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At least 253 records · Page 14

Reverse Micelle Based Synthesis of Microporous Materials in Microgravity

Formation of zincophosphates from zinc and phosphate containing reverse micelles (water droplets in hexane) has been examined. The frameworks formed resemble that made by conventional hydrothermal synthesis. Dynamics of crystal growth are however quite different, and form the main focus of this study. In particular, the formation of zincophosphate with the sodalite framework was examined in detail. The intramicellar pH was found to have a strong influence on crystal growth. Crystals with a cubic morphology were formed directly from the micelles, without an apparent intermediate amorphous phase over a period of four days by a layer-bylayer growth at the intramicellar pH of 7.6. At a pH of 6.8, an amorphous precipitate rapidly sediments in hours. Sodalite was eventually formed from this settled phase via surface diffusion and reconstruction within four days. With a rotating cell, it was possible to minimize sedimentation and crystals were found to grow epitaxially from the spherical, amorphous particles. Intermediate pH's of 7.2 led to formation of aggregated sodalite crystals prior to settling, again without any indication of an intermediate amorphous phase. These diverse pathways were possible due to changes in intramicellar supersaturation conditions by minor changes in pH. In contrast, conventional syntheses in this pH range all proceeded by similar crystallization pathways through an amorphous gel. This study establishes that synthesis of microporous frameworks is not only possible in reverse micellar systems, but they also allow examination of possible crystallization pathways.

Dutta, Prabir K.↗

Step Bunching: Influence of Impurities and Solution Flow

Step bunching results in striations even at relatively early stages of its development and in inclusions of mother liquor at the later stages. Therefore, eliminating step bunching is crucial for high crystal perfection. At least 5 major effects causing and influencing step bunching are known: (1) Basic morphological instability of stepped interfaces. It is caused by concentration gradient in the solution normal to the face and by the redistribution of solute tangentially to the interface which redistribution enhances occasional perturbations in step density due to various types of noise; (2) Aggravation of the above basic instability by solution flowing tangentially to the face in the same directions as the steps or stabilization of equidistant step train if these flows are antiparallel; (3) Enhanced bunching at supersaturation where step velocity v increases with relative supersaturation s much faster than linear. This v(s) dependence is believed to be associated with impurities. The impurities of which adsorption time is comparable with the time needed to deposit one lattice layer may also be responsible for bunching; (4) Very intensive solution flow stabilizes growing interface even at parallel solution and step flows; (5) Macrosteps were observed to nucleate at crystal corners and edges. Numerical simulation, assuming step-step interactions via surface diffusion also show that step bunching may be induced by random step nucleation at the facet edge and by discontinuity in the step density (a ridge) somewhere in the middle of a face. The corresponding bunching patterns produce the ones observed in experiment. The nature of step bunching generated at the corners and edges and by dislocation step sources, as well as the also relative importance and interrelations between mechanisms 1-5 is not clear, both from experimental and theoretical standpoints. Furthermore, several laws controlling the evolution of existing step bunches have been suggested, though unambiguous conclusions are still missing. Addressing these issues is the major goal of the present project. The theory addressing the above problem, experimental methods, several figures which include: (1) the spatial wave numbers at which the system is neutrally stable as a function of growth velocity for linear kinetics and supersaturation for nonlinear kinetics; (2) a schematic of the experiment of lysozyme crystal growing under conditions of natural convection; (3) fluctuations in time, t, of the normal growth rate, R(t), vicinal slope, p(t) and Fourier Spectra of R(t), discussions and conclusions are presented.

