The Possible Topologic structure Types of Orthopyroxene with Space Group P21ca

The possible topologic structure types of orthopyroxene with space group P21ca comprise four kinds of tetrahedral chains and four kinds of octahedral sites.all of which are non-equivalent in symmetry,In these structure types,the skew of the octahedral layers has a sequence of --,There are sixteen possible combination forms for the rotation type of tetradral chain.Twelve of them violate Thompson ‘s sparity rule and the remainder constitutes two pairs.In each pair,the two polar forms show a relationship of anti-orientation for their polar a-axes.Thus,there are only two possible different topologic structure types for P21ca-orthopyroxene.The ratios of O-rotated and S-rotated tetrahedral chains for these two structure types are 3:1 and 1:3,respectively,In the view S-rotated tetrahedral chains for these two structure types are 3:1 and 1:3,respectively,In the view of crystallochemical principle,the most likely form is the one with a ratio of 3:1,and its constitutions of two stacks of I-beam,which are non-equivalent both in symmetry and in topology,are and the configurations of the two types of M2 sites are P.P and P.N,respectively,A complementary twinning on(100) would be formed between the anti-oriented structure pairs,and their twin boundary is exactly equivalent to the inversion boundary,Moreover,it is possible that the ordered structure would appear when the atom ratio of Mg:Fe is equal to 3:1 as well as to 1：1。

The possible topologic structure types of orthopyroxene with space groupP2 1 ca

The possible topologic structure types of orthopyroxene with space group P2₁ca comprise four kinds of tetrahedral chains and four kinds of octahedral sites, all of which are non-equivalent in sym metry. In these structure types, the skew of the octahedral layers has a sequence of ++ --. There are sixteen possible combination forms for the rotation type of tetrahedral chain. Twelve of them violate Thompson ’s parity rule and the remainder constitutes two pairs. In each pair, the two polar forms show a relationship of anti-orientation for their polara-axes. Thus, there are only two possible different topologic structure types for P2₁ca orthopyroxene. The ratios of Orotated andS- rotated tetrahedral chains for these two structure types are 3:1 and 1:3. respectively. In the view of crystallochemical principle, the most likely form is the one with a ratio of 3:1, and its constitutions of two stacks of I-beam, which are non-equivalent both in symmetry and in topology, areO+ O O-O O+S O-S +O S-O S+ or +O O-O O+ and the configurations of the two types of M2 sites areP.P and P.N, respectively. A complementary twinning on (100) would be formed between the anti-oriented structure pairs, and their twin boundary is exactly equivalent to the inversion boundary. Moreover, it is possible that the ordered structure would appear when the atom ratio of Mg:Fe is equal to 3:1 as well as to 1:1. This work was financially supported by the National Natural Science Foundation of China.