Polyhedral crystal

P. D Ambra. Numerical simulation of polyhedral crystal growth based on a mathematical model arising from nonlocal thermomechanics. Contin Mech Thermodyn 9 91, 1997. 

Morphology also depends on the driving force or chemical potential difference (g/ kt) in the crystallization process this is related to the supersaturation of the system. A low driving force favours polyhedral crystals, whereas with a very high driving... 

On crystal faces bounding a polyhedral crystal, step patterns resembling the contour lines on a topographic map or striations in one direction are observable depending on the nature of the face. These show the process of crystal growth or dissolution at an atomic level, and are referred to as the surface morphology or surface microtopography. 

Polyhedral crystals bounded by flat crystal feces usually take characteristic forms controlled by the symmetry elements of the crystal (point) group to which the crystal belongs and the form and size of the unit cell (see Appendix A.5). When a unit cell is of equal or nearly equal size along the three axes, crystals usually take an isometric form, such as a tetrahedron, cube, octahedron, or dodec-... 

Figure 2.1. Various forms exhibited by crystals, (a) Polyhedral crystals (b) hopper crystal (c) dendritic crystal (snow crystal, photographed by the late T. Kobayashi) (d) step pattern observed on a hematite crystal (0001) face (e) internal texture of a single crystal (diamond-cut stone, X-ray topograph taken by T.Yasuda) (f) synthetic single crystal boule. Si grown by the Czochralski method (g) synthetic corundum grown by the Verneuil method.

We discussed iu Section 3.12 that there is a mutual relation among spherulitic, dendritic, hopper, and polyhedral crystals, with respect to the driving force. We will see how these mutual relatious appear in real systems, using, as representative examples, low-temperature suow crystals (vapor phase growth) and high-temperature silicate crystals growiug iu silicate solutiou phases. 

T. Kuroda, T. Irisawa, and A. Ookawa, Growth of a polyhedral crystal and its morphological stability,/. Crystal Growth, 42,1977,41-6... 

Another advantage of the PBC theory is its ability to predict not only the bulk morphology of a polyhedral crystal, but also the morphology of growth layers developing on F faces. When growth layers are polygonal, the step direction is assumed to be defined by the PBC theory. These predictions cannot be made by the BFDH law. 

As can be seen in the Nakaya diagram in Fig. 3.23, snow crystals grown in a reduced vapor supply (smaller driving force) appear as polyhedral crystals... 

Even if crystals grow from the same aqueous solution, there are differences in Habitus. NaC103 crystals, for example, grow easily as polyhedral crystals, whereas NH Cl crystals always grow as dendrites, and NaCl crystals appear as hopper crystals. If Pb or Mn ions are added, cubic crystals of NaCl bounded by flat 100 faces may be obtained quite easily, but if NaCl is grown in pure solution all crystals take a hopper form, unless great care is taken to keep the supersaturation very low. These differences occur because the solute-solvent interaction energies, and, as a result, the values of Ap,/kT and A/x/kT, are different for different crystals. 

These three features correspond to the two-dimensional morphology of a crystal, and are directly related to the problems of the three-dimensional morphology of polyhedral crystals. Habitus and Tracht. This is because the normal growth rate R which determines Habitus and Tracht is related in the following way to the height of a step, h, the advancing rate of the step, v, and the step separation, A. ... 

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