![Chapter 5 - 19
Diffusion and Temperature
• Diffusion coefficient increases with increasing T.
D Do exp
Qd
RT
= pre-exponential [m2/s]
= diffusion coefficient [m2/s]
= activation energy [J/mol or eV/atom]
= gas constant [8.314 J/mol-K]
= absolute temperature [K]
D
Do
Qd
R
T](https://image.slidesharecdn.com/diffusionfinalppt-220828085320-a7b03c5e/85/diffusion-final-PPT-ppt-19-320.jpg)
diffusion final PPT.ppt
- 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
- 2. Chapter 5 - 2 After studying this chapter you should be able to do the following: 1. Name and describe the two atomic mechanisms of diffusion. 2. Distinguish between steady-state and non steady state diffusion. 3.(a) Write Fick’s first and second laws in equation form and define all parameters. (b) Note the kind of diffusion for which each of these equations is normally applied. 4. Write the solution to Fick’s second law for diffusion into a semi-infinite solid when the concentration of diffusing species at the surface is held constant. Define all parameters in this equation. Learning Objectives
- 3. Chapter 5 - 3 Diffusion Diffusion - Mass transport by atomic motion Many reactions and processes that are important in the treatment of materials rely on the transfer of mass either within a specific solid (ordinarily on a microscopic level) or from a liquid, a gas, or another solid phase.This is necessarily accomplished by diffusion. Mechanisms Gases & Liquids – random (Brownian) motion Solids – vacancy diffusion or interstitial diffusion
- 4. Chapter 5 - 4 Ni Cu Ni Cu Cu Ni
- 5. Chapter 5 - 5 • 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 & Rethwisch 8e. Diffusion After some time This process, whereby atoms of one metal diffuse into another, is termed inter diffusion, or impurity diffusion.
- 6. Chapter 5 - 6 • Self-diffusion: In an elemental solid, atoms also migrate. Label some atoms Diffusion A B C D After some time A B C D Diffusion also occurs for pure metals, but all atoms exchanging positions are of the same type; this is termed self-diffusion.
- 7. Chapter 5 - 7 DIFFUSION MECHANISMS From an atomic perspective, diffusion is just the stepwise migration of atoms from lattice site to lattice site. In fact, the atoms in solid materials are in constant motion, rapidly changing positions. For an atom to make such a move, two conditions must be met: (1) there must be an empty adjacent site, and (2) the atom must have sufficient energy to break bonds with its neighbor atoms and then cause some lattice distortion during the displacement.This energy is vibrational in nature. At a specific temperature some small fraction of the total number of atoms is capable of diffusive motion, by virtue of the magnitudes of their vibrational energies. This fraction increases with rising temperature.
- 8. Chapter 5 - 8 Diffusion Mechanisms Vacancy Diffusion: • atoms exchange with vacancies • applies to substitutional impurities atoms • rate depends on: -- number of vacancies -- activation energy to exchange. increasing elapsed time
- 9. Chapter 5 - 9 Diffusion Mechanisms • Interstitial diffusion – smaller atoms can diffuse between atoms. More rapid than vacancy diffusion Adapted from Fig. 5.3(b), Callister & Rethwisch 8e.
- 10. Chapter 5 - 10 Diffusion • How do we quantify the amount or rate of diffusion? s m kg or s cm mol time area surface diffusing mass) (or moles Flux 2 2 J J slope dt dM A l At M J M = mass diffused time • Measured empirically – Make thin film (membrane) of known surface area – Impose concentration gradient – Measure how fast atoms or molecules diffuse through the membrane
- 11. Chapter 5 - 11 Steady-State Diffusion dx dC D J Fick’s first law of diffusion C1 C2 x C1 C2 x1 x2 D diffusion coefficient Rate of diffusion independent of time Flux proportional to concentration gradient = dx dC 1 2 1 2 linear if x x C C x C dx dC The negative sign in this expression indicates that the direction of diffusion is down the concentration gradient, from a high to a low concentration.
