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 Flux: # of atoms passing through a plane of unit area per unit time.  diffusion is a time-dependent process.  the mass transfer rate is often needed.  mass transfer = diffusion flux (J) (kg/m2·s; atoms/ m2·s)

C1C1 C2C2 x1x1 x2x2 C X J Let the solute concentration be C 1 at point x 1 and C 2 at point x 2. The concentration gradient is since C 2 < C 1.

Fick’s First Law

D is called the diffusivity or the diffusion coefficient.

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 Diffusion  Diffusing 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:

DoDo D T

log D o log D 0 The plot of log D vs. 1/T is a straight line of slope = The intercept of this line with the log D axis is log D o at

Diffusion Example: Determine D cu in Ni at 500°C. Q d = 256 kJ/mol D O = 2.7 x m 2 /sec T = = 773 K R = 8.31 J/mol-K D = 1.33 x m 2 /sec

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. t1t1 t2t2 t0t0

Factors Influencing Diffusion  Diffusion 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 Q gb < Q v, 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-grained Fine-grained