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Experiments on nuclear orientation at low temperatures Lamarche, Gilles 1956

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Faculty of Graduate Studies P R O G R A M M E O F T H E F I N A L O R A L E X A M I N A T I O N F O R 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 GILLES LAMARCHE B . A . , College Brebeuf, Montreal B.Sc, Universite de Montreal M . A . , University of British Columbia FRIDAY, DECEMBER 28th, 1956, at 11:00 a.m. IN R O O M 300, PHYSICS BUILDING C O M M I T T E E IN C H A R G E / D E A N G . M . S H R U M , Chairman J . M . D A N I E L S C . A . M C D O W E L L J . B . B R O W N C . REID G . M . V O L K O F F G . R . T O U G A S J . B . W A R R E N ~ R. R . J E F F E L S External Examiner: N . K U R T I University of Oxford EXPERIMENTS O N N U C L E A R O R I E N T A T I O N A T L O W TEMPERATURES A B S T R A C T At the low temperatures attainable by the technique of adiabatic demagne-tization, it is possible to produce under certain favorable conditions an almost complete orientation in space of the nuclear spins. Observation of the gamma radiation emitted by such an assembly of oriented radioactive nuclei often shows an anisotropy in the intensity with respect to the direction of observation. From this anisotropy it is possible to deduce the multipole order of the electromagne-tic radiation, the change in angular momentum occurring in the transition that precedes it, and the value of the nuclear magnetic moment of the emitter. Using Bleaney's method for nuclear alignment, two isotopes were studied. Firstly, Yb in cerium magnesium nitrate in the temperature range from 1.2° K . to 0.005° K . The same isotope was also investigated in Oxford in ytterbium ethyl sulphate, and the object of our experiment was to find out if, given two salts suitable for nuclear alignment, the interaction in the crystal could affect'the anisotropy. It was found to be the case. While the Oxford experiment revealed a sizeable anisotropy, none was observed in our own. The absence of anisotropy is attributed in our case partly to magnetic interaction between the paramagnetic ions and partly to a relatively long lifetime of the excited state of Lu" 5 from which the gamma-ray is emitted: a deorientation of the nuclei before emission ruins the effect. This is not the case in the ethyl sulphate. The second isotope Pr" 2 was also investigated by Bleaney's method from 4.2° K . to 0.005° K . The possible values of anisotropy to be expected were 0.33, 1.00, or —1.00. The experiment clearly showed that there was no anisotropy. It is almost certain that the details of "the decay shemes so far proposed are in-correct. Either the spin of Pr'4 2 is 0, not 2 as has been suggested, or the decay chain which ends in the gamma-ray observed includes a state of spin 0 before the emission of the gamma-ray. An explanation which must be considered, how-ever, is that the properties of the praseodymium ion in this crystal lattice are not fully understood. Finally, a series of experiments have been performed in an attempt to detect calorimetrically the nuclear quadrupole specific heat of I and Br in covalent com-pounds. This investigation was a contribution to the problem of nuclear align-ment by Pound's method, and was part of a research ^program initiated by J. M . Daniels at Oxford. The observation of the effect was rendered impossible be-cause the nuclear ionic relaxation-time'fo'r'the establishment of an equilibrium in temperature was longer'than'expected. PUBLICATIONS A theoretical investigation of the Nuclear Resonance Absorption Spectrum of AF ' in Spodumene G. Lamarcb_e and.G. M . _Yolkoff, Canadian Journal of Physics, 31, 1010, 1953. Further Calculations on the Nuclear Resonance Spectrum.of A l " in Spodumene G. M . Volkoff and G. Lamarche, Canadian Journal of Physics, 32, 492, 1954. Experiments to Detect and Determine Calorimetrically Nuclear Quadropole Hyperfine Structure A communication by J. M . Daniels and G. Lamarche, Conference de Physique des basses temperatures, Paris, 1955. G R A D U A T E STUDIES Field of Study: Physics Quantum Mechanics G. M . Volkoff Group Theory in Quantum Mechanics W . Opechowski Electromagnetic Theory W . Opechowski Magnetism W . Opechowski Nuclear Physics K . C. Mann Low Temperature Physics J. M . Daniels Theory of Measurements A . M . Crooke'l, Special Theory of Relativity H . Koppe Quantum Theory of Radiation F. H . S. Cornish Physics of the Solid State J. S. Blakemore and J. B. Brown Other Studies: Differential Equations T. E. Hul l Advanced Theory of Functions W . H . Simons The Theory of the Chemical Bond.- . C. Reid Theory of Metals and Alloys H . P. Myers EXPERIMENTS ON NUCLEAR ORIENTATION AT LOW TEMPERATURES by GILLES LAMARCHE B.A., College Brebeuf, Montreal, 1947 B.So. Unlverslte" de Montreal, 1950 M.A., University of B r i t i s h Columbia, 1953 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of Physica We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December, 1956 1 ABSTRACT At the low temperatures attainable by the technique of adiabatic demagnetization, It i s possible to produce under certai n favorable conditions an almost complete orientation i n space of the nuclear spins. Observation of the gamma radiatio n emitted by such an assembly or oriented radioactive nuclei often shows an anisotropy i n the int e n s i t y with respect to the d i r e c -t i o n of observation. From t h i s anisotropy i t l a possible to dee duce the multipole order of the electromagnetic radiation, the change i n the angular momentum occuring i n the t r a n s i t i o n that precedes i t , and the value of the nuclear magnetic moment of the i emitter. 5 u i Using Bleaney's method for nuclear alignment, two 1SQ-'> topes were studied. F i r s t l y , Yb*^5 i n cerium magnesium nitrate] i n the temperature range from 1.2° K. to 0.005° K. The same Isotope was also investigated i n Oxford i n ytterbium ethyl sul- ? phate and the object of our experiment was to f i n d out i f , given two s a l t s suitable f o r nuclear alignment, the Interactions i n the c r y s t a l could a f f e c t the anisotropy. It was found to be the case,. While the Oxford experiment revealed a sizeable anisotropy, none was observed i n our own. The absence of anisotropy i s attributed i n our case p a r t l y to magnetic i n t e r a c t i o n between the paramagnet-i c Ions and p a r t l y to a r e l a t i v e l y long l i f e t i m e of the excited state of Lu^5 from which the #-ray i s emitted: a deorlentation of the nucleus before emission ruins the e f f e c t . This Is not the case i n the ethyl sulphate. i i The second Isotope Pr was also investigated by Bleaney's method from 4.2° K. to 0 .005° K. The possible values of anisotropy to be expected were 0 . 33 , 1.00, or - 1 . 0 0 . The ex-periment c l e a r l y showed that there was no anisotropy. It i s a l -most certa i n that the d e t a i l s of the decay schemes so f a r pro-, posed are incorrect. E i t h e r the spin of Pr i s 0 , not 2 as has been suggested or the decay chain which ends i n the tf-ray ob-served includes a state of spin 0 before the emission of the Y -ray. An explanation which must be considered, however, i s (that the properties of the praseodymium ion i n t h i s c r y s t a l l a t t i c e ' )' I • are not f u l l y understood. F i n a l l y , a series of experiments have been performed i n an attempt to detect c a l o r l m e t r i c a l l y the nuclear quadrupole s p e c i f i c heat of I and Br i n covalent compounds. This i n v e s t i -gation was a contribution to the problem of nuclear alignment by Pound's method, and was part of a research program i n i t i a t e d by J . M. Daniels at Oxford. The observation of the e f f e c t was rendered impossible because the nuclear-ionic relaxation time f o r the establishment of an equilibrium i n temperature of the nuclear spin system was larger than expected. In presenting t h i s thesis 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 Universit}' of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available f o r reference and study. I further agree that permission f o r extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by h i s representative. I t i s under-stood that copying or publication of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Physics The University of B r i t i s h Columbia, Vancouver #, Canada. Date December, 19,56  i i i ACKNOWLEDGEMENTS I would l i k e i n the f i r s t place to express my g r a t i -tude to Dr. J . M. Daniels, who suggested the problems and helped me i n every phase of the work. I am thankful to him f o r having investigated many of the t h e o r e t i c a l aspects of the project and f o r having c a r r i e d out many of the calculations that are given i n t h i s t h e s i s . I wish also to thank Miss B. Fulton f o r assistance during every experiment, f o r typing the thesis, and f o r looking a f t e r the many d e t a i l s Involved In e d i t i n g a t h e s i s , The work could not have been earrl'ed through without the excellent coop-eration of Mr. H. Zerbst who i s responsible for the production of the l i q u i d helium and who manages the equipment i n the low temperature laboratory. I wish to acknowledge also the s t a f f of the workshop fo r continued assistance i n a l l phases of the work. I thank e s p e c i a l l y Mr. J . Lees and Mr. E. Price f o r t h e i r cooper-ation i n problems related to t h e i r f i e l d of work. I am g r a t e f u l also f o r the help of Mr. Laos i n handling the radioactive samples. The members of both the Van de Graaf and the Beta Spec-troscopy laboratories deserve s p e c i a l acknowledgement f o r t h e i r advice and help i n matters Involving nuclear physics. I would l i k e to thank equally a l l the members of the Low Temperature group who have helped i n the many long experiments. F i n a l l y , I wish to acknowledge g r a t e f u l l y the follow-ing i n s t i t u t i o n s who have provided me with f i n a n c i a l assistance: Le Ministers du blen-etre s o c i a l et de l a Jeunesse de l a Province de Quebec, f o r a bursary, the National Research Council f o r two summer asslstantship3, and 1'Association canadienne fran-caise pour l'avanceraent des sciences, for a bursary. TABLE OF CONTENTS Page INTRODUCTION I 1 CHAPTER I A FEW PRELIMINARY REMARKS ON THE ANGULAR DISTRIBUTION OF GAMMA RADIATION FROM ORIENTED NUCLEI 4 A The methods of ori e n t a t i o n ...... 4 1. The Brute Force method 7 2. Pound*s method 8 3 . The method of Rose and Gorter, and Bleaney's method 8 ( B The atfguTar d i s t r i b u t i o n of gamma radiation .. 13 CHAPTER II DESCRIPTION OF THE APPARATUS 20 A The apparatus for adiabatlc demagnetization .. 20 1. The cryostat 22 2. The sample tubes 24 3. The s u s c e p t i b i l i t y briclge 25 v, 4. The magnets e. 26 B Gamma ray detection equipment 32 C A control experiment, the gamma ra d i a t i o n anisotropy from aligned Co&0 37 CHAPTER I I I AN ATTEMPT AT THE NUCLEAR ORIENTATION OF YTTERBIUM 175 40 t Introduction' • 40 A Theoretical aspects 41 1. The decay scheme of Y b 1 ^ 41 2. Yb* 4* ion i n the cerium magnesium nijbrate l a t t i c e and the expected hyperfine structure .; 43 3» Radiation anisotropy to be expected from the 396 kev. t r a n s i t i o n 49 B Experimental d e t a i l s 51 1. The cooling agent 5^  2. Preparation of the samples 52 3. Procedure 53 4. Treatment of the experimental data •• 56 C Results and Discussion 57 1. Results 57 2. Discussion • 5@ CHAPTER IV THE EXPERIMENT ON PRASEODYMIUM 142 62 A Theoretioal aspects 62 1. The reason f o r studying P r 1 ^ 2 62 2. The decay scheme 62 3. Paramagnetic properties of P r + + + .... 63 4. Anisotropy expected 64 B Experimental aspect 65 C Results and Discussion ..................... 65 CHAPTER V AN ATTEMPT ON CALORIMETRIC DETECTION OF THE NUCLEAR SPECIFIC HEAT 70 The problem ....•..•*.. 70 A The technique 74 B Experiments with the para-iodo benzene and para-toluene sulphonates c 75 1. The samples o . 76 2. The procedure , 79 3 . Results o . 80 C The experiment on bromine In bromate s a l t s .. 81 BIBLIOGRAPHY • 85 v i i LIST OF ILLUSTRATIONS to follow page Figure 1 Energy Levels i n Zero Magnetic F i e l d f o r S . 1/2, I • 7/2 11 Figure 2 Vacuum System 22 Figure 3 Mutual Inductance Bridge . 25 Figure 4 Block Diagram of Counter Array - i p S Figure 5 Photomultlpllers and Cathode Followers 33 Figure 6 Amplifier and Discriminator 35 Figure 7 (a) Anisotropy of Co^° Radiation 37 (b) Cobalt T-ray Speotrum • 37 Figure 8 Maximum Anisotropy i n Intensity of the }f-ray expected f o r various mixtures of CN2 and./2>2 pf E l and.H2 51 Figure 9 Results of the Y b 1 ^ 5 Experiment 57 Figure 10 Results of the Nuclear S p e c i f i c Heat Experiment, samples E - l arid E-2 . . . . . . . . . . . . 78 Figure 11 Results of the Nuclear S p e c i f i c Heat Experiment, samples E-3 and E-4 78 Figure 12 (a) t y p i c a l warming up curves f o r E-5-and f o r p o l y c r y s t a l l l n e CepMg-z(N0-»Wo. 6H 20 . . . . . . . ? . .? 83 (b) expected slopes f o r samples E -6 and E-5 showing the various corresponding contributions 83 Plate I (a) View of the solenoid on i t s movable support (b) View of the apparatus f o r adiabatio demagnetization Plate II Photograph of crystallographic data on the benzene sulphonates 30 30 76 1 INTRODUCTION The experiments described i n t h i s thesis are a l l re-lated to problems of nuclear alignment at low temperatures. Ob-servation of the radiatio n emitted from a system of oriented nuclei often permits the determination of some parameters in. the decay scheme of the radioisotope and of the value of the magnetic moment of the nucleus. Many methods have been proposed to obtain oriented sys-tems of n u c l e i . A review of these methods and of the results so f a r obtained i s found f o r instance i n the paper of Blin-Stoyle, Grace, and Halban (1955)« We have studied the angular d i s t r i b u t i o n of ^ - r a d i a -t i o n from P r ^ 2 and Yb*^5 oriented i n cerium magnesium ni t r a t e by the method proposed by Bleaney. In the case of Yb^-*, the decay scheme i s f a i r l y well established, and the purpose of the experiments was, not only to determine i f possible the magnetic moment of Yb^"*, but also, i n conjunction with experiments at Oxford, to obtain information about the destruction of the anis-otropic Jf-ray pattern by c r y s t a l l i n e i n t e r a c t i o n s . These exper-iments are described i n Chapter I I I . P r ^ 2 appeared to have a simple and well understood decay scheme, and the purpose of these experiments was to deter-mine i t s magnetic moment. The c r y s t a l l i n e environment of the Pr ion i s such that interactions should not a f f e c t the polar diagram and,the interpretation should be simple. No anisotropy was found at temperatures as low as 0.005° K., and the conclus-ion Is tentatively drawn that the published deoay schemes of Pr ^ c are not correet. The res u l t s are discussed i n Chapter IV. Another series of experiments was ca r r i e d out to i n -vestigate the f e a s i b i l i t y of orienting nuclei by Pound's method. < • If nuclear alignment!ib a c r y s t a l i s possible, thene should be also a Schottky anomaly i n the s p e c i f i c heat due to the change In population of the hyperfine l e v e l s . The p r i n c i p a l obstacle so f a r to the r e a l i z a t i o n of Pound's method has been the fac t that, i n general, the nuclear 3 p i n - l a t t i c e relaxation times are too long to permit cooling of the n u c l e i i n the time available for an experiment. It was hoped that the relaxation time could be shortened by including i n the c r y s t a l some paramagnetic ions to provide a mechanism of coupling between the nuclei and the l a t t i c e . Measurements of the s p e c i f i c heat should then Indicate whether or not the nuclei BPS oooled by the presence or absence, of t h i s Sohottky anomaly. A r e a l experimental d i f f i c u l t y i s that o, —5 o these s p e c i f i c heats are very small {CT^/R ^ 10 K.). Iodine i n magnesium para-iodobenzene sulphonate and bromine in zinc bromate were cooled by being mixed with cerium magnesium n i t r a t e and subjected to adlabatic demagnetization. No Schottky anomaly was observed, but i n the warming up curves some evidence was found f o r a relaxation time of about 3 minutes. These experiments were abandoned a f t e r i t was decided that no useful quantitative information could be obtained unless the heat leak could be cut down by several orders of magnitude, an operation which would present considerable technical d i f f i c u l t y . These experiments are discussed i n Chapter V. 3 F i n a l l y , i n Chapter I I , the apparatus i s described. In order to carry out these experiments, a cryostat was b u i l t to produce temperatures of the order of 10 K. by adlabatic de-magnetization. A solenoid cooled i n l i q u i d nitrogen producing 18 kilogausB f o r 10 kilowatts input was b u i l t i n order to per-form the adiabatic demagnetizations. In addition, the equip-ment fo r counting ^-rays was set up. 4 CHAPTER I A FEW PRELIMINARY REMARKS ON THE ANGULAR DISTRI-BUTION CF GAMMA RADIATION FROM ORIENTED NUCLEI A The methods of orientation Before discussing how and what Information on radio-active isotopes can be obtained from a system of oriented n u c l e i , l e t us review b r i e f l y the d i f f e r e n t methods by which orientation can be achieved at the low temperatures attained by adiabatic demagnetization. Suppose the nucleus has a magnetic moment Jx , spin I, and e l e c t r i c quadrupole moment Q. If we could i s o l a t e I t , i t would be i n a 21+1-fold degenerate state. In the presence of a f i e l d , e l e c t r i c or magnetic,' t h i s degeneracy i s p a r t i a l l y or t o t a l l y removed. When the d i r e c t i o n of the f i e l d i s taken as the axis of quantization, each d i f f e r e n t state with i t s magnetic quantum number m can be regarded as corresponding to d i f f e r e n t orientations of the nuclear spin with respect to t h i s axis. When we are dealing with a large number of nuclei placed i n i d e n t i c a l surroundings the d i s t r i b u t i o n of the nuclei among the various levels Is governed by the Boltzman d i s t r l b u ^ t i o n function which t e l l us that