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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 UNIVERSITY, CHANDIGARH, 1 9 6 3 A THESIS 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 t h i s t h e s i s in p a r t i a l fu 1 f i lmenf of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that 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 reference and Study. I f u r t h e r agree that permission f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . It i s understood that copying or p u b l i c a t i o n of t h i s thes.is f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department of The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date 3o j C f j j - i -Supervisor: C. A. McDowell ABSTRACT The techniques o f EPR, ENDOR and double ENDOR were employed with a view to 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 heavier n u c l e i i n the 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 KH 2As0 4, KD 2As0 4, RbH 2As0 4, mixed KH 2P0 4-KH"2As04 and the a n t i f e r r o e l e c t r i c compound NH 4H 2As0 4 < The paramagnetic 4- 3-centre A s 0 4 , formed by the capture o f an e l e c t r o n by an A s 0 4 i o n , was used as a mic 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 accurate i n t e r p r e t a t i o n o f the As hyperfine s t r u c t u r e 4-i n the EPR spectra o f A s 0 4 . The use o f EPR to obtain 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" centre i n KH 2As0 4 a t 4.2°K have y i e l d e d accurate superhyperfine parameters. The r e s u l t s provide evidence 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 and 0 H- parts of the 0-H 0 bond i n such systems. A new method has been proposed f o r determining the signs of hyper-f i n e couplings 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 to the 4-A s 0 4 c e n t r e i n KH 2As0 4. A n a l y s i s of the temperature dependence of 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. At lower 75 temperatures, however, the c o r r e l a t i o n times f o r the As and the proton motions are found to be e s s e n t i a l l y the same. This 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. - i i -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. This development may extend the range of a p p l i c a b i l i t y o f the ENDOR technique. - i i i -TABLE OF CONTENTS Page ABSTRACT i LIST OF TABLES vi LIST OF FIGURES v i i ACKNOWLEDGEMENTS x i i GLOSSARY OF SYMBOLS USED x i i i CHAPTER ONE: INTRODUCTION 1 CHAPTER TWO: THEORETICAL 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 20 2.2.2 Superhyperfine Parameters through ENDOR measurements 25 2.2.3 Signs of the Hyperfine tensors 31 2.3 Motion Effects in hyperfine structure 33 2.4 Interpretation of the spin Hamiltonian parameters . 38 CHAPTER THREE: EXPERIMENTAL DETAILS 40 3.1 Preparation and Crystal structure of the Arsenates and Phosphates 40 3.2 The Irradiation Units 45 i 3.3 The EPR Spectrometers 45 3.3.1 The X-band Spectrometers 45 3.3.2 The K-band Spectrometer 46 - iv -Page 3.4 The ENDOR Spectrometer 46 3.5 ENDOR Technique '. 50 3.6 The Arrangement for Double ENDOR 53 CHAPTER FOUR: RESULTS AND DISCUSSION 55 4.1 EPR studies of AsoJ" centre 56 4.2 ENDOR of AsoJ" centre in KH2As04 79 4.3 ENDOR Data and Analysis 87 4.3.1 Signs of the Hyperfine and Superhyperfine Couplings .' 87 4.3.2 Angular variation of ENDOR transit ion 96 4.4 Correlation of EPR and ENDOR results 99 4.5 Discussion 101 A. HYPERFINE INTERACTION 101 Arsenic 101 Oxygen 102 'Close' protons 102 'Far' protons 105 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 crystals 128 4.8 CONCLUSIONS 131 - V -Page APPENDIX A: Experimental Arrangement for Electron-Nuclear Tr iple Resonance 135 APPENDIX B: EPR studies of the 'other' paramagnetic centres 140 REFERENCES 145 - vi _ LIST OF TABLES Table Page 4-1 Spin Hamiltonian parameters f o r the AsO^ centre at 296°K 68-69 4-2 Spin Hamiltonian parameters for the AsO^ centre at low (indicated) temperatures 78 3 Calculated values of 2 < S z >^  for the given set of 7 ^ As spin Hamiltonian parameters 88 4 Comparison of the observed r a t i o s v t / v T f o r a ' i ' l 'close' proton for the possible combinations of the 75 proton and As hyperfine couplings 89 (felt/ vCloSGJ 5 Observed and calculated values of ' and v i t , — c a -using the graphical procedure described in the text 95 6 Observed and calculated values, using the numerical diagonalisation procedure 97 7 Pri n c i p a l 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 in KH ?AsO d ..... 98 - v i i -LIST OF FIGURES Figure Page 1 Schematic energy level diagram for an S=J_ and 3 1= j system 23 2 Structure of KH^PO^-type crysta ls , unit-cell in space group I42d after J . West 42 3 (a) Displacement of atoms in Kh^PO^-type crystals at the Curie point 44 (b) c-axis projection of the crystal structure of KH2As04 below the Curie point, 97°K 44 (c) c-axis projection of the crystal structure of NH 4H 2As0 4 below the Curie point 216°K 44 4 Block diagram of the ENDOR spectrometer 47 5 Schematic representation of ENDOR signal 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 KH2As04 for H||c at 300°K at X-band (v=9.45 GHz). The lines from the As0 4 centre are marked at the top whereas the lines from the other centres (unidentified) are marked at the bottom 61 8 EPR spectrum of x-irradiated KH2As04 for H||c, at X-band (v=9.448 GHz) and at 4.2°K. T ] , T 3 , T 5 and T ? are the normally allowed and T 2 , T 4 and Tg are the - vi i i -Figure Page normally forbidden transitions belonging to the Aso|~ centre (see text) 62 9 EPR spectrum of x-irradiated KH^AsO^ for H||c at 300°K taken at K-band (v=24.150 GHz) 63 10 EPR spectrum of x-irradiated KD2As04 for H||c, at X-band (v=9.450 GHz) and at 300°K 65 11 EPR spectrum of x-irradiated RbH2As04 for H||c at X-band (v=9.435 GHz) taken at * 300°K 66 12 X-band (v= 9.325 GHz) spectrum of x-irradiated NH4 H 2As0 4 for H | j c at ^296°K 67 13 Comparison of proton superhyperfine features on 75 the lowest and the highest f i e l d As hyperfine 4-l ine in the EPR spectrum of the AsO^ centre in x-irradiated KH2As04 70 14 Angular variation of the spl i t t ings associated with the lowest f i e l d l ine ( I= )^ in the ab plane of x-irradiated KD 2As0 4 at 77°K 73 15 Angular variation of the sp l i t t ing associated with 75 the lowest f i e l d As hyperfine l ine for the As0 4 " centre in various (marked) crystals at low (indicated) temperatures 74 3 75 16 Electr ic f i e l d effects on the As' hyperfine component for H||X in x-irradiated KH2As04 at 77°K 77 4-17 Typical proton ENDOR signals from the As0 4 centre in x-irradiated KHoAs0„ at 4.2°K 80 - ix -Figure Page 18 Spl i t t ing of the 'c lose ' and the ' fa r ' proton ENDOR transitions for the case of H 2° away from the c-axis 82 19 Angular variation of the ' fa r ' proton ENDOR transitions in (a) the ac and (b) ab plane of x-irradiated KH2As04 83 20 Angular variation of the 'c lose ' proton ENDOR transit ions in the ac (or be) plane for (a) 75 the highest and (b) the lowest f i e ld As hyperfine transit ion in x-irradiated Kh^AsO^ at 4.2°K 84 21 Angular variation of the 'c lose ' proton ENDOR transitions in the ab plane of x-irradiated KH2As04 for (a) the highest f i e l d and (b) the lowest f i e ld A s 7 5 hyperfine transit ion at 4.2°K 85 4-22 Double ENDOR signals for protons around an AsO^ centre in x-irradiated KH2As04 for H||c at 4.2°K 9.1 23 Graphical representation of Eq. (39) (see text) for the ' f a r ' proton ENDOR transitions in x-irradiated KH2As04 H||c at 4.2°K 93 24 Graphical representation of Eq. (39) for the 'c lose ' protons in x-irradiated KH2As04 for H||c and 4.2°K 94 25 Temperature dependence of the powder EPR spectra for x-irradiated KH9AsO/,. Only the features - X -Figure Page 75 3 associated with the As mi=~z hyperfine transit ion for the AsO^" centre are shown (see text) 112 4-26 EPR spectra of the AsO^ centre in powder samples of x-irradiated Nh^r^AsO^ at the indicated temperatures. 75 3 Only the features associated with the As transit ion are shown .114 27 Temperature dependence of the spl i t t ings associated 75 with the lowest f i e ld As hyperfine transit ion for H| |X in various crystals 117 75 28 Correlation times for the motion of As and of protons, calculated from the temperature dependence 75 of As and proton hyperfine structure 120 2 1 29 Plot of v = —5- as a function of the reduced T temperature (T-T ) : 123 30 Angular variation of the spl i t t ings associated with 75 the lowest f i e ld As hyperfine l ine in the ab plane of Kh^AsO^ at the indicated temperature 127 31 Typical proton ENDOR transitions in mixed KH2P04 -KH2As04 crystals 130 32 Schematic representation of energy levels for an S=h system 136 33 Electron-Nuclear Tr iple Resonance signals for the 4-protons around the AsO^ centre in x-irradiated KrLAsO d, at 4.2°K and H||c 138 - xi -Figure Page 34 EPR spectrum at X-band (v=9.325 GHz) of NH* radical for HJ Ic in x-irradiated NH^AsG^ at room temperature 144 - x i i -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 (Department of Physics, IIS 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. Farmer for his continued advice and help. Several very stimulating discussions with Professors W.C. Lin and R.F. Snider, Dr. F.G. Herring and especially with Dr. J.A.R. Coope are also grateful ly acknowledged. I am thankful to Messrs. D.E. Kennedy, J.R. Dickinson and J . Tait and Dr. J .A. Hebden for supplying computer subroutines and,together with other colleagues,for general help. I thank Professor R. Blinc (University of Ljubljana and Nuclear Institute J . Stefan, Ljubljana, Yugoslavia) for his kind g i f t of single crystals of KD 2As0 4, RbH 2As0 4 and CsH 2As0 4. My thanks are also due to Messrs. J . Sal los, T. Markus, S. Rak and E. Matter for invaluable technical 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 under-standing and my parents-in-law for help and encouragement especially during the early stages of this work. Lastly, I am grateful to my parents who underwent a lot of hardships for giving me a university education. - x i i i -GLOSSARY OF SYMBOLS USED A = The tensor A h = Planck's constant (fl = -R-) e = the electronic charge c = the velocity of l ight in vacuum m = the electron rest mass Pj = the momentum vector of the i-th electron r\j = position vector of the i-th. electron g e = the g-value of the free electron g^ = the nuclear g-factor 3 = the absolute value of the Bohr magneton = ^ 3 n = the nuclear magneton _S = the electron spin angular momentum vector J_ = the nuclear spin angular momentum vector 6 . . = the Kronecker delta "13 6 (r i j )= the Dirac delta-function X = spin orbit coupling constant = orbital hyperfine coupling constant = charge on i-th nucleus. - 1 -CHAPTER ONE  INTRODUCTION In recent years the I^PO^-type of ferroelectr ics and anti-ferroelectr ics have received considerable attention, partly because of their applications in industry and partly because the microscopic nature of fer roe lect r ic i ty and ant i ferroe lectr ic i ty in these compounds is not yet fu l l y understood. Additional interest resulted because these compounds belong to one of the simplest hydrogen-bonded structures and detailed knowledge of their properties, which often depend upon the details 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 ferroelectr ic properties of Kr^PO^ (KDP) and isomorphous crystals 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 ferroelectr ic transit ion in the KDP-type of crystals. S later , in analogy with the case of i ce , 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 ta t i s t i ca l mechanics he showed that a transit ion should occur (the theory predicts one of the f i r s t order), the transit ion being essential ly a change from a disordered system of hydrogen bonds above the transit ion 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 di f f rac t ion work of J . West as early as 1930. Thirteen years after Slater proposed his model, the ordering of the hydrogens was veri f ied 4 through neutron d i f f ract ion experiments by Bacon and Pease at Harwell, 5 and Peterson, Levy and Simonsen at Oak Ridge, thus presenting strong experimental evidence for the essential correctness of S later 's basic assumptions. Moreover, the entropy change at the t rans i t ion, 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 ts isomorphic crystals shifted their 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 cation, i t f a i l s to explain the large shif ts in the Curie points observed when K is replaced by L i , - 3 -Na, Rb, Cs,etc. The role of heavy ions is evident also from the fact that the magnitude of the observed spontaneous polarization can be accounted for mainly on the basis of the large displacements of the heavy ions accompanying the ferroelectr ic transit ion. To explain the effect of deuteration on the Curie points and the observation of certain low frequency modes in the infrared o spectra of these compounds, Blinc proposed that the disorder of the hydrogen nuclei (protons) in the paraelectric phase is a dynamic one, in that the protons perform a tunneling motion from one equilibrium site in the hydrogen-bond (H-bond) to the other. This modification of the Slater model is often referred to as the Blinc or the Slater-g Blinc model of the ferroelectr ic t ransi t ion. Schmidt and Uehling were the f i r s t to obtain direct experimental evidence for such a motion for the case of deutaons in I^PO^ (DKDP), through the deuteron resonance relaxation measurements. It has since been confirmed by the more recent neutron-scattering experiments^. Recent in f rared^ and 12 Raman scattering experiments on the KDP-type of crysta ls , however, present quite conf l ict ing 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. Results of the more recent NMR^ and EPR^ experiments are, on the other hand, believed to be in better agreement with the Slater-Blinc model,although the interpretation of these results does not appear to be conclusive]'' On the other hand, Cochran 1 5 ' ^ 6 and independently Anderson^7 introduced another model, now known as the Cochran model, which is based on the following ideas in la t t ice dynamics. It can be shown - 4 -that in some ionic cr partly ionic crystals a long wavelength transverse optical frequency may become imaginary in the harmonic approximation resulting in an ins tab i l i t y of the lat t ice with respect to this normal mode; this causes a change in the crystal structure and hence the occurrence of the ferroelectr ic transit ion. The theory is based on the argument that in ionic crystals la t t ice vibrations are accompanied by polarization osc i l lat ions which create a local f i e l d 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 forces, the crystal becomes unstable against this mode. Above the Curie point anharmonic interactions stabi l i se the system making the observable frequency w real and posi t ive, 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 la t t ice displacements associated with this mode become unstable and produce a 'displacive ' ferroelectr ic phase transi t ion. This model could sat is factor i ly describe phase transitions in BaTiOg—type ferroe lectr ics . As such, however, i t did not prove suitable for KDP type ferroelectr ics . This latter has been ascribed to the neglect of any direct role of the protons in the mechanism of the phase transit ion in the original Cochran model, as 1 g is indicated by the more recent work of Kobayashi , discussed later. 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 la t t i ce . They demonstrated that the Curie point of the isolated proton system is s igni f icant ly lowered when the la t t i ce - 5 -interaction is taken into account. In their theory, however, the dynamical aspects of the phase transit ion are not discussed and, in part icular , no explanation is offered for the large distortions 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 Bl inc '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 ferroelectr ic phase transit ion in KDP-type of c rys ta ls , assuming that there exist two possible configurations for a (K-XO )^ complex along the symmetry axis (c-axis) of the crysta l . These configurations correspond to the two possible orientations of the permanent dipoles along this axis. According to their theory, ferroelectr ic phase transitions 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 effect observed in the Curie points of these crysta ls , although other properties l ike the observed magnitude of saturated polarization.no i so -tope effect in saturated polarization and the large displacements of the heavy ions at the Curie points can be sat is factor i l y explained. 18 23 In the meanwhile Kobayashi ' proposed the so called mixed model in which the ionic motion along the c-axis is also taken into account without assuming an order-disorder type transit ion for the ionic system. In this model the proton tunneling mode couples strongly - 6 -with the optical mode of (K-XO )^ la t t ice vibration along the c-axis and the frequency of one of the coupled modes tends to zero as the temperature approaches the Curie point, T . Below T , this mode is frozen i n , causing a large displacement of the heavy ions, and thus resulting in a large spontaneous polarization 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 model,i .e. the frequency of a transverse optical mode tends to zero as T-»-T , the exact mechanism of the ferroe lectr ic transit ion i t s e l f is c l a r i f i ed . 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 la t t ice vibrations compel the frequency of transverse optical vibration to tend to 7Bro.The assumption of a strong proton la t t i ce coupling in the Kobayashi model is based on the well established experimental fact that,whereas the ferroelectr ic transit ion in KDP-type of crystals is triggered by a cooperative ordering of hydrogens, the spontaneous polarization arises due to the large displacements of the heavy ions along the c-axis. The Kobayashi model thus offers an explanation for most of the properties associated with the ferroe lectr ic or ant i ferroelectr ic transitions in the crystals . Although the Kobayashi model is believed to be the most general for explaining the phase transit ion phenomenon, the basic assumptions employed by Kobayashi have, so fa r , received no direct experimental confirmation, although most of the available experimental techniques have been employed with a view to examining the va l id i ty - 7 -of such assumptions. In particular there is l i t t l e or no quantitative data on the low frequency (K-PO )^ and (K-AsO^) vibrations, 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 ignif icant isotope effect in the temperature dependence of the frequency of the coupled mode, the Kobayashi model predicts a s ign i -f icant isotope ef fect , thus providing a c r i t i c a l test for examining the va l id i ty of one or the other model. Some experimental evidence for the existence of the "ferro-24 e lect r ic mode" in KDP has been obtained by Arfjev et al . They observed a vibrational band in the far infrared region whose frequency behaved anomalously with temperature T according to to oc (T-T ). 