**At-a-Glance**

*MedeA*^{®}[1] *Special Quasirandom Structures* provides quick access to
efficient modeling of binaray, ternary, and pseudo-ternary random
alloys crystallizing in cubic or hexagonal lattices.

**Key Benefits**

- Quick access to the most common alloy structures
- Straightforward specification of the alloy composition
- Automated creation of the quasirandom alloy crystal structure

The efficient and at the same time realistic modelling of substitutionally random alloys has been a challenge for very long. For many years, two main kinds of approaches were routinely used. The virtual crystal approximation (VCA) and the coherent potential approximation (CPA) focus on averaging the atomic potentials and the atomic scattering matrices, respectively [2] [3], but have difficulties taking local structural distortions into account. Supercell approaches allow a more realistic description, but are computationally demanding, and suffer from limited control of the statistics. Representing alloys as special quasirandom structures (SQS) offers a very elegant solution to this dilemma. The basic idea consists of arranging the different alloying atoms on lattice sites of relatively small unit cells, such that their most relevant radial correlation functions mimic those of a perfectly random structure [4] [5]. The validity and usefulness of this approach has been demonstrated in numerous applications for a variety of alloys [6] [7] [8].

Art begins when randomness ends. Although randomness enriches it.

P. Reverdy, French poet

*MedeA Special Quasirandom Structures* provides an easy-to-use access to
quasirandom structures. As shown in the figure below, it only requires
input of the type of alloy, the underlying crystal structure, the lattice
parameters, and the types of the constituent atoms. With this minimal
information, *MedeA Special Quasirandom Structures* generates a crystal
structure, which fulfills the above mentioned requirement of approximating
the physically most relevant radial correlation functions of a perfectly
random structure.

As an example, a 64-atom structure of a CuAu metal alloy is displayed in
the figure below. It was generated by *MedeA Special Quasirandom Structures*,
and uses a 2 \(\times\) 2 \(\times\) 2 supercell of a
face-centered cubic conventional unit cell. Cu and Au atoms are then
distributed over the 64 sites following the SQS algorithm.

As another example, a 64-atom structure of an InGaAs_{2}semiconductor alloy, as generated by *MedeA Special Quasirandom Structures*,
is shown in the figure below. It is based on 2 \(\times\) 2 \(\times\) 2
supercell of the zincblende unit cell. Whereas the As atoms form a regular
sublattice, In and Ga atoms are distributed over the other sublattice as
determined by the SQS algorithm.

- Straightforward generation of quasirandom crystal structures for binary, ternary, and pseudoternary alloys with face-centered cubic, base-centered cubic or hexagonal close-packed lattices
- Specification of the key ingredients as the underlying ideal structure, as well as the types of the constituent atoms, with an intuitive user interface
- Quasirandom structures generated by
*MedeA Special Quasirandom Structures*can be used just like ordered structures,*e.g.*in structure relaxations using*MedeA VASP*or vibrational analysis using*MedeA Phonon*

- Setup of crystal structures for binary, ternary, and pseudoternary alloys with cubic or hexagonal lattices

*MedeA Environment*

To learn more about a systematic approach to alloy design using *MedeA’s* Universal CLuster Expansion method, check out our datasheet on MedeA UNCLE.

[1] | MedeA and Materials Design are registered trademarks of Materials Design, Inc. |

[2] | B. Velicky, S. Kirkpatrick, and H. Ehrenreich,
Phys. Rev. 175, 747 (1968)
(DOI) |

[3] | R. J. Elliott, J. A. Krumhansl, and P. L. Leath,
Rev. Mod. Phys. 46, 465 (1974)
(DOI) |

[4] | A. Zunger, S. H. Wei, L. G. Ferreira, and J. E. Bernard,
Phys. Rev. Lett. 65, 353 (1990)
(DOI) |

[5] | S. H. Wei, L. G. Ferreira, J. E. Bernard, and A. Zunger,
Phys. Rev. B 42, 9622 (1990)
(DOI) |

[6] | K. C. Hass, L. C. Davis, and A. Zunger,
Phys. Rev. B 42, 3757 (1990)
(DOI) |

[7] | R. Magri, S. Froyen, and A. Zunger,
Phys. Rev. B 44, 7947 (1991)
(DOI) |

[8] | C. Wolverton and V. Ozolins,
Phys. Rev. B 73, 144104 (2006)
(DOI) |

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