no l e v e l w i l l be p r e f e r e n t i a l l y populated ,unless kT i s of the same order or smaller than the hyperfine s p l i t t i n g . At room temperature, t h i s s p l i t t i n g Is always very small compared to kT even in the largest external, molecular, or atomic f i e l d s . However, i f the temperature i s low enough and the lowest l e v e l i s a pure "magnetic quantum state m", I.e., a state 5. with a magnetic quantum number m, a l l or nearly a l l the nuclear spina can be pictured as pointing i n the same d i r e c t i o n along the axis of quantization. This situation i s usually referred to as a " p o l a r i z a t i o n " of the system of n u c l e i . Under s i m i l a r temperature conditions but with the lowest l e v e l corresponding to a mixture of magnetic states -f m and — m, some of the spins may be pictured as pointing In one d i r e c t i o n , along the d i r e c t -ion of the axis of quantization, while most of the others would point -in the opposite d i r e c t i o n . We say that we have a case of "alignment" of n u c l e i . F i n a l l y , i t may happen that the lowest l e v e l even at the very low temperatures referred to i s a mixture of states with various quantum numbers m. In t h i s case the degree of orientation may be rather small. From these remarks we see that to investigate the conditions "for orientation we need' i n the f i r s t place a know-ledge of the energy l e v e l s of the nucleus i n the various f i e l d s , external or molecular. This Information i s to a great extent i derived from paramagnetic resonance and pure quadrupole reson-ance experiments and for t h i s reason we s h a l l base our discuss-ions on the study of the spin Hamlltonlan, generally used to describe the energy of the paramagnetic ions Including the h.f.s., which takes account of the i n t e r a c t i o n of the f i e l d s with the nucleus. The spin Hamlltonlan can be written for our purposes " 9t - 8 „ / 3 H Z S z 4 S L / 3 ( H X S X + H Y S Y ) + DQsl - 1/3 S ( S - r l ) ] + A S Z I Z + B ( S X I X + Syly) f - 1/3 K I - 1 ) ] -/fc^N / I" where g and g, are the values of g, the spectroscopic s p l i t t i n g " factor along and perpendicular to the axis y3,/3jj the electronic and nuclear magneton, respectively. H* the external f i e l d ,S* the e f f e c t i v e spin of the electron f o r the p a r t i c -u l a r Ion T the nuclear spin A, B, and Q, are parameters which represent the coupling of the electron s h e l l with the nucleus-D i s a parameter which represents the coupling of the electron with the c r y s t a l l i n e f i e l d This Hamiltonlan takes into account the following: the e f f e c t of the external magnetic f i e l d H on the e f f e c t -ive e l e c t r o n i c spin S of the paramagnetic ion and on the nuclear spin I. •the f i r s t and second order effect of the c r y s t a l l i n e f i e l d on the ion through the parameters g and D respectively (the D term i s zero unless S > £ ) the e f f e c t of the f i e l d also on the nucleus d i r e c t l y through the parameter Q related to the quadrupole moment of the nucleus and'the f i e l d gradient of the surroundings, and i n d i r e c t l y , through the parameters A and B. On the other hand i t neglects to take into account the energy of interaction between the electronic spins, e i t h e r spin-spin coupling or exchange i n t e r a c t i o n . This omission i s not always j u s t i f i e d . Let us remark f i n a l l y that t h i s is a convenient form of the spin Hamiltonlan even i f i t presupposes that the c r y s t a l l i n e f i e l d possesses a x i a l symmetry or better. Extension to lower symmetry can be made readily but for nuclear alignment a x i a l or spherical symmetry i s more Interesting. 7. Four methods of orientation which can be described with t h i s Hamlltonlan, although they are not a l l based on para-magnetic properties of the atoms, have been proposed. We s h a l l discuss b r i e f l y a l l of them, but emphasize only those which are of immediate in t e r e s t i n t h i s t h e s i s . There are a number of excellent review a r t i c l e s from which we mention the following: Bleaney and others (1954), Blln-Stoyle and others (1953 and 1955), Daniels (1952), Halban (1955), and K u r t i (1956). In each method we simplify the discussion by assuming that only certain interactions are present•,and influence the nucleus, while i n actual cases the other interactions also may • have a small e f f e c t on the energy. 1. The Brute Force method The f i r s t method requires that a large magnetic f i e l d be applied on the nuclei while they are at a very low tempera-ture. Any nucleus can qualify f o r t h i s method i f i t s magnetic moment i s d i f f e r e n t from zero. It need not be placed i n any p a r t i c u l a r surroundings as long as large Internal f i e l d s are avoided which would compete with the external f i e l d . Internal f i e l d s can be as large as 10^ gauss, while i t i s d i f f i c u l t to produce f i e l d s of 75 to 100 kilog'auss i n the laboratory. The nuclear energy lev e l s are described by the l a s t term of the Ham-l l t o n l a n above. They are equal to y</^ Hm/I. The nuclear degen-eracy i s completely l i f t e d and each l e v e l corresponds to only one orientation of the nuclear spin i n space, i . e . , we have nuc-lear p o l a r i z a t i o n . The large magnets necessary (giving f i e l d s of the order of 100 kllogauss) and the low temperatures at which 8. t h i s f i e l d must be applied to the sample (temperatures of the order of 0.01° K.) to obtain an observable p o l a r i z a t i o n make t h i s method, simple i n p r i n c i p l e , one of the most d i f f i c u l t . Only re-cently has i t been attempted with success by K u r t i and others (1956). 2. Pound'8 method Pound's method; Pound (1949), takes advantage of the large i n t e r a c t i o n that e x i s t s between the e l e c t r i c quadruple moment of the nucleus and the e l e c t r i c f i e l d gradient of i t s surroundings in certain covalently bonded atoms. In t h i s case the nuclear degeneracy i s only p a r t i a l l y l i f t e d as the interac-t i o n i s calculated from the term Q^I 2 - 1/3 1(1 t 1)J and each state i s made up of states t_ m for-each m. This means that only an alignment i s obtained. No successful use of t h i s method has yet been reported. This i s explained by the fact that i t i s d i f f i c u l t ' to f i n d ,a c r y s t a l showing large quadrupole s p l i t t i n g and also containing In the same l a t t i c e a. paramagnetic ion which would contribute to the cooling of the sample; In t h i s method, as in the method of Bleaney below, i t i s es s e n t i a l to use a single c r y s t a l ^ so that the nuclei when oriented along the quantization axis defined by St. the molecular f i e l d s , are also oriented in space, whereas in the ( other two methods the external f i e l d i s assumed to define t h i s 'i axis no matter what the i n t e r n a l f i e l d s are. In Chapter V we s h a l l discuss i n more d e t a i l some aspects of the problems•pre-sented by t h i s method. 3. The method of Rose and Gorter. and Bleaney's method Both methods are based on the paramagnetic properties of certain ions whose nuclei are of Interest and they exploit the large magnetic f i e l d s created at the si t e of the nucleus by the o r b i t a l motion of the electrons responsible for the paramag-netic properties of the ions. The f i e l d on the nucleus i s then of the order of 100 to 1,000 kllogauss and produces nuclear l e v e l s p l i t t i n g s of the order of 0.01° to 0.1° K. When the temperature of the sample containing these ions Is s u f f i c i e n t l y lowered some nuclear orientation should occur i f there Is a means of orienting the electronic o r b i t s . ' \ ,i The difference between the methods proposed by Rose i, 'i  (19*8) and Gorter (1948) on the one hand and by Bleaney (1951a' and b) on the other i s a difference i n the way the electronic o r b i t s are oriented. The names of Rose and Gorter are assoc-iated together since they both suggested independently the use of a small external magnetic f i e l d to orient the orbits even i f they have suggested d i f f e r e n t ways of cooling the n u c l e i . A few hundred gauss only i s necessary and t h e i r technique consists i n demagnetizing a d i a b a t i c a l l y from a f i e l d of many kilogauss a sample previously i n thermal contact with a helium bath at 1° K. to a residual f i e l d of a few hundred gauss. Magnetic cooling takes place to an extent depending on the i n i t i a l f i e l d and temperature and also the f i n a l f i e l d which should polarize to a great extent the electronic o r b i t s . If the cooling has brought the system to a s u f f i c i e n t l y low temperature some order w i l l set i n among the nuclei and some p o l a r i z a t i o n w i l l r e s u l t . I t i s ' not necessary to use a single c r y s t a l i n t h i s case; a compressed powder, f o r instance, should be s u f f i c i e n t since the axis of 10. c p o l a r i z a t i o n i s defined by the external f i e l d . However, as Bleaney (1951a) has pointed out, i n many cases of intere s t i t i s important not only to use single c r y s t a l s , but also to orient them c a r e f u l l y in the residual f i e l d . Bleaney's method i s based on the fact that In crystals where a large anisotropy of 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 s known to ex i s t , the orbits are aligned automatically along and opposite to the axis of the c r y s t a l l i n e f i e l d and cooling w i l l bring about alignment when the temperature Is low enough not only to order the el e c t r o n i c spins, but also to populate mostly the lowest nuclear l e v e l s . For a better understanding of the mech-anism by which nuclear orientation i s obtained by the h.f. s . methodB of Bleaney and of Rose and Gorter, i t i s necessary to , consider the system of electrons and nucleus as a whole, espe.c- , i a l l y when the ef f e c t i v e spin Is This system has d i f f e r e n t energies f o r d i f f e r e n t r e l a t i v e orientations of the nuclear spin with respect to the electronic spin and the d i f f e r e n t orientat-ions of the whole with respect to the c r y s t a l axis. In the f i n a l a nalysis, however, i t can be regarded that the nuclear orientation takes place along the c r y s t a l axis, and the energy of the various nuclear states i s obtained d i r e c t l y from the spin Hamlltonlan once the relevant parameters are known. For th i s reason, in the example given below we treat the problem formally. Bleaney's method has the advantage over the method of Rose and Gorter that lower temperatures can be reached since the demagnetization from which the cooling i s obtained i s done to zero f i e l d . I t i s es s e n t i a l with this, method that the sample be a single c r y s t a l or many single c r y s t a l s w^th p a r a l l e l c r y s t a l l o -11. graphic orientation i n apace and with only one-ion pe/r unit c e l l since the axis of alignment i s defined by the Intramolecular f i e l d s " o f each c e l l . This s u p e r f i c i a l d escription of the methods have of course to be supplemented i n each Individual case by a careful a n a lysis of the spin Hamiltonlan. In order to throw some l i g h t on how much a discussion could be conducted we s h a l l discuss i n [ some d e t a i l an example given by Bleaney. v This Is the case of an ion where the e f f e c t i v e spin 5 i s £ and the nuclear spin I i s 7/2. It i s a case of p a r t i c u l a r Interest to us since i t happens that these values f i t Yb^-> i n the s i t u a t i o n described i n Chapter I I I . We w i l l assume that the only terms of importance in the Hamiltonlan are the following: AS 2I z-f B ( S X I X S v I y ) . A S 2 I 2 + £ B ( 3 + I _ + S_I t) where S + , I + , etc. are defined i n the usual manner. Then the only non zero off-diagonal elements are: <£,m-l| S +I.)-£,m> =/ 1(1+1) - m(m-l) <-£,m+l| S_I + | i,m> - / 1(1+1) - m(ra+l) The secular determinant i s then formed and factorized into sub-determinants which a l l appear twice except one. The energy levels are e a s i l y obtained and can be displayed as functions of the para-meters A and B as follows: 7 A ; -At\l 36A2 + 28 B 2 ; -At J 16A 2 + 48B 2 ; - A ± ^ 4 A 2 -+ 60B2 ; -A± 8B, where a f a c t o r £ has been omitted. 12. We thus have nine energy l e v e l s , two singlets and seven doublets, which merge into only two when B - A and of which the two sing-l e t s merge when B » 0. In order to i l l u s t r a t e more c l e a r l y the behavior of a l l the levels together as A and B are Varied we have, plotted them i n figure 1. In the l e f t hand half of the graph, A Is kept equal to 1, while B i s varied from 0 to 1. On the right side, B I s l e f t equal to 1 and A passes from 1 to 0 thus displaying a l l the possible r a t i o s of the two parameters. A and B of course are generally found by the methods of paramagnetic resonance and many data are found summarized i n Bleaney and Stevens (1953) and i n Bowers and Owen (1955). If not, i t i s sometimes possible to obtain an estimate of them as we have done i n Chapter III f o r Yb. The simplest case to discuss i s when B'» 0. The a l i g n -ment then takes place i n the d i r e c t i o n of the axis of the c r y s t a l . The energy levels each contain nuclear states consisting of £ m, and are eauidistant by an amount equal to A/2. When the temper-ature i s lowered to a value A/2k the nuclei populate p r e f e r e n t i -a l l y the state i 7/2. Indeed, the r e l a t i v e populations given by cosh (Am/kT) f o r 7/2:5/2:3/2:1/2 are In the r a t i o 1.00:0.37:0.14: 0.07 f o r t h i s temperature. If now both A and B are d i f f e r e n t from zero, but with B<A, the s i t u a t i o n i s more d i f f i c u l t to analyze at a glance. Nuclear alignment along the c r y s t a l axis remains possible, but as B increases the conditions are less and less favorable. Let us note that the lev e l s remain i n the same order, i . e . , they do not cross each other but they contain admixed with the states tm, states-(m +• 1) or states -(m - 1), except f o r the l e v e l 13-t i which on the other hand s p l i t s i n two, and, f o r one of the extreme l e v e l s which also does not get any admixture. The a l i g n -ment i s along the same axis but the s p l i t t i n g between levels de-' creases as B increases. The admixture becomes more and more Im-portant, and must be taken into account when ca l c u l a t i n g the pop-u l a t i o n s . ' Of course i n t h i s discussion we have assumed, as, we have done when p l o t t i n g the graph,' that A was a posi t i v e number. However, i t should be realized that i f the pattern were reversed the condition f o r alignment when B i s d i f f e r e n t from zero but s t i l l small compared to A would be better. In this case, the lowest l e v e l has m with no -admixture of other m-states. If B 3 A, a l l levels merge to form two levels with 9-fold and 7-fold degeneracy corresponding respectively to new quantum numbers 4 and 3 of t o t a l angular momentum. No alignment can be expected i n t h i s case at any temperature since each energy l e v e l contains a l l possible nuclear orientations. When B>A, the lowest l e v e l i s always a state made up only of m a t | and the s p l i t t i n g between t h i s l e v e l and the next i s much smaller. In t h i s case the alignment takes place i n a plane perpendicular to the c r y s t a l axis, and the sign of A does not a f f e c t greatly the discussion. B The angular d i s t r i b u t i o n of gamma radiation The i n t e n s i t y of gamma radiation from randomly oriented nu c l e i i s i s o t r o p i c . However, when the nuclei are oriented, an an-isotropy i s found which depends on the nature of the radiation emitted. A knowledge of that anisotropy gives Information'similar 14. to that of angular correlation studies at room temperature. In the l a t t e r case a co r r e l a t i o n i s established between two radia-tions occuring i n cascade by accepting only the pulses which are i n coincidence along two directions as a function of the angle between them. Analysis of these results reveals in gener-a l the multipole order of the tra n s i t i o n s and helps in es t a b l i s h -ing a correct decay scheme. If there i s a single gamma ray, the correlation meth-ods can only be applied when the gamma ray i s preceded by cer-tain forbidden ^ - t r a n s i t i o n s . I t 1 B i n cases where angular c o r r e l a t i o n methods f a l l that nuclear o r i e n t a t i o n : Is p a r t i c u -i * l a r l y u s e f u l . Also, from the v a r i a t i o n of the anisotropy of the radiation with temperature and a knowledge of the s o l i d state properties of the sample, the magnetic moment of the radioactive isotope can be deduced. The angular dependence of the Intensity of radiation from a system of oriented nuclei can be deduced from the theory of electromagnetic radiation and of angular momentum. The r a d i -ation emitted by excited nuclei can be c l a s s i f i e d according to the angular momentum carried away by the photon or the p a r t i c l e from the quantized nuclear source, and the par i t y change Involved i n t h e ' t r a n s i t i o n . If the angular momentum carried away from the nucleus i s JL then the radiation i s said to be of multipole order The nature of the radiation can be either magnetic or e l e c t r i c : i f we denote by a minus sign a change i n pa r i t y and by a plus sign no change i n p a r i t y , then the following rules define t h i s nomenclature: / £ - (-1) f o r a 2 -pole magnetic t r a n s i t i o n 15. (-1) for a 2 -pole e l e c t r i c t r a n s i t i o n The angular d i s t r i b u t i o n depends on the multipole order, and not on p a r i t y . On the other hand, the po l a r i z a t i o n of the elec-tromagnetic wave determines the nature of the radiation, since e l e c t r i c and magnetic radiations have a d i f f e r e n t kind of polar-i z a t i o n . The analysis of the angular d i s t r i b u t i o n of radiation • -i and t h e i r p o l a r i z a t i o n from a system of oriented .nuclei has been given by Spiers (1949), and by Steenberg (.1952) and (1953). > :-In our analysis, Chapter III and Chapter IV, we have used a s l i g h t l y d i f f e r e n t approach. Instead of using the formulae given in the papers referred to, we developped the necessary formulae for each separate case s t a r r i n g from the wave function f o r the photon and using the rules of addition of angular momenta. Pol a r i z a t i o n of the radiation Is not considered here since no experiment has been attempted i n that d i r e c t i o n . One of the simplest cases Is when there i s emission of a beta ray to an excited state of the daughter nucleus, followed by a gamma ray deexcltation to the ground state. Let us then i l l u s t r a t e schematically the si t u a t i o n as follows: J C X J Depending on how much of the atjt-ual decay scheme i s known, i t i s then a matter of assigning d i f f e r -ent possible values to the spin of the various l e v e l s , compatible with the value of the spin for the ground state which i s usually known. From a l l these schemes the angular 16. d i s t r i b u t i o n dependence on the angle i s worked out and then compared to the experimental r e s u l t s to find the best f i t . The procedure i s as follows. F i r s t l y , we determine the polar diagram for the l i m i t i n g case where a l l radioactive nuclei are e f f e c t i v e l y aligned, i . e . , are in a d e f i n i t e nuclear substate M. We can write at once: where ( j - J ^ J - J - t - J x C J J1J 9 Mm^ m^  a r e ' t h e W 1 5 n e r o r Clebsch-Gordan c o e f f i c i e n t s that can be evaluated from the tables given i n Condon and Shortley (1953)« Now we can evaluate for a l l m^  that appear i n th i s summation , (Z)™1 - T~ p«5l J 2 Jo ry m2 ( A m 0 ;"'< , ^ J l " m 0 T m 2 = m x ral m2 m 0 A J 2 T J 0 ; f where the ^ are the components of the normalized wave functions f o r the photons of multipole order 2^2 . Should the t r a n s i t i o n Involve a mixture of radiations, a l l t h e i r wave func-tions are considered and the r e l a t i v e importance of the radia-tions of d i f f e r e n t orders i s taken into account by introducing weighting factors c< , (3 , ^  , where oc2 + f^ 2 + # 2 + • • • = !