6.1.Lattice Defects and Diffusion 105 TABLE 6.1 Selected diffusion constants (volume diffusion) Mechanism Do m2 Solute Host material Q [ev] Self diffusion Cu Cu 7.8×10-5 2.18 Al Al 1.7×10-5 1.40 Fe a-Fe 2.0×10-4 2.49 Si Si 32×10-4 4.25 Interstitial C a-Fe(BCC) 6.2×10-7 0.83 diffusion y-Fe (FCC) 1.0×10-5 1.40 Interdiffusion Zn Cu 3.4×10-5 1.98 Cu Al 6.5×10-5 1.40 Cu Ni 2.7×10-5 2.64 Ni Cu 2.7×10-4 2.51 Al Si 8.0×10-4 3.47 fused by an interstitial mechanism.This mechanism is quite com- mon for the diffusion of carbon in iron or hydrogen in metals but can also be observed in nonmetallic solids in which the dif fusing interstitial atoms do not distort the lattice too much.The activation energy for interstitial diffusion is generally lower than that for diffusion by a vacancy mechanism(see Table 6.1),par- ticularly if the radius of the interstitial atoms is small compared to that of the matrix atoms.Another contributing factor is that the number of empty interstitial sites is generally larger than the number of vacancies.In other words,Ef(see above)is zero in this case. Interstitialcy If the interstitial atom is of the same species as the matrix,or if Mechanism a foreign atom is of similar size compared to the matrix,then the diffusion takes place by pushing one of the nearest,regular lattice atoms into an interstitial position.As a result,the former interstitial atom occupies the regular lattice site that was previ- ously populated by the now displaced atom.Examples of this mechanism have been observed for copper in iron or silver in AgBr. Other Diffusion by an interchange mechanism,that is,the simultaneous Diffusion exchange of lattice sites involving two or more atoms,is possible but energetically not favorable.Another occasionally observed Mechanisms mechanism,the ring exchange,may occur in substitutional,body- centered cubic solid solutions that are less densely packed.In this case,four atoms are involved which jump synchronously,one po- sition at a time,around a circle.It has been calculated by Zenerfused by an interstitial mechanism. This mechanism is quite com￾mon for the diffusion of carbon in iron or hydrogen in metals but can also be observed in nonmetallic solids in which the dif￾fusing interstitial atoms do not distort the lattice too much. The activation energy for interstitial diffusion is generally lower than that for diffusion by a vacancy mechanism (see Table 6.1), par￾ticularly if the radius of the interstitial atoms is small compared to that of the matrix atoms. Another contributing factor is that the number of empty interstitial sites is generally larger than the number of vacancies. In other words, Ef (see above) is zero in this case. If the interstitial atom is of the same species as the matrix, or if a foreign atom is of similar size compared to the matrix, then the diffusion takes place by pushing one of the nearest, regular lattice atoms into an interstitial position. As a result, the former interstitial atom occupies the regular lattice site that was previ￾ously populated by the now displaced atom. Examples of this mechanism have been observed for copper in iron or silver in AgBr. Diffusion by an interchange mechanism, that is, the simultaneous exchange of lattice sites involving two or more atoms, is possible but energetically not favorable. Another occasionally observed mechanism, the ring exchange, may occur in substitutional, body￾centered cubic solid solutions that are less densely packed. In this case, four atoms are involved which jump synchronously, one po￾sition at a time, around a circle. It has been calculated by Zener Interstitialcy Mechanism Other Diffusion Mechanisms 6.1 • Lattice Defects and Diffusion 105 TABLE 6.1 Selected diffusion constants (volume diffusion) Mechanism Solute Host material D0 m s 2 Q [eV] Self diffusion Cu Cu 7.8 105 2.18 Al Al 1.7 105 1.40 Fe -Fe 2.0 104 2.49 Si Si 32 104 4.25 Interstitial C -Fe (BCC) 6.2 107 0.83 diffusion C -Fe (FCC) 1.0 105 1.40 Interdiffusion Zn Cu 3.4 105 1.98 Cu Al 6.5 105 1.40 Cu Ni 2.7 105 2.64 Ni Cu 2.7 104 2.51 Al Si 8.0 104 3.47