DEPENDENCE OF THE 3RD-ORDER COEFFICIENTS IN LANDAU-FREE-ENERGIES FOR BCC-]FCC STRUCTURAL TRANSITION ON HYDROGEN CONCENTRATION IN ZIRCONIUM HYDRIDES

Young's modulus E and the modulus of rigidity G of zirconium hydrides ZrHx(0.9 less than or equal to x less than or equal to 1.65) at 941 an d 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 i n the bcc beta phase, slightly increase linearly in the beta + delta p hase, and then decrease in the fcc delta phase. On the basis of a phen omenological free energy in terms of strain components taking account of space group symmetry, two types of Landau expansion of the free ene rgies for the beta phase in terms of the strain components which play an important role in the structural phase transition between the beta and the delta phases are examined. The observed E and G are assumed to be the same as the second-order coefficients of the free energy for t he Bain distortions, which occur at the structural phase transition. T he dependence of the third-order coefficients on c permits the expande d frets energies to describe the fact that the beta phase is more stab le than the delta phase at low c. (C) 1997 American Institute of Physi cs.