The monograph "Shaped Crystal Growth" by V. A. Tatarchenko is the first systematic of the macroscopic crystallization theory. The theory is based on the stable statement growth conception, which means that self-stabilization is present in the system, with growth parameter deviations occurring under the action of external perturbations attenuating with time. The crystallization rate is one of the parameters responsible for crystal defect formation. Steady-state crystal growth means that crystallization rate internal stabilization is present, thus allowing more perfect crystals to grow. Most important is the fact that the crystal shape (an easily observed parameter) is one of the stable-growth characteristics when growing crystals without any contact with the crucible walls. This means that constant-cross-section crystal growth is to a certain extent evidence of crystallization process stability. The principles of the stable crystal growth theory were developed by the author of the monograph in the early 1970s. Due to the efforts over the past 20 years of V. A. Tatarchenko, his disciples (V. A. Borodin, S. K. Brantov, E. A. Brener, G. I. Romanova, G. A. Satunkin et al) and his followers (B. L. Timan, 0. V. Kolotiy et al) the theory has been completed, which is demonstrated by this monograph. The characteristic feature of the theory is its trend towards solving practical problems that occur in the process of crystal growth."

An introduction to structure determination by x-ray crystallography, primarily for final-year undergraduate studies in crystallography, chemistry, and chemical physics, and introductory postgraduate work in this area of crystallography. This substantially revised edition (2nd, 1985) adds a chapter o

In its combination of an advanced teaching standpoint with an emphasis on new perspectives and recent advances in the study of liquids formed by simple molecules, Molecular Liquids: New Perspectives in Physics and Chemistry provides a clear, understandable guide through the complexities of the subject. A wide range of topics is covered in the areas of intermolecular forces, statistical mechanics, the microscopic dynamics of simple liquids, thermodynamics of solutions, nonequilibrium molecular dynamics, molecular models for transport and relaxation in fluids, liquid simulations, statistical band shape theories, conformational studies, fast-exchange dynamics, and hydrogen bonding. The experimental techniques covered include: neutron scattering, X-ray diffraction, IR, Raman, NMR, quasielastic neutron scattering, and high-precision, time-resolved coherent Raman spectroscopy.

Solitons are a well-known and intriguing aspect of nonlinear behavior in a continuous system such as a fluid: a wave propagates through the medium without distortion. Liquid crystals are highly ordered systems without a rigid, long-range structure. Solitons in liquid crystals (sometimes referred to as "walls") have a wide variety of remarkable properties that are becoming important for practical applications such as electroluminescent display. This book, the first review of the subject to be published, contains not only surveys of the existing literature, but presents new results as well.

Cellular growth, especially its pattern formation, has been studied both experimentally and numerically. In situ observations of faceted cellular growth have clearly revealed cellular interactions in the array of cells. For the first time, the true time-dependent faceted cellular array growth has been modelled properly. It has been found that pattern formation is determined by cellular interactions in the array. Readers of the book will obtain a general view of the field of pattern formation in crystal growth, and in-depth and up-to-date knowledge of faceted cellular array growth, which occurs in semiconductor crystals.

With the development of diverse analytical chemistry techniques, the discovery of rich and numerous properties pertaining to bicontinuous liquid crystal structures has yielded beneficial applications in medicine, consumer products, materials science, and biotechnology. Presenting contributions from 24 experts worldwide, Bicontinuous Liquid Crystals presents a comprehensive overview of these structures with a practical approach to applying them in manufacturing and laboratory processes. This book considers the cubic, mesh, ribbon, and sponge equilibrium phases of bicontinuous structures. It begins with a historical perspective and a theoretical platform for study, followed by a detailed discussion of physical chemistry, properties, and structural characteristics of the different phases. The text interrelates the most useful analytical methods for the characterization of the behavior and stability of liquid crystalline phases based on structure, geometry, composition-dependent changes, temperature, dispersion, and other factors. These techniques include differential geometry, thermodynamics, local and global packing, and the study of conformational entropy. The book also highlights tools for mathematically visualizing bicontinuous systems. This provides an excellent foundation for the authors' examination of the latest studies and applications, such as controlled release, materials development, fabrication, processing, polymerization, protein crystallization, membrane fusion, and treatment of human skin. Bicontinuous Liquid Crystals represents current trends and innovative ideas in the study of bicontinuous liquid crystals. Divided into three sections, it provides a complete overview of theoretical and modeling aspects, physical chemistry and characterization, and applications in this active field of research.

Molecular chirality is one of the fundamental aspects of chemistry. Chirality properties of molecules have implications in a wide variety of subjects, ranging from the basic quantum mechanical properties of simple of a few atoms to molecular optical activity, asymmetric synthesis, systems and the folding pattern of proteins. Chirality, in both the geometrical and the topological sense, has also been the subject of investigations in various branches of mathematics. In particular, new developments in a branch of topology, called knot theory, as well as in various branches of discrete mathematics, have led to a novel perspective on the topological aspects of molecular chirality. Some of the mathematical advances have already found applications to the interpretation of new concepts in theoretical chemistry and mathematical chemistry, as well as to novel synthetic approaches leading to new molecules of exceptional structural properties. Some of the new developments in molecular chirality have been truly fundamental to the theoretical understanding and to the actual practice of many aspects of chemistry. The progress in this field has been very rapid, even accelerating in recent years, and a review appears more than justified. This book offers a selection of subjects covering some of the latest developments. Our primary aim is to clarify some of the basic concepts that are the most prone to misinterpretation and to provide brief introductions to some of those subjects that are expected to have further, important contributions to our understanding of molecular properties and chemical reactivity.

