The surface tensions of Pb,Sn, and Pb-Sn alloys

The surface tensions of 99.9999 pct Pb and Sn and of alloys made from lead and tin of the same purity have been measured by the sessile-drop method. The surface tension of lead was determined from the melting point, the surface tension of tin from 200°C (32°C of supercooling) and the surface tensions of the Pb−Sn alloys from the respective liquidus temperatures, all, up to a temperature of about 560°C. Within the limits of experimental error, data for both pure metals plot in a rectilinear fashion with negative slopes, thus: γ_lead=472.7−0.085t(±5) dyne/cm γ_tin=569.0−0.080t((±5) dyne/cm The surface tensions of Pb−Sn alloys are not straight-line functions of temperature and the evidence indicates that the temperature coefficients of surface tension are slightly positive at the liquidus temperature.     

Theoretical Estimation of Temperature-Dependent Surface Tension of Liquid Antimony,Boron, and Sulfur

A theoretical calculation of the temperature-dependent surface tension of liquid antimony, boron, and sulfur in the temperature ranges 904 K to 1200 K (631 °C to 927 °C), 2349 K to 3085 K (2076 °C to 2812 °C) and 388 K to 453 K (115 °C to 180 °C), respectively, in the framework of Eyring theoretical consideration is explored. A reasonable agreement between the calculated and measured reported values is detected. The surface tensions of the three elements decrease linearly with temperature, with a change of 5.7 pct, 15 pct, and 16 pct, and the calculated surface tension data are expressed as γ = 388–0.0749 (T-Tm), γ = 1200–0.259 (T-Tm), and γ = 71–0.183 (T-Tm) (mJ/m²) for Sb, B, and S, respectively. Moreover, the surface tension was calculated, at melting point, for liquid metalloids and liquid nonmetals.     

The high temperature phase diagrams for zirconium-molybdenum and hafnium-molybdenum

The high temperature regions of the Zr−Mo and Hf−Mo binary phase diagrams have been constructured from temperature-composition data obtained by gravimetric and pyrometric methods. The liquidus curves were obtained directly from the measurements of saturation solubilities of molybdenum (single crystal) in liquid Zr and Hf. The solubility results are supported by electron microprobe analyses which identify the formation of thin (∼10 μm) layers of nearly stoichiometric compounds ZrMo₂ and HfMo₂ on the surface of the single crystal molybdenum below the respective peritectic temperatures 1918±5 and 2206±5°C. These thin layers and the negligible diffusion zones of Zr and Hf in single crystal molybdenum do not significantly affect the measured solubilities. The diffusion coefficient of Hf in Mo-single crystal at 2080°C is ∼5×10⁻¹² m² s⁻¹. The melting, solidus, liquidus, eutectic and peritectic temperatures were directly measured by pyrometrically observing the partial or complete destruction of “black-body” conditions inside an effusion cell with the appearance of a liquid phase that forms a highly reflecting mirror. The melting points of Zr and Hf metals, 1860±3 and 2228±3°C, respectively, are in good agreement with previously assessed values. The respective eutectic temperatures peratures and compositions 1551±2°C, 29.0±0.5 at. pct Mo and 1896±3°C, 40.5 at. pct Mo, are considerably more precise and only in fair agreement with previously measured or estimated values. The liquidus composition at the peritectic temperature for the Zr−Mo binary is precisely fixed at 54.0±1.0 at. pct Mo and that for the Hf−Mo binary is 61 ±3 at. pct Mo. The thermodynamic activities of molybdenum in the liquid Zr−Mo alloy indicate positive deviations from Raoult's Law. temporarily attached to the Chemistry Division, Argonne National Laboratory, Argonne IL 60439 This work was performed at Argonne National Laboratory under the auspices of the U.S. Energy Research and Development Administration     

Surface Tension of Liquid Alkali,Alkaline, and Main Group Metals: Theoretical Treatment and Relationship Investigations