Chernov, A. A.↗

Profile Evolution Simulation in Etching Systems Using Level Set Methods

Semiconductor device profiles are determined by the characteristics of both etching and deposition processes. In particular, a highly anisotropic etch is required to achieve vertical sidewalls. However, etching is comprised of both anisotropic and isotropic components, due to ion and neutral fluxes, respectively. In Ar/Cl2 plasmas, for example, neutral chlorine reacts with the Si surfaces to form silicon chlorides. These compounds are then removed by the impinging ion fluxes. Hence the directionality of the ions (and thus the ion angular distribution function, or IAD), as well as the relative fluxes of neutrals and ions determines the amount of undercutting. One method of modeling device profile evolution is to simulate the moving solid-gas interface between the semiconductor and the plasma as a string of nodes. The velocity of each node is calculated and then the nodes are advanced accordingly. Although this technique appears to be relatively straightforward, extensive looping schemes are required at the profile corners. An alternate method is to use level set theory, which involves embedding the location of the interface in a field variable. The normal speed is calculated at each mesh point, and the field variable is updated. The profile comers are more accurately modeled as the need for looping algorithms is eliminated. The model we have developed is a 2-D Level Set Profile Evolution Simulation (LSPES). The LSPES calculates etch rates of a substrate in low pressure plasmas due to the incident ion and neutral fluxes. For a Si substrate in an Ar/C12 gas mixture, for example, the predictions of the LSPES are identical to those from a string evolution model for high neutral fluxes and two different ion angular distributions.(2) In the figure shown, the relative neutral to ion flux in the bulk plasma is 100 to 1. For a moderately isotropic ion angular distribution function as shown in the cases in the left hand column, both the LSPES (top row) and rude's string method (bottom row) predict tapered profiles. The LSPES uses an AD with a FWHM = 13.5 degrees, and rude's model uses a ratio of sheath voltage to ion temperature of 50. The more anisotropic IADs produce profiles with more vertical sidewalls and a wider bottom surface, as shown in the right hand column. Here, the LSPES has an AD with a FWHM = 2 degrees, and rude's model uses a ratio of 500 of sheath voltage to ion temperature. The agreement between the LSPES and rude's model is excellent in both cases. We will present etching profiles generated by the LSPES, including calculations of the re-emitted fluxes of both neutrals and ions off of the profile walls. In addition, we will show the effect of geometric structures (overhangs, etc.) on the etching profiles. Other physical aspects, such as surface diffusion, will also be included in the model.

Hwang, Helen H.↗

Dot-Projection Photogrammetry and Videogrammetry of Gossamer Space Structures

This paper documents the technique of using hundreds or thousands of projected dots of light as targets for photogrammetry and videogrammetry of gossamer space structures. Photogrammetry calculates the three-dimensional coordinates of each target on the structure, and videogrammetry tracks the coordinates versus time. Gossamer structures characteristically contain large areas of delicate, thin-film membranes. Examples include solar sails, large antennas, inflatable solar arrays, solar power concentrators and transmitters, sun shields, and planetary balloons and habitats. Using projected-dot targets avoids the unwanted mass, stiffness, and installation costs of traditional retroreflective adhesive targets. Four laboratory applications are covered that demonstrate the practical effectiveness of white-light dot projection for both static-shape and dynamic measurement of reflective and diffuse surfaces, respectively. Comparisons are made between dot-projection videogrammetry and traditional laser vibrometry for membrane vibration measurements. The paper closes by introducing a promising extension of existing techniques using a novel laser-induced fluorescence approach.

Pappa, Richard S.↗

Jupiter System Data Analysis Program: Mechanisms, Manifestation, and Implications of Cryomagmatism on Europa

The objectives of the work completed under NASA Grant NAG5-8898 were (i) to document and characterize the low-albedo diffuse surfaces associated with triple bands and lenticulae, (ii) to determine their mechanisms of formation, and (iii) to assess the implications of these features for the resurfacing (in space and time) of the Europa and the nature of the Europan interior. The approach involved a combination of processing and analysis of Solid State Imaging data returned by the Galileo spacecraft during the primary and extended mission phases, together with numerical modeling of the physical processes interpreted to the observed features. We have modeled the formation of Europan triple explosive venting of cryoclastic material from bands and lenticulae halos by two processes: (i) a liquid layer in the Europan interior, and (ii) lag deposit formation by the thermal influence of subsurface cryomagmatic intrusions. We favor the latter hypothesis for explaining these features, and further suggest that a liquid water or brine intrusion is required to provide sufficient lateral heating of surface ice to explain the 25 km size of the largest features. (Solid ice diapirs, even under the most favorable conditions, become thermally exhausted before they heat significant lateral distances). We argue that water circulating in open fractures, or repeated cryomagmatic 'diking' events would provide sufficient thermal input to produce the observed features. Thus our work argues for the existence of a liquid beneath Europa's surface. Our results might most easily be explained by the presence of a continuous liquid layer (the putative Europan ocean); this would concur with the findings of the Galileo magnetometer team. However, we cannot rule out the possibility that discrete liquid pockets provide injections of fluid closer to the surface.

