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ISSUES TO ADDRESS...

CHAPTER 5: DIFFUSION IN SOLIDS. 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?. SELF DIFFUSION.

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ISSUES TO ADDRESS...

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  1. CHAPTER 5:DIFFUSION IN SOLIDS 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?

  2. SELF DIFFUSION • Self-diffusion: In an elemental solid, atoms, and therefore vacancies, jump around! Label some atoms After some time C C A D D A B B Energy Random Walk! Distance R at TK The atoms oscillate between these two positions r0 at 0K

  3. TEMPERATURE GRADIENT: Driving Force for Self Diffusion T1 T3 <T1 A atoms vacancies A T2 > T1 The “A” atom is an isotope of the element “A”.

  4. INTERDIFFUSION: Concentration Gradient is the driving Force for Diffusion • Interdiffusion: In an alloy, atoms tend to migrate from regions of large concentration to the regions of low concentration. Initially After some time Adapted from Figs. 5.1 and 5.2, Callister 6e.

  5. DIFFUSION MECHANISM Substitutional Diffusion: • applies to substitutional impurities • atoms exchange with vacancies • rate depends on: --number of vacancies --activation energy to exchange.

  6. DIFFUSION SIMULATION • Simulation of interdiffusion across an interface: • Rate of substitutional diffusion depends on: --vacancy concentration --frequency of jumping. (Courtesy P.M. Anderson)

  7. DIFFUSION MECHANISM Interstitial Diffusion: • Applies to interstitial impurities. • More rapid than the diffusion of substitutional atoms, because it does not require the presence of vacancies. • Simulation: shows the jumping of a smaller atom (gray) from one interstitial site to another in a BCC structure. The interstitial sites considered here are at midpoints along the unit cell edges. (Courtesy P.M. Anderson)

  8. MODELING DIFFUSION: FLUX • Flux: • Directional Quantity • Flux can be measured for: --vacancies --host (A) atoms --impurity (B) atoms

  9. CONCENTRATION PROFILES & FLUX • Concentration Profile, C(x): [kg/m3] Adapted from Fig. 5.2(c), Callister 6e. • Fick's First Law: 2 Diffusion coefficient [m /s] flux in x-dir. dC 2 [kg/m - s] = - J D concentration x dx 4 gradient [kg/m ] • The steeper the concentration profile, the greater the flux!

  10. STEADY STATE DIFFUSION • Steady State: the concentration profile doesn't change with time. • Apply Fick's First Law: • If Jx)left = Jx)right , then • Result: the slope, dC/dx, must be constant (i.e., slope doesn't vary with position)!

  11. EXAMPLE: STEADY STATE DIFFUSION • Steel plate at 700C with geometry shown: Adapted from Fig. 5.4, Callister 6e. • Q: How much carbon transfers from the rich to the deficient side?

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