Linear Function Of Composition Research Articles

PHASE RELATIONS AND CHARACTERIZATION OF SOLID SOLUTIONS IN THE SnBi2Te4–PbBi2Te4 AND SnBi4Te7–PbBi4Te7 SYSTEMS

Phase equilibria in SnBi2Te4¬–PbBi2Te4 and SnBi4Te7–PbBi4Te7 systems were studied using differential thermal analysis (DTA) and X-ray diffraction (XRD) techniques. It has been shown that both systems are characterized by the formation of a continuous series of solid solutions with a tetradymite-like layered structure. The lattice parameters of solid solutions are linear functions of composition

Augmented Adam-Gibbs model for glass melt viscosity and configuration entropy as functions of temperature and composition

As the temperature of glass melt increases, its structure approaches the state of a simple liquid while the configuration entropy approaches a maximum value. We describe this gradual change using a power law function of inverse temperature. The Adam-Gibbs model for glass viscosity as a function of temperature and glass composition augmented in this way is greatly simplified when applied to common glass families occupying moderate composition regions, such as float glass or nuclear waste glasses, on which properties can be approximated as linear functions of composition. The parsimonious model thus obtained is preferable for use in optimizing glass formulation and mathematical modeling of glass melting and forming. For multicomponent glasses with N viscosity-affecting components, the augmented Adam-Gibbs model requires 2N + 3 adjustable parameters. The model efficacy is demonstrated by fitting the model to a viscosity-temperature-composition dataset for low-activity nuclear waste glasses.

An efficient implementation for the solution of auxiliary composition fields in multicomponent phase field models

We present a new approach for incorporating CALPHAD thermodynamics in phase field models using linear spline functions. In this method, we discretize an n-component composition space with a mesh of n-1 dimensional elements that have linear shape/interpolation functions, therefore representing any thermodynamic quantity as a linear function of composition. Following this approach, the solution of auxiliary solute compositions in phase field simulations is straightforward and significantly faster compared to standard Redlich-Kister polynomials based method. At the same time, we obtain high accuracy in solutions when compared with reference calculations where excess energy is represented using Redlich-Kister polynomials. The salient features of the model are highlighted through examples of α/β phase transformation in a ternary Ti-Al-V diffusion couple.

The Effect of Glass Composition Containing RE Oxide Waste Glass on Liquidus Temperature

ABSTRACTThe liquidus temperature (TL) of rare earth (RE) was determined for alumino-borosilicate glasses for treating americium and curium that have been studied previously. Their work covers a wide range of glass composition with various crystalline phases as primary phase. Present work is aimed at understanding the effect of glass composition on TL for waste glasses designed for vitrifying RE oxides wastes. In a sufficiently narrow composition region, this effect can be represented by a first-order model fitted measured TL versus composition data. Test glasses were formulated by varying of component fractions one-at-a-time. The glasses contained SiO2, B2O3, and Al2O3 as glass formers and Nd2O3 with CeO2 as simulated RE waste. Twenty glasses were made to investigate crystallization as a function of temperature and glass composition. The primary crystalline phase was Ce-borosilicate (Ce3BSi2O10), secondary phases were Al-containing crystals (Al2O3 and Al10Si2O19), and crystalline CeO2. A first-order model was fitted to crystal fraction versus glass composition data. Generally, SiO2 and B2O3 tend to suppress crystallization, Al2O3 has little effect, and, as expected, RE components (Nd2O3 and CeO2) promote it. The correlation coefficient, R2, was 0.89 for the primary crystalline phase TL as a linear function of composition.

Potential Orthopyroxene, Clinopyroxene and Olivine Reference Materials for In Situ Lithium Isotope Determination

Over 1400 electron probe and 700 ion probe microanalyses were performed on eleven mineral separates to evaluate their potential as reference materials for in situ Li isotopic determination. Our results suggest the homogenous distributions of major elements, Li and its isotopes for each sample. Hence, these samples are suitable to be used as reference materials for in situ measurements of Li abundance and Li isotopes by secondary ion mass spectrometry (SIMS) or laser ablation‐inductively coupled plasma‐mass spectrometry (LA‐ICP‐MS). These samples have the advantage of mitigating probable matrix effects during calibration owing to the wide range of compositions. The effect of composition on the δ7Li of olivine measured by SIMS is a linear function of composition, with δ7Li increasing by 1.0‰ for each mole per cent decrease in forsterite component.

