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. 

Sunday, September 21, 2014

The role of the student in superior education

My third post about superior education deals with its leading actor: the student. I have the honor and opportunity to work with the best applicants to an exact sciences carrier in Brazil: the "Politécnico". Nevertheless I need to exercise some critic.
First of all, there is a universe of distance between the student in the junior years and the same student in the late years of the course. Some years ago I attributed this to a lack of satisfaction with the chosen carrier, but nowadays I believe the students are also to blame. In my opinion the student, submitted for years to the evaluation system I described in my last post, give up learning, concentrating instead in obtaining the necessary grades for approval. I am being, probably, too severe. I have also good students in the classroom (I teach in the 7th and 8th semesters), but I just feel they are not as interested as in the first years.
One possible explanation for this, which was pointed out many times before, is that, paradoxically, our student is too good. Frequently he (or she) was the best student, the most intelligent, in his (her) class in the secondary school (the Brazilian equivalent to the American highschool, or the German Gymnasium). This student usually got good grades without the need to study hard (I know this because I was one of these students), the result is that he (or she) didn't learn how to study properly. When he (she) enters the Escola Politecnica, suddenly, there are others who are, as much or even more intelligent than him (her). Not every student can cope with this renewed situation. In addition, this student didn't learn how to study and the lectures in the first years of the Escola Politecnica (mostly Mathematics and Physics) are not as simple as the ones he attended before. This, added to the poorly prepared written tests, leads to the recipe of a tragedy.
I had the privilege to work with a brilliant student, Dr. Bruno Geoffroy Scuracchio. Today he is the responsible engineer for innovation in an autopart supplier industry. Our first contact was just after I got hired in the Escola Politecnica. I supervised him in a junior research project, the final course dissertation, a master dissertation and finally, the PhD thesis. I knew he had some trouble to finish his course, in particular, I knew he had to attend the "Integral and differential calculus III" discipline in the last year (this is originally a third semester discipline). Once, in an informal chat, I asked him how difficult it was and his answer surprised me: not difficult at all. He told me he attended the lectures to know what was the subject, solved the exercises corresponding to that subject, solved doubts with the professor, and used about two hours a week for studying, after doing all this he got the grade for approval already in the second test (out of three). Further, he said that if he did that the first time he attended that discipline, he would not be reproved. I thought that if we are not teaching our junior students this, we are doing a clumsy job.
This lack of discipline in studying is easier to show with an example. I am an enthusiast of network learning, as my good (virtual) friend, Prof. Ewout ter Haar defines (also known in my country as distance learning). Once, some years ago, I was responsible for coordinating a discipline with a large number of students (820). I decided to substitute  a written test by one applied online using the moodle system administered by Prof. ter Haar. I didn't know, but this was the first attempt to do this with such a large discipline. I gave five days per week as a deadline for the tests and monitored the number of students who solved them. One day Prof. ter Haar sent me the figure below, showing the bandwidth charges of the servers.
As one sees, there are some plateaus in the charge, this is not that difficult to understand, the student probably used the evenings to solve the test. The problems are the levels of these plateaus. Only about 220 students (out of 820) solved the first test within three days, about 530 students did it until the fourth day. The charge growth in the last day was faster than exponential. It was a hell of a crash test to the servers (and they survived). The interesting is to see that the plateau levels decrease with time, meaning more and more students left the test to solve in, literally, the last minutes of the deadline.
This last example is a characteristics of our students (in fact, of the Brazilians), to leave everything to do in the last minute, We should do a better job in teaching our students, especially in the first years of the course, to avoid this.