Thermodynamic Properties Of Solid Solutions Research Articles

Theory prediction of band structures, densities of states, mechanical and thermodynamic properties of solid solutions BaxK1-xBi0.92Mg0.08O3

The band structures, densities of states, mechanical and thermodynamic properties of solid solutions BaxK1-xBi0.92Mg0.08O3 have been systematically investigated using the pseudopotential plane-wave method based on the first-principles simulation. The obtained lattice parameters are in accordance with the experimental test data. The electronic band structure indicates the metallic character of the considered compound. And the Ef is principally originated from the Bi/Mg:s, p and the O:2p states. The predicted elastic constants Cij reveals that BaxK1-xBi0.92Mg0.08O3 is mechanically stable. The polycrystalline modulus such as Young's modulus E, shear modulus G and bulk modulus B are obtained in the framework of the Voigt-Reuss-Hill arithmetic mean approximation. Cauchy pressure Cp and B/G ratio are further investigated in order to probe the ductile/brittle nature of solid solutions. Additionally, the anisotropy is forecasted by the Zener factor Z, AG, Au and 3D surface of E. Finally, the Vickers hardness Hv and the Debye temperature θD have been obtained. We believe that our theoretical results can provide information for further experimental and theoretical researches.

Thermodynamic properties of solid solutions in the PbSe—AgSbSe2 system

The results of the study of the PbSe—AgSbSe2 system by measuring the emf of concentration chains with respect to PbSe in a temperature range of 300–450 K are presented. The formation in the system of a wide (37–100 mol.% AgSbSe2) region of solid solutions based on AgSbSe2 is shown. The partial thermodynamic functions of PbSe and lead in the alloys are calculated from the equations of the temperature dependences of the emf. The standard thermodynamic functions of formation and standard entropies of solid solutions (2PbSe)x(AgSbSe2)1−x (x = 0.4, 0.6, 0.8, and 0.9) are calculated by the integration of the Gibbs—Duhem equation over the PbSe—AgSbSe2 section using the literature data on the corresponding thermodynamic data for compounds PbSe and AgSbSe2.

Vaporization features of CeO2[sbnd]ZrO2 solid solutions at high temperature

Ceria-zirconia solid solutions are the important materials for the application in catalysis and the energy conversion. However, the existing data on the thermodynamic properties of ceria-zirconia solid solutions which is used to distinguish their stability is controversial. In the present work, equilibrium ceria-zirconia solid solutions with 90, 50, 24 and 9 mol.% CeO2 were manufactured using the original sol-gel reverse co-precipitation method with further prolonged thermal treatment for 5–50 h at 973–1373 K. Comprehensive characterizations of the precursor powders obtained were performed via SEM, STA, XRD, ESCA and PSD-analysis. According to XRD observations combined with Rietvield refinement and ESCA the equilibrium solid solutions without an admixture of Ce3+ in the condensed phase were obtained after the calcination of samples at 1373 K. Knudsen effusion mass spectrometry was used to study the vaporization processes and the thermodynamic properties of solid solutions in the CeO2ZrO2 system at 2150 K. Similar dependence of the CeO2 activity on the condensed phase composition was obtained for solid solutions with various ceria contents, which ensured the equilibrium evaporation. The schematic evaporation process for xCeO2-(100-x)ZrO2 solid solutions at 2100–2500 K was suggested for the first time. It was found, that high temperature behavior of CeO2ZrO2 system significantly differs from its behavior at lower temperatures, i.e. 873–1373 K, when Ce (IV) to Ce (III) reduction takes place.

Thermodynamic properties of the La2 O3 -ZrO2 system by Knudsen effusion mass spectrometry at high temperature.

