e.g. Grace and Halban 1 9 5 2 ) . As part of a program to exploit the p o t e n t i a l -142 i t i e s of such experiments, we have oriented Pr i n cerium magnesium n i t r a t e by t h i s method and have observed and measured an anisotropy i n the emission of the 1 .57 mev /-ray which occurs i n the decay of t h i s nucleus. A value of the magnetic moment 142 of the Pr nucleus has been deduced from these measurements. Experimental.: The experimental technique which we used i s e s s e n t i a l l y that described i n d e t a i l by Bleaney et a l (1954) and we mention the features pertinent to t h i s experiment. A solution of a few milligrams of praseodymium n i t r a t e i n heavy water was i r r a d i a t e d i n the B.E.P.O. p i l e at Harwell to an a c t i v i t y of some 10 m i l l i c u r i e s . I t was then brought to Vancouver by C.P.A.'s transpolar f l i g h t , and the active solution was poured into a saturated solution of about 10 grams of cerium magnesium n i t r a t e . Single c r y s t a l s were then grown from t h i s solution i n a vacuum dessicator over concentrated sulphuric acid. Because of the short h a l f l i f e of the isotope special care must be taken to accelerate the growth of the c r y s t a l s . This was done by preparing beforehand s e v e r a l small w e l l formed c r y s t a l s of cerium magnesium n i t r a t e . These are then used as seeds from which l a r g e c r y s t a l s can be e a s i l y and q u i c k l y obtained i n the r a d i o a c t i v e saturated s o l u t i o n . We found i t p o s s i b l e to ob t a i n w i t h i n l e s s than 18 hours some 20 w e l l formed s i n g l e c r y s t a l s w i t h a t o t a l weight of about 4 grams and a t o t a l counting r a t e of about 100/second i n the counting apparatus w i t h the s c i n t i l l a t i o n c r y s t a l s placed at a,distance of 10 cm from the source. The c r y s t a l s which are f l a t p l a t e s of t r i g o n a l symmetry were glued w i t h p a r a l l e l c r y s t a l l o g r a p h i c o r i e n t a t i o n on a s t r i p of mica. The s t r i p of mica was t a u t l y suspended by short nylon threads i n the g l a s s sample holder which i s then sealed and mounted i n the c r y o s t a t . The detectors are a l i g n e d w i t h r e s -pect to the plane of the mica by t a k i n g d i s t a n t o b j e c t s i n the la b o r a t o r y as reference p o i n t s . The c r y s t a l s were cooled by a d i a b a t i c demagnetization from an i n i t i a l f i e l d of about 20 k i l o g a u s s and temperatures of 1.3°K t o temperatures of about -•5 3x10 -'OK. A f t e r demagnetization, the magnet was removed and two s c i n t i l l a t i o n counters placed i n p o s i t i o n round the specimen i n some 20 seconds. One s c i n t i l l a t i o n c r y s t a l was placed along the t r i g o n a l a x i s of the r a d i o a c t i v e c r y s t a l s , about 10 cm. from the source, and the other was placed at a s i m i l a r distance i n a d i r e c t i o n at r i g h t angles t o t h i s a x i s . The pulses due to gamma rays of energy g r e a t e r than 1 Mev were counted. During the p e r i o d when the c r y s t a l s warmed up from the low temperature a t t a i n e d on demagnetization t o the helium bath temperature of 1 . 3 ° K, from 10 to 20 minutes according t o the c o n d i t i o n s p r e v a i l i n g during an experiment, the counting r a t e was measured i n the two counters, and the temperature of the c r y s t a l s was measured u s i n g a mutual inductance and a b a l l i s t i c galvanometer (Chapter II p. 2 9 , Bleaney et a l 195*0. A f t e r the a c t i v e c r y s t a l s had warmed to 1.3°K, the counting r a t e was observed f o r a wh i l e t o t e s t the s t a b i l i t y of the counters, and f o r n o r m a l i z a t i o n purposes. In the second s e r i e s of experi-ments an e x t e r n a l f i e l d of a few hundred gauss was a p p l i e d t o the r a d i o a c t i v e c r y s t a l s by p l a c i n g Helmholtz c o i l s around the dewar wi t h the f i e l d along the t r i g o n a l a x i s . When these c o i l s were used the s c i n t i l l a t i o n c r y s t a l s were coupled t o the photo-m u l t i p l i e r s s h i e l d e d from the s t r a y f i e l d as described i n Chapter I I . Decay Scheme 142 The decay scheme of 1 9 . 2 hour Pr has been studied by v a r i o u s workers, I n c l u d i n g Gideon et a l ( 1 9 4 9 ) , Jensen et a l ( 1 9 5 0 ) , Bartholomew and Kinsey ( 1 9 5 3 ) , Polm et a l (1954) and Sterk et a l ( 1 9 5 5 ) . The decay scheme suggested by Polm et a l (1954) i s shown i n Figure 4 . P r 1 2 * 2 decays to Nd 1 / | 2 i n two branches.: a beta of 2 . 1 6 6 Mev t o the ground s t a t e and a much l e s s intense beta of O .586 Mev to the only low energy e x c i t e d 142 l e v e l of Nd fo l l o w e d by a 1 .57 Mev gamma ray t r a n s i t i o n to the ground s t a t e . The arguments f o r t h i s decay scheme are, 142 b r i e f l y , as f o l l o w s . Nd i s an even-even nucleus; I t s ground s t a t e t h e r e f o r e i s 0 + . The 2 . 1 6 6 Mev i f - r a y has 45 log f t = 7.8, and the f i r s t special shape appropriate to a beta 14P t r a n s i t i o n with A I = 2, yes; the spin and p a r i t y of FT are thus 2-. The other beta t r a n s i t i o n has log f t = 7.1 and allowed shape; i t i s therefore suggested that i t i s f i r s t f o r -bidden with A I = 0 or + 1, yes. Since the f i r s t excited states of nearly a l l even-even nu c l e i so f a r measured have spin and 142 p a r i t y 2+, the excited state of Nd i n t h i s scheme i s assigned spin and p a r i t y 2+, and the / - r a y i s assumed to be E2. Results was obtained from the magnetic s u s c e p t i b i l i t y measurements, using the rel a t i o n s h i p given by Daniels and Robinson ( 1 9 5 3 ) . The Curie-Weiss A for our specimen was determined by comparing the measured value of the magnetic temperature T a f t e r demagnetization with the value calculated from the i n i t i a l magnetic f i e l d and the i n i t i a l temperature. Its value was 2.6 millidegrees which i s a reasonable value according to Daniels and Robinson ( 1 9 5 3 ) . where I ^ and 1 ^ are the normalized counting rates i n directions p a r a l l e l and perpendicular 1 respectively to the t r i g o n a l axis of the c r y s t a l s . Values of £ f o r the same temperature range, but from d i f f e r e n t demagnetizations, were The absolute temperature of the radioactive c r y s t a l s We can define the anisotropy parameter € by the relation.: € averaged to improve s t a t i s t i c s . 46 The r e s u l t s of the measurements are shown In Figures 5 and 6 i n which £ i s p l o t t e d as a f u n c t i o n of l/T. Figure 5 i s f o r the case where an e x t e r n a l magnetic f i e l d of 320 gauss i s a p p l i e d p a r a l l e l to the t r i g o n a l a x i s of the c r y s t a l s . This f i e l d s t r e n g t h was chosen a f t e r p r e l i m i n a r y measurements d i d not show any appreciable d i f f e r e n c e between r e s u l t s obtained u s i n g f i e l d s of 1 6 0 , 250 and 400 gauss along t h i s a x i s . In each f i g u r e the s o l i d curve i s the curve of the form 6 = a/T 2 which best f i t s the data. For zero e x t e r n a l magnetic f i e l d a = 4 . 9 5 x 10~ 7 o-K" 2, f o r an e x t e r n a l f i e l d of 320 gauss a = 1 8 . 7 x 1 0" 79K - 2. These r e s u l t s may be compared w i t h those obtained at Oxford i n a 142 s i m i l a r experiment w i t h Pr i n c e r t a i n magnesium n i t r a t e (Johnson 1 9 5 8 ). From t h e i r p u b l i s h e d curves we can estimate the value of a. In the case of zero e x t e r n a l f i e l d a. = 8 . 7 x 1 0~ 7 oK~ 2. Since t h i s value i s l a r g e r than ours by a f a c t o r of about 1 .7 the agreement i s somewhat poor. In the case of an e x t e r n a l mag-n e t i c f i e l d of 300 gauss where a = 22 x 1 0 " 7 o K " 2 ( O x f o r d ) the agreement I s q u i t e good. The value of the nuc l e a r magnetic 14? moment of Pr i s estimated from the l a t t e r curve as shown below. The Oxford group a l s o observed t h a t the anisotropy d i d not increase at a given temperature i n e x t e r n a l f i e l d s l a r g e r than 300 gauss. The p o s s i b i l i t y was considered that bremsstrahlung from the 2 . 1 6 6 Mev ( 3 - r a y could be counted as /- r a y s and reduce the observed an i s o t r o p y . C a l c u l a t i o n s based on formulae i n Siegbahn (1955) showed that t h i s e f f e c t i s n e g l i g i b l e . 47 The t h r e s h o l d of the d i s c r i m i n a t o r was set at 1 Mev t o get a good counting r a t e . In t h i s case one must consider the reduc-t i o n of anisotropy due to s c a t t e r e d gamma rays . Such a c a l -c u l a t i o n was made by Bleaney et a l (1954) f o r the case of Co i n an apparatus which i s e s s e n t i a l l y s i m i l a r t o ours. I t was found t h a t t h i s c o r r e c t i o n i s q u i t e n e g l i g i b l e f o r values of £ as low as 0.04, and we have t h e r e f o r e ignored i t . I t i s very u n l i k e l y t h a t the l i f e t i m e of the gamma e m i t t i n g s t a t e i s g r e a t e r than about 10~^3 seconds (Weisskopf's formula p r e d i c t s a l i f e t i m e of IO - 1 2* second f o r an E l t r a n s i t i o n , and 1 0 ~ 1 2 second f o r an E2 t r a n s i t i o n ) hence l o s s of anisotropy due to p r e c e s s i o n i n the c r y s t a l l i n e f i e l d s can be discounted. Discussion.: The double n i t r a t e s MgMg^NO^) 1 2 2 4 HgO where M i s one of La,Ce, or P r , are isomorphous and form mixed c r y s t a l s i n a l l p r o p o r t i o n s . The paramagnetic resonance spectrum of the s t a b l e 141 i s o t o p e , Pr , as an i m p u r i t y i n lanthanum magnesium n i t r a t e , has been observed by Cooke and Duffus ( 1 9 5 5 ) , who assigned to t h i s i o n the spin Hamiltonian.: H z s z + A S z I z + \ s x + A y s y •••• -U) -1 where g = 1 . 5 5 A = 0 . 0 7 7 cm A = Average \j A* + Xo-0.04 cm" _ ,-vn I ML r>n ^" S = 1/2 I = 5/2 and the z - a x i s i s the t r i g o n a l a x i s of the c r y s t a l s . The Pr' 48 ion has an even number of electrons, and hence the energy le v e l s need not be doublets (Kramer's theorem). However the symmetry of the double n i t r a t e c r y s t a l i s such that the ground state i s an accidental doublet. Strains and other d i s t o r t i o n s can cause a s p l i t t i n g of t h i s doublet, and i t has been sug-gested that t h i s i s the o r i g i n of the A — t e r m . There i s no unique value of ^  , a d i f f e r e n t value being appropriate for each ion, but an "average"value of A °an be assigned. A i s probably structure-sensitive. The most general spin Hamiltonian with t r i g o n a l symmetry has terms Q (3 (H S + H S ) and 0-L x x y y B (S I + S„I ) i n addition to those i n equation ( l ) . To the v x x y y' ^ v ' accuracy of published measurements, both g j ^ and B are zero. In the case where S = 1/2, g ^ = B = 0 and h = 0 , magnetic interactions between the ions do not af f e c t the angular d i s t r i -bution of gamma rays (Daniels 1 9 5 7 ) . In th i s case also, an external magnetic f i e l d applied along the z-axls has no ef f e c t on the angular d i s t r i b u t i o n (Daniels 1 9 5 7 ) . Case a) I f the decay scheme i s 2 —°-5> 2 — ^ 0 ( i . e . the (3 - V p a i r c a r r i e s o f f no angular momentum) the normalized i n t e n s i t y d i s t r i b u t i o n s Im{9) for the various m-states of the parent nucleus are: I (6) = 5/16 T T ( 1 - cos^e ) +2 I (8) = 5/16 T (1 - 3 cos 2 0 + 4 cos 4e ) (2) +1 I n ( G ) = 5/16 T ( 6 c o s 2 S - 6 cos 4& ) 49 1 o Case b) I f the decay scheme i s 2 —=-> 2 } 0 ( i . e . the (3- V p a i r c a r r i e s o f f one unit of angular momentum) the normalized i n t e n s i t y d i s t r i b u t i o n s are.: I O) = 5/16 TT (1 - cos^0 + 2/3 cos46> ) +2 2 a • 41 2 A o/o _ 4 I (S) = 5/16 TT (1/2 + 5/2 cos^e - 8/3 c o s 4 6 ) . . . (3) +1 I 0 ( 8 ) = 5/16 T ( 1 - 3 cos26> + 4 c o s 4 Q ) We may calculate the polar diagram as a function of temperature from the r e l a t i o n : I (6) « £ V m )• •••• tT) where Wm are the temperature dependent r e l a t i v e populations of the substates m. In a state of thermal equilibrium we may assume a Boltzmann d i s t r i b u t i o n consequently.: - m/kT Wm = -5 1 . . . . (5) I l e " ^ ^ where E m i s the energy of a nucleus i n substate m. I f the energy E m i s small r e l a t i v e to kT we may expand the numerator -E /kT 2 o o e m = 1 - Ejj/kT + Em/2kZTd (6) and we may neglect terms of higher order. In the absence of an external f i e l d the energy levels are given from the Hamiltonian equation (1) by.: E m = ± l / 2 J (A m) 2 + A 2 ... # l ( 7 ) where m i n the nuclear magnetic quantum number and takes on the values 2,1,0,-1,-2. I f we define the anisotropy by f = I ( "V*) - I (0) I ( T/A ) the c a l c u l a t i o n y i e l d s f o r case a) £ = / U J * 1 - 3A . . . . (8) and f o r case b) I f A, and A are small r e l a t i v e to kT t h i s procedure Is v a l i d . However since the anisotropy i s ap p r e c i a b l y increased i n the presence of an e x t e r n a l f i e l d along the t r i -gonal a x i s these approximations are q u i t e suspect. We t h e r e f o r e proceed to i n v e s t i g a t e the behaviour of the energy l e v e l s when a magnetic f i e l d i s a p p l i e d along the t r i g o n a l a x i s ( I . e . the z - a x i s ) . The energy l e v e l s are then given by: Em = ± * \j ( S„PH + A m ) 2 + A 2 ....(10) I f we used the approximation given i n equation (6) the expressions (8) and (9) would then contain an a d d i t i o n a l term i n (g (3H ) 2 i n the denominator and would be l e s s v a l i d . 51 We note that as ( g ^ @H) i n c r e a s e s r e l a t i v e to a and A the energy l e v e l s become separated and the separation between the d i f f e r e n t m-states approaches the f u l l value of A / 2 . This corresponds to the separation i n zero f i e l d w i t h A= o. For instance i f we assume g^^H = 2A, and A ~ A, we o b t a i n l e v e l s at + 3 . 0 4 A , + 2.55A, + 2.06A, + I . 5 8 A , and + 1.12A. Since the measurements w i t h magnetic f i e l d s g r eater than 320 gauss d i d not i n d i c a t e any increase i n the anisotropy at a given temperature we assume th a t i n a magnetic f i e l d of 320 gauss the l e v e l s have a t t a i n e d the f u l l s e p aration of A/2. We may then proceed i n the f o l l o w i n g manner. Let + EJJI — +_ EQ + mA/2 where E Q i s some constant energy term. We then expand the numerator i n equation (5) +E m/kT ±E0AT + mA/2kT ^ + E f t/kT o A T [ l + BL. + 1 mA 2 1 |_ 2kT 8 kT J (11) where we neg l e c t higher order terms. Since|E o| >• A/2 we may n e g l e c t the terms c o n t a i n i n g the f a c t o r e~ E°/ k^ and we note E /kT t h a t the f a c t o r e 0 / cancels out. Hence we c a l c u l a t e I (©) of equation (4) and o b t a i n f o r the anisotropy defined above the f o l l o w i n g expressions.: Case a) «£*:; = 3 k* (12) 16 k2T 6= 3 a 2 .... (13) 32 k T From the anisotropy measured i n a f i e l d of 320 gauss and equations (12) and (13) we determine the h y p e r f i n e s t r u c t u r e constant A/k. We f i n d Case a) A/k = G .0032°K Case b) A/k = 0.0045°K I f we assume th a t A = 0, upon s u b s t i t u t i o n of these values f o r A/k i n t o the appropriate expression given i n equa-t i o n s (8) and (9) we note t h a t t h i s does not introduce a p p r e c i a b l e r e d u c t i o n of the anisotropy f o r values of T as low as 0 .005°K. For instance the denominator becomes 1 . 13 and 1 . 2 3 i n case a) and b) r e s p e c t i v e l y at t h i s temperature. The decrease of the anisotropy i n zero f i e l d must then be a t t r i b u t e d t o the term i n A . We may estimate the magnitude of the term A r e q u i r e d t o reduce the anisotropy to the zero f i e l d measurements using the exact expression f o r 1 ( 0 ) and c a l c u l a t i n g the anisotropy £ at var i o u s temperatures f o r ' s e v e r a l values of A • These c a l c u l a t i o n s show th a t a A ~ IOA and C£ 7A giv e s a good f i t t o our r e s u l t s f o r case a) and case b) r e s p e c t i v e l y . From the values of A/k determined above we may 142 estimate the nuclear magnetic moment of P r . Since the f i e l d on the praseodymium nucleus i s due to the 4f e l e c t r o n s h e l l , independent of the i s o t o p e , t h i s f i e l d i s H = A l i t l I i 4 i / / i i i 1 = A i 4 2 I i 4 2 / ^ l 4 2 * F o r t h e s t a b l e isotope p r l 4 l £ n e v a i u e s a r e known = 3 . 