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In analogy to ferromagnetic and paramagnetic materials, the term Curie temperature (T C) is also applied to the temperature at which a ferroelectric material transitions to being paraelectric. Hence, T C is the temperature where ferroelectric materials lose their spontaneous polarisation as a first or second order phase change occurs.
There are two other measures of susceptibility, the molar magnetic susceptibility (χ m) with unit m 3 /mol, and the mass magnetic susceptibility (χ ρ) with unit m 3 /kg that are defined below, where ρ is the density with unit kg/m 3 and M is molar mass with unit kg/mol: =; = =.
In a paramagnetic system, that is, a system in which the magnetization vanishes without the influence of an external magnetic field, assuming some simplifying assumptions (such as the sample system being ellipsoidal), one can derive a few compact thermodynamic relations. [4]
where C is a material-specific Curie constant, T is the absolute temperature, and T C is the Curie temperature, both measured in kelvin. The law predicts a singularity in the susceptibility at T = T C. Below this temperature, the ferromagnet has a spontaneous magnetization. The name is given after Pierre Curie and Pierre Weiss.
[1]: 117 The formula above is known as the Langevin paramagnetic equation. Pierre Curie found an approximation to this law that applies to the relatively high temperatures and low magnetic fields used in his experiments. As temperature increases and magnetic field decreases, the argument of the hyperbolic tangent decreases.
Compounds at temperatures below the Curie temperature exhibit long-range magnetic order in the form of ferromagnetism. Another critical temperature is the Néel temperature, below which antiferromagnetism occurs. The hexahydrate of nickel chloride, NiCl 2 ·6H 2 O, has a Néel temperature of 8.3 K. The susceptibility is a maximum at this ...
reduced temperature minus 1, T − T c / T c f: specific free energy: C: specific heat; −T ∂ 2 f / ∂T 2 J: source field (e.g. P − P c / P c where P is the pressure and P c the critical pressure for the liquid-gas critical point, reduced chemical potential, the magnetic field H for the Curie point) χ
A number of actinide compounds are ferromagnets at room temperature or exhibit ferromagnetism upon cooling. Pu P is a paramagnet with cubic symmetry at room temperature, but which undergoes a structural transition into a tetragonal state with ferromagnetic order when cooled below its T C = 125 K.