St. Petersburg Mining University (Saint-Petersburg, Russia):

Zakharova A. A., Postgraduate Student, zakharova.alena27614@gmail.com
Voytekhovsky Yu. L., Professor, Doctor of Geological and Mineralogical Sciences, Professor, Voytekhovskiy_YuL@pers.spmi.ru

A statistical approach has been proposed that allows strictly defining the structure of a rock (ore), isolating fields of various structures in barycentric diagrams, and comparing them with the processing results. An original method is proposed for predicting the washability defined as the separation of apatite grains from polymineral aggregations at the crushing and flotation stages. It develops and formalizes the current approach that combines the mineral composition of ores, their structures and textures into a multifactor semiquantitative model. The method is based on the calculation of the probabilities (frequencies) of all types of intergranular contacts recorded in a symmetric matrix under a microscope in petrographic thin sections. Its canonical diagonal shape allows identifying the rock (ore) structure type. The algebraic theory of quadratic forms is used to demonstrate that the structure identified using this method corresponds to one of the types of n-dimensional nondegenerate quadratic surfaces, where n is the number of minerals in the rock (ore). The structure is invariant for a certain fluctuation in the probabilities of intergranular contacts. The calculated probabilities uniquely identify the imaging point in the corresponding barycentric diagram. The Hardy–Weinberg boundary is important as it corresponds to the ideal uniform mixing of minerals and the balance of various intergranular contacts for any modal composition of rocks (ores). It allows distinguishing fields of different structures in barycentric diagrams. The method proposed offers a means to identify ores with different washability characteristics at early exploration stages.

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