NationMaster - Encyclopedia: Curie's law

In a paramagnetic material Curie's law relates the magnetization of the material to the applied magnetic field and temperature. Paramagnetism is the tendency of the atomic magnetic dipoles, due to quantum-mechanical spin, in a material that is otherwise non-magnetic to align with an external magnetic field. ... Magnetization is a property of some materials (e. ... In physics, magnetism is a phenomenon by which materials exert an attractive or repulsive force on other materials. ... Fig. ...

$mathbf{M} = C cdot frac{mathbf{B}}{T}$

$mathbf{M}$ is the resulting magnetisation

$mathbf{B}$ is the magnetic flux density of the applied field, measured in teslas

T

is absolute temperature, measured in kelvins

C

is a material-specific Curie constant

This relation was discovered experimentally (by fitting the results to a correctly guessed model) by Pierre Curie. The tesla (symbol T) is the SI derived unit of magnetic flux density (or magnetic induction). ... The Kelvin scale is a thermodynamic (absolute) temperature scale where absolute zeroâ€”the lowest possible temperature where nothing could be colder and no heat energy remains in a substanceâ€”is defined as zero kelvin (0 K). ... The Curie constant appears in Curies law, which relates the magnetic field and the temperature to the magnetisation of a paramagnetic substans. ... Pierre Curie (May 15, 1859, Paris â€“ April 19, 1906, Paris) was a French physicist and a pioneer in the study of crystallography, magnetism, piezoelectricity and radioactivity. ...

Derivation (Statistical Mechanics)

Magnetization of a paramagnet as a function of inverse temperature.

A simple model of a paramagnet concentrates on the particles which compose it, call them paramagnetons. Assume that each paramagneton has a magnetic moment given by : $vec{mu}$ . Energy of a magnetic moment in a magnetic field is given by Image File history File links Magnetization2. ... Image File history File links Magnetization2. ... Simple Illustration of a paramagnetic probe made up from miniature magnets. ... A bar magnet. ...

$E=-vec{mu}cdotvec{B}$

To simplify the calculation, we are going to work with a 2-state paramagnet, that is, the particle can either align its magnetic moment with the magnetic field, or against it. No other orientations are possible. If so, then such particle has only two possible energies

E 0 = μ B

and

E 1 = - μ B

With this information we can construct the partition function of one paramagneton In statistical mechanics, the partition function Z is an important quantity that encodes the statistical properties of a system in thermodynamic equilibrium. ...

$Z = sum_{n=0}^{infty} e^{-E_nbeta} = e^{-mu Bbeta} + e^{mu Bbeta} = 2 coshleft(mu Bbetaright)$

When one seeks the magnetization of a paramagnet, one is interested in the likelihood of a paramagneton to align itself with the field. In other words, one seeks the expectation value of orientation $μ$ .

$leftlanglemurightrangle = sum_{n=0}^{infty} mu_n Pleft(mu_nright) = sum_{n=0}^{infty} mu_n {e^{-mu_n Bbeta}over Z} = {1over Z}sum_{n=0}^{infty}{partial_{beta}e^{-mu_n Bbeta}over B} = {1over B}{1over Z} partial_{beta} Z$

$leftlanglemurightrangle = {1over 2 B coshleft(mu Bbetaright)} 2 mu B sinhleft(mu Bbetaright) = mu tanhleft(mu Bbetaright)$

This is magnetization of one paramagneton, total magnetization of the solid is given by

$M = Nleftlanglemurightrangle = N mu tanhleft({mu Bover k T}right)$

The formula above is known as the Langevin Paramagnetic equation. Pierre Curie found an approximation to this law that applies to the reasonably high temperatures and low magnetic fields used in his experiments. Let's see what happens to the magnetization as we specialize it to large $T$ and small $B$ . As temperature increases and magnetic field decreases, the argument of hyperbolic tangent decreases. Another way to say this is Paramagnetism is the tendency of the atomic magnetic dipoles, due to quantum-mechanical spin, in a material that is otherwise non-magnetic to align with an external magnetic field. ...

$left({mu Bover k T}right) << 1$

this is sometimes called the Curie regime. We also know that if $| x | < < 1$ , then

$tanh x approx x$

$mathbf{M}(Trightarrowinfty)={Nmu^2over k}{mathbf{B}over T}$

Q.E.D.

Applications

It is the basis of operation of magnetic thermometers, that are used to measure very low temperatures.

Categories: Electric and magnetic fields in matter | Eponymous laws The Curie-Weiss law describes the magnetic susceptibility of a ferromagnet in the paramagnetic region above the Curie point: where is the magnetic susceptibility C is a material-specific Curie constant T is absolute temperature, measured in kelvins Tc is the Curie temperature, measured in kelvins The susceptibility has a... Simple Illustration of a paramagnetic probe made up from miniature magnets. ... Pierre Curie (May 15, 1859, Paris â€“ April 19, 1906, Paris) was a French physicist and a pioneer in the study of crystallography, magnetism, piezoelectricity and radioactivity. ...

Results from FactBites:

MSN Encarta - Marie Curie (942 words)
	The Curies shared the 1903 Nobel Prize in physics with a colleague, and Marie Curie was awarded the 1911 Nobel Prize in chemistry.
	Curie was born Maria Skłodowska on November 7, 1867, in Warsaw, Poland, and her nickname while growing up was Manya.
	Marie Curie went on to study the chemistry and medical applications of radium, and in 1911 she was awarded the Nobel Prize in chemistry in recognition of her work in discovering radium and polonium and in isolating radium.

More results at FactBites »

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Applications

See also

Derivation (Statistical Mechanics)