Incommensurate Crystals, Liquid Crystals, and Quasi-Crystals (Nato Science Series B:, 166)

In this NATO-sponsored Advanced Research Workshop we succeeded in bringing together approximately forty scientists working in the three main areas of structurally incommensurate materials: incommensurate crystals (primarily ferroelectric insulators), incommensurate liquid crystals, and metallic quasi-crystals. Although these three classes of materials are quite distinct, the commonality of the physics of the origin and descrip­ tion of these incommensurate structures is striking and evident in these proceedings. A measure of the success of this conference was the degree to which interaction among the three subgroups occurred; this was facili­ tated by approximately equal amounts of theory and experiment in the papers presented. We thank the University of Colorado for providing pleasant housing and conference facilities at a modest cost, and we are especially grate­ ful to Ann Underwood, who retyped all the manuscripts into camera-ready form. J. F. Scott Boulder, Colorado N. A. Clark v CONTENTS PART I: INCOMMENSURATE CRYSTALS A. Theory A PHENOMENOLOGICAL THEORY OF THE TRANSITION SEQUENCE INCLUDING AN INCOMMENSURATE (COMMENSURATE) PHASE SANDWICHED BY REENTRANT COMMENSURATE (INCOMMENSURATE) PHASE - Yoshihiro Ishibashi . . . . . 1 DAUPHINE-TWIN DOMAIN CONFIGURATIONS IN QUARTZ AND ALUMINUM PHOSPHATE - M. B. Wa lker . . . . . . . . . . 9 ELASTIC AND INELASTIC SCATTERING FROM QUASI-PERIODIC STRUCTURES - T. Janssen and R. Currat . . . . . 19 ARE EXOTIC CONSEQUENCES OF INCOMMENSURABILITY IN SOLIDS EXPERIMENTALLY OBSERVABLE? - J. B. Sokoloff. 35 B. Theory - Numerical l1ethods THE APPLICATION OF AXIAL ISING MODELS TO THE DESCRIPTION OF MODULATED ORDER - Julia Yeomans . . 45 TWO-DIMENSIONAL MODELS OF COMMENSURATE-INCOMMENSURATE PHASE TRANSITIONS - Palll D. Beale . . . Front Matter....Pages i-ix A Phenomenological Theory of the Transition Sequence including an Incommensurate (Commensurate) Phase Sandwiched by Reentrant Commensurate (Incommensurate) Phase....Pages 1-8 Dauphiné-Twin Domain Configurations in Quartz and Aluminum Phosphate....Pages 9-18 Elastic and Inelastic Scattering from Quasi-Periodic Structures....Pages 19-33 Are Exotic Consequences of Incommensurability in Solids Experimentally Observable?....Pages 35-43 The Application of Axial Ising Models to the Description of Modulated Order....Pages 45-54 Two-Dimensional Models of Commensurate-Incommensurate Phase Transitions....Pages 55-61 Growth Kinetics in a Frustrated System: The Quenched Axial Next-Nearest-Neighbor Ising Model....Pages 63-73 Electron Microscopy of Incommensurate Structures....Pages 75-89 Effect of Transverse Electric Fields on the Incommensurate Phase of NaNO 2 ....Pages 91-104 Light Scattering from Incommensurate Insulators; Mainly BaMnF 4 ....Pages 105-118 Brillouin Scattering Study of Incommensurate Crystals....Pages 119-126 Experimental Results Related to the Normal-Incommensurate Phase Transition in A 2 MX 4 Compounds....Pages 127-138 Some Aspects of Raman Scattering from A 2 BX 4 Compounds....Pages 139-150 Intrinsic Defects in Insulating Incommensurate Crystals....Pages 151-162 Thermal Hysteresis, Solitons and Domain Walls....Pages 163-176 Thermal Memory and Phase Conjugation Experiments in Incommensurate Barium Sodium