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.     

Density and Surface Tension of Liquid Fe-Mn Alloys

The density and surface tension of liquid Fe-Mn alloys were determined by using the sessile drop method at 1823  K (1550 °C). The density of liquid Fe-Mn alloys decreased with increasing Mn content. When the molar volume was plotted with respect to the mole fraction of Mn, a linear relationship was obtained. Consequently, it was found that there is no excess volume in liquid Fe-Mn alloy. The surface tension of liquid Fe-Mn alloys was found to decrease with increasing Mn content. The current experimental data were higher than the reported results but close to the calculated results using Butler’s equation.     

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.     

Application of a thermodynamic database to the calculation of surface tension for iron-base liquid alloys

Thermodynamic models based on Butler's equation for surface tension of liquid alloys has been discussed. In alloys, in which activities of components deviate largely from Raoult's law, the calculated surface tensions are found to be affected by the selection of the ratio of the coordination number in the surface phase to that in the bulk phase. Then, the surface tension of liquid Fe-Al, Fe-Co, Fe-Cr, Fe-Mn, Fe-Mo, Fe-Ni, Fe-Si, Fe-Ti and Fe-W binary alloys and liquid Fe-Cr-Ni ternary alloys have been calculated from thermodynamic data in a database constructed by Kaufman. The calculated results reproduce the concentration dependence of the surface tension in those alloys reported so far, but their absolute values are dependent upon the selection of surface tension values for pure elements.     

Associative adsorption on liquid iron

The depression of the surface tension of a liquid metal by a binary surface compound which is formed from a pair of solutes is considered. The necessary thermodynamic equations are developed for the case in which the solutes are not separately surface active. It is shown that the published experimental results for liquid Fe-Cr-C alloys are fully consistent with the formation of the surface compound “CrC” and that the results for Fe-Si-C alloys might indicate coverage by “SiC”.     

Growth of the solid-liquid region during one-dimensional solidification of binary alloys. Part II

The solidification behavior of finite slabs of Fe-Si, Fe-P, and Fe-S alloys is calculated assuming: negligible diffusion in solid; complete diffusion in the liquid; equal solid and liquid densities; and constant temperature at the cooling surface. The effects of alloy parameters,e.g., solute distribution ratio, eutectic temperature and composition, and the initial concentration of solute in the molten alloys on the growth of the solid-liquid region (mushy zone) are explored. It is found that the thickness of the mushy zone relative to the solidified shell becomes greater with decreasing solute distribution ratio.     

Theoretical Calculations of the Surface Tension of Liquid Transition Metals

The surface tension of pure liquid mercury in the temperature range 273 K to 523 K (0 °C to 250 C°) was calculated using our previously reported equation. The results were compared with the experimental data and showed a good agreement. The surface tension of mercury decreases linearly with temperature, confirming a negative slope, and therefore shows the usual linear temperature dependence. The calculated surface excess entropy (0.21) is in excellent consistence with the experimental value (0.22). The surface tension also was calculated for many d-block metals (Ti, Zr, Fe, Co, Ni, Cu, Zn, Cd, Ag, Au, Pd, and Pt) at their melting points. The calculated values were compared with the existing experimental data.     

The liquid film migration in a sintered Fe-Cr-C base alloy

In an Fe-5Cr-lMo-2Cu-0.5P-3C (wt pct) alloy prepared by liquid-phase sintering at 1120 °C, the intergranular liquid films migrate during cooling and isothermal heat treatment at temperatures where the solid and liquid phases coexist. The liquid film migration (LFM) occurs extensively even during rapid cooling, apparently because of a large driving force. The migrating liquid films solidify to form network carbides. In the regions swept by the migrating liquid films, the concentrations of the substitutional solute atoms are slightly different from those in the original grains. When cooled rapidly, martensite is abundant in these regions. It is possible that the driving force for LFM in this alloy stems in part from the C concentration change associated with the concentration changes of the slowly diffusing substitutional solute atoms.     

Simplified computation of macrosegregation in multicomponent aluminum alloys

An approximate method for calculating the macrosegregation in a multicomponent aluminum alloy is proposed. This method is based on the use of a predefined solidification path (i.e., relation between the solute concentration in the liquid phase and the solid fraction) instead of addressing the fully coupled micro-macrosegregation problem. In determining the solidification path, it is assumed that the total solute concentration is constant, and that the solidification history is the same everywhere in the casting. In this manner it becomes quite easy to take into account how the macrosegregation development is affected by the solute diffusion in the dendrites and the precipitation of secondary phases, provided that such effects are accounted for in the model used for determining the solidification path. In order to demonstrate the approximate method, the inverse segregation formation at a chill surface of an Al-4 pct Mg-0.2 pct Fe-0.15 pct Si-0.3 pct Mn (AA5182) alloy is calculated. In this case study, the solidification path is determined prior to the macrosegregation computation by a microsegregation model discussed elsewhere, and the solid and liquid densities are related to the concentrations of the different alloying elements by a simple mixture law without distinguishing between the different solid phases that are formed. The accuracy of the approximate method is discussed by considering a binary alloy. It turns out that the macrosegregation formation at a chill surface of an Al-4 pct Mg alloy is fairly close to that resulting from a modeling in which the variation of the total solute concentration is taken into account. Furthermore, the mixture law is compared to a more elaborate treatment of the densities involving both primary and eutectic solid phases. This comparison is carried out for an Al-4.5 pct Cu alloy for which literature data exist. The mixture law is found to give a reasonable accuracy in the calculated macrosegregation.     

