Temperature penetration depth

The shallow penetration of ion implantation would in itself make it appear useless as a technique for engineering appHcations however, there are several situations involving both physical and chemical properties in which the effect of the implanted ion persists to depths fat greater than the initial implantation range. The thickness of the modified zone can also be extended by combining ion implantation with a deposition technique or if deposition occurs spontaneously during the ion implantation process. In addition, ion implantation at elevated temperatures, but below temperatures at which degradation of mechanical properties could occur, has been shown to increase the penetration depths substantially (5). 

The terms in Eq. (6) include the gravitational constant, g, the tube radius, R, the fluid viscosity, p, the solute concentration in the donor phase, C0, and the penetration depth, The density difference between the solution and solvent (ps - p0) is critical to the calculation of a. Thus, this method is dependent upon accurate measurement of density values and close temperature control, particularly when C0 represents a dilute solution. This method has been shown to be sensitive to different diffusion coefficients for various ionic species of citrate and phosphate [5], The variability of this method in terms of the coefficient of variation ranged from 19% for glycine to 2.9% for ortho-aminobenzoic acid. 

Using the data in Question 5, at what temperature (°C) will the penetration depth be 5 pm after 2 h of heating ... 

First, we will consider thin objects - more specifically, those that can be approximated as having no spatial, internal temperature gradients. This class of problem is called thermally thin. Its domain can be estimated from Equations (7.11) to (7.12), in which we say the physical thickness, d, must be less than the thermal penetration depth. This is illustrated in Figure 7.7. For the temperature gradient to be small over region d, we require... 

This type of solution is called a similarity solution where the affected domain of the problem is proportional to yfat (the growing penetration depth), and the dimensionless temperature profile is similar in time and identical in the i) variable. Fluid dynamic boundary layer problems have this same character. 

Figure 6. Comparison of XPS depth profiles for Cs in obsidian at various temperatures (broken lines) with predicted penetration depths based on profiles calculated by Equation 4 (solid lines).

In practice, the application of x-ray measurement techniques to thin films involves some special problems. Typical films are much thinner than the penetration depth of commonly used x-rays, so the diffracted intensity is much lower than that from bulk materials. Thin films are often strongly textured this, on the other hand, results in improved intensity for suitable experimental conditions but complicates the measurement problem. Measurements at other than ambient temperature, not usually attempted with bulk materials, constitutes additional complexity. Since typical strains are on the order of 1 X 10 , measurements of interplanar spacing with a precision of the order of 1 X 10 are needed for reasonably accurate results hence, potential sources of error must be kept to a low level. In particular, the sample displacement error can be a major source of difficulty with a heated sample. The sample surface must remain accurately on the axis of the instrument during heating. 

Due to the low penetration depth of X-rays in heavy element samples, XRD patterns are not always significant for the structure of the bulk. In analogy to observations made on rare earth metal foils, fee phases observed occasionally after heating and interpreted as high temperature phases of the actinide metals, might be the product of a reaction between the metal surface and residual gas leading, e.g. to hydride etc. 

When Hj < Hcl, B = 0 in the interior of the superconducting cylinder as shown in Figure 1(b), but magnetic flux enters the walls for a distance A ( 1400 A for fields parallel to the a-b plane in YBajCujOy at low temperatures (23)). Provided the sample is of macroscopic size, the penetration depth is negligible, but it... 

It is found that for metals, low temperature field evaporation almost always produces surfaces with the (1 x 1) structure, or the structure corresponding to the truncation of a solid. A few such surfaces have already been shown in Fig. 2.32. That this should be so can be easily understood. For metals, field penetration depth is usually less than 0.5 A,1 or much smaller than both the atomic size and the step height of the closely packed planes. Low temperature field evaporation proceeds from plane edges of these closely packed planes where the step height is largest and atoms are also much more exposed to the applied field. Atoms in the middle of the planes are well shielded from the applied field by the itinerant electronic charges which will form a smooth surface to lower the surface free energy, and these atoms will not be field evaporated. Therefore the surfaces produced by low temperature field evaporation should have the same structures as the bulk, or the (lxl) structures, and indeed with a few exceptions most of the surfaces produced by low temperature field evaporation exhibit the (1 x 1) structures. 

In a microwave cavity a standing wave pattern is generated, which depends of course on a multiple of the wavelength of the radiation (12.5 cm at 2.45 GHz), and therefore depending on the dielectric properties and size of the sample one can get considerable variations in temperature. The penetration depth, Dp, of the radiation is clearly an important consideration. 

For ideal solutions, the partial pressure of a component is directly proportional to the mole fraction of that component in solution and depends on the temperature and the vapor pressure of the pure component. The situation with group III-V systems is somewhat more complicated because of polymerization reactions in the gas phase (e.g., the formation of P2 or P4). Maximum evaporation rates can become comparable with deposition rates (0.01-0.1 xm/min) when the partial pressure is in the order of 0.01-1.0 Pa, a situation sometimes encountered in LPE. This problem is analogous to the problem of solute loss during bakeout, and the concentration variation in the melt is given by equation 1, with l replaced by the distance below the gas-liquid interface and z taken from equation 19. The concentration variation will penetrate the liquid solution from the top surface to a depth that is nearly independent of zlDx and comparable with the penetration depth produced by film growth. As result of solute loss at each boundary, the variation in solute concentration will show a maximum located in the melt. The density will show an extremum, and the system could be unstable with respect to natural convection. 

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