Mott’s and Frank’s rules!

For the past few weeks, I have been trying to read up all the dislocation theory that I managed not-learn till now. During my not infrequent visits to the library, in addition to picking up the text books on dislocation theory (Weertman, Read, Hirth and Lothe), I happened to pick up some of the conference proceedings, which make a fascinating reading. I think, the history of dislocations is a materials science story waiting to be told; and when told, Oh! what a story it is going to be!

For example, according to Frank, Bilby had a programme–of formulating all physics in the language of dislocation theory; it would be really interesting to see how such a programme has influenced the development of materials science.

In this post I want to tell you some of the interesting stuff I found in one of the proceedings, namely, Dislocations and properties of real materials: Proceedings of the conference to celebrate the fiftieth anniversary of the concept of dislocation in crystals, The Institute of Metals, London, 1985–Get this volume from your library and have fun!

Mott:

So I went to see G.I. (Taylor) in Cambridge–and asked him what was the origin of the dislocations, Of course he did not know, and all I remember of the conversation is his remark “my paper is a model, not a theory”.

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…I shall always remember vividly the day when one of his young men, I think it was Mike Whelan, came into my room and said “Prof., come and see a moving dislocation”.

Frank:

I found all that elasticity mathematics rather difficult, but I found it easier to concentrate on the screw dislocation, with only one displacement variable, instead of two for the edge. So I became particularly fond of the screw dislocation. Mott and Nabarro liked to work with edge dislocations., because they liked two-dimensional diagrams. I was less afraid than they were of the third dimension, and more afraid of algebra.

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We had great fun in Bristol in those days, working out all sorts of dislocation properties at high speed, cutting all the corners, using what I used to call Mott’s Rule: “All definite integrals you don’t know are unity” and Frank’s rule: “The logarithms of infinity is 4 \pi”.

Of course the same paper has the story that Prof. Robert Cahn describes in his Coming of Materials Science about Frank-Read sources (involving Frank, Read, Eshelby, and Fisher).

A Cottrell:

I once wrote, in 1953, that work hardening was the first problem to be attempted by dislocation theory and may well prove the last to be solved. I feel I can still say the same today.

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The trouble with these very complex dislocation groupings–which Nabarro and I used to call “birds’ nests” some years ago–is that they defy the two traditional methods of theoretical physics: the method of reduction to elementary unit process; and the statistical method of kinetic theory.

If I remember my discussions with Praj correctly, I think even in early 2000, Prof. Cottrell has not changed his opinion–I could not get the proper references on the net though–all I could get is this page of Prof. Cottrell; so, there goes an open problem for you to think about, and I’ll leave you with that.