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By M. A. Rigdon, R. E. Grace

The dissociation of cupric oxide to cuprous oxide and oxygen was studied with a microbalmce technique at 700" to 750°C. In this temperature range the dissociation pressure of the reaction 2CuO= Cu2O + 1/2 O2 was: The theory of near-equilibriwm reaction rates predicts a linear relationship between reaction rate and the Gibbs free-energy change for small values of AF/RT. This correlation is found to be valid for AF/RT = -0.1 or approximately 200 cal per mole away from equilibrium. THE theory of reaction rates near equilibrium as developed from classical thermodynamics suggests a small range of linear behavior between the overall reaction rate and the free-energy change accompanying the process. The extent of this linear correlation is generally unknown, even to the order of magnitude. The idea of linearity is also found in the formal mathematics of coupled transport phenomena, e.g., chemical diffusion, thermal diffusion, thermoelectricity, and so forth. The linear array of forces and fluxes which leads to various main and cross coefficients is predicated upon linearity between reaction rates and the bulk thermodynamics which govern the process. The general case in reaction kinetics is well-known: the magnitude of the free-energy change does not cor- relate with observed reaction kinetics, irrespective of whether the process occurs by diffusion or chemical reaction or both. The real need is to investigate specific reaction paths near equilibrium in order to learn of the limitations in attempting to correlate reaction rates and thermodynamics. It is the main purpose of this paper to examine the dissociation kinetics of cupric oxide under conditions of known driving force where the dissociation process is likely to occur by chemical reaction. A secondary objective is to obtain equilibrium data for the CuO-Cu20-O2 system. In a prior paper Edmiston and race' investigated reduction kinetics of wustite in H2-H2O gas mixtures. The present study was carried out in oxygen according to the following reaction:

Jan 1, 1969

By Ernest Darby

WHEN bronze is melted in open-flame furnaces a considerable amount of slag is formed during the melting operation. This slag may be incidental to the melting practice or it may be formed intentionally by slag-forming constituents added to the furnace charge to provide a covering for the melted metal. When this slag is removed from the furnace, it contains, in addition to the free metal carried with it by the skimming operation, a considerable amount of metal as oxide either combined or mechanically mixed with it. By the usual crushing and washing methods this metallic oxide generally goes to the tailings pile, so diluted by other foundry waste that its recovery is economically impossible. If this furnace slag is not mixed with other foundry waste, practically all of the metal oxide as well as the free metal may be recovered by some form of smelting operation. The first side of the problem to be considered is the amount of slag produced. It may not be true that the majority of foundries have no record of the amount of slag made, but it is certainly true that a very great many either have no record or pay little attention to it. Usually the collection of furnace slag for one normal week's run will be sufficient to determine the advisability of its being handled in a different manner from the crushing and concentrating generally employed. If a large representative sample of the accumulation is crushed and concentrated and the recovery compared with the results of a careful assay, it will be found that a large percentage of the total metal content was lost in the washing process. The percentage of loss will be greater than the metallic oxide content, as some free metal in extremely fine particles always is carried away in grains of slag: From such a comparison, it may be determined whether or not the slag should be melted, sold or treated as before. An example of an actual test of this kind is given below.

Jan 1, 1928

By N. H. Murlenberg, T. M. Drown

It is often a tedious matter to get a solution of pig iron or steel, for the determination of phosphorus, which is absolutely free from silica. Where pig iron rich in silicon is dissolved in hydrochloric or nitric acid in the usual procedure, it is necessary, not only to evaporate the solution to complete dry ness, but to heat the dry residue for some beam in an air-bath to a temperature of about 120° C. The oxide of iron is thus rendered insoluble in nitric acid, and is only slowly dissolved by hydrochloric acid. In the method of determining silicon by nitric and sulphuric acid, described in the Transactions of the Institute, Vol. VII, page 346, arid Vol. VIII, page 508, we obtain in one or two hours a solution of the iron in the form of ferric sulphate entirely free from silica, and containing free sulphuric acid. It occurred to Us that this solution might be made available for the determination of the phosphorus by the molybdate method. The following experiments mere tried with unsatisfactory results. 1st. The iron was precipitated by ammonia, the precipitate filtered, washed, and dissolved in nitric acid. 2d. The iron was precipitated as basic acetate and dissolved in nitric acid. 3d. The solution was neutralized by ammonia, and nitric acid added in small excess. In all these cases the phosphorus obtained by precipitating by ammonium molybdate and magnesia-mixture was too low. The following method was then tried with success. The filtrate from the silica and graphite was evaporated to small bulk and heated in a porcelain dish on a sand-bath. until fumes of sulphuric acid ceased to escape. The dry residue was taken up with dilute nitric acid and the solution precipitated by ammonium molyldate. The phosphorus was weighed as magnesium pyrophosphate. The results were satisfactory. To save time, the original solution of the iron in nitric and sulphuric acids was evaporated to dryness and heated as before until