• This procedure i s i l l u s t r a t e d more f u l l y in Chapter •III f o r the case of Lu^5 where the 396 kev. t r a n s i t i o n i s ass-umed to involve a mixture E l - M2. Returning now to the case of a pure multipole 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 17. c r y s t a l axi3 and the d i r e c t i o n of emission Is obtained by forming T 7/2*T?/2 the product ^ 2 T ^ / 2 a n d i r i t e 6 r a t l n 8 this l a t t e r expression over a l l space but not over the angle ©. (If we integrate over © as well then t h i s expression becomes equal to uni t y ) . Thus we n n d ! :„<«>- f | « p r$i ; | - p y Y~ f J J J l /^l J2Joft m'Y n ,2(0 I Bo| • rofTm2 mV*»2 • B 1 ^ l ^ o P J A.J21J0I • M' - mj_ _j 09 IHQ The eigenfunctions pj and*PjQ form orthonormal sets orthogonal to each other so that f i n a l l y 1 ' mT +m 2 »oT»2 L M m m i L l W O J A. J 2 * J 2 This i s an expression of the form: i M (e) a 1 + a M cos 2© + bjj cos^e + + £n eds 2 ^ e where 2 i s the multipole order involved. When the radiation Is not a pure multipole, t h i s ex-pression contains the parameters c<, ^  , ^  , mentioned e a r l i e r . I t should be remarked that when the prob a b i l i t y i s formed from |(p • there are non-zero cross terms with factorsc<jJ , c t ^ , . . . . which appear. I t turns out that they modify considerably the angular dependence. If there i s a cascade of two or more gamma rays to the ground state, then the formulae become somewhat more involved, since repeated use of the rules f o r the summation of angular mom-enta have to be practiced. 18. A useful measure of the polar diagram Is the so-called anisotropy £ which Is a r b i t r a r i l y defined as: f - 1^/2) - 1(0) 1072) 's I t i s a parameter which i s most e a s i l y deduced from the experi-mental data and Is i n most cases the maximum e f f e c t that can be observed. It i s s u f f i c i e n t to use simultaneously two counters, one along the axis of alignment and the other penpendicular to it'. The v a r i a t i o n of the anisotropy as a function of tempera-ture Is readily obtained as the s a l t warms up from the lowest temperature to the temperature of the helium bath i f the temper-ature i s monitored during that time. The l i m i t i n g anisotropy i s obtained by extrapolation of these results to the temperature where the nuclear saturation i s complete. In general, an unam-blguouB value can be obtained, and the correct decay scheme can often be decided from this value. Steenberg (1953b) has obtained formulae for the aniso-tropy as a function of temperature f o r the 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 described above. Using h i s notation, we have for any temperature I (6) « ST % I M ( e ) M where the WM are the temperature dependent r e l a t i v e populations of the substates M. The complete a n a l y t i c a l expressions for WM aire rather complicated. Steenberg gives f o r each method of nuc-l e a r alignment a perturbation c a l c u l a t i o n carried to the second order.' We are more interested here, however, i n his approxiraa-t i o n when the lowest l e v e l i s f a r from being saturated. For Bleaney's method t h i s i s : V M and % » 1 j l + 1 A 2 1~3M2 - J U «f 1)1 * P a (wt) U " A ^ This formula applies when A / 2 k T « 1 and B 2 / A 2 « 1. The f i t t i n g of these formulae to the experimental curve allows an estimate of the nuclear magnetic moment to be made i f A and 8 are known. 20. CHAPTER II DESCRIPTION OF THE APFARATUS A The apparatus f o r adlabatlc demagnetization Temperatures below l°-&. are reached by adlabatlc demagnetization of various paramagnetic substances. This method of obtaining low temperatures i s well known and we re f e r f o r a more complete description to papers by Hull (1947) , Garret (1954), Ambler and Hudson (1955) , de Klerk and Steenland (1955) . In t h i s section only d e t a i l s relevant to our apparatus are given. In the simple kind of cryostat we used, the paramag-netic s a l t , compressed e l l i p s o i d or single c r y s t a l s , i s suspended r i g i d l y inside a vacuum container or "sample tube" surrounded by a mutual inductance c o i l which i s part of a b a l l i s t i c galvano-meter c i r c u i t used in 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 temperature. The sample tube and the c o i l are immersed in l i q u i d helium contained i n the usual set of dewars. Provision i s made to pump over the l i q u i d helium so that Its temperature can be lowered from 4 . 2 ° to 1.2° K. The s a l t i s magnetized isothermally at 1.2° K. The heat of magnetization i s carried away from the s a l t to the l i q u i d bath by a small residual amount of helium gas, referred to as exchange gas. The exchange gas i s l a t e r pumped through a high vacuum system. A f t e r a few minutes of pumping, the f i e l d i s removed, and the temperature of the s a l t drops by an amount which depends on the paramagnetic substance used, the i n i t i a l temperature, and the magnetic f i e l d . The f i e l d strength necessary to carry the experiments i undertaken generally varies from 5 to 30 kilogauss. This labor-atory w i l l have shortly a Weiss-type electromagnet and a motor generator designed to produce such f i e l d s over a region of 6 M diameter and a gap of over 2 M to accommodate our dewars. Unfor-tunately t h i s magnet was not available during the course of the experiments described i n t h i s thesis and we used a small e l e c t r o -magnet which at f u l l power gave a f i e l d of some 6 .5 kilogauss with a 2 M gap. Much e f f o r t was put i n the design, construction, and t r i a l of smaller sample tubes and s u s c e p t i b i l i t y c o i l s to be used with a d i f f e r e n t set of dewars which permits a gap of only 1" and f i e l d s up to 10 kilogauss. L i t t l e success was obtained and t h i s project was dropped i n favor of the design arid construe-t i o n of a l i q u i d nitrogen cooled solenoid. I t i s a well''known f a c t that iron-free core solenoids have a gffeat advantage over v I electromagnets as f a r as weight, cost and construction are con-'I 1 earned. However, the problem of cooling and i n general the necessary large e l e o t r l c a l power needed to feed them often out-weighs the advantages. Such i s not the case i f the coolant i s -l i q u i d nitrogen, since the cooling can be effected e a s i l y , and the power necessary i s some 6 times smaller. When thi s was r e a l i z e d we decided to experiment on such a solenoid. The con-sumption of l i q u i d nitrogen i s r e l a t i v e l y low; besides t h i s , a large capacity l i q u i d a i r machine was i n s t a l l e d i n the physics department before the work described in t h i s thesis was completed. In t h i s section we w i l l describe the cryostat, the sample tube, the s u s c e p t i b i l i t y bridge, and the magnets. 22. 1. The cryostat The apparatus f o r adlabatlc demagnetization has two vacuum systems: a high vacuum system whose main function i s to insulate the sa l t thermally before demagnetization, and a large capacity system to get the helium b o i l i n g under reduced pressure. Figure 2 i l l u s t r a t e s the high vacuum system. It con-s i s t s of a mercury d i f f u s i o n pump preceded by a rotary pump and followed by a l i q u i d a i r trap. I t produces a vacuum of the order of 10""^  mm. of Hg. A 5 l i t r e reservoir with i t s own rrrercury manometer can be evacuated from the high vacuum side and serves as back vacuum f o r the d i f f u s i o n pump when i t i s desired to stop temporarily the rotary pump to reduce the vi b r a t i o n on the appar-atus. The sample tube can be evacuated through two paths. Also, provisions are made to evacuate the syphon used i n the , trans f e r of l i q u i d helium, and the high vacuum side of the raer-I cury and of the o i l manometers. , 1 The exchange gas can be obtained from the 30d cm.^ \ ' I- j reservoir which also has lts^.own mercury manometer, or alterna-t i v e l y by taking fresh helium gas from, the helium bath through the pressure l i n e leading to the manometers. To read the pressure arid help i n detecting leaks i n the system, two gauges, two manometers and three discharge tubes have been attached. A P l r a n l gauge i s used to give an in d i c a t i o n of the pressure down to about one micron of Hg, and a P h i l l i p s gauge f o r pressures 100 times smaller. Both these gauges are so C . > D T O S I P H O N J A C K E T l L I T R E J M 4> D O U T 0 4> R O T A R Y P U M P O U T R E S E R V O I R PIRANI G A U G E LIQUID AIR T R A P M E R C U R Y DIFFUSION P U M P D M D I S C H A R G E T U B E M A N O M E T E R T O S A M P L E —t T U B E PHILLIPS G A U G E • O U T M _K H E L I U M B A T H M Hg 120 cm. M Oil IOO cm. FIGURE 2 VACUUM SYSTEM to fo l low p a g e ZZ 23. placed that they can be used to read the pressure i n the sample tube, as well as other parts of the system when desired. The three discharge tubes are conveniently located to help i n leak detection and to show the nature and the approxi-mate pressure of the gas at these points. The high tension f o r the discharge tubeB i s obtained from an automobile spark c o i l . To pump over the l i q u i d helium bath, a large capacity ! ii , Kinney mechanical pump has been i n s t a l l e d In a room adjacent,to the laboratory and i s linked to the apparatus by a 4" pipe. The pressure over the helium bath i s read on a mercury manometer from atmospheric pressure down to about 40 mm. of Hg. For lower pressures, an o i l manometer i s used. The density of t h i s o i l (Aplezon B) i s 15*85 times smaller than that of mercury. At maximum pumping speed, a temperature of 1.2° K. can be obtained; to 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 on the cap which seals the l i q u i d helium dewar. There are two sets of dewars a v a i l a b l e . Both seta, a l i q u i d helium dewar which f i t s into a l i q u i d a i r dewar, are made of pyrex and s i l v e r e d . The outer diameter of the t a i l s are as follows: Set A: He 0.67" L. A 0.90" Set B: He 1.50" L« A* ••«••••• 2«00 The l i q u i d helium i s obtained from a C o l l i n s l i q u l f i e r commercially available from A. D. L i t t l e Company, and i s stored i n a 25 l i t r e l i q u i d helium can which serves as transport v e s s e l . 24. The transfer of helium from t h i s can to the cryostat Is done with ease by creating a small overpressure i n the can. Repeatedly a . 2.0 l i t r e quantity has been transferred into the cryostat with a loss of only 0.5 l i t r e which evaporates i n cooling the dewar to the temperature of helium. ; 2 . The sample tubes The sample tube i n our case consists e s s e n t i a l l y of a vacuum t i g h t container i n which the paramagnetic substance can be suspended, linked to the high vacuum system through a radia-t i o n trap. ' f .' A metal sample tube s i m i l a r to the one described by Daniels (1952) was f i r s t used. The s a l t Is r i g i d l y suspended by nylon threads In a metal cradle which i s I t s e l f held In place i n the metal case. The advantage of the arrangement consists i n the ease with which the sample tube can be opened or closed and the s a l t put i n place with the proper tension. However, the Woods metal used to seal i t introduces magnetic ef f e c t s which are a disadvantage i n c a l i b r a t i n g the magnetic thermometer. A c a l i b r a t i o n done i n the absence of the sample gave temperature dependent deflexions of the galvanometer, and^ the paramagnetism of the metal varied from experiment to experiment. To avoid t h i s d i f f i c u l t y and to get more r e l i a b l e c a l i -bration, a glass sample tube was designed. The s a l t i s suspended between glass hooks at top and bottom. To insure tautness, a non-magnetic phosphor bronze spring c o i l was used s a t i s f a c t o r i l y . To Introduce the assembly i n the sample tube, the glass i s broken 2 5 . near the bottom. The threads are hooked at the top and at the bottom parts and the glass tube Is sealed again. To avoid damage from the hot flame during sealing of the glass, part of the nylon thread i s replaced by t h i n tungsten wire. The sample tube used throughout most experiments has an outer diameter of 17 mm. which gives a good f i t with the sus-c e p t i b i l i t y c o i l . The available inside diameter i s approximately 15 mra.j t h i s allows e l l i p s o i d s and samples of £* diameter to be suspended without touching the walls. Black e l e c t r i e a l tape was wound on a l l open portions of the glass to serve as radiation s h i e l d . A B mentioned above, sample tubes of smaller diameters, to be used with the smaller set of dewars, were also designed and t r i e d . The outside diameter of thest had to be under 10 mm. This reduced the size of the sample to . The variety of sa'raple tubes of these dimensions Includes german s i l v e r containers ;with german s i l v e r cradle as well as glass sample tubes. Because of the spaoe avail a b l e , the s u s c e p t i b i l i t y c o i l s were wound d i r e c t l y on the sample tubes. However, f o r reasons that are no.t!t,too ,clear to us we had no success with these. <• -i 3« The s u s c e p t i b i l i t y bridge The bridge to 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 3» The mutual Inductance c o i l around the paramagnetic sample i s 1 wouM on a bakelite former and consists of two secondaries i n opposition separated by a gap of 1", and a primary extending a t o t a l length of 5". One secondary i s 1M In length, while the A AMMETER WITH 0 . 0 5 0 TO 5 . 