An improved theoretical method for calculating the surface tension of liquid metals is proposed. A recently derived equation that allows an accurate estimate of surface tension to be made for the large number of elements, based on statistical thermodynamics, is used for a means of calculating reliable values for the surface tension of pure liquid alkali, alkaline earth, and main group metals at the melting point, In order to increase the validity of the model, the surface tension of liquid lithium was calculated in the temperature range 454 K to 1300 K (181 °C to 1027 °C), where the calculated surface tension values follow a straight line behavior given by γ = 441 – 0.15 (T-Tm) (mJ m⁻²). The calculated surface excess entropy of liquid Li (–dγ/dT) was found to be 0.15 mJ m⁻² K⁻¹, which agrees well with the reported experimental value (0.147 mJ/m² K). Moreover, the relations of the calculated surface tension of alkali metals to atomic radius, heat of fusion, and specific heat capacity are described. The results are in excellent agreement with the existing experimental data.     

Surface tension of zinc: The positive temperature coefficient

The positive temperature coefficient of the surface tension of molten zinc has been confirmed experimentally with a maximum-bubble-pressure (MBP) system. The possible effects of the high vapor pressure of molten zinc on the surface tension have been checked by making the measurements at atmospheric pressure and repeating at 1,800 Torr. The measurements were made on 99.999 pct zinc in the range from 436 to 806°C in an improved twin-tube MBP system. Results are that, over the given temperature range, the surface tension (γ) of zinc is given by γ (dynes/cm) = 839.7 − 125.7 e^−0.00941(T−419.5) The temperature (T) is in degrees centigrade. A total of 130 experimental values were determined with a correlation index of 0.98 with the equation. Comparisons of this result with others in the literature are discussed.     

Diffusivity of hydrogen in liquid nickel and copper

The diffusivity of hydrogen in liquid nickel was determined from 1468° to 1550°C by a capillary gas-reservoir technique. The diffusion cell was semiinfinite in length and consisted of Specpure nickel in an alumina capillary. An argon and hydrogen gas flow maintained a constant hydrogen potential at the metal/gas interface. A controlled furnace hot zone of length 23 cm was obtained using eight separate windings of Pt-40 pct Rh wire. The temperature profile in this zone was adjusted so that the top of the cell was hotter than the bottom, to eliminate convection. The experiments were terminated by a rapid nonaqueous quench. The diffusion columns were then sectioned and analyzed by vacuum extraction. Diffusivities were calculated using a solution to Fick’s Second Law. At 1468°C,D = 3.17 x 10⁻³ sq cm per sec with σ = ±0.76 × 10⁻³; at 1550°C,D = 3.48 × 10⁻³ sq cm per sec with σ = ±0.54 × 10⁻³. The diffusivity of hydrogen in liquid copper was determined using a shallow melt and analyzing for the total diffusate content; at 1101°C,D = 0.99 x 10⁻³ sq cm per sec with a = ±0.25 × 10⁻³; at 1201°C,D = 1.26 × 10⁻³ sq cm per sec with σ = ±0.16 × 10⁻³. Formerly with the Nuffield Research Group in Extraction Metallurgy at Imperial College, London, England This paper is based upon a thesis submitted by J. H. WRIGHT in partial fulfillment of the requirements of the degree of Doctor of Philosophy at the University of London.     

A new method to dynamically measure the surface tension,viscosity, and density of melts

A new formulation has been developed to describe the fluid dynamics of a liquid draining through an orifice under the influence of gravity. The model relates experimental quantities of head and flow rate, with surface tension, viscosity, and density, facilitating the calculation of all three properties. Experiments performed with molten aluminum at temperatures from 937 to 1173 K indicate that surface tension (N/m) and density (kg/m³) are [0.871 − 0.155 × 10⁻³ (T − T _liq)] and [2390 − 0.15 (T − T _liq)], which is within 6.5 and 2.5 pct, respectively, of values reported in the literature. The viscosity has been determined to be 5.2 × 10⁻⁴ Nsm⁻², which is significantly less than data reported from other sources. The method is unique because the measurements are performed under highly dynamic conditions.     