Fagents, Sarah A.↗

Gravitational Effects on Distortion in Sintering

During sintering a powder compact gains strength through low-temperature interparticle bonding, usually induced by solid-state surface diffusion, followed by further strength contributions from high-temperature densification. In cases where a liquid phase forms, sintering densification is accelerated and shape retention is sustained while open pores remain and contribute capillary forces. Unfortunately, sintering densification requires the compact become thermally softened to a point where creep strain rates reach levels near 10(exp -2)/s when the liquid forms. On the other hand, thermal softening of the powder compact substantially reduces the strength at high temperatures. Therefore, the in situ strength evolution during sintering is a primary focus to separate compact densification (as required for high performance) with minimized distortion (as required for net-shaping). With respect to gravitation effects on distortion during sintering there are two points of substantial weakness - prior to significant interparticle bonding and during final pore closure. This research is focused on understanding the competition among interparticle neck growth, densification, thermal softening, grain boundary wetting, capillary effects associated with liquid wetting and residual porosity, and gravity. Most surprising is the apparent role of gravity, where the deviatoric stress acting on the powder structure induces skeletal formation that reduces distortion. In contrast with theory, microgravity samples exhibit more distortion yet fail to fully densify. Results are presented on the experimental concepts supporting an emerging model of sintering strength evolution that enables understanding of both distortion and densification. The experiments have relied on tungsten heavy alloys, various combinations of dihedral angle, pore size, initial porosity, liquid:solid ratio, and heating rates. On Earth, the dominant factor with respect to distortion is the starting body heterogeneity. Current modeling efforts are seeking some means to uniformly predict the distortion based on a starting pore structure heterogeneity parameter. Densification is largely unaffected by the initial pore structure, but distortion is highly variable, suggesting that nonuniform pore closure might be a significant parameter during sintering. With respect to flight experiments, plans include removal of the solid body forces acting on the solid grains, allowing stabilization of the pore structure and examination of the buoyancy effects with regard to distortion. In microgravity there is the surprising result that compacts do not densify, yet distort a factor that is contrary to all current sintering models. Densification without distortion during liquid phase sintering was achieved by manipulating microstructure and its evolution during sintering. Microstructure parameters such as the solid volume fraction, dihedral angle, initial porosity, and pore size were varied to measure densification and distortion behavior during LPS using W-Ni-Cu alloys. Green compacts were formed using ethylene-bis-stearamide as a pore-forming agent with the amount of polymer controlling the initial porosity. Different initial pore sizes were generated by varying the polymer particle size. Dihedral angle was varied by changing the Ni:Cu ratio in the alloys. Finally, the solid volume fraction was adjusted via the tungsten content. Distortion was quantified using profiles determined with a coordinate measuring machine to calculate a distortion parameter. Sintering results showed that solid volume fraction and dihedral angle are the dominant factors on densification and distortion during liquid phase sintering. Distortion decreases with increasing solid volume fraction and dihedral angle, while initial porosity and pore size have no observable effect on distortion at nearly full densification. Various strategies emerge to improve distortion control in liquid phase sintering.

German, Randall M.↗

Crystal Growth Rate Dispersion: A Predictor of Crystal Quality in Microgravity?

In theory macromolecular crystals grow through a process involving at least two transport phenomena of solute to the crystal surface: diffusion and convection. In absence of standard gravitational forces, the ratio of these two phenomena can change and explain why crystal growth in microgravity is different from that on Earth. Experimental evidence clearly shows, however, that crystal growth of various systems is not equally sensitive to reduction in gravitational forces, leading to quality improvement in microgravity for some crystals but not for others. We hypothesize that the differences in final crystal quality are related to crystal growth rate dispersion. If growth rate dispersion exists on Earth, decreases in microgravity, and coincides with crystal quality improvements then this dispersion is a predictor for crystal quality improvement. In order to test this hypothesis, we will measure growth rate dispersion both in microgravity and on Earth and will correlate the data with previously established data on crystal quality differences for the two environments. We present here the first crystal growth rate measurement data for three proteins (lysozyme, xylose isomerase and human recombinant insulin), collected on Earth, using hardware identical to the hardware to be used in microgravity and show how these data correlate with crystal quality improvements established in microgravity.