12 S imi lar ly , 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 c) rather than (T-T ). 25 T Subsequently Brody and Cummins , using the Bri l louin scattering 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 similar conclusions 31 through P NMR T^  measurements. Recent NMR experiments of Blinc and Mai i^13^ Blinc and Bjorkstam 1 3 b and of others 2 7 > 2 8 > 2 9 have been interpreted as favoring the Blinc model as compared to other models. 30 However, more recent infrared spectroscopic measurements of Sato , 33 neutron scattering experiments of the Cochran group and infrared 34 spectroscopic and Mossbauer measurements of the Pel ah group, favor - 8 -the soft mode type models. Very recently Popova et al . as well 32 as White et a l . observed an isotope effect in the temperature dependence of the frequency of the soft mode (observed f i r s t by 1 o Kaminow and Damen as mentioned ea 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 ferroelectr ic mode has been reported, i t is not clear whether this 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) type crysta ls , on the other hand, no such data has as yet appeared. These considerations show that no clear picture has yet emerged for the mechanism of the phase transit ion in the KDP-type of crystals. Therefore, more accurate and detailed experimental data, especially on the role of the heavy ions, appear to be necessary for a fu l l e r understanding of the transit ion phenomenon in these crystals . 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 transit ion in the KDP type of crysta ls . Since these crystals 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-irradiation of 4-KDA results in the formation of a stable paramagnetic AsO^ centre due to the capture of an electron. No appreciable structural change - 9 -seems to occur on the formation of this centre which is hydrogen-bonded to other AsO^ units in the crystals. The unpaired electron has been shown to enter an A-|-type molecular orbital centered on the 3- 75 AsO^ ion, resulting in a large hyperfine interaction with the As nucleus (I =•?). Each of the As hyperfine lines shows further, par t ia l l y 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 for a detailed investigation of the nature of hydrogen bonding as well as the 75 dynamics of the hydrogen bond protons, and of the As nuclei in the ferroe lectr ic crystals KDA and KI^AsO^ (DKDA); and also in the anti-ferroe lectr ic crystals of Nh^h^AsO^ (ADA) in their paraelectric phases. It is perhaps important to mention here that similar studies on pure KDP crystals could not be performed because x-irradiation of KDP 4-crystals does not y ie ld the corresponding PO^ radical in any measurable quantities. However, the present studies show that prolonged irradiat ion of KDP at room temperature results in the formation of a paramagnetic centre which has been identi f ied as the 2- 37 P0 4 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 invest i -gating hydrogen bonding in KDP. Instead, we doped KDP with varying 3- 4-amount of the AsO^ ions and obtained the AsO^ centres in KDP. EPR and ENDOR investigations of the doped crystals y ie ld information on the structure of these (ferroelectr ic) , sol id solutions. The results indicate that EPR and ENDOR are perhaps the most helpful techniques for investigating the structural properties of these ferroelectr ic - 10 -sol id solutions. In Chapter II are outlined the details of the theoretical background necessary for the interpretation of the EPR and ENDOR measurements. In addit ion, 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 latter f a i l s due to unfavorable experimental conditions. The detai ls of the experimental arrangement, together with some preparatory and structural properties of the investigated crysals, are described in Chapter III. In Chapter IV are presented the results of the EPR, ENDOR and Double ENDOR experiments and their interpretation. Appendix A contains the detai ls 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 appl icabi l i ty of the ENDOR technique to a wider variety of samples than is possible at present. Appendix B contains 4-a brief description of the studies of the radicals other than AsO^ produced as a result of the i rradiat ion of the samples. - 11 -, CHAPTER TWO  THEORETICAL INTRODUCTION The present chapter contains an outline of the theoretical background necessary for the interpretation of the results of EPR and ENDOR studies of a paramagnetic system embedded in a crystal l a t t i ce . The treatment is brief since i t has already been the subject of discussion in several excellent review art ic les " and 39-43 books. For reasons of sel f suff ic iency, however, and later reference, a brief summary of the theoretical approach leading to the derivations of the formulae used in the present work wil 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 for elucidating the properties of paramagnetic systems. Its principle is quite - 12 -simple. If a molecular or an atomic system, possessing a magnetic moment, and therefore having a degenerate ground state, is placed in a steady magnetic f i e l d , the degeneracy is l i f t ed and the levels undergo a Zeeman sp l i t t i ng . Simultaneously this system is also subjected to a high frequency electro-magnetic f i e l d so that transitions 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 stat ic magnetic f i e l d is varied and one can plot out the energy levels as functions of the s tat ic f i e l d . For the general case of a paramagnetic c rys ta l , idea l ly , one should solve the Schrb'dinger equation for the electrons and the nuclei in the entire crystal in the presence of the applied magnetic f i e l d H. This , however, is not possible at the present time and one is thus forced to simplify this many-body problem. Perturbation theory methods have proved to be invaluable here. One thus begins by considering a general Hamiltonian for the entire system, retaining the dominant terms as the zeroth order ones and treating the smaller ones as perturbations. As a start ing point, we note that, in general, the dominant contribution to the magnetism of a molecular complex comes from the electrons. Many nuc le 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 electrons, the system may be approximately represented by a system of electrons moving in the f i e l d of the nuclei in the crysta l . The - 13 -41 Hamiltonian for this system may be written as : + z e _ + ^ + # ( } (i) (« ) i<k r-j^  ss s i i ,<x ^ i a y — — (a) (a) " E a 9 n fyi- — + VEQ + s m a 1 ' 1 terms.due to r e l a t i v i s t i c corrections (1) The f i r s t term is the kinetic energy; the second is the potential energy of the electrons in the f i e ld of the nucleus and of the surrounding ions; the third 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.  rHss represents the term due to magnetic interaction among the electrons, represents that due to magnetic interaction between the electron and the nuclear spins, and the next term expresses the interaction between the magnetic moment of the nuclei and the magnetic moment due to the orbital motion of the electrons. ^ g ^ f y I_^H_ represents the nuclear Zeeman interaction and the last term describes the interaction between the e lectr ic f i e l d gradients and the e lectr ic quadrupole moment of the nucleus. Al l the symbols used have their usual meanings and have been defined in the Glossary. To simplify the form of Eq. (1 ), i t is convenient to choose a gauge for which A = h H_xr (2) the origin being taken at the nucleus. By substituting Eq. (2) in Eq. (1), the kinetic energy of an electron can be written as: - 14 -a <*+f*>2 - £ + Is? fl-rxp - 4a (axr)2 - {£ + «.H + | Y (Hxr) 2 Thus Eq. (1) may be w r i t t e n as at. [E. t'p ( i'» 2 -*isi£J + I. .«?_]• v , L i 2m r i 1 < k r i k c r y s t p2 2 + V s p i n - o r b i t + ^ . ( k + j f e f (bxr) + BH.g eS + * $ s + a f s I M U l W . E ^ ^ l ( a ? H + V q (3) where L = z i ^ K S = I s^K i - — i — Here the term i n the square bracket i s the s p i n independent pa r t of our system and i s u s u a l l y by f a r the dominant term, ^ c r y s t 1 S ^ e P ° t e n t 1 ' a 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 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 gS), the e l e c t r o n i c Zeeman term, i s mainly r e s p o n s i b l e f o r the paramagnetism. The f i f t h term, •gjrc' 2 i(Hxr\j) i s the one mainly r e s p o n s i b l e f o r diamagnetism and the remaining terms have already been d e f i n e d . We have neglected 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 to be much sm a l l e r than the other terms i n the Hamiltonian. Now the problem of studying the p o s i t i o n of 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 - 15 -to determining the eigenvalues and eigenfunctions of <fl. This problem is most usefully attacked in stages, using the perturbation theory methods. This can be seen by examining the order of magnitude of the different parts o f $ , l i s ted below: 5 -1 1. free ion (complex): spin independent part 10 cm 2. crystal f i e l d 10 4 cm _ 1 2 -1 3. spin-orbit interaction 10 cm 4. electronic Zeeman term lcm"^ 5. electronic spin-spin interaction Icm"^ 6. electron-nuclear interaction 0.1 cm"'' -4 -1 7. other terms 10 cm The position of the crystal f i e l d term in this table is s l ight ly variable, and i t may be weaker than the spin-orbit term in some cases. In addit ion, in the present experiments we are interested in the energy levels with non-negligible occupancy at room temperature or below. Hence the properties of levels more than, 3 -1 say, 10 cm above the ground level can be ignored as direct contributors to the magnetic properties at or below room temperature. Also spin-spin interactions play no role in the present studies and simi lar ly we wi l l drop the term representing the diamagnetic interaction. It wi l l be further assumed that the many atom Hamiltonian can be written as a sum of single atom Hamiltonians i .e. ^ = £ *i& a ) , where a ft(a)=A + X l . S + BH.(L+g eS) + 4- I ( a ) + ^ s r t ( a \ l ( a - l i + V EQ } (4) - 16 -where a labels the atoms and represents the spin-independent part ofH. Since, in general, the energies associated with the various terms in Eq. 4 d i f fe 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 ike the one represented by Eq. (4), are, correct to the second order in A and H, the eigenvalues of an operator involving only the spin variables. This operator is now called the spin Hamiltonian operator. We wi 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 % = % +2C-1, where ^t^AL.S + BH.(L+g S). Since 2£Q ,HQ can be taken as the zeroth order Hamiltonian and ^ can be considered as a perturbation on i t . Using the second order perturbation theory, the effective Hamiltonian operator corres-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.) 0 e n*o ] . J u —J_ 1 e 1 ( En " E0> (5) where the eigenfunctions |0> , |1>, refer to the eigenstates of ft,, |0> corresponding to the lowest eigenvalue of*^ Q . To simplify Eq. (5) further, a tensor A• . is introduced and is defined in terms of the matrix elements of L, by - 17 -A „ - E < o | L i | n x n | L j | o > n ° (6) The tensor indices i , j refer to Cartesian coordinates' and the summation convention is assumed for them. Also since <0|ljn> is imaginary and equal to -<n|Jj0>, A^j is real and symmetrical and i f EQ is the lowest eigenvalue, i t is also positive def in i te . Now Eq. (5) can be written as 8 e B ( « i j - " l j » s 1 H J - A 1 J s 1 s J - A 1 j H 1 H J ( 7 ) In this equation, EQ is the unperturbed energy. The second term is the magnetic energy of a spin system with a g factor , 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 studies, we are concerned with free radical systems, this term is not applicable, hence i t wi l l not be discussed further. Similarly the last term in Eq. (7) can be dropped because i t is spin independent and hence shifts a l l the levels equally. With these remarks and using tensor notation Eq. (7) can be written as h" = EQ + H.g.S (9) It is now re lat ive ly simple to take into account the electron-nucleus interactions. One may just augment Eq. (9) by adding to i t the t e r m s ' g l . j _ , ^ s I , - g n$ nH.I and V^g. However, for the effect of s t . I , further s impl i f icat ion occurs. 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 ise to a term, called orbital hyperfine term, wj^ , given by " J r t - ^ l j ' j (10) and simi lar ly the cross term between j>t.J_ and J_ give r ise to a term proportional to H_.I_ i .e. which is a correction to the nuclear Zeeman term - g n 3 n H . L However, for free radical systems ( l ike the one considered in the present work) both of these correction terms are negligibly small and hence they wil l not be discussed further. Next consider the term Jf!^ which represents the magnetic interactions between the electronic and the nuclear spin magnetic moments. It is usual to write this term as ' * s i • V y ^ ) ! 2 ^ ^ ' - ^ * £ I.S«(r)]dv y» 5 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 interact ion, while the third term gives the Fermi contact interaction. This expression is l inear in the spin variables Ix, I , Iz, S x , Sy and S z and may therefore be written in the form 36SI = a L S + Z B i k I i S k (12) 1 9 ^ = x , y , z where a = §2- g e Bg n 6 n l * ( o ) | 2 (13) B 1 k = W „ ^ - ^ l ^ | 2 d v ( 1 4 ) The tensor B_ is 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 XI XS X + B y I yS y • B ZI ZS Z (15) - 19 -In the tensor notation, Eq. (15) can be rewritten as ^SI = C"16) where A x = a + Bx > A y = a + B , A z = a + Bz (17) and since B is traceless a = 1 ( 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 direct ly to the Hamiltonian for our system. Thus, relat ive to E , the 'complete 1, effective 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 ) (19) — § — £ — = — n n —' where the term V £ Q has been expressed, as usual, as V E Q = I . Q . I (20) The operator^now contains only the electron and the nuclear spin operators and the various 'coupling parameters', g , A, Q etc. It is noted that in obta in ing^, the formidable many-body problem has been replaced by a relat ively simple spin problem, in which the coupling effects involving the electronic wavefunctions have been 'absorbed' into a number of parameters. This is precisely w h y ^ i s cal led the spin Hamiltonian (operator). - 20 -On adopting the spin Hamiltonian formalism for the description of a paramagnetic system, a clear div is ion of labour is achieved by the separation of the work of determining the 'coupling parameters' from that of their interpretation. We wi l l now br ief ly describe f i r s t , how the parameters of the spin .—• Hamil tonian $£may be obtained through the analysis of the para-magnetic resonance spectra and wi l l then indicate how these parameters might be interpreted in terms of the molecular properties. 2.2 Determination of the spin Hamiltonian Parameters 2.2.1: Spin Hamiltonian parameters from EPR measurements: Consider the case of an electron coupled strongly with a single nucleus and assume that the EPR spectra show axial symmetry about a certain d i rect ion, called the z-axis, as is found to be the case for most of the EPR spectra observed above about 310°K in the present studies. (The more general case of an electron interacting simultaneously with several nuclei and where the EPR spectra do not show axial symmetry presents no conceptual d i f f i cu l t i e s although i t becomes much more cumbersome to discuss). The spin Hamiltonian for this system is ^EPR V ( 9 1 1 B H ) S. + ^ ^ + A ^ + S y y -" Vn H Iz + B l l ( I z • 1 / 3 l 2 )' ( 2 1 ) where is a parameter describing the axial ly symmetric quadrupole coupling. The eigenstates may be labelled by the eigenvalues mp of the commuting operator ? z = S z + I 2 < Then \%> = \mri ± > according - 21 -as m$ -*• ± 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 basis |ms,nij>, where m.j = m F ~ m S ! <n£. mF - m;|^EpR|ms, mp - ms> « hig^m + (m F - % ) ( A i r 2 g n 3 n H ) ] + b + ^ [ 1 ( 1 + 1) - m2 + hi*' %A|.[I(I + 1) - m2 + hi* -JsCg^BH + (m F + JsMA^ + 2g n3 nH) + b_ (22) + 2 where b~ = [(nip + h) ~ 1(1 + 1 ) B n - T n e eigenvalues are E(m F, ±) = - { V A N + m F g n e n H + + 1 ) - ( m r ^ ] B l l } ^ s { ( g n e H + ( A n - 2o^)mr: + 9 n 6 n H ) 2 + ' A £ [ I ( I + 1) - (m 2 - J*)]}'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 Tan 2a [41(1 + 1) - 4m2 + iT^Aj. g n B H + ( A n - 2 B n ) m F + g ^ H (25) - 22 -4-Consider now the s p e c i f i c case o f the AsO^ center 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 of 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 that 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 hyperfine i n t e r a c t i o n of 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 of the s p i n H a m i l t o n i a n ' ^ p R 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 of the energy l e v e l s of the 4-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. T r a n s i t i o n s T-|, Tg, Tg and T^ are observed whenever the microwave magnetic f i e l d v e c t o r 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 allowed, 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 2 , T^ and T g , on the other hand, are 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 constant 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 f o r these seven EPR t r a n s i t i o n s are given e x p l i c i t l y by Multiple! Energy Levels No Eigenfunction Eigenvolue 2 ^= |i,t> E, 1 ^ = C o s a , | i f i > + S ina , | - l J ) E 2 O % = C o s e g i f - i ) + S i n a o l ^ i ) E 3 = i g „ / S H + j A „ - l g n / Q n H r i i ' A „ - g n / Q n H +1 [(gn/3H + A „ + g n / S n H T + 3A^J 2 : -iA,^ [(g„ /3H + g n /^H )2 + 4 A 2 ]^ -1 = C o s q , | i ,-|) + Sin g, |~i,%> E, = g n / 3 n H + | [ (g , / 3 H- A, 1 + g n /3 n H) 2 + 3A2]= 6 7 8 -2 *s= tvt> -1 »//. = Cosa,|-i;i> E =-i CosaJ-i, i ) - Sin a | Cos a [-i . f>- S i n a , | i t i ) aa./SHflA 1 1 + |gn^,H Sin a,I l;f> E 6 = -iAl+gn/3nH-i[cg,/3H- A „ + g n £ n H ) 2 + 3 A 2 ] ~ 2 'iA,,- 9n A, H-i [ ( g „ / S H - t - A „ + g n / S n H 3 A 2 ] 2 E E F i g . 