Jan 1, 1882

By N. H. Muhlenberg

IT is often a tedious matter to get a solution of pig iron or steel, for the determination of phosphorus, which is absolutely free from silica. Where pig iron rich in silicon is dissolved in hydrochloric or nitric acid in the usual procedure, it is necessary, not only to evaporate the solution to complete dryness, but to heat the dry residue for some hours in an air-bath to a temperature of about 120° C. The oxide of iron is thus rendered insoluble in nitric acid, and is only slowly dissolved by hydrochloric acid. In the method of determining silicon by nitric and sulphuric acid, described in the Transactions of the Institute, Vol. VII, page 346, and Vol. VIII, page 508, we obtain in one or two hours a solution of the iron in the form of ferric sulphate entirely free from silica, and containing free sulphuric acid. It occurred to us that this solution might be made available for the determination of the phosphorus by the molybdate method. The following experiments were tried with unsatisfactory results. 1st. The iron was precipitated by ammonia, the precipitate filtered, washed, and dissolved in nitric acid. 2d. The iron was precipitated as basic acetate and dissolved in nitric acid. 3d. The solution was neutralized by ammonia, and nitric acid added in small excess. In all these cases the phosphorus obtained by precipitating by ammonium molybdate and magnesia-mixture was too low. The following method was then tried with success. The filtrate from the silica and graphite was evaporated to small bulk and heated in a porcelain dish on a sand-bath, until fumes of sulphuric acid ceased to escape. The dry residue was taken up with dilute nitric acid and the solution precipitated by ammonium molyhdate. The phosphorus was weighed as magnesium pyrophosphate. The results were satisfactory. To save time, the original solution of the iron in nitric and sulphuric acids was evaporated to dryness and heated as before until

Jan 1, 1882

By C. F. Austin, J. K. Pringle

In view of the many large differences in structure and physical properties between metals, plastics, and most rock materials, a continuing experimental petrodynamics program has been established at the U. S. Naval Ordnance Test Station. Part of this program has been to test the concepts of scabbing and corner fracturing in a typical coarse-grained rock. The results of this experimental program have shown very interesting differences between the formation of fractures in rock and the formation of fractures in other materials such as metals and plastics which are often used as models for rock behavior studies. The gross behavior of coarse-grained brittle solids subjected to impulsive loading has undergone abundant empirical investigation by mining organizations and by mineral research agencies. However, the fundamental response of coarse-grained brittle solids to impulsive loading has received little detailed study in recent years. The various organizations and agencies interested in rock-like brittle materials have broadly applied the stress wave interaction concepts of the impulsive failure of metallic samples to the behavior of granular brittle materials 1,2,3,4,5,6 Using the metallic sample approach for stress wave induced fracturing, an understanding of the fracture behavior of brittle materials which perhaps is not always appropriate has been established in the open literature. An excellent summary of the metallic sample approach is provided by ref. 7 which summarizes the general beliefs prevalent at present regarding the impulsive behavior of brittle solids: "In the blasting process, rock breakage occurs primarily from tensile slabbing, beginning at a free face and proceeding back toward the explosive charge. The tensile waves formed by the reflection of incident compressive waves from two or more free faces will collide in the rock, resulting in large localized tensile stresses. Fractures formed by the interaction of these tensile stresses begin at the apex of the free face planes and progress back into the rock as shown...."