8 n.m., A.,,, » 0 . 0 7 7 cm'1 = 0.111°K I t i s then a simple matter to substitute into these formulae to f i n d y*"1^2 * T h e r e s u l t i s : f^\l\2. = n u c l e a r magnetons i f the f%~v p a i r c a r r i e s o f f no angular momentum, o r = 0.15 nuclear magnetons i f the ^ - ^ p a i r c a r r i e s o f f one unit of angular momentum. 54 Par t I I Nuclear O r i e n t a t i o n Experiments with Y b l 7 5 I n t r o d u c t i o n To f u r t h e r e x p l o i t the p o t e n t i a l i t i e s of o r i e n t i n g n u c l e i by the magnetic h y p e r f i n e s t r u c t u r e method we performed experiments to o r i e n t Yb"^-* as an i m p u r i t y i n cerium magnesium n i t r a t e . When these i n v e s t i g a t i o n s were s t a r t e d , i t was d i s -covered t h a t a group at Oxford were preparing to a l i g n t h i s i s o t o p e . At tha t time, very l i t t l e was known about the e f f e c t of i n t e r a c t i o n s between neighbouring paramagnetic ions on the angular d i s t r i b u t i o n of gamma rays from an assembly of a l i g n e d n u c l e i , except t h a t such e f f e c t s could be larg e (Grace et a l 60 1954). In a d d i t i o n , only one i s o t o p e , Co , had been a l i g n e d i n more than one c r y s t a l l i n e environment (Bleaney et a l 1954, Ambler et a l 1953)• Since the Oxford group planned to o r i e n t 175 Yb x J i n the et h y l s u l p h a t e l a t t i c e , and we planned t o a l i g n i t i n the double n i t r a t e l a t t i c e , i t was thought t h a t these i n v e s t i g a t i o n s might complement each other and y i e l d i n f o r m a t i o n about the e f f e c t s of i n t e r a c t i o n s . The r e s u l t s of the i n v e s t i -g a t i ons at Oxford have been pu b l i s h e d (Grace et a l 1957) and are indeed very d i f f e r e n t from ours. Experimental The technique used t o o r i e n t the ytterbium was e x a c t l y the same as tha t used to o r i e n t praseodymium described i n Par t I of t h i s chapter. The s t a r t i n g m a t e r i a l f o r these i n v e s t i g a t i o n s was YbpO^ separated by the i o n exchange method, and suppl i e d to us by Dr. P.H. Spedding of the Ames I n s t i t u t e . One m i l l i g r a m was i r r a d i a t e d i n the NRX p i l e at Chalk R i v e r , t o an a c t i v i t y of about 5 m i l l i c u r i e s . On r e c e i p t of the i r r a d i a t e d sample, the quartz capsule was crushed under about 20 cc. of water con-t a i n e d i n a platinum c r u c i b l e . A s p e c i a l j i g was used f o r t h i s o p e r a t i o n . About s i x drops of concentrated s u l p h u r i c a c i d were added, and the whole was evaporated to dryness, f i r s t on a sand bath and afterwards under a heat lamp. The residue was then d i s s o l v e d i n about 20 or 30 cc. of water. This s o l u t i o n was f i l t e r e d i n t o a beaker and about 15 cc. of saturated s o l u t i o n of cerium magnesium n i t r a t e was added. C r y s t a l s were grown from seeds placed i n t h i s s o l u t i o n i n a vacuum d e s s i c a t o r over s u l p h u r i c a c i d . The double n i t r a t e s of the r a r e earths e x i s t only f o r the r a r e earths from La t o Gd, and ytterbium magnesium n i t r a t e does not e x i s t as such. However, some ytterbium does go i n t o the c r y s t a l l a t t i c e . A f t e r a c r y s t a l was removed from the s o l u t i o n , i t was washed w i t h d i s t i l l e d water t o remove any s o l u -t i o n from i t s s u r f a c e , and d r i e d w i t h f i l t e r paper, t o preclude the p o s s i b i l i t y t h a t the a c t i v i t y i s due t o a l a y e r of d r i e d o f f s o l u t i o n on the surf a c e . The c r y s t a l s were g e n e r a l l y c l e a r enough f o r the observer to see t h a t they contained no l a r g e i n c l u s i o n s of s o l u t i o n . On one occasion, a sample of YbgO^ became contaiminated i n the i r r a d i a t i o n , and the s o l u t i o n from which the c r y s t a l s were grown emitted a gamma ray of about 001 0 -0.01 - £ r '/T i 1—o—1 1 rooi > 300 0.01 h 6 J 0 -0.01 t 0.01 h 0 -0.01 h 0 100 T 150 O 260 GAUSS • 380 " € 510 O 700 11 0 P4 T 100 o T 150 O 60 GAUSS • 100 ' " C 160 " 175 FIGURE 8 Yb " 396 keVy -RAY Upper graph - Zero external f i e l d . Middle graph - fields along the trigo-nal axis. Lower graph - fields perpendicular to the trigonal axis. 56 700 kev energy, yet t h i s gamma ray was completely absent from the c r y s t a l s grown from t h i s s o l u t i o n . In t h i s way we are sure t h a t the ytterbium does go i n t o the c r y s t a l l a t t i c e ; i t i s most reasonable t o assume th a t i t goes i n t o a r a r e - e a r t h p o s i t i o n , although there i s no d i r e c t evidence f o r t h i s . The s p e c i f i c a c t i v i t y of the c r y s t a l s was about 1/30 that of the s o l u t i o n . Decay Scheme: 175 The p r i n c i p a l f e a t u r e s of the decay scheme of Yb ^ are shown i n Figu r e J. This decay scheme has been studi e d by a v a r i e t y of i n v e s t i g a t o r s de Waard ( 1 9 5 5 ) , A k e r l i n d et a l ( 1 9 5 5 ) , Marty ( 1 9 5 5 ) , Mize et a l (1 9 5 5 a , b ) , Cork et a l (1956) and has been analyzed t h e o r e t i c a l l y by Chase and W i l e t s ( 1 9 5 6 ) . We s h a l l t h e r e f o r e assume th a t the decay scheme i s e s t a b l i s h e d c o r r e c t l y . During the i r r a d i a t i o n of n a t u r a l y t t e r b i u m , three is o t o p e s are formed, 4 . 2 day Yb 1"^, 3 2 . 4 day Y b 1 ^ , a n d 6 . 7 day L u 1 ^ . However, about 10 times as much Y b 1 ^ as Y b 1 6 9 or L u 1 7 7 i s produced (Cork et a l 1950) and the 396 y 175 kev J-ray of Yb has a gr e a t e r energy than any other from any of the three i s o t o p e s . Y b 1 ^ 9 has a '/-ray of 300 kev, 175 but t h i s i s l e s s intense than the 282 kev y~ray of Yb . Results.: Measurements were made on both the 396 kev /-ray and a l s o on the 282 kev / - r a y ; f o r the former a bottom cut d i s c r i m i n a t o r was used, set t o pass the photopeak of the 396 kev / - r a y ; f o r the l a t t e r a s i n g l e channel k i c k s o r t e r was 0-01 0 J I 100 2" I I 200 /-300 T - 0-01 0.01 0 0.01 h 0.01 0.01 i hi i) 100 1 150 T o 260 GAUSS o 380 " c 510 3 700 100 0 T 150 o 6 0 GAUSS • 100 " € 160 " 175 F I G U R E «J Yb 2 8 2 k e V y - R A Y Upper graph - no external magnetic f i e l d . Middle graph - fields along the trigonal axis. Lower graph - fields perpendicular to the trigonal axis. used, set to pass only the photopeak of t h i s / - r a y . Measure-ments were made wit h zero e x t e r n a l magnetic f i e l d , w i t h f i e l d s of 2 6 0 , 38O, 5 1 0 , and 700 gauss p a r a l l e l t o the t r i g o n a l c r y s t a l l i n e a x i s , and w i t h f i e l d s of 6 0 , 1 0 0 , and 160 gauss pe r p e n d i c u l a r t o t h i s a x i s . In no case was any s i g n i f i c a n t a nisotropy of / - r a d i a t i o n observed at any temperature. The r e s u l t s f o r the 396 kev /-ray are shown i n Figure 8 and the r e s u l t s f o r the 282 kev tf"-ray i n Figure 9« From measurements of the anisotropy of these two V-rays from Y b 1 7 ^ o r i e n t e d In ytterbium e t h y l s u l p h a t e , Grace et a l (1957) deduced a value f o r the magnetic moment of Y b 1 7 ^ . i t I s 0 . 1 5 + 0.04 n u c l e a r magnetons; the s i g n i s not known. The 396 kev /-ray and the 282 kev y-ray are both M2 w i t h a small admixture E l . The experiments so f a r c a r r i e d out do not g i v e c o n s i s t e n t values f o r the mixing r a t i o s of these V-rays (Grace et a l 1 9 5 7 ) . Discussion.: No one has observed paramagnetic resonance i n Y b + + + i n the double n i t r a t e l a t t i c e , hence the s p i n Hamiltonian i s not known. An estimate of the constants i n the s p i n Hamiltonian was made. Since the d e t a i l s of these c a l c u l a t i o n s are presented elsewhere (J.L.G. Lamarche 1956) we w i l l only i n d i c a t e the general procedure and the r e s u l t s . We assume that the c r y s t a l l i n e f i e l d a c t i n g on the ytterbium i o n i s the same as t h a t a c t i n g on the cerium i o n ; the c o e f f i c i e n t s f o r the expansion of t h i s f i e l d i n a s e r i e s of 58 s p h e r i c a l harmonics are given by Judd (1955a). We assume tha t the formula given by E l l i o t t and Stevens (1953a) f o r the ra d i u s of the 4f s h e l l , i s a p p l i c a b l e i n the case of' Yb . Using these values of c r y s t a l f i e l d parameters and i o n i c r a d i i , we can work out an energy m a t r i x f o r the ytterbium i o n us i n g the method and formulae given by Stevens (1952), E l l i o t t and Stevens (1952, 1953a, b ) , and Judd (1955a, b ) . The r e s u l t s of these c a l c u l -a t i o n s are as follows.: whereas the f r e e Y b + + + i o n has J = 7/2 and an e i g h t - f o l d degenerate ground s t a t e , i n the double n i t r a t e environment, t h i s degenerate l e v e l i s s p l i t i n t o 4 doublets whose energies are - 2.26, +39.4, +0.4, and -37.5 cm. - 1. The s t a t e w i t h energy -2.26 cm 1 i s the doublet spanned by e t h y l s u l p h a t e . The lowest energy l e v e l i s the one at -37*5 cm i. This i s spanned by the wave f u n c t i o n . and lowest i n the .... (2) and We assume a s p i n Hamiltonian of the form g ii (3H ZS Z + g j 0 ( H x S x + HySy) + A S z I z + B ( S X I X + S y I y ) (3) The g values i n t h i s s p i n Hamiltonian can be obtained from.: co ' • • * • 3 x = a | < + J L x + ^ x | - > | ^ | < T | | A | | ^ l ^ | - > ) • • • (5) where the | j -A. || are constants given f o r each rare e a r t h . Thus we f i n d f o r Yb + + H" i n cerium magnesium n i t r a t e : 9 i = 4- 2 .It-*-9 The extent of the h y p e r f i n e s t r u c t u r e i s given by A I and B I. These can be evaluated by the f o l l o w i n g formulae.: A I - 4.|SfVl. ( ±3.) < J | | N j| J><4 | J zj- f> . . . . (6) a i - * ^ / * * < £ ) < j I I » l l * X + k l - > • • • • ( 7 ) r where the J| N J| are again constants given f o r each ra r e e a r t h . Here again we use our i n i t i a l assumption to _ o 4-+4- oil o~3 approximate r -> which f o r Y i r " has the value 91 X 10 & H A . 175 Assuming t h a t the magnetic moment of Yb • i s 0.15 nuclear magnetons (Grace et a l 1957) and d i v i d i n g by the Boltzmann f a c t o r , we o b t a i n A I = 0.024°K B I = 0.017°K 6o I t i s t r u e t h a t i t i s r a t h e r o p t i m i s t i c to expect such a c a l c u l a t i o n t o gi v e a r e s u l t which i s q u a n t i t a t i v e l y c o r r e c t , but u n f o r t u n a t e l y no b e t t e r estimate of the p r o p e r t i e s of the ytterbium i o n i n t h i s l a t t i c e e x i s t s . On the b a s i s of these estimates, we should expect to observe nuclear o r i e n t a t i o n under the c o n d i t i o n s of our experiments. In view of the e s t a b l i s h e d f a c t that s i z e a b l e a n i s o -t r o p i c s of both the 396 kev S"-ray and the 282 kev S'-ray have been observed from o r i e n t e d Y b 1 7 ^ n u c l e i (Grace et a l 1957), the absence of an anisotropy i n zero f i e l d i n our experiment can be explained by one or more of the f o l l o w i n g hypotheses.: ( i ) The ytterbium i o n does not enter the l a t t i c e i n a r a r e - e a r t h p o s i t i o n , ( i i ) The s p i n Hamiltonian i s I s o t r o p i c ; i . e . g ^ = g ^ and A = B. ( i i i ) Magnetic I n t e r a c t i o n s i n the double n i t r a t e c r y s t a l destroy the alignment of the ytterbium n u c l e i . ( i v ) The / - e m i t t i n g s t a t e I s l o n g - l i v e d and prec e s s i o n 175 of the e x c i t e d Lu nucleus i n the i n t e r n a l atomic f i e l d s destroys the alignment before the emission of the y'-ray. As f o r the hypothesis ( i i ) , the a p p l i c a t i o n of an e x t e r n a l magnetic f i e l d i n any d i r e c t i o n should cause an aniso-tropy of ^-emission to appear (Gorter 1958; Rose 19^9; Ambler et a l 1953)• Since t h i s does not occur, the p o s s i b i l i t y of the other hypotheses must a l s o be considered. 61 Hypothesis ( i i i ) i s c e r t a i n l y a p p l i c a b l e i n t h i s case. The theory of the e f f e c t of i n t e r a c t i o n s has been given by Daniels (1957), and an order of magnitude c a l c u l a t i o n based on the formulae given there shows th a t the magnetic i n t e r f e r e n c e can be much g r e a t e r than the f o r c e s which tend to o r i e n t the n u c l e i . N a i v e l y , the I n t e r n a l f i e l d at a r a r e - e a r t h s i t e i s about 30 gauss; t h i s w i l l produce a s p l i t t i n g of the ground s t a t e of about 0.01°K, whereas the f o r c e s which tend to produce s p a t i a l o r i e n t a t i o n are of the order of magnitude of (A - B) 1 I, or about 0.007°K. However, the a p p l i c a t i o n of an e x t e r n a l f i e l d l a r g e r than the i n t e r n a l f i e l d of 30 gauss should cause an a n i s o t r o p y to appear, and t h i s i s not so. r e s u l t s , and a l s o to e x p l a i n the d i f f e r e n c e between our r e s u l t s and those obtained at Oxford. In the s p i n Hamiltonian f o r +++ the Yb i o n i n the e t h y l s u l p h a t e , gj_= Oa B. Under these circumstances, the angular d i s t r i b u t i o n of J^-rays i s not a f -f e c t e d by p r e c e s s i o n of the X-emitting nucleus. This i s e a s i l y seen, f o r the angular d i s t r i b u t i o n of af-rays i s given by an expression of the form X where g i s a s t a t i s t i c a l d i s t r i b u t i o n (e.g., Boltzmann) Y-emitting nucleus, and f i s an operator which represents the angular d i s t r i b u t i o n of ^ - r a y s (see e.g., Daniels 1957). Because of the a x i a l symmetry of the i o n and i t s environment Hypothesis ( i v ) i s q u i t e s u f f i c i e n t t o e x p l a i n our (8) f a c t o r , ""y^is a wave-function of the i o n c o n t a i n i n g the 62 i n a r e p r e s e n t a t i o n w i t h S diagonal only the diagonal elements of p appear i n the r e s u l t . I f there i s p r e c e s s i o n f o r a time t before the emission of the / - r a y , P must i n t h i s r e p r e s e n t a t i o n and hence the diagonal elements of Thus the angular d i s t r i b u t i o n of / - r a d i a t i o n i n ytterbium e t h y l s u l p h a t e i s not a f f e c t e d by p r e c e s s i o n . This i s not so f o r the more general s p i n Hamiltonian which presumably a p p l i e s to the double n i t r a t e . I t i s d i f f i c u l t to estimate the l i f e -time necessary to wipe out a l l the anisotropy which should be t h e r e . I f we take as a rough c r i t e r i o n that the l i f e t i m e should be about as long as i t would take f o r the e x c i t e d 175 Lu nucleus to precess i n the atomic magnetic f i e l d , the r e s u l t i s about 1 0 ~ 1 0 seconds. Chase and W i l e t s (1956) have explained t h a t f o r both / - r a y s , the E l t r a n s i t i o n i s s t r o n g l y i n h i b i t e d , and the l i f e t i m e should be about t h a t appropriate to an M2 t r a n s i t i o n . Weisskopf's formula f o r the l i f e t i m e of -8 a 400 kev M2 e m i t t i n g s t a t e gives 10 seconds; since the t r a n s i t i o n i n Yb"*"^ i s a c o l l e c t i v e t r a n s i t i o n , not a s i n g l e nucleon t r a n s i t i o n , a l i f e t i m e of at l e a s t 10 seconds i s more l i k e l y . A question a r i s e s whether the s p i n Hamiltonian of the ytterbium i o n should be used during the p r e c e s s i o n , s i n c e a f t e r the ^-emission the e l e c t r o n i c c o n f i g u r a t i o n should be t h a t of lutecium, which i s not magnetic. This depends p r i n c i p a l l y on the l i f e t i m e s of the 4f s t a t e s . These are exp f + i £f t / p exp are independent of t . probably about 10 t o 10 seconds, t y p i c a l l i f e t i m e s f o r o p t i c a l t r a n s i t i o n s , and i n the absence of f u r t h e r i n f o r m a t i o n the use of the ytterbium s p i n Hamiltonian i s j u s t i f i a b l e . Thus, i t appears th a t hypothesis ( i v ) i s adequate to e x p l a i n our r e s u l t s . This c o n c l u s i o n has r e c e n t l y been confirmed by V a r t a p e t i a n (1957) who measured a l i f e t i m e of 3 . 