Hysteresis-free measurements

Therefore, in most cases, pH values measured at high temperatures in dilute solution should be considered approximate values only. In cases where the investigators address this problem and are careful to select a suitable electrode (namely, one that manufacturers claim to have almost hysteresis-free pH measurement and a stable isopotential point over the temperature range), the error associated with electrode performance will be small, and differences in reported pH values will correspond to differences in actual pH. In cases where pH is measured in concentrated sucrose solutions, the reported pH value should be considered as a nominal value only, and the differences in nominal pH values might not correspond to actual differences in hydrogen ion activity. 

Figure 9.28 illustrates the electro-optic responses observed at two 0 s 0° and 30°, where 0 is the angle between the layer normal and one of the crossed polarizer directions. As shown in Figure 9.28 [92], the electric field dependence of transmittance at 0 = 0° shows the typical thresholdless, hysteresis free, V-shaped switching. From the electro-optic measurements at every 5° of 0, the transmittance T versus 0 was obtained at given electric fields. Figure 9.29(a) shows three examples of T versus 0 curves at applied fields of 0, +6, and 6 V/pm [92]. The transmittance T is described by... 

The variation in optieal transmittanee as a funetion of simultaneously measured resistivity in Lai-yYyH c alloy films is shown in fig. 94. For y < 0.30, the films were eompletely hysteresis free and have a sharp optieal transition, where as for 0.46 < y < 0.67, the optieal transition proeeeds more gradually and some hysteresis was present. The films with y 0.86, exhibit large hysteresis effeets. Exeept for the film with y = 0.67 (not shown in the figure), whieh was on the borderline of the fee-hex phase transition, for all other films the transmittanee versus resistivity eurves were observed to reaeh the final shape after the first absorption-desorption eyele. For the film with y = 0.67, the eyele was observed to beeome reprodueible from the third loading eyele onwards. 

The pressure-eomposition isotherm for a typieal Lui-yYyllx (Lao.55Yo.45H c) is shown in fig. 95. In agreement with the optieal and X-ray diffraetion measurements, the isotherms were observed to be hysteresis free and with out any plateau, indieating that these alloy films remains fee for all x > 2. Van Gogh et al. (2001), fitted the isotherms to the Laeher s equation (Laeher, 1938) and ealeulated the partial molar heat of solution AH. For example for Lao.54Yo.46H c alloy, the heat of solution AH was found to be —38.1 kJ/mole H. 

The isomorphous substitution of framework aliunimun in faujasite-type zeolites was evidenced by chemical analysis, XRD (unit cell contraction), mid-infra-red spectroscopy (shift of lattice vibrations) and adsorption measurements (hysteresis-free adsorption isotherms) [147] and later by Si MAS NMR spectroscopy [149,150,153] (see Fig. 5). 

The evaluation of Gi at Xi+, and Xj.i is a check for possible hysteresis in the calculation and is a measure of the statistical error for the free energy change. 

When wood below the fiber-saturation point interacts with water, heat is evolved, and there are changes in the free energy and entropy of the sorbed water. Furthermore, the wood exerts swelling forces that can be measured. These effects can be treated by classical thermodynamic methods although moisture sorption by wood is not a perfectly reversible process because sorption hysteresis is involved, as was pointed out in the section on Moisture Sorption Isotherms (p. 136). 

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