Thermodynamic optimization of the Na<Subscript>2</Subscript>O-B<Subscript>2</Subscript>O<Subscript>3</Subscript> pseudo-binary system

The Na₂O-B₂O₃ system is thermodynamically optimized by means of the CALPHAD method. A two-sublattice ionic solution model, (Na⁺¹)_P(O⁻²,BO₃ ⁻³,B₄O₇ ⁻²,B₃O_4.5)_Q, has been used to describe the liquid phase. All the solid phases were treated as stoichiometric compounds. A set of thermodynamic parameters, which can reproduce most experimental data of both phase diagram and thermodynamic properties, was obtained. Comparisons between the calculated results and experimental data are presented.     

Thermodynamic reassessment of the BaO-B2O3 system

The BaO-B₂O₃ pseudobinary system is assessed. A two-sublattice ionic solution model, (Ba²⁺) _P (O²⁻, BO ₃ ³⁻ , B₄O ₇ ²⁻ , B₃O_4.5) _Q , is adopted to describe the liquid phase. All the solid phases are treated as stoichiometric compounds. A set of parameters consistent with most of the available experimental data on both phase diagram and thermodynamic properties is obtained by using CALPHAD technique. A comparison between the calculated results and experimental data as well as a previous assessment is presented.     

Thermodynamic reassessment of the BaO-B2O3 system

The BaO-B₂O₃ pseudobinary system is assessed. A two-sublattice ionic solution model, (Ba²⁺) _P (O²⁻, BO₃³⁻, B₄O₇²⁻, B₃O_4.5) _Q , is adopted to describe the liquid phase. All the solid phases are treated as stoichiometric compounds. A set of parameters consistent with most of the available experimental data on both phase diagram and thermodynamic properties is obtained by using CALPHAD technique. A comparison between the calculated results and experimental data as well as a previous assessment is presented.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the CrO-Cr2O3, CrO-Cr2O3-Al2O3, and CrO-Cr2O3-CaO systems

Available thermodynamic and phase diagram data have been critically assessed for all phases in the CrO-Cr₂O₃, CrO-Cr₂O₂-Al₂O₃, and CrO-Cr₂O₂-CaO systems from 298 K to above the liquidus temperatures and for oxygen partial pressures ranging from equilibrium with metallic Cr to equilibrium with air in the case of the first two systems and toP _{O 2} = 10⁻³ atm for the CrO-Cr₂O₃-CaO system. All reliable data have been simultaneously optimized to obtain one set of model equations for the Gibbs energy of the liquid slag and all solid phases as functions of composition and temperature. The modified quasichemical model was used for the slag. The models permit phase equilibria to be calculated for regions of composition, temperature, and oxygen potential where data are not available.     

The quaternary system B2O3-PbO-SiO2-ZnO: Thermodynamics and phase diagram

We evaluated the six binary phase diagrams, B₂O₃-PbO, B₂O₃-SiO₂, B₂O₃-ZnO, PbO-SiO2, PbO-ZnO, and SiO₂-ZnO, to obtain a consistent picture for the quaternary system B₂O₃-PbO-SiO₂-ZnO. We used all the available thermodynamic data: enthalpies of mixing, activity data, complete phase diagrams, and miscibility gaps. The agreement between the various sets of data is good. We also calculated the enthalpy of formation of the ternary compound 5PbO-B₂O₃-SiO₂. Δ_fH/R of 1/8 [5PbO-B₂O₃-SiO₂] =-(2.104 ± 0.057) kK.     

Thermodynamic Description of $${\hbox{SrO-Al}_{2}\hbox{O}_{3}}$$ System and Comparison with Similar Systems

The Al₂O₃-SrO binary system has been studied using the CALPHAD technique in this paper. The modeling of Al₂O₃ in the liquid phase is modified from the traditional formula with the liquid phase represented by the ionic two-sublattice model as (Al³⁺, Sr²⁺) _P (, O²⁻) _Q . Based on the measured phase equilibrium data and experimental thermodynamic properties, a set of thermodynamic functions has been optimized using an interactive computer-assisted analysis. The calculated results are compared with experimental data. A comparison between this system and similar systems is also given.     

