Showing co-relationships between elements and minerals in a three-dimensional matrix

Abstract

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 the distribution of those species. 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 took 30 key elements chosen by the research team 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 can already show interesting 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?"

For future works using the three dimensional matrix, many other ideas have been proposed and discussed within the research team. 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, thus to estimate the extent to which the element triplets occur with greater or lesser frequency. 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 be other properties. Using cation and anion oxidation states, not elements may allow use to see more dramatic correlation based on redox.

Full text

Showing co-relationships between elements
and minerals in a three-dimensional matrix
Xiaogang Ma1,2 (max@uidaho.edu), Daniel Hummer3, Robert Hazen4, Joshua Golden5,
Peter Fox2, Michael Meyer4
1 University of Idaho, Moscow, ID; 2 Rensselaer Polytechnic Institute, Troy, NY; 3 Southern Illinois University,
Carbondale, IL; 4 Carnegie Institution for Science, Washington, DC; 5 University of Arizona, Tucson, AZ
Background
• 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.
Ideas for Future Work
This three-dimensional matrix visualization
method is applicable to many other systems.
• 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.
Case Study 1: Co-Existence of Key Elements in
Minerals
• 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.
• Developed function to manipulate the matrix, so a user can rotate the
matrix, highlight certain cubes or patterns by taking logarithmic
calculation of values, and slice one or more planes out from the matrix to
see patterns in a 2D context.
Data Sources
http://rruff.info/
http://rruff.info/ima/
IMA Database of Mineral Properties
Created and maintained by the RRUFF Project
in partnership with the IMA.
http://www.mindat.org/
Computer Technologies
• jQuery (https://jquery.com/) for parsing
datasets
• Three.js (http://threejs.org/) for the 3D cube
matrix visualization
• A few other libraries and JavaScript
programming for interactive data analysis
Case Study 3: Co-relations between Primary and
Secondary Cobalt Minerals
• Minerals are arranged by their 1st occurrence time (Old to young: left to
right along X axis; top to bottom along Y axis).
• Values in cells represent the number of localities at which both of the
minerals occur.
Case Study 2: Impact of A Third Element on
Correlation Between Two Existing
Elements in Minerals
• Constructed a 72 x 72 x 72 matrix for 72 mineral-forming elements, and
used a chi-squared test to generate p-values to be filled in that matrix.
• The aim is to answer the question "Does the presence of element Z affect
the correlation between elements X and Y in mineral species?"
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