Thermodynamic modeling of the Mn–P and Fe–Mn–P systems in the full composition was carried out using the CALculation of PHAse Diagrams (CALPHAD) method based on the critical evaluation of all available phase equilibria and thermodynamic data. The liquid and solid solutions were described using the Modified Quasichemical Model and Compound Energy Formalism, respectively. The Gibbs energies of the binary stoichiometric iron and manganese phosphides were determined based on reliable experimental data. The ternary (Fe,Mn)₃P, (Fe,Mn)₂P and (Fe,Mn)P phosphides were modeled as solid solutions with mutual substitution between Fe and Mn atoms. The Gibbs energy of the liquid solution was predicted using the Toop interpolation technique with P as an asymmetric component, without any ternary parameters. The thermodynamic properties of P in the entire composition region and the liquidus of the ternary system were well reproduced. Based on the thermodynamic models with optimized parameters, unexplored phase diagrams and thermodynamic properties of the Fe–Mn–P system were predicted.

基于对所有可用相平衡和热力学数据的严格评估，使用PHAse图的计算（CALPHAD）方法对整个成分中的Mn-P和Fe-Mn-P系统进行热力学建模。分别使用改进的拟化学模型和化合物能量形式主义描述了液体和固体溶液。基于可靠的实验数据确定了二元化学计量的铁和磷化锰的吉布斯能。三元（Fe，Mn）₃ P，（Fe，Mn）₂P和（Fe，Mn）P磷化物被建模为在Fe和Mn原子之间相互取代的固溶体。液体的吉布斯能量是使用Toop插值技术预测的，其中P为不对称成分，没有任何三元参数。很好地再现了P在整个组成区域和三元体系液相线中的热力学性质。基于具有优化参数的热力学模型，预测了Fe-Mn-P体系的未探索相图和热力学性质。