Kephart, Richard D.↗

Science Archives in the 21st Century: A NASA LAMBDA Report

Lambda is a thematic data center that focuses on serving the cosmic microwave background (CMB) research community. LAMBDA is an active archive for NASA's Cosmic Background Explorer (COBE) and Wilkinson Microwave Anisotropy Probe (WMAP) mission data sets. In addition, LAMBDA provides analysis software, on-line tools, relevant ancillary data and important web links. LAMBDA also tries to preserve the most important ground-based and suborbital CMB data sets. CMB data is unlike other astrophysical data, consisting of intrinsically diffuse surface brightness photometry with a signal contrast of the order 1 part in 100,000 relative to the uniform background. Because of the extremely faint signal levels, the signal-to-noise ratio is relatively low and detailed instrument-specific knowledge of the data is essential. While the number of data sets being produced is not especially large, those data sets are becoming large and complex. That tendency will increase when the many polarization experiments currently being deployed begin producing data. The LAMBDA experience supports many aspects of the NASA data archive model developed informally over the last ten years-that small focused data centers are often more effective than larger more ambitious collections, for example; that data centers are usually best run by active scientists; that it can be particularly advantageous if those scientists are leaders in the use of the archived data sets; etc. LAMBDA has done some things so well that they might provide lessons for other archives. A lot of effort has been devoted to developing a simple and consistent interface to data sets, for example; and serving all the documentation required via simple 'more' pages and longer explanatory supplements. Many of the problems faced by LAMBDA will also not surprise anyone trying to manage other space science data. These range from persuading mission scientists to provide their data as quickly as possible, to dealing with a high volume of nuisance (spam) messages. Because so many data center problems and solutions are common across individual data centers and disciplines it would be very valuable to establish some new systems of communication - such as informal email lists for administrators and developers. But resources are very limited, so new timeconsuming and inefficient mechanisms - like too-frequent and too-structured meetingsshould be avoided. Although there are great advantages to being small, agile and independent, there are also some areas where science data centers within and without NASA could be better coordinated - for the assignment of persistent identifiers; to encourage the early adoption of useful standards and technologies; etc. Some super-structure to facilitate such coordination might be beneficial as long as it doesn't begin to control the other work of the archives, and become a "methodology police". In this respect the CCSDS "Reference Model for an Open Archive Information System" is a little worrying. It may be that the closer a data center gets to following such a detailed prescription, the less effective it will become. It is much better to have an informal coordination process than a bureaucratic straight-jacket.

Butterworth, P.↗

Analysis of Nonlinear Shrinkage for the Bound Metal Deposition Manufacturing using Multi-scale Approach

We consider problem of nonlinear shrinkage of the metal part during bound metal deposition manufacturing on the ground and in zero-G. To analyze this problem we developed multi-scale physics-based approach that spans atomistic dynamics at the scale of nanoseconds and the full part shrinkage at the time scale of hours. Using this approach we estimated the key parameters of the problem including grain boundary width, coefficient of surface diffusion, initial redistribution of particles during debinding stage, micro-structure evolution from round particles to densely packed grains and corresponding change of the total and chemical free energy, and sintering stress. The introduced method was used to predict shrinkage at the level of two particles, filament cross-section, sub-model, and the whole green, brown, and metal parts. To further improve accuracy and reliability of the shrinkage predictions we propose concept of intelligent additive manufacturing of metal powders in space that combines the strengths of both physics-based and data-driven methods of analysis of AM.

bound metal deposition↗

On the Alleviation of Background Noise for the High-Lift Common Research Model Aeroacoustic Test

Microphone array measurements of the airframe noise from the High-Lift Common Research Model (CRM-HL) in the NASA Langley 14- by 22- Foot Subsonic Tunnel were initially hindered by extraneous noise sources. The steps taken to reduce the background noise in the open-jet test section for the aeroacoustic test are described in this paper. Adhesive-backed felt was used to attenuate noise resulting from the interaction of the test section shear layer with the collector and diffuser surfaces, scrubbing noise from the floor perforated panels, as well as an extraneous noise source produced near the junction of the model and the floor when the model was producing significant lift. The effects of the felt on noise attenuation and acoustic reflections are discussed. Following the CRM-HL test, scrubbing noise measurements from a floor basket with a perforated top panel were acquired in the Quiet Flow Facility to compare the performance of different perforated panel covers and their respective effects on the noise spectra. Aside from a smooth, hard wall, the felt cover was found to produce the minimum scrubbing noise of all the materials tested.

