108 6·Atoms in Motion ←一TK volume diffusion FIGURE 6.4.Schematic representation of grain-boundary an Arrhenius diagram.Generally a loga- Inf diffusion rithmic scale (base 10)and not an In scale is used.The adjustment from In to log is a factor of 2.3.The difference be- tween volume diffusion and grain bound- ary diffusion is explained in the text.The slopes represent the respective activation energies. 1/TK-]→ in every 25 seconds.At the melting point of iron (1538C)the jump rate dramatically increases to 2 X 1011 per second. 6.1.4 Arrhenius equations are generally characterized by an exponential Arrhenius term that contains an activation energy for the process involved as well as the reciprocal of the absolute temperature.It is quite Diagrams customary to take the natural logarithm of an Arrhenius equation. For example,taking the natural logarithm of Eg.(6.3)yields: nf=a6-(份)片 (6.4) This expression has the form of an equation for a straight line, which is generically written as: y=b+mx. (6.5) Staying with the just-presented example,one then plots the ex- perimentally obtained rate using a logarithmic scale versus 1/T as depicted in Figure 6.4.The (negative)slope,m,of the straight line in an Arrhenius diagram equals QkB,from which the acti- vation energy can be calculated.The intersect of the straight line with the y-axis yields the constant fo.This procedure is widely used by scientists to calculate activation energies from a series of experimental results taken at a range of temperatures. 6.1.5 Self-diffusion is random,that is,one cannot predict in which di- Directional rection a given lattice atom will jump if it is surrounded by two or more equivalent vacancies.Indeed,an individual atom often Diffusion migrates in a haphazard zig-zag path.In order that a bias in the direction of the motion takes place,a driving force is needed.Dri-in every 25 seconds. At the melting point of iron (1538°C) the jump rate dramatically increases to 2 1011 per second. Arrhenius equations are generally characterized by an exponential term that contains an activation energy for the process involved as well as the reciprocal of the absolute temperature. It is quite customary to take the natural logarithm of an Arrhenius equation. For example, taking the natural logarithm of Eq. (6.3) yields: ln f
ln f0   k Q B  T 1 . (6.4) This expression has the form of an equation for a straight line, which is generically written as: y
b mx. (6.5) Staying with the just-presented example, one then plots the ex￾perimentally obtained rate using a logarithmic scale versus 1/T as depicted in Figure 6.4. The (negative) slope, m, of the straight line in an Arrhenius diagram equals Q/kB, from which the acti￾vation energy can be calculated. The intersect of the straight line with the y-axis yields the constant f0. This procedure is widely used by scientists to calculate activation energies from a series of experimental results taken at a range of temperatures. Self-diffusion is random, that is, one cannot predict in which di￾rection a given lattice atom will jump if it is surrounded by two or more equivalent vacancies. Indeed, an individual atom often migrates in a haphazard zig-zag path. In order that a bias in the direction of the motion takes place, a driving force is needed. Dri- 108 6 • Atoms in Motion volume diffusion grain-boundary diffusion 1/T [K–1] ln f T [K] FIGURE 6.4. Schematic representation of an Arrhenius diagram. Generally a loga￾rithmic scale (base 10) and not an ln scale is used. The adjustment from ln to log is a factor of 2.3. The difference be￾tween volume diffusion and grain bound￾ary diffusion is explained in the text. The slopes represent the respective activation energies. 6.1.4 Arrhenius Diagrams 6.1.5 Directional Diffusion