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where is the Entropy, is the Volume and is the number of particles in the system. Note that in this case, is the energy added to the system by the insertion of the paramagnet. The total energy in the space occupied by the system includes a component arising from the energy of a magnetic field in a vacuum.
In rare cases, the diamagnetic contribution can be stronger than paramagnetic contribution. This is the case for gold , which has a magnetic susceptibility less than 0 (and is thus by definition a diamagnetic material), but when measured carefully with X-ray magnetic circular dichroism , has an extremely weak paramagnetic contribution that is ...
The element hydrogen is virtually never called 'paramagnetic' because the monatomic gas is stable only at extremely high temperature; H atoms combine to form molecular H 2 and in so doing, the magnetic moments are lost (quenched), because of the spins pair. Hydrogen is therefore diamagnetic and the same holds true for many other elements ...
Magnetic susceptibility indicates whether a material is attracted into or repelled out of a magnetic field. Paramagnetic materials align with the applied field and are attracted to regions of greater magnetic field. Diamagnetic materials are anti-aligned and are pushed away, toward regions of lower magnetic fields.
The magnetization is the negative derivative of the free energy with respect to the applied field, and so the magnetization per unit volume is = , where n is the number density of magnetic moments. [1]: 117 The formula above is known as the Langevin paramagnetic equation.
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.
In this case, it will be shown that (+ +), which, combined with the constant k, shows that paramagnetic materials can have energy maxima but not energy minima and diamagnetic materials can have energy minima but not energy maxima. That is, paramagnetic materials can be unstable in all directions but not stable in all directions and diamagnetic ...
Barium is chemically similar to magnesium, calcium, and strontium, but more reactive. Its compounds are almost invariably found in the +2 oxidation state. As expected for a highly electropositive metal, barium's reaction with chalcogens is highly exothermic (release energy). Barium reacts with atmospheric oxygen in air at room temperature.