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.

Friday, February 6, 2015

The wonders of education

When I was a first year student at the Physics course of the University of São Paulo, I struggled with Calculus, as most of my colleagues. I remember the sense of incapacity, when I wrote tests, getting negligible grades, because of some error in integrating weird combinations of functions, which would never see the light in a true application (after many years I learned that those tests were tainted, wrong, and not my knowledge, but at that time I didn't know that). The interesting was, that I observed my older colleagues, who where on the fourth or fifth year, had no problem with calculus.

Then, an interesting idea came to my mind: learning has more to do with the time you spend in the university, than with the actual lecture you attend. Of course, one cannot bring this to the extreme to say that a student that spends all the time of his study in the university's cafeteria will learn as much as the student who attends all the lectures.

I believe that attending the lectures is vital for learning, but not because of what the professor teaches, it is because of the how he teaches. Education has this "magical" property, you spend some time hearing a professor talking about some subject, and you learn, indeed. Sometimes the professor teaches by hypnotism. I remember the lectures on thermodynamics I had with Prof. Ferdinando Luiz Cavallante, during my Master in Engineering study. I swear to you, when I needed some key concepts on thermodynamics (reference states, Raoult and Henry laws, activity, thermodynamic potential) I saw in my mind Prof, Cavallante talking! But these are not the general cases, most professors (myself including) are simply boring. So, how do this work?

I believe, this "time dependency" of learning is tied to the subject I posted before "on the role of the professor".  It is a matter of exercising. Exercising the brain. As with any other activity which requires exercising (football playing, sewing clothes, playing a video game) learning requires practicing, but practicing of what? I believe the key issue are the mental processes going on in the brain of the student. The professor repeats many arguments which the student has to follow, even if he is asleep. In any of them, the student has to follow the logic behind of what the professor teaches. This logic expands the student's mind. One single event, has limited influence, but repeating this process over and over again has a cumulative effect on the student's brain, until education reaches the ultimate goal, to teach the student how to learn by himself. This requires time.