Quartz constants 99

Cinnamic acid, 50 mg/100 mL in sodium phosphate buffer Thiourea, 30 mg/100 mL in sodium phosphate buffer Cuvettes, glass and quartz Constant-temperature bath at 25-30°C... 

Using Eqs. VI-30-VI-32 and data from the General References or handbooks, plot the retarded Hamaker constant for quartz interacting through water and through n-decane. Comment on the relative importance of the zero frequency contribution and that from the vuv peak. 

A thin film of hydrocarbon spread on a horizontal surface of quartz will experience a negative dispersion interaction. Treating these as 1 = quartz, 2 = n-decane, 3 = vacuum, determine the Hamaker constant A123 for the interaction. Balance the negative dispersion force (nonretarded) against the gravitational force to find the equilibrium film thickness. 

Kinetic measurements were performed employii UV-vis spectroscopy (Perkin Elmer "K2, X5 or 12 spectrophotometer) using quartz cuvettes of 1 cm pathlength at 25 0.1 C. Second-order rate constants of the reaction of methyl vinyl ketone (4.8) with cyclopentadiene (4.6) were determined from the pseudo-first-order rate constants obtained by followirg the absorption of 4.6 at 253-260 nm in the presence of an excess of 4.8. Typical concentrations were [4.8] = 18 mM and [4.6] = 0.1 mM. In order to ensure rapid dissolution of 4.6, this compound was added from a stock solution of 5.0 )j1 in 2.00 g of 1-propanol. In order to prevent evaporation of the extremely volatile 4.6, the cuvettes were filled almost completely and sealed carefully. The water used for the experiments with MeReOj was degassed by purging with argon for 0.5 hours prior to the measurements. All rate constants were reproducible to within 3%. 

A Perkin-Elmer 5000 AAS was used, with an electrically heated quartz tube atomizer. The electrolyte is continuously conveyed by peristaltic pump. The sample solution is introduced into the loop and transported to the electrochemical cell. A constant current is applied to the electrolytic cell. The gaseous reaction products, hydrides and hydrogen, fonued at the cathode, are flowed out of the cell with the carrier stream of argon and separated from the solution in a gas-liquid separator. The hydrides are transported to an electrically heated quartz tube with argon and determined under operating conditions for hydride fonuing elements by AAS. 

In 1963, McQueen, Fritz, and Marsh (J. Geophys. Res. 68, p. 2319) suggested that the high-pressure shock-wave data for fused quartz (Table 1) and the data for crystal quartz pg = 2.65 g/cm, Co = 1.74 km/s and s = 1.70, both described the shock-induced high-pressure phase of SiOj, stishovite pg = 4.35 g/cm ), above 50 GPa. Assume Ej-j, = 1.5 kJ/g show that these shock data are consistent with a constant value of y = 0.9 in the 50-100 GPa range. 

Fig. 4.3. Typical normalized piezoelectric current-versus-time responses are compared for x-cut quartz, z-cut lithium niobate, and y-cut lithium niobate. The y-cut response is distorted in time due to propagation of both longitudinal and shear components. In the other crystals, the increases of current in time can be described with finite strain, dielectric constant change, and electromechanical coupling as predicted by theory (after Davison and Graham [79D01]).

The measured relationships between piezoelectric polarization and strain for x-cut quartz and z-cut lithium niobate are found to be well fit by a quadratic relation as shown in Fig. 4.4. In both materials a significant nonlinear piezoelectric effect is indicated. The effect in lithium niobate is particularly notable because the measurements are limited to much smaller strains than those to which quartz can be subjected. The quadratic polynomial fits are used to determine the second- and third-order piezoelectric constants and are summarized in Table 4.1. Elastic constants determined in these investigations were shown in Chap. 2. 

In the case of x-cut quartz there is excellent agreement between second-order constants determined in the shock-compression studies and ultrasonic... 

The ratio of third- to second-order piezoelectric constants has also been determined for x-cut quartz with the acceleration pulse loading method [77G05]. Two experiments yielded values for Cm/Cu of 15.0 and 16.6 compared to the ratio of 15.3 [72G03] determined from the fit to the 25 shock loading experiments. 

