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Adiabatic demagnetization apparatus for nuclear orientation Gorling, Robert Lloyd Albert 1970

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AN ADIABATIC DEMAGNETIZATION APPARATUS FOR NUCLEAR ORIENTATION by ROBERT LLOYD ALBERT GORLING B.A., U n i v e r s i t y of B r i t i s h Columbia, 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of Physics We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1970 In present ing th i s thes i s in p a r t i a l f i l l f i lment of the requirements fo r an advanced degree at the Un iver s i t y of B r i t i s h Columbia, I agree that the L ibrary sha l l make i t f r ee l y ava i l ab le for reference and study. I fu r ther agree tha permission for extensive copying of th i s thes i s f o r s cho la r l y purposes may be granted by the Head of my Department or by h i s representat ives . It is understood that copying or pub l i ca t i on o f th i s thes i s fo r f i nanc i a l gain sha l l not be allowed without my wr i t ten permiss ion. Department of Physics ^ The Un ivers i ty of B r i t i s h Columbia Vancouver 8, Canada Date A p r i l 15. 1970 ABSTRACT A cryostat has been b u i l t f o r cooling specimens to temperatures of the order of a hundredth of a K e l v i n by thermal contact with an a d i a b a t i c a l l y demagnetized paramagnetic s a l t p i l l . The apparatus was designed f o r performing nuclear o r i e n t a t i o n experiments. This thesis describes the construction of the apparatus and experimental tests studying the nuclear 60 o r i e n t a t i o n of Co i n an i r o n plate. The paramagnetic s a l t used was chromium potassium alum i n an alum- glyc e r i n e s l u r r y . In a d d i t i o n to the chrome alum p i l l a guard p i l l of manganous ammonium sulphate was used between the alum p i l l and the IK helium bath. The p i l l s were supported and thermally i s o l a t e d by German s i l v e r spacers. A copper heat l i n k was embedded i n the alum-glycerine s l u r r y and soldered to the specimen to provide thermal contact. Several heat l i n k s were used ranging from a bundle of f i v e thousand copper wires to a copper f o i l "concertina" arrangement. A Ventron. niobium-titanium superconducting solenoid which produced f i e l d s up to 48 kilogauss was used f o r the magnetic cooling. A superconducting p o l a r i z i n g solenoid was used to magnetically saturate the p o l y c r y s t a l l i n e i r o n plate. 60 Anisotropics i n the gamma r a d i a t i o n i n t e n s i t y from Co of 7 to 11 per cent corresponding to temperatures of 37 to 45 m K were observed. i i TABLE OF CONTENTS Page ABSTRACT . . . . . . . . . . i i LIST OF TABLES v i LIST OF FIGURES v i i CHAPTER I INTRODUCTION 1.1 Anisotropy of Radiation from Oriented Nuclei . . 1 1.2 S t a t i c Nuclear Orientation 3 1.3 Experimental Nuclear Or i e n t a t i o n 4 i ) Low Temperature 4 i i ) The Macroscopic Axis . . . . . . . . . . . 5 i i i ) Thermometry 5 iv) The Experiments 5 1.4 Contact Cooling 5 1.5 The Hyperfine F i e l d and the E f f e c t i v e F i e l d . . . 6 1.6 Mechanisms f o r Hyperfine F i e l d s i n Metals . . . . 9 i ) Exchange P o l a r i z a t i o n . 9 i i ) Transferred Hyperfine Structure 10 i i i ) RKKY. . 12 1.7 Other Experimental Techniques . 13 i ) NMR . 13 i i ) Resonant Destruction of Nuclear 14 Orientation (NMR-ON) i i i ) Mossbauer E f f e c t . 14 iv ) Perturbed Angular Correlations 14 v) Nuclear S p e c i f i c Heat 14 CHAPTER I I THE 'LOW TEMPERATURE APPARATUS 2.1 The Outer Cryostat 16 i i i Page CHAPTER I I (continued) i ) The Glass Dewars 16 i i ) L i q u i d Nitrogen F i l l e r 17 i i i ) L i q u i d Helium Transfer 17 iv) B o i l - O f f Rate 19 2.2 The Demagnetization and the Remnant F i e l d 19 i ) The Solenoid 19 i i ) The Remnant F i e l d 20 i i i ) NMR F i e l d Measurement of Demagnetization . . 21 Solenoid 2.3 The P o l a r i z i n g Solenoid 21 2.4 Magnetic Saturation of Specimen . 23 2.5 The Inner Cryostat 25 i) D e s c r i p t i o n . . . ; 25 i i ) The IK Helium Bath . . . . 25 i i i ) Solder Joins i n Inner Cryostat 25 2.6 The Vacuum Requirements and Low Temperature . . . 29 Vacuum Techniques i ) The Inner and Outer Jackets 29 i i ) Other Pumping Requirements 30 2.7 The Paramagnetic S a l t Assembly . 30 i ) Chrome Potassium Alum P i l l 30. i i ) The Guard P i l l 31 i i i ) The Spacers 31 2.8 The Heat Link and the Specimen Temperature . . . . 31 2.9 Vibrations 35 2.10 Experimental Procedure 36 CHAPTER IH NUCLEAR ORIENTATION OF 6°Co IN IRON 3.1 The Temperature Dependence of the Anisotropy of . 40 6 0 C o i v Page CHAPTER I I I (continued) 3.2 The Preparation of the Source 42 3.3 The Detectors and E l e c t r o n i c C i r c u i t r y 42 3.4 The Experiments: Data and Results . . . . . . . . 44 i ) The Raw Data 44 i i ) Corrections to the Raw Data 46 i i i ) The Results 48 CHAPTER IV FUTURE MODIFICATIONS OF THE APPARATUS 4.1 Low Temperature 61 i ) Heat Leaks to the Demagnetized System . . . 61 i i ) The Remnant F i e l d 62 i i i ) The IK Helium Bath 62 i v ) L i q u i d Helium Loss 62 4.2 Resonant Destruction of Nuclear Ori e n t a t i o n . . 62 4.3 Detectors 63 i ) Ge(Li) Detectors . 63 i i ) S i ( L i ) Detectors . 63 REFERENCES 64 v LIST OF TABLES Table Page 2.1 NMR F i e l d C a l i b r a t i o n 22 2.2 Typ i c a l Low Temperature Run 38 3.1 The 6°Co Runs . . . . . . . 49 v i I . • . • LIST OF FIGURES Figure Page 2.1 The Outer Cryostat (Schematic) 17 2.2 Saturation of Iron Foil 24 2.3 Saturation of Specimen (In Situ Experiment). . . . 26 2.4 Inner Cryostat and Demagnetization Assembly . . . 28 2.5 The Spacers 32 2.6 The Specimen Temperature 34 3.1 The Decay Scheme of 6 0Co 41 3.2 The 6 0Co Thermometer 43 3'.3 The Gamma Radiation Detection Apparatus (Schematic) 45 3.4 Run 1 54 3.5 Run 2 55 3.6 Run 3 - An Uninterrupted Run 56 3.7 Runs 4 and 5 57 3.8 Run 6 58 3.9 Run 7 59 v i i ACKNOWLEDGEMENTS I wish to thank Dr. B. G. T u r r e l l f o r h i s constant encouragement and assistance throughout this work. Of the many members of the Physics Department who have contributed t e c h n i c a l assistance to the work, I e s p e c i a l l y want to thank Mr. John Lees and Mr. E. P. Williams who b u i l t and maintained the glassware. v i i i CHAPTER I INTRODUCTION In this chapter some of the basic theory and procedures w i l l be introduced. The s p a t i a l anisbtropy of gamma r a d i a t i o n from a system of. The mechanisms of s t a t i c nuclear o r i e n t a t i o n are b r i e f l y presented i n terms of a hyperfine Hamiltonian.. The e l e c t r o n i c contributions to magnetic hyperfine i n t e r a c t i o n s w i l l be b r i e f l y introduced with an emphasis on d i l u t e impurities i n ferromagnetic metals. The technique of nuclear o r i e n t a t i o n i n c l u d i n g a discussion of contact cooling i s given. In ad d i t i o n a b r i e f discussion of some of the other techniques used i n the study of hyperfine f i e l d s i s presented. 1.1 Anisotropy of Radiation from Oriented Nuclei Given a system of n u c l e i of spin J. and magnetic momentyU , a magnetic f i e l d H w i l l s p l i t the ground state into 2 1 + 1 sub-levels equally spaced i n energy by^uH/I. In thermal equilibrium the population of these l e v e l s i s given by the Boltzman d i s t r i b u t i o n . For the Mth l e v e l , where -I <M< I, the normalized occupation i s where E i s the energy of the Mth sub-level and a i s the normalization M o constant. For the magnetic i n t e r a c t i o n above the occupation i s oriented n u c l e i i s discussed i n terms of c e r t a i n o r i e n t a t i o n parameters. a M = a Q exp ( y k T ) I t i s common i n angular c o r r e l a t i o n work to describe the relevant p r o p e r t i e s of the nucleus by an i r r e d u c i b l e tensor • For problems of c y l i n d r i c a l symmetry i t i s only the terms x T = P (M //J(I + 1)J 2 ) H 4 which are i n v o l v e d . In t h i s expression P^ i s the Legendre polynomial. The f i r s t three terms have simple p h y s i c a l meaning. E x p l i c i t l y they are: T00 = 1 5 T10 = M / [ I ( I + '* T20 = C 3 m 2 " I ( I + D l /2I (I+D The f i r s t term i s i s o t r o p i c and i s set equal to one f o r n o r m a l i z a t i o n . The second term expresses what i s c a l l e d the " p o l a r i z a t i o n " of the nucleus i n the d i r e c t i o n of q u a n t i z a t i o n . The t h i r d term expresses the "alignment". The o r i e n t a t i o n of the e n t i r e system of n u c l e i i n a bulk sample of m a t e r i a l i s given by the e x p e c t a t i o n values < T q Q } , s u i t a b l y normalized. 2 The n o t a t i o n used throughout t h i s work i s that of Gray and S a t c h l e r who def i n e the o r i e n t a t i o n parameter = 2 (2 0 + 1 ) % C (I 0 I ; M 0) a M , M where C i s the Clebsh-Gordon c o e f f i c i e n t . The parameter has been t a b u l a t e d 3 f o r some important Hamiltonians by B l i n - S t o y l e and Grace . I f the n u c l e i i n t h i s system emit nuclear r a d i a t i o n decaying to a new s t a t e (of d e f i n i t e angular momentum) then angular momentum must be conserved. The ex p r e s s i o n f o r the t r a n s i t i o n p r o b a b i l i t y f o r gamma r a d i a t i o n reduces to W ( Q ) = Z B ^ U ^ F ^ P ^ cos ( 0 ) 1 ) < 21, 2L ->) even This expression gives the normalized i n t e n s i t y of the gamma r a d i a t i o n as a f u n c t i o n of the angle 0 from the q u a n t i z a t i o n a x i s . In t h i s e x p r e s s i o n the U s f a c t o r s express the r e - o r i e n t a t i o n e f f e c t of any unobserved 3 t r a n s i t i o n s from the i n i t i a l state preceding the observed gamma decay. The F ̂  factors r e f e r to the observed t r a n s i t i o n . These two factors and F ^ are functions of the preceding and f i n a l states of the t r a n s i t i o n and the angular momentum of the r a d i a t i o n . "L" i s the highest multipole component of the observed t r a n s i t i o n . For observed t r a n s i t i o n s not con- serving p a r i t y - b e t a r a d i a t i o n -the requirement that 0 be even i s dropped. A f u l l d iscussion of th i s scheme including the form of F y and U ̂  i s given i n reference 4. A us e f u l experimental parameter i s the anisotropy, £ , given by, r = W(90°) - W(o°) W(90°) 1.2 S t a t i c Nuclear Orientation Only at temperatures where the s p l i t t i n g of the nuclear sub-levels i s comparable to the thermal energy, that i s , \ - EM+1 ^ k T ' i s appreciable nuclear o r i e n t a t i o n achieved. For a t y p i c a l magnetic i n t e r - a c t i o n 1 n.m. , I 0? 