${\mathrm{ZnGeN}}_2$ is sought as a semiconductor with comparable lattice constant to GaN and tunable band gap for integration in optoelectronic devices. Configurational disorder on the cation sublattice of ${\mathrm{ZnGeN}}_2$ can strongly modify the electronic structure compared to the ordered material, and both ordered and disordered forms of ${\mathrm{ZnGeN}}_2$ are candidates for light-emitting diodes and other emitters. The nonisovalent character of the disordered species (${\mathrm{Zn}}^{2+}$ and ${\mathrm{Ge}}^{4+}$) subjects the cation ordering to strong short-range order effects. To model these effects, we use Monte Carlo (MC) simulations utilizing a cluster expansion to approximate formation enthalpy. Representative disordered configurations in 1024-atom supercells are relaxed in density functional theory calculations. From the MC structures, we extract a short-range order parameter (the N-cation coordination motif), and two long-range order parameters (Bragg-Williams and stretching parameters), and examine their correlations. We perform a thermodynamic integration to determine the mixing entropy and free energy. ${\mathrm{ZnGeN}}_2$ exhibits a first-order phase transition with pronounced discontinuities in enthalpy and entropy, as well as in the structural order parameters. We discuss the relationship between the effective temperature used in the MC simulation and the growth temperatures in experiment in relation to the crossover from the nonequilibrium to the equilibrium growth regime. This work expands on current models of site disorder in ${\mathrm{ZnGeN}}_2$ and provides atomic structure models with a systematic variation of the degree of cation disorder.

中文翻译：

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使用基于簇的蒙特卡洛探测ZnGeN2中的构型无序

${\mathrm{锌锗}}_2$寻找一种具有与GaN相当的晶格常数和可调谐带隙的半导体，以集成到光电子器件中。阳离子亚晶格上的构型无序。${\mathrm{锌锗}}_2$ 与有序材料相比，可以极大地改变电子结构，有序和无序形式的 ${\mathrm{锌锗}}_2$是发光二极管和其他发射器的候选人。无序物种的非等价特征（${锌}^{2+}$ 和 ${\mathrm{通用电器}}^{4+}$）使阳离子有序作用于短程有序效应。为了模拟这些影响，我们使用蒙特卡罗（MC）模拟，利用簇扩展近似地层焓。在密度泛函理论计算中放宽了1024原子超级电池中的代表性无序构型。从MC结构中，我们提取了一个短程有序参数（N阳离子配位基序）和两个远程有序参数（Bragg-Williams和拉伸参数），并检查了它们的相关性。我们执行热力学积分以确定混合熵和自由能。${\mathrm{锌锗}}_2$表现出一阶相变，在焓和熵以及结构序参数方面具有明显的不连续性。我们讨论了MC模拟中使用的有效温度与实验中的生长温度之间的关系，这些温度与从非平衡到平衡生长机制的转换有关。这项工作扩展了当前的网站疾病模型${\mathrm{锌锗}}_2$ 并为原子结构模型提供了阳离子无序度的系统变化。