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Magnetic resonance studies of some X-irradiated hydrogen-bonded arsenates Dalal, Nar Singh 1971

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MAGNETIC RESONANCE STUDIES OF SOME X-IRRADIATED HYDROGB4-BONDED ARSENATES BY  NAR SINGH DALAL  M.Sc.,  PANJAB U N I V E R S I T Y ,  CHANDIGARH, 1 9 6 3  A T H E S I S SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  I N THE DEPARTMENT OF CHEMISTRY  WE ACCEPT T H I S THESIS AS CONFORMING TO THE REQUIRED STANDARD  THE UNIVERSITY OF BRITISH COLUMBIA SEPTEMBER 1 9 7 1  In p r e s e n t i n g  this thesis  i n p a r t i a l fu 1 f i l m e n f of the r e q u i r e m e n t s f o r  an advanced degree a t the U n i v e r s i t y of B r i t i s h Columbia, I agree the  L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and  I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e f o r s c h o l a r l y purposes may by h i s r e p r e s e n t a t i v e s .  be g r a n t e d by  written  gain  Department o f The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada Date  3o  publication  s h a l l not be a l l o w e d w i t h o u t  permission.  jCfjj  thesis  Department or  It i s u n d e r s t o o d t h a t c o p y i n g or  of t h i s thes.is f o r f i n a n c i a l  Study.  c o p y i n g of t h i s  the Head of my  that  my  - i -  Supervisor:  C.  A.  McDowell  ABSTRACT The techniques o f EPR, ENDOR and double ENDOR were employed with a view t o o b t a i n i n g d e t a i l e d i n f o r m a t i o n on hydrogen-bonding and on the r o l e o f protons and h e a v i e r n u c l e i i n t h e phase t r a n s i t i o n s i n the X - i r r a d i a t e d f e r r o e l e c t r i c s K H A s 0 , KD As0 , RbH As0 , mixed KH P0 2  4  2  4  2  4  2  4  KH" As0 and the a n t i f e r r o e l e c t r i c compound N H H A s 0 The paramagnetic centre A s 04- , formed by the capture o f an e l e c t r o n by an A s 03- i o n , was 2  4  4  2  4<  4  4  used as a m i c r o s c o p i c probe. EPR i n v e s t i g a t i o n s , combined with the use o f e l e c t r i c f i e l d s , 75 have r e s u l t e d i n an a c c u r a t e i n t e r p r e t a t i o n o f the As h y p e r f i n e s t r u c t u r e 4i n t h e EPR s p e c t r a o f A s 0  4  . The use o f EPR t o o b t a i n the d i e l e c t r i c  h y s t e r i s i s loop has been demonstrated f o r the f i r s t time. ENDOR s t u d i e s o f the AsoJ" c e n t r e i n K H A s 0 a t 4.2°K have 2  y i e l d e d a c c u r a t e s u p e r h y p e r f i n e parameters. f o r c o v a l e n t c h a r a c t e r i n both the 0-H 0-H  4  The r e s u l t s provide evidence and 0  H- p a r t s o f the  0 bond i n such systems. A new method has been proposed f o r determining the s i g n s o f hyper-  f i n e c o u p l i n g s f o r $=% systems and has been i l l u s t r a t e d by a p p l i c a t i o n t o the 4A s 0 c e n t r e i n KH As0 . A n a l y s i s o f the temperature dependence o f the EPR s p e c t r a i n d i c a t e s 75 t h a t both the As and the protons perform jump-type motions. A t lower 75 4  2  4  temperatures, however, the c o r r e l a t i o n times f o r the As motions a r e found t o be e s s e n t i a l l y the same.  and the proton  T h i s provides experimental  evidence f o r the r e c e n t l y p o s t u l a t e d coupled p r o t o n - l a t t i c e motion i n these systems.  - ii-  A method f o r performing E l e c t r o n - N u c l e a r T r i p l e Resonance experiments has been demonstrated. T h i s development may extend the range of a p p l i c a b i l i t y o f the ENDOR technique.  - iii -  TABLE OF CONTENTS  Page ABSTRACT  i  LIST OF TABLES  vi  LIST OF FIGURES  vii  ACKNOWLEDGEMENTS  xii  GLOSSARY OF SYMBOLS USED  xiii  CHAPTER ONE:  INTRODUCTION  CHAPTER TWO:  THEORETICAL  1 11  INTRODUCTION  11  2.1  The spin Hamiltonian  16  2.2  Determination of spin Hamiltonian Parameters  20  2.2.1  Spin Hamiltonian Parameters from EPR measurements  2.2.2  20  Superhyperfine Parameters through ENDOR measurements  25  Signs of the Hyperfine tensors  31  2.3  Motion Effects in hyperfine structure  33  2.4  Interpretation  38  2.2.3  CHAPTER THREE: 3.1  of the spin Hamiltonian parameters .  EXPERIMENTAL DETAILS  Preparation and Crystal structure of the Arsenates and Phosphates  3.2  40  The Irradiation  40 Units  45  The EPR Spectrometers  45  3.3.1  The X-band Spectrometers  45  3.3.2  The K-band Spectrometer  46  i 3.3  - iv -  Page 3.4  The ENDOR Spectrometer  3.5  ENDOR Technique  3.6  The Arrangement for Double ENDOR  CHAPTER FOUR:  46 '.  RESULTS AND DISCUSSION  4.1  EPR studies of  4.2  ENDOR of  4.3  ENDOR Data and Analysis 4.3.1  53 55  AsoJ" centre  56  AsoJ" centre in KH As0 2  4  79 87  Signs of the Hyperfine and Superhyperfine Couplings  4.3.2  50  .'  Angular v a r i a t i o n of ENDOR t r a n s i t i o n  87 96  4.4  Correlation of EPR and ENDOR results  4.5  Discussion  101  A.  101  HYPERFINE INTERACTION  99  Arsenic  101  Oxygen  102  'Close' protons  102  'Far'  105  protons  B.  HYDROGEN BONDING  106  C.  FERROELECTRICITY  108  D.  SUMMARY  109  4.6  Temperature dependence of the EPR spectra  110  4.7  Studies on KDP-KDA mixed c r y s t a l s  128  4.8  CONCLUSIONS  131  - V -  Page APPENDIX A:  Experimental Arrangement for ElectronNuclear T r i p l e Resonance  APPENDIX B:  EPR studies of the 'other' centres  REFERENCES  135 paramagnetic 140 145  - vi _ LIST OF TABLES Table 1  2  Page 4Spin Hamiltonian parameters f o r the AsO^ centre at 296°K 4Spin Hamiltonian parameters f o r the AsO^ centre at low (indicated) temperatures  3  68-69  78  Calculated values of 2 < S >^ f o r the given set of z  7 ^  4  As spin Hamiltonian parameters Comparison of the observed ratios v / v f o r a 'i ' l 'close' proton f o r the possible combinations of the 75 proton and As hyperfine couplings t  T  (felt/  5  vCloSGJ  —  ca-  using the graphical procedure described i n the text  95  Observed and calculated values, using the numerical diagonalisation procedure  7  89  ' and v i  Observed and calculated values of t,  6  88  97  Principal values and d i r e c t i o n cosines of one of the s i t e s f o r 'close' and 'far' protons i n KH AsO ..... ?  d  98  -vii  -  LIST OF FIGURES  Figure 1  Page Schematic energy level diagram for an S=J_ and 3 1= j system  2  23  Structure of KH^PO^-type c r y s t a l s , u n i t - c e l l  in  space group I42d a f t e r J . West 3  (a)  42  Displacement of atoms in Kh^PO^-type  crystals  at the Curie point  44  (b) c-axis projection of the crystal KH As0 2  (c)  4  structure of  below the Curie p o i n t , 97°K  c-axis projection of the crystal NH H As0 4  2  4  44  structure of  below the Curie point 216°K  4  Block diagram of the ENDOR spectrometer  5  Schematic representation of ENDOR signal  44 47 intensity  as a function of the applied microwave power  52  6  Block diagram of the Double ENDOR experiment  54  7  EPR spectrum of x-irradiated KH As0 for H||c 2  at  4  300°K at X-band (v=9.45 GHz). The l i n e s from the As0 centre are marked at the top whereas the lines 4  from the other centres  (unidentified)  are marked at  the bottom 8  61  EPR spectrum of x-irradiated KH As0 for H||c,  at  X-band (v=9.448 GHz) and at 4.2°K.  and T  2  are the normally allowed and T , T 2  4  T , T , T ]  4  3  5  and Tg are the  ?  - vi i i Figure  Page normally forbidden t r a n s i t i o n s belonging to the Aso|~ centre (see text)  9  62  EPR spectrum of x-irradiated KH^AsO^ for H||c  at  300°K taken at K-band (v=24.150 GHz) 10  63  EPR spectrum of x-irradiated KD As0 for H||c, 2  4  at  X-band (v=9.450 GHz) and at 300°K 11  65  EPR spectrum of x-irradiated RbH As0 for H||c 2  4  at  X-band (v=9.435 GHz) taken at * 300°K 12  X-band (v= 9.325 GHz) spectrum of x-irradiated NH H As0 2  13  66  4  for H | j c at ^296°K  67  Comparison of proton superhyperfine features on the lowest and the highest f i e l d As  75  hyperfine  4-  l i n e in the EPR spectrum of the AsO^ x-irradiated KH As0 2  14  4  centre in 70  4  Angular v a r i a t i o n of the s p l i t t i n g s associated with the lowest f i e l d l i n e ( I=^)  in the ab plane  of x-irradiated KD As0 at 77°K 2  15  73  4  Angular v a r i a t i o n of the s p l i t t i n g associated with 75 the lowest f i e l d As  hyperfine l i n e for the  A s 0 " centre in various (marked) c r y s t a l s at low 4  (indicated)  temperatures  74 3  16  E l e c t r i c f i e l d effects on the  75 As'  hyperfine  component for H||X in x-irradiated KH As0 at 2  4  77°K  77 4-  17  Typical proton ENDOR signals from the As0 x-irradiated KH As0„ at 4.2°K o  4  centre in 80  - ix -  Figure 18  Page S p l i t t i n g of the ' c l o s e ' and the ' f a r '  proton  ENDOR t r a n s i t i o n s for the case of H 2° away from the c-axis 19  82  Angular v a r i a t i o n of the ' f a r ' t r a n s i t i o n s in (a)  the ac and (b) ab plane of  x-irradiated KH As0 2  20  proton ENDOR  83  4  Angular v a r i a t i o n of the ' c l o s e ' proton ENDOR t r a n s i t i o n s in the ac (or be) plane f o r  (a) 75  the highest and (b) the lowest f i e l d As hyperfine t r a n s i t i o n in x-irradiated Kh^AsO^ at 4.2°K 21  84  Angular v a r i a t i o n of the ' c l o s e ' proton ENDOR t r a n s i t i o n s in the ab plane of x-irradiated KH As0 2  4  for (a)  lowest f i e l d A s  the highest f i e l d and (b) 7 5  the  hyperfine t r a n s i t i o n at 4.2°K  85  422  Double ENDOR signals for protons around an AsO^ centre in x-irradiated KH As0 for H||c at 4.2°K 2  23  4  Graphical representation of Eq. (39) for the ' f a r '  (see text)  proton ENDOR t r a n s i t i o n s in  x-irradiated KH As0 H||c at 4.2°K 2  24  9.1  93  4  Graphical representation of Eq. (39) for the ' c l o s e ' protons in x-irradiated KH As0 for H||c 2  4  and 4.2°K 25  94  Temperature dependence of the powder EPR spectra for x-irradiated KH AsO/,. 9  Only the features  - X -  Figure  Page associated with the As  75  3 m  i ~z =  hyperfine t r a n s i t i o n  for the AsO^" centre are shown (see text) 26  4-  EPR spectra of the AsO^  112  centre in powder samples  of x-irradiated Nh^r^AsO^ at the indicated temperatures. 75  3  Only the features associated with the As t r a n s i t i o n are shown 27  .114  Temperature dependence of the s p l i t t i n g s associated with the lowest f i e l d As  75  H| |X in various crystals  28  hyperfine t r a n s i t i o n for  Correlation times for the motion of As  75  117  and of  protons, calculated from the temperature dependence of As 29  75  and proton hyperfine structure 2  120  1  Plot of v = —5- as a function of the reduced T  30  temperature (T-T )  :  Angular v a r i a t i o n of the s p l i t t i n g s associated with 75  the lowest f i e l d As  hyperfine l i n e in the ab  plane of Kh^AsO^ at the indicated temperature 31  127  Typical proton ENDOR t r a n s i t i o n s in mixed KH P0 2  KH As0 2  32  4  4  crystals  130  Schematic representation of energy levels for an S=h system  33  123  136  Electron-Nuclear T r i p l e Resonance signals for the 4-  protons around the AsO^  centre in x-irradiated  KrLAsO , at 4.2°K and H||c d  138  - xi -  Figure 34  Page EPR spectrum at X-band (v=9.325 GHz) of NH*  radical  for HJ Ic in x-irradiated N H ^ A s G ^ at room temperature  144  -xii  -  ACKNOWLEDGEMENTS  I wish to express my great indebtedness to my research supervisor, Professor C A . McDowell, for his guidance and help throughout the course of the present work. Sincere thanks are due to Dr. R. Srinivasan Physics, IIS  (Department of  Bangalore, India) for his introducing me to the ENDOR  technique and for his untiring help and stimulating discussions at various stages of this research. I am grateful to Professor J.B. and help. and R.F.  Several very stimulating discussions with Professors W.C.  I am thankful to Messrs. D.E.  Dickinson and J . T a i t and Dr. J . A .  Kennedy,  Hebden for supplying computer  subroutines and,together with other colleagues,for general help. thank Professor R. Blinc J.  Lin  Snider, Dr. F.G. Herring and e s p e c i a l l y with Dr. J . A . R . Coope  are also g r a t e f u l l y acknowledged. J.R.  Farmer for his continued advice  (University  I  of Ljubljana and Nuclear Institute  Stefan, Ljubljana, Yugoslavia) for his kind g i f t of single c r y s t a l s of  K D A s 0 , RbH As0 2  4  2  4  and C s H A s 0 . 2  4  My thanks are also due to Messrs. J . and E. Matter for invaluable technical  S a l l o s , T. Markus, S. Rak  help.  Grateful acknowledgement is made of the receipt of several assistantships from the Department of Chemistry and of the award of a B.C. Sugar Refinery Scholarship and of a U.B.C. scholarship. I thank my wife, Jyotsna, for her much needed help and understanding and my parents-in-law for help and encouragement e s p e c i a l l y during the early stages of this work.  Lastly,  I am grateful to my parents who  underwent a l o t of hardships for giving me a university education.  - xiii GLOSSARY OF SYMBOLS USED  A  =  The tensor A  h  =  Planck's constant (fl = -R-)  e  =  the e l e c t r o n i c charge  c  =  the v e l o c i t y of l i g h t in vacuum  m  =  the electron rest mass  Pj  =  the momentum vector of the i-th  r\j  =  position vector of the i-th.  g  =  the g-value of the free electron  g^  =  the nuclear g-factor  3  =  the absolute value of the Bohr magneton = ^  =  the nuclear magneton  _S  =  the electron spin angular momentum vector  J_  =  the nuclear spin angular momentum vector  6..  =  the Kronecker delta  e  3  n  "13  electron  electron  6(rij)=  the Dirac delta-function  X  =  spin o r b i t coupling constant  =  o r b i t a l hyperfine coupling constant  =  charge on i-th nucleus.  -1 -  CHAPTER ONE INTRODUCTION  In recent years the I^PO^-type of f e r r o e l e c t r i c s and antif e r r o e l e c t r i c s have received considerable a t t e n t i o n , partly because of t h e i r applications in industry and partly because the microscopic nature of f e r r o e l e c t r i c i t y and a n t i f e r r o e l e c t r i c i t y yet f u l l y understood.  in these compounds i s not  Additional i n t e r e s t resulted because these  compounds belong to one of the simplest hydrogen-bonded structures and d e t a i l e d knowledge of t h e i r p r o p e r t i e s , which often depend upon the d e t a i l s of the hydrogen-bond network in these systems, might be helpful for a further understanding of the nature of the hydrogen bond i t s e l f . The f e r r o e l e c t r i c properties of Kr^PO^ (KDP) and isomorphous c r y s t a l s were f i r s t discovered by Busch and Scherrer^  in 1935.  However,  - 2 -  i t was only in 1941 that Slater  proposed his famous 'Order-disorder'  model of the f e r r o e l e c t r i c t r a n s i t i o n in the KDP-type of c r y s t a l s . Slater,  in analogy with the case of i c e , made the assumptions that the  hydrogen of the O-H-0 bond is situated in a double minimum potential 3_ well and that there are only two hydrogens close to any given XO^ group (X=P or As).  With these assumptions and using s t a t i s t i c a l  mechanics he showed that a t r a n s i t i o n should occur (the theory predicts one of the f i r s t o r d e r ) , the t r a n s i t i o n being e s s e n t i a l l y a change from a disordered system of hydrogen bonds above the t r a n s i t i o n point (called the Curie temperature, T )  to an ordered arrangement below i t .  It must be mentioned that when Slater proposed his model, the positions of the hydrogen atoms were not precisely known, although the room temperature crystal  structure of KDP was known through the x-ray 3 d i f f r a c t i o n work of J . West as early as 1930. Thirteen years after  Slater proposed his model, the ordering of the hydrogens was v e r i f i e d through neutron d i f f r a c t i o n experiments by Bacon and Pease 5  and Peterson, Levy and Simonsen  4  at Harwell,  at Oak Ridge, thus presenting strong  experimental evidence for the essential correctness of S l a t e r ' s basic assumptions.  Moreover, the entropy change at the t r a n s i t i o n , as  calculated on the basis of this model, was also found to be in good agreement with the experimental values^.  On the other hand, i t was  soon discovered that deuteration of KDP and i t s isomorphic c r y s t a l s s h i f t e d t h e i r Curie points by nearly a factor of two^, which could not be accounted for on the basis of the Slater model.  Moveover, since  the Slater model neglects the role of the c a t i o n , i t f a i l s to explain the large s h i f t s in the Curie points observed when K is replaced by L i ,  - 3 -  Na, Rb, C s , e t c .  The role of heavy ions is evident also from the fact  that the magnitude of the observed spontaneous p o l a r i z a t i o n can be accounted for mainly on the basis of the large displacements of the heavy ions accompanying the f e r r o e l e c t r i c  transition.  To explain the e f f e c t of deuteration on the Curie points and the observation of certain low frequency modes in the infrared o spectra of these compounds, Blinc hydrogen nuclei (protons)  proposed that the disorder of the  in the p a r a e l e c t r i c phase is a dynamic  one, in that the protons perform a tunneling motion from one equilibrium s i t e in the hydrogen-bond (H-bond) to the other.  This modification  of the Slater model is often referred to as the Blinc or the SlaterBlinc model of the f e r r o e l e c t r i c t r a n s i t i o n .  Schmidt and Uehling  g  were the f i r s t to obtain d i r e c t experimental evidence for such a  motion f o r the case of deutaons in I^PO^ resonance relaxation measurements.  It  (DKDP), through the deuteron  has since been confirmed by the  more recent neutron-scattering experiments^.  Recent i n f r a r e d ^ and  12 Raman scattering  experiments on the KDP-type of c r y s t a l s ,  however,  present quite c o n f l i c t i n g results regarding the interpretation of the data in terms of double minimum potential well model of the 0-H-O bond  with any appreciable tunneling.  NMR^ and EPR^  Results of the more recent  experiments are, on the other hand, believed to be  in better agreement with the Slater-Blinc model,although  the  i n t e r p r e t a t i o n of these results does not appear to be conclusive]'' On the other hand, C o c h r a n ' ^ 15  6  and independently Anderson^  introduced another model, now known as the Cochran model, which is based on the following ideas in l a t t i c e dynamics.  It  can be shown  7  - 4 -  that in some ionic cr partly i o n i c crystals a long wavelength transverse optical frequency may become imaginary in the harmonic approximation resulting in an i n s t a b i l i t y of the l a t t i c e with respect to this normal mode; this causes a change in the crystal hence the occurrence of the f e r r o e l e c t r i c t r a n s i t i o n .  structure and  The theory is  based on the argument that in ionic c r y s t a l s l a t t i c e vibrations  are  accompanied by p o l a r i z a t i o n o s c i l l a t i o n s which create a local  field  interacting with the ions through long range Coulomb forces.  If,  for  a given normal mode, these long range forces have the same magnitude but are of opposite sign to that of the short range f o r c e s , the crystal becomes unstable against this mode.  Above the Curie point anharmonic  interactions s t a b i l i s e the system making the observable frequency w real and p o s i t i v e , but temperature dependent.  The anharmonic contri-  bution decreases with decreasing temperature as to ec (T-T ), and approaches zero as T->T  so that the l a t t i c e displacements associated  with this mode become unstable and produce a ' d i s p l a c i v e ' phase t r a n s i t i o n .  ferroelectric  This model could s a t i s f a c t o r i l y describe phase  t r a n s i t i o n s in BaTiOg—type f e r r o e l e c t r i c s .  As such, however,  did not prove suitable for KDP type f e r r o e l e c t r i c s .  This l a t t e r  it has  been ascribed to the neglect of any d i r e c t role of the protons in the mechanism of the phase t r a n s i t i o n in the o r i g i n a l Cochran model, as is indicated by the more recent work of Kobayashi  1g  , discussed l a t e r .  On the basis of the aforementioned considerations, Blinc and 19 Ribaric  were the f i r s t to allow the interaction of the proton system  with the l a t t i c e .  They demonstrated that the Curie point of the  isolated proton system is s i g n i f i c a n t l y lowered when the  lattice  - 5 -  i n t e r a c t i o n is taken into account.  In t h e i r theory, however,  the  dynamical aspects of the phase t r a n s i t i o n are not discussed and, in p a r t i c u l a r , no explanation is offered for the large d i s t o r t i o n s of the heavy ions accompanying the ordering of the proton system at the Curie point. 20 Meanwhile, after the pioneering ideas of de Gennes  ,  21 22 Tokunaga and Matsubara  '  have reformulated B l i n c ' s model in terms  of a pseudospin system, with the main emphasis on the importance of the ionic motion along the c-axis.  For example, they discussed a new  order-disorder model for the f e r r o e l e c t r i c phase t r a n s i t i o n in KDP-type of c r y s t a l s , assuming that there e x i s t two possible configurations for a (K-XO^) complex along the symmetry axis (c-axis) of the c r y s t a l . These configurations correspond to the two possible orientations of the permanent dipoles along this a x i s .  According to t h e i r  theory,  f e r r o e l e c t r i c phase t r a n s i t i o n s would occur by an order-disorder arrangement of the two possible configurations even without the cooperation of the proton system in the hydrogen bonds.  As might be  expected, this model does not explain the large isotope e f f e c t observed in the Curie points of these c r y s t a l s , although other properties l i k e the observed magnitude of saturated p o l a r i z a t i o n . n o i s o tope e f f e c t in  saturated p o l a r i z a t i o n and the large displacements of  the heavy ions at the Curie points can be s a t i s f a c t o r i l y explained. 18 23 In the meanwhile  Kobayashi  '  proposed the so c a l l e d mixed model  in which the i o n i c motion along the c-axis is also taken into account without assuming an order-disorder type t r a n s i t i o n for the i o n i c system.  In this model  the proton tunneling mode couples strongly  - 6 -  with the optical mode of (K-XO^) l a t t i c e vibration along the c-axis and the frequency of one of the coupled modes tends to zero as the temperature approaches the Curie p o i n t , T .  Below T , t h i s mode is  frozen i n , causing a large displacement of the heavy ions, and thus re sulting in a large spontaneous p o l a r i z a t i o n along the c-axis.  It  must be emphasised that although the basic idea behind the Kobayashi model is the same as that of the Cochran m o d e l , i . e . the frequency of a transverse optical mode tends to zero as T-»-T , the exact mechanism of the f e r r o e l e c t r i c t r a n s i t i o n i t s e l f is c l a r i f i e d .  In the Kobayashi  model i t is the proton ordering in the double well potential  system  of the hydrogen bonds that makes the frequency of the coupled mode tend to zero, in contrast to the case of the Cochran model where the anharmonic terms in the l a t t i c e vibrations compel the frequency of transverse optical vibration to tend to 7Bro.The assumption of a strong proton l a t t i c e coupling in the Kobayashi model i s based on the well established experimental fact that,whereas  the  ferroelectric  t r a n s i t i o n in KDP-type of crystals is triggered by a cooperative ordering of hydrogens, the spontaneous p o l a r i z a t i o n arises due to the large displacements of the heavy ions along the c-axis.  The Kobayashi  model thus offers an explanation f o r most of the properties associated with the f e r r o e l e c t r i c or a n t i f e r r o e l e c t r i c  transitions in the c r y s t a l s .  Although the Kobayashi model is believed to be the most general for explaining the phase t r a n s i t i o n phenomenon, the basic assumptions employed by Kobayashi have, so f a r , received no d i r e c t experimental confirmation, although most of the available experimental techniques have been employed with a view to examining the  validity  -7 -  of such assumptions.  In p a r t i c u l a r there is l i t t l e or no quantitative  data on the low frequency (K-PO^) and (K-AsO^) v i b r a t i o n s , the existence of which is fundamental to the Kobayashi model, as well as to, the Cochran model.  However, whereas the Cochran model predicts no  s i g n i f i c a n t isotope e f f e c t in the temperature dependence of the frequency of the coupled mode, the Kobayashi model predicts a s i g n i f i c a n t isotope e f f e c t , thus providing a c r i t i c a l the v a l i d i t y  test for examining  of one or the other model.  