Diffusion substitutional

It can be shown from the Chilton-Colbum analogy (6) that under identical flow conditions the ratio of foi to b2 is equal to the 1/3 power of the ratio of the respective diffusivities. Substituting and combining Equations 11 and 12 leads to... 

Carbon diffuses in solid silicon both substitutionally and interstitially. It has been experimentally confirmed that carbon diffuses substitutionally in... 

SOLUTION We will use the Vignes method to estimate the MS diffusivity. Substituting the numerical values for the infinite dilution diffusivities and the mole fraction into Eq. 

When pores are big enough and pressures are high enough so that ordinary bulk diffusion is operative in the catalyst pores, then we can get a corresponding formula for ha, the value of h to be used with bulk diffusion. Substituting (40) and (10) into (33) gives... 

Perturbations in the axial velocity must be balanced by radial diffusion. Substituting for... 

Equimolar Counterdiffusion in Binary Cases. If the flux of A is balanced by an equal flux of B in the opposite direction (frequently encountered in binary distillation columns), there is no net flow through the film and like is directly given by Fick s law. In an ideal gas, where the diffusivity can be shown to be independent of concentration, integration of Fick s law leads to a linear concentration profile through the film and to the following expression where (P/RT)y is substituted for... 

Carbon Dioxide Transport. Measuring the permeation of carbon dioxide occurs far less often than measuring the permeation of oxygen or water. A variety of methods ate used however, the simplest method uses the Permatran-C instmment (Modem Controls, Inc.). In this method, air is circulated past a test film in a loop that includes an infrared detector. Carbon dioxide is appHed to the other side of the film. AH the carbon dioxide that permeates through the film is captured in the loop. As the experiment progresses, the carbon dioxide concentration increases. First, there is a transient period before the steady-state rate is achieved. The steady-state rate is achieved when the concentration of carbon dioxide increases at a constant rate. This rate is used to calculate the permeabiUty. Figure 18 shows how the diffusion coefficient can be deterrnined in this type of experiment. The time lag is substituted into equation 21. The solubiUty coefficient can be calculated with equation 2. 

Boron and carbon form one compound, boron carbide [12069-32-8] B C, although excess boron may dissolve ia boron carbide, and a small amount of boron may dissolve ia graphite (5). Usually excess carbon appears as graphite, except for the special case of boron diffused iato diamonds at high pressures and temperatures, eg, 5 GPa (50 kbar) and 1500°C, where boron may occupy both iaterstitial and substitutional positions ia the diamond lattice, a property utilized ia synthetic diamonds (see Carbon, diamond, synthetic). 

These expressions can also be used for the case of external mass transfer and solid diffusion control by substituting D, for 8pDpi/( p + ppK)) and/c rp/(ppK)D,i) for the Biot number. 

Dispersion The movement of aggregates of molecules under the influence of a gradient of concentration, temperature, and so on. The effect is represented hy Tick s law with a dispersion coefficient substituted for molecular diffusivity. Thus, rate of transfer = —Dj3C/3p). 

Dispersion model is based on Fick s diffusion law with an empirical dispersion coefficient substituted for the diffusion coefficient. The material balance is... 

Chemical erosion can be suppressed by doping with substitutional elements such as boron. This is demonstrated in Fig. 14 [47] which shows data for undoped pyrolitic graphite and several grades of boron doped graphite. The mechanism responsible for this suppression may include the reduced chemical activity of the boronized material, as demonstrated by the increased oxidation resistance of B doped carbons [48] or the suppressed diffusion caused by the interstitial trapping at boron sites. 

In some materials, semiconductors in particular, interstitial atoms play a crucial role in diffusion. Thus, Frank and Turnbull (1956) proposed that copper atoms dissolved in germanium are present both substitutionally (together with vacancies) and interstitially, and that the vacancies and interstitial copper atoms diffuse independently. Such diffusion can be very rapid, and this was exploited in preparing the famous micrograph of Figure 3.14 in the preceding chapter. Similarly, it is now recognised that transition metal atoms dissolved in silicon diffuse by a very fast, predominantly interstitial, mechanism (Weber 1988). 

Another subsidiary field of study was the effect of high concentrations of a diffusing solute, such as interstitial carbon in iron, in slowing diffusivity (in the case of carbon in fee austenite) because of mutual repulsion of neighbouring dissolved carbon atoms. By extension, high carbon concentrations can affect the mobility of substitutional solutes (Babu and Bhadeshia 1995). These last two phenomena, quenched-in vacancies and concentration effects, show how a parepisteme can carry smaller parepistemes on its back. 

Kinetic studies have shown that the enolate and phosphorus nucleophiles all react at about the same rate. This suggests that the only step directly involving the nucleophile (step 2 of the propagation sequence) occurs at essentially the diffusion-controlled rate so that there is little selectivity among the individual nucleophiles. The synthetic potential of the reaction lies in the fact that other substituents which activate the halide to substitution are not required in this reaction, in contrast to aromatic nucleophilic substitution which proceeds by an addition-elimination mechanism (see Seetion 10.5). 

The substituent effects on the H-bonding in an adenine-uracil (A-U) base pair were studied for a series of common functional groups [99JPC(A)8516]. Substitutions in the 5 position of uracil are of particular importance because they are located toward the major groove and can easily be introduced by several chemical methods. Based on DFT calculation with a basis set including diffuse functions, variations of about 1 kcal/mol were found for the two H-bonds. The solvent effects on three different Watson-Crick A-U base pairs (Scheme 100) have been modeled by seven water molecules creating the first solvation shell [98JPC(A)6167]. 

The grafting reaction depends upon the degree of substitution as well as the kind of pulp used. Introducing acetyl groups in the cellulose chains (high substitution) causes a large reduction of its swellability, which reduces the diffusion of the reactants. Thus, acetylation lowers the graftability of the cellulose. 

Changes in the atomic correlations are enabled by atomic jumps between neighbouring lattice sites. In metals and their substitutional solutions point defects are responsible for these diffusion processes. Ordering kinetics can therefore yield information about properties of the point defects which are involved in the ordering process. 

The poor efficiencies of coal-fired power plants in 1896 (2.6 percent on average compared with over forty percent one hundred years later) prompted W. W. Jacques to invent the high temperature (500°C to 600°C [900°F to 1100°F]) fuel cell, and then build a lOO-cell battery to produce electricity from coal combustion. The battery operated intermittently for six months, but with diminishing performance, the carbon dioxide generated and present in the air reacted with and consumed its molten potassium hydroxide electrolyte. In 1910, E. Bauer substituted molten salts (e.g., carbonates, silicates, and borates) and used molten silver as the oxygen electrode. Numerous molten salt batteiy systems have since evolved to handle peak loads in electric power plants, and for electric vehicle propulsion. Of particular note is the sodium and nickel chloride couple in a molten chloroalumi-nate salt electrolyte for electric vehicle propulsion. One special feature is the use of a semi-permeable aluminum oxide ceramic separator to prevent lithium ions from diffusing to the sodium electrode, but still allow the opposing flow of sodium ions. 

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