Foundations of Materials Science and Engineering Lecture Note 8 (Chapter 5 Diffusion)

Transcription

1 Foundations of Materials Science and Engineering Lecture Note 8 (Chapter 5 Diffusion) May 13, 2013 Kwang Kim Yonsei University kbkim@yonsei.ac.kr Y O N Se I

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3 Introduction Processing Using Diffusion Furnace for heat treating steel using carburization. Carburizing is the addition of carbon to the surface of low-carbon steels at temperatures ranging from 1560 F to 1740 F. Hardening is achieved when a high carbon martensitic case with good wear and fatigue resistance is superimposed on a tough, low-carbon steel core.

4 Introduction Processing Using Diffusion Case hardening or surface hardening is the process of hardening the surface of a metal, often a low carbon steel, by diffusing elements into the material's surface, forming a thin layer of a harder alloy. Carbon atoms diffuse into the iron lattice atoms at the surface. This is an example of interstitial diffusion. The C atoms make iron (steel) harder. Result: The presence of C atoms makes iron (steel) harder.

5 Introduction Processing Using Diffusion Carbide band saw blade can cut through case hardened materials.

6 Introduction Doping by Diffusion Integrated circuits (ICs), found in numerous electronic devices have been fabricated using doping techniques. The base material for these ICs is silicon that has been doped with other materials. More precisely, controlled concentrations of impurities have been diffused into specific regions of the device to change the properties (improve electrical conductivity).

7 Introduction Doping silicon with phosphorus for n-type semiconductors: 1. Deposit P rich layers on surface. silicon 0.5 mm magnified image of a computer chip 2. Heat it. 3. Result: Doped semiconductor regions. light regions: Si atoms silicon light regions: Al atoms Adapted from Figure 18.27, Callister & Rethwisch 8e.

8 Introduction Diffusion - Phenomenon of material/matter transport by atomic motion Often think of diffusion in a medium where atoms are relatively free to move around such as liquids and gases Materials processing Many materials are heat treated to achieve necessary properties: prefer to develop methods that will allow relatively high diffusion rates to achieve an efficient/cost-effectively process (e.g. alloying, case hardening etc ) Mechanisms Gases & Liquids random (Brownian) motion Solids vacancy diffusion or interstitial diffusion

9 Introduction Diffusion Diffusion - Mass transport by atomic motion. Diffusion is a consequence of the constant thermal motion of atoms, molecules and particles that results in material moving from areas of high to low concentration. Mechanisms Brownian motion is the seemingly random movement of particles suspended in a liquid or gas. Solids vacancy diffusion or interstitial diffusion.

10 Introduction DIFFUSION DEMO 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. t o x (mm) t 1 t 2 t 3 x o x 1 x 2 x 3 time (s)

11 Diffusion

12 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 & Rethwisch 8e.

13 Diffusion Self-diffusion: In an elemental solid, atoms also migrate. C C D A B A B D

14 Diffusion Mechanism Atoms in solid materials are in constant motion, rapidly changing positions. For an atom to move, 2 conditions must be met: 1. There must be an empty adjacent site, and 2. The atom must have sufficient (vibrational) energy to break bonds with its neighboring atoms and then cause lattice distortion during the displacement. At a specific temperature, only a small fraction of the atoms is capable of motion by diffusion. This fraction increases with rising temperature. There are 2 dominant models for metallic diffusion: 1. Vacancy Diffusion 2. Interstitial Diffusion

15 Diffusion Mechanism Vacancy Diffusion: atoms exchange with vacancies applies to substitutional impurities atoms rate depends on: -- number of vacancies -- activation energy to exchange. -- frequency of jumping increasing elapsed time

16 Diffusion Mechanism ACTIVATION ENERGY FOR DIFFUSION Initial state Intermediate state Final state Energy Activation energy Also called energy barrier for diffusion

17 Diffusion Mechanism Atom needs enough thermal energy to break bonds and squeeze through its neighbors. Energy needed energy barrier Called the activation energy E m (like Q) Energy Atom E m Vacancy Distance Diagram for Vacancy Diffusion Diffusion Thermally Activated Process

18 Diffusion Mechanism Interstitial diffusion smaller atoms (H, C, O, N) can diffuse between atoms. More rapid than vacancy diffusion due to more mobile small atoms and more empty interstitial sites.

19 Diffusion Mechanism PROCESSING USING DIFFUSION (1) Case Hardening: -- Example of interstitial diffusion is a case hardened gear. -- Diffuse carbon atoms into the host iron atoms at the surface. 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.

20 Introduction Doping silicon with phosphorus for n-type semiconductors: 1. Deposit P rich layers on surface. silicon 0.5 mm magnified image of a computer chip 2. Heat it. 3. Result: Doped semiconductor regions. light regions: Si atoms silicon light regions: Al atoms Adapted from Figure 18.27, Callister & Rethwisch 8e.

