Presentation is loading. Please wait.

Presentation is loading. Please wait.

ENGR-45_Lec-06_Diffusion_Fick-1.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Registered Electrical.

Similar presentations


Presentation on theme: "ENGR-45_Lec-06_Diffusion_Fick-1.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Registered Electrical."— Presentation transcript:

1 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Registered Electrical & Mechanical Engineer Engineering 45 Solid State Diffusion-1

2 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 2 Bruce Mayer, PE Engineering-45: Materials of Engineering Learning Goals - Diffusion  How Diffusion Proceeds  How Diffusion Can be Used in Material Processing  How to Predict The RATE Of Diffusion Be Predicted For Some Simple Cases Fick’s FIRST and second Laws  How Diffusion Depends On Structure And Temperature

3 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 3 Bruce Mayer, PE Engineering-45: Materials of Engineering InterDiffusion  In a SOLID Alloy Atoms will Move From regions of HI Concentration to Regions of LOW Concentration  Initial Condition  After Time+Temp

4 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 4 Bruce Mayer, PE Engineering-45: Materials of Engineering SelfDiffusion  In an Elemental Solid Atoms are NOT in Static Positions; i.e., They Move, or DIFFUSE  Label Atoms  After Time+Temp  How to Label an ATOM? Use a STABLE ISOTOPE as a tag –e.g.; Label 28 Si (92.5% Abundance) with one or both of  29 Si → 4.67% Abundance  30 Si → 3.10% Abundance

5 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 5 Bruce Mayer, PE Engineering-45: Materials of Engineering Diffusion Mechanisms  Substitutional Diffusion Applies to substitutional impurities Atoms exchange position with lattice-vacancies Rate depends on: –Number/Concentration of vacancies (N v by Arrhenius) –Activation energy to exchange (the “Kick-Out” reaction)

6 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 6 Bruce Mayer, PE Engineering-45: Materials of Engineering Substitutional Diff Simulation  Simulation of interdiffusion across an interface  Rate of substitutional diffusion depends on: Vacancy concentration Jumping Frequency

7 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 7 Bruce Mayer, PE Engineering-45: Materials of Engineering Interstitial Diff 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.

8 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 8 Bruce Mayer, PE Engineering-45: Materials of Engineering Diffusion in Processing Case1  Example: CASE Hardening Diffuse carbon atoms into the host iron atoms at the surface. Example of interstitial diffusion is a case Hardened gear.  Result: The "Case" is hard to deform: C atoms "lock" xtal planes to reduce shearing hard to crack: C atoms put the surface in compression Shear Resistant Crack Resistant

9 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 9 Bruce Mayer, PE Engineering-45: Materials of Engineering Doping Silicon with Phosphorus for n-type semiconductors: Process: 1. Deposit P rich layers on surface. 2. Heat it. 3. Result: Doped semiconductor regions. Diffusion in Processing Case2

10 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 10 Bruce Mayer, PE Engineering-45: Materials of Engineering Modeling Diffusion - Flux  Flux is the Amount of Material Crossing a Planar Boundary, or area-A, in a Given Time x-direction Unit Area, A, Thru Which Atoms Move  Flux is a DIRECTIONAL Quantity

11 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 11 Bruce Mayer, PE Engineering-45: Materials of Engineering Concentration Profiles & Flux  Consider the Situation Where The Concentration VARIES with Position i.e.; Concentration, say C(x), Exhibits a SLOPE or GRADIENT  The concentration GRADIENT for COPPER Concentration of Cu (kg/m 3 ) Concentration of Ni (kg/m 3 ) Position, x Cu fluxNi flux xx CC

12 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 12 Bruce Mayer, PE Engineering-45: Materials of Engineering Fick’s First Law of Diffusion  Note for the Cu Flux Proceeds in the POSITIVE-x Direction (+  x) The Change in C is NEGATIVE (–  C)  Experimentally Adolph Eugen Fick Observed that FLUX is Proportional to the Concentration Grad Fick’s Work (Fick, A., Ann. Physik 1855, 94, 59) lead to this Eqn (1 st Law) for J Position, x Cu fluxNi flux xx CC

