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Single phonon x‐ray scattering from alkali halides I. The influence of eigenvectors
Author(s) -
Reid J. S.
Publication year - 1971
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220480217
Subject(s) - eigenvalues and eigenvectors , scattering , phonon , reciprocal lattice , halide , sensitivity (control systems) , alkali metal , phonon scattering , physics , debye , mathematical analysis , chemistry , computational physics , condensed matter physics , mathematics , optics , quantum mechanics , inorganic chemistry , diffraction , engineering , electronic engineering
Variations in the eigenvectors given by a number of force models for the alkali halides are examined for wave vectors lying along the: [1,0,0], [1,1,0], and [1,1,1] directions. Among the models considered are least‐squares‐fitted shell models for NaF, NaCl, NaBr, NaI, KCl, and KBr. Substantial differences in the eigenvectors given by different models for one material are found, even when the models fit phonon frequencies well. In addition it is found that the fractional variation of the eigenvectors with temperature is similar to the fractional variation of the square of the phonon frequencies. The method of determining the ratio of the eigenvectors of the two ions from the one‐phonon X‐ray scattering is discussed, and the sensitivity of this method is numerically examined. Although this sensitivity varies widely in reciprocal space it is possible to choose values of the scattering vector where this ratio can be determined to about ± 0.03 for a 20% accuracy in the one‐phonon scattering. The effect of the eigenvectors on the Debye‐Waller factors is also considered and shown to produce an uncertainty in the B k values of the order of 1% at 300 ° K. It is concluded that measurements of the X‐ray intensity scattered by a transverse mode could distinguish between the eigenvector ratios given by fitted shell models and models determined by macroscopic data. Measurements to an accuracy of 1% could further distinguish different good shell models.