Twin planes

Fig. 5. Silver haUde grain morphologies for (a) cubic, precipitated in an environment having a silver ion concentration, [Ag" ], of ca 2.5 x 10 mol/L (b) octahedral, ca 6.0 x 10 mol/L and (c) tabular microcrystals, ca 1.0 x 10 ° mol/L. A cross section of a tabular grain revealing double parallel twin planes...

In ordinary diamond (2inc-blende stmcture) the wrinkled sheets He in the (111) or octahedral face planes of the crystal and are stacked in an ABCABC sequence. In real crystals, this ABCABC sequence continues indefinitely, but deviations do occur. For example, two crystals may grow face-to-face as mirror images the mirror is called a twinning plane and the sequence of sheets crossing the mirror mns ABCABCCBACBA. Many unusual sequences may exist in real crystals, but they are not easy to study. 

It is well known that in rutile-like structures the planes [Oil] and [0 3 1] are twinning planes. Hence, Chabre and Pannetier concluded that twinning faults in the planes [0 2 1] and [0 6 1] (the equivalent planes in the ramsdel-lite doubled unit cell) are the explanation for some features in the diffraction patterns of y — Mn02 e.g., the lineshift of the (1 1 0) reflection toward lower angles or the merging of the reflection groups (h 2 1 )/(h 4 0) and (h 6 1 )/(h 0 2). 

Figure 6. Projection of the manganese atoms in the ramsdellite lattice onto the be-plane. The oxygen atoms are not shown. The twinning planes [02l (above) and [061] (below) are marked with arrows. The twins at these planes are generated by rotating the shaded ramsdellite cells by either 60° or 120° around the a-axis. (Adapted from Ref. [47].)...

Twins are intergrown crystals such that the crystallographic directions in one part are related to those in another part by reflection, rotation, or inversion through a center of symmetry across a twin boundary. Twinned crystals are often prized mineralogical specimens. When twins are in contact across a well-defined plane (which is not always so), the boundary is generally called the composition plane. The only twins that are considered here will be reflection twins, where the two related parts of the crystal are mirror images (Fig. 3.22). The mirror plane that relates the two components is called the twin plane. This is frequently, but not always, identical to the plane along which the two mirror-related parts of the crystal join, that is, the composition plane. Repeated parallel composition planes make up a polysynthetic twin (Fig. 3.23). 

Figure 3.22 A (101) twin plane in rutile, Ti02. The two parts of the crystal are related by mirror symmetry. The unit cells in the two parts are shaded.

Twin geometry may refer to just one set of atoms in the crystal rather than all. This type of twinning is met, for example, in cases where a fraction of octahedral or tetrahedral cation sites in a close-packed array of anions are occupied in an ordered fashion. The close-packed anion array remains unchanged by the twin plane, which applies to the cation array alone (Fig. 3.24). These boundaries are of low energy and are often curved rather than planar. In oxides such as spinel, MgAl204, in which cations are distributed in an ordered fashion over some of the octahedral and tetrahedral sites, boundaries may separate regions that are twinned with respect to the tetrahedral cations only, the octahedral cations only or both. 

In some circumstances twin planes can alter the composition of a crystal. These consequences are described in Chapter 4. 

As in the case of twin planes, the antiphase relationship may affect only one part of the structure, for example, the cation substructure, while leaving the anion substructure unchanged. This is particularly common when the anion array can be considered to consist of a close-packed array of ions, which remains unchanged by the antiphase boundary (Fig. 3.28). 

Twin planes are most frequently internal boundaries across which the crystal matrix is reflected (Section 3.11). Some twin planes do not change the composition of the crystal while at others atoms are lost and a composition change can result. If faults that alter the composition are introduced in considerable numbers, the crystal will take on the aspect of a modular material and show a variable composition. 

The term chemical twinning (CT) is used to refer to repeated ordered twin planes that change the stoichiometry of the bulk significantly. New coordination polyhedra that do not occur in the parent structure are a feature of chemical twinning, and the occupation of these generates a number of new stuctures. Both aspects are illustrated by the PbS-Bi2S3 system. 

Figure 4.25 101 twinning in Ti02 (rutile) (a) Ti twin plane, no composition change (b) O twin plane, oxygen loss and (c) O twin plane, oxygen gain. 

Figure 4.26 Chemical twinning in the lead bismuth sulfosalts (a) idealized structure of galena, PbS, projected onto (110) (b) idealized structure of heyrovskyite and (c) idealized structure of lillianite. Shaded diamonds represent MS6 octahedra, those at a higher level shown lighter. Bi atoms are represented by shaded spheres, those at a higher level shown lighter. The twin planes are 113 with respect to the galena cell, and the arrows indicate planes of close-packed S atoms.

Twin planes play an important role in decreasing the current-carrying capability of the compounds, and they make device fabrication difficult. 

---