Some experimental evidence for the existence of the "ferro24 e l e c t r i c mode" in KDP has been obtained by Arfjev observed a vibrational  et al  .  band in the far infrared region whose frequency  behaved anomalously with temperature T according to to oc (T-T Similarly,  They  12  Kami now and Damen  ).  observed in KDP a vibrational band  around 100 c m " \ at room temperature, which f a l l s in the range of frequencies predicted by the Cochran model.  However, the temperature  2 dependence of to was found to be a function of (T-T ) rather than (T-T ). 25 Subsequently Brody and Cummins , using the B r i l l o u i n scattering c  T  technique, observed in KDP a mode whose frequency changed with  temperature as (T-T ),  as predicted by the Cochran or Kobayashi model. 26  Simultaneously  Blinc and Zumer  also reached s i m i l a r conclusions  31 through P NMR T^ measurements. and Recent NMR experiments of been Blinc and of others > > have Mai i^ ^ Blinc and B j o r k s t a m 13  13b  2 7  2 8  2 9  interpreted as favoring the Blinc model as compared to other models. However, more recent infrared spectroscopic measurements of Sato neutron scattering experiments  33  30  ,  of the Cochran group and infrared  spectroscopic and Mossbauer measurements  34  of the Pel ah group, favor  - 8 -  the soft mode type models. 32 as White et a l .  Very recently Popova et a l .  as well  observed an isotope e f f e c t in the temperature  dependence of the frequency of the soft mode (observed f i r s t by 1  Kaminow and Damen  o  as mentioned e a r l i e r ) ,  which supports the  Kobayashi model against the Cochran model, although neither of the models helps to explain the detailed shapes of the observed bands. It  is emphasized that in KDP and DKDP, although the existence  of a f e r r o e l e c t r i c mode has been reported, i t is not c l e a r whether t h i s mode represents a pure l a t t i c e , a quasi-spin type proton tunneling or a mixed proton-lattice mode.  For the Kh^AsO^ (KDA)  c r y s t a l s , on the other hand, no such data has as yet appeared.  type These  considerations show that no clear picture has yet emerged for the mechanism of the phase t r a n s i t i o n in the KDP-type of c r y s t a l s . Therefore, more accurate and detailed experimental data, e s p e c i a l l y on the role of the heavy i o n s , appear to be necessary for a f u l l e r understanding of the t r a n s i t i o n phenomenon in these c r y s t a l s . In the present work we have employed the techniques of Electron Paramagnetic Resonance (EPR), Electron-Nuclear Double Resonance (ENDOR) and Double ENDOR with a view to understanding the part played by protons as well as the role of heavy ions in the mechanism of the phase t r a n s i t i o n in the KDP type of c r y s t a l s .  Since  these c r y s t a l s are not naturally paramagnetic, they were x-irradiated to introduce paramagnetic centres in them, following Hampton, Herring, 35 35 Lin and McDowell . Hampton et a l . have shown that x - i r r a d i a t i o n of  4-  KDA results in the formation of a stable paramagnetic AsO^ due to the capture of an e l e c t r o n .  centre  No appreciable structural  change  - 9 -  seems to occur on the formation of this centre which is hydrogenbonded to other AsO^ units in the c r y s t a l s .  The unpaired electron  has been shown to enter an A-|-type molecular o r b i t a l centered on the 375 AsO^ i o n , r e s u l t i n g in a large hyperfine interaction with the As nucleus (I partially  =•?).  Each of the As  hyperfine lines shows f u r t h e r ,  resolved structure due to the superhyperfine  interaction 4-  of the unpaired electron with the H-bond protons.  The AsO^  centre,  therefore, appeared to be,an ideal microscopic probe f o r a detailed investigation of the nature of hydrogen bonding as well as the  75 dynamics of the hydrogen bond protons, and of the As f e r r o e l e c t r i c crystals  nuclei in the  KDA and KI^AsO^ (DKDA); and also in the anti-  f e r r o e l e c t r i c c r y s t a l s of Nh^h^AsO^ (ADA) in t h e i r paraelectric phases. It  i s perhaps important to mention here that s i m i l a r studies on pure  KDP c r y s t a l s could not be performed because x - i r r a d i a t i o n of KDP 4c r y s t a l s does not y i e l d the corresponding measurable q u a n t i t i e s .  PO^  radical in any  However, the present studies show that  prolonged i r r a d i a t i o n of KDP at room temperature results in the formation of a paramagnetic centre which has been i d e n t i f i e d as the 2P0  4  37 centre  .  Since this centre is formed due to the rupture of one  of the hydrogen bonds, i t is not a very convenient probe for i n v e s t i gating hydrogen bonding in KDP. Instead, we doped KDP with varying 34amount of the AsO^ ions and obtained the AsO^ centres in KDP. EPR and ENDOR investigations of the doped c r y s t a l s y i e l d information on the structure of these ( f e r r o e l e c t r i c ) , s o l i d solutions.  The results  indicate that EPR and ENDOR are perhaps the most helpful techniques for investigating the structural properties of these  ferroelectric  - 10 -  solid solutions. In Chapter II  are outlined the d e t a i l s of the  theoretical  background necessary for the interpretation of the EPR and ENDOR measurements.  In a d d i t i o n , we also discuss a new, graphical procedure  for obtaining the signs of the hyperfine interaction constants.  This  method can complement the method of Double ENDOR when the l a t t e r  fails  due to unfavorable experimental conditions.  The d e t a i l s of the  experimental arrangement, together with some preparatory and structural properties of the investigated c r y s a l s , are described in Chapter  III.  In Chapter IV are presented the results of the EPR, ENDOR and Double ENDOR experiments and t h e i r i n t e r p r e t a t i o n .  Appendix A contains the  d e t a i l s of the technique of Electron-Nuclear Triple-Resonance which has been demonstrated for the f i r s t time and which may be quite important for a further understanding of the phenomenon of ENDOR and for extending the a p p l i c a b i l i t y of the ENDOR technique to a wider variety of samples than is possible at present.  Appendix B contains  4a b r i e f description of the studies of the radicals other than AsO^ produced as a r e s u l t of the i r r a d i a t i o n of the samples.  - 11 -  ,  CHAPTER TWO THEORETICAL  INTRODUCTION The present chapter contains an outline of the theoretical background necessary f o r the interpretation of the results of EPR and ENDOR studies of a paramagnetic lattice.  system embedded in a crystal  The treatment is b r i e f since i t has already been the  subject of discussion in several excellent review a r t i c l e s  "  and  39-43 books.  For reasons of s e l f s u f f i c i e n c y , however, and l a t e r  reference, a b r i e f summary of the theoretical approach leading to the derivations  of the formulae used in the present work w i l l be given  here. The technique of paramagnetic resonance, f i r s t introduced by Zavoisky, has by now become a well known method f o r elucidating the properties of paramagnetic systems.  Its  p r i n c i p l e is quite  - 12 -  simple.  If  a molecular or an atomic system, possessing a magnetic  moment, and therefore having a degenerate ground s t a t e , is placed in a steady magnetic f i e l d , the degeneracy is l i f t e d and the undergo a Zeeman s p l i t t i n g .  levels  Simultaneously this system is also  subjected to a high frequency electro-magnetic f i e l d so that t r a n s i t i o n s may be induced between the Zeeman levels when they have the appropriate energy separations.  The consequent absorption  of energy, therefore, shows a series of maxima as the s t a t i c magnetic f i e l d is varied and one can plot out the energy levels as functions of the s t a t i c  field.  For the general case of a paramagnetic c r y s t a l ,  ideally,  one should solve the Schrb'dinger equation for the electrons and the nuclei in the entire crystal f i e l d H.  in the presence of the applied magnetic  T h i s , however, is not possible at the present time and one  i s thus forced to simplify this many-body problem. theory methods have proved to be invaluable here.  Perturbation One thus begins  by considering a general Hamiltonian f o r the entire system, retaining the dominant terms as the zeroth order ones and treating the smaller ones as perturbations. As a s t a r t i n g point,  we note t h a t , in general, the  dominant contribution to the magnetism of a molecular complex comes from the electrons.  Many n u c l e i , however, possess magnetic moments  and thus do make some contributions to the Hamiltonian representing the system.  Since the nuclei are very massive compared to the  e l e c t r o n s , the system may be approximately represented by a system of electrons moving in the f i e l d of the nuclei in the c r y s t a l .  The  - 13 -  Hamiltonian f o r this system may be written as  +  z  e _ ^  i<k r-j^  +  (a)  "  E  a n 9  #  +  ss  (  si  }  i ,<x ^  ia  41  :  (i) y  —  («)  —  (a)  fyi-  —  +  V  EQ  +  '  s m a 1  1  terms.due to  relativistic  corrections The f i r s t term is the k i n e t i c energy;  (1)  the second is the potential  energy of the electrons in the f i e l d of the nucleus and of the surrounding i o n s ;  the t h i r d expresses the interaction between the  electron spin and the external f i e l d ;  the fourth is the spin-orbit  interaction term and the f i f t h is the potential energy of the repulsion between the electrons.  H  r  ss  represents the term due to  magnetic i n t e r a c t i o n among the e l e c t r o n s ,  represents that due  to magnetic i n t e r a c t i o n between the electron and the nuclear s p i n s , and the next term expresses the interaction between the magnetic moment of the nuclei and the magnetic moment due to the o r b i t a l motion of the electrons.  ^ g ^ f y I_^H_ represents the nuclear  Zeeman i n t e r a c t i o n and the l a s t term describes the interaction between the e l e c t r i c f i e l d gradients and the e l e c t r i c quadrupole moment of the nucleus.  A l l the symbols used have t h e i r usual  meanings and have been defined in the Glossary. To simplify the form of Eq. (1 ),  i t is convenient to  choose a gauge f o r which A  = h H_xr  the o r i g i n being taken at the nucleus. in Eq. (1),  (2) By substituting Eq.  (2)  the k i n e t i c energy of an electron can be written as:  - 14 -  a <* f*> - £ +  2  Is? fl-rxp -  +  4a  (axr)  2  - {£ + «.H + | Y  (Hxr)  Thus Eq. (1) may be w r i t t e n as at.  [E. 'p '» i 2m (i  2  t  -*isi£ . .«?_]• J + I  L  i  r  1 < k  r  +  V  spin-orbit *  $ s  a f  +  +  s  ik  cryst  2 ^ . ( k + j f e f (bxr) p  +  I  ,  v  2  +  B  M U l W . E ^ ^ l (  H.g S e  a  ? H  +  V  q  (3)  L = z i ^ K S = I s^K i — i—  where  Here the term i n the square b r a c k e t i s the s p i n independent p a r t o f our system and i s u s u a l l y by f a r the dominant term, ^cryst  1 S  ^  e  P°t  ent1  ' l energy due to the e l e c t r o s t a t i c f i e l d o f a  the neighbours, c a l l e d the c r y s t a l f i e l d .  The t h i r d term i s the  s p i n - o r b i t term, whereas 3H.. ( L + g S ) , the e l e c t r o n i c Zeeman term, i s g  m a i n l y r e s p o n s i b l e f o r the paramagnetism. •gjrc'  2  i(Hxr\j)  i s the one  The f i f t h term,  mainly r e s p o n s i b l e f o r diamagnetism and  the remaining terms have a l r e a d y been d e f i n e d .  We have n e g l e c t e d  the terms r e p r e s e n t i n g the r e l a t i v i s t i c c o r r e c t i o n s because t h e i r c o n t r i b u t i o n i s found t o be much s m a l l e r than the o t h e r terms i n the H a m i l t o n i a n . Now the problem o f s t u d y i n g the p o s i t i o n o f resonance t r a n s i t i o n s between the Zeeman l e v e l s (and hence EPR) i s e q u i v a l e n t  2  - 15 -  to determining the eigenvalues and eigenfunctions of <fl.  This  problem is most u s e f u l l y attacked in stages, using the perturbation theory methods.  This can be seen by examining the order of  magnitude of the d i f f e r e n t parts o f $ , l i s t e d below: 1.  2.  free ion (complex): crystal f i e l d  5  spin independent part  10 cm  -1  10 cm 4  2  _1  -1  3.  spin-orbit i n t e r a c t i o n  10 cm  4.  e l e c t r o n i c Zeeman term  lcm"^  5.  e l e c t r o n i c spin-spin i n t e r a c t i o n  Icm"^  6.  electron-nuclear interaction  0.1 cm"''  7.  other The termsposition of the crystal f i e l d term in this  -4  10 cm table  -1  i s s l i g h t l y v a r i a b l e , and i t may be weaker than the spin-orbit term in some cases. In a d d i t i o n , in the present experiments we are  interested  in the energy levels with non-negligible occupancy at room temperature or below. 3  Hence the properties of levels more than,  -1  say, 10 cm  above the ground level  can be ignored as d i r e c t  contributors to the magnetic properties at or below room temperature. Also spin-spin interactions play no role in the present studies and s i m i l a r l y we w i l l drop the term representing the diamagnetic interaction.  It w i l l be further assumed that the many atom  Hamiltonian can be written as a sum of single atom Hamiltonians ^  = £ *i& a  ft( =A a)  a )  i.e.  , where  + X l . S + BH.(L g S) + +  e  4-I  ( a )  +^srt \l -li ( a  ( a  +  V  EQ  (4)  }  - 16 -  where  labels the atoms and  a  represents the spin-independent part  Since, in general, the energies associated with the various  ofH.  terms in Eq. 4 d i f f e r from each other quite appreciably, the Hamiltonian  can be conveniently handled by the method of 44  successive perturbations, as shown f i r s t by Pryce  and in more  45 detail  by Abragam and Pryce.  These authors have shown that the  energy levels of a system l i k e the one represented by Eq. are, correct to the second order in A and H, the operator involving only the spin variables. c a l l e d the spin Hamiltonian operator.  (4),  eigenvalues of an  This operator is now  We w i l l  indicate below the  various steps to obtain the form of this operator used in almost a l l of the paramagnetic resonance studies. 2.1  The spin Hamiltonian Consider f i r s t a paramagnetic system where the nuclear spin  1=0.  Then Eq. (4)  becomes  Since 2£  ,H  Q  and ^  Q  % = %  +2C- , where ^t^AL.S + BH.(L+g S). 1  can be taken as the zeroth order Hamiltonian  can be considered as a perturbation on i t .  Using the second  order perturbation theory, the e f f e c t i v e Hamiltonian operator c o r r e s ponding to K ' can be written as iC' = E +g BH.S - E <o|L.|n >< n|L.|o > (xS. + g BH•)(xS-+g BH.) n*o ] . J u —J_ 0  e  1  (n E  where the eigenfunctions  " 0>  refer to the eigenstates o f ft,,  |0> corresponding to the lowest eigenvalue o f * ^ . Q  Eq.  (5)  1  (5)  E  |0> , |1>,  e  To simplify  f u r t h e r , a tensor A• . i s introduced and i s defined in terms  of the matrix elements of L, by  - 17 -  A„-  <o|Li|nxn|Lj|o>  E  °  n  (6)  The tensor indices i , j refer to Cartesian coordinates' and the summation convention is assumed f o r them.  Also since <0|ljn> is  imaginary and equal to -<n|Jj0>, A ^ j is real and symmetrical and if Eq.  E  Q  is the lowest eigenvalue, i t is also p o s i t i v e d e f i n i t e .  Now  (5) can be written as  8eB(«ij-"lj» 1 J- 1J 1 J- 1j 1 J s  In this equation, E  Q  H  A  s  s  A  H  H  is the unperturbed energy.  ( 7 )  The  second term is the magnetic energy of a spin system with a g f a c t o r , in general anisotropic and represented by the tensor  9«''9e<«1J-V  (8)  2 and -X A . .S-S.  is the second order spin-orbit contribution to  spin-spin coupling.  In the present s t u d i e s , we are concerned with  free radical systems, be discussed f u r t h e r .  this term is not applicable, hence i t w i l l not S i m i l a r l y the l a s t term in Eq. (7) can be  dropped because i t is spin independent and hence s h i f t s a l l equally.  the  levels  With these remarks and using tensor notation Eq. (7) can be  written as h" = E It  Q  + H.g.S  is now r e l a t i v e l y  (9) simple to take into account the  electron-nucleus i n t e r a c t i o n s .  One may just augment Eq. (9) by  adding to i t the t e r m s ' g l . j _ , ^ , - g $ H.I and V^g. s I  the e f f e c t of s t . I ,  n  n  further s i m p l i f i c a t i o n occurs.  However, for In exact  analogy to the terms iL.S^ or iH.L_, the f i r s t order contribution of  - 18 -  the term ^l.I_ vanishes.  However, in the second order, the cross  terms between At^._S_ and £L.J_ give r i s e to a term, called o r b i t a l hyperfine term, wj^,  given by  "Jrt-^lj'j  (10)  and s i m i l a r l y the cross term between j>t.J_ and  J_ give r i s e to a  term proportional to H_.I_ i . e . which i s a correction to the nuclear Zeeman term - g 3 H . L n  However, f o r free radical systems ( l i k e  n  the one considered i n the present work) both of these correction terms are n e g l i g i b l y small and hence they w i l l not be discussed further. Next consider the term Jf!^ which represents the magnetic interactions between the e l e c t r o n i c and the nuclear spin magnetic moments.  It i s usual to write this term as  '*si •  V y ^ ) !  ^ ^ ' - ^  2  y» 5  * £ I.S«(r)]dv  v* 3  (11)  the integration being over the spatial coordinates.  The f i r s t  two terms in the integral represent the usual dipole-dipole i n t e r a c t i o n , while the t h i r d term gives the Fermi contact interaction. I, x  I , I, z  This expression i s l i n e a r i n the spin variables S , Sy and S and may therefore be written in the form I S (12) SI = a L S + Z B x  z  36  i k  1  where  i  9^ x,y,z  k  =  a = §2- g B g 6 l * ( o ) | e  B  1k  =  W  „  n  ^  n  -  ^  l  (13)  2  ^  |  d  2  v  (  1  4  )  The tensor B_ i s traceless and symmetric and can be diagonalized. Then representing the principal axes by x , y , z we obtain  3 t  S  I  .  a  I.S + B I S X  X  X +  B I S y  y  y  •B I S Z  Z  Z  (15)  - 19 -  In the tensor notation, Eq. (15) can be rewritten as ^SI where A  x  = a + B  and since B is  C" ) 16  =  A  x>  y  =a + B ,  A  z  =a + B  (17)  z  traceless  1  a =  ( A  x  +  A  + y  V  (18)  The remaining two terms, g ^ H . I  and V^g, representing  respectively the nuclear Zeeman and the Quadrupole interactions are usually much smaller and can be added d i r e c t l y to the Hamiltonian f o r our system.  Thus, r e l a t i v e to E , the 'complete , e f f e c t i v e 1  Hamiltonian representing a system consisting of a single electron interacting with several nuclei may be written as «tf = H.g.S + y(r-A*S-gae H . f t l ^ f ) — § — £ —= — n n —'  (19)  where the term V Q has been expressed, as usual, as £  V  E Q  =  (20)  I . Q . I  The operator^now contains only the electron and the nuclear spin operators and the various g , A, Q etc.  It  'coupling parameters',  is noted that in o b t a i n i n g ^ , the formidable  many-body problem has been replaced by a r e l a t i v e l y  simple spin  problem, in which the coupling effects involving the e l e c t r o n i c wavefunctions have been 'absorbed' into a number of parameters. This is precisely w h y ^ i s c a l l e d the spin Hamiltonian  (operator).  - 20 -  On adopting the spin Hamiltonian formalism f o r the description of a paramagnetic system, a clear d i v i s i o n of labour is achieved by the separation of the work of determining the 'coupling parameters' from that of their i n t e r p r e t a t i o n .  We w i l l  now b r i e f l y describe f i r s t , how the parameters of the spin  .—•  Hamil tonian $£may be obtained through the analysis of the paramagnetic resonance spectra and w i l l then indicate how these parameters might be interpreted in terms of the molecular p r o p e r t i e s . 2.2  Determination of the spin Hamiltonian Parameters  2.2.1:  Spin Hamiltonian parameters from EPR measurements: Consider the case of an electron coupled strongly with  a s i n g l e nucleus and assume that the EPR spectra show axial symmetry about a certain d i r e c t i o n , c a l l e d the z-axis, as is found to be the case f o r most of the EPR spectra observed above about 310°K in the present s t u d i e s .  (The more general case of an electron  i n t e r a c t i n g simultaneously with several nuclei and where the EPR spectra do not show axial symmetry presents no conceptual d i f f i c u l t i e s although i t becomes much more cumbersome to d i s c u s s ) . The spin Hamiltonian f o r this system is ^EPR  V(  9 1 1  B H ) S. + ^  ^  + A  ^  +S y y -  " Vn z H I  where coupling.  +  B  ll  ( I  z  •  1 / 3 l2)  '  ( 2 1 )  is a parameter describing the a x i a l l y symmetric quadrupole The eigenstates may be labelled by the eigenvalues mp of  the commuting operator ?  z  =S  z  + I  2  <  Then \%> = \m  ri  ± > according  - 21 -  as m -*• ± h i n the high f i e l d l i m i t .  For a given nip, the matrix  $  °^^EPR  1 S  a t  n i o s t  2 x 2  ' namely, i n the b a s i s |m ,nij>, where m.j = s  F ~ S <n£. m - m;|^ |m , m - m > «  m  m  !  F  EpR  s  p  s  + (m - % ) ( A 2 g 3 H ) ] + b  hig^m  F  i r  n  n  %A|.[I(I + 1 ) - m + hi*  2  -JsCg^BH + (m + J s M A ^ + 2 g 3 H ) + b_ (22)  2  +  ^ [ 1 ( 1 + 1 ) - m + hi*'  +  F  n  n  2  where b~ = [(nip + h)  ~ 1(1 + ) n 1  B  eigenvalues are  T n e  E(m , ±) = - { V A gn n )-( r^ ll ^ s { ( g e H + ( A - 2o^)mr: + 9 6 H ) + ' A £ [ I ( I + 1 ) - (m - J*)]}' + m  N  F  e  H +  +  1  m  ] B  2  n  }  F  n  n  2  n  5  (23)  The e i g e n s t a t e s |s> may be w r i t t e n |mp, + > = Cosa|J5,mp-%>  + Sina|-%,mp + %>,  |m.p, - > =-Sina|55,mp - h> + Cosa|-^,m + %>, F  (24)  where [41(1 + 1) - 4m + iT^Aj. 2  Tan 2a  g BH+ ( A - 2B )m n  n  n  F  +g ^ H  (25)  - 22 -  4Consider now the s p e c i f i c case o f the AsO^ c e n t e r i n x - i r r a d i a t e d s i n g l e c r y s t a l s o f Kh^AsO^.  E a r l i e r room  35  temperature EPR s t u d i e s o f t h i s system show t h a t the EPR s p e c t r a are a x i a l l y symmetric.  The dominant f e a t u r e s o f the s p e c t r a a r i s e  from the h y p e r f i n e i n t e r a c t i o n o f the unpaired e l e c t r o n with the As  (I = TJO nucleus.  Thus, t h i s system may be  d e s c r i b e d i n terms  o f the s p i n H a m i l t o n i a n ' ^ p given by Eq. (21) f o r the case o f 1=2 2* A schematic r e p r e s e n t a t i o n o f the energy l e v e l s o f the 4R  AsO^  c e n t e r , assuming A-^ to be p o s i t i v e (as w i l l be shown l a t e r )  i s given i n F i g . 1.  The v e r t i c a l arrows show the seven EPR  t r a n s t i o n s observed i n general i n the experiments.  Transitions  T-|, Tg, Tg and T^ are observed whenever the microwave magnetic f i e l d vector  has a component p e r p e n d i c u l a r to H and obey the  usual s e l e c t i o n r u l e Amp = ±1.  Other Amp =  ±1 t r a n s i t i o n s  are a l s o a l l o w e d , but occur i n d i f f e r e n t frequency ranges, or are much weaker.  T r a n s i t i o n s T , T^ and T , on the o t h e r hand, are 2  g  observed when H ^ has a component p a r a l l e l to H, and obey the corresponding s e l e c t i o n r u l e Amp = 0.  For a c o n s t a n t microwave  frequency v, n e g l e c t i n g the quadrupole term which i s found to be n e g l i g i b l e , the resonance f i e l d s H. = hV t r a n s i t i o n s are g i v e n e x p l i c i t l y by  f o r these seven EPR  Multiple! No  Eigenfunction  Energy Levels  ^=  |i,t>  1  ^=Cosa,|i i>+  Sina,|-lJ)  E  O  % = Cosegi -i)+  Sinaol^i)  E  f  f  = C o s q , | i ,-|) + Sin g, |~i,%>  -2 * = s  -1  tvt>  »//. = Cosa,|-i;i>  7  CosaJ-i, i ) -  8  Cos a [ - i . f > -  Fig. 1  2  = ig„/SH + j A „ - l g Q H r ii ' A „ - g Q H + 1 [(g/3H + A „ g / S H T + 3A^J  3  : -iA,^ [(g„ /3H + g  E,  2  -1  6  Eigenvolue  n /  n  2  n /  E, =  E  n  +  n  n  2  n  = -ai a . / S H f l A  1 1  n  /^H ) + 4 A ]^  g / 3 H + | [ ( g , / 3 H - A, n  n  2  g / 3 H ) + 3A ]= n  1+  2  n  + |g ^,H n  Sin a,I l;f>  E = -iA g /3 H-i[cg,/3H- A „ g £ H )  Sin a |  E  Sina,|i i) t  6  E  l+  n  n  2  +  n  n  2  + 3  A ]~ 2  'iA,,- 9n A, H-i [ ( g „ / S H - t - A „ + g S H 3 A ] n /  n  2  Schematic energy l e v e l diagram f o r an S=% and I=y, a x i a l system.  2  2  - 24 -  = hv = hg ^  +A  u  - ^g 6  n  n  + [g  n H l  + A„ + g^H, ) , 2  l l 3 H l  + 3A_L ]^ 2  T  2  = hv = [g^BHg +  T  3  = hv = - g g H  T  = hv =  T  = hv = - g 6 H  4  5  n  n  [( BH GIL  n  n  T  ?  = hv = [ ( g = hv =  9 l l  l l B  6H  H  7  g i l  n  + ^[  5  +9  3 H )  n  n  3H  + g B H )  4  11  6  N  + ^[(  3  + %[(g 3H T  A  g i l  1 1  - g 6 H n  n  4  3H  - A  5  - A  6  n  +  7  n  2  2  + A,  3  SAJL ]' ,  +  2  2  +g ^ )  }  2  + g 3 H ) n  n  g g H ) n  + SAj ]*, 2  2  + 4Aj_ ] , + g ^ )  5  5  n  6  2  5  !s  2  2  +  + [(g^e^ -  . * + 3A  ±  2  ]\  2h?f\ +g B H ) n  n  7  2  +  Z^f.  (26) From an inspection of Eqns. (26), i t w i l l be noticed that this set of seven equations contains only four unknowns: g-j-j, g^, and Aj_ and thus these parameters can be extracted through the seven EPR t r a n s i t i o n s observed in these experiments. It might be pointed out here that for the more general case of a system which can only be described by orthorhombic symmetry i t is neither easy nor convenient to obtain exact equations those given in Eqns. (26). theory methods.  like  One is then forced to use the perturbation  A very general method of obtaining the spin  Hamiltonian parameters for a paramagnetic system is that due to B y f l e e t , 46 Chong, Hebden and McDowell  .  The basic tool of the approach is again  the method of successive perturbations to obtain the eigenfunctions  - 25 of the spin Hamiltonian correct to the t h i r d order in the perturbation parameters.  T h i s , therefore, allows one to obtain the energy  l e v e l s of the system correct to the seventh order in the perturbation parameters.  This approach has been described more f u l l y in the  Ph.D. thesis of J . A .  Hebden ' who also,wrote, a computer programme 4 7  based on this approach. At this stage we must point out that although the gross 4-  features in the hyperfine structure of the AsO^  center could be  studied through the EPR technique, the resolution of EPR is  inadequate  75 for studying the further s p l i t t i n g of the As  hyperfine l i n e s .  This  further s p l i t t i n g (of the hyperfine l i n e s ) , c a l l e d the superhyperfine structure ( s h f s ) , arises because of the much smaller  interactions  with the ligand n u c l e i , in our case the protons of the O-H-0 bonds. These smaller interactions could be studied through the technique of Electron-Nuclear Double-Resonance (ENDOR) in the manner described next. 2.2.2  Determination of superhyperfine parameters through ENDOR measurements: 49 / The technique of ENDOR, introduced by Feher  the observation of Nuclear t r a n s i t i o n s via EPR.  %  (1957),  is  For studying  hyperfine i n t e r a c t i o n s , this technique i s much more powerful  than  e i t h e r EPR or NMR because by i t s application one can obtain the higher s e n s i t i v i t y of the EPR technique as well as the higher resolution possible with the use of the NMR technique.  We shall now give a  b r i e f o u t l i n e of i t s p r i n c i p l e s and of the derivation of some formulae used l a t e r for obtaining the shfs parameters. The necessity f o r performing ENDOR experiments arises because the EPR spectrum of a paramagnetic centre in a s o l i d usually shows only the resolved hyperfine structure (HFS)  of the central  nucleus.  The  - 26 -  HFS interaction of the unpaired electron with many other nuclei of the l a t t i c e s p l i t s each of these resolved HFS lines into a large number of very c l o s e l y spaced l i n e s , which may overlap and consequently y i e l d a structureless broadening of the HFS l i n e .  It  is thus  this increased width of the HFS lines in s o l i d samples which usually l i m i t s the resolution of the EPR technique. (50b) Portis into two types:  has shown that EPR l i n e broadening can be c l a s s i f i e d homogeneous broadening and inhomogeneous broadening.  Homogeneous broadening occurs when the energy absorbed from the microwave f i e l d is d i s t r i b u t e d to a l l  spins and thermal equilibrium  is maintained in the spin system during resonance.  In the case of  inhomogeneous broadening the erergy is transferred only to those spins whose local f i e l d s s a t i s f y the resonance condition.  The v a r i a t i o n  in the local f i e l d s of d i f f e r e n t spins may correspond to variations  in  the local magnetic f i e l d s due to random orientations of neighbouring nuclei in the host c r y s t a l .  They may also be due to random strains  and e l e c t r i c f i e l d s which produce s l i g h t l y d i f f e r e n t g-values at these centres.  In either case, the set of a l l electron spins which have  the same magnetic environment constitutes a 'spin packet'.  A large  number of such ' s p i n packets' then constitute an inhomogeneously broadened EPR l i n e . It  is the case of the 'inhomogeneously broadened' EPR lines  where ENDOR can be of great help for studying the small couplings unresolved in the EPR spectra.  hyperfine  In the ENDOR experiments  one e s s e n t i a l l y measures the NMR t r a n s i t i o n frequencies of the nuclei  - 27 -  t h a t a r e coupled t o t h e unpaired e l e c t r o n .  F o r reasons o f  s e n s i t i v i t y , however, d i r e c t measurement o f the n u c l e a r resonance i s u s u a l l y n o t p o s s i b l e , and one thus employs t h e enhancement p r o p e r t i e s o f the double resonance techniques.  In t h e ENDOR  experiments one causes an i n c r e a s e o f the d i f f e r e n c e i n t h e p o p u l a t i o n o f the nuclear s p i n l e v e l s by s a t u r a t i o n o f t h e EPR t r a n s i t i o n s and then the nuclear resonance t r a n s i t i o n s a r e detected through the d e s a t u r a t i o n o f t h e EPR t r a n s i t i o n s as a r e s u l t o f t h e occurrence o f t h e nuclear resonances.  An ENDOR experiment i s thus  an NMR experiment i n which t h e e f f e c t i v e s e n s i t i v i t y i s s e v e r a l orders o f magnitude g r e a t e r than t h a t p o s s i b l e with usual NMR technique i n v o l v i n g t h e same number o f n u c l e i and i n f a v o u r a b l e cases approaches t h e s e n s i t i v i t y o f EPR. From the above c o n s i d e r a t i o n s , i t can be seen t h a t the s p i n Hamiltonian  necessary f o r d e s c r i b i n g an ENDOR experiment  may be w r i t t e n as *  Here^ p E  R  - tPR  +  2  ^ENDtm  < > 2 7  i s t h e s p i n Hamiltonian  f o r the s t r o n g l y  coupled  e l e c t r o n - n u c l e a r s p i n system ( r e s p o n s i b l e f o r the r e s o l v e d  hyperfine  s t r u c t u r e ) and has t h e form given by an operator o f t h e type represented by Eq.  <K,  (19).  E N D  Q  R  includes t h e term i n v o l v i n g the  (a)  s e t o f the nuclear s p i n s , {_I '} and has t h e form #C  ENDOR  4 =  I a=  (l 1  ( a )  . A  ( a )  •S-  g  n  a )  B H n  .I  ( a )  ).  (28)  - 28 -  We can here assume t h a t the parameters d e f i n i n g ^ are a l r e a d y known. A l s o the e i g e n v e c t o r s | c > and the E° of ^ £  P R  E P R  eigenvalues  d e f i n e d as before, by tt |e> ERR  - E||e>,  (  2  9  )  are a l s o supposed to have been found e x a c t l y (or to any s u f f i c i e n t approximation).  Note t h a t the states|£> r e f e r to the s t r o n g l y  coupled system o n l y , and d e f i n e a s e t o f hyperfine m u l t i p l e t s , l a b e l l e d by £. The s u b l e v e l s w i t h i n each m u l t i p l e t s are due to the d e s c r i b e d by ^£^ QR-  o f the s e t of n u c l e a r spins  U  energy a s s o c i a t e d with ^^QOR  1 S m u c n  presence  Since the  s m a l l e r than t h a t a s s o c i a t e d  with <^£p , ^ENDOR may be d i s c u s s e d i n a language which omits a l l R  r e f e r e n c e to the s t r o n g l y coupled system by d e f i n i n g , f o r each m u l t i p l e t 5 , an e f f e c t i v e H a m i l t o n i a n ^ , which i s an operator i n the space o f the s t a t e s o f the weakly coupled spins { 1 ^ }  only. (50a)  For the  weak c o u p l i n g assumed, a p e r t u r b a t i o n expansion i s v a l i d , thus we may  write  *  5  = E|  +-<5|*  E N D 0 R  |e>  +  g: <e VENDOR 1 ^ ' VENDOR' 6  ><G  (E° - E°J K  5  G >  +  ••••  (30)  Although, i n p r i n c i p l e , the second or the higher order terms i n Eq.(30) should be r e t a i n e d f o r o b t a i n i n g the energy l e v e l s given b y 3 ^  and  hence the ENDOR t r a n s i t i o n f r e q u e n c i e s , these terms were not found to be necessary f o r the ENDOR s p e c t r a obtained i n the present s t u d i e s . Neglecting these terms, we then simply have  - 29 -  %  = E° + I {-g 6 n  E  *  ?  a  n  H.I + <S> . ^  ( a )  .I  ( a )  }  (31)  where <S>  = <e|S|5>.  ?  (  3  2  We note therefore that the energy levels involved in the ENDOR t r a n s i t i o n s depend upon a p a r t i c u l a r multiplet £ through the spin p o l a r i s a t i o n vectors <S_>^, determined e n t i r e l y For small electron-nuclear coupling in^jrpR <S> _£ =  w  e  by^p^.  have approximately  ± h_ k, where _ k i s a unit vector in the f i e l d d i r e c t i o n and  Eq. (30) then leads to the usual f i r s t order hyperfine l e v e l s .  In  general, however, <S>^ varies both in magnitude and d i r e c t i o n from one m u l t i p l e t to another.  In the general case, because the  v a r i a t i o n in the d i r e c t i o n of the ENDOR t r a n s i t i o n s f o r a p a r t i c u l a r nucleus are expected to depend in a complicated way on (n)  all  the elements of the tensor A/ ' so that the analysis i s  complicated.  I f , however, the f i e l d i s oriented along an n-fold  symmetry axis o f ^ p R * to a l l  n  > , 2 , then <S>^ must be t o t a l l y  rotations generated by C  p  and must therefore have the  d i r e c t i o n of the symmetry a x i s , i . e . field.  symmetric  the same d i r e c t i o n as the  The d i r e c t i o n of spin p o l a r i s a t i o n i s then independent of  £, so that <  § r >  =  < S > F Jl,  (33)  the symmetry axis here being supposed to l i e in the z d i r e c t i o n . In this case at most three components of A ^ ,  namely A ^ " L  A ^ ,  )  - 30 -  A^zy  appear in  (the contribution of nucleus a to the sum  in Eq.[31]), so that these can be determined by a quadratic f i t of the ENDOR measurements.  Furthermore, i f the nucleus a has no  s i g n i f i c a n t quadrupole coupling, then only two parameters, namely A^ ( A  and [ A ^ ~\  z  U))2  zz  [ U) ] 2  =  A  z 2  (or, e q u i v a l e n t s _ (a)^2 (A  a  r  i  e  n v o  and A = ( A ^ f +  l v e d , and these can be  determined from a simple linear p l o t .  4  a)  In fact we have  \n H k.A' = -gnaVa H..Ii^ + +<S <sz>> r k.A n -— t,=•  (a  ( a )  r  h ^ (a  (34)  which has eigenvalues E  where |a|  M  = m  (a)|_ (a) g  B n  H  <S >  +  z  c  k.A|,  ( ) 35  = /aTa denotes the magnitude of a vector, so that the  (a)  Amj  '=  ±1  ENDOR frequency associated with the nucleus a,  multiplet £, and EPR t r a n s i t i o n 5 < v  ( a )  E,S  =  v(?!r) E,S  =  | - v ^ •< ^  +  = [(v  ( a )  )  2  » is  > r <S > z  - 2v  sr  ( a )  sr  r  k . A|  (36) .  <S > A ) + < S > ( A ( a  zz  5  2  z  ( a ) 2  ^  ) J 7  z z  3 5  ( 3 7 )  Since f o r most free radical cases, <S >^ % ±h, one can Z  (a) obtain the values of the principal components of the tensor A/ ' by measuring the ENDOR transitions when H is along the principal axes. If the orientation of the principal axes is only approximately known,  (a) the principal values of the components of the A/ ' tensor may be inferred from the plots of the difference of the ENDOR frequency and the NMR frequency against the angle between the crystal!ineaxes and the d i r e c t i o n of the magnetic f i e l d .  ,  - 31 -  For a more general case when the parameters of show only orthorhombic symmetry, and when the orientation of the (a)  p r i n c i p a l directions for the tensors A/ ' is not known, the expression for  the ENDOR t r a n s i t i o n frequencies becomes very complicated.  It  is then found to be essential to use computer diagonalisation  of  (^pp  +  ^E;NDOR^'  present studies.  ^  w o  c o m  P t u  programmes were employed in the  e r  The f i r s t programme, c a l l e d ENDOR, is a simple  one which assumes. <S >^ = ±% but then y i e l d s the least-squaresz  adjusted values f o r the elements of the tensor S (a)  (a)  .  The  values for the p r i n c i p a l components of A/ ' and the orientation of the p r i n c i p a l directions with respect to the crystal axes are then refined further with the use of the computer programme FIELDS, which has been described before. 2.2.3  Determination of the signs of the hyperfine tensors. One of the more interesting outcomes of the present  investigations is the development of a method to obtain the signs of the hyperfine tensors through EPR, ENDOR and double ENDOR measurements.  To explain this we note that Eq. (37) can be  written as where  yU,r) yu.n  = [A  ( a ) 2  ]  x(e,r) -  z z  (38)  = [{v(?,r)) -(v ^ ) ]/2v^l<s > , 2  )  2  r  and  (39) x(?,r) = + < S > / ( 2 v ^ l ) . z  5  Note here that the parameters  (A^ )J A  and A J ^  can be determined  - 32 -  from the slope and intercept of a plot of y ( ? , £ ' ) against x ( ? , £ ' ) , as the EPR t r a n s i t i o n s E, <—> £" are varied.  In p a r t i c u l a r the  () a  sign of A  z 2  ' and an overall sign on the EPR couplings (which affects  the resonance f i e l d  , hence the states  \K> and hence S >^) <  can both be determined for the orientation H||z.  Also, i f  Z  the  (a)'  z-directi on coincides with a principal d i r e c t i o n of A Eq. (37) becomes v uir E,£  ) ±  vA {  = ± <S>  z ?  , then from  v  (40)  A£) zz  In this case a simple comparison of ratios of the measured quantities (a) (a) F » to ratios of the calculated spin p o l a r i s a t i o n  V  1  t 5  v  s  sr  magnitudes <S >^ i s s u f f i c i e n t to determine s i g n s . Z  If the principal  (a) d i r e c t i o n of A/ ' is not exactly along the symmetry a x i s , but s t i l l quite close to i t , then Eq. (40)  can be obtained as an approximation. (a)  may be very accurate f o r multiplets for which S >^ <  Z  A  z z  and  (a)  v  v  ' have the same sign while at the same time quite  f o r those which have opposite signs.  inaccurate  The.analysis of the ENDOR  experiments on the AsO^j" centre in KH^AsO^ provides a good example f o r testing these ideas. Of course the procedure outlined above y i e l d s the sign f o r the components of the hyperfine tensors only for H||z, where the z-directi on coincides with a two (or higher) f o l d symmetry axis f o ^ f r p R '  Relative signs of the hyperfine components for other  directions can then be obtained through ENDOR measurements on a single hyperfine t r a n s i t i o n  for various magnetic f i e l d o r i e n t a t i o n s .  It  - 33 -  Additional double ENDOR measurements may be necessary f o r very weakly coupled n u c l e i .  The presently described method is believed  to be important in that i t can compliment double ENDOR-studies in favourable cases. 2.3  Motional effects in hyperfine  structure  In the theoretical discussion outlined in the previous s e c t i o n s , i t has been i m p l i c i t l y assumed that a l l  paramagnetic  resonance spectra can be analysed in terms of the perfectly sharp resonant t r a n s i t i o n s between spin energy levels which are the stationary states of a d e f i n i t e and f i x e d Hamiltonian.  This is a  very useful approach but i t is also quite u n r e a l i s t i c because every molecule interacts with i t s surroundings and these  interactions  l i m i t the l i f e times of the spin s t a t e s , broadening the energy level. lattice  In f a c t i t i s well known that an i n t e r a c t i o n , c a l l e d spini n t e r a c t i o n , between the spin system and the surrounding  l a t t i c e i s essential for the success of the paramagnetic resonance experiment.  In the present work, although we do require the  existence of favourable s p i n - l a t t i c e relaxation conditions, we w i l l not be d i r e c t l y concerned with the subject of s p i n - l a t t i c e r e l a x a t i o n . On the other hand, the presence of molecular motion in the paramagnetic system can also d r a s t i c a l l y a f f e c t the appearance of the resonance spectra expected on the basis of the ( s t a t i c ) spinHamiltonian of the form given by Eq. (19), provided that the time scale of the motion involved coincides with the time scale of the paramagnetic resonance experiment.  For the systems investigated  -  34  -  here, the anticipated time scales f o r the molecular motion are ^ 10~^° sec which thus f a l l  in the domain of the EPR techniques.  In f a c t , using as probes the effects of molecular motion on the EPR spectra, we have been able to obtain valuable information on the dynamics of the processes involved in the f e r r o e l e c t r i c t r a n s i t i o n phenomena in the Kh^PO^-type  of c r y s t a l s .  Therefore,  we w i l l now present a b r i e f account of the effects of molecular motion on EPR spectra.  The discussion is again b r i e f because i t 52-54  has already been given in detail  in several review a r t i c l e s .  The effects of motion on the paramagnetic resonance spectra may be v i s u a l i z e d as follows.  From a c l a s s i c a l point of  view, free electrons precess at about 1 0 ^ Hz in typical  laboratory  4  f i e l d s of about 10  gauss.  Motions,in the environments of the  magnetic nuclei and electrons which produce f l u c t u a t i n g magnetic f i e l d s with frequency components at the precessional frequencies of these spins, can cause spin f l i p s and, therefore, may have observable effects on t h e i r spectra.  Because of the weakness  of the i n t e r a c t i o n of the nuclei and of unpaired electrons s i m i l a r effects may also be observed for the magnetic resonance spectra in paramagnetic s o l i d s .  The precessional frequencies of  nuclear or e l e c t r o n i c magnetic moments are often time-dependent because of the fluctuations in the weak local magnetic f i e l d s . If  the fluctuations are s u f f i c i e n t l y r a p i d , only an average f i e l d w i l l  act on each spin and a single resonance w i l l r e s u l t .  On the other  hand, very slow f i e l d fluctuations w i l l allow each spin to precess  - 35 -  at a frequency c h a r a c t e r i s t i c of i t s environment so that a number of resonances may appear.  It  is emphasized that here rapid  and slow refer to a comparison of the frequency of f i e l d f l u c t u a t i o n with the differences in precessional frequencies of spins in the various local f i e l d s . even slow  Since local f i e l d differences are often small,  processes (undetectable by x-ray or neutron d i f f r a c t i o n  techniques) can have observable effects in magnetic resonance. Two basic approaches are employed to study the effects of the molecular motion on magnetic resonance spectra.  These are  55 56 the modified Bloch equation treatment  '  and the relaxation  57 treatment.  The modified Bloch equation treatment covers the f u l l  range of rates from the f u l l y averaged spectra to the spectra showing d i s t i n c t species.  However, i t is based on the assumption that the  process of molecular motion does not induce any t r a n s i t i o n between the Zeeman levels of the spins hence c a l l e d the , ' a d i a b a t i c  1  approach.  On the other hand, the relaxation matrix method is more general because by this method even the 'non a d i a b a t i c '  effects can be studied  although,for nearly a l l the spectra investigated so f a r , such effects are considered insignificant.  The relaxation matrix method is  applicable only in the f a s t rate region i . e . , averaged spectra are observed.  in the region where  A l s o , i t turns out that because  of the complexities in the c a l c u l a t i o n s , at the present state the density matrix method is useful  only for obtaining  qualitative  information on the molecular motion a f f e c t i n g the spectra.  It  been further shown that in the f a s t rate region both, the relaxation matrix method and the modified Bloch method,yield the  has  - 36 -  same r e s u l t s .  Since we were interested in obtaining quantitative  information on both the slow and the f a s t exchange rates, we  used  the modified Bloch equation treatment f o r the present investigations. Consider f i r s t the normal (unmodified) Bloch equations. These are a phenomenological  set of d i f f e r e n t i a l  equations  describing the relaxation of the bulk magnetisation  M.  Referred to a set of axes rotating about the Z-axis at an angular -co, these equations are  frequency of  * %  • v_  +  ( „) v  v  H- - ( „ „ - . ) u - 0  +  (41)  . o.  '(«)  dM _ | where T-| and T  2  +  M|zMo  .  Y  H  I  V  =  0  (43)  are respectively the spin l a t t i c e and the spin-spin  relaxation times.  Defining now  the complex transverse magnetisation  as G = u + iv ,  a quantity a =-y-  (44)  - i (to - c o ) , and f o r the case of no saturation,  Eqns. (41) and (42) can be written as ^ | + aG = -iyh^M. Now  suppose that several s i t e s e x i s t between which the  system can coexist.  (45) paramagnetic  If the rate of conversion of one s i t e into  another i s very slow, then f o r each form an equation s i m i l a r to Eq. (45) can be w r i t t e n / that i s  - 37 -  N  d G  "dt Here  N N "WoN  A  +  G  =  ( 4 6 )  = T ^ - i('u^-«.)» e t c . , where <^ is the resonance frequency 2  f o r the s i t e N.  However, as the rate of exchange of the radical  between the d i f f e r e n t s i t e s becomes comparable to the frequency differences between l i n e s , Eq. (46) is not adequate.  The  modification was made f i r s t by Gutowsky, McCall and S l i c h t e r and l a t e r treated in more detail by the Gutowsky group 55 56 others  '  .  59  CO  and by  It has been shown that i f the exchange is f i r s t  order, then the modified Bloch equations f o r a system with N d i f f e r e n t s i t e s are dG  w  "df SHere k X  NN  A  +  =— ,  T  G  " WON J +  =  N  ( k  x x " G  W  .  <> 4 7  being the mean l i f e time of the s i t e x.  X  X  A  The total complex magnetisation G is given by G = £ G •N  M  IN  and the imagninary part of G then gives the absorption l i n e shape. Miyagawa and I t o h ^ have shown that f o r an N-site system, where a l l interconversions are equally probable, the general solution of G_ may be written as  G ~  G  by  ° sl s  lYHlM T  5  N  f  -  1  S  (48)  NO-I f ) s  s=l x ) " . f = (N + a where x is the mean l i f e f o r a given radical s i t e and f s  s  1  (49) i s defined  - 38 -  Eqns. (47) and (48) are d i r e c t l y applicable for N=2 or N=3.  Computer programmes based on Eqns. (47) and (48) are a v a i l -  a b l e , and a modified version of such a computer programme was supplied to the author by Mr. David Kennedy of the Chemistry Department, U.B.C.  The d e t a i l s of the programme w i l l be described  in the Ph.D. thesis of Mr. Kennedy.  Here i t appears enough to  state that the input data of the programme are the l i n e separations (to-co ), the estimated relaxation time T 0  2  and the l i f e time x.  The output of the programme goes to a p l o t t i n g sub-routine, supplied by Mr. John T a i t , also of the Chemistry Department, U.B.C. the p r i n t out is a simulated EPR spectrum.  Thus  By comparing these  simulated spectra with the experimental spectra the l i f e t i m e of the various s i t e s at d i f f e r e n t temperatures have been computed. Further d e t a i l s of the f i t t i n g procedure and the information obtained w i l l be presented i n Chapter 2.4  IV.  Interpretation of the spin Hamiltonian parameters The spin Hamiltonian parameters which are of s i g n i f i c a n c e  f o r the present studies are the tensor g , A. and possibly Q.  The  i n t e r p r e t a t i o n for tensor g can be obtained with the help of Eq.  (7).  In the absence of the nuclear magnetism, and the small diamagnetic e f f e c t s , the operator representing the magnetic moment is obtained by d i f f e r e n t i a t i n g the Hamiltonian with respect to the magnetic f i e l d , i.e.  U - - U  •  6  j.S  Hence, the quantity 8cj.S_ represents f a i r l y accurately the electronic magnetic moment operator and i s , therefore, of great physical  interest.  - 39 -  The strong hyperfine tensor £ is s i m i l a r l y of great interest.  By examining Eqns. (11-17), i t can be seen that the  i s o t r o p i c p a r t , a, of the hyperfine tensor density of the unpaired electron  |^(r. )| A  a  s p e c i f i e s the t  t  n  e  nucleus A.  Also,  the anisotropic parts show the symnetry of the centre and give further quantitative  information about the wavefunction since they  are weighted means of the type 3 C  °'3 " 6  1  I » (r)l dx,  (50)  2  where 9 is the angle with respect to a principal axis of the hyperfine i n t e r a c t i o n . The weaker, superhyperfine interactions of the unpaired e l e c t r o n , studied through ENDOR, provide the same information as obtained through the determination of the tensor A. representing the stronger hyperfine i n t e r a c t i o n s .  ENDOR can also resolve  quadrupole interactions and in that case one can obtain information about the gradient of the e l e c t r i c f i e l d as determined by the d i s t r i b u t i o n of a l l  nuclei and electrons in the c r y s t a l .  - 40 -  CHAPTER THREE EXPERIMENTAL DETAILS 3.1  Preparation  and C r y s t a l  Structure  The s i n g l e c r y s t a l s all  grown by s l o w l y  t h e s e compounds.  o f the A r s e n a t e s and Phosphates.  o f KDP, KDA, ADA and mixed KDP-KDA were  evaporating  the s a t u r a t e d aqueous s o l u t i o n s of  C h e m i c a l l y pure KDA and KDP were s u p p l i e d by Merck  and ADA was o b t a i n e d from A l f a  Inorganics.  The c r y s t a l s  were  t r a n s p a r e n t and p r i s m a t i c i n shape as d e s c r i b e d byWycko f f a n d G r o t h . 6  Deuterated  KDP, KDA, and mixed KDP-KDA were o b t a i n e d by d i s s o l v i n g  the  undeuterated compounds i n D2O, r e f l u x i n g f o r about two days and r e p e a t i n g the p r o c e s s twice b e f o r e growing the c r y s t a l s . d e u t e r a t e d compounds had growth h a b i t s u n d e u t e r a t e d ones. Professor B l i n c ,  Crystals  s i m i l a r to those o f  One DKDA s i n g l e c r y s t a l  and t h i s was used i n the  the  was k i n d l y s u p p l i e d by  initial  experiments.  from  - .41 -  X-ray '  and neutron d i f f r a c t i o n  experiments have shown  that in t h e i r high temperature p a r a e l e c t r i c phase these c r y s t a l s belong to the tetragonal  (142d) space group with four molecules per unit c e l l .  The structure is most e a s i l y pictured as b u i l t up from K (or NH ) 4  and X0 (X=P or As) groups. 4  units  Each of the XO^ groups consists of the  X(P or As) atom surrounded by four O's at the corners of a tetrahedron which is nearly but not exactly regular, being compressed by about 2% along the tetrad a x i s .  Each of the XO^ groups is hydrogen-bonded to  the four neighboring X0 u n i t s . 4  The time average position of each  hydrogen atom is located symmetrically between the upper oxygen of one X0  4  tetrahedron and a lower oxygen of a neighboring one, these  two tetrahedra being related to each other by a rotation of approximately 32° about the tetragonal c-axis of the c r y s t a l .  A schematic  diagram of the unit c e l l as determined by West, is given in F i g . 2. In t h e i r low temperature phase these crystals may be c l a s s i f i e d in two categories: without NH . 4  those containing NH^ i o n , and those  We w i l l f i r s t consider the structure of KDP, DKDP, KDA  and DKDA, which thus belong to the second category. The low temperature form of these crystals is orthorhombic, space group Fdd2.  In this form the 4-fold axis in the c-direction  disappears and the two other orthorhombic axes, X and Y, appear at 45° from the tetragonal a and b axes, respectively.  However, the X  and the Y directions are d e f i n i t e only in single domain c r y s t a l s because the presence of a domain structure results in a random interchange of the X and the Y d i r e c t i o n s .  A l s o , as a r e s u l t of the o  phase t r a n s i t i o n , the K and the P (or As) atoms move, each about 0.05 A,  - 42-  Fig.  2  Structure of K H A s 0 2  4  (or  c r y s t a l s , a f t e r J . West?  KH P0 )-type 2  4  - 43 -  towards each other.  The hydrogens are found to be arranged in such a  way that in a given domain, for example, they are a l l Oxygens or a l l  near 'lower'  Oxygens.  near 'upper'  A schematic diagram showing  the displacements of the various atoms is given in F i g . 3(a), c-axis projection of the crystal  and a  structure showing the positions of  the H's in the f e r r o e l e c t r i c phase is depicted in F i g .  3(b).  For the case of the ammonium s a l t , ADA, the t r a n s i t i o n takes place to an a n t i f e r r o e l e c t r i c phase and the crystals shatter during the transition.  The low-temperature structure of this crystal  is also  orthorhombic but i s quite d i f f e r e n t from those of the c r y s t a l s belonging to the second category, in that for the former case the axes do not coincide with the base diagonals of the (small) tetragonal c e l l do the c r y s t a l s of the KDP-type), but along the side.  (as  In the tetragonal  (high temperature) structure there are axes of symmetry along the c e l l side and along the c e l l diagonals forming two independent sets.  The  low temperature structure of the ammonium compounds retains the f i r s t set whereas the structures of the c r y s t a l s in the second category retain the second set.  The space group of the ammonium compounds is P2^2^2^;  and there are four formula-units per c e l l . unit c e l l  is given i n F i g . 3(c).  A c-axis projection of the  It w i l l be noticed that here, for a  given domain, one hydrogen is near an 'upper' and the other near a 'lower'  oxygen of the AsO^ group.  In the v e r t i c a l d i r e c t i o n as well  as in the plane of the diagram every component of each vector representing an interatomic distance or displacement is balanced by an equal component in the opposite d i r e c t i o n .  This is a consequence of  the space group and does not depend upon a detailed knowledge of the  - 44 -  3(a)  Displacement of atoms in KH^AsO^-type c r y s t a l s at T  c  (b) c-axis projection, of crystal structure of Kh^AsO and (c)  of N H ^ A s C ^ below T  - 45 -  individual coordinates of the atoms.  It means that these  crystals  cannot possess spontaneous p o l a r i z a t i o n ; this is in agreement with experimental observations.  It must be mentioned that a structure  possessing this symmetry was indeed predicted by.Nagamiya the crystal  , before  structure was determined by the x-ray d i f f r a c t i o n  techniques. 3.2  The Irradiation Units The crystals were i r r a d i a t e d with a Mach'lett, type OEG-60  50 KV, 20mA X-ray tube or a ^Co  Y-ray source for several  room temperature and also at 77°K.  hours at  Most of the measurements described  in the present work, were made on crystals  i r r a d i a t e d by x-rays at  room temperature since no new features were noticed by using crystals i r r a d i a t e d at 77°K or by using the Y-irradiated 3.3 3.3.1  crystals.  The EPR Spectrometers The X-band Spectrometers For preliminary examination of the EPR spectra at X-band  (^9.3 GH ), the Varian E-3 spectrometer proved to be the most convenient. 2  More accurate measurements were made on a home-made EPR spectrometer, 54 c a l l e d ESR-1 in the group and described more f u l l y elsewhere  .  It  is  a modified version of the Varian V-4502 spectrometer, using 100 KHz magnetic f i e l d modulation and a 12", rotatable Varian electromagnet having a VFR 2501 F i e l d i a l Mk.II. measured with a Hewlett-Packard  The microwave frequency was  5246L frequency counter, using a  5256A Plug-in. u n i t , and the magnetic f i e l d was c a l i b r a t e d with a Magnion N.M.R. probe and a magnetometer constructed by the Group, Department of Chemistry, U. B. C.  Electronics  - 46 -  The variable temperature experiments were performed using the E-3 or the ESR-1 spectrometer, in conjunction with a Varian Variable Temperature unit. from about 350° to 77°K.  The measurements were made over the range The s t a b i l i t y of the temperature bath is  about I h° , and the temperatures were measured with a copper-constantan thermocouple. 3.3.2  The K-band Spectrometer With a view to having an aid in the i d e n t i f i c a t i o n of the  many overlapping EPR signals due to the several r a d i c a l s obtained in the i r r a d i a t e d c r y s t a l s , some EPR measurements were made with a spectrometer operating at a frequency of about 24 GHz.  This spectrometer  uses the same electronics and the magnetic f i e l d accessories as the ESR-1.  The cavity used is a Magnion model C-TC-10-UVK, locked  e l e c t r o n i c a l l y to the frequency of the Klystron, Varian type EM-1138. 3.4  ENDOR Spectrometer The ENDOR spectrometer used in these experiments has been  b u i l t around an x-band EPR spectrometer u t i l i s i n g the single sideband superheterodyne p r i n c i p l e with an intermediate frequency of 30MHz. F i g . 4 shows a block diagram of the set up. with a Hewlett-Packard power.  A Varian V-153C klystron  716B power supply is the source of microwave  The kystron frequency is s t a b i l i s e d by phase locking to the  harmonic of a thermally controlled crystal o s c i l l a t o r by the use of a synchroniser, LFE model 244. to 2 parts in 10  7  The klystron frequency was thus controlled  (over half hour periods).  A provision was  available  in this synchronizer to continuously vary the s t a b i l i s e d microwave  -  47 -  KYLSTRON  KYLSTRON  POWER SUPPLY  ISOLATOR  20d B DIRECTIONAL COUPLER  SYNCHRONISER  ATTENUATOR  PRECISION ATTENUATOR  MATCHED  LOAD  TOTTO  MAGIC TEE  MICROWAVE SWITCH  BALANCED MIXER  ISOLATOR  MIXER  N  FIELDIAL M A R K JL t  SCANNING UNIT  PHASE SHIFTER  ISOLATOR  »1Hz  30r  A M P L IFIER RF  D E T E CTOR  TO  and  MHz. MULTIPLIER, AMPLIFIER  FILTER CAVITY  CRO  MANET POWER SUPPLY  30  ISOLATOR  DETECTOR  S A M P L E CAVITY  5 MHz  MOD COILS  LOW P A S S FILTERS R F AMPLIFIERS  t  AUDIO P O W E R AMPLIFIER  RF SIGNAL GENERATOR  AUDIO AMPLIFIER  FREQUENCY COUNTER  DIGITAL — A N A L O G CONVERTER  Fig. 4  L O C K IN SYSTEM  X,Y  RECORDER  i  Block diagram o f the ENDOR spectrometer.  - 48 -  frequency within small l i m i t s , once a p a r t i c u l a r crystal s e l e c t e d , by p u l l i n g the frequency of the c r y s t a l .  harmonic was  This was found very  useful as no provision for variation of the sample cavity  frequency  was necessary in the spectrometer. A portion of the microwave power was coupled out of the main waveguide run by a 20db coupler and fed into a balanced modulator for the generation of sidebands.  Varactor diodes type IN460A manufactured  by Microwave Associates were used for this and they were driven by 10mA of current each at 30MHz, which was obtained f o r convenience by m u l t i plying a 5MHz output available from the synchronizer, and amplifying suitably.  The balanced modulator was tuned such that the output power  at O o , the c a r r i e r frequency, was minimum, and that in the two sidebands at ( u o t 30)MHz were maximum. Q transmission cavity  By passing t h i s output through a high  (Model 585-BS2 of PRD Electronics  I n c . ) , one s i d e -  band alone (in our case, ( u o + 30)MHz) i s selected and used as local o s c i l l a t o r for the superheterodyne detection at the balanced detector using two IN23G diodes. The main branch of microwave power at the c a r r i e r frequency is led through a series of attenuators to the cavity through a magic T bridge.  The cavity i s a rectangular one operating in a T E ^ ^  The crystal  could be mounted at the position of the maximum microwave  magnetic f i e l d either on the end plate or the narrow v e r t i c a l the cavity.  mode.  side of  The r e f l e c t e d power from the cavity was led through the  t h i r d arm of the magic T to the balanced detector, mentioned e a r l i e r . A microwave switch is also included in this arm for convenience of displaying the cavity frequency on an o s c i l l o s c o p e .  - 49 -  The detected i . f . model IF31BP I.F. width of 8-MHz.  at 30MHz was f i r s t amplified by a LEL  amplifier which had a gain of 450 with a 3db bandThe output after detection by a IN34 crystal  is  processed by a lock-in a m p l i f i e r , PAR model 121, which could be set to operate at any frequency between 1.5Hz and 150KHz.  The output of  the lock-in is recorded either on an x-y recorder or a s t r i p  chart  recorder. The Zeeman magnetic f i e l d was provided by a Varian 9" pole face rotatable electromagnet with a Mark II supply.  Fieldial  system power  A signal proportional to the magnetic f i e l d was  available  from the power supply to drive the x axis of the x-y recorder. Magnetic f i e l d modulation at a variable audio frequency was produced by means of modulation c o i l s wound on the magnet polepieces. The modulation c o i l s were driven from the reference frequency output of the PAR lock-in a f t e r suitable power a m p l i f i c a t i o n .  The f a c i l i t y  of a variable modulation frequency was found essential to obtain optimum EPR and ENDOR signal i n t e n s i t i e s at low temperatures. For work at 4 . 2 ° K , a glass double dewar system with l i q u i d nitrogen in the outer and l i q u i d helium in the inner dewar was employed.  The entire cavity dipped in l i q u i d helium but care was  taken to prevent i t from entering the  cavity.  For ENDOR work a second radio frequency was introduced at the sample s i t e by means of a single loop of wire located in the plane of the microwave magnetic f i e l d and surrounding the sample inside the c a v i t y . for the c o i l .  High f i e l d superconducting Nb-Zr wire was used  The r . f .  source is a Marconi signal generator 1066B,  - 50 -  which has a frequency range 10MHz to 480MHz which can be frequency modulated by an external audio signal to a depth of 5 to lOOKHz.  In  the range 0.5 to 10MHz, a G.R. model 1001A o s c i l l a t o r which had been modified for f.m. was used.  The signal output of the generator is  f i r s t amplified successively by two wideband amplifiers type 460AR and 460BR, and then by a IFI  Hewlett-Packard,  model 5000, d i s t r i b u t e d  a m p l i f i e r which could d e l i v e r a maximum power of 30W into 50 ohms. The amplified output was led through a set of r.f.  low pass  filters  in which the c u t o f f frequency could be suitably selected to suppress harmonics generated by the amplifier system, to the ENDOR loop in the cavity  by means of a coaxial cable.  The coaxial cable connection was  kept as short as practicable and no serious attempt was made to match the loop to the amplifier over the entire range of frequencies used in these i n v e s t i g a t i o n s , i . e . ,  1 to 30MHz.  The r.f.  current in the  ENDOR loop was found to vary with change of frequency, but not very r a p i d l y and this was not found to be troublesome when f.m. detection was used for ENDOR, as described in detail r.f.  in the next section.  frequency is monitored by a Hewlett-Packard  The  5246L counter and  i t s d i g i t a l output after analog conversion by Hewlett-Packard  type  580A, drives the x-axis of an x-y recorder for display of ENDOR s i g n a l s . 3.5  ENDOR Technique The method used by us to observe ENDOR is the  ENDOR technique in the absorption mode.  stationary  ENDOR lines have been observed  and recorded at 4.2°K in KH As0 crystals in the ac, be, and ab planes 2  4  (the axes refer to the tetragonal system), and on several tions.  EPR t r a n s i -  F i r s t the crystal was mounted accurately with the required  - 51 -  plane h o r i z o n t a l .  Then, the EPR spectrum was recorded and a p a r t i c u l a r  l i n e selected for ENDOR study.  The microwave power level  for maximum  EPR signal was determined and the EPR t r a n s i t i o n was p a r t i a l l y  satura-  ted by increasing the microwave power by 3db' or so above this  (see F i g .  5).  The magnetic f i e l d was then set precisely at the center of the  derivative  EPR l i n e and the magnetic f i e l d modulation switched o f f .  With the lock-in amplifier gain increased about hundred f o l d and the time constant increased to 10 seconds, the r . f . through the loop was switched on.  The r . f .  current (^5 watts)  was swept by driving the  tuning shaft of the signal generator by a slow reversible synchronous motor, such that the sweep rate was not faster than lOOKHz per minute in any frequency band.  The frequency modulation used on the r.f.  was  at an audio frequency rate (usually 41Hz), and the depth of modulation which depended on ENDOR linewidth was usually between 40KHz and lOOKHz.  ENDOR signals recorded in this manner gave signal to noise  ratios which in most cases were better than 5 to 1, and in some cases as good as 60 to 1.  However, in certain directions the signal to  noise ratios were quite poor and highest possible r.f.  powers and  careful adjustment of the magnetic f i e l d to the exact centre of the EPR t r a n s i t i o n was necessary to record the s i g n a l .  A careful study of  the ENDOR i n t e n s i t y has,however, not been made. Once the ENDOR lines for a p a r t i c u l a r EPR l i n e for a given orientation in the s p e c i f i e d plane were a l l  located and recorded on  the x-y recorder, the accurate measurement was made as follows.  The  f.m. was switched o f f and the signal generator frequency manually adjusted to the center of each recorder ENDOR l i n e as monitored by  Fig. 5  Schematic p l o t of ENDOR s i g n a l i n t e n s i t y as a f u n c t i o n of the microwave power.  applied  - 53f -  the x-y r e c o r d e r , and then the s t a t i c frequency was read o f f from the frequency counter. 3.6  The Arrangement f o r Double ENDOR The experimental arrangement used f o r performing the Double 65  ENDOR experiments i s s i m i l a r t o t h a t d e s c r i b e d by Cook and Whiffen  .  I t i s based on t h e X-band ENDOR spectrometer d e s c r i b e d i n the previous s e c t i o n , 3.4. A schematic diagram o f the experimental setup i s g i v e n i n F i g . 6. Here both o f the s i g n a l generators (the Marconi-type 1066B and the General Radio-type 1001 A), a r e used s i m u l t a n e o u s l y . The procedure we used i s f i r s t t o s e l e c t the microwave power, the magnetic f i e l d and the frequency o f one o f the o s c i l l a t o r s t o correspond t o the optimum c o n d i t i o n s f o r a normal ENDOR experiment.  Keeping these  c o n d i t i o n s f i x e d , the second, unmodulated o s c i l l a t o r i s then swept such t h a t i t s frequency corresponds t o one o f t h e ENDOR t r a n s i t i o n s due to another nucleus.  I f t h e i n t e n s i t y o f the f i r s t ENDOR t r a n s i t i o n  i n c r e a s e s as a r e s u l t o f t h e simultaneous s a t u r a t i o n o f the second ENDOR t r a n s i t i o n then these two ENDOR t r a n s i t i o n s w i l l belong t o d i f f e r e n t subsets o f the e l e c t r o n i c Zeeman l e v e l s , and hence t h e double ENDOR s i g n a l can be r e l a t e d t o the r e l a t i v e sign o f the hyperf i n e c o u p l i n g s g i v i n g r i s e t o these two s i m u l t a n e o u s l y s a t u r a t e d ENDOR transitions.  The p o s s i b i l i t y o f any spurious r . f . pickup was  minimised by i n c o r p o r a t i n g a low pass f i l t e r i n the r . f . system.  The  same experimental s e t was a l s o used f o r t e s t i n g the f e a s i b i l i t y o f performing E l e c t r o n - N u c l e a r Triple-Resonance experiments, to be d e s c r i b e d i n Appendix A o f the p r e s e n t work.  41 c / s Oscillator  General Radio signal generator  H-P counter  3  Marconi signal generator Wide b a n d amplifiers  jx X - band Superheterodyne E.S.R. s p e c t r o m e t e r  I 5 0 f i line  Fig. 6  41 c / s phase detector  Sample cavity Hall Probe  Block diagram of the Double ENDOR and Electron-Nuclear T r i p l e Resonance experiments.  XY Recorder  Fieldial Mark H  in  - 55 -  CHAPTER FOUR EXPERIMENTAL RESULTS AND DISCUSSION  The present chapter contains the results and discussion of the EPR and ENDOR investigations on x and "r-irradiated KDA and KDP-KDA (mixed) c r y s t a l s and of the EPR investigations on DKDA, ADA and RbDA. The observed EPR spectra are in general quite complex since they a r i s e due to the simultaneous presence of several paramagnetic centres formed during the i r r a d i a t i o n process.  Some of these centres can,  however, be s e l e c t i v e l y destroyed through careful annealing of the i r r a d i a t e d samples, thus rendering the spectra easier to i n t e r p r e t . 4A l l these centres except AsO^ have been t e n t a t i v e l y  interpreted to  form as a r e s u l t of the rupture of either one or more hydrogen bonds or some OH groups.  4On the other hand, the AsO, centre, i d e n t i f i e d by  - 56 -  Hampton et a l .  , is formed following the capture of an extra electron  3_ by an AsO^ ion and thus no appreciable change is found to accompany /lithe formation of this centre. The AsO^ centre thus appeared to be  the most suitable for investigating the structural properties of the KDA-type of c r y s t a l s .  The present investigations thus deal mainly  with the investigations of this centre and we now begin with the description of the EPR studies.  4.1  4EPR studies of AsO^j centre At the time the present studies were taken up (1967),  35 Hampton et a l . had shown that the main paramagnetic species formed 4-  during the x - i r r a d i a t i o n of KDA single crystals was the AsO^  centre. 4-  B r i e f l y , the i d e n t i f i c a t i o n of the paramagnetic species as an AsO^ centre is based on the following observations.  The gross features  in the EPR*spectrum of this centre can be analysed in terms of a strong hyperfine interaction of an unpaired electron with a single nucleus possessing a spin I=-|, indicating that the paramagnetic centre contains an arsenic atom.  Detailed analysis of the spectra for the  various orientations of the crystal with respect to the external magnetic f i e l d leads to a nearly i s o t r o p i c but s i g n i f i c a n t l y 4-  symmetric hyperfine tensor, as expected for an AsO^  axially  centre.  Semi empirical LCAO molecular o r b i t a l calculations were then performed 4for the AsO^  radical with symmetry D j trapped in KDA. 2c  The  calculations showed that the odd electron enters a molecular o r b i t a l with A-|-symmetry.  The i s o t r o p i c part of the hyperfine  interaction  tensor was calculated from this theory to be ^2100 MHz which was  - 57 -  considered as a reasonable value when compared with the experimental value of 3038.6 MHz.  On the other hand, the calculated value (^lMHz)  of the anisotropic part of the hyperfine tensor was found to be much too small in comparison with the experimental value, ^2i5MHz, of the anisotropic component along the d i r e c t i o n of the crystal  c-axis.  This  difference was believed to a r i s e , l a r g e l y , due to the neglect of the spin-polarization effects of the B and E-type o r b i t a l s . At this stage i t may be noted, as pointed out by Hampton et 35 -al,  that the observed gross features in the hyperfine structure could  be equally well explained on the basis that this paramagnetic centre is As02» rotating about the c r y s t a l l i n e c-axis.  However, superhyperfine  75 structure was observed on each As  l i n e which was s p l i t into a quintet  with the components having the i n t e n s i t y r a t i o of 1:4:6:4:1.  The  superhyperfine structure was attributed to the interaction of the unapired electron with the four protons in the hydrogen bonds surrounding an AsO^ group.  Thus the detection of the superhyperfine strucutre  was offered as a strong basis for suggesting that the paramagnetic 4-  system was held r i g i d l y in the l a t t i c e and hence for favoring the AsO^ 14  against the AsO^ centre.  Subsequent work of Blinc et a l .  on KDA and  also on DKDA confirmed that the superhyperfine structure arises indeed due to the hydrogen-bond protons.  In a d d i t i o n , they also carried out  detailed investigations on the temperature dependence of the proton and deuteron superhyperfine structure in KDA and DKDA respectively. It was observed that below about 220°K, the quintet pattern of the proton superhyperfine structure changed to a t r i p l e t whose components show the i n t e n s i t y pattern of 1:2:1, c h a r a c t e r i s t i c cf  - 58 -  that due to the hyperfine interaction  from  two equivalent protons.  No change in the spectra was observed at the Curie point (97°K) and the spectra were found to be the same even at 4.2°K. shows that whereas at higher temperatures a l l  .This observation  the four hydrogen-protons  contribute equally to the superhyperfine structure, below 220°K only two of them dominate the superhyperfine i n t e r a c t i o n . These results are explained in terms of the dynamic orderg disorder model proposed e a r l i e r by Blinc  himself.  As was mentioned  in chapter 1, this model is based on the assumption that in the paraelectric phase, the hydrogens move between the two equilibrium s i t e s in the hydrogen bonds.  In the f e r r o e l e c t r i c phase, however,  they get l o c a l i s e d in one of the two available sites in such a way that only two of them, c a l l e d ' c l o s e ' protons, are nearer to any given As0  4  group.  The other two protons of the hydrogen bonds get  l o c a l i s e d in the equilibrium s i t e s which are farther away with respect to the oxygens of this As0 protons.  4  group and hence they are c a l l e d the  'far'  The EPR results were explained by assuming that the super-  hyperfine i n t e r a c t i o n is i s o t r o p i c and that the coupling constant for the ' c l o s e ' protons, a ^ for the ' f a r '  protons, a ^  , was. ffc29MHz whereas the coupling constant was taken to be zero.  