1) this requires a temperature of the order of a hundredth of a degree and a f i e l d of the order of a hundred k i l o - o e r s t e d . In general other hyperfine i n t e r a c t i o n s can be involved. A phenomenological spin Hamiltonian^ i n an external f i e l d i s , Y\ = u_.R + M 0 [ g l l H S + g . ( H S + H S ) ] " — y u 11 z z J - x x y y + [A s I + B (S I + S I )] z z x x y y + CD S 2 - 1/3S (S '+ l ) ] + C P f I 2 - 1/3 I (I + 1)}] z z J where ^ i s the e f f e c t i v e spin determined by the m u l t i p l i c i t y of the low ly i n g e l e c t r o n i c energy l e v e l s . The f i r s t term i n the Hamiltonian gives the "brute force" method of achieving nuclear o r i e n t a t i o n . I t requires the a p p l i c a t i o n of an external 5 6 f i e l d t y p i c a l l y 10 to 10 oersted. The terms i n gj| and g ^ are Zeeman e l e c t r o n i c terms which or i e n t the e f f e c t i v e spin i n an external f i e l d . For a ferromagnet the "external f i e l d " H w i l l include the Lorentz f i e l d of the e l e c t r o n i c dipole moments . In the Gorter-Rose method of nuclear o r i e n t a t i o n , the p o l a r i z a t i o n of the e f f e c t i v e spin by the Zeeman i n t e r a c t i o n w i l l produce o r i e n t a t i o n of the nuclear spin by the hyperfine terms i n A and B. I f A dominates B then the nucleus aligns along the e f f e c t i v e spin; i f B dominates then the nucleus aligns perpendicular to the e f f e c t i v e spin. The term i n D represents the e l e c t r o n i c i n t e r a c t i o n with 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 and can also produce nuclear o r i e n t a t i o n through the hyperfine terms i n A and B (provided S > ^ ) . This i s the Bleaney method. I t i s also feas- i b l e to produce nuclear o r i e n t a t i o n through the i n t e r a c t i o n of the nuclear quadropole moment and the e l e c t r i c f i e l d gradient as given i n the P term. 1.3 Experimental Nuclear Orientation The actual apparatus used i n this work i s very b r i e f l y introduced i n t his section. i ) Low Temperature The low temperature i s produced by a d i a b a t i c demagnetization of a chrome potassium alum s l u r r y . Magnetic f i e l d s up to 48 k i l o - o e r s t e d were produced i n a superconducting solenoid. When the alum i s a d i a b a t i c a l l y demagnetized from 20 k oe. per degree i t cools to .012°K. At this temperature there i s a magnetic ordering trans- i t i o n with a large s p e c i f i c heat anomaly. A copper heat l i n k embedded i n the s a l t and soldered to the source provides the thermal contact between the s a l t and the r a d i o a c t i v e specimen. 5 i i ) The Macroscopic Axis To observe macroscopic e f f e c t s of nuclear o r i e n t a t i o n an axis of quantization must be defined. Since the f i e l d s which o r i e n t the n u c l e i are e l e c t r o n i c i n o r i g i n i t i s necessary to a l i g n the e l e c t r o n i c spins. In this experiment they are aligned by the exchange f i e l d of the iron . Thus the p o l y c r y s t a l l i n e i r o n f o i l i s magnetically saturated by a superconducting solenoid to remove the domains. i i i ) Thermometry The most s u i t a b l e method of thermometry i s the observation of the anisotropy of gamma r a d i a t i o n of aligned n u c l e i f o r which a l l the o r i e n t a t i o n and decay scheme parameters are known. ^ C o i s used i n this experiment because i t has been well studied both for nuclear and hyperfine parameters, and also because i t has a r e l a t i v e l y high anisotropy at temperatures of approximately .01 K. iv) The Experiments A f t e r demagnetization, the count rates at 0° and 90° to the axis of quantization were observed. The count rates were normalized to the i s o t r o p i c rates observed at helium bath tempera- tures . . > . 1.4 Contact Cooling There are three d i s t i n c t thermal b a r r i e r s g i v i n g termperature gradients between the source and the p i l l . F i r s t , the heat must be con- ducted across the alum-copper i n t e r f a c e . The heat i s conducted across by phonons. L i t t l e ^ has given the t h e o r e t i c a l formula, 4 4 Q = k A (T^ - T 2*) where A i s the contact surface area. The value of the constant k seems to vary with the experimental set-up. The best value obtained experi- mentally^ _ s k = 7.5 x 10 erg sec (k) cm The conductivity of the copper i s due p r i m a r i l y to the conduction electrons. Hence, the heat must be transferred from conduction electrons to phonons. L i t t l e has shown for t h i s b a r r i e r that, Q = 1 . 0 x 1 0 1 0 ( T 1 5 - T 2 5 ) erg s e c " 1 cm"3, where the rate i s given per un i t volume. The volume over which the transfer can take place i s given by the mean fr e e path of the phonons, L = 4.0 x 10" 3 ( T _ 1 ) cm. The t h i r d thermal b a r r i e r arises simply from the conductivity of the copper: Q = k ( T x - T 2) A L" 1 where k = l.O-x-10 7 (T) erg s e c " 1 K _ 1. The actual experimental considerations and c a l c u l a t i o n of the source temperature as a function of the heat input i s given i n Chapter I I . 1.5 The Hyperfine F i e l d and the E f f e c t i v e F i e l d The magnetic i n t e r a c t i o n Hamiltonian for an el e c t r o n of o r b i t a l angular momentum X , spin angular momentum _s, with a nucleus of spin 1 i s given by - + C1 • i - 3 (s • r o ) ( r 0 • r ~3> + C I • I S C r ) < > " 3>J} Here, f3 i s the Bohr magneton and r Q i s the u n i t vector between the nucleus and e l e c t r o n . The f i r s t term i n the sum i s the o r b i t a l contribution; the second i s the d i p o l a r i n t e r a c t i o n between the spins of the e l e c t r o n and nucleus; the t h i r d i s the Fermi contact term. The Fermi contact term represents the i n t e r a c t i o n of the nucleus with that e l e c t r o n that has a f i n i t e p r o b a b i l i t y of being at the nuclear s i t e . The f i r s t two terms are both zero f o r S-state (X = 0) electrons. The contact term i s non-zero f o r , and only f o r , S-state electrons. I t i s convenient to think of the i n t e r - a c t i o n i n the form of a magnetic f i e l d of the e l e c t r o n a t the nucleus as follows, I f the i n t e r a c t i o n i s diagonal i n H^ and I, the nuclear energy l e v e l s are given by ^ I EM= < H h . f . > M — . The three terms i n the Hamiltonian each give r i s e to a magnetic f i e l d ; the t o t a l f i e l d i s t h e i r vector sum. The o r b i t a l f i e l d , f o r L-S coupling i s , H L=<^ _e < L > < r "3> In the 3d t r a n s i t i o n metals the o r b i t a l angular momentum i s nearly quenched (< L } = 0) by the c r y s t a l l i n e e l e c t r i c f i e l d so that this con- t r i b u t i o n i s small. From the r e l a t i o n s L + S = J ; L + 2 S = g J we have L - - ( g - 2) S. Hence, \ - ̂  2(3 ( g - 2) < s><r-3>, f o r 3d t r a n s i t i o n metals. For rare earth metals the s p i n - o r b i t coupling i s dominant. Hence, the o r b i t a l hyperfine f i e l d from the 4f electrons i s the dominant contribution. The s p i n - d i p o l a r f i e l d i s ( i n L-S coupling) HD "Ti h§ <S>0~-3>0 - 3 c o s 2 6 > . The angle 0 i s taken between the vector giving the nuclear spin and the p o s i t i o n vector g i v i n g a small volume element of e l e c t r o n i c spin. The averages i n © and T are taken over the electron o r b i t ; the average i n S i s an ensemble average over the occupied spin states. The contact f i e l d i s given by H = ^ 2 6 < s > < r _ 3 > s 4 rr s provided, however, that^T* ^ i s the same f o r a l l the spin states averaged i n the f a c t o r ^ S } . Large hyperfine f i e l d s can r e s u l t i f KjT- 3/> i s not the same f o r both spins i n an S-state o r b i t a l . H can be wr i t t e n s i n a form which c l e a r l y shows the non-zero value of the S-state wave- function at the nuclear s i t e ( i n c.g.s. u n i t s ) : for one S el e c t r o n . The hyperfine f i e l d which has been discussed i s not measured d i r e c t l y . What i s measured i s the e f f e c t i v e f i e l d given by Seff - 4.f. +4 + So ^ i s the hyperfine f i e l d , H ^ i s the Lorentz f i e l d of the magnetic dipoles surrounding the "atomic s i t e " . H q i s the e x t e r n a l l y applied f i e l d and DM i s • t h e demagnetizing f i e l d of the surface "magnetic poles" i n terms of a demagnetizing (geometrical) factor and the magnetization of the sample. Notice that the sign of ^ can be determined by varying the magnitude of H q and noting i f increases or decreases. 1.6 Mechanisms f or Hyperfine F i e l d s i n Metals This section w i l l give mechanisms whereby hyperfine f i e l d s a r i s e i n metals and p a r t i c u l a r l y at an impurity s i t e i n a metal. i ) Exchange P o l a r i z a t i o n Conventional Hartree-Fock c a l c u l a t i o n s ignored the dif f e r e n c e i n spin up and spin down states i n c a l c u l a t i n g the wave functions. Hence a l l states equally populated with spin up and down (such as core S-states) give zero hyperfine f i e l d i n t h i s scheme. "Spin-polarized" (unrestricted) c a l c u l a t i o n s consider the exchange i n t e r a c t i o n between unpaired electrons and core "closed s h e l l " g electrons. A simple but p h y s i c a l l y meaningful model has been given which explains the r e s u l t s . The exchange i s found to act as an a t t r a c t i v e force between p a r a l l e l spins. For example, i n a ferromagnetic metal the unpaired 3d spin up electrons a t t r a c t the core S electrons of the same spin outwards towards the high density of 3d electrons. The e f f e c t i s to produce a 3 2 di f f e r e n c e i n the^r" y , or |T ^ \ , values of the spin states. A net hyperfine f i e l d from the Fermi contact term r e s u l t s : Freeman and Walson have shown that this f i e l d could be -5 x 10"* oersted i n m e t a l l i c i r o n (out of a t o t a l f i e l d of -3.3 x lO^oersted. This e f f e c t i s c a l l e d core " p o l a r i z a t i o n " . The 4s conduction e l e c t r o n c o n t r i b u t i o n would be of opposite sign; the conduction electrons of spin up are pulled inwards because they l i e p r i m a r i l y outside the 3d spins. The 4s electrons of spin up are lowered i n energy, hence, the spin up band w i l l f i l l with 10 more electrons up to the Fermi l e v e l than the spin down band. This produces a net spin up contribution-conduction e l e c t r o n p o l a r i z a t i o n - i n the 4s band. Because the spin up electrons are pul l e d inwards by the up spins, a net spin down p o l a r i z a t i o n i s l e f t near the c e l l boundary ( i n s p i t e of the net spin up p o l a r i z a t i o n ) . Indeed, positron a n n i h i l a t i o n 9 experiments i n i r o n and n i c k e l have measured such a net spin down . A better analysis of the conduction e l e c t r o n problem i s given by the Ruderman-Kittel-Kasuya-Yosida approach presented below. The e f f e c t s w i l l be seen to be much less " p r e d i c t a b l e " than given by the simple model. F r i e d e l and Daniels have proposed a model f or the hyperfine f i e l d s on period V elements from s i l v e r to iodine as d i l u t e impurities i n a 3d t r a n s i t i o n m etal 1^. The model uses the conduction e l e c t r o n e f f e c t s discussed above. I f a normally diamagnetic atom i s placed s u b s t i t u t i o n a l l y i n an i r o n l a t t i c e (for example), provided the e l e c t r o s t a t i c perturbation i n the l a t t i c e i s small enough, the impurity w i l l "see" the negative spin p o l a r i z a t i o n of the outer region of the i r o n atoms. A negative hyper- f i n e f i e l d w i l l r e s u l t (from the contact i n t e r a c t i o n ) . However, i f the atom has a large e l e c t r o s t a t i c i n t e r a c t i o n , compared to the i r o n , with the conduction electrons the nucleus w i l l see the net spin of the conduction band. Since t h i s i s spin-up, a p o s i t i v e f i e l d w i l l r e s u l t . i i ) Transferred Hyperfine Structure P o l a r i z a t i o n of electrons on an impurity atom can occur from transferred hyperfine i n t e r a c t i o n . In add i t i o n , the f i e l d on the host can be affe c t e d . Two mechanisms can account f o r this p o l a r i z a t i o n : the " P a u l i d i s t o r t i o n e f f e c t " or admixture, and covalent bonding. These e f f e c t s have been used to q u a l i t a t i v e l y explain transferred hyperfine structure on ligands i n d i e l e c t r i c s o l i d s 8 such as MnF„ and KMnF . The free atom core e l e c t r o n i c states of the solute are not i n general orthogonal to the ferromagnetic e l e c t r o n states of the host f o r the same spin states. I f (fi^ i s an o r b i t a l appropriate to the f e r r o - magnet and X > X are appropriate to the core of the solute, they w i l l have an overlap i n t e g r a l 0 between them. These wavefunctions can be Schmidt orthogonalized obtaining the set ( i - s 2 ) ^ [ <p+- - sX +]; x t ; X^ or the equivalent set ^ ; X+.; (i - s 2)" % IX., - s c^'J . The free atom states of spin up on both the host (near neighbours to the impurity) and the'solute are "strengthened". The impurity nucleus w i l l see a net spin up p o l a r i z a t i o n of core electrons giving a p o s i t i v e f i e l d . Because the host ferromagnetic wavefunction is.strengthened, the host core p o l a r i z a t i o n w i l l increase g i v i n g a p o s i t i v e f i e l d . Because the host ferromagnetic wavefunction i s strengthened, the host core polar- i z a t i o n w i l l increase giving a larger negative co n t r i b u t i o n to i t s hyper- f i n e f i e l d . There i s an a d d i t i o n a l binding energy f o r the electrons i f they are shared (molecular o r b i t a l s ) by neighbouring atoms. Pa u l i exclusion prevents f i l l e d states sharing electrons, hence, to f i r s t order, only (J) and X , can mix. The new set of wavefunctions i s r ( i - s)-*_c[^ - sX^] ; ; d - 2 sT + r 2 >~* [ x + + r < p + ] • This mixing corresponds to having the core spin down el e c t r o n spend time i n the ferromagnetic atom spin down state. ~8~ i s the weighting or "covalent" mixing f a c t o r . The e f f e c t on the impurity i s to reduce the 12 net spin down giving a p o s i t i v e f i e l d ( i n a d d i t i o n to the p o s i t i v e admixture f i e l d ) . On the host the ferromagnetic spin i s reduced, reducing the core p o l a r i z a t i o n and the f i e l d . Admixture and covalent bonding must both be considered i n the wavefunctions f o r the conduction band and the ferromagnetic band i n the pure metal. The two mechanisms are of opposite sign i n the core polar- i z a t i o n . The net e f f e c t on the hyperfine f i e l d i s not known but i t could be as large as the d i r e c t contribution to the f i e l d by the conduc- t i o n electrons through the contact term. D. A. S h i r l e y et a l . have recently suggested that transferred hyper- f i n e s t r u c t u r e could be the dominant e f f e c t f o r iodine and xenon impurities i n 3d t r a n s i t i o n metals''"'''. Furthermore, i t has been suggested from studies of systematics of hyperfine f i e l d s i n impurities i n 3d t r a n s i t i o n ferromagnetics that the core p o l a r i z a t i o n i s . p o s i t i v e and constant ( i n a 12 given host) across a period . Transferred hyperfine i n t e r a c t i o n would po s s i b l y contribute to such a mechanism. i i i ) RKKY The Ruderman-Kittel-Kasuya-Yosida (RKKY) i n t e r a c t i o n r e f e r s to the e f f e c t of a l o c a l magnetic moment on the conduction e l e c t r o n spin d i s t r i b u t i o n . The net e f f e c t on the conduction band i s to lower the energy of the spin states p a r a l l e l to the l o c a l moment. However, the " l o c a l " e f f e c t can be of eit h e r sign and p r a c t i c a l l y any magnitude. In fa c t , the spin density o s c i l l a t e s . Indeed, c a l c u l a t i o n s have shown that the net l o c a l induced spin density (as would be seen by neutron d i f f r a c t i o n ) can be 180° out of phase with the s character of the spin density at 13 that point (as would be seen by a nucleus at the point) . The c a l c u l a - tions were done 'for i r o n and gadolinium. Such r e s u l t s i l l u s t r a t e the complexity of the conduction electron problem as well as the great progress 13 presently being made by t h e o r i s t s . 1.7 Other Experimental Techniques In t h i s s e c t i o n some of the other experimental methods used to determine hyperfine f i e l d s w i l l be compared to nuclear o r i e n t a t i o n . i ) NMR Nuclear magnetic resonance (NMR) measures the hyper- f i n e f i e l d d i r e c t l y (hi) = gH I ) . Furthermore, because of the accuracy to which the frequency can be measured accurate determination of the f i e l d i s possi b l e . However, the ferromagnetic nuclear magnetic resonances are generally very broad and pulsed techniques are u s u a l l y used. Very d i l u t e impurities cannot be studied d i r e c t l y because of the weakness of the s i g n a l . Very f i n e powders with p a r t i c l e s i z e less than the radio frequency s k i n depth are u s u a l l y required. NMR measures the hyperfine f i e l d i n the domain walls unless the specimen i s magnetically saturated or strong radio frequency pulses are used. i i ) Resonant Destruction of Nuclear Orientation (NMR-ON) 18 Mathias has performed an experiment using the de s t r u c t i o n of nuclear o r i e n t a t i o n to detect nuclear magnetic resonance. A small radio frequency ( r . f . ) s i g n a l c o i l i s set up i n the demagnetization chamber around the specimen source, oriented so the r . f . i s perpendicular to the p o l a r i z i n g f i e l d . The r . f . power output of the c o i l must be kept small to prevent excessive heating of the source. The resonant detection method has several advantages. The accuracy of measurement i s much higher - approaching that of normal NMR. Further- more, the hyperfine f i e l d i s determined d i r e c t l y (OJ = ^ f^)' removing the requirement of accurate thermometry. Changing the magnitude of the p o l a r i z i n g f i e l d allows determination of the sign of the hyperfine f i e l d 14 because of the high p r e c i s i o n . Furthermore, complete s a t u r a t i o n of domains i s not required. This i s very u s e f u l i n rare earth metals and cobalt. Indeed, the method has been shown to be just as a p p l i c a b l e to non-ferromagnetic metals i n s p i t e of the loss of the r . f . enhancement. • The NMR-ON si g n a l contains a f i n e structure c o n s i s t i n g of k maxima i f the s t a t i s t i c a l o r i e n t a t i o n tensor i s of rank k. This feature has u s e f u l a p p l i c a t i o n s . i i i ) Mossbauer E f f e c t Mossbauer e f f e c t ( r e c o i l l e s s absorption of gamma rad i a t i o n ) has been used to study the hyperfine i n t e r a c t i o n s on a l i m i t e d number of "Mossbauer n u c l e i " (which includes ~*7Fe) i n various e l e c t r o n i c environments. Indeed, the "isomer s h i f t " has been very u s e f u l i n determining the amount of s-character i n the orb i t a l - hyper- f i n e f i e l d . i v ) Perturbed Angular Correlations Perturbed angular c o r r e l a t i o n s measure the hyperfine f i e l d on an intermediate state of a nuclear decay. I t requires s u f f i c i e n t l y l o n g - l i v e d states that s i g n i f i c a n t r o t a t i o n of the s p a t i a l anisotropy of r a d i a t i o n occurs. Coincidence counting neces- s i t a t e s long counting times. PAC has been combined with NMR. v) Nuclear S p e c i f i c Heat At high temperatures the population d i s t r i b u t i o n of the nuclear spin l e v e l s w i l l be uniform, that i s , random o r i e n t a t i o n , but at low temperatures those spin states having lower energy w i l l be preferred. This r e d i s t r i b u t i o n of the nuclear spin states gives r i s e to a large c o n t r i b u t i o n C^ to the s p e c i f i c heat (Schottky anomaly) i n the temperature. region where i t i s s i g n i f i c a n t . C^ has a maximum for kT ^ e f f ^ 1 2 and i s proportioned to 1/T at the high temperature end (T S IK). Hence 15 a low temperature apparatus i s requ i red . Helium three cryostats are most f requent ly used but demagnetization and hel ium four cryostats are a l so used. Other contr ibut ions to the t o t a l s p e c i f i c heat ( e l e c t r o n i c , l a t t i c e and sp in wave) have d i f f e r e n t temperature dependence and become smal l at low temperature so that C„ can be separated and hence H r r can be deter -r N e f f mined. Small impurity contr ibut ions can give s i g n i f i c a n t e f f e c t s i f they a f f e c t the magnetic s ta te ( for example, by the formation of l o c a l moments). High pu r i t y specimens are required unless such e f f e c t s are being s tud ied. Besides supplementing and complementing in format ion obtained by other methods s p e c i f i c heat measurements can provide a r e l i a b l e estimate o f , say, the p o s i t i o n of the NMR s i gna l which can give more accurate r e s u l t s . CHAPTER II THE LOW TEMPERATURE APPARATUS This chapter i s concerned with the design, construction and opera- t i o n of the low temperature apparatus used i n these experiments. The f i r s t s e c t i o n deals with the outer cryostat which r e f e r s to the part of the machine producing l i q u i d helium temperature (4 K). This involves the outer dewars, l i q u i d helium transfer and the superconducting solenoid (and t h e i r power s u p p l i e s ) . An inner cryostat allows the production of temperatures below 4 K by pumping on l i q u i d helium. The paramagnetic s a l t p i l l s used f o r the demagnetization and the specimen source are con- tained i n the inner cryostat. Heat leaks to the demagnetized system are discussed as w e l l as the actual contact cooling of the source. An experi ment to determine the f i e l d of the demagnetization solenoid by NMR, and a check of the satu r a t i o n of the source are given. A t y p i c a l low tempera ture run i s presented. Also mentioned i n the chapter are some of the problems encountered using the apparatus. 2.1 The Outer Cryostat The outer cryostat consisted of glass l i q u i d nitrogen and helium dewars. Contained i n the outer cryostat were the demagnetization and p o l a r i z i n g solenoids, the inner cryostat and pumping and e l e c t r i c a l l i n e s The outer cryostat i s shown i n Fig.2.1. i ) The Glass Dewars a) The l i q u i d nitrogen, or outer dewar was a glass dewar sealed with a 'hard' vacuum i n the interspace. I t was supplied with a v e r t i c a l s l i t i n the s i l v e r i n g so the l i q u i d l e v e l could be determined. 