6.3 Origin and spatial distribution of dislocations 123

Figure 6.4. Forms of growth sector boundaries depending on the relation between RA and RB.

growth will be interrupted by impurity adsorption and grows again with a high growth rate. As a result, growth banding appears intermittently, and the growth sector will appear, but will soon disappear (because of the high normal growth rate). In the growth sector formed by the morphologically most important crystal face, growth at near steady state is realized and growth banding is indistinct; this is because fluctuations in environmental conditions affect the growth rate far less than in growth sectors of rough or morphologically less important faces.

If conditions fluctuate during the growth process, the degree to which the growth rates are modified will change on different crystal faces. As a result, the growth sector boundaries will change from straight, to barrel, to reverse trumpet type in crystals bounded by two faces A and B, depending on whether RA RB,

RA RB, or RA RB, respectively.

6.3Origin and spatial distribution of dislocations

Dislocations are linear distortions of the lattice, and, unlike point defects, they are energetically undesirable. However, real crystals contain dislocations in the order 106 8/cm2, most of which are induced into the crystals during growth, and they also contribute to promoting the growth. As long as something occurs to generate a mismatch of the lattice planes, a dislocation will be generated, even though it is energetically unfavorable. In Fig. 6.5, X-ray topographs of two crystals, one grown from a seed with etched surface and another grown from an as-grown seed are compared (ref. [11], Chapter 7).

In Fig. 6.5(b), it is seen that dislocations in the seed are inherited, and that only a small number of dislocations generate from the seed surface, whereas in Fig. 6.5(a) most of the dislocations are newly generated on the seed surface. These newly generated dislocations start from initial liquid inclusions trapped at etch pits. The dislocations originate due to the failure of matching of lattice planes when inclusions

124 Perfection and homogeneity of single crystals

(a)

(b)

Figure 6.5. X-ray topographs demonstrating the differences in inheritance and generation of dislocations when (a) an etched crystal and (b) an as-grown crystal are used as seed crystals (ref. [11], Chapter 7). The crystal here is Ba(NO3)2, grown from

aqueous solution. g Burgers vector; S seed crystal.

–

are enclosed. Dislocations generated from inclusions are seen in the X-ray topograph of quartz shown in Fig. 6.1(c).

Phenomena similar to inclusions (in respect to the origin of dislocation generation) are encountered at various stages of real crystal growth processes. For example, (1) when neighboring side branches meet in dendritic growth, (2) where two adjacently growing crystals come into contact, (3) at grain boundaries of slightly misoriented components in lineage structure or split growth, and (4) where one macro-step meets another macro-step while advancing on a smooth surface from different growth centers. Depending on the situation, dislocations

6.3 Origin and spatial distribution of dislocations 125

(a)

(b)

Figure 6.6. (a) Spiral growth hillocks observed on a (111) face of a Ba(NO3)2 crystal grown from aqueous solution. (b) Corresponding X-ray topograph. Only numbered dislocations act as active growth centers; the others do not contribute to the growth (ref. [11], Chapter 7).

with large Burgers vectors will be generated due to large lattice mismatch, and macro-steps with large step heights will advance from the outcrop on a smooth surface. However, such dislocations are energetically unfavorable, and tend to dissociate into elemental dislocations with small Burgers vectors and elemental spiral steps.

Not all the dislocations outcropped on a crystal surface are active growth centers. In Fig. 6.6, the distribution of growth hillocks on a (111) face of an as-grown Ba(NO3)2 crystal is compared with the distribution of dislocations revealed by X-ray

126Perfection and homogeneity of single crystals

topography. It is clearly seen in this figure that, among many dislocations, only some act as active growth centers.

The spatial distribution of dislocations in single crystals may differ greatly depending on the mode of growth of the crystal. In crystals grown from the melt, a condensed ambient phase using seed crystals, dislocations are mainly generated from the surface and from inside the seed. These dislocations are inherited by the growing crystal unless an appropriate method is applied to prevent this from occurring. Thus, a technique called Dash necking is used. This is a method of removing dislocations inherited from and generated on the surface of a seed crystal; it involves thinning the diameter of the growing crystal, until the crystal is of an appropriate length, and then subsequently increasing the diameter again.

The most commonly encountered distribution of dislocations in crystals grown from solution or vapor phase (dilute ambient phases) by natural nucleation and without seed may be observed as dislocation bundles starting from the center of a crystal and running nearly perpendicular to the habit faces. In addition to these dislocations, smaller dislocation bundles originating from inclusions may be observed. See Figs. 6.1(e) and 6.5 for examples.

References

1 M. J. Buerger, The significance of block structure in crystals, Am. Min., 17, 1922, 177–91

2 M. J. Buerger, The lineage structure of crystals, Z. Krist, 89, 1934, 195–220

3 M. Seal, Structure in diamond as revealed by etching, Am. Min., 50, 1965, 105–23

4T. Miyata, K. Tsubokawa, and M. Kitamura, Observation of synthetic emeralds by scanning cathodoluminescence method, J. Gemmol. Soc., Japan, 18, 1993, 3–14