In physics, the free electron model is a possible model for the behaviour of electrons in a crystal structure. The core idea is that the valence electrons detach themselves completely from their ions and form an "electron gas". A Superconductor demonstrating the Meissner Effect Physics (from the Greek, φυσικός (physikos), natural, and φÏσις (physis), nature) is the science of the natural world dealing with the fundamental constituents of the universe, the forces they exert on one another, and the results produced by these forces. ... Properties The electron is a fundamental subatomic particle that carries a negative electric charge. ... Rose des Sables (Sand Rose), formed of gypsum crystals In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. ... In chemistry, valance electrons are the electrons located within the outermost energy level of an atom. ... // An ion is an atom or group of atoms with a net electric charge. ...
While this model is the simplest model, it reproduces the main electronic properties of metals. The two fundamental asumptions are:
the independent electron approximation that considers the electrons as independent. Electron screening is one justification for ignoring electron-electron interactions.
the electrons move in a constant energy potential (the structure of the material is completely ignored). Bloch's Theorem states that a periodic potential (such as a regular array of atoms) cannot scatter a travelling wave electron.
The electronic Hamiltonian for a multi-electron molecule in atomic units is: where is the vector position of electron with vector components in Bohr radii, is the charge of fixed nucleus a in units of the elementary charge, is the vector position of nucleus with vector components in Bohr radii. ... It has been suggested that this article or section be merged with Scalar potential. ... A Bloch wave or Bloch state is the wavefunction of a particle (usually, an electron) placed in a periodic potential. ...
Predictions of the model
This very simple model of metals more or less correctly predicts:
Gaselectron diffraction (GED) is one of the applications of electron diffraction techniques.
The geometrical structure of molecules can be obtained directly from the observed electron diffraction pattern by using this method.
The total scattering intensity is given as a function of the momentum transfer, which is defined as the difference between the wave vector of the incident electron beam and that of the scattered electron beam and has the reciprocal dimension of length.
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