Vaporization Coefficients

Definition The vaporization coefficient, is usually defined as the ratio of the actual flow of gaseous decomposition product J to the flow Jmax coming from an effusion cell, in which, it is assumed, decomposition products are in an ideal equilibrium with the reactant. For many substances, as found from comparative Knudsen-Langmuir TG measurements, -C 1, i.e., their free-surface decomposition proceeds much more slowly than would be expected from effusion observations. It is a common practice to explain this discrepancy by a multistage character of the evaporation process, by surface relief peculiarities or by impurities and defects (imperfections) in the reactant lattice. 

Analysis L vov and Novichikhin [1] were the first to relate this effect to the difference between the actual decomposition scheme and the supposed scheme of decomposition directly to equilibrium products (as in an effusion cell). Initial gasification of all of the products, including low-volatility components (metals or metal oxides) is assumed, followed by partial or complete release of gaseous products in a chemical form different from the equilibrium composition. 

The contributions of these factors to the decomposition coefficient are presented separately for reactants decomposing to gaseous products only (Table 11.1) and to gaseous and solid products (Table 11.2). Reactants are listed in order of decreasing coefficient Ov The coefficients were determined from the experimentally obtained magnitudes of the equilibrium pressures Peqp for the primary evaporation products found by means of the third-law method (see Chapter 16), and from theoretically calculated equilibrium pressures Peq for the final (equilibrium) products. Analysis of these data yielded the following conclusions. 

Reactant T (K) Primary Products -Peqp Equilibrium Products Peq (bar) (y. r 

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Not all molecules striking a surface necessarily condense, and Z in Eq. VII-2 gives an upper limit to the rate of condensation and hence to the rate of evaporation. Alternatively, actual measurement of the evaporation rate gives, through Eq. VII-2, an effective vapor pressure Pe that may be less than the actual vapor pressure P. The ratio Pe/P is called the vaporization coefficient a. As a perhaps extreme example, a is only 8.3 X 10" for (111) surfaces of arsenic [11]. 

Finally, it is to be expected that the evaporation coefficient of a very stable compound, such as alumina, which has a large heat of sublimation resulting from the decomposition into the elements, will be low. Since the heat of evaporation must be drawn from the surface, in die case of a substance widr a low thermal conductivity such as an oxide, the resultant cooling of the surface may lead to a temperature gradient in and immediately below the surface. This will lower die evaporation rate compared to that which is calculated from the apparent, bulk, temperature of the evaporating sample as observed by optical pyromeuy, and thus lead to an apparently low free surface vaporization coefficient. This is probably die case in the evaporation of alumina in a vacuum. 

Chemically similar substances have comparable vaporization coefficients, so that rates of vaporization, J, can be predicted from determined using equilibrium data. Beruto and Searcy [121] have suggested the similar use of the decomposition coefficient providing that due consideration is given to the occurrence of unstable intermediates. 

Specific heat at 25°C Latent heat of fusion Latent heat of vaporization Coefficient of linear expansion at 25°C Thermal conductivity at 25°C... 

Kempter did not record weight loss after each heating interval. However, the data set enables us to qualitatively determine whether the presence of a He atmosphere changes the congruently vaporizing composition as a function of temperature, and to determine the approximate values of the vaporization coefficients ANb and Ac in He. 

The data of Drowart (3 ) show a significant drift while those of Grieveson ( ) do not, but the latter should be corrected for C2Si(g) and CSi2(g) which are present in amounts of about 4 and 3%, respectively, at 2000 K. Silicon carbide may have a small vaporization coefficient, since rates of free evaporation reported by Voronin (6) and Ghoshtagore (7 ) yield apparent pressures which are smaller by factors of 1/30 to 1/10000. 

Gole [41] has distinguished the following modes of vaporization, (i) Simple solids which show no unusual barriers to evaporation and condensation (their vaporization and condensation coefficients are close to unity) e.g. monatomic elements such as Zn. (ii) "Retarded" vaporization of molecular and ionic solids (measured vaporization coefficients are very much smaller than those predicted from... 

Interpretation of vaporization coefficients Studying of the atomization mechanism Production of technological materials (lime, soda, alumina)... 

AgaO [4] a vacuum and introduction of concept of vaporization coefficient [32]... 

Interpretation of the decomposition mechanism along the lines of the Knudsen-Langmuir approach is based on the difference between the real vaporization rate of a reactant from a free surface (after Langmuir) and that of the same reactant in practically equilibrium conditions from effusion cells (after Knudsen). The ratio of these rates is called the vaporization coefficient, Oy. Its value turns out in many cases to be smaller (quite frequently, by several orders of magnitude) than unity. As pointed out by Somorjai and Lester [3] All the information on the evaporation mechanism is hidden into a correction factor which is applied to adjust the deviation of the evaporation rate far from the maximum evaporation rate in equilibrium. ... 

Historical Background A regularity fairly close to the one considered above has been discovered in studies of the decompositions of metal nitrides [8-12]. The analysis of the stoichiometry of the primary products formed during the decompositions of nitrides was based on early works [8-11] on the kinetic data available in the literature, in particular, on the results of the determination of vaporization coefficients. The reliability of these data, especially for Langmuir... 

Table 11.1 The vaporization coefficients for reactants decomposing into gaseous products ... 

Misconception and its Interpretation The low magnitudes of the vaporization coefficients for many substances (effusion method, which is used for estimations of the maximum decomposition rate or of the equilibrium pressure of the product. The ratio of the equilibrium pressure inside the cell, P q, to the effusion pressure, P g, is governed by [3] ... 

Table 16.5 Calculated (theory) and experimental values of vaporization coefficients for...

The discrepancies between the calculated and experimental vaporization coefficients of P, As, and Sb do not exceed an order of magnitude (Table 16.5), which is quite acceptable taking into account the experimental errors. The correlation between the composition of products formed in vaporization of phosphorus, arsenic and antimony, and the crystal structures of these elements was discussed in Sect. 10.3. 

The calculated vaporization coefficients of both oxides are given in Table 16.8. The considerably lower coefficient for HgO is due to the lower vaporization temperature, at which the relative content of atomic oxygen deviates from the equilibrium content more strongly. On the whole, the thermochemical analysis reliably confirms the mechanism of dissociative vaporization of ZnO and HgO with the release of atomic oxygen. The correlation between the composition of the primary products and the crystal structure of both oxides was discussed in Sect. 10.1. 

Table 16.8 Calculated values of the vaporization coefficients for zinc and mercury oxides...

Introduction The vaporization of cadmium and zinc sulfides, seienides, and tellurides has been thoroughly examined in many studies [24-30]. The authors of these papers report that the vaporization coefficients of these compounds are in the range 0.1-0.3, which suggests that, not oniy the most stable diatomic molecules, but also free S, Se, and Te atoms can be detached from the surface in the course of vaporization. Using the primary data from [24-30], the corresponding molar enthalpies are compared with the values calculated for the equilibrium vaporization scheme. The thermodynamic functions given in Table 16.13 were used in the calculations. The final results are presented in Table 16.14. 

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