Evolving ideas about osmosis and capillary fluid exchange

When a solute is dissolved in water at (T, pel), the temperature and external pressure applied to the solution, the water in the solution is altered as is pure liquid water at (T, pel - piH2Ol). The liquid water and the water in the solution are in equilibrium when piH2Ol is the osmotic pressure of the water in the solution. Every partial molar property of the water in the solution at (T, pel), including its vapor pressure, chemical potential, volume, internal energy, enthalpy and entropy, is identical with the same molar property of pure liquid water at (T, pel - piH2Ol). This elementary fact was deduced by Hulett in 1903 from a thought experiment; he concluded that the internal tension in the force bonding the water is the same in both solution and pure liquid water, in equilibrium, at these differing applied pressures. Hulett's understanding of osmosis and the means by which the water was altered by the solute were neglected and abandoned. Competing ideas included the notions that the solute attracts the water into the solution and that the solute lowers the activity (or concentration) of the water in the solution. These ideas imply that the solute acts on the solvent at the semipermeable membrane separating the solution and water. Hulett's theory of osmosis requires that the solute alter the water at the free surface of the solution where the solute exerts an internal pressure on the boundary of the solution retaining the solute. Fluid exchange across the capillary endothelium is influenced, in part, by colloidal proteins in the plasma. The role of the proteins in capillary fluid exchange must be reinterpreted based on Hulett's view, the only valid view of osmosis.     

Segregation and wetting transition at dislocations

We investigate solute segregation and wetting transition at dislocations and the corresponding drag effect on dislocation glide using a continuum model developed previously for grain boundary and based on gradient thermodynamics. The dislocation core structure and stress field are described by the newly developed phase field model. This study differs from much previous work because it takes into account not only the long-range elastic interactions but the short-range chemical interactions between solute atoms and dislocation core as well as among solute atoms themselves. The latter leads to the prediction of a wetting transition at the dislocation core with respect to varying temperature, solute concentration, or dislocation velocity. The transition temperatures obtained during heating and cooling are different from each other, leading to a hysteresis loop in the solute concentration-temperature plot and the solute concentration-velocity plot. These predictions could provide new insights into the phenomena of sharp yield point drop and strain aging observed in metal alloys. This article is based on a presentation made in the “Hillert Symposium on Thermodynamics & Kinetics of Migrating Interfaces in Steels and Other Complex Alloys,” December 2–3, 2004, organized by The Royal Institute of Technology in Stockholm, Sweden.     

铅锑合金共沸及气液相平衡研究

根据气液相平衡理论设计了测定合金气液相平衡的试验设备并测定了铅锑合金气液相平衡数据。测定结果证实了铅锑合金存在共沸现象,共沸现象发生在铅锑合金中锑摩尔含量为10%~20%。并采用分子相互作用体积模型计算了铅锑合金的活度组元的系数,平均相对偏差和平均标准偏差分别为±0.08%和±0.005,证明该模型适用于计算铅锑合金活度系数。结合气液相平衡理论应用该模型计算并绘制了铅锑合金气液相平衡相图（T-x-y图）,计算结果并没有出现共沸现象并且与试验结果偏差很大。通过分析可知,纯金属的饱和蒸气压的准确性、金属挥发时分子形式、液态金属原子间结合力、液态金属表面张力和黏度等都会影响合金气液相平衡的计算结果,而目前的气液相平衡理论都没有考虑这些因素。本研究指出,下一步合金气液相平衡研究工作的重点是从试验角度测定纯金属的饱和蒸气压,在此基础上结合原子间结合力和分子挥发状态发展目前的气液相平衡理论,使其适用于计算共沸合金体系,从而更好地指导真空蒸馏。     

The effect of temperature on the surface tension and adsorption functions of the Fe-S-O melts – an analysis based on interaction parameters

The present investigation analyses the thermodynamic behaviour of the surfaces and adsorption as a function of temperature and composition in the Fe-S-O melts based on the Butler's equations. The calculated values of the surface tensions exhibit an elevation or depression depending on the type of the added solute at a concentration which coincides with that already present in the system. Generally, the desorption of the solutes as a function of temperature results in an initial increase followed by a decrease in the values of the surface tension. The observations are analyzed based on the surface interaction parameters which are derived in the present research.     

