Electronic properties
Properties of materials such as electrical conduction and heat capacity are investigated by solid state physics. An early model of electrical conduction was the Drude model, which applied kinetic theory to the electrons in a solid. By assuming that the material contains immobile positive ions and an "electron gas" of classical, noninteracting electrons, the Drude model was able to explain electrical and thermal conductivity and the Hall effect in metals, although it greatly overestimated the electronic heat capacity.
Arnold Sommerfeld combined the classical Drude model with quantum mechanics in the free electron model (or DrudeSommerfeld model). Here, the electrons are modelled as a Fermi gas, a gas of particles which obey the quantum mechanical FermiDirac statistics. The free electron model gave improved predictions for the heat capacity of metals, however, it was unable to explain the existence of insulators.
The nearly free electron model is a modification of the free electron model which includes a weak periodic perturbation meant to model the interaction between the conduction electrons and the ions in a crystalline solid. By introducing the idea of electronic bands, the theory explains the existence of conductors, semiconductors and insulators.
The nearly free electron model rewrites the Schrodinger equation for the case of a periodic potential. The solutions in this case are known as Bloch states. Since Bloch's theorem applies only to periodic potentials, and since unceasing random movements of atoms in a crystal disrupt periodicity, this use of Bloch's theorem is only an approximation, but it has proven to be a tremendously valuable approximation, without which most solidstate physics analysis would be intractable. Deviations from periodicity are treated by quantum mechanical perturbation theory.
Heat capacity (usually denoted by a capital C, often with subscripts), or thermal capacity, is the measurable physical quantity that shows the amount of heat required to change the temperature of a substance by a given amount. In the International System of Units (SI), heat capacity is expressed in units of joule(s) (J) per kelvin (K).
Derived quantities that specify heat capacity as an intensive property, i.e, independent of the size of a sample, are the molar heat capacity, which is the heat capacity per mole of a pure substance, and the specific heat capacity, often simply called specific heat, which is the heat capacity per unit mass of a material. Occasionally, in engineering contexts, a volumetric heat capacity is used. Because heat capacities of materials tend to mirror the number of atoms or particles they contain, when intensive heat capacities of various substances are expressed directly or indirectly per particle number, they tend to vary within a much more narrow range.
Temperature reflects the average kinetic energy of particles in matter while heat is the transfer of thermal energy from high to low temperature regions. Thermal energy transmitted by heat is stored as kinetic energy of atoms as they move, and in molecules as they rotate. Additionally, some thermal energy may be stored as the potential energy associated with higherenergy modes of vibration, whenever they occur in interatomic bonds in any substance. Translation, rotation, and a combination of the two types of energy in vibration (kinetic and potential) of atoms represent the degrees of freedom of motion which classically contribute to the heat capacity of atomic matter (loosely bound electrons occasionally also participate). On a microscopic scale, each system particle absorbs thermal energy among the few degrees of freedom available to it, and at high enough temperatures, this process contributes to a specific heat capacity that classically approaches a value per mole of particles that is set by the DulongPetit law. This limit, which is about 25 joules per kelvin for each mole of atoms, is achieved by many solid substances at room temperature (see table below).
For quantum mechanical reasons, at any given temperature, some of these degrees of freedom may be unavailable, or only partially available, to store thermal energy. In such cases, the specific heat capacity will be a fraction of the maximum. As the temperature approaches absolute zero, the specific heat capacity of a system also approaches zero, due to loss of available degrees of freedom. Quantum theory can be used to quantitatively predict specific heat capacities in simple systems.
