Thermodynamic assessment of the C Cr Ti system—Supported by DFT calculations

The thermodynamic description of the CCrTi ternary system has been reassessed. The main reason was to adjust the solubility limit of Cr in MC (M = Cr, Ti), but also to take the solubility of Ti in M3C2 and M7C3 into account. Another reason was that the thermodynamic descriptions of all the three constituent binary systems (CCr, CTi and CrTi) had been revised after the previously published description of the CCrTi system. Important metastable end-members and interaction parameters were calculated using Density Functional Theory (DFT). For fcc-CrC and Ti3C2, DFT was used together with a recently published method to calculate the molar Gibbs energy as a function of temperature (Gm(T)). For fcc-CrC also the magnetic contribution and the magnetic transition temperature, i.e. the Curie temperature (TC), were included. DFT was also used to calculate Gibbs energy of formation at 0 K for Ti7C3 and to calculate the molar excess Gibbs energy contribution, and TC, as a function of Ti composition in MC. DFT calculated parameters were compared with experiments or previous assessments. Selected experimental information from literature was then used to optimize parameters that are difficult to calculate with DFT, e.g. interaction parameters for the liquid phase and temperature dependence for interaction parameters in the solid phases. The resulting thermodynamic description, which is based on critically reviewed binary descriptions, reproduces the experimental solidification sequence, found in literature, equally well as the previous description of the CCrTi system. Furthermore, in contrast to the previous description, the new description also reproduces the most recent experimentally determined solubility of Cr in MC and takes the solubility of Ti in M3C2 and M7C3 into account. Finally the new description uses DFT calculated metastable end-members and interaction parameters, which gives more reliable predictions, especially at low temperatures.