Preparation of Materials Lecture 6

Transcription

1 PY3090 Preparation of Materials Lecture 6 Colm Stephens School of Physics PY3090 6

2 iffusion iffusion Mass transport by atomic motion Mechanisms Gases & Liquids random (Brownian) motion Solids vacancy diffusion or interstitial diffusion

3 iffusion Interdiffusion: In an alloy, atoms tend to migrate from regions of high concentration to regions of low concentration. Initially After some time 3

4 iffusion Self-diffusion: In an elemental solid, atoms also migrate. Label some atoms C A B After some time C A B 4

5 iffusion Mechanisms Vacancy iffusion: atoms exchange with vacancies applies to substitutional impurities atoms rate depends on: --number of vacancies --activation energy to exchange. increasing elapsed time 5

6 iffusion Mechanisms Interstitial diffusion smaller atoms can diffuse between atoms. More rapid than vacancy diffusion 6

7 Processing Using iffusion Case Hardening: --iffuse 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. 7

8 Carburising of steel 8

9 Carburising of steel 600 δ 400 T( C) L 00 γ (austenite) γ +L 48 C L+Fe 3 C α 600 α +γ γ +Fe 3 C 77 C T eutectoid α +Fe 3 C Fe 3 C (cementite) (Fe).4% C o, wt% C 9

10 Processing Using iffusion oping silicon with phosphorus for n-type semiconductors: Process: 0.5mm. eposit P rich layers on surface.. Heat it. silicon 3. Result: oped semiconductor regions. magnified image of a Si chip light regions: Si atoms silicon light regions: Al atoms 0

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

12 Steady-State State iffusion Rate of diffusion independent of time Flux proportional to concentration gradient dc dx C C Fick s first law of diffusion C C J dc dx x x x diffusion coefficient if linear dc dx ΔC Δx C x C x

13 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? ata: diffusion coefficient in butyl rubber: 0 x0-8 cm /s surface concentrations: C 0.44 g/cm 3 C 0.0 g/cm 3 3

14 Example (cont). Solution assuming linear conc. gradient C paint remover glove x x t b 6 C skin J - ata: dc dx C x C x 0x0-8 cm /s C 0.44 g/cm 3 C 0.0 g/cm 3 x x 0.04 cm J (0 x 0-8 cm (0.0 g/cm 0.44 g/cm /s) (0.04 cm) 3 3 ).6 x 0-5 g cm s 4

15 iffusion and Temperature iffusion coefficient increases with increasing T. o exp Q d RT o Q d R T diffusion coefficient [m /s] pre-exponential [m /s] activation energy [J/mol or ev/atom] gas constant [8.34 J/mol-K] absolute temperature [K] 5

16 iffusion and Temperature has exponential dependence on T (m /s) C in γ-fe 600 C in α-fe T( C) interstitial >> substitutional 0-4 Fe in γ-fe Fe in α-fe Al in Al C in α-fe C in γ-fe Al in Al Fe in α-fe Fe in γ-fe K/T 6

17 7 Example: At 300ºC the diffusion coefficient and activation energy for Cu in Si are (300ºC) 7.8 x 0 - m /s Q d 4.5 kj/mol What is the diffusion coefficient at 350ºC? ln ln ln T T R Q d T 0 0 ln ln and ln ln T R Q R Q d d

18 Example (cont.) exp Q R d T T (7.8 x 0 m /s) 4,500 J/mol exp 8.34 J/mol - K 63 K 573 K 5.7 x 0 - m /s 8

19 Non-steady State iffusion 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 Fick s Second Law C t C x 9

20 Non-steady State iffusion Copper diffuses into a bar of aluminum. Surface conc., Cs of Cu atoms bar pre-existing concentration, C o of copper atoms B.C. at t 0, C C o for 0 x at t > 0, C C S C C o for x 0 (const. surf. conc.) for x 0

21 Solution: ( x,t ) C C s C C o o erf x t C(x,t) ) Conc. at point x at time t erf (z)) Gaussian error function C S C(x,t) π z e y 0 dy C o

22 Non-steady State iffusion Sample Problem: An FCC iron-carbon alloy initially containing 0.0 wt% C is carburized at an elevated temperature and in an atmosphere that gives a surface carbon concentration constant at.0 wt%. If after 49.5 h the concentration of carbon is 0.35 wt% at a position 4.0 mm below the surface, determine the temperature at which the treatment was carried out. Solution: use equation C( x, t) C C C s o o erf x t

23 Solution (cont.): C( x,t ) C C C s o o erf x t t 49.5 h C x 0.35 wt% C o 0.0 wt% x 4 x 0-3 m C s.0 wt% C( x, t) C C C s o o erf x t erf( z) erf(z)

24 Solution (cont.): We must now determine from table the value of z for which the error function is z erf(z) z z z Now solve for z x t x 4z t x 4z t (4 x 0 (4)(0.93) 3 m) (49.5 h) h 3600 s.6 x 0 m /s 4

25 To solve for the temperature at which has above value, we use a rearranged form of o exp Q d RT T Q R( ln ln) for diffusion of C in FCC Fe o.3 x 0-5 m /s Q d 48,000 J/mol o d T (8.34 J/mol - K)(ln.3x0 48,000 J/mol 5 m /s ln.6x0 m /s) T 300 K 07 C 5