Anisotropic elastic constants and thermal expansivities in monocrystal CrB2, TiB2, and ZrB2

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The elastic constants and thermal expansivities in monocrystals of three transition-metal diborides with the AlB2 structure, CrB2, TiB2, and ZrB2, have been investigated in the temperature ranges from 300 to 1373 K and from 300 to 1073 K. The anisotropic parameters deduced from the measured elastic constants and thermal expansivities indicate that of the three diborides, the anisotropy is the most and least significant in CrB2 and ZrB2, respectively. The factors determining the significance in anisotropy in atomic bonding in AlB2-type diborides are analyzed by an approach similar to the valence-force-field method and are discussed in terms of the deformation of the electronic charge around the metal atoms occurring to fit themselves in the (0 0 0 1) basal plane.