Jan 1, 1964

By J. M. Steininger

The mechanism of flotation of sphalerite with sulthydryl compounds of different acidities has been interpreted in terms of chemisorption of unionized collector molecules on hydroxylated zinc surface sites. At a constant collector concentration of 1.5 x 10 -4 M, the upper pH limit of flotation has been found to be directly and closely related to the negative logarithm of the collector acidity constant, pKa The experimental results indicate that flotation is prevented when about 95% of the collector is ionized. At low pH, collector adsorption decreases because of the reduction in number of hydroxylated zinc surface sites. These two effects explain why sphalerite does not float with the more acidic sulfhydryl compounds. Typical anionic collectors for sulfide minerals are short chain xanthates or dithiophosphates which are nearly completely ionized in the generally alka- line flotation circuits.1,2 Flotation mechanisms have therefore been usually interpreted in terms of ionic collector adsorption and competition with ionic depressants of the same sign as the collector. A few attempts have been made, however, to consider adsorption of neutral collector molecules. Contact angle measurements obtained by Wark and cox3 have been interpreted by Cook and Nixon4 as representing adsorption of the free acid molecules on sulfide minerals such as pyrite, galena, chalcopyrite, and sphalerite. Cook and Nixon tried to show that the free acid concentration of the collector was substantially constant along the curves relating collector addition and minimum pH for bubble adherence. However, in a review of the subject,5 Sutherland presented new data on the flotation of pyrite with mercaptobenzothiazole which did not support the hypothesis of constant concentration of either collector ions or collector free molecules. He further showed that, with the assumption of constant occupation of surface sites, both theories lead to relations between pH and collector addition having similar mathematical expressions. In fact, with the more likely assumption of variable occupation of surface sites which results in more complex relationships, it appears impossible to

Jan 1, 1968

By Anson G. Betts

A solution of lead-fluosilicate, containing an excess of fluosilicic acid, has been found to work very satisfactorily as an electrolyte for refining lead. It conducts the current well, iseasily handled and stored, non-volatile and stable under electrolysis, may be made to contain a considerable amount of dissolved lead, and is easily prepared from inexpensive materials. It possesses, however, in common with other lead electrolytes, the defect of yielding a deposit of lead lacking in solidity, which grows in crystalline branches toward the anodes, causing short circuits. But if a reducing-action (practically accomplished by the addition of gelatine or glue) be given to the solution, a perfectly solid and dense deposit is obtained, having very nearly the same structure as electrolytically-deposited copper, and a specific gravity of about 11.36—that of cast-lead. Lead-fluosilicate may be crystallized in very soluble, brilliant crystals, resembling those of lead-nitrate and containing four molecules of water of crystallization, with the formula PbSiF,,4H20. This salt dissolves at 150 C. in 28 per cent. of its weight of water, making a sirupy solution of 2.38 sp. gr. Heated to 60° C., it melts in its water of crystallization. A neutral solution of lead-fluosilicate is partially decomposed on heating, with the formation of a basic insoluble salt and free fluosilicic acid, which keeps the rest of the salt in solution. This decomposition ends when the solution contains, perhaps, 2 per cent. of free acid; and the solution may then be evaporated without further decomposition. The solutioi~s desired for refining are not liable to this decomposition, since they contain much more than 2 per cent. of free acid. The electrical conductivity depends mainly on the acidity of the solution. My first experiments were carried out without the addition of gelatine to the fluosilicate solution. The lead-deposit con-

Jan 1, 1904

By George S. Evans

Certain American operators bclieve that desulphurizing in the ladle offers a means of increasing blast-furnace and open-hearth yields with the possibility of improvements in quality of the steel. In fact, several producers have experimented with practically all of the known desulphurizing agents, including both standard grades of the alkalies and special preparations that have been offered from time to time during the past several years. Some of these are regularly being used today in large-scale commercial operations, with good results. Also, it is the practice to treat off-sulphur casts in the blast-furnace ladle at a number of plants. It is not known, however, that anyone in the steel industry (American) has ever adequately equipped a plant for desulphurizing blast-furnace metal in an efficient manner as regular operating practice. The purpose of this paper is to illustrate the importance of correct equipment and proper handling for obtaining uniform and efficient results. As will be shown, at the temperature of molten iron the alkalies are instantly neutralized by any free slag present, dissipating their desulphurizing value. Entrained silicates are rapidly washed out of the metal bath by the highly basic soda slags and will be satisfied ahead of desulphurizing reactions with FeS. More or less of the reagent will always be used up through reactions with the refractory lining. Desulphuriza-tion will be limited to the action of the free alkali then remaining in the slag. Causes for the erratic results generally found with desulphurizing tests in blast-furnace transfer ladles would include, among other things, variations in the quantity of furnace slag coming down with the metal, and differences in the percentage of kish and entrained silicates in the different casts. As the alkalies instantly unite with any free slags or silicates present, these, with any kish coming off, both dilute the reagent and reduce the surface contact between the slag and metal, thereby retarding the desulphurizing reactions.

