Quartz parameter values

Each parameter value reported in the monitor file must be divided by the actual exposure time in order to yield a reasonable value. For this purpose one of the channels should be reserved and count the heartbeats of an oscillator quartz. 

Zq is the acoustic impedance of AT-cut quartz its value is 8.8 x 10 kg m s Strictly speaking, Zq is a complex quantity Z + iZ", where Z" accounts for internal friction. Zq is often considered to be real. When this happens, the fundamental frequency/f must also be a real number (see end of Sect. 2). The Sauerbrey equation fails to account for viscoelasticity and also, when applied in liquids, cannot distinguish between the adsorbed material itself and solvent trapped inside the adsorbed film. When a mass is derived by means of the Sauerbrey equation, the interpretation of this mass parameter is sometimes difficult. The terms Sauerbrey mass and Sauerbrey thickness are used in order to indicate that the respective parameters have been calculated by the simple Sauerbrey equation. 

Summary of Parameter Values for Quartz, Gold (and Titanium), and Water... 

Circuit parameter values of the crystal are largely influenced by the angle at which the quartz is cut from the raw quartz slab (precut form). One of the most popular cuts is the AT-cut, which typically is operated in a thickness shear mode between 1 and 200 MHz. Also, above 25 MHz, the AT-cut quartz crystal typically operates in an overtone mode. The AT-cut is usually made from a Y-bar, which simply indicates that the maximum dimension of the crystal is in the Y direction. Also, the actual cut is defined as a cut with angle, 9 = 35° 15 with respect to the z axis. Another popular cut is the BT-cut this is a cut made at an angle of —49° with respect to the z axis. The BT-cut crystals are usually Y-cut also, and the BT-cut crystals are more likely to be appHed in an overtone mode, although fundamental mode oscUlation is also common. 

TABLE 3.2 Typical Equivalent Circuit Parameter Values for Quartz Crystals... 

The inductance L is associated with the mass of the quartz slab, and the capacitance Q is associated with the stiffness of the slab. Finally, the resistance Ri is determined by the loss processes associated with the operation of the crystal. Each of the equivalent parameters can be measured using standard network measurement techniques (see Sec. 3.1.6). Table 3.2 Hsts typical parameter values. 

Fig. 5. The /rSR spectra from fused quartz at room temperature and silicon at 77 K, each in a magnetic field of 10 mT. For quartz, the two high-frequency lines result from muonium with a hyperfine parameter close to that in vacuum. The two high-frequency lines in Si result from Mu, and their larger splitting arises because the hyperfine parameter is less than the vacuum value (0.45 Afree). The lowest line in each sample comes from muons in diamagnetic environments. The lines from 40 to 50 MHz in Si arise from Mu. From Brewer et al. (1973).

Selected values of (1000 A)1/2 for quartz = mineral lsO, and pyrite = mineral 34S equilibria are found in Table 9.2. In other cases, especially at lower temperature, the temperature dependence of IE s on mineral formation may be more complicated and require empirical fits of the form, in a = Ci/T + C2/T2 or in a = Co + Ci/T + C2/T2, the C s are empirical least squares fitting parameters. 

Fig. 25. Kinetics for the recombination of H atoms by Pyrex and quartz. Experimental points o, Wood and Wise [91] A,Tsu and Boudart [64a] , Smith [54], Theoretical lines [(Ng) = 1014cm 3] —, Wood and Wise [91] calculated for the model of de Boer and van Steenis [98] (see Table 8 for values of the energy parameters).

The most extensive test which has been made of this conduction model for thermal explosion is to be found in the work of Vanp e on the explosion of CH2O + O2 mixtures. He used a calibrated thread of 10 per cent Rh-Pt alloy of 20 m diameter (jacketed by a 50-m quartz sleeve) suspended at the center of a cylindrical vessel to measure directly his reaction temperature during the induction periods preceding explosion. By Uvsing He and Ar as additives and vessels of different diameters he was able to verify the dependence of the critical explosion limits on vessel size and on thermal conductivity of the gas mixture. In addition, he was able to check the maximum predicted temperature at the center of the vessel just prior to explosion and also the value of 8c = 2 [Eq. (XIV.3.12)], the critical explosion parameter for cylindrical vessels. Finally, with a high-speed camera, he was able to show directly that the explosions in this system do start at the center, the hottest region, " and propagate to the walls. 

