The purpose of the study is refining of the proposed earlier unified three-dimensional model for the positioning of chemical elements, minerals, and rocks in the earth's crust, as well as working out its description terminology and model system properties specification. The research methods included the logical and mathematical analysis of the model based on atomic weights of chemical elements, their valences and electronegativity, as well as on the atomic weights of chemical elements present in the composition of minerals and calculation of multidimensional proportionality indexes for each of given characteristics. The methods were used for further development of the previously introduced assumption that within the three-dimensional model minerals are arranged in the ascending order of the index of multidimensional proportionality of atomic weights of chemical elements in their composition, similarly to the way the chemical elements are positioned in the model according to the increase of their atomic weights. Both rocks and minerals are arranged in the ascending order of this index, whereas rocks correspond to a certain mineral in terms of the multidimensional proportionality index. As a result of the study, a general analysis of the system properties of vertical spatial groups of chemical elements of the model was carried out with groups being divided into two types depending on the presence of a gas or a solid chemical element in the first position. The variation patterns of chemical element valencies and electronegativity were studied in these spatial groups. Also, the analyses of multidimensional data were performed for the elements of these groups. The values of the multidimensional index were calculated for the first 760 minerals using the Agemarker open source program. The analysis of multivariate data confirmed the division of groups into two types. Having analyzed their mutual arrangement, the authors suggested the existence of gas channels of chemical element migration and determined possible migration paths of chemical elements in the three-dimensional model under the formation of some minerals. The relative position of some fields was considered in order to confirm the spatial characteristics of the three-dimensional model. The authors have introduced a new paradigm of geological research positioning minerals and rocks in a three-dimensional model and determining possible migration paths of chemical elements when minerals and rocks are formed.

The purpose of the study is refining of the proposed earlier unified three-dimensional model for the positioning of chemical elements, minerals, and rocks in the earth's crust, as well as working out its description terminology and model system properties specification. The research methods included the logical and mathematical analysis of the model based on atomic weights of chemical elements, their valences and electronegativity, as well as on the atomic weights of chemical elements present in the composition of minerals and calculation of multidimensional proportionality indexes for each of given characteristics. The methods were used for further development of the previously introduced assumption that within the three-dimensional model minerals are arranged in the ascending order of the index of multidimensional proportionality of atomic weights of chemical elements in their composition, similarly to the way the chemical elements are positioned in the model according to the increase of their atomic weights. Both rocks and minerals are arranged in the ascending order of this index, whereas rocks correspond to a certain mineral in terms of the multidimensional proportionality index. As a result of the study, a general analysis of the system properties of vertical spatial groups of chemical elements of the model was carried out with groups being divided into two types depending on the presence of a gas or a solid chemical element in the first position. The variation patterns of chemical element valencies and electronegativity were studied in these spatial groups. Also, the analyses of multidimensional data were performed for the elements of these groups. The values of the multidimensional index were calculated for the first 760 minerals using the Agemarker open source program. The analysis of multivariate data confirmed the division of groups into two types. Having analyzed their mutual arrangement, the authors suggested the existence of gas channels of chemical element migration and determined possible migration paths of chemical elements in the three-dimensional model under the formation of some minerals. The relative position of some fields was considered in order to confirm the spatial characteristics of the three-dimensional model. The authors have introduced a new paradigm of geological research positioning minerals and rocks in a three-dimensional model and determining possible migration paths of chemical elements when minerals and rocks are formed.

The topicality of the research comes from the need to obtain new knowledge about the manifestation of the periodic law in nature. Research aim is to associate the periodic system of chemical elements with the chemical composition and structure of natural objects. The research method suggests the creation of a solid model of the periodic system of chemical elements along with its comparison with ore formation objects as well as the manifestation of chemical elements isomorphism and some natural processes geochemistry. Research results. The solid version of the periodic table of the first 95 chemical elements together with a conventional zero element is proposed. Each volume cell characterizes a chemical element with an elementary crystal lattice of simple substance. Similar models can be composed of minerals and rocks associating with material substance of the earth's crust. 16 vertical groups in the model are arranged in a snake-like pattern. The model of the earth's crust with the “cubes” of chemical elements, minerals and mineral associations is proposed. The elements of adjacent spatial groups are naturally concentrated in combination, showing isomorphism while minerals enter the crystal lattice. The relative position of adjacent “cubes” follows the rule of translation in mutually perpendicular directions. The chemical elements of the first group can correspond spatially to volcanoes as well as mud volcanoes. The place of the zero chemical element is considered to be occupied by the elements of adjacent spatial groups. It is assumed that the faces of the “cube” of chemical elements are permeable areas through which chemical elements can be transferred. Summary. The confirmation of the model follows while considering ore formations, isomorphism of chemical elements in minerals and geochemistry of volcanic processes. 46 "Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal". No. 1. 2020 ISSN 0536-1028 Key words: chemical elements; solid model of periodic system; ore formations; isomorphism in crystals; geochemistry of volcanic processes.