Temperature and Pressure Dependence

We can combine many of the above points to rmderstand the variation in the minimum direct and indirect energy gaps in semiconductors with hydrostatic pressure and temperature. 

Hydrostatic pressure is uniform over the surface of a body and can be compressive or tensile. Compressive forces on an isotropic material push atoms slightly closer 

Si and GaAs data from Sze (1981). [6] Remaining data from the CRC Handbook of Chemieal Physics, 2001. [3] When no value is given it may be assumed that B 300K. 

Theoretically, the opposite dependence of direct and indirect gaps on pressure could be used to convert indirect gap materials to direct gaps. However, a negative pressure (tensile stress) would have to be applied to achieve this conversion. Ceramics, including semiconductors, tend to be weaker in tension than in compression. Even by placing the indirect material in a strained-layer superlattice (see Chapter 7), which can achieve the highest tensile stress levels, it has been impossible to convert indirect semiconductors to direct gaps before the stress is relieved by formation of dislocations or by fracture. 

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Zhu L, Chen W, Hase W L and Kaiser E W 1993 Comparison of models for treating angular momentum in RRKM calculations with vibrator transition states. Pressure and temperature dependence of CI+C2H2 association J. Phys. Chem. 97 311-22... 

Pressure and Temperature Dependent Properties of Black Powder Propellants , Jour of the MIT Rocket Society (Jan 1974) 73) U.A. Lehi-... 

Thallous halides offer a unique possibility of studying the stereochemistry of the (chemically) inert electron pair, since their structures and their pressure and temperature-dependent phase transitions have been well established. Thallium (1) fluoride under ambient conditions, adopts an orthorhombic structure in the space group Pbcm which can be regarded as a distorted rocksalt structure (Fig. 2.4). In contrast to TIF, the thallium halides with heavier halogens, TlCl, TlBr and Til, adopt the highly symmetric cubic CsCl structure type under ambient conditions [46]. Both TlCl and TlBr, at lower temperatures, undergo phase transitions to the NaCl type of structure [47]. 

The cyclotrimerization of alkynes to aromatic compounds, observed to occur efficiently on reduced Ti02 (001) surfaces during TPD experiments, can also be carried out as a genuinely catals tic reaction at low pressures. A kinetic model of the cyclotrimerization reaction describing the pressure and temperature dependence of the behavior observed was constructed (Scheme 1). 

One rather unfortunate aspect of the M + hydrocarbon (and M + OX) reactions mentioned thus far is that the products of the reactions were not detected directly, but were instead inferred via the pressure and temperature dependencies of the measured rate constants for metal reactant consumption and by comparison to ab initio calculations. Exceptions are the reactions of Y, Zr + C2H4 and C3H6, for which the Weisshaar group employed the 157 nm photoionization/mass spectrometry technique to identify the products of the reaction as those resulting from bimolecular elimination of H2.45 47 95... 

J. Rimmelin and G. Jenner, Tetrahedron, 30, 3081 (1974). A recent measurement of the pressure and temperature dependence of die electrocyclic ring-closure of Z-l,3,5-hexatriene to 1,3-cyclohexadiene in the range of 200 to 2500 bar and 100 to 125 °C does not show a significant temperature dependence of die activation volume (M. K. Diedrich and F. -G. Klarner, unpublished results). 

For flow rate measurements the volume or, more conveniently, the mass flow is suitable. In the first case a pressure- and temperature-dependent calibration is necessary if the gas does not show ideal behavior. This also applies for heat conductivity as the measured quantity often used in flow meters. Currently, real pressure- and temperature-independent measurement of a hydrogen mass flow of a hydrogenation remains problematic on the laboratory scale, at least for low substrate concentrations. 

UNIMOL Calculation of Rate Coefficients for Unimolecular and Recombination Reactions, Gilbert, R. G., Jordan, M. J. T. and Smith, S. C. Department of Theoretical Chemistry, Sydney, Australia (1990). Fortran computer code for calculating the pressure and temperature dependence of unimolecular and... 

A quite different group of experiments is concerned with the investigation of dye lasers themselves, or of lasers based on the photodissociation of molecules. Studies of the time behavior, concentration, or pressure and temperature dependence of fluorescence and... 

Warnatz, J. 1981. Concentration-, pressure-, and temperature-dependence of the flame velocity in hydrogen-oxygen-nitrogen mixtures. Combustion Science Technology 26 203-14. 

Nickolaisen, S. L., R. R. Friedl, and S. P. Sander, Kinetics and Mechanism of the CIO + CIO Reaction Pressure and Temperature Dependences of the Bimolecular and Termolecular Channels and Thermal Decomposition of Chlorine Peroxide, J. Phys. Chem., 98, 155-169(1994). 

Evacuable chambers Ideally, one would like to be able to vary the pressure and temperature during environmental chamber runs in order to simulate various geographical locations, seasons, and meteorology and to establish the pressure and temperature dependencies of reactions. Varying the pressure and temperature also allows one to simulate the upper atmosphere (e.g., to study stratospheric and mesospheric chemistry). 

