The following figure illustrates the icet workflow. Here, classes are shown in blue, input parameters and data in orange, and functionalities invoked via external libraries are indicated in green.
The typical workflow involves the following steps:
initialize a cluster space (via
ClusterSpace) by providing a prototype structure (typically a primitive cell), the species that are allowed on each site as well as cutoff radii for clusters of different orders
construct a cluster expansion (via
ClusterExpansion) by combining the cluster space with a set of parameters obtained by optimization
The final cluster expansion can be used in a number of ways. Most commonly one
creates a cluster expansion calculator (via
ClusterExpansionCalculator) for a specific
supercell structure and subsequently carries out Monte Carlo
simulations via the mchammer module
It is also possible to use a cluster expansion (via
ClusterExpansion) directly to make predictions for arbitrary
supercells of the primitive prototype structure, obtained e.g., by
A cluster space (represented by the
class) is defined by providing a prototype structure (usually a primitive
cell), the species allowed on each site, and a set of cutoffs for each
(cluster) order to be included, as demonstrated in the tutorial section that
illustrates the basic construction of a cluster expansion. It contains the set of clusters
(pairs, triplets, quadruplets etc.) and orbits into which a structure
can be decomposed. (An orbit is a set of symmetry equivalent clusters, see
figure below). Such a decomposition is referred to as a cluster vector.
In simpler terms, a cluster vector is a numerical representation of an alloy structure, and a cluster space enables such representations to be obtained.
A structure container (represented by the
StructureContainer class) is a collection of structures along with
their cluster vectors. Structure containers allow one to easily compile
structures for training and validation, as demonstrated in the tutorial on
basic construction of a cluster expansion. They can also be written to file for
Optimizers allow one to train the effective cluster interactions (ECI) associated with each orbit in the cluster space.
This functionality is maintained in the trainstation package, the documentation of which can be found here and which provides optimizer classes such as
A cluster expansion (CE; represented by the
ClusterExpansion class) is obtained by combining a cluster space with
a set of parameters as illustrated in the tutorial on basic construction
of a cluster expansion. CEs are the
main output of the icet model construction cycle. While they are
specific for a given prototype structure and cluster space they are not tied
to a specific supercell structure. CEs can be written to file for later use.
Cluster expansion calculators¶
A cluster expansion calculator (represented by the
ClusterExpansionCalculator class) is needed in order
to carry out Monte Carlo simulations via the mchammer
module. They are generated by applying a CE to a
specific supercell and are subsequently used to initialize a Monte Carlo
ensemble as shown in
the MC tutorial section.