Dependence Of The Third-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 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 beta phase, slightly increase linearly in the beta + delta phase, and then decrease in the fcc delta 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 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 the Bain distortions, which occur at the structural phase transition. The dependence of the third-order coefficients on c permits the expanded frets energies to describe the fact that the beta phase is more stable than the delta phase at low c. (C) 1997 American Institute of Physics.