1 Schematic energy l e v e l diagram f o r an S=% and I=y, a x i a l system. - 24 -= hv = hgu^ + A n - ^ g n 6 n H l + [ g l l 3 H l + A „ + g ^ H , ) 2 , + 3A_L 2]^ T2 = hv = [g^BHg + A N + 9 n 3 n H 2 ) 2 + SAJL2]'5, T3 = hv = - g n g n H 3 + ^ [ ( g i l 3 H 3 + A, } + g ^ ) 2 + S A j 2 ] * , T4 = hv = [(G I LBH 4 + g n B n H 4 ) 2 + 4Aj_2] ! s, T5 = hv = -g n 6 n H 5 + ^ [ g i l 3 H 5 + g ^ ) 2 . * + %[ (g 1 1 3H 5 - A n + g n 3 n H 5 ) 2 + 3 A ± 2 ] \ T6 = hv = [ ( g l l B H 6 - A 1 1 + g n g n H 6 ) 2 + 2h?f\ T ? = hv = 9 l l 6 H 7 - g n 6 n H 7 + [ ( g^e^ - + g n B n H 7 ) 2 + Z^f. (26) From an inspection of Eqns. (26), i t wi 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 transitions 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 l ike those given in Eqns. (26). One is then forced to use the perturbation theory methods. A very general method of obtaining the spin Hamiltonian parameters for a paramagnetic system is that due to Byfleet, 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 third order in the perturbation parameters. This , therefore, allows one to obtain the energy levels of the system correct to the seventh order in the perturbation parameters. This approach has been described more fu l l y in the Ph.D. thesis of J .A. Hebden4'7 who also,wrote, a computer programme 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 sp l i t t ing of the As hyperfine l ines . This further sp l i t t ing (of the hyperfine l ines ) , called the superhyperfine structure (shfs), arises because of the much smaller interactions with the ligand nucle 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 (1957), is the observation of Nuclear transitions via EPR. For studying hyperfine interactions, this technique is much more powerful than either EPR or NMR because by i ts application one can obtain the higher sens i t iv i ty of the EPR technique as well as the higher resolution possible with the use of the NMR technique. We shall now give a brief outline of i ts principles and of the derivation of some formulae used later for obtaining the shfs parameters. The necessity for performing ENDOR experiments arises because the EPR spectrum of a paramagnetic centre in a sol id 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 la t t ice sp l i ts each of these resolved HFS lines into a large number of very closely spaced l ines , which may overlap and consequently y ie ld a structureless broadening of the HFS l ine . It is thus this increased width of the HFS lines in sol id samples which usually l imits the resolution of the EPR technique. (50b) Portis has shown that EPR l ine broadening can be c lass i f ied into two types: homogeneous broadening and inhomogeneous broadening. Homogeneous broadening occurs when the energy absorbed from the microwave f i e l d is distributed 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 ie lds sat isfy the resonance condition. The variation in the local f ie lds of different spins may correspond to variations in the local magnetic f ie lds due to random orientations of neighbouring nuclei in the host crysta l . They may also be due to random strains and e lect r ic f ie lds which produce s l ight ly different 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 'spin packets' then constitute an inhomogeneously broadened EPR l ine . It is the case of the 'inhomogeneously broadened' EPR lines where ENDOR can be of great help for studying the small hyperfine couplings unresolved in the EPR spectra. In the ENDOR experiments one essential ly measures the NMR transit ion frequencies of the nuclei - 27 -tha t are coupled to the unpaired e l e c t r o n . For reasons of s e n s i t i v i t y , however, d i r e c t measurement of the nu c l e a r resonance i s u s u a l l y not p o s s i b l e , and one thus employs the enhancement p r o p e r t i e s o f the double resonance techniques. In the ENDOR experiments one causes an in c r e a s e of the d i f f e r e n c e i n the populat i o n of the nuclear s p i n l e v e l s by s a t u r a t i o n of the 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 are detected through the d e s a t u r a t i o n of the EPR t r a n s i t i o n s as a r e s u l t o f the occurrence o f the nuclear resonances. An ENDOR experiment i s thus an NMR experiment i n which the e f f e c t i v e s e n s i t i v i t y i s seve r a l orders of 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 the same number of n u c l e i and i n favo u r a b l e cases approaches the s e n s i t i v i t y of 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 sp 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 * -2tPR + ^ENDtm < 2 7 > H e r e ^ E p R i s the sp 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 re s o l v e d h y p e r f i n e s t r u c t u r e ) and has the form given by an operator of the type represented by Eq. (19). <K, E N D Q R includes the 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 the form #C 4 ENDOR = I ( l ( a ) . A ( a ) • S - g n a ) B n H . I ( a ) ) . (28) a = 1 - 28 -We can here assume that the parameters d e f i n i n g ^ E P R are already known. Als o the eigenvectors | c > and the eigenvalues E° of ^ £ P R d e f i n e d as before, by ttERR|e> - 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 that 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 se t of 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 presence of the s e t of nuclear spins d e s c r i b e d by ^£ U^QR- Since the energy a s s o c i a t e d with ^^ QOR 1 S m u c n s m a l l e r than t h a t a s s o c i a t e d with <^£p R, ^ ENDOR may be d i s c u s s e d i n a language which omits a l l 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 of the s t a t e s of the weakly coupled spins { 1 ^ } only. For the (50a) weak coupling 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 w r i t e * 5 = E| +-<5 | * E N D 0 R | e > + g: <e VENDOR 16^><G' VENDOR' G > + •••• (E° - E°J K 5 (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 = E° + I {-g n 6 n H.I + <S> .^ ( a ).I ( a )} (31) * ? a where <S>? = <e|S|5>. ( 3 2 ) We note therefore that the energy levels involved in the ENDOR transitions depend upon a particular multiplet £ through the spin polarisation vectors <S_>^ , determined entirely b y ^ p ^ . For small electron-nuclear coupling in^jrpR w e have approximately <S> = ± h k, where k is a unit vector in the f i e ld direction and _£ _ _ Eq. (30) then leads to the usual f i r s t order hyperfine levels. In general, however, <S>^  varies both in magnitude and direction from one multiplet to another. In the general case, because the variation in the direction of the ENDOR transitions for a particular nucleus are expected to depend in a complicated way on (n) al l the elements of the tensor A/ ' so that the analysis is complicated. If, however, the f i e l d is oriented along an n-fold symmetry axis o f ^ p R * n > , 2 , then <S>^  must be tota l ly symmetric to a l l rotations generated by C p and must therefore have the direction of the symmetry axis, i .e. the same direction as the f i e l d . The direction of spin polarisation is then independent of £, so that < § > r = <S>F Jl, (33) the symmetry axis here being supposed to l i e in the z direct ion. 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 signi f icant quadrupole coupling, then only two parameters, namely A ^ z and [ A ^ ~\zz (or, equivalents and A = ( A ^ f + ( A U ) ) 2 = [ A U ) 2 ] z 2 _ ( A(a)^2 a r e i n v o l v e d , and these can be determined from a simple linear plot. In fact we have \ H . I ^ + <S > rk.A' n - — z t,- =• 4a) = -g n a V a n H . i ( a ) + <s r k .A ( a h ( a ^ (34 ) which has eigenvalues E M = m ( a ) | _ g ( a ) B n H + <S z> c k.A|, ( 3 5) where |a| = /aTa denotes the magnitude of a vector, so that the (a) Amj ' = ±1 ENDOR frequency associated with the nucleus a, multiplet £, and EPR transit ion 5 < > r » is v ( a ) = v ( ? ! r ) = | - v ^ •< + <S z> r k . A| (36) . E,S E,S ^ = [ ( v ( a ) ) 2 - 2 v ( a ) <S > A ( a ) + < S > 2 ( A ( a ) 2 ) 7 J 3 5 , s r s r 5 zz z ^ z z ( 3 7 ) Since for most free radical cases, <SZ>^ % ±h, one can (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 direction 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) principal directions for the tensors A/ ' is not known, the expression for the ENDOR transit ion frequencies becomes very complicated. It is then found to be essential to use computer diagonalisation of (^pp + ^ E ; N D O R ^ ' ^ w o c o m P u t e r programmes were employed in the present studies. The f i r s t programme, called ENDOR, is a simple one which assumes. <Sz>^ = ±% but then yields the least-squares-(a) adjusted values for the elements of the tensor S . The (a) values for the principal components of A/ ' and the orientation of the principal 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 y U , r ) = [ A ( a ) 2 ] z z x ( e , r ) - (38) where y u . n = [ { v ( ? , r ) ) 2 - ( v r ^ ) ) 2 ] / 2 v ^ l < s > , and (39) x(?,r) = + < S z > 5 / ( 2 v ^ l ) . Note here that the parameters ( A^ A ) J and AJ^ can be determined - 32 -from the slope and intercept of a plot of y ( ? , £ ' ) against x ( ? , £ ' ) , as the EPR transitions E, <—> £" are varied. In particular the (a) sign of A z 2 ' and an overall sign on the EPR couplings (which affects the resonance f i e ld , hence the states \K> and hence <S Z>^) can both be determined for the orientation H||z. Also, i f the (a)' z-directi on coincides with a principal direction of A v , then from Eq. (37) becomes v u i r ) ± v{A = ± <S> A £ ) (40) E,£ z ? zz In this case a simple comparison of ratios of the measured quantities (a) (a) V F 1 v » to ratios of the calculated spin polarisation t 5 s s r magnitudes <SZ>^ is suff ic ient to determine signs. If the principal (a) direction of A/ ' is not exactly along the symmetry axis, but s t i l l quite close to i t , then Eq. (40) can be obtained as an approximation. It (a) may be very accurate for multiplets for which <S Z>^ A z z and (a) v v ' have the same sign while at the same time quite inaccurate for those which have opposite signs. The.analysis of the ENDOR experiments on the AsO j^" centre in KH^AsO^ provides a good example for testing these ideas. Of course the procedure outlined above yields the sign for the components of the hyperfine tensors only for H||z, where the z-directi on coincides with a two (or higher) fold symmetry axis fo^f rpR ' Relative signs of the hyperfine components for other directions can then be obtained through ENDOR measurements on a single hyperfine transit ion for various magnetic f i e ld orientations. - 33 -Additional double ENDOR measurements may be necessary for very weakly coupled nuclei . 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 sections, i t has been impl ic i t ly assumed that a l l paramagnetic resonance spectra can be analysed in terms of the perfectly sharp resonant transitions between spin energy levels which are the stationary states of a definite and fixed Hamiltonian. This is a very useful approach but i t is also quite unreal ist ic because every molecule interacts with i ts surroundings and these interactions l imit the l i f e times of the spin states, broadening the energy l eve l . In fact i t is well known that an interact ion, called spin-lat t ice interact ion, between the spin system and the surrounding la t t i ce is essential for the success of the paramagnetic resonance experiment. In the present work, although we do require the existence of favourable spin-latt ice relaxation conditions, we wil l not be direct ly concerned with the subject of spin-latt ice relaxation. On the other hand, the presence of molecular motion in the para-magnetic system can also drast ica l ly affect the appearance of the resonance spectra expected on the basis of the (static) spin-Hamiltonian 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 for the molecular motion are ^ 10~^° sec which thus f a l l in the domain of the EPR techniques. In fac 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 ferroelectr ic transit ion phenomena in the Kh^PO^-type of crystals . Therefore, we wi l l now present a brief account of the effects of molecular motion on EPR spectra. The discussion is again brief because i t 52-54 has already been given in detail in several review ar t i c les . The effects of motion on the paramagnetic resonance spectra may be visualized as follows. From a c lassical point of view, free electrons precess at about 1 0 ^ Hz in typical laboratory 4 f ie lds of about 10 gauss. Motions,in the environments of the magnetic nuclei and electrons which produce fluctuating magnetic f ie lds 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 their spectra. Because of the weakness of the interaction of the nuclei and of unpaired electrons similar effects may also be observed for the magnetic resonance spectra in paramagnetic so l ids . The precessional frequencies of nuclear or electronic 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 suf f ic ient ly rapid, only an average f i e l d wi l l act on each spin and a single resonance wil l result . On the other hand, very slow f i e l d fluctuations wil l allow each spin to precess - 35 -at a frequency characterist ic of i ts 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 ld fluctuation with the differences in precessional frequencies of spins in the various local f i e lds . Since local f i e l d differences are often small, even slow processes (undetectable by x-ray or neutron d i f f ract ion 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 fu l l range of rates from the fu l l y averaged spectra to the spectra showing d is t inct species. However, i t is based on the assumption that the process of molecular motion does not induce any transit ion between the Zeeman levels of the spins hence called the , 'adiabatic 1 approach. On the other hand, the relaxation matrix method is more general because by this method even the 'non adiabatic' 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 fast rate region i . e . , in the region where averaged spectra are observed. Also, i t turns out that because of the complexities in the calculat ions, at the present state the density matrix method is useful only for obtaining qualitat ive information on the molecular motion affecting the spectra. It has been further shown that in the fast rate region both, the relaxation matrix method and the modified Bloch method,yield the - 36 -same results. Since we were interested in obtaining quantitative information on both the slow and the fast exchange rates, we used the modified Bloch equation treatment for the present investigations. Consider f i r s t the normal (unmodified) Bloch equations. These are a phenomenological set of differential equations describing the relaxation of the bulk magnetisation M. Referred to a set of axes rotating about the Z-axis at an angular frequency of -co, these equations are * • v _ + ( v „ ) v . o. (41) % + H- - ( „ „ - . ) u - 0 ' ( « ) dM _ | +M|zMo . Y H I V = 0 (43) where T-| and T 2 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 , (44) a quantity a =-y- - i (to -co) , and for the case of no saturation, Eqns. (41) and (42) can be written as ^ | + aG = -iyh^M. (45) Now suppose that several sites exist between which the paramagnetic system can coexist. If the rate of conversion of one site into another is very slow, then for each form an equation similar to Eq. (45) can be written/ that is - 37 -d G N "dt + A N G N = " W o N ( 4 6 ) Here = T 2 ^ - i('u^-«.)» e t c . , where <^  is the resonance frequency for the s i te N. However, as the rate of exchange of the radical between the different sites becomes comparable to the frequency differences between l ines , Eq. (46) is not adequate. The C O modification was made f i r s t by Gutowsky, McCall and Sl ichter 59 and later treated in more detail by the Gutowsky group and by 55 56 others ' . It has been shown that i f the exchange is f i r s t order, then the modified Bloch equations for a system with N different sites are dGw " d f + ANGN = " WON + J N ( k x G x " W . <47> SHere k = — , T being the mean l i f e time of the si te x. X X X A The total complex magnetisation G is given by G = £ GM •N I N and the imagninary part of G then gives the absorption l ine shape. Miyagawa and I toh^ have shown that for an N-site system, where a l l interconversions are equally probable, the general solution of G_ may be written as G - lYHlM°Tsl f s G ~ N 5 - 1 S (48) NO-I f s) s=l where x is the mean l i f e for a given radical s i te and f is defined by f s = (N + a s x ) " 1 . (49) - 38 -Eqns. (47) and (48) are direct ly applicable for N=2 or N=3. Computer programmes based on Eqns. (47) and (48) are ava i l -able, 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 details of the programme wil 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 ine separations (to-co0), the estimated relaxation time T 2 and the l i f e time x. The output of the programme goes to a plotting sub-routine, supplied by Mr. John Ta i t , also of the Chemistry Department, U.B.C. Thus the print out is a simulated EPR spectrum. By comparing these simulated spectra with the experimental spectra the l i fet ime of the various sites at different temperatures have been computed. Further detai ls of the f i t t i ng procedure and the information obtained wi l l be presented in Chapter IV. 2.4 Interpretation of the spin Hamiltonian parameters The spin Hamiltonian parameters which are of significance for the present studies are the tensor g, A. and possibly Q. The interpretation for tensor g can be obtained with the help of Eq. (7). In the absence of the nuclear magnetism, and the small diamagnetic ef fects , the operator representing the magnetic moment is obtained by di f ferent iat ing 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 similarly of great interest. By examining Eqns. (11-17), i t can be seen that the isotropic part, a, of the hyperfine tensor specifies the density of the unpaired electron |^(r.A)| a 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 2dx, (50) where 9 is the angle with respect to a principal axis of the hyperfine interaction. The weaker, superhyperfine interactions of the unpaired electron, studied through ENDOR, provide the same information as obtained through the determination of the tensor A. representing the stronger hyperfine interactions. ENDOR can also resolve quadrupole interactions and in that case one can obtain information about the gradient of the e lectr ic f i e ld as determined by the distr ibut ion of a l l nuclei and electrons in the crysta l . - 40 -CHAPTER THREE EXPERIMENTAL DETAILS 3 .1 Preparat ion and Crysta l S t ructure of the Arsenates and Phosphates. The s i ng l e c r y s t a l s of KDP, KDA, ADA and mixed KDP-KDA were a l l grown by slowly evaporating the saturated aqueous so lu t ions of these compounds. Chemical ly pure KDA and KDP were suppl ied by Merck and ADA was obtained from A l f a Inorganics. The c r y s t a l s were transparent and pr i smat i c in shape as descr ibed byWycko f f 6 and Groth. Deuterated KDP, KDA, and mixed KDP-KDA were obtained by d i s so l v i ng the undeuterated compounds in D2O, r e f l ux ing fo r about two days and repeat ing the process twice before growing the c r y s t a l s . Crys ta l s from deuterated compounds had growth habits s i m i l a r to those of the undeuterated ones. One DKDA s ing le c r ys ta l was k ind ly suppl ied by Professor B l i n c , and th i s was used in the i n i t i a l experiments. - .41 -X-ray ' and neutron d i f f ract ion experiments have shown that in their high temperature paraelectric phase these crystals belong to the tetragonal (142d) space group with four molecules per unit c e l l . The structure is most easily pictured as bui l t up from K (or NH4) units and X04(X=P or As) groups. 