16 S t o p c o c k I n n e r dewar Outer dewar Dewar su p p o r t p l a t e s Dewar cap • Vacuum l i n e s B a f f l e s - R a d i a t i o n t r a p •Inner c r y o s t a t D e m a g n e t i z a t i o n s o l e n o i d S c a l e : 2 i n . : 1 cm. i ! i The Outer C r y o s t a t ( S c h e m a t i c ) FIGURE 2.1 18 b) The l i q u i d helium dewar, or inner dewar, was supplied with a stopcock to the interspace. A glass dewar i s somewhat porous to helium gas and w i l l become " s o f t " a f t e r exposure. To remove traces of helium gas i n the interspace the dewar i s flushed with a i r or nitrogen gas. The inner dewar i s l e f t with a s o f t vacuum of a i r or nitrogen to enable e f f i c i e n t precooling to l i q u i d nitrogen tempera- tures. The gas i n the interspace freezes out upon i n i t i a l transfer of l i q u i d helium leaving a "hard" vacuum. The inner dewar was supplied with a viewing s l i t to determine the l i q u i d l e v e l . The inner dewar space was equipped with a safety pressure-release valve to prevent pressure build-up from helium b o i l - o f f , e s p e c i a l l y a f t e r the quenching of the superconducting solenoids. i i ) L i q u i d Nitrogen F i l l e r Because the s a l t p i l l was made with a gly c e r i n e base i t was necessary to keep i t cold (frozen s o l i d ) at a l l times to prevent dehydration of the s a l t . This required that l i q u i d nitrogen be maintained i n the outer dewar between runs. An automatic f i l l - ing device was used f o r this purpose. i i i ) L i q u i d Helium Transfer I t i s e s s e n t i a l that e f f i c i e n t use of the cold e f f l u e n t helium gas be made to precool the system during a l i q u i d helium transfer. This requires that the l i q u i d must be deli v e r e d to the bottom of the dewar where i t b o i l s o f f . The e f f l u e n t gas then cools the magnets and the inner cryostat as i t r i s e s . An extension on the helium transfer syphon to the bottom of the inner dewar was used. However, i t was found that i f the en t i r e transfer syphon and extension were l e f t i n place a f t e r the transfer with the outside end of the syphon closed o f f thermal o s c i l l a t i o n s were set up i n the l i q u i d . These o s c i l l a t i o n s quickly b o i l e d o f f the l i q u i d helium. The problem was solved by leaving 19 the extension permanently inside the dewar with a b a y o n e t - f i t t i n g into which the transfer syphon was inserted. The actual tr a n s f e r was performed using a pressure head of about 3 cm. of mercury pressure. A f t e r precooling the system to l i q u i d nitrogen temperature the i n i t i a l transfer took about an hour to complete and used approximately twelve l i t r e s of l i q u i d helium. Three to f i v e l i t r e s were used i n r e t r a n s f e r r i n g into the cold system. iv) B o i l - O f f Rate The b o i l - o f f of l i q u i d helium was about 200 cc. per hour i n t i a l l y . As the l e v e l f e l l the rate lowered. The l i q u i d remained above the demagnetization solenoid f or about f i v e hours allowing one or two counting runs before the l i q u i d was "topped up". 2.2 The Demagnetization Solenoid and the Remnant F i e l d i ) The Solenoid The demagnetization solenoid was supplied by Ventron Instruments, Magnion D i v i s i o n (Burlington, Mass.). The i n s i d e diameter was 2 i n . , the outer diameter was 4 i n . and the a c t i v e winding length was 7 i n . I t was wound with niobium-titanium wire and supplied a f i e l d of 50 k i l o - o e r s t e d from a current of 62 amperes. For normal operation a current of about 55 amperes was used providing a f i e l d of 45 k i l o - o e r s t e d . A p e r s i s t e n t heat-switch was supplied with the solenoid allowing operation f o r long periods of time without energy l o s s . The solenoid's power supply was equipped to automatically shut o f f i f the magnet "quenched" (went normal). The quench f a c i l i t y prevented excessive heating of the solenoid and l i q u i d helium both. In the case of a quench the energy stored i n the magnetic f i e l d was p a r t i a l l y d i s s i p a t e d i n a diode connected across the solenoid leads outside the cryostat. The high current leads to the solenoid were wrapped around the pump- 20 ing l i n e s for e f f i c i e n t cooling. They were tapered down i n s i z e from "B and S" s i z e number 10 at the top of the cryostat to number 18 at the solenoid. i i ) The Remnant F i e l d When a superconducting magnet i s f i r s t magnetized and then demagnetized s o - c a l l e d p e r s i s t e n t currents flow i n 15 the solenoid. These currents give r i s e to a r e s i d u a l or remnant f i e l d The remnant f i e l d must be small f o r e f f i c i e n t cooling of the paramagnetic s a l t s . I t can be r e a d i l y shown that i f the applied f i e l d i s H at i n i t i a l o temperature T q and the f i n a l f i e l d i n the 'sample including any e f f e c t i v e " i n t e r a c t i o n f i e l d " i s FL. then the f i n a l temperature, T^, i n the adiabatic demagnetization i s given by H^/H Q = T^/T q where must be interpreted as a magnetic temperature. I t i s possible to remove the remnant f i e l d by heating the solenoid above i t s superconducting t r a n s i t i o n temperature. However, th i s i s very inconvenient l a r g e l y because of the large l i q u i d helium loss involved. A method which avoids a c t u a l l y removing the f i e l d from the solenoid i s l i f t i n g the magnet above the s a l t p i l l . Besides t e c h n i c a l d i f f i c u l t y t h i s method involves a possible v i b r a t i o n a l heat leak. The remnant f i e l d can be reduced by "sweeping the f i e l d " . The current i n the magnet i s reversed a few times with successively decreasing amplitude. Excessive sweeping must be avoided to prevent eddy current and hy s t e r e s i s heating of the demagnetization assembly. By manually reversing the current by about 8 amperes the f i e l d as measured external to the magnet by a search c o i l was reduced by a f a c t o r of as much as t h i r t y . Magnetic s h i e l d i n g was used to attempt to reduce the remnant f i e l d at the s i t e of the p i l l . Mu metal shields the remnant f i e l d yet reduces the magnetizing f i e l d by only a k i l o - o e r s t e d . The s h i e l d was a cylinder of "Netic" mu metal supplied by P e r f e c t i o n Mica Company, Magnetic Shielding 21 D i v i s i o n (Chicago). The cylinder was about 1/16 i n . thick, by 2 i n . diameter, by 9 i n . length. I t was wrapped from annealed f o i l , each layer being magnetically separated by aluminum f o i l . I t was found that f or f i n a l temperatures greater than .03 K the remnant f i e l d had no measurable e f f e c t on the f i n a l temperature (using chrome potassium alum). i i i ) NMR F i e l d Measurement of Demagnetization Solenoid The demagnetization solenoid was c a l i b r a t e d ( f i e l d produced by a given current) by observing the nuclear magnetic resonance of aluminum i n powder form. Aluminum has a large NMR s i g n a l . I t was chosen because the resonance frequency of aluminum was i n the frequency range of the a v a i l a b l e marginal o s c i l l a t o r f o r the f i e l d used. The powder was mixed with o i l and placed i n a glass tube which was positioned i n the centre of the solenoid. Around this specimen tube was wound a c o i l the inductance of which was determined by t r i a l to give o s c i l l a t i o n at about 22 M Hz which corresponds to a f i e l d of 20 Kgauss (11.10 M Hz/10.00 KG). The marginal o s c i l l a t o r was modulated at audio frequencies by a transducer or 'wobbulator'. The applied f i e l d was swept at 40 gauss per minute. The linewidth of aluminum i s 8 gauss so that the s i g n a l took about 12 seconds to sweep through. The NMR s i g n a l was monitored by a l o c k - i n a m p l i f i e r and recorded on a s t r i p - c h a r t recorder. The r e s u l t s are given i n Table 2.1. 2. 3 The P o l a r i z i n g Solenoid The p o l a r i z i n g solenoid was wound from superconducting niobium-257<, zirconium wire. I t was designed to give an approximately uniform saturat- ing f i e l d over the specimen yet to give n e g l i g i b l e f i e l d at the demagnet- i z a t i o n s a l t . The c o i l was wound with three separated sections on a brass 22 TABLE 2.1 NMR FIELD CALIBRATION Resonant Current i n Frequency Magnet F i e l d F i e l d/Current Run (MHZ) (amp.) (11.1 MHZ/10KG) (KG/amp.) 1 23.36 26.2 21.0 .802 Sweeping f i e l d up 2 23.14 26.2 20.8 .795 Sweeping f i e l d down 3 19.38 22.0 17.45 .794 Sweeping f i e l d down 23 former. The source was situated between the lower two sections which were wound i n the same sense. The t h i r d s e c t i o n was wound i n the opposite sense to compensate the f i e l d produced by the lower sections at the demagnetization s a l t . The f i e l d at the source was estimated to be a h a l f kilogauss per ampere current; the f i e l d at the s a l t about 2% of the f i e l d at the source. An experiment which can be used to check the e f f e c t - iveness of the solenoid i s described i n the next section. The superconducting leads of the solenoid were spot welded to platinum wires which were s o f t soldered to copper leads. The current was supplied by a 12-volt storage battery through a t r a n s i s t o r i z e d current control u n i t capable of handling up to seven amperes. 2.4 Magnetic Saturation of Specimen I t was necessary to do an experiment to determine the sat u r a t i o n of the i r o n f o i l source. A f o i l i d e n t i c a l to the source was placed i n a magnetic f i e l d i n the o r i e n t a t i o n used i n the nuclear o r i e n t a t i o n apparatus. Fixed i n the f i e l d on each side of the f o i l was a c o i l aligned with i t s axis p a r a l l e l to the f i e l d . The c o i l s were connected i n seri e s adding through a galvonometer. The experiment was performed by snatching the f o i l out of the f i e l d and measuring the current induced i n the c o i l s . This was repeated f o r d i f f e r e n t values of the f i e l d . The d e f l e c t i o n of the galvonometer, D, i s proportional to the d i f f e r e n c e i n the magnetic induction B f o r the f o i l and for a i r i n the applied f i e l d H 0: D oC B .. - B . oC M. m F o i l a i r (H) where M i s the net magnetization of the f o i l . At sa t u r a t i o n D i s constant fo r changing applied f i e l d . The r e s u l t s of the experiment are shown i n 2.0 0.5 1.0 1.5 2.0 H ( k i l o - o e r s t e d ) S a t u r a t i o n - o f I r o n F o i l FIGURE 2.2 25 F i g . 