Thermodynamics of segregation in alloys

The segregation process is described in terms of thermodynamic equations that use concepts of excess partial molar free energies and activity coefficients. Using such generalized equations, simplified equations are developed that can be used to check the segregation behavior in terms of thermodynamic quantities that are generally available in the literature. These simplified equations can be used to represent segregation semiquantitatively in many situations, including those where the elements form highly stable chemical compounds, such as sulfides, borides, and phosphides. The validity of our equations is checked by comparing the calculated segregation values with those observed on the surface of Ni, Cr, Al, Y, and NiCrAl(Y) alloys containing small concentrations of sulfur.     

Thermodynamics of Ca-Ga alloys

The enthalpies of formation of the intermetallic compounds CaGa₄, Ca₃Ga₈, and CaGa₂, at 298.15 K, were determined by high-temperature liquid gallium solution calorimetric measurements to be −24.9 ± 4.9 kJ·g at.⁻¹, −25.4 ± 2.4 kJ·g at.⁻¹, and −38.8 ± 4.8 kJ·g at.⁻¹, respectively. The enthalpies of formation of CaGa₄ at 988 K and that of Ca₃Ga₈ at 1070 K were determined, using precipitation calorimetry, to be −28.2 ± 1.7 kJ·g at.⁻¹ and −22.5 ± 1.4 kJ·g at.⁻¹, respectively. The integral enthalpy of mixing of the (Ca-Ga) liquid alloys (ΔH ⁰) measured at 1309 K are described by the following Redlich-Kister equation:

Thermodynamics of Ti in Ag-Cu alloys

The thermodynamic activities of Ti at dilution in a series of Ag-Cu alloys and eutectic Ag-Cu alloys containing In or Sn were measured using a galvanic cell technique employing a ThO₂-8 pct Y₂O₃ electrolyte. The equilibrium oxide phase formed by the reaction of Ti (X_Ti > 0.004) in the Ag-Cu alloy melts with an A1₂O₃ or ZrO₂ crucible was Ti₂O (s). The free energy of formation of Ti₂O (s) was estimated from available thermodynamic data. Titanium activities were calculated from measured oxygen potentials and the free energy of formation of Ti₂O (s). Titanium in the eutectic Ag-Cu melt showed a positive deviation from ideal solution behavior at 1000°C, and its activity coefficient at infinite dilution was about 6.5 relative to pure solid Ti. Indium and Sn did not increase the activity coefficient of Ti in eutectic Ag-Cu melts. Silver increased the Ti activity coefficient in the Ag-Cu-Ti melts significantly. The Ti activity coefficient value in liquid Ag was about 20 times higher than in eutectic Ag-Cu melt at 1000 °C.     

Thermodynamics of molten Li-Sn alloys

The activity of Li in molten Li-Sn alloys was continuously varied and monitored electrochemically in cells of the type Al-LiAl/glass electrolyte/Sn/glass electrolyte/Al-LiAl. The temperature (320 to 380 °C) and compositional dependence of the Li activity coefficient, γ_Li, was found to follow a quadratic expression of the form In γ_Li = A + B(1 − X_Li)² up to 30 mole pct lithium. Further, the liquidus temperature, T_L, was found to follow TL(°C) = 642 X_Li + 188 for 0.20 X_Li 0.44 over the temperature range 320 to 470 °C. The partial and integral molar heats of solution were calculated and the results indicate that strong attractive forces exist between Sn and Li. These forces are strong enough to induce substantial ordering in the melt to an extent that the integral molar entropy of mixing at high Li contents (36 mole pct) is negative.     

Thermodynamics of austenitic Fe-C alloys

New data on the activity of carbon in austenite have been obtained by CO₂/CO equilibration of Fe-C alloys in the temperature range 900° to 1400°C. Equations for the thermodynamic properties of carbon and iron in austenite are obtained from the data combined with selected data from the literature. A slightly modified phase diagram is presented. The stability of cementite is also determined from data published earlier and the results of the present study. Parameters of the various models of the behavior of carbon in austenite taken from the literature are also calculated from the data.     

Thermodynamics of phosphorus in carbon-saturated manganese-based alloys

The interaction coefficient of phosphorus with silicon in a Mn-Si-C_sat alloy has been measured at 1573 K, equilibrating CaC₂, C, and Ca₃P₂ in a quartz capsule to keep the phosphorus partial pressure as high as 33.7 Pa. The activity coefficient of phosphorus in the melts increases with increasing silicon content, and the interaction parameter between silicon and phosphorus in the melts at carbon saturation ε^Si_P, C_sat was found to be 10.4. The activity of phosphorus in a carbon-saturated Fe-Mn alloy was also determined at temperatures of 1573 to 1673 K using a chemical equilibration technique between BaO-BaF₂ fluxes and Fe-Mn-C_sat with manganese mass contents ranging from 0 to 85.3 %. A slight decrease in the activity coefficient of phosphorus in Fe-Mn-C_sat alloys was observed with increasing manganese content, as a reflection of a stronger interaction between manganese and phosphorus than that between iron and phosphorus. The value for e^Mn_P,Csat was found to be -0.0029 between 1573 and 1673 K.     