Zirconia doped with a lanthanum oxide system is of high interest due to its exceptional thermal stability for the development of high-performance ceramics. It possesses the beneficial properties of pure zirconia, such as heat resistance, mechanical strength and inertness, but also eliminates its main disadvantage, i.e. brittleness. At high temperatures, components of such systems may vaporize selectively, leading to significant change in composition, and hence, the thermal resistance, phase stability and performance of the ceramic materials. Therefore, information on the vaporization processes and thermodynamic properties of the La2 O3 -ZrO2 system is of great importance. Knudsen effusion mass spectrometry was used to study the vaporization processes and thermodynamic properties of solid solutions in the La2 O3 -ZrO2 system at 2110 K. Pure La2 O3 was used as a reference substance. Comprehensive characterization of the precursors and ceramics was performed via SEM, STA, XRD and PSD analysis. Zirconia-doped lanthania precursor powders and ceramics with La2 O3 of 33.3, 50, 70 and 90 mol.% content were manufactured by solid-state synthesis and the original cryochemical technique. La, LaO, ZrO and ZrO2 were found to be the main vapor species over the samples studied. The activities and thermodynamic properties of La2 O3 were calculated. Via XRD analysis it was shown that the phase composition of xLa2 O3 -(100-x)ZrO2 powders (x = 0.33, 0.5, 0.7 and 0.9 mol. fraction) significantly depends on the synthesis technique chosen. According to the XRD results combined with Rietveld refinement of the patterns, 33.3 La2 O3 -66.7 ZrO2 ceramics after solid-state synthesis are composed of well-formed cubic pyrochlore-type La2 Zr2 O7 with 5 wt.% admixture of monoclinic and cubic ZrO2 whereas 33.3 La2 O3 -66.7 ZrO2 precursor powders after cryochemical synthesis correspond to low-crystalline La(OH)3 . The components of the La2 O3 -ZrO2 system evaporate separately: there is no temperature range where lanthanum and zirconium gaseous species are present together. It was found that the activities of lanthania have low negative deviation from the ideal case.

Relaxation method for constructing the interaction potentials of metal–nonmetal atomic pairs

An algorithm that employs the method of successive relaxation for determining the parameters of the pairwise interaction potential of iron and nonmetallic atoms that implicitly considers the redistribution of electron density between atoms is developed. The parameters of the interatomic interaction potential are calculated for ten pairs of elements: Fe–P, Fe–S, Fe–B, Fe–V, Fe–Mo, Fe–Cr, Fe–Mn, Fe–Si, Fe–Ni, and Fe–Al. The structural and thermodynamic properties of solid solutions based on iron and pure materials, and some pairwise interaction potentials constructed earlier in the Lennard–Jones form for identical metal atoms and homogeneous pairs of different metal–metal atoms, are used in these calculations.

Mass spectrometric study of thermodynamic properties of BaO-CeO2. The formation enthalpy of BaCeO3 (solid)

Barium cerate with additions of rare-earth or 3-d metal oxides is widely used for production of solid electrolytes, ionic, and electron–ionic conductors. Knudsen effusion mass spectrometry was used to study vaporization processes and thermodynamic properties of solid solutions in the BaO – CeO2 system at the temperature 2000 K. Ba, BaO, CeO and CeO2 were found as the main vapor species over the samples studied. Activity values and Gibbs energy of BaO and CeO2 in the samples studied were calculated. The activities of barium and cerium oxides in the concentration range of the homogeneous melt (70–32 mol. % of BaO) and in the region from 32 to 5 mol % of BaO (solid solution of CeO2 + liquid) have low negative deviations from the ideal case. The determined value of the standard formation enthalpy of solid barium cerate is equal to −1692 ± 17 kJ/mol.

Relationship between the thermodynamic excess properties of mixing and the elastic moduli in the monazite-type ceramics

Using ab initio quantum chemistry we computed the excess thermodynamic properties and the elastic moduli for a series of monazite-type single substitution solid solutions (Ln1−xLnxPO4). We found that the Margules interaction parameters of all the solid solutions can be described by a simple function of the endmembers volume mismatch ΔV, i.e. W(kJ/mol)=0.616(ΔV(cm3/mol))2. We show that the obtained relationship could be also derived by considering the strain energy resulting from the substitution of cations of different sizes, knowing the Young's modulus and the volumes of endmembers. This indicates that the strain resulting from the structural incorporation of cations is a major factor responsible for arising of the excess properties in monazite-type ceramics. Our results show thus a way to estimate the excess thermodynamic properties of solid solutions from the structural and elastic parameters, namely the endmembers volumes and the Young's modulus, which could be easily measured or computed.

Thermodynamic properties of solid solutions in the Ag-Au-Cu system

Data on the Cu content in native gold and silver and the Ag and Au contents in native copper are summarized. The standard thermodynamic functions of solid solutions in the Au-Cu and Ag-Cu binary systems and the Ag-Au-Cu ternary system have been estimated. The corresponding calculation module is prepared for the Selektor software.