4 X 10~°' seconds f o r t h i s s t a t e . CHAPTER IV NUCLEAR ORIENTATION EXPERIMENTS IN ANTIFERRO-MAGNETIC SINGLE CRYSTALS Pa r t I Nuclear O r i e n t a t i o n Experiments w i t h Mn-^ and Co^° i n Antiferromagnetic S i n g l e C r y s t a l s I n t r o d u c t i o n I t had been suggested by Daunt (1951) and Gorter (1951) that n u c l e i might be a l i g n e d i n antiferromagnetic s i n g l e c r y s t a l s at low temperatures. At the Neel temperature and at lower temperatures a negative exchange i n t e r a c t i o n pro-duces an a n t i p a r a l l e l o r d e r i n g of the e l e c t r o n i c moments along p r e f e r r e d d i r e c t i o n s of the c r y s t a l l a t t i c e . The magnetic hy p e r f i n e i n t e r a c t i o n then at s u i t a b l y low temperatures should cause an appreciable nuclear alignment. At the time we i n i t i a t e d the work described i n t h i s chapter, the only attempt t o detect nuclear o r i e n t a t i o n i n an antiferromagnetic s i n g l e c r y s t a l had been made i n Leiden w i t h an u n d i l u t e d c o b a l t ammonium sulphate c r y s t a l and no e f f e c t g r e a t e r than 1$ was reported (Poppema 1 9 5 4 ) . Although Mn^4 (Grace et a l 1954) and C e 1 4 1 (Ambler et a l 1 9 5 5 , 1956) had been a l i g n e d i n cerium magnesium n i t r a t e at 0 .003°K where an antiferromagnetic t r a n s i t i o n i s b e l i e v e d to occur i t was not c l e a r whether the alignment was enhanced or reduced at the Neel temperature. At any r a t e these measurements d i d not 64 y i e l d i n f o r m a t i o n on n u c l e a r alignment below the Neel tempera-t u r e . The negative r e s u l t s of the Leiden group w i t h cobalt ammonium sulphate which has a Neel temperature at 0 .085°K (Ga r r e t t 1951) l e d us t o expect that a substance w i t h a higher t r a n s i t i o n temperature might be more s u i t a b l e . Measurements at about 1°K and lower on a n t i f e r r o -magnetic MnF 2 w i t h a t r a n s i t i o n temperature at 6j°K i n d i c a t e d the presence of a considerable n u c l e a r s p e c i f i c heat and t h i s substance was proposed as very promising f o r nuclear o r i e n -t a t i o n (Cooke 1 9 5 7 ) . S i n g l e c r y s t a l s of MnF 2 are q u i t e d i f f i -c u l t t o grow however. We decided to t r y i n s t e a d another a n t i -ferromagnetic s a l t of manganese which i s r e a d i l y c r y s t a l l i z e d from the s o l u t i o n . We s e l e c t e d MnCl 24H 0 although i t s Neel temperature i s some orders of magnitude lower than MnF 2. When these measurements proved s u c c e s s f u l we t r i e d another s a l t of manganese, MnBr 24H 2 9 i n order t o confirm t h i s method of o r i e n -t i n g n u c l e i . 54 The a n i s o t r o p i e s observed f o r the Mn gamma r a d i a t i o n w i t h these c r y s t a l s r e q u i r e d s e v e r a l hours t o a t t a i n a maximum value. Gradual c o o l i n g of the c r y s t a l may account f o r t h i s phenomenon but i t may a l s o be due to some extent to long n u c l e a r r e l a x a t i o n times i n antiferromagnetic m a t e r i a l s . In such a case t h i s method of o r i e n t i n g n u c l e i would be of l i t t l e value. A l t e r n a t i v e l y however nuclear alignment i n ant i f e r r o m a g n e t i c m a t e r i a l s might y i e l d i n f o r m a t i o n on nuclear r e l a x a t i o n phenomena i n t h i s c l a s s of substances. 66 A s e r i e s of experiments was launched i n order to explore the p o s s i b i l i t i e s and general f e a t u r e s of nuclear alignment i n ant i f e r r o m a g n e t i c s i n g l e c r y s t a l s and a l s o to gain some i n s i g h t i n t o the nu c l e a r r e l a x a t i o n mechanism i n such substances. In t h i s chapter we rep o r t on the r e s u l t s of e x p e r i -ments completed to date. Prom the l a r g e number of antiferromagnetic compounds t h a t are known and have been i n v e s t i g a t e d we s e l e c t e d a few s a l t s of cob a l t and manganese f o r t h i s experimental survey. Cobalt and manganese each have an is o t o p e which i s p a r t i c u l a r l y 60 s u i t a b l e f o r t h i s type of i n v e s t i g a t i o n . The isotopes Co and 54 Mn are r e a d i l y a v a i l a b l e , l o n g - l i v e d gamma e m i t t e r s ; they have simple and w e l l known decay schemes and lar g e n u c l e a r magnetic moments. Further the o r i e n t a t i o n of these n u c l e i has been w e l l i n v e s t i g a t e d i n paramagnetic s a l t s . Dr. Myer Bloom po i n t e d out t o the author that t h e o r e t i c a l work p r e d i c t e d a strong dependence of the nuclear r e l a x a t i o n time on the Neel temperature of the a n t i f e r r o -magnetic m a t e r i a l s (Van Kranendonk and Bloom 1 9 5 6 ). Indeed w i t h a l l other f a c t o r s approximately constant f o r d i f f e r e n t s a l t s of a given i o n "¥ ~< T^ , where T i s the nuclear r e l a x a t i o n time and T N i s the Ne'el temperature. For t h i s reason we thought i t might be i n f o r m a t i v e to i n v e s t i g a t e s a l t s w i t h t r a n s i t i o n temperatures d i f f e r i n g by some order of magnitude. We l i s t the s a l t s i n which nuclear alignment has been s t u d i e d and i s reported i n t h i s t h e s i s , w i t h t h e i r 67 Neel temperature. MnCl 4H 0 . . . 1.6°K CoCl 6H 0 . . . 3.0°K 2 2 2 2 MnBr 24H 20 . . . 2.2°K C o C N H ^ C S O ^ 6 ^ 0 . . . 0.085°K MnSiP 66H 2 0 . . . 0.1°K The question a l s o arose whether nuclear alignment would occur f o r n u c l e i of f o r e i g n ions incorporated as I m p u r i t i e s i n the l a t t i c e of an antiferromagnetic c r y s t a l . A f u r t h e r p o s s i b i l i t y dependent upon t h i s i s that the nuclear r e l a x a t i o n time might be ap p r e c i a b l y d i f f e r e n t f o r each type of nucleus i n a c r y s t a l . This would then provide us with a technique to i n v e s t i g a t e the nuclear r e l a x a t i o n time and to d i s t i n g u i s h between t h i s phenomenon and the process of gradual c o o l i n g of the c r y s t a l l a t t i c e . T o study t h i s p o i n t we incorporated fin a small amount of Co i n s i n g l e c r y s t a l s of MnCl 4H 0 and 2 2 54 MnSiP 6H ) and made some p r e l i m i n a r y measurements with Mn i n 6 2' CoCl 26H 2 0 and C o ( N H 4 ) 2 ( S 0 4 ) 2 6 H 2 0 . The r e s u l t s obtained w i t h s i n g l e c r y s t a l s of each s a l t are presented s e p a r a t e l y . In each case we g i v e the mor-phology of the c r y s t a l , the Neel temperature, and the p r e f e r r e d a x i s of antiferromagnetic o r d e r i n g . In the c r y s t a l s used i n these experiments, w i t h the exception of Co(NH 4) 2(S0 4) 26H 2 0 , i t i s not yet known whether t h i s p r e f e r r e d d i r e c t i o n c o r r e s -ponds to only one set of sub l a t t i c e s . Experimental Procedure S a l t s i n the antiferromagnetic s t a t e cannot i n general be cooled by a d i a b a t i c demagnetization and s a l t s which 68 are paramagnetic at l i q u i d helium temperatures but undergo an antiferromagnetic t r a n s i t i o n at lower temperatures w i l l not c o o l a p p r e c i a b l y below the Neel temperature (Ambler and Hudson 1 9 5 5 ) . In the s a l t s we have used the Neel temperature i s e i t h e r i n the l i q u i d helium range or at temperatures t h a t are s t i l l r e l a t i v e l y h i g h f o r a s i g n i f i c a n t degree of n u c l e a r alignment t o be expected. Hence to study the n u c l e a r a l i g n -ment w e l l i n t o the a n t i f e r r o m a g n e t i c r e g i o n e x t e r n a l c o o l i n g of the antiferromagnetic c r y s t a l s i s r e q u i r e d . T h i s was accomplished by p l a c i n g the s i n g l e c r y s t a l s i n good thermal contact w i t h a paramagnetic c o o l i n g s a l t . Since i t may be cooled t o temperatures of the order of 0.01°K by a d i a b a t i c demagnetization from moderate values of H/T and has a l a r g e s p e c i f i c heat we used potassium chrome alum as the c o o l i n g agent. Two techniques f o r e x t e r n a l c o o l i n g have been used i n our work. In the simpler and e a r l i e r technique the c r y s t a l s were covered w i t h aplezon o i l B and embedded between c y l i n d e r s of compressed potassium chrome alum powder. This w i l l be r e f e r r e d t o as technique A. In the l a t e r and more elaborate method some hundred and f i f t y No. 36 B & S enamelled copper wires w i t h a t o t a l surface of about 60 cm 2 were s o f t soldered to a t h i n copper d i s c of 1 cm. diameter. The space between the wires was f i l l e d w i t h f i n e potassium chrome alum powder and apiezon o i l B, and the assembly was pressed i n t o a " p i l l " a t some 5 tons/cm. 2 pressure. This produced a c y l i n d e r w i t h a f l a t copper d i s c at one end. The 69 c r y s t a l was then sandwiched between two such p i l l s and the space between was f i l l e d w i t h Apiezon N grease. This w i l l be r e f e r r e d t o as technique B. This more e f f e c t i v e method of c o o l i n g a c r y s t a l was adopted by the author at the suggestion of Dr. J.C. Wheatley. The f i r s t method was used i n e a r l i e r experiments and when the second arrangement was adopted most of the experiments performed w i t h the f i r s t technique were repeated. When the p i l l s c o n t a i n i n g copper wire were used the magnetic f i e l d was removed slow l y over some 5 minutes i n the a d i a b a t i c demagnetization t o avoid eddy current h e a t i n g . In general one small s i n g l e c r y s t a l of about 0.25 gram weight or l e s s c o n t a i n i n g 5 t o 10 m i c r o c u r i e s of r a d i o a c t i v e Mn-^  and/or Co was used. The c r y s t a l s were grown from seeds some 20 cubic mm. i n volume to a s i z e 2 t o 3 times g r e a t e r . T h i s means t h a t the r a d i o a c t i v e n u c l e i were lo c a t e d i n the outer l a y e r of the c r y s t a l . In a l l the r e s u l t s presented i n t h i s chapter one s i n g l e c r y s t a l was used i n the experiment. In the case of MnClg^HpO and MnBrg^HgO co n t a i n i n g experiments were a l s o performed w i t h the same amount of r a d i o a c t i v e m a t e r i a l d i s t r i b u t e d i n s e v e r a l s mall c r y s t a l s sandwiched between s e v e r a l c y l i n d e r s of c o o l i n g s a l t i n the same assembly. For each experiment we give the approximate dimensions of the c r y s t a l used. U s u a l l y the assembly of potassium chrome alum c y l i n d e r s had a t o t a l length of about 8 cm., and a diameter of 1.1 cm. The temperature of the potassium chrome alum was measured us i n g a mutual Inductance and b a l l i s t i c galvanometer, as the assembly warmed up a f t e r adlabatic demagnetization. The c a l i b r a t i o n of the magnetic thermometer i n the l i q u i d helium range gives an experimental r e l a t i o n between the galvanometer d e f l e c t i o n and the magnetic tempera-ture. This i s of the form £ = a Q + a-j/T. Readings of the b a l l i s t i c galvanometer a f t e r adiabatic demagnetization give a magnetic temperature T m of the KCr Alum from t h i s r e l a t i o n . On account of demagnetizing e f f e c t s d i f f e r e n t values of T m may be obtained with specimens of d i f f e r e n t shapes. The accepted procedure i s to determine the magnetic temperature for a spherical specimen where we now denote t h i s magnetic temperature by T*. The magnetic temperatures T m obtained for a pressed p i l l assembly can be converted to the tempera-tures T* for a spherical specimen when the appropriate cor-r e c t i o n factor i s known using the r e l a t i o n T m + A = T * where A i s the correction f a c t o r . For a specimen e l l i p s o i d a l i n shape t h i s correction factor may be calculated and the correction factor for a sample of any a r b i t r a r y shape may be determined empirically. The correction factor f o r an e l l i p s o i d of large a x i a l r a t i o w i l l be approximately equal to that f o r a c y l i n d r i c a l sample of the same length to diameter r a t i o . Previous workers i n t h i s laboratory have determined a correction factor of 0.025°K f o r a c y l i n d r i c a l pressed p i l l of KCr Alum with a length to diameter r a t i o of J. This i s the value we have used throughout our work. 71 Several workers have studied the r e l a t i o n between the magnetic temperature T and the absolute temperature T of KCr Alum (de K l e r k et a l 1 9 4 9 , Keesom 1 9 4 8 , Bleaney 1 9 5 0 , D a n i e l s and K u r t i 1954, Ambler and Hudson 1 9 5 4 ) . Although the r e s u l t s d i f f e r markedly i n the lowest temperature range, agreement i s f a i r l y good at higher temperatures. We have adopted the values given by Bleaney (1950) t o a s s i g n absolute temperatures t o the potassium chrome alum i n our work. Recent measurements on e x t e r n a l c o o l i n g (Miedema et a l 1958) i n the range between 0.5°K to 0.04°K have shown that the r a t e of c o o l i n g of a c r y s t a l i n a set up very s i m i l a r t o technique B, could be described by the r e l a t i o n : § - A'i (1* - Tf ) . . . . ( 1 ) at the higher temperatures and by the r e l a t i o n . : = Ao ( T 4 - T 4\ .... (2) at the lowest temperatures, and by a combination of these formulae at intermediate temperatures. A^ and Ag are para-meters determined from the experiment, T w and T c are the temperature of the warm c r y s t a l and the c o o l i n g agent r e s p e c t i v e l y . These r e l a t i o n s i n d i c a t e t h a t as the temperature i n c r e a s e s we can expect b e t t e r correspondence between the tem-perature of the KCr Alum and that of the antiferromagnetic c r y s t a l i n our experiments. Since the antiferromagnetic c r y s t a l i n our experiments contains a r a d i o a c t i v e i sotope i t w i l l be a generator of heat and t h i s w i l l f u r t h e r i n crease the temperature d i f f e r e n c e between T w and T q . At "high" temperatures the f o l l o w i n g approximation i s valid.: € = a/T 2 .... (3) where £ i s the gamma ray an i s o t r o p y , T i s the absolute tem-perature and a i s a constant. Using t h i s r e l a t i o n we can check the consistency of our temperature assignments. A p p l i c a t i o n of t h i s r e l a t i o n to our data shows th a t i n s e v e r a l cases the a n i s o t r o p i c s observed are c o n s i s t e n t w i t h the temperatures measured i n the range above 0 .05°K. We may then compare the a n i s o t r o p i c s observed i n our experiments w i t h those observed w i t h the same isotope i n paramagnetic c r y s t a l s at the same temperatures. Prom t h i s comparison we may g a i n some i n s i g h t i n t o the hyper-f i n e s t r u c t u r e c o u p l i n g i n anti f e r r o m a g n e t i c c r y s t a l s . The gamma ray counters were placed about 10 cm. from the r a d i o a c t i v e source. G e n e r a l l y one counter was placed along the a x i s of p r e f e r r e d d i r e c t i o n and the other along some other c r y s t a l l o g r a p h i c a x i s p e r p e n d i c u l a r to the f i r s t . The axes chosen are given f o r each experiment. The procedure f o l l o w e d i n the experiments was the f o l l o w i n g . The anisotropy and temperature were measured as a f u n c t i o n of time from the end of the demagnetization as the potassium chrome alum warmed up. Exchange gas was then introduced i n the sample holder t o warm the s a l t t o the temperature of the l i q u i d helium bath and a n o r m a l i z a t i o n count was taken. The n o r m a l i z a t i o n count was taken f o r 73 i n t e r v a l s of some minutes during about an hour to check the s t a b i l i t y of the counters. The curve given i n each case i s the r e s u l t of one run. However i n each case s e v e r a l runs were made t o check the r e p r o d u c i b i l i t y of the r e s u l t s . The r e s u l t s are presented i n the f i g u r e s In the f o l l o w i n g manner.: measurements of the anisotropy and the in v e r s e of the magnetic temperature ( l / T ) are p l o t t e d as a f u n c t i o n of time from the end of the demagnetization. Although a l a r g e r number of temperature readings were taken In a run than shown, only enough p o i n t s are given to i n d i c a t e the v a r i a t i o n of temperature w i t h time. The curve of the aniso-tropy e x h i b i t s three main f e a t u r e s i n succession: a) an incr e a s e t o a maximum value, b) a l e v e l l i n g o f f or pl a t e a u at t h i s maximum value f o r a time which i n some cases can be of s e v e r a l hours d u r a t i o n , and f i n a l l y c) a decrease. The i n c r e a s i n g p o r t i o n of the curve may throw some l i g h t on nuc l e a r r e l a x a t i o n times. The broad p l a t e a u has to date only served to t a x the patience of the e x p e r i m e n t a l i s t . This could provide however an opportunity f o r nuclear magnetic resonance i n v e s t i g a t i o n s on o r i e n t e d r a d i o a c t i v e n u c l e i (Tolhoek and de Groot 1951» Bloembergen and Temmer 1953, Abragam 1956). Such endeavours are i n progress i n t h i s l a b o r a t o r y at the time of w r i t i n g of t h i s t h e s i s and we are indebted to Dr. Myer Bloom f o r p o i n t i n g out t h i s p o s s i b i l i t y to us. The decreasing p o r t i o n enables us t o determine the anisotropy M n 5 4 ( 2 9 i d ) 2 + 0 + 0.842 Cr 54 0 FIGURE 10 D E C A Y S C H E M E O F Mn 54 5 + OO ( 5 . 