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By E. M. Cox, A. S. Skapski, N. H. Nachtrieb, M. C. Bachelder

D. T. ROGERS*—The conclusions drawn in this paper have important practical significance to the steelmaker and the metallurgist if, in practice, it is demonstrated that metallic copper in the charge will pick up sulphur from the furnace atmosphere and thus increase the sulphur content of the bath. The problem of residual copper arising out of increasing copper in the scrap available to the industry is, in itself, a matter of concern to the steel maker. If, in addition to the often detrimental effects of high residual copper upon the physical properties of some important steel grades, there is to be a complication of the sulphur problem, then we have a set of conditions that bodes no good for the open hearth melter and the open hearth metallurgist. M. B. BEVER*— Investigations of gas-metal equilibria continue to be of interest, especially as new possibilities for improving experimental techniques emerge. Higher purity of reacting substances, better refractories, improved methods of temperature control and an increased awareness of the pitfalls of high-temperature equilibrium work are

Jan 1, 1950

By J. Winlock

To have been chosen by you to give the Howe Memorial Lecture is the greatest honor I have ever had and I should like to have you know that I appreciate it deeply. Many years ago I had the privilege and the pleasure of working with Professor Howe in the private laboratory which he had established in his home at Bedford Hills, New York. Without doubt he was one of the world's greatest metallurgists and so you can imagine what a difficult task it has been for me to live up to his teachings. Every morning Professor Howe would outline the work he wanted done and the recollections of those conferences are clear to me to this day. Sometimes he would ask me to ride in his automobile and the chauffeur had full instructions to go no more than fifteen miles an hour. If he did so, Professor Howe was sure to rap upon the man's shoulder with his cane. I assure you, however, Professor Howe's thinking was not at that rate. His homely advice, his patience and his perfect control of the English language still impress me. Many times I heard him dictate a complicated paper on metallurgy and never find it necessary to change a single word. There are no better words to describe the character of Professor Howe, in my opinion, than those used by Professor Sauveur when he presented the John Fritz Medal to him in 1917: "Lover of justice and humanity Public servant and public benefactor, Master of the English Language, Loyal and devoted friend, Untiring and unselfish worker in an important field of science." I hope you will bear with me with the same patience and understanding which he used to give to me. The peculiar behavior of steel at the yield point has long been known and has been the subject of much research, both in this country and abroad.',' Many theories, including some of mine and my colleagues, have been suggested, but none of them, in our opinion, fully explains to our satisfaction why the phenomena occur. Of particular importance has been the work of Nadai,3 Siebel and Pomp,' Sachs and Fiek,5 Rawdon,0 Kenyon and Burns,' Gensamer," Gensamer and Meh1,0 Davenport and Bain,'" Fell," Deutler,12 Brinkman,13 MacGregor,14 Hollomon,15 Cot-trell,16 and Palm." The question of what is occurring during this singular behavior is not only of interest from an academic point of view, but is of great practical importance for at least two reasons: 1—The highly localized plastic flow which occurs during the deep drawing of light-gage steel gives rise to surface markings which seriously mar its appearance, Fig. 1. If the forces causing the deformation are primarily tensile forces, these surface markings occur as depressions in the surface. Whereas, if the forces causing the deformation are primarily compressive, irregular lines of elevations occur. These surface markings are known as Luder's lines, Hartmann lines, the Piobert affect, and, in the shop, as "stretcher strains." 2—The steel is in the most suitable condition for deep drawing after the yield point phenomena have been removed. When this is done, the steel may be deep drawn more easily and to a greater extent.' It should be mentioned that steel is not the only metal which shows this peculiar behavior at the yield point. Stretcher strains occur, also, during the deformation of some copper-nickel-zinc alloys." The purpose of this paper is not an attempt to describe what causes the steel to behave in this peculiar manner, but an attempt: l—to describe what is taking place at the yield point; and 2—to show the influence of the rate of deformation on the tensile properties of some plain carbon steels. As is well-known, there are two methods of deforming a metal in tension: 1—by actually hanging an increasing amount of dead weight on the metal; or 2—by deforming the metal at some given rate or rates by means of oil pressure cylinders, screws, etc. With the first method, the load is always present and, clearly, no drop in load can ever occur while the steel is deforming. With the second method, the registered load is the resistance of the steel to the deformation being imposed upon it. The second method is the one most widely used, and is the one referred to throughout this paper. In order to describe clearly what is occurring at the yield point in steel, it will help, I believe, if a description is first given of what occurs when alumi-