Thermodynamic properties of the Lu2O3–ZrO2 solid solutions by Knudsen effusion mass spectrometry at high temperature

The zirconium oxide based ceramics with addition of rare-earth metal oxides is widely used for production of high temperature materials. Knudsen effusion mass spectrometry was used to study vaporization processes and thermodynamic properties of solid solutions in the ZrO2–Lu2O3 system at the temperature 2700K. The Lu, LuO, ZrO and ZrO2 were found as the main vapor species over the samples studied. The ZrO2 and Lu2O3 activities, the Gibbs free energy of formation, the excess Gibbs free energy of formation in the samples studied were calculated. The activities of lutetium oxide in all concentration range of condensed phase have low negative deviation from ideal case whereas zirconium dioxide activities have strong negative deviation from ideal case.

Evaluation of the thermodynamic properties of solid solutions of titanium, chromium, cobalt, and nickel in silicon using a two-sublattice model

We have evaluated the thermodynamic properties of solid solutions of titanium, chromium, cobalt, and nickel in silicon using a two-sublattice model. Our results demonstrate that the thermodynamic data obtained can be used in thermodynamic calculations.

Solid electrolytes in the binary system RbNO 3–RbNO 2

Conductivity and thermodynamic properties of solid solutions (1−x)RbNO 3–xRbNO 2 were investigated over entire concentration range of 0 < x < 1. As shown by differential thermal analysis and conductivity measurements, the introduction of a small concentration of nitrite into rubidium nitrate leads to an decrease in the temperature of phase transitions IV↔III and III↔II, so that highly conducting phase III becomes stable at low temperatures. The introduction of smaller NO 2 − anions results in the increase in the conductivity of the RbNO 3-III phase, the activation energy and a pre-exponential factor of conductivity decrease with the doping and III–IV transition becomes diffusive. A possible reason of these effects is a strong influence of nitrite ions to the orientational disorder of the anionic sublattice of RbNO 3.

The thermodynamic properties of solid solutions of manganese and iron in silicon

The thermodynamic properties of solid solutions of manganese and iron in silicon were estimated using the model of two sublattices. The possibility of using the values obtained in thermodynamic calculations was demonstrated.

First-principles study of binary special quasirandom structures for the Al–Cu, Al–Si, Cu–Si, and Mg–Si systems

Based on special quasirandom structures (SQS’s) and first-principles calculations, enthalpies of mixing have been predicted for four binary fcc solid solutions in the Al–Cu, Al–Si, Cu–Si, and Mg–Si systems at nine compositions ( x = 0.0625 , 0.125, 0.1875, 0.25, 0.5, 0.75, 0.8125, 0.875, 0.9375, where x is the mole fraction of A atoms in the A–B binary system). The present results are compared with previous first-principles calculations and thermodynamic modeling results available in the literature. In order to provide insight into the understanding of mixing behavior for these solid solutions, the spatial charge density distributions in these binary solid solutions are also analyzed. The results obtained herein indicate that the SQS model can be used to estimate the thermodynamic properties of solid solutions, especially for metastable phases, the thermodynamic qualities of which are rarely measured.

On the decomposition of solid solutions of magnesium in aluminum

A nonequilibrium version of measuring the electromotive force during a continuous decrease in the temperature at a rate of 5–7 °C/min is used to study the thermodynamic properties of solid solutions of magnesium in aluminum. The studies show that the abrupt change in the potential of an alloy containing 20–30 mol % Mg at 370–380°C reliably correlates with the decomposition of the solid solution formed at 450°C.

First-principles calculations of the structural and thermodynamic properties of bcc, fcc and hcp solid solutions in the Al–TM (TM = Ti, Zr and Hf) systems: A comparison of cluster expansion and supercell methods

The thermodynamic properties of solid solutions with body-centered cubic (bcc), face-centered cubic (fcc) and hexagonal close-packed (hcp) structures in the Al–TM (TM = Ti, Zr and Hf) systems are calculated from first-principles using cluster expansion (CE), Monte-Carlo simulation and supercell methods. The 32-atom special quasirandom structure (SQS) supercells are employed to compute properties at 25, 50 and 75 at.% TM compositions, and 64-atom supercells have been employed to compute properties of alloys in the dilute concentration limit (one solute and 63 solvent atoms). In general, the energy of mixing (Δ m E) calculated by CE and dilute supercells agree very well. In the concentrated region, the Δ m E values calculated by CE and SQS methods also agree well in many cases; however, noteworthy discrepancies are found in some cases, which we argue originate from inherent elastic and dynamic instabilities of the relevant parent lattice structures. The importance of short-range order on the calculated values of Δ m E for hcp Al–Ti alloys is demonstrated. We also present calculated results for the composition dependence of the atomic volumes in random solid solutions with bcc, fcc and hcp structures. The properties of solid solutions reported here may be integrated within the CALPHAD formalism to develop reliable thermodynamic databases in order to facilitate: (i) calculations of stable and metastable phase diagrams of binary and multicomponent systems, (ii) alloy design, and (iii) processing of Al–TM-based alloys.

