# 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.

## Optimization and machine learning¶

ARDR

Automatic relevance determination regression (ARDR) is an optimization algorithm provided by scikit-learn

compressive sensing

Compressive sensing (CS), also known as compressive sampling, is an efficient method for constructing sparse solutions for linear systems.

CV
cross validation

Cross validation (CV) is commonly employed to evaluated the transferability and accuracy of linear problems.

LASSO

The least absolute shrinkage and selection operator (LASSO) is a method for performing variable selection and regularization in problems in statistics and machine learning.

kernel ridge regression

Kernel ridge regression (KRR) combines ridge regression with the kernel trick.

RFE

In machine learning recursive feature elimination (RFE) is a popular feature selection process in model construction.

regularization

Regularization, is commonly used in machine learning to combat overfitting and for solving underdetermined systems.

## 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 $$N_{sites}$$ MC trial steps, where $$N_{sites}$$ 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].