The effect of chromium on the activity coefficient of sulfur in liquid Fe−Cr−S alloys

The effect of chromium on the activity coefficient of sulfur in the ternary system Fe−Cr−S has been determined in the temperature range 1525° to 1755°C for chromium concentrations of up to 40 wt pct, using a levitation melting technique in H₂−H₂S atmospheres. The first order free energy interaction coefficient,e _S ^Cr , which is derived on the assumption that the thermal diffusion error is constant for both binary Fe−S and ternary Fe−Cr−S melts under controlled levitation conditions, is given by the relationship:e _S ^Cr =−94.2/T+0.040 The first order enthalpy and entropy interaction coefficients are found to beh _S ^Cr =−430±70 ands _S ^Cr =−0.183±0.007 respectively. These results are in good agreement with recently published data.     

Enthalpies of formation of borides of iron,cobalt, and nickel by solution calorimetry in liquid copper

The enthalpies of formation at 1385 ±2 K of the following crystalline borides have been determined by high temperature solution calorimetry using liquid copper as the calorimetric solvent. Fe₂B-67.87 ±8.05 kJ mol⁻¹, Co₂B -58.1 ±7.0 kJ mol⁻¹, Ni₂B -67.66 ±4.12 kJ ml⁻¹, FeB-64.63 ±4.34 kJ mol⁻¹, CoB -69.52 ±6.0 kJ mol⁻¹, and NiB -40.2 ±3.77 kJ mol⁻¹. The enthalpy of fusion of NiB has been determined to be 28.25 ±1.54 kJ mol⁻¹ at its melting point of 1315 K. New data are reported also for the enthalpies of solution of iron, cobalt, and nickel in copper, and for the enthalpies of interaction between these metals and boron in dilute solutions in liquid copper.     

Activities of oxygen in liquid Bi,Sn, and Ge from electrochemical measurements

Modified coulometric titrations on the galvanic cell: O in liquid Bi, Sn or Ge/ZrO₂( + CaO)/Air, Pt, were performed to determine the oxygen activities in liquid bismuth and tin at 973, 1073 and 1173 and in liquid germanium at 1233 and 1373 K. The standard Gibbs energy of solution of oxygen in liquid bismuth, tin and germanium for 1/2 O₂ (1 atm) →O (1 at. pct) were determined respectively to be ΔG° (in Bi) = −24450 + 3.42T (±200), cal· g-atom⁻¹ = − 102310 + 14.29T (±900), J·g-atom⁻¹, ΔG° (in Sn) = −42140 + 4.90T (±350), cal· g-aton⁻¹ = −176300 + 20.52T (± 1500), J-g-atom⁻¹, ΔG° (inGe) = −42310 + 5.31 7 (±300), cal·g-atom⁻¹ = −177020 + 22.21T(± 1300), J· g-atom⁻¹, where the reference state for dissolved oxygen was an infinitely dilute solution. It was reconfirmed that the modified coulometric titration method proposed previously by two of the present authors produced far more reliable results than those reported by other investigators. TOYOKAZU SANO, formerly a Graduate Student, Osaka University     

The density and surface tension of dilute liquid Na-In alloys and comparison with liquid Na-Cd alloys

The density and surface tension of five liquid Na-ln alloys, containing between 0.5 and 7 at. pct In, have been measured in the temperature range 170° to 400°C using a maximum bubble pressure technique which incorporates an automatic pressure measuring and recording device. The results are compared with corresponding data reported previously for Na-Cd alloys. The gram-atomic volumes of the Na-ln alloys, calculated from the densities, indicate a substantial contraction on alloying which is, on average, about double that for the Na-Cd alloys and qualitatively consistent with thermodynamic data for the two systems. The surface tension of liquid sodium is increased slightly on adding indium, indicating a lower indium concentration in the surface than in the bulk, in contrast to the marked surface active behavior of cadmium. The surface excess concentrations of indium and cadmium are calculated using Gibbs’ adsorption equation. The surface excess entropy, estimated from the temperature dependence of the surface tension, is compared and briefly discussed for the two systems.     

