Crystal deformation

Most probable positions of the chains are determined by the use of a characteristic vector r. This vector is representative of an average network chain of N links (the average links per chain). It deforms affinely whereas the actual network chains might not, and its value depends only upon network deformation. Crystallization leaves r essentially unaltered since the miniscule volume contraction brought about by crystallization can be ignored. But real network chains are severely displaced by crystallization. These displacements, however, must be compatible with the immutability of r. So in a sense, the characteristic vector r limits the configurational variations of the chains to those consistent with a fixed network shape and size at a given deformation. 

Owing to the very high intensity of SR, exposure times on nuclear plates are typically ten minutes, whereas for such a slow emulsion, exposures are of the order of days in the laboratory. This reduction in timescale is particularly important for multiple exposure topographs of deformed crystals. 

Swelling cellulose I by means of liquid ammonia and precipitating the substance leads to the formation of cellulose III, which also differs from I by virtue of its deformed crystal lattice, in which the /9-angle is approximately 58° (Legrand [26]. 

The radiation-induced color changes in inorganic materials (Ref 145) led to a comprehensive study by Rosenwasser, Dreyfus and Levy (Ref 148) on Na azide, which turns to brownish yellow when subjected to radiation. Subsequently, when mechanically deformed crystals of Na and K azide were irradiated with 107R gamma radiation, Dreyfus and Levy (Ref 69) observed the formation of pyramidal etch pits which occurred mainly in regions where imperfections were located at the surface. These were also evident in ammonium perchlorate crystals (Ref 255)... 

Deformed crystals. If a semi-crystalline polymer is deformed while undergoing crystallization, oriented lamellae form instead of spherulites. 

Kulda J (1984) A novel approach to dynamical neutron diffraction by a deformed crystal. Acta Cryst A40 120-126... 

The potential at a point r in a perfect crystal is given by K(r). If the crystal is now deformed by the presence of a defect, then the potential at point r will be different from V(t) because the potential at a point depends on the positions of the atoms in the neighborhood. If we assume that the deformation is not too severe (i.e., the deformation is a slowly varying function of position), then the potential at point r in the deformed crystal will be equivalent to the potential at point (r—R) in the undeformed crystal. R, in general, is a function of position and is called the displacement function. Thus, in a deformed crystal, the potential at a point r is given by... 

For the two-beam approximation there is only one operating reflection g, and for the deformed crystal the corresponding Fourier coefficient is... 

In specimens deformed to several percent strain (or more) at low to intermediate temperatures and stresses, where neither work-hardening nor recovery processes predominate, dislocations tend to tangle into localized walls (Kirby and McCormick 1979 McCormick 1977 McLaren et al. 1970 Morrison-Smith et al. 1976). These walls behave as optical phase objects and give rise to the deformation lamellae that are commonly observed in deformed crystals by optical microscopy (see Section 1.3 and McLaren et al. 1970). Similar walls of tangled dislocations develop in metals in the power-law-breakdown creep regime where both recovery-controlled and glide-controlled deformation mechanisms are operative (see, e.g., Drury and Humphreys 1986). 

Stress estimates based on measurements of p, d, and D in naturally deformed crystals also assume (i) steady-state deformation, at the cessation of which the evolved microstructure is frozen in, (ii) a simple deformation history, and (iii) experimental data that can be extrapolated to geological conditions. 

The hard-ray diffraction technique allows a fast characterization of the lattice distortions for sample size in the centimeter range or more. The spatial resolution is low, but this technique showed the predominance of excess screw dislocations to accommodate the torsion deformation in all deformed crystals. A negligible contribution of edge dislocations was evidenced, which is consistent with the loading conditions. 

Fig. 8-26 Formation of Debye arcs on Laue patterns of deformed crystals.

A modification of the Guinier-Tennevin method can reveal additional information about a deformed crystal [8.12, 8.13]. If a Seller slit with horizontal plates is placed in the incident beam and the crystal is twisted about a vertical axis, the original vertical-line Laue spot broadens into a striated region composed of fine inclined lines, and the inclination of these lines is a measure of the torsional strain in the crystal (Fig. 8-30(c)). 

The derivations for the strained semiconductors follow closely the classical works of Pikus and Bir " (or refer to for the valence-band). The position vector of a specific atom in the primitive cell in the undeformed crystal is described byr=(x,y,z). The position vector of the same atom in the same primitive cell in the deformed crystal is described byr = (x, y,z ). These two vectors are connected through the strain... 

GRO 88] GROMA I., UNGAR T., WILKENS M., Asymmetric x-ray line broadening of plastically deformed crystals. I. Theory. J. Appl. Cryst, vol. 21, p. 47-53,1988. 

The major mechanical forces that affect chemical processes—coupling P->C—are mechanical stresses or pressures that deform crystal lattices, affect the solid density and chemical potentials, and cause disaggregation or aggregation of solid particles on a macroscopic scale. The reverse coupling of the chemical effects on solids—C- P -includes a very broad category of chemical reactions in a solid state, reactions of mineral or biogenic solids with waters and atmospheric gases, and corrosion of metals. 

Fig. 9.06. Motion of an edge dislocation in a crystal undergoing slip deformation, (a) The undeformed crystal. (b, c) Successive stages in the motion of the dislocation from right to left, (d) The deformed crystal.

Much of this data has been or will be published elsewhere [5-10]. The data shows that the lattice and molecules of plastically deformed crystals experience significant and semi-permanent deformation. From this, insights are obtained that permit the development of an approximate deformed lattice potential for shocked or impacted crystals. Shear bands have been observed in shocked or impacted crystals. Some of shear bands show that molten material had been extruded from deep within the bands. These are possibly the source of the hot spots thought to be responsible for initiation during shock or impact. On the basis of these and other experimental observations it is concluded that energy dissipation and localization during plastic deformation is likely to be responsible for initiation of chemical reaction. 

Section (2) develops a theoretical account of plastic deformation and energy dissipation at the atomic or molecular level. The AFM observations show that plastic deformation of shocked or impacted crystals can significantly deform both the crystal lattice and its molecular components. These molecular and sub-molecular scale processes require a quantum mechanical description and necessarily involve the lattice and molecular potentials of the deforming crystals. A deformed lattice potential is developed which when combined with a quantum mechanical account of plastic flow in crystalline solids will be shown to give reasonably complete and accurate descriptions of the plastic flow and initiation properties of damaged and deformed explosive crystals. The deformed lattice potential allows, for the first time, the damaged state of the crystal lattice to be taken into account when determining crystal response to shock or impact. 

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