Ground-state characterizations of systems predicted to exhibit $L{1}_1$ or $L{1}_3$ crystal structures

Despite their geometric simplicity, the crystal structures $L{1}_1$ (CuPt) and $L{1}_3$ (CdPt${}_3$) do not appear as ground states experimentally, except in Cu-Pt. We investigate the possibility that these phases are ground states in other binary intermetallic systems, but overlooked experimentally. Via the synergy between high-throughput and cluster-expansion computational methods, we conduct a thorough search for systems that may exhibit these phases and calculate order-disorder transition temperatures when they are predicted. High-throughput calculations predict $L{1}_1$ ground states in the systems Ag-Pd, Ag-Pt, Cu-Pt, Pd-Pt, Li-Pd, Li-Pt, and $L{1}_3$ ground states in the systems Cd-Pt, Cu-Pt, Pd-Pt, Li-Pd, Li-Pt. Cluster expansions confirm the appearance of these ground states in some cases. In the other cases, cluster expansion predicts unsuspected derivative superstructures as ground states. The order-disorder transition temperatures for all $L{1}_1$/$L{1}_3$ ground states were found to be sufficiently high that their physical manifestation may be possible.

Figure 1

Low-temperature ground states for the binary system Ag-Pd as determined by the combined effort of HT and CE. The other curve shows the energy of the random alloy as computed by the CE. Crystal structures listed above the plot that are in bold and with an asterisk next to them indicate ground states.

Figure 2

Low temperature ground states for the binary system Pd-Pt as determined by the combined effort of HT and CE. All stable phases found by the CE are unsuspected and therefore not predicted by HT. Metallurgical challenges may prevent these unsuspected phases from being seen experimentally. The other curve shows the energy of the random alloy as computed by the CE. Crystal structures listed above the plot that are in bold and with an asterisk next to them indicate ground states.

Figure 3

Low-temperature ground states for the binary system Li-Pd as determined by the combined effort of HT and CE. $L{1}_3$ appears as a ground state in this system as well as two unsuspected Li-rich phases (hcp-982 and bcc-9) and one unsuspected Pd-rich phase (fcc-625). The other curves show the energy of the random alloy for the different lattices considered by CE methods. Crystal structures listed above the plot that are in bold and with an asterisk next to them indicate ground states. UOP designates the unknown ordered phase.

Figure 4

Low-temperature ground states for the binary system Li-Pt as determined by the combined effort of HT and CE. $L{1}_3$ appears as a ground state in this system as well as one unsuspected Li-rich phase (hcp-982) and one unsuspected Pd-rich phase (fcc-625). The other curves show the energy of the random alloy for the different lattices considered by CE methods. Crystal structures listed above the plot that are in bold and with an asterisk next to them indicate ground states. UOP designates the unknown ordered phase.

Figure 5

Low-temperature ground states for the binary system Cu-Pt as determined by the combined effort of HT and CE. The low-temperature regime at Cu-rich composition is characterized by three phases not previously observed. One other unsuspected phase is found at Pt-rich composition (fcc-625). The other curve shows the energy of the random alloy as computed by the CE. Crystal structures listed above the plot that are in bold and with an asterisk next to them indicate ground states. UOP designates the unknown ordered phase.

Figure 6

Low-temperature ground states for the binary system Ag-Pt as determined by the combined effort of HT and CE. AgPt ($L{1}_1$) is a low-temperature ground state for this system. The other curve shows the energy of the random alloy as computed by the CE. Crystal structures listed above the plot that are in bold and with an asterisk next to them indicate ground states. UOP designates the unknown ordered phase.

Figure 7

Ground-state crystal structures for the binary system Cd-Pt as determined by the combined effort of HT and CE. HT predictions dominate the Cd-rich portion of the phase diagram, with D0${}_{11}$ and Hg${}_2$Pt being the only stable Cd-rich phases. This system is predicted to exhibit the rarely seen phase $L{1}_3$ for Pt-rich composition. Crystal structures listed above the plot that are in bold and with an asterisk next to them indicate ground states. UOP designates the unknown ordered phase.

Figure 8

Low-temperature ground states for the binary system Pt-Zn as predicted by the combined effort of HT and CE. The phase with structure $L{1}_3$ is a low-temperature ground state for this system at composition Pt${}_3$Zn. The other curves show the energies of the random alloys for the different lattices considered by CE method. Crystal structures listed above the plot that are in bold and with an asterisk next to them indicate ground states. UOP designates the unknown ordered phase.