Dependence of the third-order coefficients in Landau free energies for bcc→fcc structural transition on hydrogen concentration in zirconium hydrides

Abstract

Young’s modulus E and the modulus of rigidity G of zirconium hydrides ZrHx(0.9⩽x⩽1.65) at 941 and 1001 K have been obtained as a function of hydrogen concentration c by measuring resonance frequencies for bending and torsion vibrations of a polycrystalline wire. As c increases, observed E and G increase in the bcc β phase, slightly increase linearly in the β+δ phase, and then decrease in the fcc δ phase. On the basis of a phenomenological free energy in terms of strain components taking account of space group symmetry, two types of Landau expansion of the free energies for the β phase in terms of the strain components which play an important role in the structural phase transition between the β and the δ phases are examined. The observed E and G are assumed to be the same as the second-order coefficients of the free energy for the Bain distortions, which occur at the structural phase transition. The dependence of the third-order coefficients on c permits the expanded free energies to describe the fact that the β phase is more stable than the δ phase at low c.