The Theory of Crystal Structure AnalysisStructure analysis is based on the phenomena of the diffraction of radia tion by materials. In the first ten to twenty years after Laue's discovery, a very complete theory was developed for the diffraction of x-rays and, later, of electrons. This theory led to equations by means of which it was possible to compute the intensity pattern for a given structure. The theory of structure analysis came to mean that of the diffraction of radiation. In 1935, Patterson pointed out a way leading to the solution of the inverse problem: the finding of the structure from a given intensity distribution pattern. At first the conservatism of researchers, and then the war, hampered the de velopment and broad application of the ideas set forth in this work. It was only during the last ten years that all the rich possibilities of the Patterson method - the method of the analysis of the convolution of the electron density - were brought to light and applied in practice. |
Contents
Mathematical Introduction | 1 |
Principles of the Theory | 19 |
Structure Amplitudes and Products as Random | 67 |
Copyright | |
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Common terms and phrases
absolute magnitude accuracy addends analyze atomic factor atomic functions average axes in P-function axis basic calculated Cauchy's inequality center of inversion center of symmetry centrosymmetric centrosymmetric crystal computed connecting determinant Consequently convolution correlation cos² Crystal Fedorov space curve determining signs deviation diffraction distribution function electron density equal equation example experimental F² series Fedorov space group formula Fourier transform g₁ Gaussian heavy atom hypersymmetry Images of symmetry indices inequality integral intensity interatomic functions interatomic vectors inversion center magnitude maxima mean square method nodes number of atoms obtain origin of coordinates particle planes in P-function possible reciprocal lattice reciprocal space reflections reliably positive scattering amplitude self-convolution spherical structure analysis structure products symmetry axes symmetry planes tion space Translation group trigonometric tudes unitary structure amplitude x-ray zero Ση