Twinning of crystals

M.V. Klassen-Neklyudova, Mechanical Twinning of Crystals, Consultant Bureau, New York... 

Klassen-Nekludova M.V. Mechanical twinning of crystals. Moscow, 1960 (in Russian). 

The results of recent electron diffraction studies of selected areas of single kaolin crystals have thrown considerable doubt on the usefulness of such symbols. These studies are revealing that zones with different stacking patterns exist within minute kaolin crystals and that micro-twinning of crystals is common. Under these circumstances, the adoption of any current system of polymorphic symbols represents an oversimplification of the true structure. A much more complex system of symbols will be necessary, but its development must await the publication of many more detailed experimental results. 

Aoki, Y. and Nakamuto, Y., 1984. Penetration twins of potassium chloride. Journal of Crystal Growth, 67, 579-586. 

Aquilano, D. and Franchini-Angela, M., 1985. Twin laws of calcium oxalate trihydrate (COT). Journal of Crystal Growth, 73, 558-562. 

Mantovani, G., Vaccari, G., Accorsi, C.A., Aquilano, D. and Rubbo, M., 1983. Twin growth of sucrose crystals. Journal of Crystal Growth, 62, 595-602. 

Prasad, P.B.V., 1985. Twinning in palmitic acid crystals. Journal of Crystal Growth, 72, 663-669. 

DOia/TigAl. These materials possess a lamellar structure consisting of layers of twin-related TtAl and layers of TigAl in single crystalline form they are called "polysynthetically twinned (PST) crystals" (for a recent review see Yamaguchi, et al. 1995). 

Table 1 Analysis of X-ray diffraction pattern of icosahedrally twinned cubic crystals of MnAl6...

So-called Icosahedral and Decagonal Quasicrystals Are Twins of an 820-Atom Cubic Crystal... 

The powder patterns obtained by X-ray diffraction and selected area electron diffraction do represent averages over very large numbers of particles but the averaging over size, orientation and imperfection of crystals removes much of the important information, especially that on the correlations of properties,e.g, the orientational relationship of adjacent crystal regions or the dependence of twinning on size. 

The occurrence of twinned crystals is a widespread phenomenon. They may consist of individuals that can be depicted macroscopically as in the case of the dovetail twins of gypsum, where the two components are mirror-inverted (Fig. 18.8). There may also be numerous alternating components which sometimes cause a streaky appearance of the crystals (polysynthetic twin). One of the twin components is converted to the other by some symmetry operation (twinning operation), for example by a reflection in the case of the dovetail twins. Another example is the Dauphine twins of quartz which are intercon-verted by a twofold rotation axis (Fig. 18.8). Threefold or fourfold axes can also occur as symmetry elements between the components the domains then have three or four orientations. The twinning operation is not a symmetry operation of the space group of the structure, but it must be compatible with the given structural facts. 

International Tables for Crystallography, Vol. D Physical Properties of Crystals (A. Authier, ed.), Chap. 3.1 (J.-C. Toledano, V. Janovec, V. Kospky, J.F. Scott, P. Boek) Structural phase transitions Chap. 3.2 (V. Janovec, Th. Hahn, H. Klapper) Twinning and domain structures. Kluwer, 2003. 

Twins are commonly found or formed in all types of crystals. Their boundaries are of two general types coherent and incoherent. The coherent boundaries are usually also symmetric, so they offer little resistance to dislocation motion. However, the incoherent ones are not symmetric and may resist dislocation motion considerably. 

In the paramagnetic regime, the evolution of the EPR line width and g value show the presence of two transitions, observed at 142 and 61 K in the Mo salt, and at 222 and 46 K in the W salt. Based on detailed X-ray diffraction experiments performed on the Mo salt, the high temperature transition has been attributed to a structural second-order phase transition to a triclinic unit cell with apparition of a superstructure with a modulation vector q = (0,1/2, 1/2). Because of a twinning of the crystals at this transition, it has not been possible to determine the microscopic features of the transition, which is probably associated to an ordering of the anions, which are disordered at room temperature, an original feature for such centrosymmetric anions. This superstructure remains present down to the Neel... 

Figure 8.11 Transformation of a tetragonal crystal, with lattice parameters aT = bT, into a multiply twinned orthorhombic crystal with lattice parameters a0, bQ. The twinned regions are often called domains and the boundaries may occur on a variety of crystallographic planes.

By means of our experimental method (twin+single crystal kinetics) steady state growth morphology can be predicted as a function of supersaturation and temperature. 

Therefore a particular method was chosen (4). We worked on a statistical population of crystals in order to minimize the dispersion and on simultaneous measurement of all faces in order to compare their growth rate under the same conditions of supersaturation and temperature. Therefore classical (R,o ) isotherms were obtained. Experimentally we grew at the same time and in the same solution a single crystal and twin. Whereas growth rate measurements of the forms hOL are relatively simple (thanks to the fact that the b axis is a binary axis) (Figure lb), the kinetic measurements of the p 110 and p llO forms are more difficult. 

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