Model For Composition Dependence Research Articles

Distribution of REE between amphibole and pyroxenes in the lithospheric mantle: An assessment from the lattice strain model

Abstract Amphibole and pyroxenes are the main reservoirs of rare earth elements (REEs) in lithospheric mantle that has been affected by hydrous metasomatism. In this study, we developed semi-empirical models for REE partitioning between orthopyroxene and amphibole and between clinopyroxene and amphibole. These models were formulated on the basis of parameterized lattice strain models of mineral–melt REE partitioning for orthopyroxene, clinopyroxene, and amphibole, and they were calibrated using major element and REE data of amphibole and pyroxenes in natural mantle samples from intraplate setting. The mineral–melt REE partitioning models suggest that amphibole is not in equilibrium with coexisting pyroxenes in the mantle samples, and that the amphibole crystallized at a lower temperature than that of the pyroxenes. We estimated the apparent amphibole crystallization temperature using major element compositions of the amphibole and established temperature- and composition-dependent models that can be used to predict apparent pyroxene–amphibole REE partition coefficients for amphibole-bearing peridotite and pyroxenite from intraplate lithospheric mantle. Apparent pyroxene–amphibole REE partition coefficients predicted by the models can be used to infer REE contents of amphibole from REE contents of coexisting pyroxenes. This is especially useful when the grain size of amphibole is too small for trace element analysis.

An ab-initio study on the thermodynamics of disulfide, sulfide, and bisulfide incorporation into apatite and the development of a more comprehensive temperature, pressure, pH, and composition-dependent model for ionic substitution in minerals

AbstractThe mineral apatite, Ca10(PO4)6(F,OH,Cl)2, incorporates sulfur (S) during crystallization from S-bearing hydrothermal fluids and silicate melts. Our previous studies of natural and experimental apatite demonstrate that the oxidation state of S in apatite varies systematically as a function of oxygen fugacity (fO2). The S oxidation states –1 and –2 were quantitatively identified in apatite crystallized from reduced, S-bearing hydrothermal fluids and silicate melts by using sulfur K-edge X-ray absorption near-edge structure spectroscopy (S-XANES) where S 6+/ΣS in apatite increases from ~0 at FMQ-1 to ~1 at FMQ+2, where FMQ refers to the fayalite-magnetite-quartz fO2 buffer. In this study, we employ quantum-mechanical calculations to investigate the atomistic structure and energetics of S(-I) and S(-II) incorporated into apatite and elucidate incorporation mechanisms.One S(-I) species (disulfide, S22−) and two S(-II) species (bisulfide, HS−, and sulfide, S2−) are investigated as possible forms of reduced S species in apatite. In configuration models for the simulation, these reduced S species are positioned along the c-axis channel, originally occupied by the column anions F, Cl, and OH in the end-member apatites. In the lowest-energy configurations of S-incorporated apatite, disulfide prefers to be positioned halfway between the mirror planes at z = 1/4 and 3/4. In contrast, the energy-optimized bisulfide is located slightly away from the mirror planes by ~0.04 fractional units in the c direction. The energetic stability of these reduced S species as a function of position along the c-axis can be explained by the geometric and electrostatic constraints of the Ca and O planes that constitute the c-axis channel.The thermodynamics of incorporation of disulfide and bisulfide into apatite is evaluated by using solid-state reaction equations where the apatite host and a solid S-bearing source phase (pyrite and Na2S2(s) for disulfide; troilite and Na2S(s) for sulfide) are the reactants, and the S-incorporated apatite and an anion sink phase are the products. The Gibbs free energy (ΔG) is lower for incorporation with Na-bearing phases than with Fe-bearing phases, which is attributed to the higher energetic stability of the iron sulfide minerals as a source phase for S than the sodium sulfide phases. The thermodynamics of incorporation of reduced S is also evaluated by using reaction equations involving dissolved disulfide and sulfide species [HnS(aq)(2−n) and HnS(aq)(2−n); n = 0, 1, and 2] as a source phase. The ΔG of S-incorporation increases for fluorapatite and chlorapatite, and decreases for hydroxylapatite, as these species are protonated (i.e., as n changes from 0 to 2). These thermodynamic results demonstrate that the presence of reduced S in apatite is primarily controlled by the chemistry of magmatic and hydrothermal systems where apatite forms (e.g., an abundance of Fe; solution pH). Ultimately, our methodology developed for evaluating the thermodynamics of S incorporation in apatite as a function of temperature, pH, and composition is highly applicable to predicting the trace and volatile element incorporation in minerals in a variety of geological systems. In addition to solid-solid and solid-liquid equilibria treated here at different temperatures and pH, the methodology can be easily extended to different pressure conditions by just performing the quantum-mechanical calculations at elevated pressures.

