# Algorithm for Generating Derivative Structures

@article{Hart2008AlgorithmFG, title={Algorithm for Generating Derivative Structures}, author={G. Hart and R. Forcade}, journal={Physical Review B}, year={2008}, volume={77}, pages={224115} }

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

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#### References

SHOWING 1-10 OF 42 REFERENCES

Derivative Crystal Structures

- Chemistry
- 1947

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 popular… Expand

Direct enumeration of alloy configurations for electronic structural properties

- Materials Science, Physics
- 2005

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 of… Expand

The enumeration and symmetry-significant properties of derivative lattices. III. Periodic colourings of a lattice

- Mathematics
- 1995

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 their… Expand

Properties of crystal lattices: the derivative lattices and their determination

- Physics
- 1972

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 for… Expand

Colour lattices and spin translation groups. General case

- Mathematics
- 1981

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 and… Expand

Coincidence-site lattices

- Chemistry
- 1973

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 or… Expand

Where are nature’s missing structures?

- Physics
- 2007

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 vehicle… Expand

Automating First-Principles Phase Diagram Calculations

- Computer Science, Physics
- 2002

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

- Computer Science
- Int. J. High Perform. Comput. Appl.
- 1991

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

- Computer Science, Physics
- 2002

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