Diffusion temperature

Thermal diffusivity Temperature sensitivity Temperature difference Thickness of tube Aspect ratio, relation of Cp/Cy Fluid dielectric constant Wall zeta potential Dimensionless temperature Friction factor, Debye length Mean free path Dynamic viscosity Kinematic viscosity Bejan number Density... 

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... 

Fig. 6. Deuterium concentration profiles in LPE grown p-type GaAs Si (p 7x 1018 cm-3) exposed to a rf deuterium plasma for 90 min. at different temperatures (rf power density = 0.2 W/cm2). For these diffusion temperatures, the plateau region is well defined with a deuterium solubility slightly above the silicon acceptor concentration. J. Chevallier era/., Mat. Res. Soc. Symp. Proc. 104, 337 (1988). Materials Research Society. 

Under adiabatic conditions with external diffusion, temperature and concentration differences will develop between the bulk of the fluid and the surface of the catalyst. The rate of reaction is the rate of diffusion, r = kga(Cg-Cs) and the heat balance is... 

There are two possible directions for both the atoms in both the first and second atomic jumps. If the jumping direction is completely random and the two atoms have the same probability of performing a jump, then these atomic jumps are said to be uncorrelated. A correlation factor, /, has been introduced for the two atomic jumps, which is defined as the extra probability that the atom making the first jump will also make the second jump in the forward direction. The rest of the probability, (1 — /), is then shared equally for either of the two atoms jumping in either of the two directions. Two experimental displacement distributions measured at 299 K and 309 K fit best with a Monte Carlo simulation with / = 0.1 and /=0.36, respectively. The correlation factor increases with diffusion temperature as can be expected. It is interesting to note that when/= 1, only a and steps can occur. 

The temperature dependence of the diffusion parameter for all coals could be described by Arrhenius plots. Figure 1 shows typical plots for two of the bituminous coals. Table II summarizes the activation energy and preexponential data for all coals, where D /r = D. /r. exp(- /2RT). Since r should be independent of diffusion temperature, the activation energy... 

First attempts to produce p-type ZnO were reported in the 1950s by Lander from Bell Labs [40]. He introduced alkali atoms, especially lithium, into intrinsic ZnO crystals. Depending on the concentration and the diffusion temperature, lithium acts both as a donor (interstitial Li1 ) as well as an acceptor. The lithium becomes an acceptor by displacing a zinc ion from a lattice site according to the equation ... 

The process of particle collision is governed by physical factors such as diffusion, temperature, fluid shear, particle and fluid density, and the size of particles and aggregates. Whether particles will adhere when they collide is considered to be a function of conditions at the interface between the two solid particles and the fluid medium. Chemical interactions at the solid-liquid interface are responsible for the development of surface charge and potential, the electric diffuse layer, and hydration and hydrophobic effects which determine the probability of particle attachment. 

Continuum diffusion (Kn 1). Hie different species of a mixture move relative to each other under the influence of concentration gradients (ordinary or concentration diffusion), temperature gradients (thermal diffusion) or external forces (forced diffusion). Here molecule-wall collisions are neglected. 

Figure 8. Dependence of the conversion on the catalyst density (gr-catalyst/cc-void). Base case. No removal of hydrogen occurs by diffusion Temperature = 600°C.

In sealed-tube diffusion of A1 from an A1 metal source, reaction occurs with the quartz walls of the tube, with O2 and with moisture (residual after evacuating the ampule). Possible reactions at the diffusion temperature are ... 

Liquid doping sources are usually of two forms (1) a solution of dopant material is directly applied to the semiconductor surface and dried prior to diffusion or (2) a carrier gas is bubbled through the liquid source and the source molecules are carried into an open-tube furnaee. Doping may then occur from the gas phase or from a deposited solid phase on the semiconductor. Also, in some cases solid sources deposited on semiconductors become liquid at diffusion temperatures (e.g., borosilicate glasses containing ca. 30 mol% B2O3 become liquid at 1000°C)L... 

