Mathematical Techniques in Crystallography and Materials Science

1. Front Matter

   Pages i-viii

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2. Matrices: Definitions and Fundamental Operations

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   Pages 1-19

3. Symmetry of Finite Objects

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   Pages 20-40

4. Symmetry of Infinitely Repeated Patterns

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   Pages 41-48

5. Vectors

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   Pages 49-57

6. Tensors

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   Pages 58-76

7. Data Fitting

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   Pages 77-92

8. Estimation of Uncertainty

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   Pages 93-104

9. Significance and Accuracy

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   Pages 105-118

10. Constrained Crystal Structure Refinement

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    Pages 119-133

11. Back Matter

    Pages 134-192

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In the course of 30 years as a practicing crystallographer I have frequently been faced with the necessity of finding out a little bit about some general branch of mathematics with which I was previously unfamiliar. Under these circumstances I have usually followed the common practice of seeking out some colleague who would be expected to have a thorough knowledge of the subject. I would then find myself faced either with an involved lecture in which the colleague would attempt to distill a lifetime of experience into a form that was comprehensible to a novice with a very different background, or with a book about the subject, written by a specialist, that contained far more information than I really wanted to know. I would have to separate the few kernels of useful material from a large volume of what would probably be wheat to someone else, but was chaff to me. In the course of that time I have acquired a collection of books to which I frequently refer. Most of these have a small number of thoroughly dog-eared pages, along with many that have scarcely been opened. During the same period I have been privileged to associate and collabo­ rate with a number of materials scientists who were not trained as crystal­ lographers, but whose interests required them to understand particular details of some structural problem.

• Materials
• Matrix (Math.)
• Statistik
• Symmetrische Gruppe
• Tensorrechnung
• Vektorrechnung
• algebra
• crystallography
• kernel
• knowledge
• materials science
• mathematics
• model
• uncertainty

• National Bureau of Standards, USA

  Edward Prince

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