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 axis. Each of the XO^ groups is hydrogen-bonded to the four neighboring X0 4 units. 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 approxi-mately 32° about the tetragonal c-axis of the crysta l . A schematic diagram of the unit ce l l as determined by West, is given in Fig. 2. In their low temperature phase these crystals may be c lass i f ied in two categories: those containing NH^  ion, and those without NH4. We wi 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 definite only in single domain crystals because the presence of a domain structure results in a random interchange of the X and the Y directions. Also, as a result of the o phase t rans i t ion, the K and the P (or As) atoms move, each about 0.05 A, - 4 2 -F i g . 2 Structure of K H 2 A s 0 4 (or KH 2 P0 4 )-type crysta ls , after J . West? - 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 near 'upper' Oxygens or a l l near 'lower' Oxygens. A schematic diagram showing the displacements of the various atoms is given in Fig. 3(a), and a c-axis projection of the crystal structure showing the positions of the H's in the ferroelectr ic phase is depicted in Fig. 3(b). For the case of the ammonium sa l t , ADA, the transit ion takes place to an ant i ferroelectr ic phase and the crystals shatter during the transi t ion. The low-temperature structure of this crystal is also orthorhombic but is quite different from those of the crystals belonging to the second category, in that for the former case the axes do not coincide with the base diagonals of the (small) tetragonal cel l (as do the crystals of the KDP-type), but along the side. In the tetragonal (high temperature) structure there are axes of symmetry along the cel l side and along the cel 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 crystals 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 . A c-axis projection of the unit cel l is given in Fig. 3(c). It wi 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 vertical direction as well as in the plane of the diagram every component of each vector repre-senting an interatomic distance or displacement is balanced by an equal component in the opposite direct ion. 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 crystals at T c (b) c-axis projection, of crystal structure of Kh^AsO and (c) of NH^AsC^ below T - 45 -individual coordinates of the atoms. It means that these crystals cannot possess spontaneous polar izat ion; this is in agreement with experimental observations. It must be mentioned that a structure possessing this symmetry was indeed predicted by.Nagamiya , before the crystal structure was determined by the x-ray di f f ract ion techniques. 3.2 The Irradiation Units The crystals were irradiated with a Mach'lett, type OEG-60 50 KV, 20mA X-ray tube or a ^Co Y-ray source for several hours at room temperature and also at 77°K. Most of the measurements described in the present work, were made on crystals irradiated by x-rays at room temperature since no new features were noticed by using crystals irradiated at 77°K or by using the Y-irradiated crystals. 3.3 The EPR Spectrometers 3.3.1 The X-band Spectrometers For preliminary examination of the EPR spectra at X-band (^9.3 GH 2), the Varian E-3 spectrometer proved to be the most convenient. More accurate measurements were made on a home-made EPR spectrometer, 54 called ESR-1 in the group and described more fu l l y elsewhere . It is a modified version of the Varian V-4502 spectrometer, using 100 KHz magnetic f i e ld modulation and a 12", rotatable Varian electromagnet having a VFR 2501 Fie ldia l Mk.II. The microwave frequency was measured with a Hewlett-Packard 5246L frequency counter, using a 5256A Plug-in. unit , and the magnetic f i e ld was calibrated with a Magnion N.M.R. probe and a magnetometer constructed by the Electronics Group, Department of Chemistry, U. B. C. - 46 -The variable temperature experiments were performed using the E-3 or the ESR-1 spectrometer, in conjunction with a Varian Variable Temperature unit. The measurements were made over the range from about 350° to 77°K. The s tab 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 ident i f icat ion of the many overlapping EPR signals due to the several radicals obtained in the irradiated crysta ls , 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 ld accessories as the ESR-1. The cavity used is a Magnion model C-TC-10-UVK, locked electronical ly to the frequency of the Klystron, Varian type EM-1138. 3.4 ENDOR Spectrometer The ENDOR spectrometer used in these experiments has been bui l t around an x-band EPR spectrometer u t i l i s i ng the single sideband superheterodyne principle with an intermediate frequency of 30MHz. Fig. 4 shows a block diagram of the set up. A Varian V-153C klystron with a Hewlett-Packard 716B power supply is the source of microwave power. The kystron frequency is stabi l ised by phase locking to the harmonic of a thermally controlled crystal osc i l l a tor by the use of a synchroniser, LFE model 244. The klystron frequency was thus controlled to 2 parts in 10 7 (over half hour periods). A provision was available in this synchronizer to continuously vary the stabi l ised microwave - 47 -K Y L S T R O N K Y L S T R O N POWER SUPPLY ISOLATOR 20d B DIRECTIONAL COUPLER SYNCHRONISER 5 MHz A T T E N U A T O R B A L A N C E D MIXER 3 0 MHz. MULTIPLIER, AMPLIFIER PRECISION A T T E N U A T O R M A T C H E D TOTTO LOAD ISOLATOR FILTER CAVITY PHASE SHIFTER MAGIC T E E S A M P L E CAVITY N MICROWAVE SWITCH ISOLATOR MIXER M A N E T POWER SUPPLY and FIELDIAL MARK JL t D E T E C T O R CRO ISOLATOR 3 0 r A M P L »1Hz IFIER R D E T E F CTOR TO MOD COILS LOW PASS FILTERS R F AMPLIFIERS t AUDIO POWER AMPLIFIER RF SIGNAL GENERATOR AUDIO AMPLIF IER LOCK IN S Y S T E M X,Y RECORDER SCANNING UNIT FREQUENCY COUNTER DIGITAL —ANALOG C O N V E R T E R i F i g . 4 Block diagram o f the ENDOR spectrometer. - 48 -frequency within small l im i t s , once a particular crystal harmonic was selected, by pull ing the frequency of the crysta l . 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 for convenience by mult 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 carr ier frequency, was minimum, and that in the two sidebands at ( u o t 30)MHz were maximum. By passing this output through a high Q transmission cavity (Model 585-BS2 of PRD Electronics Inc.), one side-band alone (in our case, ( u o + 30)MHz) is selected and used as local osc i l l a tor for the superheterodyne detection at the balanced detector using two IN23G diodes. The main branch of microwave power at the carr ier frequency is led through a series of attenuators to the cavity through a magic T bridge. The cavity is a rectangular one operating in a TE^^ mode. 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 vertical side of the cavity. The reflected power from the cavity was led through the third arm of the magic T to the balanced detector, mentioned ear l ier . A microwave switch is also included in this arm for convenience of displaying the cavity frequency on an oscil loscope. - 49 -The detected i . f . at 30MHz was f i r s t amplified by a LEL model IF31BP I.F. amplifier which had a gain of 450 with a 3db band-width of 8-MHz. The output after detection by a IN34 crystal is processed by a lock-in amplif ier , 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 str ip chart recorder. The Zeeman magnetic f i e ld was provided by a Varian 9" pole face rotatable electromagnet with a Mark II F ie ldial system power supply. A signal proportional to the magnetic f i e ld was available from the power supply to drive the x axis of the x-y recorder. Magnetic f i e ld modulation at a variable audio frequency was produced by means of modulation coi ls wound on the magnet polepieces. The modulation coi ls were driven from the reference frequency output of the PAR lock-in after suitable power amplif ication. The f a c i l i t y of a variable modulation frequency was found essential to obtain optimum EPR and ENDOR signal intensit ies at low temperatures. For work at 4.2°K, a glass double dewar system with l iquid nitrogen in the outer and l iquid helium in the inner dewar was employed. The entire cavity dipped in l iquid 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 site by means of a single loop of wire located in the plane of the microwave magnetic f i e ld and surrounding the sample inside the cavity. High f i e ld superconducting Nb-Zr wire was used for the c o i l . 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 osc i l la tor 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 Hewlett-Packard, type 460AR and 460BR, and then by a IFI model 5000, distributed amplifier which could deliver a maximum power of 30W into 50 ohms. The amplified output was led through a set of r.f. low pass f i l t e r s in which the cutoff 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 investigations, i . e . , 1 to 30MHz. The r.f. current in the ENDOR loop was found to vary with change of frequency, but not very rapidly and this was not found to be troublesome when f.m. detection was used for ENDOR, as described in detail in the next section. The r.f. frequency is monitored by a Hewlett-Packard 5246L counter and i ts d ig i ta l output after analog conversion by Hewlett-Packard type 580A, drives the x-axis of an x-y recorder for display of ENDOR signals. 3.5 ENDOR Technique The method used by us to observe ENDOR is the stationary ENDOR technique in the absorption mode. ENDOR lines have been observed and recorded at 4.2°K in KH2As04 crystals in the ac, be, and ab planes (the axes refer to the tetragonal system), and on several EPR t rans i -t ions. F i rst the crystal was mounted accurately with the required - 51 -plane horizontal. Then, the EPR spectrum was recorded and a part icular l ine selected for ENDOR study. The microwave power level for maximum EPR signal was determined and the EPR transit ion was part ia l ly satura-ted by increasing the microwave power by 3db' or so above this (see Fig. 5). The magnetic f i e l d was then set precisely at the center of the derivative EPR l ine and the magnetic f i e ld modulation switched off . With the lock-in amplifier gain increased about hundred fold and the time constant increased to 10 seconds, the r.f. current (^ 5 watts) through the loop was switched on. The r.f. 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 transit ion was necessary to record the signal. A careful study of the ENDOR intensity has,however, not been made. Once the ENDOR lines for a particular EPR l ine for a given orientation in the specified 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 off and the signal generator frequency manually adjusted to the center of each recorder ENDOR l ine as monitored by F i g . 5 Schematic p l o t of ENDOR si 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 a p p l i e d microwave power. - 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 th a t d e s c r i b e d by Cook and Whiffen . I t i s based on the 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 given 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), are used simultaneously. The procedure we used i s f i r s t to s e l e c t the microwave power, the magnetic f i e l d and the frequency o f one of the o s c i l l a t o r s to correspond to 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 to one of the ENDOR t r a n s i t i o n s due to another nucleus. I f the 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 creases as a r e s u l t o f the 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 to 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 the double ENDOR s i g n a l can be r e l a t e d to the r e l a t i v e sign o f the hyper-f i n e couplings g i v i n g r i s e to these two simultaneously s a t u r a t e d ENDOR t r a n s i t i o n s . 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 of performing E l e c t r o n - N u c l e a r Triple-Resonance experiments, to be des c r i b e d i n Appendix A of the present work. Genera l Radio s igna l g e n e r a t o r 41 c / s O s c i l l a t o r 3 M a r c o n i s i g n a l genera to r Wide band a m p l i f i e r s I X - band S u p e r h e t e r o d y n e E.S.R. s p e c t r o m e t e r 5 0 f i l ine 41 c / s phase d e t e c t o r H - P coun te r jx X Y R e c o r d e r Sample c a v i t y Hal l P robe F ie ld ia l M a r k H in Fig. 6 Block diagram of the Double ENDOR and Electron-Nuclear Tr iple Resonance experiments. - 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) crystals and of the EPR investigations on DKDA, ADA and RbDA. The observed EPR spectra are in general quite complex since they arise due to the simultaneous presence of several paramagnetic centres formed during the irradiat ion process. Some of these centres can, however, be selectively destroyed through careful annealing of the irradiated samples, thus rendering the spectra easier to interpret. 4-All these centres except AsO^ have been tentatively interpreted to form as a result of the rupture of either one or more hydrogen bonds 4-or some OH groups. On the other hand, the AsO, centre, identif ied by - 56 -Hampton et al. , is formed following the capture of an extra electron 3_ by an AsO^ ion and thus no appreciable change is found to accompany /li-the formation of this centre. The AsO^ centre thus appeared to be the most suitable for investigating the structural properties of the KDA-type of crystals . The present investigations thus deal mainly with the investigations of this centre and we now begin with the description of the EPR studies. 4-4.1 EPR studies of AsO j^ centre At the time the present studies were taken up (1967), 35 Hampton et al. had shown that the main paramagnetic species formed 4-during the x-irradiation of KDA single crystals was the AsO^ centre. 4-Br ie f l y , the ident i f icat ion 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 ld leads to a nearly isotropic but s igni f icant ly axia l ly 4-symmetric hyperfine tensor, as expected for an AsO^ centre. Semi empirical LCAO molecular orbital calculations were then performed 4-for the AsO^ radical with symmetry D2cj trapped in KDA. The calculations showed that the odd electron enters a molecular orbital with A-|-symmetry. The isotropic 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 direction of the crystal c-axis. This difference was believed to ar ise , largely, due to the neglect of the spin-polarization effects of the B and E-type orbi ta ls . At this stage i t may be noted, as pointed out by Hampton et 35 -a l , 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 crysta l l ine c-axis. However, superhyperfine 75 structure was observed on each As l ine which was sp l i t into a quintet with the components having the intensity ratio 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 surround-ing 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 ig id ly in the la t t ice 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 addit ion, 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 ip le t whose components show the intensity pattern of 1:2:1, characterist ic 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. .This observation shows that whereas at higher temperatures a l l the four hydrogen-protons contribute equally to the superhyperfine structure, below 220°K only two of them dominate the superhyperfine interaction. These results are explained in terms of the dynamic order-g disorder model proposed ear l ier 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 sites in the hydrogen bonds. In the ferroelectr ic phase, however, they get local ised in one of the two available sites in such a way that only two of them, called 'c lose ' protons, are nearer to any given As0 4 group. The other two protons of the hydrogen bonds get local ised in the equilibrium sites which are farther away with respect to the oxygens of this As0 4 group and hence they are called the ' fa r ' protons. The EPR results were explained by assuming that the super-hyperfine interaction is isotropic and that the coupling constant for the 'c lose ' protons, a ^ , was. ffc29MHz whereas the coupling constant for the ' fa r ' protons, a ^ was taken to be zero. Also, for a given AsO^ group, the l i f e time T of a given protonic configuration (called a Slater configuration), is related to the frequency v of proton exchanges between the different sites around a given AsO^ group, through the relat ion v=j. If now v>| aclose - afar|^29Mz, the effective superhyperfine coupling constant wil l be that due to the time average 'of a , and a . , i .e. 14.5 MHz. In this case the unpaired electron c 1. tar - 59 -wil l show equal coupling with al l the four protons surrounding an 4-AsO^ centre. The resulting superhyperfine structure wil l be a quintet, as observed experimentally. However, when the exchange frequency is lower than | close - f a r | , the electron wil l 'see' the instantaneous hyperfine f i e lds . Since a c lis^29MHz and a f f l r £ 0, only two protons now contribute to the superhyperfine structure, which wil l therefore be a 1:2:1 t r ip 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 'frozen i n ' . 