Phase change and hysteresis

Phase Change and Hysteresis in PEMFCs 287 Table 7.5 Material parameters and reference values. 

Simulations of octahedral molecular clusters at constant temperature show two kinds of structural phase changes, a high-temperature discontinuous transformation analogous to a first-order bulk phase transition, and a lower-temperature continuous transformation, analogous to a second-order bulk phase transition. The former shows a band of temperatures within which the two phases coexist and hysteresis is likely to appear in cooling and heating cycles Fig. 10 the latter shows no evidence of coexistence of two phases. The width of the coexistence band depends on cluster size an empirical relation for that dependence has been inferred from the simulations. 

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. 

First-order phase transitions exhibit hysteresis, i.e. the transition takes place some time after the temperature or pressure change giving rise to it. How fast the transformation proceeds also depends on the formation or presence of sites of nucleation. The phase transition can proceed at an extremely slow rate. For this reason many thermodynamically unstable modifications are well known and can be studied in conditions under which they should already have been transformed. 

In Figure 8.5, w is the distance between the heating and cooling curves at the point where a = 0.5 is called the hysteresis width. This temperature may be quite small, or it may amount to several degrees depending on the nature of the phase transition and the heating rate. Many substances exhibit this type of behavior as a result of a phase change. 

The only salt of the [Fe(bpp)2]2+ ion for which crystal structural data have been obtained above and below the transition temperature is the nitroprus-side, [Fe(bpp)2][Fe(CN)5NO], which crystallises anhydrous. The cation is high spin at room temperature. This salt displays an abrupt transition with a narrow hysteresis loop, T1/2j=181 K and T1/2t=184 K. The transition is accompanied by a phase change at 298 K the crystal is tetragonal with space... 

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