110 6·Atoms in Motion (a) FIGURE 6.5.(a)Steady- state diffusion through a slab.(b)Linear con- centration gradient which stays constant with time by constantly supplying solute atoms on the left and remov- ing the same number of atoms on the right side (b) of the slab.Ca and CB are two assumed sur- face concentrations, where Ca>CB. frequency of the atoms,f,which we introduced above [Equation (6.3)].This interrelationship reads: D=名A2f, (6.9) where A is the diffusion jump distance which is,in isotropic sys- tems,identical with the interatomic distance. Fick's first law [Eq.(6.6)]may be used to describe steady-state flow.One assumes for this case an infinite source and an infi- nite sink,respectively,on the opposite ends of a plate of metal that causes a constant flow of solute atoms through a given area.Steady-state flow is observed,for example,when gases (such as hydrogen or oxygen)diffuse through metals as a con- sequence of a constant (but different)gas pressure on each side of a plate.This requires a supply of gas atoms on one side and a removal of the same amount of gas atoms on the other side. As an example,hydrogen-filled gas tanks for fuel-cell-propelled automobiles are empty after about two months.(Hand tools in university labs seem to disappear by a similar mechanism.) 6.1.7 Fick's second law deals with the common case for which the con- Nonsteady- centration gradient of a diffusing species,A,in the host material, B,changes gradually with time (Figure 6.6).The nonsteady-state State (or dynamic)case is governed by the partial differential equation: Diffusion =D℃ (6.10) atfrequency of the atoms, f, which we introduced above [Equation (6.3)]. This interrelationship reads: D
1 6 2f, (6.9) where  is the diffusion jump distance which is, in isotropic sys￾tems, identical with the interatomic distance. Fick’s first law [Eq. (6.6)] may be used to describe steady-state flow. One assumes for this case an infinite source and an infi￾nite sink, respectively, on the opposite ends of a plate of metal that causes a constant flow of solute atoms through a given area. Steady-state flow is observed, for example, when gases (such as hydrogen or oxygen) diffuse through metals as a con￾sequence of a constant (but different) gas pressure on each side of a plate. This requires a supply of gas atoms on one side and a removal of the same amount of gas atoms on the other side. As an example, hydrogen-filled gas tanks for fuel-cell-propelled automobiles are empty after about two months. (Hand tools in university labs seem to disappear by a similar mechanism.) Fick’s second law deals with the common case for which the con￾centration gradient of a diffusing species, A, in the host material, B, changes gradually with time (Figure 6.6). The nonsteady-state (or dynamic) case is governed by the partial differential equation:   C t
D   2 x C 2 , (6.10) 6.1.7 Nonsteady￾State Diffusion 110 6 • Atoms in Motion (b) (a) C C X A J FIGURE 6.5. (a) Steady￾state diffusion through a slab. (b) Linear con￾centration gradient which stays constant with time by constantly supplying solute atoms on the left and remov￾ing the same number of atoms on the right side of the slab. C and C are two assumed sur￾face concentrations, where C ! C.