Faulted crystals

An example of such a disordered crystal is shown in Figure 8.4a. The material is SrTi03, which adopts the perovskite structure. The faulted crystal can be best described with respect to an idealised cubic perovskite structure, with a lattice parameter of 0.375 nm, (Figure 8.4b). The skeleton of the material is composed of comer-linked TiC>6 octahedra, with large Sr cations in the cages that lie within the octahedral framework. The planar defects, which arise where the perovskite structure is incorrectly stacked, lie upon [110] referred to the idealised cubic stmcture (Figure 8.4c). 

Fig. 9.20 The temperature dependence of the shear modulus, n = C55, of HDPE from Karasawa et al. (1991) is shown by the upper curve. The lower curve presents an attenuated form based on expectations for a faulted crystal (from Argon et al. (2005) courtesy of...

Figure 29. Diffraction by a faulted crystal A) Effect of a translation interface with vector Ro< B) Effect of a di.splacement field C) Schematic of the expressions for transmitted and scattered beam amplitude for a foil containing a general interface parallel to the foil surfaces...

Figure B3.3.13. Intersecting stacking faults in a fee crystal at the impact plane induced by collision with a momentum mirror for a square cross section of side 100 unit cells. The shock wave has advanced half way to the rear ( 250 planes). Atom shading indicates potential energy. Thanks are due to B Holian for tliis figure.

Extended defects range from well characterized dislocations to grain boundaries, interfaces, stacking faults, etch pits, D-defects, misfit dislocations (common in epitaxial growth), blisters induced by H or He implantation etc. Microscopic studies of such defects are very difficult, and crystal growers use years of experience and trial-and-error teclmiques to avoid or control them. Some extended defects can change in unpredictable ways upon heat treatments. Others become gettering centres for transition metals, a phenomenon which can be desirable or not, but is always difficult to control. Extended defects are sometimes cleverly used. For example, the smart-cut process relies on the controlled implantation of H followed by heat treatments to create blisters. This allows a thin layer of clean material to be lifted from a bulk wafer [261. 

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. 

Scherrer equation to estimate the size of organized regions Imperfections in the crystal, such as particle size, strains, faults, etc, affect the X-ray diffraction pattern. The effect of particle size on the diffraction pattern is one of the simplest cases and the first treatment of particle size broadening was made by Scherrer in 1918 [16]. A more exact derivation by Warren showed that. 

The key here was the theory. The pioneers familiarity with both the kinematic and the dynamic theory of diffraction and with the real structure of real crystals (the subject-matter of Lai s review cited in Section 4.2.4) enabled them to work out, by degrees, how to get good contrast for dislocations of various kinds and, later, other defects such as stacking-faults. Several other physicists who have since become well known, such as A. Kelly and J. Menter, were also involved Hirsch goes to considerable pains in his 1986 paper to attribute credit to all those who played a major part. 

T. Sinno, R. A. Brown, W. Van Ammon, E. Dornberger. Point defect dynamics and the oxidation-induced stacking-fault ring in Czochralski-grown silicon crystals. J Electrochem Soc 145 302, 1998. 

Uranium, too, is widely distributed and, since it probably crystallized late in the formation of igneous rocks, tends to be scattered in the faults of older rocks. Some concentration by leaching and subsequent re-precipitation has produced a large number of oxide minerals of which the most important are pitchblende or uraninite, U3O8, and camotite, K2(U02)2(V04)2.3H20. However, even these are usually dispersed so that typical ores contain only about 0.1% U, and many of the more readily exploited deposits are nearing exhaustion. The principal sources are Canada, Africa and countries of the former USSR. 

For the smaller particles which Include only a few tens or hundreds of atoms, any twinning or faulting reduces the range of ordering to the extent that the pattern can not be Interpreted In the same way as a pattern from an extended crystal. The Individual single-crystal regions may contain only two or three atomic planes. Interpretation can be made only by calculation of patterns from postulated models for the configurations of atoms (22). 

Other kinds of defects could give rise to peak broadening, for example the staking faults. In this case, the equation taking into account this phenomenon depends on the peculiar structure of the crystals and the analysis can be more complex some defects, in fact, introduce profile asymmetry and a shift in the position of some selected peaks [26]. 

Crystals are distinguished by the regular, periodic order of their components. In the following we will focus much attention on this order. However, this should not lead to the impression of a perfect order. Real crystals contain numerous faults, their number increasing with temperature. Atoms can be missing or misplaced, and dislocations and other imperfections can occur. These faults can have an enormous influence on the properties of a material. 

If the stacking faults occur only rarely (say, every 105 layers on average), the result is a polysynthetic twinned crystal (cf. Fig. 18.8, p. 223). Depending on the frequency of the stacking faults, there is a smooth transition between crystals with stacking faults and poly synthetic twinning. 

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