Burgers vector theories

Hill et al. [117] extended the lower end of the temperature range studied (383—503 K) to investigate, in detail, the kinetic characteristics of the acceleratory period, which did not accurately obey eqn. (9). Behaviour varied with sample preparation. For recrystallized material, most of the acceleratory period showed an exponential increase of reaction rate with time (E = 155 kJ mole-1). Values of E for reaction at an interface and for nucleation within the crystal were 130 and 210 kJ mole-1, respectively. It was concluded that potential nuclei are not randomly distributed but are separated by a characteristic minimum distance, related to the Burgers vector of the dislocations present. Below 423 K, nucleation within crystals is very slow compared with decomposition at surfaces. Rate measurements are discussed with reference to absolute reaction rate theory. 

However, for some other epoxy-amine systems, experimental monotonous decrease from epoxy-rich to amine-rich formulations (Yamini and Young, 1980 Won et al., 1990). This means that the proportionality constant between ay and (Tg — T) must vary along the series (P relaxations and physical aging may be invoked as some of the possible factors accounting for the observed trends). For these series, Bowden s theory, with the Burger vector increasing with the amount of hardener, provided a very good lit of experimental data. 

Note y = surface energy, D = volume diffusivity, Ds = surface diffusivity, Db = grain boundary diffusivity, ij = viscosity, b = Burgers vector, k = Boltzman s constant, p = density, S = width of grain boundary diffusion path, P = pressure, M = molecular weight, and 2 = atomic volume. Source From R. M. German, Sintering Theory and Practice (New York Wiley, 1996). Reprinted with permission of John Wiley Sons, Inc. 

Here Gm( c) are the shear moduli of the two materials, A is the thickness of the softer layer, b is the Burgers vector of the dislocation, and

angle between the dislocation slip plane in the layer M(l) and the interface M(l)/M(2). This theory predicts that the strength (and hardness) depends mainly on the relative difference between the shear moduli (Gm(2) - Gm ))/ Gm(2) + Gm(i)) and the angle tp. For small period but still Ai 4b the enhancement reaches an asymptotic value of... 

Vector b(y,t) is called the dislocation by Eshelby [1973] and is identical to the Burgers vector in the dislocation theory of crystalline motion. From Eq. 7.10, it leads to the following equation, assuming the equilibrium of traction t = 0) between the crack surfaces. 

All the expressions given above for discli-nation and focal curve energies are similar to those for screw and edge dislocations in true crystals [9,15], but the situation is different for translation dislocations in smectics. The presence of a screw dislocation of weak Burgers vector does not introduce any splay and does not really modify the layer thickness even at small distances [16]. The energy is reduced to a core term and therefore interaction terms are absent in the frame of the linear theory. This is not the case for edge dislocations in this approximation [106], and one has the expression ... 

Fig. 27. Kink pair energy as a function of the kink-kink separation d (in Burgers vector unit) for various shear strain values (fuU lines). Fits from elasticity theory are reported as dashed lines. After PizzagaUi...

As we note in Section 7.2, the permanent deformation of most crystalline materials is by the motion of dislocations. In addition, the Burgers vector is an element of the theory that has been developed to explain this type of deformation. 

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