Optimization of site occupancies in minerals using quadratic programming

Abstract Atomic sites with multiple substituents are common in minerals, and correct site assignment of substituents in structure refinement is of fundamental importance. Substituents must be assigned to particular sites to fit the observed site scattering and chemical analysis, but the assignments are rarely made with mathematical rigor. We propose a quadratic programming approach to calculating optimal site assignments, thereby providing crystallographers with a mathematically robust starting point for the determination of site occupancies. Our program, OCCQP, implements this approach within the widely used MATLAB programming environment. User-defined weights may be assigned to the structural formula, site scattering, and bond-valence sums. The program is useful for evaluation of site occupancies in newly refined structures and re-evaluation of previously published structures with ad hoc site assignments.

[1]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[2]  C. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[3]  D. R.,et al.  Empirical Bond-Strength-Bond-Length Curves for Oxides , 2001 .

[4]  B. Craven,et al.  Internal molecular vibrations from crystal diffraction data by quasinormal mode analysis , 1985 .

[5]  Charles L. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[6]  I. D. Brown,et al.  Bond‐valence parameters obtained from a systematic analysis of the Inorganic Crystal Structure Database , 1985 .

[7]  I. Brown.  14 - The Bond-Valence Method: An Empirical Approach to Chemical Structure and Bonding , 1981 .

[8]  William L. Goffe,et al.  SIMANN: FORTRAN module to perform Global Optimization of Statistical Functions with Simulated Annealing , 1992 .

[9]  F. Hawthorne.  Quantitative characterization of site-occupancies in minerals , 1983 .

[10]  P. Burns,et al.  Reassignment of cation site occupancies in tourmaline: Al-Mg disorder in the crystal structure of dravite , 1993 .

[11]  M. O'Keeffe.  The prediction and interpretation of bond lengths in crystals , 1989 .

[12]  Matts Roos,et al.  MINUIT-a system for function minimization and analysis of the parameter errors and correlations , 1984 .

[13]  J. Grice,et al.  A new anhydrous amphibole from the Hoskins mine, Grenfell, New South Wales, Australia: Description and crystal structure of ungarettiite, NaNa2(Mn2+2Mn3+3 )Si8O22O2 , 1995 .

[14]  Michael O'Keeffe,et al.  Bond-valence parameters for solids , 1991 .

[15]  G. Artioli,et al.  Cation partitioning versus temperature in (Mg0.70Fe0.23)Al1.97O4 synthetic spinel by in situ neutron powder diffraction , 1999 .