The use of optimization methods---and thermodynamic implications---in mineralogy

This research has been bound together by one common theme: optimization. Chapters one and two are examples of traditional crystal structure refinements. Chapter three explains the site assign problem and documents a new approach to the problem. Chapter four extends the method to high temperatures; chapter five extracts the thermodynamic information found in the site occupancies. The appendix is a user's manual for OccQP.; In chapter one the structure and formula of brackebuschite was redefined. Also, the crystal chemistry of the d4 Mn 3+ ion in oxygen-based minerals is reviewed. Chapter two presents the refinement of redledgeite. It and its synthetic equivalent are important as a solid-state repository for toxic heavy-metal waste.; With chapter three, the traditional methods of determining site occupancies in minerals come in to question. The approach is based on crystal-structure data and chemical analyses of the compound, without making prior assumptions. This method provides the flexibility to evaluate trade-offs inherent in assigning occupancies on the basis of a single criterion. Multiple criteria may be used and their relative importance adjusted interactively. The optimizations yield excellent results.; Chapter four builds upon the foundation established in chapter three. This chapter is a reexamination of the cation partitioning of the same spinel used in chapter three. This method led to strikingly different results from the authors of the original study, supporting the general view that spinel undergoes a lambda transition at ∼1000K.; Chapter five extends the thermodynamic formulations for spinel. Most thermodynamic studies of spinels have focused on simple end-member compositions, meaning only two cations—at most—are distributed among the octahedral and tetrahedral sites. This chapter considers a 2–3 spinel having three cation species and vacancies. The standard thermodynamic technique is to consider migration of cations between octahedral and tetrahedral positions as reactions. The stability coefficient K_D gives the changes in Gibbs free energy of distribution, and statistical mechanics yields the entropy of distribution.