SHOWING CO-RELATIONSHIPS BETWEEN ELEMENTS AND MINERALS IN A THREE-DIMENSIONAL MATRIX

The geoscience community has discovered more than 5000 mineral species so far. Studies are under way to explore the physical and chemical characteristics of those minerals as well as the spatial and temporal patterns in their distribution. In this work we aim to explore the co-relationships between those mineral species and the 72 mineral-forming elements, and we have carried out a few case studies since the beginning of 2016. In the first pilot study, we considered 30 key mineral-forming elements and constructed a 30 x 30 x 30 matrix, with the same list of elements along each axis. Each matrix element was first filled with the raw number of minerals in which elements X, Y, and Z coexist, and then rendered with a color according to the value of the number. With such a simple visualization the three-dimensional matrix reveals intriguing patterns in the co-relationships between elements and minerals. We also developed function to manipulate the matrix, so a user can rotate the matrix, highlight certain cubes or patterns, and slice one or more planes out from the matrix to see patterns in a two-dimensional context. In another case study we constructed a 72 x 72 x 72 matrix for all the 72 mineral-forming elements, and used a chi-squared test to generate values to be filled in that matrix. The aim of that case study is to answer the question: Does the presence of element Z affect the correlation between elements X and Y in mineral species?

This three-dimensional matrix visualization method is applicable to many other systems. For example, we can calculate the expected numbers of minerals with X + Y + Z based on average crustal abundances and compare the observed and expected numbers. In this way we estimate the extent to which the element triplets occur with greater or lesser frequency than would be expected based on average crustal abundances. Each axis can have multiple associated parameters. For example, we can also add data on electronegativity, ionic radius, atomic number, period, crustal abundance, etc. By using those parameters, we can order elements along the three axes automatically to test different clusterings of elements. Besides mineral counts, the value in each cube can also represent other properties. Using cation and anion oxidation states in place of chemical elements may allow us to see dramatic correlations based on redox.