Chapter 5 Diffusion

Skip Sec. 5-7, 5-8 and 5-9.

Homework No. 6

Problems 4-17, 4-19, 4-32, 4-47, 4-48, 5-9, 5-15, 5-23, 5-26, 5-60

The levels of atomic arrangement in materials: (a) Inert gases have no regular ordering of atoms. (b, c) Some materials, including steam and glass, have ordering only over a short distance (d) Metals and many other solids have a regular ordering of atoms that extends through the material.

Introduction Difference between liquid-state and solid –state diffusion is the

slower diffusion rate in the solid.

Tight atomic structure of atoms has an impact on the diffusion of atoms or ions within the solid.

The energy requirements to squeeze most atoms or ions through a perfect crystal structure are so high that diffusion is nearly impossible.

Vacancy Diffusion

What is needed to make solid-state diffusion practical?

POINT DEFECTS!!!

V

Vacancy Diffusion

atom interchange from a normal lattice position to an adjacent vacant lattice site.

the extent of vacancy diffusion is controlled by the concentration of these defects.

the direction of vacancy motion is opposite to direction of diffusing atoms.

both self-diffusion and interdiffusion occur by this mechanism.

Diffusion Concepts processes reactions in solid state occur by spontaneous

rearrangement of atoms into a more stable state.

for reactions to proceed from an unreacted to a reacted state, atoms must have enough energy to overcome an activation energy barrier.

Diffusion Concepts

Stepwise migration of atoms from a lattice point to another.

In a solid material atoms are in constant motion.

Conditions for atom migration: empty adjacent site. atom must have enough energy to break bonds and cause lattice distortion

during displacement.

diffusive motion influenced by atom vibrational energies f(T)

Interstitial Diffusion

migration of interstitial atoms

from and interstitial position to

adjacent empty one. Typical

interstitial atoms: hydrogen,

carbon, nitrogen, and oxygen.

In most metals interstitial diffusion occurs much more rapidly than vacancy diffusion.

Activation Energy for Diffusion

a diffusing atom must squeeze past neighbor atoms to reach new site.

Energy must be supplied to force atom to its new position activation energy, Q.

normally less energy is required to squeeze an interstitial atom past the surrounding atoms.

Steady State Diffusion

dt

dM

A

1

tA

MJ

Flux: # of atoms passing through a plane of unit area per unit time.

diffusion is a time-dependent process.diffusion is a time-dependent process. the mass transfer rate is often needed.the mass transfer rate is often needed. mass transfer = diffusion flux mass transfer = diffusion flux (J) (J)

(kg/m2·s; atoms/ m2·s)(kg/m2·s; atoms/ m2·s)

C1

C2

x1 x2

C

X

JLet the solute concentration be C1 at point x1 and C2 at point x2. The concentration gradient is

,012

12

xx

CC

dx

dC

since C2 < C1.

dx

dCDJ

Fick’s First Law

D is called the diffusivity or the diffusion coefficient.

),e(eX E/kTQ/RT where X = probability that an atom moves,

Q = activation energy per mole,

E = activation energy per atom,

T = temperature in K.

1

0

X

T

Factors Influencing DiffusionDiffusing Species: the magnitude of the diffusion coefficient D is indicative of

the rate at which atoms diffuse. temperature has a profound effect on diffusion rates:

TR

QDlnDln d

o

1

RTQ

expDD dO

TR.

QDlogDlog d

o

132

Do

D

T

log Do

log D

T

10

The plot of log D vs. 1/T is a straight line of slope =

2.3R

Q

The intercept of this line with the log D axis is log Do at 0.

T

1

Diffusion

Example: Determine Dcu in Ni at 500°C. Qd = 256 kJ/mol

DO= 2.7 x 10- 5 m2/secT = 500 + 273 = 773 KR = 8.31 J/mol-K

D = 1.33 x 10-22 m2/sec

77331.8

256000exp107.2 5D

Factors Influencing Diffusion

Arrhenius plot of relationship between diffusion coefficient and reciprocal of temperature for different elements.

Activation Energy for Diffusion

Factors Influencing Diffusion Diffusing Species: The crystal structure of the metal affects the diffusion rate:

Diffusivities of different elements in BCC-Fe are higher than in FCC-Fe at the same temperature (e.g. 910ºC).

Reasons for faster diffusion in BCC compared with FCC iron: BCC iron lattice is slightly more open; it has lower packing factor than FCC. BCC lattice has a coordination number of 8 compared with 12 in FCC fewer bonds

must be broken when elements diffuse in BCC iron.

G.F. Carter. “Principles of Physical & Chemical Metallurgy”. American Society for Metals (1979)

Non-steady State Diffusion (Fick’s Second Law – not covered) steady-state diffusion not commonly encountered in

engineering materials.

in most cases the concentration of solute atoms at any point in the material changes with time non-steady state diffusion.

t1

t2

t0

Factors Influencing DiffusionDiffusion is faster along grain boundaries than through

grains: More open structure at grain boundaries than the interior grain. Much lower activation energy for diffusion in grain boundaries compared

transgranular diffusion.

G.F. Carter. “Principles of Physical & Chemical Metallurgy”. American Society for Metals (1979).

Grain boundary

Volume

log D

1/T

Since Qgb < Qv , the slope of the Arrhenius plot is less steep for the part of D due to grain boundary diffusion than for the part of D due to volume diffusion.

1/T

log D

Coarse-grainedFine-grained