2 y ) ft- 0.312 Mev 4+ 2+ 0+ 1 1 N i 6 0 • 2.505-1.333 0 FIGURE U D E C A Y S C H E M E O F Co 60 74 versus temperature curve arid thus t o compare our r e s u l t s w i t h other data. Hence i n t h i s r e g i o n we i n d i c a t e the absolute temperature of the potassium chrome alum at convenient p o i n t s . The presence of the copper wire throughout the KCr Alum w i l l help e q u a l i z e the temperature throughout the volume of the sample. Nevertheless i t i s p o s s i b l e that an appreciable heat leak w i l l introduce s i g n i f i c a n t temperature g r a d i e n t s i n the length and ra d i u s of the KCr Alum specimen thereby rendering the r e s u l t s q u a n t i t a t i v e l y i n a c c u r a t e . To minimize t h i s source of e r r o r we have endeavoured t o reduce the heat leak. T h i s of course means t h a t a run w i l l l a s t f o r s e v e r a l hours and increas e s the p o s s i b i l i t y of d r i f t i n the e l e c t r o n i c s , thereby n e c e s s i t a t i n g s e v e r a l check runs. 54 60 Decay Scheme of Mn and Co .: 54 In Figure 10 we present the decay scheme of Mn (Grape et a l 1954, Strominger et a l 1 9 5 8 ) . Mn^4 decays by e l e c t r o n capture t o an e x c i t e d s t a t e of C r ^ which de-excites by gamma emission to the ground ;state. The gamma t r a n s i t i o n was found t o be E2 (Grace e t ; . a l ) . The ground s t a t e of Mn^4 may have e i t h e r spin' 2 or 3 . Thus two decay schemes are 1 2 0 2 possible.: 3 ^.2 >©. and 2 >2 > 0 . In F igure 11 we present the main fea t u r e s of the decay scheme of Co (Strominger et a l 1 9 5 8 ) . Co decays by @ emission t o an e x c i t e d s t a t e of N i which de-excites by a cascade gamma emission t o the ground s t a t e . The p a i r c a r r i e s o f f one u n i t of angular momentum and the gamma Mn CL- 4 H 20 FIGURE 12 Co CL • 6 H 20 c [ " " " " — - f ia I J FIGURE 20 75 t r a n s i t i o n s are E 2 . The decay scheme may then be represented as f o l l o w s : 5 —i-> 4 2 > 2 2 > 0. McCl 4H^0 General Information The Neel temperature i s 1.6 K (Friedberg and Wasscher 1 9 5 3 ) . Manganous c h l o r i d e c r y s t a l l i z e s i n the monoclinic system and i t s e x t e r n a l morphology i s described i n Groth (1906) whose nomenclature we use. The e x t e r n a l appearance i s shown i n Figure 12 where the a- and b-planes are a l s o i n d i -cated. The a-plane i s g e n e r a l l y q u i t e pronounced and may be e a s i l y i d e n t i f i e d . (3 = 9 9 0 2 5 ' . According t o Gijsman (1957) and P o u l i s and Gijsman (1958) the d i r e c t i o n of easy magnetization i s the c r y s t a l l o -graphic c - a x i s , and the next p r e f e r r e d a x i s i s the b - a x i s . We measured the r a d i a t i o n along these axes hence the anisotropy parameter € i s given by: € = where the s u b s c r i p t s r e f e r t o the axes. The c r y s t a l s used were t h i n and f l a t , about 1 mm. p t h i c k and w i t h an e f f e c t i v e surface of about 1 .5 cm each. (We define the e f f e c t i v e surface as the t o t a l surface of the c r y s t a l i n d i r e c t contact w i t h the copper d i s c s at the end 0.07 r 0.06 0.05 0-04 0.03 0.02 0.01 0 25 20 15 10 5 I-0 _ I > ' T D O °o o J I I I I I I I I o O o o o o O O o o o o o J I L J L _ i L. 0 F I G U R E 13 50 100 150 T I M E [min] M n 5 4 in Mn C L - 4 H , 0 of the KCr Alum p i l l s . The area of the sides of the c r y s t a l i s not taken i n t o account.) R e s u l t s and D i s c u s s i o n Mn 5 4 i n McCl 24H 2 0 Figure 13 shows the r e s u l t of a run where the a n i s -otropy i n c r e a s e s t o a p l a t e a u . I t w i l l be n o t i c e d that the manganese n u c l e i were i n f a c t a l i g n e d along the p r e f e r r e d a x i s ( c - a x i s ) . The anisotropy r e q u i r e s some 100 minutes to reach a maximum. This p a r t i c u l a r run was performed u s i n g technique A. The experiment was repeated u s i n g technique B to c o o l the c r y s t a l . The r e s u l t s were e s s e n t i a l l y the same and w i t h i n s t a t i s t i c a l accuracy n e i t h e r the r a t e of growth of the anisotropy nor the maximum value reached were enhanced. Figure 14 shows the r e s u l t s of a run where the coolant s a l t was allowed t o warm u n t i l a d e f i n i t e drop i n the anisotropy was observed. I t w i l l be n o t i c e d that the anisotropy s t a r t s t o decrease at a temperature of about 0.12°K. The c r y s t a l i n t h i s experiment a l s o contained 60 60 some Co , hence some of the gamma r a d i a t i o n from the Co was counted i n the pulse height a n a l y z e r channel set t o accept the photopeak of the Mn^ gamma r a d i a t i o n . Since t h i s background r a d i a t i o n was i s o t r o p i c w i t h i n l e s s than 1% the aniso t r o p y observed was correspondingly reduced. The pur-pose of t h i s experiment was t o e s t a b l i s h the temperature at which the anisotropy decreased, hence the p o i n t s p l o t t e d i n 0 0 6 0.05 0-04 0-03 0.02 0.01 0 0 0 5 0 ° K i { } 1 j ! j M i 0.060"K | 0.070 ° K ( ° o £ 0.080 ° K | 0-090°K 0-100 ° K 0 I I 0 ° K 0-l20°K Ml ° K I ' 0.130 O.I40°K| 14 12 10 8 T 6 4 J T , l r o 60 120 180 240 300 360 T I M E [min] 420 480 540 600 FIGURE M n 5 4 IN Mn C l 2 ' 4 H 2 0 Figure 14 were not co r r e c t e d f o r t h i s background. In the case where the background i s i s o t r o p i c we may c a l c u l a t e the c o r r e c t anisotropy from the r e l a t i o n ; £ ^ =/^b + ifigd \ E0 where £ c i s the cor r e c t e d a n i s o t r o p y , £"Q i s the observed 5 4 a n i s o t r o p y , l b i s the i n t e n s i t y of r a d i a t i o n from the iyfcr along the b - a x i s , and I B g d i s the background r a d i a t i o n due mainly t o Co r a d i a t i o n . This c o r r e c t i o n f a c t o r may be appreci a b l e s i n c e the photopeak of the 842 kev gamma ray of 54 Mn c o i n c i d e s w i t h the Cornpton p l a t e a u from the 1.33 and 6 0 1 . 1 7 Mev gamma rays of Co . Since I. changes w i t h the 54 n u c l e a r alignment of the Mn n u c l e i , the c o r r e c t i o n f a c t o r w i l l a l s o vary. I t may be assumed constant however when small a n i s o t r o p i c s are i n v o l v e d since then 1^  changes by a few percent o n l y . Further the c r y s t a l s are prepared so tha t I b ^Bgd * T o d e t e r m i n e the c o r r e c t i o n f a c t o r we measure t h i s background r e l a t i v e t o the Co^° count w i t h a Co^° source. In t h i s experiment the c o r r e c t i o n f a c t o r was 2i 1.45. These experiments I n d i c a t e t h a t the assembly of o n u c l e i c o o l s only t o a temperature of about 0 . 1 2 K. E x p e r i -ments described l a t e r show t h a t w i t h e s s e n t i a l l y the same c o o l i n g arrangement and w i t h c r y s t a l s of about the same e f f e c t i v e surface to volume r a t i o the n u c l e i and t h e r e f o r e the c r y s t a l l a t t i c e may be cooled t o a temperature of — 0 . 0 6 ° K . We may then conclude t h a t the n u c l e a r s p i n r e l a x a t i o n time of manganese n u c l e i In t h i s l a t t i c e i s 78 s e v e r a l hours at 0.12°K. Van Kranendonk and Bloom (1956) g i v e the f o l l o w i n g expression f o r the nuclear r e l a x a t i o n time, v a l i d f o r very low temperatures. *Y = C e T A / T (4) where C i s a p r o p o r t i o n a l i t y f a c t o r and may be c a l c u l a t e d from t h e i r paper, T A i s a measure of the anisotropy energy. This r e s u l t i s based on the s p i n wave model of a n t i f e r r o -magnetic substances. Assuming only d i p o l e - d i p o l e i n t e r a c t i o n between the nu c l e a r spins and e l e c t r o n i c spins and using t h e i r d e t a i l e d expression f o r a temperature T = 0.1°K the nu c l e a r r e l a x a t i o n time was estimated t o be C£ 500 hours. The c o n t r i b u t i o n of h y p e r f i n e i n t e r a c t i o n to the n u c l e a r s p i n r e l a x a t i o n i s neglected In these c a l c u l a t i o n s and may be very s i g n i f i c a n t . Experimental work on the r e l a x a t i o n time of protons i n CuCl 22H 2 0 shows a more r a p i d i n c r e a s e of f w i t h decrease of temperature (Hardeman et a l 1956) than p r e d i c t e d by t h i s expression. Cooke and Edmonds (1958) r e p o r t a nuclear s p i n r e l a x a t i o n time of about 7 minutes at 0.5°K i n MnP^ from s p e c i f i c heat measurements. Hence i t i s not s u r p r i s i n g t h a t the nuclear system remains at a temperature of CZ 0.12°K f o r s e v e r a l hours even i f the c r y s t a l l a t t i c e i s appr e c i a b l y c o l d e r . An anisotropy of 01 0 . 0 7 at a temperature of d 0.12°K 54 i s comparable to the anisotropy of Mn observed i n paramagnetic 0.07 0.06 0.05 0.04 0-03 0.02 0.01 0 55 x 5*-5 5 5 x ' 5 $ 5 ^ 5 M * T *5 J 1 1 1 1 I I I L 25 k Q ' T * 20 15 10 5 h 0 o o o o o o o o o o o o 0 O o J 1 1 1 1 1 1 1 1 0 9 0 0 0 0 120 240 360 480 600 TIME [miri] F IGURE I* M n 5 4 in M n B r 2 ' 4 H 2 0 cerium magnesium n i t r a t e at t h i s temperature. This i s i n agreement w i t h the 'expectation t h a t the h y p e r f i n e ' s t r u c t u r e c o u p l i n g of Mn + + i s independent of the s o l i d s t a t e . C o 6 0 i n MnC^4H 0 2 2 R e s u l t s and D i s c u s s i o n Co^° was introduced as an Impurity i n s i n g l e c r y s t a l s of MnCl^H^O and the anisotropy of the gamma r a d i a -t i o n was measured along the same a x i s as i n the experiment discussed above. Several runs were made and a small aniso-tropy was measured. The anisotropy averaged f o r the various runs g i v e s 0 .0075+ 0 . 0 0 2 5 . This e f f e c t i s very small and i n such cases some s u s p i c i o n always remains that i t may be spurious. I t i s conceivable t h a t the c o b a l t n u c l e i do not a l i g n along the c - a x l s . MnBr^4H_0 General Information,: / o , The Neel temperature i s given as 2 . 2 K (Gijsman 1955) and 2.4°K (Henry 1 9 5 4 ) . This s a l t c r y s t a l l i z e s i n the monoclinic system and i t s e x t e r n a l morphology I s described i n Groth ( 1 9 0 6 ) . I t s e x t e r n a l appearance i s very s i m i l a r to MnClp^H^O shown i n Figure 1 2 . (3 = 9 9 ° 6 ' . The d i r e c t i o n of easy magnetization corresponds to the c r y s t a l l o g r a p h i c c - a x i s (Bolger 1955 Gijsman 1 9 5 5 ) . The 022 r 0.20 0.18 0.16 lo o I 0.14 0-12 r 010 0.08 0.06 0.04 0.02 0 s * 5 i o o o o 5 i 0.045 0 0 5 0 ° K 0 0 6 0 °K o o 0 0 7 0 0 K t 0.080°^ 22 20 18 16 14 '/-T 10 8 J , x. 0 60 FIGURE U 120 180 240 T I M E [min] M n 5 4 300 360 420 in M n S i F f i 6 H p O 80 anisotropy parameter i s defined as i n the experiment w i t h MhCl 24H 0 . Th<s c r y s t a l s were b u l k i e r than the MnCl^H^O c r y s t a l s , and were about 2 mm. t h i c k and had an e f f e c t i v e surface of 2 about 1.5 cm each. R e s u l t s and D i s c u s s i o n The c r y s t a l was cooled u s i n g technique A. The measurements were not repeated when technique B was adopted. Figure 15 shows £ and 1/T as f u n c t i o n s of time from demagnetization. I t i s n o t i c e d t h a t the anisotropy i n c r e a s e s extremely slowly and only reaches a maximum a f t e r some 8 hours. Since the Neel temperature f o r t h i s s a l t I s higher than t h a t f o r MnCl 4H 0 we may a t t r i b u t e t h i s t o a longer r e l a x a t i o n 2 2 time. MnSiF 6H„0 General Information The Neel temperature i s 0.1°K (Ohtsubo et a l 1958). The c r y s t a l s are t r i g o n a l and grow i n hexagonal p i l l a r s p a r a l l e l to the t r i g o n a l a x i s (Groth 1906). The p r e f e r r e d a x i s i s along the hexagonal a x i s (Ohtsubo et a l 1958). The anisotropy parameter i n these experiments i s defined by I - I e = j i _ .... (5) 1 81 where I i s the normalized i n t e n s i t y of r a d i a t i o n along the hexagonal a x i s , and I p i s the i n t e n s i t y i n some a r b i t r a r y d i r e c t i o n i n the hexagonal plane. The c r y s t a l was about 0 . 1 5 mm. t h i c k w i t h an e f f e c t i v e surface of about 0 . 8 cm 2. Mn 5 4 i n MnSiP 66H 2 0 R e s u l t s and Di s c u s s i o n Figure 16 shows the r e s u l t s of a t y p i c a l run. I t i s n o t i c e d t h a t the anisotropy grows more r a p i d l y than i n the two previous experiments and the maximum corresponds to a tem-perature of r ^ 0 . 0 5 o K . In other runs (not shown) the coolant s a l t was allowed to warm up to T = 0.12°K, i . e . above the N^el temperature of manganese f l u o s i l i c a t e . In Table I we l i s t the values of £ , T and a ( c a l c u l a t e d from = a/T 2) obtained from these runs. Table I T a 0 . 0 4 5 °K 0 . 2 0 5 4 . 0 2 0 . 0 5 0 0 . 1 8 7 4 . 6 7 0 . 0 6 0 0 . 1 5 4 5 . 5 5 0 . 0 7 0 0 . 1 1 3 5 . 5 3 0 . 0 8 0 O.O83 5 . 3 2 0 . 0 9 0 O.O63 5 . 1 0 0 . 1 0 0.047 4 . 7 0 0 . 1 1 0 . 0 3 9 4 . 6 0 0 . 1 2 0 . 0 3 2 4 . 3 7 82 The decrease i n a at the lower temperatures i s probably due t o poor thermal e q u i l i b r i u m and the f a c t t h a t the approximation £ = a/T i s no longer v a l i d . I t i s a l s o n o t i c e d t h a t a decreases g r a d u a l l y at higher temperatures. Further runs are i n progress to v e r i f y t h i s r e s u l t . At corresponding temperatures the a n i s o t r o p i e s measured are smal l e r by a f a c t o r of about 2/3 from those observed w i t h 54 Mn i n cerium magnesium n i t r a t e i n an e x t e r n a l f i e l d (600 and 1000 gauss) but 3/2 l a r g e r than those observed i n zero e x t e r n a l f i e l d i n t h i s s a l t (Grace et; a l 1954, Bishop et a l 1 9 5 4 ) . Paramagnetic resonance i n v e s t i g a t i o n s of Mn + + i n magnesium f l u o s i l i c a t e , z i n c f l u o s i l i c a t e and bismuth magnesium n i t r a t e have been reported (Arakawa 1 9 5 4 , Bleaney and Ingram 1951 a, Trenam 1 9 5 3 ). The values of D and A i n the s p i n Hamiltonian of Mn + + i n these d i f f e r e n t s a l t s are l i s t e d i n Table I I . The temperature at which these measure-ments were c a r r i e d out and the d i l u t i o n are a l s o g i v e n . Table I I S a l t MgSiF^6H o 0 6 d-ZnSiF^H^O 6 2 T - 1 D cm A cm~'L 0 20 K 1/3 - 0 . 