MTLS 509 Statistical Mechanics of Simple Materials

Overview

Statistical Mechanics bridges between the continuum world of Thermodynamics and the atomic nature of matter - specifically addressing the macroscopic ramifications of atomic level details. Notwithstanding that the strength of Statistical Mechanics rests upon this sensitivity to detail, a surfeit of detail makes it difficult to see the connection between, on one hand, (continuum) thermodynamic properties and, on the other, the (granular) atomic description of matter. As a result, while it is, in principle, possible to start with a Quantum Mechanical description of, say, water and to deduce the behavior of the tides, it is certainly, impractical - although, with the aid of extremely powerful computers, less impractical than even a few years ago.

Even if it were relatively straightforward to incorporate a full, atomic (and sub-atomic) level description of matter into a Statistical Mechanical treatment, such would not necessarily be the best course. The high level of detail needed to understand, for instance, why Argon and Methane are different, would tend to obscure questions such as why the critical point behaviors of the two gases are the same. In order to see the forest in spite of the trees, it is often necessary to neglect much of the detail on the “tree” level.

I have tried to hold as closely as possible to simple models of materials. Even so, the general features of a surprisingly wide range of macroscopic properties can be understood – ranging from the temperature dependence of the heat capacity of a crystal to the formation of a Black Hole.

In order to avoid the elegant and complex mathematics of “detailed” models, it is necessary that the particles do not directly see each other. Techniques beyond those presented in this course are needed to truly do justice to the particle-particle attractions and repulsions as depicted in, for instance, a Lennard-Jones potential. It is only in the last chapter that some of these techniques are briefly touched upon.

In simple terms, the systems that this course addresses are Ideal Gases. Ideal Gases, yes, but of many exotic varieties: Fermions and Bosons; Phonons and Photons; Relativistic and Non-Relativistic. In every field of Materials Physics, a simple, Ideal model defines much of the language of the field. It is the treatment of these model systems of which the course consists.