- 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 = 110x10-8 cm2/s – surface concentrations: C2 = 0.02 g/cm3 C1 = 0.44 g/cm3
- 13. Chapter 5 - 13 s cm g 10 x 16 . 1 cm) 04 . 0 ( ) g/cm 44 . 0 g/cm 02 . 0 ( /s) cm 10 x 110 ( 2 5 - 3 3 2 8 - J Example (cont). 1 2 1 2 - x x C C D dx dC D J D tb 6 2 glove C1 C2 skin paint remover x1 x2 • Solution – assuming linear conc. gradient D = 110x10-8 cm2/s C2 = 0.02 g/cm3 C1 = 0.44 g/cm3 x2 – x1 = 0.04 cm Data:
- 14. Chapter 5 - 14 Non-steady State Diffusion • The concentration of diffusing species is a function of both time and position C = C(x,t) • In this case Fick’s Second Law is used 2 2 x C D t C Fick’s Second Law
- 15. Chapter 5 - 15 Non-steady State Diffusion Adapted from Fig. 5.5, Callister & Rethwisch 8e. B.C. at t = 0, C = Co for 0 x at t > 0, C = CS for x = 0 (constant surface conc.) C = Co for x = • Copper diffuses into a bar of aluminum. pre-existing conc., Co of copper atoms Surface conc., C of Cu atoms bar s Cs
- 16. Chapter 5 - 16 Solution: C(x,t) = Conc. at point x at time t erf (z) = error function erf(z) values are given in Table 5.1 CS Co C(x,t) Dt x C C C t , x C o s o 2 erf 1 dy e y z 2 0 2 Adapted from Fig. 5.5, Callister & Rethwisch 8e. Gaussian error function,
- 17. Chapter 5 - FACTORS THAT INFLUENCE DIFFUSION • Diffusing Species • The magnitude of the diffusion coefficient D is indicative of the rate at which atoms diffuse. • Temperature Diffusion coefficient increases with increasing T. 17
- 18. Chapter 5 - 18 Diffusion and Temperature Adapted from Fig. 5.7, Callister & Rethwisch 8e. (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 Dinterstitial >> Dsubstitutional C in a-Fe C in g-Fe Al in Al Fe in a-Fe Fe in g-Fe 1000K/T D (m2/s) 0.5 1.0 1.5 10-20 10-14 10-8 T(C) 1500 1000 600 300
- 19. Chapter 5 - 19 Diffusion and Temperature • Diffusion coefficient increases with increasing T. D Do exp Qd RT = pre-exponential [m2/s] = diffusion coefficient [m2/s] = activation energy [J/mol or eV/atom] = gas constant [8.314 J/mol-K] = absolute temperature [K] D Do Qd R T
- 20. Chapter 5 - • The activation energy may be thought of as that energy required to produce the diffusive motion of one mole of atoms. 20 D Do exp Qd RT
- 21. Chapter 5 - DIFFUSION IN SEMICONDUCTING MATERIALS • One technology that applies solid-state diffusion is the fabrication of semiconductor integrated circuits (ICs).Each integrated circuit chip is a thin square wafer having dimensions on the order of 6 mm by 6 mm by 0.4 mm; furthermore, millions of interconnected electronic devices and circuits are embedded in one of the chip faces. Single-crystal silicon is the base material for most ICs. In order for these IC devices to function satisfactorily, very precise concentrations of an impurity (or impurities) must be incorporated into minute spatial regions in a very intricate and detailed pattern on the silicon chip; one way this is accomplished is by atomic diffusion. 21
- 22. Chapter 5 - OTHER DIFFUSION PATHS • Atomic migration may also occur along dislocations, grain boundaries, and external surfaces.These are sometimes called “short- circuit” diffusion paths inasmuch as rates are much faster than for bulk diffusion. However, in most situations short-circuit contributions to the overall diffusion flux are insignificant because the cross sectional areas of these paths are extremely small. 22
- 23. Chapter 5 - 23 Diffusion FASTER for... • open crystal structures • materials w/secondary bonding • smaller diffusing atoms • lower density materials Diffusion SLOWER for... • close-packed structures • materials w/covalent bonding • larger diffusing atoms • higher density materials Summary