Volume and Surface Properties of a Bismuth-Containing Separating Nickel Melt

The influence of a bismuth impurity on the properties of solid and liquid alloys in the concentration range that obeys Henry’s law is considered. The structural and physicochemical properties, specifically, the density and the surface tension, of real melts are studied on relatively pure metals. The changes in the properties of the melts are estimated from changes in the temperature dependences of the density and the surface tension upon heating and cooling and in the concentration dependences of these parameters at a constant temperature. These dependences exhibit a correlation between the volume and surface properties of the melts: the density and the surface tension increase or decrease simultaneously. The introduction of bismuth in the nickel melt is accompanied by the appearance of a relatively strong compression effect (i.e., a decrease in the melt volume). At a certain bismuth content in the melt, the compression effect weakens because of the appearance of an excess phase or its associates and melt separation.     

On the thermodynamics of adsorption at interfaces as it influences decohesion

Earlier computations on the work of separation of boundaries with adsorbed solute atmospheres are reconsidered in terms of reversible work cycles. Special attention is given to two limiting cases. These are the separation of a material interface under fully equilibrated conditions, for which the chemical potential of the adsorbed solute remains constant, and separation under constrained conditions for which the surface excess solute concentration remains constant (i.e., the same on the two newly created free surfaces as present initially on the unstressed interface). The results are consistent with the limiting cases treated before and include the extension to more general cases of solute interactions, including multi-component systems. The work terms are conveniently represented on diagrams of chemical potentialvs surface excess solute concentration. A general separation process is then represented as a path in this diagram which begins on the adsorption isotherm for the unstressed interface and ends on the adsorption isotherm for the pair of newly created surfaces.     

The temperature independent plateau stress of solid solution crystals

A calculation of the plateau stress in solid solution crystals is presented assuming an arbitrarily oriented dislocation loop of lengthL, that moves under an applied stress. At high concentrations of solute atoms the dislocation segment does not interact with an individual solute atom but instead with all the solute atoms along the dislocation segment within a certain radius. The macroscopic flow stress is assumed to be determined by the maximum force that is encountered when a dislocation is moved over a distance equal to the distance between the position at zero stress and the critical position of an activated Frank-Read source. If the dislocation segment is assumed to be large compared to atomic distances, the interaction with groups of atoms will lead to an athermal process and therefore can explain the origin of the temperature independent flow stress in solid solution crystals. From this model the flow stress can be calculated with the help of statistical methods similar to those used in calculations of the movement of Bloch walls in magnetic materials. Besides the proper temperature dependence of the plateau stress the above model yields a dependence of the plateau stress upon the square root of the solute concentration, a result that is in good agreement with the measurements on silver, gold, and copperbased alloys. A linear relation between the solid solution hardening parameter dT/d√c and the strength of the solute atoms is obtained which is confirmed by the experimental results on copper-based alloys.     

The compressibilities of liquid Sn-Tl,In-Bi,Sn-ln,Bi-Sb,and Bi-Cd-Tl alloys

The velocity of 5 mHz ultrasonic waves was measured from the liquidus temperature up to a maximum of 500∮ to 650° for a certain number of liquid metals and alloys. A semiempirical model of the metallic liquid state was developed to fit the numerical data by varying its six parameters. This model was based on widely admitted assumptions and on an additional hypothesis concerning the excess volume redistribution among the atoms of the liquid. The six calculated parameters were found to have a physical meaning and could be related to the crystalline molar volume at 0∮K, to the activation energy for self-diffusion, and to the geometrical characteristics of hard-sphere dense random packings, for the low-melting polyvalent metals and alloys.     

Dissolution of carbon from coal-chars into liquid iron at 1550 °C

Carbon-dissolution studies were carried out on four coal-chars (ash content ranging from 9.04 to 12.61 wt pct), using the carburizer-cover method, and the rates of carbon transfer into liquid iron at 1550 °C were determined. A theoretical model was developed for estimating the interfacial area of contact between the chars and the liquid iron. Using a force-balance approach, the partial penetration of the particles was calculated numerically and the total solid/liquid contact area was evaluated for a range of system parameters. The wettability was found to have a very significant effect on the area of contact. An improvement in wetting reduced the upward force due to surface tension, thereby increasing the downward penetration of particles in the liquid and the contact area. While two chars showed a monotonic increase in carbon pickup by the liquid iron, a two-stage behavior was observed for the remaining two chars. Stage I, which corresponds to short times of contact, showed a much higher rate of carbon dissolution, as compared to stage II during later times. The slow rate of carbon dissolution in stage II was attributed to high levels of interfacial blockage by reaction products, which resulted in many fewer areas of contact between the carbonaceous material and the liquid iron. First-order dissolution rate constants (×10³ ms⁻¹) were computed for stage I in all chars, and the observed trend was as follows: 0.01795 (Char 1)>0.00954 (Char 4)>0.0061 (Char 3)>0.00274 (Char 2). These results compare well with the dissolution rate constants quoted in the literature. Char 1, which had the highest rate constant, also had the lowest concentration of reducible oxides (e.g., silica) among all chars. The consumption of solute carbon through silica reduction could affect the carbon levels in the liquid iron. Due to reduction reactions, the experimentally measured rates of carbon dissolution are expected to be slower than the inherent rates of carbon dissolution into the liquid metal. This study shows strong evidence that chemical reactions at the interface play an important role in determining the rate of char dissolution into liquid metal.