The Screening effect and the Shielding effect
Screening effect
From Wikipedia, the free encyclopedia
In solids, especially in metals and semiconductors, the electrostatic screening or screening effect reduces the electrostatic field and Coulomb potential of an ion inside the solid. Like the electric field of the nucleus is reduced inside an atom or ion due to the shielding effect, the electric fields of ions in conducting solids are further reduced by the cloud of conduction electrons. The screened Coulomb potential is expressed as[1]
![V(r)={\frac {Ze}{r}}\exp[{-qr}]](https://wikimedia.org/api/rest_v1/media/math/render/svg/5f794e546c05f31b854f4cc2fa53138dc4aafbb4)
where Z is the atomic number, e is the elementary unit charge, r is the distance to the nucleus of the embedded ion, and q is the screening parameter that determines the range of the potential. The screening parameter q plays an important role in theoretical models in solid-state physics.[2] The screened electrostatic potential, like the Yukawa potential, has a simple Fourier transform, expressed as
The screened potential determines the inter atomic force and the phonon dispersion relation in metals. The screened potential is used to calculate the electronic band structure of a large variety of materials, often in combination with pseudopotential models.
Shielding effect
From Wikipedia, the free encyclopedia
See also: Effective nuclear charge
The shielding effect describes the attraction between an electron and the nucleus in any atom with more than one electron shell. Shielding effect can be defined as a reduction in the nuclear charge on the electron cloud, due to a difference in the attraction forces of the electrons on the nucleus. It is also referred to as the screening effect or atomic shielding.
Cause[edit]
In hydrogen, or any other atom in group 1A of the periodic table (those with only one valence electron), the force on the electron is just as large as the electromagnetic attraction from the nucleus. However, when more electrons are involved, each electron (in the n-shell) experiences not only the electromagnetic attraction from the positive nucleus, but also repulsion forces from other electrons in shells from 1 to n. This causes the net force on electrons in outer shells to be significantly smaller in magnitude; therefore, these electrons are not as strongly bonded to the nucleus as electrons closer to the nucleus. This phenomenon is often referred to as the orbital penetration effect. The shielding theory also contributes to the explanation of why valence-shell electrons are more easily removed from the atom.
The size of the shielding effect is difficult to calculate precisely due to effects from quantum mechanics. As an approximation, we can estimate the effective nuclear charge on each electron by the following:
Where Z is the number of protons in the nucleus and is the average number of electrons between the nucleus and the electron in question. can be found by using quantum chemistry and the Schrödinger equation, or by using Slater's empirical formulas.
is the average number of electrons between the nucleus and the electron in question.
In Rutherford backscattering spectroscopy the correction due to electron screening modifies the Coulomb repulsion between the incident ion and the target nucleus at large distances.
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