Phase Stability and Diagrams from First Principles

Segregation of Pt(28)Rh(27) bimetallic nanoparticles: a first-principles study

Based on a first-principles calculation combined with the cluster expansion technique and Monte Carlo statistical simulation, the segregation behavior of a Pt(28)Rh(27) cuboctahedral nanoparticle is examined. From the effective cluster interaction of the nanoparticle, we see a similar weak ordering tendency inside the nanoparticle to that for Pt-Rh bulk alloy. Below the bulk melting temperature of around 1700 K, we find strong Pt segregation to the surface of the nanoparticle. This is due mainly to larger Pt on-site segregation energy for surface sites than that for subsurface and core sites. In order to examine the segregation behavior of the Pt(28)Rh(27) nanoparticle, we find that the ordering contribution is essential, which reverses the preferable segregation between edge and (100) sites. A ground-state atomic arrangement of the Pt(28)Rh(27) nanoparticle at T = 0 K is predicted, where all the Pt atoms are located at surface sites, particularly at the vertex site of the lowest coordination number.

Cluster expansion approach for transmutative lattice systems

We propose a cluster expansion (CE) technique that can express any function of atomic arrangement on any given lattice with the same number of lattice points in a single formalism. In the proposed CE, two types of spin variable, σ and τ, on the base lattice and virtual lattice, respectively, are introduced. The former spin variable specifies the occupation of the constituent elements for each lattice point. The latter specifies the positions of each lattice point. Basis functions constructed from the two types of spin variable satisfy completeness and orthonormality for any atomic arrangement on given lattices. As examples, the proposed CE is applied to one- and three-dimensional lattices in a binary system, which clarifies the concept of base and virtual lattices, how the functions of atomic arrangements are expressed in terms of the two types of spin variable, and the efficiency and convergence of the proposed CE with a finite number of clusters and input structures.