A l s o , for a given  AsO^ group, the l i f e time T of a given protonic configuration (called a Slater c o n f i g u r a t i o n ) , is related to the frequency v of proton exchanges between the d i f f e r e n t sites around a given AsO^ group, through the r e l a t i o n v=j.  If  now v>| close - far|^29Mz, the a  a  effective  superhyperfine coupling constant w i l l be that due to the time average 'of a , and a . , i.e. 14.5 MHz. In this case the unpaired electron c tar  1.  - 59 -  w i l l show equal coupling with a l l  the four protons surrounding an  4AsO^  centre.  The r e s u l t i n g superhyperfine structure w i l l be a q u i n t e t ,  as observed experimentally. lower than | close hyperfine f i e l d s .  However, when the exchange frequency is  f a r | , the electron w i l l  Since a is^29MHz and a cl  f f l r  'see'  the instantaneous  £ 0, only two protons  now contribute to the superhyperfine s t r u c t u r e , which w i l l be a 1:2:1  therefore  t r i p l e t with a coupling constant £ 29MHz, as observed  experimentally below 220°K.  No change in the spectrum can occur at  the Curie point since on the EPR scale the motion is already in'.  'frozen  Using modified Bloch equations (introduced in chapter II),  Blinc  14 et a l .  could obtain the proton exchange frequencies over a range  from about 230°K to 210°K and concluded that the exchange frequencies v=— could be f i t t e d to the expression T=T T  E  / k T with E=0.2 eV and to=4cm  Oc  4-  A s i m i l a r exchange between deuterons around an AsO^ was also observed in y-irradiated  DKDA.  centre  At room temperature, a barely  resolved nine l i n e deuteron superhyperfine structure  indicating  ^->>| close - f a r | was observed, which appeared to change over to a a  a  quintet at lower temperatures.  No r e l i a b l e detailed studies could be  made here because of the lack of resolution in the EPR spectra. For l a t e r discussion i t should be noted here that from these observations, Blinc et a l l  4  have concluded that the  t r a n s i t i o n in KDP-type of c r y s t a l s order-disorder model.  ferroelectric  is best described by the dynamic  In p a r t i c u l a r , these results were interpreted  as evidence against the existence of a ' f e r r o e l e c t r i c mode  1  proton displacements in this class of c r y s t a l s .  involving  Similar conclusions  have been drawn l a t e r for the proton dynamics in mixed KDP-KDA  - 60 -  ferroelectric crystals^ ^) 4  a  s  w  e  n  a  s  -j ADA-type of n  antiferroelectric  + i 14(c)  crystals  v  4The present investigations of the AsO^ the observation that a l l  centre started with  the previous workers had assumed that the  proton superhyperfine i n t e r a c t i o n is largely i s o t r o p i c and, in p a r t i c u l a r , that the ' f a r ' electron.  protons show no coupling with the unpaired  On the other hand, the previous studies indicated that  the  4hyperfine e f f e c t s in the EPR of the As0  centre may provide very  4  s i g n i f i c a n t information on hydrogen bonding and f e r r o e l e c t r i c i t y Kh^PO^-type c r y s t a l s .  in the  A systematic EPR and ENDOR investigation of  4the AsO^  centre in these compounds was therefore undertaken. Fig. 7, 8 and 9 show typical  KDA for H||c.  EPR spectra of x-irradiated  The spectra shown in F i g . 7 and 8 were recorded at  X-band (^9.456GHz) at 300 and 4.2°K r e s p e c t i v e l y , whereas F i g . 9 represents a spectrum observed at 300°K at K-band (24.15GHz).  As  mentioned e a r l i e r these spectra contain lines due to four other centres  (discussed b r i e f l y in Appendix B ) ,  in addition to EPR  4due to the As0 centre, indicated by v e r t i c a l 4  lines  arrows at the top of 4-  the spectra.  The EPR lines belonging to the AsO^  are quite  distinct  because they are the only ones that show proton superhyperfine structure.  Note that the superhyperfine structure pattern is quintet  at 300°K but t r i p l e t at 77°K.  Moreover at 4.2°K some of the r a d i c a l s  do not appear, presumably because of longer electron-spin relaxation, times associated with them.  lattice  Also note that in F i g . 8 the  normally forbidden (Amp=0) lines also appear because for that case the microwave f i e l d had a component along the magnetic f i e l d H.  AsQa PO  2_  L i  250  G  3300G  Fig. 7  EPR o f x - i r r a d i a t e d Kh^AsO, f o r H||c a t X-band (9.45 GHz), T= 300°K. See text f o r l a b e l i n g o f the s p e c t r a l l i n e s .  Fig. 8  EPR o f i r r a d i a t e d KH As0 , H||c, a t X-band (9.448 GHzl and 4.2°K. See t e x t f o r l a b e l l i n g o f the t r a n s i t i o n s . 2  4  AsCf  6700 i  r  7200  7700  8 210 0  8 7r 00  9 2 i0 0  9 7r0 0  «-H ( G A U S S ) Fig. 9  EPR of KH As0 at K-band (24.150 HGz), H||c, T=300°K. 2  4  10,200  10,700  - 64 .  Although the hyperfine structure in the room temperature EPR 435 spectrum of AsO^ in KDA had been analysed by Hampton et al . , we have reinvestigated i t by u t i l i s i n g measurements also on the three normally forbidden Amp=0 l i n e s , shown by T^,  and Tg in F i g . 1.  Moreover in our analysis we have also included the nuclear Zeeman term which had been omitted in the e a r l i e r studies.  The parameters  35 given by Hampton et a l .  predicted l i n e positions to within 4 Gauss  with the i n c l u s i o n of the nuclear Zeeman term.  It  is suspected  that the addition of a small quadrupole term may improve the  fit,  but t h i s has not been t r i e d yet. 4Typical room temperature EPR spectra of the AsO^ in x-irradiated DKDA, RbDA and ADA in Figs. 10, 11 and 12.  centre  for H||c are shown respectively  The spin Hamiltonian parameters for these  c r y s t a l s and those for KDA are given in Table 1. An interesting aspect of the present room temperature EPR studies is the observation of a rapid change in the proton superhyperfine structure as the orientation is changed from that of H||c. F i g . 13(a) and (b)  show a comparison of the superhyperfine pattern on  the lowest f i e l d A s Hie r e s p e c t i v e l y .  7 5  hyperfine l i n e , for the orientations H||c and  F i g . 13(c) and ( c )  show the proton structure on  75  the highest f i e l d As F i g . 13(a)  l i n e for H i e  It w i l l be noted that whereas  is a p a r t i a l l y resolved quintet  with the component  i n t e n s i t y r a t i o 1 : 4 : 6 : 4 : 1 , the H|| c-axis patterns, F i g . 13(b) and 13(c) are respectively a s i n g l e t and a p a r t i a l l y resolved t r i p l e t with 1:2:1  as the r a t i o f o r the i n t e n s i t i e s of the components. The 35  quintet feature was observed f i r s t by Hampton et a l .  who also  AsO'  4-  J cn on  24  2.9  3.4  3.9  4.4  4.9  -H(KGauss)  F i g . 10  EPR o f x - i r r a d i a t e d KD As0 f o r H||c a t X-band (9.450 GHz) and 300°K. 2  4  1.4 1.9 F i g . 11  2.4  EPR of x-irradiated  2.9  3.4  H(KGauss)  3.9  4.4  4.9  RbH As0 at X-band, (9.435 GHz) for H||c and at ^300°K. 2  4  - 68 -  TABLE 1 4Spin Hamiltonian  parameters for AsO^  centre at 296°K.  £, m and n  refer to the crystal a, b and c system.  Direction Cosines Crystal  g  KDA (Ref.35)  z  X  m  0.000  0.000  II  H  3253.5+4 MHz  -  -  -  n  1.000 0.000  II  II  II  2.0046+.0008 z A = 3253.2+0.2 MHz  0.000  0.000  1.000  2.0000+0.0.0011  -0.000  =  =  z  g  y  A g  A  g  y x  =  =  2922.3+0.3 MHz —  =  2.0011+0.0010  x= 2926.5+0.3 MHz z  =  A,=  z  2.0057+0.0004 3245.3+0.3 MHz  2.0063+0.0004 y A = 2927.0+0.3 MHz y x 2.0084+0.0003 2935.3+0.2 MHz x g  =  g  =  A  z  =  A  z  =  g  y  =  A  A  II  II  II  1.000  1.000 11  -0.000  "  -0.000 II  -0.000  II  0.000  0.000  1.000  II  II  II  -0.000 II  1.000 II  II  -0.000 II  1.000  -0.000  -0.000  0.000  0.000  1.000  II  II  II  II  II  II  =  g  RbDA  2.0021  9 ! 3 = 2.0014 (\y = 2931.3+5 MHz x '  g  DKDA  =  V A  KDA  l  Principal value  y x  =  2.0137+0.0011 3200+1 MHz 2.0342+.0010 2909+1 MHz —  II  1.000 II  -0.000 II  •  2.0352+0.0011 =  -0.000  2912+1 MHz  1.000 II  -0.000 II  -0.000 II  - 69- -  TABLE 1 (continued)  Direction ICosines Crystal  Principal  value  g = 2.0069+.0010 A = 3255+1 MHz  m  I  n  0.000  0.000  1. 000  II  II  II  z  ADA  g = 2.0033+.0015 Ay= 2906+1 -MHz  -0.4848 II  y  g = 2.0098+.0015 A  =  A  2930+1 MHz  0.8746  "  0.8746 it  0.4848  0. 000 II  0. 000 II  T~  AO  13  GAUSS  1  I  3 0 0  2 0 GAUSS  0  K  1  I  Superhyperfine f e a t u r e s on m^j and m =|-As in the EPR o f AsO?" c e n t r e i n K r L A s C v T  AO G A U S S  hyperfine lines  - 71 -  interpreted i t to arise due to a mainly i s o t r o p i c superhyperfine inter4action of the four protons surrounding the AsO^  centre.  hand, the H^c feature has not been mentioned before.  On the other  The H]_c-axis  spectrum, however, gives a clear i n d i c a t i o n that the superhyperfine interaction is very a n i s o t r o p i c .  Another interesting feature of the  Hie spectra is that the resolution of the superhyperfine structure improves as the magnetic f i e l d increases.  We find that ENDOR  experiments were very helpful in explaining the room temperature EPR spectra.  This point w i l l be taken up again and we now describe the  EPR measurements at lower temperatures. 14 As observed f i r s t by Blinc et a l . v i r t u a l l y the same at 4.2 as those at 77°K.  the EPR spectra are The gross features of  the low temperature spectra are almost the same as those of the room temperature spectra.  Marked changes, however, occur in the f i n e r  d e t a i l s of the EPR spectra.  In F i g . 1 3 ( a ' ) , (b )  the spectra observed at 4 . 2 ° K .  1  and ( c ' )  are shown  The corresponding room temperature  spectra are shown in the same figure at the top.  It  is now  observed that for H||c, F i g . 1 3 ( a ' ) , the superhyperfine structure consists of a (1:2:1) t r i p l e t of almost the same total  pattern  separation as that of the corresponding higher temperature pattern, F i g . 13(a),  These observations have been understood^ in terms of a 4  dynamic order-disorder model, although here, again, superhyperfine interaction has been assumed to be e s s e n t i a l l y i s o t r o p i c .  This  assumption is seen to be in error when the angular variation of the EPR spectra at 77 or 4.2°K is studied.  F i g . 13 also shows a compari-  son of the superhyperfine patterns on the lowest f i e l d hyperfine  - 72 -  component of the AsO^ centre for Hie, as mentioned e a r l i e r . -  It may  be noted that in addition to the s p l i t t i n g s being d i f f e r e n t , F i g . 13(b') shows an e s p e c i a l l y interesting feature when compared with 13(b): 75 the lowest f i e l d As  hyperfine l i n e s p l i t s , apparently, into four  components, compared to the room temperature case, where i t does not show any s p l i t t i n g at a l l . To understand the features on the lowest f i e l d hyperfine l i n e , an i r r a d i a t e d crystal  of DKDA was used.  observed spectra showed that in F i g . 13(b')  A comparison of the the A s ^ hyperfine  line  i t s e l f s p l i t s into two components and that in the case of KDA, the four l i n e pattern was actually due to two separate hyperfine t r a n s i t i o n s , one of which remains single while the other s p l i t s into a triplet, protons.  1:2:1  i n d i c a t i v e of a superhyperfine i n t e r a c t i o n with two equivalent These observations show that the superhyperfine  is highly a n i s o t r o p i c .  interaction  Moreover, this additional s p l i t t i n g of the  hyperfine components (regardless of the superhyperfine  splittings)  is found to decrease rapidly as the magnetic f i e l d is increased, to the extent that i t is hardly resolved on any other except the lowest 75 f i e l d As  hyperfine components as seen for the highest f i e l d l i n e in  Fig. 13(c').  For the lowest f i e l d l i n e , however, the number of  components as well as the magnitude of the s p l i t t i n g changed as the magnetic f i e l d orientation was varied in the crystal  ab plane.  In  order to avoid the interference due to proton superhyperf ine s p l i t t i n g s , again a DKDA crystal  was chosen for these studies.  F i g . 14 shows the 75  angular v a r i a t i o n of these s p l i t t i n g s associated with the lowest As hyperfine l i n e in the ab plane of DKDA at 77°K.  Similar  variation  X(orY)  i o 14  i  10  1  1  1  1  1  1  20  30  40  50  60  70  WANGLE  1  so  FROM T E T R A G O N A L a AXIS 3  Angular variation of the s p l i t t i n g s associated with nij=^ l i n e in the ab plane of x-irradiated KDgAsO^ at 77°K. refer to the two d i f f e r e n t domains.  The single and the dotted lines  1  90  - 74 -  0  .  KDA.216K  F i g . 15  Angular variation of s p l i t t i n g s associated 75  with the As at d i f f e r e n t  3  m  i 2 '' ' =  1  n e  "*  n  v  a  crystals. «  i  n  '  o  u  s  crystals  - 75 -  was observed for KDA and ADA a l s o .  It  is seen from F i g . 15 that  in  general there are four distinguishable s i t e s for an AsO " centre for 4  all  these c r y s t a l s .  However, t h i s number reduces to only two for the  cases of H||b, and when H is oriented at an angle of 45° with respect to crystal  a and b axes, corresponding to points A or B in F i g . 14.  In a d d i t i o n , there is a puzzling feature that the remaining hyperfine lines show hardly any s i m i l a r s p l i t t i n g at a l l H in the crystal  symmetry planes.  for any orientation of  Before obtaining the parameters  of the spin Hamiltonian describing these spectra, we w i l l now show that the observed variations of the gross features  in the EPR spectra can be explained in terms  in the crystal  structure of KDA o r ,  equivalently,  of DKDA . 67  The c r y s t a l  structure of KDA in the f e r r o e l e c t r i c phase  has been discussed in Chapter III.  Assuming that no s i g n i f i c a n t  d i s t o r t i o n of the l a t t i c e takes place on the formation of this  centre  i t w i l l be seen that for the case of a polarised c r y s t a l , there are 4only two d i s t i n c t orientations for an AsO^  centre and that  these  two orientations should be related to each other by a rotation of approximately 16° about the c r y s t a l l i n e c-axis.  However, in an  unpolarised c r y s t a l , twinning ( i . e . , domain structure)  is present  and X and Y d i r e c t i o n s can be interchanged, doubling the number of 4possible s i t e s for the As0  4  centre.  Hence, for an a r b i t r a r y  orientation of H in the ab plane of DKDA, each hyperfine l i n e expected to s p i t into four components.  is  This is precisely what is  seen in F i g . 14 where the v a r i a t i o n of the l i n e s a r i s i n g due to two d i f f e r e n t f e r r o e l e c t r i c domains is shown by continuous and dotted  - 76 -  lines.  It  is also evident from F i g . 14 that when H is along the X or  Y d i r e c t i o n , the components a r i s i n g from two d i f f e r e n t l y  oriented  tetrahedra c o i n c i d e , the remaining s p l i t t i n g being e n t i r e l y due to the domain structure.  On the other hand, when H is along a or along b,  the components belonging to the two domains c o i n c i d e , the remaining s p l i t t i n g now being e n t i r e l y due to the two d i f f e r e n t l y oriented AsO^ tetrahedra. To confirm these results f u r t h e r , we repeated the EPR study on KDA at 77°K in the ab plane with a p o l a r i s i n g dc e l e c t r i c across the crystal  and p a r a l l e l to i t s c-axis.  f i e l d s up to ± 12 KV/cm were used.  Variable  field  electric  For the cases of H along X or H  along Y, we observed the expected v a r i a t i o n of the hyperfine  line  i n t e n s i t i e s with the magnitude and the d i r e c t i o n of the applied e l e c t r i c f i e l d , as shown in F i g . 16.  Also no e l e c t r i c f i e l d  effects  could be observed for the case with H||a or H||b-thus f u l l y confirming our model. In f a c t , we could plot the hysteresis loop for applied f i e l d s between ± 12KV/cm by taking the p o l a r i s a t i o n in the crystal  to  be proportional to the difference in the intensity of the two l i n e s . The hysteresis loop was found to be symmetrical and the coercive force determined to be 5.5±0.5KV/cm.  This value is in reasonable agreement  with that determined through d i e l e c t r i c studies  ^.  The angular v a r i a t i o n of the hyperfine t r a n s i t i o n s can be described by the spin Hamiltonian (21), with the parameters g and A having orthorhombic symmetry. Table 2.  The principal values are given in  Here, as before, the z d i r e c t i o n is the d i r e c t i o n of the  c-axis, and x and y are the two other mutually orthogonal d i r e c t i o n s .  -  78  -  TABLE  2  Spin Hamiltonian parameters f o r AsO ~ centre at low (indicated) A  temperatures .  i, m andn refer to the crystal a , b and c system.  Direction Cosines Crystal  Temperature  Principal  (°K)  value  g =2.0007+0.0004 z  A =3199.0+0.1 z  KDA  4.2  g  MHz  =1.9953+0.0005  A =2833.5+0.8 y  g  MHz  =2.0114+0.0010  A  =2895.0+0.3  MHz  m  .l 0.0000 II  -0.4848 M  0.8748  0.0000  n 1.000  II  0.8746  0.000  II  II  +0.4848  0.000  II  II  II  0.000  0.000  1.000  II  II  II  A g =2.0003+0.001 z  A =3200+5 z  DKDA  4.2  g  MHz  =2.0001+0.002  A =2830+5 y  g  MHz  =2.0005+0.002  A  =2890+5  MHz  -0.4848 II  0.8746  0.8746 n 0.4848  0.000 II  0.000  II  II  0.000  0.000  1.000  II  II  A  g =2.005+.001 z  A =3240+5 z  ADA  230  g 3  y  MHz  =2.002+0.002  -  " -0.4848 ll  A = 2 8 9 5 + 5 MHz g =2.007+0.003 y  0.8746 II  0.000 II  y  0.8746  0.4848  0.000  y  A  =2920+5  MHz  II  n  II  - 79 It can now be seen that the presence of the orthorhombic s i t e symmetry together with a large second order e f f e c t in the As  75  75  structure is responsible for the other three As remaining u n s p l i t .  hyperfine  hyperfine lines  Moreover, i f x and y are taken to coincide with  the projections of the top and the bottom edges of the AsO^ tetrahedra, these results show the tetrahedra to be rotated by 16° on either side of the orthorhombic X (or Y) mirror plane.  Thus below T , the r e s u l t  for KDA and DKDA are in agreement with the structural  data. 4-  Analysis of e s s e n t i a l l y s i m i l a r observations of the AsO^ centre in NH^AsO^ has also been done and the spin Hamiltonian parameters obtained are also given in Table 2.  Corresponding spectra  for RbDA have not yet been analysed. Note, however, from F i g . 15 that for these c r y s t a l s , over a range of 'vlOO below T .  0  above T , the EPR spectra show the symmetry of those  This has been explained by considering the effects of  molecular motion on the EPR spectra and is discussed in section 4.5. 4.2  ENDOR of  AsoJ" centre in KH As0 :2  4  To understand the superhyperfine features, ENDOR spectra were recorded at intervals of 5° or less with the magnetic f i e l d being turned around the three mutually perpendicular crystas axes a, b and c.  ENDOR studies were made on a l l of the seven As  t r a n s i t i o n s observed in our experiments.  hyperfine  A large e f f e c t was observed  due to the change of the nuclear spin state of As m u l t i p l e t to another.  75  75  from one hyperfine  Typical ENDOR spectra are shown in F i g . 17.  The spectra are the simplest for the case of H||c, F i g . and 17(b).  17(a)  They consist of three d i s t i n c t sets of l i n e s ,  - 80 -  (far) ^(close)  J  (close)  (a)H//C  H = 4854 G Q  1  1—//-^ ,  p-  .  •,(close)  (b)H/^C  H = 2624 G q  9  8  10  ii  ~ i —  12  (far)  I  23  13  (far)  24 M H z  (close)  (c)HlC  H = 2608 G q  ~~1  9  i—  10  11  12  13  177  18  19 M H z  F i g . 17 T y p i c a l proton ENDOR s i g n a l s from the A s O " c e n t r e i n ' KrLAsO, a t 4.2°K. 4  - 81 -  centered around the free proton NMR frequency for the magnetic f i e l d corresponding to the EPR t r a n s i t i o n saturated.  The set closest to  the free proton NMR frequency consists of a group of 4 lines in either d i r e c t i o n whereas each of the other two sets consists of j u s t one line.  For the case of the magnetic f i e l d H oriented along an  a r b i t r a r y d i r e c t i o n in the crystal  planes, each of these two sets  also consists of a number of lines (maximum 4) (see F i g . 18) and the t h i r d s e t , near the free proton NMR frequency, consists of many more unresolved l i n e s .  In the present s t u d i e s , we have concentrated only  on the two sets of ENDOR lines r e s u l t i n g from the two largest superhyperfine couplings.  For example in F i g . 17(b) these two sets are  formed by the l i n e at 23.40 MHz assigned to the ' c l o s e ' protons, and the l i n e at 12.80 MHz assigned to the ' f a r '  protons.  that because the superhyperfine coupling due to ' f a r '  It  is now clear  proton is so  small (^ one Gauss), i t is not resolved in the EPR spectra at 4.2°K even for the case of  H||c.  In general the nature of the angular variations of the ENDOR t r a n s i t i o n s on various hyperfine multiplets from F i g . 19,20 and 21.  Here 2(v^ - V p )  is the same as seen  is plotted because this  is  approximately equal to the hyperfine coupling for the corresponding direction. 'close'  Four t r a n s i t i o n s each are in general observed for the  and the ' f a r '  protons, in accordance with the crystal  structure of KDA in the f e r r o e l e c t r i c phase.  However, when H is  oriented in the ab plane, the ENDOR spectra obtained by saturating the lowest f i e l d hyperfine t r a n s i t i o n are d i s t i n c t from those obtained by saturating most other EPR t r a n s i t i o n s .  A comparison is given in  F i g . 18  S p l i t t i n g of the ' c l o s e ' proton ENDOR transitions for H oriented 2° from the c-axis.  'Far'  protons also show similar s p l i t t i n g .  -io°  O  -Angle f r o m  IO  90°  c-axis CO  co  Angle from  F i g . 19  a-axis  Angular v a r i a t i o n o f the ' f a r ' proton ENDOR t r a n s i t i o n s i n (a) be (or ac) and (b) ab plane o f x - i r r a d 1 a t e d Kh^AsO^. Each curve ( l a b e l l e d x^ o r ) r e f e r s t o a d i s t i n c t ' f a r ' proton s e t .  F i g . 20  Angular v a r i a t i o n o f the ' c l o s e ' p r o t o n ENDOR t r a n s i t i o n s i n the ac (or be) plane o f KH-AsO* f o r (a) the h i g h e s t and (b) the lowest f i e l d A s h y p e r f i n e t r a n s i t i o n s a t u r a t e d . Each curve ( l a b e l l e d B. or A.) r e f e r s to a d i s t i n c t ' c l o s e ' p r o t o n s e t . 7 5  - 85 -  ANGLE FROM TETRAGONAL a AXIS  21  Angular v a r i a t i o n of the ' c l o s e ' proton ENDOR transitions in the ab plane of x-irradiated KhLAsO, for (a) the highest f i e l d and (b) the lowest fTeld A s hyperfine t r a n s i t i o n at 4 . 2 ° K . 7 5  - 86 -  F i g . 21, which shows the ENDOR spectra for the ' c l o s e ' protons in 75 the ab plane of KDA when the lowest and the highest f i e l d As lines are saturated.  It  EPR  seems rather puzzling at f i r s t when one  obtains ENDOR signals from four d i s t i n c t s i t e s in one case, F i g . 21(a), but from only two in the other case, F i g . 21(b),  However,  this  observation also finds a natural explanation when the presence of the f e r r o e l e c t r i c domain structure in the EPR spectra was taken into account. In the case of F i g . 21(b), the magnetic f i e l d H is set to s a t i s f y conditions corresponding to point A in F i g . 14, and then kept constant throughout the angular v a r i a t i o n study.  It w i l l be seen  that for ENDOR, the EPR condition is then s a t i s f i e d mainly for the l i n e s from the two s i t e s in a single domain and only two t r a n s i t i o n s are therefore expected (and observed) in the ENDOR experiments. Similarly,  by s a t i s f y i n g the EPR conditions corresponding to point  B in F i g . 14, the two other t r a n s i t i o n s  (from two sites in the other  domain) could be observed exclusively.  For the case of ENDOR on the  highest f i e l d t r a n s i t i o n , F i g . 21(a), however, since the s p l i t t i n g s due to the two sites or the two domains remain unresolved in EPR,  all  the four t r a n s i t i o n s are expected to occur simultaneously and this is precisely what is observed in F i g . 21(a).  These arguments were  further confirmed by observing the effects of polarising f i e l d s on the ENDOR t r a n s i t i o n s . and then cooled to 4.2°K.  electric  The crystal was polarised at 77°K  The polarising e l e c t r i c f i e l d was then  removed and the ENDOR t r a n s i t i o n s were observed.  The expected  changes in the ENDOR l i n e i n t e n s i t i e s were c l e a r l y seen, thus lending  -  firm  support  switching  4.3  t o o u r model  following  1.  82 ferroelectrics.  of  h u n d r e d ENDOR m e a s u r e m e n t s  two  were  made  by f o l l o w i n g  procedures:  F o r H | | c , ENDOR m e a s u r e m e n t s EPR t r a n s i t i o n s .  