Point Defect Properties from Metal Diffusion Experiments — What Does the Data Really Tell Us?

1997 ◽  
Vol 469 ◽  
Author(s):  
Srinivasan Chakravarthit ◽  
Scott T. Dunham
Keyword(s):  
Point Defect ◽  
Equilibrium Concentration ◽  
Simulation Software ◽  
Published Data ◽  
Vacancy Diffusion ◽  
Metal Diffusion ◽  
Float Zone ◽  
Equilibrium Concentrations ◽  
Parameter Values ◽  
Carbon Concentrations

Point defect properties, including diffusivities and equilibrium concentrations for both interstitials and vacancies, are commonly extracted from metal diffusion experiments, and these values are widely used in process simulation software. However, in many cases, these parameter values were extracted using oversimplified models which ignore interactions between interstitial and vacancy diffusion mechanisms. Questions about the accuracy of these parameters have come from ab-initio defect calculations which conclude that vacancies diffuse faster than interstitials, in contrast with published reports on metal diffusion which find vacancies diffuse much more slowly than interstitials. We have reanalyzed published data for zinc and platinum diffusion and find that it is possible to match all of the data using fast vacancy diffusivity. The most direct evidence for slow vacancy diffusion (and a high equilibrium concentration) comes from platinum diffusion experiments. However, we are able to reproduce these results with fast V diffusion and carbon/interstitial clustering, using carbon concentrations typical of Czochralski and float zone silicon (1016cm−3). We evaluate the effectiveness of metal diffusion experiments in determining point defect parameters, and find that it is not possible to reliably determine both diffusivities and equilibrium concentrations for both interstitials and vacancies from metal diffusion results.

Thermal Equilibrium Concentrations and Effects of Ga Vacancies in n-TYPE GaAs

1993 ◽  
Vol 300 ◽  
Author(s):  
Teh Y. Tan ◽  
Homg-Ming You ◽  
Ulrich M. Gösele
Keyword(s):  
Temperature Dependence ◽  
Point Defect ◽  
Thermal Equilibrium ◽  
Quantitative Data ◽  
Equilibrium Concentration ◽  
Negative Temperature ◽  
Positive Temperature ◽  
Self Diffusion ◽  
N Doping ◽  
Equilibrium Concentrations

ABSTRACTWe have calculated the thermal equilibrium concentrations of the various Ga vacancy species in GaAs. That of the triply-negatively-charged Ga vacancy, V3Ga has been emphasized, since it dominates Ga self-diffusion and Ga-Al interdiffusion under intrinsic and ndoping conditions, as well as the diffusion of Si donor atoms occupying Ga sites. Under strong n-doping conditions, the thermal equilibrium V3Ga concentration, CeqvGa.3−(n), has been found to exhibit a temperature independence or a negative temperature dependence, in the sense that the CeqvGa.3−(n) value is either unchanged or increases as the temperature is lowered. This is contrary to the normal positive temperature dependence of point defect theerqmal equilibrium concentrations, which decreases as the temperature is lowered. This CeqvGa.3−(n) property provides explanations to a number of outstanding experimental results, either requiring the interpretation thatV3−Ga has attained its thermal equilibrium concentration at the onset of each experiment, or requiring mechanisms involving point defect non-equilibrium phenomena. Furthermore, there exist also a few quantitative data which are in agreement with the presently calculated results.

The Effect of Carbon/Self-Interstitial Clusters on Carbon Diffusion in Silicon Modeled by Kinetic Monte Carlo Simulations

2000 ◽  
Vol 610 ◽  
Author(s):  
R. Pinachoa ◽  
M. Jaraíz ◽  
H. J. Gossmann ◽  
G. H. Gilmer ◽  
J. L. Benton ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Kinetic Monte Carlo ◽  
Carbon Diffusion ◽  
Interstitial Concentration ◽  
Carbon Structures ◽  
Kinetic Monte Carlo Simulations ◽  
Equilibrium Concentrations ◽  
Low Solubility ◽  
Carbon Concentrations ◽  
Diffusion Profiles

