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.     

Phase equilibria and multiphase reaction diffusion in the Cr-C and Cr-N systems

The phase formation in the Cr-C and Cr-N systems was investigated using reaction diffusion couples. The carbides were prepared by reaction of chromium metal with graphite powder in the range 1143 to 1413 °C in argon atmosphere; the nitride samples by reaction of the metal with N₂ (≤31 bar) in the range 1155 to 1420 °C. While the carbide samples showed the three chromium carbide phases in form of dense diffusion layers between 1100 and 1400 °C, porosity occurred at temperatures above 1400 °C. The composition of the phase bands was measured by the means of electron probe microanalysis. For the Cr₂₃C₆ phase, a slightly higher C composition was found than given in the literature. In Cr-N diffusion couples both the δCrN_1−x and βCr₂N formed phase bands at T≥1150 °C. Because decomposition processes occurred upon cooling, quenching experiments were carried out in the range 1370 to 1420 °C at 31 bar N₂ to stabilize the phases. The EPMA investigations of the homogeneity ranges yielded a large increase of the homogeneity range for δCrN_1−x with increasing temperature. The nonmetal diffusion coefficients in all phases of both systems were calculated from layer growth and/or from concentration profiles. In δCrN_1−x the N diffusivity was found to be strongly dependent on the composition. The Vickers microhardnesses of the various phases were obtained by measuring the diffusion layers.     

Phase equilibria and multiphase reaction diffusion in the Cr-C and Cr-N systems

The phase formation in the Cr-C and Cr-N systems was investigated using reaction diffusion couples. The carbides were prepared by reaction of chromium metal with graphite powder in the range 1143 to 1413 °C in argon atmosphere; the nitride samples by reaction of the metal with N₂ (≤31 bar) in the range 1155 to 1420 °C. While the carbide samples showed the three chromium carbide phases in form of dense diffusion layers between 1100 and 1400 °C, porosity occurred at temperatures above 1400 °C. The composition of the phase bands was measured by the means of electron probe microanalysis. For the Cr₂₃C₆ phase, a slightly higher C composition was found than given in the literature. In Cr-N diffusion couples both the δCrN_1−x and βCr₂N formed phase bands at T≥1150 °C. Because decomposition processes occurred upon cooling, quenching experiments were carried out in the range 1370 to 1420 °C at 31 bar N₂ to stabilize the phases. The EPMA investigations of the homogeneity ranges yielded a large increase of the homogeneity range for δCrN_1−x with increasing temperature. The nonmetal diffusion coefficients in all phases of both systems were calculated from layer growth and/or from concentration profiles. In δCrN_1−x the N diffusivity was found to be strongly dependent on the composition. The Vickers microhardnesses of the various phases were obtained by measuring the diffusion layers.     

Thermodynamic study of the phase equilibria in the Sn−Ti−Zn ternary system

The Sn−Ti−Zn ternary phase diagram has been constructed using the CALPHAD technique. The Ti−Zn binary system phase boundaries were determined using differential scanning calorimetry and the solid-liquid diffusion couples method. In addition, the formation energy of some stoichiometric compounds was obtained using first-principle band energy calculations. For the ternary system, some alloys were prepared by equilibration at 600 or 700 °C, and the compositions of the precipitates were analyzed using electron probe microanalysis. Thermodynamic assessment of the Ti−Zn and Sn−Ti−Zn systems was performed based on the experimental information and by adopting reported values of the thermodynamic properties of the Sn−Zn and Sn−Ti binary systems. Microstructural observation showed that Sn₃Ti₅Zn₁₂ exists in the ternary system. Seven types of invariant reaction on the Sn-rich liquidus surface of the ternary system are predicted by the phase diagram calculations. The ternary eutectic point falls at 0,0009 mass% Ti and 8.69 mass% Zn, at T=192.40°C, which is slightly lower than the calculated eutectic point of Sn−Zn binary alloy (T=192.41°C). Based on these results, a nonequilibrium solidification process using the Scheil model was simulated. This paper was presented at the International Symposium on User Aspects of Phase Diagrams, Materials Solutions Conference and Exposition, Columbus, Ohio, 18–20 October, 2004.     

Thermodynamics of the liquid Co-Cu system and calculation of phase diagram

Knudsen-cell mass spectrometric measurements have been carried out in the liquid phase of the Co-Cu system in the concentration range 25.0 to 85.9 at. % Cu in the temperature range 1347 to 1587 °C. The molar excess Gibbs energy, enthalpy and entropy of mixing, as well as the thermodynamic activities of components in the liquid Co-Cu system were determined using the composition and temperature dependence of the ratio of intensities of ⁵⁹Co and ⁶³Cu ions. The results show that a subregular solution model would fit measured data well (2-parameter thermodynamically adapted power (TAP) series: C _n ^H in J·mol⁻¹; C ₁ ^H =35,961, C ₂ ^H =−5573.2; C _n ^S in J·mol^−1·K−1; C ₁ ^S =5.54, C ₂ ^S =−3.35). A special experiment verified solid-liquid phase equilibrium at 1327 °C and the phase diagram was calculated.     