Heat capacity, configurational heat capacity and fragility of hydrous magmas

The glassy and liquid heat capacities of four series of dry and hydrous natural glasses and magma as a function of temperature and water content (up to 19.9mol%) were investigated using differential scanning calorimetry (DSC). The analyzed compositions are basalt, latite, trachyte and pantellerite. The results of this study indicate that the measured heat capacity of glasses (Cpg) is a linear function of composition and is well reproduced by the empirical model of Richet (1987). For the investigated glasses, the partial molar heat capacity of water can be considered as independent of composition, in agreement with Bouhifd et al. (2006). For hydrous liquids, the heat capacity (Cpliq) decreases nonlinearly with increasing water content. Previously published models, combined with the partial molar heat capacity of water from the literature, are not able to reproduce our experimental data in a satisfactory way. We estimated the partial molar heat capacity of water (CpH2O) in hydrous magma over a broad compositional range. The proposed value is 41±3Jmol−1K−1. Water strongly affects the configurational heat capacity at the glass transition temperature [Cpconf (Tg)]. An increases of Cpconf (Tg) with water content was measured for the polymerized liquids (trachyte and pantellerite), while the opposite behavior was observed for the most depolymerized liquids (basalt and latite). Structural and rheological implications of this behavior are discussed in light of the presented results.

Vapor–Liquid Equilibria of Binary Associating Fluids Using a Cubic Equation of State with Limited Data

The vapor–liquid equilibria of binary associating fluids containing alcohols are described using a cubic equation of state, van der Waals mixing rules, and a binary interaction parameter. The binary interaction parameter is a linear function of composition. The binary interaction parameter is also a strong function of temperature. The temperature dependency was derived by combining van der Waals mixing rules with GE mixing rules followed by approaching infinite dilution limiting condition. Employing pure component parameters with literature values of infinite dilution activity coefficients, the vapor–liquid equilibria of systems containing alcohols were predicted satisfactorily. In the absence of experimental or estimated infinite dilution activity coefficients, the model can be coupled with the nonrandom two-liquid activity coefficient model to accurately correlate experimental vapor–liquid equilibrium data.

Interaction between lead bromide and barium bromide

The phase diagram of the PbBr2-BaBr2 system over the entire concentration range is studied for the first time by differential thermal analysis and X-ray powder diffraction analysis. No new compounds are formed in the system. The phase diagram is represented by a continuous series of solid solutions (type I by Rooseboom’s classification). The unit cell parameters change as a linear function of composition.

Effect of inert components (Y2O3, Al2O3, and Ga2O3) on the chemistimulating effect of the Sb2O3 activator of GaAs thermal oxidation

Chemistimilated thermal oxidation of gallium arsenide was studied using Sb2O3 activator oxide in compositions with Ga2O3, Al2O3, and Y2O3 inert components. For Sb2O3-Y2O3 compositions, the thickness of the resulting oxide layer on GaAs was found to be a linear function of composition over the enter range of the compositions. For antimony oxide compositions with Ga2O3 and Al2O3 inert components, nonadditivities were observed near the component ordinates. For the Sb2O3-Ga2O3 system, the chemistimulating efficiency noticeably weakened at low concentrations of the inert component. The linear trend observed for this system within 0–60 mol % Sb2O3 is additively determined by the oxide layer thickness on GaAs in the presence of Sb2O3 and in the absence of activator. In the presence of inert Al2O3, the chemistimulating effect was enhanced near the Al2O3 ordinate and the resulting function was nonadditive with respect to the thicknesses reached in the presence of the individual components.

Lattice parameters and dielectric properties of (1 − x)Bi(Mg1/2Ti1/2)O3 · xBiCoO3 perovskite solid solutions

(1 − x)Bi(Mg1/2Ti1/2)O3 · xBiCoO ceramics have been prepared at high pressures (6 GPa) and temperatures (1370–1570 K). Perovskite solid solutions have been obtained in the composition ranges 0 0.8) has a tetragonal structure (sp. gr. P4mn). In the range 0.6 < x < 0.8, the ceramics consisted of the two perovskite phases. The lattice parameters of the solid solutions with x < 0.6 are linear functions of composition. The dielectric properties of the orthorhombic solid solutions have been studied using impedance spectroscopy. The temperature dependences of dielectric permittivity ɛ′ and dielectric loss tanδ exhibit different behaviors at low and high temperatures. With increasing x, the boundary between these regions shifts from about 450 to 300 K. At high temperatures, both ɛ′ and tanδ rise steeply. The dc conductivity of the solid solutions with x < 0.6 exhibits Arrhenius behavior. The activation energies for charge transport in the ceramics studies are presented.

