Predicting low-thermal-conductivity Si-Ge nanowires with a modified cluster expansion method

We introduce the cluster-expansion ghost-lattice method, which extends the applicability of existing clusterexpansion software, to cluster expand structures of arbitrary finite and infinite geometries in a fast, unique, and transferable way. The ghost site that is introduced zeroes the cluster function of any cluster which includes it. This enables the use of bulk clusters grouped by bulk symmetries in nonbulk systems and distinguishes the cluster-expansion ghost-lattice method from a regular ternary cluster expansion with an inactive vacuum atom type. Even though the method does not treat surface terms, it can be used as an efficient way to obtain the bulk term in D. Lerch et al. [Modell. Simul. Mater. Sci. Eng. 17, 055003 (2009)]. We use the method to learn the thermal conductivity of Si-Ge nanowires, oriented along the [111] direction on a diamond lattice, versus their configuration of Si and Ge atoms. Once learned, the ghost-lattice cluster-expansion method is shown to be able to predict the lowest-thermal-conductivity nanowire configuration, in agreement with the configuration found in M. Chan et al. [Phys. Rev. B 81, 174303 (2010)].