Experimental determination and thermodynamic calculation of phase equilibria in the Fe−Mn−Al system

The phase equilibria among the face-centered cubic (fcc), body-centered cubic (bcc), and βMn phases at 800, 900, 1000, 1100, and 1200 °C were examined by electron probe microanalysis (EPMA), and the A2/B2 and B2/D0₃ ordering temperatures were also determined using the diffusion couple method and differential scanning calorimetry (DSC). The critical temperatures for the A2/B2 and B2/D0₃ ordering were found to increase with increasing Mn content. Thermodynamic assessment of the Fe−Mn−Al system was also undertaken with use of experimental data for the phase equilibria and order-disorder transition temperatures using the CALPHAD (Calculation of Phase Diagrams) method. The Gibbs energies of the liquid, αMn, βMn, fcc, and ε phases were described by the subregular solution model and that of the bcc phase was represented by the two-sublattice model. The thermodynamic parameters for describing the phase equilibria and the ordering of the bcc phase were optimized with good agreement between the calculated and experimental results. This paper was presented at the International Symposium on User Aspects of Phase Diagrams, Materials Solutions Conference and Exposition, Columbus, Ohio, 18–20 October, 2004.     

Thermodynamics of the liquid Co-Cu system and calculation of phase diagram

Knudsen-cell mass spectrometric measurements have been carried out in the liquid phase of the Co-Cu system in the concentration range 25.0 to 85.9 at. % Cu in the temperature range 1347 to 1587 °C. The molar excess Gibbs energy, enthalpy and entropy of mixing, as well as the thermodynamic activities of components in the liquid Co-Cu system were determined using the composition and temperature dependence of the ratio of intensities of ⁵⁹Co and ⁶³Cu ions. The results show that a subregular solution model would fit measured data well (2-parameter thermodynamically adapted power (TAP) series: C _n ^H in J·mol⁻¹; C ₁ ^H =35,961, C ₂ ^H =−5573.2; C _n ^S in J·mol^−1·K−1; C ₁ ^S =5.54, C ₂ ^S =−3.35). A special experiment verified solid-liquid phase equilibrium at 1327 °C and the phase diagram was calculated.     

Critical assessment and thermodynamic calculation of the ternary system C-Hf-Zr (Carbon-Zirconium-Hafnium)

Based on an assessment of the available experimental thermochemical and phase diagram information available, the phase equilibria of the C-Hf-Zr system were calculated. The G of the individual phases was described with thermodynamic models. The liquid phase was described as a substitutional solution using the Redlich-Kister formalism for excess G. Graphite was treated as a stoichiometric phase. The solid solutions of carbon in α(Hf,Zr) and β(Hf,Zr), as well as the non-stoichiometric phase (Hf,Zr)C_1−x, were represented as interstitial solid solutions using the compound energy model with two sublattices. The parameters in the models were determined by computerized optimization using selected experimental data. A detailed comparison was made between calculation and experimental data.     

Thermodynamic properties and phase equilibria in the Cr-P system

A Knudsen effusion method with mass-spectrometric analysis of gaseous phase has been applied to investigate the thermodynamic properties of the chromium phosphides (1341 to 1704 K) and Cr-P liquid alloys (1664 to 1819 K). Simultaneously, DSC has been used to measure heat capacities of chromium phosphides Cr₃P and Cr₁₂P₇ in the temperature range of113 to 873 K. The entropies of formation of chromium phosphides calculated according to the second and third laws of thermodynamics agree within the limits of experimental error. The Gibbs energies of formation of the phosphides from solid Cr and P₂ gas have been approximated with the following equations (in J/mol): A_fG⁰(Cr₃P) = −(244 112 ±2800) + (70.95 ±1.80)T ΔG⁰(Cr₁₂2P₇) = −(1563 678 ±15 350) + (440.6 ±9.90)T Thermodynamic properties of liquid solutions have been described with the ideal associated-solution model assuming that CrP, Cr₂P, Cr₃P, and Cr₃P₂ complexes exist in the melt. The phase diagram computed with the help of the thermodynamic data agrees with the published information.     