Solid solutions in the Ag2Se-PbSe-Bi2Se3 system

The phase equilibria in the pseudoternary system Ag2Se-PbSe-Bi2Se3 have been studied using differential thermal analysis, x-ray diffraction, and microhardness measurements. The results have been used to construct the T-x phase diagram along the AgBiSe2-PbSe join and the 900-K section of the ternary phase diagram. The AgBiSe2-PbSe system contains a continuous series of cubic solid solutions with the NaCl structure. Their lattice parameter is an almost linear function of composition (a = 5.822–6.125 A). The formation of the solid solutions stabilizes the high-temperature phase of AgBiSe2: PbSe dissolution in this compound markedly reduces its polymorphic transformation temperature (590 K), down to room temperature at ≃ 10 mol % PbSe. In the Ag2Se-PbSe-Bi2Se3 system, the γ-phase exists in a broad region around the AgBiSe2-PbSe pseudobinary join.

Lithium isotope analysis of olivine by SIMS: Calibration of a matrix effect and application to magmatic phenocrysts

High-spatial resolution analysis of light element isotope variations by secondary-ion mass spectrometry (SIMS) has numerous applications in geochemistry and cosmochemistry. Recent attention has focused on 7Li/ 6Li variations in magmatic phenocrysts to infer the volatile degassing history of their parent magmas, and on minerals from mantle samples to determine source-region processes and the recycling history of mantle reservoirs. In these studies the effect of mineral composition on the 7Li/ 6Li ratio measured by SIMS has been considered secondary, and generally disregarded. We show, using a suite of nine olivines analyzed by MC-ICP-MS or TIMS, that there is a substantial effect of composition on the 7Li/ 6Li ratio of olivine measured by SIMS. For magnesian olivine (74 < Fo < 94) the effect is a linear function of composition, with δ 7Li increasing by 1.3‰ for each mole percent decrease in forsterite component. At higher Fe contents, the relationship ceases to be linear. The composition range over which linear behavior is exhibited appears to depend on instrumental conditions. A calibration of this matrix effect over the linear range is presented, assuming the measurement of 7Li/ 6Li relative to an olivine standard of known composition. Application of this calibration to a suite of olivines separated from basaltic lavas from Ko'olau, Hawai'i demonstrates that the matrix effect is responsible for a geologically spurious correlation between δ 7Li and Mg#. However, after correction, the olivines retain evidence of Li isotope heterogeneity, the degree and nature of which differs in each of the four separates studied. These results emphasize the importance of compositional correction for SIMS measurement of δ 7Li in olivine, particularly in zoned crystals, and support previous conclusions that Li isotope variability in igneous materials is subject to late-stage disturbance. The significant matrix effect demonstrated for olivine suggests that matrix effects in other minerals require further evaluation.

Molar Volume and Composition of Oxides of the Same Metal

The relation between the molar volume of metal oxides and their composition has been discussed. In order to compare molar volume of oxides with different compositions, the volume per one mole of oxygen atoms (Ma/bO) was used. It has been found that molar volumes of oxide phases of the same metal in the composition range 2 > a/b > 0.5 are linear functions of composition. This type of relationship has been proposed as an additional criterion to classify an oxide as a compact structure. Furthermore, in the case of oxides with metal ions in higher oxidation states (Mz+ > M4+) the increase of the molar volume (relative to the MO2 oxides) and the formation of framework structures have been found. Molar Volume and Composition of Oxides of the Same Metal Andrzej Stoklosa*, Barbara Laskowska Molar volumes of oxide phases of the same metal in the composition range 1>a/b>0.3 are linear functions of composition.