Thermodynamics of inclusion formation in Fe-Cr-Ti-N alloys

The thermodynamics of titanium in Fe-Cr alloys and of inclusion formation in Fe-Cr-N-Ti alloys was investigated. A metal-nitride-gas equilibration technique was used to measure the activity of titanium. The equilibrium titanium content of the metal that is in equilibrium with pure solid titanium nitride and nitrogen gas at 1 atm was determined. The activity coefficients of titanium it(f_Ti) relative to 1 wt pct standard state in Fe were calculated for Fe-Cr alloys from the experimental results. The first-order interaction coefficient between titanium and chromium, e _Ti ^Cr , was determined to be 0.024 at 1873 K. The solubility of nitrogen in Fe-Cr alloys was measured and was found to increase with chromium content, which is in agreement with previous work. Thermodynamic calculations were made in order to predict under what conditions titanium nitride will form in 409 stainless steel and was compared with inclusions found in plant samples. The inclusion stability diagrams for 304 stainless steel and Fe-18 pct Cr and Fe-9 pct Cr alloys were computed.     

Thermodynamics of inclusion formation in Fe-Ti-C-N alloys

The thermodynamics of the formation of titanium carbonitride in liquid iron-titanium-carbon-nitrogen alloys were investigated in order to predict under what conditions it will form in liquid steel. A metal-carbonitride equilibration technique was used. Titanium carbonitride of a desired composition was made by mixing and high-temperature sintering of very fine powders of titanium nitride and carbide. The formation of titanium carbonitride was confirmed by lattice parameter measurements on the samples before and after the experiments. The equilibrium concentrations of titanium, carbon, and nitrogen in equilibrium with a specific titanium carbonitride were obtained at 1873 K. Activities of titanium carbide and nitride relative to pure solid titanium carbide and nitride were calculated. It was found that titanium carbonitride solid solution is almost ideal. From the results, calculations were performed to predict at which composition various carbonitrides will form.     

Thermodynamics of formation of Y-Co alloys

The Gibbs free energies, enthalpies, and entropies of phase formation were determined for nine Y-Co intermediate phases from electromotive force measurements. Solid CaF₂ was employed as the electrolyte, and emf measurements were made over the temperature range 850 K to 1200 K. The data indicate that the Gibbs free energies of formation per mole of Y reactant are nearly constant for the four Y-poor phases. Such behavior is associated with the close structural similarity of these phases. The present experimental Gibbs energy data at 973 K are compared with those of the Th-Fe, Th-Co, Th-Ni, La-Co, La-Ni, and Y-Fe systems. It was observed that the Gibbs free energy of formation can be empirically correlated with the total number of valence electrons in these alloy systems. The enthalpy of formation of an equiatomic Y-Co alloy was determined to be −27.1 kJ/mole atoms. This experimental value is in good accord with the theoretical predictions of the Miedema and Watson-Bennett models.     

Thermodynamics of formation of Th-Co alloys

Electromotive force cells have been used to determine the Gibbs free energies, enthalpies, and entropies of formation for Th₂Coi₇, ThCo₅, Th₂Co₇, ThCo, and Th₇Co₃. Solid CaF₂ was employed as the electrolyte, and measurements were made over the temperature range 917‡ to 1233‡K. Comparison of the Th-Co enthalpy values with Th-Ni values shows that the relative bond strengths associated with thorium-transition metal interactions in the two systems invert between the thorium-poor and thorium-rich regions. Formerly Graduate Student, Department of Metallurgy, Iowa State University.     

Thermodynamics of formation of Y-Ni alloys

The Gibbs free energies, enthalpies, and entropies of phase formation were determined for nine Y-Ni intermediate phases from electromotive force measurements. With CaF₂ solid electrolyte, emf measurements were made over the temperature range 900 to 1225 K. The Gibbs energies of formation per mole of Y reactant were found to be nearly constant for the four Y-poor phases; this is in keeping with the close structural relationship among these four phases. The Gibbs energies of formation of the Y-Ni phases at 973 K have been compared with those of the Th-Fe, Th-Co, Th-Ni, La-Co, La-Ni, Y-Fe, and Y-Co systems, and an increasing bond strength with increasing number of bonding electrons is evident. Comparison of the experimental values for the enthalpies of formation of the Y-Ni phases has been made with values predicted by the Miedema model and by the Watson-Bennett model. Both predictions yield values that are within ±50 pet of the experimental values which is the range of scatter that is normally expected from these simple models. Formerly Graduate Assistant, Department of Materials Science and Engineering, Iowa State University.     