Importance of the Relative Static Permittivity in electrolyte SAFT-VR Mie Equations of State

The influence and importance of the relative static permittivity (RSP) in electrolyte equations of state is examined for the case of aqueous sodium chloride. Using the SAFT-VR Mie model, the Debye-Hückel (DH) or Mean-Spherical Approximation (MSA) terms, as well as the Born-solvation term, are used to formulate an electrolyte equation of state. The RSP is obtained from a variety of models, each differing in their dependencies; we consider constant, temperature-, density- and composition-dependent models. For a fair comparison between different combinations of electrostatic and RSP models, all ion-related parameters are obtained a priori. A novel combining rule is proposed to obtain the unlike parameters between solvents and ions; its reliability is examined for a variety of electrolyte systems. We also compare its performance relative to parameterised electrolyte models. Both the DH and MSA terms yield similar results for almost all properties and conditions. The RSP models used have the more-significant impact. Liquid densities and solvent saturation pressures showed limited changes between RSP models whereas osmotic coefficients, mean ionic activity coefficients and carbon dioxide solubilities observed drastically different behaviour. Analysing the contributions of the various terms to the activities of each species in an electrolyte mixture reveals an important balance between the Born-solvation and the DH or MSA terms where the RSP models have a significant influence over this balance, particularly when these carry a solvent- or ion-composition dependence.

Thermodynamic database of zeolites and new method of their thermodynamic properties evaluation for a wide temperature range

A database on the thermodynamic properties of zeolites has been created. It contains the published raw experimental measurements of heat capacities, heat contents and enthalpies of formation for 46 zeolites at T=0−1000K. This is about 1/3 higher than in previous reviews and databases. The zeolites from the database consist from H2O and oxides of Li, Na, K, Tl, Ca, Mg, Sr, Ba, Fe, Al and Si. All experimental data were approximated by sums of Einstein-Planck functions in the entire temperature range. Heat capacity anomalies were described by addition of extra terms to the sum. A new additive composition dependent model for estimation of thermodynamic properties of zeolites was suggested. It's based on the collected data and is valid for a wide temperature range.

Atomic channel occupation in disordered η-Al5Fe2 and in two of its low-temperatures phases, η″ and η‴

High-temperature, disordered η-Al5Fe2 intermetallic and its low-temperature long-range ordered structures have been investigated in the whole homogeneity range from 70.6 to 73.0 at.% Al based on selected area electron diffraction data and powder X-ray diffraction data. Using these data, the channel site occupation in the disordered η phase has been revised and a composition-dependent model with mixed occupation of the channels by both Al and Fe atoms was derived. It leads to an average number of atoms per channel and unit cell of approx. 1.5 in the whole homogeneity range. Below about 350 °C, four different phases exhibiting long-range order of the channel atoms appear to exist. Here the atomic ordering in the Al-poorest and Al-richest of these low-temperature phases, η″ and η‴ is reported. Both these phases can be characterized as incommensurately modulated composite crystal structures. Thereby, in both phases, the first composite subsystem contains atoms of the framework structure generating channels which are filled by atoms described by the second composite subsystem. The subsystems of the η″ phase have orthorhombic superspace groups Xmcm(00g)0s0 and Immm(00g)0s0 keeping the basic metric of the parent η phase. The subsystems of the η‴ can be described by the monoclinic superspace groups P21/c(0b0)00 and P21/c(0b0)s0 providing a lattice correspondence am = 1/2(a+b), bm = c and cm = a+b to the orthorhombic parent η phase. Although the number of atoms per channel is approx. 1.5 in η″ and η‴ phases, the channels are differently correlated with each other which is attributed to different Fe content in the channels inherited from the channel occupation in the disordered η phase.

