Quartz molar volume

Silica (Si02) exists in several forms, including quartz (molar volume 22.69 cm moU ) and cristobalite (molar volume 25.74 cm moU ). 

As shown in Table VI, the tetrahedra in PON are less regular than in Si02 because of the presence of two different anions. The molar volumes of the ct-quartz and /3-cristobalite phases of PON are compared in Fig. 7, as a function of pressure (200, 203). 

Fig. 7. Molar volumes of quartz and cristobalite polymorphs of PON as a function...

The occurrence of the moganite-type phase in PON confirms that moganite is really a new structure type in AX2 compounds. The molar volumes at ambient of the three phases, cristobalite, moganite, and quartz (22.58, 21.05, and 20.64 cm3, respectively) follow the same trend as in silica. The smaller size of the P02N2 tetrahedron relative to that of Si04 (cf. Table VI) widens the pressure fields of stability, so that PON appears to be very useful to shed light on the detailed behavior of silica, which is still ill defined. 

Here, rqtz is the rate of quartz precipitation (mol s-1 from a kg of water) and My is the mineral s molar volume (22.7 cm3 mol-1). Figure 26.4 shows the resulting sealing rates calculated for several traversal times. For a At of one year, for example, we expect the fracture to become occluded near its high-temperature end over a time scale of about 10 000 years. 

Fig. 26.6. Variation in mineral volumes over a kinetic reaction path designed to illustrate Ostwald s step sequence. The calculation traces the reaction at 25 °C among the minerals amorphous silica (tine line), cristobalite (medium line), and quartz (bold line). The top diagram shows results plotted against time on a linear scale the time scale on the bottom diagram is logarithmic. The decrease in total volume with time reflects the differing molar volumes of the three minerals.

Another problem is an uncertainty involved in the estimation of the double-layer thickness. This thickness is often calculated from the size of the solvent molecule, using macroscopic data (e.g., the molar volume) under a doubtful assumption about the shape of the molecule, which is often taken as spherical. There are some indications, also provided by modern experimental techniques (X-ray spectroscopy, quartz crystal microbalance, QCM), that the density of water near the interface can change drastically (see later discussion). 

The amount of H2O in amorphous silica (number n of H2O molecules per unit formula) varies between 0.14 and 0.83 (Frondel, 1962). Nevertheless, the thermodynamic properties of the phase are not particularly affected by the value of n (Walther and Helgeson, 1977). The molar volume of opal is 29 cm /mole. The same volume of a-quartz may be adopted for chalcedony see table 5.68 for the other polymorphs. 

When comparing ionic porosity of different minerals, for self-consistency, the same set of ionic radii should be used, and the same temperature and pressure should be adopted to calculate the molar volume of the mineral. Table 3-3 lists the ionic porosity of some minerals. It can be seen that among the commonly encountered minerals, garnet and zircon have the lowest ionic porosity, and feldspars and quartz have the highest ionic porosity. More accurate calculation of IP may use actual X-ray data of average inter-ionic distance and determine the ionic radius in each structure. 

The molar volumes of Si and quartz, the densest form of SiC>2, are 12.1 and 22.8 cm3 mol-1, respectively deposited amorphous silica will have an even larger molar volume. 

Scott and Brickwedde found for the molar volumes of ordinary and para-hydrogen at 14°-20 4°K. in a fused quartz pyknometer ... 

The molar volumes lead to (dAG ydP)r = AV°= 1.66 cmVmol, from which we conclude that an increase in pressure slightly favors corundum and quartz over sillimanite. Given the conversion factor 1 cm bar = 0.02390 cal, we obtain... 

Other codes came later. One was the implementation of DFT in the well-known CRYSTAL code [61], already mentioned. Originally CRYSTAL was a Hartree-Fock package. Suppported by a large development collaboration, CRYSTAL is widely distributed and has a much more user-friendly interface than GTOFF. At least with default settings and basis sets, however, CRYSTAL appears to give peculiar results sometimes. The most recent example is a predicted double min-imiun for the a-quartz equilibrium structure at very different molar volumes per formula unit [62]. No other DFT study of a-quaitz equilibrium had found this behavior, but they were all plane-wave/pseudopotential or cellular basis. We do not find it either [63]. See discussion below. 

Indeed, the quantum-chemical structure optimizations confirm the preference of V + for lower coordination numbers. Under the assumption of zero pressure, the lowest energy is found for the case of a-cristobalite (four-fold coordination, molar volume = 41.1 cm /mol), followed by quartz (four-fold, 33.2 cm /mol), followed by anatase (six-fold, 19.8 cm /mol), followed by bad-deleyite (seven-fold, 16.6 cm /mol) and several others. In order to arrive at stable structures, however, a minimum thermochemical requirement is that the total energy of VON is lower than those of its educts. Here we rely on the plausible reaction... 

Secondly, we performed an MD simulation of heating quartz up to 1300 K. We have mainly used a system of 432 particles for the periodic boundary condition, while 324- and 576-particle systems have also been studied for comparison. MD results for the temperature dependence of the molar volume and cell parameters shows quite good agreement with experimental data (Fig. 6) [43]. The volume expansion coefficient abruptly... 

