Questions and Answers, Year 2, Metals and Alloys

Why is it that at high temperatures most diffusional flux is through the lattice rather than the grain boundaries?

Diffusion through the grain boundary is ALWAYS faster than through the lattice. Grain boundaries have a more open structure.

However, a FLUX is the mass transport through a unit area, in a unit time. If you take a random section through the microstructure, the area presented by the lattice is far greater than than presented by the grain boundaries.

Therefore, at high temperatures where the difference between lattice diffusivity and boundary diffusivity is relatively small, the larger area presented by the lattice more than makes up for the smaller lattice diffusivity. Hence, the net mass transport consists more of diffusion through the lattice than through the grain boundaries.

At low temperatures, the boundary diffusivity is many orders of magnitude greater than lattice diffusivity, so the greater cross-section presented by the lattice does not compensate for its low diffusivity. Grain boundary diffusion makes the greater contribution to the net flux at low temperature.

A quantitative expression of these ideas can be found in a simple derivation presented in Lecture 2 of the Part IB Metals and Alloys Course.

Why is intersitial atom diffusion so much easier than substitutional atom diffusion?

Atoms in substitutional sites generally diffuse by a vacancy mechanism. The activation energy for diffusion can be partitioned into two components, the first due to the distortion of the lattice as the atom moves from one equilibrium position to another. The second component comes from the need to create a vacancy in the adjacent site into which the atom can jump.

This second component is absent for interstitial atoms because interstitial vacancies are more common than occupied interstices for all solutions with reasonable concentrations of interstitial atoms.

For more information, see

Lecture 1, Diffusion
Lecture 2, Diffusion

What evidence is there that diffusion occurs by a vacancy mechanism? After all, isn't the concentration of vacancies incredibly small?

There are a number of mechanisms for the diffusion of atoms in susbtitutional sites. For example, the ring mechanism in which a group of atoms in a "ring" arrangement simultaneously swap positions; or a pair of atoms make a coordinated move to swap positions. Both of these require an equal flow of matter in opposite directions. The vacancy mechanism does not, since the mass flow is balanced exactly by an equal and opposite vacancy flow. In a diffusion couple where the interface is identified with inert markers which are fixed to the laboratory frame, the couple will tend to migrate relative to the markers when diffusion is by a vacancy mechnism. This "Kirkendall Effect" is conclusive evidence for the vacancy mechanism.

I am a chemical engineering student at Universidad del Valle in Colombia, South America. I  found an article on Aluminum-Silicon casting alloys by  Robert Cornell. This article is very interesting, I need more information on  Al-12Si  such as physical properties, suppliers etc. If you can give me any help with related information. I would be very grateful.

I am afraid I cannot give you information about suppliers other than to suggest you get in touch with Alcan or Alcoa.

The typical mechanical properties of an Al-12Si wt% sand casting are as follows: yield strength 62 MPa, ultimate tensile strength 178 MPa and a tensile elongation to failure of 7%.

This alloy is used for the preparation of 55Al-Zn. I need to know the density of the alloy.

The densities of aluminium and silicon are 2.71 and 2.33 g cm^-3 respectively. Assuming a rule of mixtures, the average density of Al-12Si wt% should be 2.66 g cm^-3

For a bainitic railway steel, is it possible that the heat treatment due to friction from train wheels would eventually normalise the structure? How might one make the structure more stable, since it is fundamentally a metastable structure (I think)?

The heat treatment of the surface due to friction, especially during braking, is restricted to a very small depth below the surface. This surface layer also sees severe deformation. These two factors operate for all microstructures. Whether the temperature reaches one where austenite is formed is debatable.

Pearlite is, in the context of your question, more stable, but undergoes these same processes of localised heating and deformation.

Article on rail steels

At high temperature most diffusional flux is through the lattice. Why then are turbine blades made of single crystals in order to reduce the flux(and consequently creep) by having fewer grain boundaries (as was stated in lectures) ?

Note that although, at sufficiently high temperatures, the flux is predominantly through the lattice, the contribution from grain boundaries may not be insignificant.

You could do a simple calculation. Take the self diffusion coefficient for nickel, assume that the activation energy for diffusion through the grain boundaries is half that through the lattice, and hence calculate an apparent diffusivity as a function of temperature. You can assume a grain size of about 100 micron. Compare this apparent diffusivity with lattice diffusivity for a temperature of about 1273 K. You should find that the boundaries make a significant difference over a turbine blade life time of between 5000-10000 hours.

If a plate shape precipitate grows by a reconstructive mechanism and produces IPS shape deformation, would you expect an increase or decrease in the lengthening and thickening growth rates when the pre-transformed matrix is deformed significantly?   

In a reconstructive mechanism, the defects in the parent material are eliminated by transformation. Therefore, there is a gain in the free energy change associated with transformation. It follows that growth rates should be accelerated and this is always found to be the case for reconstructive transformations.

I just wanted to "pick your brain" on impurity diffusion:
you get this in iron systems. For example, with heat treatment you can
get impurities to diffuse. I just wondered if you are into
simulation of this sort of thing ?

We have similar stuff in solid state physics, for example in
silicon and silicon dioxide systems. You can introduce impurities and with heat treatment, the impurities diffuse
mostly through the grain boundaries. Is there a definiitve model on this? or can you refer me
a book on this ?

The best reference on this is Christian's Theory of Transformations in Metals and Alloys , (1975), 2nd edition, Pergamon Press, Oxford, Chapter 9, which contains everything you need to know about diffusion and about structure-sensitive diffusion.

There are many instances where we diffuse solutes into the surface of iron. Carburisation is one such process. See worked example 16 of my Part IB course on Metals and Alloys.