2.2. The s a t u r a t i o n f i e l d was taken as 1.5 k i l o g a u s s . This f i e l d r e q u i r e d a c u r r e n t of about 3\ amperes i n the p o l a r i z i n g s o l e n o i d . Another experiment was performed to determine s a t u r a t i o n during an a c t u a l nuclear o r i e n t a t i o n experiment. The degree of nuclear o r i e n t a t i o n measured by the anisotropy was measured as a f u n c t i o n of the current i n the p o l a r i z i n g s o l e n o i d . The r e s u l t s are shown i n F i g . 2.3. Although no change i n a n i s o t r o p y was observed f o r currents from two to f o u r amperes no f i r m conclusions could be reached because of the l a r g e e r r o r s . 2.5 The Inner Cryostat i ) D e s c r i p t i o n The inner c r y o s t a t and demagnetization assembly are shown i n F i g . 2.4. The outer can was used as a vacuum j a c k e t to i s o l a t e t h e r m a l l y the IK pumped helium bath. The helium bath i n the f i n a l arrangement completely surrounded the demagnetization assembly. The inner j a c k e t must.be evacuated to i s o l a t e t h e r m a l l y the demagnetized s a l t p i l l s . However, i t i s a l s o used w i t h helium exchange gas to remove the heat of magnetization. The pumping l i n e s from the outer j a c k e t . t o the bath j a c k e t are t h i n - w a l l e d s t a i n l e s s s t e e l . i i ) The IK Helium Bath The helium bath was f i l l e d from the 4 K helium r e s e r v o i r through the pumping l i n e . A needle v a l v e c o n t r o l l e d from the top of the apparatus was used to admit the l i q u i d . The bath would be evacuated to a low pressure; then the needle v a l v e was opened a l l o w i n g the l i q u i d to f l o w i n . Approximately 70 cc. of l i q u i d could be admitted t h i s way. The bath was pumped down by a 5 cubic f e e t per minute pump (Cenco Hyvac 14). Pressures of about .3 mm. mercury were obtained. This represents a temperature i n the bath of ^ 1.2 K. The heat of magnetization flows i n t o the bath. The maximum heat 8- 42 6 2 - 32 18 12 2 8 - 2 0 2 4 p o l a r i z i n g c u r r e n t (amperes) Note: The numbers b e s i d e t h e d a t a p o i n t s i n d i c a t e the r e l a t i v e time ( i n m i n u t e s ) from d e m a g n e t i z a t i o n o f • th e r e a d i n g . See a l s o runs 4 and 5 i n Chapter I I I from which t h i s d a t a i s t a k e n ( f i g u r e 3 - 7 ) . S a t u r a t i o n o f Specimen {In S i t u E x p e r i m e n t ) FIGURE 2 . 3 . 27 input for isothermal magnetization i s given by Q = T A S = T R l n ( 2 J + l ) , where J i s the angular momentum of the paramagnetic ions. For 50 grams of chrome potassium alum and 50 grams of manganous ammonium sulphate at 1 K the heat of magnetization i s ^ 5 j o u l e s which b o i l s o f f a- \\ cc. of l i q u i d helium. The major loss of helium occurs when i t i s pumped down. About one h a l f the volume.is l o s t i n cooling i t s e l f , the jackets and p i l l s . The heat leak to the bath from the outer jacket by gas conduc t i v i t y -4 i s at most 1 x 10 W. which i s 1/10 cc. of l i q u i d helium per hour. The heat leak down the pumping l i n e s i s at most 5 x 10 4 W. or 1/2 cc/hr. D i r t i n the pumping l i n e can increase the heat leak by r a i s i n g the surface area f o r s u p e r f l u i d creep. The system has been run for as long as s i x hours and two demagnetizations without running out of l i q u i d helium. i i i ) Solder Joins i n Inner Cryostat The jackets i n the inner cryostat were soldered using low melting point solders to prevent other solder joins from melting during heating. The inner jacket was soldered with a non-eutectic a l l o y made by melting Wood's metal and radio grade s o f t solder together to give an o v e r - a l l melting point about 100°C. The bath jacket and outer jacket were soldered with Wood's metal (melting point = 70°C). Soldering the bath jacket would not melt the inner jacket s e a l . The solder joins were heated with a natural gas-air torch. Stay-Clean f l u x , a very corrosive f l u x , was found u s e f u l . I t was necessary to ensure there was no touch between the vacuum jackets. A simple test could be made. The can was soldered i n place, then l e f t hanging f r e e l y by the solder j o i n . The can was tapped l i g h t l y with a metal rod. I f the can was not touching i t would r i n g c l e a r l y . \ \ // I" \ -Needle v a l v e •Helium ( I K ) b a t h Guard p i l l S p a c e r •-< D e m a g n e t i z a t i o n s o l e n o i d Chrome alum p i l l Wire heat l i n k P o l a r i z i n g s o l e n o i d Specimen S c a l e : l i n . : 1 c m . I n n e r C r y o s t a t and D e m a g n e t i z a t i o n Assembly FIGURE 2.4 29 2.6 The Vacuum Requirements and Low Temperature Vacuum Techniques There are a number of vacuum requirements i n the apparatus. The inner jacket, helium bath (which was discussed i n section 2.5), outer jacket, the inner dewar space and the inner dewar interspace a l l require use of low pressure. , i ) The Inner and Outer Jackets The inner and outer jackets require very high vacuum f o r thermal i s o l a t i o n yet they require also the use of helium exchange gas. The inner jacket should be capable of main- ta i n i n g a vacuum of the order of 10 ^ mm. of mercury (measured at room temperature) during a demagnetization without external pumping. The outer jacket should be able to maintain a -pressure of 2 x 10 ^ mm. of mercury without pumping (with the helium bath pumped down). These require- ments were met using a 2 i n . metal o i l - f r a c t i o n a t i n g d i f f u s i o n pump (Consolidated Vacuum Corporation, PMC-115) pumping through a glass manifold system i n t o 3/8 i n . copper pipe to the cryostat. The d i f f u s i o n pump requires a rotary fore-pump (Cenco Hyvac 7) of at l e a s t 3 cubic f e e t per second. The outer jacket would be pumped down to 5 x 10 ^ mm. of mercury before pumping the helium bath. Then the outer jacket was shut o f f . Upon pumping the bath the outer jacket pressure would f a l l to ^ 2 x 10 ^ mm. of mercury pressure. Pumping on the inner jacket was eliminated (pumping rates are very low at low temperatures) by using the following technique. The exchange gas pressure i n the inner jacket was set at .01 mm. of mercury before the bath was pumped. Upon pumping the bath the pressure i n the inner jacket -4 would f a l l to less than 2 x 10 mm. of mercury. Upon demagnetization - 6 the pressure would f a l l to less than 5 x 10 mm. of mercury (through absorption of the exchange gas i n the p i l l s ) . 30 The pumping manifold contained a cold trap to prevent pump vapours from contaminating the system. The helium exchange gas was supplied by a glass f l a s k connected to the manifold. Inner and outer jacket pressures were measured at the manifold by cold cathode P h i l l i p s gauges. i i ) Other Pumping Requirements The helium bath was pumped to .3 mm. of mercury by a 1 i n . pumping l i n e . The pressure was measured by mercury and o i l manometers at high pressure and by a thermocouple -3 gauge at low pressure (1 to 10 mm. of mercury range) f o r accurate measurement. There i s a large gas load upon i n i t i a l pumping of the bath which requires a f a i r l y large pump. A f i v e cubic feet per minute pump was found to be s u f f i c i e n t . I t was required that the l i q u i d helium 4 K reser v o i r and the inner dewar interspace be flushed with helium gas. Any rotary pump served these vacuum needs. The backing l i n e s of the manometers were pumped by the fore-pump of the d i f f u s i o n pump. 2.7 The Paramagnetic S a l t Assembly i ) Chrome Potassium Alum P i l l The chrome potassium alum s a l t p i l l (see F i g . 2.4) was made from a s l u r r y of alum and glycerine. The mixture becomes a glass at low temperatures g i v i n g good thermal contact to the heat l i n k . The s l u r r y was made by mixing f i n e l y ground chrome alum powder with a 50-50 s o l u t i o n of glyc e r i n e and alum-saturated water. The consistency was that of a t h i n jam. The mixture was added as uniformly as possible to the wire or copper f i n heat l i n k . The e n t i r e assembly was then put i n the b a k e l i t e p i l l . A 33 ohm Allan-Bradley r e s i s t o r had pre- v i o u s l y been f i x e d i n contact with the alum mixture i n the top of the p i l l . This r e s i s t o r was used as a thermometer above 1K to measure the precooling of the p i l l and as a heater a f t e r demagnetization for warming the specimen assembly p r i o r to taking normalization counts. The leads to the r e s i s t o r were constantan wire (80 ohms per foot) wrapped many times around the' supporting tubes above the alum p i l l . i i ) The Guard P i l l The manganous ammonium sulphate s a l t p i l l served as a guard p i l l against leaks down the supports to the chrome alum. Manganous ammonium sulphate demagnetizes to about a tenth of a degree K e l v i n i n a f i e l d of a few kilogauss. The p i l l was made from ground manganous ammonium sulphate powder. I t was contained i n a l i g h t brass can. Twelve copper f i n s were soldered i n the can to give a surface area 2 of 100 cm . i i i ) The Spacers The thermal i s o l a t i o n between the two s a l t p i l l s and between the guard p i l l and the bath was provided f o r by spacers. Each spacer was made from 6 1 mm. outer diameter by .1 mm. wall german s i l v e r tubes each about 2\ cm. long s o f t soldered i n brass end pieces. The arrangement of the tubes provided high r i g i d i t y and low s e c t i o n a l area. The arrangement i s shown i n F i g . 2.5. The heat leak to the chrome alum down the spacer i s expected to be less than 20 erg/min. 2.8 The Heat Link and the Specimen Temperature The heat l i n k between the source and demagnetization p i l l was made from about 5000 B and S gauge 44 copper wires. The wires were enamel- coated to prevent eddy current heating during the demagnetization and to prevent corrosion by the chrome alum. The surface area i n contact with 2 the alum was about 900 cm . The ends of the wires were cleaned with s t r i p v a r enamel remover and s o f t soldered into a standard 3/8 i n . copper coupling. The coupling was hard soldered to a 3/8 i n . copper rod to 32 The Spacers FIGURE-2.5 • 3 3 which the i r o n specimen f o i l was s o f t soldered. The i r o n f o i l was f i r s t " tinned" using Stay Clean solder f l u x and then soldered to the copper using the same f l u x . A copper f o i l heat l i n k with a contact area of 800 2 cm was also used. The copper wires or f o i l were fastened to the b a k e l i t e s a l t p i l l container and held s t r a i g h t and r i g i d by a low temperature epoxy r e s i n . The heat removed from the copper heat l i n k and a l l other materials must be absorbed by the alum. The l a t t i c e heat capacities are a l l n e g l i g i b l e below 1°K compared to the e l e c t r o n i c s p e c i f i c heat of the copper. Cooling the copper removes heat dQ ='CdT, where C i s the e l e c t r o n i c s p e c i f i c heat. This heat flows to the alum g i v i n g an increase i n entropy as given by dQ = TdS. Integrating from IK to 1/100 K using C = .888 x I O - 4 RT gives: S = 1 x 10" 4 j ( K ) " 1 This f i g u r e i s about .005% of the t o t a l entropy removed by the magnetization and i s n e g l i g i b l e . Using the t h e o r e t i c a l r e s u l t s given i n the introduction, a curve gi v i n g the f i n a l temperature of the source against the heat leak into the wires has been pl o t t e d i n F i g . 