The concept of reciprocal space is over 100 years old, and has been of particular use by crystallographers in order to understand the patterns of spots when x-rays are diffracted by crystals. However, it has a much more general use, especially in the physics of the solid state. In order to understand what it is, how to construct it and how to make use of it, it is first necessary to start with the so-called real or direct space and then show how reciprocal space is related to it. Real space describes the objects we see around us, especially with regards to crystals, their physical shapes and symmetries and the arrangements of atoms within: the so-called crystal structure. Reciprocal space on the other hand deals with the crystals as seen through their diffraction images. Indeed, crystallographers are accustomed to working backwards from the diffraction images to the crystal structures, which we call crystal structure solution. In solid state physics, one usually works the other way, starting with reciprocal space to explain various solid-state properties, such as thermal and electrical phenomena. In this book, I start with the crystallographer's point of view of real and reciprocal space and then proceed to develop this in a form suitable for physics applications. Note that while for the crystallographer reciprocal space is a handy means of dealing with diffraction, for the solid-state physicist it is thought of as a way to describe the formation and motion of waves, in which case the physicist thinks of reciprocal space in terms of momentum or wave-vector k-space. This is because, for periodic structures, a characteristic of normal crystals, elementary quantum excitations, e.g. phonons and electrons, can be described both as particles and waves. The treatment given here, will be by necessity brief, but I would hope that this will suffice to lead the reader to build upon the concepts described. I have tried to write this book in a suitable form for both undergraduate and graduate students of what today we call "condensed matter physics."

This suberb text is designed to introduce the fundamentals of the subject of statistical mechanics at a level suitable for students who meet the subject for the first time. The treatment given is designed to give the student a feeling for the topic of statistical mechanics without being held back by the need to understand complex mathematics. The text is concise and concentrates on the understanding of fundamental aspects. Numerous questions with worked solutions are given throughout.

Crystal Clear takes you behind the scenes in the life of one of the most prominent scientists of the twentieth century, William Lawrence Bragg (WLB) - an innovative genius, who together with his father, William Henry Bragg (WHB) founded and developed a whole new branch of science, X-ray Crystallography. The main body of the text contains the hitherto unpublished autobiographies of both WLB and his wife, Alice. Alice Bragg was a public figure in her own right. She was Mayor of Cambridge and National Chairman of the Marriage Guidance Council among other roles. She and WLB were as different as chalk and cheese. Their autobiographies complement each other to give a rounded picture of the real personalities behind their public appearance. They write of their travels, their family life, their friends and their joys and sorrows. They write most of all about each other. Their younger daughter, Patience Thomson, provides anecdotes and vignettes, bringing her parents to life. She has also included extracts from previously unpublished letters and from articles which Alice Bragg wrote for National newspapers. The result is an unusual insight into the lives of two distinguished people. The two accounts reveal a fascinating interaction between these two characters, neither of whom could have achieved on this scale without the other. There is an underlying love story here which humanises and transforms. This is a unique book, adopting an original viewpoint, which will take the reader far beyond the scope of a normal biography.

This suberb text is designed to introduce the fundamentals of the subject of statistical mechanics at a level suitable for students who meet the subject for the first time. The treatment given is designed to give the student a feeling for the topic of statistical mechanics without being held back by the need to understand complex mathematics. The text is concise and concentrates on the understanding of fundamental aspects. Numerous questions with worked solutions are given throughout

Crystals have fascinated us for centuries with their beauty and symmetry, and have often been invested with magical powers. The use of X-ray diffraction, first pioneered in 1912 by father and son William and Lawrence Bragg, enabled us to probe the structure of molecules, and heralded the scientific study of crystals, leading to an understanding of their atomic arrangements at a fundamental level. The new discipline, called X-ray crystallography, has subsequently evolved into a formidable science that underpins many other scientific areas. Starting from the determination of the structures of very simple crystals, such as that of common salt, today it has become almost routine to determine the positions of tens of thousands of atoms in a crystal. In this Very Short Introduction Mike Glazer shows how the discoveries in crystallography have been applied to the creation of new and important materials, to drugs and pharmaceuticals and to our understanding of genetics, cell biology, proteins, and viruses. Tracing the history of crystallography, he analyses astonishing developments in new sources of X-rays, as well as of neutrons, and in electron microscopy, and considers the impact they have on the study of crystals today. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

The concept of reciprocal space is over 100 years old, and has been of particular use by crystallographers in order to understand the patterns of spots when x-rays are diffracted by crystals. However, it has a much more general use, especially in the physics of the solid state. In order to understand what it is, how to construct it and how to make use of it, it is first necessary to start with the so-called real or direct space and then show how reciprocal space is related to it. Real space describes the objects we see around us, especially with regards to crystals, their physical shapes and symmetries and the arrangements of atoms within: the so-called crystal structure. Reciprocal space on the other hand deals with the crystals as seen through their diffraction images. Indeed, crystallographers are accustomed to working backwards from the diffraction images to the crystal structures, which we call crystal structure solution. In solid state physics, one usually works the other way, starting with reciprocal space to explain various solid-state properties, such as thermal and electrical phenomena. In this book, I start with the crystallographer's point of view of real and reciprocal space and then proceed to develop this in a form suitable for physics applications. Note that while for the crystallographer reciprocal space is a handy means of dealing with diffraction, for the solid-state physicist it is thought of as a way to describe the formation and motion of waves, in which case the physicist thinks of reciprocal space in terms of momentum or wave-vector k-space. This is because, for periodic structures, a characteristic of normal crystals, elementary quantum excitations, e.g. phonons and electrons, can be described both as particles and waves. The treatment given here, will be by necessity brief, but I would hope that this will suffice to lead the reader to build upon the concepts described. I have tried to write this book in a suitable form for both undergraduate and graduate students of what today we call "condensed matter physics".