- 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
- 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,
- 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.
- 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.
- Cutoffs define the longest allowed distance between two atoms in a
cluster for each order.
- An orbit is defined as a set of symmetry equivalent clusters.
- Cluster expansion
- Cluster expansions 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.
- The parameters of a CE are usually referred to as
effective cluster interactions (ECIs).
- Monte Carlo (MC) simulations are an effective method for
sampling a multi-dimensional space.