C-vacancy concentration in cementite, Fe₃C_1-z, in equilibrium with α-Fe[C] and γ-Fe[C]

New data are presented on the ambient-temperature values of the orthorhombic lattice parameters of cementite (θ, Fe₃C_1-z). The cementite was obtained by electrolytically etching away the ferrite or martensite from quenched dual-phase Fe-C alloys equilibrated at 823 K ≤ T ≤ 1323 K, i.e. in the α (ferrite) + θ or γ (austenite) + θ two-phase fields, followed by quenching. In qualitative agreement with earlier data (Petch, 1944), the decrease in the lattice parameters a and c and the simultaneous increase in b with increasing equilibration temperature T can be attributed to an increase in the fraction of C vacancies, z, in Fe₃C_1-z in equilibrium with the corresponding Fe[C] terminal solid-solution phase (α or γ). The experimental data are compared with results on C-vacancy-induced lattice-parameter changes obtained by first-principles calculations performed within the framework of density-functional theory (DFT). The anisotropy of the changes in the lattice parameters a, b and c predicted by DFT agrees qualitatively with the experimentally observed changes occurring with increasing equilibration temperature. Eventually, the equilibration-temperature dependence of the unit-cell volume of the cementite, V = abc, was used to calculate T-dependent values of the vacancy fraction z, thereby yielding data for the α + θ/θ and γ + θ/θ phase boundaries in the metastable phase diagram of Fe-Fe₃C. In particular, the α + θ/θ phase boundary determined could be interpreted in terms of Gibbs energy of C-vacancy formation in cementite, whereby its enthalpy contribution agrees well with the results of the first-principles calculations.