Compositional dependence of Raman frequencies in ternaryGe1−x−ySixSnyalloys

The Ge-Ge, Si-Si, and Si-Ge Raman frequencies in ${\mathrm{Ge}}_{1\ensuremath{-}x\ensuremath{-}y}{\mathrm{Si}}_{x}{\mathrm{Sn}}_{y}$ alloys were measured for $x\ensuremath{\leqslant}0.2$ and $y\ensuremath{\leqslant}0.1$. The Ge-Ge and Si-Si mode frequencies are found to be linear functions of composition over the measured range. The coefficients obtained from linear fits to the experimental data are similar to those measured in binary alloys incorporating Si, Ge, or Sn, suggesting that the linear behavior extends over the entire range of possible compositions $(x,y)$ to include the binary alloys as special cases. The linear coefficients are shown to follow a universal behavior that results from the scaling of phonon dispersion curves in Si, Ge, and $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$.

Synergistic Effect between Components of Mixtures of Cationic Amphipaths in Transfection of Primary Endothelial Cells

To date, the primary approach to improving the transfection properties of cationic lipids has been the synthesis of new kinds of cationic amphipaths. Recently, however, it was found that combining two cationic lipid derivatives having the same head group but tails of different chain lengths can provide another, and often superior, approach to higher transfection efficiency. For example, the combination of medium-chain and long-chain homologues of O-ethylphosphatidylcholine transfected DNA into primary human umbilical artery endothelial cells (HUAECs) more than 30-fold more efficiently than did either compound separately. Here it is reported that this synergism of mixtures is not limited to O-ethylphosphatidylcholine homologues, but is also exhibited by other common cationic amphipathic transfection reagents; for example, combining DC-Chol (3beta-[N',N'-dimethylaminoethane)-carbamol] cholesterol), dimethylditetradecylammonium bromide, or DMTAP (1,2-dimyristoyl-3-trimethylammonium-propane) with EDOPC increased transfection significantly both in the absence and in the presence of serum. Furthermore, combining a poorer transfection agent-dimethyldioctadecylammonium bromide-with dimethylditetradecylammonium bromide increased transfection by about an order of magnitude with a maximum at an intermediate composition. Lack of synergy occurred with some mixtures, such as DMTAP and DOTAP (1,2-dioleoyl-3-trimethylammonium-propane), in which case transfection activity was a linear function of composition both in the absence and presence of serum. Although the mechanism of enhanced transfection by mixtures is not fully understood, the existence of a number of optimal mixtures with diverse cationic compounds indicates that attention to mixture formulations can lead to greatly improved transfection by cationic amphipathic carriers.

Thermodynamics of open two-phase systems with coherent interfaces: Application to metal–hydrogen systems

We develop a thermodynamic theory for the absorption/desorption of interstitial atoms by a solid crystalline host forming a coherent mixture of two phases with different compositions of interstitial solutes. It is shown that the misfit-generated strain produces a macroscopic energy barrier between the transforming phases. The energy barrier is proportional to the macroscopic volume and thus cannot be surmounted by the thermally assisted nucleation of the new phase. The barrier splits the phase-transition pressure (temperature) into two pressures (temperatures): one during increase of pressure (cooling) and another during decrease of pressure (heating). The difference between these pressures (temperatures) determines the system hysteresis. It is also shown that the chemical potential of interstitials within the two-phase region of the coherent phase diagram is a linear function of composition rather than a constant, as is the case in the absence of coherency strains. We apply the theory to the absorption/desorption of H atoms by a metal that is free to exchange hydrogen atoms with an external source (reservoir). The theory explains the ubiquitous hysteresis in the ‘plateaus’ of the pressure–composition isotherms and the critical pressure–composition point for the disappearance of the hysteresis. The proposed theory is generic in the sense that it is applicable to any open interstitial systems forming coherent hydrides or other interstitial phases in the host lattice of the same symmetry.