Properties of Helium bubbles in Fe and FeCr alloys

We investigate three aspects of He that are relevant for its behavior in FeCr alloys. (i) the EOS of pure He, as an auxiliary element to relate pressure and density inside a bubble; (ii) He bubbles in FeCr alloys, to explore the influence of Cr as solute and at α′ precipitates on the He precipitation behavior; (iii) the growth mechanism of a He bubble in Fe and Fe 15 at% Cr under the particular conditions of a He-rich and vacancy poor environment. This last case represents an extreme situation that reveals the maximum pressures that can be achieved by a bubble before the matrix yields. We observe the emission of interstitial dislocation loops as the mechanisms by which the bubble creates room to host the He atoms. We use molecular dynamics and Monte Carlo computer simulations based on a new ternary FeCr–He empirical potential, which is an extension of our previous composition-dependent model for FeCr (A. Caro et al., Phys. Rev. Lett. 95 (2005) 075702).

Composition dependent model for the prediction of syngas ash deposition in turbine gas hotpath

An improved physical model to predict flyash deposition is developed and discussed in this paper. This model differs from its predecessor ( Rozati et al., in press; Sreedharan and Tafti, 2009) by accounting for deposition of syngas ash particles below the ash softening temperature. The modified deposition model is based on the critical viscosity approach. To test this model, deposition of ash particles impacted on a flat, 45° wedge shape geometry is computed and the results obtained from the numerical model are compared to Crosby et al. (2007). Large Eddy Simulation (LES) is used to model the flow field and flyash particles are modeled using a discrete Lagrangian framework. Results quantify deposition for 4 μm particles of various ash composition samples. Most of the deposition occurs at the stagnation region of the target plate. At 1456 K, out of all the ash samples considered in this study, WY and ND ash sample show the highest capture efficiency (15%) and KL1 ash sample exhibits the lowest capture efficiency (0.02%). In general, capture efficiencies for all ash samples followed an exponential trend with temperature. Additionally, this model is also compared to results obtained from the flat plate deposition experiments conducted here at Virginia Tech using PVC particles ( Wood et al., 2010). In the case of PVC particles, the sticking probability in the deposition model assumed an exponential increase in deposition rate with temperature and was calibrated with one experimental data point. The results obtained from this model for PVC particles showed excellent agreement with the experimental measurements over a range of temperatures.

Particle size dependence of the elastic modulus of particulate filled PMMA near its Tg

Models for composition dependence of elastic modulus of particulate filled polymers inherently assume modulus of the matrix independent of particle content and size. In this letter, experimental evidence is presented for existence of a critical particle size below which elastic modulus of the matrix becomes strongly dependent on the particle content due to the extensive chain stiffening. It is also suggested that below the critical particle size, specific interface area should replace volume fraction as the structural variable.

Rheology of vegetable oil analogs and triglycerides

AbstractThe rheological properties of two complex mixtures of short‐chain triglycerides were experimentally determined. Dynamic or absolute viscosities of the mixtures were measured for shear rates of 0.32 to 64.69 s−1 at temperatures between 25 and 80°C. The compositions of the mixtures were based on the oil of the plant species Cuphea viscosissima VS‐320, a natural source of short‐chain triglycerides. The dynamic viscosities of these mixtures were compared to those of a traditional vegetable oil (peanut oil) and diesel fuel. The results of this comparison were used to make estimates of the performance of such triglyceride mixtures as diesel fuel substitutes, since viscosity can be a key indicator of fuel performance for possible substitute diesel fuels. The crystallization temperatures of these two mixtures were also determined experimentally, and the effects of crystallization on fuel performance were projected. Additionally, the dynamic viscosities of pure triglycerides from C6∶0 to C18∶0 at 75°C were plotted vs. chain length. These viscosities were measured at high shear rates (>6 s−1) where dynamic viscosity is shear‐independent. An obvious trend in the relationship between triglyceride chain length and viscosity was observed. A second‐order regression was used to obtain an equation for this relationship. This equation was used as a model for composition dependence of viscosity. This model was applied to the viscosities of the triglyceride mixtures examined here. There was good agreement between the model and the actual, measured viscosity values determined in this study.