13 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 13 Bruce Mayer, PE Engineering-45: Materials of Engineering Fick’s First Law cont.  Consider the Components of Fick’s 1 st Law Position, x Cu fluxNi flux xx CC  J  Mass Flux in kg/m 2 s Atom Flux in at/m 2 s  dC/dx = Concentration Gradient In units of kg/m 4 or at/m 4  D  Proportionality Constant Units Analysis

14 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 14 Bruce Mayer, PE Engineering-45: Materials of Engineering Fick’s First Law cont.2  Units for D Position, x Cu fluxNi flux xx CC  D → m 2 /S  One More CRITICAL Issue Flux “Flows” DOWNHILL –i.e., Material Moves From HI-Concen to LO-Concen The Greater the Negative dC/dx the Greater the Positive J –i.e.; Steeper Gradient increases Flux  The NEGATIVE Sign Indicates:

15 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 15 Bruce Mayer, PE Engineering-45: Materials of Engineering Diffusion and Temperature  Diffusion coefficient, D, increases with increasing T → D(T) by: D  DoDo exp       – QdQd RT = pre-exponential constant factor [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 DoDo QdQd R T

16 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 16 Bruce Mayer, PE Engineering-45: Materials of Engineering Diffusion Types Compared  Some D vs T Data 1000 K/T D (m 2 /s) C in  -Fe C in  -Fe Al in Al Fe in  -Fe Fe in  -Fe T(  C)  The Interstitial Diffusers C in α -Fe C in γ-Fe  Substitutional Diffusers > All Three Self- Diffusion Cases The Interstitial Form is More Rapid

17 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 17 Bruce Mayer, PE Engineering-45: Materials of Engineering STEADY STATE Diffusion  Steady State → Diffusion Profile, C(x) Does NOT Change with TIME (it DOES change w/ x) Example: Consider 1-Dimensional, X-Directed Diffusion, J x Concentration, C, in the box does not change w/time. J x(right) J x(left) x  For Steady State the Above Situation may, in Theory, Persist for Infinite time To Prevent infinite Filling or Emptying of the Box

18 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 18 Bruce Mayer, PE Engineering-45: Materials of Engineering Steady State Diffusion cont  Since Box Cannot Be infinitely filled it MUST be the case: J x(right) J x(left) x  Now Apply Fick’s First Law  Thus, since D=const  Therefore While C(x) DOES change Left-to-Right, the GRADIENT, dC/dx Does NOT –i.e. C(x) has constant slope

19 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 19 Bruce Mayer, PE Engineering-45: Materials of Engineering Example SS Diffusion  Iron Plate Processed at 700 °C under Conditions at Right  Find the Carbon Diffusion Flux Thru the Plate  For SS Diffusion   dC/dx  f(x) i.e., The Gradient is Constant  For const dC/dx C 1 = 1.2kg/m 3 C 2 = 0.8kg/m 3 Carbon rich gas 10mm Carbon deficient gas x1x1 x2x2 0 5mm D=3x m 2 /s Steady State → CONST SLOPE

20 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 20 Bruce Mayer, PE Engineering-45: Materials of Engineering Expl SS Diff cont  Thus the Gradient  Use In Fick’s 1 st Law  or C 1 = 1.2kg/m 3 C 2 = 0.8kg/m 3 Carbon rich gas 10mm Carbon deficient gas x1x1 x2x2 0 5mm D=3x m 2 /s Steady State → CONST SLOPE

21 ENGR-45_Lec-06_Diffusion_Fick-1.ppt 21 Bruce Mayer, PE Engineering-45: Materials of Engineering WhiteBoard Work  Problem Similar to 5.9 Hydrogen Diffusion Thru  -Iron  -Fe:  = 7870 kg/m 3


Download ppt "ENGR-45_Lec-06_Diffusion_Fick-1.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Registered Electrical."

Similar presentations


Ads by Google