Modern crystallographic methods originate from the synergy of two main research streams, the small-molecule and the macro-molecular streams. The first stream was able to definitively solve the phase problem for molecules up to 200 atoms in the asymmetric unit. The achievements obtained by the macromolecular stream are also impressive. A huge number of protein structures have been deposited in the Protein Data Bank. The solution of them is no longer reserved to an elite group of scientists, but may be attained in a large number of laboratories around the world, even by young scientists. New probabilistic approaches have been tailored to deal with larger structures, errors in the experimental data, and modest data resolution. Traditional phasing techniques like ab initio, molecular replacement, isomorphous replacement, and anomalous dispersion techniques have been revisited. The new approaches have been implemented in robust phasing programs, which have been organized in automatic pipelines usable even by non-experts. Protein structures, which 50 years ago could take months or even years to solve, can now be solved in a matter of hours, partly also due to technological advances in computer science. This book describes all modern crystallographic phasing methods, and introduces a new rational classification of them. A didactic approach is used, with the techniques described simply and logically in the main text, and further mathematical details confined to the Appendices for motivated readers. Numerous figures and applicative details illustrate the text.

Crystallography is an interdisciplinary science covering a wide area, from biology to earth sciences, mathematics and materials science. Its role is growing, owing to the contribution crystallography can offer to the understanding of such diverse fields as biological structures, high-temperature superconductors, mineral properties, and phase transitions. The book describes both the theoretical bases and applications of different areas interacting with crystallography. As with the first and second editions, it is organized as a collection of chapters written by recognized specialists, with all contributions being harmonized into a unified whole. The main text is devoted to the presentation of basics; the appendices deal with specialist aspects. In this third edition topics have been updated so as to document the present state of the art: emphasis is placed upon areas of current research.
To facilitate learning and make teaching more effective, new illustrations have been introduced. As with the second edition, a software package is included via the book's OUP web site: modern graphics will help users to better understand the basics of this science via three-dimensional images, simulation of experiments, and exercises.

Direct methods are, at present, applied to a large variety of cases: X-ray, neutron or electron data; single crystal and powder data; small molecules and macromolecules. While direct methods solved in practice the phase problem for small molecules, their application to macromolecules is recent and still undergoing strong development. The fundamentals of the methods are described: in particular it is shown how the methods can be optimized for powder, neutron or electron data, and how they can be integrated with isomorphous replacement, molecular replacement and anomalous dispersion techniques. Maximum Entropy methods are also described and discussed. Sets of test structures are used to verify, throughout the various chapters, the mathematical techniques there described and to provide practical examples of applications. This book will appeal to a wide variety of readers - offering both a comprehensive description of direct methods in crystallography and an invaluable reference tool. The first three chapters can be considered as an introduction to the field, with sufficient material to constitute a university course and for allowing the expert use of most direct methods programs. Subsequent chapters are aimed at graduate students and working crystallographers. Basic results are described and discussed in the main body of the text, while the appendices compliment these with in depth mathematical details. The quoted literature is extremely wide and the interested reader can find suggestions for future work and further reading throughout the book.

Crystallography is an interdisciplinary science covering a wide area, from biology to earth sciences, mathematics and materials science. Its role is growing, owing to the contribution crystallography can offer to the understanding of such diverse fields as biological structures, high-temperature superconductors, mineral properties, and phase transitions. The book describes both the theoretical bases and applications of different areas interacting with crystallography. As with the first and second editions, it is organized as a collection of chapters written by recognized specialists, with all contributions being harmonized into a unified whole. The main text is devoted to the presentation of basics; the appendices deal with specialist aspects. In this third edition topics have been updated so as to document the present state of the art: emphasis is placed upon areas of current research.
To facilitate learning and make teaching more effective, new illustrations have been introduced. As with the second edition, a software package is included via the book's OUP web site: modern graphics will help users to better understand the basics of this science via three-dimensional images, simulation of experiments, and exercises.