Magnesium-lithium ͑Mg-Li͒ alloys are among the lightest structural materials. Although considerable work has been done on the Mg-Li system, little is known regarding potential ordered phases. A first and rapid analysis of the system with the high-throughput method reveals an unexpected wealth of potentially stable low-temperature phases. Subsequent cluster expansions constructed for bcc and hcp superstructures extend the analysis and verify our high-throughput results. Of particular interest are those structures with greater than 13 at. % lithium, as they exhibit either partial or complete formation as a cubic structure. Order-disorder transition temperatures are predicted by Monte Carlo simulations to be in the range 200-500 K.
I. MOTIVATION AND BACKGROUNDEmerging technologies increasingly depend on the production of ultralight-weight materials. Magnesium-lithium ͑Mg-Li͒ alloys are the lightest metallic alloys, having densities near that of plastics, 1-3 and are strong enough to be used in a variety of high-performance applications. In particular, Mg-Li alloys are good candidates for material applications in industries such as aerospace and automotive manufacturing. 4 As an alloying agent in magnesium, lithium is advantageous principally because of its low density and cubic crystal structure. The addition of lithium converts the hexagonalclose-packed ͑hcp͒ structure of natural magnesium to a more ductile and formable body-centered-cubic ͑bcc͒ alloy. Addition of 13 at. % Li partially converts the alloy to a cubic structure and content exceeding 33 at. % results in total conversion. 5 Although the Mg-Li system has been studied extensively, 5-11 evidence suggesting the formation of ordered phases is notably sparse. Diffusionless transformations of the martensitic type have been observed in pure Li, and similar transformations occur in low-temperature magnesium alloyed lithium at certain concentrations. 11,12 Binary ordered phases have not been conclusively identified, however, and any instances contained in the literature are indeterminate. 6,9,13,14 The results of high-throughput ͑HT͒ ab initio calculations performed with the AFLOW package ͑described later͒ show, however, that the heat of formation is negative for a large number of potential structure types, implying the existence of at least one thermodynamically stable ordered phase ͑Fig. 1͒.
II. FIRST-PRINCIPLES METHODFollowing the HT results, we have made predictions of Mg-Li ordered phases using the cluster-expansion ͑CE͒ method-a first-principles-based approach in which input data is mapped to a truncated Ising-type Hamiltonian. The configurational Hamiltonian allows for a fast ground-state search ͑GSS͒ over many derivative superstructures. 16 The CE method was applied to the Mg and Li lattice configurations ͑bcc and hcp, respectively͒. Although minimum-energy configurations may exist outside those considered, superstructures derived from the parent lattices of the alloy constituents generally include the lowest-energy configurations. This assumption is ...