Figure 5 illustrates the optimized temperature sets for the Ising ferromag-net obtained by several iterations of the above feedback loop. After feedback of the local diffusivity temperature points accumulate near the critical temperature Tc = 2.269 of the transition. This is in analogy to the optimized histograms for the extended ensemble simulations where resources where shifted towards the critical energy of the transition, see Fig. 2. 

Fig. 8. Optimized temperature sets with 20 temperature points for the parallel tempering simnlation of the 36-residue protein HP-36. The initial temperatnre set covers a temperatnre range 250 K < T < 1000 K and concentrates temperatnre points at low temperatures similar to a geometric progression. After the feedback of the local diffusivity temperature points accumulate around the hehx-coil transition at T fs 500 K where the strong suppression of the local diffusivity points to a severe bottleneck...

The basic concept of diffusion refers to the net transport of material within a single phase in the absence of mixing (by mechanical means or by convection). Both experiment and theory have shown that diffusion can result from pressure gradients (pressure diffusion), temperature gradients (thermal diffusion), external force fields (forced diffusion), and concentration gradients. Only the last type is considered in this book that is, the discussion is limited to diffusion caused by the concentration difference between two points in a stagnant solution. This process, called molecular diffusion, is described by Pick s laws. His first law relates the flux of a chemical to the concentration gradient ... 

For Al bonds on Au or vice versa, the Kirkendall effect leads to a well known failure mechanism [37]. The Kirkendall effect results from the different diffusion coefficients of Au and Al in different phases of the system AlAu [38]. The Al2Au phase ( purple phase ), which is always present, plays a crucial role. The diffusion coefficient of Al through Al2Au is much higher than that of Au. As a result, voids are created as soon as the temperature reaches the diffusion temperature, which reduces the stability of the bond contact. 

The depth of the recrystallised layer is very small, of the order of 0.01 -0.1 pm. Thus, a possible way to eliminate its effect on p-n junction properties is to perform a drive-in diffusion of aluminium from the epitaxial layer. Unfortunately, the diffusivity of aluminium from an epitaxial layer is extremely slow in SiC. The diffusivity is 3 - 5 orders of magnitude lower than that observed for diffusing aluminium from the vapour phase [70]. The authors of [69] had to employ very high diffusion temperatures, over 2500 °C. The anneal produced a shift of the p-n junction into the crystal bulk and the electrical properties were substantially improved. However, this could not provide the elimination of the weak points of the junctions. The characteristics of the p-n junctions were worse than those with the recrystallised layer removed by sublimation etching. In addition, the surface evaporation and graphitisation at temperatures above 2500 °C severely reduces the reproducibility of the results. 

It has been shown recently [75] that the diffusion of boron and aluminium in SiC occurs by a mechanism very similar to that of gold in silicon, i.e. it breaks the equilibrium of intrinsic point defects in the system. Thus, if aluminium concentration is high and the diffusion temperature is not too high, the enhanced diffusion will take place along dislocations. In the vicinity of an imperfection the p-n junction profile will be distorted, and a needle-shaped projection will appear (FIGURE 17(c)). This suggests a very strong electric field concentration and microplasma formation in a reverse-biased p-n junction. 

To go from the behavior of the diffusion coefficient to the phenomenon of the glass transition and the relation between simulated and real systems, we need to consider (J) the observed diffusivity-temperature relation over the full temperature range, and (2) the relation between diffusivity and relaxation time, and between real and apparent thermodynamic properties. The first of these we consider now the second is taken up in the Section IIl.C. 

House et al. (1999) recognized that problems associated with thermal history could be circumvented by taking advantage of the fact that He ages of samples held close to the closure temperature will rapidly achieve the steady state age where He production and diffusive loss are in balance (Wolf et al. 1998). Provided a sample is in steady state, the measured age and downhole temperature provide a diffusivity-temperature pair that is completely independent of the laboratory measurements. Samples thought to be in steady state in boreholes from the Otway Basin, Australia, yielded diffusivities in excellent agreement with the extrapolated laboratory data (Fig. 2). Unfortunately the downhole temperatures from these industry wells are not very well known, so some uncertainty remains. 

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