## Thursday, February 19, 2015

### Isopleths and phase diagrams

I work with phase diagrams in materials science. More specifically, I calculate phase diagrams using ab initio methods. In many occasions in the past, I came across the term "isopleth". to designate a projection of a high order phase diagram in the form of a composition - temperature diagram in which all composition variables are kept constant except one (of course two if we consider the base "solvent"). The diagram below is an example, it shows the 20 wt% Cr isopleth in system Fe-Cr-C as calculated using the Thermo-Calc program with the solid solution 2.0 database.
Those who are familiar with the Fe-C diagram will recognize some familiar points, like something which resembles the eutectic reaction and something which resembles the peritectic reaction, this familiarity is useful in interpreting the phase relations in this complex phase diagram. This diagram may also be used to understand basic phase relations in some special grades of ferritic stainless steels.
I wished to use this concept in my own language, this would lead to "isopletas" in a simple, literal, translation. I already discussed with my colleagues of the Brazilian Materials Phase Diagram Committee in the past, and although many of them meant this was "allowed", no one was really quite sure of it. Today I decided to investigate.
I did a google search for the term "isopleth" and discovered some interesting facts. First the word is derived from Greek (as I already suspected), through iso + pleth(os), which means equal + large number (or quantity). Most references in phase diagram literature conform the definition I knew (reproduced at the beginning of this post), but in formal online dictionaries I found only one reference to this definition. I found out, on the contrary, that the term is quite used in physical geography to denote contour lines of a given quantity (wind velocity is often mentioned) in a map. I searched for the term "isopleta" and discovered that this meaning (contour line) is also used in Portuguese geographical literature.
Comparing with the suggested etymology this makes sense, it seems to me that the original meaning of a synonym for isolines is the correct one. What about the term in phase diagram literature? It looks to me the the term was "borrowed" without much care and designates something quite different.
In summary, I believe it is safe to use the term "isopleta" in Portuguese to designate the same thing as the English specialized literature does. One has to consider this has a quite different meaning in Physical Geography and Cartography. The safer solution would be to look after some other word to designate these special projections in phase diagram. One thing is, however, clear. The term cannot be used to designate any composition temperature section of a multicomponent phase diagram, only those in which all other components are kept constant deserve this name.