Calorimetric determination of energetics of solid solutions of UO 2+ x with CaO and Y 2O 3

Quantitative study of thermodynamic properties of solid solutions of UO 2+ x with divalent and trivalent oxides is important for predicting the behavior of oxide fuel. Although early literature work measured vapor pressure in some of these solid solutions, direct calorimetric measurements of enthalpies of formation have been hampered by the refractory nature of such oxides. First measurements of the enthalpies of formation in the systems UO 2+ x –CaO and UO 2+ x –YO 1.5, obtained by high-temperature oxide melt solution calorimetry, are reported. Both systems show significantly negative (exothermic) heats of formation from binary oxides (UO 2, plus O 2 and CaO or YO 1.5, as well as from UO 2 plus UO 3 and CaO or YO 1.5), consistent with reported free energy measurements in the urania–yttria system. The energetic contributions of oxygen content (oxidation of U 4+) and of charge balanced ionic substitution as well as defect clustering are discussed. Behavior of urania–yttria is compared to that of corresponding systems in which the tetravalent ion is Ce, Zr, or Hf. The substantial additional stability in the solid solutions compared to pure UO 2+ x may retard, in both thermodynamic and kinetic sense, the oxidation and leaching of spent fuel to form aqueous U 6+ and solid uranyl phases.

Thermodynamic Investigation of the Redox Properties of Ceria−Zirconia Solid Solutions

The thermodynamic properties of solid solutions of ceria and zirconia, having the general formula Ce1-yZryO2, were studied as a function of temperature and oxygen fugacity by measuring the oxygen content of samples equilibrated in H2/H2O mixtures between 873 and 1173 K. The thermodynamic redox properties were found to be a strong function of oxide composition but were independent of sample surface area and calcination temperature. Ceria−zirconia solid solutions were much more easily reduced than CeO2, so that thermodynamic values such as the enthalpy of oxidation for ceria are not the same as for the solid solution. All of the reduction isotherms for the ceria−zirconia solutions exhibited a plateau in the oxygen stoichiometry at the higher oxygen fugacities accessible using H2/H2O mixtures, suggesting special stabilities for certain reduction states in the solid solutions.

Computer simulation of mineral solid solutions

We discuss how two techniques, based on (1) lattice dynamics (lattice statics) simulations and (2) Monte Carlo methods may be used to calculate the thermodynamic properties of solid solutions and highly disordered systems. The lattice dynamics calculations involve a full free-energy structural optimisation of each of a number of configurations, followed by thermodynamic averaging. The Monte Carlo simulations include the explicit interchange of cations and use the semi-grand canonical ensemble for chemical potential differences. Both methods are readily applied to high pressures and elevated temperatures without the need for any new parameterisation. We discuss the application of the Monte Carlo technique to the study of surfaces. A range of examples, including binary oxides, spinels, carbonates and surface segregation, is used to illustrate the methods.

Beyond the point defect limit: Simulation methods for solid solutions and highly disordered systems

We discuss how two techniques, based on (1) lattice statics/lattice dynamics simulations and (2) Monte Carlo methods may be used to calculate the thermodynamic properties of solid solutions and highly disordered systems. The lattice statics/lattice dynamics calculations involve a full free-energy structural optimization of each of a number of configurations, followed by thermodynamic averaging. The Monte Carlo simulations include the explicit interchange of cations and use the semigrand canonical ensemble for chemical potential differences. Both methods are readily applied to high pressures and elevated temperatures without the need for any new parameterization; at agreement between the two techniques is better at high pressures where anharmonic terms are smaller. Vibrational contributions to thermodynamic quantities of mixing are examined. A range of examples, including binary oxides, garnets and carbonates, are used to illustrate the methods.

Prediction of the thermodynamic properties of binary continuous solid solutions by infinite dilute activity coefficients

A new thermodynamic model based on the free volume theory and the lattice model was proposed for solid solutions. A significant advantage of the model lies in its ability to predict the thermodynamic properties of solid solutions using only the binary infinite dilute activity coefficients and the predicted values are in good agreement with their experimental data. This shows that the model with a good physical basis is reliable, convenient and economic.