Hysteresis width

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. 

Somewhat unusual pressure dependence of the nature of the spin transition curve has been found for chain-like SCO systems containing substituted bridging triazole ligands [163, 164]. Although the transition is displaced to higher temperatures with increase in pressure, the shape of the transition curve, unusually, is effectively constant, i.e. there is no significant change in the hysteresis width and the transition remains virtually complete. This has been taken to indicate that the cooperativity associated with the transitions in these and related systems is confined within the iron(II) triazole chains. 

The influence of pressure has also been used to tune the ST properties of these ID chain compounds. Application of hydrostatic pressure ( 6 kbar) on [Fe(hyptrz)3] (4-chlorophenylsulfonate)2 H20 (hyptrz=4-(3 -hydroxypro-pyl)-l,2,4-triazole) provokes a parallel shift of the ST curves upwards to room temperature (Fig. 5) [41]. The steepness of the ST curves along with the hysteresis width remain practically constant. This lends support to the assertion that cooperative interactions are confined within the Fe(II) triazole chain. Thus a change in external pressure has an effect on the SCO behaviour comparable to a change in internal electrostatic pressure due to anion-cation interactions (e.g. changing the counter-anion). Both lead to considerable shifts in transition temperatures without significant influence on the hysteresis width. Several theoretical models have been developed to predict such SCO behaviour of ID chain compounds under pressure [50-52]. Figure 5 (bottom) also shows the pressure dependence of the LS fraction, yLS, of... 

Figure 4. Schematic showing a hysteresis loop for the CdSe nanociystals with the smearing of the thermodynamic transition pressure caused by the finite nature of the nanocrystal particle. The thermodynamic transition pressure is offset from the hysteresis center to emphasize that in first-order solid-solid transformations, this pressure is unlikely to be precisely centered. The lower plot shows the estimated smearing for CdSe nanocrystals as inversely proportional to the number of atoms in the crystal, at two temperatures, as discussed in the text. Note that nanocrystals are not ordinarily synAesized or studied in sizes smaller than 20 A in diameter. This figure shows that this thermal smearing is insignificant compared to the large hysteresis width in the CdSe nanociystals studied (25-130 A in diameter), such that the transition is bulk-like from this perspective. This means that observed transformations occur at pressures far from equilibrium, where there is little probability of back reaction to the metastable state once a nanociystal has transformed. In much smaller crystals or with larger temperatures, the smearing could become on the order of the hysteresis width, and the crystals would transform from one stmcture to the other at thermal equilibrium.

Figure 6. Hysteresis loop dependence on (A) relaxation time and (B) temperature for the transformation in 25-A diameter CdSe nanociystals. In (A), the rate constants are determined from time-dependent decays at 463 K, such as those shown in Figure 5. Activation volumes determined from the slopes using Equation (2) are -17 and +65 A in the forward and reverse transitions, respectively. The activation volumes are assumed to be constant over the pressure ranges under study to simplify the analysis. In (B), the temperature data are compiled from measurements of the rate constant for In (k) = -3.5 at the given temperatures. The inset is a sample hysteresis loop measured for 35 A nanocrystals with the hysteresis width indicated. The loop starts at low pressure and proceeds in the direction of the arrows, as the normalized ratio of sample transformed is monitored [Used by permission of the editor of Science, from Jacobs et al (2001), Fig. 3].

Figure 7. Hysteresis width versus nanocrystal size at room temperature and a relaxation time of 3 minutes. The width for the largest sample is a lower limit beeause the 126-A diameter nanociystals remain trapped in the high-pressure roeksalt stracture as the pressure is released (Jacobs, in preparation). In the inset, AS is the entropic barrier and ke is Boltzmann s constant. [Used by permission of the editor of Science, from Jacobs et al. (2001), Fig. 4.]...

The nearly constant hysteresis width is important because it means that, at least in CdSe, the size-dependence of the hysteresis width is not sensitive to the kinetics. The upstroke transition pressure can nevertheless shift with nanocrystal size due to thermodynamic effects, as discussed earlier in this chapter (see SURFACE EFFECTS... above). Some geophysically-relevant systems may not exhibit full hysteresis loops because the high-pressure phase remains metastable as the pressure is released. Thus, special care should be taken to consider both the thermodynamics and kinetics in interpreting hysteresis measurements on such systems. 

Cui, J. Chu, Y. S. Famodu, O. O. Furuya, Y. Hattrick-Simpers, J. James, R. D. Ludwig, A. Thienhaus, S. Wuttig, M. Zhang, Z. Takeuchi, I., Combinatorial search of thermoelastic shape-memory alloys with extremely small hysteresis width, Nat. Mater. 2006, 5, 286-290... 

Solvate molecules incorporated into the crystal lattice can strongly influence the spin crossover behaviour. A representative series is given by [Fe(2-pic)3]Cl2 sol complexes (Table 9.6). These systems differ in their structure and the hydrogen bonding network. Consequently the spin crossover behaviour (transition temperature, hysteresis width, abruptness) is different. 

A pronounced change in the absorption spectrum which accompanies the spin transition can be utilised to select an appropriate optical response function (e.g. a difference between HS and LS absorption at a certain wavenumber). The optical response function possesses a shape which copies the shape of the (xT) versus T curve of the magnetic measurements, including the hysteresis width. The hysteresis is utilised as an information-keeping function (memory effect). 

FIGURE 7.13. (a) Static hysteresis of macroscopic polarization P E) and (b) dielectric susceptibility x E) = dPjdE for an FLC cell. A14 is defined as the hysteresis width. 

Additionally, the rubbing strength was controlled. The largest value of the hysteresis width was obtained when both sides were unrubbed. 

Step 1 With the process initially at or near steady state, estimate the process output noise level by calculating its stamdard deviation (input signal where the input signal will switch d around a nominal value u. Designate the corresponding nominal value of the process output as the reference output value r. 

Characteristic transformation temperatures depend strongly on composition (see table on next page and the previous section on chemistry). Typical hysteresis widths range from 10 C (18 °F) for certain titanium-nickel-copper alloys, to 40 to 60 °C (72 to 108 °F) for binary alloys, to 100 °C (180 °F) for titanium-nickel-niobium alloys. 

Tests of a superelastic titanium-nickel wire at three temperatures. Alloy contains 50.6 at.% nickel. Three modes of degradation occur simultaneously during the isothermal superelastic cycling of titanium-nickel alloys walking, or an accumulation of permanent set (top), a change in yield stress (middle) and a reduction in the hysteresis width (bottom). 

Recently, PPy has been used to construct a reference electrode for an Ru02 thin-film pH sensor [93], The solid-state miniaturized PPy-coated ITO (indium tin oxide) reference electrode showed improved properties such as lower drift rate and narrower hysteresis width in comparison to a commercial Ag/AgCl electrode. 

Figure 14.1.2 shows a thermal hysteresis width of about 37 K with T = 231 K and = 194 K (T(.t = critical temperature in low-spin- high-spin transition in the warming mode, while T l = critical temperature in high-spin low-spin transition in the cooling mode Tj/2 is the temperature for which there is 50 percent of the low-spin complex). 

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