Evaluation of the reduction of iron oxide from liquid slags using a graphite rotating disk

The rotating disk methodology has been used for examination of the reduction of FeO from CaO-FeO-SiO₂ liquid slags (20 and 60 pct FeO) with a CaO/SiO₂ ratio equal to 0.66 and 1.27, in the temperature range 1350 °C to 1420 °C. It has been found that the reduction proceeds under diffusion control. The calculated diffusion coefficients fall in the range 0.76·10⁻⁷ to 1.6·10⁻⁶ cm²/s. Comparison of these values with those given in the literature suggests that the calculated coefficients are related to the diffusion of oxygen ions in the slag. The calculated thickness of the limiting diffusion layer, δ, ranges from 0.65·10⁻³ to 5.25·10⁻³ cm, depending on the reduction conditions. The largest decrease in the limiting diffusion layer thickness takes place at low rotational speeds, i.e., 100 and 400 rev/min. The maximum value of the mass transfer coefficient is 1.71·10⁻³ cm/s for reduction from slag with a CaO/SiO₂ ratio of 1.27, 60 pct FeO, at 1420 °C and 2000 rev/min, and the minimum value is 0.27·10⁻⁴ cm/s for reduction from slag with a CaO/SiO₂ ratio of 0.66, 20 pct FeO, at 1350 °C and 100 rev/min. Good agreement has been found between experimental and calculated reduction rates at low disk rotations (100 and 400 rev/min).     

Thermodynamics of liquid Al-Na alloys determined by using CaF2 solid electrolyte

The purpose of this work has been to establish activity data on sodium in liquid aluminum-sodium alloys at temperatures applied by the industry in liquid metal refining processes. A coulometric titration technique using a galvanic cell employing CaF₂ as a solid electrolyte has enabled measurements to be done under very clean and well-defined conditions over the entire range of compositions from highly diluted up to nearly sodium-saturated solutions. Sodium in liquid aluminum of 99.9999 pct purity is found to exhibit strong negative deviation from Henry’s law, corresponding to a large negative self-interaction coefficient ɛ _Na ^Na as expressed by the equation ɛ _Na ^Na =16,318−(191.1·10⁵ K)·T ⁻¹. This behavior is normal for elements, which exhibit strong positive deviation from Raoult’s law and is explained by formation of Na clusters. The activity coefficient at infinite dilution, γ _Na ^o , is expressed by the equation: RT ln γ _Na ^o =86,729−26.237T. The magnitude of γ _Na ^o from this equation agrees with the value predicted from the Miedema’s semiempirical model. Sodium in liquid Al-Si5 pct alloy of 99.9999 pct purity exhibits strong positive deviation from Henry’s law, which is in agreement with earlier investigations of the activity of sodium in liquid Al-Si alloys. The activity coefficient of sodium in pure liquid aluminum at saturation, γ _Na ^sat , is expressed by RT ln γ _Na ^sat =−67,476+102.33T, which gives for the sodium concentration at saturation x _Na ^sat =exp(8115.5/T−12.307). This implies that the solubility of sodium in liquid aluminum at temperatures around the melting point of aluminum is about 10 times higher than previously reported and decreases rapidly with increasing temperature, possibly due to a decreasing stability of Na clusters. Analysis of the experimental conditions used by previous investigators supports these findings.     

Experimental determination of solid-liquid interfacial energy for Zn solid solution in equilibrium with the Zn-Al eutectic liquid

The equilbrated grain boundary groove shapes for the Zn solid solution in equilibrium with the Zn-Al eutectic liquid were observed by rapid quenching. From the observed grain boundary groove shapes, the Gibbs-Thomson coefficient and the solid-liquid interfacial energy for the Zn solid solution in equilibrium with the Zn-Al eutectic liquid have been determined to be (5.80±0.18) × 10⁻⁸ Km and (93.496±7.57) × 10⁻³ Jm⁻² with the numerical method and from the Gibbs-Thomson equation, respectively. The grain boundary energy for the same material has been calculated to be (182.302±18.23)×10⁻³ Jm⁻² from the observed grain boundary groove shapes. The thermal conductivities of the solid and liquid phases for Zn-5 wt pct Al and Zn-0.5 wt pct Al alloys have also been measured.     

