Section 3.3.1. Crystal aggregates and intergrowths

(i) Arbitrary intergrowth: Aggregation of two or more crystal grains with arbitrary orientation, i.e. without any systematic regularity. Examples are irregular aggregates of quartz crystals (Bergkristall) in a geode and intergrown single crystals precipitated from a solution. To this category also belong untextured polycrystalline materials and ceramics, as well as sandstone and quartzite.

(ii) Parallel intergrowth: Combination of two or more crystals with parallel (or nearly parallel) orientation of all edges and faces. Examples are dendritic intergrowths as well as parallel intergrowths of spinel octahedra (Fig. 3.3.1.1a) and of quartz prisms (Fig. 3.3.1.1b). Parallel intergrowths frequently exhibit re-entrant angles and are, therefore, easily misinterpreted as twins.

Figure 3.3.1.1 | top | pdf | Parallel intergrowth (a) of spinel octahedra and (b) of hexagonal quartz prisms. Part (a) after Phillips (1971, p. 172), part (b) after Tschermak & Becke (1915, p. 94).

In this context the term mosaic crystal must be mentioned. It was introduced in the early years of X-ray diffraction in order to characterize the perfection of a crystal. A mosaic crystal consists of small blocks (size typically in the micron range) with orientations deviating only slightly from the average orientation of the crystal; the term `lineage structure' is also used for very small scale parallel intergrowths (Buerger, 1934, 1960a, pp. 69–73).

(iii) Bicrystals: This term is mainly used in metallurgy. It refers to the (usually synthetic) intergrowth of two single crystals with a well defined orientation relation. A bicrystal contains a grain boundary, which in general is also well defined. Usually, homophase bicrystals are synthesized in order to study the structure and properties of grain boundaries. An important tool for the theoretical treatment of bicrystals and their interfaces is the coincidence-site lattice (CSL). A brief survey of bicrystals is given in Section 3.2.2 ; a comparison with twins and domain structures is provided by Hahn et al. (1999).

(iv) Growth sectors: Crystals grown with planar faces (habit faces), e.g. from vapour, supercooled melt or solution, consist of regions crystallized on different growth faces (Fig. 3.3.1.2). These growth sectors usually have the shapes of pyramids with their apices pointing toward the nucleus or the seed crystal. They are separated by growth-sector boundaries, which represent inner surfaces swept by the crystal edges during growth. In many cases, these boundaries are imperfections of the crystal.

Figure 3.3.1.2 | top | pdf | (a) Optical anomaly of a cubic mixed (K,NH4)-alum crystal grown from aqueous solution, as revealed by polarized light between crossed polarizers: (110) plate, 1 mm thick, horizontal dimension about 4 cm. (b) Sketch of growth sectors and their boundaries of the crystal plate shown in (a). The {111} growth sectors are optically negative and approximately uniaxial with their optical axes parallel to their growth directions [birefringence up to ; Shtukenberg et al. (2001)]. The (001) growth sector is nearly isotropic (). Along the boundaries A between {111} sectors a few small {110} growth sectors (resulting from small {110} facets) have formed during growth. S: seed crystal.

Frequently, the various growth sectors of one crystal exhibit slightly different chemical and physical properties. Of particular interest is a different optical birefringence in different growth sectors (optical anomaly) because this may simulate twinning. A typical example of this optical anomaly is shown in Fig. 3.3.1.2.

The phenomenon optical anomaly can be explained as follows: as a rule, impurities (or dopants) present in the solution are incorporated into the crystal during growth. Usually, the impurity concentrations differ in symmetrically non-equivalent growth sectors (which belong to different crystal forms), leading to slightly changed lattice parameters and physical properties of these sectors. Surprisingly, optical anomalies may occur also in symmetrically equivalent growth sectors (which belong to the same crystal form): as a consequence of growth fluctuations, layers of varying impurity concentrations parallel to the growth face of the sector (`growth striations') are formed. This causes a slight change of the interplanar spacing normal to the growth face. For example, a cubic NaCl crystal grown on cube faces from an aqueous solution containing Mn ions consists of three pairs of (opposite) growth sectors exhibiting a slight tetragonal distortion with tetragonality 10<sup>−5</sup> along their growth directions, and, hence, are optically uniaxial (Ikeno et al., 1968). Although this phenomenon closely resembles all features of twinning, it does not belong to the category `twinning', because it is not an intrinsic property of the crystal species, but rather the result of different growth conditions (or growth mechanisms) on different faces of the same crystal (growth anisotropy).

An analogous effect may be observed in crystals grown from the melt on rounded and facetted interfaces (e.g. garnets). The regions crystallized on the rounded growth faces and on the different facets correspond to different growth sectors and may exhibit optical anomalies.

The relative lattice-parameter changes associated with these phenomena usually are smaller than 10⁻⁴ and cannot be detected in ordinary X-ray diffraction experiments. They are, however, accessible by high-resolution X-ray diffraction.

(v) Translation domains: Translation domains are homogeneous crystal regions that exhibit exact parallel orientations, but are displaced with respect to each other by a vector (frequently called a fault vector), which is a fraction of a lattice translation vector. The interface between adjoining translation domains is called the `translation boundary'. Often the terms antiphase domains and antiphase boundaries are used. Special cases of translation boundaries are stacking faults. Translation domains are defined on an atomic scale, whereas the term parallel intergrowth [see item (ii) above] refers to macroscopic (morphological) phenomena; cf. Note (7) in Section 3.3.2.4.

(vi) Twins: A frequently occurring intergrowth of two or more crystals of the same species with well defined crystallographic orientation relations is called a twin (German: Zwilling; French: macle). Twins form the subject of the present chapter. The closely related topic of domain structures is treated in Chapter 3.4 .