AbstractA new model for carbon diffusion in silicon that explains carbon diffusion during annealing at 850°C and 900°C in superlattice carbon structures grown by MBE is implemented using the Monte Carlo atomistic simulator DADOS. Carbon concentrations in the delta layers are 2×1020 cm−3, exceeding by far the solid solubility. The simple kick-out mechanism which incorporates the well established values of the product of diffusivity and equilibrium concentrations of intrinsic point defects and in-diffusion experiments of carbon in silicon does not explain the observed C diffusion profiles. A more detailed analysis of the experiments shows that, in order to fit them, a more unstable Ci is required. Therefore, we include the formation of clusters in the simulations. The formation of carbon/Si self-interstitial clusters promotes the premature break-up of Ci and the increase of the Si self-interstitial concentration in the carbon rich regions and, consequently, provides a better fit to the experiments. The low solubility of carbon in silicon at the annealing temperatures explains why these clusters are formed, even under conditions where the self-interstitial concentration is below the equilibrium value.

Model of rice (Oryza sativa) yield reduction as a function of weed interference

Weed Science ◽  
1997 ◽  
Vol 45 (2) ◽  
pp. 218-224 ◽  
Author(s):  
Karl W. VanDevender ◽  
Thomas A. Costello ◽  
Roy J. Smith
Keyword(s):  
Weed Management ◽  
Management Strategies ◽  
Economic Assessment ◽  
Richards Equation ◽  
Yield Reduction ◽  
Published Data ◽  
Weed Species ◽  
Individual Parameter ◽  
Alternative Weed Control ◽  
Parameter Values

Economic assessment of weed management strategies in rice is dependent upon a quantitative estimate of the yield impact of a given weed population. To assist rice producers in making such assessments, a mathematical model was developed to predict rice yield reduction as a function of weed density and duration of interference. The nonlinear empirical model was a unique 3-dimensional adaptation of the Richards equation with 4 parameters. Using published data, individual parameter values were fitted for each of 6 weed species interfering with either conventional or semi-dwarf statured rice cultivars. The functional form of the equation produced surfaces that were qualitatively consistent with available data and experience regarding rice-weed biology. Hence, predictions from the model should be useful and reliable in assessing the economic impact of weeds and in determining the feasibility of alternative weed control treatments for various field scenarios.

scholarly journals Tunable Mn Oxidation State and Redox Potential of Birnessite Coexisting with Aqueous Mn(II) in Mildly Acidic Environments

Minerals ◽  
2020 ◽  
Vol 10 (8) ◽  
pp. 690
Author(s):  
Juan Liu ◽  
Yixiao Zhang ◽  
Qian Gu ◽  
Anxu Sheng ◽  
Baogang Zhang
Keyword(s):  
Oxidation State ◽  
Organic Pollutant ◽  
Equilibrium Concentration ◽  
Aquatic Environments ◽  
Oxidation Potentials ◽  
Average Oxidation State ◽  
Subsurface Environments ◽  
Equilibrium Concentrations ◽  
Kinetics Of ◽  
Manganese Oxide Mineral

As the dominant manganese oxide mineral phase in terrestrial and aquatic environments, birnessite plays an important role in many biogeochemical processes. The coexistence of birnessite with aqueous Mn2+ is commonly found in the subsurface environments undergoing Mn redox cycling. This study investigates the change in Mn average oxidation state (AOS) of birnessite after reaction with 0.1–0.4 mM Mn2+ at pH 4.5–6.5, under conditions in which phase transformation of birnessite by Mn2+ was not detectable. The amount of Mn2+ uptake by birnessite and the equilibrium concentration of Mn(III) proportionally increased with the initial concentration of Mn2+. The Mn AOS of birnessite particles became 3.87, 3.75, 3.64, and 3.53, respectively, after reaction with 0.1, 0.2, 0.3, and 0.4 mM Mn2+ at pH 5.5. Oxidation potentials (Eh) of birnessite with different AOS values were estimated using the equilibrium concentrations of hydroquinone oxidized by the birnessite samples, indicating that Eh was linearly proportional to AOS. The oxidation kinetics of bisphenol A (BPA), a model organic pollutant, by birnessite suggest that the logarithms of surface area-normalized pseudo-first-order initial rate constants (log kSA) for BPA degradation by birnessite were linearly correlated with the Eh or AOS values of birnessite with AOS greater than 3.64.