0 0 A. SHUNTS C EXTERNAL COMPENSATOR G TINSLEY GALVANOMETER WITH TELESCOPE AND SCALE P PARAMAGNETIC SAMPLE S, SECONDARY SURROUNDING THE SAMPLE IN THE HELIUM BATH S 2 SECONDARY COMPENSATING PARTIALLY S x IN HELIUM BATH T REVERSING SWITCH L I Q U I D H E L I U M B A T H F I G U R E 3 M U T U A L I N D U C T A N C E B R I D G E to follow pag« other i s l ^ " . The sample i s placed inside the shorter secondary at the centre of the former. The longer secondary, near the end of the former serves to compensate largely the e f f o r t of the other. Another compensator, at room temperature, can be varied 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 . Reference to the diagram of figure 3 can be supplemented by the following data on the s u s c e p t i b i l i t y c o i l . S i has 3200 turns and S2 , 3,620 of No. 40 B & S S.S.C. copper wire which at room ;temperature has a d.c. resistance of 1,600 ohms. The primary has 576 turns of v . No. 36 B & S D.S.C. copper wire with a resistance of 74 ohms. 4. The magnets The Electromagnet; The electromagnet available Is a 4" pole face diameter, iron core, adjustable gap, water cooled type which produces at maximum power a f i e l d of 6 .5 kilogauss f o r a 1" gap. The current i s controlled by a p a i r of water ' cooled rheostats. It i s mounted on a carriage r o l l i n g on a railway and can be moved e a s i l y to and from the cryostat. The current i s s t a b i l i z e d manually. The f i e l d has been ca l i b r a t e d against current with a search c o i l and a f l u x -meter. Also a few proton resonance readings were taken as a check on our c a l i b r a t i o n . However, i n view of the facts that the magnet has a rather large hysteresis e f f e c t , that the gap has to be adjusted frequently, that the position of the windings was l i a b l e to change from time to time, and f i n a l l y , that the ammeter was not r e l i a b l e to better than 2%$ an error i n reading 27. the f i e l d as large as 5$ Is not Impossible. Many experiments have been done with t h i s magnet and many res u l t s at low f i e l d s were obtained from i t i n the e a r l i e r part of t h i s work, but more and more, jrfhenever possible, the l i q u i d nitrogen cooled solenoid replaced i t . j The l i q u i d nitrogen cooled solenoids: The problem of designing and constructing high power solenoids f or' adia'batlo demagnetization has been treated by many 'authors to which refer- 1 'i ence should be made: Daniels (1952 and 1953), L i n and Keuffman (1953), B i t t e r (1936). Water cooled solenoids have been b u i l t to give f i e l d s up to 100 kllogauss, and d i s s i p a t i n g thousands of kilowatts. For a long time, cooling of solenoids by a l i q u e f i e d gas, a i r , n i t o -gen, or hydrogen, has been considered, but i t Is not u n t i l recent-ly that i t came into use. Liquefied gases are rather expensive and f o r t h i s reason very few laboratories made use of t h i s idea. The design of these solenoids Is e s s e n t i a l l y the same as that of the more conventional water cooled type. We s h a l l not give a detailed discussion of design f o r maximum e f f i c i e n c y and homogeneity as we simply made use of some formulae derived in the papers mentioned above. We have constructed two such solenoids. Solenoid No. 1 has a core of 1.66" diameter, and solenoid No. 2 has a core of 2 .15" . The cooling i s done by immersion of the solenoid i n a l i q u i d nitrogen bath i n such a way that the l i q u i d penetrates the winding completely. The gas boil s away when power i s d i s s i -pated i n the c o l l . This requires that the solenoid be wound on 28. a strong but t h i n spool leaving at the ends the minimum of mater-i a l to l e t the l i q u i d flow f r e e l y Into i t end Just enough to support the windings. For f i e l d s below 20 kilogauss, i t was not necessary to take into account the stresses created by the forces developped when a large current flows through the wire. The cross section of the winding i s calculated so that i t w i l l give the maximum f i e l d available for the power dissipated with a reasonable homogeneity at the centre over a region large enough to contain the sample. The following formula gives a very useful relationship between the f i e l d and the power d i s s i -pated i n a solenoid of rectangular cross-section. where H, i s the magnetic i n t e n s i t y i n kilogauss, G, a shape fac t o r which can be calculated or found i n table and graph, c f . Cockcroft (1928), ^, the r e s i s t i v i t y of the wire at the temperature of use, the f i l l i n g f a c t o r , the r a t i o of the volume occupied by the wire to the t o t a l volume available f o r the : winding, a-j_, the inner radius of the winding i n centimeters, W, the power dissipated by the solenoid in.kilowatts. a^ and p are f i x e d at the start when the choice of the radius and the nature of the wire and the cooling agent^tre made. depends on the size and shape of the wire as well as the space l e f t to permit the flow of the coolant. The shape factor G can be varied but again f o r maximum e f f i c i e n c y i t i s possible to f i x the shape so that i t s value comes close to 0.17. 29. The resistivity of the copper wire varies rapidly around 90° K. , and as the purity of the wire was not known i t was diff icult to evaluate its value to better than 10$, and so to predict the field strength to a greater precision. The ques-tion of homogeneity of the field was also taken into considera-tion in designing solenoid No. 2. It is known that improvement from a simple rectangular cross section winding Is obtained by breaking the section into two parts and leaving a gap In the centre, to produce an arrangement similar to the Helmholtz colls. Dimensions and data on solenoid No. 1.. t \ - t * . . . at a-, . O.83" : a 2 B 2.24" b =1.96" a. « &2 - 2.7 p « _b_ m 2.4 *1 0 » 0.173 resistance of the solenoid at liquid N 2 temperature 0.4 ohms resistivity, estimated 2.5»10~7 ohra/cm. ^ calculated 0.6 Hence, for H - 15 kQ., W * 6.5 kW. Optimum value for <x • 3, j3» 2, Dimensions and data on solenoid No. 2. Tcnn gjr_ ao - 3.38" b a 3.38" d a 0.25" OC * ag a 3*0 *1 30. 5 • b_ « 3 .0 \ e d _ » 0.17 a i G . 0.17 Assuming the same values f o r P and ^ we f i n d that for H a 15 kG., W = 8.0 kW. (experimentally W - 9 .8 kW.) Weight: 50 p o u n d B , : , The solenoid No. 1 was wound on a thin aluminum spool with No. 14 B & S enamel magnet wire. Every two layers, from 10 ' to 20 cardboard s t r i p e , wide and 0 .025 M thick, and extending out at both ends of the spool, were placed on the winding to i n -sure that there would be a path l e f t for the l i q u i d nitrogen to permeate the entire winding. The solenoid was held in place around the dewar by wires attached to the cryostat. r The solenoid No. 2 was wound on a thin brass tubing. The sides of the sppol as well as the gap was made out of £ w bakelite plates. Same size wire and method were used as i n No. 1 . Solenoid No. 2 was used i n experiments on nuclear a l i g n -ment where a set of y -ray detectors must be placed near the sample a f t e r demagnetization. For this reason, i t was suspended with i t s l i q u i d nitrogen bath on a support which moves v e r t i c a l l y i n a dexlon framework as can be seen i n plate I. The assembly, solenoid and bath, i s so counterbalanced by weights that i t can be moved e a s i l y by hand. The l i q u i d nitrogen bath was a copper ban surrounded by a protective layer of styrofoam to minimize the b o i l i n g rate. During the period of magnetization the l e v e l i n the bath i s kept at constant height by pouring the l i q u i d View of solenoid No. 2 on i t s movable support PLATE I to follow page 30 3 i : d i r e c t l y from the l i q u i d a i r cans through £" siphons. The power i s available from a couple of motor gener-ators which w i l l give up to 30 kW. each. To control the current, a large KOH e l e c t r o l y t i c bath was constructed and used as a rheo-sta t . A simple device allows the anode to be lowered in the s o l -ution at w i l l and the current can be s t a b i l i z e d manually with ease. A good Weston ammeter with a 100 ampere shunt gives an accuracy of fe% at f u l l scale. Only the second solenoid was c a r e f u l l y calibrated as i t turned out to be the only one consistently used. It was c a l -ibrated at room temperature and low f i e l d with a search c o i l . However, this c a l i b r a t i o n was dubious and Mr. L. Robinson of the Nuclear Magnetic Resonance group offered to do some f i e l d meas-urements f o r us. Two consistent readings at d i f f e r e n t currents and f r e -quencies have been obtained at the centre. The. accuracy of the ammeter sets the*%lmit to the precision with which the f i e l d can be known. To' 1%, the solenoid i s known to give 168 G/amp. More readings were obtained* at l£ M from the centre, the f i e l d drops by less than 1%; at 2£", It had decreased by some 5% of the value it' had at the centre. I t was thus concluded that to the accuracy ' quoted, and with the size of the sample used throughout, the s o l -enoid was a r e l i a b l e ' source of magnetic f i e l d for the purpose of f adlabatlc demagnetization. , '. Solenoid No. 1 was designed to be used d i r e c t l y around the t a i l of the helium dewar having i n view the highest f i e l d f o r the lowest possible d i s s i p a t i o n of energy. This was achieved, • but the l i q u i d a i r dewar available was not long enough to cover 32. the l i q u i d helium dewar with ar r e s u l t i n g high evaporation rate of the l i q u i d helium, and a high i n i t i a l temperature for'demag-netization. Also, the necessity of removing the solenoid in experiments on nuclear alignment made thi s arrangement of l i t t l e value. However, the experience acquired i n the construction and t r i a l of t h i s solenoid proved us e f u l . This solenoid No. 2 has been i n use at f u l l power for many hours and has proved s a t i s f a c t o r y . It waa soon realized that when i t i s used at f u l l power (approximately 10 kW.), I t is Important that the l e v e l of the l i q u i d nitrogen be held a few inches above the windings. Up to now i t has been on at f u l l power fo r only fiv e minutes at a time. It may be that longer periods at high f i e l d s w i l l require better spacing i n the winding. It i s inter e s t i n g to note f i n a l l y that the solenoid can be lowered to the f l o o r a f t e r demagnetization to allow f o r the detector to be set i n place, without any change i n the warm-ing up rate of the sample. Also, the vi b r a t i o n Introduced by1 the b o i l i n g nitrogen does not a f f e c t the demagnetization. t B Gamma ray detection equipment ' For the detection and recording of the anisotropy of gamma radiation we used s c i n t i l l a t i o n countera. We w i l l describe i n t h i s section the necessary equipment which consists of Nal cr y s t a l s , photomultlpllers, cathode followers, l i n e a r amplifiers, amplitude discriminators, and s c a i e r s . The radiation i s recorded simultaneously i n two dire c t i o n s as the radioactive sample warms up from the lowest temperature attained i n the apparatus f o r adiabatlc demagnetization described i n the preceding section. This implies that we have two separate channels, as the block diagram i n figure 4 should make c l e a r . The Nal (Tl) s c i n t i l l a t i o n c r y s t a l , the photomulti-p l i e r with i t s potential d i v i d e r , and the cathode follower form *a portable u n i t . The c r y s t a l i s I f " in diameter, 1 M long, and was obtained ready mounted from Harshaw Co. It Is held In o p t i c a l contact on the RCA 6342 photomultiplier by Dow Corning F l u i d 200. The phototube i s magnetically shielded against the stray f i e l d s by a Mumetal tubing. The p o t e n t i a l applied to the cathode, the dynodes and the anode i s obtained from a chain of r e s i s t o r s as shown on figure 5 which also displays the cathode follower c i r c u i t s . Two cathode followers have been placed so that positive and negative pulses could be obtained from the photomultiplier. In the set up described below, only negative pulses were used. . . A more elaborate mounting i s required to study the radiation when a small magnetic f i e l d i s applied on the sample to obtain nuclear p o l a r i z a t i o n with the Rose-Gorter method. The detectors have to be placed in close proximity to the source and to the magnetic f i e l d which i s obtained from a p a i r of Helmholtz c o i l s . The magnetic f i e l d i s of the order of a few hundred gauss, and the stray f i e l d s on the photomultlpliers i s enough to disturb completely the action of the phototube. To soive t h i s d i f f i c u l t y we placed the photomultiplier as f a r away from the s c i n t i l l a t i o n c r y s t a l as was f e a s i b l e , a l u c i t e pipe providing the path f o r the l i g h t . The l u c i t e rods, l£" i n diameter and 7" and 12" long, were well polished, and i n contact with the .IQUID H E L I U M A N D O X Y 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 A M P L DISCRIM T U D E INATOR t S C A L . E R I T I M E R C A T H FOLLC O D E DWER 1 LINE A M P L : A R IFIER A M P L DISCRIM T U D E 1NATOR f S C A L E :R n F I G U R E 4 B L O C K D I A G R A M O F T H E C O U N T E R A R R A Y to follow page 33 F I G U R E 5 P H O T O M U L T I P L I E R A N D C A T H O D E F O L L O W E R . to fol low page 34. photomultipllers and the c r y s t a l s , using again the D. C. 200. I t was mounted r i g i d l y , but contact of the l u c i t e pipe with the supports was c a r e f u l l y avoided as t h i s may have reduced the transmission i n the pipe. The lengths of 7" and 12 H were de-cided upon as i t was found that the e f f e c t of the stray f i e l d could be completely avoided at these distances provided we used 3ome addit i o n a l magnetic shielding over the Mumetal s h i e l d . This additional shielding consists of a soft iron tubing with a £ M wall placed over the phototube. To detect along the d i r e c t i o n of the f i e l d such an arrangement would not provide much shielding. We t r i e d to use . a curved pipe; apart from the d i f f i c u l t y of mounting such a , pipe avoiding contact with the wall of the pipe, we realized that too much of the l i g h t could escape. We could have used some white coating on the l u c i t e , but f i n a l l y we preferred to place t h i s unit with a straight pipe p a r a l l e l to the other, and perpendicular to the f i e l d , but so placed that" the c r y s t a l would be,In the l i n e of the f i e l d , presenting to the source i t s c y l i n -d r i c a l surface; geometrically, f o r the dimensions of the c r y s t a l used, the cross section exposed to the source i s about the same as i f the c r y s t a l was mounted i n the more conventional manner with i t s base facing the source. Many t r i a l s were then under-taken with the f i e l d on to ascertain that the photomultipllers so mounted and i n t h e i r proper place f o r the experiment were not affected by the stray f i e l d s . To mount the detector units, and the Helmholtz pair, a table forming a sort of goniometer was b u i l t . This table was fi x e d to a carriage that could be moved eas i l y Into place under 35. the dewar allowing the counting to start not l a t e r than 30 sec-onds a f t e r the end of the demagnetization. The alignment of the detectors with respect to the sample was done p r i o r to the exper-iment and consisted of a l i g n i n g one unit with respeot to the plane of the mica on which the radioactive c r y s t a l s were mounted. For instance, i n the case of the double n i t r a t e , the c r y s t a l i s i n the form of a f l a t hexagonal plate. The p r i n c i p a l axis of the c r y s t a l i s normal to the f l a t c r y s t a l . It was then s u f f i c -ient to glue the c r y s t a l , with i t s f l a t portion on the mica. Then a f i r s t counter was placed In l i n e with t h i s plane. The d i r e c t i o n of the other counter was obtained on the goniometer ' with respect to the f i r s t one. The error Involved i n l i n i n g up the detectors was estimated to be less than 2°. •_ The pulses from the cathode follower were fed into a ' li n e a r pulse a m p l i f i e r through low impedance cables. The ampli-f i e r s have been b u i l t following closely the c i r c u i t and the lay-out of the commercially available Linear Amplifier Model 218 of Atomic Instrument Co. It consists of two separate three stage amplifiers with negative feedback loops. The c i r c u i t i s given i n figure 6. I t accepts negative pulses. The gain i s controlled at the input by a potentiometer providing an adjustment of the signal between 50% and 100$ of Its maximum value". A coarse gain control follows which gives roughly steps of 2. The gain of the amplif i e r i s 6,000 f o r a rise time of some 0.7 microsecond, and a pulse duration of 5 microsecond. Some modifications of the o r i g i n a l c i r c u i t have*been made. The filamenta on a l l tubes have been set at a d.c. p o t e n t i a l of 40 vo l t s with respect to the chassis. Some time constants between 2 5 0 0 + 2 6 5 v. FIGURE 6 A M P L I F I E R A N D D I S C R I M I N A T O R to follow page 35 36 . the various stages have also been modified to cut down' the noise. F i n a l l y , the l a s t stage consists of the double trlode 12AV7 since' the 5687 tube used in the o r i g i n a l was not a v a i l a b l e . The per-formance of the amplifier does not seem to have been affected by th i s replacement. The signal at the output i s a p o s i t i v e pulse with amp-litude between 0 and 100 v o l t s . The amplitude discriminator Is mounted on the same chassis and i s the usual Schmidt t r i g g e r • c i r c u i t . It i s also shown In figure 6 . The output from the discriminator i s also a pos i t i v e pulse, but with constant ampli-i tude of 40 v o l t s . These pulses are d i f f e r e n t i a t e d before being fed to the scaler which w i l l accept only negative pulses of a ! microsecond duration. This explains why a l l through the, c i r c u i t f ' ,• '' . , . «. 