Further the pressure and temperature dependences of all the transport coefficients involved have to be specified. The solution of the equations of change consistent with this additional information then gives the pressure, velocity, and temperature distributions in the system. A number of solutions of idealized problems of interest to chemical engineers may be found in the work of Schlichting (SI) there viscous-flow problems, nonisothermal-flow problems, and boundary-layer problems are discussed. 

Elementary reactions are initiated by molecular collisions in the gas phase. Many aspects of these collisions determine the magnitude of the rate constant, including the energy distributions of the collision partners, bond strengths, and internal barriers to reaction. Section 10.1 discusses the distribution of energies in collisions, and derives the molecular collision frequency. Both factors lead to a simple collision-theory expression for the reaction rate constant k, which is derived in Section 10.2. Transition-state theory is derived in Section 10.3. The Lindemann theory of the pressure-dependence observed in unimolecular reactions was introduced in Chapter 9. Section 10.4 extends the treatment of unimolecular reactions to more modem theories that accurately characterize their pressure and temperature dependencies. Analogous pressure effects are seen in a class of bimolecular reactions called chemical activation reactions, which are discussed in Section 10.5. 

P.H. Stewart, C.W. Larson, and D. Golden. Pressure and Temperature-Dependence of Reactions Proceeding via a Bound Complex. 2. Application to 2CH3 C2H5 + H. Combust. Flame, 75 25-31,1989. 

From this equation, we can see that the total nonideality correction (in braces) contains a negative contribution (first bracketed term) that is indeed proportional to the attractions constant a, while the positive contribution (second bracketed term) is proportional to the finite-volume repulsions constant b, as was supposed in the interpretation of experimental Z behavior in Fig. 2.2. One can also see that the attractions term is linearly proportional to density n/V, whereas the repulsions term is proportional to squared density (,njV)2, so that the former must always prevail at low density (low P) and the latter at high density (high P), as was shown in Fig. 2.2. Furthermore, one can recognize from the 1 /RT prefactor that the entire nonideality correction must diminish with increasing P, as was noted in Fig. 2.3. Thus, regardless of the particular values chosen for a and b, the Van der Waals equation is expected to exhibit both pressure and temperature dependences that are qualitatively consistent with the observed Z(P, T) behavior. 

At the pressure P, knowing the interaction parameter, and the vapour pressure of the monomer, Po, the volume-fraction, tj), of the monomer sorbed can be estimated from Equation 5.4-9. Figure 5.4-6 shows the pressure- and temperature dependence of the volume fraction of absorbed propylene in a given amorphous polypropylene [12],... 

Finally, the great bulk of published polymerization studies have been conducted on a vacuum line at 25°C and < 1 atm. Such activity measurements may be the most accurate of all, in their own way. Unfortunately, the experimenters often draw conclusions about the commercial world, to which such studies have little connection. Polymerization is not just the addition of ethylene to a chain. It involves a complicated series of reactions—reduction, alkylation, propagation, and termination—all of which are pressure and temperature dependent. Therefore, vacuum line techniques are not always reliable indicators of a catalyst s performance under commercial conditions.2 To study polymerization, there is no substitute for making polymer. 

Imagine that you have two more gas samples inside cylinders with movable pistons (Figure 9.9). One cylinder contains 1 mol of a gas and the other cylinder contains 2 mol of the gas at the same temperature and pressure as the first. Common sense says that the gas in the second cylinder will have twice the volume of the gas in the first cylinder because there is twice as much of it. According to Avogadro s law, the volume of an ideal gas at a fixed pressure and temperature depends on its molar amount. If the amount of the gas is halved, the gas volume is halved if the amount is doubled, the volume is doubled. 

A particularly convenient way to picture the pressure and temperature dependency of a pure substance in a closed system without air present is to use what is... 

Thus, a proper choice of ls and Zr can minimize the pressure and temperature dependence of these devices. 

This factor may be calculated for room temperature and atmospheric pressure from tabulated sums of ionic radii obtained from X-ray data (Shannon and Prewitt, 1969, 1970). However, it must be recognized that the thermal expansions and the compressibilities of the (A-O) and (M-O) bonds are different, which makes t both pressure and temperature dependent. In the case of a transition-metal atom M, the thermal expansion of the (A-O) bond is the larger, which makes... 

For the precise measurement of gas flow (steam) at varying pressures and temperatures, it is necessary to determine the density, which is pressure and temperature dependent, and from this value to calculate the actual flow. The use of a computer is essential to measure flow with changing pressure or temperature. Figure 10 illustrates an example of a computer specifically designed for the measurement of gas flow. The computer is designed to accept input signals from commonly used differential pressure detectors, or from density or pressure plus temperature sensors, and to provide an output which is proportional to the actual rate of flow. The computer has an accuracy better than +0.1% at flow rates of 10% to 100%. 

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