1 SUPERSTRUCTURES AND CHARGE-DENSITY WAVES IN DISTORTED AND INTERCALATED LAYER MATERIALS A thesis presented for the degree of Doctor of Philosophy in the University of London by Christopher Brian Scruby Imperial College of May 1976 Science and Technology 2 acbtopctUvres Els Trio-ouv Heb.12 v 2. 3 ABSTRACT Transmission electron and X-ray diffraction studies, and high resolution phase-contrast electron microscopy, have shown that, except for NbS2,all the Group Va transition metal layer dichalcogenides are unstable with respect to periodic structural deformation in some temperature range. Inmommen- surate and commensurate distorted phases have been identified in 1T TaS2, 4Hb TaS2, IT VSe2 and 2H TaSe2. The deformations remain incommensurate in 2H NbSe2. The three distorted phases of IT TaS make this compound 2 unique; two are incommensurate. A detailed model of the deform- ation structure of 1T (room temperature phase) has been prop- 2 osed from diffractometer data, in which groups of metal atoms form planar clusters. The distortion modes on the Ta sublattice are predominantly LA, and on the S sublattice TA1 out of phase with the Ta by 2T/3. There are thus periodic variations in layer thickness and rhombohedral stacking of deformations. There is a 30% increase in deformation amplitude at the 1T -1.1T transition, and a further 15 % from 1T to 1T 1 2 2 3' 1T and 1T 3TaS also show some degree of metal clustering. 1 2 At the transition to the 15a x f a superlattice (1T3) there is a deformation stacking change to give a triclinic cell. The deformation structures of the other materials are related to IT TaS2, but mostly with reduced displacements. The superstructures are interpreted in terms of lattice deformations which are coupled to charge-density waves in the conduction d-bands. This arises as a consequence of the cond- ensation of phonons into modes softened by an enhanced Kohn Anomaly. The phase transitions occur at temperatures in agree- ment with electrical measurements, and the charge-density wave • 4 model is used to try and explain the anomalous properties of these materials. The transformations are also discussed in terms of energy gaps which are opened up by the deformation potential at the Fermi level. The distortion wave vector spans the Fermi Surface and the changes with temperature are discussed on this basis. Charact- eristic diffuse scattering observed in octahedral polytypes, is interpreted as a direct image of the Fermi Surface. It becomesnecessary to develop scattering theory for a distorted structure, and incommensurate superstructures are discussed in some detail. The intercalation complex of pyridine with 2H TaS was 2 also studied, and a model proposed for the structure. Most important is a stacking change of the host lattice:— AcA BcB AcAlAbA, on intercalation. The possible relation- ship between this complex and charge-density waves is discussed. 5 TABLE OF CONTENTS Page LIST OF FIGURES 11 LIST OF TABLES 22 1 INTRODUCTION 24 1.1 General 24 1.2 Structural Properties 27 1.2.1 The Undistorted Materials 28 1.2.2 Other Polytypes of the Undistorted 31 Materials 1.2.3 The Distorted Tellurides 32 1.3 Electronic Properties 34 1.3.1 Electronic Band Structure 34 1.3.2 Electrical and Magnetic Measurements 37 1.3.3 Superconductivity 43 1.4 Intercalation 44 2 SCATTERING OF RADIATION BY SUPERSTRUCTURES 48 2.1 Scattering by a Regular Lattice of Atoms 48 2.2 Diffraction by a Layer Material 49 2.2.1 Stacking of the Layers 49 2.2.2 Effects of Intercalation 51 • 2.3 Superstructures 52 2.3.1 Indexing Commensurate Superstructures 53 •2.3.2 Indexing Incommensurate Superstructures 54 2.4 Single Periodic Distortion of a Lattice 55 2.4.1 Distorted Monatomic Lattice 56 2.4.2 Redistribution of Scattered Intensity 58 2.4.3 Equivalence of Commensurate and 59 Incommensurate Analysis. 2.4.4 Choice of Analysis Close to Limiting 63 Case 6 2.5 Multiple Distortions in a Lattice 64 2.5.1 Phase Correlation 64 2.5.2 Matrix Cell Containing More than One 66 Atom 2.5.3 Symmetry-Related Distortions 70 2.5.4 Symmetry-Related Distortions and Phase 74 2.5.5 Distortion Mode 75 2.6 Non-Sinusoidal Deformations 77 2.6.1 Fourier Components, 221, 2Q2, 223 8o 2.6.2 Fourier Components, P1, P2, P3 81 2.6.3 Special Non-Sinusoidal Functions 82 2.6.4 Diffraction from 1-D C9mmensurate 85 Clusters 2.6.5 Diffraction from 1-D Incommensurate 86 Clusters 2.6.6 Effect of Omitting Higher Fourier 88 Components 3 THE KOHN ANOMALY AND CHARGE-DENSITY WAVES 89 3.1 Electronic Susceptibility and Screening 89 3.2 Phonons and the Kohn Anomaly 91 3.2.1 Free Electron Model - Spherical Fermi 