2.6. I t has been assumed a l l wires or N f i n s make f u l l contact with the alum. A specimen source r a d i a t i o n strength of 17 microcurie emitting one Mev. of energy absorbed i n the source (beta r a d i a t i o n ) gives a heat leak of about one erg per sec. In these experiments source heating was kept below one tenth of an erg per sec. Heating of. the source by gas conductivity from the walls of the inner jacket can be calculated to an order of magnitude. An expression heat i n p u t t o heat l i n k ( e r g / s e c ) The Specimen. Temperature FIGURE 2.6 f o r the heat transfer i s ' -2 Q = const • a • p • (T- T.) W cm o mm i / for two p a r a l l e l surfaces at temperatures and T^. Here the constant i s .028 f o r helium and a , the accommodation c o e f f i c i e n t , i s not greater o than 0.5 for.normal laboratory s i t u a t i o n s . The gas pressure, p , i s mm - 6 measured i n mm. of mercury at room temperature. For a pressure 1 x 10 2 mm. of mercury and an exposed copper surface area of 50 cm the heat leak i s Q = 8 erg sec \ This gives a predicted lowest temperature of .020 K at the specimen. Unfortunately, the actual p a r t i a l pressure of helium gas i s not r e a d i l y known because of outgassing of v o l a t i l e vapours-near the pressure gauge. These vapours are not expected to reach the p i l l or wire assembly. Eddy currents induced by v i b r a t i o n of the copper i n the magnetic f i e l d could be a s i g n i f i c a n t heat leak i f the current path i s long. A heat conducting sleeve over the heat l i n k and alum p i l l , but not i n contact with them, thermally anchored to the guard p i l l would reduce the gas conductivity heat leak and the heat leak caused by adsorption of helium gas on the wires and alum p i l l . However, i n p r a c t i c e such a s h i e l d gives only a marginal improvement. 2.9 Vibrations Vibrations can present a s i g n i f i c a n t heat leak i n the demagnetized system. Indeed, even at IK the v i b r a t i o n s can heat the p i l l at low exchange gas pressure. The major sources of v i b r a t i o n s of the apparatus are expected to a r i s e from the b u i l d i n g i t s e l f through the f l o o r or any other mechanical contact, from pumps i n c l u d i n g d i f f u s i o n pumps, from bubbling of the l i q u i d 36 r e f r i g e r a n t s and from handling the apparatus. I t i s extremely important that resonant conditions be avoided. Hence everything i n or on the apparatus must be f i r m l y attached and the e n t i r e assembly made as r i g i d as p o s s i b l e . The apparatus was b u i l t on an aluminum Dexion frame r e i n f o r c e d as much as possi b l e . The enti r e assembly was placed on s t e e l spring v i b r a t i o n i s o l a t o r s . Cement blocks were placed i n the bottom f o r damping. The pumping l i n e s inside the cryostat were re i n f o r c e d f o r r i g i d i t y . The demagnetization assembly was made as r i g i d as possible. The bath pump was connected to the apparatus by f l e x i b l e rubber tubing. At the pump i t s e l f , the pumping l i n e was f i r m l y anchored to the b u i l d i n g . During the demagnetization personal contact with the apparatus was avoided. Both the d i f f u s i o n pump and the mechanical fore-pump were stopped. In s p i t e of these precautions some v i b r a t i o n s were s t i l l present i n the apparatus and could be detected by an accelerometer. The extent of the v i b r a t i o n heat leak has not been determined. However, only a f t e r a l l these steps had been taken could runs be done with consistent success. 2.10 Experimental Procedure The demagnetization solenoid was charged to 44 kilogauss (55 amperes) with the helium bath i n i t i a l l y at 1.2 K. Occasionally, to save time or to c a l i b r a t e the p i l l r e s i s t o r ( i n the magnetic f i e l d ) the magnetization was done at 4.2K, the bath being pumped a f t e r or during magnetization. The outer jacket would be pumped to about 5 x 10 t o r r . The i n i t i a l exchange gas pressure i n the inner jacket was set at .01 t o r r at 4.2K as described i n s e c t i o n 2.6 i ) . At 1.2K the inner jacket pressure would f a l l to 2 x -4 10 torr or l e s s . During magnetization the inner jacket pressure would 37 -3 r i s e to about 5 x 10 t o r r . The bath pressure would r i s e s l i g h t l y (depending on the pump speed). A f t e r the magnetization the inner jacket pressure and the resistance of the carbon r e s i s t o r i n the p i l l were monitored. When these measurements indicated cooling had completed (about 25 minutes) the demagnetization was begun. The demagnetization should be done s u f f i c i e n t l y slowly to keep eddy currents induced as small as possible yet s u f f i c i e n t l y f a s t to quickly lower the inner jacket pressure and keep v i b r a t i o n a l eddy current heating small. I n i t i a l l y , the f i e l d was reduced at a rate of 6 kilogauss per minute. The inner jacket pressure would quickly f a l l . When the f i e l d had reduced to 4 to 5 kilogauss the demagnet- i z a t i o n was stopped u n t i l the exchange gas pressure stopped f a l l i n g (1-2 minutes). I t i s desi r a b l e to remove the exchange gas at a high temperature i f p o s s i b l e ( d Q = T d S ) . The demagnetization was recommenced at a rate of 3 kilogauss per minute u n t i l no current was flowing. The p o l a r i z i n g c o i l was charged to 3 amperes. The current i n the demagnetization solenoid was reversed to sweep out the remnant f i e l d . When the remnant f i e l d as measurured by search c o i l outside the cryostat was reduced as low as possi b l e the counters were c a r e f u l l y put i n place and gamma ray counting was started. By th i s time the inner jacket pressure gauge reading would — 6 be 2 - 5 x 10 t o r r . When s u f f i c i e n t cold counts had been taken the p i l l would be warmed by e l e c t r i c a l l y heating the carbon r e s i s t o r i n i t . For a d d i t i o n a l runs the magnet was recharged and the procedure repeated. A t y p i c a l low temperature run as taken from the log book i s given i n Table 2.2. 38 TABLE 2.2 TYPICAL LOW TEMPERATURE RUN This table gives the procedure as taken from the laboratory notebook f o r run 7 i n Table 3.1. Time System precooling overnight with l i q u i d nitrogen. Helium exchange gas i n outer, inner and bath jackets. 14:15 L i q u i d helium transfer i s i n progress. L i q u i d helium i s i n bottom of dewar. Transfer pressure head i s 2 cm. mercury. :35 Transfer completed. About 12 l i t r e s of l i q u i d helium were used. Resistance of carbon r e s i s t o r i n chrome alum p i l l (Rp) i s 1.23K ohm. Bath f i l l e d . :50 Beginning pumping of outer jacket. 15:24 Outer jacket shut o f f . Outer jacket pressure i s 5\ x 10 t o r r . This i s s u f f i c i e n t l y low to pump bath. Inner jacket pressure i s .005 torr (at 4.2K). Rp = 1.23K ohm (no magnetic f i e l d ) . :35 Begin magnetization (at 4.2K). :41 Magnet i s i n p e r s i s t e n t mode at 55 amp. Bath was r e f i l l e d to r e p l e n i s h any l i q u i d l o s t i n magnetization. :43 Rp = 1.38K ohm W i l l begin pumping bath. 16:27 Outer jacket pressure i s 3 x 10 ^ t o r r . :30 Rp = 15.IK ohm -4 Inner jacket pressure i s 1.8 x 10 t o r r . :40 Rp = 15.2K ohm. Assume p i l l has cooled to bath temperature. 39 Inner jacket pressure i s 7 x 10 ^ t o r r . Bath pressure i s approximately .3 t o r r . This pressure means the bath temperature i s 1.1K. D i f f u s i o n and backing pumps turned o f f i n preparation f o r demagnetization. Begin demagnetization. Demagnetization completed. P o l a r i z i n g solenoid charged to 3 amp. Commencing counting. Inner jacket pressure i s \\ x 10 t o r r . Measure remnant f i e l d with search c o i l : d e f l e c t i o n of +3 cm. Swept f i e l d by reversing current i n demagnetization solenoid to -8 amp. Measure remnant f i e l d : d e f l e c t i o n of -1/3 cm. P i l l warmed by e l e c t r i c a l l y heating r e s i s t o r i n chrome alum p i l l . Commencing normalization counts. -4 Inner jacket pressure i s 1.8 x 10 t o r r . End of f i r s t run. Anisotropy achieved 87o. Begin next magnetization, etc. CHAPTER I I I NUCLEAR ORIENTATION OF Co IN IRON The nuclear physics aspects of the experiment are considered i n 60 thi s chapter. The choice of Co as a thermometer i s discussed. The preparation of the source and the e l e c t r o n i c set-up i s also discussed. F i n a l l y the actual low temperature experimental data i s presented and the analysis of the r e s u l t s . 60 3.1 The Temperature Dependence of the Anisotropy of Co 6 0 Co was chosen f o r three reasons: i ) Its nuclear and hyperfine parameters are well known; i i ) I t has a large anisotropy at a hundredth of a degree Kelvin; and i i i ) I t i s r e a d i l y a v a i l a b l e and dissolves e a s i l y i n i r o n . 60 The decay scheme f o r Co i s shown i n F i g . 3.1. The magnetic moment of ^ C o i s equal to 3.754 (-8) nuclear magnetons 1^. The hyperfine f i e l d of d i l u t e cobalt i n i r o n f o i l i s 290 k i l o g a u s s 1 ^ . The equations for the i n t e n s i t y of r a d i a t i o n given i n Chapter I reduce to W(0) = 1 + U 2 F 2 B 2 + U 4 F 4 B 4 W(TT/2) = 1 - h U 2 F 2 B 2 + 3/8 U 4 F 4 B 4 The U c o e f f i c i e n t s reduce'to (see reference 4, p. 1206) U. = ( - 1 ) < I 0 + I 1 " V ( 2 I 0 + 1 ) ( 2 I 1 + 1) % W ( I i W o > . where 1^, I are the angular momenta for the i n i t i a l and f i n a l states of the unobserved t r a n s i t i o n and L^ i s the angular momentum c a r r i e d away i n 40 — - 4+ 2.505 Mev decay (1.172 Mev 2+ 1.333 Mev decay (1.333 Mev 0 + The Decay Scheme of Co FIGURE 3.1 42 this t r a n s i t i o n . W i s the Racah c o e f f i c i e n t . The F c o e f f i c i e n t s are given i n reference 4, p. 1197. Using these r e s u l t s the parameters are U 2 F 2 = -0.421; U 4 F 4 = -0.243 for both gamma decays. The B c o e f f i c i e n t s are given i n reference 3. The f i n a l temperature dependence of W(0) , W(90°) and 67 i s given i n F i g . 3.2. 3.2 The Preparation of the Source , 6 0 The Co source was prepared from a cobalt chloride s o l u t i o n con- ta i n i n g ^ C o with v i r t u a l l y no ~^Co c a r r i e r present. The cobalt i s less e l e c t r o p o s i t i v e than i r o n . Hence, when drops of cobalt s o l u t i o n are placed on the i r o n f o i l , the f o i l i s spontaneously plated by cobalt. The f o i l was annealed at 950°C for 24 hours i n a dry hydrogen atmosphere. The a c t i v i t y of the source was determined by counting against a known strength source. The source was then etched and i t s strength remeasured. As there was no decrease i n a c t i v i t y i t was concluded that the cobalt had di f f u s e d w e l l into the ir o n . The f i n a l a c t i v i t y was about 2\ microcuries. 