Phase transitions, ferroelectricity and collective motions

Microwave relaxation can be very useful for the study of phase transitions in protonic materials and their existence (and origin) can be evidenced by considering the following parameters. 

A plot of l/As vs. temperature T allows the extrapolated Curie-Weiss temperature and the corresponding C constant in the expression (Ae) = (T — Tq)/C (Table 25.1) to be measured. The Curie constant C is defined by the relation C = Np /k. The constant Tq is related to the exchange integral which takes into account the dipole-dipole interaction. In the case of a first order transition, Tq must be lower the T.  

Previous low frequency studies have failed to detect the ferro-para-electric nature of the I - II transition and CSHSO4 was considered as the only non-ferroelectric material of the MHXO4 family of compounds with an infinite chain structure. This is probably due to the low dipole moment value and to the fact that Asj and As4 susceptibilities vary in opposite directions. 

Analysis of As plots recorded on H3OUO2PO4.3H2O also gives a better description of the phase transition mechanism . In particular, the dimensionality effect concerning the ferroelectric sublattice can be deduced from As analysis. The extrapolated Curie-Weiss temperatures are about 210 K (Table 25.1) for the H2O sublattice (ferroelectric order, in the layer) and 170 K for orientation (dipole perpendicular to the layer), the C 

The relaxation time can be deduced from the Debye-like drcular arc. A plot of T values versus the inverse of temperature (10 /r) (Fig. 25.4) allows a measure of activation energy (Fig. 25.5). The separation of domains already discussed above is clearly visible, from fast reorientational motions of dipolar polyatomic ions such as HX04 and HjO to slow reorientation of NH4 ions. Motions of water molecules cover a broad region they are slow in gel, medium in superionic materials (e.g. HUP) and fast in liquid water. 

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