A comparison of the structure of liquid alloys derived from thermodynamic and diffraction studies

A significant amount of research on the thermodynamic properties of molten alloys is undertaken for obtaining insights into their structure . The partial and integral molar enthalpies, entropies and volumes of mixing provide some general information on the nature and strength of atomic bonds and the distribution of atoms. However, until recently it has been difficult to derive specific quantitative information because the excess entropy of mixing contains configurational , vibrational , electronic , and sometimes magnetic contributions which cannot be easily separated.

Correlations between structure and thermodynamic properties of spinels and their applications in technology

Measurements a/the Gibbs' energy enthalpy and entrupy vffarmation oj chromites, vanadites and alumlnat.:s 0/ F", Ni. Co'. Mn, Zn Mg and Cd, using solid oxide galvanic cells over a ternperature range extending approximately lOOO°C, have shown that the '~'Ilir"!,,, J'JrIl/iJ~ tion 0/ cubic 2-3 oxide spinel phases (MX!O,), from component oxide (MO) with rock-salt and X.Os whir c(1f'l/!ldwn st!'llt'lw,·. call b,' represented by a semi-empirical correlalion, ~S~ = --LiS + L'i,SM +~S~:"d(±O.3) cal.deg-1 mol-1 where /',.SM Is the entropy 0/calian mixing oillhe tetrahedral alld octahedral sites o/the spinel and Sr:~ is tlie enfropy associaf,'d Wifh Ih,' randomization a/the lahn-Telier distortions. A review a/the methods/or evaluating the cation distriblltion lfl spille!s suggeJ{j' l/r,l! Ihe most promising scheme is based Oil octahedral site preference energies from the crystal field theory for the Iral1silioll IIIl'f"! IlIIL';. For I/""-Irallsifioll melal cal ions site preference energies are derived relative /0 thol'lt fLI, [ransilion metal ions from measured high tClllP('ftJi ure Cal iUlI disll iiJuriol1 in spine! phases thar contail! one IransilioJl metal and another non-transition metal carion. For 2-3 srinds compulatiorrs b,IS"J Oil i.!c[J;' Temkin mixing on each catioll subialtice predici JistributionJ that are In fair agreement with X-ray and 1I1'IIIrOll ditTraction, /IIdg""!ic dll.! electrical propcrries, and spectroscopic measurements. In 2-4 spineis mixing vI ions do not foliow strictly ideal slllIistli:al Jaws, Th,' OIl/up) associated with the randomizalion 0/the Jllhn-Teller dislOriioll" appear to be significant, only ill spinels witll 3d'. 3d', 3d' (ifld~UI' iOtls in tetrahedral and 3d' and 3d9 ions in octahedral positions. Application 0/this structural model for predicting the thermodynamic proputies ofspinel solid .,olutiofl5 or,' illustrated. F,lr complex systems additional contributions arising from strain fields, redox equilibria and off-center ions have to be qllalllififti. The entropy correlation for spinels provides a method for evaluating structure tran:.jormafiofl entropies in silllple o.\id.-s, ["founlllion on the relative stabilities ofoxides in different crystallCtructures is USe/III for computer ea/culaliof! a/phase dfugrullls ofIlIrer,',,1 III (N.lll1ie5 by method, similar to thost: used by Kaufman and Bernstein for refractory alloy systems. Examples oftechnoiogical appliCation tnclude the predictioll ofdeoxidation equilibria in Fe-Mn-AI-O s),slelll at 1600°C duj ,'Ulllpltfalion 0/phase relutions in Fe-Ni-Cr-S system,

Phase relationships in the system Cr W O and thermodynamic properties of CrWO4 and Cr2WO6

The phase diagram of the Cr-W-O system at 1000° C was established by metallographic and X-ray identification of the phases present after equilibration in evacuated silica capsules. Two ternary oxide phases, CrWO4 and Cr2WO6 were detected. The oxygen potential over the three-phase mixtures, W+Cr2O3 s+CrWO4, WO2.90+CrWO4+Cr2WO6 and Cr2O3+CrWO4+Cr2WO6, were measured by solid state cells incorporating Y2O3 stabilized ZrO2 electrolyte and Ni+NiO reference electrode. The Gibbs' energies of formation of the two ternary phases can be represented by the following equations

A derivation of thermodynamic quantities of liquid alloys from their structure factors

A method of deriving the thermodynamic properties of mixing in liquid alloys Delta G, Delta S and Delta H, from low-Q scattering data has been presented. As an example, the method has been demonstrated with liquid Na-Ga alloys for which both thermodynamic and diffraction data have recently been obtained by the authors.

