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Symmetry (geometry)

About: Symmetry (geometry) is a(n) research topic. Over the lifetime, 7710 publication(s) have been published within this topic receiving 113087 citation(s).

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Abstract: The dichotomy method for indexing powder diffraction patterns for low-symmetry lattices is studied in terms of an optimization of bound relations used in the comparison of observed data with the calculated patterns generated at each level of the analysis. A rigorous mathematical treatment is presented for monoclinic and triclinic cases. A new program, DICVOL91, has been written, working from the cubic end of the symmetry sequence to triclinic lattices. The search of unit cells is exhaustive within input parameter limits, although a few restrictions for the hkl indices of the first two diffraction lines have been introduced in the study of triclinic symmetry. The efficiency of the method has been checked by means of a large number of accurate powder data, with a very high success rate. Calculation times appeared to be quite reasonable for the majority of examples, down to monoclinic symmetry, but were less predictable for triclinic cases. Applications to all symmetries, including cases with a dominant zone, are discussed.

1,409 citations

01 Jan 1990

1,116 citations

Journal ArticleDOI
Abstract: It is remarked that left-right symmetry of the starting gauge interactions is a "natural" symmetry if it is broken in no way except possibly by mass terms in the Lagrangian. The implications of this result for the unification of coupling constants and for parity nonconservation at low and high energies are stressed.

996 citations

Journal ArticleDOI
Abstract: In this paper, Rossmann & Blow describe how they have detected the existence of partial, approximate symmetry from a knowledge of the intensities alone. The effect of noncrystallographic symmetry, whether partial or total, results in decreasing the size of the structure to be determined, while the number of observable intensities remains the same.

858 citations

Journal ArticleDOI
Abstract: SIR88 is an integrated package of computer programs for the solution of crystal structures. The package is based on the estimation of one- and two-phase structure seminvariants and three- and four-phase structure invariants according to the theory of representations [Giacovazzo (1977). Acta Cryst. A33, 933–944; (1980). Acta Cryst. A36, 362–372]. The program works in all the space groups and in most cases it is able to provide the correct solution without user intervention. Some prior information like the availability of a partial structure or of pseudotranslational symmetry is easily exploited to obtain the structure solution.

768 citations

No. of papers in the topic in previous years