TOPIC 2: 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?

Diffusion Diffusion - Mass transport by atomic motion in materials (solids, liquids or gases) Mechanisms Gases & Liquids – random (Brownian) motion Solids – vacancy diffusion or interstitial diffusion Diffusion mechanism depends on material

Why diffusion is important? Heat treatment (phase transformation from solid to solid) Solidification (liquid to solid) Surface hardening of steel (carburising, nitriding, etc…) Coatings sintering of ceramics

Diffusion in solid materials Temperature should be high enough to overcome energy barriers to atomic motion Heat : causes atoms to vibrate Vibration amplitude : increases with temperature Melting occurs when vibrations are sufficient to rupture bonds

Two types of diffusion in crystalline solids: impurity diffusion or interdiffusion Occurs in a solid material with more than one type of element (such as an alloy) (2) Self-diffusion Occurs in chemically pure materials (only one type of atoms)

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

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

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

Diffusion mechanism Atoms are constantly in motion and vibrating Change of atomic position requires: Vacant site Energy to break atomic bonds Two types of diffusion mechanism: Vacancy diffusion or substitutional diffusion Interstitial diffusion

Diffusion Mechanisms Vacancy Diffusion: • atoms exchange with vacancies • applies to substitutional impurities atoms Both self diffusion and interdiffusion occur by this mechanism • rate depends on: --number of vacancies --activation energy to exchange.

Diffusion Mechanisms Interstitial diffusion – smaller atoms can diffuse between atoms. this is essentially mechanism in amorphous materials such as polymer membranes Adapted from Fig. 5.3 (b), Callister 7e. More rapid than vacancy diffusion because the interstitial atoms are smaller, thus more mobile. Also, there are more empty interstitial positions than vacancies.

INTERSTITIAL SIMULATION • Applies to interstitial impurities. • More rapid than vacancy diffusion. • 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)

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. Adapted from chapter-opening photograph, Chapter 5, Callister 7e. (Courtesy of Surface Division, Midland-Ross.) • Result: The presence of C atoms makes iron (steel) harder.

Steady-State Diffusion Rate of diffusion independent of time (no change in concentration of solute atoms with time) Flux proportional to concentration gradient = C1 C2 x x1 x2 Fick’s first law of diffusion D  diffusion coefficient

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 cm2/s surface concentrations: C1 = 0.44 g/cm3 C2 = 0.02 g/cm3

Example (cont). Solution – assuming linear conc. gradient Data: glove paint remover skin D = 110 x 10-8 cm2/s C2 = 0.02 g/cm3 C1 = 0.44 g/cm3 x2 – x1 = 0.04 cm Data: C2 x1 x2

Diffusion and Temperature • Diffusion coefficient increases with increasing T. Arrhenius equation: D = Do exp æ è ç ö ø ÷ - Qd R T = 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]

Diffusion and Temperature D has exponential dependence on T 1000 K/T D (m2/s) C in a-Fe C in g-Fe Al in Al Fe in a-Fe Fe in g-Fe 0.5 1.0 1.5 10-20 10-14 10-8 T(C) 1500 1000 600 300 D interstitial >> D substitutional C in a-Fe C in g-Fe Al in Al Fe in a-Fe Fe in g-Fe 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.)

What is the diffusion coefficient at 350ºC? Example: At 300ºC the diffusion coefficient and activation energy for Cu in Si are D(300ºC) = 7.8 x 10-11 m2/s Qd = 41.5 kJ/mol What is the diffusion coefficient at 350ºC? transform data D Temp = T ln D 1/T

Example (cont.) T1 = 273 + 300 = 573 K T2 = 273 + 350 = 623 K D2 = 15.7 x 10-11 m2/s

Non-steady State Diffusion The concentration of diffusing species is a function of both time and position C = C(x,t). In most cases non-steady state diffusion is occurs, where the concentration of solute atoms at any point in the materials changes with time. e.g. If carbon is being diffused in the surface of a steel camshaft to harden its surface, the concentration of carbon under the surface at any point will change with time as the diffusion process progresses. In this case Fick’s Second Law is used In the non-steady state the concentration profile develops with time. Fick’s Second Law

Summary Diffusion FASTER for... Diffusion SLOWER for... • open crystal structures • smaller diffusing atoms • lower density materials Diffusion SLOWER for... • close-packed structures • larger diffusing atoms • higher density materials