Order–disorder transformations and phase equilibria in strongly nonstoichiometric compounds

First-principles phase diagram calculations for the HfC–TiC, ZrC–TiC, and HfC–ZrC solid solutions

“…3͒. Without taking F vib into account we calculate X C = 0.5, but with F vib it shifts to X C = 0.41, in good agreement with experimental work 9 and thermodynamic modeling 13,14 ͑Table II͒. By including F vib the consolute temperature is reduced from 3350 to 2695 K ͑ϳ20%͒.…”

“…The consolute composition, however, is at X C = 0.50 ͑Table II͒. Experimental data 8,9 and their thermodynamic assessment, 14 even when combined with ab initio computations on ordered intermediate compounds, 13 exhibit stronger asymmetry. In HfC-TiC, including vibrational contributions to the free energy reduces T C by about 7% from 2275 to 2120 K, within the uncertainty of experimental values 8,9 ͑Table II͒.…”

“…37 Formation energies in HfC-ZrC are more like those in AlN-GaN, 37 i.e., consistent with complete miscibility at room temperature, also inferred from the thermodynamic assessment of the system. 14 The CEs were fit to a moderate number of structures to obtain a good CVS ͑Table I͒. They include pair interactions only, or pair plus one triplet interaction ͑Table I and Fig.…”

“…Such thermodynamic models have also been applied to group IV carbides. [13][14][15] Although these methods are useful to fit phase diagram data and approximate thermodynamic functions, it is desirable to compute phase diagrams strictly from knowledge of the constituent atoms without empirical parameters. To calculate phase equilibria the Gibbs free energy must be known for competing structures over a wide range of concentrations, and consequently the formation energy ͑⌬E f ͒ must be computed for a large number of phases along the solid solution.…”

Thermodynamic Modeling in Reduced Activation Steels

“…51) A comprehensive review on pseudo binary systems based on carbides (including the TaC-VC 0.88 system) can be found in Ref. 52).…”