Jan 1, 1954

By C. B. Post, G. V. Luerssen

It is generally recognized that non-metallic inclusions in steel come from two principal sources. First are the chemical reactions in the furnace, or in subsequent deoxidation, resulting in slag which does not free itself from the metal. Much information has been published concerning these chemical reactions and their control through proper attention to slag viscosity, composition of deoxidizers, and other qualities. The studies of this subject by C. H. Herty, Jr. and others through the medium of physical chemistry have yielded much information for the steelmaker. The second source is erosion of ladle refractories, such as lining brick, stoppers, nozzles and runners, causing entrapped particles of globules of fluxed silicate material. In contrast with the large amount of information available on the first source, relatively little has been published on the subject of erosion which, in the case of basic electric melted steel, is the principal source of nonmetallics. This is probably due to the fact that the problem was assumed to be one of simple mechanical erosion, which could be solved primarily by modification of ladle practices. Good improvements have been made by elimination of slurries in the ladle, better ladle and runner refractories, and more attention to pouring temperatures. It is doubtful, however, that this problem has been recognized in its true light since it is not one of simple mechanical erosion but rather one of chemical reaction between the metal and the refractories; and in this sense is as much a problem of physical chemistry as the reactions involved in the actual steelmaking process. The influence of ladle refractories on the resulting cleanness of steels was early recognized by A. McCancel who examined large inclusions in steels made by both acid and basic practices. His chemical analyses showed the large influence exerted by the manganese content of the steel on erosion of the ladle and nozzles used in those days. The presence of MnO in such inclusions led McCance to the hypothesis that both basic and acid steels react chemically with the ladle refractories so that small globules of fluxed refractories are carried in the stream into the molds. This early work of McCance was checked by one of the present authors on basic electric bearing-steel, and it was found that on steels containing as low as 0.40 pct manganese the fluxed surface of the ladle lining after delivering such a heat showed as high as 25 pct MnO by actual analysis. Furthermore, by lowering the manganese content of the steel to 0.20 pct, ladle erosion was decreased with a corresponding decrease in silicate inclusions in the steel. Limitations placed on the manganese content for the required inherent properties made it impossible to pursue this line further, and subsequent attention was concentrated on improved ladle refractories, care in keeping the ladle clean and free from loose refractories up to the time of tapping, and pouring the steel at optimum temperature. Our study of the chemical reactions at the metal-brick interface between steel and ladle refractories was revived in 1939 as a result of an experimental observation made on the cleanness of alloy steels of the SAE types. This observation showed that the relative cleanness of such steels made in basic electric arc furnaces of 12 ton capacity and poured in ingots ranging from 1100 to 2200 lb weight was determined to a large extent by the ratio of the manganese and silicon contents, provided other steelmaking variables such as tapping temperature, pouring temperature, pouring time, amount of aluminum added for grain size control, and degree of deoxidation in the furnace were kept reasonably constant. Detailed studies made on the deoxidation and slag practice during the refining period of basic electric furnace practice showed that these two variables exerted some influence on the resulting cleanness of steel in the form of bars and forgings. The important variable, the manganese-silicon balance, was not apparent until heats were made in succession by the best furnace practice kept under fairly rigid metallurgical control. Another observation pertinent to this work concerned the similarity in the microscope of slag particles causing magnaflux or step-down indications in subsequent rolled bars, and the patches of slag frequently seen on the surface of ingots. These patches are generally believed to come from the glassy metal-brick interface in the ladle and represent an entrapment of such glass (both from the ladle brick and nozzle) in the metal as it flows over the refractories in the neighborhood of the nozzle. These glassy particles are carried down into the mold with the liquid steel, and gradually coalesce into a slag "button" which floats on the surface of the steel as it rises in the molds. Periodically the button is washed to the side of the ingot where it is trapped between the surface of the ingot and the mold, later appearing as a slag patch on the surface of the ingot after stripping. Even though most of the small glassy particles coalesce into a slag button while the ingot is being poured, it is logical to suspect this step in the steelmaking process as being a source of slag lines large enough to cause trouble

