Algorithm for Generating Derivative Structures

  title={Algorithm for Generating Derivative Structures},
  author={G. Hart and R. Forcade},
  journal={Physical Review B},
We present an algorithm for generating all derivative superstructures--for arbitrary parent structures and for any number of atom types. This algorithm enumerates superlattices and atomic configurations in a geometry-independent way. The key concept is to use the quotient group associated with each superlattice to determine all unique atomic configurations. The run time of the algorithm scales linearly with the number of unique structures found. We show several applications demonstrating how… Expand
Generating derivative structures at a fixed concentration
We present an algorithm for generating derivative superstructures for large unit cells at a fixed concentration. The algorithm is useful when partial crystallographic information of an ordered phaseExpand
Generating derivative superstructures for systems with high configurational freedom
Abstract Modeling alloys requires the exploration of all possible configurations of atoms. Additionally, modeling the thermal properties of materials requires knowledge of the possible ways ofExpand
Efficient stochastic generation of special quasirandom structures
The proposed method optimizes the shape of the supercell jointly with the occupation of the atomic sites, thus ensuring that the configurational space searched is exhaustive and not biased by a pre-specified supercell shape. Expand
Supercell program: a combinatorial structure-generation approach for the local-level modeling of atomic substitutions and partial occupancies in crystals
The all-in-one approach to process point disordered structures, powerful command line interface, excellent performance, flexibility and GNU GPL license make the supercell program a versatile set of tools for disordered structure manipulations. Expand
Sublattice enumeration. IV. Equivalence classes of plane sublattices by parent Patterson symmetry and colour lattice group type.
  • J. S. Rutherford
  • Mathematics, Medicine
  • Acta crystallographica. Section A, Foundations of crystallography
  • 2009
The Dirichlet generating functions for the number of sublattices fixed under each symmetry operation of the parent Patterson group may be combined to count the number of crystallographicallyExpand
Increasing the Computational Efficiency of Combinatoric Searches
Increasing the Computational Efficiency of Combinatoric Searches Wiley Spencer Morgan Department of Physics and Astronomy, BYU Master of Science A new algorithm for the enumeration of derivativeExpand
Finding the Stable Structures of N1-xWx with an Ab Initio High-Throughput Approach
Abstract : One of the major goals of electronic-structure calculations is the prediction of crystal structures as a function of composition [1 3]. Determining the possible configurations of aExpand
Uncovering compounds by synergy of cluster expansion and high-throughput methods.
This work presents an integrated approach of CE and high-throughput ab initio calculations (HT) applicable to the full range of compositions in binary systems where the constituent elements or the intermediate ordered structures have different lattice types. Expand
UNCLE: a code for constructing cluster expansions for arbitrary lattices with minimal user-input
We present a new implementation of the cluster expansion formalism. The new code, UNiversal CLuster Expansion (UNCLE), consolidates recent advances in the methodology and leverages one newExpand
Favoured local structures in liquids and solids: a 3D lattice model.
A lattice spin model - the FLS model on a face-centered cubic lattice - is introduced where this geometry can be arbitrarily chosen among a discrete set of 115 possible FLS, and crystalline groundstates are found for all choices of a single FLS. Expand


Derivative Crystal Structures
There exists a class of crystal structures which are derived from others by generalization. These are here designated derivative structures. A special case of derivative structure is the popularExpand
Direct enumeration of alloy configurations for electronic structural properties
We present and apply an approach to directly enumerate the band gaps and effective masses of all possible zinc blende-based alloy configurations whose unit cell contains up to a specified number ofExpand
The enumeration and symmetry-significant properties of derivative lattices. III. Periodic colourings of a lattice
In the triclinic case, structures that can be described in terms of arrangements of a set number of possible subunits occupying the unit cells of an underlying lattice may be enumerated by theirExpand
Properties of crystal lattices: the derivative lattices and their determination
Derivative lattices are classified as super, sub and composite, on the basis of the properties of the transformation matrices relating them to the lattice from which they are derived. A method forExpand
Colour lattices and spin translation groups. General case
A method of deriving d-dimensional crystallographic colour lattices with no symmetry conditions on the basis vectors is given. A number of nonequivalent n-colour lattices is evaluated for d ≤ 4 andExpand
Coincidence-site lattices
Coincidence-site lattices are characterized mathematically, in the general case, by a method that can be applied to a pair of original lattices of any symmetry, either metrically identical orExpand
Where are nature’s missing structures?
Our society’s environmental and economic progress depends on the development of high-performance materials such as lightweight alloys, high-energy-density battery materials, recyclable motor vehicleExpand
Automating First-Principles Phase Diagram Calculations
The proposed algorithm formalizes the most difficult step of phase diagram calculations, namely the determination of the “cluster expanison,” which is a compact representation of the configurational dependence of the alloy’s energy. Expand
Stability, Electronic Structure, and Phase Diagrams of Novel Inter- Semiconductor Compounds
It is described here how the use of state- of-the-art techniques in both quantum and statistical mechanics can lead to predictions of new, stable, and ordered semiconductor alloys. Expand
The Alloy Theoretic Automated Toolkit: A User Guide
A concise user guide is presented outlining the steps required to obtain thermodynamic information from ab initio calculations of alloy thermodynamic properties from first-principles. Expand