Gibbs energy coupling of phase stability and thermochemistry in the HfNb system

Abstract

The thermodynamic properties of the HfNb system are little known from experimental data. There have been conflicting reports about the phase diagram, and no measurements have been presented of the thermochemical properties. As a consequence, there is a lack of information on the Gibbs energy ( G m) of its various stable phases, which is necessary in order to establish systematically the thermal properties of transition metal alloys, and to model ternary and higher order phase diagrams based on HfNb. This problem is studied in the present paper by applying a theoretical method which relies on the coupling between thermochemistry and phase diagrams. The approach involves the analysis and synthesis of selected phase equilibrium data using models for G m of bcc, hcp and liquid, and the evaluation of a set of optimum model parameters through a computer optimisation technique. The G m functions arrived at in this way are used in constructing, by calculation, a phase diagram for the HfNb system, and in analysing the composition and structure dependence of the enthalpy of formation. Detailed comparisons are reported with estimates from the Miedema method and other predictive approaches, and with the behaviour of the related systems HfTa, ZrNb and ZrTa, which have recently been analysed.