Critical thermodynamic evaluation and optimization of the MgO-Al2O3, CaO-MgO-Al2O3, and MgO-Al2O3-SiO2 Systems

A complete literature review, critical evaluation, and thermodynamic modeling of the phase diagrams and thermodynamic properties of all oxide phases in the MgO-Al₂O₃, CaO-MgO-Al₂O₃, and MgO-Al₂O₃-SiO₂ systems at 1 bar total pressure are presented. Optimized model equations for the thermodynamic properties of all phases are obtained that reproduce all available thermodynamic and phase equilibrium data within experimental error limits from 25 °C to above the liquidus temperatures at all compositions. The database of the model parameters can be used along with software for Gibbs energy minimization to calculate all thermodynamic properties and any type of phase diagram section. The modified quasichemical model was used for the liquid slag phase and sublattice models, based upon the compound energy formalism, were used for the spinel, pyroxene, and monoxide solid solutions. The use of physically reasonable models means that the models can be used to predict thermodynamic properties and phase equilibria in composition and temperature regions where data are not available.     

Assessment of the Sr-Mn-O system

A thermodynamic assessment of the Sr-Mn-O system is presented. The main practical relevance of this system is that it contains the perovskite phase SrMnO₃, which is the Sr-rich end member of the phase (La,Sr) MnO₃, that finds widespread use as a cathode material for solid oxide fuel cells (SOFCs) and has recently attracted a lot of attention due to its interesting giant magnetoresistive properties. The thermodynamic parameters are optimized by applying the CALPHAD method. The SrMnO_3−z phase exists in two modifications, a layered hexagonal modification at low temperatures and a perovskite modification at high temperatures. Both modifications show considerable oxygen deficiencies, which are modeled using the compound energy model. The sublattice occupation of the phases is (Sr²⁺) (Mn³⁺, Mn⁴⁺)(O²⁻, Va)₃. On reducing Mn⁴⁺ to Mn³⁺, oxygen vacanices are formed. The phase SrMn₃O_6−z also shows an oxygen deficiency, which is modeled in an identical way. The Ruddlesden-Popper phases Sr₂MnO₄ and Sr₃Mn₂O₇, and the phases Sr₇Mn₄O₁₅ and Sr₄Mn₃O₁₀ are modeled as stoichiometric phases. The ionic liquid is modeled using the two-sublattice model for ionic liquids. The stability and thermodynamic data on many of the phases in this system are poorly known. For this reason, some aspects of this assessment must be regarded as tentative.     

Influence of B2O3 additives on microstructure and electrical properties of ZnO-Bi2O3-Sb2O3-based varistors

B₂O₃-doped ZnO-Bi₂O₃-Sb₂O₃-based varistors were fabricated by conventional ceramic technique. The microstructure and electrical properties were investigated by SEM, XRD and electrical measurements. With the addition of B₂O₃, the liquid-assisted sintering based on Bi₂O₃ was improved, and the Bi₂O₃-B₂O₃ glass and Zn₃(BO₃)₂ phase were formed on the grain boundaries. The doping of B₂O₃ markedly improved the varistor performance of the ZnO-Bi₂O₃-Sb₂O₃-based varistors. The nonlinear coefficient of the sample with 3.5 mol% B₂O₃ sintered at 1100 °C reached 56 and the leakage current was only 0.3 μA.     

Thermodynamics and phase diagrams in the binary systems Na2O-SiO2, Na2O-GeO2, Na2O-B2O3, Li2O-B2O3, CaO-B2O3, SrO-B2O3, and BaO-B2O3

We applied our model to the enthalpy of mixing data of the binary systems Na₂O-SiO₂, Na₂O-GeO₂, Na₂O-B₂O₃, Li₂O-B₂O₃, CaO-B₂O₃, SrO-B₂O₃, and BaO-B₂O₃. The most stable composition in the liquid, that is where the enthalpy of mixing is most negative, is with a metal-oxygen ratio of 4 to 3, for monovalent metals (Na and Li) and 3 to 4 for divalent metals (Ba and Ca) in liquid silicates or borates. The same applies to the CaO-SiO₂, CaO-Al₂O₃, PbO-B₂O₃, PbO-SiO₂, ZnO-B₂O₃, and ZnO-SiO₂ systems. The oxygen to metal ratio, its constant value in various types of systems, reflects and describes the structure of the liquid. Using the analyzed enthalpies of mixing data and the available phase diagrams, we calculated the enthalpies of formation of the various binary compounds. The results are in excellent agreement with data in the literature that were obtained from direct solid-solid calorimetry.     

