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.

Thermo-lp（热力学-线性规划，Thermodynamics-Linear Programing）是一款采用C与Python语言编写的计算程序，用于评估有限温度下MAX相的热力学成形能力，涵盖组态熵、电子熵与振动熵。该程序以声子态密度（phonon density of states，PDOS）与电子态密度（electron density of states，EDOS）为核心输入参数，可针对内置结构与热力学数据池中的各晶体结构，计算其在0 K至2000 K温度区间内的吉布斯自由能。Thermo-lp可借助线性规划优化算法，对目标MAX相对多种竞争杂质的整体热力学稳定性开展高度可靠的评估。得益于约束线性规划流程的集成应用，该程序还可同时构建并优化目标MAX相的合成路径。本程序以四元Cr₂TiAlC₂ o-MAX化合物为典型示例，通过成功预测该体系在1724 K退火温度下热力学上最可行的合成路径与最可能生成的杂质，验证了其各项功能的有效性。