In this article, the structural phase stability of the KXP (X = Cr & Mo) compounds in the half-Heusler structure were investigated. The stability of the KXP compound was taken into account in the three phases α, β, and $\gamma$ of the half-Heusler structure within various ferromagnetic (FM), antiferromagnetic (AFM), and nonmagnetic (NM) states. Total energy calculations, as well as cohesive energy calculations, indicated that for each KXP compound the β phase of the half-Heusler structure in the FM state has the lowest energy compared to the other phases α and $\gamma$. For all structural phases of the KMoP compound, the positive amount of the formation energy predicts that the compound cannot be grown in the hypothetical half-Heusler structure and prefers to decompose into stable phases of the constituent elements. The hull distance calculations justify that, unlike KMoP, the β and $\gamma$ phases of the half-Heusler KCrP compound can be considered to be thermodynamically stable and suitable for experimental synthesis. Based on the elastic results, it can be argued that, unlike $\alpha$ phase, both β and $\gamma$ phases of the KCrP compound in the FM state satisfy the conditions of mechanical stability. Moreover, $\gamma$ phase of the KCrP compound is stiffer than $\beta$ phase, while $\beta$ phase has a more ductile nature compared to $\gamma$ phase. In agreement with the elastic results, the phonon scattering calculations showed that both β and $\gamma$ phases of the half-Heusler KCrP compound are dynamically stable and can be synthesized, while the α phase is regarded to be an unstable phase. The electronic calculations indicated that the KCrP compound in the different phases β and $\gamma$ possess a half-metallic property with the highly desired Curie temperature, making it a potential candidate for use in spintronic devices.

在本文中，研究了半赫斯勒结构中 KXP (X = Cr & Mo) 化合物的结构相稳定性。KXP 化合物的稳定性在三相α、β和$\gamma$各种铁磁 (FM)、反铁磁 (AFM) 和非磁 (NM) 状态下的半赫斯勒结构。总能量计算以及内聚能计算表明，对于每种 KXP 化合物，FM 状态下半赫斯勒结构的β相与其他相α和$\gamma$. 对于 KMoP 化合物的所有结构相，正的形成能预示着该化合物不能在假设的半赫斯勒结构中生长，而是倾向于分解为组成元素的稳定相。船体距离计算证明，与 KMoP 不同，β和$\gamma$半赫斯勒 KCrP 化合物的相可以被认为是热力学稳定的，适合实验合成。基于弹性结果，可以说，不像$\alpha$相，β和$\gamma$FM 状态的 KCrP 化合物的相满足机械稳定性条件。而且，$\gamma$ KCrP 化合物的相比 $\beta$ 相，而 $\beta$ 相相比，相具有更强的延展性 $\gamma$阶段。与弹性结果一致，声子散射计算表明β和$\gamma$半赫斯勒 KCrP 化合物的相是动态稳定的，可以合成，而α相被认为是不稳定的相。电子计算表明，KCrP 化合物在不同相β和$\gamma$ 具有高度理想的居里温度的半金属特性，使其成为用于自旋电子器件的潜在候选者。