Computation of thermodynamic properties of liquid ferrous alloys from structural measurements

Relation between X-ray scattering intensities, mean square thermal fluctuations and thermodynamic properties. High temperature X-ray diffraction study of liquid Fe-Ni and Fe-Si alloys using reflection and transmission geometries. Calculation of the structure factor as a function of wave vector. Extrapolation to zero wave vector. Calculation of the concentration-concentration correlation function defined by A. B. Bhatia and D. E. Thorton. Computation of thermodynamic quantities of mixing A G, LlH and LlS for the binary alloys. Comparison with direct thermodynamic measurements reported in the literature.

Mass spectrometric and electrochemical studies of thermodynamic properties of liquid and solid phases in the CaO Al2O3 system

The activities of CaO and Al2O3 in lime-alumina melts were studied by Knudsen cell-mass spectrometry at 2060 K. Emf of solid state cells, with CaF2 as the electrolyte, was measured from 923 to 1223 K to obtain the free energies of formation of the interoxide compounds. The results are critically evaluated in the light of data reported in the literature on phase equilibria, activities in melts, and stabilities of compounds. A coherent set of data is presented, including the previously unknown free energy of formation of CaO.6Al2O3 and the temperature dependence of activities in the liquid phase.

Revision of thermodynamic data on MnO Al2O3 melts

The high temperature region of the MnO-A1203 phase diagram has been redetermined to resolve some discrepancies reported in the literature regarding the melting behaviour of MnA1,04. This spinel was found to melt congruently at 2108 (+ 15) K. Theactivity of MnOin MnO-Al,03 meltsand in the two phase regions, melt + MnAI,04 and MnAI2O4 + A1203, has been determined by measuring the manganese concentration in platinum foils in equilibrium under controlled oxygen potentials. The activity of MnO obtained in this study for M ~ O - A I ,m~el~ts is in fair agreement with the results of Sharma and Richardson.However. the alumina-rich melt is found to be in equilibrium with MnAl,04 rather than AI2O3. as suggested by ~ha rmaan d Richardson. The value for the acthity of MnO in the M~AI ,O,+ A1,03 two phaseregion permits a rigorous application of the Gibbs-Duhem equation for calculating the activity of A1203 and the integral Gibbs' energy of mixing of MnO-A1203 melts, which are significantly different from those reported in the literature.

Thermodynamic properties of Fe3O4 FeAl2O4 spinel solid solution

The Gibbs energy of mixing for the system Fe3O4-FeAl2O4 was determined at 1573 K using a gas-metal-oxide equilibration technique. Oxide solid solution samples were equilibrated with Pt foils under controlled CO+CO2 gas streams. The equilibrium iron concentration in the foil was determined by chemical analysis. The cation distribution between tetrahedral and octahedral sites in the spinel crystal can be calculated from site-preference energies and used as an alternate method of determining some thermodynamic properties, including the Gibbs energy of mixing. The solvus occurring at low temperatures in the system Fe3C4-FeAl2C4 was used to derive the effect of lattice distortion due to cation size difference on the enthalpy of mixing and to obtain a better approximation to the measured thermodynamic quantities.

Thermodynamic properties of Fe3O4 FeV2O4 and Fe3O4 FeCr2O4 spinel solid solutions

Solid solutions of Fe304-FeV204 and Fe304-FeCr204 were prepared and equilibrated with Pt under controlled streams of CO/CO, gas mixtures at 1673 K. The concentration of Fe in Pt was used to determine the activity of Fe304 in the solid solutions. The activity of the second component was calculated by Gibbshhem integration. From these data, the Gibbs energy of mixing was derived for both systems. The experimental results and theoretical values which are determined from calculated cation distribution compare favorably in the case of vanadite solid solutions but not in the case of chromite solid solutions. The difference is attributed to a heat term arising from lattice distortion due to cation size difference. The positive heat of mixing will give rise to a miscibility gap in the system Fe304-FeCr204 at lower temperatures.

Computation of thermodynamic properties of quaternary and higher order systems from binary data using shortest distance composition paths

Equations for the computation of integral and partial thermodynamic properties of mixing in quarternary systems are derived using data on constituent binary systems and shortest distance composition paths to the binaries. The composition path from a quarternary composition to the i-j binary is characterized by a constant value of (Xi − Xj). The merits of this composition path over others with constant values for View the MathML source or Xi are discussed. Finally the equations are generalized for higher order systems. They are exact for regular solutions, but may be used in a semiempirical mode for non-regular solutions.

