Spiral Growth of the Surface of Carborundum Crystals

The theory of crystal growth, based on the theory of dislocations, predicts that, at small supersaturations, screw dislocations emerging on the surface of a crystal can serve as growth centers, and spiral terraces should form on the surface of the crystal. The height of the terraces should be equal to the lattice constant; their width can be calculated. If the growth rate does not depend on the crystallographic direction, then the terraces form an ordinary Archimedean spiral with its center at the dislocation. In the case of a strong dependence of the growth rate on the crystallographic direction, the shape of the spiral is distorted, reflecting the symmetry of the crystal. The authors of the summarized notes*) succeeded, with the aid of a phase microscope and also by methods of multiple-beam interferometry, in observing such “growth spirals” on the surface of carborundum crystals and thereby obtaining convincing confirmation of the above theory.

The surface of the crystal under investigation was coated with a thin silver film (by evaporation in vacuum), whose reflection coefficient reached approximately 90%. The observed value in reflected light, with the use of multiple-beam interferometry methods, was due to the silvered surface performing, as usual, the role of one of the plates of the interferometer. Crystals of two types were studied: rhombohedral \((c = 37.7\ \text{Å})\) and hexagonal \((c = 15.1\ \text{Å})\). In the latter case, the spiral near the dislocation clearly revealed the hexagonal symmetry of the crystal; as the radius of the turns of the spiral increased, however, they became more and more rounded (Figs. 1 and 2, б). In this case the width of the terrace increased in proportion to the distance from the dislocation (approximately proportional to the distance).

Fig. 1.

In the case of rhombohedral crystals, the crystalline structure had practically no effect on the form of the spiral (Fig. 2, а).

In most cases, there was not one but several dislocations on the surface of the crystal (predominantly of one direction), and their number sometimes reached \(10^4\) per \(\text{cm}^2\). Examples of the formation of spiral—

) A. J. Verma, Nature 167*, 939 (1951); S. Amelineckx, ibid.

terraces in these cases are shown in Fig. 2, a and b (in Fig. 2, a the dislocations have opposite directions).

Determination of the critical radius of the growth nuclei gave a value of 2 μ; the critical supersaturation was 0.2%. The methods of multiple-beam interferometry made it possible to determine the height of the terraces with great accuracy. In the case of hexagonal crystals the measurements were made in two different ways for two different spirals.

Fig. 2.

The values obtained agreed well with one another (15.1 and 15.2 Å; the greatest possible error, 2 Å) and were in complete agreement with the data of X-ray structural analysis ($c = 15.1$ Å). Thus, the terrace height proved indeed to be equal to the lattice constant. Incidentally, one of the authors observed, alongside terraces of this height, also higher terraces (up to 35 Å, see Fig. 1); however, he does not specify the conditions under which such a terrace height was observed.

R. G.