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 ted to the expression T=T E/kT with E=0.2 eV and to=4cm T O c 4-A similar exchange between deuterons around an AsO^ centre was also observed in y-irradiated DKDA. At room temperature, a barely resolved nine l ine deuteron superhyperfine structure indicating ^->>|aclose - a f a r | was observed, which appeared to change over to a quintet at lower temperatures. No re l iable detailed studies could be made here because of the lack of resolution in the EPR spectra. For later discussion i t should be noted here that from these observations, Blinc et a l l 4 have concluded that the ferroelectr ic transit ion in KDP-type of crystals is best described by the dynamic order-disorder model. In part icular , these results were interpreted as evidence against the existence of a ' ferroelectr ic mode1 involving proton displacements in this class of crystals. Similar conclusions have been drawn later for the proton dynamics in mixed KDP-KDA - 60 -ferroelectr ic c rys ta l s^ 4 ^) a s w e n a s -jn ADA-type of ant i ferroelectr ic + i 14(c) crystals v 4-The present investigations of the AsO^ centre started with the observation that a l l the previous workers had assumed that the proton superhyperfine interaction is largely isotropic and, in part icular , that the ' f a r ' protons show no coupling with the unpaired electron. On the other hand, the previous studies indicated that the 4-hyperfine effects in the EPR of the As0 4 centre may provide very s ignif icant information on hydrogen bonding and fer roe lect r ic i ty in the Kh^PO^-type crystals. A systematic EPR and ENDOR investigation of 4-the AsO^ centre in these compounds was therefore undertaken. Fig. 7, 8 and 9 show typical EPR spectra of x-irradiated KDA for H||c. The spectra shown in Fig. 7 and 8 were recorded at X-band (^9.456GHz) at 300 and 4.2°K respectively, whereas Fig. 9 represents a spectrum observed at 300°K at K-band (24.15GHz). As mentioned ear l ier these spectra contain lines due to four other centres (discussed br ief ly in Appendix B), in addition to EPR lines 4-due to the As0 4 centre, indicated by vertical arrows at the top of 4-the spectra. The EPR lines belonging to the AsO^ are quite d is t inct 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 ip l e t at 77°K. Moreover at 4.2°K some of the radicals do not appear, presumably because of longer electron-spin la t t ice relaxation, times associated with them. Also note that in Fig. 8 the normally forbidden (Amp=0) lines also appear because for that case the microwave f i e ld had a component along the magnetic f i e ld H. L AsQa P O 2_ 250 G i 3 3 0 0 G F i g . 7 EPR of x - i r r a d i a t e d Kh^AsO, f o r H||c at X-band (9.45 GHz), T= 300°K. See text f o r l a b e l i n g of the s p e c t r a l l i n e s . F i g . 8 EPR of i r r a d i a t e d KH 2As0 4, H||c, at 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 . A s C f i r 1 r i r 6 7 0 0 7 2 0 0 7 7 0 0 8 2 0 0 8 7 0 0 9 2 0 0 9 7 0 0 «-H (GAUSS) 10,200 10,700 Fig. 9 EPR of KH2As04 at K-band (24.150 HGz), H||c, T=300°K. - 64 . Although the hyperfine structure in the room temperature EPR 4- 35 spectrum of AsO^ in KDA had been analysed by Hampton et al . , we have reinvestigated i t by u t i l i s ing measurements also on the three normally forbidden Amp=0 l ines , shown by T^, and Tg in Fig. 1. Moreover in our analysis we have also included the nuclear Zeeman term which had been omitted in the ear l ier studies. The parameters 35 given by Hampton et a l . predicted l ine positions to within 4 Gauss with the inclusion of the nuclear Zeeman term. It is suspected that the addition of a small quadrupole term may improve the f i t , but this has not been tr ied yet. 4-Typical room temperature EPR spectra of the AsO^ centre in x-irradiated DKDA, RbDA and ADA for H||c are shown respectively in Figs. 10, 11 and 12. The spin Hamiltonian parameters for these crystals 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 super-hyperfine structure as the orientation is changed from that of H||c. Fig. 13(a) and (b) show a comparison of the superhyperfine pattern on the lowest f i e ld A s 7 5 hyperfine l i ne , for the orientations H||c and Hie respectively. Fig. 13(c) and ( c ) show the proton structure on 75 the highest f i e ld As l ine for H i e It wi l l be noted that whereas Fig. 13(a) is a par t ia l ly resolved quintet with the component intensity rat io 1:4:6:4:1, the H|| c-axis patterns, Fig. 13(b) and 13(c) are respectively a singlet and a par t ia l ly resolved t r ip le t with 1:2:1 as the ratio for the intensit ies of the components. The 35 quintet feature was observed f i r s t by Hampton et a l . who also A s O ' 4-J 2 4 2.9 3.4 3.9 4.4 4.9 - H ( K G a u s s ) cn on F i g . 10 EPR of x - i r r a d i a t e d KD 2As0 4 f o r H||c a t X-band (9.450 GHz) and 300°K. 1.4 1.9 2.4 2.9 3.4 3.9 4.4 4.9 H(KGauss) Fig. 11 EPR of x-irradiated RbH2As04 at X-band, (9.435 GHz) for H||c and at ^300°K. - 68 -TABLE 1 4-Spin Hamiltonian parameters for AsO^ centre at 296°K. £, m and n refer to the crystal a, b and c system. Direction Cosines Crystal Principal value l m n g z = 2.0021 0.000 0.000 1.000 KDA V 3253.5+4 MHz II H (Ref.35) 9 X - ! 3 = 2.0014 y - - 0.000 A x = ' (\ = 2931.3+5 MHz II II II g z = 2.0046+.0008 0.000 0.000 1.000 Az= 3253.2+0.2 MHz II II KDA g y = 2.0000+0.0.0011 -0.000 1.000 -0.000 A = 2922.3+0.3 MHz II 11 " y — g x = 2.0011+0.0010 1.000 -0.000 -0.000 Ax= 2926.5+0.3 MHz II II II g z = 2.0057+0.0004 0.000 0.000 1.000 DKDA A , = 3245.3+0.3 MHz II II II z g y = 2.0063+0.0004 -0.000 1.000 -0.000 A = 2927.0+0.3 MHz II II II y g x = 2.0084+0.0003 1.000 -0.000 -0.000 A x = 2935.3+0.2 MHz II II II g z = 2.0137+0.0011 0.000 0.000 1.000 A z = 3200+1 MHz II II II RbDA g y = 2.0342+.0010 -0.000 1.000 -0.000 A = 2909+1 MHz II II II y — • 2.0352+0.0011 1.000 -0.000 -0.000 A x = 2912+1 MHz II II II - 69- -TABLE 1 (continued) Direction I Cosines Crystal Principal value I m n g = 2.0069+.0010 0.000 0.000 1. 000 Az= 3255+1 MHz I I I I I I ADA g = 2.0033+.0015 y --0.4848 0.8746 0. 000 Ay= 2906+1 MHz I I it I I g = 2.0098+.0015 0.8746 0.4848 0. 000 A = 2930+1 MHz A " I I T ~ 3 0 0 0 K AO GAUSS 1 I 2 0 GAUSS 1 I AO GAUSS 13 Superhyperfine features on m^j and mT=|-As hyperfine l i n e s in the EPR o f AsO?" centre i n KrLAsCv - 71 -interpreted i t to arise due to a mainly isotropic superhyperfine inter-4-action of the four protons surrounding the AsO^ centre. On the other hand, the H^ c feature has not been mentioned before. The H]_c-axis spectrum, however, gives a clear indication that the superhyperfine interaction is very anisotropic. Another interesting feature of the Hie spectra is that the resolution of the superhyperfine structure improves as the magnetic f i e ld increases. We find that ENDOR experiments were very helpful in explaining the room temperature EPR spectra. This point wi 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 . the EPR spectra are v i r tua l ly the same at 4.2 as those at 77°K. 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 iner detai ls of the EPR spectra. In Fig. 13(a') , (b 1) and (c') are shown the spectra observed at 4.2°K. The corresponding room temperature spectra are shown in the same figure at the top. It is now observed that for H||c, Fig. 13(a') , the superhyperfine structure consists of a (1:2:1) t r ip l e t of almost the same total pattern separation as that of the corresponding higher temperature pattern, Fig. 13(a), These observations have been understood^4 in terms of a dynamic order-disorder model, although here, again, superhyperfine interaction has been assumed to be essential ly isotropic. This assumption is seen to be in error when the angular variation of the EPR spectra at 77 or 4.2°K is studied. Fig. 13 also shows a compari-son of the superhyperfine patterns on the lowest f i e ld hyperfine - 72 -component of the AsO^- centre for Hie, as mentioned ear l ier . It may be noted that in addition to the spl i t t ings being d i f ferent , Fig. 13(b') shows an especially interesting feature when compared with 13(b): 75 the lowest f i e ld As hyperfine l ine s p l i t s , apparently, into four components, compared to the room temperature case, where i t does not show any sp l i t t ing at a l l . To understand the features on the lowest f i e ld hyperfine l ine , an irradiated crystal of DKDA was used. A comparison of the observed spectra showed that in Fig. 13(b') the A s ^ hyperfine l ine i t s e l f sp l i ts into two components and that in the case of KDA, the four l ine pattern was actually due to two separate hyperfine transit ions, one of which remains single while the other sp l i ts into a 1:2:1 t r i p l e t , indicative of a superhyperfine interaction with two equivalent protons. These observations show that the superhyperfine interaction is highly anisotropic. Moreover, this additional sp l i t t ing of the hyperfine components (regardless of the superhyperfine spl i t t ings) is found to decrease rapidly as the magnetic f i e ld 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 ine in Fig. 13(c ' ) . For the lowest f i e l d l i ne , however, the number of components as well as the magnitude of the sp l i t t ing 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 sp l i t t ings , again a DKDA crystal was chosen for these studies. Fig. 14 shows the 75 angular variation of these spl i t t ings associated with the lowest As hyperfine l ine in the ab plane of DKDA at 77°K. Similar variation X(orY) i i 1 1 1 1 1 1 1 1 o 10 20 30 4 0 50 60 70 so 90 W A N G L E FROM T E T R A G O N A L a AX I S 3 14 Angular variation of the spl i t t ings associated with nij=^ l ine in the ab plane of x-irradiated KDgAsO^ at 77°K. The single and the dotted lines refer to the two different domains. - 74 -0 . KDA.216K Fig. 15 Angular variation of spl i t t ings associated 75 3 with the As m i = 2 ' ' 1 ' n e "*n v a n ' o u s crystals at different crystals. « i - 75 -was observed for KDA and ADA also. It is seen from Fig. 15 that in general there are four distinguishable sites for an AsO 4" centre for a l l these crysta ls . However, this 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 Fig. 14. In addit ion, there is a puzzling feature that the remaining hyperfine lines show hardly any similar sp l i t t ing at a l l for any orientation of H in the crystal symmetry planes. Before obtaining the parameters of the spin Hamiltonian describing these spectra, we wil l now show that the observed variations in the EPR spectra can be explained in terms of the gross features in the crystal structure of KDA or, equivalently, of DKDA67. The crystal structure of KDA in the ferroelectr ic phase has been discussed in Chapter III. Assuming that no s ignif icant distort ion of the la t t i ce takes place on the formation of this centre i t wi l l be seen that for the case of a polarised c rys ta l , there are 4-only two d is t inct orientations for an AsO^ centre and that these two orientations should be related to each other by a rotation of approximately 16° about the crysta l l ine c-axis. However, in an unpolarised c rys ta l , twinning ( i . e . , domain structure) is present and X and Y directions can be interchanged, doubling the number of 4-possible sites for the As0 4 centre. Hence, for an arbitrary orientation of H in the ab plane of DKDA, each hyperfine l ine is expected to spit into four components. This is precisely what is seen in Fig. 14 where the variation of the l ines arising due to two different ferroelectr ic domains is shown by continuous and dotted - 76 -l ines. It is also evident from Fig. 14 that when H is along the X or Y d i rect ion, the components arising from two dif ferent ly oriented tetrahedra coincide, the remaining sp l i t t ing being entirely due to the domain structure. On the other hand, when H is along a or along b, the components belonging to the two domains coincide, the remaining sp l i t t ing now being entirely due to the two dif ferent ly oriented AsO^ tetrahedra. To confirm these results further, we repeated the EPR study on KDA at 77°K in the ab plane with a polarising dc e lectr ic f i e ld across the crystal and paral lel to its c-axis. Variable e lectr ic f ie lds up to ± 12 KV/cm were used. For the cases of H along X or H along Y, we observed the expected variation of the hyperfine l ine intensit ies with the magnitude and the direction of the applied e lectr ic f i e l d , as shown in Fig. 16. Also no e lectr ic f i e l d effects could be observed for the case with H||a or H||b-thus fu l l y confirming our model. In fact , we could plot the hysteresis loop for applied f ie lds between ± 12KV/cm by taking the polarisation in the crystal to be proportional to the difference in the intensity of the two l ines. 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 ie lect r ic studies ^ . The angular variation of the hyperfine transitions can be described by the spin Hamiltonian (21), with the parameters g and A having orthorhombic symmetry. The principal values are given in Table 2. Here, as before, the z direction is the direction of the c-axis, and x and y are the two other mutually orthogonal directions. - 7 8 -T A B L E 2 Spin Hamiltonian parameters for AsOA~ centre at low (indicated) temperatures . i, m and n refer to the crystal a, b and c system. Direction Cosines Crystal Temperature ( ° K ) Principal value . l m n g z = 2 . 0 0 0 7 + 0 . 0 0 0 4 0 . 0 0 0 0 0 . 0 0 0 0 1 . 0 0 0 A z = 3 1 9 9 . 0 + 0 . 1 MHz II II KDA 4 . 2 g = 1 . 9 9 5 3 + 0 . 0 0 0 5 A y = 2 8 3 3 . 5 + 0 . 8 MHz g = 2 . 0 1 1 4 + 0 . 0 0 1 0 A = 2 8 9 5 . 0 + 0 . 3 MHz A - 0 . 4 8 4 8 M 0 . 8 7 4 8 II 0 . 8 7 4 6 II + 0 . 4 8 4 8 II 0 . 0 0 0 II 0 . 0 0 0 II g z = 2 . 0 0 0 3 + 0 . 0 0 1 0 . 0 0 0 0 . 0 0 0 1 . 0 0 0 DKDA 4 . 2 A z = 3 2 0 0 + 5 MHz g = 2 . 0 0 0 1 + 0 . 0 0 2 A y = 2 8 3 0 + 5 MHz g = 2 . 0 0 0 5 + 0 . 0 0 2 A =2890+5 MHz A II - 0 . 4 8 4 8 II 0 . 8 7 4 6 II II 0 . 8 7 4 6 n 0 . 4 8 4 8 II II 0 . 0 0 0 II 0 . 0 0 0 g z = 2 . 0 0 5 + . 0 0 1 0 . 0 0 0 0 . 0 0 0 1 . 0 0 0 A z = 3 2 4 0 + 5 MHz " II II A D A 2 3 0 g = 2 . 0 0 2 + 0 . 0 0 2 3 y -A y = 2 8 9 5 + 5 MHz - 0 . 4 8 4 8 ll 0 . 8 7 4 6 II 0 . 0 0 0 II g = 2 . 0 0 7 + 0 . 0 0 3 y y A = 2 9 2 0 + 5 MHz 0 . 8 7 4 6 II 0 . 4 8 4 8 n 0 . 0 0 0 II - 79 -It can now be seen that the presence of the orthorhombic site symmetry 75 together with a large second order effect in the As hyperfine 75 structure is responsible for the other three As hyperfine lines remaining unspl i t . 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 result for KDA and DKDA are in agreement with the structural data. 4-Analysis of essential ly similar 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 Fig. 15 that for these crysta ls , over a range of 'vlOO 0 above T , the EPR spectra show the symmetry of those below T . 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 2As0 4:-To understand the superhyperfine features, ENDOR spectra were recorded at intervals of 5° or less with the magnetic f i e ld being turned around the three mutually perpendicular crystas axes a, b and 75 c. ENDOR studies were made on al l of the seven As hyperfine transit ions observed in our experiments. A large effect was observed 75 due to the change of the nuclear spin state of As from one hyperfine multiplet to another. Typical ENDOR spectra are shown in Fig. 17. The spectra are the simplest for the case of H||c, Fig. 17(a) and 17(b). They consist of three d is t inct sets of l ines , - 80 -^(close) J (a)H//C (far) (close) H Q = 4854 G 1 1—//-^ , p- . •,-( b ) H / ^ C H q= 2624 G (close) 8 9 (far) ( c ) H l C Hq= 2608 G 10 i i ~~1 9 i — 10 11 ~ i — 12 12 I 13 (far) 2 3 24 MHz (close) 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 AsO 4" ce n t r e i n ' KrLAsO, a t 4.2°K. - 81 -centered around the free proton NMR frequency for the magnetic f i e ld corresponding to the EPR transit ion saturated. The set closest to the free proton NMR frequency consists of a group of 4 lines in either direction whereas each of the other two sets consists of just one l ine. For the case of the magnetic f i e ld H oriented along an arbitrary direction in the crystal planes, each of these two sets also consists of a number of lines (maximum 4) (see Fig. 18) and the third set , near the free proton NMR frequency, consists of many more unresolved l ines. In the present studies, we have concentrated only on the two sets of ENDOR lines resulting from the two largest super-hyperfine couplings. For example in Fig. 17(b) these two sets are formed by the l ine at 23.40 MHz assigned to the 'c lose' protons, and the l ine at 12.80 MHz assigned to the ' f a r ' protons. It is now clear that because the superhyperfine coupling due to ' fa r ' 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 transitions on various hyperfine multiplets is the same as seen from Fig. 19,20 and 21. Here 2(v^ - V p ) is plotted because this is approximately equal to the hyperfine coupling for the corresponding direct ion. Four transitions each are in general observed for the 'c lose ' and the ' far ' protons, in accordance with the crystal structure of KDA in the ferroelectr ic phase. However, when H is oriented in the ab plane, the ENDOR spectra obtained by saturating the lowest f i e ld hyperfine transit ion are d ist inct from those obtained by saturating most other EPR transit ions. A comparison is given in Fig. 18 Spl i t t ing of the 'c lose ' proton ENDOR transitions for H oriented 2° from the c-axis. 'Far' protons also show similar sp l i t t ing . -io° O IO - A n g l e f r o m c - a x i s 90° A n g l e f r o m a - a x i s F i g . 19 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^ or ) r e f e r s to a d i s t i n c t ' f a r ' proton s e t . CO co F i g . 