Jan 1, 1938

By George S. Evans

Certain American operators bclieve that desulphurizing in the ladle offers a means of increasing blast-furnace and open-hearth yields with the possibility of improvements in quality of the steel. In fact, several producers have experimented with practically all of the known desulphurizing agents, including both standard grades of the alkalies and special preparations that have been offered from time to time during the past several years. Some of these are regularly being used today in large-scale commercial operations, with good results. Also, it is the practice to treat off-sulphur casts in the blast-furnace ladle at a number of plants. It is not known, however, that anyone in the steel industry (American) has ever adequately equipped a plant for desulphurizing blast-furnace metal in an efficient manner as regular operating practice. The purpose of this paper is to illustrate the importance of correct equipment and proper handling for obtaining uniform and efficient results. As will be shown, at the temperature of molten iron the alkalies are instantly neutralized by any free slag present, dissipating their desulphurizing value. Entrained silicates are rapidly washed out of the metal bath by the highly basic soda slags and will be satisfied ahead of desulphurizing reactions with FeS. More or less of the reagent will always be used up through reactions with the refractory lining. Desulphuriza-tion will be limited to the action of the free alkali then remaining in the slag. Causes for the erratic results generally found with desulphurizing tests in blast-furnace transfer ladles would include, among other things, variations in the quantity of furnace slag coming down with the metal, and differences in the percentage of kish and entrained silicates in the different casts. As the alkalies instantly unite with any free slags or silicates present, these, with any kish coming off, both dilute the reagent and reduce the surface contact between the slag and metal, thereby retarding the desulphurizing reactions.

Jan 1, 1938

By C. H. P. Lupis, R. Hocine, G. Bernard

The necessary and sufficient conditions for the stability of a multicomponent phase with respect to infinitesinzal fluctuations are derived and transformed to be written in terms of activity coeffcients and mole fractions rather than in terms of the customary second deritlatives of the free energy. NECESSARY conditions for the stability of a multi-component system were derived by Gibbs as early as 1876.' However, as the usefulness of these conditions is greatly enhanced by the simplicity of their translation in terms of functions of common usage, the present contribution establishes these conditions in terms of activities or activity coefficients-and mole fractions. It was shown in another article2 that not only may these conditions be used for the prediction of the appearance of new phases, but they may also provide a check on the orders of magnitude of the interaction coefficients involved. "Spinodal" decomposition is said to occur when, at constant temperature and pressure, the system is unstable with respect to infinitesimal fluctuations in composition. As a result, the "phases" which appear may be attained through continuous changes in the system rather than discontinuous ones, and, consequently, the free energy of these phases may be described by a unique continuous free-energy function. For a binary system, the familiar curve of Fig. 1 illustrates the case we wish to extend to a multicom-ponent system. The conditions to be written pertain to the decomposition of a system of n moles into moles of phase moles of phase v, ...hen moles of phase 9, where the phases a, ...v, ...9 are—at least initially-arbitrarily close in composition to that of the original phase. Each A, is positive and since the total number of moles n in the system remains constant: Each phase v contains hv(nl +dnY) moles of component (I), ...xV(ni +dny) of component + dnk) moles of component (m). The total number of moles ni in the system remaining also constant, it is clear that:

Jan 1, 1968

By R. D. Pehlke, J. F. Elliott

The equilibrium pressure of nitrogen gas over pure silicon metal and silicon nitride has been measured in the temperature range 1400° to 1700°C. From the experimental data, the standard free energies and enthalpies of formation of Si3N4(a) have been calculated as functions of temperature over the above temperature range. Utilizing data in the literature and the results of this investigation, the specific heat, molar enthalpy, molar entropy, standard enthalpy of fornation, and standard free energy of fornation are estimated for the temperature range 298° to 1400°C. THE high-temperature thermodynamic properties of many metallic nitrides are not well established at present. This is a serious deficiency because nitrogen and nitride-forming metals are important alloying additions to steels, and knowledge of the interaction between nitrogen and these elements is essential to a better understanding of the behavior of steels. Metallic nitrides also are used as refractory materials. Consequently, the investigation reported here was undertaken to provide more complete information on the standard entropy and free energy of formation of silicon nitride. The experimental technique provided a direct measurement of the equilibrium pressure of nitrogen gas in the range of 1413 to 1700°C for the reaction: 3 Si(1) + 2N2 (g) = Si3N4 (a) [ 1 ] and below 1413oC for the reaction: 3Si(c) + 2N2(g) = Si3N4(a) [2] APPARATUS The experimental system consisted of a crucible assembly, a reaction chamber, and a gas supply and vacuum system. The Crucible Assembly which contained the equilibration specimen and molybdenum radiation shields with a susceptor for induction heating is shown in Fig. 1. Two covered, high-purity alumina crucibles, one nested within the other, contained the susceptor, shields and specimen. Central openings in the upper shield and crucible covers permitted on optical pyrometer to be sighted into the central cavity of the specimen. The specimen itself was a 5/8 OD by 1-in.