Continues the aim of Structure reports to present critical accounts of all crystallographic structure determinations of metals and of inorganic compounds. Published for the International Union of Crystallography. Annotation copyright Book News, Inc. Portland, Or.

Diese Arbeit enthiilt zwei grof3ere Fallstudien zur Beziehung zwischen theo- retischer Mathematik und Anwendungen im 19. Jahrhundert. Sie ist das Ergebnis eines mathematikhistorischen Forschungsprojekts am Mathemati- schen Fachbereich der Universitiit-Gesamthochschule Wuppertal und wurde dort als Habilitationsschrift vorgelegt. Ohne das wohlwollende Interesse von Herrn H. Scheid und den Kollegen der Abteilung fUr Didaktik der Mathema- tik ware das nicht moglich gewesen: Inhaltlich verdankt sie - direkt oder indirekt - vielen Beteiligten et- was. So wurde mein Interesse an den kristallographischen Symmetriekon- zepten, dem Thema der ersten Fallstudie, durch Anregungen und Hinweise von Herrn E. Brieskorn geweckt. Sowohl von seiner Seite als auch von Herrn J. J. Burckhardt stammen uberdies viele wert volle Hinweise zum Manuskript von Kapitel I. Herrn C. J. Scriba mochte ich fur seine die gesamte Arbeit betreffenden priizisen Anmerkungen danken und Herrn W. Borho ebenso fUr seine ubergreifenden Kommentare und Vorschlage. Beziiglich der in Kapitel II behandelten projektiven Methoden in der Baustatik des 19. Jahrhunderts gilt mein besonderer Dank den Herren K. -E. Kurrer und T. Hiinseroth fUr ihre zum Teil sehr detaillierten Anmerkungen aus dem Blickwinkel der Geschichte der Bauwissenschaften. Schliefilich geht mein Dank an alle nicht namentlich Erwiihnten, die in Gesprachen, technisch oder auch anderweitig zur Fertig- stellung dieser Arbeit beigetragen haben. Fur die vorliegende Publikation habe ich einen Anhang mit einer Skizze von in unserem Zusammenhang besonders wichtig erscheinenden Aspekten der Theorie der kristallographischen Raumgruppen hinzugefUgt. Ich hoffe, daB er zum Verstiindnis des mathematischen Hintergrunds der historischen Arbeiten des ersten Kapitels beitragt.

This book presents a computational scheme for calculating the electronic properties of crystalline systems at an ab-ini tio Hartree-Fock level of approximation. The first chapter is devoted to discussing in general terms the limits and capabilities of this approximation in solid state studies, and to examining the various options that are open for its implementation. The second chapter illustrates in detail the algorithms adopted in one specific computer program, CRYSTAL, to be submitted to QCPE. Special care is given to illustrating the role and in: fluence of computational parameters, because a delicate compromise must always be reached between accuracy and costs. The third chapter describes a number of applications, in order to clarify the possible use of this kind of programs in solid state physics and chemistry. Appendices A, B, and C contain various standard expressions, formulae, and definitions that may be useful for reference purposes; appendix D is intended to facilitate the interpretations of symbols, conventions, and acronyms that occur in the book. Thanks are due to all those who have contributed to the implementation and test of the CRYSTAL program, especially to V.R. Saunders and M. Causal, and to F. Ricca, E. Ferrero, R. Or lando, E. Ermondi, G. Angonoa, P. Dellarole, G. Baracco

In the last decade mathematical crystallography has found increasing interest. Siginificant results have been obtained by algebraic, geometric, and group theoretic methods. Also classical crystallography in three-dimen sional Euclidean space has been extended to higher dimen sions in order to understand better the dimension independent crystallographic properties. The aim of this note is to introduce the reader to the fascinating and rich world of geometric crystallography. The prerequisites for reading it are elementary geometry and topological notations, and basic knowledge of group theory and linear algebra. Crystallography is geometric by its nature. In many cases, geometric arguments are the most appropriate and can thus best be understood. Thus the geometric point of view is emphasized here. The approach is axiomatic start ing from discrete point sets in Euclidean space. Symmetry comes in very soon and plays a central role. Each chapter starts with the necessary definitions and then the subject is treated in two- and three-dimensional space. Subsequent sections give an extension to higher dimensions. Short historical remarks added at the end of the chapters will show the development of the theory. The chapters are main ly self-contained. Frequent cross references, as well as an extended subject index, will help the reader who is only interested in a particular subject."

In the last decade mathematical crystallography has found increasing interest. Siginificant results have been obtained by algebraic, geometric, and group theoretic methods. Also classical crystallography in three-dimen sional Euclidean space has been extended to higher dimen sions in order to understand better the dimension independent crystallographic properties. The aim of this note is to introduce the reader to the fascinating and rich world of geometric crystallography. The prerequisites for reading it are elementary geometry and topological notations, and basic knowledge of group theory and linear algebra. Crystallography is geometric by its nature. In many cases, geometric arguments are the most appropriate and can thus best be understood. Thus the geometric point of view is emphasized here. The approach is axiomatic start ing from discrete point sets in Euclidean space. Symmetry comes in very soon and plays a central role. Each chapter starts with the necessary definitions and then the subject is treated in two- and three-dimensional space. Subsequent sections give an extension to higher dimensions. Short historical remarks added at the end of the chapters will show the development of the theory. The chapters are main ly self-contained. Frequent cross references, as well as an extended subject index, will help the reader who is only interested in a particular subject."