0 2 1 5 - 0 . 0 0 9 0 20° 2/3 - 0 . 0 0 8 0 - 0 . 0 0 9 0 290 - 0 . 0 2 7 4 - 0 . 0 0 9 2 20 - 0 . 0 1 3 4 - 0 . 0 0 9 1 D i l u t i o n t 1/20 t o 150 1/1000 The measurements w i t h magnesium f l u o s i l i c a t e (Arakawa 1954) i n d i c a t e d the presence of s i x magnetic complexes . 0 0 4 5 ° K 0 050 K 0.20 0.18 0-16 0-14 012 N 0-10 0 0 8 0-06 0 O 4 0 0 2 0 0-060° K O 0 .070°K o o o 0.080 ° K 0.090 ° K o O.IOO°K 0. I I0 °K O o 0.120 ° K o o F I G U R E 17 6 0 CO O U I N M n S i lv6H,0 -J- 1 1 1 I L 5 £ - 1 — 1 1 1 I L 14 13 12 10 / - p 9 8 7 6 0 4 0 8 0 120 160 2 0 0 2 4 0 280 TIME [min] 320 3 6 0 4 0 0 4 4 0 4 8 0 5 2 0 560 83 i n the u n i t c e l l . The s i x complexes are equivalent but are o o r i e n t e d at an angle of about 7 t o the hexagonal a x i s . T h i s c o n t r a s t s w i t h the measurements on z i n c f l u o s i l i c a t e (Bleaney and Ingram 1951a) which i n d i c a t e d one magnetic i o n per u n i t c e l l . At any r a t e the d i s t o r t i o n i n v o l v e d i s too small t o account f o r the r e d u c t i o n i n a n i s o t r o p y . Since the magnitude of the D term i n manganese f l u o s i l i c a t e i s unknown at present no d e t a i l e d c a l c u l a t i o n s have been c a r r i e d out. 60 i i ) Co i n MnSiF£6 HgO The r e s u l t s of a t y p i c a l run are shown i n Figure 1 7 . This p a r t i c u l a r run was c a r r i e d out a f t e r a demagnetization w i t h H/T of 13 Kilogauss/degree K s i n c e i t was d e s i r e d to shorten the d u r a t i o n of the experiment. I t i s n o t i c e d t h a t the c o b a l t n u c l e i were a l i g n e d along the p r e f e r r e d a x i s . W i t h i n s t a t i s t i c a l .accuracy the anisotropy observed f o r the 60 54 Co r a d i a t i o n i s equal t o t h a t of the Mn^ r a d i a t i o n and a l s o e x h i b i t s a small decrease i n the value of the parameter a at higher temperatures. The a n i s o t r o p i c s are c o n s i d e r a b l y 6o l a r g e r than any p r e v i o u s l y measured w i t h Co i n any para-magnetic s a l t at corresponding temperatures. For i n s t a n c e Co1 p o l a r i z e d i n cerium magnesium n i t r a t e w i t h an e x t e r n a l f i e l d of 400 gauss g i v e s an anisotropy of about 0 . 1 at 0 .05°K compared t o 0 . 1 8 at 0 .05°K i n t h i s s a l t . Bleaney and Ingram (1951b) have stud i e d the paramagnetic resonance of C o + + i n z i n c f l u o s i l i c a t e and determined the value of A and B i n 60 FIGURE 18 External morphology of Co(NH 4 ) a ( S 0 i J 2 6 H 2 0 crystal 84 i n the s p i n Hamiltonian. I t i s evident from a comparison of these r e s u l t s w i t h the values of A and B f o r C o + + i n the z i n c Tutton s a l t s and bismuth magnesium n i t r a t e that the s p i n Hamiltonian does not account f o r the discrepancy. No attempt has been made to date t o e x p l a i n t h i s l a r g e anisotropy. The runs seemed to i n d i c a t e that the anisotropy of 60 54 Co increased more r a p i d l y than t h a t of Mn i n t h i s same l a t t i c e (compare Figure 16 and 1 7). Hence a c r y s t a l c o n t a i n -60 54 i n g both Co and Mn was prepared. P r e l i m i n a r y measure-ments (not shown) w i t h t h i s c r y s t a l i n d i c a t e that the a n i s o -t r o p i c s increase at the same r a t e . C o ( N H 4 ) 2 ( S 0 4 ) 2 6 H 2 0 General Information Cobalt ammonium sulphate i s a Tutton s a l t . The Tutton s a l t s are an isomorphous s e r i e s w i t h the formula M " XO4 M£ X0 4 6 H 2 0 ; where M" i s a d i v a l e n t metal of the i r o n group ( T i , V, Cr, Mn, Fe, Co, N i , Cu, Zn, Mg), M1 i s a monovalent metal (K, Rb, Ce, NH4, T l ) and X i s one of (S, Se, C r ) . The s a l t s form monoclinic c r y s t a l s whose morpho-logy has been described by Tutton ( 1 9 0 5 , 1913 , 1 9 1 6 ) . The e x t e r n a l appearance i s shown i n Figure 1 8 , where a l s o the v a r i o u s c r y s t a l axes are d e p i c t e d . The b-axls i s perpendi-c u l a r t o the a-c plane; the a and c-axes are i n c l i n e d at an n O angle p ~ 1 0 5 . The p r i n c i p a l axes of magnetic s u s c e p t i b i l i t y are denoted by K , K0, and K , and are mutually p e r p e n d i c u l a r . K.^  and Kg are r e s p e c t i v e l y the d i r e c t i o n s of maximum and minimum s u s c e p t i b i l i t y and l i e i n the a-c plane; K^ c o i n c i d e s w i t h b. We denote by the angle from a to K-^  i n the acute angle between a and c. In the b-K^ plane l i e the two t e t r a -gonal axes denoted by T 1 and T 2; each makes the same angle o( w i t h K . There are two d i v a l e n t c a t i o n s i n the u n i t c e l l of the c r y s t a l , and each i s surrounded by a c r y s t a l f i e l d of roughly t e t r a g o n a l symmetry due mainly t o a d i s t o r t e d o c t a -hedron of s i x water molecules. One t e t r a g o n a l a x i s , say T^, ( i . e . the a x i s of d i s t o r t i o n of the octahedron) I s the mirror-image of the other, Tg, i n the c r y s t a l l o g r a p h l c a-c plane. The p o s i t i o n s of the c r y s t a l l o g r a p h l c and magnetic axes and of the t e t r a g o n a l axes are shown i n Figure 1 8 . For the C o + + i o n we have taken ^ = 4 0 ° , &< = 3 3 ° as given by G a r r e t t ( 1 9 5 1 ) . The magnetic p r o p e r t i e s of a s i n g l e c r y s t a l of cob a l t ammonium sulphate have been e x t e n s i v e l y s t u d i e d by G a r r e t t (1951) between 1°K and 0.04°K. He found the Ndel temperature to be 0.084°K. From l e s s r e l i a b l e measurements Malaker (1951) r e p o r t s a Neel temperature of 0 .125°K. G a r r e t t 1 s work a l s o shows th a t the t e t r a g o n a l axes are the p r e f e r r e d axes of magnetization i n the antiferromagnetic s t a t e . The anisotropy parameter may then be defined as.: P = "^2 " \ . . . (7) 0 . 0 7 0 . 0 6 0 . 0 5 t 0 . 0 4 6 Y- 0 nr 0-03 0 T 0 . 0 2 0.01 0 J L 2 0 h lo o _l L J u i J L T ? I 1 15 10 o o o o o o o o o o 0.045 ° K O O 0 .050 °K 0.060 ° K 0.070 ° K FIGURE 19 Co 6 0 in Co(NH 4)2(S0^) 26He0 0 -I 1 I I L 0 6 0 2 0 8 0 2 4 0 T I M E [min] where a n (* I j ^ a r e the normalized i n t e n s i t i e s of r a d i a t i o n along the and K2 axes r e s p e c t i v e l y . The c r y s t a l was about 3 mm. t h i c k and had an 2 e f f e c t i v e surface of about 1.2 cm . R e s u l t s and D i s c u s s i o n The r e s u l t s of a run are shown i n Figure 19. The r e s u l t s show t h a t the a n i s o t r o p i c s observed are about equal to those measured i n experiments w i t h Co i n paramagnetic Tutton s a l t s at the corresponding temperatures. We may then conclude t h a t the e f f e c t i v e f i e l d at the nucleus i s not s i g n ! f i c a n t l y modified i n the antiferromagnetic s t a t e f o r t h i s s a l t . The magnetic f i e l d f o r a d i a b a t i c demagnetization was a p p l i e d p a r a l l e l t o the a - a x i s , hence p e r p e n d i c u l a r t o the b-axis (K^ a x i s ) and at an angle of 40° to the a x i s The entropy removed i s given by the r e l a t i o n . : S/R = -y tanh y + In'cosh y .... (8) where J f ^ , Jfg and being the d i r e c t i o n cosines of the a p p l i e d f i e l d r e l a t i v e to the p r i n c i p a l axes of e i t h e r set of i o n s . The p r i n c i p a l i o n i c g-values were found from resonance e x p e r i ments (Bleaney and Ingram 19^9) to be 6.2 (along a t e t r a g o n a l a x i s ) , 3.0 and 3.0. In our experiments H/T c£ 1 .5 x 10 gauss/degree. We then c a l c u l a t e y = 1 . 9 6 which y i e l d s a value of S/R = 0 . 6 0 f o r the entropy removed. Prom the curve of S/R versus T given i n G a r r e t t (1951) t h i s i n d i c a t e s a c o o l i n g of the co b a l t ammonium sulphate c r y s t a l t o m 0.055°K upon a d i a b a t i c demagnetization. I t appears from our r e s u l t s (see Figure 19) t h a t the system of n u c l e i r e q u i r e d a few minutes to c o o l t o t h i s temperature. As we mentioned e a r l i e r , the Leiden group reported negative r e s u l t s ( w i t h i n 1$) from an attempt t o detect nuclear o r i e n t a t i o n of Co i n a s i n g l e c r y s t a l of t h i s s a l t (Poppema 195*0 • Considering the i n i t i a l values of H/T used f o r a d i a b a t i c demagnetization and G a r r e t t ' s values of S/R versus T, t h e i r c r y s t a l was c e r t a i n l y cooled to tem-peratures below 0 .05°K (they c l a i m f i n a l temperatures between 0 .02°K and 0.04°K). However i n s u f f i c i e n t d e t a i l s are given i n t h e i r r eport (Poppema 195*0 t o assess f u l l y the meaning of t h e i r experiment. To c l a r i f y the s i t u a t i o n we i n v e s t i g a t e d the anisotropy as a f u n c t i o n of time from demagnetization and of the s u s c e p t i b i l i t y of the specimen w i t h Co i n a s i n g l e c r y s t a l of c o b a l t ammonium sulphate embedded between two pressed p i l l s of co b a l t ammonium sulphate. The temperature of the co b a l t ammonium sulphate p i l l s should be about 0 . 0 5 5 ° t o 0 .0$0°K a f t e r demagnetization. The magnetic f i e l d was p a r a l l e l to the K-L a x i s of the s i n g l e c r y s t a l , hence i t should be a few m i l l l d e g r e e s c o l d e r immediately a f t e r demagnetization 88 We have observed an anisotropy of about 0 . 0 3 5 which seems .to appear immediately a f t e r demagnetization and decreases to , about 0 . 0 2 as the s u s c e p t i b i l i t y of the specimen reaches a 54 maximum. Our c r y s t a l a l s o contained some Mn and f o r t h i s i s o t o p e we observed an anisotropy of ^ 0 . 0 7 decreasing to CZ 0.04 at t h e . s u s c e p t i b i l i t y maximum. A s i m i l a r experiment w i t h manganese f l u o s i l i c a t e has been performed. A s i n g l e 54 c r y s t a l of MnSiP^6H^0 c o n t a i n i n g Mn was embedded between o c. two pressed p i l l s of MnSiF , 6 HO powder. The assembly was cooled by a d i a b a t i c demagnetization from i n i t i a l values of H/T CZ 15 Kilogauss/degree. In two runs the s u s c e p t i b i l i t y a f t e r demagnetization was p r a c t i c a l l y constant f o r two hours. The anisotropy £ observed during t h i s p e r i o d was a l s o constant w i t h a value 2^  0 . 0 3 5 . In a t h i r d run the anisotropy was measured a f t e r the s u s c e p t i b i l i t y had shown a small but d e f i n i t e i n c rease t o a constant value. The aniso-tropy observed at t h i s constant,value was a l s o 0 . 0 3 5 . I t i s not known at present whether MnSiPg6H^0 c o o l s apprec-i a b l y below 0.1°K upon a d i a b a t i c demagnetization. These experiments show th a t n u c l e a r alignment occurs when a sub-stance w i t h a low Neel temperature i s cooled by a d i a b a t i c demagnetization. C o C l 2 6 HgO General Information CoClgSHgO c r y s t a l l i z e s i n the monoclinic system, and i t s e x t e r n a l morphology has been described by Groth Co CI2-6H20 X of POWDER X II to c - AXI S X 1 to c - A X I S - o ° ° ° o o ° ° 0 0 o o o n o O O O Q  u o o °°o O o o o o o o o o o 0 o o 1 1 1 1 1 1 o o o 1 1 1 1 1 1 1 . _L .. . 1 1 1 1 1 1 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 . 0.6 0.8 / V V FIGURE 21 Susceptibility of CoCl 2 6H 2 0 versus temperature in powder and i n single crystal. 89 ( 1 9 0 6 ) . The e x t e r n a l appearance i s shown i n Figure 20 where the a- and c- planes are a l s o i n d i c a t e d . (3 = 1 2 2 ° 1 9 ' . The s a l t was found t o become antiferromagnetic at o about 3 K from s u s c e p t i b i l i t y measurements of the powder (Baseda and Kanda 1957)• From s u s c e p t i b i l i t y measurements wit h s e v e r a l l a r g e c r y s t a l s we determined roughly the pre-f e r r e d a x i s of magnetization. These measurements i n d i c a t e t h a t the p r e f e r r e d a x i s i s p e r p e n d i c u l a r t o the c r y s t a l l o -graphlc c-plane ( i . e . the a x i s p e r p e n d i c u l a r t o the cleavage p l a n e ) . The r e s u l t s of these measurements are shown i n Figure 21 where £ , the galvanometer d e f l e c t i o n i s propor-t i o n a l t o the s u s c e p t i b i l i t y 'X. , according to the r e l a t i o n £ - a D X + a i ( a Q a n d a-jL are constants f o r any one curve but may be d i f f e r e n t f o r each c u r v e ) . With respect to the c-plane we define the anisotropy parameter by £ = ^ " X A (10) where I A i s the normalized r a d i a t i o n i n t e n s i t y i n the d i r e c t i o n p e r p e n d i c u l a r t o the c-plane and Ip i s the normalized i n t e n s i t y i n some a r b i t r a r y d i r e c t i o n i n the c-plane. The c r y s t a l was about 3 mm. t h i c k w i t h 1 .0 cm^ e f f e c t i v e surface,. R e s u l t s and D i s c u s s i o n C o 6 0 i n CoCl 26H 2 0 F i g u r e 22 shows the r e s u l t s of a t y p i c a l run. The a n i s o t r o p i e s are ap p r e c i a b l y s m a l l e r than those observed w i t h 0.18 0.16 0.14 o CoCI 2 6H 2 0 FIGURE 22 M n 5 4 C o 6 0 012 0.10 0.08 0.06 o o 0-045' O o o 0 0 5 0 ° K o o o o o o O 0 6 0 0 K O o O ° o o o 0-070 ° K O o o o o 18 16 o 0.080 ° K O 14 12 10 8 0.090 0 K 0.04 0.02 I I I I 1 I I 0 60 T IME [min] 120 180 240 300 360 42Q 90 60 Co at corresponding temperatures i n paramagnetic c r y s t a l s . I t i s conceivable t h a t there are more than one magnetic i o n per u n i t c e l l w i t h d i f f e r e n t o r i e n t a t i o n s . The s u s c e p t i b i l i t y and anisotropy measurements would then given an e f f e c t averaged over these se t s of i o n s . Work i s i n progress i n t h i s depart-ment under the d i r e c t i o n of Dr. Myer Bloom to I n v e s t i g a t e the proton resonance i n the paramagnetic and antiferromagnetic s t a t e s of t h i s s a l t . I t may be t h a t the p r e f e r r e d d i r e c t i o n i s a c t u a l l y at an appreciable angle t o the c - a x i s . Our deter-mination of the p r e f e r r e d a x i s was only approximate and we d i d not measure the s u s c e p t i b i l i t y f o r intermediate angles t o the c-plane. Greater accuracy i n t h i s respect was not attempted since the main purpose of t h i s experiment was to determine whether the c o b a l t n u c l e i would show an alignment i n an antiferromagnetic s a l t of c o b a l t w i t h a r e l a t i v e l y h i g h Neel temperature and t o estimate the temperature to which these n u c l e i might e a s i l y be cooled. MoT i n CoCl 26H 20 Figure 22 shows the r e s u l t s of a t y p i c a l run. The a n i s o t r o p i e s are c o r r e c t e d f o r the background r a d i a t i o n from the Co°^ i n the sample according t o the r e l a t i o n : .... (11) where 6^ and £ G o are the observed a n i s o t r o p i e s f o r the Mn"^ and Co^° r e s p e c t i v e l y , I C o and 1^ are the normalized 91 i n t e n s i t i e s of r a d i a t i o n i n the plane from the Co" 0 and Mn-3 r e s p e c t i v e l y . We assumed the r a t i o I Q Q / I ^ was constant i n applying t h i s c o r r e c t i o n although l t w i l l vary a few percent w i t h temperature. 60 The Co anisotropy i s too small t o enable us t o draw any conclusions w i t h respect to the r e l a t i v e r a t e of c o o l i n g of the d i f f e r e n t i s o t o p e s . I t i s n o t i c e d t h a t the Mn-' anisotropy i s equal t o th a t observed at corresponding temperatures i n cerium magnesium n i t r a t e i n an e x t e r n a l f i e l d of 600 gauss (Bishop et a l 1 9 5 4 ) . 