Diffusion temperature variation

The mobility or diffusion of die atoms over the surface of die substrate, and over the film during its formation, will occur more rapidly as the temperature increases since epitaxy can be achieved, under condition of ctystallographic similarity between die film and the subsuate, when the substrate temperamre is increased. It was found experimentally that surface diffusion has a closer relationship to an activation-dependent process than to the movement of atoms in gases, and the temperamre dependence of the diffusion of gases. For surface diffusion the variation of the diffusion coefficient widr temperature is expressed by the Anhenius equation... 

There is experimental evidence to suggest that anion and cation diffusion can have different mechanisms [70]. The temperature variation of the diffusion coefficients of 1,1 P and 7 Li in aPEO-LiPF6 shows quite different trends. The 31P diffusion coefficients follow a VTF-type de-... 

During the course of these calculations it is obviously necessary to employ property values characteristic of the volume element in question. Rate constants are extremely sensitive to temperature variations diffusivities will vary as T1/2 or T3/2, depending on whether Knudsen or ordinary bulk diffusion dominates. 

The third curious point has to do with the overall time variation of the rate of loss of tritium at the diffusion temperatures and is illustrated by Fig. 14, a selection taken from detailed data presented by Ichimiya and Furuichi (1968). The fraction of the originally dissolved tritium remaining in the sample decreases from 1 to 0 as the annealing time goes from 0 to... 

The temperature in a sewer depends on a number of different conditions, e.g., climate, source of wastewater and system characteristics. The microbial community developed in a sewer is typically subject to annual temperature variations and, to some extent, a daily variability. Different microbial systems may be developed under different temperature conditions, and process rates relevant for the microorganisms vary considerably with temperature. Long-term variations may affect which microbial population will develop in a sewer, whereas short-term variations have impacts on microbial processes in the cell itself as well as on the diffusion rate of substrates. 

Fig. 32a, b. Temperature variation of a. the geometrical parameters jump distance r and distance L between neighbouring chains, b. Residence time x and diffusion constant D... 

The diffusion coefficients, as expected, increase with increasing temperature. Variation of the diffusion coefficient as a function of temperature can be expressed in terms of the Arrhenius equation, which, in logarithmic form, is... 

Heat transfer is an extremely important factor in CVD reactor operation, particularly for LPCVD reactors. These reactors are operated in a regime in which the deposition is primarily controlled by surface reaction processes. Because of the exponential dependence of reaction rates on temperature, even a few degrees of variation in surface temperature can produce unacceptable variations in deposition rates. On the other hand, with atmospheric CVD processes, which are often limited by mass transfer, small susceptor temperature variations have little effect on the growth rate because of the slow variation of the diffusion with temperature. Heat transfer is also a factor in controlling the gas-phase temperature to avoid homogeneous nucleation through premature reactions. At the high temperatures (700-1400 K) of most... 

During cell/stack operation, water content in the membrane is affected by the local intensive variables, such as local temperature, water vapor concentration in the gas phase, gas temperature and velocity in the channel, and the properties of the electrode and gas diffusion media. The power fluctuation can result in temperature variation inside the cell/stack, which will subsequently change the local membrane water content. As the water content in the membrane tends to be non-uniform and unsteady, this results in operation stresses. When the membrane uptakes water from a dry state, it tends to expand as there is no space for it to extend in plane and it can wrinkle up as schematically shown in Fig. 4 when the membrane dries out, the wrinkled part may not flatten out, and this ratcheting effect can cause the pile up of wrinkles at regions where membrane can find space to fold. The operation stress is typically cyclic in nature due to startup-shutdown cycles, freeze-thaw cycles, and power output cycles. 

The generation of heat always accompanies the operation of a fuel cell. The heat is due to inefficiencies in the basic fuel-cell electrochemical reaction, crossover (residual diffusion through the fuel-cell solid-electrolyte membrane) of fuel, and electrical heating of interconnection resistances. Spatial temperature variation can occur if any of these heat-generating processes occur preferentially in different parts of the fuel cell stack. For example, non-uniform distribution of fuel across the surfaces of electrodes, different resistances between the interconnections in a stack, and variations among... 

The second explanation for the solvent isotope effect arises from the dynamic medium effect . At 25 °C the rotational and translational diffusion of DjO molecules in D20 is some 20% slower than H20 molecules in H20 (Albery, 1975a) the viscosity of D20 is also 20% greater than H20. Hence any reaction which is diffusion controlled will be 20% slower in D20 than in H20. This effect would certainly apply to transition state D in Fig. 3 where in the transition state the leaving group is diffusing away. A similar effect may also apply to the classical SN1 and SN2 transition states, if the rotational diffusion of water molecules to form the solvation shell is part of the motion along the reaction co-ordinate in the transition state. Robertson (Laughton and Robertson, 1959 Heppolette and Robertson, 1961) has indeed correlated solvent isotope effects for both SN1 and SN2 reactions with the relative fluidities of H20 and D20. However, while the correlation shows that this is a possible explanation, it may also be that the temperature variation of the solvent isotope effect and of the relative fluidities just happen to be very similar (see below). 

In one formulation, dyes with similar rates of diffusion should be used. Very quickly diffusing dyes sublime easily, contaminate the fixing aggregate, and produce dyeings that have a low fastness to thermofixation. The color yield of very slowly diffusing dyes is sensitive to temperature variations. 

Figure 2.9 Arrhenius plot showing temperature variation of nohle gas diffusion coefficients. Samples 1-3 are glass melts 4, 5, and 14 are vitreous silica 6 is commercial glass 7 and 14 are B203 8-10 are mixtures of alkali oxides with B203, Si02, and A1203 11 and 12 are obsidians 13 and 15 are Si02. Reproduced from Hiyagon (1981).

Figure 2.10 Arrhenius plot showing temperature variation of He diffusion coefficient in carbonado (diamond), a indicates the size (in micrometers) of the pulverized powder. Note that the diffusion is characterized by two distinct activation energies. Reproduced from Zashu and Hiyagon (1995).

Also Senkan et al. (6) and Schehl et al. (3) have shown that for methanation, the material balance equation can be solved independently of the energy balance equation in diffusion-limited cases, because the effects of temperature variation on gas properties essentially cancel each other. It is therefore justified to consider the isothermal model for the purpose of yield optimization. 

Having mentioned the correlative capabilities of this model, one can consider its semi-predictive abilities. It was mentioned that a number of diffusion data taken from a limited range of penetrant concentrations are required to calculate two of the parameters of the model. Once these parameters have been determined, one can make theoretical predictions for diffusion coefficients over a wider range of penetrant concentration or temperature variation. This is a critical test for any theoretical model,... 

Temperature variations. Essentially all kinetic phenomena are temperature dependent ion diffusion (in both electrolyte and active materials), electron transfer, desolvation, adsorption, etc. Additionally, thermodynamic equilibrium constants are temperature dependent, so any temperature variations within the cell will produce uneven plating and stripping, electrode shape change effects and uneven utilization again leading to compromised performance. 

The temperature records in Fig. 4.19 correlate well with this classification. The conduit type revealed significant temperature variations, in good agreement with the known seasonal variations of karstic flow, whereas the springs with the diffuse type of flow revealed steady temperatures. Once the temperature pattern was established by calibration against other observa-... 

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