Freeze-out region

When ln( ) is plotted against 1/T, the slope is -AE/2fc. This is characteristic of what is known as the freeze-out region and the observed slope can be used to determine the... 

Figure 20.6 shows the carrier concentration in -doped Si calculated from the above analysis plotted against 1/T. The intrinsic, saturation, and freeze-out regions can easily be identified. 

One can easily see that if n p, Eh reduces to -1/ne. Hall measurements are easiest to interpret in doped materials when either n 3> p orn < p. Otherwise one is faced with four unknowns, which require other measurements to resolve. For example, except for the difference between electron and hole mobilities, the Hall effect would be zero for intrinsic materials. One can also see that doing Hall measurements as a fimction of temperature offers a means of determining the occupancy number and energy levels of the various impurity states in the freeze-out region through Equation 20.22. 

At low temperatures, not all of the donors (or acceptors) are ionized and the number of carriers (or p) exp —(AE/2fcT), where A is the ionization energy of the donor (or acceptor). This energy can be determined by making Hall measurements in this freeze-out region. 

The circumstellar chemistry is often subdivided into three main zones, which are determined by a comparison of the characteristic dynamic flow time, R/vx, with the chemical reaction times (Lafont et al. 1982 Omont 1987 Millar 1988). (i) In the region closest to the star (perhaps R 1014 cm), the density is sufficiently high that three-body chemical reactions occur in a time short compared to the dynamic time. In this regime, we expect the chemical abundances to approach thermodynamic equilibrium, (ii) Somewhat further away from the star (1014 cm < R < 1016 cm), there is a freeze-out of the products of the three-body reactions (McCabe et al. 1979). In this region, two-body reactions dominate the active chemistry, (iii) Finally, far from the star (R > 1016 cm), the density becomes sufficiently low that the only significant chemical processing is the photodestruction that results from absorption of ambient interstellar ultraviolet photons by the resulting molecules that flow from the central star. 

With temperature, density and Ye as free parameters, many choices of initial NSE compositions may clearly be made, involving a dominance of light or heavy nuclides, as illustrated in Fig. 24. However, in view of its relevance to the supernova models, an initial NSE at temperatures of the order of 1010 K is generally considered. It favours the recombination of essentially all the available protons into a-particles (the region noted NSE n,o in Fig. 24). The evolution of this initial composition to the stage of charged-particle induced reaction freeze-out has been analyzed in detail by [60], and we just summarize here some of its most important features that are of relevance to a possible subsequent r-process ... 

This curve cannot represent the situation over the entire range of composition. As Xg 1, we would expect solid B to freeze out far above the temperatures indicated by the curve in this region. If the solution is ideal, the same law holds for substance B ... 

Figure 6.18 shows the solid-liquid temperature-composition phase diagram of silver and copper at 1.00 atm. There are two one-phase regions of limited solid solubility, labeled a and /3. A tie line in the area between the a and P regions represents two coexisting saturated solid solutions, one that is mostly silver and one that is mostly copper. The tie line at 779°C connects the points representing the two solid phases and one liquid phase that can be at equilibrium with the two solid phases. The point representing this liquid phase is called the eutectic point. If a liquid that has the same composition as the eutectic is cooled, two solid phases will freeze out when it reaches the eutectic temperature, with compositions represented by the ends of the tie line. 

In normal operation, caution should be exercised to prevent liquid from forming during the expansion cycle in reciprocating expanders. Liquid in the expansion space can cause both erosion and corrosion of the equipment. Serious mechanical problems can also arise if any liquid freezes out in the expander cylinder. Care should therefore be taken to avoid expansion of the gas into the vapor-liquid and triple point regions of the refrigerant. 

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