Calculation of Lindgård and Mouritsen’s free energy using recently measured moduli of elasticity for hydrogen in zirconium

Abstract

The Young’s modulus E and the modulus of rigidity G of ZrHx (0≤x<0.9) were measured as functions of temperature between 300 and 1300 K for Zr and of hydrogen concentration at 941 and 1001 K in the previous paper. The abrupt change of the observed G for Zr at a critical temperature determines all the unknown coefficients of the free energy (LM free energy) derived by Lindgård and Mouritsen, who discussed the structural phase transition between the α (a hexagonal closed-packed structure) and β (a body centered cubic structure) phases in a Landau theory [Phys. Rev. Lett. 57, 2458 (1986)]. LM free energy is modified so as to include effects of interstitial hydrogen atoms at low hydrogen concentration. A modified LM free energy which represents the transition from the α to β phase through the α+β phase is obtained by introducing an order parameter proportional to hydrogen concentration. The order parameter multiplied by a lattice constant is the displacement between the position of Zr atom in the α phase and its position in the β phase.