Jan 1, 1960

By George S. Evans

CERTAIN American operators believe that desulphurizing in the ladle offers a means of increasing blast-furnace and open-hearth yields with the possibility of improvements in quality of the steel. In fact, several producers have experimented with practically all of the known desulphurizing agents, including both standard grades of the alkalies and special preparations that have been offered from time to time during the past several years. Some of these are regularly being used today in large-scale commercial operations, with good results. Also, it is the practice to treat off-sulphur casts in the blast-furnace ladle at a number of plants. It is not known, however, that anyone in the steel industry (American) has ever adequately equipped a plant for desulphurizing blast-furnace metal in an efficient manner as regular operating practice. The purpose of this paper is to illustrate the importance of correct equipment and proper handling for obtaining uniform and efficient results. As will be shown, at the temperature of molten iron the alkalies are instantly neutralized by any free slag present, dissipating their desulphurizing value. Entrained silicates are rapidly washed out of the metal bath by the highly basic soda slags and will be satisfied ahead of desulphurizing reactions with FeS. More or less of the reagent will always be used up through reactions with the refractory lining. Desulphurization will be limited to the action of the free alkali then remaining in the slag. Causes for the erratic results generally found with desulphurizing tests in blast-furnace transfer ladles would include, among other things, variations in the quantity of furnace slag coming down with the metal, and differences in the percentage of kish and entrained silicates in the different casts. As the alkalies instantly unite with any free slags or silicates present, these, with any kish coming off, both dilute the reagent and reduce the surface contact between the slag and metal, thereby retarding the desulphurizing reactions.

Jan 1, 1938

W. M. Courtis, Detroit, Mich.: Except for free-gold ores, I have always believed in scorification. I think the crucibleassay gives silver low. We found this out at the Wyandotte works in assaying Silver Islet ore. The mine-managers made us, and also the check-assayera, run one of the duplicates by

Jan 1, 1896

By R. Hogg, D. W. Fuerstenau

Based on a simplified model for the motion of particulate materials in horizontal, rotating cylinders, approximate expressions have been derived relating the power consumption of a tumbling mill to its dimensions and speed of rotation and to the amount and nature of the charge. The basic assumptions underlying the model are that there is no slip between the charge and the mill shell, that the free surface of the charge remains essentially planar during rotation, and that there is no transfer of momentum from the material flowing down the free surface back to the mill shell. The relationships formulated from this model have been shown to be in excellent agreement with experimental results taken from the literature. While the requirements of the model are most clearly met at low speeds of rotation, the results appear to be valid even for speeds up to 70-80% of the critical speed. Poorer agreement between theory and experiment is found when the charge consists of relatively large particles (balls) and when the filling of the mill exceeds 50% of the available volume. Qualitative explanations of these deviations have been offered.

Jan 1, 1973

By Walter J. Johnson

The coals in northern Wyoming and Montana are free-burning and non-caking and range from lignite to bituminous C in rank. Strip and underground mining are employed to supply railroad, utility, industrial, and domestic fuel. The market area includes Iowa, Nebraska, Minnesota, North and South Dakotas, Wyoming, Montana, the Pacific Northwest, and western Canada.

