Motion and Disorder in Crystal Structure Analysis: Measuring and Distinguishing Them

Abstract

Dynamic processes in crystalline solids are reflected in the atomic displacement amplitudes determined, together with the atomic coordinates, by crystal structure analysis. The interpretation of such amplitudes poses two severe problems: (a) The relative phases of the atomic displacements are lost; and (b) the amplitudes may reflect disorder in the structure and systematic error in the diffraction experiment in addition to motion, but the three contributions cannot be separated on the basis of measurements at a single temperature. Several approximate ways to solve these problems, e.g. rigid-body and segmented-rigid-body analysis, are reviewed together with their limitations. A more recent approach that represents a significant advance with respect to both difficulties is also described: Crystal structures are determined over a range of temperatures; the mean square amplitude quantities are interpreted by taking explicit account of their temperature dependence, i.e. by exploiting the difference in behavior of a microscopic oscillator in the low-temperature, quantum regime and in the high-temperature, classical regime. A distinction between low-frequency and high-frequency motion, disorder, and systematic error becomes possible with this model; this is illustrated with the help of case studies.