2.  and the domain  and A n a l y s i s  Several the  -  o f the domain s t r u c t u r e  i n the KDA-type  ENDOR D a t a  87  The a n g u l a r  This  variation  were  data  made f o r a l l  is discussed  seven  i n Section  o f t h e ENDOR l i n e s  were  4.3.1.  carried  out  75 on  the highest  crystal 4.3.1 S i g n s  and the lowest  planes.  This  field  is discussed  As  lines  in different  in Section  4.3.2.  o f t h e H y p e r f i n e and S u p e r h y p e r f i n e c o u p l i n g s We w i l l  now o u t l i n e  the a p p l i c a t i o n o f the procedure d i s -  7^ cussed and  in 2.3.2  those  of the At  direction  signs  of  tensor  'close' cos  of a  [2a  (H  ' i i n F i g . 1 a n d nip=2,  of  < S  of  >£ U=mF,+).  e  F P  superhyperfine couplings.  shown t h a t  proton,  couplings .)]  is quite  c  h  e  the p r i n c i p a l  close  c a n be u s e d  for H||c.  and t h e r a t i o s  r  t  r  a  n  s  i  t  i  °  n  T a b l e 4 shows T-j, T  observed  2  T  i  t  o  to the the  Table 3 gives  the  quantities  i4+() • 4° ^' a  p  o f the  to obtain  of the  t, c, a  hyperfine coupling  p r i n c i p a l component  s h o u l d be t h e same  EPR t r a n s i t i o n  the experimentally  have  Thus E q . (40)  Hip  for  each  ' f a r ' proton  'close'  proton  T-j  for  o f t h e As "  the l a r g e s t  o f the c - a x i s .  v  z  and the  with  i °+(v- 4"^ E  the s i g n s  t h e ENDOR s t u d i e s  associated  of the  values  'close'  4.2°K,  superhyperfine direction  to o b t a i n  Ti  1  ' as the c o r r e s p o n d i n g  the observed  Ty', as w e l l and t h e o r e t i c a l l y  values  of  v  1  ratios  ( j c  o s e  )(j.)  as a comparison expected  for  values  of  _ 88 _  TABLE 3  Values of 2 < S  z  >^ = cos (2a ^_), nip = 1 , 0 , - 1 , m  for the resonance f i e l d s H 2931  EPR Transition  T  l  T  2  T  3  T  4  T  5  T  6  T  7  MHz, g H  n  T  and'g &  = 2.0021  =2  <  using A-p  T  n  S  z  >  1  n  =2  <  S  MHz, Aj^ =  = 3254  = 7.292  z  x >  Q  10"  calculated  4  MHz/gauss. =2  <  s'  Gauss  1349.9  0.8110  0.5423  0.1043  1692.2  0.8442  0.6272  0.2816  2154.5  0.8775  0.7208  0.4810  2653.8  0.9033  0.7855  0.6361  3235.3  0.9246  0.8398.  0.7469  3938.6  0.9436  0.8862  0.8431  4863.2  0.9576  0.9187  0.8962  z  >_-,  -89 TABLE 4 Comparison of the observed r a t i o s v = p |  Vj  V  2< S As  E  P  R  Transition Saturated J  75  z  C  o s e  ^  (T..)  - v  /v for a ' c l o s e ' proton, where i 1 to the corresponding values of  ,  T  T  > , for the possible combinations of signs of the proton and hyperfine couplings.  V  T.  experimental (MHz)  Observed rat.os , v  T /  V  T  Calculated values of 2< S > 75 for the signs of As and close z  1  1  proton couplings +,-  T  l  T  2  T  3  T  4  T  5  T  6  T  7  T  +,+  indicated -,+  15.431  1.000  1,000  0.8110  1.000  0.1043  13.048  0.8456  0.8442  0.8442  0.2816  0.2816  13.528  0.8767  0.8775  0.7208  0.4810  0.7208  12.210  0.7849  0.7855  0.7855  0.7855  0.7855  12.960  0.8399  0.8398  0.7469  0.8398  0.9246  13.001  0.8425  0.8431  0.8431  0.9422  0.9422  13.812  0.8952  0.8962  1.000  0.9576  1.000  - 90 -  2 <S  z  >£• for the four possible combinations of the signs of the As  and the ' c l o s e ' proton couplings.  The comparison c l e a r l y  shows  that,  75 for the c-axis d i r e c t i o n , the sign of As  hyperfine coupling is  p o s i t i v e whereas that of a ' c l o s e ' proton superhyperfine coupling is negative.  Combined with the results of the detailed angular  variation  studies of the ENDOR l i n e p o s i t i o n s , this leads to the conclusion that  75 the sign of the As  hyperfine coupling is p o s i t i v e whereas that of  a ' c l o s e ' proton superhyperfine coupling is The sign f o r the ' f a r '  negative.  proton coupling could not be unambi-  guously determined by this simple procedure since the p r i n c i p a l directionsassociated with ' f a r '  proton coupling tensor  s i g n i f i c a n t l y from the crystal-axis d i r e c t i o n s .  deviate  The double ENDOR  technique was then applied to obtain the r e l a t i v e signs of the and the ' f a r '  proton coupling tensors.  F i g . 22 i l l u s t r a t e s  'close'  the  double ENDOR signals obtained by saturating the ENDOR t r a n s i t i o n v  £^+ ^ r  a n c  l sweeping the second r . f .  o s c i l l a t o r through frequencies  corresponding to the other ENDOR t r a n s i t i o n s involving the and the ' f a r '  protons.  Since the double ENDOR enhancement signals  for both the ' c l o s e ' and t h e ' f a r ' signs of the ' c l o s e ' and the ' f a r ' same.  protons have the same phase, the proton couplings, for H||c,  In view of the r e s u l t that the general nature of the  and the ' f a r '  'close'  is the  'close'  proton tensor is the same, we conclude that the sign  of the ' c l o s e ' and the ' f a r '  proton tensor is the same.  To check the consistency of the procedure we have also used Eq. (39), and the graphical procedure, for both the higher, ta)  ()  MT-) and the lower, viENDOR transition$T. observed. t,+ i ' » ' t,-1 ^ a  i  The values  - 92 -  of ( A ' ' k z and the magnitude of A a  determined from the slope and the  z z  intercepts of the graph agree f a i r l y well with those determined from the detailed angular variation studies. The lower ENDOR t r a n s i t i o n frequencies depend more c r i t i c a l l y on r e l a t i v e values of ( A ^ )  and A ^ than the higher.  F i g . 23 shows  z z  the graphical representation of Eq. (39) for ' c l o s e ' and F i g . 24 for 'far'  proton ENDOR t r a n s i t i o n frequencies.  values of  A comparison of the observed  j(T.j) with those calculated using the values of (A )  (a) and A  from graph of F i g . 23 and 24 is given in Table 5.  z z  The close  agreement between the calculated and the observed ENDOR frequencies lends a firm support to the v a l i d i t y of our procedure. It must be mentioned, however, that the best f i t to the (a) observed ENDOR frequencies for the two sets of data v)- ' for each t, -  type of proton was found to be given by two s l i g h t l y d i f f e r e n t values of ( A ^  z z  vl°^(T. )  and A ^  obtained by plotting the data for v £ ° ] ( T . ) and  separately, although the f i t of Table (5)  is considered  reasonably good, and the deviations are within the ENDOR l i n e width (100-150KHz).  The s l i g h t , apparently systematic differences between (a)  (a)  the best f i t s for the two d i f f e r e n t sets v£ j and v£  are attributed  to small errors in the description of the EPR parameters, in p a r t i c u l a r 75  to the fact that the As  coupling tensor is not exactly axial  at  4.2°K and we have neglected the (small) quadrupole interaction term. These corrections could be included a n a l y t i c a l l y  as a perturbation.  On the other hand, the e f f e c t of inclusion of terms second order in the proton coupling constants or of d i r e c t nuclear-nuclear coupling, appears to be n e g l i g i b l e since there is no clear evidence of the  F i g . 23  Graphical representation of Eq. (39)  (see text) for the  'far'  proton ENDOR transitions in x-irradiated KhLAsO, H||c at 4 . 2 ° K .  Fig. 24  Graphical representation of Eq. (39) for the  'close'  protons in x-irradiated KHLAsO, f o r H||c and 4.2°K.  TABLE 5  Observed and calcualted (MHz)  2  Transition Saturated  using  as obtained from F i g . 24 and of J j c  960.3 (MHz) EPR  values of v^l^  v^  Observed  o s e  = -3.56 MHz and ( A ^  )  u s  ing A ^  1 o s e  ^  f a r  b  = 30.25 MHz and  2  z  =  3 3  ( ( A  -  5 4  c l o s e  ))  from F i g . 23.  a r )  (MHz)  Calculated  v  f a r ) E  Observed  (MHz)  Calculated  v^  Observed  o s e  >  (MHz)  Calculated  v ^  Observed  2  zz  0  5  ^  (MHz)  Calculated  4.679  4.685  7.888  7.866  21.178  21.14  7.068  7.07  6.023  6.012  8.920  8.910  20.253  20.18  6.262  6.25  8.057  8.060  10.929  10.916  22.701  22.67  10.010  10.060  12.827  12.823  23.410  23.33  12.568;  12.562  15.401  15.390  26.735  26.64  15.425  15.369  18.318  18.329  30.037  29.84  19.088  19.063  22.400  22.394  34.518  34.40  6.312  6.32  - 96 -  presence of non-additive effects i n the experimental ENDOR spectra. In any case there i s no ambiguity i n the conclusion that the sign of 75 As  hyperfine coupling i s p o s i t i v e while those o f the 'close' and the  'far' protons are both negative. 4.3.2 Angular v a r i a t i o n s of ENDOR transitions From the discussion i n Chapter II and that i n the previous Section, i t i s c l e a r that the observation of v t r a n s i t i o n s on the 75 lowest f i e l d and v _on the highest f i e l d As hyperfine component involves the least c o r r e c t i o n due to admixture of the electron spin 75 F+  F  states by the As  hf i n t e r a c t i o n .  Hence d e t a i l e d measurements  r e l a t i n g to these lines only, as a function of angle i n the three c r y s t a l planes were made. F i g . 19, 20 and 21 show the observed v a r i ations, as mentioned  earlier.  The observed ENDOR frequencies were f i r s t f i t t e d by the least-squares-adjustment procedure to the eigenvalues o f  ^jr|y|n.oR  75 using the computer IBM 360/67. This neglects the e f f e c t of As hyperfine on mixing the electron spin states but the error due to this was estimated to be ^ 100 KHz. Subsequently the computer program, FIELDS became a v a i l a b l e . This program was adopted to predict ENDOR l i n e positions by d i r e c t diagonalisation of ^ " p + ^ E N D O R ^ ' °^ l M i states obtained from S=%, I ^ ^ = i and I ^ = h. E  i n  R  a  asi  s  m  s  m  >  As  2  The observed ENDOR frequencies were f i t t e d by adjusting the parameters of  ^E^QOR  (  t n e  parameters f o r <^p_p having been R  determined already). Table 6 shows a typical f i t of the observed and  - 97 -  TABLE 6 Observed and calculated values, using the superhyperfine  parameters  given in Table 7, of ENDOR t r a n s i t i o n frequencies for protons 4surrounding an AsO^ centre in Kh^AsO^, at 4.2°K. 3 m •= — l i n e was saturated in each case. I 2  The As  75  T  Orientation of H  V  Observed (MHz)  (close) E,-  (far) E,Calculated (MHz)  Observed (MHz)  Calculated (MHz)  H11 a  17.855  17.858  24.110  24.112  H||b  17.439  17.445  10.647  10.643  Hi Ic  19.103  19.091  6.293  6.293  - 98 -  TABLE 7  Superhyperfine parameters determined through ENDOR of protons 4-  surrounding an AsO^  centre in KH^AsO^.  1 , m, n refer to the  tetragonal a, b, c system. Site  Principal Value (MHz)  A  =  1  m  n  8.907  0.9943  -0.0751  0.0752  = -16.848  0.0397  0.9189  0.3926  = -33.496  -0.0986  -0.3874  0.9166  0.7255  0.3750  0.5771  A  'Close'  A A  y  z  A  =  v  2.168  A  'Far'  A  A  y  =  -3.388  0.6702  0.5757  -0.4684  =  -7.405  -0.1566  0.7266  0.6690  - 99 -  calculated ENDOR t r a n s i t i o n s and the superhyperfine tensors for protons thus obtained are given in Table 7.  'close'  The f i t was achieved to  within a standard deviation of 20 KHz for 'close'protons and 15 KHz for  'far'  protons.  The better f i t f o r ' f a r '  inherent narrow linewidth  protons r e f l e c t s  their  80 KHz), as compared to close protons.  No nuclear spin-spin interaction was detected in these i n v e s t i g a t i o n s ; however, i t is possible that the higher l i n e width of the ' c l o s e ' proton ENDOR lines may be due to unresolved nuclear-nuclear s p l i t t i n g . 4.4  Correlation of EPR and ENDOR results An examination of Table 6 shows that  (a)  The superhyperfine i n t e r a c t i o n is considerably anisotropic  both f o r ' c l o s e ' and ' f a r ' (b)  protons.  The strength of the interaction for the ' f a r '  protons is about  a f i f t h of that of the ' c l o s e ' protons and i s therefore not resolved in EPR. (c)  The principal axes of the ' c l o s e ' proton i n t e r a c t i o n nearly  coincide with the a , b and c directions defined in the c r y s t a l tetragonal phase.  These observations c l a r i f y the aspects  in i t s  relating  to superhyperfine structure mentioned in Section 4.1 on EPR r e s u l t s . Let us reconsider F i g . 13 again in the l i g h t of these r e s u l t s . (i)  When H|jc,  the four ' c l o s e ' proton positions are  equivalent with a coupling constant ^-SOMHzand the four ' f a r '  protons  are equivalent with a coupling constant of ^-3MHz (from F i g . 19 and 20).  Hence, at room temperature, where rapid motion of the protons  between ' c l o s e ' and ' f a r '  s i t e s is taking place, an equivalent  - 100 -  coupling of -33/2 = -16.5MHz to four equivalent protons should be observed.  This is seen to agree with F i g . 13(a). (ii)  When H| j a a x i s , i t is noticed that the four  proton positions and the four ' f a r ' only in p a i r s .  Since a l l  equivalent  the 0-H...0 bonds in the crystal  along a and b axes, l e t us c a l l the 0-H...0 bond p a r a l l e l  proton positions are  the pair of ' c l o s e '  'close'  lie  nearly  protons lying on  to the a axis as the ' a ' type protons and,  correspondingly, the other pair as ' b ' type protons.  It  is then seen  that the following four coupling constants are operative for the  eight  possible proton p o s i t i o n s : 1.  ' a ' type ' c l o s e '  2.  ' a ' type ' f a r '  3.  ' b ' type ' c l o s e '  4.  ' b ' type ' f a r '  protons - 18MHz ;  protons,- 4.5MHz protons,  9MHz  protons, -0.5MHz  At room temperature there is averaging between the coupling constants of the ' a ' type ' c l o s e '  and ' f a r '  protons giving an average coupling  of ^ -11.25MHz and of the ' b ' type ' c l o s e ' and ' f a r ' coupling constant of °» 4.25MHz.  protons giving a  Hence the observed structure  show two proton couplings with equivalent pairs of protons. the coupling of 4.25 MHz is unobservable by EPR.  should However,  Hence, what is seen  is a coupling of -11.25MHz to two equivalent protons giving a t r i p l e t . This is exactly what we see in F i g . 13(c). At low temperature stopped and a l l  ( 4 . 2 ° K ) a l l motion should be  effectively  four coupling constants should be operative.  3 of the coupling constants are too small to be seen c l e a r l y  However, in  EPR.  Only the f i r s t coupling of -18MHz to two protons is expected to be  - 101 -  seen.  As explained in the section on EPR r e s u l t s , due to orthorhombic 75  symmetry we would expect the low f i e l d As  hyperfine l i n e to s p l i t  into two with one of the lines corresponding to the s i t e with two ' a ' type ' c l o s e ' protons and two ' b ' type ' f a r '  protons and the other  corresponding to two ' b ' type ' c l o s e ' protons and two ' a ' type protons.  It  'far'  is clear from the tabulation of the coupling constants  that only one of the lines is expected to show clear proton s p l i t t i n g , while the other one is broad with no resolved proton s p l i t t i n g , in complete accord with the spectrum in F i g . It  13(b).  is c l e a r , therefore, that the ENDOR results have been  essential for the complete understanding of the proton superhyperfine structure at room temperature and at 4.2°K. B l i n c , Cevc and Schara's 14 e a r l i e r results for the simple special case of H|[c have thus been I P  found to f i t 4.5  in with our model.  Discussion A.  HYPERFINE INTERACTION Arsenic  35 Hampton et al.  have noted that the large positive  interaction  75 with the As  nucleus arises because of the predominance of 4s and 5s  character in the atomic o r b i t a l of arsenic involved in the m.o. of A-| symmetry into which the odd electron enters.  An estimate of the  f r a c t i o n of the unpaired spin population on the As s o r b i t a l s from the observed i s o t r o p i c hyperfine interaction leads to the figure of 36%.  The observed anisotropic i n t e r a c t i o n , though small, cannot be  f u l l y accounted for by the p a r t i c i p a t i o n of 4d 2 As o r b i t a l alone in 2  - 102 -  the A-j s t a t e , and probably a complete c a l c u l a t i o n involving the contribution from the spin p o l a r i z a t i o n of inner As p and d o r b i t a l s is necessary. Oxygen Although a considerable p o s i t i v e spin density is presumably 4present on the oxygens of the AsO^  u n i t , no hyperfine i n t e r a c t i o n can  be seen as 0 ^ has no nuclear moment.  An order of magnitude estimate  would lead to a figure of 16% for the f r a c t i o n of the unpaired electron spin on each oxygen.  0 ^ enrichment of this crystal  would  y i e l d valuable d i r e c t data on the spin density on the oxygen as well as the hybridization on each oxygen. A c a l c u l a t i o n from the structural data of Frazer and 62 4 Pepinsky and Bacon and Pease shows that the As-O-H angle is close to 3 1  108° which would lead us to expect a sp 'Close' Isotropic  interaction:  be -13.812MHz from Table 6.  hybridization at the oxygens.  protons The contact interaction is seen to  This corresponds to a f r a c t i o n 0.97% of  the unpaired electron in the hydrogen Is o r b i t a l .  Although i t appears  most l i k e l y that the mechanism for t h i s i s o t r o p i c i n t e r a c t i o n is the same as the one now f a m i l i a r in free radicals i.e.  the exchange  p o l a r i z a t i o n of the 0-H <j bond by the a spin density on oxygen, i t i s d i f f i c u l t to make a c o r r e l a t i o n of this r e s u l t with the observations in other r a d i c a l s .  The extensive EPR data and calculations available 68 in the l i t e r a t u r e for the 0-H radical in irradiated ice and other  - 103 -  crystals  69  are unfortunately not d i r e c t l y applicable to our case.  This is because in these cases  a) one of the bonds of the oxygen  is broken so as to leave the 0-H fragment with an unpaired ir electron on the oxygen, and  b) the 0-H bond lengths are d i f f e r e n t .  Anisotropic i n t e r a c t i o n : -  It  is noticed that the traceless  anisotropic interaction has the p r i n c i p a l values 22.72, -3.04 and -19.68 MHz, which shows i t to be f a r from a x i a l .  This can be  understood from the following model for the dipolar i n t e r a c t i o n . (a)  The p o l a r i z a t i o n of the 0-H a bond, referred to already  w i l l lead to a negative spin density in the bond.  The 8 spin in the  0-H bond w i l l lead to a dipolar i n t e r a c t i o n which w i l l be axial with respect to the 0-H bond. (b)  The a spin d i s t r i b u t e d over the entire AsO^ tetrahedral  unit may be approximated by an electron with a spin at the arsenic site.  This point charge model is crude but is used in the absence  of a better approximation. s i t u a t i o n rather w e l l .  It appears, however, to describe the  The unpaired electron at the arsenic  site  w i l l have a dipolar interaction with the proton,which w i l l be axial with the As-H d i r e c t i o n as the a x i s .  The magnitude of t h i s  interaction  can be calculated to be 4.2 MHz under the above approximation using the atomic positions from the neutron d i f f r a c t i o n investigation which gives the As-H distance to be 2.2 A . 0  An examination of the angular v a r i a t i o n shows that the 'close'  proton interaction i s dominated by the mechanism (a).  This  explains why in the ab plane the anisotropy is so l a r g e , whereas  in  the ac plane one of the protons shows a similar v a r i a t i o n to that in the ab plane and the other shows only a small v a r i a t i o n due almost  - 104 -  e n t i r e l y to the mechanism ( b ) .  I t i s found t h a t the non-axial  tensor may i n f a c t be decomposed i n t o two a x i a l tensors with the symmetry a x i s o f one being along the 0-H bond d i r e c t i o n and t h a t of the other along the As-H d i r e c t i o n .  The two t e n s o r s (estimated by  a n a l y s i n g the angular v a r i a t i o n ) are g i v e n ( i n MHz) below.  /15.8  0.0  0.0  •7.9  y  0.0  0.0  ]  with symmetry along 0-H d i r e c t i o n  0.0  and /-9.4  0.0  [  0.0  4.7  I  0.0  0.0  0.0  |  w i t h symmetry along As-H d i r e c t i o n  The value of 4.7 MHz compares reasonably w e l l w i t h the value of 4.2  MHz  as deduced from the s t r u c t u r a l data under approximation (b) i n the manner d e s c r i b e d e a r l i e r .  A comparison f o r the d i p o l a r i n t e r a c t i o n  o f a ' c l o s e ' proton with the unpaired e l e c t r o n on the oxygen o f the 0-H fragment cannot be evaluated a t the present stage s i n c e the d e t a i l e d e l e c t r o n i c s t r u c t u r e of an AsO^ group i n c l u d i n g the f o u r surrounding hydrogens i s not y e t known.  However, the observed good  agreement between the d i p o l a r i n t e r a c t i o n parameters obtained through the a n a l y s i s of the ENDOR r e s u l t s and those c a l c u l a t e d on the b a s i s of the c r y s t a l s t r u c t u r e , f o r the As-H t e n s o r , lends support to our view 4t h a t the formation o f AsO^ of  KDA.  c e n t r e causes l i t t l e change i n the l a t t i c e  - 105 It  is noted that the 0-H d i r e c t i o n s when projected on the  ab plane are along a and b axes according to the crystal data.  structure  The OH bonds, however, appear to deviate from the ab plane by  a few degrees in the ac plane.  Bjorkstam's  deuteron resonance  r e s u l t s ^ show this to be the case and although the present 7  cannot confirm t h i s , they do not contradict  results  it.  Far Protons Isotropic  interaction:-  The contact interaction is found  to be -2.875 MHz, which means a spin density of 0.20% on the Is  orbital  of proton.  in  Using the spin p o l a r i z a t i o n model mentioned e a r l i e r  connection with the ' c l o s e ' proton, this c l e a r l y shows that the hydrogen bonds in this case are p a r t i a l l y  covalent.  It  0...H  is not possible  for the spin p o l a r i z a t i o n mechanism to give r i s e to spin density on the Is hydrogen atom o r b i t a l  i f the hydrogen bond were purely i o n i c .  We w i l l return to a discussion of this important point in the next section. Anisotropic Interaction:-  A decomposition of the observed  tensor, using the procedure outlinedfor the ' c l o s e ' proton tensor possible.  The two d i p o l a r tensors may be written as:  ,with the symmetry axis along  is  - 106 the 0...H d i r e c t i o n , and -4.6  0.0  0.0  0.0  2.3  0.0  0.0  0.0  2.3  with the symmetry a x i s along the As-H d i r e c t i o n .  As mentioned  e a r l i e r , i t has not been p o s s i b l e t o c a l c u l a t e the d i p o l a r p a r t o f the tensor r e s u l t i n g from t h e unpaired e l e c t i o n s p i n d e n s i t y on the oxygen o f t h e 0...H bond.  For the As-H case, however, t h e v a l u e  of 2.8 MHz c a l c u l a t e d on the b a s i s o f c r y s t a l s t r u c t u r e compares f a v o r a b l y with the v a l u e o f 2.3 MHz given above.  Note a l s o t h a t f o r  the f a r protons the a n i s o t r o p i c i n t e r a c t i o n i s dominated by the d i p o l a r i n t e r a c t i o n o f the proton with the unpaired s p i n on the a r s e n i c atom. T h i s i s why Fig.l9(a) shows angular v a r i a t i o n s i m i l a r t o the angular 75 v a r i a t i o n on the lowest f i e l d As  h y p e r f i n e component, F i g . 14.  On the other hand, the a n i s o t r o p i c p a r t o f the ' c l o s e ' proton superh y p e r f i n e t e n s o r i s dominated by the i n t e r a c t i o n o f the proton with the unpaired e l e c t r o n s p i n d e n s i t y a t the oxygen atom.  T h i s can be  understood q u a l i t a t i v e l y because o f the ^ - n a t u r e o f the d i p o l a r 75 i n t e r a c t i o n and the d i s t r i b u t i o n o f t h e s p i n d e n s i t y a t As oxygen atoms.  B.  and the  HYDROGEN BONDING  KDA has turned out t o be an i d e a l system f o r s t u d y i n g the nature o f the hydrogen bond.  Here the H i s l o c a t e d between two  oxygens belonging t o two d i f f e r e n t AsO* u n i t s a t a d i s t a n c e of 1.06A  0  I  -  107  -  from one o f them. The hydrogen bond was d e s c r i b e d by P a u l i n g ^ ,  and by  72  Lennard-Jones  and Pople  73  on a p u r e l y e l e c t r o s t a t i c  model.  Subsequently  74  Coulson  and Tsubomura  p o i n t e d out the inadequacy o f the  s t a t i c model and emphasized the importance o f the structures  i n v o l v i n g charge t r a n s f e r .  valence-bond  The s t r o n g e s t e v i d e n c e  covalency  i n the hydrogen bond appears to come from the  intensity  of c e r t a i n  infrared  electro-  transitions  for  increased  and some data on d i p o l e  75  moments  .  