Curie's Law

Curie's law

[′kyu̇r‚ēz ‚lȯ] (electromagnetism) The law that the magnetic susceptibilities of most paramagnetic substances are inversely proportional to their absolute temperatures.

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, O₂, 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 = Nμ²H/3kT, where N is the number of molecules and k is Boltzmann’s constant. Thus,

(2) Χ = M/H = Nμ²/3kT and C = Nμ²/3k

In 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 Nμ², 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 = Nμ²_{n, eff}/3kT = C_n/T, where μ_{n, eff} is the effective magnetic moment of the nucleus and C_n is the nuclear Curie constant.

REFERENCE

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

单词	curie's law
释义	Curie's law Curie's law n (General Physics) the principle that the magnetic susceptibility of a paramagnetic substance is inversely proportional to its thermodynamic temperature. See also Curie-Weiss law Curie's Law Curie's law [′kyu̇r‚ēz ‚lȯ] (electromagnetism) The law that the magnetic susceptibilities of most paramagnetic substances are inversely proportional to their absolute temperatures. 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, O₂, 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 = Nμ²H/3kT, where N is the number of molecules and k is Boltzmann’s constant. Thus, (2) Χ = M/H = Nμ²/3kT and C = Nμ²/3k In 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 Nμ², 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 = Nμ²_{n, eff}/3kT = C_n/T, where μ_{n, eff} is the effective magnetic moment of the nucleus and C_n is the nuclear Curie constant. REFERENCE Vonsovskii, S. V. Magnetizm. Moscow, 1971.
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