Spirals, growth

Spiral growth is a mechanism that is expected only on smooth interfaces. The assistance provided by screw dislocations is not necessary in the growth of rough interfaces, where an adhesive-type growth operates. 

As explained above, three fundamental models of crystal growth mechanism were established in relation to the roughness of interfaces these are illustrated in Fig. 3.14. At present, there is no other known growth mechanism that is essentially different from these three. Therefore, we shall analyze the morphology of crystals, the main topic of this book, based on these three growth mechanisms. 

---

If spiral growth occurs due to the existence of screw dislocations, the results depend upon whether the diffusion length ijy is smaller or larger than the typical separation of the spiral arms i. In the first case the situation hardly changes from the purely kinetic situation without diffusion, but in the second case interaction between steps comes into effect [90] and phenomena such as step bunching [91] take place. We can estimate qualitatively the... 

Massive barite crystals (type C) are also composed of very fine grain-sized (several xm) microcrystals and have rough surfaces. Very fine barite particles are found on outer rims of the Hanaoka Kuroko chimney, while polyhedral well-formed barite is in the inner side of the chimney (type D). Type D barite is rarely observed in black ore. These scanning electron microscopic observations suggest that barite precipitation was controlled by a surface reaction mechanism (probably surface nucleation, but not spiral growth mechanism) rather than by a bulk diffusion mechanism. 

Fig. 5.50 Spiral growth of Cu from a 0.5 m CuS04 + 0.5 m H2S04 electrolyte, 25°C, current density 15 mA cm-2, magnification 1250x. (From H. Seiter, H. Fischer, and L. Albert, Electrochim. Acta, 2, 97, 1960)...

Stack of lamellar crystals generated by spiral growth at one or more screw dislocations. Note The axial displacement over a full turn of the screw (Burgers vector) is usually equal to one lamellar thickness. 

It became necessary to understand how crystals grow at the atomic level so as to form a deeper understanding of why crystals can take a variety of forms. This was achieved through the layer growth theory put forward in the 1930s by Volmer, Kossel, and Stranski on the structure and implication of the solid-liquid interface, the spiral growth theory by Frank in 1949, and the theory of morphological... 

Growth mechanism adhesive-type two-dimensional nucleation growth or spiral growth ... 

The concept of dislocations was theoretically introduced in the 1930s by E. Orowan and G. I. Taylor, and it immediately played an essential role in the understanding of the plastic properties of crystalline materials, but it took a further twenty years to understand fully the importance of dislocations in crystal growth. As will be described in Section 3.9, it was only in 1949 that the spiral growth theory, in which the growth of a smooth interface is assumed to proceed in a spiral step manner, with the step serving as a self-perpetuating step source, was put forward [7]. 

Figure 3.15. Areas where rough and smooth interfaces are expected. The growth rate versus the driving force relations expected for the three models of growth are indicated on the growth rate, R (vertical), axis versus the driving force (A/x/kT) diagram. Curve A shows the spiral growth mechanism B represents the two-dimensional nucleation growth mechanism C denotes the adhesive-type mechanism.

---