1 the pulses have been kept 5 microseconds of duration,. The scalers with a maximum counting rate of 1000 counts per second are Berkeley Decimal Scalers Model 2105. To obtain repeated and well defined counting periods automatically through-out the warming up period of the sample, a timer has been assem-bled consisting of a system of relays and gears operating from the pendulum of a clock. It was set to allow 10 seconds of count-ing and 6 seconds f o r reading the counts. The exact duration of the counting period i s not too Important since i t i s the r a t i o of counting rates i n the two channels that i s of Importance, and the scalers start and stop simultaneously with our device. The el e c t r o n i c equipment has been submitted to a number of tests to Insure that Its behavior.was s a t i s f a c t o r y . The four d i f f e r e n t detector units were placed near a Se?5 source obtained from Mr. H. 3chneider and the spectra obtained using as discrim-inator a single channel pulse analyser were compared to a spec-trum obtained with a d i f f e r e n t set up i n t/ie Beta Spectroscopy Laboratory. With the size of our c r y s t a l s , and the usual char-a c t e r i s t i c s of the RCA 6342 used, the resolution was as expected The two units used In the Rose-Gorter method also had a good resolution, even though the l i g h t pipes have the e f f e c t of de-creasing the resolution. F i n a l l y , the s t a t i s t i c s of countings have always been checked and were found defective only i n the case where the H. T. power supply was found to be unstable. The performance of our amplitude discriminator can be seen from the spectra f o r Co^O appearing In figure 7« We would l i k e to remark that t h i s spectrum is not quite as good as can be obtained from a single channel analyser. This i s because our spectrum was obtained from an i n t e g r a l bias curve using the method of differences, which increases the, s t a t -i s t i c a l e rrors. C A control experiment, the gamma radiation anisotropy from ' aligned C o 6 0 . Because i n the f i r s t few t r i a l s we did not detect any anisotropy from aligned Y b 1 ^ (see Chapter I I I ) , we deoided'as' a check on our equipment as well as to ascertain the adequacy of our techniques, to repeat an experiment where the anisotropy should be unmistakable. Since some Co^O was immediately available we decided to use th i s isotope. The experiment, which i s an application of Bleaney's method, was s i m i l a r to our experiment on Y b 1 ^ and u p Pr . For th i s experiment we followed cl o s e l y the d e t a i l s of F I G U R E 7 b C O B A L T If - RAY S P E C T R U M to fol low p a g e 37 38. an experiment of Bleaney and others (1954). We w i l l not attempt here to give a l l the d e t a i l s which are found i n the reference mentioned above. We w i l l only out-l i n e the main points. The procedure i s the same as that des-cribed i n Chapters III and IV. The decay scheme of Co^° i s well established and i s given here: Ci bO o (5.2}f) ^ This i s a p a r t i c u l a r l y easy emitter to deal with using our detection equipment, since the discriminator can be set anywhere. Indeed^ the two gamma rays have the same polar 2 diagram. In fa c t , the discrimina-tors have been set In the region of Q the Compton plateau, as well as Just below the two photopeaks. Some 4 grams of (1% Co, 12% Cu, 87% Zn) Rb 2 (SO^ISHgO single c r y s t a l s containing i n a l l less than 50 ^  ouries of Co^° were grown from an aqueous so l u t i o n . The c r y s t a l s were mounted on a piece of mica i n such a way that the crystallographic axis 3 of a l l c r y s t a l s pointed along the same d i r e c t i o n . This sample was attached i n the sample tube and cooled by the usual method of adlabatlc demagnetization. The r e l a t i o n s h i p between T* (the magnetic temperature) and T (the thermodynamic temperature) In our experiment was assumed to be the same as that arrived at by the Oxford group. The counters were placed along the and the Kg axis of the c r y s t a l s . The counts were recorded along these two d i r -E 2 e2 HI 60 39 . ectlons f o r 10 second periods during the warm up time (approxi-mately 10 minutes). A l l along the temperature was recorded with the mutual inductance bridge previously c a l i b r a t e d from 4.2° to 1.2° K. The anisotropy was then calculated and related to the temperature. The pesults of two runs are averaged and displayed in figure 7, where the curve obtained at Oxford i s also given as a means of comparison. V/e have thus proven to our s a t i s f a c t i o n that the equip-ment and the techniques we used are adequate and should permit to es t a b l i s h the presence or the absence of an anisotropy. Our experimental points, i t w i l l be noticed, do not f i t too well the previous experiment of the Oxford group. This can be attributed to many f a c t o r s . F i r s t l y , the rel a t i o n s h i p between the magnetic and absolute temperature Is not known f o r the exact composition of our c r y s t a l which may d i f f e r appreciab-ly from that arrived at at Oxford. Also, the shape of the sample influences this r e l a t i o n and there i s no way of comparing quant- • i t a t l v e l y this f a c t o r . F i n a l l y , i t Is unfortunate that the c a l -lb r a t i o n of the magnetic thermometer f o r t h i s experiment was / rather poor, so that there i s a large undertainty i n the tempeir- • ature. We made no attempt at getting a better agreement or at c o n t r o l l i n g the factors which brought about the disagreement, since the object of thi s experiment, to check the performance of the equipment, was achieved. We may add that the d i f f i c u l t y experienced i n the c a l -i b r a t i o n of the thermometer t h i s time was unusual as compared to some 50 other sat i s f a c t o r y c a l i b r a t i o n s with d i f f e r e n t samples. 40. CHAPTER III AN ATTEMPT AT THE NUCLEAR ORIENTATION OF YTTEREIUM 175 Introduction At the suggestion of Dr. Daniels It was decided to attempt an experiment on nuclear alignment of Y b ^ ^ i n cerium magnesium ni t r a t e to Investigate the.decay ^ scheme of t h i s i s o -tope and especially to decide on the order of the multipole t r a n s i t i o n of the 396 kev. gamma ray and i f possible determine the magnitude of the nuclear magnetic moment of t h i s radio-isotope. CegMg^(N0^)^2'24H20 acts as the cooling agent. Ytter-t bium, to our knowledge, does not exist as a double n i t r a t e , but introduced into the l a t t i c e as an impurity i t should replace , some of the Ce*"** Ions. It was then expected that the nature of the c r y s t a l l i n e f i e l d at the s i t e of the YD*"*"*" ion would be such as to permit the a p p l i c a b i l i t y of Bleaney's method and that at the low temperatures available a sizeable anisotropy would be detected from which the multipole order of the t r a n s i t i o n and the muclear magnetic moment could be deduced. The decay of Yb^ -75 has been studied by several authors (see the following section) and the c o n f l i c t i n g assignments of the mixture E l - M2 or Ml - E2 of the 396 kev. t r a n s i t i o n warran-ted further research on t h i s isotope.. Also, n u c l e i i n that reg-ion of the periodic table are known to be better understood i n terms of the c o l l e c t i v e model theory of the nucleus than by the single p a r t i c l e model and as a re s u l t are of great current i n -t e r e s t . By the time t h i s project "Was well under way, i t came to our attention that Dr. H. Meyer of the Clarendon Laboratory, Oxford, England, also intended to Investigate t h i s nucleus, and i t was agreed that we should carry forward our attempt to orient the nucleus in the cerium magnesium n i t r a t e l a t t i c e while the group at Oxford would attempt to orient i t i n the ytterbium ethyl sulphate l a t t i c e . A comparison of the resu l t s of the two experiments was expected to throw l i g h t on the problem of magnet-i c interaction on the gamma ray d i s t r i b u t i o n , a problem of i n t e r -est not only i n the f i e l d of oriented nuclei but also that of angular correlation i n general (see, f o r instance, the review a r t i c l e of Frauenfelder (1955) )• A Theoretical aspects 1 • The decay scheme of Yb^ -75 The decay of Y b 1 ^ has been studied by de Waard (1955), Akerlind and others (1955), Marty (1955), Mize and others (1955a, b), Chase and Wilets (1956), and Cork and otherB (1956). The decay scheme arrived at by Mlze and others i s shown below. 42. The gamma transitions indicated by the dashed lines are of lesser intensity than the others. The double lines Indi-cate the 396 kev. transition of immediate interest in this thesis. While for small and medium values 6f Z and in the neighborhood of the magic numbers the shell model has obtained a great success in predicting the various excited levels, the reg-1 ions of 60<Z<80 and 88<N<120 as well as Z > 88 and N > 136 give many confirmations of the applicability of the model of Bohr and Mottelson (1955) to these nuclei. A qualitative explan-ation for this is the following: the nuclei having a great num-ber of neutrons and protons outside the closed shell, the closed shells themselves are greatly deformed and collective motion of the nuclear mass is expected. In f irst approximation, the motion of the nuclei can be separated into intrinsic motion of the nuc-leons in the nuclear fields and into collective motion of vibra-tion and rotation. At low energy only rotational motion Is ob-served and under the assumptions mentioned the first few rotat-ional excited states can be evaluated. It is found that for even-even nuclei: 0 Erot.- -hL • K I + D where c§ is the moment of inertia of the nucleus and where the spin I can take only the values 0, 2, 4, . . . . It is found that the rotational levels a l l have the same parity as the fundament-al level. In nuclei where the atomic number A is odd, the rotatr ional levels have spins I Q , I Q + 1, I Q + 2; where I Q Is the fundamental level and the energy is given by: E R O T . - JzL + 1) - I 0 U 0 -t 1')] *3. and the same pa r i t y . * If t h i s applies to ytterbium, since f o r low energy there i s no v i b r a t i o n a l e x c i t a t i o n , I 0 i s the^sum of the compo-nent of angular momentum of the unpaired nucleons along the nuc-lear symmetry axis. Here I Q = 7 /2 + . The f i r s t excited state at 114 kev. would be the f i r s t r o t a t i o n a l l e v e l with a spin of 9/2 + and the second at 251 kev. with 11 /2 + . This i s i n good agreement with the predicted energy r a t i o 20/9 of the two .levels. The 396 kev. l e v e l , assigned 9 /2 -, corresponds on the other hand to a d i f f e r e n t excitation of the nuclei and i s the lowest l e v e l of t h i s new series of e x c i t a t i o n s . If the p a r i t y assignment l a right, the t r a n s i t i o n s to the stable state can only be a E l - M2 mixture. The only estimate of the l i f e time of the 396 kev. ft l e v e l i s given by de Waard who f i x e d i t s upper l i m i t to 6*10 seconds. Exci t a t i o n of the f i r s t two r o t a t i o n a l l e v e l s , 114 and 251 kev., by alpha'particles are reported by Heydenburg and Temmer (1955), but no mention i s made of the e x c i t a t i o n to the 396 kev. l e v e l . This would be an i n d i c a t i o n that the l i f e t i m e of the l e v e l i s rather long. 2 . Yb*** ion In the cerium magnesium n i t r a t e l a t t i c e and the  expected hyperflne structure The Yb 4 +* ion has 13 electrons i n the 4f electronic , s h e l l and i t can be pictured as having a single hole and thus would behave in somewhat the same fashion as a Ce ' f + t ion which has a single electron i n t h i s s h e l l . The ground term i s known to be 2 F and the spin o r b i t i n t e r a c t i o n s p l i t s t h i s state into 1' 44. two l e v e l s , the lowest having J = 7 /2 and the other, 5 / 2 , separ-ated by 10,300 cm.""1". It Is r e c a l l e d that contrary to the case of the Iron group, in the rare earths the spin o r b i t coupling Is fa r more important than the c r y s t a l l i n e f i e l d e f f e c t which comes only as a perturbation on the former. An attempt to observe the ytterbium paramagnetic res-onance at 3 cm. i n the cerium magnesium n i t r a t e l a t t i c e was kind-ly undertaken f o r us by Mr. H. Wesemeyer of t h i s laboratory at the temperature of helium, but i t was not detected. However, we proposed the following estimate of the electronic energy l e v e l s of ytterbium in the cerium magnesium n i t r a t e . l a t t i c e as. a guide ' for the interpretation of the r e s u l t s of our attempt at aligning' this nucleus. Such an estimate i s possible because the theory has been worked out i n great d e t a i l for the paramagnetic proper-t i e s of the rare earths i n the double n i t r a t e s and the ethyl sulphates by Stevens (1952) , E l l i o t t and Stevens (1952, 1953a,b), and by Judd (1955a,b) which we have followed step by step. We w i l l assume i n this c a l c u l a t i o n that a) the c r y s t a l l i n e f i e l d at the Yb4"*"*' ion i s the same as the f i e l d would be for the Ce ion. b) the assumption proposed by E l l i o t t and Stevens (1953a) obtained from the screening constant method, notably that 7* c* (Z - 55) , i s s t r i c t l y applicable In the case of Yb***". In the double n i t r a t e of the rare earths and magnesium, the c r y s t a l l i n e f i e l d Is found to be of the C symmetry. Expan-sion of the potential function f o r this symmetry can be expressed 4 5 . i n cartesian coordinates by: V 0 = Ag ( 3 z 2 - r 2 ) 4- Ag ( 3 5 Z 4 - 3 0 r 2 Z 2 + 3r 4) + A| ( 231z 6 - 3 1 5 r 2 z 4 1 0 5 r 4 z 2 - 5 r 6 ) + A* (x 6 - 15x 4 y 2 + 1 5 x 2 y 4 - y 6 ) +- A? z(x 3 - 3xy2) o ' •+ A% ( H z 3 - 3zr 2 )(x 5 - 3 x y 2 ) To deal with t h i s rather complicated Hamiltonlan, and others similar, Stevens((1952) has developped a technique which s i m p l i -f i e s greatly the c a l c u l a t i o n s . It is the method of operator equivalents, whereby th i s complicated Hamiltonlan can be written In terms involving only the well-known angular momentum opera-tors acting on the angular momentum elgenfunctlons. These oper-atorsequivalents -are found f o r a l l the terms of our p o t e n t i a l operator in the various papers quoted above. Thus we can make this transformation r e a d i l y . It is: V Q s A| r 2 « F < | 3 J Z 2 - J ( J • D l > • A£ r ^ P F < ; | 3 5 J Z 4 - 30J (J + U J Z 2 + 2 5 J Z 2 - 6J ( J+l) -3 J 2 ( J > 1) 2J t A° r 5 ^ F< | 2 3 U Z 6 - 315J (J+1 )J Z 4 + 735J z 4 • 1 0 5 J 2 ( J * l ) 2 J z 2 - 525J(J+1)J Z 2 + 294JZ 2 - S J ^ U + l ) 3 • 40J2(J+-1)2 - 6 J ( J+ i ) |> 4 A g ^ J F £ < | + J . 6 | > ? + Al r*|SF K | j z ( J f 5 + J.3) + ( V 5 * J - 3 ) J a | > + A | r ^ A F i < j i u z 3 . 3 J ( J ^ I ) J 2 - 59J z ) (J t 5 4-J. 3) -f ( J * 3 * J > ? ) ( 1 U Z 5 - 3J(J+l)Jz - 59 J z l> A™ i s a c o e f f i c i e n t related to the strength of the c r y s t a l l i n e f i e l d , while r^1 is the mean value of the nth power of the r a d i a l distance of the 4f electron. The numerical factors oc, (3 , and ft 46. depend on the Ion and are tabulated f o r a l l the^ rare earths. There Is a m u l t i p l i c a t i v e f a c t o r F which appears when the equiv-alence between the two representations i s worked out. It varies with the d i f f e r e n t operators and the various values of J . F i n -a l l y , the operators Involving various products of J x , J v , and J z are tabulated f o r a l l useful values of J . There remains only the A™ r** which have not been determined experimentally. This i s where our assumptions become important. Judd (1955a) gives the,A™ r n f o r Ce i n cerium magnesium n i t r a t e . If we assume that the f i e l d at the Yb*** i s the same and also that P 5 varies according to the r e l a t i o n given i n our second assumption, then the calculations can be effected. Thus, using the values quoted, we have i • 4 ? ± 2800 cat."1 i 2 5 0 cm. 4 ± 850 76 A 0 r 6 - 60 - 5 . 5 A° r2 - 70 -31 + 900 + 180 A? 7 - 3 0 -6 -1 With these values and the values obtained from the papers quoted above we can form the energy eigenvalue determinant. It w i l l be an 8 x 8^determinant. I t f a c t o r l z e s e a s i l y into two i d e n t i c a l l x l determinants and two equivalent 3 x 3 determinants. The o f f - diagonal terms of the other set have a l l opposite sign, so that they are equivalent. 47 3/2 - 2 . 2 6 - E 0 0 0 7 /2 0 -17.27- E 26 .8 10.70 1/2 0 26.8 25.43 -E 12.45 - 5 / 2 0 10.70 12.45 - 5 . 8 5 - E k 0 Numerical solution of this determinant y i e l d s f o r the energy levels the values: 43 .50 , -2.26, - 1 0 . 1 0 , and -31 . 01 . A l l these are doublets and i t i s obvious that the lowest doub-l e t i s cer t a i n l y not the l e v e l with elgenstate J z »"*J3/2. I t Is one with the mixture (-»-7/2, +1/2 , - 5 / 2 ) and ( - 7 / 2 , - 1 / 2 , +5/2) If now we assume that the lowest doublet i s the one corresponding to the largest negative energy eigenvalue, i . e . , to E = - 3 1 . 0 1 , Its elgenstate i s a line a r combination of |+^and | —^ where , |+> - - 0.902 I +7/2> • 0 .385|+l/2> + 0.195 | - 5 / 2 > | - ) « + 0.902 I -7 /2> + 0.385 I - l / 2 > - 0.195 I +5/2 > using the notation and the sign rule given by the authors. From thi s the g values can be obtained, since / g, = a | < . | L , + 2sz|+>| . a | < j | | A l | j > « | j , l + > l . 6 i = 2 | < + | L X + 2 S X | - > | = 2|<j||AHj><-f|j x|->l where the ^ J | | A I I are constants given f o r each rare earth. Thus we fin d for YD*"*"*" i n the cerium magnesium n i t r a t e : g|| = 6.46 g x - 1.74 F i n a l l y , the h.f.B. constants A and B <Bf the spin Hamlltonlan can be evaluated by the following formulae: where the <J|JN||j)are again constants given f o r each rare,earth. Here again we use our I n i t i a l assumption b) to approximate r~3 which f o r Yb*4** has the value 91 • 1 0 2 4 A* F i n a l l y , d i v i d i n g by the Boltzman fac t o r , we obtain: A l - 0.250° K./ N. M» '"BI - 0.0672° K./N . M. Using t h i s r a t i o A/B « 0.27, and r e f e r r i n g to figure 1 of Chap-t e r I where we plotted the energy levels as a function of the parameters A and B f o r the case S - 1/2 and I - 7/2, we see that from, t h i s point of view the method of 'Bleaney f o r nuclear alignment should apply, since the lowest nuclear l e v e l i s almost a pure eigenstate with m - ±7/2 and the spacing of the le v e l s i s not much d i f f e r e n t from what i t would be i f B • 0. Because of the uncertainty in the signs, the lowest l e v e l w i l l be wither 100$ ±7/2 or e mixture Involving 99$ ±7/2. and only l $ t 5/2. Furthermore, the s p l i t t i n g between the two lowest levels should be of the .order of 0.03° K./N.'M. If the value of. the magnetic moment 0.2 N.M. found by the Oxford group (unpublished) i s accep-ted, then the separation would correspond to 0.006° K. which i s of the order of the lowest temperature obtained by adlabatlc de-magnetization of the cerium magnesium n i t r a t e , and an almost com-plete saturation of the lowest l e v e l should occur. 49. 3* Radiation anisotropy to be expected from the 396 kev. t r a n s i t i o n Under the assumption that the lowest nuclear l e v e l i s a pure state ) ± 7/2^ we proceed to calculate the l i m i t i n g polar diagram f o r the 396 kev. gamma ray of ytterbium. The set of assumptions that we have to make to carry • out t h i s estimate i s the following: a) Yo^-* has a spin of 7/2, and a l l nuclei are i n the magnetic substate ±|7/2>. b) the beta t r a n s i t i o n to the 396 kev. l e v e l involves a change In angular momentum of A j m±l. c) the t r a n s i t i o n from the 396 kev. l e v e l to the ground state Is a mixture of dipole and quadrupole radiations. d) the excited state at 396 kev. has a spin. 9/2, while the ground / state has one of 7/2. These assumptions are based on the previous discussion of the decay scheme found i n the l i t e r a t u r e and they are indicated on the following s i m p l i f i e d decay scheme: ; Yb 1 7 5 K 50< Here 1 \ represents the wave function of the i n i t i a l state of the system, j ^ i , the wave function associated with the emission of the beta p a r t l c l e , ( ^ ) t h a t of the intermediate state, y *? represent the normalized photon wave functions and the ground state of the system Is represented by • From the theorems of addition of angular momentum we have f o r the beta t r a n s i t i o n : iT I"»A sJkM I a~' n Vt % ' r\Vl A ° , r ^ ' r-\ 5* (kx X '- C * % ^ ft + C * * 0 0 * P l C * * > * Applying the same theorems we f i n d an expression f o r ( ^ j ^ * This expression contains two parameters oi and W whlph characterize the ' i, contribution from the dlpole and the quadrupole radiation respep-? 