Derivation of phase diagrams : A new methodology was derived for theoretical derivation of stability and metastability regions of clay minerals in an aqueous environment. Some errors in older methods have been rectified. Derived diagrams show good fit with experimental results. A program in Mathematica has been developed for this purpose. It is also possible to derive the phase diagrams of mineral groups with data for several minerals included in each group.

Evaluation of standard free energies of formation of clay minerals 

An empirical method has been developed to overcome the limited availability of experimental data on standard free energies of formation (DG0f) of variable composition clay minerals. Using this method, it is possible to derive DG0f of any clay mineral with only knowledge of its chemical composition. Development of this procedure involved solving a complex mathematical problem for an iterative least squares fitting of data in an exponential equation containing a residual. This method provides very close estimates of DG0f with experimental data and is a versatile means of deriving standard free energies of formation of clay minerals. A program in C and another in Mathematica has been developed.

What's 

Describing clay mineral compositions with fuzzy mathematics 

A novel approach has been  proposed which allows the quantification of compositional vagueness in clay minerals. The method involves the use of advanced statistics for derivation of fuzzification parameters and further development of a methodology for evaluation of membership functions or belongingness of a mineral to its own group as well as the quantification of its resemblances to other groups. This method provides a means of grading clay minerals, evaluating how ‘good’ a sample is, and defining the extent of transition to other phases. It could provide a framework for the analysis of other complex chemical systems in geology and metallurgy.

Fuzzy phase diagrams for clay minerals : This represents the integration of fuzzy mathematics with thermodynamics and geochemistry, resulting in the opening up of a novel approach for modelling of geochemical processes. The first ever fuzzy phase diagrams constructed, show graded zones of clay mineral occurrences. The 2-D and 3-D diagrams depict grades of mineral occurrences under varying chemical environments and give excellent agreement with experimental observations. A program in Mathematica has been developed for the purpose.  

Clay Mineral Classification & Grading

Statistical analysis can be use to classify a clay mineral into their groups or subgroups. Only the composition data is needed. This method can complement or substitute experimental methods for determination of the nature of a clay mineral.