Mechanochemical synthesis of Al2O3-TiB2 nanocomposite powder from Al-TiO2-H3BO3 mixture

Alumina-titanium diboride nanocomposite (Al₂O₃-TiB₂) was produced using mixtures of titanium dioxide, acid boric and pure aluminum as raw materials via mechanochemical process. The phase transformation and structural characterization during mechanochemical process were utilized by X-ray diffractometry (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), and thermogravimetric analyses (TG-DTA) techniques. A thermodynamic appraisal showed that the reaction between TiO₂, B₂O₃ and Al is highly exothermic and should be self-sustaining. XRD analyses exhibited that the Al₂O₃-TiB₂ nanocomposite was formed after 1.5 h milling time. The results indicate that increasing milling time up to 40 h had no significant effect other than refining the crystallite size.     

Enthalpy of formation of selected mixed oxides in a CaO-SrO-Bi2O3-Nb2O5 system

The heats of drop-solution in 3Na₂O + 4MoO₃ melt at 973 K and 1073 K for calcium and strontium carbonates, Bi₂O₃, Nb₂O₅ and several stoichiometric mixed oxides in CaO-Nb₂O₅, SrO-Nb₂O₅ and Bi₂O₃-Nb₂O₅ systems were measured using a Setaram Multi HTC-96 calorimeter. The values of enthalpy of formation from constituent binary oxides at 298 K, Δ_oxH, were derived for the mixed oxides under investigation: Δ_oxH(CaNb₂O₆) = −132.0 ± 23.8 kJ mol⁻¹, Δ_oxH(Ca₂Nb₂O₇) = −208.0 ± 31.9 kJ mol⁻¹, Δ_oxH(SrNb₂O₆) = −167.9 ± 19.1 kJ mol⁻¹, Δ_oxH(Sr₂Nb₂O₇) = −289.2 ± 37.5 kJ mol⁻¹ and Δ_oxH(BiNbO₄) = −41.9 ± 11.1 kJ mol⁻¹. Additionally, the values Δ_oxH for other mixed oxides with different stoichiometries were estimated on the basis of these experimental results.     

Synthesis and luminescent properties of Ln3+ (Ln3+ = Eu3+, Dy3+) -doped Bi2ZnB2O7 phosphors

The new phosphors Bi2ZnB2O7:Ln3+ (Ln3+ =Eu3+,Dy3+) were synthesized by solid-state reaction technique.The obtained phosphors were investigated by means of X-ray powder diffraction (XRD),photoluminescence excitation and emission spectra with the aim of enhancing the fundamental knowledge about the luminescent properties of Eu3+ and Dy3+ ions in the Bi2ZnB2O7 host lattice.XRD analysis shows that all these compounds are of a single phase of Bi2ZnB2O7.The excitation and emission spectra of Bi2ZnB2O7:Ln3+ (Ln3+ =Eu3+,Dy3+) at room temperature show the typical 4f-4f transitions of Eu3+ and Dy3+,respectively.The hypersensitive transitions of 5D0→7F2 (Eu3+) and 4F9/2→ 6H13/2 (Dy3+) are relatively higher than those of the insensitive transitions in Bi2ZnB2O7.It is conceivable that the Bi2ZnB2O7 structure provides asymmetry sites for activators (Eu3+,Dy3+).The optimum concentrations of Eu3+ and Dy3+ ions in Bi2ZnB2O7 phosphors are both x =0.05.     

