Magnetism paramagnetism

For conventional Ising-spin systems, Pising(o ) takes on the expected simple forms namely, either Puingiq) = < (0) in the (high-temperature, zero magnetization) paramagnetic phase or the double-peaked Pising(o ) = 5(q + M ) + 6 q — M ) for temperatures below the Curie critical temperature, T < Tc. 

Fig. 9. Bulk moduli of four austenitic stainless steels. Irregular behavior below 80 K can be interpreted from Doring s model as the difference in elastic properties at constant magnetization (paramagnetic) and constant magnetic field (antiferromagnetic in this case).

Phase stability of nanostructures has been one of the central issues in nanoscience and technology. For a given specimen of a fixed size, phase transition takes place when the temperature is raised to a certain degree. The value of the critical temperature (Tc) varies with the actual process of phase transition. The Tq values are different for the magnetic-paramagnetic, ferroelectric-non-ferroelectric, solid-solid, solid-liquid, and liquid-vapor phase transitions of the same specimen. Generally, solid-size reduction depresses the Tc of a nanosolid because atomic undercoordination lowers cohesive energy of atomics in the skin. 

The little atomic magnets are of course quantum mechanical, but Weiss s original theory of paramagnetism and ferromagnetism (1907) [7] predated even the Boln atom. He assumed that in addition to the external magnetic field Bq, there was an additional internal molecular field B. proportional to the overall magnetization M of the sample. 

The two primary causes of shielding by electrons are diamagnetism and temperature-independent paramagnetism (TIP). Diamagnetism arises from the slight unpairing of electron orbits under the influence of the magnetic field. This always occurs so as to oppose the field and was first analysed by Lamb [7]. A simplified version of his fomuila. 

Kowalewski J 1996 Paramagnetic relaxation in solution Encyclopedia of Nuclear Magnetic Resonance ed D M Grant and R K Harris (Chichester Wiley) pp 3456-62... 

NMR is an important teclnhque for the study of flow and diflfiision, since the measurement may be made highly sensitive to motion without in any way influencing the motion under study. In analogy to many non-NMR-methods, mass transport can be visualized by imaging the distribution of magnetic tracers as a fiinction of time. Tracers may include paramagnetic contrast agents which, in particular, reduce the transverse... 

The negative sign in equation (b 1.15.26) implies that, unlike the case for electron spins, states with larger magnetic quantum number have smaller energy for g O. In contrast to the g-value in EPR experiments, g is an inlierent property of the nucleus. NMR resonances are not easily detected in paramagnetic systems because of sensitivity problems and increased linewidths caused by the presence of unpaired electron spins. 

Other magnetic measurements of catalysts include electron paramagnetic resonance and magnetic susceptibility. Although those are not as common as NMR, they can be used to look at the properties of paramagnetic and ferromagnetic samples. Examples of these applications can be found in the literature [87. 

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