2 t i v e l y . The parameters are such that tt, + ^> - 1. Then )^ and The polar diagram which describes the p r o b a b i l i t y of emission i n a given d i r e c t i o n 9 i s obtained by expanding .the ex-pressions given above, forming the product ^ly^ a n d i n * , e S r a ~ ti n g t h i s l a t t e r expression over a l l space, but not over the angle 6. If we should integrate over © as well then t h i s expression would be equal to unity. We f i n d thus: 'hi % 1 (e) « I \lfi* ' ^ d t ' r A -t B cos 2e + c cos 4e where A = 283. of + 5 x 907 n2 +Kll x 15 77«£ 2 22 l J V 11 * 2 | l c c 2 ^ 5 * 1073 ft2 -Jl-x^ 77x3x«£ B c = R x 1820 a2 33 r 51. The anisotropy i s given by: ' . s > £ = I( /2) - 1(0) = - B f O < " » , K /2) A . , . e - n?>? + 31.? p 2 - 357.5 x ; ; 141 . 5 * 2 2 0 6 . 1 f 2 - f 119 x 2 « ^ The anisotropy and the polar diagram w i l l depend on the r e l a t i v e Bigns of <x, and . These signs are related to the phases of the emitted r a d i a t i o n . If the phases are the same, thenotjS^O and i f they d i f f e r than«£><0. The anisotropy i s given f o r a l l r a t i o s i n figure;© f o r l i k e and unlike phases. If the r a t i o arrived at by Mize and others (1955) i s assumed, we show i n the figure what anisotropy should be expected. Thus fo r M2/E1 a 0.20 the anisotropy f o r l i k e and unlike phases would be respectively 0.69 and -5.89. If the t r a n s i t i o n was of pure dlpole nature, the anisotropy would be 0.816 while i f pure quadrupole, i t would be -0.155' Let us note f i n a l l y that there are two mixtures of dlpole and w quadrupole radiations which would give zero anisotropy. These are f o r l i k e phases and either 97*5$ dlpole with 2.5$ quadrupole or 0.2$ dlpole with 99.8$ quadrupole, both mixtures being very unlikely i f we can r e l y on the values quoted i n the l i t e r a t u r e . If there Is no extranuclear e f f e c t to disturb the alignment, an anisotropy i s expected to be observable at a low enough temperature. B Experimental d e t a i l s ^ 1. The cooling agent CegMg^NO})^* 2^ H 2 ° constitutes an e x c e l l -t' £ = T.tor/2) - 1 ( 0 ) ICir/a) F IGURE 8 MAXIMUM A N I S O T R O P Y IN INTENSITY O F T H E Y— RAY E X P E C T E D F O R V A R I O U S M I X T U R E S O F oL' A N D ^ O F E l AND M 2 to fol low page 51 ent magnetic cooling agent whose properties are.well known. Cooke, Duffus, and Wolf (1953) have studied its magnetic proper-ties above 1° K. Daniels and Robinson (1953) have determined the relation between its entropy and the absolute temperature below' 1° K . and have shown that its susceptibility follows „ „ „ . K. It is interesting to note that for S/R^0.45, the temperature is almost constant and equal to 3»08 . 10~3 ° K . Also, the salt has a large susceptibility and having no h.f .s . as well as small dipole-dipole and exchange interactions, the specific heat is small. The specific heat con-stant CT2/R - 6.4 . 10"6 °K. The cerium magnesium nitrate crystallizes into flat hexagonal crystals, the principal axis being perpendicular to the plane. The g values are gjj = 0.25 and g^ - 1.84. For mag-netic cooling the field Is applied along a direction in the plane. If an external field Is to be used, as in the Rose-Gorter method, i t oer\ be lined up along the axis and the change in temperature that results Is comparatively small. 2. Preparation of the sample One milligram of Y^O^ of normal isotopic composition is. irradiated for four days in the large neutron flux of the Chalk River Reactor! to a total radioactivity of 5 milllcurles. Most of the radioactivity is due to the Isotope Y b 1 7 5 . Yb16^ and Yb*"*^  are also present, but their undesirable gamma- radia-tion is less important than that of Yb*""^  for reasons of lesser abundance, shorter half l i fe , or smaller neutron cross-section. Besides this, a l l the v- rays from Yb 1 ^ and Yb*77 have energies 53 . less than 300 kev. and do not i n t e r f e r e i n the anisotropy meas-urement of the 396 kev. peak. The radioactive material, i n powder form, i s sealed "In a vycor capsule and must be crushed. This i s d'one In a platinum dish containing a very weak solution of sulphuric acid since the YbgO-j i s e a s i l y soluble only i n such a solution.. Then the solu-t i o n i s slowly evaporated to dryness, f i r s t over a Bunsen burner and l a t e r under a heat lamp i n a fume hood. The ytterbium dissolved In the dish In as small an a-mount of d i s t i l l e d water as possible i s added to a concentrated aqueous solution of cerium magnesium n i t r a t e . It i s possible by t h i s technique to get nearly h a l f of the t o t a l a c t i v i t y into solution. The cerium magnesium n i t r a t e c r y s t a l s .containing traces of radioactive ytterbium are grown by evaporation of the solution i n a vacuum desslcator over sulphuric acid. , The sample for nuclear alignment consists of some 3 to 4 grams of such crystals glued on a piece of mica which' i s i t s e l f suspended by nylon threads i n the sample tube of the cry-, ostat. The nuclear detectors are aligned on the goniometer with respect -to the plane of the mica. By taking distant objects In the laboratory as reference points, the alignment of the detect-ors can be obtained to better than 2 ° . 3« Prooedure Once the sample i s i n proper place In the sample tube Joined to the high vacuum system and surrounded by the mutual inductance c o i l used In measuring the s u s c e p t i b i l i t y and deter-mining the magnetic temperature, the dewars are put in place, 54. precooled to l i q u i d nitrogen temperature, and then the l i q u i d helium Is transferred. The f i r s t part of the experiment consists i n c a l i b r a -t i n g the magnetic thermometer. For t h i s , i t i s important that the sample be In good thermal contact with the l i q u i d helium bath, and therefore a proper amount of exchange gas must be In-troduced into the sample tube. For each point of the c a l i b r a t i o n , four readings of the galvanometer d e f l e c t i o n are made at 30 sec-ond i n t e r v a l s between which the pressure i s read. An average of the four galvanometer readings and the three pressure readings i s made. From tables, the temperature of the l i q u i d i s obtained. Reducing the pressure to lower values, other points are obtained: a t o t a l of eight or nine points form the basis f o r the c a l i b r a -t i o n . A least square f i t gives the experimental r e l a t i o n between 5 the galvanometer de f l e c t i o n and the temperature. I t ' i s of'the form p { 6 s a x + a Q , T - A !• ' i When the sample Is a spheroid, A can be evaluated, c f . K u r t i and Simon (1938). With the sample used f o r nuclear alignment t h i s i s not possible. However, we obtain t h i s value emperically since the relationship between the entropy and the thermodynamic temp-erature i s given by Daniels and Robinson (1953). For the magnetic cooling, the solenoid i s brought into p o s i t i o n around the dewars and a f i e l d of some 17 kilogauss i s applied. Af t e r one minute, the heat of magnetization has been transferred to the helium bath. The tap to the high vacuum sys-tem i s opened. Pumping away the exchange gas requires a few minutes. The a d i a b 8 t i c dernngnetization las t s for about 3 0 seconds as the magnetic f i e l d Is slowly and regularly reduced to' zero. The solenoid i s lowered and the detectors are brought into place.. The recording of the radiation s t a r t s . Periods of counting l a s t -ing from 10 to 5 0 seconds, depending on the rate "at which the sample warms up, are taken with short Intervals i n between f o r recording the counts. Both scalers are started and stopped sim-•ultandously from a single-throw double-pole switch, e i t h e r by hand or by the automatic t i n e r . Meanwhile the magnetic suscept-i b i l i t y readings are taken at 3 0 second Intervals during the whole warming up period. The time i s read on two chronometers which are started simultaneously at the Instant the adlabatic demagnetization ends. When the s a l t has reached the temperature of the h e l i -um bath, some exchange gas i s Introduced again into the sample tube and then a normalizing count i s taken on both channels. This gives the counting rate i n each channel when the radiatio n i s known to be i s o t r o p i c . When an external f i e l d i s applied along the c r y s t a l axis to help i n p o l a r i z i n g the nuclei (Rose-G-orter method), the procedure i s si m i l a r as f a r as the isothermal magnetization and the adiabatlc demagnetization are concerned. The detectors i n t h i s case are the units with l i g h t pipes and additional magnetic shie l d i n g . On the goniometer table a p a i r of Helmholtz c o i l s are mounted. This assembly i s r o l l e d into place around the dew-ars and the current through the Helmholtz p a i r i s switched on and kept at a constant value. The scaler readings, the time, and the s u s c e p t i b i l i t y are recorded i n the usual fashion. The s u s c e p t i b i l i t y readings are not to our knowledge affected by th i s external f i e l d . In a l l experiments the f i e l d applied was 180 10 gauss and homogeneous over the sample to 1% or better of Its value at the centre. 4. Treatment of the experimental data a) From a knowledge of the magnetic f i e l d and temperature before demagnetization, the magnetic temperature T^* a f t e r demagnetiza-tion can be found from the data given by Daniels and Robinson (1953)* The observed value of the galvanometer defl e c t i o n Immediately aft e r demagnetization, §Qt i s obtained by extrapo-l a t i n g measured values of £ back to the Instant of demagneti-zation. A. i s then obtained from the r e l a t i o n V 3 a i + A b) If the number of counts on channel I (along the axis) i s , say,- I Q , while the number of counts f o r the saine^ period on chan-nel II (along the plane) i s Inyg* while the normalizing counting rates f o r channel 1 and II are respectively S Q and Sr/g» then the aniBOtropy i s f = 1 - *o S V 2 lT/2 S 0 This value i s then related to l / T . c) From the many demagnetizations, an average £ corresponding to an average (l/T) can be computed. The standard deviation for each" of the resultant experimental points i s computed. If each 57. channel has N average counts per period and the number of periods averaged f o r a given point i s n, the standard deviation f o r l - £ i s 1 J _ x|_2. N V n C Results and Discussion " " " 1 1 I I I 1. Results a) F i r s t we have Investigated the 396 kev. t r a n s i t i o n by Bleaney's method. We did many runs on at least three d i f f e r e n t samples. We w i l l , however, quote the r e s u l t s f o r the l a s t sample only since they were by f a r the most r e l i a b l e . Observation below 0.01° K. lasted f o r over one hour a f t e r 18 successful adiabatic demagnet-iz a t i o n s . Ko anisotropy greater than ±0.005 was found. The av-erages £ obtained are displayed as a function of (1/T) In figure 9 . The results obtained f o r the same isotope In Ytterbium ethyl sulphate by the Oxford group (unpublished) are indicated approx-imately as a means of comparison. b) Since the anisotropy observed in the ytterbium ethyl sulphate for the 282 kev. t r a n s i t i o n was much larger, we made an attempt to.observe this t r a n s i t i o n and detect t h i s anisotropy. A few observations soon convinced us that there was no such e f f e c t i n our case. The results of a few successful runs on t h i s t r a n s i t -ion are shown also on the graph of figure 9* / c) Because of the p o s s i b i l i t y that the magnetic f i e l d created at • the s i t e of the Yb + +* by the Ce** 4 might be such as to destroy the alignment along the c r y s t a l axis, we have Investigated the 396 kev. t r a n s i t i o n by the method of Rose and Gorter. o x> Q «Q J (0 01 -J + 0 0 2 + , o - o i \— - o o i t -- O 0 2 t— 2 8 2 kev. ( O X F O R D ) • 2 8 2 kev. O 3 9 6 kev. X-ray of Yb /-ray of Yb 175 175 in C e 2 M a 3 ( N 0 3 ) a - 2 4 H^O i. 150 5 P 2 0 0 J _ D r 2 5 0 T 6 3 9 6 kev ( O X F O R D ) F I G U R E 9 R E S U L T S O F T H E Y b 1 7 5 E X P E R I M E N T 58 A f i e l d of 180 £10 gauss was applied along the axis of the cr y s t a l s during the period of observation. No anisotropy could be detected during the long periods of warming up (20 roln-o utes). Contrary to our expectations, the lowest temperature reached was above 0 .05° K. We soon re a l i z e d that the paramagnet-ic sample, because of the.method of suspension used, had "actually rotated i n the sample tube. The sample was then mounted more r i g i d l y i n a l a s t run, during which the sample did not turn i n the f i e l d . No anisotropy was recorded within;,the l i m i t s of experimental error which, be-cause of the f a s t warming up rate, was not better than 1%. That the sample had not turned Is evidenced by the f a c t that the temp-eratures recorded i n the presence of the f i e l d were as low, as 0.009° K. as expected. ^ , ' ^  . • i 2 . Discussion The unexpected negative re s u l t s obtained cannot be ex-plained unambiguously. A certain number of p o s s i b i l i t i e s present themselves which we s h a l l f i r s t l i s t and then survey c r i t i c a l l y . a) The Yb*"*"*" did not occupy the Ce4"*"*" l a t t i c e s i t e i n the c r y s t a l , bi) Our estimate of the values of A and B are e n t i r e l y wrong be- . cause the Yb*4"* has distorted the l a t t i c e . c) The magnetic int e r a c t i o n i n the c r y s t a l Is s u f f i c i e n t to ruin the mechanism of alignment. d) The mixture of quadrupole to dipole Is such as to give £ • 0« e) The lifetime X o f t n e 396 kev. l e v e l i s so long that there i s a deorientation of the nucleus before the radiation i s emitted. f ) The nuclear magnetic moment i s so small that a much lower temperature has to be reached before any sizeable anisotropy w i l l be observed. V 1 a) Ytterbium magnesium n i t r a t e has never been c r y s t a l l i z e d as such and the p o s s i b i l i t y that i n our sample the ytterbium was not i n the l a t t i c e cannot e n t i r e l y be rejected. However, the c r y s t a l s obtained from the radioactive Ce2Ms^(K0-j^2«S4H20 solution showed a f a i r amount of r a d i o a c t i v i t y . Each c r y s t a l coming out of the solution was c a r e f u l l y washed with d i s t i l l e d water and immediately dried with clean f i l t e r paper to avoid having some amount of solution drying on the c r y s t a l . Also, the c r y s t a l s were well formed and clea r ; no trace of the solu-t i o n trapped i n the c r y s t a l s has ever been noticed. On the other hand i t i s d i f f i c u l t to suppose that the ytterbium can occupy any other s i t e i n the l a t t i c e than the cerium s i t e . b) If the ytterbium ion d i s t o r t s the l a t t i c e s u f f i c i e n t l y , our estimate Is no longer v a l i d . However, i f A • 0 and B / 0,an alignment along the plane could then lead to some anisotropy In the -ray. If A ¥ B, then the experiment i n the presence of a magnetic f i e l d (paragraph c ) , even i f the sample has rotated,• i s s t i l l a v a l i d Indication-that such 1B not the case. c) Magnetic in t e r a c t i o n between the dipoles, cerium and y t t e r -bium, may have affected the mechanism of nuclear alignment i n a way si m i l a r to that which was reported i n the Mn-^ experiment of Grace and others (1954) even though the Yb ions w i l l not be i n a f i e l d ' as large as the one the divalent Mn*"*" ions are i n . This destructive e f f e c t does not take place In the ytterbium ethyl 6 0 . i sulphate because gj_ = B a 0, S = 1 / 2 . Although t h i s can be proven more rigorously i t can be seen that i t i s so. The e f f e c t of the Ce ion can be represented by a magnetic f i e l d . Only the component of th i s f i e l d p a r a l l e l to the axis has any e f f e c t on ytterbium since gj_ » 0 . Since also S » 1 / 2 and B - 0 , we expect the f i e l d to have no e f f e c t In the ^  -ray d i s t r i b u t i o n . This i s not the case i n the cerium magnesium n i t r a t e . d) As we have already mentioned above, the r a t i o of quadrupole to dlpole observed by the various authors are quite d i f f e r e n t i • ' from the values which would give £ « 0 . This p o s s i b i l i t y Is . I. not considered any further. , • e) If the life t i m e of the 3 9 6 kev. l e v e l "C ^ 1 0 * ~ 1 0 second, 1 there may be a deorlentation of the spin before the emission of the y -ray and the anisotropy would be l o s t . This p o s s i b i l i t y i s important i n our case and not so i n the ethyl sulphate l a t t i c e where B s 0 . In t h i s case the alignment i s not des-troyed because the quantization of the nuclear spins along the axis, say z, w i l l not be affected. Indeed £ A S Z I Z , I Z J a 0 and ' i t can be shown that a l l the moments are invariant with time. On the other hand, the moments involving terms l i k e I x , l y vanish by symmetry. Such i s not the case i n the cerium magnesium l a t t -ice at the site of the Yb* , + + when B / 0 and I z does not necess-a r i l y commute with the Hamlltonlan. This remains one of the p o s s i b i l i t i e s that cannot be rejected u n t i l the value of t" i s better known. Chase and Wllets ( 1 9 5 6 ) remark that i t i s expect-ed that the E l t r a n s i t i o n from the 9 / 2 - to the 7/2 + level s w .