Curie s law

Insofar that Curie s law is true, /left is independent of temperature, for that is how we arrived at Eq. (5.5). In practice. Curie s law is rarely obeyed exactly and, occasionally, it is quite seriously flouted. Nevertheless it is still conventional to quote /ieff values but it is then necessary to quote them over a range of temperatures. Although we might just as well report susceptibility values in these circumstances, conventions die hard. In any case, the temperature variation for /ieff immediately and transparently reveals any departures from Curie s Law in a way that the temperature variation of susceptibilities might not. 

There may, however, be specific reasons to study a signal over an extended temperature range. For one, a linear increase in EPR amplitude with the inverse of the temperature (Curie s law) is proof that a spin system is a two-level system, i.e., an S = 1/2 or an effective S = 1/2 system. More importantly, in complex multicenter metalloproteins, overlapping spectra may be deconvoluted by virtue of their Tu value being different if two centers, a and b, have rMa < TMb then at TMb the spectrum of center a is broadened and that of center b is not. It is once more emphasized that these types of studies require determination of (anisotropic) saturation behavior at all relevant temperatures. 

In paramagnetic resonance experiments, the sample is usually placed in a large constant magnetic field H0, whose direction is taken as that of the z axis. This field determines the quantum levels of the individual spins and polarizes them according to Curie s law. In a typical nuclear resonance experiment, a radiofrequency field H1( perpendicular to H0 and rotating in the x,y plane is applied to the sample. The response of the system is, under stationary conditions, described by the radiofrequency susceptibility %(co). The rotating field is given by... 

Magnetic thermometry 1. Electron paramagnetism 0 001-35 Magnetic susceptibility Curie s law plus corrections l/k T plus corrections ... 

Curie s Law and Its Application to Assignments of the Ground-State Multiplicity... 

Although for most metals x is independent of the temperature, for many substances it is inversely proportional to the absolute temperature, T, as expressed by Curie s law ... 

A simple method for determining the temperature inside the sample volume of an NMR probe is the quantitative evaluation of the absolute intensity using Curie s law (Eq. (25)). However, this approach is limited to systems that heat the sample volume only and not the radio frequency coil or other electronic parts of the probe. A heating of the radio frequency coil strongly influences the quality factor of the NMR probe and leads to an additional change of the signal intensity and, therefore, renders the quantification of intensity more complicated. 

It is important to note the quantitative character of NMR spectroscopy. By use of an internal or external intensity standard, a spin counting via the comparison of the signal intensities can be performed. In the case of an external intensity standard, the same spectroscopic parameters must be used, and the effect of Curie s law (Eq. (25)) in experiments at elevated temperatures has to be taken into account. 

The basic features of the Mb111 (Ns) spectrum are similar to those of cyanoferrimyoglobin (Fig. 14). Only one set of hyperfine-shifted resonances is observed, but the hyperfine shifts are larger and the lines broader than in MbmCN. Furthermore the temperature dependences of the resonances positions show drastic deviations from Curie s law (Eq. 4). Similar data were also obtained for azidoporphyrin-iron(III) complexes in pyridine solution 116). 

Studies on proton shifts in aqueous solutions of lanthanide perchlorates showed irregular sign variation of the shifts in the series and quite different from 170 shifts. This observation led to the idea that proton shifts are predominantly due to dipolar contributions. Further the proton shifts departed from Curie s law significantly [17]. The relative dipolar shifts and their temperature dependence can be predicted by Bleaney s theory [18]. For now Eu3+ and Sm3+ are not considered. 

To understand cross polarization and its many variants, we need several new concepts. These concepts include spinlocking (one element of this double-resonance pulse sequence), rotating-frame relaxation times, spin temperature and Curie s law, and finally, establishing contact, or mixing, between spin systems by means of applied rf. 

Write down an expression for Curie s law pertaining to paramagnetic materials and for the Curie-Weiss law pertaining to ferromagnetic or antiferromagnetic materials. 

Show that when Curie s Law applies to a magnetic... 

A quantity called the effective magnetic moment is obtained by measuring the Curie constant. If a substance obeys Curie s law, Eq. 8.7 holds over the paramagnetic region and Cmoi is given by the slope of the versus 1 /T plot. If is then substituted... 

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