6.1.Lattice Defects and Diffusion 107 FIGURE 6.3.Schematic representation of a diffusion channel caused by an edge dislocation.(Disloca- tion-core diffusion.) ary diffusion.One should keep in mind,however,that,except for thin films,etc.,the surface area comprises only an extremely small fraction of the total number of atoms of a solid.Moreover, surfaces are often covered by oxides or other layers which have been deliberately applied or which have been formed by contact with the environment.Thus,surface diffusion represents gener- ally only a small fraction of the total diffusion. Dislocation- Finally,a dislocation core may provide a two-dimensional chan- Core nel for diffusion as shown in Figure 6.3.The cross-sectional area of this core is about 4d2,where d is the atomic diameter.Very Diffusion appropriately,the mechanism is called dislocation-core diffusion or pipe diffusion. 6.1.3 Rate The number of jumps per second which atoms perform into a Equation neighboring lattice site,that is,the rate or frequency for move- ment,f,is given again by an Arrhenius-type equation: f=fo exp (6.3) where fo is a constant that depends on the number of equivalent neighboring sites and on the vibrational frequency of atoms (about 1013 s-1).Q is again an activation energy for the process in question. We see from Eq.(6.3)that the jump rate is strongly tempera- ture-dependent.As an example,one finds for diffusion of carbon atoms in iron at room temperature(Q=0.83 ev)about one jumpary diffusion. One should keep in mind, however, that, except for thin films, etc., the surface area comprises only an extremely small fraction of the total number of atoms of a solid. Moreover, surfaces are often covered by oxides or other layers which have been deliberately applied or which have been formed by contact with the environment. Thus, surface diffusion represents gener￾ally only a small fraction of the total diffusion. Finally, a dislocation core may provide a two-dimensional chan￾nel for diffusion as shown in Figure 6.3. The cross-sectional area of this core is about 4d2, where d is the atomic diameter. Very appropriately, the mechanism is called dislocation-core diffusion or pipe diffusion. The number of jumps per second which atoms perform into a neighboring lattice site, that is, the rate or frequency for move￾ment, f, is given again by an Arrhenius-type equation: f
f0 exp  k Q BT  , (6.3) where f0 is a constant that depends on the number of equivalent neighboring sites and on the vibrational frequency of atoms (about 1013 s1). Q is again an activation energy for the process in question. We see from Eq. (6.3) that the jump rate is strongly tempera￾ture-dependent. As an example, one finds for diffusion of carbon atoms in iron at room temperature (Q
0.83 eV) about one jump 6.1 • Lattice Defects and Diffusion 107 FIGURE 6.3. Schematic representation of a diffusion channel caused by an edge dislocation. (Disloca￾tion-core diffusion.) Dislocation￾Core Diffusion 6.1.3 Rate Equation