3.3 The Detectors and E l e c t r o n i c C i r c u i t r y The gamma radiations were normally detected by sodium iodide c r y s t a l s c i n t a l l a t i o n detectors. The c r y s t a l s were 2" x 2" mounted on a photo- m u l t i p l i e r . The photomultipliers were very s e n s i t i v e to magnetic f i e l d s which meant they had to be shielded from the p o l a r i z i n g f i e l d . S u f f i c i e n t s h i e l d i n g was provided by a s o f t i r o n pipe 3" diameter by 1/4" wall thickness (with a very low impurity gamma r a d i a t i o n a c t i v i t y ) which was slipped over mu metal which was wrapped around the detector and spaced with copper f o i l . The e f f e c t of the p o l a r i z i n g c o i l on the counting rate was smaller than the s t a t i s t i c a l counting error provided the detectors were £ W(TT/2) 44 not too close to the outer dewar. In any event, the counts were normalized with the same f i e l d s present i f possible. Any change i n the gain of the detectors could be detected on the multi-channel analyser discussed below. The e l e c t r o n i c s used are shown schematically i n F i g . 3.3. The re s o l u t i o n of the system was s u f f i c i e n t to separate the ̂ C o gamma ray photopeaks almost to the baseline. The multichannel analyser was used ( i n the pulse height analysis mode) to set the sing l e channel analyser windows and to determine any change i n gain of the system. I t was also used to obtain spectra so that the r a d i a t i o n background could be stripped o f f the photopeaks. In addition, the analyser has a m u l t i - s c a l i n g mode which can be used to run up the counts from each detector switching channels automatically a f t e r a given counting time. The counts can then be punched out on tape. In th i s way the actual counting time w i l l be increased because the delay of recording the counts i s eliminated. Also, errors i n recording are eliminated. The warm-up of the source can be r e a d i l y seen on the o s c i l l o s c o p e output at any time. The punched tape output can r e a d i l y be used f o r computer analysis of the data. In one run a Ge(Li) s o l i d state detector was used i n the equatorial plane. I t gave very good r e s o l u t i o n of the two ̂ C o gamma photopeaks well past the baseline. This detector was not af f e c t e d by the magnetic f i e l d s present. 3.4 The Experiments: Data and Results i ) The Raw Data I t was usual to take a few sets of counts s h o r t l y before the demagnetization or a f t e r the demagnetization but before the p o l a r i z i n g solenoid was charged i n order to obtain some idea of the normalization counts. They were also u s e f u l f o r determining any change C r y o s t a t Source S c i P r e • S c i P r e SCA Sea Timer S c i Sodium i o d i d e s c i n t i l l a t i o n d e t e c t o r P r e P r e a m p l i f i e r L.A. L i n e a r a m p l i f i e r SCA S i n g l e c h a n n e l a n a l y z e r Sea S c a l e r MCA M u l t i - c h a n n e l a n a l y z e r and r o u t i n g The Gamma R a d i a t i o n D e t e c t i o n A p p a r a t u s ( S c h e m a t i c ) FIGURE 3 - 3 ' 4 6 i n the gain of the detectors i n the f i e l d of the p o l a r i z i n g solenoid. When the demagnetization was completed (inc l u d i n g sweeping the f i e l d ) the experimental counting was commenced. The scalers were operated e i t h e r by hand or by a master'timer. Counts were u s u a l l y taken f o r 1 0 0 to 2 0 0 sec. periods. The scaler d i g i t a l readings were recorded by hand. A f t e r the sample was warmed the normalization counts were taken. Care was taken to ensure that no change i n the magnetic f i e l d s on the counters occurred during the run (unless such changes were part of a experiment). The warm counts were taken for the same period as the cold counts to get an idea of the random v a r i a t i o n s . A few long warm counts would then be taken to reduce the s t a t i s t i c a l error. The raw counts f o r a number of runs are shown i n Table 3 . 1 . The window settings of the sin g l e channel analysers were us u a l l y set to show the t o t a l counts i n both the 1 . 1 7 and 1 . 3 3 Mev photopeaks of 6 0 the Co since both gamma rays show the same anisotropy. i i ) Corrections to the Raw Data The i s o t r o p i c background of the laboratory must be subtracted from the raw counts taken during the experi- ments. For the runs reported i n this work the i s o t r o p i c background was less than 17> of the t o t a l counts. In the normalized counts the c o r r e c t i o n i s less than l / 5 7 o and has been neglected. The a n i s o t r o p i c background i n the photopeaks from scattered r a d i a t i o n must also be subtracted. In the present experiment no higher energy radiations were present to give back- 6 0 ground to the Co photopeaks. Hence, t h i s c o r r e c t i o n i s n e g l i g i b l e . 6 0 The h a l f - l i f e of Co i s 5 . 2 years. Hence, no c o r r e c t i o n need be applied f o r the decay of the source during the run. There i s a c o r r e c t i o n f or the "smearing out" of the anisotropy due 47 to the s o l i d angle subtended by the counters. The s p a t i a l d i s t r i b u t i o n s of r a d i a t i o n was shown i n Chapter I to be of the form: W ( e ) = S k± P i (cos 6 ) This f u n c t i o n must be m o d i f i e d to i n c l u d e the s o l i d angle subtended by the counter from the source as f o l l o w s • f W (6) djfl W (0) / d n. XL where omega i s the s o l i d angle of the counter. I t has been shown that f o r c y l i n d r i c a l counters the form of the d i s t r i b u t i o n f u n c t i o n i s unchanged but that each term becomes m u l t i p l i e d by an a t t e n u a t i o n f a c t o r independent 18 of the angle of o b s e r v a t i o n . Hence, w' (9) = 2A. P. ( C O S 9 ) k ^ * ) where o< i s the l i n e a r h a l f - a n g l e subtended by the c y l i n d r i c a l counter. The a t t e n u a t i o n c o e f f i c i e n t s k^ can be c a l c u l a t e d d i r e c t l y by i n t e g r a t i n g 19 the Legendre polynomials g i v i n g : k 2 = h cos o< (1 + cos c*. ) 2 k^ = 1/8 cos »< (1 + cos <K )(7 cos o< - 3 ) . In the experimental runs reported i n t h i s t h e s i s the counters used 2" x 2" c r y s t a l d e t e c t o r s , except one run which used a Ge(Li) s o l i d s t a t e d e t e c t o r i n the e q u a t o r i a l plane. The a x i a l counter was 6" from the source and the e q u a t o r i a l counter was 5" from the source. Using the approximation of 2" c y l i n d r i c a l counters and a p o i n t source the attenua- t i o n c o e f f i c i e n t s are k 2 = .97 and k^ = .90 48 f o r both counters. For anisotropy 6 of 10% or less the c o r r e c t i o n to £ i s less than -J-l/37o. This c o r r e c t i o n has been neglected. The geometry of the Ge(Li) detector was not known; however, the attentuation was small and the c o r r e c t i o n factor has been ignored. i i i ) The Results The analysis of several runs are given i n Table 3.1 and F i g s . 3.4 to 3.9. In run 2 (Fig. 3.5) the e f f e c t of reversing the p o l a r i z i n g f i e l d i s shown. Also shown i s the length of run before warming occurs. At 30 minutes a f t e r the demagnetization the anisotropy was s t i l l observable. Run 3 i n F i g . 3.6 gives an uninterrupted run showing the warming of the p i l l beginning about 20 minutes a f t e r demagnetization. Runs 4 and 5 (Fig. 3.7) show the e f f e c t of d i f f e r e n t p o l a r i z i n g f i e l d s . In these two runs the demagnetization assembly and conditions were the same.. In this case warming occurs too quickly to draw s i g n i f i c a n t conclusions about the e f f e c t of the p o l a r i z i n g solenoid. The e f f e c t of the remnant f i e l d was studied i n run 6 (Fig. 3.8). The p i l l was unshielded. The remnant f i e l d was gradually swept out. No s i g n i f i c a n t change i n anisotropy was noticed although the remnant f i e l d was reduced by a factor of ten (as measured by a search c o i l external to the c r y o s t a t ) . In run 7 (Fig. 3.9) only 8 g. of chrome alum was used i n the p i l l . However, a s i g n i f i c a n t l y long run was performed with a r e l a t i v e l y high anisotropy (7.47„). This would i n d i c a t e that the amount of alum used normally, 30 - 60 g., was s u f f i c i e n t for cold times of about a h a l f hour. During the course of the runs, several chrome alum mixtures were used; two wire heat l i n k s and one f i n heat l i n k were used and two specimen sources were t r i e d . No s i g n i f i c a n t d ifferences i n r e s u l t s were noticed i n any case. 49 TABLE 3.1 Normalized Raw* Raw' Normalized (90 ) Counting Counts Equa- (0) Equa- T Time Period A x i a l t o r i a l A x i a l t o r i a l £ % (K) A l l errors quoted represent one standard deviation i n the counting s t a t i s t i c s Run 1 (24th July, 1968) Basic counting period 6 minutes 9:03 Demagnetized P o l a r i z i n g f i e l d = 0 (Pseudo warm count) 2 min.* 19041 27573 P o l a r i z i n g f i e l d = 4A 08 6 min. 17739 29158 .937*17. 1.048*1% ( 1 0 ^ 1 ) % .038^.001 15 " 17667 28743 .932 1.037 (10.*1)% .038 21 " 17484 28878 .923 1.039 (ll.±l)% .036 29 . " 17736 28762 .937 1.032 (9.^1)% .043 Normalization Counts 12 min." 19071 27783^ 6 min. 18715 27710 >(l8940) (27794) . 6 min. 18904 27921J Run 2 (7th October, 1968) Basic counting period 300 seconds P o l a r i z i n g f i e l d = OA. 8:55 (3x) 100 sec. 13803 74052 P o l a r i z i n g f i e l d = 4A. :57 3x 100 sec. 13417 73766 .973*1^% 1.020^% (4.7*1^)% .059*. 008 9:03 " 13363 73516 .969 1.018 (5 - 1 ^ ) % .056 P o l a r i z i n g f i e l d reversed :27 " 13469 73298 .976 1.010 (3.4^1^)% .07 O r i g i n a l p o l a r i z i n g f i e l d :45 3 x 1 0 0 13448 72756 .984 1.005 (2*1^)% .1 i.06 Normalization 3 x 100 13788 72309 *The raw counts not i n basic counting period are m u l t i p l i e d by the fac t o r necessary to make them comparable to the basic counting period. Time Raw Counting Counts Pe r i o d A x i a l Raw' Counts Equa- t o r i a l Normalized Normalized (90 ) (0) A x i a l Equa- t o r i a l e % T (K) Run 3 (1st November, 1968) B a s i c counting p e r i o d 12:34 Demagnetization. P o l a r i z i n g current = OA. 300 seconds (3x) 100 sec. 12441 42813 P o l a r i z i n g f i e l d = 4A. 12: 37 3 x 100 sec. 11992 43010 .976 . 996 (2 •* l i > ) % .1 *. 06 46 11910 43746 .959 1. 010 (5 • * 1 ^ ) % .056*. 006 52 11942 43517 .962 1. 005 (3.3*1%)% .07 58 12156 43194 .979 . 999 ( 2 . * ! % ) % .1 *. 06 1: 02 " 12363 43322 .995 1. 002 (• 7*1%)% .049*. 006 1: 06 12499 43767 1.005 1. 012 (• 7*1%)% .049 N o r m a l i z a t i o n 1100 s e c * 12410 43220 Run 4 (7th June, 1969) Ba s i c counting p e r i o d 3 minutes 5 35 Demagnetization, P o l a r i z a t i o n Current & 3 Amp s. 3 min. 4513 16022 .955 1 021 (6. 5*2)% .05 * 006 it 4473 16240 .946 1 035 (7. 6*1%)% .046* 006 n 4476 15895 .947 1 013 I I 4558 15890 .964 1 013 (7. 2*1%)% .049* 006 I I 4394 16097 . .931 1 028 I I 4562 15987 .966 1 020 (6. 6*1%)% .049* .006 I I 4512 16229 .955 1 037 P o l a r i z i n g f i e l d + 4 Amp. 6 :02 4 min. 4500 15950 .952 1 .018 (6. 