Hysteresis temperature domain

Figure 2. Steady state hysteresis in the conversion-inlet temperature domain...

This class of smart materials is the mechanical equivalent of electrostrictive and magnetostrictive materials. Elastorestrictive materials exhibit high hysteresis between strain and stress (14,15). This hysteresis can be caused by motion of ferroelastic domain walls. This behavior is more compHcated and complex near a martensitic phase transformation. At this transformation, both crystal stmctural changes iaduced by mechanical stress and by domain wall motion occur. Martensitic shape memory alloys have broad, diffuse phase transformations and coexisting high and low temperature phases. The domain wall movements disappear with fully transformation to the high temperature austentic (paraelastic) phase. 

A similar study by O Brien and coworkers utilized bilayers composed of a shorter chain diacetylenicPC (9) and DSPC or DOPC [37]. Phase separation was demonstrated in bilayers by calorimetry and photopolymerization behavior. DSC of the 9/DSPC (1 1) bilayers exhibited transitions at 40 °C and 55 °C, which were attributed to domains of the individual lipids. Polymerization at 20 °C proceeded at similar rates in the mixed bilayers and pure 9 bilayers. A dramatic hysteresis effect was observed for this system, if the bilayers were first incubated at T > 55 °C then cooled back to 20 °C, the DSC peak for the diacetylenicPC at 40 °C disappeared and the bilayers could no longer be photopolymerized. The phase transition and polymerizability of the vesicles could be restored simply by cooling to ca. 10 °C. A similar hysteretic behavior was also observed for pure diacetylenicPC bilayers. Mixtures of 9 and DOPC exhibited phase transitions for both lipids (T = — 18 °C and 39 °C) plus a small peak at intermediate temperatures. Photopolymerization at 20 °C initially proceeded at a similar rate as observed for pure 9 but slowed after 10% conversion. These results were attributed to the presence of mixed lipid domains... 

Figure 2.4 Strain-field curves for < 001 > oriented 0.91PbZn1/3Nb2/303-0.09PbTi03 single crystals. The sample in (a) was poled at room temperature, where the resulting domain state is unstable (due to induction of tetragonal material associated with the curved morphotropic phase boundary), yielding substantial hysteresis. In (b) the crystal was poled at low temperatures to keep it in the rhombohedral phase. When measured at room temperature, the piezoelectric response is much more linear and non-hysteretic, due to the improved stability of the ferroelectric domain state. Data courtesy of S. E. Park.

The hysteresis loop of a single-domain single crystal of BaTiCF is shown in Fig. 2.46(a). The almost vertical portions of the loop are due to the reversal of the spontaneous polarization as reverse 180° domains nucleate and grow. The almost horizontal portions represent saturated states in which the crystal is single domain with a permittivity er of 160 (see Fig. 2.40(d)) measured in the polar direction. The coercive field at room temperature when the loop is developed by a 50Hz supply is 0.1 MVm-1 and the saturation polarization is 0.27 Cm-2. For fields in the approximate range 10 to 100 V mm 1 the hysteresis loop takes the form of a narrow ellipse, a Rayleigh loop, with its major axis parallel to the almost horizontal part of the fully developed loop. 

When a critical field (Ec) is reached, which is near to the coercive field, the domains switch direction as a whole involving considerable hysteresis loss. This loss is proportional to the area of the loop, so that for the single crystal in Fig 2.46(a) it amounts to about 0.1 MJm-3. At 100Hz the power dissipated as heat would be 100 MW m-3, which would result in a very rapid rise in temperature. The dissipation factor (tan (5) is also very high at high field strengths, but becomes small at low field strengths, as described above. Modifications to the composition diminish the loss still further. 

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