Jan 12, 1953

By J. E. McDonald, J. G. Eberhart

A model is discussed from which the work of adhcslon .tor liquid transition metals on aluminum oxide surfaces can he calculated, A close-packed (00011 oxygen surface on A12O3 is assumed with two different types of surface sites: one type involving metal-oxygen bonds and the other man der Waals into actions. The work of adhesion is thus expressed as the sum of these two bonsding free energies. Calculated works of adhesion for nickel, titanium, chromium, and zirconium on sapphire agree well with the experimentally determined quantities. The model is extentled to the calculation of the work of adhesion and shear stress required to remove a thin metal film from a sapphire substrate and is in good agreement with experimental values. The obsewed dependence of the work of adhesion on the free energy of oxide formation of the metal is shown to also provide an interpretation of the tittle dependence of thin-film adhesion. THIS paper presents a model for the type of bonding which occurs across a metal-A12O3 interface. The model is used to explain the results of two types of experiments in which such an interface exists: 1) the adhesion of thin metal films on Al2O3 substrates and 2) the wetting of A12O3 by liquid metal drops. The adhesion of thin films to various substrates has been the subject of a variety of investigations.'-' Benjamin and weaver3 and Bowie,6 using the scratch test developed by Heavens,10 studied the adhesion of metallic films to glass substrates. Their observations for noble-metal film adhesion agree well with an adhesion model involving a van der Waals type of bonding between the film and the substrate. For films of metals whose free energy of oxide formation. ?F°f, has a negative value. Benjamin and weaver3 and Bowie6 found a time-dependent adhesion with an initial value that can be interpreted in terms of van der Waals interactions but a larger terminal value which was related to ?F°f, Karnow-sky and Estill7 deposited films on sapphire at elevated temperatures and noticed no time dependence of film adhesion but a similar correlation with ?F°f. Because of the kinetic problems associated with thin-film adhesion it is desirable to examine adhesion in an equilibrium system. The wetting behavior of liquid-metal drops on Al2O3 provides such a system. Systems of this metal-ceramic type have been studied extensively.11 Humenik and Kingeryl2 have measured the wetting of A12O3 (and other substrates) by several metals and have pointed out that the wetting ability of these metals increases with increasing values of -?F°f. It is thus seen that thin-film adhesion and metal wetting on A12O3 are both related to the tendency of the metal to react with the surface oxide ions of the Al2O3 substrate and, because of this, both phenomena should be explainable by an appropriate model for the metal-Al2O3 interfacial bonding. In the sections that follow, wetting and adhesion data on A2O3 are reviewed and a model is presented by which these phenomena can be interpreted. ANALYSIS OF WETTING EXPERIMENTS In an equilibrium system involving a liquid-metal drop on a solid Al2O3 substrate, the work of adhesion, WAD, is defined by the Dupre, equation as WAD = ?s + ?L -?sL [1] where ?s and ?L are the surface free energies of the solid substrate and the liquid drop, respectively, and ?sL is the interfacial free energy. The work of adhesion is the work required to separate a unit area of the solid-liquid interface into two surfaces. The work of adhesion is usually determined from a sessile-drop experiment in which yL and the contact angle, ?, are measured. The Young-Dupr6 equation is then used to calculate WAD Wad = ?L (1+ cos ?) [2] The literature of this subject has been examined and Table I shows work of adhesion data for various liquid metals as measured on A12O3 substrates. The standard free energy of oxide formation of the metal at the temperature of the wetting experiment, ?F°f . is also tabulated in kcal per g-atom of oxygen. The data is grouped according to the gaseous atmos-

