Thermo-lp: A computational tool to evaluate reaction thermodynamics for synthesizing M_{n+1}AX_n (MAX) phases based on linear programming optimization method

Thermo-lp (Thermodynamics-Linear Programing) is a computational program written in C and Python for evaluating the thermodynamic formability of MAX phases at the finite temperature, including configurational, electronic, and vibrational entropies. The program uses the phonon density of states (PDOS) and electron density of states (EDOS) as the main inputs to obtain the Gibbs free energy in a temperature range from 0 K to 2000 K for each crystal structure in the self-contained structural and thermodynamic data pool. Thermo-lp offers a highly reliable evaluation of the overall thermodynamic stability of a target MAX phase with respect to many competing impurities using linear programing optimization algorithm. Thermo-lp program is also capable to simultaneously compose and optimize the synthetic pathways for the target MAX phase due to the implementation of constrained linear programing procedure. The capabilities of Thermo-lp program are demonstrated using the quaternary Cr_2TiAlC_2 o-MAX compound as the typical example by successfully predicting the thermodynamically most feasible synthetic route, and the most likely impurities at 1724 K for the annealing temperature.