Thermodynamic Analysis of the Nb–Ti–B Ternary Phase Diagram

Abstract

A thermodynamic analysis of the Nb–Ti–B ternary system was carried out by estimating the unknown thermodynamic properties of binary and ternary borides by using a first-principles method. The calculated value for the binary TiB₂ phase was in reasonable agreement with those found by experiment. Due to a lack of experimental values concerning thermodynamic properties of the ternary system, the formation enthalpies for the Nb₃B₂–Ti₃B₂, NbB–TiB (Cmcm), NbB–TiB (Pnma), Nb₅B₆–Ti₅B₆, Nb₃B₄–Ti₃B₄, and NbB₂–TiB₂ pseudo-binary sections were also determined by constructing various kinds of superstructures for binary borides. The thermodynamic functions determined using these theoretical values, as well as the available experimental information on the phase fields, successfully revealed the phase equilibria in the Nb–Ti–B ternary system across the entire composition and all temperature ranges.