Tie lines and activities in the system NiO-MgO-SiO2 at 1373 K

The isothermal section of the phase diagram for the system NiO-MgO-SiO₂ at 1373 is established. The tie lines between (Ni_xMg_1-x )O solid solution with rock salt structure and orthosilicate solid solution (Ni_yMg_1-y)Si_0.5O₂ and between orthosilicate and metasilicate (Ni_zMg_1-z)SiO₃ crystalline solutions are determined using electron probe microanalysis (EPMA) and lattice parameter measurement on equilibrated samples. Although the monoxides and orthosilicates of Ni and Mg form a continuous range of solid solutions, the metasilicate phase exists only for 0 < Z < 0.096. The activity of NiO in the rock salt solid solution is determined as a function of composition and temperature in the range of 1023 to 1377 using a solid state galvanic cell. The Gibbs energy of mixing of the monoxide solid solution can be expressed by a pseudo-subregular solution model: ΔG^ex = X(l - X)[(-2430 + 0.925T)X + (-5390 + 1.758T)(1 - X)] J/mol. The thermodynamic data for the rock salt phase are combined with information on interphase partitioning of Ni and Mg to generate the mixing properties for the orthosilicate and the metasilicate solid solutions. The regular solution model describes the orthosilicate and the metasilicate solid solutions at 1373 K within experimental uncertainties. The regular solution parameter ΔG^ex/Y(1-Y) is -820 (±70) J/mol for the orthosilicate solid solution. The corresponding value for the metasilicate solid solution is -220 (±150) J/mol. The derived activities for the orthosilicate solid solution are discussed in relation to the intracrystalline ion exchange equilibrium between Ml and M2 sites. The tie line information, in conjunction with the activity data for orthosilicate and metasilicate solid solutions, is used to calculate the Gibbs energy changes for the intercrystalline ion exchange reactions. Combining this with the known data for NiSi_0.5O₂, Gibbs energies of formation of MgSi_0.5O₂, MgSiO₃, and metastable NiSiO₃ are calculated. The Gibbs energy of formation of NiSiO₃, from its component oxides, is equal to 7.67 (±0.6)kJ/mol at 1373K.     

Phase diagram calculations of ZrO2-based ceramics with an emphasis on the reduction/oxidation equilibria of cerium ions in the ZrO2-YO1.5-CeO2-CeO1.5 system

Phase diagram calculations that were made previously for the ZrO₂-MO _m/2 (m = 2, 3, 4) systems and for the ZrO₂-YO_1.5-MO _m/2 (M = transition metals) systems have been extended to the ZrO₂-YO_1.5-CeO₂(-CeO_1.5) system to make an attempt to explain (1) thermogravimetric (TG) results as a function of oxygen potential, (2) electronic conductivity as a function of oxygen potential, and (3) a miscibility gap observed in air. The interaction parameters for the CeO₂-CeO_1.5-YO_1.5 system were obtained from the reported oxygen nonstoichiometry in CeO_2−x and rate earth doped ceria, (Ce,RE)O_2−δ . The interaction parameters for the ZrO₂-CeO₂ subsystem were obtained so as to reproduce the observed miscibility gap at 1273 K. Those thermodynamic properties can reproduce consistently the experimental behaviors of the electronic conductivity and the TG results in the (Zr_1−x Ce _x )_0.8Y_0.2O_1.9 solid solutions; these indicate the enhancement of reduction of CeO₂.     

Surface tension and thermodynamic properties of liquid Ag-Bi solutions

With the maximum bubble pressure method, the density and surface tension were measured for five Ag-Bi liquid alloys (X _Bi=0.05, 0.15, 0.25, 0.5, and 0.75), as well as for pure silver. The experiments were performed in the temperature range 544–1443 K. Linear dependences of both density and surface tension versus temperature were observed, and therefore the experimental data were described by linear equations. The density dependence on concentration and temperature was derived using the polynomial method. A similar dependence of surface tension on temperature and concentration is presented. Next, the Gibbs energy of formation of solid Bi₂O₃, as well as activities of Bi in liquid Ag-Bi alloys, were determined by a solid-state electromotive force (emf) technique using the following galvanic cells: Ni, NiO, Pt/O ⁻²/W, Ag _X Bi _(1−X), Bi ₂ O _3(s). The Gibbs energy of formation of solid Bi₂O₃ from pure elements was derived: =−598 148 + 309.27T [J · mol⁻¹] and =−548 008 + 258.94T [J · mol⁻¹]; the temperature and the heat of the α → δ transformation for this solid oxide were calculated as 996 K and 50.14 J · mol⁻¹. Activities of Bi in the liquid alloys were determined in the temperature range from 860–1075 K, for five Ag-Bi alloys (X _Ag=0.2, 0.35, 0.5, 0.65, 0.8), and a Redlich-Kister polynomial expansion was used to describe the thermodynamic properties of the liquid phase. Using Thermo-Calc software, the Ag-Bi phase diagram was calculated. Finally, thermodynamic data were used to predict surface tension behavior in the Ag-Bi binary system.     

