Symmetry-adapted configurational modelling of fractional site occupancy in solids

A methodology is presented, which reduces the number of site-occupancy configurations to be calculated when modelling site disorder in solids, by taking advantage of the crystal symmetry of the lattice. Within this approach, two configurations are considered equivalent when they are related by an isometric operation; a trial list of possible isometric transformations is provided by the group of symmetry operators in the parent structure, which is used to generate all configurations via atomic substitutions. We have adapted the equations for configurational statistics to operate in the reduced configurational space of the independent configurations. Each configuration in this space is characterized by its reduced energy, which includes not only its energy but also a contribution from its degeneracy in the complete configurational space, via an entropic term. The new computer program SOD (site-occupancy disorder) is presented, which performs this analysis in systems with arbitrary symmetry and any size of supercell. As a case study we use the distribution of cations in iron antimony oxide FeSbO4, where we also introduce some general considerations for the modelling of site-occupancy disorder in paramagnetic systems.

[1]  Peter R. Slater,et al.  Atomic-Scale Investigation of Defects, Dopants, and Lithium Transport in the LiFePO4 Olivine-Type Battery Material , 2005 .

[2]  P. Dederichs,et al.  Corrected atomic limit in the local-density approximation and the electronic structure of d impurities in Rb. , 1994, Physical review. B, Condensed matter.

[3]  C. Catlow,et al.  Cation distribution and magnetic ordering in FeSbO4 , 2003 .

[4]  C. Catlow,et al.  A computer modeling study of redox processes on the FeSbO4 (100) surface , 2007 .

[5]  Neil L. Allan,et al.  Ordering in spinels—A Monte Carlo study , 2003 .

[6]  Blöchl,et al.  Projector augmented-wave method. , 1994, Physical review. B, Condensed matter.

[7]  P. Davies,et al.  Cation Ordering in Pb(Mg1/3Nb2/3)O3–Pb(Sc1/2Nb1/2)O3 (PMN–PSN) Solid Solutions , 2002 .

[8]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[9]  M. Islam,et al.  Cation doping and oxygen diffusion in zirconia: a combined atomistic simulation and molecular dynamics study , 1998 .

[10]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[11]  I. Todorov,et al.  Simulation of mineral solid solutions at zero and high pressure using lattice statics, lattice dynamics and Monte Carlo methods , 2004 .

[12]  P. B. Wilson,et al.  A computational study of the effect of Li–K solid solutions on the structures and stabilities of layered silicate materials—an application of the use of Condor pools in molecular simulation , 2005 .

[13]  C. Catlow,et al.  Distribution of Cations in FeSbO 4 : A Computer Modeling Study , 2004 .

[14]  The effect of cation coordination on the properties of oxygen vacancies in FeSbO4 , 2006 .

[15]  C. Catlow,et al.  Electronic structure and magnetic coupling inFeSbO4: A DFT study using hybrid functionals andGGA+Umethods , 2006 .

[16]  G. Kresse,et al.  Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set , 1996 .

[17]  N. Allan,et al.  Beyond the point defect limit: solid solutions, phase diagrams and trace-element partitioningPresented at the 78th International Bunsen Discussion Meeting on , 2003 .

[18]  Georg Kresse,et al.  Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements , 1994 .

[19]  LOW-ENERGY RELATIVISTIC EFFECTS AND NONLOCALITY IN TIME-DEPENDENT TUNNELING , 1999, quant-ph/0006110.

[20]  J. Perdew.  Generalized gradient approximation for the fermion kinetic energy as a functional of the density , 1992 .

[21]  J. Zaanen,et al.  Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators. , 1995, Physical review. B, Condensed matter.

[22]  A. Zunger,et al.  Self-interaction correction to density-functional approximations for many-electron systems , 1981 .

[23]  V. Heine,et al.  Scaling of thermodynamic mixing properties in garnet solid solutions , 2001 .

[24]  V. Anisimov,et al.  Band theory and Mott insulators: Hubbard U instead of Stoner I. , 1991, Physical review. B, Condensed matter.

[25]  J. Holden,et al.  Identification of the space group and detection of cationic ordering in iron antimonate using conventional and convergent-beam electron diffraction , 1987 .

[26]  N. Allan,et al.  Monte Carlo simulation of GaN/InN mixtures , 2005 .

[27]  Hafner,et al.  Ab initio molecular dynamics for open-shell transition metals. , 1993, Physical review. B, Condensed matter.

[28]  Kresse,et al.  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. , 1996, Physical review. B, Condensed matter.

[29]  J. Holden,et al.  The superlattice in iron antimonate: The detection of cationic ordering by electron diffraction , 1986 .

[30]  Georg Kresse,et al.  Electronic correlation effects in transition-metal sulfides , 2003 .

[31]  A. R. Ruiz-Salvador,et al.  A computer simulation study of distribution, structure and acid strength of active sites in H-ZSM-5 catalyst , 2000 .

[32]  C. I. Sainz-Díaz,et al.  Computational methods for the study of energies of cation distributions: applications to cation-ordering phase transitions and solid solutions , 2001, Mineralogical Magazine.