Electromotive force study of the liquid silver-bismuth-tin alloys

The Ag−Bi−Sn alloy system has been assessed twice, so far, for its potential applications as a lead-free solder material. The first assessment was based on binary data only; the second assessment introduced ternary parameters. It was noted in conclusion that more experimental studies were needed, especially for the liquid phase. The electromotive force (emf) measurement method was used in this study to determine the thermodynamic properties of liquid Ag−Bi−Sn alloys using solid electrolyte galvanic cells as shown below: Re, Ag−Bi−Sn, SnO₂ |Yttria Stabilized Zirconia| Ni, NiO, Pt, Re, Sn, SnO₂ |Yttria Stabilized Zirconia| Ni, NiO, Pt. Alloy compositions for in vestigation were chosen along three constant Bi-to-Sn ratio lines (1/3, 1, and 3) and with the silver content changing from 10 up to 90 at.%, every 10 at.%, resulting in a total of 27 different alloy samples. The temperature of the measurements varied from 975 to 1400 K. A linear dependence of the emf on temperature was observed for all compositions, and the appropriate line equations were derived. Excess partial Gibbs energies of Sn were then calculated at 1200 K and compared with the results of the calculations of both assessments; Gibbs energy of formation of SnO₂ was determined as well. It was then shown that our new emf data fit better to the binary formalism-based calculations than to the second assessment results.     

Computation of metastable phases in tungsten-carbon system

Metastable phase equilibria in the W-C system are presented in the vicinity of the metastable reactions involving W₂C, WC_1−x , and WC. Metastable phase boundaries were obtained by reproducing the stable boundaries using optimized Gibbs energy formulations and extrapolating them into regions of metastability. Four metastable reactions were obtained: a metastable congruent melting reaction of WC at 3106 K, a metastable eutectic reaction between WC_1−x and graphite at 2995 K, a metastable eutectic reaction between W₂C and WC at 2976 K, and a metastable eutectic reaction between W₂C and graphite at 2925 K. The reaction enthalpies and entropies associated with these transitions are also computed using the available Gibbs energy data. Furthermore, possible kinetic paths that could lead to metastability are discussed.     

Phase equilibria in the cobalt oxide-copper oxide system

Thermodynamic properties were determined for the system cobalt oxide-copper oxide by means of an electromotive force (EMF) measurement techniques using galvanic cells with calciastabilized zirconia (CSZ) as the solid electrolyte and with air as the reference electrode according to the following schemes: CuO, Cu₂O | CSZ | air and CoO-CuO, Cu₂O CSZ | air for composition variables y=X_Cu/(X_Co+X_cu equal to 0.05, 0.15, 0.25, 0.35, 0.45, 0.667, and 0.8; and within the temperature interval 1200–1350 K. Thermodynamic properties calculated directly from EMF values were combined with the available literature data on phase equilibria, and thermodynamic properties of solid phases in the Co-Cu-O system were assessed. Both terminal solid solutions, (Co,Cu)O and (Cu,Co)O, were described by a sublattice model with Redlich-Kister excess term. The interaction parameters for both (Co,Cu)O and (Cu,Co)O solid solutions and the Gibbs energy of formation for the intermediate phase Cu₂CoO₃ were obtained. The Gibbs energies of fictive end-members: monoclinic “CoO” and “CuO” with rock salt structure were derived as well. The phase diagrams were calculated using the assessed thermodynamic parameters. The (T, y) phase diagram was calculated for existence under ambient air. The property diagrams log₁₀P(O₂) versus composition and activity of CuO versus composition were calculated at 1273 K. The results of our calculations were in a good agreement with available experimental data. This paper was presented at CALPHAD XXX International Conference on Phase Diagram Calculations in York, UK, May 27–June 1, 2001, and appeared in the Conference Abstracts on Page 75.     

Computation of metastable phases in tungsten-carbon system

Metastable phase equilibria in the W-C system are presented in the vicinity of the metastable reactions involving W₂C, WC_1−x , and WC. Metastable phase boundaries were obtained by reproducing the stable boundaries using optimized Gibbs energy formulations and extrapolating them into regions of metastability. Four metastable reactions were obtained: a metastable congruent melting reaction of WC at 3106 K, a metastable eutectic reaction between WC_1−x and graphite at 2995 K, a metastable eutectic reaction between W₂C and WC at 2976 K, and a metastable eutectic reaction between W₂C and graphite at 2925 K. The reaction enthalpies and entropies associated with these transitions are also computed using the available Gibbs energy data. Furthermore, possible kinetic paths that could lead to metastability are discussed.     