20 Angular v a r i a t i o n o f the ' c l o s e ' proton 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 7 5 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 ' proton s e t . - 85 -ANGLE FROM TETRAGONAL a AXIS 21 Angular variation of the 'c lose' proton ENDOR transitions in the ab plane of x-irradiated KhLAsO, for (a) the highest f i e ld and (b) the lowest fTeld A s 7 5 hyperfine transit ion at 4.2°K. - 8 6 -Fig. 21, which shows the ENDOR spectra for the 'c lose' protons in 75 the ab plane of KDA when the lowest and the highest f i e ld As EPR lines are saturated. It seems rather puzzling at f i r s t when one obtains ENDOR signals from four d is t inct sites in one case, Fig. 21(a), but from only two in the other case, Fig. 21(b), However, this observation also finds a natural explanation when the presence of the ferroelectr ic domain structure in the EPR spectra was taken into account. In the case of Fig. 21(b), the magnetic f i e ld H is set to satisfy conditions corresponding to point A in Fig. 14, and then kept constant throughout the angular variation study. It wi l l be seen that for ENDOR, the EPR condition is then sat isf ied mainly for the l ines from the two sites in a single domain and only two transitions are therefore expected (and observed) in the ENDOR experiments. S imi lar ly , by satisfying the EPR conditions corresponding to point B in Fig. 14, the two other transitions (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 rans i t ion, Fig. 21(a), however, since the spl i t t ings due to the two sites or the two domains remain unresolved in EPR, a l l the four transitions are expected to occur simultaneously and this is precisely what is observed in Fig. 21(a). These arguments were further confirmed by observing the effects of polarising e lectr ic f ie lds on the ENDOR transit ions. The crystal was polarised at 77°K and then cooled to 4.2°K. The polarising e lectr ic f i e ld was then removed and the ENDOR transitions were observed. The expected changes in the ENDOR l ine intensit ies were clearly seen, thus lending - 87 -f i r m s u p p o r t t o o u r model o f t h e domain s t r u c t u r e and the domain 82 s w i t c h i n g i n t h e K D A - t y p e o f f e r r o e l e c t r i c s . 4.3 ENDOR Data and A n a l y s i s S e v e r a l h u n d r e d ENDOR measurements were made by f o l l o w i n g t h e f o l l o w i n g two p r o c e d u r e s : 1. F o r H | | c , ENDOR measurements were made f o r a l l s e v e n EPR t r a n s i t i o n s . T h i s d a t a i s d i s c u s s e d i n S e c t i o n 4 . 3 . 1 . 2. The a n g u l a r v a r i a t i o n o f t h e ENDOR l i n e s were c a r r i e d o u t 75 on t h e h i g h e s t and t h e l o w e s t f i e l d As l i n e s i n d i f f e r e n t c r y s t a l p l a n e s . T h i s i s d i s c u s s e d i n S e c t i o n 4 . 3 . 2 . 4.3.1 S i g n s o f the 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 t h e a p p l i c a t i o n o f the p r o c e d u r e d i s -7^ c u s s e d i n 2 . 3 . 2 t o o b t a i n the s i g n s o f t h e As " h y p e r f i n e c o u p l i n g and t h o s e o f t h e ' c l o s e ' and the ' f a r ' p r o t o n s u p e r h y p e r f i n e c o u p l i n g s . A t 4 . 2 ° K , t h e ENDOR s t u d i e s have shown t h a t the p r i n c i p a l d i r e c t i o n a s s o c i a t e d w i t h the l a r g e s t p r i n c i p a l component o f the s u p e r h y p e r f i n e t e n s o r o f a ' c l o s e ' p r o t o n , i s q u i t e c l o s e t o the d i r e c t i o n o f the c - a x i s . Thus E q . (40) c a n be used t o o b t a i n the s i g n s o f t h e ' c l o s e ' p r o t o n c o u p l i n g s f o r H | | c . T a b l e 3 g i v e s the v a l u e s o f cos [2a ( H F P . ) ] and the r a t i o s o f t h e q u a n t i t i e s Hip t, c, ivE°+(v- 4"^for e a c h e p r t r a n s i t i ° n T i t o i4a+(Ti) • 4°1^'for ' i ' 1 T-j i n F i g . 1 and nip=2, s h o u l d be t h e same as the c o r r e s p o n d i n g r a t i o s o f < S z > £ U = m F , + ) . T a b l e 4 shows t h e o b s e r v e d v a l u e s o f v ( c j o s e ) ( j . ) f o r e a c h EPR t r a n s i t i o n T - j , T 2 Ty', as w e l l as a c o m p a r i s o n o f t h e e x p e r i m e n t a l l y o b s e r v e d and t h e o r e t i c a l l y e x p e c t e d v a l u e s o f _ 88 _ TABLE 3 Values of 2 < S z >^  = cos (2am^_), nip = 1 , 0 , - 1 , calculated for the resonance f ie lds H T using A-p = 3254 MHz, Aj^  = 2931 MHz, g n = 2.0021 a n d ' g n & n = 7 .292 x 1 0 " 4 MHz/gauss. EPR H T =2 < S z >1 =2 < S z >Q =2 < s ' z >_-, Transition Gauss T l 1349 .9 0 .8110 0 .5423 0 .1043 T 2 1692 .2 0 .8442 0 .6272 0 .2816 T 3 2 1 5 4 . 5 0 .8775 0 .7208 0 .4810 T 4 2 6 5 3 . 8 0 .9033 0 .7855 0.6361 T 5 3235 .3 0 .9246 0 .8398 . 0 .7469 T 6 3 9 3 8 . 6 0 .9436 0 .8862 0.8431 T 7 4 8 6 3 . 2 0 .9576 0 .9187 0 .8962 -89 -TABLE 4 Comparison of the observed ratios v T / v T for a 'c lose ' proton, where i 1 Vj = V p C | o s e ^ (T..) - v , to the corresponding values of 2< S z > , for the possible combinations of signs of the proton and 75 As hyperfine couplings. Calculated values of 2< S z > T 75 1 for the signs of As and close proton couplings indicated +,- +,+ -,+ T l 15.431 1.000 1,000 0.8110 1.000 0.1043 T 2 13.048 0.8456 0.8442 0.8442 0.2816 0.2816 T 3 13.528 0.8767 0.8775 0.7208 0.4810 0.7208 T 4 12.210 0.7849 0.7855 0.7855 0.7855 0.7855 T 5 12.960 0.8399 0.8398 0.7469 0.8398 0.9246 T 6 13.001 0.8425 0.8431 0.8431 0.9422 0.9422 T 7 13.812 0.8952 0.8962 1.000 0.9576 1.000 E P R V T . Observed rat.os Transition - , Saturated experimental v T / V T 1 J (MHz) - 90 -2 < S z >£• for the four possible combinations of the signs of the As and the 'c lose ' proton couplings. The comparison clearly shows that, 75 for the c-axis d i rect ion, the sign of As hyperfine coupling is positive whereas that of a 'c lose' proton superhyperfine coupling is negative. Combined with the results of the detailed angular variation studies of the ENDOR l ine posit ions, this leads to the conclusion that 75 the sign of the As hyperfine coupling is positive whereas that of a 'c lose ' proton superhyperfine coupling is negative. The sign for the ' fa r ' proton coupling could not be unambi-guously determined by this simple procedure since the principal directionsassociated with ' fa r ' proton coupling tensor deviate s igni f icant ly from the crystal-axis directions. The double ENDOR technique was then applied to obtain the relat ive signs of the 'c lose ' and the ' fa r ' proton coupling tensors. Fig. 22 i l lustrates the double ENDOR signals obtained by saturating the ENDOR transit ion v £^+ r ^ a n c l sweeping the second r.f. osc i l l a tor through frequencies corresponding to the other ENDOR transitions involving the 'c lose' and the ' fa r ' protons. Since the double ENDOR enhancement signals for both the 'c lose ' and the ' far ' protons have the same phase, the signs of the 'c lose' and the ' fa r ' proton couplings, for H||c, is the same. In view of the result that the general nature of the 'c lose ' and the ' fa r ' proton tensor is the same, we conclude that the sign of the 'c lose ' 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) (a) MT-) and the lower, vi- ENDOR transition$T. observed. The values t,+ i i ' » ' t,-1 ^ - 92 -of (A ' a ' kz and the magnitude of A z z determined from the slope and the intercepts of the graph agree f a i r l y well with those determined from the detailed angular variation studies. The lower ENDOR transit ion frequencies depend more c r i t i c a l l y on relat ive values of (A^ ) and A z z ^ than the higher. Fig. 23 shows the graphical representation of Eq. (39) for 'c lose' and Fig. 24 for ' fa r ' proton ENDOR transit ion frequencies. A comparison of the observed values of j(T.j) with those calculated using the values of (A ) (a) and A z z from graph of Fig. 23 and 24 is given in Table 5. The close agreement between the calculated and the observed ENDOR frequencies lends a firm support to the va l id i ty 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 ight ly different values of ( A ^ z z and A ^ obtained by plotting the data for v £ ° ] ( T . ) and vl°^(T. ) separately, although the f i t of Table (5) is considered reasonably good, and the deviations are within the ENDOR l ine width (100-150KHz). The s l igh t , apparently systematic differences between (a) (a) the best f i t s for the two different sets v£ j and v£ are attributed to small errors in the description of the EPR parameters, in particular 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 analyt ical ly as a perturbation. On the other hand, the effect of inclusion of terms second order in the proton coupling constants or of direct nuclear-nuclear coupling, appears to be negligible since there is no clear evidence of the Fig. 23 Graphical representation of Eq. (39) (see text) for the ' fa r ' proton ENDOR transitions in x-irradiated KhLAsO, H||c at 4.2°K. Fig. 24 Graphical representation of Eq. (39) for the 'c lose ' protons in x-irradiated KHLAsO, for H||c and 4.2°K. TABLE 5 Observed and calcualted values of v^l^ using = -3.56 MHz and ( A ^ f a r b 2 z = 3 3 - 5 4 (MHz)2 as obtained from Fig. 24 and of J c j o s e ) u s i n g A ^ 1 o s e ^ = 30.25 MHz and ( A ( c l o s e ) ) 2 960.3 (MHz) from Fig. 23. zz EPR Transition Saturated v ^ a r ) (MHz) v E f a r ) (MHz) v ^ o s e > (MHz) v ^ 0 5 ^ (MHz) Observed Calculated Observed Calculated Observed Calculated Observed Calculated 4.679 6.023 8.057 10.010 12.568; 15.425 19.088 4.685 6.012 8.060 10.060 12.562 15.369 19.063 7.888 8.920 10.929 12.827 15.401 18.318 22.400 7.866 8.910 10.916 12.823 15.390 18.329 22.394 21.178 20.253 22.701 23.410 26.735 30.037 34.518 21.14 20.18 22.67 23.33 26.64 29.84 34.40 7.068 6.262 7.07 6.25 6.312 6.32 - 96 -presence of non-additive effects in the experimental ENDOR spectra. In any case there i s no ambiguity in the conclusion that the sign of 75 As hyperfine coupling i s positive while those of the 'close' and the 'far' protons are both negative. 4.3.2 Angular variations of ENDOR tra n s i t i o n s From the discussion in Chapter II and that i n the previous Section, i t is clear that the observation of v F + t r a n s i t i o n s on the 75 lowest f i e l d and v F_on the highest f i e l d As hyperfine component involves the least correction due to admixture of the electron spin 75 states by the As hf int e r a c t i o n . Hence detailed measurements r e l a t i n g to these l i n e s only, as a function of angle in the three c r y s t a l planes were made. Fig. 19, 20 and 21 show the observed v a r i -ations, as mentioned e a r l i e r . 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 of ^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 available. This program was adopted to predict ENDOR l i n e positions by d i r e c t diagonalisation of ^ " E p R + ^ E N D O R i n a ^ a s i ' s °^ l M m s mi > states obtained from S=%, I^ A s^= i and I ^ = h. 2 The observed ENDOR frequencies were f i t t e d by adjusting the parameters of ^ E ^ Q O R ( t n e parameters f o r <^p_pR having been 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 transit ion frequencies for protons 4- 75 surrounding an AsO^ centre in Kh^AsO^, at 4.2°K. The As 3 mT•= — l ine was saturated in each case. I 2 Orientation of H (far) V E ,-(close) E,-Observed (MHz) 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 1 m n (MHz) A = 8 .907 0 . 9 9 4 3 -0 .0751 0 . 0 7 5 2 A 'Close' A y = - 1 6 . 8 4 8 0 . 0 3 9 7 0 . 9 1 8 9 0 .3926 A z = - 3 3 . 4 9 6 - 0 . 0 9 8 6 - 0 . 3 8 7 4 0 . 9 1 6 6 0 . 3 7 5 0 0 .5771 0 .5757 - 0 . 4 6 8 4 0 . 7 2 6 6 0 . 6 6 9 0 A v = 2 . 1 6 8 0 . 7 2 5 5 A 'Far' A y = - 3 . 3 8 8 0 . 6 7 0 2 A = - 7 . 4 0 5 - 0 . 1 5 6 6 - 99 -calculated ENDOR transitions and the superhyperfine tensors for 'c lose ' protons thus obtained are given in Table 7. The f i t was achieved to within a standard deviation of 20 KHz for 'close'protons and 15 KHz for ' fa r ' protons. The better f i t for ' fa r ' protons ref lects their inherent narrow linewidth 80 KHz), as compared to close protons. No nuclear spin-spin interaction was detected in these investigations; however, i t is possible that the higher l ine width of the 'c lose ' proton ENDOR lines may be due to unresolved nuclear-nuclear sp l i t t i ng . 4.4 Correlation of EPR and ENDOR results An examination of Table 6 shows that (a) The superhyperfine interaction is considerably anisotropic both for 'c lose ' and ' fa r ' protons. (b) The strength of the interaction for the ' f a r ' protons is about a f i f t h of that of the 'c lose ' protons and is therefore not resolved in EPR. (c) The principal axes of the 'c lose ' proton interaction nearly coincide with the a, b and c directions defined in the crystal in i ts tetragonal phase. These observations c la r i f y the aspects relating to superhyperfine structure mentioned in Section 4.1 on EPR results. Let us reconsider Fig. 13 again in the l ight of these results . (i) When H|jc, the four 'c lose ' proton positions are equivalent with a coupling constant -^SOMHzand the four ' fa r ' protons are equivalent with a coupling constant of ^-3MHz (from Fig. 19 and 20). Hence, at room temperature, where rapid motion of the protons between 'c lose ' and ' fa r ' sites 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 Fig. 13(a). ( i i ) When H| j a axis , i t is noticed that the four 'c lose' proton positions and the four ' fa r ' proton positions are equivalent only in pairs. Since al l the 0-H...0 bonds in the crystal l i e nearly along a and b axes, let us cal l the pair of 'c lose' protons lying on the 0-H...0 bond paral lel 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 posit ions: 1. ' a ' type 'c lose ' protons ; - 18MHz 2. ' a ' type ' f a r ' protons,- 4.5MHz 3. 'b ' type 'c lose ' protons, 9MHz 4. 'b ' type ' fa r ' protons, -0.5MHz At room temperature there is averaging between the coupling constants of the ' a ' type 'c lose ' and ' fa r ' protons giving an average coupling of ^ -11.25MHz and of the 'b ' type 'c lose ' and ' far ' protons giving a coupling constant of °» 4.25MHz. Hence the observed structure should show two proton couplings with equivalent pairs of protons. However, the coupling of 4.25 MHz is unobservable by EPR. Hence, what is seen is a coupling of -11.25MHz to two equivalent protons giving a t r ip l e t . This is exactly what we see in Fig. 13(c). At low temperature (4.2°K) a l l motion should be effect ively stopped and a l l four coupling constants should be operative. However, 3 of the coupling constants are too small to be seen clearly 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 resul ts , due to orthorhombic 75 symmetry we would expect the low f i e ld As hyperfine l ine to sp l i t into two with one of the lines corresponding to the s i te with two 'a ' type 'c lose ' protons and two 'b ' type ' far ' protons and the other corresponding to two 'b ' type 'c lose' protons and two ' a ' type ' far ' protons. It is clear from the tabulation of the coupling constants that only one of the lines is expected to show clear proton sp l i t t i ng , while the other one is broad with no resolved proton sp l i t t i ng , in complete accord with the spectrum in Fig. 13(b). It is c lear , 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 inc, Cevc and Schara's 14 I P ear l ier results for the simple special case of H|[c have thus been found to f i t in with our model. 4.5 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 orbital of arsenic involved in the m.o. of A-| symmetry into which the odd electron enters. An estimate of the fraction of the unpaired spin population on the As s orbitals from the observed isotropic hyperfine interaction leads to the figure of 36%. The observed anisotropic interact ion, though small, cannot be fu l l y accounted for by the participation of 4d22 As orbital alone in - 102 -the A-j state, and probably a complete calculation involving the contribution from the spin polarization of inner As p and d orbitals is necessary. Oxygen Although a considerable positive spin density is presumably 4-present on the oxygens of the AsO^ unit , no hyperfine interaction can be seen as 0 ^ has no nuclear moment. An order of magnitude estimate would lead to a figure of 16% for the fraction of the unpaired electron spin on each oxygen. 0 ^ enrichment of this crystal would y ie ld valuable direct data on the spin density on the oxygen as well as the hybridization on each oxygen. A calculation from the structural data of Frazer and 62 4 1 Pepinsky and Bacon and Pease shows that the As-O-H angle is close to 3 108° which would lead us to expect a sp hybridization at the oxygens. 