Niobate....Pages 177-186 Phasons in Quasi-Crystals and Incommensurate Liquid Crystals....Pages 187-204 The Frustrated Spin-Gas Theory of Multiply Reentrant Liquid Crystals....Pages 205-213 Macroscopic Description of Ferroelectric Chiral Smectic C* Liquid Crystals....Pages 215-222 On the Molecular Theory of Smectic-A Liquid Crystals....Pages 223-233 Order Electricity at Smectic Liquid Crystal Interfaces....Pages 235-240 Macroscopic Variables in Commensurate and Incommensurate Condensed Phases, Quasicrystals and Phasmids....Pages 241-248 How the Smectic a Phase Adapts to two Incommensurate Periods in Asymmetric Liquid Crystalline Systems....Pages 249-258 An Incommensurate Smectic A Phase....Pages 259-270 The Nematic and Smectic-A 1 Phases in DB7NO 2 : High Resolution X-Ray Study and Synthesis....Pages 271-281 X-Ray Diffraction by Incommensurate Liquid Crystals....Pages 283-296 Anomalous Heat Capacity Associated with the Incommensurate SmA Phase in DB 7 OCN + 80CB....Pages 297-303 Thermal Conductivity Studies and Free-Standing Liquid-Crystal Film Calorimetry as Two Applications of the AC Calorimetric Technique....Pages 305-313 Quasiperiodic Patterns with Icosahedral Symmetry....Pages 315-326 Frustration and Order in Rapidly Cooled Metals....Pages 327-336 Local Atomic Environments in the Manganese-Aluminum Icosahedral Phase....Pages 337-348 X-Ray Scattering from Two-Dimensional Liquids Modulated by a Periodic Host: Theory, Simulation and Experiment....Pages 349-358 Artificially Structured Incommensurate Materials....Pages 359-365 Back Matter....Pages 367-368 In this NATO-sponsored Advanced Research Workshop we succeeded in bringing together approximately forty scientists working in the three main areas of structurally incommensurate materials: incommensurate crystals (primarily ferroelectric insulators), incommensurate liquid crystals, and metallic quasi-crystals. Although these three classes of materials are quite distinct, the commonality of the physics of the origin and descripƯ tion of these incommensurate structures is striking and evident in these proceedings. A measure of the success of this conference was the degree to which interaction among the three subgroups occurred; this was faciliƯ tated by approximately equal amounts of theory and experiment in the papers presented. We thank the University of Colorado for providing pleasant housing and conference facilities at a modest cost, and we are especially grateƯ ful to Ann Underwood, who retyped all the manuscripts into camera-ready form. J.F. Scott Boulder, Colorado N.A. Clark v CONTENTS PART I: INCOMMENSURATE CRYSTALS A. Theory A PHENOMENOLOGICAL THEORY OF THE TRANSITION SEQUENCE INCLUDING AN INCOMMENSURATE (COMMENSURATE) PHASE SANDWICHED BY REENTRANT COMMENSURATE (INCOMMENSURATE) PHASE - Yoshihiro Ishibashi ... . 1 DAUPHINE-TWIN DOMAIN CONFIGURATIONS IN QUARTZ AND ALUMINUM PHOSPHATE - M.B. Wa lker ... ... 9 ELASTIC AND INELASTIC SCATTERING FROM QUASI-PERIODIC STRUCTURES - T. Janssen and R. Currat ... . 19 ARE EXOTIC CONSEQUENCES OF INCOMMENSURABILITY IN SOLIDS EXPERIMENTALLY OBSERVABLE? - J.B. Sokoloff. 35 B. Theory - Numerical l1ethods THE APPLICATION OF AXIAL ISING MODELS TO THE DESCRIPTION OF MODULATED ORDER - Julia Yeomans . . 45 TWO-DIMENSIONAL MODELS OF COMMENSURATE-INCOMMENSURATE PHASE TRANSITIONS - Palll D. Beale ..