Prediction of binary hard-sphere crystal structures.

We present a method based on a combination of a genetic algorithm and Monte Carlo simulations to predict close-packed crystal structures in hard-core systems. We employ this method to predict the binary crystal structures in a mixture of large and small hard spheres with various stoichiometries and diameter ratios between 0.4 and 0.84. In addition to known binary hard-sphere crystal structures similar to NaCl and AlB2, we predict additional crystal structures with the symmetry of CrB, gammaCuTi, alphaIrV, HgBr2, AuTe2, Ag2Se, and various structures for which an atomic analog was not found. In order to determine the crystal structures at infinite pressures, we calculate the maximum packing density as a function of size ratio for the crystal structures predicted by our GA using a simulated annealing approach.

[1]  N. Ashcroft,et al.  Weighted-density-functional theory of nonuniform fluid mixtures: Application to freezing of binary hard-sphere mixtures. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[2]  P. A. Monson,et al.  Substitutionally ordered solid solutions of hard spheres , 1995 .

[3]  Alfons van Blaaderen,et al.  Self-assembly route for photonic crystals with a bandgap in the visible region. , 2007, Nature materials.

[4]  A. Oganov,et al.  Crystal structure prediction using ab initio evolutionary techniques: principles and applications. , 2006, The Journal of chemical physics.

[5]  P. Pusey,et al.  Stability of the binary colloidal crystals AB2 and AB13. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  T. Hales The Kepler conjecture , 1998, math/9811078.

[7]  M. Dijkstra,et al.  Fabrication of large binary colloidal crystals with a NaCl structure , 2009, Proceedings of the National Academy of Sciences.

[8]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[9]  D. Frenkel,et al.  Entropy-driven formation of a superlattice in a hard-sphere binary mixture , 1993, Nature.

[10]  B. Hartke Global geometry optimization of clusters using genetic algorithms , 1993 .

[11]  Vincent H. Crespi,et al.  Predictions of new crystalline states for assemblies of nanoparticles: Perovskite analogues and 3-d arrays of self-assembled nanowires , 2003 .

[12]  Matt Probert,et al.  A periodic genetic algorithm with real-space representation for crystal structure and polymorph prediction , 2006, cond-mat/0605066.

[13]  Jorge Nocedal,et al.  A Limited Memory Algorithm for Bound Constrained Optimization , 1995, SIAM J. Sci. Comput..

[14]  Alfons van Blaaderen,et al.  Layer-by-Layer Growth of Binary Colloidal Crystals , 2002, Science.

[15]  Bartlett,et al.  Superlattice formation in binary mixtures of hard-sphere colloids. , 1992, Physical review letters.

[16]  C. Patrick Royall,et al.  Ionic colloidal crystals of oppositely charged particles , 2005, Nature.

[17]  Christos N. Likos,et al.  Complex alloy phases for binary hard-disc mixtures , 1993 .

[18]  Ho,et al.  Molecular geometry optimization with a genetic algorithm. , 1995, Physical review letters.

[19]  D. Frenkel,et al.  The stability of the AB13 crystal in a binary hard sphere system , 1993 .

[20]  Jonathan K. Kummerfeld,et al.  The densest packing of AB binary hard-sphere homogeneous compounds across all size ratios. , 2008, The journal of physical chemistry. B.

[21]  Bartlett,et al.  Superlattice formation in mixtures of hard-sphere colloids , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[22]  J. V. Sanders,et al.  Close-packed structures of spheres of two different sizes II. The packing densities of likely arrangements , 1980 .

[23]  S. Yoshimura,et al.  ORDER FORMATION IN BINARY MIXTURES OF MONODISPERSE LATEXES , 1985 .

[24]  K.-S. Cho,et al.  Three-dimensional binary superlattices of magnetic nanocrystals and semiconductor quantum dots , 2003, Nature.

[25]  Yong L. Xiao,et al.  Genetic algorithm: a new approach to the prediction of the structure of molecular clusters , 1993 .

[26]  Gerhard Kahl,et al.  Predicting equilibrium structures in freezing processes. , 2005, The Journal of chemical physics.

[27]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[28]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[29]  R. Koole,et al.  Binary superlattices of PbSe and CdSe nanocrystals. , 2008, Journal of the American Chemical Society.

[30]  E. Parthé Space filling of crystal structures A contribution to the graphical presentation of geometrical relationships in simple crystal structures , 1961 .

[31]  M. Dijkstra,et al.  Stability of LS and LS2 crystal structures in binary mixtures of hard and charged spheres. , 2009, The Journal of chemical physics.