'Close' protons Isotropic interact ion: The contact interaction is seen to be -13.812MHz from Table 6. This corresponds to a fraction 0.97% of the unpaired electron in the hydrogen Is orb i ta l . Although i t appears most l ike ly that the mechanism for this isotropic interaction is the same as the one now famil iar in free radicals i.e. the exchange polarization of the 0-H <j bond by the a spin density on oxygen, i t is d i f f i c u l t to make a correlation of this result with the observations in other radicals. The extensive EPR data and calculations available 68 in the l i terature for the 0-H radical in irradiated ice and other - 103 -69 crystals are unfortunately not d irect ly 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 dif ferent. Anisotropic interaction:- It is noticed that the traceless anisotropic interaction has the principal values 22.72, -3.04 and -19.68 MHz, which shows i t to be far from axia l . This can be understood from the following model for the dipolar interaction. (a) The polarization of the 0-H a bond, referred to already wi l l lead to a negative spin density in the bond. The 8 spin in the 0-H bond wi l l lead to a dipolar interaction which wi l l be axial with respect to the 0-H bond. (b) The a spin distributed over the entire AsO^ tetrahedral unit may be approximated by an electron with a spin at the arsenic s i te . This point charge model is crude but is used in the absence of a better approximation. It appears, however, to describe the situation rather well . The unpaired electron at the arsenic s i te wil l have a dipolar interaction with the proton,which wil l be axial with the As-H direction as the axis. The magnitude of this interaction can be calculated to be 4.2 MHz under the above approximation using the atomic positions from the neutron d i f f ract ion investigation which gives the As-H distance to be 2.2 A 0 . An examination of the angular variation shows that the 'c lose ' proton interaction is dominated by the mechanism (a). This explains why in the ab plane the anisotropy is so large, whereas in the ac plane one of the protons shows a similar variation to that in the ab plane and the other shows only a small variation 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 that of the other along the As-H d i r e c t i o n . The two tensors (estimated by a n a l y s i n g the angular v a r i a t i o n ) are given ( i n MHz) below. /15.8 0.0 y 0.0 and /-9.4 [ 0.0 I 0.0 The value of 4.7 MHz compares reasonably well with 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 des 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 of a ' c l o s e ' proton with the unpaired e l e c t r o n on the oxygen of the 0-H fragment cannot be evaluated at 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 basis 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 4-that the formation of AsO^ c e n t r e causes l i t t l e change i n the l a t t i c e o f KDA. 0.0 •7.9 0.0 ] with symmetry along 0-H d i r e c t i o n 0.0 0.0 4.7 0.0 | w i t h symmetry along As-H d i r e c t i o n 0.0 - 105 -It is noted that the 0-H directions when projected on the ab plane are along a and b axes according to the crystal structure data. The OH bonds, however, appear to deviate from the ab plane by a few degrees in the ac plane. Bjorkstam's deuteron resonance resul ts 7 ^ show this to be the case and although the present results cannot confirm th is , they do not contradict i t . to be -2.875 MHz, which means a spin density of 0.20% on the Is orbital of proton. Using the spin polarization model mentioned earl ier in connection with the 'c lose ' proton, this clearly shows that the 0...H hydrogen bonds in this case are part ia l ly covalent. It is not possible for the spin polarization mechanism to give r ise to spin density on the Is hydrogen atom orbital i f the hydrogen bond were purely ionic . We wil l return to a discussion of this important point in the next section. tensor, using the procedure outlinedfor the 'c lose ' proton tensor is possible. The two dipolar tensors may be written as: Far Protons Isotropic interaction:- The contact interaction is found Anisotropic Interaction:- A decomposition of the observed ,with the symmetry axis along - 106 -the 0...H d i r e c t i o n , and -4.6 0.0 0.0 2.3 0.0 0.0 0.0 2.3 0.0 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 to 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 the unpaired e l e c t i o n s p i n d e n s i t y on the oxygen of the 0...H bond. For the As-H case, however, the value of 2.8 MHz c a l c u l a t e d on the basis of 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 value o f 2.3 MHz given above. Note a l s o that 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 of the proton with the unpaired s p i n on the a r s e n i c atom. This i s why Fig.l9(a) shows angular v a r i a t i o n s i m i l a r to the angular 75 v a r i a t i o n on the lowest f i e l d As hyperfine 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 'clo s e ' proton super-hyperfine tensor 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. This can be understood q u a l i t a t i v e l y because of the ^ - n a t u r e of 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 of the sp i n d e n s i t y a t As and the oxygen atoms. B. HYDROGEN BONDING KDA has turned out to be an i d e a l system f o r studying the nature o f the hydrogen bond. Here the H i s l o c a t e d between two oxygens belonging to 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 of them. The hydrogen bond was descr ibed by P a u l i n g ^ , and by 7 2 Lennard-Jones and Pople on a purely e l e c t r o s t a t i c model. Subsequently 7 3 74 Coulson and Tsubomura pointed out the inadequacy of the e l e c t r o -s t a t i c model and emphasized the importance of the valence-bond s t ruc tures invo l v ing charge t r ans f e r . The strongest evidence fo r covalency in the hydrogen bond appears to come from the increased i n t ens i t y of c e r t a i n in f ra red t r a n s i t i o n s and some data on d ipo le 7 5 moments . The study of contact hyperf ine i n t e r a c t i on of protons can a lso y i e l d d i r e c t informat ion on charge t r ans fe r and covalency in the hydrogen bond. Such a study fo r .p ro tons in f ree r ad i c a l s by EPR has not t i l l now shown evidence fo r th i s e f f e c t because the i n t e r a c t i on i s expected to be very small and therefore d i f f i c u l t to reso lve . The higher r e s o l u t i o n poss ib l e with the ENDOR technique i s , however, expected to reveal t h i s e f f e c t . As pointed out in the previous s e c t i o n , the p o l a r i z a t i o n of the 0 . . .H hydrogen bond by an unpaired spin dens i ty on oxygen produces a 3 sp in in the Is o r b i t a l of hydrogen. Unfortunately a de t a i l ed theory c o r r e l a t i n g the spin dens i ty on oxygen with the observed contact i n t e r a c t i on i s not a v a i l a b l e . S u f f i c i e n t experimental data on s i m i l a r systems i s a lso not a v a i l a b l e . However, i t seems reasonable to s ta te that the contact hyperf ine i n t e r a c t i on observed in the two pos i t i onso f the proton may be'-direct ly proport iona l to t he i r cova lenc ies in the two p o s i t i o n s . In other words the r a t i o of the covalency in the 0-H bond to that in the 0 . . .H bond may be roughly equal to the r a t i o of the corresponding i s o t r o p i c i n t e r a c t i on - 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 th 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 ight of the crude approximations employed here. Such evidence from ENDOR when available on many systems may prove to be useful data on which detailed calculation of the covalency in the hydrogen bond may be made. C. FERROELECTRICITY The EPR experiments at 77 and 4.2°K have clear ly shown the effects of ferroelectr ic domains. In fact the experiments have shown the f eas ib i l i t y of examining by EPR and ENDOR each domain separately in a multidomain crysta l . This enables a study of sublattice po la r i -zation which might be valuable where unfavourable relaxation conditions make d ie lec 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 ferroelectr ic phase now makes available parameters necessary for a detailed and accurate study of the temperature dependence of proton superhyperfine structure. Such studies can y ie ld valuable information on proton dynamics in the paraelectric phase of this crysta l . We have recently completed such a study which wil l be reported elsewhere. - 109 -D. SUMMARY 4-This study emphasizes the fact that the AsO^ center in Kr^AsO^ is an ideal paramagnetic probe to study several aspects of fer roe lect r ic i ty and hydrogen bonding in this crysta l . The center is formed with remarkably l i t t l e damage to the la t t i ce as the discussion of the symmetry of the anisotropic proton hyperfine structure shows 3_ clear ly . The extra unpaired electron captured by the AsO^ unit goes into an A-| antibonding orbital with apparently l i t t l e damage to the surroundings. The study of hyperfine structure for the hydrogen bonded ' fa r ' proton which was completely unresolved in EPR and resolved only by ENDOR, has provided direct evidence of covalency in the hydrogen bond. The precise data regarding the hyperfine interaction obtained through ENDOR can form the basis for detailed calculations relating to the nature of the hydrogen bond in sol ids. The use of the ENDOR technique in demonstrating the nature of ordering of protons in the two ferroelectr ic domains, which confirms Slater 's model, has been shown. EPR is l ike ly 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 wi 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. Such studies have been made and are described next. - 110 -4.5 Temperature dependence of the EPR rpectra As mentioned in Chapter I, the d ie lect r ic and other properties of the KDP-type crystals can be understood best in terms 18 of the Kobayashi model of the ferroelectr ic transit ion in these crysta ls . 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 ferro-e lectr ic mode has been obtained for K D P 1 2 ^ and D K D P 1 2 ^ . It i s , however, not clear whether the observed mode represents a pure la t t ice mode which is not connected with the proton disorder, a quasi spin-wave type proton tunneling mode, or a mixed proton-lattice mode. In the KDA-type crysta ls , the corresponding Raman and neutron d i f f ract ion data is not available. These crysta ls , however, have been investigated 13 in detail 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 l i t t l e information on the temperature dependence of the motion of either 75 As or hydrogens and, hence, on that of the coupled proton-lattice 75 mode. The lack of data on the motion of As and protons in these crystals may be ascribed to the fact that the anticipated frequencies f a l l in the range of 10^ Hz, at room temperature and this is a bit too low for Raman, I.R. and neutron scattering experiments. However, this range of frequencies fa l l s 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. - I l l -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 ear l i e r , only the lowest f i e ld A s 7 5 hyperfine l ine shows further sp l i t t ing when cooled to 'lower' temperatures. We wi l l therefore concentrate mainly on the changes 75 in the spectral features associated with the lowest f i e l d As hyperfine transi t ion. Fig. 25 shows the features associated with the lowest f i e ld 75 As t rans i t ion, recorded at the various temperatures for the case of the powdered sample: of KDA. At room temperature the two main l ines at about 1230 and 1370 Gauss are just the 'pa ra l l e l ' and the 'perpendicular' features associated with the t rans i t ion, with the hyperfine parameters given in Table 1. It is seen from the inspection of Fig. 25 that only the ' pa ra l l e l ' component shows the presence of the proton superhyperfine structure, characterist ic of four equivalent spin % nuclei (protonsin our case). This can be easily understood on the basis of the ENDOR results which have shown that the superhyperfine couplings are highly anisotropic and the largest principal component l ies close to the c-axis direction of the crysta l . On lowering the temperature the superhyperfine features on the 'pa ra l l e l ' component start to change from the quintet towards a t r ip le t structure and, simultaneously the single l ine corresponding to the 'perpendicular' position starts to sp l i t into two. At about 215°K (though s t i l l about - 112 -KH 2 As04 ( POWDER ) 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 Fig. 25 Temperature dependence of the powder EPR spectra for x-irradiated KH9AsCL. Only the features associated with 75 3 4-the As m i = 2 hyperfine transit ion for the AsO^ centre are shown (see text). _ 113 _ 115° above the Curie point) the superhyperfine structure changes from a quintet to a t r ip le t with the components having the intensity pattern of 1:2:1. Note that here the hyperfine parameters already ref lect the orthorhombic symmetry whereas, on the basis of the known crystal structure of KDA, the EPR spectra are expected to ref lect only an axial symmetry in the paraelectric phase, below 97°K. In Fig. 26 are presented the similar spectra observed for the case of the powdered samples of the ant i ferroelectr ic compound ADA. Note again that even at about 330°K, (again about 115° above the Curie point) the spectra ref lect the features of those expected below T c in this system. Two important conclusions follow from these studies. F i r s t , these results present a rather clear demonstration of the fact that the known tetragonal symmetry in the paraelectric 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 last inference is important in that i f this is proved to be indeed the case, these studies could provide a rather direct evidence of the much-sought-after proton la t t i ce coupled mode motion in these systems. Another very interesting feature of Fig. 25 and 26 is that over a range of about 70° , the EPR spectra ref lect simultaneously the features of those due to axial and non-axial symmetry. This observation indicates that there are perhaps two mechanisms involved which have different activation energies and which affect the EPR spectra d i f ferent ly . Of course, the recent NMR experiments have - 114 -Fig. 26 EPR spectra of the AsO^~ centre in powder samples of x-irradiated NHAH»AsOA at the indicated temperatures. - 115 -shown the presence of r o t a t i o n o f the AsO^ groups and i f As n u c l e i are assumed to 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 observations could be explained. 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 the dynamics of 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 of the temperature dependence of the EPR 4-s p e c t r a o f the AsO^ centre i n the s i n g l e c r y s t a l s o f KDA, DKDA and ADA. The basis 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 desc r i b e d as 4-f o l l o w s . As explained e a r l i e r , EPR s t u d i e s of the AsO^ centre 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 four 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 of these s i t e s were shown to be due to the ex i s t e n c e o f the two d i f f e r e n t l y o r i e n t e d AsO^ te 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 to a r i s e from the ex 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 to the orderi n g o f protons i n the hydrogen bonds accompanied by the displacement of As and K ions along the c-axis a t the Curie p o i n t , two s i t e s are i n general expected f o r a l l the 4- / • x o r i e n t a t i o n s o f the AsO^ ce n t r e . I f , however, the (K-AsO^) system i s i n motion, according to the Kobayashi or the Cochran models, the 4-number of s i t e s f o r the AsO^ cen t r e could be one, or 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 the r o t a t i o n of the A s 0 4 t e t r a h e d r a and of the motion of As 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 be l i e v e d to be h e l p f u l f o r the understanding of the d e t a i l s of the powder EPR spectra too. - 116 -The present study shows that only one site is observed for 4-the 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 points, the EPR spectra already ref lect the symmetry of those sites expected and observed in ferroelectr ic phases of KDA and DKDA. This is c learly seen by examining Fig. 15 which shows the angular variation of the group of EPR lines (each arising from a distinct orientation of the AsO^~ centre) associated with lowest-field 3 hyperfine component n i j ~ which alone shows this sp l i t t ing as explained previously. For comparison the angular variation of the same group for the ferroelectr ic phase of KDA at 77°K is also included, see Fig. 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 different 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 ines , disappears. Moreover, as the temperature is raised further, 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). S imi lar ly , as the temperature is lowered below that corresponding to the collapsing of the individual components, the separation between 4-the lines corresponding to the dif ferent ly oriented AsO^ centres increases, until i t reaches to a maximum of about 35 Gauss, see Fig. 27. - 117 -2CH i ^ j , , , , , , — 240 260 280 300 320 340 360 380 — T ( K ) Fig. 27 Temperature dependence of the spl i t t ings associated with the 75 lowest f i e ld As hyperfine transit ion for H||X in various crystals . - 118 -This 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 of the As hyperfine i n t e r -a c t i o n as well as those due to the proton hyperfine 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 only 75 e x p l a i n e d i n terms of 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 of As was s t u d i e d 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 tetragonal 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 s i m p l e s t . 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 basis 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), at 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 o r i e n t e d t e t r a h e d r a . 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 . I t must be f u r t h e r mentioned t h a t f o r H||X, 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 7 ^ hyperfine s t r u c t u r e . 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 superhyper-fine structure because for that direction a l l the arsenic sites are 75 equivalent, and thus the slowing of the As motion do.es not seem to affect the EPR spectra. 75 To evaluate the correlation times for the motion of As nucleus, as well as for the protons, a computer programme based on the formalism of the modified Bloch equations was used. For the case 75 of the As motion, the sp l i t t ing between the EPR lines due to the two AsO^- 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 calculations. For the case of the protons the spl i t t ings for H||c for the case of both the 'c lose ' and the ' far ' protons were measured to be 10.80 Gauss l and 1.50 Gauss respectively, 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 ise 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 correlation times, x , were obtained. The data are shown in Fig. 28 where I n - is plotted against 1°-?-°-. Several important features can be noted from inspection of Fig. 28. F i rst of a l l i f we assume that the motions are thermally l 1 correlated, then the plot of 1 n - against - should be l inear , the T T - 120 -c 2 3 . 0 0 2 2 . 0 0 21.00 2 0 . 0 0 19.00 18.00 17.00 16.00 15.00 Protons in K H 2 A s 0 4 , H / / c A s 7 5 in KH 2 As0 4 ) H//X A s 7 5 in KD 2 As0 4 ,H//X A s 7 5 in N H 4 H 2 A s 0 4 l H / / X Protons in N H 4 H 2 A s 0 4 , H / / c 2.80 3.20 3.60 4 .00 4 . 4 0 4 .80 5.20 I O 3 — * » -T °K 7 5 Fiq. 28 Correlation times for the motion of As and of protons, 7 5 calculated from the temperature dependence of As and proton hyperfine structure. - 121 -slope being the activation 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 inear regions each, with slopes in eV and preexpontial factors in Hz of: 0.25, 1.0 x 1 0 1 3 ; 0.12, 3.9 x 1 0 1 0 ; 0.2, 3.2 x 1 0 1 2 for the motion of A s 7 5 and 0.5, 2.8 1 0 1 8 ; 0.15, 2.5 x 1 0 1 1 ; 0.2, 3.2 x 1 0 1 2 for the motion of protons. 75 It is clear that the motion of As nucleus and protons are governed by different processes at higher temperature but the same process governs the motion of both types of nuclei at lower temperatures. These studies thus present direct evidence for the existence of a 75 strong coupling between the motion of the protons and that of the As nuclei . Similar coupling is also observed for the case of ADA, where 75 the activation 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 1 0 ; 0.12, 1.4 x 10 9 and those for the proton motion: 0.25, 7.9 x 1 0 1 0 ; 0.33, 8 x 1 0 1 1 . The 75 same quantities for the motion of As in DKDA were determined to be 0.3, 13.6 x 1 0 1 3 ; 0.13, lx 1 0 1 1 ; 0.09, 5 x 10 9 for the case of H||X. We have so fa r , not been able to obtain correlation 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 clearly shows that below about 250°K, the same process governs the motion of 75 deuterons and As and this may be taken as an evidence for the l existence of the coupled mode motion in this material also. v=- can 75 T be interpreted as the frequency of exchange of the As and of protons - 122 -in their respective double minimum positions. 