Solid-solution aqueous-solution reactions between jarosite (KFe 3(SO 4) 2(OH) 6) and its chromate analog

The sulfate mineral jarosite (KFe 3(SO 4) 2(OH) 6), its chromate analog (KFe 3(CrO 4) 2(OH) 6), and seven precipitates with intermediate compositions (KFe 3(Cr XS (1-X)O 4) 2(OH) 6) were synthesized. The unit cell volume of the precipitates is closely represented by a linear function of composition, suggesting a continuous solid solution. This solid solution dissolves stoichiometrically according to KFe 3(Cr XS (1−X)O 4) 2(OH) 6 + 6H +→ K ++ 3Fe 3+ + 2X CrO 4 2− + (2 − 2X) SO 4 2− + 6H 2O and reaches stoichiometric saturation after approximately 40 d. Log K SS values calculated from samples taken after 1090 d are consistently lower than what would be expected for an ideal solid solution, indicating that the excess free energy of mixing, G E, is negative. G E calculated from the log K SS values can be closely modeled by the one-parameter Guggenheim expansion G E = X CrJar X Jar RT a 0 where a 0 is −4.9 ± 0.8, X CrJar and X Jar are the mole fractions of KFe 3(CrO 4) 2(OH) 6 and KFe 3(SO 4) 2(OH) 6 in the solids, R is the gas constant, and T the absolute temperature. Based on the calculated excess free energy, a Lippmann diagram with a modified abscissa was constructed.

Critical locus and vapor–liquid equilibria of HFC32–HFC125 system

We measured vapor–liquid equilibria (VLE) and critical locus for the system of difluoromethane (HFC32)–pentafluoroethane (HFC125) ranging from 318.15 to 349.15 K. Composition differences between vapor and liquid phases on the P–( x– y) diagram were very small. The critical locus can be classified as type I behavior according to the system of van Konynenburg–Scott. The system of HFC32 and HFC125 is unusual in that the larger component in molecular weight has a lower critical temperature and vapor pressure than the smaller component. Using binary interaction parameter m ij expressed as a linear function of composition and temperature, we obtained excellent correlation of the experimental data with an extended BWR equation of state.

Lattice vibrational modes in synthetic tremolite-Sr-tremolite and tremolite-richterite solid solutions

Powder IR spectra of synthetic richterite-tremolite and Sr-tremolite-tremolite solid solutions were obtained in the spectral range between 1400 and 600 cm−1. Under the consideration of the crystal structure and the Wykoff positions of the atoms in the primitive unit cell, the number, type and symmetry of vibrational modes were deduced. The space group of tremolite C2h was used as the factor group leading to 16 theoretical stretching vibrations in the IR range caused by the Si4O11∞-ribbon. The energy of the internal vibrations of the Si4O11∞-ribbon is a function of the relative bond strengths and masses of nearby ions. For the amphiboles a one-mode behavior was observed for all the Si-O, Si-O-Si and O-Si-O stretching vibrations, indicating no clustering in the two solid solution series. In both solid solution series the vibrational energy of the stretching vibrations is a linear function of composition. In the system richterite-tremolite a shift of the stretching frequencies of the Si4O11∞-ribbon over the whole compositional range of up to 30 cm−1 was observed. In contrast, for Sr-tremolite-tremolite the maximum shift was only 5 cm−1. These quite small band shifts allow the (Si4O11)∞-ribbon to be treated as an isolated entity for factor group analysis. Nevertheless, by the two exchange mechanisms, Ca(M4) ? Sr(M4) and □(A) Ca(M4) ? Na(A)Na(M4), the FWHHs increased and the amplitudes decreased, indicating a slight distortion of the ribbon. For Sr-tremolite-tremolite only a linear expansion of the lattice was observed. In the series richterite-tremolite individual bond angles of the SiO4 tetrahedra are additionally changed, causing the higher energy shift of the bands. The strongest and sharpest bands were observed for the end member tremolite. The one-mode behavior of the Si4O11-double chain indicates that there is no short-range order of Na/Ca and Ca/Sr at the M4 sites of these amphiboles.

T-x-s phase diagram of compositionally orderable (1-x) PbSc1/2Nb1/2O3-xPbSc1/2Ta1/2O3 solid solution

(1-x) PbSc1/2Nb1/2O3-xPbSc1/2Ta1/2O3 solid solution crystals have been grown in the whole range of compositions by spontaneous crystallization. The temperature Tt of compositional order-disorder phase transition was found to be a linear function of composition ′ The ferroelectric phase transition temperature Tc also depends linearly on ′ both for crystals with high and low degree of ordering s. On the base of the results obtained a tentative T-′—s phase diagram for (1-x) PbSc1/2Nb1/2O3-xPbSc1/2Ta1/2O3 solid solutions have been calculated.