Equation Weiss

The function of I2g> (T) in the vicinity of the phase transition to centrosymmetric conditions usually has a linear character. Such behavior corresponds to ferroelectrics that undergo type II phase transitions and for which the SHG signal, l2Curie temperature is described by the Curie - Weiss Equation ... 

Information about the structure of Pd and Pt is provided by the paramagnetic susceptibility of the metals, interpreted by the Weiss equation... 

The use of H2O2 and Fe(II) for oxidation was reported by Fenton in 1894, and was proposed to involve hydroxyl radicals by Haber and Weiss (equation 69) 269 reaction was developed by Waters in the 1940s and then by... 

Curie s equation applies to gases, solutions, and some crystals. For other crystals a more general equation, the Weiss equation, may be used (derived by P. Weiss in 1907). Weiss assumed that the local magnetic field orienting the dipoles is equal to the applied field plus an added field proportional to the magnetic volume polarization M ... 

In a graph of 1/xmoiar against T, the points lie on a straight line if the Weiss equation is valid. Measurements for three salts of cobalt(II) are shown in Figure X-l. It is seen that the curves are straight lines except at very low temperatures. Their slopes are the same the slope is the reciprocal of the Curie constant, and accordingly the cobalt (II) atom has the same magnetic moment in the three substances. 

Yamada et al. [9,10] demonstrated that the copolymers were ferroelectric over a wide range of molar composition and that, at room temperature, they could be poled with an electric field much more readily than the PVF2 homopolymer. The main points highlighting the ferroelectric character of these materials can be summarized as follows (a) At a certain temperature, that depends on the copolymer composition, they present a solid-solid crystal phase transition. The crystalline lattice spacings change steeply near the transition point, (b) The relationship between the electric susceptibility e and temperature fits well the Curie-Weiss equation, (c) The remanent polarization of the poled samples reduces to zero at the transition temperature (Curie temperature, Tc). (d) The volume fraction of ferroelectric crystals is directly proportional to the remanent polarization, (e) The critical behavior for the dielectric relaxation is observed at Tc. 

In an analogous maimer, the complete form of the Curie-Weiss equation is ... 

The relationship, i = 2.83 "VX (T+ A ) shows that changes in susceptibility could result from changes in the moment (i.e.,changes in oxidation state) and/ or from changes in the Weiss interaction constant, A. The susceptiblity, X, is related to the interaction constant,A, by the Curie-Weiss equation ... 

This Weiss equation is applicable to surface and shallow subsurface water within a limited temperature range. For more complex conditions (higher temperature and salinity) it is necessary to determine directly activities coefficient of nonpolar components using corresponding equations of state of solutions. For instance, according to Pitzer model... 

Table 2.30 Ray Weiss equations constants (2.291) for the determination of Bunsen solubility coefficient, ml-1 atm... 

Ideally the graph is linear, with a slope of 1/C and an intercept on the T axis of (Figure 11.18). Frequently, the point of intercept, Tq, is slightly different from the measured value of T, and the Curie-Weiss equation is often written in the form... 

The mean density pix, t) of a system of independent particles that undergo a CTRW obeys the same equation as the PDF pix, t), which can be written in the form of a generalized Master equation. The Montroll-Weiss equation (2.45) can be rewritten for p(, i) and rearranged as... 

Applying the Fourier-Laplace (F-L) transform to (3.28) and (3.30), we obtain the Fourier-Laplace transform of the PDF p(x, t), the Montroll-Weiss equation,... 

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