Thermodynamic properties and phase boundaries of Co O solutions

The thermodynamic properties of liquid unsaturated Co--O solutions have been determined by electrochemical measurements using (Y sub 2 O sub 3 )ThO sub 2 as solid electrolyte. The cell can be represented as, Pt. MoO sub 2 + Mo | (Y sub 2 O sub 3 )ThO sub 2 | O sub Co , tungsten, Pt, Emf of the cell was measured as a function of oxygen concentration in liquid Co at 1798, 1873 and 1973K. Least-mean squares regression analysis of the experimental data gives for the free energy of solution of diatomic oxygen in liquid Co Delta G exp 0 sub O(Co) = --84935--7.61 T ( plus/minus 400) J/g-atom and self interaction parameter for oxygen epsilon exp O sub O = --97240/T + 40.52 ( plus/minus 1) where the standard state for O is an infinitely dilute solution in which the activity is equal to atomic percent. The present data are discussed in comparison with those reported in the literature and the phase diagram for the Co--O system. 18 ref.--AA.

Thermodynamic properties of Cr Mo solid alloys

The activity of Cr in solid Cr-Mo alloys has been measured at 1873 K using a metal-oxide-gas equilibrium technique. Thin foils of Mo were equilibrated with solid Cr203 under flowing gas mixtures of argon, hydrogen and watervapourof known composition. The equilibrium concentration of Cr in Mo was determined by chemical analysis. These measurements indicate positive deviations from Raoult's law. The activity data obtained in the study at 1873 K are combined with free energy of mixing at 1471 K, calorimetric enthalpy of mixing at 1673 K, and experimental evidence of phase separation at lower temperatures, reported in the literature, to obtain an optimised set of thermodynamic parameters for the Cr-Mosystem in the solid state.

Thermodynamic study of Fe2O3 Fe2(SO4)3 equilibrium using an oxyanionic electrolyte (Na2SO4 I)

The emf of the cell, Pt, Ar + O2 + SO2 + SO3/Na2SO4-I/Fe2O2 + Fe2(SO4)3, Pt, has been measured in the temperature range 800 to 1000 K, using a gas mixture of known input composition as the reference electrode. The equilibrium composition of the reference gas at the measuring temperatures was computed using the thermodynamic data on the gaseous species reported in the literature. A mixture of ferric oxide and sulfate was kept in a closed system to ensure establishment of equilibrium partial pressure at the electrode. The cell was designed to avoid physical contact between Fe2(SO4)3 and Na2SO4 electrolyte. Uncertainties arising from the formation of sulfate solid solution were thus eliminated. The Gibbs’ energy of formation of ferric sulfate calculated from the emf is discussed in comparison with data reported in the literature. There is no evidence for the formation of oxysulfates in the Fe-S-0 system. Based on the results obtained in the present study for Fe2(SO4)3 and literature data for other phases, chemical potential diagrams have been constructed for the Fe-S-O system at 900 and 1100 K.

Thermodynamic properties of Pt5La, Pt5Ce, Pt5Pr, Pt5Tb and Pt5Tm intermetallics

The Gibbs’ energies of formation of Pt5La, Pt5Ce, Pt5Pr, Pt5Tb and Pt5 Tm intermetallic compounds have been determined in the temperature range 870–1100 K using the solid state cell:Ta,M + MF3 /CaF2 /Pt5 M + Pt + MF3 ,TaTaM+MF3CaF2Pt5M+Pt+MF3Ta.The reversible emf of the cell is directly related to the Gibbs’ energy of formation of the Pt5M compound. The results can be summarized by the equations:DGf° á Pt5 La ñ = - 373,150 + 6 ·60 T( ±300 )J mol - 1 DGf° á Pt5 Ce ñ = - 367,070 + 5 ·79 T( ±300 )J mol - 1 DGf° á Pt5 Pr ñ = - 370,540 + 4 ·69 T( ±300 )J mol - 1 DGf° á Pt5 Tb ñ = - 372,280 + 4 ·11 T( ±300 )J mol - 1 DGf° á Pt5 Tm ñ = - 368,230 + 4 ·89 T( ±300 )J mol - 1 Unknown control sequence '\hfill'relative to the low temperature allotropic form of the lanthanide element and solid platinum as standard states The enthalpies of formation of all the Pt5M intermetallic compounds obtained in this study are in good agreement with Miedema’s model. The experimental values are more negative than those calculated using the model. The variation of the thermodynamic properties of Pt5M compounds with atomic number of the lanthanide element is discussed in relation to valence state and molar volume.