Titlebook: Direct Methods of Solving Crystal Structures; Henk Schenk Book 1991 Springer Science+Business Media New York 1991 DSI_D012

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Structure Invariants, Seminvariants and Origin Definition,f the crystal; this means that in the three-dimensional lattice, generated by the basic vectors, the lattice points represent positions that are translational equivalent, i.e. points that have identical surroundings in the same orientation. In order to define a crystal structure completely it is suf

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Determinantal Inequalities Lead to Triplet and Quartet Relationships,equalities hold: .where the (complex) normalized structure factor E. is defined by . H is an arbitrary reciprocal lattice vector, Z. is the atomic number and r. the position vector of the atom labeled j, N is the number of atoms in the unit cell, and ..

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Symbolic Addition,ads to very fast-running programs; structures are solved in a fraction of the time necessary to carry out a complete multisolution approach (Peschar, 1991; Schenk and Kiers, 1983; Overbeek and Schenk, 1978; Schenk, 1971). For an Advanced Study Instute there is one more advantage: the procedures used

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Quartets and Other Phase Relationships,e choice of origin are called structure invariants. When it is possible to estimate the phase sum of an invariant, this sum is generally called a phase relationship. Although in principle a phase relationship is always a structure invariant, it is sensible to make the distinction between all invaria

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The Joint Probability Distribution of Three Structure Factors Leading to a Distribution for the Triof three structure factors via its characteristic function. Assuming an a priori probabilistic model of uniformly and independently distributed atoms, the calculations result in the well-known Cochran distribution for the triplet phase sum.

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Some Applications of Probability Theory in Direct Methods,ion problem. Crystals, which are usually defined in terms of the long range ordering they display, might appear to be poor samples on which to apply a mathematical model devised to deal with random experiments. It is the realization that the periodically repeating motif could itself be depicted as c

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