Solute diffusion in liquid nickel measured by pulsed ion beam melting

Measurements of liquid-phase diffusion coefficients for dilute tungsten and molybdenum in molten nickel were made using a pulsed ion-beam melting technique. A high-intensity beam of nitrogen ions is focused on the surface of a nickel substrate that was implanted with known concentration profiles of W and Mo. Melting of the surface to a depth of ∼1 μm allows broadening of the implant profiles while molten. Solute concentration-depth profiles were determined before and after melting using Rutherford backscattering spectrometry. Using a series of numerical simulations to estimate the melt history and diffusional broadening for mean liquid temperatures in the range 1755 to 2022 K, an effective diffusion coefficient is determined in each case by comparison to the measured depth profiles. This is found to be (2.4±0.2)×10⁻⁵ cm²/s for W and (1.6±0.4)×10⁻⁵ cm²/s for Mo, with an additional systematic uncertainty of ±0.5×10⁻⁵ due to instrumental and surface effects.     

Nitrogen solubility in complex liquid Fe−Cr−Ni alloys

Measurements of nitrogen solubility were performed in a series of liquid iron-chromium-nickel alloys near the composition of the commercial superalloy INCOLOY^* 800 (I:21 pct Cr, 33 pct Ni, bal. Fe). This work was carried out at 1450 to 1600°C and up to one atmosphere of nitrogen gas pressure. Sieverts' law was obeyed by nitrogen in all the alloys. Changes were observed in the compositions of all the melts studied, mainly due to the chromium loss by volatilization. These changes necessitated nitrogen solubility measurements in a series of alloys immediately surrounding alloy I. The experimental results have been prepared as a regression polynomial equation for the logarithm of nitrogen solubility as a function of temperature and reported weight percentages of chromium and nickel in the alloys. The standard Gibbs free energy of nitrogen solution in a region around alloy I is given as ΓG ^o=−58,700+48.20T Joules/g atom N. At 1600°C, the temperature coefficient of nitrogen solubility in I is −2.65×10⁻⁴ pct N/K. The shape of a portion, of the nitrogen solubility surface for the Fe−Cr−Ni system near to alloy I at 1600°C is defined.     

The solubility of hydrogen in liquid binary Al-Li alloys

The solubility of hydrogen in liquid binary aluminum alloys with 1, 2, and 3 wt pct lithium has been determined for the temperature range of 913 to 1073 K and pressure 5.3 × 10⁴ to 10.7 × 10⁴ Pa, using an appropriate version of Sieverts’ method. The results fit the Van’t Hoff isobar and Sieverts’ isotherm and the solubility,S, is given by: Al-1 pct Li: log(S/S°) − 1/2 log(P/P°) = −2113/T/k + 2.568 Al-1 pct Li: log(S/S°) − 1/2 log(P/P°) = −2797/T/k + 3.329 Al-1 pct Li: log(S/S°) − 1/2 log(P/P°) = −2889/T/k + 3.508 whereS° is a standard value of solubility equal to 1 cm³ of diatomic hydrogen measured at 273 K and 101,325 Pa per 100 g of metal, andP° is a standard pressure equal to 101,325 Pa. Added lithium progressively increases the solubility of hydrogen in liquid aluminum, due more to its effect on the entropy of solution of hydrogen, through its influence on the liquid metal structure than to an increase in the solute hydrogen atom binding enthalpy.     

