Curie transition

Because of very high dielectric constants k > 20, 000), lead-based relaxor ferroelectrics, Pb(B, B2)02, where B is typically a low valence cation and B2 is a high valence cation, have been iavestigated for multilayer capacitor appHcations. Relaxor ferroelectrics are dielectric materials that display frequency dependent dielectric constant versus temperature behavior near the Curie transition. Dielectric properties result from the compositional disorder ia the B and B2 cation distribution and the associated dipolar and ferroelectric polarization mechanisms. Close control of the processiag conditions is requited for property optimization. Capacitor compositions are often based on lead magnesium niobate (PMN), Pb(Mg2 3Nb2 3)02, and lead ziac niobate (PZN), Pb(Zn 3Nb2 3)03. 

Ironis very reactive chemically and oxidizes readily. It has four allotropic forms, one of which (a) is magnetic with a Curie transition point of770°C. Ithasadensity of7.6g/cm, ameltingpointof 1536°C, athermal expansion of 12.6 ppm/°C at 25°C, a thermal conductivity of 0.80 W/ cm °C at25°C and an electrical resistivity of 9.71 iohm-cm at 20°C. 

In copolymers of group B the Curie transition appears in the differential scanning calorimetric curve as a broad peak, extending over a temperature interval which narrows down with increasing VF2 content. The transition... 

The melting temperature and melting enthalpy are, however, unchanged under poling and are only slightly affected by crystallization conditions since the influence of the preparation conditions is lost during the Curie transition. It is noteworthy that the enthalpy at the Curie transition Ah (up) increases with the... 

The ferroelectric all-trans diffraction maximum is always significantly broader than its paraelectric counterpart. Figure 14a shows as an example the variation of the integral width of the WAXD peak with temperature through the Curie transition for the 60/40 copolymer. In the high temperature range, p... 

Fig. 16a-c. Schematic model of the lamellar structure of the copolymer in the, a. high temperature range (paraelectric phase) b. Curie transition region and c. low temperature region L and I denote respectively the long period and the average crystal thickness comprising a mixture of non ferroelectric and ferroelectric domains... 

On cooling, the opposite behavior of the microhardness, increase with decreasing temperature, is observed. However, the Curie transition temperatures are shifted towards lower temperatures. 

Fig. 19. Dependence of crystal hardness upon unit cell density through the Curie transition...

As an example of the Curie transition for other VF2/F3E compositions, measurements of e and e" as a function of temperature and f = 1 kHz are shown in Figs. 25a and 25b. The complex permittivity function of polymeric materials has been shown to follow the Havriliak-Negami phenomenological equation [99] ... 

The distance between neighboring chains L has been evaluated from the experimental EISF, and r and t from the experimental asymptotic values of HWHM. Figure 32a shows that L increases strongly from 1 up to 4.8 A with temperature while the jump parameter r varies only slightly (between 0,8 and 1.6 A). At 340 K the r and L values are nearly the same indicating that at the onset of the Curie transition all the free volume available is occupied by the jump. 

A simple quantitative model, with no adjustable parameters, is developed for the finite size effect of ferroelectric particles on the Curie transition temperature. As the size of ferroelectric particles decreases, the Curie temperature decreases. Based on our model for lattice contraction and the Landau-Ginsburg-Devonshire (LGD) phenomenological theory, size effects on Curie temperature of lead zirconate titanate PbZri. Ti Oj (PZT, x > 0.6) are considered. It is shown that Curie temperature of PZT (x > 0,6) decreases with decreasing particle size. The predictions of our equation are in agreement with the experimental results. 

The heat capacities of sintered specimens of LaN and NdN were measured from 1.2°K. to 45°K. by Veyssie, et al. 185). LaN shows a slight anomaly attributed to magnetic impurities NdN has a peak at 27.6 zh 0.1°K. corresponding to a (ferromagnetic) Curie transition. Debye 0 values are 300° and — 360 °K., respectively, but the data do not cover an adequate range to permit evaluation of the thermodynamic properties. 

Figure 4.19 illustrates the relationship between the Curie transition temperature as determined from microhardness and as measured by calorimetry. Only for the 80/20 composition is there an uncertainty in the correlation, due to the overlapping of the Curie temperature with the melting point. 

Figure 4.18. Temperature dependence of the microhardness (a) during heating and (b) during cooling of the 60/40 (O), 70/30 (A), 80/20 ( ) VF2-F3E copolymers. The filled symbols denote the Curie transition region between ferroelectric (low T) and paraelectric (high T) and paraelectric (high T) behaviour. (From Balta Calleja, Santa Cruz et al, 1992.)...

Lovinger AJ, Funikawa T, Davis GT, Broadhurst MG (1983) Crystallographic changes characterizing the Curie transition in three ferroelectric copolymers of vinylidene fluoride and trifluoroethylene. Polymer, 24 1225,1233... 

A simple estimate shows that magnetic order is not the result of a real magnetic field. The order of magnitude of the magnetic interaction energy for one spin, PBHy, can be compared with the thermal energy at the Curie transition, lc7 ... 

Lovinger AJ, Furukawa T (1983) Curie transitions in copolymers of vinylidene fluoride. Ferroelectrics 50 227... 

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