Gas phase diffusion

SiH2Cl2 + NH3- Si3N4 167 One-dimensional model of wafer space, onedimensional model of flow region, multiple component diffusion, gas phase and surface reactions, entrance effects, comparison with data, and numerical solution. 

Another key problem with diffusive sintering is that it can occur by several diffusion mechanisms as shown in Fig. 9.33. Viscous and plastic flow are two simple possibilities but another five are readily distinguished, including solid-state diffusion, grain boundary diffusion, surface diffusion, gas phase transport, and liquid layer transport. These inevitably form a neck at the particle contact, to reduce the sharp curvature of the contact region. 

For a binary mixture of two components A and B in the gas phase, the mutual diffusion coefficient such as defined in 4.3.2.3, does not depend on composition. It can be calculated by the Fuller (1966) method ... 

Vreugdenhil A J and Butler I S 1998 Investigation of MMT adsorption on soils by diffuse reflectance infrared spectroscopy DRIFTS and headspace analysis gas-phase infrared spectroscopy HAGIS Appl. Organomet. Chem. 

The Beckstead-Derr-Price model (Fig. 1) considers both the gas-phase and condensed-phase reactions. It assumes heat release from the condensed phase, an oxidizer flame, a primary diffusion flame between the fuel and oxidizer decomposition products, and a final diffusion flame between the fuel decomposition products and the products of the oxidizer flame. Examination of the physical phenomena reveals an irregular surface on top of the unheated bulk of the propellant that consists of the binder undergoing pyrolysis, decomposing oxidizer particles, and an agglomeration of metallic particles. The oxidizer and fuel decomposition products mix and react exothermically in the three-dimensional zone above the surface for a distance that depends on the propellant composition, its microstmcture, and the ambient pressure and gas velocity. If aluminum is present, additional heat is subsequently produced at a comparatively large distance from the surface. Only small aluminum particles ignite and bum close enough to the surface to influence the propellant bum rate. The temperature of the surface is ca 500 to 1000°C compared to ca 300°C for double-base propellants. 

Activated carbons for use in Hquid-phase appHcations differ from gas-phase carbons primarily in pore size distribution. Liquid-phase carbons have significantly more pore volume in the macropore range, which permits Hquids to diffuse more rapidly into the mesopores and micropores (69). The larger pores also promote greater adsorption of large molecules, either impurities or products, in many Hquid-phase appHcations. Specific-grade choice is based on the isotherm (70,71) and, in some cases, bench or pilot scale evaluations of candidate carbons. 

For prediction of gas phase diffusion coefficients in multicomponent hydi ocarbon/nonKydi ocai bon gas systems, the method of Wilke shown in Eq. (2-154) is used. 

Many more correlations are available for diffusion coefficients in the liquid phase than for the gas phase. Most, however, are restiicied to binary diffusion at infinite dilution D°s of lo self-diffusivity D -. This reflects the much greater complexity of liquids on a molecular level. For example, gas-phase diffusion exhibits neghgible composition effects and deviations from thermodynamic ideahty. Conversely, liquid-phase diffusion almost always involves volumetiic and thermodynamic effects due to composition variations. For concentrations greater than a few mole percent of A and B, corrections are needed to obtain the true diffusivity. Furthermore, there are many conditions that do not fit any of the correlations presented here. Thus, careful consideration is needed to produce a reasonable estimate. Again, if diffusivity data are available at the conditions of interest, then they are strongly preferred over the predictions of any correlations. 

The Shei wood-number relation for gas-phase mass-transfer coefficients as represented by the film diffusion model in Eq. (5-286) can be rearrangecTas follows ... 

The gas-phase rate coefficient fcc is not affecded by the fact that a chemic reaction is taking place in the liquid phase. If the liquid-phase chemical reaction is extremely fast and irreversible, the rate of absorption may be governed completely by the resistance to diffusion in the gas phase. In this case the absorption rate may be estimated by knowing only the gas-phase rate coefficient fcc of else the height of one gas-phase transfer unit Hq =... 

