2004 Student Research Conference:

17th Annual Student Research Conference

17th Annual Student Research Conference

**Thermodynamic Properties of Fermions in an Energy Band Structure**

Adair P. Crowe

Dr. Eduardo Velasco, Faculty Mentor

We want to study some thermodynamic properties of a system of fermions in an energy band structure. In particular, we wish to study the behavior of the coefficient of thermal expansion and the ratio of the coefficient of thermal expansion to the isothermal compressibility as the temperature of the system approaches zero. The third law of thermodynamics implies, in most cases, that this last ratio will approach zero as the temperature approaches zero. However, we want to show that in this case this is not true, even as the third law is satisfied. To accomplish this, we used a mathematical model of fermions based on realistic semiconductors. We analyzed a statistical mechanical model of our system using software able to compute and make plots of the relationships between the thermodynamic variables of interest at very low temperatures. We then compared these results with the prediction of the third law of thermodynamics.

**Keywords:** fermions, thermodynamics, band structure

**Topic(s):**Physics

**Presentation Type:** Oral Paper

**Session:** 37-3

**Location:** VH 1010

**Time:** 2:45