The determination of piezoelectric constants from current pulses is based on interpretation of wave shapes in the weak-coupling approximation. It is of interest to use the wave shapes to evaluate the degree of approximation involved in the various models of piezoelectric response. Such an evaluation is shown in Fig. 4.5, in which normalized current-time wave forms calculated from various models are shown for x-cut quartz and z-cut lithium niobate. In both cases the differences between the fully coupled and weakly coupled solutions are observed to be about 1%, which is within the accuracy limits of the calculations. Hence, for both quartz and lithium niobate, weakly coupled solutions appear adequate for interpretation of observed current-time waveforms. On the other hand, the adequacy of the uncoupled solution is significantly different for the two materials. For x-cut quartz the maximum error of about 1%-1.5% for the nonlinear-uncoupled solution is suitable for all but the most precise interpretation. For z-cut lithium niobate the maximum error of about 8% for the nonlinear-uncoupled solution is greater than that considered acceptable for most cases. The linear-uncoupled solution is seriously in error in each case as it neglects both strain and coupling. 

Constants determined from data reported in reference [68G05] and from the piezoelectric studies of X-cut quartz are shown in Table 4.3. The coefficients are found to be constant over the range of strain indicated. 

The piezoelectric constant studies are perhaps the most unique of the shock studies in the elastic range. The various investigations on quartz and lithium niobate represent perhaps the most detailed investigation ever conducted on shock-compressed matter. The direct measurement of the piezoelectric polarization at large strain has resulted in perhaps the most precise determinations of the linear constants for quartz and lithium niobate by any technique. The direct nature of the shock measurements is in sharp contrast to the ultrasonic studies in which the piezoelectric constants are determined indirectly as changes in wavespeed for various electrical boundary conditions. 

The most distinctive aspect of the shock work is the determination of higher-order piezoelectric constants. The values determined for the constants are, by far, the most accurate available for quartz and lithium niobate, again due to the direct nature of the measurements. Unfortunately it has not been possible to determine the full set of constants. Given the expense and destructive nature of the shock experiment, it is unlikely that a full set of higher-order piezoelectric constants can be determined. A less expensive investigation of higher-order constants could be conducted with the ramp wave or acceleration wave loading experiment described in the chapter. 

The PL spectrum and onset of the absorption spectrum of poly(2,5-dioctyloxy-para-phenylene vinylene) (DOO-PPV) are shown in Figure 7-8b. The PL spectrum exhibits several phonon replica at 1.8, 1.98, and 2.15 eV. The PL spectrum is not corrected for the system spectral response or self-absorption. These corrections would affect the relative intensities of the peaks, but not their positions. The highest energy peak is taken as the zero-phonon (0-0) transition and the two lower peaks correspond to one- and two-phonon transitions (1-0 and 2-0, respectively). The 2-0 transition is significantly broader than the 0-0 transition. This could be explained by the existence of several unresolved phonon modes which couple to electronic transitions. In this section we concentrate on films and dilute solutions of DOO-PPV, though similar measurements have been carried out on MEH-PPV [23]. Fresh DOO-PPV thin films were cast from chloroform solutions of 5% molar concentration onto quartz substrates the films were kept under constant vacuum. 

Wall-to-bed heat-transfer coefficients were also measured by Viswanathan et al. (V6). The bed diameter was 2 in. and the media used were air, water, and quartz particles of 0.649- and 0.928-mm mean diameter. All experiments were carried out with constant bed height, whereas the amount of solid particles as well as the gas and liquid flow rates were varied. The results are presented in that paper as plots of heat-transfer coefficient versus the ratio between mass flow rate of gas and mass flow rate of liquid. The heat-transfer coefficient increased sharply to a maximum value, which was reached for relatively low gas-liquid ratios, and further increase of the ratio led to a reduction of the heat-transfer coefficient. It was also observed that the maximum value of the heat-transfer coefficient depends on the amount of solid particles in the column. Thus, for 0.928-mm particles, the maximum value of the heat-transfer coefficient obtained in experiments with 750-gm solids was approximately 40% higher than those obtained in experiments with 250- and 1250-gm solids. 

The reactor is an 8-mm i.d. quartz tube located in a tube furnace. The quartz tube is packed with 20 by 30 mesh catalyst particles. The catalyst bed is positioned in the tube using quartz wool above and below the bed, with quartz chips filling the remainder of the reactor. The furnace temperature is controlled by a thermocouple inserted into the reactor tube and positioned about 3 mm above the catalyst bed. This allows operation at constant feed temperature into the reactor. 

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