Observation of operating conveyors indicates that the solids are rarely uniformly dispersed in the gas phase. With infrequent exceptions, the particles move in a laminar pattern, following a streamline along the duct wall where the flow velocity is at a minimum. Complete or even partial diffusion in the gas phase is rarely experienced even with low-specific-gravity particles. Air velocities may approach 20 to 30 m/s. It is doubtful, however, that even finer and lighter materials reach more than 80 percent of this speed, while heavier and larger... 

For gas-phase diffusion in small pores at lowpressure, the molecular mean free path may be larger than the pore diameter, giving rise to Knudsen diffusion. Satterfield (Ma.s.s Tran.sfer in Heterogeneous Catalysis, MIT, Cambridge, MA, 1970, p. 43), gives the following expression for the pore dimisivity ... 

Surface diffusivities are generally strongly dependent on the fractional surface coverage and increase rapidly at surface coverage greater than 80 percent [see for example Yang et al., AIChB J., 19, 1052 (1973)]. For estimation purposes, the correlation of Sladek et al. [Ind. Bng. Chem. Fundam., 13, 100 (1974)] can be used to predict surface diffusivities for gas-phase adsorption on a variety of adsorbents. 

FIG. 25-18 Biophysical model for the hiolayer. Cg is the concentration in the gas phase. The two concentration profiles shown in the hiolayer (C ) refer to (1) elimination reaction rate limited, and (2) diffusion hmited. (SOURCE Redrawn from Ref. 26.)... 

For the analysis heat and mass transfer in concrete samples at high temperatures, the numerical model has been developed. It describes concrete, as a porous multiphase system which at local level is in thermodynamic balance with body interstice, filled by liquid water and gas phase. The model allows researching the dynamic characteristics of diffusion in view of concrete matrix phase transitions, which was usually described by means of experiments. 

A situation which is frequently encountered in tire production of microelectronic devices is when vapour deposition must be made into a re-entrant cavity in an otherwise planar surface. Clearly, the gas velocity of the major transporting gas must be reduced in the gas phase entering the cavity, and transport down tire cavity will be mainly by diffusion. If the mainstream gas velocity is high, there exists the possibility of turbulent flow at tire mouth of tire cavity, but since this is rare in vapour deposition processes, the assumption that the gas widrin dre cavity is stagnant is a good approximation. The appropriate solution of dre diffusion equation for the steady-state transport of material tlrrough the stagnant layer in dre cavity is... 

It follows from this discussion that all of the transport properties can be derived in principle from the simple kinetic dreoty of gases, and their interrelationship tlu ough k and c leads one to expect that they are all characterized by a relatively small temperature coefficient. The simple theory suggests tlrat this should be a dependence on 7 /, but because of intermolecular forces, the experimental results usually indicate a larger temperature dependence even up to for the case of molecular inter-diffusion. The Anhenius equation which would involve an enthalpy of activation does not apply because no activated state is involved in the transport processes. If, however, the temperature dependence of these processes is fitted to such an expression as an algebraic approximation, tlren an activation enthalpy of a few kilojoules is observed. It will thus be found that when tire kinetics of a gas-solid or liquid reaction depends upon the transport properties of the gas phase, the apparent activation entlralpy will be a few kilojoules only (less than 50 kJ). 

There is a qualitative distinction between these two types of mass transfer. In the case of vapour phase transport, matter is subtracted from the exposed faces of the particles via dre gas phase at a rate determined by the vapour pressure of the solid, and deposited in the necks. In solid state sintering atoms are removed from the surface and the interior of the particles via the various diffusion vacancy-exchange mechanisms, and the centre-to-cenU e distance of two particles undergoing sintering decreases with time. 

The measurement of oxygen diffusion is usually made by the use of as die labelling isotope. If a gas containing an initial concentration C, of in O , and Co is the initial conceiiuation of in a right cylinder oxide sample of thickness 21, and a is the ratio of oxygen atoms in the original gas phase compared widi that in the solid, dieii after a time t, when the concentration in the gas phase is C/... 

---