21 Diffusion Flux

22 Diffusion Flux

23 Diffusion Flux

24 Diffusion Flux How do we quantify the rate of diffusion? moles (or mass) diffusing mol J Flux or cm s Measured empirically Make thin film (membrane) of known surface area Impose concentration gradient Measure how fast atoms or molecules diffuse through the membrane kg surface areatime 2 2 m s J M At l A dm dt M = mass diffused time J slope

25 Steady State Diffusion Steady-state diffusion across a thin plate Rate of diffusion is independent of time; the diffusion flux does not change with time. The concentration profile shows the concentration (C) vs the position within the solid (x); the slope at a particular point is the concentration gradient.

26 Steady State Diffusion Steady State: the concentration profile doesn't change with time. Flux proportional to concentration gradient = dc dx C 1 C 1 Fick s first law of diffusion C 2 C 2 J D dc dx if linear dc dx x 1 x 2 x D diffusion coefficient C x C x 2 2 C x 1 1 D : independent of time

27 Steady State Diffusion 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 1 = 0.44 g/cm 3 C 2 = 0.02 g/cm 3

28 Steady State Diffusion Example: Chemical Protective Clothing (CPC) Solution assuming linear conc. gradient C 1 paint remove r glove x 1 x 2 2 t b 6D C 2 skin J - D dc dx C D x 2 2 C x Data: D = 110 x 10-8 cm 2 /s C 1 = 0.44 g/cm 3 C 2 = 0.02 g/cm 3 x 2 x 1 = 0.04 cm 1 1 J (110 x 10-8 cm 2 (0.02 g/cm 0.44 g/cm /s) (0.04 cm) 3 3 ) 1.16 x 10-5 g cm 2 s

29 Diffusion Coefficient Diffusion coefficient increases with increasing T. D D o exp Q d RT D D o Q d R T = diffusion coefficient [m 2 /s] = pre-exponential [m 2 /s] = activation energy [J/mol or ev/atom] = gas constant [8.314 J/mol-K] = absolute temperature [K]

30 Diffusion Coefficient DIFFUSION AND TEMPERATURE Diffusivity increases with T. diffusivity D D o exp Q d RT pre-exponential [m 2 /s] (see Table 5.2, Callister 6e) activation energy [J/mol],[eV/mol] (see Table 5.2, Callister 6e) gas constant [8.31J/mol-K] Remember vacancy concentration: N V = N exp(-qv/kt) QV is vacancy formation energy (larger this energy, smaller the number of vacancies) Qd is the activation energy (larger this energy, smaller the diffusivity and lower the probability of atomic diffusion)

31 Diffusion Mechanism ACTIVATION ENERGY FOR DIFFUSION Initial state Intermediate state Final state Energy Activation energy Also called energy barrier for diffusion

32 Diffusion Coefficient Factors that influence diffusion The diffusing species, host material and temperature influence the diffusion coefficient. For example, there is a significant difference in magnitude between self-diffusion and carbon interdiffusion in α iron at 500 C.

33 Diffusion Coefficient Diffusion coefficient increases with increasing T. D has exponential dependence on T T(C) D (m 2 /s) Dinterstitial C in -Fe C in -Fe >> D substitutional Al in Al Fe in -Fe Fe in -Fe K/T

34 Diffusion Coefficient Example: At 300ºC the diffusion coefficient and activation energy for Cu in Si are D(300ºC) = 7.8 x m 2 /s, Q d = 41.5 kj/mol What is the diffusion coefficient at 350ºC? D transform data ln D lnd 2 lnd Temp = T lnd 2 0 lnd Q R 1 d 1 T2 D2 ln D 1 and Q R d lnd T2 T1 lnd 1/T 0 Q R d 1 T1

35 Diffusion Coefficient D 2 D 1 exp Q R d 1 T2 1 T 1 T 1 = = 573K T 2 = = 623K D 2 (7.8 x m 2 /s) 41,500 J/mol exp J/mol - K K K D 2 = 15.7 x m 2 /s

36 Non-steady State Diffusion The concentration of diffusing species is a function of both time and position C = C(x,t). More likely scenario than steady state. In this case, Fick s Second Law is used. Fick s Second Law C t D 2 C 2 x

37 Non-steady State Diffusion Copper diffuses into a bar of aluminum. Surface conc., Cs of Cu atoms bar pre-existing conc., C o of copper atoms Cs B.C. at t = 0, C = C o for 0 x at t > 0, C = C S for x = 0 (constant surface conc.) C = C o for x = 37

38 Non-steady State Diffusion C x,t C C C s o o 1 erf 2 x Dt C(x,t) = Conc. at point x at time t erf (z) = error function C S 2 z 2 e y 0 dy C(x,t) C o Diffusion depth given by: x i Dt i

39 Non-steady State Diffusion

40 Diffusion in ionic solids Which do you expect to diffuse faster, cations or anions? Smaller cations will usually diffuse faster. But analogous to charge neutrality required for defect formation, each ion will need counter charge to move with it (e.g. vacancy, impurity or free electrons or holes).

41 Diffusion in Solids Diffusion FASTER for... open crystal structures lower melting T materials materials w/secondary bonding smaller diffusing atoms lower density materials Diffusion SLOWER for... close-packed structures higher melting T materials materials w/covalent bonding larger diffusing atoms higher density materials