9.4 Morphology of single crystals 179

Figure 9.8. Structural form of diamond as predicted from PBC analysis.

9.4Morphology of single crystals

9.4.1Structural form

If PBC analysis (see Section 4.2) is performed based on the crystal structure of diamond (Fig. 9.1), we see that {111} is an F face containing three PBCs, and that {110} is an S face containing one PBC. On the other hand, since dangling bonds on the surface are perpendicularly oriented in successive atomic layers, {100} can be regarded as having a sort of double-decker structure, with no PBCs included, and so it should be classified as a K face. From this analysis, it is expected that {111} is the only smooth face on which layer or spiral growth can take place, whereas {100} corresponds to a rough interface which grows by an adhesive-type mechanism.

The {110} face is an S face, on which layer or spiral growth is not expected, and the face may appear by the piling up of the edges of the steps of the growth layers on {111} faces. Therefore, the morphology of a single crystal of diamond that can be expected based only on structural characteristics, entirely neglecting the effect of environmental conditions, is an octahedron bounded by largely developed {111} faces, accompanied by narrow, striated {110} faces, with no {100} faces appearing as crystal faces, as shown in Fig. 9.8. On {111} faces, growth or spiral layers with triangular form of the same orientation as the triangle of the face will be observed, whereas {110} faces are characterized by the development of striations, and {100} faces (if they appear) will exhibit rough and rugged surfaces.

Growth forms are the forms of a crystal determined by the structural characteristics and the effects due to environmental conditions. Assuming that a growing crystal is bounded by two F faces only, the Tracht of the crystal is determined by the

180Diamond

relative normal growth rate of two F faces R, i.e. RA: RB. If both faces grow by the spiral growth mechanism, the R values are determined by the height of the spiral

growth layer h, the advancing rate of the step v, and the step separation 0 in the following form: R hv/ 0. Since 0 19rc, and rc is related to the free energy of the step

2, and the driving force 3, the factors affecting R are (1) the ambient phase, i.e. whether it is a vapor or solution phase; (2) the solute–solvent interaction energies, i.e. the solvent component; (3) the driving force and growth conditions; (4) the impurities; and (5) the temperature and pressure. On the other hand, when a growing crystal is bounded by an F face and a K face (or an S face), the solute–solvent interaction or impurity adsorption may sometimes suppress the R value of a K face, and the K face, which should disappear from the crystal, may develop as large as a habit-controlling face. Conversely, there is a possibility that a K face (or an S face) transforms into an F face, or that an F and an S face transform into a K face.

9.4.2 Characteristics of {111}, {110}, and {100} faces

The most commonly encountered forms of single crystals of diamond in nature are octahedral or forms bounded by curved faces originating therefrom. Although Seal concluded that all {110} faces appeared by dissolution [2], it is seen in one of Seal’s own photographs (Fig. 6.1(c)) that a (110) face with straight striations appears by a series of alternating micro-facets of (111) and (111). Although it must be accepted that the larger, rounded {110} faces (in reality, these are {hhl} faces) appear by dissolution, there are cases in which {110} faces appear due to growth. Such {110} faces are stepped faces characterized by striations only. {110} faces showing these types of characteristics (Fig. 9.9) are often encountered among micro-diamond crystals of micrometer size. In contrast to this, step patterns due to the development of growth layers have never been observed on {100} faces; only rugged surfaces are seen on this face, as shown clearly in Fig. 9.2. Since natural diamond crystals bounded by {100} faces always show the surface characteristics seen in Fig. 9.2, the term cuboid instead of cube is used.

On the {111} face of the diamond crystal from Siberia (Fig. 9.10), which is only partially dissolved, triangular growth hillocks with the same orientation as the triangle of the face are observed. The height of the steps of the growth layers consisting of the growth hillocks is less than 0.5 nm. It is confirmed that there is a P- type trigon at each summit of the respective growth hillocks, which correspond to the outcrops of screw dislocations, as identified by X-ray topography (Fig. 9.11), and so it can be concluded that the crystal grew by the spiral growth mechanism on {111} faces [12]. It is a characteristic of dislocations of this type that a bundle of dislocations originate from the center of a crystal and radiate nearly perpendicularly to the {111} surface; they have Burgers vector 110 .

9.4 Morphology of single crystals 181

Figure 9.9. SEM photograph of {110} faces appearing by growth, characterized by the

development of straight striations parallel to the edge of {111}.

9.4.3Textures seen inside a single crystal

Slight deviations in physical perfection and chemical homogeneity in nearly perfect single crystals can be visualized by etching, X-ray topography, cathodoluminescence methods, etc. These deviations provide superb records, revealing fluctuations in growth rate and partitioning of impurity elements through the growth process, as already discussed in Chapter 6.

As discussed above, most natural diamond crystals are characterized by dislocation bundles originating from the center of a crystal and running nearly perpendicularly to the {111} surface with a growth banding pattern parallel to {111}. There are, however, crystals showing complicated curved banding patterns, the origin of which will be a subject for future study.

Some crystals exhibit a texture called a center-cross pattern, the origin of which was, at one time, a subject of controversy, as to whether the origin was by growth or by plastic deformation. The center-cross pattern is schematically illustrated in Fig. 9.12; it corresponds to a texture shown by the growth sectors of two coexisting crystal faces, {111} and {100}. This pattern indicates that the arms of the cross correspond to the growth sectors of {100}, which disappear at the later stage of