Evolution of symmetry index in minerals

Abstract

Crystal structures of minerals are defined by a specific atomic arrangement within the unit‐cell, which follows the laws of symmetry specific to each crystal system. The causes for a mineral to crystallize in a given crystal system have been the subject of many studies showing their dependency on different formation conditions, such as the presence of aqueous fluids, biotic activity and many others. Different attempts have been made to quantify and interpret the information that we can gather from studying crystal symmetry and its distribution in the mineral kingdom. However, these methods are mostly outdated or at least not compatible for use on large datasets available today. Therefore, a revision of symmetry index calculation has been made in accordance with the growing understanding of mineral species and their characteristics. In the gathered data, we observe a gradual but significant decrease in crystal symmetry through the stages of mineral evolution, from the formation of the solar system to modern day. However, this decrease is neither uniform nor linear, which provides further implications for mineral evolution from the viewpoint of crystal symmetry. The temporal distribution of minerals based on the number of essential elements in their chemical formulae and their symmetry index has been calculated and compared to explore their behaviour. Minerals with four to eight essential elements have the lowest average symmetry index, while being the most abundant throughout all stages of mineral evolution. There are many open questions, including those pertaining to whether or not biological activity on Earth has influenced the observed decrease in mineral symmetry through time and whether or not the trajectory of planetary evolution of a geologically active body is one of decreasing mineral symmetry/increasing complexity.

Molecular assembly indices of mineral heteropolyanions: some abiotic molecules are as complex as large biomolecules

“… Hystad and colleagues [ 38 ] have demonstrated that more than 3000 additional mineral species on Earth exist, but have yet to be discovered and described. New mineral species are being discovered at a rate of approximately 100 species per year [ 39 ], and many of those display complex, previously unknown structures [ 34 , 40 ]. …”

Crystal Structure Complexity and Approximate Limits of Possible Crystal Structures Based on Symmetry-Normalized Volumes

“…An additional constraint arises from the mobility of chemical elements in depth of Earth where no partial melts occur and where only metasomatosis through supercritical fluids acts as a potential means of mobilizing and segregating less common elements [23]. Moreover, chemically bonded water augments the number of potential mineral species in general [11,24]. maining high Z data that are not silicates are phosphate-, arsenate-, borate-, or molybdate framework structures.…”

The Average Symmetry Index of Minerals Co-Varies with Their Hydrogen Content, Rarity, and Paragenetic Mode

“…In the effort to develop a more accurate metric of symmetry through time, in this paper, we did not only use the maximum multiplicities of holohedral classes of each crystal system but rather the maximum multiplicities of all 32 point groups. This approach resulted in a formula similar to the one given by Bermanec et al [30]:…”

“…Starting with the pioneering work of Naumann [3], who investigated the distribution of 546 mineral species within crystal systems, several researchers have considered the world of mineral symmetry from a statistical standpoint [4][5][6][7][8][9][10]. Bermanec and colleagues [11] investigated symmetry distributions among 5674 International Mineralogical Association Minerals 2024, 14, 387 2 of 11 (IMA)-approved minerals species as of October 2022 from https://rruff.info/ima (accessed on 5 March 2024).…”

“…Bermanec et al [29,30] revised symmetry index calculations from Yushkin et al [15], Dolivo-Dobrovol'sky [14], and Urusov [16] and applied calculations to characterize the decrease in average symmetry indices throughout the stages of mineral evolution described by Hazen and colleagues [31,32]. Because the Dolivo-Dobrovol'sky approach was based on the multiplicity of a holohedral point group of a crystal system, it could also be easily adapted and used for other point groups and space groups.…”