Understanding Diffusion in Processing: Importance and Prediction of Rates

1. Chapter 5 - 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? Chapter 5: Diffusion in Solids

2. Chapter 5 - 2 Diffusion Diffusion - Mass transport by atomic motion Migration of atoms from lattice site to lattice site. Two conditions must be met: 1. There must be an empty adjacent site. 2. Atoms must have sufficient energy to break bonds with its neighbor atoms. Mechanisms Gases & Liquids random (Brownian) motion Solids vacancy diffusion or interstitial diffusion

3. Chapter 5 - 3 Interdiffusion : In an alloy, atoms tend to migrate from regions of high conc. to regions of low conc. Initially Adapted from Figs. 5.1 and 5.2, Callister 7e . Diffusion After some time

4. Chapter 5 - 4 f01_05_pg110 f02_05_pg111 Inter diffusion A process whereby atoms of one metal difuse into another.

5. Chapter 5 - 5 Self-diffusion : In an elemental solid, atoms also migrate. Label some atoms After some time Diffusion A B C D

6. Chapter 5 - 6 Diffusion Mechanisms Vacancy Diffusion: atoms exchange with vacancies applies to substitutional impurities atoms rate depends on: --number of vacancies (vacancy diffusion is a function of the number of these defects that are present) --activation energy to exchange. increasing elapsed time

7. Chapter 5 - 7 Diffusion Mechanisms Interstitial diffusion smaller atoms can diffuse between atoms. More rapid than vacancy diffusion Adapted from Fig. 5.3 (b), Callister 7e .

8. Chapter 5 - 8 Adapted from chapter-opening photograph, Chapter 5, Callister 7e. (Courtesy of Surface Division, Midland-Ross.) Case Hardening : --Diffuse carbon atoms into the host iron atoms at the surface. --Example of interstitial diffusion is a case hardened gear. Result: The presence of C atoms makes iron (steel) harder. Processing Using Diffusion

9. Chapter 5 - 9 Diffusion How do we quantify the amount or rate of diffusion? Diffusion flux (J): mass or equivalently number of atoms M diffusing through and perpendicular a unit cross sectional area per unit of time Measured empirically Make thin film (membrane) of known surface area Impose concentration gradient Measure how fast atoms or molecules diffuse through the membrane

10. Chapter 5 - 10 Steady-State Diffusion Ficks 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 Flux proportional to concentration gradient =

11. Chapter 5 - 11 Concentration Profile , C(x): [kg/m 3 ] 11 Fick's First Law: The steeper the concentration profile, the greater the flux! Adapted from Fig. 5.2(c), Callister 6e . CONCENTRATION PROFILES & FLUX

12. Chapter 5 - 12 Example: Chemical Protective Clothing (CPC) Methylene chloride is a common ingredient of paint removers. Besides being an irritant, it also may be absorbed through skin. When using this paint remover, 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: diffusion coefficient in butyl rubber: D = 110 x10 -8 cm 2 /s surface concentrations: C 2 = 0.02 g/cm 3 C 1 = 0.44 g/cm 3

13. Chapter 5 - 13 Example (cont). glove C 1 C 2 skin paint remover x 1 x 2 Solution assuming linear conc. gradient D = 110 x 10 -8 cm 2 /s C 2 = 0.02 g/cm 3 C 1 = 0.44 g/cm 3 x 2 x 1 = 0.04 cm Data:

14. Chapter 5 - 14 Diffusion and Temperature Diffusion coefficient increases with increasing T . D D o exp Q d R T = pre-exponential [m 2 /s] = diffusion coefficient [m 2 /s] = activation energy [J/mol or eV/atom] = gas constant [8.314 J/mol-K] = absolute temperature [K] D D o Q d R T

15. Chapter 5 - 15 Diffusion and Temperature Adapted from Fig. 5.7, Callister 7e . (Date for Fig. 5.7 taken from E.A. Brandes and G.B. Brook (Ed.) Smithells Metals Reference Book , 7th ed., Butterworth-Heinemann, Oxford, 1992.) D has exponential dependence on T D interstitial >> D substitutional C in -Fe C in -Fe Al in Al Fe in -Fe Fe in -Fe 1000 K/ T D (m 2 /s) C in -Fe C in -Fe Al in Al Fe in -Fe Fe in -Fe 0.5 1.0 1.5 10 -20 10 -14 10 -8 T ( C) 1500 1000 600 300

16. Chapter 5 - 16 t02_05_pg119

17. Chapter 5 - 17 Example: At 300C the diffusion coefficient and activation energy for Cu in Si are D (300C) = 7.8 x 10 -11 m 2 /s Q d = 41.5 kJ/mol What is the diffusion coefficient at 350C? transform data D Temp = T ln D 1/ T

18. Chapter 5 - 18 Example (cont.) T 1 = 273 + 300 = 573 K T 2 = 273 + 350 = 623 K D 2 = 15.7 x 10 -11 m 2 /s