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 ract ion experiments point to preferential vibrations of heavy ions along c-axis , no quantitative data is avai lable, but this has been 18 21 22 78 79 postulated by several authors recently. ' ' ' ' Furthermore, although the EPR studies do not y ie ld direct information on the motion of K+ or NH^ ion, 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 identif ied as the coupled proton-lattice mode in these crystals. To check whether the observed exchange frequencies follow the 2 v a (T-T ) relat ionship, plots of v versus /T-Tc were made, see Fig. 29. These plots were not l inear over the entire range of the invesi-gated temperatures, but they became linear at lower temperature as T->TC. Since this result 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 AT-T ) plots for the deuterated and the undeuterated crystals . On the basis of the Kobayashi model the slopes of these plots wil l be quite d i f ferent , being strongly dependent on the tunneling frequencies of the protons or the deuterons in their 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 that 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 description of the phase transit ion here. Inspection of Fig. 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 transit ion mechanism at lower temperatures the slopes are not appreciably different and this point is not c lear ly 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 correlation times is too large to arrive at definite conclusions. It is believed that EPR experiments using much lower microwave frequencies wi l l be quite helpful to c la r i f y this point further. We also l ike to point out that over a large range of temperatures the plots of Inv versus ln(T-T ) are reasonably l inear , pointing to the relationship of the form va(T-T c ) n . It is emphasized that such a relationship is not predicted by any of the current models of the ferroelectr ic transitions 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 crystals has also been pointed out. Another feature to be noted from these plots is that, at 75 corresponding temperatures, the motion of As and of protons is the slowest in ADA and the fastest in KDA. 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 clearly understood, i t might also be a result 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^ units. This could be checked further by investigating the temperature dependence of the NH^  motion. We note that NH^  radicals 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 correlation times, i t wi 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 wil 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 units, 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 ax i s i n these compounds. The e f f e c t of 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 a x i s of t h i s ' r o t a t i o n ' . 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 observing the temperature dependence of 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 best 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 th 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 at 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 of the lowest 75 4-f i e l d As hyperfine l i n e i n the EPR spectrum of the AsO^ c e n t r e i n KDA and ADA at temperatures where the a x i a l and the non-axial f e a t u r e s are observed simultaneously 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 ASO4 t e t r a h e d r a i s more or l e s s smeared out. This i s a strong 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 course, the recent 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 of a slow r o t a t i o n of 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 process, f o r example, proton exchange between various 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 of the AsO, u n i t s . I t seems c l e a r , i n any - 127 -20H (a) KhL AsQ,, T= 2 5 0 0 K (b) N H 4 H 2 A s0 4 , T= 3 2 4 ° K 10 3 0 5 0 7 0 9 0 ' Angle from tetragonal "a" axis Fig. 30 Angular variation of the spl i t t ings associated with the lowest f i e ld A s 7 5 transit ion for KH2As04 and NH4H2As04 at the indicated temperatures. - 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^ units, the two processes having different activation energies. 4.6 Studies on KH2P04-KH2As04 mixed crystals It is well known that by mixing two ferroelectr ic 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 ie lect r ic for use in a given range of temperature and the study of the structural details of the mixed crystals thus acquires practical importance. For low concentration of the "impurity" constituent, EPR and in particular ENDOR, can prove very helpful for elucidating structural details here. We have employed these techniques with a view to investigating the structural details of the mixed KDP-KDA crysta ls , KDA being mixed with KDP in concentrations ranging from one to about 20% by weight. 14 Again at the time we started our studies, 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 paraelectric 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 75 parameters describing the As hyperfine structure at room temperature - 129 -as well as at 77°K are essential ly the same as those of the AsO^" centre in KDA. To investigate the l ine broadening mechanism, the l ine shapes of the hyperfine transitions were examined as a function 4-of the concentration of the As0 4 centres. The concentration was changed by x-irradiating the mixed crystals for widely different periods of time. The results showed the absence of the 1 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 drast ica l ly changed, an ENDOR investigation was undertaken. For a crystal containing about 20% of KDA, and for H||c and Hie the ENDOR spectra obtained by saturating Ty and T 3 hyperfine transitions is shown in Fig. 31 . 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 4-v ic in i ty of the AsO^ centre mixed crystal is essential ly identical with those for pure KDA. We may thus conclude that KDA molecules just substitute the KDP molecules at random la t t i ce sites and the distort ion of the la t t ice caused by these produces random crysta l l ine f ie lds which then broaden the hyperfine lines to widths large enough to render the superhyperfine structure, unobservable at higher temperatures. - 130 -.(close) (far) (a) H//c,4850G | rr/ [ 6 7 18 20 22 24 26 M H z .(far) (b) Hic,2615G , / f a r ) Z / ( c l o s e ) i r 8 10 — i r # — r 12 18 20 M H z Fig. 31 Typical proton ENDOR transitions in mixed KH2P04 KH2As04 crystals. - 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 transit ion 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 sol ids. Detailed ENDOR studies, involving also the use of externally applied e lectr ic f ie lds present additional evidence for the 4 -correctness of the model of the AsO^ centre in KDA type crysta ls , proposed ear l ier by Hampton et a I3.5 Combined with the EPR studies, 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 sites 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 far. However, the ENDOR studies y ie ld accurate data on the hydrogen-bond proton superhyperfine coupling constants and the data can form the basis for any accurate quantum mechanical calculation of hydrogen bonding in the presently investigated systems. It 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 studies, 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 possible, for the f i r s t time, to use protons as microscopic probes for investigating the ferroelectr ic domain structure in the 4-EPR spectra of the AsO^ centre in these crysta ls . Also the use of externally applied e lectr ic f i e ld has shown the feas ib i l i t y of using EPR as a technique of plotting hysteresis loop and this technique can complement the d ie lec t r i c and other studies for studying sub-lattice polarisation 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^ centre in these compounds. The results y ie ld direct experimental evidence for the existence of the coupled proton-lattice mode motion in these 75 systems and show that both the protons and the As nuclei perform a jump type motion in their respective double minima. These observations provide experimental basis for the su i tab i l i t y of the pseudo-spin type description 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 displacive type transit ion not only for protons but also for the heavier nuclei . These studies are thus in broad agreement with the Kobayashi model. These results also indicate that the ferroelectr ic mode observed in the Raman scattering experiments at room temperature is the col lect ive 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 ferroelectr ic mode observed in the Raman experiments, whereas 75 the As motion is much slower. As the temperature is decreased, the 75 motion of protons slows down faster than that of As nuclei until the correlation times for the two motions become essential ly ident ical . At higher temperatures the magnitudes of the proton correlation times 76 are consistent with those obtained from the recent NMR and Raman experiments. On the other hand, no previous data has been available 75 on the motion of the As nucleus in these compounds. F ina l ly , the present studies also demonstrate that in the paraelectric phase the known tetragonal symmetry of these crystals is only a time average of two orthorhombic ones. It 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 site 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 scale, our experiments clearly demonstrate that this is indeed the case. Our resul ts , however, do not contradict the d i f f ract ion experiments, but they rather ref lect 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 wil l stimulate further interest for making more specif ic estimates of the hydrogen-bonding parameters and of the ferroelectr ic mode motion in these compounds., since accurate data obtained here may serve as basis for such calculations. 135 APPENDIX A Experimental Arrangement for Electron-Nuclear Tr iple Resonance In the course of extensive ENDOR studies on the AsO^" centre in x-ray irradiated single crystals of KH^AsO^, we have observed for the f i r s t time steady.state ENDOR transitions predicted 86 87 ear l ier by Feher, and independently by Freed, and named Electron-Nuclear Tr ip le Resonance by the lat ter . Although the Electron-Nuclear Double Resonance (ENDOR) technique has already proved to be quite powerful for the analysis of complex EPR spectra, detai ls of the processes operative during the ENDOR phenomenon are not yet quite clear (thus l imiting the potent ia l i t ies of ENDOR as a general technique). Progress has, however, been made recently in the understanding of l iquid-state ENDOR enhancements. " These enhancements were theoretical ly 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 electron-spin-flip rate (Wg). It has been observed, however, that for protons in most l iquid samples Wg>>WN, resulting in very poor ENDOR enhancements. But i t was predicted as early as 86 87 1958 by Feher, and more recently by Freed that s ignif icant steady state ENDOR enhancements should be obtained even in these unfavorable cases i f both the NMR transit ions, - 136 -corresponding to a particular set of equivalent nuclei as shown in Fig. 32 for the case s=%, l~h, are simultaneously saturated. Freed has named this the technique of Electron-Nuclear Triple 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 Tr iple Resonance experiments. B A m s . m I 2^ , *2 h v . W. A' — —\y • -2/ -1 Fig. 32 Energy levels for a system with S-h and I=%. See text for detai ls . 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 osc i l l a tor (General Radio-type 1001 A) feeds the same - 137 -ENDOR loop surrounding the sample under study. To this extent the 66 arrangement is similar 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 transitions corresponding to a second type of nucleus, the sign of the intensity changes being related to the signs of the hyperfine coupling constants of the two types of nuclei . The procedure we used is 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 osc i l la tors 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 inal output terminal of the amplif ier system there appears optimum power at the two frequencies given by Eq. (A). We find that in our amplifying system (as also in most amplifiers) conditions for obtaining the necessary non-linearity can easily be achieved and therefore the method of generating the two frequencies given by Eq. (A) is quite simple. When the hyperfine constant, a, in Eq. (A) is only approximately known, one of the osc i l la tors is swept in frequency (the second one being kept osc i l la t ing at constant frequency equal to the free nuclear Zeeman frequency), and thus we can obtain the t r ip le resonance spectrum. 4-The method has been tested on the AsO^ centre in X-ray-irradiated KH 2As0 4. The ENDOR (in fact the triple-resonance) enhancements were obtained at the expected frequencies, (see Fig. 33). - 138 -! j ! j- 1 1 • 1 1 1—^ i i i i i i ' i ' i 9.852 10002 11.04 11.239 11.683 12.703 13000 | 23.380 23.6854 Mc/s 23.280 F i g . 33(a) DOUBLE ENDOR AND TRIPLE RESONANCE SIGNALS IN X-IRRADIATED KH 2As0 4 (b) HYDROGEN-BOND ENDOR OF THE AsO^'CENTRE IN X-IRRADIATED KH 2As0 4 H//c-axis, T = 4.2°K, MICROWAVE FREQ. = 9369.75 Mc/s. - 1 3 9 -The triple-resonance signals were s l ight ly 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 situation is not expected to ar ise. Experiments were carried out on different EPR lines and consistent results were obtained. As a f inal check against the poss ib i l i ty of a two-photon absorption process giving the observed Triple-Resonance signals, 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 applicable. - 140 -APPENDIX B EPR studies of the 'Other' Paramagnetic Centres In the course of the present, studies i t was observed (as mentioned in the last chapter) that prolonged x or y-irradiation leads to the formation of several paramagnetic centres in a l l the crystals 4-investigated here. Unlike the case with the AsO^ centre, the EPR spectra of these 'other' centres are very anisotropic and, in general, as many as eight sites arc observed for the possible orientations of these centres. When the magnetic f i e ld H is oriented in the crystal planes, the number of the possible orientations reduces to only four. Moreover, for H||c, a l l these sites become equivalent, thus the EPR spectra are observed to be the simplest. Fig. 7 shows a typical EPR spectrum of x-irradiated Kr^AsO^, obtained for H||c. The EPR 4-spectrum of the AsO^ centre is quite d ist inct 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. This spectrum is marked with four arrows at the top of Fig. 7. In addition to the four EPR lines due to the AsO 4 - centre, fourteen other strong transitions also appear in the EPR spectrum. From the intensity and the linewidth studies these transitions may be assigned to four different paramagnetic centres. Three of these paramagnetic centres, indicated by the markers at the bottom of Fig. 7 and 8, possess a central atom having a nuclear spin 1=3/2. Since no isotope effect was observed in the EPR spectra, this central atom - 141 -is ident i f ied as the As nucleus. The ' g 1 values for these centres are very close to the free electron g value. To check this assignment further, some spectra were recorded at K-band microwave frequencies. For H||c, such a spectrum is shown in Fig. 9. 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 transitions to these different paramagnetic centres. Also when the irradiated crystals were annealed at various temperatures, some of these centres grow up in concentra-t ion at the cost of others. Similarly the l i f e times of different centres are different and spectra recorded over a period of about one month after i rradiat ion of a crystal show that the intensity behavior of a l l the l ines assigned to a particular centre is indeed the same. Angular variation of these spectra have been studied with the magnetic f i e ld in the three crystal planes. Angular variation of the EPR spectra of a l l these three centres is observed to be v i r tua l l y the same. Preliminary analysis of these spectra shows that the hyperfine parameters describing the spectra of a l l these centres are a l i ke , except for their actual magnitudes. Comparison. 2- 9 3 , 9 4 with the spectra of the AsO^ centre indicates that these centres belong to this class of radica ls , although the .exact mechanism for their formation is not yet clear. It is noted here that after these studies had been completed, a preliminary report on the EPR studies of these three 8 3 centres in KDA and ADA has appeared. The conclusions obtained in this report are similar to ours, although no details 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 P04~ centre in Fig. 7. Angular variation of this spectrum shows that in general eight sites are allowed for the possible orientations of this centre. The doublet sp l i t t ing is almost isotropic and equals about 106 at room temperature, but the g tensor is highly anisotropic, 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 2- 95 96 the parameters of the PO^ 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 ^ crystals . Observation of similar spectra in ^ A s O ^ further showed that protons are not responsible for the observed doublet hyperfine structure. Experiments on KDA crystals doped with KDP showed corresponding increase in the intensity 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 def inite ident i f icat ion 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 of the microwave power. With the present superheterodyne spectrometer, i t was, therefore, not possible to obtain ENDOR enhancements. Almost identical spectra were observed for the case of DKDA, RbDA and ADA. In ADA we also observed the spectrum due to - 143 -NHg radicals. A typical spectrum of the NH^  rad ica l , observed for Hj1c is shown in Fig. 34. The spectrum is essential ly 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 str iking changes as the temperature is changed. 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