background noise↗

Multi-Scale Modelling of the Bound Metal Deposition Manufacturing of Ti6Al4V

Nonlinear shrinkage of the metal part during manufacturing by bound metal deposition, both on the ground and under microgravity, is considered. A multi-scale physics-based approach is developed to address the problem. It spans timescales from atomistic dynamics on the order of nanoseconds to full-part shrinkage on the order of hours. This approach enables estimation of the key parameters of the problem, including the widths of grain boundaries, the coefficient of surface diffusion, the initial redistribution of particles during the debinding stage, the evolution of the microstructure from round particles to densely-packed grains, the corresponding changes in the total and chemical free energies, and the sintering stress. The method has been used to predict shrinkage at the levels of two particles, of the filament cross-section, of the sub-model, and of the whole green, brown, and metal parts.

Nonlinear shrinkage↗

Homogeneity Study of ZrC, NbC, and TaC Binary Carbide Fuels for the Application of Nuclear Thermal Propulsion

In alignment with NASA and DARPA goals, efforts towards Nuclear Thermal Propulsion (NTP) have increased in recent years. As progress is made, a main challenge still exists; the fuel in an NTP system must survive the extreme environment experienced during operating conditions. Three fuel forms have been studied including a ceramic-metallic matrix, a ceramic-ceramic matrix, and solid solution carbides. Solid solution carbides were studied previously as a fuel for NTP and was shown to be a promising technology; however, the programs were canceled before demonstration in an NTP engine test. Of the refractory metal carbides of interest, zirconium carbide (ZrC), niobium carbide (NbC) and tantalum carbide (TaC) were studied. ZrC, NbC, and TaC powders were consolidated in monocarbide (ZrC, NbC, TaC) and bi-carbide (ZrC-NbC, ZrC-TaC, NbC-TaC) forms using spark plasma sintering (SPS), with 50-50 mol% compositions of the bi-carbides of interest. The time and temperature conditions to achieve a completely homogeneous solid solution for the mixed carbides is of interest for NTP fuel applications, since this homogeneity is considered to be essential for this fuel form. Homogeneity is typically not achieved during sintering, as surface diffusion (predominant for sintering to near ideal density) tends to occur at lower temperatures than bulk volumetric diffusion (required for solute interdiffusion to achieve a homogeneous solid solution). High temperature isochronal annealing was performed to identify the conditions to achieve a chemically homogeneous sample. The solute interpenetration vs annealing temperature was quantified using energy dispersion spectroscopy (EDS) in a scanning electron microscope (SEM). X-ray diffraction (XRD) was used to accurately measure the phase stability and lattice parameter as a function of annealing conditions. The diffusion data from each sample was then used to determine self-diffusion coefficients for interdiffusion of the Nb, Zr, and Ta solutes and compared to existing literature values. The minimum annealing conditions to achieve complete chemical homogeneity for each carbide was determined.

nuclear thermal propulsion↗

Effective Dielectric Passivation Scheme in Area-Selective Front/Back Poly-Si/SiOx Passivating Contact Solar Cells

Explored different dielectric passivation schemes on lifetime samples after removing poly-Si completely. Showed that SiNx/Al2O3 had the best passivation properties on SiOx/n+ c-Si in diffused surface. Applied SiNx/Al2O3 stack on poly-Si/SiOx passivating contact device and showed large improvement in Jsc, with best device efficiency of 21.8%. Future work: CV measurement of dielectric stacks to obtain Qf and Dit.

dielectric↗

Value Proposition of UV-Absorbers in PV Module Encapsulation

Various common crystalline silicon cell technologies were exposed to UVA radiation (1.24 Wm-2 nm-1 at 340 nm peak) on the front and back faces at 45 degrees Celsius for periods up to 3000 h, representing about 3 y of solar exposure in Phoenix, Arizona, USA. The resulting degradation of the open-circuit voltage and short-circuit current is presented. Of the various cell types examined, significant levels of degradation were seen in all cases. Less degradation was generally found after UV irradiation of cell fronts and older cell types, whereas a bifacial PERC type exposed on the rear showed about 25% degradation in short circuit current, attributable to lack of a diffused surface field. Selected cells were exposed to UV irradiation with the addition of long pass UV filters to replicate UV-absorbers in encapsulants. Modern cell designs are sensitive to UV-ID because of reduced or eliminated front and back surface field and increased dependence on high quality surface passivation. Single transformation of the independent variable (t, kW h/m^2) could be used to achieve a linear model of the data to extrapolate to 50 y. Solar Advisor Model (SAM) shows appropriate filtering of UV-irradiation can improve LCOE and net present value of plant. Some advanced cell types are seen to be UV-resistant (cell level solutions also exist). Solutions therefore exist on the cell, glass, and encapsulant level. Changes over time in each of these would also need to be considered (solarization, encapsulant browning...).

