Verifying predictions of the $L{1}_3$ crystal structure in Cd-Pt and Pd-Pt by exhaustive enumeration

In 2001, S. Müller and A. Zunger [Phys. Rev. Lett. 87, 165502 (2001)] predicted a never-before-observed crystal structure in Ag-Pd. Recently, Curtarolo predicted the same structure to be stable in Pt-Cd and Pt-Pd [S. Curtarolo et al., CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 29, 163 (2005)]. The predicted structure is unique in several ways. Though never seen in any other face-centered-cubic-based intermetallic binary compound or ordered alloy, it is relatively simple—it contains only four atoms per unit cell. Furthermore, the structure is the only one of this small size, except the $L{1}_2$ structure, that cannot be characterized as a simple stacking of layers where each layer contains only one kind of atom. We construct a first-principles-based Hamiltonian and search it for the thermodynamically stable (lowest energy) structures. Using a (practically) exhaustive enumeration of about three million of the most likely candidate structures, we find that this new structure, designated $L{1}_3$, is indeed a ground state in both Cd-Pt and Pd-Pt. Experimental efforts to validate the predictions are underway.

Figure 1

(Color) The first 17 binary structures derived from the fcc lattice. All have four atoms/cell or less. Structures shown with a green plane can be characterized as a stacking of pure A and B atomic layers. For example the $L{1}_0$ structure (upper left) is an alternating $\left({\text{A}}_1{\text{B}}_1\right)$ sequence of layers stacked in the [001] direction. All of the two- and three-atoms/cell structures have physical manifestations. Of the four-atoms/cell structures only four have physical manifestations. Three of the others (yellow backgrounds) have been predicted to exist[1] but not yet observed. The other five (purple backgrounds) have never been observed or predicted to exist in any system.

Figure 2

(Color online) Input energies and corresponding fitted values for Cd-Pt (left) and Pd-Pt (right). The energy scales on the plots are not the same. Input energies are indicated by open circles and the corresponding fitted value is indicated by a bold cross. If the fitting errors were zero, each cross would coincide exactly with its circle.

Figure 3

(Color online) Ground state searches for Cd-Pt (left) and Pd-Pt (right). For each case, the energies of approximately three million structures were computed and compared. The red crosses indicate the energy of each structure, the black diamonds the ground states. The solid black line indicates the convex hull. The $L{1}_3$ structure is found to be a ground state at 75% Pt in Cd-Pt and at 25% and 75% Pt in Pd-Pt, as predicted by the datamining approach.