also y i e l d  The study o f c o n t a c t h y p e r f i n e direct  hydrogen bond. not t i l l is  i n t e r a c t i o n o f protons can  i n f o r m a t i o n on charge t r a n s f e r and c o v a l e n c y  Such a study f o r . p r o t o n s i n f r e e r a d i c a l s  now shown e v i d e n c e f o r t h i s  expected to be very  effect  because the  small and t h e r e f o r e d i f f i c u l t  this  interaction  polarization  hydrogen bond by an u n p a i r e d s p i n d e n s i t y on oxygen orbital  detailed  the s p i n d e n s i t y on oxygen with  theory c o r r e l a t i n g  observed c o n t a c t data on s i m i l a r  interaction systems i s  is  o f hydrogen.  not a v a i l a b l e .  a l s o not a v a i l a b l e .  r e a s o n a b l e to s t a t e t h a t the c o n t a c t  Unfortunately  Sufficient However,  covalencies  equal  i n the two p o s i t i o n s .  a  the experimental seems observed  proportional  to  In o t h e r words the r a t i o  i n the 0-H bond to t h a t i n the 0 . . . H  t o the r a t i o  it  hyperfine i n t e r a c t i o n  i n the two p o s i t i o n s o f the p r o t o n may b e ' - d i r e c t l y  the c o v a l e n c y  The  however,  produces a 3 s p i n i n the Is  their  has  effect.  As p o i n t e d out i n the p r e v i o u s s e c t i o n , the o f the 0 . . . H  by EPR  the  to r e s o l v e .  h i g h e r r e s o l u t i o n p o s s i b l e with the ENDOR t e c h n i q u e i s , expected to r e v e a l  in  of the c o r r e s p o n d i n g i s o t r o p i c  of  bond may be roughly interaction  - 108 -  constants i . e .  equal to -13.81/-2.87=4.8.  This figure may be compared 73  with the expression given by Coulson and Danielsson  for t h i s , which  for the distances involved in our case turns out to be 4.3.  The  agreement may be considered to be good in the l i g h t of the crude approximations employed here. Such evidence from ENDOR when available on many systems may prove to be useful data on which detailed c a l c u l a t i o n of the covalency in the hydrogen bond may be made. C.  FERROELECTRICITY  The EPR experiments at 77 and 4.2°K have c l e a r l y shown the effects of f e r r o e l e c t r i c domains.  In fact the experiments have shown  the f e a s i b i l i t y of examining by EPR and ENDOR each domain separately in a multidomain c r y s t a l .  This enables a study of s u b l a t t i c e p o l a r i -  zation which might be valuable where unfavourable relaxation conditions make d i e l e c t r i c measurements d i f f i c u l t . The determination of the accurate data on the hyperfine interaction of the protons in the f e r r o e l e c t r i c phase now makes available parameters necessary for a detailed and accurate study of the temperature dependence of proton superhyperfine structure.  Such  studies can y i e l d valuable information on proton dynamics in the paraelectric phase of this c r y s t a l .  We have recently completed such  a study which w i l l be reported elsewhere.  - 109 D.  SUMMARY  4This study emphasizes the f a c t that the AsO^  center in  Kr^AsO^ is an ideal paramagnetic probe to study several aspects of ferroelectricity  and hydrogen bonding in this c r y s t a l .  The center  is  formed with remarkably l i t t l e damage to the l a t t i c e as the discussion of the symmetry of the anisotropic proton hyperfine structure shows  3_ clearly.  The extra unpaired electron captured by the AsO^  unit  goes into an A-| antibonding o r b i t a l with apparently l i t t l e damage to the surroundings. The study of hyperfine structure for the hydrogen bonded 'far'  proton which was completely unresolved in EPR and resolved only  by ENDOR, has provided d i r e c t evidence of covalency in the hydrogen bond.  The precise data regarding the hyperfine i n t e r a c t i o n obtained  through ENDOR can form the basis for detailed calculations  relating  to the nature of the hydrogen bond in s o l i d s . The use of the ENDOR technique in demonstrating the nature of ordering of protons in the two f e r r o e l e c t r i c domains, which confirms S l a t e r ' s model, has been shown.  EPR is l i k e l y to prove very  useful in the study of the dynamics of proton motion in this  crystal  14 as has been demonstrated by Blinc et a l .  The complete parameters  now obtained w i l l permit a more detailed study of the proton and 75 As  dynamics through more detailed study of temperature dependence 75  of both As  hf and proton shf structure.  made and are described next.  Such studies have been  - 110 4.5  Temperature dependence of the EPR rpectra As mentioned in Chapter I,  the d i e l e c t r i c and other  properties of the KDP-type crystals can be understood best in terms 18  of the Kobayashi crystals.  model of the f e r r o e l e c t r i c t r a n s i t i o n in these  Many experiments have been done with a view to detecting the  proton-lattice coupled mode motion, the existence of which is fundamental to this model.  Experimental evidence for the existence of a f e r r o -  e l e c t r i c mode has been obtained for K D P  1 2  ^  and D K D P  1 2  ^.  It  however, not clear whether the observed mode represents a pure  is, lattice  mode which is not connected with the proton d i s o r d e r , a quasi spinwave type proton tunneling mode, or a mixed proton-lattice mode.  In  the KDA-type c r y s t a l s , the corresponding Raman and neutron d i f f r a c t i o n data is not a v a i l a b l e .  These c r y s t a l s , however, have been investigated 13  in d e t a i l through NMR techniques.  Although the NMR and NQR  results  point to the existence of a strong coupling between the motion of protons and of the l a t t i c e , these experiments have yielded  little  information on the temperature dependence of the motion of either As  75  mode.  or hydrogens and, hence, on that of the coupled proton-lattice 75  The lack of data on the motion of As  and protons in these  c r y s t a l s may be ascribed to the fact that the anticipated frequencies fall  in the range of 1 0 ^ Hz, at room temperature and this is a b i t  too low for Raman, I.R.  and neutron scattering experiments.  this range of frequencies f a l l s  However,  in the range where EPR is known to be  the most suitable technique and a detailed investigation of the temperature dependence of the EPR spectra was thus taken up.  - Ill  -  The EPR spectra were recorded at the X-band microwave frequencies, using a Varian variable temperature accessory, together with a copper-constantan thermocouple to measure the sample temperature, the accuracy of the temperature bath being ^ 1 ° . Preliminary experiments were done on the powder samples of KDA, DKDA and ADA.  As explained e a r l i e r , only the lowest f i e l d A s  hyperfine l i n e shows further s p l i t t i n g when cooled to temperatures.  7 5  'lower'  We w i l l therefore concentrate mainly on the changes 75  in the spectral features associated with the lowest f i e l d As  hyperfine  transition. F i g . 25 shows the features associated with the lowest  field  75 As  t r a n s i t i o n , recorded at the various temperatures for the case  of the powdered sample: of KDA.  At room temperature the two main  l i n e s at about 1230 and 1370 Gauss are j u s t the ' p a r a l l e l ' and the 'perpendicular' features associated with the t r a n s i t i o n , with the hyperfine parameters given in Table 1.  It  is seen from the inspection  of F i g . 25 that only the ' p a r a l l e l ' component shows the presence of the proton superhyperfine s t r u c t u r e , c h a r a c t e r i s t i c of four equivalent spin % nuclei  (protonsin our case).  This can be e a s i l y understood on  the basis of the ENDOR results which have shown that the superhyperfine couplings are highly anisotropic and the largest principal component l i e s close to the c-axis d i r e c t i o n of the c r y s t a l .  On lowering the  temperature the superhyperfine features on the ' p a r a l l e l ' component s t a r t to change from the quintet towards a t r i p l e t structure and, simultaneously the single l i n e corresponding to the position starts to s p l i t into two.  'perpendicular'  At about 215°K (though s t i l l  about  - 112 -  K H As0 4 ( POWDER ) 2  T=300°K T=272°K T = 263°K T=253°K T=256°K T=250°K T=22S°K T=224°K  1400  F i g . 25  Temperature dependence of the powder EPR spectra for x-irradiated KH AsCL. Only the features associated with 75 3 4the As i 2 hyperfine t r a n s i t i o n for the AsO^ centre 9  m  =  are shown (see  text).  _ 113 _  115° above the Curie point)  the superhyperfine structure changes from  a quintet to a t r i p l e t with the components having the intensity pattern of 1:2:1.  Note that here the hyperfine parameters already  r e f l e c t the orthorhombic symmetry whereas, on the basis of the known c r y s t a l structure of KDA, the EPR spectra are expected to r e f l e c t only an axial symmetry in the paraelectric phase, below 97°K. In F i g . 26 are presented the s i m i l a r spectra observed for the case of the powdered samples of the a n t i f e r r o e l e c t r i c compound ADA. Note again that even at about 330°K, (again about 115° above the Curie point) the spectra r e f l e c t the features of those expected below T  c  in this system. Two important conclusions follow from these studies.  First,  these results present a rather clear demonstration of the fact that the known tetragonal symmetry in the p a r a e l e c t r i c phase of these compounds is only a time average of two orthorhombic ones.  And  second, at lower temperatures the time scale of the motion of the 75 protons and of the As  nuclei appears to be the same.  This l a s t  inference is important in that i f this is proved to be indeed the case, these studies could provide a rather d i r e c t evidence of the much-sought-after proton l a t t i c e coupled mode motion in these systems. Another very interesting feature of F i g . 25 and 26 is that over a range of about 7 0 ° , the EPR spectra r e f l e c t simultaneously the features of those due to axial and non-axial symmetry.  This  observation indicates that there are perhaps two mechanisms involved which have d i f f e r e n t a c t i v a t i o n energies and which a f f e c t the EPR spectra d i f f e r e n t l y .  Of course, the recent NMR experiments have  -  F i g . 26  114 -  EPR spectra of the AsO^~ centre in powder samples of x-irradiated NH H»AsO at the indicated temperatures. A  A  - 115 -  shown the presence o f r o t a t i o n o f the AsO^ groups and i f As  nuclei  are assumed t o be possessing a t u n n e l i n g motion between two q u i l i b r i u m s i t e s , then these o b s e r v a t i o n s c o u l d be e x p l a i n e d .  To o b t a i n a d d i t i o n a l  i n f o r m a t i o n on t h e dynamics o f the p r o t o n - l a t t i c e motion, we undertook a systematic i n v e s t i g a t i o n o f t h e temperature dependence o f the EPR 4s p e c t r a o f the AsO^ c e n t r e i n the s i n g l e c r y s t a l s o f KDA, DKDA and ADA. The b a s i s o f the s i n g l e c r y s t a l s t u d i e s can be d e s c r i b e d as 4f o l l o w s . As explained e a r l i e r , EPR s t u d i e s o f the AsO^ c e n t r e i n 82 KDA and DKDA have shown  t h a t i n the f e r r o e l e c t r i c phase f o u r  o r i e n t a t i o n s f o r t h i s c e n t r e a r e , i n g e n e r a l , observed.  Two o f these  s i t e s were shown t o be due t o t h e e x i s t e n c e o f t h e two d i f f e r e n t l y o r i e n t e d AsO^ t e t r a h e d r a i n the u n i t c e l l o f these c r y s t a l s , whereas the other two were proved t o a r i s e from the e x i s t e n c e o f the two o p p o s i t e l y p o l a r i z e d domains.  I f t h e r e f o r e the l a t t i c e i s completely  r i g i d i n the p a r a e l e c t r i c phase, the f e r r o e l e c t r i c t r a n s i t i o n being e n t i r e l y due t o t h e o r d e r i n g o f protons i n the hydrogen bonds accompanied by the displacement o f As and K ions along the c - a x i s a t the C u r i e p o i n t , two s i t e s a r e i n general expected f o r a l l the 4- c e n t r e . I f , however, the (K-AsO^) / • x system o r i e n t a t i o n s o f the AsO^ i s i n motion, according t o the Kobayashi o r the Cochran models, the 4number o f s i t e s f o r t h e AsO^ c e n t r e could be one, o r more, depending upon the s t a t e o f the motion i n the system. Moreover, the e f f e c t s 75  of t h e r o t a t i o n o f the A s 0 t e t r a h e d r a and o f the motion o f As 4  and  protons can here be s t u d i e d f a i r l y independently and t h i s was b e l i e v e d to be h e l p f u l f o r the understanding o f t h e d e t a i l s o f the powder EPR spectra too.  - 116 -  The present study shows that only one s i t e is observed for 4the orientation of the AsO^  centre at very high temperatures, 253°K  and above for the case of KDA and DKDA, and 333°K and above for the case of ADA.  At lower temperatures, even though s t i l l  about 80°  above the Curie p o i n t s , the EPR spectra already r e f l e c t the symmetry of those s i t e s expected and observed in f e r r o e l e c t r i c phases of KDA and DKDA.  This is c l e a r l y seen by examining F i g . 15 which shows the  angular v a r i a t i o n of the group of EPR lines (each a r i s i n g from a distinct orientation of the AsO^~ centre) associated with lowest-field 3  hyperfine component n i j ~ previously.  which alone shows this s p l i t t i n g as explained  For comparison the angular v a r i a t i o n of the same group  for the f e r r o e l e c t r i c phase of KDA at 77°K is also included, see F i g . 15(b).  It  is further noted from the spectra recorded with the  magnetic f i e l d H in the crystal ab plane, that the range of temperatures 4-  at which these d i f f e r e n t orientations of the AsO^  centre become  indistinguishable from each other is also the range of the temperature  75  where the superhyperfine structure due to protons, on each of the As EPR l i n e s , disappears.  Moreover, as the temperature is raised f u r t h e r ,  the linewidth decreases, from a value of 30-40 Gauss, (at  the  coalescence temperature where the sites collapse) to a residual linewidth of 5 Gauss at approximately 77°K (almost corresponding to that of the individual components at very low temperatures). Similarly,  as the temperature is lowered below that corresponding to  the collapsing of the individual components, the separation between 4the lines corresponding to the d i f f e r e n t l y oriented AsO^  centres  increases, u n t i l i t reaches to a maximum of about 35 Gauss, see F i g . 27.  - 117 -  2CH i  ^  240  j  ,  ,  ,  ,  260  280  300  320  340  —  F i g . 27  ,  360  ,—  380  T(K)  Temperature dependence of the s p l i t t i n g s associated with the 75  lowest f i e l d As crystals.  hyperfine t r a n s i t i o n for H||X in various  -  -  118  T h i s happens when the c r y s t a l s are s t i l l i n t h e i r high temperature 75 phase and i s observed f o r t h e s p l i t t i n g s o f the As  hyperfine i n t e r -  a c t i o n as well as those due to the proton h y p e r f i n e i n t e r a c t i o n s . These r e s u l t s c l e a r l y r u l e out the r i g i d - l a t t i c e model f o r the f e r r o e l e c t r i c t r a n s i t i o n i n these c r y s t a l s , s i n c e they can be o n l y 75 e x p l a i n e d i n terms o f the presence of motion of both As  n u c l e i as  well as protons, i . e . they demonstrate the e x i s t e n c e o f p r o t o n - l a t t i c e coupled modes as we s h a l l show below. 75 The temperature dependence of the motion o f As  was  studied  from 4.2°K to 345°K with the Zeeman f i e l d H o r i e n t e d along the t e t r a g o n a l a(b) a x i s as well as along the orthorhombic axes, points X (or Y) i n F i g . 14 where the EPR s p e c t r a are found to be the simplest.  On the basis of the c r y s t a l s t r u c t u r e i t w i l l be e a s i l y  seen t h a t f o r the case o f H||X,  the l i n e s due to the two d i f f e r e n t l y  o r i e n t e d AsO^ t e t r a h e d r a c o i n c i d e , and on the b a s i s of the r i g i d l a t t i c e model only one s i t e i s expected u n t i l a t (or very near) the Curie p o i n t , when the a r s e n i c n u c l e i get d i s p l a c e d and the two domains formed.  On the other hand, f o r the case of H||a  (or b ) , a t any  temperature, two and only two l i n e s are expected because of the two d i f f e r e n t l y oriented tetrahedra.  The i s o t r o p i c s p e c t r a observed i n  the ab plane at high temperatures show t h a t the AsO^ groups are undergoing motion which i s f a s t enough to smear out the d i s t i n c t i o n between the two types of t e t r a h e d r a . t h a t f o r H||X,  I t must be f u r t h e r mentioned  no proton superhyperfine s t r u c t u r e i s r e s o l v e d and t h i s  d i r e c t i o n i s thus more s u i t a b l e f o r the studying o f the motional e f f e c t s on the A s ^ h y p e r f i n e s t r u c t u r e . 7  On the other hand, the H||c d i r e c t i o n  - 119 -  was chosen for studying the motional effects in the proton superhyperfine structure because for that d i r e c t i o n a l l  the arsenic sites  are  75 equivalent, and thus the slowing of the As  motion do.es not seem to  a f f e c t the EPR spectra. To evaluate the c o r r e l a t i o n times for the motion of As  75  nucleus, as well as for the protons, a computer programme based on the formalism of the modified Bloch equations was used. of the As  AsO^  75  For the case  motion, the s p l i t t i n g between the EPR lines due to the two  centres belonging to the two oppositely polarised domains was l measured to be 33 Gauss, and was estimated to be 8 Gauss. -  T  2  Although the actual lineshapes were neither pure Lorentzians nor Gaussians, Lorentzian shapes were assumed for these c a l c u l a t i o n s . For the case of the protons the s p l i t t i n g s for H||c for the case of both the ' c l o s e ' and t h e ' f a r '  protons were measured to be 10.80 Gauss l  and 1.50 Gauss r e s p e c t i v e l y , as measured by ENDOR.  was estimated  to be 3.5 Gauss and contrary to the procedure of Blinc et a l . no allowance was made for those Slater configurations which give r i s e to zero dipole moment for an h^AsO^ group.  It  is emphasized that this  is an approximation which, however, is believed to be quite good at temperatures close to ^ 300°K as well as at low temperatures approaching the Curie point.  By comparing the theoretical  and the experimental  spectra, the c o r r e l a t i o n times, x , were obtained. in F i g . 28 where I n -  The data are shown  is plotted against 1°-?-°-.  Several important features can be noted from inspection of Fig.  28.  F i r s t of a l l  i f we assume that the motions are thermally  l c o r r e l a t e d , then the plot of 1 n - against - should be l i n e a r , 1  T  T  the  - 120 -  23.00 22.00  Protons in K H A s 0 , H / / c 2  21.00  4  As  7 5  in K H A s 0 H / / X  As  7 5  in K D A s 0 , H / / X  As  7 5  in N H H A s 0 H / / X  2  4)  2  4  4  2  4 l  Protons in N H H A s 0 , H / / c  20.00  4  2  4  19.00  c  18.00 17.00 16.00 15.00  2.80  3.20 3.60 4 . 0 0 4 . 4 0 4 . 8 0 5.20 — * » -  IO  3  T°K 75  Fiq.  28  Correlation times for the motion of As  and of protons, 75  calculated from the temperature dependence of As proton hyperfine structure.  and  - 121 -  slope being the a c t i v a t i o n energy of the potential energy barrier to the motion.  We notice that for the case of KDA, which could be  studied the most extensively, both the graphs can be broken into three l i n e a r regions each, with slopes in eV and preexpontial in Hz o f :  0.25, 1.0 x 1 0  the motion of A s  7 5  1 3  ; 0.12, 3.9 x 1 0  and 0.5, 2.8 1 0  1 8  1 0  ; 0.2, 3.2 x 1 0  ; 0.15, 2.5 x 1 0  1 1  factors 1 2  for  ; 0.2, 3.2 x 1 0  1 2  for the motion of protons. 75 It  is c l e a r that the motion of As  nucleus and protons are  governed by d i f f e r e n t processes at higher temperature but the same process governs the motion of both types of nuclei at lower temperatures. These studies thus present d i r e c t evidence for the existence of a strong coupling between the motion of the protons and that of the As  nuclei.  75  Similar coupling i s also observed for the case of ADA, where 75  the a c t i v a t i o n energy and the preexponential factors for the As motion are:  0.5, 1 x 1 0  1 2  ; 0.25, 7.9 x 1 0  those for the proton motion:  1 0  ; 0.12, 1.4 x 10 and  0.25, 7.9 x 1 0  9  1 0  ; 0.33, 8 x 1 0 .  The  1 1  75 same quantities f o r the 0.3, 13.6 x 1 0  1 3  motion of As  ; 0.13, lx 1 0  1 1  in DKDA were determined to be  ; 0.09, 5 x 10 for the case of 9  H||X.  We have so f a r , not been able to obtain c o r r e l a t i o n times for the motion of deuterons because of the lack of resolution in the EPR spectra.  However, comparison of the results for the deuteron 76 75 intrabond motion in DKDA with our results on As c l e a r l y shows  that below about 250°K, the same process governs the motion of deuterons and As  75  and this may be taken as an evidence for the  existence of the coupled mode motion in this material a l s o . be interpreted as the frequency of exchange of the As  75  l v = - can T  and of protons  - 122 -  in t h e i r respective double minimum p o s i t i o n s .  For the protons this  conclusion can be drawn in analogy with the NMR, EPR,  IR,  Raman, and  75 neutron scattering data.  For the case of As  although X-ray  d i f f r a c t i o n experiments point to preferential along c-axis  vibrations of heavy ions  , no quantitative data is a v a i l a b l e , but this has been 18 21 22 78 79  postulated by several authors recently.  '  '  '  '  Furthermore,  although the EPR studies do not y i e l d d i r e c t information on the motion of K  or NH^ i o n , symmetry considerations allow us to identify the 7" • > observed motion of As as that of the (K-AsO^) or (NH^-AsO^) systems +  75  along the c-axis.  Thus the coupled proton-As  motion may be i d e n t i f i e d  as the coupled proton-lattice mode in these c r y s t a l s . 2  To check whether the observed exchange frequencies follow the  v a (T-T ) r e l a t i o n s h i p , plots of v versus /T-Tc were made, see F i g . 29.  These plots were not linear over the entire range of the invesi-  gated temperatures, but they became l i n e a r at lower temperature as T->T . C  Since this r e s u l t is expected on the basis of both the Cochran and the Kobayashi mechanisms, i t supports both the models equally.  However,  the observation that at higher temperatures the exchange frequencies 75 for the proton motion are much higher than those for the As  motion  and that the cross-over takes place at lower temperatures, favors the Kobayashi over the Cochran mechanism.  One could also check this point  further by comparing the slopes of the v versus A T - T ) plots for the deuterated and the undeuterated c r y s t a l s .  On the basis of the  Kobayashi model the slopes of these plots w i l l be quite d i f f e r e n t , being strongly dependent on the tunneling frequencies of the protons or the deuterons in t h e i r double minimum potential wells.  No such  52  F i g . 29  P l o t s of v=- against [T-T ] \  Notation on the p l o t s corresponds to t h a t i n F i g . 28  The i n s e t shows enlarged v e r s i o n of the p o r t i o n marked by the dotted l i n e s .  - 124 -  large difference i s , however, expected on the basis of the Cochran d e s c r i p t i o n of the phase t r a n s i t i o n here. Inspection of F i g . 28 also shows that at higher temperatures 75  the slopes of the plot  for the As  motion in KDA is much larger than  the slopes of the corresponding plot in DKDA.  Although this seems to  support the Kobayashi type description of the t r a n s i t i o n mechanism at lower temperatures the slopes are not appreciably d i f f e r e n t and this point is not c l e a r l y understood.  It must be mentioned that in the 75  region of the lowest investigated temperatures the motion of As  as  well as that of the protons is already f a i r l y frozen on the EPR scale and the experimental uncertainty  in the magnitudes of the  extracted c o r r e l a t i o n times is too large to a r r i v e at d e f i n i t e conclusions.  It  is believed that EPR experiments using much lower  microwave frequencies w i l l be quite helpful to c l a r i f y this point further. We also l i k e to point out that over a large range of temperatures the plots of Inv versus ln(T-T ) are reasonably pointing to the r e l a t i o n s h i p of the form v a ( T - T ) . c  n  It  linear,  is emphasized  that such a r e l a t i o n s h i p is not predicted by any of the current models of the f e r r o e l e c t r i c t r a n s i t i o n s here.  In this regard i t may 76  be noted that in the recent work of Blinc et a l .  a similar realtion-  ship for deuteron T-| (though not for T) in DKDA type c r y s t a l s has also been pointed out. Another feature to be noted from these plots is that,  at  75  corresponding temperatures, the motion of As slowest in ADA and the f a s t e s t in KDA.  and of protons is the  Of course, this observation is  - 125 -  not unexpected since the Curie point for ADA is the highest whereas that for KDA is the lowest.  