Jan 1, 1965

By J. Szekely, G. P. Martins

A formulation is given for describing the rate of expansion of spherical bubbles rising in liquids the freeboard of which is evacuated. The computer solution of the resultant differential equations has shown that, for low freeboard pressures (less than about 5 mm Hg), on approaching the free surface the bubbles expand much less rapidly than predictable from equilibrium considerations. In other words, in this region the pressure inside the bubbles will be significantly larger than the static pressure in the liquid corresponding to the position of the bubble. These theoretical predictions were confirmed by experimental work, using two-dimensional air bubbles rising in mercury. The important consequence of these findings is that the expansion of gas bubbles in vacuum degassing operations will be a great deal less than expected from hydrostatic considerations. This would lead to a significant reduction in the available interfacial area and may explain the apparent poor efficiency of many vacuum degassing units. VACUUM degassing as a treatment for liquid steel has gained widespread popularity in recent years; the number of known installations exceeds several hundred at the present time.' Although much information is available on both the thermodynamics of the system and the overall performance of various industrial units, much less is known about the fundamental aspects of the process kinetics.2-4 The basic physical situation common to virtually all vacuum degassing operations is the interaction between gas bubbles (swarms of bubbles) and the surrounding molten metal, held in a container, the freeborad of which is at a low absolute pressure. Once formed (or introduced from an external source) the bubbles will ascend, due to the buoyancy forces, and, during this ascent, a significant increase in their volume will occur. This progressive increase in the bubble volume is due to two factors: a) the continuous reduction in the static pressure acting on the bubble during its rise; and b) mass transfer into the bubble from the surrounding molten steel. In a recent paper Richardson and Bradshaw developed equations5 for describing mass transfer into gas bubbles from molten metals at reduced pressures. However, in deriving these expressions it was assumed that the pressure inside the bubble was identical to the static pressure in the adjacent liquid. In other words, the volume of the bubble was considered to be in equilibrium with the pressure of the fluid adjacent to it. This assumption, thus their analysis presented, was thought to be reasonably accurate for most of the bubble's ascent; however, it was unlikely to be valid in the immediate vicinity of the free surface, held at a low pressure. It was pointed out in the discussion6 that the region close to the surface may be of considerable importance as both the driving force and the interfacial area available for mass transfer are at their highest value here. The ' 'anomalous" behavior of gas bubbles when approaching a free surface at low pressures was recently confirmed in a preliminary investigation by Szekely and Martins. ?1 Here high-speed motion photography was used to study air bubbles rising in a column of n-tetradecane with a freeboard pressure of 0.1 mm Hg. It was found that significant distortion of the bubbles occurred on approaching the free surface; furthermore, the expansion observed was much less than what one could expect from hydrostatic considerations, i.e., factor a previously discussed. It follows from the foregoing that a detailed study of these phenomena would be justified both from fundamental considerations and because of their potential relevance to technology. The purpose of the paper is to present a more realistic formulation for the expansion of a gas bubble approaching a low-pressure region, together with a comparison of the theoretical prediction with experimental measurement. An inert bubble will be considered in the first instance; it is thought that the understanding of the fluid mechanics is an essential first step toward the realistic formulation of the mass transfer process. This latter problem will be the subject of a subsequent publication. FORMULATION The Physical Model. Consider a spherical bubble, of initial radius Ro, rising in a fluid, having a density pL. Initially let the bubble be at a distance H from the free surface, and at a pressure Pgo, as illustrated in Fig. 1. Pgo, the initial pressure in the bubble, is given by the following equation: pgo = Po = Ptp +pLgH [ la] where Po is the pressure in the liquid corresponding to the initial position of the bubble and Ptp is the pressure at the free surface. The fluid pressure at

Jan 1, 1970

By F. H. Buttner, E. R. Funk, H. Udin

A. P. Greenough (University College, swansea, Great Britain)—I have recently made some experiments on the deformation of silver wire at high temperature in an atmosphere of oxygen-free nitrogen. The observa-tions which 1 made confirm the main conclusion of this paper, that the most satisfactory mechanism so far suggested to explain the deformation which takes place

Jan 1, 1953

By John Chipman

THE equilibrium between titanium in liquid iron and titanium oxides has been studied by Hadley and Derge.' They have shown that a minimum occurs in the oxygen content of the metal between 0.1 and 1.0 pct Ti, but its exact level was not fixed. The oxide phase in this minimum range was principally TiO, containing some iron oxide. On the other hand, for concentrations above 5 pct Ti the oxide phase was TiO and the oxygen content of the metal increased rapidly with increasing titanium content. From their observations and the free energy of Ti0 and TiOz reported by Kelley and ah,' it is possible to derive approximate values for the activity coefficients of titanium and oxygen in liquid iron-titanium alloys and the conditions for equilibrium in steel deoxidation. Neglecting possible departures from the stoichio-metric composition, the condition of equilibrium with Ti0 may be expressed as follows: TiO= Ti_ + C) log K = log NTl + log [% O] + log yTi + log fQ Here as a matter of convenience the titanium concentration is expressed in mol fraction while that of oxygen is in weight percent. The activity coefficients are yTi and fo. The value of log fo approaches zero as the concentration of titanium approaches zero, while that of log yTi approaches a limiting value of In Fig. 1 the sum of log NTi + log [% 0] is plotted for mol fractions of titanium between 0.05 and 0.50. The smooth extrapolation gives a value of —4.15 which corresponds to log K — log y:i . We therefore have the equation: According to the data of Kelley and Mah,' the free energy of formation of Ti0 at 1900°K is -82,400 cal. The free energy of solution of half a mol of oxygen in iron, taking 1 pct 0 as the standard state, is -29,300 cal. From these we write: From these equations the activity coefficient of titanium at infinite dilution in iron is found to have a value of 0.011 or log y°. = -1.96. This is only an approximate value but is certainly better than the estimated 0.05 in Basic Open Hearth Steelmaking To obtain approximate values for the activity coefficient at intermediate concentrations, it is as- sumed that log yTi(l is constant and equal to -1.96. This corresponds to a value of E;: = 3 In yTi/aNTi = 9.0 which is not unreasonable We now have the value for the activity of titanium and the percentage of oxygen in equilibrium with TiO. It is therefore a simple matter to calculate the activity coefficient of oxygen which is shown in Fig. 2. The effect of titanium is rather large, being comparable to that of vanadium, but not so large as has been reported for aluminum. The slope of the line at low concentrations corresponds to E: = aln yo/ aNTi=-0.37. At concentrations below 1 pct Ti the deoxidation constant and oxygen content for equilibrium with TiO, can be calculated from the foregoing data and the free energy of formation of TiO,, which according to Kelley and Mah is -144,600 cal at 1900°K. The free energy of solution of oxygen has been given; that of Ti to form a dilute solution with 1 pct Ti as the standard state is RT ln (0.5585 y:i/47.9) = -34,800 cal. From these data we find (for concentrations in wt pct): TiO, = Ti + 2 -0; hFTgO0= + 51,200 cal log if =-5.89 The interaction coefficients, concentrations being expressed as wt pct, are e;: = alogfTi/a[% Ti] = +0.048 and e:' = a logfo,/a[ojTi] = -0.187. The calculation gives the following results which, in view of the impurity of the oxide phase, must be regarded as approximate:

