Structural Studies of Ferroelectrics of The

STRUCTURAL STUDIES OF FERROELECTRICS OF THE BORACITE AND KH P0 TYPE WILLIAM JOHN HAY DOCTOR OF PHILOSOPHY UNIVERSITY OF EDINBURGH 1978 The research described in this thesis was the unaided work of the author, unless otherwise indicated. Where the research was done in collaboration--with others, there was a significant contribution by the author. ACKNOWLEDGEMENTS I would like to express my gratitude to all those who have helped to make this work possible. In particular my personal thanks go to my supervisor Dr R J Nelmes for his guidance, assistance and encouragement. I am very grateful to Professors N Feather and W Cochran for extending to me the facilities of the Department of Physics at Edinburgh University; to the Science Research Council for granting me access to the facilities of A.E.R.E., Harwell; to Professor Woolfson for extending to me the facilities of the Department of Physics at York University; and to Dr P Main of York University for his kindness and assistance. I would like to thank the Atomic Energy Authority for the award of a research studentship. Finally I would also like to thank the staff of A.E.R.E., Harwell for their kindness and assistance, my friends and colleagues at Edinburgh for their help and encouragement, Mrs P Wood for her patient and painstaking work in preparing this thesis and my wife and family for their unstinted encouragement and support. ABSTRACT This thesis is concerned with structural studies of ferroelectric crystals, in particular the structure of CsD 2AsO 4 in its tetragonal paraelectric phase and orthorhombic ferroelectric phase and the structures of Co 3B7O13 I and Cu 3B7O13Br in their cubic paraelectric phases. Both X-ray and neutron single-crystal diffraction techniques were used. The methods of constrained least-squares refinement and significance testing were used to determine the significance of certain structural feat- ures of interest. Details of the development of a technique for the collection of single- crystal data from an unpoled and physically unconstrained crystal in its ferroelectric phase are given. The structural studies of tetragonal CsD 2 AsO4 revealed that the D ions are disordered in double minimum potential wells. In the orthorhombic phase the D ions order onto one of their two possible sites in the tetragonal phase. The displacements of the Cs, As and 0 ions are related to the choice of site of the D ion on the 0 ..... 0 bond. The As ions move away from the 0 ions which the D ions have moved towards. The unusual feature of the ferroelectric transition in Cs(DH 1 ) 2AsO4 suggests an inhomogeneous mixing of the hydrogen and deuterium concentration. The studies of Co 3B7O 13 I and Cu 3B7O 13Br show that it is not necessary to postulate disorder to explain the crystal structures of these boracites in their cubic phase. Table of Contents Page Chapter 1 - Introduction 1 1.1 Objectives 1 1.2 Ferroelectricity and ferroelectric phase transitions 1 1.3 Materials studied and present work 8 Chapter 2 - Sample Preparation 12 2.1 Cs(T) H ) AsO 12 x l-x 2 4 2.1.1 Crystal samples for neutron structural 12 experiments 2.1.2 Crystals for transition investigation 13 2.2 Boracites 14 2.2.1 Co-I boracite 15 2.2.2 Cu-Br boracite 15 Chapter 3 - Methods of Study 16 3.1 Introduction 16 3.2 X-ray and neutron diffraction 17 3.3 X-ray and neutron structure factors 22 3.4 Instruments and data collection 24 3.5 Data handling procedures 28 0 3.6 Data analysis 31 3.6.1 Crystallographic least squares refinement 31 3.6.2 Constrained refinement and significance testing 32 Page Chapter 4 - A Specific Technique Developed for the Investigation 35 of the Ferroelectric Phase of Cs(D H ) AsO x1-x2 4 4.1 Introduction 35 4.2 Method 36 4.3 Data collection 39 4.4 Data reductiOn 39 4.5 Discussion 41 Chapter 5 - Structural Studies of Cs(D H 1 ) 2AsO4 (nominal x = 41 0.67) in the Parelectric and Ferroelectric Phases 5.1 Introduction 43 5.2 Present work 55 5.3 Structural studies of Cs(D H 1 ) 2AsO4 (nominal x = 0.67) 56 5.3.1 The tetragonal phase of Cs(D H 1 ) 2 AsO4 at room 56 temperature (292 K) 5.3.2 The tetragonal phase of Cs(D H 1 ) 2As04 at T0+5°K 59 (T = 208°K) 5.3.3 The orthorhombic phase of Cs(D H1 ) 2As04 at 77°K 63 5.4 Discussion 68 Chapter 6 - The Tetragonal Bragg Peak in Ferroelectric 73 Cs(D H ) AsO xl-x2 4 Page Chapter 7 - Structural Studies of Boracites 80 7.1 Introduction 80 7.2 Present work 93 7.3 The cubic phase of cobalt iodine boracite, Co 3B7O13 I, 96 at room temperature (291 °K) 7.3.1 Experiment 96 7.3..2 Refinements and constraints 97 7.3.3 Structure 101 7.4 The cubic phase of copper bromine boracite, Cu. 3B7O 13Br, 103 at room temperature (291 °K) 7.4.1 Experiment 103 7.4.2 Refinements and constraints 105 7.4.3 