Formulas for the Calculation of Temperatures and Concentrations of Carbon Responsible to the Parar Equilibrium of the Main Phases in Medium Sheet Steels

2019 ◽  
Vol 822 ◽  
pp. 44-52
Author(s):  
Pavel Zhitelev ◽  
Darya Serzhenko
Keyword(s):  
Chemical Composition ◽  
Reference Data ◽  
Calculated Data ◽  
Medium Carbon ◽  
Sheet Steels ◽  
Thermo Calc Software ◽  
Temperature Ranges ◽  
Analytical Formulas ◽  
Equilibrium Concentrations ◽  
Carbon Concentrations

With the help of the Thermo-Calc software package, arrays of calculated data were created for carbon concentrations in ferrite and austenite, corresponding to the para-equilibrium of these phases and their para-equilibrium with cementite, as well as for the corresponding temperatures A1 and A3. Marked arrays were obtained in wide temperature ranges for ranges of carbon concentrations and the most important substitution alloying elements (Mn; Si; Cr; Ni; Mo), covering the respective ranges for medium carbon and moderately alloyed steels. Analytical formulas were developed on the basis of the reference data arrays for calculating para-equilibrium concentrations of carbon in ferrite and austenite (depending on temperature and chemical composition), as well as temperatures A1 and A3 (depending on chemical composition), which allow to reproduce with high accuracy the results obtained using Thermo-Calc.

scholarly journals The asymptotic iteration method for the angular spheroidal eigenvalues with arbitrary complex size parameter c

2006 ◽  
Vol 84 (2) ◽  
pp. 121-129 ◽  
Author(s):  
T Barakat ◽  
K Abodayeh ◽  
B Abdallah ◽  
O M Al-Dossary
Keyword(s):  
Excellent Agreement ◽  
Iteration Method ◽  
Full Range ◽  
Numerical Results ◽  
Asymptotic Iteration Method ◽  
Published Data ◽  
Size Parameter ◽  
Arbitrary Complex ◽  
Parameter Values

The asymptotic iteration method is applied to calculate the angular spheroidal eigenvalues [Formula: see text] (c) with arbitrary complex size parameter c. It is shown that the numerical results obtained for [Formula: see text] (c) are all in excellent agreement with the available published data over the full range of parameter values [Formula: see text] m, and c. Some representative values of [Formula: see text] (c) for large real c are also given.PACS No.: 02.70.–c.

Assessment of the Public Radiation Protection and Economic Activity Safety in the Area of the Developed Uranium Deposit

2020 ◽  
Vol 65 (2) ◽  
pp. 11-16
Author(s):  
A. Titov ◽  
N. Shandala ◽  
D. Isaev ◽  
M. Semenova ◽  
V. Seregin ◽  
...  
Keyword(s):  
Economic Activity ◽  
Equilibrium Concentration ◽  
Dose Equivalent ◽  
Economic Activities ◽  
The Public ◽  
Equivalent Rate ◽  
Ambient Dose Equivalent ◽  
Equilibrium Concentrations ◽  
Effective Doses ◽  
The Town

Purpose: To analize radiation situation in the vicinity of mine number one of the Lermontov Production Association “Almaz” in the areas of the public residence and economic activities. Material and methods: During the study, methods of pedestrian gamma surveys with a portable spectrometric complex MKS-01A “Multirad-M” and short-term measurements of radon equivalent equilibrium concentration with aerosol alpha radiometer RAA-20P2 “Poisk” were used. Results: Along the main roads used by the population for walks and rest, the values of the gamma ambient dose equivalent rate vary within the range between 0.10 and 0.86 μSv/h. Local areas with excess of the remediation criterion (0.6 μSv / h), established by the Sanitary Rules for elimination, conservation and changing functions of facilities for radioactive ore mining and milling (SP LKP-91), are located on the ascent of Beshtau Mountain from the side of the Town of Pyatigorsk (near tunnels and dumps). Along other routes, the remediation criteria are met. External effective doses to the population in a single passage of the routes vary from 1.0 to 1.6 µSv. The highest contribution to the dose from manmade radiation does not exceed 30 %. The highest external doses (4.3 μSv at the contribution of manmade radiation about 70 %) can be realized when resting near the most contaminated parts of the dumps or tunnel mouths. The equivalent equilibrium concentrations of radon progenies in air along the routes did not exceed 60 Bq/m3. The effective internal dose due to inhalation intake of radon and its progenies will not exceed 3 μSv when single passing routes. Conclusions: In the main areas of the residence and economic activity of the population in the vicinity of mine number 1 , the radiation situation at some locations does not comply with the requirements of the SP LKP-9, however, it does not pose a threat to public health.

