The asymmetry of the formation energy Δ E f( x) is greater for Ti 1− xHf xN than Ti 1− xZr xN, with less solubility on the smaller cation TiN-side, and similar asymmetries were predicted for the corresponding phase diagrams. We predict consolute temperatures ( T C), at which miscibility gaps close, for Ti 1− xZr xN to be 1400 K, for Ti 1− xHf xN to be 700 K, and below 200 K for Zr 1− xHf xN.
We have studied the phase equilibria of three ceramic quasibinary systems Ti 1− xZr xN, Ti 1− xHf xN and Zr 1− xHf xN (0 ≤ x ≤ 1) with density functional theory, cluster expansion and Monte Carlo simulations.
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