| Abstract Scope |
Thermal expansion allows a material to minimize its free energy at finite temperature. At equilibrium, second derivatives of the free energy give the Maxwell relationship ∂S/∂P = -∂V/∂T. The right-hand side is thermal expansion, and it can be obtained as the pressure derivative of the entropy S on the left-hand side. There are multiple types of entropy, including vibrational, magnetic, electronic, and their interactions. Their pressure-induced changes can be used to quantify thermal expansion. An example will be shown for quantifying the entropy in a popular mechanical model of negative thermal expansion by bond bending in ScF3. Other examples include a competition between magnetic and vibrational entropy in the thermal expansion of ferromagnetic materials, and an anomalously large change in the thermal expansion of FeTi due to changes in electronic structure. The importance of two different vibrational contributions to thermal expansion, anharmonic and quasiharmonic, will be discussed. |