# Curie's Law

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Related to Curie's Law: Marie Curie, Curie constant

## Curie's law

[′kyu̇r‚ēz ‚lȯ]## Curie’s Law

the temperature dependence of the specific magnetic susceptibility *Χ* of certain paramagnetic substances having the form

(1) *Χ* = *C/T*

where *T* is the absolute temperature and *C* is a constant for the particular substance (Curie constant). The law was established by P. Curie in 1895. It is obeyed by gases (oxygen, O_{2}, and nitric oxide, NO), vapors of alkali metals, dilute liquid solutions of paramagnetic salts of rare-earth elements, and some paramagnetic salts in the crystalline state; such salts contain between the ions, which are the carriers of the magnetic moment μ, groups of atoms, such as molecules of water of crystallization or ammonia, that have no moment and prevent interaction of the ions.

The classical theory of Curie’s law is based on the statistical analysis of the properties of a system (“gas”) of weakly interacting atoms, molecules, or ions that have magnetic dipole moments. In the absence of an external magnetic field, the moments μ of molecules are randomly oriented. A magnetic field *H* produces orientation of the moments along the field, which is counteracted by the thermal motion of the particles. For the magnetization of unit mass of the substance in a weak magnetic field at temperature *T*, statistical analysis yields the quantity *M = Nμ ^{2}H/3kT*, where

*N*is the number of molecules and

*k*is Boltzmann’s constant. Thus,

(2) *Χ* = *M/H = Nμ ^{2}/3kT* and

*C*=

*Nμ*

^{2}/3kIn strong magnetic fields and at low temperatures, the thermal motion does not disturb the orientation of the magnetic moments and the magnetization *M* tends toward the value *Nμ ^{2}*, that is, toward saturation, and Curie’s law is inapplicable. If there is appreciable interaction of the ions—carrying the magnetic moments—with one another and with nonmagnetic ions of the crystal lattice, the magnetic susceptibility of paramagnetic substances obeys the Curie-Weiss law rather than Curie’s law.

Quantum mechanical calculations (J. H. Van Vleck, 1932) lead to a dependence of *Χ* on *T* for paramagnetic substances similar to that in equation (1). Curie’s law is also applicable to the paramagnetism of nuclei. In the absence of a significant interaction between the spins of the nuclei and electrons in atoms, the nuclear paramagnetic susceptibility (per 1 mole) is *Χ*_{n} = *Nμ*^{2}_{n, eff}/3kT = *C _{n}/T*, where μ

_{n, eff}is the effective magnetic moment of the nucleus and

*C*is the nuclear Curie constant.

_{n}### REFERENCE

Vonsovskii, S. V.*Magnetizm*. Moscow, 1971.