92 P a r t I I Nuclear O r i e n t a t i o n Experiments  w i t h I 1 3 1 and B r 8 2 i n  Antiferromagnetic S i n g l e C r y s t a l s I n t r o d u c t i o n Recent i n v e s t i g a t i o n s of the n u c l e a r magnetic 19 resonance of F y i n MnF 2,CoF 2, and FeFg have shown a hyper-f i n e s t r u c t u r e i n t e r a c t i o n t o e x i s t between the f l u o r i n e n u c l e i and the magnetic e l e c t r o n s (Shulman and J a c c a r i n o 1 9 5 6 , 1957 , 1958j J a c c a r i n o et a l 1957; J a c c a r i n o and Shulman 1957; Baker and Hayes 1 9 5 7 ) . The f r e e f l u o r i n e i o n ( 2 s 2 2p^) i s diamagnetic and can have no hy p e r f i n e i n t e r -19 a c t i o n w i t h the F ^ nucleus. However, i n a paramagnetic and antiferromagnetic s o l i d the surrounding ions may a l t e r the ground s t a t e i o n c o n f i g u r a t i o n and a hy p e r f i n e i n t e r a c t i o n can r e s u l t . I t has been shown t h a t these I n t e r a c t i o n s depend upon the s p i n o r i e n t a t i o n of the magnetic i o n . There are s e v e r a l mechanisms which might create paramagnetism at the f l u o r i n e s i t e . The two most apparent are; the t r a n s f e r of an e l e c t r o n from the f l u o r i n e i o n and the formation of covalent bonds between the two i o n s . Both mechanisms have been invoked t o e x p l a i n the r e s u l t s of nuclear 19 magnetic resonance of F i n va r i o u s substances. This e l e c t r o n t r a n s f e r a l s o provides a l i k e l y mechanism f o r i n d i r e c t or super exchange I n t e r a c t i o n between the magnetic ions i n the ant i f e r r o m a g n e t i c s t a t e (Anderson 1 9 5 0 , Cooke 1 9 5 7 ). In 93 e i t h e r case the unpaired e l e c t r o n remaining on the F~ i o n w i t h s p i n p a r a l l e l or a n t i p a r a l l e l t o that of the paramag-n e t i c i o n produces a r e l a t i v e l y l a r g e f i e l d at the f l u o r i n e nucleus and hence a h y p e r f i n e s t r u c t u r e coupling i f the nucleus has a magnetic moment. The alignment of the s p i n of the unpaired e l e c t r o n i s coupled to the alignment of the para-magnetic i o n . In MnFg below the Ne'el temperature the Mn"1"4" spins are a n t i f e r r o m a g n e t i c a l l y ordered w i t h the spins ± 5/2 r e s p e c t i v e l y p a r a l l e l and a n t i p a r a l l e l t o a c r y s t a l a x i s . As the temperature i s lowered and the magneti-z a t i o n approaches s a t u r a t i o n i n each s u b l a t t i c e the alignment of the unpaired e l e c t r o n of the f l u o r i n e i o n becomes more 19 complete. From t h e i r measurements of the F , resonance at temperatures from 1.3°K to 20°K J a c c a r i n o and Shulman estimate th a t the h y p e r f i n e s p l i t t i n g parameter A/k i s of the order of 16 x l C f ^ c m " 1 . A h y p e r f i n e s t r u c t u r e i n t e r a c t i o n has a l s o been reported f o r the c h l o r i n e i o n i n c e r t a i n t i g h t l y bound magnetic complexes such as JjEr Clg] — i n potassium c h l o r o i r i d a t e K g l r Gig, and ammonium c h l o r o i r i d a t e ( N H ^ ) 2 I r C l 2 ( G r i f f i t h s and Owen 1954; G r i f f i t h s et a l 1 9 5 3 ; Cooke 1957) which become antiferromagnetic at 3«3°K and 2.1°K r e s p e c t i v e l y (Cooke 1 9 5 7 ) . This h y p e r f i n e c o u p l i n g has a l s o been i n t e r p r e t e d i n terms of a s i m i l a r mechanism of e l e c t r o n t r a n s f e r between the diamagnetic and paramagnetic components (Stevens 1 9 5 3 ) . I f a h y p e r f i n e s t r u c t u r e i n t e r a c t i o n e x i s t s f o r the c h l o r i n e and bromine n u c l e i i n MnClg4 HgO and MnBr 2 4 H 2 0 through one of the mechanisms mentioned above then at 5-0 + K r8 2 I f 2.648 1.475 0.777 0 FIGURE ^ DECAY SCHEME OF Br 82 ~ 2x 10 s Xe 131 m 4.8 x 10 , 0s IT X. 131 I 0.722 0.637 0.364 0.164 0.080 0 F I G U R E M DECAY SCHEME OF 131 o s u i t a b l y low temperatures, say 0 . 0 1 K, we might expect an appreciable o r i e n t a t i o n of these n u c l e i along the p r e f e r r e d d i r e c t i o n of antiferromagnetic o r d e r i n g i n s i n g l e c r y s t a l s of 82 these s a l t s . Bromine has a gamma e m i t t i n g i s o t o p e , Br , hence o r i e n t a t i o n of t h i s nucleus may be detected by measuring 82 the anisotropy of the r a d i a t i o n . F u r t h e r Br i s known to have a f a i r l y l a r g e n u c l e a r magnetic moment of 1 .6 nuclear magnetons, (Green et a l 1 9 5 7 ) . C h l o r i n e does not have any s u i t a b l e isotopes f o r t h i s type of measurement however s t a b l e 131 i o d i n e enriched w i t h gamma e m i t t i n g I which has a l s o a lar g e nuclear magnetic moment of 2 . 5 6 n u c l e a r magnetons ( F l e t c h e r and Amble 1958) may be introduced as an i m p u r i t y at the c h l o r i n e s i t e s i n MnCl 24 R^O and at the bromine s i t e s i n MnBr 4 H 2 0 . For these reasons we have thought i t 2 131 worthwhile to measure the gamma ray d i s t r i b u t i o n from I In s i n g l e c r y s t a l s of MnCl 24 HgO and MnBr 4 HgO and of 82 Br i n MnBr 24 HgO. In Figure 23 we show the decay scheme of I 1 3 1 ^ 3 82 i n Figure 24 the decay scheme of Br Procedure and R e s u l t s I 1 3 1 i n MnCl 24 HgO and MnBr 24 HgO 131 I was produced by neutron bombardment of t e l l u r i u m metal i n the Chalk R i v e r Reactor i n the r e a c t i o n Te" » 1 3° ( n , / ) T e 1 3 1-^> I 1 3 1 . A f t e r chemical s e p a r a t i o n I 1 3 1 i s commercially a v a i l a b l e i n Nal i n b a s i c s o l u t i o n of NoHSO^. One cubic centimeter of t h i s d i l u t e s o l u t i o n c o n t a i n i n g 131 1 m i l l i c u r i e of I ^ a c t i v i t y was poured i n t o 1 c c . of s a t u r -ated s o l u t i o n of MnCl 24 E^O or MnBr g4 R^O. A c r y s t a l seed some 20 cubic m i l l i m e t e r i n volume was placed i n the s a t u r -ated s o l u t i o n and allowed t o increase t o double the o r i g i n a l s i z e . The c r y s t a l was c a r e f u l l y r i n s e d w i t h d i s t i l l e d water and d r i e d w i t h f i l t e r paper. I t was n o t i c e d t h a t only a small f r a c t i o n of the s p e c i f i c a c t i v i t y could be introduced i n the c r y s t a l . To check th a t t h i s a c t i v i t y d i d not r e s i d e i n a t h i n f i l m on the surface of the c r y s t a l we weighed a c r y s t a l and measured i t s a c t i v i t y . Then some of the outer l a y e r was d i s s o l v e d , the c r y s t a l was weighed again a f t e r d r y i n g and i t s a c t i v i t y was measured. The a c t i v i t y remain-i n g i n the c r y s t a l corresponded f a i r l y w e l l w i t h the volume of i t s r e s i d u a l a c t i v e l a y e r . 131 When the I and i t s chemical c a r r i e r are mixed w i t h the saturated s o l u t i o n of manganous c h l o r i d e (or mangan-ous bromide) a f i n e suspension forms i n the l i q u i d . A f t e r the l i q u i d was passed through a f i l t e r paper and t h i s sus-pended m a t e r i a l removed i t was n o t i c e d that a l a r g e r p o r t i o n 131 of the I J a c t i v i t y remained on the f i l t e r paper than i n the r e s i d u a l s o l u t i o n . A small amount of t h i s f i n e suspension l a t e r appeared i n the s o l u t i o n as the c r y s t a l grew. I t i s 131 then p o s s i b l e t h a t the I a c t i v i t y i n the c r y s t a l i s a c t u a l l y i n c l u d e d i n t h i s f i n e suspension and merely becomes trapped i n the body of the c r y s t a l as i t grows. The pro-cedure o u t l i n e d above was repeated w i t h MnBr^ and HgO and 96 the same d i s t u r b i n g phenomenon observed. The c r y s t a l was embedded w i t h Apiezon o i l B between two pressed p i l l s of K Cr Alum and mounted i n the c r y o s t a t . A f t e r a d i a b a t i c demagnetization we counted the 368 kev gamma ray u s i n g both a low cut d i s c r i m i n a t o r to pass the photopeak of t h i s gamma ray and pul s e s of higher energy, and a s i n g l e channel k i c k s o r t e r to accept only the photopeak of t h i s gamma ray. The a c t i v i t y was measured simultaneously along the b-axis and along the c - a x i s . S e v e r a l runs w i t h I 1 3 1 i n MnCl 4 H o 0 and MnBr 4 HO 2 2 2 2 s i n g l e c r y s t a l s f a i l e d t o i n d i c a t e any anisotropy g r e a t e r than 0 . 5 $ . In Table I I I we l i s t the temperature of the K Cr Alum a f t e r demagnetization and i t s temperature at the time exchange gas was allowed i n the sample; as w e l l as the time elapsed w h i l e the KCr Alum warmed up from the i n i t i a l to the f i n a l temperature f o r each run. The formula of the c r y s t a l used i s a l s o g i v e n . 82 Br i n MnBr 2 4 H 2 0 One cc. of saturated s o l u t i o n of MnBr 2 4 HgO i n a quartz ampoule was i r r a d i a t e d to an a c t i v i t y of 5 m i l l i c u r i e s 82 of Br i n the neutron f l u x of the B.E.P.O. p i l e at Ha r w e l l . I t was then brought to Vancouver by C.P.A.'s t r a n s p o l a r f l i g h t . The a c t i v e s o l u t i o n was t r a n s f e r r e d to a small beaker and a c r y s t a l seed of MnBr 2 4 HgO 20 cubic mm. i n volume was placed i n t h i s s o l u t i o n and allowed t o grow to twice i t s o r i g i n a l volume. A f t e r r i n s i n g and dr y i n g the c r y s t a l was o.56 Mev 10' c E CO Z) o o I0; 10' o 0.77 Mev o o o n O O „ o O o o o 1.03 Mev o o o o o o 1.30 Mev 1.45 Mev o o o o o o o FIGURE 3 5 Br 8 2 S P E C T R U M o 10 J L 10 20 30 40 50 V O L T S 60 70 80 90 97 embedded wi t h Apiezon o i l B between two pressed p i l l s of KCr Alum and mounted i n the c r y o s t a t . As can be seen from Figure 24 the decay scheme of 82 Br i s q u i t e complex. We measured the f i v e most intense gamma ray s ; e.g., 1 . 4 5 , 1 . 3 0 , 1 . 0 3 , 0 . 7 7 , 0 . 5 6 mev. These are represented by a double l i n e i n Figure 24. We used a bottom cut d i s c r i m i n a t o r to count the gamma ray of highest energy and a s i n g l e channel k i c k s o r t e r set at the photopeak of each lower gamma ray i n succession. A t y p i c a l spectrum i s shown i n Figure 25 where the counting r a t e i s p l o t t e d against the voltage s e t t i n g of the pulse height analyzer. 82 Br has a h a l f l i f e of 35 hours. In order t o o b t a i n adequate s t a t i s t i c s f o r each gamma ray and t o e l i m i n a t e preparing a second sample we performed a l l the measurements using two separate d u p l i c a t e e l e c t r o n i c systems and operated continuously u n t i l the a c t i v i t y of the sample had died out. This was made p o s s i b l e by e n l i s t i n g the a s s i s t a n c e of Mr. H. Schneider, a graduate student i n t h i s l a b o r a t o r y who assembled the second system of e l e c t r o n i c s and a l t e r n a t e d w i t h the author i n conducting the experiments. In Table I I I we l i s t the r e s u l t s under the fc^-ray observed, the i n i t i a l and f i n a l temperature of the K Cr Alum, and the time elapsed w h i l e the alum warmed up from the i n i -t i a l t o the f i n a l temperature. No anisotropy g r e a t e r than 0 . 0 0 5 was observed f o r any of the Y"-rays. 98 Discussion,: Although there I s a strong p o s s i b i l i t y that the io d i n e d i d not replace the c h l o r i n e or bromine ions i n our c r y s t a l s , the negative r e s u l t s obtained can be a t t r i b u t e d to two main causes. The method used f o r c o o l i n g the c r y s t a l s was c e r t a i n l y crude and i t i s very d o u b t f u l that temperatures even as low as 0.05°K were obtained. I f there i s a hyper-82 131 f i n e s t r u c t u r e coupling f o r Br and I -> i n these s a l t s and 19 i t i s of the same magnitude as that measured f o r F , tem-peratures lower than 0 .05°K would be r e q u i r e d f o r a s i g n i f i -cant anisotropy t o appear. Further n u c l e a r r e l a x a t i o n times of the order of 30 sec. at 4.2°K and 90 sec. at 1.3°K were 19 / observed f o r F i n MnFg (Jaccarino and Shulman 1957 , J a c c a r i n o and Walker 1 9 5 8 ). I t i s p o s s i b l e that even i f the c r y s t a l l a t t i c e were cooled to temperatures of the order of 0.05°K and lower, s i g n i f i c a n t a n i s o t r o p i e s would r e q u i r e an i m p r a c t i c a l l y long time t o develop. CHAPTER V NUCLEAR ORIENTATION EXPERIMENTS IN FERROMAGNETIC SUBSTANCES Introduction.: The Oxford group e s t a b l i s h e d t h a t nuclear o r i e n t -a t i o n could be produced i n a ferromagnetic substance by measur-60 i n g the anisotropy of Co i n a s i n g l e c r y s t a l of c o b a l t metal (Grace et a l 1 9 5 5 , 1 9 5 7 ) . We undertook t o i n v e s t i g a t e nuclear o r i e n t a t i o n i n binary a l l o y s of ferromagnetic sub-stances i n order t o determine whether a hyperfine s t r u c t u r e coupling occurred i n both components of such a b i n a r y a l l o y and t o obta i n thereby some in f o r m a t i o n on the e l e c t r o n i c con-f i g u r a t i o n i n ferromagnetic a l l o y s . In p r e p a r a t i o n f o r t h i s p r o j e c t the author used a r a d i o a c t i v e s i n g l e c r y s t a l of Cobalt metal to acquire experience w i t h techniques of c o o l i n g o m e t a l l i c samples to temperatures w e l l below 0 . 0 5 K. In the course of t h i s work a s i g n i f i c a n t discrepancy was n o t i c e d between the anisotropy measured at a given temperature and the r e s u l t s reported by the Oxford group (Grace et a l 1 9 5 7 ) . 60 In p a r t I we describe the i n v e s t i g a t i o n s w i t h Co i n a cobal t s i n g l e c r y s t a l and i n p a r t I I we discuss the p r o j e c t and describe the p r e l i m i n a r y work on nuc l e a r o r i e n t a t i o n i n a ferromagnetic binary a l l o y . 99 100 Part I 60 Nuclear Orientation of Co i n a Cobalt Metal Single C r y s t a l Experimental Procedure and Results.; A single c r y s t a l of cobalt metal, rectangular i n shape, 0 . 1 3 x 0 . 1 3 x 0 . 3 0 cm. i n s i z e , was prepared by Dr. Peter Myers i n the metallurgy department of t h i s u n i v e r s i t y and placed at our disposal. This single c r y s t a l was i r r a d i a t e d to an a c t i v i t y of 3 microcuries i n the neutron f l u x of the Chalk River Reactor. In a l l experiments with t h i s c r y s t a l the anisotropy i s defined with respect to the hexagonal axis by the r e l a t i o n ; £ = ^"Plane "^Axis ^Plane w h e r e i l A X i s and Ipiane a r e respectively the normalized inten-s i t i e s of radiatio n In the d i r e c t i o n p a r a l l e l to the hexagonal axis of the c r y s t a l and i n any a r b i t r a r y d i r e c t i o n p a r a l l e l to the basal plane. In a preliminaty experiment the c r y s t a l was wetted with glycerine and embedded between two pressed p i l l s of K Cr Alum. The whole sample was cooled by adiabatic demagnetization and observations made as the sample warmed up. With t h i s crude arrangement a maximum anisotropy 5f 0 . 0 5 was observed. Prom measurements using a si m i l a r arrange-ment the Oxford group reported a maximum anisotropy 2i 0 . 0 1 5 (Grace et a l 1 9 5 5 ) . 0.12 r 0.10 -0.08 0-06 -0.04 0.02 0 O 0 0 4 5 ° K I 0 . 0 5 0 ° K ° ~ o' 1 ° ° o o o 1 I 0.060 ° K 0 0 1 I 0 0 7 0 K 0.080 ° K o o O n I o l „ 1 o o J o o o o o 25 2 0 V 10 - 5 * 4 0 2 0 4 0 6 0 F I G U R E C o 6 0 IN COBALT CRYSTAL 8 0 100 120 T I M E [min] 140 160 1801 200 Anisotropy before heat treatment when crystal i s cooled by one copper strip of 6 cm.' surface. Square dots indicate Oxford results at corresponding temperatures. 