ENGINEERING,SOLAR ENERGY↗

Lithium extraction composite for recovery of lithium from brines, and process of using said composition

A lithium extraction composite comprising: (i) a porous support and (ii) particles of a lithium-selective sorbent material coated on at least one surface of the support, wherein the support has a planar membrane, fiber (or rod), or tubular shape. A method for extracting and recovering a lithium salt from an aqueous solution by use of the above-described composition is also described, the method comprising (a) flowing the aqueous source solution through a first zone or over a first surface of the lithium extraction composite to result in selective lithium intercalation in the lithium-selective sorbent material in the first zone or first surface; and (b) simultaneously recovering lithium salt extracted in step (a) from said lithium-selective sorbent material by flowing an aqueous stripping solution through a second zone or over a second surface of the lithium extraction composite in which lithium ions from the first zone or first surface diffuse.

Bhave, Ramesh R.↗

Effect of metal encapsulation on bulk superconducting properties of niobium thin films used in qubits

Niobium metal occupies nearly 100% of the volume of a typical 2D transmon device. While the aluminum Josephson junction is of utmost importance, maintaining quantum coherence across the entire device means that pair-breaking in Nb leads, capacitive pads, and readout resonators can be a major source of decoherence. The established contributors are surface oxides and hydroxides, as well as absorbed hydrogen and oxygen. Metal encapsulation of freshly grown surfaces with non-oxidizing metals, preferably without breaking the vacuum, is a successful strategy to mitigate these issues. While the positive effects of encapsulation are undeniable, it is important to understand its impact on the macroscopic behavior of niobium films. We present a comprehensive study of the bulk superconducting properties of Nb thin films encapsulated with gold and palladium/gold, and compare them to those of bare Nb films. Magneto-optical imaging, magnetization, resistivity, and London and Campbell penetration depth measurements reveal significant differences in encapsulated samples. Both sputtered, and epitaxial Au-capped films exhibit the highest residual resistivity ratio and superconducting transition temperature, as well as the lowest upper critical field, London penetration depth, and critical current. These results are in good agreement with the microscopic theory of anisotropic normal and superconducting states of Nb. We conclude that pair-breaking in the bulk of niobium films, driven by disorder throughout the film rather than just at the surface, is a significant source of quantum decoherence in transmons. We also conclude that gold capping not only passivates the surface but also affects the properties of the entire film, significantly reducing the scattering rate due to defects likely induced by surface diffusion if the film is not protected immediately after fabrication.

Datta, Amlan [Ames Lab; Iowa State U.]↗

Cooperative mechanisms behind nanoscale smoothing on metal surfaces: From adatom diffusion to step nucleation

Many technologies require stable or metastable surface morphology. Here, in this paper we study the factors that control the metastability of a common feature of rough surfaces: “hillocks.” We use low energy electron microscopy to follow the evolution of the individual atomic steps in hillocks on Pd(111). We show that the uppermost island in the stack often adopts a static, metastable configuration. Modeling this result shows that the degree of the metastability depends on the configuration of steps dozens of atomic layers lower. Our model allows us to link surface metastability to the atomic processes of surface evolution.

Fernandes Cauduro, Andre Luis↗

Application of the MOS C-V technique to determine impurity concentrations and surface parameters on the diffused face of silicon solar cells

An experimental and theoretical investigation of the feasibility of using the MOS C-V (capacitance-voltage) technique to determine impurity and surface state concentrations on the diffused face of Si solar cells with Ta2O5 coatings. Impurity concentration 10 A from the diffused surface is found to be 2.9 times 10 to the 20th power per cu cm. Charge density in surface and oxide states is 2.1 times 10 to the 13th power per sq cm. These data agree with theoretical predictions.-

Weinberg, I.↗