Friday, September 26, 2014

On the Bragg-Williams-Gorsky model

I am writing a manuscript about ordered compounds stability and decided to produce a small paragraph about history of this subject. One of the topics of this paragraph is the Bragg-Williams-Gorsky model, which is a milestone in the investigation of the phenomena. For this I downloaded the original manuscript by the authors and was surprised by the insight it gave to me on this fascinating era of investigation in physical metallurgy. In particular, it corrected a mistaken notion I had, but I will return to the point later.
First of all, the reading of this work, plus a few other references, show that the current division of physics into experimentalists and theoreticians was non existent at that time, the works are mostly experimental works dealing with aspects of the ordering transformation like resistivity measurements, corrosion experiments, crystallographic investigations and even plastic deformation, with the authors developing some theoretical background in varying degrees. This proves a point I raised in a previous post in the blog, namely, that specialization in science is a modern (or even post-modern) phenomenon.
Bragg and Williams give credit to Tammann as the one who "first envisaged" the notion of ordered compounds in 1919. This is backed up by  previous publications by other authors, quoted in the manuscript. It is amazing to observe the careful way the authors dealt with a notion which is so common today, namely of the ordering/disordering transformations, which, today is a matter of introductory textbooks.
The authors also acknowledge previous work by other research groups, which predated their work. According to them, they became aware of these theoretical treatments after the publication of a first work in the series, these were works by Borelius, Johanson and Linde, by Gorsky and by Dehlinger and Graf.
Reading these papers, it becomes clear that the works by Borelius, Johanson and Linde (published in 1928) and by Dehlinger and Graf contained only part of the ideas which compose what we know today as the Bragg-Williams-Gorsky model, but the same is not true for the work by Gorsky, published in 1928 (which, therefore, predates the work by Bragg and Williams in seven years!), which gives a full derivation of the model in terms of the laws of statistical mechanics (this author, however, uses the ordering energy as energetic parameter for the calculation). This was the erroneous notion I had. Someone, I don't remember who, told me once that Gorsky's  contribution was minimal and limited to including the magnetic degrees of freedom in the model. This is wrong. Based on the description in the manuscript by Bragg and Williams, we may accept that the theory was derived in parallel by their group and by Gorsky in Leningrad, so, this author's contribution of the model is, at least, as important as the one of Bragg and Williams.
A further interesting note. Reading the work by Borelius, Johanson and Linde, I discovered that the authors discuss the famous formula:
which allows an interpretation of the stability of a compound in terms of the interatomic bonds, the compound would become stable if delta<0 meaning the compound becomes stable if the interactions between unlike atoms becomes stronger than in the pure componentes:
"Trotz der Einfachheit dieser Formel durfte sie doch von wenig Nutzen sein, weil der Anordnung der Paare benachbarter Atome wahrscheinlich keine wesentliche physikalische Bedeutung zukommt." (page 309) Translating: "In spite of its simplicity, this formula should be of little use, since the ordering of pairs of neighboring atoms present no important physical meaning". This view is similar to one that I defend, namely that the interactions energies are just a convenient way to write down the energy of a crystal, but we should not attempt to interpret them as having a physical origin.
So in summary, calling the model Bragg-Williams-Gorsky is not only an option, it is mandatory, for the sake of history. 

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