10J To Improve the c o o l i n g of the c r y s t a l i t was mounted on a copper s t r i p i n the f o l l o w i n g manner. The c r y s t a l was i n s e r t e d i n a small hole cut i n the middle of a copper s t r i p and t h i s assembly was copper p l a t e d together. The s t r i p of copper was 3 cm.long, 1 cm. wide and 0.08 cm. t h i c k , i . e . the t o t a l c o o l i n g surface was about 6 cm . This s t r i p of copper was sandwiched between two h a l f c y l i n d e r s of pressed K Cr Alum powder and the space between f i l l e d w i t h a sludge of K Cr Alum and g l y c e r i n e . The sample was mounted In the c r y o s t a t w i t h the t h i n edge of the copper s t r i p p a r a l l e l t o the demagnetiz-i n g f i e l d i n order t o avoid eddy c u r r e n t s . The r e s u l t s of two t y p i c a l runs are shown i n Figure 26 and 27. In Figure 26 the a n i s o t r o p i e s expected from the Oxford r e s u l t s at the measured temperatures of the K Cr Alum are i n d i c a t e d by square dots. I t i s n o t i c e d t h a t the aniso-t r o p i e s we observed are 3 to 4 times l a r g e r than the former. U n f o r t u n a t e l y we have performed only two runs l i k e that shown i n t h i s f i g u r e . Further i t was r e a l i z e d only a f t e r the nature of the c r y s t a l had probably been a l t e r e d t h a t the 2 c o o l i n g surface provided (6 cm. ) was c e r t a i n l y inadequate. Dr. J.C. Wheatley during a v i s i t to our l a b o r a t o r y i n d i c a t e d 2 to the author t h a t the Oxford group had provided some 200 cm of c o o l i n g surface by l i n k i n g s e v e r a l hundred f i n e copper wires t o t h e i r c r y s t a l . Using t h i s s u p e r i o r arrangement they obtained the r e s u l t s shown i n Figure 26 (Grace et a l 1957) and a maximum anisotropy d 0.15 ( E u r t i 1957) at the lowest temperatures. Q O O o O o 0.060 ° K 0.06 0.04 0.02 20 o o O 0.070 °K 12 FIGURE 27 8 Anisotropy at "high" temperatures of Co^° in cobalt metal single crystal before heat treatment. Crystal cooled via copper strip of 6 cm^  surface. 40 60 T I M E [min] 80 100 1209 1 140 77 102 In the experiment shown i n Figure 27 the c o o l i n g s a l t upon demagnetization f a i l e d t o c o o l to the temperature expected from the i n i t i a l value of H/T. This probably-occurred because not enough exchange gas was present t o conduct away the heat of magnetization. In t h i s run and others s i m i l a r to i t we were endeavouring t o reduce the f i n a l heat leak by u s i n g a very small amount of exchange gas (say 0 . 1 5 microns) during the magnetization of some 5 to 10 minutes i n order t o leave very l i t t l e r e s i d u a l gas a f t e r pumping f o r 20 t o 25 minutes. When adequate exchange gas was used the r e s u l t of the previous f i g u r e was obtained. The r e s u l t s shown i n Figure 27 are given to show t h a t the c o b a l t c r y s t a l could not have been cooled t o a temperature lower than 0.05°K si n c e the c o o l i n g s a l t i t s e l f d i d not c o o l below t h i s temperature. This run and the others l i k e i t a l s o confirm -t h a t the a n i s o t r o p i e s observed are appr e c i a b l y l a r g e r than those reported by the Oxford group In the same temperature range. The c o b a l t s i n g l e c r y s t a l was then heated f o r some o ten minutes at about 1000 C and quenched to room temperature. With the same c o o l i n g and mounting arrangement described above new observations were made on the s i n g l e c r y s t a l . The r e s u l t s of such a run are shown i n Figure 2 8 . A comparison of the r e s u l t s shown i n Figure 26 and 28 i n d i c a t e s that the anisotropy i s now reduced by a f a c t o r of about 2 . 5 at the equivalent temperatures. o o o o o 0.06 r 0-05 0-0 4 0.03 0.02 0-01 0 o 0 20 o o 1 27 26 25 24 23 T 22 20 FIGURE 28 60 Co i n cobalt metal single crystal. Anisotropy after heat treatment, when crystal i s cooled via one copper strip 2 of 6 cm surface. Compare with Figure 26, 4-40 60 TIME [min] 80 100 103 I t was thought at the time that the d r a s t i c heat treatment had i n some way ruine d our co b a l t s i n g l e c r y s t a l . Dr. J.C. Wheatley's v i s i t to our l a b o r a t o r y r e f e r r e d t o above occurred at t h i s time and upon h i s suggestions we proceeded to improve the c o o l i n g of our c r y s t a l . S e v e r a l arrangements were attempted and the techniques which y i e l d e d the best r e s u l t s were the following.: (a) The c r y s t a l was copper p l a t e d In a copper s t r i p 1 .5 cm x 1 .0 cm. x 0 . 0 8 cm i n s i z e . To t h i s assembly we s o f t soldered some two hundred 36 B & S enamelled copper wires w i t h a t o t a l 2 surface of about 150 cm . Pine K Cr Alum powder was i n t r o -duced between the wires and wetted w i t h Apiezon o i l B. This 2 assembly was pressed together t o a pressure of 3 tons/cm . The r e s u l t s of a run with t h i s set up are shown In Figu r e 29 where the square dots again i n d i c a t e the a n i s o t r o p i e s expected according to the Oxford work, (b) In another s e r i e s of experiments we s o f t soldered the c r y s t a l and copper s t r i p assembly mentioned i n (a) to a copper sheet 10 cm by 12 cm. and 0 . 0 0 5 cm t h i c k . This sheet was fo l d e d Into p a r a l l e l s t r i p s and K Cr Alum powder wetted w i t h Apiezon o i l B i n t r o -duced between the f o l d s . This assembly was then pushed t i g h t l y i n t o a l u c i t e c o n t a i n e r . The r e s u l t s of a run wit h t h i s arrangement are shown i n Figure 30 where the square dots again' i n d i c a t e a n i s o t r o p i e s according t o the Oxford group. I t i s n o t i c e d t h a t the a n i s o t r o p i e s now measured are s t i l l somewhat l a r g e r than the Oxford values by a f a c t o r o 0.14 r ° 0-12 0-1.0 0-08 0.06 0-04 0-02 0 o o A 18 16 o o o o 0.045 ° K o o o o o o 0.050 °K O O O 0 . 0 6 0 ° K O O cr o o o 0-070°W O O o o o o ° o 0 14 7_ T 12 H 10 A 8 r 60 Uo in COBALT C R Y S T A L J L J L 0 20 40 60 80 140 160 180 200 FIGURE 29 100 120 T I M E [min] Anisotropy after heat treatment when crystal i s cooled via copper wires with 150 cm surface. Square dots represent Oxford results. T 104 of 1.6 i n Figure 29 and about 1.4 i n Figure 30 although they are app r e c i a b l y s m a l l e r than those observed w i t h the untreated c r y s t a l at equivalent temperatures. The maximum a n i s o t r o p i e s reached i n Figures 29 and 30 are r e s p e c t i v e l y 0.12 and od. 0.10. Several runs w i t h the arrangements described In (a) and (b) confirmed these values. The Oxford group has reported a maximum anisotropy of 0.15 ( K u r t i 1957). The d i f f e r e n c e between our values and the Oxford one may s t i l l be due t o the sup e r i o r c o o l i n g technique used by the Oxford group. However other aspects may be more s i g n i f i c a n t i n the explanation of t h i s d i f f e r e n c e . The Oxford c r y o s t a t and s o l e n o i d enable t h i s group to demagnet-i z e from H/T values of about 30 as compared with H/T values of 16 i n our case. In our experiments w i t h samples c o n t a i n i n g l a r g e amounts of copper wire and copper f o i l we have never been able t o reach the Cu r i e temperature, say T*d 0.033°, of K Cr Alum. The temperatures reached a f t e r a d i a b a t i c demagneti-z a t i o n w i t h arrangements (a) and (b) were only T*a 0.05°K and T*2f 0.06°K (see Figures 29 and 30). We may a t t r i b u t e t h i s f a i l u r e to eddy current h e a t i n g i n the copper since w i t h our i n i t i a l H/T values we should a t t a i n the Curie temperature and indeed we u s u a l l y reach t h i s temperature w i t h a sample c o n s i s t i n g only of K Cr Alum. Samples w i t h l a r g e r surfaces of copper wire or f o i l cooled to temperatures higher than those i n d i c a t e d above and i n a l l experiments w i t h samples c o n t a i n i n g copper wire or f o i l the f i n a l temperatures reached 0-14 0-12 0.10 0.08 006 -0.04 0.02 0 o o 0 0 0 4 5 ° K T5 ° o I 0 0 5 0 0 K 0.060 ° K i 0.070 ° K 0 1 O ' 0.080°tC 1 1 14 12 10 8 I 0 20 40 60 FIGURE 30 Co 6 0 IN COBALT CRYSTAL 80 100 120 140 160 TIME [min] 180 Anisotropy after heat treatment when crystal i s cooled via a copper sheet 2 with 200 cm surface. Square dots represent Oxford results. 220 240 by a d i a b a t i c demagnetization depended on the time taken to remove the f i e l d . I t i s to be expected t h a t eddy current e f f e c t s would be l e s s a ppreciable u s i n g a s o l e n o i d as at Oxford since i n t h i s case the f i e l d i s p a r a l l e l t o the length of the wires or f o i l s hence the f l u x i n t e r s e c t s the smallest area of metal. D i s c u s s i o n I t i s convenient to d i s c u s s the v a r i o u s measurements 60 of the anisotropy of Co i n c o b a l t metal i n terms of the 2 parameter "a" i n the r e l a t i o n £ = a/T . This approximation i s c e r t a i n l y v a l i d at the "high" temperatures range where i t I s a p p l i e d i n these experiments. - 4 2 The Oxford work y i e l d s a value a = 1 x 10 deg (This value has r e c e n t l y been c o r r e c t e d ( K u r t i 1958) and the - 4 2 recent data g i v e s a = 0 . 7 9 x 10 deg . The r e v i s e d value came to our a t t e n t i o n a f t e r Figures 2 6 , 29 and 30 were p r i n t e d and the p o i n t s shown i n these f i g u r e s correspond to the h o value a = 1 x 10 deg .) Our measurements on the c r y s t a l a f t e r heat treatment - 4 2 g i v e a value a = 1 .5 x 10 deg and from measurements on the c r y s t a l before heat treatment we may a s s i g n a value a m l n # 3 x K T 4 deg 2. K h u t s i s h v i l i (1957) has observed a n i s o t r o p i e s of 0 . 1 0 t o 0 . 1 5 i n the temperature range 0 . 0 8 ° to 0 . 0 5 ° K. This would y i e l d values of a ^ 4 x 1 0 ~ 4 t o 6 x 1 0 ~ 4 deg 2. (Although t h i s paper contains scant i n f o r m a t i o n of the experimental d e t a i l s and i s o f t e n neglected In the l i t e r a t u r e 60 i t does confirm our view that r e s u l t s on Co i n Cobalt metal are ambiguous). The nuclear s p e c i f i c heat of cobalt metal has been measured by Heer and Erickson (1957), Heer (1958) and Arp et a l (1957). The data of Heer and Erickson (1957) and Heer (1958) give.: ¥ ^ = 4 x 1 0 - 4 _ b ( l a ) those of Arp et a l (1957) give.: 9jf. = 6.2 x 10" 4 •••• (lt>) R where C/R i s the s p e c i f i c heat per mole and R i s the gas constant. Prom these r e s u l t s we may derive a value of h. -4 p a = 1.4 x 10~ and 2.17 X 10 deg as follows.: I f we assume that the Hamiltonian f o r a cobalt atom i n the hexa-gonal cobalt metal structure i s s i m i l a r to that for the cobalt ion i n the c r y s t a l l i n e e l e c t r i c f i e l d of a x i a l symmetry i n cobalt s a l t s we may write as a f i r s t approximation.: 4 -The s p e c i f i c heat can then be written (Bleaney 1950).: A V z + B (yx + V y ) • • • • ( 2 ) C T = (A 2 + 2 B; 9) I (I + 1) = 4 x l O " 4 5 9 5 9 1 2 ....(3) where I i s the nuclear spin of cobalt 59. Also using t h i s Hamiltonian we may calculate the 60 polar diagram hence the anisotropy expected for Co gamma rays at "high" temperatures. This c a l c u l a t i o n gives.: € = ( A6o - 4o) ( |g ) .... W k2 T2 d° 2 2 I f we assume that A ^) B and drop the B terms then we obtain.: C T 2 ^ A 2 9 ( |1 )~4: x I O - 4 deg 2 and 6.2 x 10~4 .... (5) and 6 cz 60 ( A ? J ( 39 ) 2m2 k^T 28 .... (6) Since we can assume the f i e l d at the nucleus to be the same f o r the cobalt isotopes i n cobalt metal, from the re l a t i o n s H E F F = 1/2 A $ 9 I5g and ^ 6 c . H e f f = 1/2 A 6 Q I 6 O we obtain A^Q = 0.572 A ^ . The value of A^g may be c a l c u l -ated from equation (5) hence the value of A^Q i s known and upon substitution into equation (6) we obtain the r e s u l t £ = 1.4 x 10"V T 2 and 2.17 x 10~4/ T 2. We o f f e r the following q u a l i t a t i v e explanation of these r e s u l t s . Hexagonal cobalt i s formed from face-centered-cubic cobalt by a transformation on cooling below a temperature 1 o of 417 C. This transformation i s seldom i f ever complete and the structure of any p a r t i c u l a r specimen i s often a mixture of face centred-cubic and close-packed-hexagonal forms 108 (van A r k e l 1 9 3 9 ) . For instance Edwards and Lipson (1942), found about equal p r o p o r t i o n s of the cubic and hexagonal o phases i n a sample t h a t had been annealed at 1 ,100 C f o r 5 days and then at about 380° C f o r 1 week. Also small completely cubic s i n g l e c r y s t a l s of c o b a l t have been observed (Edwards and Lipson 1 9 4 2 ) . Even i n the c l o s e packed hexagonal s t r u c t u r e some face-centered cubic o r d e r i n g i s present and t h i s i s r e f e r r e d t o as a s t a c k i n g f a u l t . (Edwards and Lipson 1942, Wilson 1 9 4 2 , Houska and Averbach 1 9 5 8 , Troiana and Tokich 1 9 4 8 ) . The presence of these f a u l t s may be described i n the f o l l o w i n g way. Close-packed s t r u c t u r e s are made by p i l i n g up c l o s e -packed planes of atoms i n three d i f f e r e n t r e l a t i v e p o s i t i o n s . We may r e f e r to these p o s i t i o n s as A, B, C. In proper hexagonal close-packing only two of the p o s i t i o n s are used so t h a t the succession of planes may be represented by ABABAB .... or BCBCBC .... or CACACA .... In the face centered cubic a l l three p o s i t i o n s are used and the succession of planes may be represented by ABCABCA .... A c l o s e packed hexagonal s t r u c t u r e In which a f a u l t occurs may then be represented by the sequence ABABCBC .... In the sample mentioned above Wilson (1942) found on the average one f a u l t i n every 14 planes of atoms. In a sample heated q u i c k l y i n t o the face-centred cubic r e g i o n (600° C) and ice-quenched, Houska and Averbach (1958) a l s o found one f a u l t In every ten planes of the hexagonal c o b a l t . 109 I t i s q u i t e probable then t h a t a f t e r heat treatment our c r y s t a l contained a l a r g e p r o p o r t i o n of the face-centered-cubic phase. I t would then appear from our r e s u l t s that the presence of t h i s phase reduces the anisotropy. This seems q u i t e l i k e l y f o r i n such a s t r u c t u r e (e.g. i r o n ) the body diagonals are the p r e f e r r e d axes of o r i e n t a t i o n of the domains and i s o t r o p i c r a d i a t i o n would be expected i n t h i s case. We do not know how " p e r f e c t l y " hexagonal our c r y s t a l was p r i o r to heat treatment and the phase composition of our c r y s t a l s i n c e i t was subjected t o heat treatment has not yet been determined although work i s i n progress i n t h i s d i r e c t i o n . I f we assume, as seems reasonable, t h a t the c r y s t a l was i n i t i a l l y more hexagonal than a f t e r heat treatment we can s t a t e that the constant "a" f o r a p e r f e c t or n e a r l y p e r f e c t c l o s e packed hexagonal c r y s t a l should be of the order or gr e a t e r than -4 2 3 x 10 deg . This i m p l i e s of course t h a t the c r y s t a l used by the Oxford group f o r t h e i r i n v e s t i g a t i o n s d i d not have a p e r f e c t hexagonal composition. This e x p l a n a t i o n seems t o r e c e i v e c o n f i r m a t i o n from the r e s u l t s reported by K h u t s i s h v i l i ( 1 9 5 7 ) . I t i s i n f e r r e d from t h i s paper th a t the Russian group used f i n e c o b a l t powder embedded i n the c o o l i n g s a l t . The domains were p o l a r i z e d by a l a r g e e x t e r n a l magnetic f i e l d . I t i s known that g r i n d i n g a cob a l t specimen to a f i n e powder w i l l produce small p a r t i c l e s of, p e r f e c t or almost p e r f e c t c l o s e packed hexagonal composi-t i o n (Houska and Averbach 1-958). 