Theoretical study of the diffusion constant for self-diffusion in metals
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Relatively good GaAs solar cells can be made from poor quality substrates by making the junction deep (more than 1 micron) instead of shallow and by leaching both the p and n GaAs regions during the growth process. Air-mass-zero efficiencies of 14.7% (19% AM1) have been obtained from substrates with starting substrate thickness of 0.6 micron.
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Engineering technology programs are characterized by their focus on application and practice, and by their approximately 50/50 mix of theory and laboratory experience. Engineering technology graduates are employed across the technological spectrum and are often found in areas that deal with application, implementation, and production. Yet we know very little about the communications practices and information-use skills of engineering technology students. In this paper, we report selected results of an exploratory study of engineering technology students enrolled in three U.S. institutions of higher education. Data are presented for the following topics: career goals and aspirations; the importance of, receipt of, and helpfulness of communications and information-use skills instruction; collaborative writing; use of libraries; and the use of electronic (computer) networks.
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An experimental investigation of exhaust diffusers has been conducted to evaluate various methods of minimizing the overall pressure ratio (from chamber to ambient pressure) required to establish and maintain full expansion of the nozzle flow (altitude simulation). Exhaust-diffuser configurations investigated were (1) cylindrical diffusers, (2) diffusers with contraction, and (3) diffusers including a right-angle turn. Cylindrical diffusers were evaluated with primary nozzles of various area ratios and types, as well as two clustered configurations; the other diffusers were evaluated with individual nozzles of constant area ratio and varied type. Air was the working fluid, except for two check points obtained with JP-4 fuel and liquid-oxygen rocket engines and cylindrical diffusers. The minimum length-diameter ratio of cylindrical diffusers was about 6 for minimum pressure-ratio requirements. With cylindrical diffusers of adequate length, the pressure-ratio requirements were primarily a function of the ratio of diffuser to nozzle-throat areas and were essentially independent of primary-nozzle type (including two clustered configurations) or area ratio. The two check points obtained with rocket engines indicated the pressure-ratio requirements at given ratios of diffuser to nozzle-throat areas were lowered, as compared with the requirements with air, as a result of the reduced ratio of specific heats. The minimum length-diameter ratio of the contraction throat of convergent-divergent diffusers was also about 6 for minimum pressure-ratio requirements. With adequate contraction-throat length, the pressure-ratio requirements of such diffusers were appreciably below those of comparable cylindrical diffusers when used with conical and cutoff-isentropic nozzles, but not when used with a bell nozzle. Minimum pressure-ratio requirements of a diffuser including a simple long-radius right-angle turn at maximum diffuser area, obtained with the center of radius of the turn a minimum of 2 diffuser diameters downstream of the nozzle exit, were not appreciably above those of a comparable optimum cylindrical diffuser. A diffuser including a long-radius right-angle turn at a contraction minimum area had somewhat lower pressure-ratio requirements than the aforementioned simple turn.
Diffusion results from random motion of particles and entities. Diffusion in melts and magmas is due to thermally excited random motion of atoms, ions, and clusters, and plays a critical role in magmatic and volcanic processes. In melts and magmas, diffusion is one of the two mechanisms of mass transfer; the other being bulk flow (referred to as convection or advection). When both are present, diffusion refers to the dispersive motion relative to the mean bulk flow in a given reference frame (Richter et al. 1998). Diffusion plays critical roles in controlling magma mixing (Watson 1982; Koyaguchi 1985, 1989; Lesher 1994; Huber et al. 2009; Guo and Zhang 2020), mineral growth and dissolution rates in magmas (e.g., Watson 1982; Harrison and Watson 1983; Zhang et al. 1989; Newcombe et al. 2014; Macris et al. 2018), bubble growth and dissolution rate in magmas (Sparks 1978; Proussevitch and Sahagian 1998; Liu and Zhang 2000; Zhang 2013), and elemental and isotope fractionation during mineral 2 growth and dissolution (Jambon 1980; Richter et al. 1999, 2003; Watson and Muller 2009; Chopra et al. 2012; Watkins et al. 2014, 2017; Holycross et al. 2016, 2018). As a result, diffusion also plays an essential role in explosive volcanic eruptions and magma crystallization. Furthermore, diffusion has important applications in geospeedometry (Lasaga 1983, 1998; Zhang 1994, 2008; Trail et al. 2016; Zhang and Xu 2016). Experimental investigation of diffusion in geologically relevant silicate melts began to flourish in the 1970’s when micro-analytical measurements of diffusion profiles became available. In addition to the vast number of papers published since then, numerous books and reviews are available for diffusion in silicate melts. Hofmann et al. (1974) edited a book titled “Geochemical Transport and Kinetics” published by Carnegie Institution of Washington. This was the first landmark book summarizing the field. Lasaga and Kirkpatrick (1981) edited a book “Kinetics of Geochemical Processes” as volume 8 of the Reviews in Mineralogy (later becoming Reviews in Mineralogy and Geochemistry) series. Zhang and Cherniak (2010) edited “Diffusion in Minerals and Melts” as volume 72 of Reviews of Mineralogy and Geochemistry series, in which one chapter focused on diffusion theory, five chapters on diffusion in silicate melts (Behrens 2010; Lesher 2010; Liang 2010; Zhang and Ni 2010; Zhang et al. 2010), and other chapters were on experimental, analytical, and computational methods, and diffusion in minerals. Several textbooks covered the principles and applications of diffusion theories (Kirkaldy and Young 1987; Shewmon 1989; Cussler 1997; Lasaga 1998; Zhang 2008; Vrentas and Vrentas 2016), and two classic books covered the mathematics of diffusion (Carslaw and Jaeger 1959; Crank 1975). In preparing for this review chapter, we thought carefully about what to cover for this vast field, and decided to briefly go through the fundamentals of diffusion (more complete review can be found in Chakraborty 1995; Zhang 2008, 2010) and solutions to often-encountered 3 diffusion problems, and then focus on post-2010 diffusion studies on silicate melts and magmas. Here, melts refer to (mostly natural) silicate liquid, and magmas refer to crystal-bearing and/or bubble-bearing melts in which the continuous phase is the melt. There is a large body of work on diffusion in glasses, especially in the materials science literature, which is not covered in this review.
Theoretical Mach number distributions and boundary-layer parameters are presented for subsonic nacelle inlet diffuser geometries with length to exit diameter ratios ranging from 0.4 to 1.6 and diffuser exit area to throat area ratios ranging from 1.1 to 2.0. The major portion of the study was done with a cubic diffuser contour with the inflection point at the midpoint of the diffuser, a diffuser throat Mach number of 0.6, and a free-stream Mach number of 0.12. Calculations were performed at both model (diffuser exit diameter, 30.5 cm) and full-scale (diffuser exit diameter, 183 cm) sizes. Separation limits were defined by establishing a separation boundary on plots of diffuser area ratio as a function of diffuser length to diameter ratio. The effects of diffuser contour, inlet lip geometry, and throat Mach number on the boundary-layer characteristics are illustrated. The major results of the study indicate that the separation boundary is shifted to greater area ratios by (1) increasing the diffuser length, (2) increasing the scale of the diffuser and, (3) moving the inflection point of the diffuser contour to or ahead of the midpoint of the diffuser.