Hydrogen spin fluctuations

In the presence of both order-disorder and displacive, as in the KDP family, the two dynamic concepts have somehow to be merged. It could well be that the damping constant Zs becomes somewhat critical too (at least in the over-damped regime of the soft mode), because of the bihnear coupling of r/ and p. It would, however, lead too far to discuss this here in more detail. The corresponding theory of NMR spin-lattice relaxation for the phase transitions in the KDP family has been worked out by Blinc et al. [19]. Calculation of the spectral density is here based on a collective coordinate representation of the hydrogen bond fluctuations connected with a soft lattice mode. Excellent and comprehensive reviews of the theoretical concepts, as well as of the experimental verifications can be found in [20,21]. 

According to the spin fluctuations theory, the Curie temperature of the band ferromagnets is inversely proportional to the density of states in the subbands near the Fermi level, NT(Ef) and Nl(E ). The increase of the lattice parameters after the hydrogen atoms incorporation to the lattice induces the decrease of the degree of wave-function hybridization between the 3r/-electrons of Fe atoms and 5r/-electrons of rare-earth metal atoms. This in turn entails the decrease of density of states in both zones NT(Ef) and Ni(EF). 

The summation indicates that more than one hydrogen spin could be interacting with the phosphorus spin and that the spectral densities may be different for each of these interactions. It will be noted that the dipolar relaxation equations given are in their conventional form. However, because the P—H intemuclear distances may actually fluctuate with the nucleic acids motions, r may be incorporate explicitly into the spectral density calculations (see following discussion Keepers and James, 1982). 

The rate of relaxation is affected by magnetic field fluctuations in the local environment of excited hydrogen spins. For simple liquids such as water, the diffusion of H2O molecules by Brownian motion allows H spins to encounter and interact with other dipole magnetic moments as described by the Bloembergen-Purcell-Pound, or BPP, theory (Bloembergen et al. 1948). In cementitious materials, there are two main sources of relaxation ... 

Different response functions such as Cp and Up show maxima, and these maxima increase and seem to diverge as the critical pressure is approached, consistent with the Widom line picture discussed for other water models in the sections above. Moreover, the temperature derivative of the number of hydrogen bonds dAnB/dT displays a maximum in the same region where the other thermodynamic response functions have maxima, suggesting that the fluctuations in the number of hydrogen bonds is at a maximum at the Widom line temperature Tw. To further test whether this model system also displays a dynamic crossover as found in the other models of water, the total spin relaxation time of the system as a function of T for different... 

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