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Structural model for the ‐phase transformation
Author(s) -
Sanchez J. M.,
De Fontaine D.
Publication year - 1977
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889877013405
Subject(s) - anharmonicity , diffraction , reciprocal lattice , physics , displacement field , curvature , brillouin zone , intensity (physics) , streaking , phase (matter) , condensed matter physics , optics , chemistry , crystallography , molecular physics , geometry , quantum mechanics , mathematics , finite element method , thermodynamics
The intensity distribution observed in neutron diffraction experiments in Zr–20% Nb alloys is analyzed in terms of the essential anharmonicity in the free energy, believed to be important in the Group IV b transition metals. It is found that a second‐order approximation in the atomic displacements for calculating the diffuse intensity readily accounts for the main features of the intensity distribution. In particular, the observed ratio of intensities between certain superlattice reflections is shown to be related in a straightforward manner to the ratio of harmonic to anharmonic free‐energy coefficients. Furthermore. in order to describe the observed curvature in the diffuse streaking in some Ti and Hf alloys, the displacement field of a localized ω‐like particle is obtained by adding longitudinal displacement plane waves with wave vectors distributed on one octant of a spherical surface centered at the 〈111〉 octahedral site of the reciprocal lattice, and passing through point k m ≃ 0.71 [ 111 ]. Computer‐generated patterns of dots simulating such displacement fields were Fourier‐transformed optically, yielding diffuse intensity' in excellent agreement with the circular streaking found experimentally in electron diffraction patterns of certain Ti and Hf alloys.