^11 be in h i b i t e d to some extent. This Is attributed to deform-ation of the nucleus expected on the basis of the Bohr-Motte&son .61. strong-coupling u n i f i e d model. A r e l a t i v e l y large ? i s then ex-pected. f ) We have calculated that we could detect an £ / 0 for/p/> 0.05.' Even though the Oxford experiment confirms that the nuclear 1 mom-ent i s small, /x Is nevertheless estimated to be 0.2 N. M. ( K u r t i , unpublished). This p o s s i b i l i t y must also be rejected. Conclusion; The anisotropy o f - r a d i a t i o n can depend very s i g n i f -icantly on the nature of the s a l t In which the alignment i s a t t -empted, even i n two s a l t s which a p r i o r i should produce an a l i g n -ment. Unless the ytterbium did hot occupy the l a t t i c e s i t e i t should occupy, the reason f o r no anisotropy i s probably p a r t l y due to magnetic Interaction i n the c r y s t a l and partly due 'to . ' 1 too long a l i f e t i m e for the excited state. ; l ; This could possibly be cleared up by further experi- "\ ments with a magnetic f i e l d applied along the c r y s t a l axis. 1 F i n a l l y , i t i s i n t e r e s t i n g to note that from our est-imate of the expected properties of the ytterbium ion i t appears that i t should be possible to observe paramagnetic resonance of Yb i n lanthanum magnesium n i t r a t e . No resonance can be observed i n the ethyl sulphate since In t h i s case the lowest, doublet i n -volves only the states J z a ±3/2 and the t r a n s i t i o n i s forbidden. Such i s not the case i n the double n i t r a t e . A very sensitive P. M. R. spectrometer would be required since the Yb concentration would presumably very small. P. M. R. investigations would cer-t a i n l y help to sort out the uncertainties mentioned i n our d i s -cussion. CHAPTER IV THE EXPERIMENT ON PRASEODYMIUM 142 A Theoretical aspects 1. The reason f o r studying Pr p r142 represents a case where the re s u l t s of angular d i s t r i b u t i o n of 2f-rays emitted from oriented n u c l e i should y i e l d information about the decay scheme where the- methods of ' • t angular c o r r e l a t i o n are not applicable. I t i s fortunate,*also .that praseodymium c r y s t a l l i z e s e a s i l y i n the form of a double nitra t e which i s lsomorphous with the cerium s a l t . Also, I t i s an i d e a l case f o r nuclear alignment by Bleaney's method since B • 0. The short half l i f e of the isotope presents, however, some d i f f i c u l t y . , , 2. The decay scheme P r 1 4 2 decays to N d 1 4 2 i n two branches: a beta of 2.166 mev. to the ground state or a much less Intense beta of O.586 142 mev. to the only low energy excited l e v e l of Nd followed by a 1.572 mev. gamma ray t r a n s i t i o n to the ground state. This isotope has been studied by Gideon and others (1949), Jensen and others (1950), Bartholomew and Kinsey (1953)» Polm and others (1954), and Sterk and others (1955)* The decay scheme put forward by Polm and others (1954) i s shown below. From the Kurle plot i t i s concluded that the 2*166 mev. beta i s 1st forbidden with A I = 2 (yes). A log f t value of 7«8 makes t h i s p l a u s i b l e . The other beta has allowed shape. A log f t value of 7.1 suggests that i t i s f i r s t f o r -63. bidden withal s 0 o r i l (yes). If N d 1 4 2 i s assigned 0* then P r 1 4 2 i s 2~ compatible with the prediction of the nuclear s h e l l model i n regard to par-i t y and spin i n accordance with the rules of Nordheim f o r the i beta decay of odd-odd n u c l e i . If the f i r s t excited state of N d 1 4 2 i s 2 + then the t r a n s i t i o n from the 2" of P r 1 ^ 2 to 2* would correspond to &I = 0 (yes), but i t could also be a trans-i t i o n with A I » t l (yes) to a 1* state of Nd 1^ 2. However, be-cause of the large preponderance of 2* f i r s t excited states found i n a large number of even-even n u c l e i , the 2* choice i s 142 tentati v e l y made for t h i s excited state of Pr We hoped that our experiment could help i n c l a r i f y i n g these points and permit us to estimate the magnetic moment of P r 1 4 2 . 3. Paramagnetic properties of Pr* 4"* The paramagnetic properties of P r * + * are summarized i n Bowers and Owen (1955). The ion has 2 electrons i n the 4f s h e l l and i s i n a state 5Ha. In the double n i t r a t e at low temperatures 64. only the lowest doublet Is populated. The magnetic/complex has trigo n a l symmetry and hence an accidental doublet ground state. The ion does not have Kramers degeneracy. However, there i s a small random s p l i t t i n g due to some d i s t o r t i o n of the l a t t i c e . For t h i s reason, an extra term A i s Introduced into the spin Ham-il t o n l a n which can be written = S / //3H ZS Z • 4 S 2 I Z + A X S X + A ySy where S s 1/2 and I • 5/2 f o r P r 1 4 1 . The other properties of the ion are, at 4.2° K., g^ » 1.55 and g^ s 0, A a 0.077 and B m 0 according to Cooke and Duffus (1955). Since gj_ a B » 0 and S - 1/2, we expect no trouble from magnetic Interaction or lif e t i m e e f f e c t . A value A * 0.04 cm."*' does not perturb the energy l e v e l to an Important extdnt. The energy levels are ±. £ Q(Aro)2 + A 2 J ^. Suppose the spin of pr142 l s 2 . Then A a 0.553 and the s p l i t t i n g of the term with m s 0 has a value A a 0.04 while the s p l i t t i n g between t h i s term and the next one with m s 1 i s of the order of 0.553* It should not a f f e c t the c a l c u l a t i o n of the anisotropy at most temperatures. 4. Anisotropy expected 142 Assuming as the possible spin value f o r Pr eit h e r 1 or 2, there are 6 possible decay soheme with the following polar diagrams and l i m i t i n g anisotropies: Decay scheme Polar diagram Anisotropy 2 - 2 * 2 -2-> 0 1 - cos 46 +• 1 2 -i> 2 -2-> 0 1 - cos 2 9 + 2/3 cos 4© + 1/3 65 3 - cos 2© 1/3 1 + cos 2© . - 1 B Experimental aspect The technique used Is e s s e n t i a l l y the same as that described in Chapter III except that s p e c i a l care must be taken to accelerate the growth of the c r y s t a l because of the short half l i f e of the isotope. An aqueous solution of 1 milligram of Pr(N0-*)-x was i r r a d i a t e d for 2 days In the neutron f l u x of the B r i t i s h p i l e at Harwell and was received i n less than 30 hours a f t e r coming out of the p i l e . The radioactive solution was poured d i r e c t l y into a saturated solution of cerium magnesium n i t r a t e and the c r y s t a l l i z a t i o n was started at once In a dessicator over con-centrated sulphuric a c i d . > C Results and Discussion Within the l i m i t s of accuracy of the experiment, no anisotropy was observed i n the region from 4.2° K. to 0 .005° K. This r e s u l t i s completely unexpected from the preceding argu-ments. The p o s s i b i l i t y that a strong Bremsstrahlung upr is ing from the beta p a r t i c l e s of large energy might have completely concealed the e f f e c t was Investigated and i t was found that i t could not a f f e c t the anisotropy by more than 5$ even f o r the 1 -A* 2 0 1 -L, i -1+ o 2 i _L> o 1 - 0 ^ l _1> o 66. smallest anisotropy expected (0.33)• Also, an examination of the -spectrum with the sample i n place i n the cryostat did not indicate anything abnormal i n the rad i a t i o n . The scattering of gamma radiation was also considered but i t was found that i t s e f f e c t on the anisotropy Is small. / A control run with Co^O, as previously described (end of Chapter I I ) , was done immediately a f t e r t h i s series of exper-142 iments on Pr and under s i m i l a r conditions. An anisotropy as large as 0.3 was recorded and showed that the detectors were i n good.condition. 14? It seems unlikely that the magnetic moment of Pr ^ would be smaller than 0.01 N. M., the lower l i m i t on the moment which would give a 1% e f f e c t at 0.01° K. P r 1 4 2 has one odd pro-ton near a closed s h e l l and the magnetic moment of such a nucleuB i s generally large. Paramagnetic resonance studies have shown that the low-342 est electronic l e v e l of Pr Is an accidental doublet i n the double n i t r a t e . I t i s possible that i n the absence of a magnet-ic' f i e l d t h i s doublet i s resolved, since the Jahn-Teller e f f e c t applies when the number of electrons i s even. Should this be the case, however, i t Is d i f f i c u l t to see how the anisotropy should disappear at a l l temperatures. Let us consider, f o r example, the case where I - 1 f o r P r ^ 4 2 and the decay scheme i s 1 31^ "1 - ^ i o. The lowest doublet i s spanned by |£ 1^ and l - £ -1^'. If t h i s remains t r u l y a doublet, the angular d i s t r i b u t i o n i s 3 - cos 2©. I f t h i s doublet Is s p l i t by the Jahn-Teller e f f e c t , the two singlets are ^ — " - ^ J and the angular d i s t r i b u t i o n s from these states are: 67. 1(9) « (3 - cos 2©) + (1 - cos 2©) = 2 or (4 - cos 2©) Thus, i f the symmetric combination happens to be lowest, the l i m i t i n g anisotropy i s zero. However, quite a large anisotropy should be seen at a rather high temperature. Again, i f the nuc-lea r magnetic moment i s about 3 .5 N. M., i t s e f f e c t on the elec-tron s h e l l Is the same as that of an dxternal f i e l d of 1500 gauss. This would be considered a large f i e l d i n the paramagnetic res-onance sense, and hence the spin Hamlltonlan derived from P. M. R. should apply. Another ion, N i * + , which does not have, Kramer's , 3 degeneracy, has been extensively studied by P. M. R., and the same spin Hamlltonlan f i t s the observed facts both for large and small external f i e l d s . Although It Is a p o s s i b i l i t y that the 'spin Hamlltonlan i s not a v a l i d description of the ion at low f i e l d s , and hence the lack of anisotropy could be ascribed to th i s cause, t h i s p o s s i b i l i t y Is considered u n l i k e l y . ; 141 " 142 Pr , which has the same number of protons as Pr , has- i t s odd proton In a 4 d ^ 2 state. Examination of the neigh-boring nuclei reveals that the 5 6 y ^ 2 s t a - t © nas approximately the same energy. S i m i l a r l y , Nd^^ with the same number of neutrons 142 as Pr has i t s odd neutron i n the 5?j/2 s t a t « » but the 6h^^ 2 state also has approximately the same energy. I f , f o r example, i n P r 1 ^ 2 , the odd proton were i n a 3 S j ^ 2 s t ,ate and the odd neu-tron i n the 5 f_ , state, Nordheim's rule would predict 0" f o r 1 4 2 *he ground state of Pr and no anisotropy would be expected. The p r i n c i p a l evidence against such an hypothesis i s the fact that the ground state beta t r a n s i t i o n has the f i r s t 68. special shape, appropriate to A l s 2 (yes). However, the ex-' perimental points f o r the beta t r a n s i t i o n s arrived at by nuclear spectroscopists do not s a t i s f y the requirements f o r the o r i g i n -a l l y proposed decay scheme without a c e r t a i n amount of "adjust-ment". For example, Jensen and others (1950) were not able to obtain the correct ^-ray energy from the Kurie plots of t h e i r beta-ray measurements; and Pohm and others (1954) do not obtain consistency between the Kurie plot of the 586 kev. beta-ray ob-tained from coincidence counting, and also obtained by subtract-ing the linear corrected Kurie plot of the 2.166 mev. beta-ray , ' from the t o t a l count. If a value of 0 - f o r the spin and.parity', of the ground 14? ' state of Pr cannot be accepted, i t i s possible jthat there are levels and radiations i n the decay scheme of Pr which have been missed, and that the / - r a y i s fed through a state, of spin zero, giving no anisotropy. We have been so f a r unable to sugg-est, any plausible decay scheme of t h i s type. As has been mentioned previpusly, we do not expect the anisotropy to be seriously affected by the l i f e t i m e of the nr. eraitting state. In any case, t h i s l i f e t i m e should be short; Weia8kopf*s formula predicts 10*" 1 4 seeonds f o r an E l , 1 0 " ^ Sec-onds f o r an E2. I f t h i s l i f e t i m e were long, because perhaps the gamma-ray multipolarity i s more than quadrupole, conversion elec-trons should be expected, and these have not been reported. Fur-ther doubt on the assignment of E2 to t h i s gamma-ray i s oast by the f a i l u r e of Heydenberg and Temmer (1955) to exolte i t by Cou-lomb exci t a t i o n with 6 mev. c^P&rtlcleB. Therefore, the lack of anisotropy i n the gamma-ray d i s -69, t r l b u t i o n makes It almost certa i n that the o r i g i n a l l y proposed 14? " decay scheme and spin assignments of Pr are not correct, or are at least i n serious doubt. It would be i n t e r e s t i n g to repeat the nuclear a l i g n -ment experiment but with an external magnetic f i e l d of one k i l o -gauss since under these donditions the s o l i d s^ate properties are known. Also, a measurement of the s p e c i f i c heat of praseo-dymium magnesium n i t r a t e might help because the s p e c i f i c heat i s proportional to the sum of the squares of a l l the terms i n the spin Hamlltonlan. Any extra term would therefore show up. 70. CHAPTER V AN ATTEMPT ON CALORIMETRIC DETECTION OF THE NUCLEAR SPECIFIC HEAT The experiments to be described i n t h i s chapter were undertaken to investigate the cooling of an assembly of nuclei i n a substance where the method proposed by Pound should apply. Our r e s u l t s show c l e a r l y that the technique decided upon was not adequate f o r the investigation proposed, but we s h a l l neverthe-less give a discussion of the problem, describe the technique used, and display the results obtained, since the problem i s of interest i n r e l a t i o n to Pound's method of nuclear alignments The problem; Pound's method f o r a l i g n i n g certain nuclei depends on the coupling between the e l e c t r i c quadrupole moment of the nucleus with the surrounding e l e c t r i c f i e l d of a suitable sub-stance . As we have mentioned e a r l i e r , no successful application ' of the method has been reported as yet, and this' Is mainly because the nuclei should be In atoms covalently bonded to t h e i r neigh-bours and no suitable c r y s t a l has yet been found where t h i s s i t u -ation exists and at the same time where i t i s possible to obtain a rapid and e f f i c i e n t cooling of the n u c l e i . , ' Pound's method can be summarized as follows: assuming » that the only interaction of importance f o r the nucleus i s the coupling between the nuclear quadrupole moment and t h e ^ e l e c t r i c f i e l d gradient of the c r y s t a l at t h i s point, the 21*1 - f o l d degeneracy of the nucleus of spin I and quadrupole moment Q i s p a r t i a l l y removed. In f a c t , there w i l l be ( 2 I t l ) / 2 doublets i f 71. I i s half Integral and I doublets and one 3 i n g l e t i f I i s an i n -teger. I f , further, we assume that the f i e l d gradient i s a x i a l l y symmetric at the s i t e of the nucleus, since t h i s represents ,the best condition f o r alignment, and I f we denote th i s axis by z, then the Hamlltonlan for t h i s interaction can be written as: & - 3eQ(P z z [ l z 2 - 1/3 K l • 1)] 41(21 - 1) where ^P2Z l a the second derivative with respect to % of the e l -e c t r i c p o t e n t i a l taken at the nucleus. The energy levels are: = 3eQ<j>az [m 2 - 1/3 K l • i f ] 41(21 - 1) and they are separated by: ) J S 3*Q(j>z2 [ 2 N - l\ - / 41(21-1) n The lowest l e v e l w i l l correspond to the highest or lowest value of |m | depending on the sign of the quadrupole coupling constant eQ IP . If a single c r y s t a l or a number of single c r y s t a l s slm-i l a r l y oriented can be cooled to a temperature T ~ h j p , then the k lowest l e v e l w i l l have a population exceeding by f a r a l l the other levels and correspondingly the great majority of nuclear spins w i l l be oriented either almost p a r a l l e l and a n t l p a r a l l e l to the axis or i n a plane perpendicular to i t , i . e . , we w i l l have obtained nuclear alignment. For the usual low temperatures available at present,^0.01° K., i t i s necessary to f i n d substances i n which the s p l i t t i n g i s of the order of 100 megacycles/second. These 72. splittings are found, for Instance, In molecules having p-type covalent bonds, cf. Pound (1949). As for the question of cooling the system of nuclei, there are two possibilities. Either the crystal which contains the nuclei also contains the cooling agent, or, i f this is not the case, a thermal contact must be established between the two crystals, the cooling agent and the crystal containing the nuclei to be aligned. In the first method the problem consists of finding a substance which at the same time is a good magnetic refrigerant and contains the atom of Interest, covalently bonded. Because of the proximity of the ions and the nuclei,- there^ls a good coupling between them and i t is reasonable to expect that the nuclear temp-erature follows closely the iOnlc spin temperature. Daniels (1954), in a first attempt to align I ^ 3 \ prepared a crystal of 8% Co / 92% ZnMp-CH-^H^.S05)2.6H20 in which a small fraction of the CH^ group had been replaced by radioactive 1^31 atpms. The crystal was cooled by adlabatlc demagnetization and the inten-sity of ^-rays emitted was observed along the expected axis of alignment and perpendicular to i t . There was no directional effect recorded, and this was attributed primarily to the fact that even i f an H/T of some 15,000 gauss/degree .magnetized the i salt to about 98% of saturation, on demagnetization the temper-ature of the salt on the magnetic thermometer did not drop below 0 .1° K. because of the large interaction between the cobalt ions and the resulting large specific heat. At this temperature the degree of alignment of the iodine would be too small for the gamma radiation anisotropy to be observed. 