This may be related to the extra hydrogen  bonding that results in ADA due to the hydrogens of the NH^ ion.  More  75 puzzling is the observation that in ADA, the motion of As  and of  protons having got coupled over a certain temperature range, gets decoupled at lower temperatures.  Although this is again not c l e a r l y  understood, i t might also be a r e s u l t of the fact that at the lowest investigated temperatures, the coupling between the motion of NH^ ion and of the AsO^ units is stronger than between the motion of the protons and the AsO^ u n i t s .  This could be checked further by investigating  the temperature dependence of the NH^ motion.  We note that NH^  r a d i c a l s also form in x-irradiated ADA, and striking changes are observed in the temperature dependence of the EPR spectra of the NH^ centre.  No detailed analysis was, however, carried out, since i t  is  f e l t that for these rather long c o r r e l a t i o n times, i t w i l l be more advantageous to employ low frequency (1-2 GHz) EPR techniques.  NMR  experiments might also prove quite helpful here. These studies thus provide accurate quantitative  information  on the dynamics of the low frequency motion in these systems.  We  have, however, not yet offered an explanation for the rather unusual features observed in the temperature dependence of the powder EPR spectra, but we w i l l now take that point up. It was already indicated that the observed, simultaneous existence of the axial and the non-axial features in the powder EPR spectra, could be explained i f ,  in addition to the existence of the  jump-type motion of the AsCL and proton u n i t s , there also exists an  - 126 e f f e c t i v e r o t a t i o n type motion about the a x i a l symmetry a x i s i n these compounds.  The e f f e c t o f t h i s ' e f f e c t i v e ' , r o t a t i o n w i l l be to average  out the A and g tensor a n i s o t r o p y i n the plane p e r p e n d i c u l a r to the axis of this 'rotation'.  For s i n g l e c r y s t a l samples, i t s e f f e c t can  be s t u d i e d best by o b s e r v i n g the temperature dependence o f the s p e c t r a f o r H| j a (or b ) . S i m i l a r l y the exchange motion can be s t u d i e d b e s t f o r H11X  ( F i g . 28 f o r data ). A n a l y s i s of data f o r H||a, s i m i l a r l y shows  t h a t the a c t i v a t i o n energies f o r the processes governing the motion f o r H||X and H||a are d i f f e r e n t a t higher temperatures but they become 75 e s s e n t i a l l y i d e n t i c a l a t temperatures where the As -proton motion gets coupled. Fig.30 shows the angular v a r i a t i o n o f the lowest 75 4f i e l d As h y p e r f i n e l i n e i n the EPR spectrum of the AsO^ c e n t r e i n KDA and ADA a t temperatures where the a x i a l and the non-axial f e a t u r e s are observed s i m u l t a n e o u s l y i n the powder s p e c t r a . I t w i l l be observed t h a t here the s p l i t t i n g s observed f o r H | |a are not r e s o l v e d , i n d i c a t i n g t h a t the d i s t i n c t i o n between the two types of or l e s s smeared out.  ASO4  t e t r a h e d r a i s more  T h i s i s a s t r o n g evidence f o r the e x i s t e n c e o f  an e f f e c t i v e r o t a t i o n type motion.  Of c o u r s e , the r e c e n t NMR s t u d i e s  do p o i n t to the e x i s t e n c e o f a slow r o t a t i o n o f the AsO^ groups i n the systems.  However, the c o r r e l a t i o n times f o r the r o t a t i o n observed -3 -5 by the NMR experiments (x~.T0 sec - 10 sec) are much l a r g e r than the c o r r e l a t i o n times observed f o r the r o t a t i o n type motion here 7 -9 (T =10"  to 10  s e c ) . I t i s p o s s i b l e t h a t the e f f e c t i v e r o t a t i o n  detected i n our s t u d i e s r e s u l t s from a more complicated jumping p r o c e s s , f o r example, proton exchange between v a r i o u s S l a t e r c o n f i g u r a t i o n s which r e s u l t s i n e f f e c t i v e r o t a t i o n o f the AsO, u n i t s . I t seems c l e a r , i n any  - 127 -  (a)  KhL A s Q , , T = 2 5 0 K 0  20H  (b)  10  NH H As0 , T= 3 2 4 ° K 4  2  30  4  50  70  90'  Angle from tetragonal "a" axis Fig. 30  Angular v a r i a t i o n of the s p l i t t i n g s lowest f i e l d A s at the indicated  7 5  transition  associated with the  for KH As0  temperatures.  2  4  and NH H As0 4  2  4  - 128 -  case, that the observed unusual features in the powder EPR spectra are due to the simultaneous effectiveness of the tunneling type motion of the AsO^ nuclei and that of the rotation type motion of the AsO^ u n i t s , the two processes having d i f f e r e n t activation energies. 4.6  Studies on KH P0 -KH As0 mixed crystals 2  It  4  2  4  is well known that by mixing two f e r r o e l e c t r i c compounds  i t is possible to obtain mixed crystals whose Curie points can be varied continuously between the Curie points of the parent compounds. This property becomes important while selecting a d i e l e c t r i c for use in a given range of temperature and the study of the structural d e t a i l s of the mixed crystals thus acquires practical importance.  For  low concentration of the "impurity" constituent, EPR and in p a r t i c u l a r ENDOR, can prove very helpful for elucidating structural d e t a i l s here. We have employed these techniques with a view to investigating the structural d e t a i l s of the mixed KDP-KDA c r y s t a l s , KDA being mixed with KDP in concentrations ranging from one to about 20% by weight. 14 Again at the time we started our s t u d i e s , Blinc and Cevc  had  investigated the proton dynamics in these crystals for H||c.  They had  shown that for KDA in excess of 5% in KDP, no proton superhyperfine structure could be resolved in the p a r a e l e c t r i c phase.  This observation,  however, was not investigated further and i t formed the starting point of our studies. 4-  Detailed angular EPR studies of the AsO^  centre in these  crystals were carried out which showed that the spin Hamiltonian parameters describing the As  75  hyperfine structure at room temperature  - 129 -  as well as at 77°K are e s s e n t i a l l y the same as those of the AsO^" centre in KDA.  To investigate the l i n e broadening mechanism, the  l i n e shapes of the hyperfine transitions were examined as a function 4of the concentration of the As0  4  centres.  The concentration was  changed by x - i r r a d i a t i n g the mixed crystals for widely  different  periods of time.  1  The results showed the absence of the concentration  broadening' as the dominant mechanism for the smearing out of the proton superhyperfine structure.  To make sure that the superhyperfine  coupling had not been d r a s t i c a l l y changed, an ENDOR investigation was undertaken.  For a crystal  containing about 20% of KDA, and  and Hie the ENDOR spectra obtained by saturating Ty and T transitions is shown in F i g . 31 .  3  for  H||c  hyperfine  Comparison of these spectra with  those obtained from pure KDA (Fig. 17(a)  and (b))  shows that at these  concentrations the structure of the hydrogen bonds in the immediate 4v i c i n i t y of the AsO^  centre mixed crystal  with those for pure KDA.  is e s s e n t i a l l y  identical  We may thus conclude that KDA molecules  j u s t substitute the KDP molecules at random l a t t i c e  sites and the  d i s t o r t i o n of the l a t t i c e caused by these produces random c r y s t a l l i n e f i e l d s which then broaden the hyperfine lines to widths large enough to render the superhyperfine s t r u c t u r e , unobservable at higher temperatures.  - 130 -  .(close)  6  |  7  (a) H//c,4850G  (far)  rr/ [  18  20  22  24  26 M H z (b) Hic,2615G  .(far) ,/far)  8  i  Fig. 31  —  r  i  12  10  Z/  r#—r  18  ( c l o s e )  20 M H z  Typical proton ENDOR transitions in mixed KH P0 2  KH As0 2  4  crystals.  4  - 131 4.7  CONCLUSIONS The present studies were undertaken with a view to obtaining  detailed information on the nature of hydrogen-bonding and on the role of hydrogen bonds in the mechanism of the phase t r a n s i t i o n in compounds containing short hydrogen bonds.  The technique of ENDOR is  believed  to have been applied for the f i r s t time to study a hydrogen-bonding  81-82 problem in s o l i d s .  Detailed ENDOR s t u d i e s , involving also the use of  externally applied e l e c t r i c f i e l d s present additional evidence for the 4-  correctness of the model of the AsO^ proposed e a r l i e r by Hampton et a I .  3 5  centre in KDA type c r y s t a l s ,  Combined with the EPR s t u d i e s , the  ENDOR studies support the double minimum potential well model for the O-H-0 bond in these compounds. The ENDOR results also present evidence for the existence of covalent character for 0-H bonding in both the equilibrium s i t e s of an O-H-0 bond.  In the absence of experimental data  on the spin density at the oxygen s i t e , i t has not been possible to carry the discussion of the hydrogen-bonding in terms of the m.o. or valence bond theory very f a r .  However, the ENDOR studies y i e l d  accurate  data on the hydrogen-bond proton superhyperfine coupling constants and the data can form the basis for any accurate quantum mechanical of hydrogen bonding in the presently investigated systems.  It  calculation appears  that such information is rather d i f f i c u l t to obtain by means of other, more conventional spectroscopic methods. During the course of the present s t u d i e s , a simple graphical procedure has been developed for determining the signs of the hyperfine coupling constants for free radical  (S = h) systems.  This method can  - 132 -  complement the method of Double ENDOR in favorable cases. The higher resolution possible with the ENDOR technique has made i t p o s s i b l e , for the f i r s t time, to use protons as microscopic probes for investigating the f e r r o e l e c t r i c domain structure in the 4-  EPR spectra of the AsO^  centre in these c r y s t a l s .  Also the use of  externally applied e l e c t r i c f i e l d has shown the f e a s i b i l i t y of using EPR as a technique of p l o t t i n g hysteresis loop and this technique can complement the d i e l e c t r i c and other studies for studying sub-lattice p o l a r i s a t i o n at low temperatures. It  has been possible to obtain detailed and quantitative 75 information on the rather low frequency motion of the As nuclei  and the hydrogen bond protons, using as a microscopic probe, the 4-  temperature dependence of the hyperfine structure of the AsO^ in these compounds.  centre  The r e s u l t s y i e l d d i r e c t experimental evidence  for the existence of the coupled proton-lattice mode motion 75 systems and show that both the protons and the As jump type motion in t h e i r respective double minima.  in these  nuclei perform a These observations  provide experimental basis for the s u i t a b i l i t y of the pseudo-spin type d e s c r i p t i o n for the proton-lattice motion in these systems.  Also  no apparent change takes place in the EPR spectra at the Curie point, which may be interpreted to imply the absence of d i s p l a c i v e type t r a n s i t i o n not only for protons but also for the heavier n u c l e i .  These  studies are thus in broad agreement with the Kobayashi model. These results also indicate that the f e r r o e l e c t r i c mode observed in the Raman scattering experiments at room temperature  is  the c o l l e c t i v e proton-tunneling mode and not a coupled proton-lattice  - 133 -  mode.  This is because at room temperature and above the exchange  frequencies for the protonic motion are of the order of the frequency of the f e r r o e l e c t r i c mode observed in the Raman experiments, whereas the As  75  motion is much slower.  As the temperature is decreased, the 75  motion of protons slows down faster than that of As  nuclei  the c o r r e l a t i o n times for the two motions become e s s e n t i a l l y  until identical.  At higher temperatures the magnitudes of the proton c o r r e l a t i o n times 76  are consistent with those obtained from the recent NMR and Raman experiments.  On the other hand, no previous data has been available  on the motion of the As  75  nucleus in these compounds.  F i n a l l y , the present studies also demonstrate that in the paraelectric phase the known tetragonal symmetry of these c r y s t a l s only a time average of two orthorhombic ones.  It  is  is here noted that  recent NMR experiments also indicate that this might be the case. However, because of the time scales of these experiments, except within h° of T , the s i t e symmetry appears to be only tetragonal. Since the time scale of the motion f a l l s  in the range of the EPR time  s c a l e , our experiments c l e a r l y demonstrate that this is indeed the case. Our r e s u l t s , however, do not contradict the d i f f r a c t i o n experiments, but they rather r e f l e c t the fact that the nuclear motion coincides with the EPR time scale and that the Fermi contact coupling can be used as a sensitive microscopic probe for studying small amplitude motion. In conclusion, EPR and ENDOR appear to be quite promising techniques for investigating the nature of hydrogen bonding and the molecular motion in these compounds containing short hydrogen bonds.  - 134 -  It  is hoped that the present studies w i l l stimulate further  interest  for making more s p e c i f i c estimates of the hydrogen-bonding parameters and of the f e r r o e l e c t r i c mode motion in these compounds., since accurate data obtained here may serve as basis for such c a l c u l a t i o n s .  135  APPENDIX A Experimental Arrangement for Electron-Nuclear T r i p l e Resonance  In the course of extensive ENDOR studies on the AsO^" centre in x-ray i r r a d i a t e d single c r y s t a l s of KH^AsO^, we have observed for the f i r s t time steady.state ENDOR transitions predicted e a r l i e r by Feher,  86  and independently by Freed,  Nuclear T r i p l e Resonance by the  87  latter.  and named Electron-  Although the Electron-Nuclear Double Resonance (ENDOR) technique has already proved to be quite powerful for the  analysis  of complex EPR spectra, d e t a i l s of the processes operative during the ENDOR phenomenon are not yet quite clear (thus l i m i t i n g the p o t e n t i a l i t i e s of ENDOR as a general technique).  Progress has,  however, been made recently in the understanding of liquid-state ENDOR enhancements.  "  These enhancements were t h e o r e t i c a l l y 91 92  predicted and experimentally observed  5  to be optimum when the  lattice-induced nuclear-spin-flip rate (W^)  is comparable to the  lattice-induced e l e c t r o n - s p i n - f l i p rate (W ). g  It  has been observed,  however, that for protons in most l i q u i d samples W >>W , resulting g  N  i n very poor ENDOR enhancements. But i t was predicted as early as 86 87 1958 by Feher, and more recently by Freed that s i g n i f i c a n t steady state ENDOR enhancements should be obtained even in these unfavorable cases i f both the NMR t r a n s i t i o n s ,  - 136 -  corresponding to a p a r t i c u l a r set of equivalent nuclei as shown in F i g . 32 for the  case  s=%, l~h,  are simultaneously saturated.  Freed  has named this the technique of Electron-Nuclear T r i p l e Resonance and the technique is believed to be quite important for obtaining ENDOR information on a greater variety of samples.  We here describe  a simple arrangement to perform such Electron-Nuclear T r i p l e Resonance experiments. m  B  s.  ^2  m  I  , *2  A  hv.  W.  — —\y  • -2/ -1 A'  F i g . 32  Energy levels for a system with S-h and I=%.  See text for d e t a i l s .  The experimental arrangement is based around the X-band ENDOR spectrometer described in Chapter III.  In addition to the r f  signal generator (Marconi-type 1066 B) used for normal ENDOR work, a second o s c i l l a t o r (General Radio-type 1001 A) feeds the same  - 137 -  ENDOR loop surrounding the sample under study.  To this extent the 66  arrangement is s i m i l a r to the one used in the Double ENDOR experiment. In the Double ENDOR experiment, changes in intensity of ENDOR signals due to one type of nucleus are monitored while saturating ENDOR t r a n s i t i o n s corresponding to a second type of nucleus, the sign of the i n t e n s i t y changes being related to the signs of the hyperfine coupling constants of the two types of n u c l e i .  The procedure we  used i s f i r s t to select the microwave power and the external magnetic f i e l d to correspond to the normal ENDOR experiment.  One of the  o s c i l l a t o r s is then held at fixed frequency corresponding to the Zeeman frequency of the free nucleus in Eq. (A), and is frequency modulated to a depth of about 20 kHz at a rate of a few cycles per second.  The outputs cf the signal generators and the gains of the  amplifiers are adjusted so that at the f i n a l output terminal of the a m p l i f i e r system there appears optimum power at the two frequencies given by Eq. (A).  We find that in our amplifying system (as also in most  a m p l i f i e r s ) conditions for obtaining the necessary non-linearity can e a s i l y be achieved and therefore the method of generating the two frequencies given by Eq. (A) is quite simple. constant, a, in Eq. (A)  When the hyperfine  is only approximately known, one of the  o s c i l l a t o r s i s swept in frequency (the second one being kept o s c i l l a t i n g at constant frequency equal to the free nuclear Zeeman frequency), and thus we can obtain the t r i p l e resonance spectrum. 4-  The method has been tested on the AsO^ i r r a d i a t e d KH As0 . 2  4  The ENDOR (in fact the  centre in X-ray-  triple-resonance)  enhancements were obtained at the expected frequencies, (see F i g . 33).  - 138 -  !  i i 9.852 10002  j  !  i  j-  1  1  i  i  11.04 11.239  11.683  •  1  1  i  '  12.703 13000  i  1—^  '  F i g . 33(a) DOUBLE ENDOR AND TRIPLE RESONANCE SIGNALS IN X-IRRADIATED K H A s 0 2  4  (b) HYDROGEN-BOND ENDOR OF THE AsO^'CENTRE IN X-IRRADIATED KH As0 H//c-axis, T = 4.2°K, MICROWAVE FREQ. = 9369.75 Mc/s. 2  4  i  | 23.380 23.6854 Mc/s 23.280  -  1 3 9  -  The triple-resonance signals were s l i g h t l y broader than the corresponding ENDOR presumably due to fact that Eq. (A) does not hold exactly for the system under study.  For liquids,- however,  because of the absence of anisotropy in the hyperfine couplings, this s i t u a t i o n is not expected to a r i s e .  Experiments were carried  out on d i f f e r e n t EPR lines and consistent results were obtained.  As  a f i n a l check against the p o s s i b i l i t y of a two-photon absorption process giving the observed Triple-Resonance s i g n a l s , a low-pass r f f i l t e r was constructed.  The presence of non-linearity in the  amplifying system and the absence of the two photon absorption process was then confirmed and we believe that the method should be quite generally a p p l i c a b l e .  140  -  -  APPENDIX B EPR studies of the 'Other'  Paramagnetic  Centres  In the course of the present, studies i t was observed that prolonged x or y-irradiation  mentioned in the l a s t chapter) to the formation of several  (as  paramagnetic centres in a l l  the  leads  crystals  4-  investigated here.  Unlike the case with the AsO^  spectra of these 'other'  centre, the EPR  centres are very anisotropic and, in general,  as many as eight s i t e s arc observed for the possible orientations of these centres.  When the magnetic f i e l d H i s oriented in the  crystal  planes, the number of the possible orientations reduces to only four. Moreover, for H||c, a l l  these s i t e s become equivalent, thus the EPR  spectra are observed to be the simplest.  F i g . 7 shows a typical  EPR spectrum of x-irradiated Kr^AsO^, obtained f o r H||c.  The EPR  4-  spectrum of the AsO^  centre is quite d i s t i n c t in that i t shows the  quintet superhyperfine structure due to the four protons associated 4-  with the four O-H-0 bonds of the AsO^  centre.  marked with four arrows at the top of F i g . 7. four EPR lines due to the A s O  4-  This spectrum is In addition to the  centre, fourteen other strong  t r a n s i t i o n s also appear in the EPR spectrum.  From the  intensity  and the linewidth studies these t r a n s i t i o n s may be assigned to four d i f f e r e n t paramagnetic centres.  Three of these paramagnetic  centres, indicated by the markers at the bottom of F i g . 7 and 8, possess a central atom having a nuclear spin 1=3/2.  Since no  isotope e f f e c t was observed in the EPR spectra, this central atom  - 141 i s i d e n t i f i e d as the As  nucleus.  The ' g  1  values for these  centres are very close to the free electron g value.  To check  this assignment f u r t h e r , some spectra were recorded at K-band microwave frequencies. F i g . 9.  For H||c, such a spectrum is shown in  Since the separation between the components of these  centres was observed to be almost the same as that at X-band, i t confirms our assignment of the EPR t r a n s i t i o n s to these d i f f e r e n t paramagnetic centres.  Also when the irradiated crystals were annealed  at various temperatures, some of these centres grow up in concentrat i o n at the cost of others.  S i m i l a r l y the l i f e times of d i f f e r e n t  centres are d i f f e r e n t and spectra recorded over a period of about one month a f t e r i r r a d i a t i o n of a crystal behavior of a l l the same.  show that the intensity  the l i n e s assigned to a p a r t i c u l a r centre is indeed  Angular v a r i a t i o n of these spectra have been studied with  the magnetic f i e l d in the three crystal  planes.  Angular v a r i a t i o n  of the EPR spectra of a l l these three centres is observed to be virtually  the same.  Preliminary analysis of these spectra shows  that the hyperfine parameters describing the spectra of a l l centres are a l i k e , except for t h e i r actual magnitudes. 2-  with the spectra of the AsO^  these  Comparison.  93,94  centre indicates that these centres  belong to t h i s class of r a d i c a l s , although the .exact mechanism for their formation i s not yet It  clear.  is noted here that a f t e r these studies had been  completed, a preliminary report on the EPR studies of these three 83  centres i n KDA and ADA has appeared.  The conclusions obtained in  t h i s report are s i m i l a r to ours, although no d e t a i l s of the analysis  - 142 -  have yet been published. The fourth centre, observed in KDA is characterised by a doublet spectrum for H||c,  and marked as the P0 ~ centre in F i g . 7. 4  Angular v a r i a t i o n of this spectrum shows that in general eight sites are allowed for the possible orientations of this centre.  The  doublet s p l i t t i n g is almost i s o t r o p i c and equals about 106 at room temperature, but the g tensor is highly a n i s o t r o p i c , leading to a maximum of sixteen lines in the EPR spectra.  In the crystal ab  plane, however, the number of doublets reduces to only four. Comparison of the spin Hamiltonian parameters of this centre with 2the parameters of the PO^  95 96 centre sRows that the observed spectrum  2_ is due to P0  4  centre, formed due to the presence of phosphorous  impurities in ^ A s O ^ c r y s t a l s .  Observation of similar spectra in  ^ A s O ^ further showed that protons are not responsible for the observed doublet hyperfine structure.  Experiments on KDA c r y s t a l s  doped with KDP showed corresponding increase in the i n t e n s i t y of  31 the EPR spectra which reaffirms that P  is most probably the  nucleus responsible for the doublet hyperfine structure.  ENDOR  experiments were attempted with a view to obtaining a d e f i n i t e i d e n t i f i c a t i o n of the nucleus responsible for the doublet structure. Unfortunately, even at 4 . 2 ° K , i t was not found to be possible to saturate the EPR spectrum even with about 2 milliwatts microwave power.  of the  With the present superheterodyne spectrometer,  i t was, therefore, not possible to obtain ENDOR enhancements. Almost i d e n t i c a l spectra were observed for the case of DKDA, RbDA and ADA.  In ADA we also observed the spectrum due to  - 143 -  NHg r a d i c a l s .  A typical  Hj1c is shown in F i g . 34.  spectrum of the NH^ r a d i c a l , observed for The spectrum is e s s e n t i a l l y  identical 84 85  with that observed for this centre in irradiated NH^CIO^.  '  As mentioned in Chapter IV, the EPR spectrum of the NHg centre shows s t r i k i n g changes as the temperature is changed.  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