Phase equilibria in the cobalt oxide-copper oxide system

Thermodynamic properties were determined for the system cobalt oxide-copper oxide by means of an electromotive force (EMF) measurement techniques using galvanic cells with calciastabilized zirconia (CSZ) as the solid electrolyte and with air as the reference electrode according to the following schemes: CuO, Cu₂O | CSZ | air and CoO-CuO, Cu₂O CSZ | air for composition variables y=X_Cu/(X_Co+X_cu equal to 0.05, 0.15, 0.25, 0.35, 0.45, 0.667, and 0.8; and within the temperature interval 1200–1350 K. Thermodynamic properties calculated directly from EMF values were combined with the available literature data on phase equilibria, and thermodynamic properties of solid phases in the Co-Cu-O system were assessed. Both terminal solid solutions, (Co,Cu)O and (Cu,Co)O, were described by a sublattice model with Redlich-Kister excess term. The interaction parameters for both (Co,Cu)O and (Cu,Co)O solid solutions and the Gibbs energy of formation for the intermediate phase Cu₂CoO₃ were obtained. The Gibbs energies of fictive end-members: monoclinic “CoO” and “CuO” with rock salt structure were derived as well. The phase diagrams were calculated using the assessed thermodynamic parameters. The (T, y) phase diagram was calculated for existence under ambient air. The property diagrams log₁₀P(O₂) versus composition and activity of CuO versus composition were calculated at 1273 K. The results of our calculations were in a good agreement with available experimental data.     

The sharpness of melting maxima

The shape of melting maxima for strictly stoichiometric phases is examined by computer calculations. For a simplified case, it is found that such maxima look sharp, in apparent violation of Konovalov’s rule, if the Gibbs energy of formation of the phase is −20T _m J/mole of atoms or lower (more negative).     

Thermodynamic causes of the high diffusion rate of atoms in the superficial layer of a metallic electrode

Concentration of vacancies N _V(S) in a superficial layer (SL) of fcc lattices of Ag, Cu, and Au metals is thermodynamically estimated and analyzed. The calculations are based on a thermodynamic vacancy model of the metal SLs, by which the N _V(S) value is related to the surface Gibbs energy ΔG _s = −RTlnN _V(S). A strong ΔG _s dependence on the electrode potential and the zero point value of the metal results in the increase in N _V(S) value, which reaches nearly 10⁻² at standard potentials of the above metals. The high surface self-diffusivity of atoms (D ≅ 10⁻¹⁵ cm²/s) calculated from the in situ STM measurements of the electrode surfaces is due to the high concentration of vacancies in the metal SLs. Original Russian Text ? Yu.Ya. Andreev, 2007, published in Zashchita Metallov, 2007, Vol. 43, No. 1, pp. 18–24.     

Pyrolysis effect of group V vapor sources on the composition ranges for metal-organic vapor phase epitaxy growth of III-V semiconductors

The pyrolysis effect of NH₃ and PH₃ vapor sources on the composition ranges necessary for growing single-phase semiconductors was studied with respect to the metal-organic vapor phase epitaxy (MOVPE) of GaN and (Ga_1−x In _x )P semiconductors. The Ga-N-C-H system and the Ga-In-P-C-H system were thermodynamically analyzed respectively under the conditions of the equilibrium pyrolysis, the partial pyrolysis, and the non-pyrolysis of the vapor phase species, NH₃ and PH₃. Both the complete equilibrium and the constraint equilibrium in these two systems were calculated with the aid of the specially designed database files and Thermo-Calc software. The experimental MOVPE data from the literature were compared with calculated results. The correspondence of the theoretical prediction with the experimental data indicates that the thermodynamic analysis for the MOVPE process of GaN and (Ga_{1− x}In _x )P semiconductors needs to be considered in terms of the practical pyrolysis of NH₃ and PH₃ vapor sources. The approach of the complete thermodynamic equilibrium is applied only to some specific temperature region or certain epitaxy processes after typical pretreatment of vapor sources.     

Thermodynamic study of phase equilibria in the Ni-Si-B system

A thermodynamic analysis of the phase equilibria in the Ni-Si-B ternary system was conducted. A regular solution approximation based on a sublattice model was adopted to describe the Gibbs energies for the individual phases in the binary and ternary systems. A set of thermodynamic parameters for the individual phases was evaluated from literature data on phase boundaries and thermochemical properties. The optimized parameters reproduced the experimental data, for the most part, satisfactorily. However, in the calculated isothemal section at 850 °C, phase equilibria between the fcc phase and Ni₆Si₂B or Ni₃Si(β ₁) and Ni₆Si₂B were found instead of the experimentally observed equilibria between Ni₃Si(β ₁) and Ni₃B or Ni₅Si₂(γ) and Ni₃B. Further, in the primary crystal surface for the fcc phase, the calculated liquidus temperatures were higher than the reported values by approximately 80 °C. Therefore, it is considered that the fcc phase evaluated in the Ni-Si system by Lindhólm and Sundman is too stable.