Crystal gliding

Figure 6.2 shows one possible way in which crystal glide could occur, with one plane of atoms being sheared past an adjacent plane. In the perfect crystal, the atoms are assumed to lie directly above each other with a planar spacing d. Clearly, as the atoms are displaced, the stress will rise and pass through a maximum. Once the displacement u reaches a value of btl, i e., at the mid-shear position, the atoms would be equally as likely to complete the displacement u=b) as to return to their original positions. The stress returns to zero at this equilibrium point. For displacements larger than bl2, the atoms will be attracted into their new positions by the interatomic potential and thus the... 

Figure 6.1 Permanent deformation of a crystal produced by a) crystal glide and b) twinning. The orientation of the shading represents the crystallographic texture of the crystal.

Crystal glide plane Anion Cation Total (nm)... 

If the space group contains screw axes or glide planes, the Patterson fiinction can be particularly revealing. Suppose, for example, that parallel to the c axis of the crystal there is a 2 screw axis, one that combines a 180° rotation with... 

Flinn et al. [30] describes an experimental impact technique in which <100)-oriented LiF single crystals ( 8 ppm Mg) are loaded in a controlled manner and the multiplication of screw dislocations is measured. The peak shear stress in this relatively soft material is 0.01 GPa. For shear impulses exceeding approximately 40 dyne s/cm, dislocation multiplication is adequately described by the multiple-cross-glide mechanism [(7.24)] with m = l/bL = (2-4) X 10 m, in reasonable agreement with quasi-static measurement [2]. 

Gerk showed that Equation (2.1) is followed not only for metals, but also for ionic and covalent crystals if two adjustments are made. For covalent crystals, the temperature must be raised to a level where dislocations glide readily, but below the level where they climb readily. For ionic crystals, G (an average shear modulus) must be adjusted for elastic anisotropy. Thus it becomes ... 

When the two vectors are parallel, the crystal planes perpendicular to the line form a helix, and the dislocation is said to be of the screw type. In a nearly isotropic crystal structure, the dislocation is no longer associated with a distinct glide plane. It has nearly cylindrical symmetry, so in the case of the figure it can move either vertically or horizontally with equal ease. 

Figure 4.1 Schematic dislocation line a simple cubic crystal structure. The line enters the crystal at the center of the left-front face. It emerges at the center of the right-front face. The shortest translation vector of the structure is the Burgers Vector, b. The line bounds the glided area of the glide plane (100) from the unglided area.

Figure 4.2 Quasi-hexagonal dislocation loop lying on the (111) glide plane of the diamond crystal structure. The <110> Burgers vector is indicated. A segment, displaced by one atomic plane, with a pair of kinks, is shown a the right-hand screw orientation of the loop. As the kinks move apart along the screw dislocation, more of it moves to the right.

Figure 4.3 Glide activation energies for various covalent crystals versus their minimum energy gaps. The correlation coefficient is 0.95. Without the point for GaP, it would be much higher. 

When there are no distinct bonds crossing a glide plane, there are no distinct kinks. This is the case for pure simple metals, for pure ionic crystals, and for molecular crystals. However, the local region of a dislocation s core still controls the mobility in a pure material because this is where the deformation rate is greatest (Gilman, 1968). 

When the stress (compressive) rises to a value approaching G/10 near the Debye temperature, motion of gliding dislocations tends to be replaced by the formation of phase transformation dislocations. The crystal structure then transforms to a new one of greater density. This occurs when the compressive stress (the hardness number) equals the energy band gap density (gap/molecular volume). 

The glide planes on which dislocations move in the diamond and zincblende crystals are the octahedral (111) planes. The covalent bonds lie perpendicular to these planes. Therefore, the elastic shear stiffnesses of the covalent bonds... 

Figure 5.7 Schematic edge dislocation after Peierls. Top part of crystal, T and bottom part B, are joined between planes a and P across a glide plane with an extra half-plane of atoms ending at c. The displacement along the glide plane is b, and the glide plane spacing is a.

Dislocation motion in covalent crystals is thermally activated at temperatures above the Einstein (Debye) temperature. The activation energies are well-defined, and the velocities are approximately proportional to the applied stresses (Sumino, 1989). These facts indicate that the rate determining process is localized to atomic dimensions. Dislocation lines do not move concertedly. Instead, sharp kinks form along their lengths, and as these kinks move so do the lines. The kinks are localized at individual chemical bonds that cross the glide plane (Figure 5.8). 

Figure 5.12 Glide activation energies from high temperature data vs. energy band gaps. Note that the data for the homopolar crystals (C, SiC, Si, and Ge) lie quite close to the correlation line, while the data for The heteropolar crystals show some scatter. The reason why GaP Is an exception is not known. Also, note that the slope of the correlation line is two. 

P. Feltham and R. Banerjee, Theory and Application of Microindentation in Studies of Glide and Cracking in Single Crystals of Elemental and Compound Semiconductors, Jour. Mater. Sci., 27,1626 (1992). 

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