104 6·Atoms in Motion E atom vacancy FIGURE 6.1.Schematic representation of the diffusion of an atom from its former position into a vacant lat- tice site.An activation energy for motion,Em,has to be applied which causes a momentary and local ex- distance pansion of the lattice to make room for the passage of the atom.This two-dimensional representation shows only part of the situation.Atoms above and below the depicted plane may contribute likewise to diffusion. energy.The necessary energy of motion,E to facilitate this ex- pansion is known as the activation energy for vacancy motion, which is schematically represented by an energy barrier shown in Figure 6.1.Em is in the vicinity of leV.The average thermal(ki- netic)energy of a particle,Eh,at the temperatures of interest,how- ever,is only between 0.05 to 0.1 eV,which can be calculated by making use of an equation that is borrowed from the kinetic the- ory of particles(see textbooks on thermodynamics): Et=ikgT. (6.2) This entails that for an atom to jump over an energy barrier,large fluctuations in energy need to take place until eventually enough energy has been "pooled together"in a small volume.Diffusion is therefore a statistical process. A second prerequisite for the diffusion of an atom by this mech- anism is,of course,that one or more vacancies are present in neighboring sites of the atom;see Eq.(6.1).All taken,the acti- vation energy for atomic diffusion,Q,is the sum of Ef and Em. Specifically,the activation energy for diffusion for many ele- ments is in the vicinity of 2 eV;see Table 6.1 Interstitial If atoms occupy interstitial lattice positions(see above),they may Diffusion easily diffuse by jumping from one interstitial site to the next without involving vacancies.Interstitial sites in FCC lattices are, for example,the center of a cube or the midpoints between two corner atoms.Similarly as for vacancy diffusion,the adjacent matrix must slightly and temporarily move apart to let an inter- stitial atom squeeze through.The atom is then said to have dif-energy. The necessary energy of motion, Em, to facilitate this ex￾pansion is known as the activation energy for vacancy motion, which is schematically represented by an energy barrier shown in Figure 6.1. Em is in the vicinity of 1eV. The average thermal (ki￾netic) energy of a particle, Eth, at the temperatures of interest, how￾ever, is only between 0.05 to 0.1 eV, which can be calculated by making use of an equation that is borrowed from the kinetic the￾ory of particles (see textbooks on thermodynamics): Eth
3 2 kBT. (6.2) This entails that for an atom to jump over an energy barrier, large fluctuations in energy need to take place until eventually enough energy has been “pooled together” in a small volume. Diffusion is therefore a statistical process. A second prerequisite for the diffusion of an atom by this mech￾anism is, of course, that one or more vacancies are present in neighboring sites of the atom; see Eq. (6.1). All taken, the acti￾vation energy for atomic diffusion, Q, is the sum of Ef and Em. Specifically, the activation energy for diffusion for many ele￾ments is in the vicinity of 2 eV; see Table 6.1 If atoms occupy interstitial lattice positions (see above), they may easily diffuse by jumping from one interstitial site to the next without involving vacancies. Interstitial sites in FCC lattices are, for example, the center of a cube or the midpoints between two corner atoms. Similarly as for vacancy diffusion, the adjacent matrix must slightly and temporarily move apart to let an inter￾stitial atom squeeze through. The atom is then said to have dif￾Interstitial Diffusion 104 6 • Atoms in Motion atom vacancy Em distance E FIGURE 6.1. Schematic representation of the diffusion of an atom from its former position into a vacant lat￾tice site. An activation energy for motion, Em, has to be applied which causes a momentary and local ex￾pansion of the lattice to make room for the passage of the atom. This two-dimensional representation shows only part of the situation. Atoms above and below the depicted plane may contribute likewise to diffusion.