110 Further i f we accept the a n a l y s i s given above of the nuclear s p e c i f i c heat data of Heer and E r i c k s o n ( 1 9 5 7 ) , Heer (1958) and Arp et a l (1957) we may then conclude t h a t t h e i r specimen contained a p r o p o r t i o n of the face-centered-cubic phase. This means that i n the Hamiltonian given i n equation (2) the terms A and B are decreased. In other words the h y p e r f i n e c o u p l i n g depends on the c r y s t a l phase i n which the atom f i n d s i t s e l f . At any r a t e our r e s u l t s i n d i c a t e that the data on nuclear o r i e n t a t i o n i n c o b a l t metal i s at present ambiguous and should be f u r t h e r i n v e s t i g a t e d In conjunction w i t h x-ray a n a l y s i s before conclusions may be drawn on the h y p e r f i n e s t r u c t u r e c o u p l i n g i n the metal ( M a r s h a l l 1958) and the con-t r i b u t i o n of the p o l a r i z a t i o n of the conduction e l e c t r o n s to the e f f e c t i v e f i e l d at the nucleus. Such s t u d i e s are being pursued i n t h i s l a b o r a t o r y . I l l P a r t I I Nuclear O r i e n t a t i o n Experiments 54 w i t h Mn i n  Ferromagnetic MnBi Introduction.: In s i n g l e c r y s t a l s of ferromagnetic a l l o y s w i t h hexagonal s t r u c t u r e the domain magnetization i s g e n e r a l l y p a r a l l e l t o the hexagonal a x i s or i n the basal plane per-p e n d i c u l a r t o t h i s a x i s . Hence the unpaired e l e c t r o n spins are a l i g n e d p a r a l l e l or p e r p e n d i c u l a r t o t h i s a x i s . Since these unpaired e l e c t r o n s produce a magnetic f i e l d at the atomic n u c l e i when the system i s cooled to temperatures of o o about 0.1 to 0.01 K, the n u c l e i w i l l a l s o be o r i e n t e d p a r a l l e l or p e r p e n d i c u l a r to the hexagonal a x i s . I f the n u c l e i are gamma-emitting is o t o p e s t h i s o r i e n t a t i o n can be detected by an a n i s o t r o p i c emission of the r a d i a t i o n . Measure-ments of the anisotropy then y i e l d i n f o r m a t i o n on the f i e l d produced at the n u c l e i by the ferromagnetic e l e c t r o n s and hence on t h e i r " l o c a t i o n " . Such observations w i t h hexagonal ferromagnetic c r y s t a l s of b i n a r y a l l o y s should i n d i c a t e whether the e l e c t r o n s are l o c a l i z e d , i n which case only one component nucleus may show o r i e n t a t i o n , or i o n i z e d i n t o a band, i n which case both may show o r i e n t a t i o n . The u l t i m a t e object of t h i s p r o j e c t was t h e r e f o r e t o a s c e r t a i n whether the ferromagnetism should be described by a l o c a l i z e d Heitler-London-Heizenberg model, or a c o l l e c t i v e S l a t e r - S t o n e r model. 112 Procedure.: In face-centered cubic and body-centered cubic f e r r o -magnetic c r y s t a l s the p r e f e r r e d d i r e c t i o n s of domain magneti-z a t i o n are g e n e r a l l y p a r a l l e l t o the body diagonals of the cube or p a r a l l e l to the cubic axes (e.g. n i c k e l and i r o n ) . These are then not p a r t i c u l a r l y s u i t a b l e f o r n u c l e a r o r i e n t -a t i o n experiments. Since i n ferromagnetic c r y s t a l s of hexa-gonal s t r u c t u r e the n u c l e i may a l i g n p a r a l l e l to one a x i s or i n a d e f i n i t e plane we confined our a t t e n t i o n t o t h i s group. A search of the l i t e r a t u r e f o r ferromagnetic binary compounds of hexagonal s t r u c t u r e composed of elements w i t h gamma e m i t t i n g isotopes of adequately long h a l f - l i v e s produced a l i s t of promising a l l o y s ; e.g. MnBi, MnTe, MnSb, CrTe, FeBe. Attempts were made to ob t a i n s i n g l e c r y s t a l s of these compounds by slow c o o l i n g of the melt, In temperature gradient furnaces of var i o u s design. Numerous t r i a l s w i t h s e v e r a l of these a l l o y s produced only p o l y c r y s t a l l i n e specimens from which s i n g l e c r y s t a l s could not be separated. S p e c i a l a t t e n t i o n was given to the compound MnBi. I t i s an l n t e r m e t a l l i c compound w i t h a hexagonal, NiAs, c r y s t a l s t r u c t u r e and a high magnetic anisotropy ( G u i l l a u d 1943)• I t I s most e a s i l y magnetized along the hexagonal a x i s u n t i l the temperature i s reduced below 85°K. Below t h i s temperature i t i s most e a s i l y magnetized p a r a l l e l to the basal plane ( G u i l l a u d 1 9 4 3 , Bozorth 1951). I t s Curie temperature has been found to be about 360°C ( G u i l l a u d 1 9 4 3 , Heikes 1 9 5 5 ) . The gamma e m i t t i n g isotopes Mn^ 4 a n d B i 2 0 7 are very l o n g - l i v e d and r e a d i l y a v a i l a b l e . At the time t h i s p r o j e c t was undertaken i t was known that s i n g l e c r y s t a l s of the r e q u i r e d s i z e had been produced elsewhere by a s p e c i a l technique (Adams et a l 1 9 5 2 , Adams 1957)• This technique r e q u i r e d thorough mixing of the r e a c t i n g components by r o t a t i o n , d i f f u s i o n of the melt through the w a l l s of the c r u c i b l e and subsequent c r y s t a l l i z a t i o n on the o u tside w a l l s of the c r u c i b l e . We attempted t o d u p l i c a t e t h i s experiment w i t h c r u c i b l e s of the same composition as those used i n the o r i g i n a l work and others of various composition but without success. Two s i n g l e c r y s t a l s of some 10 cubic mm. volume each prepared by t h i s method were placed at our d i s p o s a l by Dr. E.A. Adams. We t r i e d to induce s u f f i c i e n t 54 207 Mn and B i r a d i o a c t i v i t y i n these c r y s t a l s by bombardment i n the gamma ray beam of the U. of Sask. betatron f o r 3 months. However the a c t i v i t y induced was much too weak f o r our purpose. Recently s i n g l e c r y s t a l s of MnBi have been prepared by slow c o o l i n g of the melt ( E l l i s et a l 1957) but before t h i s work came to our a t t e n t i o n we had abandoned t h i s approach f o r the one described below. Experiments elsewhere have e s t a b l i s h e d that p o l y -c r y s t a l l i n e specimens of MnBi when annealed at a temperature o of 300 C f o r about 90 hours i n a magnetic f i e l d (e.g. 8000 gauss) form an aggregate of small o r i e n t e d c r y s t a l s w i t h t h e i r p r e f e r r e d a x i s of magnetization p a r a l l e l t o the a p p l i e d f i e l d (Roberts 1 9 5 5 , W i l l i a m s et a l 1 9 5 7 a , 1957b). Hence an assembly of c r y s t a l l i t e s prepared i n t h i s way has been found 114 to be equivalent t o a s i n g l e c r y s t a l (Williams et a l 1 9 5 7 b ) . The formation of t h i s p a r a l l e l arrangement has been a t t r i -buted t o a r e c r y s t a l l i z a t i o n of the MnBi i n the magnetic f i e l d (Boothby 1958). 54 Some MnCl 2 c o n t a i n i n g Mn d i s s o l v e d i n a few drops of d i s t i l l e d water was d r i e d by g e n t l e heating on a t h i n d i s c of manganese weighing about 1 gram. This was then placed i n a molybdenum con t a i n e r and melted i n an i n d u c t i o n furnace 54 f o r a few seconds. The manganese now c o n t a i n i n g Mn was separated from the molybdenum c o n t a i n e r , ground t o a f i n e powder (200 mesh) and thoroughly mixed w i t h f i n e Bismuth powder (100 mesh) i n a p r o p o r t i o n of 45 atoms of manganese to 55 atoms of bismuth. The reason f o r the excess bismuth i s t h a t the r e a c t i o n does not go t o completion and even s i n g l e c r y s t a l s c o n tain some f r e e bismuth phase have been 54 observed ( E l l i s et a l 1957)• When studying the Mn r a d i a -t i o n i t i s of course d e s i r a b l e not to have any unreacted manganese i n the specimen although unreacted bismuth should not a l t e r the r e s u l t s . The mixed powders were placed i n a o quartz c o n t a i n e r and s i n t e r e d at 750 C f o r 12 hours, then o placed f o r some 30 hours i n a small furnace at 310 C between the poles of an electromagnet producing a f i e l d of 12 k i l o -gauss at the sample. (This procedure was adopted by the author on the b a s i s of the work of Roberts ( 1 9 5 5 ) . Our procedure i s s i m i l a r to the technique of W i l l i a m s et a l (1957b) which seems to give b e t t e r r e s u l t s but which only came to our a t t e n t i o n l a t e r . ) 115 A rod shaped p i e c e weighing about 1 .5 gram was cut from t h i s specimen and copper p l a t e d i n a copper s t r i p 2 . 5 cm long, 1 cm wide and 0 . 0 8 cm t h i c k thereby p r o v i d i n g a c o o l -2 i n g surface of some 5 cm . This assembly was embedded wi t h g l y c e r i n e between two h a l f c y l i n d e r s of pressed K Cr Alum powder and mounted i n the c r y o s t a t . R e s u l t s and Discussion,: To i n v e s t i g a t e q u a l i t a t i v e l y whether our specimen behaved as a s i n g l e c r y s t a l we performed the f o l l o w i n g t e s t . The long dimension of our MnBi sample ( 0 . 7 cm.) corresponded to the hexagonal a x i s of the o r i e n t e d c r y s t a l s , i . e . the a x i s along which the e x t e r n a l magnetic f i e l d had been a p p l i e d . The specimen was mounted so t h a t i t could r o t a t e f r e e l y and placed i n dewars wi t h u n s i l v e r e d t a i l s . The sample was p o s i t i o n e d w i t h i t s "hexagonal" a x i s p e r p e n d i c u l a r t o an e x t e r n a l f i e l d and at room temperature the torque on the sample a l i g n e d t h i s a x i s p a r a l l e l t o the f i e l d of 5 k i l o g a u s s . We cooled the specimen sl o w l y to l i q u i d a i r temperature w i t h the f i e l d on. The temperature was determined approximately by measuring the r e s i s t a n c e of a copper c o i l p laced i n the dewar. As the sample cooled the angle between the "hexagonal" a x i s and the magnetic f i e l d increased and at a temperature of about 80°K (corresponding to zero magnetic anisotropy) t h i s a x i s had adopted a d i r e c t i o n p e r p e n d i c u l a r to the f i e l d . The sample was then cooled t o l i q u i d helium temperature at which temperature a MnBi s i n g l e c r y s t a l magnetizes p r e f e r e n t i a l l y 116 i n the b a s a l plane. R o t a t i n g the magnet some 20 degrees caused the sample t o t w i s t a few degrees to r e t a i n i t s a l i g n -ment per p e n d i c u l a r to the f i e l d . 54 The amount of Mn at our d i s p o s a l when t h i s sample was prepared was u n f o r t u n a t e l y inadequate and we obtained only some 30 counts per second i n our counting apparatus. Numerous runs w i t h t h i s sample f a i l e d to show any s i g n i -f i c a n t anisotropy (greater than 2%). Since the technique used when t h i s sample was pre-pared d i f f e r e d from t h a t of W i l l i a m s et a l (1957b) i t i s p o s s i b l e t h a t i n our specimen the c r y s t a l l i t e s were not a l l w e l l o r i e n t e d i n a p a r a l l e l d i r e c t i o n . Further i n our s p e c i -men an appreciable p r o p o r t i o n of unreacted manganese may have been present. We found subsequently that a specimen prepared by s i n t e r i n g at 750°C f o r some 12 hours contained as 54 much as 40$ non-magnetic component. The presence of some Mn i n t h i s non-magnetic m a t e r i a l would gi v e an i s o t r o p i c r a d i a -t i o n d i s t r i b u t i o n and reduce any observable anisotropy. Since we expect the n u c l e i t o a l i g n i n any a r b i t r a r y d i r e c t i o n i n the b a s a l plane any anisotropy present would then be reduced by a f a c t o r of 1/2 compared t o that expected f o r 54 Mn w i t h alignment along one a x i s . The domains should how-ever a l i g n p a r a l l e l when an e x t e r n a l f i e l d of adequate strength i s a p p l i e d i n some d i r e c t i o n p a r a l l e l to the basa l plane. Measurements of the r a d i a t i o n d i s t r i b u t i o n w i t h an e x t e r n a l f i e l d of 100 gauss along the b a s a l plane a l s o f a i l e d to show any s i g n i f i c a n t a n isotropy. 117 At any r a t e the e f f e c t i v e c o o l i n g surface f o r such a r e l a t i v e l y l a r g e amount of m a t e r i a l was c e r t a i n l y inadequate. For these reasons we view the r e s u l t s obtained as i n c o n c l u s i v e . I t i s proposed to repeat these measurements with a more a c t i v e sample prepared according to the procedure of Wi l l i a m s et a l (1957b) and usi n g a much l a r g e r c o o l i n g surface. 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JACKET RESERVOIR M °0 OUT 4> TO SAMPLE - TUBE PHILLIPS GAUGE ROTARY PUMP D: DISCHARGE TUBE M: MANOMETER Hg 120 cm FIGURE / V A C U U M S Y S T E M FIGURE 9^ M U T U A L INDUCTANCE BRIDGE LIQUID HELIUM AND NITROGEN DEWARS CALORIMETER,-;AND SUSCEPTIBILITY COILS SOURCE CATHODE FOLLOWER LINEAR AMPLIFIER CATHODE FOLLOWER LINEAR AMPLIFIER AMPLITUDE DISCRIMINATOR PULSE HEIGHT ANALYZER S C A L E R .AMPLITUDE DISCRIMINATOR S C A L E R PULSE HEIGHT ANALYZER S C A L E R S C A L E R F IGURE 3 BLOCK DIAGRAM OF THE COUNTER ARRAY F I G U R E i o o no o 6 o o 6 no o 6 h G 1 ooi h £ o -o.oi o.oi o -0.01 1 t 0.01. h i T 200 300 ill] 1 - 1 I) 100 < > T I ° 150' 0 260 GAUSS • 380 " € 510 O 700 0 0 _L -o.oi h I T 100 0 T 150 O 60 GAUSS • 100 " e 160 " F I G U R E 5 Yb 396 k e V y -RAY 001 0 0.01 h e 100 1 200 I 3 0 0 t-r 0.01 0 aoi 0.01 0.01 I T (I i ± 4)100 '/- 150 T 1 o 260 GAUSS o 380 " © 5 1 0 d 700 i I"1" 100 T 150 O 60 GAUSS • 100 " © 1-60 " 175 F I G U R E J Yb"° 2 8 2 k e V y - R A Y M n 5 4 ( 2 9 i d ) 2 + 0 + 0.842 Cr 54 0 FIGURE io D E C A Y S C H E M E OF Mn 54 5 + C O (5.2y) fi~ 0.312 Mev 2 + 0+ 6 0 2.505 .333 0 FIGURE ll D E C A Y S C H E M E OF Co 6 0 -O 0.07 r 0.06 0.05 0 .04 0 0 3 0.02 0.01 0 2 5 2 0 15 10 0 i j i i i •> T D O ° o o J I I I L O O o O O O O O O O O Q O J I L J I I L J I I U 0 5 0 100 TIME [min] FIGURE n M n 5 4 in M n C L - 4 H 2 0 150 0.06 r 0.05 0-04 0.03 0-02 0.01 0 t 0.050 °K | ° 0 .060 °K | 0 .070 °K ) ° o 0.080 ° K | 0 .090°K O.IOO°K 0-IIO°K O.I20°K °°\° 0 ° K I < O.I40°K| 14 12 10 8 '/_* 6 4 1 f 9 I 0 60 120 180 240 300 360 TIME [min] 420 480 540 600 F I G U R E ' f t M n 5 4 IN M n C I 2 ' 4 H 2 0 0-07 0.06 0.05 0.04 0-03 0.02 0.01 0 §5 5 I 5 J 1 — : — _ i ; i I I i i L 0 '/r# 25 f o o T 2 0 15 10 ° ° o ° o o o ^ ° o ° ° ° o o o o o o o J I I , I I I I I 1_ L O 9 O O 120 2 4 0 3 6 0 4 8 0 6 0 0 T I M E [min] F I G U R E /5 M n 5 4 in M n B r 2 ' 4 H 2 0 0-22 r 0.20 0.18 0.16 0.14 0-12 010 0.08 0.06 0.04 0.02 0 * 5 5 5 i 5 o -5-5 'K I 5 0.045°k 0.050 0 K 1 • 0 0 6 0 0 K o o 0 0 7 0 0 K t 0.080^ 22 20 18 16 14 12 10 8 7-T 0 60 F I G U R E /& 120 180 240 300 360 T I M E [min] M n 5 4 in M n - S i F « - 6 H 2 0 4Z0 .0-045 ° K 0-050 ° K 0.20 0-18 0-16 0.14 0.12 0-10 0 0 8 0-06 0 O 4 0-02 0 0-060°K 0.070 ° K Oo 0.080 °K 0.090 ° K O.IOO ° K 0.110 °K,-0.120 ° K oo od F I G U R E / 7 i Co6 0 IN MnSi F6 • 6 H 2 0 -I 1 L 1 *; | I 5 5 j - i — 1 1 L 14 13 12 9 8 7 6 0 4 0 8 0 120 F 160 2 0 0 240 280 T I M E [min] 320 360 4 0 0 4 4 0 4 8 0 520 560 0.07 r 0 . 0 6 0 . 0 5 0 . 0 4 0.03 I o <> 11 i i 1 I 0 T 0.02 0.01 h J I I I L 2 0 r |o o o o 10 o o o o o 0.045 ° K O O O.050°K o.oeo°K 0.070 K -I 1_ I L J 1 l _ 0 6 0 120 1 8 0 2 4 0 Co Cl2- 6 H20 X of POWDER % II to c - AX I S X 1 to c - A X I S 5 4 3 S 2 - o ° ° n • - n o O O O Q ° o ^oooo^ ° o o o o o o °°o O o o o o o -o o o o o o o o o 1 1 1 I I I o 1 1 1 1 1 1 1 1 1 1 1 I I 1 0.2 0.4 " 0.6 0.8 0.2 0.4 . 0.6 0.8 0.2 0.4 . 0.6 0.8 v 1/ 1/ \, ^ T T T 0.20 r 0.18 0.16 0.14 i 1 ! 11 CoCI2-6H 20 FIGURE 22 Mn 54 I i C o 6 0 I 0.12 0.10 0 . 0 8 0 . 0 6 o 0-045* i o t ° o „ 0 0 5 0 0 K o o 5 o O 0 0 6 0 0 K o O o o o 0.070 ° K o o ° O o o o 0.080 ° K o o 18 16 14 12 10 8 0.090°K 0 . 0 4 0 . 0 2 5 5 I 3 5 5 5 5 5 _ $ 0 6 0 T I M E [min] 120 180 2 4 0 3 0 0 4 3 6 0 4 2 Q ( 4- ) (3+) ( 2 + ) 0 + Kr 8 2 I I 0 .777 0 F IGURE £ 3 DECAY S C H E M E OF Br 8 2 ~ 2x 10 1 1 s Xe 131 m 4.8 x I O " l o s IT X, 131 1 0.722 0.637 0.364 0.164 0 . 0 8 0 0 F I G U R E ,?f D E C A Y S C H E M E OF I 131 C O U N T S - m i n-i / o o ...ro "n o -i-i—i i i o 4> T 1—I I I I | -I 1 1 1—t 8 O o o o ro o 73 m OJ o o < o CO cn o CJJ 0 0 ro CO " 0 m o —I 73 C o o O o < o 0) o < O 0 0 o o o 4^  < . o < 0.12 0.10 0 .08 0-06 0 .04 0.02 0 -i 25 i i 2 0 0-045°K O n I 0 .050°K Q ° o 0 j I 0 .060°K i ° ° o l « I 0.070°K la ° o J 0 . 0 8 0 °K I o O o o d J i_ 15 V 10 0 2 0 4 0 6 0 8 0 100 120 140 T I M E [min] 160 180 T 200 F I G U R E Jl(s C o IN C O B A L T C R Y S T A L o o OJ 10 OJ in CVJ OJ ro OJ OJ OJ OJ O OJ i 1 1 1 1 1 1 r - C - 1 O GO HO 1 -o 1 I o -o ID O L L I I o 1 I o-I o-•o- 1 J I I L o CM tD m *t ro oJ — O O o O O O 6 6 6 , • 6 d 6 0.14 r 0.12 0.10 0-08 0 .06 0 .04 0 .02 0 0.045 °K I I 0.050 °K O o 0.060 °K O n O , I 0.0700W o 6 2 0 18 16 14 I G o 6 0 in COBALT C R Y S T A L fig- a? J L j i — : 1 L 12 10 8 T 0 2 0 4 0 6 0 8 0 100 120 140 160 180 2 0 0 T I M E [min] 0.14 r 0.12 [ 0.10 0.08 0.06 [ 0.04 [ 0,02 o o. o o 0 0 . 0 4 5 ° K I ° o \ 0 0 5 0 0 K ° J 0 . 0 6 0 0 K 1 0 . 0 7 0 ° K o I ° 0 | 0 . 0 8 0 ° K -. ° °°° \ 19 j i_ J L 16 14 12 10 8 F I G U R E 2 0 4 0 6 0 C o 6 0 IN COBALT C R Y S T A L 8 0 100 120 T I M E [min] 140 160 180 220 2 4 0 

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