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Unformatted text preview: LN–9 1 3.091 – Introduction to Solid State Chemistry Lecture Notes No. 9 DIFFUSION * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Sources for Further Reading: 1. Shermon, P.G., Diffusion in Solids , McGrawHill (1963). 2. Shaw, D., Atomic Diffusion in Semiconductors , Plenum (1973). 3. Park, G.S., Diffusion in Polymers , Academic Press (1968). 4. Ruoff, A.L., Materials Science , PrenticeHall (1973). * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1. DIFFUSION At any temperature different from absolute zero all atoms, irrespective of their state of aggregation (gaseous, liquid or solid), are constantly in motion. Since the movement of particles is associated with collisions, the path of a single particle is a zigzag one. However, an aggregation of “diffusing” particles has an observable drift from places of higher to places of lower concentration (fig. 1). For this reason diffusion is known as a transport phenomenon. Figure 1 Mass transport, diffusion as a consequence of existing spacial differences in concentration. In each diffusion reaction (heat flow, for example, is also a diffusion process), the flux (of matter, heat, electricity, etc.) follows the general relation: LN–9 2 Flux = (conductivity) x (driving force) In the case of atomic or molecular diffusion, the “conductivity” is referred to as the diffusivity or the diffusion constant , and is represented by the symbol D. We realize from the above considerations that this diffusion constant (D) reflects the mobility of the diffusing species in the given environment and accordingly assumes larger values in gases, smaller ones in liquids, and extremely small ones in solids. ∆ C ∆ x distance concentration ∆ C/ ∆ x → dC/dx Figure 2 Concentration gradient (constant) in the x direction The “driving force” for many types of diffusion is the existence of a concentration gradient . The term “gradient” describes the variation of a given property as a function of distance in the xdirection. If a material exhibits a linear variation of concentration with distance in the xdirection, we speak of a constant concentration gradient in the xdirection. The gradient itself is the rate of change of the concentration with distance (dc/dx), which is the same as the slope of a graph of concentration vs. position ( ∆ c/ ∆ x) (see fig. 2). Steady State and Nonsteady Diffusion Diffusion processes may be divided into two types: (a) steady state and (b) nonsteady state. Steady state diffusion takes place at a constant rate  that is, once the process starts the number of atoms (or moles) crossing a given interface (the flux) is constant with time. This means that throughout the system dc/dx = constant and dc/dt = 0. LN–9 3 Nonsteady state diffusion is a time dependent process in which the rate of diffusion is a function of time. Thus dc/dx varies with time and dc/dt ≠ 0. Both types of diffusion are0....
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 Fall '04
 DONSADOWAY
 Chemistry, Atom, Molecular diffusion, Fick, Diffusion Systems, Nonsteady Diffusion

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