CHAPTER 5: DIFFUSION

1. CHAPTER 5: DIFFUSION • Material transport by atomic motion Issues to consider: • • Types • Predicting the rate of diffusion • Factors that influence diffusion • Importance of diffusion in materials processing

2. DIFFUSION EXAMPLE: Liquids • 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.

3. DIFFUSION: Solids Types: Self-diffusion vs. Interdiffusion • Self-diffusion: Elemental solid – atoms migrate. Atom positions at some time After some time – atoms migrated

4. • Interdiffusion: Two metals (diffusion couple) adjacent to each other Apply Heat - accelerates vibrational motion Initially After some time

5. DIFFUSION MECHANISMS Vacancy Diffusion: • • atoms move to an adjacent vacant lattice site • for both self- and interdiffusion (substitutional impurities) • • rate depends on: • --number of vacancies • --activation energy

6. Interstitial Diffusion: • • Applies to interstitial • impurities. • • More rapid than • vacancy diffusion. • Smaller and hence more mobile • There are more interstitial sites than vacancies. • • Simulation: • --shows the jumping of a • smaller atom (gray) from • one interstitial site to • another in a BCC • structure.

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

8. Fick’s First Law • Concentration Profile, C(x): [kg/m3] • Fick's First Law: • • Negative sign – diffusion from higher to lower concentration. • The steeper the concentration profile, the greater the flux.

9. 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)!

10. EX: 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?

11. NON STEADY STATE DIFFUSION • Concentration profile, C(x), changes w/ time. • To conserve matter: • Fick's First Law: • Governing Eqn.:

12. EX: NON STEADY STATE DIFFUSION • Copper diffuses into a bar of aluminum. • General solution: "error function" Values given in Table 5.1, Callister 6e.

13. Factors that Influence Diffusion • Diffusing species – Table 5.2 • Temperature: Dramatic dependence

14. Diffusion Example • Ex. The Diffusion coefficients for Cu in Ni at two temperatures are given: • T (deg C) D(m /s) • 600 5.5 E-14 • 700 3.9 E-13 • Find Qd and Do. B) D at 800 deg C. 2

15. PROCESSING USING DIFFUSION • Case Hardening: --Diffuse carbon atoms into the host iron atoms at the surface. --Example of interstitial diffusion is a case hardened gear. Fig. 5.0, Callister 6e. (Fig. 5.0 is courtesy of Surface Division, Midland-Ross.) • Result: The "Case" is --hard to deform: C atoms "lock" planes from shearing. --hard to crack: C atoms put the surface in compression.

16. PROCESSING USING DIFFUSION • Doping Silicon with P for n-type semiconductors: • Process: 1. Deposit P rich layers on surface. Fig. 18.0, Callister 6e. 2. Heat it. 3. Result: Doped semiconductor regions.