73 In the second method of cooling, some means must be found to establish a fast and efficient thermal contact between two different e r y 3 t a l s . The cooling agent can be chosen at wil l but the difficulty of establishing a good thermal contact remains. In the paper referred to above, Daniels reports that it was not feasible to cool in a short time an assembly of nuclei in a purely covalent crystal to temperatures of the order of 0 .01° K. simply by Imbedding the purely covalent crystalline powder in the refrlg-erant. A mixture.of fine crystals of chromium potassium alum and para-di-lodobenzene in the proportion of one atom of iodine to each chromic ion was prepared, pressed into the form of an ellipsoid, and mounted In the sample tube of a cryestat. The final temper-ature attained upon demagnetization from different values of H/T correspond to that of the alum alone and no cooling of the Iodine system could be observed. It was concluded that the ther-mal nuclear spin-lattice relaxation time must be too long for any effect to be observed. This result;s?8s not entirely unexpected since the only route for the transfer of heat from the nuclear to the Ionic sys-tem which forms the heat sink is via the lattice. A calculation i of the relaxation for the transfer 10t heat from the nuclear spins to the lattice at theBe temperatures was done by Heitler and Teller (1936) who predicted i t to be of the order of years. The interaction between the spins and the lattice at very low temper-atures Is accomplished by the direct absorption or emission of a quantum of lattice vibration by the spin system. At 0 .01° K. there is very l i t t le energy in the lattice and the' process wi l l 74 be very long. However, R o l l i n and Hattonc(1948) observed a much Bmaller relaxation time than that predicted by H e i t l e r and T e l l e r , and they further suggested that the presence of some paramagnetic impurities i n the l a t t i c e may shorten t h i s time considerably. This can be understood since i f the nuclei and the ions are i n close proximity there w i l l be d i r e c t magnetic coupling between the ionic and nuclear dlpoles allowing an ex-change of energy to proceed without the p a r t i c i p a t i o n of the 1 l a t t i c e . Daniels (1954) has given a methcjd to estimate the nuclear io n i c relaxation time i n the case where such impurity i s present* The formulae he derived are applicable to the Mg or Zn para halogen benzene sulphonates i n which a 3mall amount of cobalt i s introduced as a paramagnetic impurity. I t i s estimated i n p a r t i c u l a r that i f the cobalt has a large number of pairs of i o n i c energy l e v e l s between which the t r a n s i t i o n s are allowed and which are separated by an energy gap equal to the nuclear quadra-pole s p l i t t i n g of the halogen, the nuclear-ionic relaxation time would be of the order of a f r a c t i o n of a second. I f such a gap does not exist i n the absence of a magnetic field*, a p p l i c a t i o n of a suitable external magnetic f i e l d w i l l give a Zeeman s p l i t t i n g of the right order. This i s achieved automatically during adla-batlc demagnetization. Whether or not the nuclei were cooled under such conditions was the problem we wished to investigate by the technique we w i l l now describe. A The technique To f i n d out If the nuclei have cooled with the rest of 75. the sample we proposed to investigate the s p e c i f i c heat anomaly which occurs at temperatures comparable to the s p l i t t i n g between the energy leve l s of these nuclei (^0.01° K.) At such temper-atures a rearrangement of the population of the energy levels takes place with a resultant s p e c i f i c heat. The substance containing the nuclei with large quadru-pole coupling constant and also containing the paramagnetic Ions used to shorten the nuclear spin relaxation time i s ground into a fine powder and mixed intimately with a fine powder of the cooling agent. This mixture i s then compressed by a force of a few tons per square inchi The cylinder obtained i s shaped into the form of an e l l i p s o i d and suspended i n place i n the cryostat. It i s then cooled by adlabatlc demagnetization from d i f f e r e n t values of H/T. Since the properties of the paramagnetic ions of the ooollng agent and of the paramagnetic impurity i n the sample are known, i t Is possible to fi n d the entropy change that occurs In the magnetic f i e l d (see f o r instance the tables of Hu l l and Hull (1941) ). I f the S-T r e l a t i o n f o r the cooling agent and the paramagnetic impurities are known, the temperature expected upon demagnetization can be evaluated and compared to that ob-tained from readings. Should the nuclei be cooled appreciably, i t w i l l be immediately observed. It was reasonable to expect that the ef f e c t should be v i s i b l e at the Instant of demagnetiz-ation sinoe the presence of the paramagnetic impurities would reduce the nuclear temperature relaxation time considerably. B Experiments with the para-lodo benzene and para-toluene  sulphonates* 76. 1. The samplea As a magnetic cooling agent the C^Mg^HO^^'^RgO was chosen for the following reasons: a) temperatures down to 0.005° K. can be obtained f o r r e l a t i v e l y small values Cjf H/T. b) the relationship between T* and T Is well known. In f a c t , T* - T f o r a l l T > 0.006° K. c) i t has a known low s p e c i f i c heat and yet a large s u s c e p t i b i l -i t y . This has the advantage^that mixtures can be made where the nuclear s p e c i f i c heat i s large compared to that of the cooling agent so that the e f f e c t can be e a s i l y detected. It should be remarked, however, that the Ce"*** ion has a very anisotropic g value i n the double n i t r a t e s ; g^ » 0.25# whereas » 1.84. I f a powder Is demagnetized* each c r y s t a l l i t e d i f f e r e n t l y oriented in the external f i e l d has i t s own tempera-ture. However, SB we have aaid above, the size of the c r y s t a l l -i t e and the very good surface contact between them should permit equilibrium to be reached r a p i d l y . Indeed, experiments with Ce Mg n i t r a t e powder alone i n compressed form have been made and the temperatures attained upon adiabatic demagnetization were found to be, within experimental error, those calculated by ass-uming a homogeneous temperature throughout the sample during demagnetization. As a substance having adequate properties f o r the  Pound method of nuclear alignment, para-iodo benzene sulphouate s a l t s were used. Crystallographic data of s i m i l a r s a l t s are summarized on Plate I I , which i s reproduced from Broomhead and NIcol (1948). In t h i s compound I Is covalently bonded to the C PLATE II Photograph of crystallographies data on the benzene sulphonate s to follow page 76 77. by a p-borid. The value of the tot&l quadrupole s p l i t t i n g Is not known i n t h i s case but i t i s believed that i t should not be too d i f f e r e n t from the value found f o r iodine i n s i m i l a r aromatic compounds and i t i s estimated to be of the order of 740 Mc./seo., i . e . , approximately 4 x 10 K. A nuclear quadrupole resonance spectrometer operating i n the region from I50 to 600 Mc./sec. was b u i l t by Miaa B. Pulton of t h i s department, and the magnes-ium s a l t i s being investigated, at t h i s time f o r us. The various para-iodo benzene sulphonate and para-toluene benzene sulphonate s a l t s form an isomorphous s e r i e s . . The cobalt s a l t was used be-cause, of a l l the possible paramagnetic constituents,It has the lowest s p e c i f i c heat. Unfortunately, the s p e c i f i c heat constant CT2/R of Co i n the Co para-iodo benzene sulphonate Is unknown and It may be as large as 6,000 x 10"°^ compared to that of Ce which i s 6.4 x 10~°\ I t i s hence important that the concentration of Co be kept to a minimum. In order to determine the contribution of the Co to the s p e c i f i c heat, i t was decided that two samples be made f o r each concentration value of Co, one containing the iodine, the I other replacing the iodine by a CH^ r a d i c a l . In t h i s way, one experiment should show a s p e c i f i c heat contributed by the C e r + * and the Co1"*" while the other experiment would give the c o n t r i -bution of Ce**** plus Co**" plus the covalently bonded iodine. It was thought at f i r s t that i f the atomic r a t i o of Ce ions to I atoms was 1:8, the s p e c i f i c heat constant of the I would be 10 times that of the cerium. An atomic r a t i o of Co/Mg 1:100 i n the sulphonate was estimated to give a s p e c i f i c heat constant f o r the cobalt ions about the same value as that f o r the 78. Ce Ions, and yet there would be s u f f i c i e n t Co ions to give ade-quate relaxation. The f i r s t experiments showed that the s p e c i f i c heat of the Co was much larger than at f i r s t estimated and the sp e o i f l c heat of the iodine, i f noticeable, was smaller than ex-pected. Accordingly, a second set of experiments was performed with the r a t i o Co/Mg 1:1000. This did undoubtedly cut down the contribution to the t o t a l s p e c i f i c heat from the Co ions, but at the same time almost i n h i b i t e d the relaxation process. With these concentrations of Co:Ce the s u s c e p t i b i l i t y of the Co Is ne g l i g i b l e , and the known T-T* r e l a t i o n f o r Ce Mg n i t r a t e was used to obtain T from T*. If the Bpeclflc heat of the'sample Is proportional to 1/T2, and S i s the entropy removed i n the i n i t i a l magnetic f i e l d , R/ S should be a straight l i n e . The resu l t s are therefore plotted In t h i s fashion i n figures 10 and 11. With the mixtures given i n the table below, the slope of the line of R/ S against T should vary'from sample E - l to sample E-2 by a fact o r 4C% which should be unmlstakeable, and the difference i n slope should be somewhat more between sample E-3 and E-4 Composition of the sample mixture E-3 E-4 20 20 1.783 0.0038 2.203 0.0047 1.787 2.208 Substance E - l " E-2 Ce2Mg 5(N0 5)x2«24H 20 20 20 MgCp-CHjCgH^SO^Jg.eHgO 1.539 Co(p-CH 5C 6H 4S0 5) 2.6H 20 0.0149 Mg(p-IC 6H 4S0 3) 2.6H 20 2.262 Co(p-IC 6H 4S0 5) 2.6H 20 0.024 Total Sulphonate 1.554 2.286 5 1 0 T mil l idegrees K. F I G U R E 10 R E S U L T S O F T H E N U C L E A R S P E C I F I C H E A T E X P E R I M E N T to fol low p a g e ^ 8 to f o l l o w p a g e 78 79. 6.95 8.27 3505 4105 4.13 5*38 2. The prooedure The f i n a l tempereture a f t e r demagnetization was obtained by leaking several readings, of the magnetic thermometer and extrap-o l a t i n g these readings back to the instant of demagnetization i n the usual way. The c a l c u l a t i o n of& 8 presents c e r t a i n novel features, since the sample i s a powder of an anisotropic paramagnetic sub-stance. From the r e l a t i o n / 3 s) a -/c>M2 ) f keeping H and T con-etant and H along the z axis while Imagining the sample to be rotated, i t Is seen that S and M must have the same transform-ation properties, i . e . , those of a tensor of rank 2. Henoe, the average value of S f o r random orientation of the c r y s t a l l i t e s i s l/3(Sjj - 2Sj_), the well known expression f o r an average of a tensor of rank 2 f o r random or i e n t a t i o n . 3^ and are the values of S f o r single c r y s t a l s with external f i e l d H p a r a l l e l and perpendicular, respectively, to the c r y s t a l axis. The time f o r the performance of the demagnetization was about 1 minute. It was found experimentally that a consis-tently low value of could be obtained i f the time f o r demag-netization were longer than 30 seconds. If I t were shorter, the f i n a l temperatures obtained were somewhat higher. This indicates that temperature equilibrium Is maintained i n the sample with these slow demagnetization rates. Ratio Ce / Sulphonate 8.0 8.0 Ratio 0e^ **/0o** 894 800 Ratio Ce*++/I 4.0 Actual r a t i o Ce**4/! 5«21 80, 3» Results The r e s u l t s of 4 successful runs on the 4 d i f f e r e n t samples are displayed i n figures 10 and 11. The two l i n e s drawn represent, as Indicated, the expected slope and the slope f o r Ce Mg n i t r a t e alone. A least squares f i t of the points gives i n each case a slope which i s nearer by f a r to the pure Ce Mg n i t -rate than to the expected slope. We can conclude that i f the Co*"* and the I have been appreciably cooled this would have happened only with a relaxa-t i o n time longer than a few minutes. This conclusion i s arrived at by consideration of the curves f o r warming up a f t e r each de-magnetization. I t i s unfortunately vary d i f f i c u l t to draw any quantitative conclusion from such considerations since with each d i f f e r e n t e l l i p s o i d ^ a d i f f e r e n t heat leak Is produced i n the sample tube. But i t would seem possible to interpret the cooling curves as i f the sample containing the iodine has two d i f f e r e n t slopes. One corresponding to the warm up of the Ce by the heat from outside and from the Co ions, and then a les s rapid change i n slope as the temperature of the various systems s t a r t warming up together with a much higher s p e c i f i c heat. The warming up of the sample containing only Ce Mg ni t r a t e has quite a d i f f e r e n t shape. Recent experiments done at Oxford by Cooke, Meyer, and Wolf (1956) would support the view that the d i f f e r e n t paramag-netic s a l t s i n physical contact can a t t a i n a homogeneous temper-ature equilibrium i n a matter of a few minutes. However, our technique does not allow us to draw any pa s i t i v e conclusions 81. about t h i s . We oan only suggest t h i s as a p o s s i b i l i t y . On the other hand, i t seems to us that the f i r s t mod-i f i c a t i o n that could be made to render th i s technique more succ-e s s f u l would be to reduce the heat leak to a minimum. We found that the heat leak was about 50 to 100 ergs/mln. I t i s possible to reduce the heat in f l u x to 1 or 2 ergs/min. by a thermal guard ring.. . Technically, It was impossible f o r us to use t h i s t r i c k . If the heat leak from outside could be reduced, i t would be possible, we bellev/e, to observe an unmistakeable change i n the slope during the warming up of the sample. Also, external heating with gamma rays combined with slow warming up would im-prove greatly the technique. It i s also possible that the amount of paramagnetic impurities used i n our experiment was by f a r too small. I f I t i s so, then another technique would have to be found because a larger concentration of cobalt would increase the s p e c i f i c heat to the point that i t would become impossible to detect the r e l -a t i v e l y small contribution of the iodine. C The experiment on bromine l n < bromate s a l t s The technique used as an attrempt to f i n d the nuclear quadrupole s p e c i f i c heat of iodine has been t r i e d as well on bromine i n bromate s a l t s . Zinc bromate was chosen and a small amount of copper was Introduced into the l a t t i c e to shorten the nuclear spin relaxation time. Although the s p e c i f i e heat of bromine i s much smaller than that of iodine, the quadrupole s p l i t t -ing i s known, and B O I S the s p e c i f i c heat constant of Cu i n Zn bromate• 82 Pure quadrupole spectra in bromates There are two stable isotopes of bromine whose nuclear properties are quite similar. Br™ B r 8 1 natural abundance 50.57$ 49.43$ magnetic moment 2.106 2.269 M. M. . spin 3/2 3/2 -24 2 electric quadrupole moment 0.30 0.25 * 10 cm. The single nuclear quadrupole transition in copper and the zinc bromate as given by K. Shlmomura and others (1954) are Cu(BrO^)2.6H20 175.70 Mc./sec, Zn(Br0 3) 2.6H 2p o 177.38 at i2°C. A splitting of this order corresponds to a temperature 0.008 K. so that the nuclear quadrupole specific heat Schottky anomaly is in the range of observation with the temperatures attainable with Ce Mg nitrate. The paramagnetic resonance spectrum of copper in Zn bromate has been investigated by Bleaney and others (1955). At 90° K. the diluted salt shows a single line with partly resolved h.f.s and its g value is nearly isotropic and equal to 2.22. At lower temperatures, a small anisotropy aets in , believed due to the Jahn-Teller effect. The crystal structure of this salt has been found by Yu and Beevers (1936). There are four bromate groups per unit cell with their axes oriented parallel to the body diagonals of a cube. Hence, this salt would be useless for producing a sys-83. tern of oriented n u c l e i , but i s s t i l l useful to test whether the bromine nuclei can be cooled. Since a l l relevant facts are known f o r the Co-Zn bro-r mates, i t was expected that the experiment would be a good test I | on our technique. i The experiment The e l l i p s o i d s used i n t h i s experiment were obtained by c r y s t a l l i z i n g together the proper amount of zinc and copper bromate and mixing the c r y s t a l l i t e s so obtained with the proper quantity of Ce;Mg n i t r a t e . E-5 contains 1% Cu, while E-6 con-tains 0.1% Cu. The expected slopes are given"*on the graph (b) of figure 12. The re s u l t s The slopes obtained were i n both cases that of Ce Mg n i t r a t e alone within the l i m i t of experimental error. However, i t i s i n t e r e s t i n g to note that f o r the sample containing the higher concentration of copper i n sample E-5 the warming up curve shows i n general a d e f i n i t e change of slope. The curve of vs. time, where , the d e f l e c t i o n on the galvanometer, i s inversely proportional to the temperature T, should be, i f the heat i n f l u x i s constant with time, a straight l i n e . Usually, however, f o r small s p e c i f i c heat and large heat i n f l u x , t h i s curve' i s not straight, but the slope varies regularly. In the case of this e l l i p s o i d , on the contrary, the vs. time curve i appears to follow two d i f f e r e n t slopes, the change from one to the other taking place a f t e r 3 minutes (see f o r instance the graph of figure 12a). I t i s tempting to interpret t h i s change FIGURE 1 2 (a) Typical warming up curves f o r E-5 and f o r p o l y c r y s t a l l i n e Ce 2Mg 5(NO^) 1 2»24H 20 (b) Expected slopes f o r sample E -6 and E-5 showing the various corresponding contributions to follow page83 84. i of slope as a change i n the rate of heat transfer. If the Ionic s p i n - l a t t i c e relaxation time was of the order of 3 minutes, then we would have aftefc that tlkme, an equilibrium between the temper-ature of the Ce ions and the Co ions, and the whole w i l l warm up much slower due to the combined s p e c i f i c heat of the two systems, and also perhaps a contribution from the bromine n u c l e i which may have cooled. If t h i s explanation Is correct, i t should be possible to f i n d the s p e c i f i c heat 60 the bromate by extrapolating the second curve back to the instant of demagnetization, and from thi s point f i n d i n g a temperature T*. T f i s then the equilibrium temperature obtained when heat i s exchanged between the Ce Mg nit r a t e and the bromate. This was not possible quantitatively, because the heat leak |n our apparatus was too large and Irregular. The only 'conclusion which can ba drawn from these ex-periments i s that i t might be possible to cool such a system of nu c l e i to temperatures of the order of .01° K. by contact with a cooling agent. There Is evidence of a relaxation time f o r t h i s process of the order of a few minutes. The slowest process i n the heat transfer i s probably the passage of heat from the Cu or Co to the Ce v i a the two l a t t i o e s . There are t h e o r e t i c a l grounds tw bfjlieving tljxat the passage of heat from the Br or I nuc l e i to the Cu or Co ions i s not a very slow process (Daniels (1954) )* but experimental v e r i f i c a t i o n of t h i s cannot be obtained from these measurements. 85 o BIBLIOGRAPHY L. Akerlind, B. Hartmann, and T. 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