Topology, mathematical quantification, and computer modeling of tectosilicate framework structures.

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  • テクトケイ酸塩フレームワーク構造のトポロジー，数量化，コンピュータモデリング
  • シリーズ造岩鉱物各論 テクトケイ酸塩フレームワーク構造のトポロジー、数量化、コンピュータモデリング
  • シリーズゾウガン コウブツ カクロン テクトケイ サンエン フレームワーク コウゾウ ノ トポロジー スウリョウカ コンピュータモデリング

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Framework structures of tectosilicates including zeolite, silica and feldspar minerals are reviewed on the basis of concentric cluster (CCL). The structural characteristics of them can be simply represented by the points (Si or Al atoms) and the lines connecting between the points. Starting from a given point, an nth CCL can be graphically defined as a set of all the points ranging from topological distance 0 to n, and all the lines responsible for the connection between them. The topological distance used here means the shortest step numbers responsible for the connection between two points, not the geometrical distance. As any kind of tectosilicate frameworks can be completely covered with the CCL by extending its topological distance from 0 to n, the topological characteristics of them are realized on a series of these CCLs. In order to quantify these CCLs, the front nodes are newly defined, and a concept of the coordination degree sequence (CDS) is introduced. In the CDS, the front nodes are characterized in terms of their topological valence numbers. The CDS can be effectively applied to the topological characterization, the classification, and the systematic computer modeling of tectoslicate frameworks. Some of application examples are shown.

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