An attempt to model the dielectric function in II-VI ternary compounds and

The dielectric function \(\) of II-VI ternaries is described by fitting experimental results at room temperature to three different models. For each individual composition, \(\) variations with photon energy E are well reproduced with only four harmonic oscillators. The model dielectric function (MDF) of Adachi which is linked to the band structure does not give better results in the description of \(\) and its derivatives are not correctly reproduced. The MDF model of Kim et al. lead to good descriptions both of \(\) and its derivatives in all the spectral range considered, and it appears the most powerful model at the present time. We have not fully succeeded in building a composition dependent model for these bulk semiconductors. The analysis of this failure reveals that, though the materials appear good, their unknown densities of defects appear uncorrelated with the composition of the ternaries. These non controlled defect densities lead mainly to erratic deviations of the broadenings near critical transitions. Though relatively small these erratic deviations on the broadenings prevent the set up of a precise composition dependent model. \(\) variations are also calculated below the fundamental gap in HgZnTe and CdZnTe. Zero frequency \(\) values are compared with known experimental results. The large variation of \(\) with composition x in \(\) prevents the revealing of the part of \(\) due to the defects. In return, the effect of the defects on the crystal polarizability is evidenced in \(\) where the variation of \(\) with x is small. This leads us to propose that the most probable values of \(\) are near 7.1 for CdTe and 6.75 for ZnTe.

A temperature-dependent model for the complex dielectric function of GaAs

In this work, we discuss a temperature-dependent model for the complex dielectric function for GaAs valid for the temperature range 31°C ≤ T ≤ 634°C. We describe our model, which is an extension of the critical point parabolic band method. This is a phenomenological method which is based on the physical processes occurring in the semiconductor, and has been previously demonstrated for composition-dependent models of the dielectric function for lattice-matched materials systems. We demonstrate the quality of the model in fitting optical data for individual temperatures, and compare our results to other established models. The data used for each fitting ranges from 1.25 to 4.5 eV. Using results obtained from the individual fits, we generate a temperature-dependent model that is valid for the range of temperatures given above. Also, we show how this model can be used to accurately determine the temperature (±2.3°C) of a material whose dielectric response has been obtained but was not included when generating the model.

A composition-dependent model for the complex dielectric function of In1 xGaxAsyP1− y lattice-matched to InP

Accurate and numerically efficient models for the complex dielectric function vs wavelength and material characteristics are essential for the use of nondestructive optical techniques such as spectroscopic ellipsometry or reflectometry. These optical techniques are commonly used for real-time and run-to-run monitoring and control of growth and etch processes to determine a material's composition and thickness. In this work, we discuss an improved composition-dependent model for the complex dielectric function for lattice-matched In1-xGaxAsyP1-y/InP systems valid over the entire composition range 0 ≤ y ≤ 1. We describe our model, which is an extension of the critical point parabolic band method and is based on the model proposed by Charles Kim et al. for the AxGa1-x/GaAs system. We demonstrate the quality of the model in fitting optical data for individual compositions and compare our results to other established models including the harmonic oscillator approximation and the model of Adachi. Using results obtained from the individual fits, we generate a composition-dependent model that is valid for the entire range of lattice-matched compositions. Also, we show how this model can be used to accurately determine the composition (±0.01) of an unknown material whose dielectric response has been obtained using spectroscopic ellipsometry or a similar technique.