# Glossary¶

## General¶

- BCC¶
Several metallic including for example elements from groups 5 (V, Nb, Ta) and 6 (Cr, Mo, W) have a body-centered cubic (BCC) ground state structure.

- FCC¶
The face-centered cubic (FCC) lattice is one of the most common crystal structures for metallic elements including e.g., the late transition metals from group 10 (Ni, Pd, Pt) and 11 (Cu, Ag, Au).

- DFT¶
The construction of force constants requires accurate reference data. Density functional theory (DFT) calculations are one of the most common source for such data.

## Crystal symmetry and clusters¶

- crystal symmetry operation¶
A crystal symmetry operation for a specific lattice means that the lattice is invariant under this operation. An operation comprises translational and rotational components.

- cluster¶
A cluster is defined as a set of points on a lattice.

- cluster size¶
The size of a cluster (commonly refered to as the cluster radius) is defined as the average distance to the geometrical center of the cluster.

- cluster space¶
The set of clusters into which a structure can be decomposed.

- cutoff¶
Cutoffs define the longest allowed distance between two atoms in a cluster for each order.

- orbit¶
An orbit is defined as a set of symmetry equivalent clusters.

## Cluster expansions¶

- cluster expansion¶
- CE¶
- CEs¶
Cluster expansions (CEs) provide a mapping between a configuration and a property of interest that can be many orders of magnitude faster than the underlying reference calculations from e.g., DFT.

- DOS¶
density of states

- ECI¶
- ECIs¶
The parameters of a CE are usually referred to as effective cluster interactions (ECIs).

- MC¶
Monte Carlo (MC) simulations are an effective method for sampling a multi-dimensional space.

- MCS¶
- MCSs¶
A Monte Carlo sweep (MCS) is defined as \(N_\mathrm{sites}\) MC trial steps, where \(N_\mathrm{sites}\) is the number of sites in the system.

- SQS¶
Special quasirandom structures, alloy supercells that mimic a random alloy using few atoms [ZunWeiFer90].

- WL¶
The Wang-Landau (WL) algorithm allows one to extract the microcanonical density of states (DOS), from which many other thermodynamic quantities can be calculated [WanLan01a].