Thermodynamics of formation of Th-Ni alloys

Electromotive force cells have been used to determine the Gibbs free energies, entropies, and enthalpies of phase formation for Th₂Ni₁₇, ThNi₅, ThNi₂, ThNi, and Th₇Ni₃. Solid CaF₂ was em ployed as the electrolyte, and it has previously been shown that CaF₂ is an ionic conductor over the temperature range of measurements, 841° to 1141°K. The experimental results can be correlated with the atomic coordinations in the crystal structures of these five Th-Ni intermediate phases. Formerly Graduate Student, Department of Metallurgy, Iowa State University     

Thermodynamics of formation of th-fe alloys

Electromotive force cells have been used to determine the Gibbs free energies, enthalpies, and entropies of formation for Th₂Fe₁₇, ThFe₅, Th₂Fe₇, ThFe₃, and Th₇Fe₃ over the temperature range 928 to 1164 K. Solid CaF₂ was used as the electrolyte. Comparisons of Th-Fe, Th-Co, and Th-Ni thermodynamic data show patterns which correlate with crystallographic and magnetic behavior. Some inferences have been drawn about the bonding interactions within the phases in these alloy systems. formerly Graduate Students, Department of Metallurgy, Iowa State University, Ames, Iowa 50010,     

Thermodynamics of dilute bcc Fe-Si alloys

The thermodynamic properties of silicon in the α-phase of the Fe-Si system in the region 0.028 <x _Si < 0.084 and 1100 < °C < 1370 has beem measured by the emf cell Mo, Si(s) | SiO₂-Li₂O | (Si-Fe)(s), Mo. The results are expressed in the form $$\log {\text{ }}\gamma _{Si}^\alpha {\text{ = 1}}{\text{.19 }} - {\text{7070/}}T + [ - 6.30 + 18,300/T]x_{Si} $$      

Thermodynamics of oxygen solutions in Fe-Ni-V melts

The oxygen solutions in Fe-Ni melts with up to 5% V are analyzed thermodynamically. The results of the works in which the fields of the vanadium-deoxidized oxide phases in iron and nickel were determined are generalized. The thermodynamic model developed for the calculation of the deoxidation of iron-nickel alloys with vanadium is shown to be adequate. The deoxidizing capacity of vanadium decreases insignificantly as the nickel content in the melt increases to 20% and increases substantially as the nickel content increases further. The oxygen solubility curves pass through a minimum, whose position changes from 2.3192% V for pure iron to 0.7669% V for pure nickel. We determined the equilibrium point [V]* between the (Fe, Ni)V₂O₄ and V₂O₃ oxide phases for alloys of six compositions at 1873 K. In nickel, [V]* is almost 200 times lower than in iron. The deoxidation of the Fe-40% Ni melt with vanadium is studied experimentally, and the experimental results agree satisfactorily with the calculated data.     

Thermodynamics of oxygen solutions in Fe-Mn melts

Oxygen solutions in Fe-Mn melts are analyzed thermodynamically. The composition of the oxide phase is determined, and the equilibrium oxygen concentrations in Fe-Mn melts are calculated over a wide composition range. The oxide phase mainly contains MnO: even at a molar fraction of manganese of 0.02 in the melt, the molar fraction of manganese oxide in the slag is more than 0.9. This is due to a much higher oxygen affinity of manganese as compared to iron; that is, manganese additives to iron considerably decrease the oxygen solubility. When the manganse content in the melt is 19.32%, the oxygen solubility curve has a minimum corresponding to an oxygen concentration of 5.136 × 10^?3%. However, a further increase in the managanese content results in an increase in the oxygen concentration in the melt. In liquid manganese, the oxygen saturation concentration at 1873 K is 0.0472%. The interaction parameter e _o(Mn) ^o (?0.207) and the activity coefficient γ _o(Mn) ^o (1.131 × 10^?4) have been calculated for the first time.     

Thermodynamics of iron-nickel alloys by mass spectrometry

A Knudsen cell-mass spectrometer combination was used to determine the activities of iron and nickel in solid and liquid iron-nickel alloys in the temperature range 1500 to 1900 K. This has provided thermodynamic data which are consistent in both the solid and liquid regions. The δH^M@#@ values obtained are in fair agreement with calorimetric data. A subregular model gives a good representation of the thermodynamic properties of this system.