0*1%)% .052* .006 3 min. 4557 15880 .965 1 . 011 I I 4602 15637 .974 .998 (2.5*1%)% .09 * .06 I I 4743 15806 .983 1 .009 I I 4633 16020 .980 1 .021 (3 3*1%)% .07 I I 4564 15731 .976 1 .002 I I 4755 15635 1.005 .998 I I 4672 15964 .988 1 .018 (3.0*2)% .08 Time Counting Period Raw Counts A x i a l Raw* Counts Equa- t o r i a l Normalized Normalized (90 ) (0) A x i a l Equa- t o r i a l € 7. T (K) :32 :48 P o l a r i z i n g f i e l d + 3 Amps. 3 min. 9 min. 9 min. 4626 4722 4611 15766 15883 15689 .986 1.000 .974 1.006 1.011 1.000 (2.0*2)% (1.1*1107. (2.6*1%)% Normalization 18 min. 18 min. 4745 4706 15662 15700 j(4726> ( 15681) Run 5 (7th June, 1969) Basic counting period Demagnetized, p o l a r i z i n g current + 3 Amps. 3 minutes .1 .14 ,09.±.06 11:23 3 min. 4602 18035 " 4559 18010 17924 4488 17855 .954 1.032 (7.6*.1%)7. .046*. 006 4527 17796 :35 4561 18159 4774 17757 .971 1.035 (6.2*.1%)% .051-*. 006 4581 18115 4589 17886 P o l a r i z i n g current + 2 Amps • :48 3 min. 4586 17888 4600 17811 .967 1.018 (5.0*1%)% .056*. 006 • i 4599 17521 :12 4723 17383 .987 1.003 (1.6*1%) 7. .12 4680 17458 Normalization 18 min.* 4800 17218 > (4765) (17364) 18 m i n / 4730 17510 J Run 6 (2nd run) (12th June, 1969) Basic counting period 3 minutes 16:30 System demagnetized Search c o i l reading of r e s i d u a l f i e l d =0.8 cm. d e f l e c t i o n 52 Time Raw Counting Counts Period A x i a l Raw Normalized Counts Normalized (90 ) Equa- t o r i a l (0) A x i a l Equa- t o r i a l T (K) ;33 :42 :54 3 min. I I 4858 19884 4788 19851 4907 19825 ,936 1.011 Sweep f i e l d . Search c o i l = +.3 cm. d e f l e c t i o n 3 min. 4840 20097 4867 20269 4812 20199 Sweep f i e l d . Search c o i l 3 min. 4976 20275 3 min. 4913 19996 " 4803 19900 4871 20124 " 4672 19779 5031 19979 ,934 1.028 .1 cm. d e f l e c t i o n .945 1.021 ,938 1.016 Normalization (7.4*1%)% .047*. 006 (9.1*1%)% (7.4*1%)% (7.7*1%)% + .002 .042-.005 ,047-.006 ,046 5 x 3 min. 5181 19645 Run 7 (1st run, 8th August, 1969) Basic counting period 200 seconds Only 8 grams of chrome alum i n p i l l Demagnetization. Search c o i l d e f l e c t i o n +3 cm. 17:08 .200 sec. 9298 9460 9332 9329 29261 29092 28830 28917 .927 .923 Swept remnant f i e l d d e f l e c t i o n = 200 sec. 9580 29309 .958 :27 " 9571 29162 11 9493 29363 .947 11 9668 29522 :40 " 9617 29313 .966 1.017 1.007 ,3 cm. 1.020 1.027 1.017 (8.8*1.2) S.4*1.2 6.1-1.2 7.8*1.2 5.0*1.2 + .007 .044-.005 .045 ,053 ,045 .056 53 £ a w* Normalized * Counts Normalized (90°) Counting Raw E q u a _ ( 0 ) E q u a _ T Time Period Axial torial Axial torial £ % (K) 200 sec. 9824 28883 9621 29083 .967 1.015 4.7*1.2 .059*.007 :51 " 9930 29107 Normalization 4 x 200 sec.* 10113 28676 . ' 12 10- W 8- 6 12 ' 18 24 time from commencement o f c o u n t i n g ( m i n u t e s ) 30 Run 1 FIGURE 3.4 x O r i g i n a l p o l a r i z i n g . f i e l d © Reversed p o l a r i z i n g f i e l d 4 4 2 f 10 20 30 time ( m i n u t e s ) 40 50 Run 2 FIGURE 3.5 6 4 0- -1 6 12 18 24 time from d e m a g n e t i z a t i o n ( m i n u t e s ) Run 3 - An U n i n t e r r u p t e d Run. FIGURE 3-6; 30 10 8 O ^ 4 2 0 -1 ? 3, 3: 3 o 4 o -2 4 o 0 Run 4 x Run 5 4 o 4 -2>: 3Q 3 9 3* 20 40 60 80 time from demagnetization (minutes) The current, in amperes, i n the p o l a r i z i n g c o i l p r i o r to the reading i s given beside each data point. Runs 4 and 5 FIGURE 3.7 10 8 .1 .1 ._. __ 20 3-Q 40 time from d e m a g n e t i z a t i o n ( m i n u t e s ) T h e . r e s i d u a l f i e l d measurements ( d e f l e c t i o n s i n cm.) a r e g i v e n b e s i d e each d a t a p o i n t . Run 6 FIGURE 3.8 00 10 -r- 8 4 o o 10 .20 30 time from commencing c o u n t i n g ( m i n u t e s 40 Note. I n t h i s run t h e r e were o n l y e i g h t grams o f chrome alum i n t h e . p i l l . Run 7 FIGURE 3.9 VO 60 The sources of possible heat leaks and the e f f e c t s of magnetic f i e l d s which cause high temperature at the specimen source have been discussed i n t h i s work. If the heating were due s o l e l y to a heat leak i t would have to be about 40 erg/sec. On the other hand, i f only 107o of the heat l i n k i s i n good contact with the alum the same r e s u l t s occur. At the present time the reason f o r the r e l a t i v e l y high f i n a l temperature i s not known. Some improvements i n the apparatus w i l l have to be made before o r i g i n a l experimental work can be c a r r i e d out. Many such changes are c u r r e n t l y being attempted including the construction of a new apparatus described i n Chapter IV. CHAPTER IV FUTURE MODIFICATIONS OF THE APPARATUS A new apparatus i s being constructed. I t i s hoped to remove some of the l i m i t a t i o n s of the present low temperature system. In a d d i t i o n some changes i n technique are being considered such as resonant destruc- t i o n of nuclear o r i e n t a t i o n and detection of beta r a d i a t i o n s . Further- more, modifications are being made to the present low temperature apparatus. . - 4.1 Low Temperature i ) Heat Leaks to the Demagnetized System The heat leak by gas conductivity and absorption of exchange gas w i l l be reduced by s h i e l d ing the chrome alum p i l l by a sleeve thermally anchored to the guard p i l l Also use of a metal high-vacuum system w i l l reduce the ( p a r t i a l ) pressure of helium i n the system. The metal system requires no vacuum grease seals i n the inner jacket l i n e which reduces the outgassing of helium. Furthermore, i t can be r e a d i l y heated to reduce outgassing. The pumping l i n e s w i l l be larger i n diameter to give higher pumping speed i f required The new support framework w i l l be r i g i d l y mounted at the base in a concrete block supported by s t e e l springs. This w i l l increase the r i g i d i thereby reducing the v i b r a t i o n a l heat leak. Furthermore, a l l pumping l i n e s to the cryostat can be f i r m l y secured outside the cryostat to keep out pump v i b r a t i o n s . The springs under the system damp out v i b r a t i o n s from the f l o o r . The chrome alum p i l l w i l l be made larger. This w i l l allow the use of more chrome alum to lengthen the "cold time". Also more wires can be 61 62 used i n the heat l i n k to increase the contact area. i i ) The Remnant F i e l d The new system has been designed to allow the demagnetization solenoid to be r a i s e d above the chrome alum. This w i l l completely remove the remnant f i e l d . I f cerium magnesium n i t r a t e were used f o r demagnetizations to lower temperatures such removal of the f i e l d could be important. i i i ) The 1 K Helium Bath The double walled helium bath presently being used w i l l be changed. Instead, an enclosed can of l i q u i d helium at the top of the inner jacket w i l l be used. The jacket w i l l be made of copper to ensure good thermal conductivity. The volume of the can w i l l be about 150 cc. which w i l l hold more l i q u i d than the present system so that r e f i l l i n g w i l l not be necessary. The use of a s i n g l e jacket leaves more room i n the demagnetization chamber. This allows the s h i e l d i n g of the p i l l and the increase i n s i z e of the p i l l . Furthermore, the inner cryostat w i l l be lengthened to allow a larger p i l l and to fur t h e r separate the p i l l from the p o l a r i z i n g solenoid. Larger pumping l i n e s i n the inner cryostat w i l l increase the pumping speed and reduce the bath pressure and temperature. iv) L i q u i d Helium Loss A l i q u i d nitrogen pot at the top of the pumping l i n e s w i l l reduce the heat leak into the 4 K helium r e s e r v o i r . The leads to the superconducting solenoid w i l l be i n thermal contact with the l i q u i d nitrogen. This should reduce the helium loss rate by a f a c t o r of at l e a s t two. 4.2 Resonant Destruction of Nuclear Orientation Resonant des t r u c t i o n of nuclear o r i e n t a t i o n was discussed i n section 1.7. The new apparatus w i l l be s u i t a b l e f or resonant experiments. A 63 small radio frequency c o i l w i l l be wound i n the demagnetization chamber around the source with i t s axis perpendicular to the axis of quantization. The r . f . power input to the source must be kept small to prevent heating. 4 . 3 Detectors i ) Ge(Li) Detectors Lithium d r i f t e d germanium s o l i d state gamma detectors have f a r greater r e s o l u t i o n than the sodium iodide s c i n t i l l a t i o n counters. This allows easier separation of gamma ray con- t r i b u t i o n s i n the r a d i a t i o n spectrum. However, the low e f f i c i e n c y of the devices require stronger sources and longer counting times to keep the s t a t i s t i c a l error low. i i ) S i ( L i ) Detectors Lithium d r i f t e d s i l i c o n s o l i d state detectors are used to detect beta r a d i a t i o n . Because the beta rays are completely attenuated by the cryostat, the detector must be placed inside the demagnetization chamber. However, the detectors have proved to be very temperature s e n s i t i v e and a device f o r warming the detector above the bath temperature may be necessary. 64 REFERENCES 1 . M. E. Rose, Elementary Theory of Angular Momentum, 179 (John Wile}' and Sons, Inc., New York, 1967). 2 T. P. Gray and G. R. Satchler, Proc. Phys. S o c , London, A68, 349, (1955). 3 R. J. Bl i n - S t o y l e and M. A. Grace, Handbuch der Physik 42, 555 (Springer, B e r l i n , 1957). ••4 S. R. De Groot, H. A. Tolhoek, and W. J. Huiskamp, Alpha-, Beta-, and Gamma-Ray Spectroscopy, Vol. 2, p. 1199 (Kai Siegbahn, editor, North Holland, Amsterdam, 1965). 5 B. Bleaney, Hyperfine Interactions (A. J. Freeman, R, B. Frandel, e d i t o r s , Academic Press, New York, 1965). 6 W. A. L i t t l e , Can. J. Phys. _37, 334 (1959). 7 A. C. Anderson, G. L. Salinger, J. C. Wheatley, Rev. S c i . I n t r . , _32, p. 1110 (1961). 8 A. J. Freeman, R. E. Watson, T r e a t i s e on Magnetism, Vol. IIA (Suhl- Rado, ed i t o r s , Academic Press, New York, 1965). 9 V. L. Sedov, L. V. Golomatina and L. A, Kondrashova, Soviet Physics JETP, 27, p. 870 (1968). 10 E. Daniel, op. c i t . , reference 5. 11 D. A. S h i r l e y , S. S. Rosenblum, and E. Matthias, Phys. Rev. 170, p. 363 (1968). 12 A. E. Balabanov and N. N. Delyagin, Soviet Physics JETP, 27_, p. 752 (1968). 13 A. J. Freeman, Hyperfine Structure and Nuclear Radiations, (E. Matthias and D. A. Shi r l e y , e d i t o r s , North-Holland Publishing Co., Amsterdam, 1968). 14 J. E. Templeton and D. A. S h i r l e y , Phys. Rev. L e t t e r s , 18, p. 240 (1967). 15 A. C. Anderson, W. R. Roach and R. E. Sarwinski, Rev. S c i . Inst., 37, p. 1024 (1961). 16 G. K. White, Experimental Techniques in' Low Temperature Physics, p. 179 (Oxford, 1959). 17- V. S. Sh i r l e y , Table of Nuclear Moments, op. c i t . , reference 13. 18 Y. Koi, A. Tsujimura, J. Phys. S o c , Japan, _16, p. 1040 (1961). 19 M. L. Rose, Phys. Rev. 91, p. 610 (1963). 20 B. G. T u r r e l l , D. P h i l . Thesis (U n i v e r s i t y of Oxford, unpublished, 1963).

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