Free electron model
Overview
Solid-state physics
Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from...
, the free electron model is a simple model for the behaviour of valence electron
Valence electron
In chemistry, valence electrons are the electrons of an atom that can participate in the formation of chemical bonds with other atoms. Valence electrons are the "own" electrons, present in the free neutral atom, that combine with valence electrons of other atoms to form chemical bonds. In a single...
s in a crystal structure
Crystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
of a metallic solid
Solid
Solid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...
. It was developed principally by Arnold Sommerfeld
Arnold Sommerfeld
Arnold Johannes Wilhelm Sommerfeld was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and groomed a large number of students for the new era of theoretical physics...
who combined the classical
Classical physics
What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...
Drude model
Drude model
The Drude model of electrical conduction was proposed in 1900 by Paul Drude to explain the transport properties of electrons in materials...
with quantum mechanical
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
Fermi-Dirac statistics
Fermi-Dirac statistics
Fermi–Dirac statistics is a part of the science of physics that describes the energies of single particles in a system comprising many identical particles that obey the Pauli Exclusion Principle...
and hence it is also known as the Drude–Sommerfeld model. The free electron Empty Lattice Approximation
Empty Lattice Approximation
The Empty Lattice Approximation is a theoretical electronic band structure model in which the potential is defined not more precisely than periodic and weak. The Empty Lattice Approximation describes a number of properties of energy dispersion relations of non-interacting free electrons that move...
forms the basis of the band structure
Electronic band structure
In solid-state physics, the electronic band structure of a solid describes those ranges of energy an electron is "forbidden" or "allowed" to have. Band structure derives from the diffraction of the quantum mechanical electron waves in a periodic crystal lattice with a specific crystal system and...
model known as nearly-free electron model
Nearly-free electron model
In solid-state physics, the nearly-free electron model is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. The model is closely related to the more conceptual Empty Lattice Approximation...
. Given its simplicity, it is surprisingly successful in explaining many experimental phenomena, especially
- the Wiedemann-Franz law which relates electrical conductivity and thermal conductivityThermal conductivityIn physics, thermal conductivity, k, is the property of a material's ability to conduct heat. It appears primarily in Fourier's Law for heat conduction....
; - the temperature dependence of the heat capacityHeat capacityHeat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...
; - the shape of the electronic density of statesDensity of statesIn solid-state and condensed matter physics, the density of states of a system describes the number of states per interval of energy at each energy level that are available to be occupied by electrons. Unlike isolated systems, like atoms or molecules in gas phase, the density distributions are not...
; - the range of binding energy values;
- electrical conductivities;
- thermal electron emissionThermionic emissionThermionic emission is the heat-induced flow of charge carriers from a surface or over a potential-energy barrier. This occurs because the thermal energy given to the carrier overcomes the binding potential, also known as work function of the metal. The charge carriers can be electrons or ions, and...
and field electron emission from bulk metals.
As in the Drude model, valence electron
Valence electron
In chemistry, valence electrons are the electrons of an atom that can participate in the formation of chemical bonds with other atoms. Valence electrons are the "own" electrons, present in the free neutral atom, that combine with valence electrons of other atoms to form chemical bonds. In a single...
s are assumed to be completely detached from their ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...
s (forming an electron gas).
