Magnetic entropy

Basic thermodynamics, statisticai thermodynamics, third-iaw entropies, phase transitions, mixtures and soiutions, eiectrochemicai systems, surfaces, gravitation, eiectrostatic and magnetic fieids. (in some ways the 3rd and 4th editions (1957 and 1960) are preferabie, being iess idiosyncratic.)... 

A second type of relaxation mechanism, the spin-spm relaxation, will cause a decay of the phase coherence of the spin motion introduced by the coherent excitation of tire spins by the MW radiation. The mechanism involves slight perturbations of the Lannor frequency by stochastically fluctuating magnetic dipoles, for example those arising from nearby magnetic nuclei. Due to the randomization of spin directions and the concomitant loss of phase coherence, the spin system approaches a state of maximum entropy. The spin-spin relaxation disturbing the phase coherence is characterized by T. ... 

The systems of interest in chemical technology are usually comprised of fluids not appreciably influenced by surface, gravitational, electrical, or magnetic effects. For such homogeneous fluids, molar or specific volume, V, is observed to be a function of temperature, T, pressure, P, and composition. This observation leads to the basic postulate that macroscopic properties of homogeneous PPIT systems at internal equiUbrium can be expressed as functions of temperature, pressure, and composition only. Thus the internal energy and the entropy are functions of temperature, pressure, and composition. These molar or unit mass properties, represented by the symbols U, and S, are independent of system size and are intensive. Total system properties, J and S do depend on system size and are extensive. Thus, if the system contains n moles of fluid, = nAf, where Af is a molar property. Temperature... 

Four of the solid solutions of Table III have excess entropies of solution which include contributions from magnetic disordering in both the alloy and in one or both of the pure components. These contributions can be quite large, and since there is no assurance... 

Magnesium cadmium, alloy (MgCd3), 128 alloy (Mg3Cd), 129 Magnetic entropy, 132 disordering, 131... 

Paramagnetic substances have a magnetic entropy associated with the random orientation of the spin of the unpaired electrons as shown in (a) below ... 

After a simple Fourier inversion of a set of magnetic structure factors MbU, one can retrieve the magnetisation density. A much better result, e.g. the most probable density map, can be obtained using the Maximum Entropy (MaxEnt) method. It takes into account the lack and the uncertainty of the information not all the Bragg reflections are accessible on the instrument, and all the values contained in the error bars are satisfactory and have to be considered. However, as this method extracts all the information contained in the data, it is important to keep in mind that it may show spurious small details associated to a low accuracy and/or a specific lack of information located in (/-space. 

Dobrzynski, L., Papoular, R.J. and Sakata, M. (1995) Internal magnetization density distributions of iron and nickel by the maximum entropy method, J. Phys. Soc. Japan, 65, 255-263. 

Notice that dephasing of the transverse magnetization does not affect Mz a T2 process involves no energy transfer but, being a spontaneous process, does involve an increase in the entropy of the spin system. 

Figure 4.1 Schematic diagram showing the thermodynamics of the demagnetization process. By changing the magnetic field from the initial value Hl to the final one Hf, with Hf < Hj a gain in magnetic entropy, ASm, occurs during the isothermal process from...

A to B, while a temperature drop, ATad, is observed during the adiabatic process A C. The maximum magnetic entropy for a system with a spin s, ftln(2s+ 1), reached at infinite temperatures, is indicated as a grey broken line. 

The origin of this heating is the changing distribution of entropy within the paramagnet with the applied field [12-14]. We can write the sum total of entropies according to Equation 9.1, where 5 total is the total entropy, SM is the magnetic entropy, 5,lattice is the lattice entropy and Selectronic is the electronic entropy of the system. 

Figure 9.1 Spin angular momenta, s, depicted as arrows, are randomly aligned in zero field, H = 0 (a), and align with the applied field, H > 0 (b), thereby decreasing the magnetic entropy of the system.

A further illustration and summary of the entropy and temperature changes involved upon moving between two magnetic fields is shown in Figure 9.2 [13]. 

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