Crystal twin plane

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. 

Whereas only hh0 can diffract with the beam along a fivefold axis of the icosatwin because of the tilt of the cubic crystals, any plane in the zone 110 of the decatwin can diffract because the seed orients the cubic crystals with this zone axis parallel to the fivefold axis of the twin. It is seen from Fig. 1 (b) that the meridional spots of decagonal FeAl are the same as for icosahedral MnAl6, representing orders of hh0, but that there are many more equatorial spots, eleven instead of three. Indices are assigned in Table II some spots involve double... 

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. 

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 introduction to this chapter mentions that crystals often contain extended defects as well as point defects. The simplest linear defect is a dislocation where there is a fault in the arrangement of the atoms in a line through the crystal lattice. There are many different types of planar defects, most of which we are not able to discuss here either for reasons of space or of complexity, such as grain boundaries, which are of more relevance to materials scientists, and chemical twinning, which can contain unit cells mirrored about the twin plane through the crystal. However,... 

In close-packed stmctures or fee crystals, twinning is introduced by stacking faults. In this case, the excess energy at the twin plane ( = composition plane) is small, and so neither generation nor concentration of dislocations is required. In... 

Sometimes twinned crystals appear to be interpenetrating, as in the calcium fluoride twin illustrated in Fig. 41 6. Here we may imagine (in the crystal nucleus) a common 111 sheet of atoms, the symmetry of which is trigonal the crystal on one side of it is rotated 60° with respect to the one on the other side. The twin plane is not always respected during subsequent growth one individual may encroach on the domain of the other, so that the junction surface in the final crystal is irregular. 

Optical properties of twinned crystals. Each individual in a twin exhibits its own optical characteristics. If a gypsum twin is seen along its b axis and examined between crossed polarizers, it can be seen that each individual extinguishes independently. The twin plane (100) is a plane of symmetry of the composite whole, and the vibration directions of the two individuals, like all the other properties, are related to each other by this plane of symmetry (see Rig. 57 a). 

The relations between the optical properties of the two individuals are clear in the case of gypsum because the crystals lie on the microscopf slide on their (010) faces, so that the (100) twin planes are parallel to the line of vision., In some crystals the twin planes are inclined to the line of vision when the crystals are lying on their principal faces so that one is looking through two crystals in which the vibration directions ar not parallel to each other. In these circumstances, in the overlapping regions extinction does not occur when the polarizers are rotated. Whed... 

However, important differences exist. Martensite and its parent phase are different phases possessing different crystal structures and densities, whereas a twin and its parent are of the same phase and differ only in their crystal orientation. The macroscopic shape changes induced by a martensitic transformation and twinning differ as shown in Fig. 24.1. In twinning, there is no volume change and the shape change (or deformation) consists of a shear parallel to the twin plane. This deformation is classified as an invariant plane strain since the twin plane is neither distorted nor rotated and is therefore an invariant plane of the deformation. 

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