Finite noncrystallographic groups, 11-vertex equi-edged triangulated clusters and polymorphic transformations in metals
Finite noncrystallographic groups, 11-vertex equi-edged triangulated clusters and polymorphic transformations in metals
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DOI：
10.1107/s2053273314015733
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发表时间：
2014-11
期刊：
影响因子：
--
通讯作者：
A. Talis;V. Kraposhin
中科院分区：
文献类型：
--
作者：
A. Talis;V. Kraposhin
揭示了一组 Mathieu 群 M11 的陪集、一组 Steiner 系统 S(4, 5, 11) 的块和 11 顶点等边三角簇之间的一一对应关系。揭示的对应关系提供了S(4,5,11)系统的结构解释：双平面2-(11,5,2)到斯坦纳系统S(4,5,11)的映射唯一地确定了11顶点四面体簇，并且S(4,5,11)系统的自同构确定了所述11顶点四面体簇的唯一变换。所述转变对应于金属多晶型转变期间的局部重建。所提出的金属多晶型转变的对称性描述与实验数据一致。
The one-to-one correspondence has been revealed between a set of cosets of the Mathieu group M11, a set of blocks of the Steiner system S(4, 5, 11) and 11-vertex equi-edged triangulated clusters. The revealed correspondence provides the structure interpretation of the S(4, 5, 11) system: mapping of the biplane 2-(11, 5, 2) onto the Steiner system S(4, 5, 11) determines uniquely the 11-vertex tetrahedral cluster, and the automorphisms of the S(4, 5, 11) system determine uniquely transformations of the said 11-vertex tetrahedral cluster. The said transformations correspond to local reconstructions during polymorphic transformations in metals. The proposed symmetry description of polymorphic transformation in metals is consistent with experimental data.