Symmetry statistics of mineral – paragenetic mode pairs

Characterizing the types of crystalline structures that form in different environments helps us to better interpret the geologic record and deepens our understanding of mineral stability. To this end, the Dolivo – Dobrovol’sky symmetry index provides a convenient way to quantify the statistical trends in the symmetry of minerals over time (Bermanec et al. 2022). Behavior of the Dolivo - Dobrovol’sky symmetry index was investigated for different paragenetic modes of minerals (Hazen and Morrison 2022). Two datasets were used and compared (code and datasets are available on https://github.com/NoaVidovic/pgm-mineral-pairs-pg). The first one used only minerals, and each mineral was considered just once. In contrast, in the mineral–paragenetic mode pair dataset, minerals were counted once for each of the paragenetic modes in which they occurred.

The paragenetic mode dataset incorporates a number of properties associated with each of more than 60 modes of formation, including relative age and order of that mode’s first appearance, estimated minimum and maximum temperature and pressure of formation, and duration. Paragenetic mode order does not substantially affect the symmetry index of minerals. However, some trends are evident when inspecting the properties of given paragenetic modes. The symmetry indices show a strong correlation with the maximum temperature, maximum pressure, and minimum pressure of paragenetic modes they belong to (Hazen et al. 2022) with correlation coefficients of 69%, 84% and 95%, respectively when using the mineral dataset. These trends show that minerals formed at higher temperature display higher overall symmetry. Trends for pressure are enigmatic: correlations show that minerals formed at higher minimum pressure tend to favor lower symmetry, whereas minerals formed at higher maximum pressure tend to favor higher symmetry.

When using the mineral–paragenetic mode dataset, the correlation coefficients are significantly lower at 42%, 30% and 89% for maximum temperature, maximum pressure, and minimum pressure, respectively. The lower correlation coefficients obtained using the mineral–paragenetic mode pairs might indicate that the paragenetic mode is not as important in terms of trends in symmetry as initially thought. On the other hand, considering a much higher correlation coefficient for the mineral dataset, perhaps there is a more dominant effect where certain P-T conditions tend to favor certain types of symmetry at equilibrium.