Adsorption of DL-alanine by allophane: effect of pH and unit particle aggregation

Clay Minerals ◽  
1999 ◽  
Vol 34 (2) ◽  
pp. 233-238 ◽  
Author(s):  
H. Hashizume ◽  
B. K. G. Theng
Keyword(s):  
Adsorption Isotherms ◽  
Linear Increase ◽  
Particle Aggregation ◽  
Published Data ◽  
Effect Of Ph ◽  
Linear Rise ◽  
Equilibrium Concentrations ◽  
Ph Dependent ◽  
High Concentrations

AbstractThe adsorption of DL-alanine at pH 4, 6 and 8 by a soil allophane has been determined. Two sets of experiments were carried out: (1) in which the allophane had been kept in a moist state throughout; and (2) in which the mineral had previously been dried at 50°C. In both instances, the adsorption isotherms showed three distinct regions as the concentration of alanine in solution was increased: (1) an initial, nearly linear, rise at low equilibrium concentrations; (2) a levelling off to a plateau at intermediate concentrations; and (3) a steep linear increase at high concentrations. For comparable concentrations of alanine in solution, adsorption decreased in the order pH 6 > pH 8 > pH 4. Irrespective of pH, however, more alanine was adsorbed by the ‘wet’ allophane than by its ‘dry’ counterpart. These observations are interpreted in terms of the morphology and aggregation of allophane unit particles together with the pH-dependent charge characteristics of allophane and alanine. The results are compared with published data on the adsorption of alanine by montmorillonite.

Phosphate sorption by soils as a measure of the phosphate requirement for pasture growth

1967 ◽  
Vol 18 (4) ◽  
pp. 601 ◽  
Author(s):  
PG Ozanne ◽  
TC Shaw
Keyword(s):  
Equilibrium Concentration ◽  
Correlation Coefficients ◽  
Laboratory Method ◽  
Phosphate Sorption ◽  
Soil Mixing ◽  
Equilibrium Concentrations ◽  
The Relationship ◽  
Pasture Plants ◽  
Different Soils

Development of a laboratory method for predicting the phosphate requirements of pasture plants, in pounds phosphorus per acre, is described. Measurement of the phosphate sorption by soil at a standard equilibrium concentration was used. Predictions made by using this method in the following year on different soils accounted for over 85% of the variability in phosphate requirement. A good correlation between phosphate sorbed and phosphate required was found. The relationship was linear over the range 0–500 p.p.m. of sorbed P. While different sampling depths, equilibrium concentrations, and degree of soil mixing affected the relationship, it remained linear and the correlation coefficients close to 0.9.

An interpretative model of carbon and nitrogentransformations applied to a residue incubation experiment

1998 ◽  
Vol 49 (3) ◽  
pp. 537 ◽  
Author(s):  
B. R. Trenbath ◽  
A. J. Diggle
Keyword(s):  
Organic Matter ◽  
Plant Residues ◽  
Published Data ◽  
Incubation Experiment ◽  
Nitrogen Immobilisation ◽  
Carbon Nitrogen Ratio ◽  
Nitrogen Ratio ◽  
Parameter Values ◽  
Interpretative Model ◽  
Residue Series

A simple model of 3 equations was devised to simulate the rates through time of gross mineralisation of nitrogen, nitrogen immobilisation, and microbial respiration relating to individual inputs into soil of plant residues of any age or type. Using published data from an incubation experiment carried out in Iowa, we applied the model to a residue newly added to soil, to the original soil organic matter (SOM), and to a mixture of these. Manipulation of the model allowed the derivation from the Iowa data of a net mineralisation index which seemed to summarise the nitrogen release characteristics of the residue in all treatments of the experiment. The equations and parameter values developed for the added residue were applied to SOM using results from unamended soil. The balance between respiration and mineralisation was found not to correspond to that expected for old organic matter near an equilibrium carbon/nitrogen ratio. Rate constants of mineralisation and respiration for SOM were adapted to overcome this apparent anomaly. To model the dynamics SOM and added residue simultaneously, the 2 sets of 3 equations were applied in parallel to 4 extreme treatments in the with-residue series (lowest and highest nitrate levels with low and high residue additions). To achieve the fits presented, only 2 of the 12 parameters required in each set of equations needed to differ between the set for SOM and that for added residue. The model reproduces well most of the primary Iowa data and also some derived results. Use of the model helped to interpret divergences between simulations and data.

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