The present study deals with accurate identification of polytypes, twins, and allotwins – oriented crystal associations of more than one polytype. The trioctahedral 1:1 layered silicate cronstedtite was studied using single-crystal X-ray diffraction data collected with a four-circle diffractometer equipped with a CCD detector. The sample from the skarn occurrence, Ouedi Beht, El Hammam, Morocco, was explored. It contains cronstedtite in fibrous massive aggregates in the central part, and euhedral crystals in surrounding veinlets and druses. The reciprocal space (RS) sections created by the diffractometer software and presented here were used to determine the OD (ordered-disordered) subfamilies (Bailey’s group A, B, C, D) and to identify polytypes. The chemical compositions of some crystals were determined thereafter by electron probe microanalysis (EPMA-WDS). Some crystals studied are more or less complicated allotwins. Polytypes were thus separated by cleaving crystals into smaller parts in many cases. All polytypes found belong to subfamilies A or D. The following polytypes of the subfamily A were identified: 2M1 (a = 5.49, b = 9.51, c = 14.40 Å, β = 97.30°, space group Cc), 1M (a = 5.51, b = 9.54, c = 7.33 Å, β = 104.5°, Cm), 3T (a = 5.51, c = 21.32 Å, P31), 6T2 (a = 5.50, c = 42.60 Å, P31). 2M1 and 3T were present as isolated crystals or separated by cleaving, otherwise all these polytypes are parts of allotwins. The 2M1 polytype is sometimes twinned by reticular pseudo merohedry with twin index n = 3 and 120° rotation about the chex axis as the twin operation. Allotwins of 1M + twinned 2M1 polytypes are also present. Another kind of twinning, with rotation by (2n+1)×60° about chex is rare. The subfamily D is represented mostly by 2H1 and 2H2 polytypes, a = 5.50, c = 14.25 Å, space groups P63cm (2H1), P63 (2H2). In addition, several six-layer (a = 5.49, c = 42.80 Å), mostly non-MDO polytypes were separated from allotwins by cleaving. In order to identify them, 24 possible stacking sequences were modeled, diffraction patterns calculated, graphical identification diagrams constructed, and comparisons made with actual RS sections. This simulation revealed that five pairs of sequences provided identical diffraction patterns. Polytypes actually found correspond to the following sequences: 1 (6T1), 5 (proposed Ramsdell’s symbol 6T3), 8+10 (6T5), 11+12 (6T4), 24 (6T6, trigonal polytypes, space group type P3), 22 (6R1), and 23 (6R2, rhombohedral polytypes, space group type R3c and R3, respectively). The RS section corresponding to the hexagonal polytype 6H2 (sequence 14) was also found. However, diffraction patterns geometrically indistinguishable can be produced by the twin with rotation by 180° about chex as a twin operation of the rhombohedral polytype 6R2 (sequence 23). Several aggregates with fiber texture of polytype 2H2 were separated from the central part. Use of EPMA-WDS revealed Fe and Si along with significant amounts of Mn and Mg. Crystals from veins were more Mn- and Mg-rich than these from the central part. Traces of Cl, S, and Al are present also.

中文翻译：

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来自摩洛哥 El Hammam 的 Ouedi Beht 的 Cronstedtite 的多型性

本研究涉及准确识别多型、双胞胎和同种双胞胎——一种以上多型的定向晶体关联。使用配备有 CCD 检测器的四圆衍射仪收集的单晶 X 射线衍射数据研究了三八面体 1:1 层状硅酸盐方铅矿。对来自摩洛哥 El Hammam 的矽卡岩矿点 Ouedi Beht 的样本进行了探索。中心部呈纤维状块状聚集体中的钙辉石，周围的细脉和晶须中含有自面体晶体。由衍射仪软件创建并在此处介绍的倒数空间 (RS) 部分用于确定 OD（有序无序）亚族（Bailey 组 A、B、C、D）并识别多型。之后通过电子探针微量分析（EPMA-WDS）确定了一些晶体的化学成分。研究的一些晶体或多或少是复杂的同分双晶。因此，在许多情况下，通过将晶体切割成更小的部分来分离多型体。发现的所有多型都属于亚科 A 或 D。确定了亚科 A 的以下多型：2M1（a = 5.49，b = 9.51，c = 14.40 Å，β = 97.30°，空间群 Cc），1M（a = 5.51 , b = 9.54, c = 7.33 Å, β = 104.5°, Cm), 3T (a = 5.51, c = 21.32 Å, P31), 6T2 (a = 5.50, c = 42.60 Å, P31)。2M1 和 3T 以孤立的晶体形式存在或通过切割分离，否则所有这些多型体都是同种异体的一部分。2M1 多型有时通过具有孪晶指数 n = 3 和围绕 chex 轴旋转 120° 作为孪生操作的网状伪三面体孪生。也存在 1M + 孪生 2M1 多型的同种异体。另一种孪生，围绕 chex 旋转 (2n+1)×60° 是罕见的。亚科 D 主要由 2H1 和 2H2 多型表示，a = 5.50，c = 14.25 Å，空间群 P63cm (2H1)，P63 (2H2)。此外，通过切割将几个六层（a = 5.49，c = 42.80 Å）主要是非 MDO 多型体与 allotwins 分离。为了识别它们，对 24 个可能的堆叠序列进行了建模，计算了衍射图案，构建了图形识别图，并与实际 RS 剖面进行了比较。该模拟揭示了五对序列提供了相同的衍射图案。实际发现的多型对应如下序列：1（6T1）、5（建议的拉姆斯德尔符号6T3）、8+10（6T5）、11+12（6T4）、24（6T6，三角多型，空间群类型P3），22（6R1）和 23（6R2，菱面体多型，空间群类型 R3c 和 R3，分别）。还发现了对应于六角多型 6H2（序列 14）的 RS 部分。然而，作为菱面体多型 6R2（序列 23）的双胞胎操作，绕 chex 旋转 180° 的双胞胎可以产生几何上无法区分的衍射图案。从中心部分分离出几个具有多型 2H2 纤维质地的聚集体。EPMA-WDS 的使用揭示了 Fe 和 Si 以及大量的 Mn 和 Mg。来自静脉的晶体比来自中心部分的晶体更富含锰和镁。还存在痕量的 Cl、S 和 Al。作为菱面体多型 6R2（序列 23）的双胞胎操作，绕 chex 旋转 180° 的双胞胎可以产生几何上无法区分的衍射图案。从中心部分分离出几个具有多型 2H2 纤维质地的聚集体。EPMA-WDS 的使用揭示了 Fe 和 Si 以及大量的 Mn 和 Mg。来自静脉的晶体比来自中心部分的晶体更富含锰和镁。还存在痕量的 Cl、S 和 Al。作为菱面体多型 6R2（序列 23）的双胞胎操作，绕 chex 旋转 180° 的双胞胎可以产生几何上无法区分的衍射图案。从中心部分分离出几个具有多型 2H2 纤维质地的聚集体。EPMA-WDS 的使用揭示了 Fe 和 Si 以及大量的 Mn 和 Mg。来自静脉的晶体比来自中心部分的晶体更富含锰和镁。还存在痕量的 Cl、S 和 Al。来自静脉的晶体比来自中心部分的晶体更富含锰和镁。还存在痕量的 Cl、S 和 Al。来自静脉的晶体比来自中心部分的晶体更富含锰和镁。还存在痕量的 Cl、S 和 Al。