The Growth of Crystals

As a class, the azides present several problems when attempting to use the well-known techniques of crystal and thin-film growth. Their instability conflicts with the successful application of most thermal approaches, and their restricted solubilities limit the usefulness of growth from aqueous solutions. For instance, growth by sublimation techniques is not feasible because the azide ion decomposes at elevated temperatures. Melt growth is limited to the azides of K, Rb, Cs, and Tl, of which only KN3 is sufficiently stable at its melting point to permit routine success. Thus, while the azides must, in general, be crystallized from solutions, precautions are also necessary to avoid hydrolytic decomposition when water is used as the solvent. 

The following general techniques for inducing solubility changes in solution have been applied to the growth of azide crystals  

Solvent evaporation temperature constant, volume decreased 

Slow cooling volume constant, temperature decreased 

---

A number of theories have been put forth to explain the mechanism of polytype formation (30—36), such as the generation of steps by screw dislocations on single-crystal surfaces that could account for the large number of polytypes formed (30,35,36). The growth of crystals via the vapor phase is beheved to occur by surface nucleation and ledge movement by face specific reactions (37). The soHd-state transformation from one polytype to another is beheved to occur by a layer-displacement mechanism (38) caused by nucleation and expansion of stacking faults in close-packed double layers of Si and C. 

Models used to describe the growth of crystals by layers call for a two-step process (/) formation of a two-dimensional nucleus on the surface and (2) spreading of the solute from the two-dimensional nucleus across the surface. The relative rates at which these two steps occur give rise to the mononuclear two-dimensional nucleation theory and the polynuclear two-dimensional nucleation theory. In the mononuclear two-dimensional nucleation theory, the surface nucleation step occurs at a finite rate, whereas the spreading across the surface is assumed to occur at an infinite rate. The reverse is tme for the polynuclear two-dimensional nucleation theory. Erom the mononuclear two-dimensional nucleation theory, growth is related to supersaturation by the equation. 

Burton, W.K., Cabrera, N. and Frank, F.C., 1951. The growth of crystals and the equilibrium structure of their surfaces. Philosophical Transactions, A243, 299-358. 

The growth of crystals—or more generally the solidification of a sohd from a fluid phase—is definitely not an equilibrium problem. Why, therefore, should we discuss here equihbrium thermodynamics, instead of treating directly, for example the coagulation of two atoms and then simply following the growth of the cluster by adding more particles with time ... 

W. Burton, N. Cabrera, F. Frank. The growth of crystals and the equiUbrium structure of their surfaces. Phil Trans Roy Soc London A 243 299, 1951. 

Brice, J., "The Growth of Crystals from Liquids , pp. 4-5. North-Holland Publ., Amsterdam, 1973. 

The growth of crystals proceeds in two subsequent-parallel stages (1) diffusion and (2) integration. 

It is interesting to note that many crystal poisons not only interfer with nucleation and the growth of crystals but may also retard their dissolution. As we have seen (Chapter 6), precipitation and dissolution of solids proceed by the attachment or detachment of ions most favorably at kink sites of the crystalline surface. Solutes such as organic substances, or phosphates may upon adsorption immobilize kinks and thus retard dissolution. 

Burton, W. K., N. Carbrera, and F. C. Frank (1951), The Growth of Crystals and the Equilibrium Structure of Their Surfaces", Phil Trans. Roy. Soc. A243, 299-358. 

The influence of -lactose on the growth of crystals of a-lactose has recently been analyzed by Visser and Bennema (68). The a- and (3-lactoses 4a and 4b are disaccharides composed of a galactose and an a- or (3-glucose moiety linked... 

Professor Curie continued his researches on the growth of crystals, and his young wife prepared for her examinations. Many chemists consider her dissertation (55) to be the most remarkable thesis ever presented for the doctorate. She continued the work begun by Becquerel, and tested most of the known elements, including a number of rare ones loaned by E.-A. Demarpay and Georges Urbain, with Prof. Curie s piezoelectric quartz electrometer, and found that thorium and uranium were the only ones whose compounds produced appreciable ionization (26, 54, 55). The radioactivity of thorium was discovered independently by Gerhardt Carl Schmidt, professor of physics at the University of Munster (25). 

In the growth of crystals from the vapor phase, the degree of the driving force is expressed by the ratio S, i.e. the ratio between the equilibrium vapor pressure and the pressure p at growth ... 

N. Cabrera and D. A. Vermilyea, The growth of crystals from solution, in Growth and Perfection ofGrystals, eds. R. H. Doremus, B. W. Roberts, and V. Turnbull, New York, John Wiley Sons, 1958... 

Solids such as KF, PbO, PbFj and BjOj are powerful solvents (flux) in the molten state for many inorganic substances and hence can be used as media for the growth of crystals. The usual technique is to dissolve the solute in a suitable combination of flux... 

Thermal uniformity in the cold zone was found to be from 0.01 to 0.02 °C, and that in the hot zone was found to be better than + 0.5 °C vertically and + 0.1 °C horizontally. Thermal gradients near the solid-liquid interface were achieved in excess of 30 °C cm " in the crystal region and up to 20 °C cm" in the melt. The growth of crystals was performed in a sealed transparent silica ampoule, which has two rooms for As source and GaAs polycrystalline, respectively, separated by a quartz diffusion barrier. For details of the growth process the reader is referred to Ref. 43. In this experiment the As source temperature T. was systematically reduced by 2 °C at 3 h intervals from 620 °C to 614 °C. 

When a solid gel has been secured, nearly fill each test tube with a solution containing 8 per cent of oxalic acid, to act as a reducing agent. The growth of crystals can be observed within a few hours, and in a few days it will... 

Various smaller molecules and ions can also inhibit the growth of crystals of calcium phosphate such as phosphocitrate, proteoglycans and trimetaphosphate. Other compounds act as accelerators. 

---