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force of attraction or repulsion between various substances, especially those made of iron and certain other metals; ultimately it is due to the motion of electric charges.
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That branch of magnetism which treats of diamagnetic phenomena and of the properties of diamagnetic bodies. Diamagnetism is a property exhibited by substances with a negative magnetic susceptibility, that is, by substances which magnetize in a direction opposite to that of an applied magnetic field. A diamagnetic substance has a magnetic permeability less than 1, and is repelled when placed near a magnet. The magnetization of diamagnetic substances is associated with the currents induced on application of a magnetic field. See Magnetic susceptibility
Although all matter exhibits diamagnetism, only those substances in which paramagnetism is absent are referred to as diamagnetic. This is because paramagnetism, if present, usually predominates, and the gross magnetic response of the material is paramagnetic. Important exceptions are the alkali and alkaline earth metals. The condition for pure diamagnetism is that all electronic spins be paired and all orbital moments either be zero or effectively cancel one another. See Paramagnetism
As stated previously, the diamagnetic response of a substance is small; only a very small fraction of the applied magnetic field is shielded from the interior of the substance by the induced diamagnetic currents. There is one case, however, in which the inducing field is completely shielded (except for small surface effects). This is the perfect diamagnetism exhibited by superconductors, and is known as the Meissner effect. See Meissner effect, Superconductivity
one type of magnetism; it is manifested in the magnetization of a substance against the direction of the external magnetic field acting on it.
Diamagnetism is inherent in all substances. When a body is placed in a magnetic field, induced ring currents, or additional circular motions of the electrons in the direction of the magnetic field, arise in the electron shell of each atom by virtue of the law of electromagnetic induction. These currents create in every atom an induced magnetic moment directed—according to the Lenz law—against the external magnetic field, regardless of whether the atom initially had a magnetic moment of its own and regardless of how it was oriented. In matter diamagnetism may be concealed to greater or lesser extent by electronic or nuclear paramagnetism, ferromagnetism, or antiferromagnetism. In purely diamagnetic substances the electron shells of the atoms (or molecules) do not have a constant magnetic moment. In the absence of an external magnetic field, the magnetic moments created by individual electrons in such atoms are compensated. In particular this obtains in atoms, ions, and molecules whose electron shells are entirely filled, such as the atoms of inert gases and molecules of hydrogen and nitrogen.
An elongated sample of a diamagnetic in a homogeneous magnetic field is oriented perpendicular to the lines of force of the field (the field intensity vector). The sample is ejected from a nonhomogeneous magnetic field in the direction of reduced field intensity.
The induced magnetic moment J acquired by 1 mole of a diamagnetic substance is proportional to the intensity of the external field H, that is, J = χ H. The coefficient X is called the molar diamagnetic susceptibility and has a negative sign, since J and H have opposite directions. The absolute value of χ is usually small (≃ l06)—for example, for 1 mole of helium, X = -1.9 x 10-6.
The currents that create diamagnetism have the simplest nature in isolated atoms. Upon exposure to an external magnetic field, all the electrons of an isolated atom acquire synchronous rotational motion around the axis that passes through the center of the atom parallel to the direction of H. This joint rotation of all of an atom’s electrons is called the Larmor precession. The contribution of each electron to the diamagnetic susceptibility of an isolated atom is
(1) Xi = -e2r2/6mc2
where e is the charge of the electron, r2 is the mean square distance of the electron from the nucleus, m is the rest mass of the electron, and c is the speed of light in a vacuum. According to formula (1) the electrons most distant from the nucleus make the greatest contribution to the diamagnetic susceptibility of a substance. Formula (1) makes possible the theoretical calculation of the diamagnetic susceptibility of a set of isolated atoms (for example, of 1 mole or 1 cm3 of a substance) if the number of electrons in the atoms and their spatial distribution are known.
At relatively low temperatures the thermal motion of atoms has a weak influence on the motion of the electrons within them. Therefore, diamagnetism has virtually no dependence on temperature.
If the atoms are not isolated from each other but interact strongly, as in liquids or solids, the electron shells of such atoms become deformed and the observed diamagnetism proves to be much less than in isolated atoms.
In metals and semiconductors part of the valence electrons can move from atom to atom throughout the entire sample (in metals the number of such “free” electrons does not depend on the temperature and is very great, whereas in semiconductors it is comparatively small at low temperatures and increases rapidly with heating). Under the influence of an external magnetic field, free electrons travel in spiral quantized orbits, also causing slight diamagnetism (Landau diamagnetism). In some substances Landau diamagnetism is very great; in bismuth and graphite, for example, the susceptibility reaches -(200-300) x 10-6 per mole.
In all of the cases examined above the diamagnetic susceptibility is weakly dependent on the intensity of the magnetic field. However, at very low temperatures periodic (oscillatory) change in susceptibility is observed in metals (such as beryllium, bismuth, and zinc) and semiconductors in strong fields upon a smooth increase in field intensity (the de Haas-Van Alphen effect).
Superconductors have the highest diamagnetic susceptibility in absolute magnitude: X = -1/4π ≃-0.8, and the magnetic induction is equal to zero—that is, the magnetic field does not penetrate the superconductor. The diamagnetism of superconductors is due to macroscopic surface currents rather than to intra-atomic currents.
REFERENCESVonsovskii, S. V. Magnetizm. Moscow, 1971.
Dorfman, Ia. G. Magnitnye svoistva i stroenie veshchestva. Moscow, 1955. Chapter 2.
Kittel, C. Vvedenie vfiziku tverdogo tela. Moscow, 1957. Chapter 8. (Translated from English.)
Kirenskii, L. V. Magnetizm, 2nd ed., Moscow, 1967.
IA. G. DORFMAN