Nespolo M, Ferraris G, Takeda H
National Institute for Research in Inorganic Materials, Research Centre for Creating New Materials, Ibaraki, Japan.
Acta Crystallogr A. 2000 Mar;56 (Pt 2):132-48. doi: 10.1107/s0108767399014907.
The geometry of the diffraction pattern from twins and allotwins of the four basic mica polytypes (1M, 2M1, 3T, 2M2) is analysed in terms of the 'minimal rhombus', a geometrical asymmetric unit in reciprocal space defined by nine translationally independent reciprocal-lattice rows. The minimal rhombus contains the necessary information to decompose the reciprocal lattice of twins or allotwins into the reciprocal lattices of the individuals. The nine translationally independent reciprocal-lattice rows are divided into three types (S, D and X): rows of different type are not overlapped by the n x 60 degrees rotations about c*, which correspond to the relative rotations between pairs of twinned or allotwinned individuals. A symbolic representation of the absolute orientation of the individuals, similar to that used for layers in polytypes, is introduced. The polytypes 1M and 2M1 undergo twinning by reticular pseudo-merohedry with five pairs of twin laws: they produce twelve independent twins, of which nine can be distinguished by the minimal rhombus analysis. The 2M2 polytype has two pairs of twin laws by pseudo-merohedry, which give a single diffraction pattern geometrically indistinguishable from that of the single crystal, and three pairs of twin laws by reticular pseudo-merohedry, which give a single diffraction pattern different from that of the single crystal. The 3T polytype has three twin laws: one corresponds to complete merohedry and the other two to selective merohedry. Selective merohedry produces only partial restoration of the weighted reciprocal lattice built on the family rows and the presence of twinning can be recognized from the geometry of the diffraction pattern.
从四个基本云母多型体（1M、2M1、3T、2M2）的孪晶和重孪晶的衍射花样几何结构出发，依据“最小菱形”进行分析。“最小菱形”是倒易空间中的一个几何不对称单元，由九条平移独立的倒易点阵行定义。最小菱形包含将孪晶或重孪晶的倒易点阵分解为各个体的倒易点阵所需的信息。九条平移独立的倒易点阵行分为三种类型（S、D和X）：不同类型的行不会因绕c*轴旋转n×60°而重叠，该旋转对应于孪晶或重孪晶个体对之间的相对旋转。引入了一种类似于用于多型体中层的个体绝对取向的符号表示。1M和2M1多型体通过网状假同形孪晶以五对孪晶律孪生：它们产生十二个独立的孪晶，其中九个可通过最小菱形分析区分。2M2多型体通过假同形孪晶有两对孪晶律，其给出的单晶衍射花样在几何上与单晶的无法区分，通过网状假同形孪晶有三对孪晶律，其给出的单晶衍射花样与单晶的不同。3T多型体有三条孪晶律：一条对应于完全同形孪晶，另外两条对应于选择性同形孪晶。选择性同形孪晶仅使基于族行构建的加权倒易点阵部分恢复，并且孪晶的存在可从衍射花样的几何结构中识别出来。
