Reciprocal temperature

Ideal Performance and Cooling Requirements. Eree carriers can be excited by the thermal motion of the crystal lattice (phonons) as well as by photon absorption. These thermally excited carriers determine the magnitude of the dark current,/ and constitute a source of noise that defines the limit of the minimum radiation flux that can be detected. The dark carrier concentration is temperature dependent and decreases exponentially with reciprocal temperature at a rate that is determined by the magnitude of or E for intrinsic or extrinsic material, respectively. Therefore, usually it is necessary to operate infrared photon detectors at reduced temperatures to achieve high sensitivity. The smaller the value of E or E, the lower the temperature must be. 

The enthalpy of the phase conversion can be determined from Eq.(6) by plotting the log of the absorption or desorption plateau pressure, P lnleau, against the reciprocal temperature as indicated in Fig. 2. When the solubility of hydrogen in the metal (or) phase is small, then AHplM AH(, where AH( is essentially the enthalpy of forma... 

Figure 2. The enthalpy, AH, of the phase transformation can be calculated from the variation of In P laleai] with reciprocical temperature in a van t Hoff plot.

Linear least squares treatments of plots of the logarithm of the vapor pressure versus the reciprocal temperature were performed. The second-law enthalpy and entropy of sublimation at the median temperature are proportioned to the slope and... 

To summarize, the surface kinetics (or near surface kinetics) is the limiting step at lower temperature and diffusion is the rate limiting step at higher temperature. It is possible to switch from one rate-limiting step to the other by changing the temperature. This is illustrated in Fig. 2.9, where the Arrhenius plot (logarithm of the deposition rate vs. the reciprocal temperature) is shown for several reactions leading to the deposition of silicon,... 

The most general representation of the isokinetic relationship is the plot of logk against the reciprocal temperature. If the Arrhenius law is followed, each... 

If 6AH, 5 AS, and a are independent of temperature, it follows that pj is a linear function of reciprocal temperature, so that eq. (73) holds... 

Increasing temperature permits greater thermal motion of diffusant and elastomer chains, thereby easing the passage of diffusant, and increasing rates Arrhenius-type expressions apply to the diffusion coefficient applying at each temperature," so that plots of the logarithm of D versus reciprocal temperature (K) are linear. A similar linear relationship also exists for solubUity coefficient s at different temperatures because Q = Ds, the same approach applies to permeation coefficient Q as well. 

We can determine the activation energy from a series of measurements by plotting the logarithm of the rate constant against the reciprocal temperature, as rearrangement of Eq. (45) sho vs ... 

Normally the activation energy for diffusion in the gas phase is much smaller than the activation energy for a catalyzed reaction, and hence, according to Eqs. (38) and (46), the overall or apparent activation energy for the diffusion-limited process is half of what it would be without transportation limitation. If we plot the rate as a function of reciprocal temperature one observes a change in slope when transport limitations starts to set in. 

If the desorption process follows straightforward first-order kinetics, one may divide the rate at any temperature by the actual coverage, and plot this logarithmically against the reciprocal temperature, to construct an Arrhenius plot. This procedure usually works well in cases where the initial coverage is sufficiently low that lateral interactions play no role. For example, it would work well for CO desorption with an initial coverage below 0.3 ML (Fig. 7.7). 

As the initial coverages of CO and O are known, and the surface is free of CO at the end of the temperature-programmed experiment, the actual coverages of CO and O can be calculated for any point of the TPD curves in Fig. 7.14. Hence, an Arrhenius plot of the rate of desorption divided by the coverages, against the reciprocal temperature yields the activation energy and the pre-exponential factor ... 

Thus, a plot of In k versus the reciprocal temperature should yield a straight line with slope -E/Rg and In ko. These two kinetic parameters are strongly interconnected even a minor change in slope evaluation will result in a major change of the intercept. Theoretically, values of rate constants at two temperatures are sufficient to estimate the activation energy ... 

I2H2O as a function of the reciprocal temperature. The points are data obtained from fits of the Mdssbauer spectra (Fig. 6.6). The broken curve is a fit to the Einstein model for a Raman process. The dotted curve corresponds to a contribution from a direct process due to interactions between the electronic spins and low-energy phonons associated with critical fluctuations near the phase transition temperature. (Reprinted with permission from [32] copyright 1979 by the Institute of Physics)... 

Dm (and Du) vary inversely with reciprocal temperature (Fig. 15). For mantle solidus garnets the correlation is reasonably good and can be used to make a first-order estimate of Dm- A more comprehensive model for Du and Dm, as a function of pressure, temperature and melt composition is provided by Salters et al. (2002). Their full expressions (for the molar partition coefficients, D ) are ... 

Figure 15. Variation in Dxh for garnet versns reciprocal temperature for experimental data sources listed in Table lb at a variety of pressures n = 33). A distinction is made between mantle solidus partition coefficients (Salters and Longhi 1999 Salters et al. 2002 McDade et al. 2003a,b) and the rest. Note the strong temperatnre dependence, which is qnalitatively similar to that incorporated in Equation (25b). The scatter is due to additional compositional controls.

Figure 22. Variation in phlogopite-melt Db with reciprocal temperature. The low temperature data of Icenhower and London (1995) define a strong linear trend. At higher temperature, no trend is apparent, and the data fall into two distinct clusters the highDea points of Green et al. (2000) and La Tourrette et al. (1995) and the low L>Ba points of Schmidt et al. (1999) and Guo and Green (1990). The cause of these differences is utuesolved.

Figure 20.2. Reciprocal temperature-rate plot for the determination of the energy of activation for the hydrogenation of 1-hexene over Wilk/STA.

A plot of In k versus reciprocal temperature (Arrhenius plot) gives a straight line. The slope of this straight line is -E/R, and therefrom E can be readily determined. Differentiating the above equation with respect to temperature, one obtains... 

Differentiation with respect to reciprocal temperature and use of the Arrhenius and van t Hoff relations gives... 

Taking the logarithm of Equation 2.1 allows plotting ln(A co) against the reciprocal temperature (Figure 2.4). In Figure 2.4 the experimental results are compared to data of a commercial Co catalyst21 and a precipitated iron material.22... 

FIGURE 2.1.1.1.1.1 Logarithm of vapor pressure versus reciprocal temperature for isobutane. 

Logarithm of Henry s law constant versus reciprocal temperature for n-pentane. 

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