In the strict sense, the dielectric constant for the bulk particles as measured here may be incorrect as applied to a hydrated surface environment which has undergone substantial changes in electrical properties upon addition of water. Levine ( ), for example, uses a value of 10 for the dielectric constant of a solvated quartz surface when the actual capacitor plate value for the solid is only 4.3. The effect of a variation in the value for the solid dielectric constant on the pH-dependence of adsorption, however, is minimal, requiring only a very small change in the value of the fitting parameter AGJ in order to produce the same results. For this reason, our use of the measured value of 16.4 for the solid should suffice, producing little error as compared to estimating a value for the solvated solid. 

Taking the average values of the equilibrium parameters (P = 2kbar, T = 600°K = 327°C) and using the consistent thermodynamic constants of grunerite, quartz, and water, we find ... 

This quantity is the source of the second harmonic and is determined from its intensity and the macroscopic optical parameters. If the intensity of the optical input is also measured and the static field strength known then the susceptibility in the equation can be calculated. In practice the intensity of the SHG is measured relative to a known standard that for solution work has usually been quartz, occasionally lithium iodate. In the gas phase a calculated value for an inert gas has been used. The macroscopic third order susceptibility has to be related to the response functions for the active molecule in the solution. 

Focussing on the first four lines of the Table 4, all of which are calibrated with the quartz standard, and can be adjusted to the same value for this standard, it is apparent that there is reasonably good agreement between the three determinations of the macroscopic nonlinearity of MNA. This consistency, taken in conjunction with the equations as written in the papers, leads to the conclusion that, with a reasonable degree of certainty, the provisionally defined quantity, F can be identified with the F of eqn (4.16). Having made this assumption, it follows that any differences in reported values that are not proportional to the small percentage differences in the F values must be the result of variations in the method employed to convert macroscopic to molecular parameters. This question is examined in the next section. 

The trans -> cis isomerisation of octafluorobut-2-ene is claimed by Schlag and Kaiser " to be a clean unimolecular reversible reaction. Studies by the static method using a seasoned quartz reaction vessel at 430-477 °C yielded the Arrhenius parameters, A = 3.4x 10 sec E = 56.4 kcal.mole L The E value is 6.4 kcal.mole lower than for the corresponding hydrocarbon - . Craig and Entemann have compared the standard enthalpy change for the cis trans isomerisation of 1,2-difluoroethylene with those for related halogenated ethylenes. The reported values are 4-928 cal.mole for difluoroethylene, 4-500 cal.mole for dichloroethylene, nearly zero for dibromoethylene, and —2000 cal.mole for diiodoethylene. 

For jS-quartz, which has an hexagonal lattice, Hylleraas (SS) has tabulated Mr, as a function of two parameters, the axial ratio c/a and a parameter , the distance of the oxygen ions from the hexagonal axis divided by a. His values are given in Table III. 

There is a marked curvature to all the elastic constants below the transition point, which reflects the variation of the order parameter and the order parameter susceptibility. No individual elastic constant or symmetry-adapted combination of elastic constants is expected to tend to zero at the transition point. In this case the agreement between observed and calculated values shown in Figure 18 implies that the model represented by Equation (28) provides a good description of the phase transition. Agreement is not as close for C33 as it is for the other elastic constants, however, suggesting that the causes of strain parallel to [001] of a-quartz have not yet been fully explained. 

Attempts to calculate actual brine compositions using existing algorithms (WATEQ — Truesdell and Jones, 1973 SOLMNEQ — Kharaka and Barnes, 1973 EQ3/6 — Wolrey, 1979) have not been very successful at present writing, owing to lack of reliable thermochemical parameters in aqueous solutions near halite saturation and in excess of 150°C. Even so, values not too different from the Edwards brine ion ratios are obtained when halite, quartz, albite, anorthite, calcite, anhydrite, celestite and fluorite are reacted to saturation, and K-feldspar and dolomite held below saturation. 

Figure 6. Spectral slope of CDOM from two lakes (Hargreaves, unpublished). S (nm ) is an exponential parameter from the relationship agjo, =ae The value of S can be computed as the absolute value of the slope when Ln(acd<, j) is plotted against wavelength over the UV and blue range. Such plots tend to be linear over UV wavelengths when DOC is high (upper curve) but can sometimes be separated into a steeper UV-B slope (280-320 nm) and shallower UV-A slope (320-380 nm) when substantial photobleaching has occurred (lower curve). These lake samples are from the upper mixed layer, June 2001 (particles removed with GF/F filter, Shimadzu UV-1601 spectrophotometer, 10 cm quartz cuvette, low DOC deionized water spectrum subtracted small glitch at 345-350 nm in lower curve is caused by spectrophotometer imperfection).

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