diffusion in solids 1

DIFFUSION IN SOLIDS: 

DIFFUSION IN SOLIDS 1 ISSUES TO ADDRESS... • How does diffusion occur? • Why is it an important part of processing? • How can the rate of diffusion be predicted for some simple cases? • How does diffusion depend on structure and temperature? Gear from case-hardened steel (C diffusion)

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2 Diffusion- Steady and Non-Steady State Diffusion - Mass transport by atomic motion Mechanisms Gases & Liquids – random (Brownian) motion Solids – vacancy diffusion or interstitial diffusion

Simple Diffusion: 

3 Simple Diffusion • Glass tube filled with water. • At time t = 0, add some drops of ink to one end of the tube. • Measure the diffusion distance, x, over some time. • Compare the results with theory.

Inter-diffusion: 

4 Inter-diffusion • Interdiffusion : In alloys, atoms tend to migrate from regions of large concentration. Initially After some time Adapted from Figs. 6.1 - 2, Callister 6e . This is a diffusion couple.

Substitution-diffusion: 

Substitution-diffusion 5 • applies to substitutional impurities • atoms exchange with vacancies • rate depends on (1) number of vacancies ; (2) activation energy to exchange . Vacancy Diffusion: increasing elapsed time

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6 Interstitial diffusion – smaller atoms diffuse between atoms. Diffusion Mechanisms More rapid than vacancy diffusion

Modeling rate of diffusion: flux: 

7 Modeling rate of diffusion: flux • Flux : • Directional Quantity • Flux can be measured for: - vacancies - host (A) atoms - impurity (B) atoms Empirically determined: – Make thin membrane of known surface area – Impose concentration gradient – Measure how fast atoms or molecules diffuse through the membrane A = Area of flow J  slope diffused mass M time

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8 • Concentration Profile , C(x): [kg/m 3 ] • Fick's First Law : D is a constant! Adapted from Fig. 6.2(c) Steady-state Diffusion: J ~ gradient of c

Steady-State Diffusion: 

9 Steady-State Diffusion • Steady State : concentration profile not changing with time. • Apply Fick's First Law: • Result: the slope, dC/dx , must be constant (i.e., slope doesn't vary with position)! • If J x ) left = J x ) right , then

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10 Steady-State Diffusion Fick’s first law of diffusion C 1 C 2 x C 1 C 2 x 1 x 2 D  diffusion coefficient Rate of diffusion independent of time J ~

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11 Example: Chemical Protection Clothing Methylene chloride is a common ingredient of paint removers. Besides being an irritant, it also may be absorbed through skin. When using, protective gloves should be worn. If butyl rubber gloves (0.04 cm thick) are used, what is the diffusive flux of methylene chloride through the glove? Data: D in butyl rubber: D = 110 x10 -8 cm 2 /s surface concentrations: Diffusion distance: C 2 = 0.02 g/cm 3 C 1 = 0.44 g/cm 3 x 2 – x 1 = 0.04 cm glove C 1 C 2 skin paint remover x 1 x 2

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12 . Fick's law is commonly used to model transport processes in foods, clothing, biopolymers, pharmaceuticals, porous soils, semiconductor doping process, etc. Where can we use Fick’s Law?

Non-Steady-State Diffusion: 

13 Non-Steady-State Diffusion • Concentration profile, C(x), changes w/ time . • To conserve matter: • Fick's First Law: • Governing Eqn.:

Non-Steady-State Diffusion: C = c(x,t): 

Non-Steady-State Diffusion: C = c(x,t) 14 concentration of diffusing species is a function of both time and position • Copper diffuses into a bar of aluminum. C s Adapted from Fig. 6.5, Callister & Rethwisch 3e . B.C. at t = 0, C = C o for 0  x   at t > 0, C = C S for x = 0 (fixed surface conc.) C = C o for x = 