The solubility of hydrogen in liquid binary Al-Li alloys

The solubility of hydrogen in liquid binary aluminum alloys with 1, 2, and 3 wt pct lithium has been determined for the temperature range of 913 to 1073 K and pressure 5.3 × 10⁴ to 10.7 × 10⁴ Pa, using an appropriate version of Sieverts’ method. The results fit the Van’t Hoff isobar and Sieverts’ isotherm and the solubility,S, is given by: Al-1 pct Li: log(S/S°) − 1/2 log(P/P°) = −2113/T/k + 2.568 Al-1 pct Li: log(S/S°) − 1/2 log(P/P°) = −2797/T/k + 3.329 Al-1 pct Li: log(S/S°) − 1/2 log(P/P°) = −2889/T/k + 3.508 whereS° is a standard value of solubility equal to 1 cm³ of diatomic hydrogen measured at 273 K and 101,325 Pa per 100 g of metal, andP° is a standard pressure equal to 101,325 Pa. Added lithium progressively increases the solubility of hydrogen in liquid aluminum, due more to its effect on the entropy of solution of hydrogen, through its influence on the liquid metal structure than to an increase in the solute hydrogen atom binding enthalpy.     

The breakup of bubbles into jets during submerged gas injection

There has never been any fundamental explanation presented for the transition from the bubbling regime to the jetting regime when gas is injected into liquid at high velocity through submerged tuyeres. This is an important issue in metallurgical processes, since the flow regime is known to influence refining rates, refractory erosion, and the penetration of the liquid into the tuyere. Based on the observation that many small droplets of liquid and gas bubbles are formed to create the jets, a combined Kelvin-Helmholtz and Rayleigh-Taylor instability analysis has been applied to bubbles forming at submerged tuyeres. For particular wavelengths of disturbances, the interface will be unstable and create bubbles and droplets. The critical injection velocity for instability depends on surface tension, tuyere diameter, and the gas-to-liquid density ratio, which can be summarized by We = 10.5(ρ*)^−1/2, where We is the Weber number based on the gas velocity and density and tuyere diameter, and ρ* is the gas-to-liquid density ratio. The importance of surface tension had not been appreciated previously for this regime of gas injection. There is considerable controversy in the literature concerning the measurement of the transition from bubbling to jetting. The 70 pct “linking” point, proposed by Ozawa and Mori, describes the situation where 70 pct of the bubbles link with the preceding bubbles and produce a reasonably steady jet. The theoretical correlation developed above predicts the velocity to reach this point ±20 pct (95 pct confidence level) in a variety of systems from six different groups of workers. The theoretical analysis demonstrates that the instabilities are primarily capillary in nature, not gravity waves, which explains the observation that orientation has little effect on the jetting transition.     

Enthalpy of formation and heat capacity of Fe-Mn alloys

The partial and integral enthalpies of mixing of liquid Fe-Mn alloys were measured as a function of the atomic fraction of iron (x) within the range of 0≤x≤0.45 at 1700±5 K, using a laboratory-built, high-temperature isoperibolic calorimeter. The minimum integral enthalphy of mixing at x=0.5 is about −820±45 J mol⁻¹. The enthalpy of formation of solid γ-Fe-Mn alloys with 30.0, 40.0, 50.0, and 57.0 at. pct Mn was determined indirectly, using the same calorimeter, by dissolving these alloys in liquid aluminium at 1409±3 K, and the minimum value amounts to −1940±70 J mol⁻¹ at x=0.5. The heat capacities of these alloys as well as the heat capacity of pure iron and α-Fe-Mn alloys with 0.95, 2.03, 2.73, and 4.30 at. pct Mn, were measured by a differential thermal analysis (DTA) technique and are described using a new analytical representation of the magnetic contribution. The composition dependencies of heat content, Curie and Neél temperatures, enthalpy of formation of α-Fe-Mn alloys, magnetic contribution to the enthalpy of pure Fe and its change due to the addition of Mn, as well as the change of enthalpy upon the γ → α transformation, were deduced from the experimental data. The results obtained were compared with experimental information available in the literature.