Curie point behavior

Ehrenfest s concept of the discontinuities at the transition point was that the discontinuities were finite, similar to the discontinuities in the entropy and volume for first-order transitions. Only one second-order transition, that of superconductors in zero magnetic field, has been found which is of this type. The others, such as the transition between liquid helium-I and liquid helium-II, the Curie point, the order-disorder transition in some alloys, and transition in certain crystals due to rotational phenomena all have discontinuities that are large and may be infinite. Such discontinuities are particularly evident in the behavior of the heat capacity at constant pressure in the region of the transition temperature. The curve of the heat capacity as a function of the temperature has the general form of the Greek letter lambda and, hence, the points are called lambda points. Except for liquid helium, the effect of pressure on the transition temperature is very small. The behavior of systems at these second-order transitions is not completely known, and further thermodynamic treatment must be based on molecular and statistical concepts. These concepts are beyond the scope of this book, and no further discussion of second-order transitions is given. 

The parallel dipolar alignment in PVDF film treated as above leads to a residual polarization, which is the basis for several proposed mechanisms that explain the piezoelectric and pyroelectric behavior of the material. Although various observations support the suggestion that PVDF is also ferroelectric, its Curie point has not been detected. (Most ferroelectrics show a phase transition at a temperature known as the Curie point above which they become paraelectric.)... 

Pyro- and Piezoelectric Properties The electric field application on a ferroelectric nanoceramic/polymer composite creates a macroscopic polarization in the sample, responsible for the piezo- and pyroelectricity of the composite. It is possible to induce ferroelectric behavior in an inert matrix [Huang et al., 2004] or to improve the piezo-and pyroelectricity of polymers. Lam and Chan [2005] studied the influence of lead magnesium niobate-lead titanate (PMN-PT) particles on the ferroelectric properties of a PVDF-TrFE matrix. The piezoelectric and pyroelectric coefficients were measured in the electrical field direction. The Curie point of PVDF-TrFE and PMN-PT is around 105 and 120°C, respectively. Different polarization procedures are possible. As the signs of piezoelectric coefficients of ceramic and copolymer are opposite, the poling conditions modify the piezoelectric properties of the sample. In all cases, the increase in the longitudinal piezoelectric strain coefficient, 33, with ceramic phase poled) at < / = 0.4, the piezoelectric coefficient increases up to 15 pC/N. The decrease in da for parallel polarization is due primarily to the increase in piezoelectric activity of the ceramic phase with the volume fraction of PMN-PT. The maximum piezoelectric coefficient was obtained for antiparallel polarization, and at < / = 0.4 of PMN-PT, it reached 30pC/N. 

Since the temperature of pyrolysis is a function of the Curie-point wire alloy composition, the wire, and consequently the sample, may be heated to that temperature only. If it is desired to evaluate several different pyrolysis temperatures, or to study the behavior of a sample material at different temperatures, it is necessary to use a different Curie-point wire for each run. Therefore, it is not possible with a Curie-point system to optimize the pyrolysis temperature of a sample by placing the material into the instrument and increasing the temperature in a stepwise fashion. 

Fig. 33. Temperature dependence of the internal field in single-crystalline Dy (left) and Ho (right). The insets show the behavior at and below the Curie point with an enlarged vertical scale. The lines are guides to the eye. After Ekstrom et al. (1997) and Schreier et al. (2000a).

NaKC4H40e 4H2O), monopotassium dihydrophosphate (KH2PO4), or barium titanate (BaTiOs). At sufficiently high temperatures ferroelectrics show normal dielectric behavior. However, below a certain critical temperamre (so called. Curie temperature), even a small electric field causes a large polarization, which is preserved even if the external field is switched off. This means that below the Curie point ferroelectric materials show spontaneous polarization. The phase transition at the Curie temperature is related to the change of the lattice symmetry of the sample. 

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