The outcome from a destined great war between humans and creatures will be decided by the courage and emotions of a few honourable and worthy individuals. Raven is the last blood line descendent from the greatest wizard known as Grackle, and he has found himself living in a time of endless uncertainty, magic and sorcery between the humans and a terrifying creature race residing upon the mysterious Planet of Phoenix. Significant emotional elements, bravery, hatred and love are the fundamental factors for either the humans or the creatures surviving existence during this epic adventure.

This book begins with an historical introduction covering the contributions of many distinguished crystallographers. From this follows a tutorial in crystal optics. Further chapters discuss the two main mechanisms of optical dissymmetry, the piezo-optic effect and the kinetic ordering of atoms. The book treats the literature comprehensively, but uses illustrations from the authors’ laboratories as the subjects of detailed analyses.

Thermal Expansion of Crystals is a comprehensive examination of the various aspects of thermal expansion of crystals. The book provides both theoretical and experimental aspects of the study of thermal expansion. Chapters are devoted to subjects on measurement methods of thermal expansion; the theory of thermal expansion; behavior of thermal expansion during the occurrence of phase transformations; and thermal expansions in ferroelectric materials. Physicists and researchers, both theoretical and experimental, in the field of thermal expansion of crystals will find this book a valuable piece of reference.

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 . . .

In this important book, the author summarizes and generalizes the results of 25 years of work in this exciting field, which has been developing extensively within the last few decades. The reader will find discussions of many crystals that were investigated in the microwave region, including low-dimensional and ferroelectric semiconductors, protonic conductors, quasi-one-dimensional H-bonded. and other order-disorder ferroelectrics. This volume is an essential reference for all scientists and graduate students whose interests are connected to the physics of ferroelectrics and related materials; the physics of structural phase transitions; and superionic conductors. It will also be of value to those interested in developing or exploiting microwave measurement techniques.