Jan 1, 1961

By W. W. Mullins

The development, by the mechanism of volume diffusion, of a grain boundary groove on an interface separating a solid phase and a saturated fluid phase is calculated under the following assumptions: 1) isotropy of the interfacial free energy 's, 2) applicability of the Gibbs-Thompson formula relating curvature and chemical potential, 3) a nearly planar groove surface. The groove profile is found to have a .fixed shape and linear dimensions that are proportional to (time)1/3. The constant of proportionality is evaluated and involves ?s in such a way that the latter my be evaluated from grooving kinetics. A grain boundary that intersects an interphase interface will tend to produce a groove along the line of intersection (Fig. 1). The ultimate motivation for the formation of the groove is the reduction in interfacial free energ that occurs as the grain boundary contracts. Smith has discussed the way in which the free energy of the interfaces determines their dihedral angles at the groove root and has given a detailed analysis of the effect of the dihedral angles upon the nature the microstructures developed in polyphase alloys. Herring2 has extended the considerations to the case in which the free energy of an interface depends on its orientation and has thus added torque terms to the condition for interface equilibrium. Although the grain boundary and the interphase interface may quickly achieve the proper equilibrium angles where they intersect, as determined by the balance of equivalent tensions and torques,"2 the groove will generally continue to grow (though with decreasing speed). Thermodynamically, this continued growth reflects the fact that the lowest free energy cannot be achieved until the entire grain boundary has been eliminated; mechanistically, the growth occurs in response to inhomogeneities of chemical potential that are caused by the constraint of fixed dihedral angles at the groove root. The latter point is illustrated in Fig. 1, which shows that atoms* near the groove are on the convex side of a cylindrically curved surface and therefore have a higher chemical potential than atoms on the flat interface beyond. Thus atoms tend to leave the curved groove shoulders and force the groove to deepen. When both phases are solid additional chemical potential gradient may arise from whatever strain fields are necessary to insure continuity of material across the interface. In the discussion that follows, this complication due to strain will not occur since we always assume one phase to be a fluid and the other a solid. The transport processes that may operate to permit growth of the groove are surface (interface)* diffusion, volume diffusion in the phase on either side of the interface, and evaporation-condensation when one phase is gaseous. (Also a melting-freezing process is responsible for groove enlargement on a solid-melt interface as discussed in Sec. VI). The theory of grain boundary grooving has been discussed in detail for the processes of surface diffusion and of one type of evaporation-condensation.3'4 The theoretical predictions for the mechanism of surface diffusion have been confirmed in an experimental study of grooving kinetics in copper.5 In this paper, the theory of groove development by volume diffusion will be presented. Volume diffusion can occur either by atomic migration in the solid S or by diffusion of S atoms in the fluid phase, or solvent, adjacent to the groove surface. As discussed in Sec. V, volume diffusion in the solid should be less important than surface diffusion in forming a groove. Apart from verifying this statement then, the main interest of the present analysis centers on diffusion in an external solvent. The solvent may be either a liquid (e.g., water, or-

Jan 1, 1961