Search results
Results From The WOW.Com Content Network
The materials do show an ordering temperature above which the behavior reverts to ordinary paramagnetism (with interaction). Ferrofluids are a good example, but the phenomenon can also occur inside solids, e.g., when dilute paramagnetic centers are introduced in a strong itinerant medium of ferromagnetic coupling such as when Fe is substituted ...
The difference between the chemical shift of a given nucleus in a diamagnetic vs. a paramagnetic environment is called the hyperfine shift.In solution the isotropic hyperfine chemical shift for nickelocene is −255 ppm, which is the difference between the observed shift (ca. −260 ppm) and the shift observed for a diamagnetic analogue ferrocene (ca. 5 ppm).
The Hamiltonian for an electron in a static homogeneous magnetic field in an atom is usually composed of three terms = + (+) + where is the vacuum permeability, is the Bohr magneton, is the g-factor, is the elementary charge, is the electron mass, is the orbital angular momentum operator, the spin and is the component of the position operator orthogonal to the magnetic field.
Molecular compounds that contain one or more unpaired electrons are paramagnetic. The magnitude of the paramagnetism is expressed as an effective magnetic moment, μ eff. For first-row transition metals the magnitude of μ eff is, to a first approximation, a simple function of the number of unpaired electrons, the spin-only formula.
The Ising model can be solved analytically in one and two dimensions, numerically in higher dimensions, or using the mean-field approximation in any dimensionality. Additionally, the ferromagnet to paramagnet phase transition is a second-order phase transition and so can be modeled using the Landau theory of phase transitions.
When Langevin published the theory paramagnetism in 1905 [12] [13] it was before the adoption of quantum physics. Meaning that Langevin only used concepts of classical physics. [17] Niels Bohr showed in his thesis that classical statistical mechanics can not be used to explain paramagnetism, and that quantum theory has to be used. [17]
Paramagnetism is a weak positive response to a magnetic field due to rotation of electron spins. Paramagnetism occurs in certain kinds of iron-bearing minerals because the iron contains an unpaired electron in one of their shells (see Hund's rules ).
It only holds for high temperatures and weak magnetic fields. As the derivations below show, the magnetization saturates in the opposite limit of low temperatures and strong fields. If the Curie constant is null, other magnetic effects dominate, like Langevin diamagnetism or Van Vleck paramagnetism.