Generalized dependence of alloy properties on multiple chemical orders

Chemical order-disorder transitions commonly exist in alloys, which serve as a degree of freedom to tune alloy properties in addition to chemical composition. The dependence of alloy properties on the order parameter is thus key for optimized alloy design. Conventionally, the dependence of alloy properties on a single order parameter has been well established. In complex alloys, there might exist multiple chemical orders; the general dependence of alloy properties on multiple chemical orders is, however, still unclear, which significantly limits the sophisticated design of complex alloys. Here, we theoretically derive the generalized dependence of alloy properties on multiple chemical orders, and validate our derived formula by explicit calculations based on first principles and a machine-learning force field for a prototypical complex alloy of ${\mathrm{GaInAs}}_{2}$, which is known for the existence of multiple chemical orders. Our study lays the foundation for the precise control of alloy performance via manipulating chemical orders.