Nano & Flexible

Device Materials Lab.11

Diff. In Dilute Substitutional Alloys

XB~0 , XA~1

• Normally DB > DA in dilute sol.

• (solute atom > solvent atom in size )

• Solute – Vacancy pair

Atomic Mobility

• DB = MBRT ( for ideal dilute solution )

• Prove that DB = MBRT [ 1 + ]B

B

Xd

d

ln

ln

Phase Transformation In Materials

Nano & Flexible

Device Materials Lab.22

Diffusion In Ternary Alloy

Example) Fe-Si-C system (Fe-3.8%Si-0.48%C) vs. (Fe-0.44%C) at 1050

oC

① Si raises the μC (chemical potential of carbon) in solution.

② MSi (sub.)≪ MC (int.), M : mobility

• Interface: local equilibrium

• System: partial equilibrium

Phase Transformation In Materials

Nano & Flexible

Device Materials Lab.33

High Diffusion path

Defect (grain boundary, dislocation, surface) : more open

structure

⇒ fast diffusion path

)exp(RT

QDD l

lol

)exp(RT

QDD b

bob

)exp(RT

QDD s

sos

Diff. along lattice

Diff. along grain boundary

Diff. along free surface

Ds > Db > Dl

But area fraction → lattice > g.b > surface

Phase Transformation In Materials

Nano & Flexible

Device Materials Lab.44

Lattice vs. Grain Boundary Diffusion

dx

dCDJ ll

dx

dCDJ bb

dx

dC

d

DD

d

dJJJ lblb )(

)(

∴ dDDD blapparent

dD

D

D

D

l

b

l

app 1or

Phase Transformation In Materials

Nano & Flexible

Device Materials Lab.5

Where Dbδ > Dld grain boundary diffusion is important

Width of grain boundary: ~ 0.5nm, grain size: 1~1000

㎛

Db > Dl ( always ), Also Qb ~ 0.5Ql in FCC materials

→ Contribution depends on temperature

Dg.b is important

below 0.75 ~ 0.8Tm

High T – lattice diff. Low T – g.b diff.

Phase Transformation In Materials

Nano & Flexible

Device Materials Lab.66

Diffusion along Pipe

g: Cross-sectional area of pipe per unit area of matrix (δ/dimension)

l

p

l

app

D

Dg

D

D 1

ex) annealed metal ~ 105disl/mm2

Pipe accommodates 10 atoms in the cross-section, matrix contains 1013 atoms mm-2

7

13

6

13

5

1010

10

10

10*10 g

Phase Transformation In Materials

Nano & Flexible

Device Materials Lab.77

Moving Boundary Problem

Mass balance

)1)(()( dxCCdtJJa

B

b

BBB

x

CD

x

CD

CCdt

dxv

b

B

a

B

a

B

b

B

)(~

)(~

)(

1

x

CDJ

b

BB

)(

~

x

CDJ

a

BB

)(

~

,

Diffusion flux determines velocity (in local equilibrium)

Reaction that passes Interface is important

→ interface (reaction) controlled

Diffusion in Multiple Binary System

Phase Transformation In Materials

Nano & Flexible

Device Materials Lab.88

Multiphase Binary System (Phase Diagram and Chemical

Potential)

Phase Transformation In Materials

Nano & Flexible

Device Materials Lab.99

Diffusion in Multiphase System

Phase Transformation In Materials

Nano & Flexible

Device Materials Lab.1010

Moving boundary problem

Phase Transformation In Materials

CB

x

CBb

CBb

dx

b

a

J J

x

CD

x

CD

CCdt

dxv

b

B

a

B

a

B

b

B

)(~

)(~

)(

1

Velocity of - interface

x

CDJ

b

B

)(

~

x

CDJ

a

B

)(

~

1)(~

)(~

1)(

dt

x

CD

x

CDdxCC

a

B

b

Ba

B

b

B

Amount of accumulated B atoms

volume = dx X 1 (unit area)

Nano & Flexible

Device Materials Lab.1111

Diffusion Controlled :

Diffusion flux 가 velocity를결정. (local equilibrium에 있을경우)

Interface (reaction) Controlled:

Interface를뛰어넘는계면반응이중요한경우

Phase Transformation In Materials

Nano & Flexible

Device Materials Lab.1212

Kinetic parameters and measurements

Phase Transformation In Materials

Thermodynamic variables : p, V, T, S, and m

Kinetic parameters : atomic diffusivities, surface and

interface energies, interfacial reaction constants, and

enthalpy (heat) of formation

When the dependence of the layer thickness (x) on time

(t) measured, we can plot x versus t and x versus t1/2

tDx~

42 Ktx

kT

EDD aexp~~

0

kT

EKK aexp0

We can get reaction constant (K), atomic diffusivity (D),

activation energy