Generally speaking, an increase in density can occur upon a polymorph transformation even without change in coordination of the nearest atoms in the structure. An example of such densiflcation is presented by the SiOz modifications, where a more compact packing of silicon-oxygen tetrahedra reduces the molar volumes in the succession cristobalite (25.9cm ) keatite (24,0cm ) quartz (22.7 cm ) -> coesite (20.0cm ). However, the transition under pressure from coesite (Nc=4) to stishovite (Nc = 6) reduces this volume much more drastically, to 13.8 cm. ... 

This behavior occurs until a certain high temperature is reached denoted and called the critical temperature. At that temperature, the constant pressure plateau shrinks into a single point (point C) called the critical point The molar volume at that point is called critical molar volume and the pressure is the critical pressure P. A gas cannot be condensed to a liquid at temperatures above and there is no clear distinction between the liquid and gaseous phases because the two states cannot coexist with a sharp boundary between them. Experimentally, if a certain amount of gas and liquid is placed inside a pressurized container with transparent quartz windows and kept below T, two layers will be observed, separated by a sharp boundary. As the tube is warmed, the boundary becomes less distinct because the densities, and therefore the refractive indices, of the liquid and gas approach a common value. When the T is reached, the boundary becomes invisible and the iridescent aspect exhibited by the fluid is called critical opalescence. Hence the following definitions can be drawn for the critical constants of a real gas. 

Thompson and Waldbaum (1967). Orville s hydrothermal ion-exchange data on the compositions of high-temperature alkali feldspars coexisting with aqueous NaCl-KCl solutions are used to derive two-coefficient Margules expressions for excess free energy and molar volume. These expressions are used to calculate the critical mixing curve and the imivariant curve for two feldspars coexisting with jadeite plus quartz (to 30 kbar). 

Here, AHj is the molar heat of transformation, and Va and vp are the molar volumes of a-quartz and p-quartz, respectively. Equation 18.81 can also be written as Equation 18.82. 

This amount of thiocyanate is sufficient for both complete reduction and complex formation. Reduction is allowed to proceed for 30 to 45 s after the addition of the thiocyanate. A bright red color can readily be observed at a technetium (VII) concentration of 0.1 ng per ml. Acetone (6 ml) is then added and the volume of the solution mixed and adjusted to 10 ml with distilled water. At this point, the color has generally developed to less than 50% of its final intensity. Quartz 1-cm glass-stoppered cells are filled with the technetiiun solution and placed in a 20 °C water-cooled spectrophotometer. The extinction will approach a maximum intensity in 1 to 3 h. The maximiun extinction occurs at 510 nm with a molar extinction coefficient and standard deviation of 47,500 + 500 in 60 vol. % of the acetone-aqueous medium. An additional examination of the analysis may be carried out by extract-... 

Then, the compositions of the essential (> 5 volume %) minerals in the rocks to be classified are defined in a composition matrix (C) and used, in conjunction with a second matrix (7) defining what minerals are employed in classification (the classifying minerals e.g., quartz, plagloclase, alkali feldspar), to obtain a third matrix (1/1/) containing a set of independent vectors containing major element coefficients. When multiplied by the un-standardized molar element quantities, they produce un-standardized molar classifying mineral quantities that are un-affected by the presence of nonclassifying minerals in the rocks. 

Reaction chambers fitting the Harrick Praying Mantis mirror optics are available commercially, and sketches or images are presented in the product description (Harrick, 2006), in the work of Weckhuysen and coworkers (Weckhuysen and Schoonheydt, 1999 Weckhuysen et al., 2000 Weckhuysen, 2002 Weckhuysen, 2003 Weckhuysen, 2004) and in a handbook article by Sojka et al. (2008). A low-pressure and a high-pressure version, suitable at pressures up to 202-303 kPa or 3.4 MPa (500 psi), are available they are characterized by a dome with either three flat, circular windows or a dome with a single quartz half-sphere shaped quartz block with a small (also half-sphere shaped) volume above the catalyst. Evacuation to pressures less than 1.33 x 10-6 hPa and a maximum temperature of 873 K (under vacuum) are specified. A low-temperature version is specified for 123-873 K and up to 202-303 kPa. In the low-pressure versions, there are several centimeters of beam path through the gas phase, so that gas phase contributions are more likely to be observed than in experiments with cells holding the sample directly at the window (this depends on the gas phase concentrations and molar absorption coefficients). 

Catalysts were tested in a fixed bed quartz tubular reactor, at atmospheric pressure, in the temperature interval 500-600 C [2]. The catalyst (particle size 0.42-0.59 mm) were mixed with SiC of the same size at a catalyst/SiC volume ratio of 1/4. The feed consisted of a mixture of alkane/oxygen/helium in a molar ratio of 4/8/78 (ethane, propane) and 5/20/75 (n-butane). In order to achieve a similar alkane conversion, samples of 0.7-1.7 g and total flow of 100-200 ml min were used to modify the contact time (W/F). 

---