A model for the prediction of lattice parameters of iron–carbon austenite and martensite

Prediction of lattice parameters of interstitial iron–carbon austenites and martensites as a function of carbon concentration and temperature are given. The model is based on the two assumptions that the change in lattice parameters of the pure Fe phase is due to the occupation by carbon atoms to the octahedral holes in the fcc austenite and the bct martensite; and on the relative change in length and vacancy concentration at the lattice sites that are in thermal equilibrium. The predicted lattice parameters of the Fe–C martensites are in a good agreement with the experimental data. However, the preparation procedures of the austenites at room temperature, causes crystal defects thereby dropping the experimental values by 0.25% from the purely ideal predicted values. The model also yield the tetragonality (c/a) of the martensite as a function of C atoms/100 Fe atoms, defined by the ideal ratio c/a = 1 + 0.01X_C.