The electronic structure, elastic, and magnetic properties of the Cr₂NbSn_1 − xPb_x quaternary Heusler alloys have been investigated using the full-potential linearized augmented plane wave (FP-LAPW) method based on density functional theory and implemented in WIEN2k code. The exchange-correlation potential is evaluated using the generalized gradient approximation (GGA) within the Perdew–Burke–Ernzerhof (PBE) parameterization. Our results provide a theoretical study for the mixed Cr₂NbSn_1 − xPb_x Heusler alloys in which no theoretical or experimental data are currently available. The AlCu₂Mnl-type (L2₁) structure is more stable than the CuHg₂Ti-type structure at equilibrium volume for the compounds. In their equilibrium L2₁ structure, all concentrations are magnetic and metallic. However, there is linear variation of the lattice parameter. The bulk modulus, the elastic constants, and the Debye temperature were studied with a variation of composition x of Pb. The mechanical results show that these compounds are mechanically stable. The quasi-harmonic Debye model, as implemented in the Gibbs code, was used to predict the thermal properties of the Cr₂NbSn_1 − xPb_x alloys. These alloys seem to be a potential candidate of spintronic devices.

中文翻译：

---

Cr 2 NbSn 1-x Pb x四元Heusler合金的结构，电子和热学性质的第一性原理计算

Cr ₂ NbSn _{1-  x} Pb _x四元Heusler合金的电子结构，弹性和磁性能已使用基于密度泛函理论的全势线性化增强平面波（FP-LAPW）方法进行了研究，并以WIEN2k代码实现。使用Perdew–Burke–Ernzerhof（PBE）参数化中的广义梯度近似（GGA）评估交换相关电位。我们的结果为混合Cr ₂ NbSn _{1-  x} Pb _x Heusler合金提供了理论研究，而目前尚无理论或实验数据。AlCu ₂ Mnl型（L2 ₁在化合物的平衡体积下，结构比CuHg ₂ Ti型结构更稳定。在它们的平衡L2 ₁结构中，所有浓度都是磁性的和金属的。但是，晶格参数存在线性变化。研究了体积模量，弹性常数和德拜温度随Pb组成x的变化。力学结果表明这些化合物是机械稳定的。用吉布斯规则实现的准谐波德拜模型用于预测Cr ₂ NbSn _{1-  x} Pb _x合金的热性能。这些合金似乎是自旋电子器件的潜在候选者。