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.

Anomalous Rare Earths and Actinides: Valence Fluctuation and Heavy Fermions focuses on the characteristics, reactions, transformations, technologies, and processes involved in the study of anomalous rare earths and actinides. The selection first offers information on lanthanides and actinides and electronic structures in cerium monopnictides. Topics include rare earth metals with fluctuating valencies, 'normal' rare earth metals, and band calculation and Fermi surface. The text then elaborates on neutron scattering studies of anomalous rare earth compounds, including magnetic neutron scattering measurements, stability and localization of magnetic moments, and condensed state. The manuscript examines the transport properties of cerium monochalcogenides and pressure-volume relationships of cerium monochalcogenides and monopnictides. The text also ponders on the theory of anisotropic magnetic behavior in hybridizing actinide systems; band hybridization effects on indirect magnetic coupling of localized moments; and neutron scattering from transuranium materials. The selection is a dependable reference for readers interested in the research on anomalous rare earths and actinides.

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 . . .