91 Surface 3.2.2 The Kohn Anomaly 94 3.2.3 Non-Spherical Fermi Surfaces 95 3.2.4 Radius of Curvature of the Fermi Surface 97 3.2.5 Phonon Image of Fermi Surface 98 3.3 Ordering and the q = 2k 101 f Instability 3.4 Charge-Density Waves and Spip-Density Waves 102 3.5 Charge-Density Waves and Energy Gaps 106 3.6 Metal-Insulator Transitions 109 3.7 Superconductivity and Charge-Density Waves 111 7 4 EXPERIMENTAL PROCEDURES 114 4.1 Materials 114 4.2 Intercalation 115 4.3 Electron Diffraction Studies 115 4.4 High-Resolution Phase Contrast Electron 116 Microscopy 4.5 X-ray Diffraction Studies 118 5 DIFFRACTION RESULTS AND INTERPRETATION: 121 TANTALUM DISULPHIDE (PYRIDINE) 5.1 Introduction 121 5.2 Tantalum Disulphide Matrix Structure 121 5.2.1 Change in Cell Dimensions on Intercalation 121 5.2.2 Tantalum-Sulphur Layer Distance 123 5.2.3 Stacking of the Tantalum Disulphide 126 Layers 5.3 Ordering of Pyridine Molecules 132 5.3.1 Pyridine Lattice 132 5.3.2 Orientation of Pyridine Molecules 142 5.4 Discussion of Structural Results 151 6 DIFFRACTION RESULTS AND INTERPRETATION: 156 IT TANTALUM DISULPHIDE 6.1 Introduction 156 6.2 Reciprocal Lattice Geometry: 159 Matrix Reflexions 6.3 Reciprocal Lattice Geometry: 159 Satellite Reflexions in 1T and 1T TaS 1 2 2 6.4 Reciprocal Lattice Geometry: 164 Satellite Reflexions in 1T TaS 3 2 6.5 Evidence for a Deformation Superstructure 165 6.6 Determination of Deformation Wave Vector 169 6.7 Stacking of Deformation Waves in Adjacent 173 Layers 8 7 DETAILED DEFORMATION STRUCTURE OF 1T TANTALUM - 177 DISULPHIDE 7.1 Introduction 177 7.2 Magnitude of In-Layer Displacements in IT TaS2 179 7.2.1 Structure Factors of M(h0.0) — Total 180 Displacement X7.2.2 Structure Factors of (10.1) and 183 - - Sh0.0 Sh0.0 --DeterminationDetermination of U Fundamental Distortion Amplitude 7.2.3 In-Layer Distortion of Sulphur Sublattice 186 7.2.4 Direction of :01Q and Mode of Deformation 188 Waves 7.2.5 Higher Fourier Components 189 (a)Wave Vector a Multiple of Fundamental 21. 7.2.6 Higher Fourier Components 192 (b)Wave Vectors, P. 7.2.7 Phases of Deformation Waves 193 7.3 Calculations Based on Detailed Model for 194 Distorted Layer 7.3.1 Summary of Initial Values for Parameters 194 7.3.2 Deformation Wave Combinations 194 7.3.3 Details of Structure Factor Calculation 197 7.3.4 Interpretation in Terms of Metal Atom 205 Clusters 7.4 Displacements Perpendicular to the Layers in 209 1T TaS 2 2 Deformation Structure 1T TaS 213 7.5 of 1 2 7.5.1 Introduction 213 7.5.2 Direction of Deformation Amplitude U 213 Q 7.5.3 Magnitude of the Displacements 215 7.5.4 Metal Atoms Clusters in 1T1 TaS2 217 7.6 Diffuse Scattering in 1T TaS 218 1 2 Deformation Structure of 1T TaS 221 .7.7 3 2 7.8 Coherence Length of the Deformation Waves 227 9 7.9 Distorted Layer Models for the Three Phases 231 8 DIFFRACTION RESULTS AND INTERPRETATION: 233 9THER OCTAHEDRAL MATERIALS 8.1 Introduction 233 8.2 4H13 Tantalum Disulphide 233 8.3 IT Vanadium Diselenide 239 8.4 IT Tantalum Diselenide 242 9 DIFFRACTION RESULTS AND INTERPRETATION: 244 TRIGONAL PRISMATIC MATERIALS 9.1 Introduction 244 9.2 2H Niobium Diselenide 244 9.3 Niobium Disulphide 250 9.4 2H Tantalum Diselenide 250 9.5 2H Tantalum Disulphide 254 10 PHASE-CONTRAST LATTICE IMAGES 255 10.1 Introduction 255 10.2 Molybdenum Disulphide 10.3 p -Molybdenum Telluride 257 10.4 1T Tantalum Disulphide 259 10.5 41113 Tantalum Disulphide 263 11 GENERAL DISCUSSION OF RESULTS 264 11.1 Summary of Structural Results 264 11.2 Electronic Origin of the Structural Deformations 270 11.3 Metal Atom Clusters and Localisation of Charge 271 11.4 Deformation Waves and the Kohn Anomaly 274 11.5 Fermi Surface Images in the Octahedral Materials 275 11.6 Fermi Surface Images in the Trigonal Prismatic 280 Materials 11.7 Inelastic Neutron Scattering Results 282 11.8 Temperature Dependence of Charge-Density Wave 286 Vector 10 11.9 Transitions to Commensurate Superstructures 287 .11.9.1 Materials with Octahedral Co-ordination 290 11.9.2 Energy Gaps at the Fermi Level 291 11.9.3 Materials with Trigonal Prismatic 293 Co-ordination 11.9.4 IT Tantalum Disulphide 294 11.10 Displacements of Anions and Stacking of 297 Charge-Density Waves 11.11 Supporting Evidence from Doping and Intercalation 298 Experiments 11.11.1 Doping Experiments 300 11.11.2 Intercalation Experiments 302 11.12 Pressure Measurements and Superconductivity 304 12 FINAL CONCLUSIONS AND FUTURE WORK 307 ACKNOWLEDGEMENTS .314 REFERENCES 315 APPENDIX 1 321 APPENDIX 2 325 APPENDIX 3 334 11 LIST OF FIGURES Page 1 The layer structure of the transition metal 28 dichalcogenides of formula, MX 2.