Surface tension and thermodynamic properties of liquid Ag-Bi solutions

With the maximum bubble pressure method, the density and surface tension were measured for five Ag-Bi liquid alloys (X _Bi=0.05, 0.15, 0.25, 0.5, and 0.75), as well as for pure silver. The experiments were performed in the temperature range 544–1443 K. Linear dependences of both density and surface tension versus temperature were observed, and therefore the experimental data were described by linear equations. The density dependence on concentration and temperature was derived using the polynomial method. A similar dependence of surface tension on temperature and concentration is presented. Next, the Gibbs energy of formation of solid Bi₂O₃, as well as activities of Bi in liquid Ag-Bi alloys, were determined by a solid-state electromotive force (emf) technique using the following galvanic cells: Ni, NiO, Pt/O ⁻²/W, Ag _X Bi _(1−X), Bi ₂ O _3(s). The Gibbs energy of formation of solid Bi₂O₃ from pure elements was derived: =−598 148 + 309.27T [J · mol⁻¹] and =−548 008 + 258.94T [J · mol⁻¹]; the temperature and the heat of the α → δ transformation for this solid oxide were calculated as 996 K and 50.14 J · mol⁻¹. Activities of Bi in the liquid alloys were determined in the temperature range from 860–1075 K, for five Ag-Bi alloys (X _Ag=0.2, 0.35, 0.5, 0.65, 0.8), and a Redlich-Kister polynomial expansion was used to describe the thermodynamic properties of the liquid phase. Using Thermo-Calc software, the Ag-Bi phase diagram was calculated. Finally, thermodynamic data were used to predict surface tension behavior in the Ag-Bi binary system.     

Study on the crystal structure of the rare earth oxyborate Yb26B12O57 from powder X-ray and neutron diffraction

Yb₂₆B₁₂O₅₇, a rare earth oxyborate previously assigned as Yb₃BO₆, has been studied by various techniques including neutron and X-ray diffraction, ¹¹B NMR spectroscopy, electron diffraction and high angle angular dark field-scanning transmission electron microscopy (HADDF-STEM). It crystallizes in the space group C2/m with cell parameters of a = 24.5780(4) Å, b = 3.58372(5) Å, c = 14.3128(3) Å and β = 115.079(1)°. The structure consists of slabs of rare earth sesquioxide and borate groups. The sesquioxide part is identified from the structural refinement, and is observed from HADDF-STEM image, while elucidation of borate groups is not straightforward. An additional oxygen atom (O31), which links two B₂O₅ groups into a B₄O₁₁ polyanion, is identified from the analysis of neutron diffraction data. The occupancy of this oxygen site is only quarter, which results in a random distribution of B₄O₁₁ and B₂O₅ groups along the b-direction. The chemical formula of ytterbium oxyborate is Yb₂₆(BO₃)₄(B₂O₅)₂(B₄O₁₁)O_24, instead of the simple stoichiometric formula Yb₃BO₆. This compound is paramagnetic but its susceptibility deviated from the Curie-Weiss law at low temperature.     

Gadolinium zinc borate glass-based low temperature Co-fired ceramics

New microwave materials based on a gadolinium zinc borate (20ZnO−20Gd₂O₃−60B₂O₃) glass with typical Al₂O₃ filler have been investigated as a dielectric candidate for low temperature co-fired ceramic (LTCC) applications. The experimental parameters, such as filler contents and firing temperature, were found to affect seriously densification, crystallization and microwave dielectric properties. The presence of ZnAl₂O₄ and GdBO₃ phases with an unexpected GdAl₃(BO₃)₄ phase were assumed to influence the final performance of the materials. In particular, the GdAl₃(BO₃)₄ phase is the consequence of chemical reactions between the glass and Al₂O₃ filler during firing. As a promising dielectric composition, the sample consisting of 20ZnO−20Gd₂O₃−60B₂O₃ and 40 wt.% Al₂O₃ filler exhibited k (dielectric constant) ∼8.1 and Q (quality factor) ∼312 at 18.6 GHz when fired at 850°C.