Structure 109 7.5 Discussion 111 Appendix A Extinction correction. Appendix B Cumulant tensors. Appendic C The observed structure amplitudes and errors, and the calculated structure factors for Cs(D H AsO at room x l-x )'2 4 temperature. Appendix D The observed structure amplitudes and errors, and the calculated structure factors for Cs(D x H ) AsO at l-x 2 4 T-i-50K (2130K). Appendix E The observed structure amplitudes, and the calculated 0 structure factors for Cs(D H ) AsO at 77 K. xl-x2 4 Appendix F The observed structure amplitudes and errors, and the calculated structure factors for Co 3B7O13 I at room temperature. Appendix G The observed structure amplitudes and errors, and the calculated structure factors for Cu 3B7O 13Br at room temperature. Appendix H Published work. References CHAPTER INTRODUCTION -1- CHAPTER 1 INTRODUCTION 1.1 Objectives The object of this work is to contribute to the understanding of the mechanisms of structural phase transitions in ferroelectric crystals by the application of the methods of crystal structure analysis. In particular this work is concerned with the determination of the crystal structures of ferroelectrics of the KH 2PO4 and boracite (i.e. Mg 3B7O 13C1) type using the techniques of X-ray and neutron diffraction. Included in this work is the development of a technique for collecting single-crystal data from an unpoled and physically unconstrained crystal in the ferroelectric phase where poling and physically constraining the crystal would normally be considered necessary. The unusual nature of the low-temperature phase transition in the material Cs(DHi_)2ASO4 is also investigated. 1.2 Ferroelectricity and Ferroelectric Phase Transitions A ferroelectric crystal is one that possesses. aspontaneous dielectric polarization which can be sr1ie1 by an externally applied electric field. The existence of a spontaneous polarization requires that a ferroelectriC crystal belongs to one of the ten crystallographic polar classes. A ferroelectric crystal is thus a pyroelectric crystal with switchable polarization. -2- Mostferroelectrics possess a spontaneous dipole moment only in a certain temperature range. At the boundary of this range the crystal undergoes a phase transition to a non-ferroelectric phase. The phases with and without a spontaneous polarization are referred to as ferroelectric and paraelectric respectively. The crystal symmetry is generally fowered on passing into the ferroelectric phase. The temperature, T, at which the transition to the ferroelectric phase occurs is known as the Curie temperature, or Curie point. Known Curie temperatures range from 7°K for potassium lithium tantalate (K3LTa5O 15 ) to 14830K for lithium niobate (LiNbO 3 ). A ferroelectric crystal may have transitions between two or more ferroelectric phases, e.g. barium titanate (BaTiO3 ) and sodium nit- rite (NaNO 2 ) have several phases between their lowest-symmetry and highest-symmetry forms. A ferroelectric crystal may also have none, one or more than one paraelectric phase, e.g. barium magnesium fluo- ride (BaMgF4 ) does not have a paraelectric phase (below its melting point at 1 bar) and Rochelle salt (NaKC 4H6 .4H20) has a paraelectric phase above 297 °K and below 255 °K. In the region of T large anomalies are usually observed in the dielectric and thermodynamic properties of the crystal. In the paraelectric phase most ferroelectrics have a Curie-Weiss type of anom- aly in the low frequency dielectric constant, E(0), (Jn the direc- tion(s) in which spontaneous polarization develos\. -3- E(0),( (T-T) ' where T is the Curie-Weiss temperature. In the case of a second order-phase transition (see below) T 0 is the same as the transition temperature T, while in the case of a first-order transition, T is lower than T C A phase transition can be described as first or second order (Pippard, 1964). A first-order ferroelectric transition has discontinuities in the static susceptibility, spontaneous polarization, unit cell volume, entropy and specific heat at the transition point. A second-order transition has discontinuities in the temperature derivatives of these properties. The theories of ferroelectricity can be divided into phenomenological theories and model theories. The development of the phenomenological theories of ferroelectricity is mainly due to Devonshire (1954), who, in a review article, summar- ized and integrated earlier theories of Mueller (1940) and Devonshire (1949, 1951). These theories consider the crystal from a macroscopic, thermodynamic point of view. The transition is exam- ined by considering the-free energy of the crystal as a function of a number of independent variables, usually temperature, stress and polarization.

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