Jan 1, 1950

By Lo-Ching Chang, J. Chipman

The perennial and increasing interest in the chemical behavior of steelmaking slags has led to numerous attempts to formulate the thermodynamic properties of these solutions. The classical view is that of a solution of the component oxides in which certain acidic oxides are more or less completely held in combination with basic or metallic oxides, the nature of the interoxide compounds being derivable from the chemical behavior of the slag or from the mineralogy of a solidified specimen. The known electrical conductivity of slags has pointed to the existence of ions in the solution and a number of attempts have been made to account for the observed facts of slag behavior on the basis of a theory of complete ionization of the solution. It is the purpose of this paper to examine, in the light of ionic theory, a number of recently published series of data on slag-metal and slag-gas equilibria, with the purpose of obtaining a more complete or more satisfactory generalization than has been possible on either of the single bases of simple compound formation or complete ionization. The attempt to formulate the ionic constitution of a complex solution is fraught with many uncertainties. An ion is not something that can be plucked from the solution and examined in detail, nor can its true formula be determined with certainty by any single experimental method. In attempting to express the composition of a slag by various ionic formulas it can be expected that alternative hypotheses of essentially equal merit will present themselves. In the present state of early development of the ionic theory of slags, it may be necessary to make some rather arbitrary choices of ionic formulas in the absence of su- cient information to yield complete certainty. Acids and Bases The classification of slag-forming oxides as acidic or basic apparently dates back into the days of Berzelius. It is difficult to see how the concept could have originated in the early twentieth century when it was fashionable to define an acid or a base as an aqueous solution containing hydrogen or hy-droxyl ions. It is, however, entirely consistent with the modern and more general theory of acids and bases. In this theory, as originally formulated by G. N. Lewis,' a basic molecule is one that has an electron pair which may enter the valence shell of another atom thus binding the two together by the electron-pair bond. An acid molecule is one which is capable of receiving such an electron pair into the shell of one of its atoms. The acid, the base, and the product of neutralization may be either ions or neutral molecules. The product of such a reaction may itself be a base or an acid if it is further capable of giving or accepting an electron pair. Thus a base is a donor of electrons, an acid, an acceptor. In oxide slags the typical and ever-present base is oxide ion, 0-—. In behavior and in importance it is analogous to hydroxyl ion, OH-, which is the typical base of aqueous solutions. There is nothing in the chemistry of slags which is quite analogous to the acid H30+ in aqueous solutions. This is not surprising for in slag systems there is nothing which can be designated as a solvent and no ubiquitous positive ion. The chemistry of slags is in fact more complex than the chemistry of aqueous solutions and the concepts which must be evoked in its study are correspondingly broader. In seeking a basis for a classification of slag-forming oxides as basic or acidic it must be remembered that these terms are not absolute but relative. A substance which acts as a base toward a second substance may act as an acid toward a third. This is less likely to happen among strong bases or acids than among the weak ones; there are numerous examples of weak acids which under the influence of a stronger acid behave as weak bases. Such substances are called amphoteric. A classification of the glass-forming oxides has been proposed by Sun and Silverman² and further developed by Sun3 in which the oxides are arranged in order of decreasing acidity or increasing basicity, each substance being potentially capable of acting as an acid toward substances below it in the list and as a base toward those above it. It is based upon the relative strengths of the metal-to-oxygen bond as determined by the energy required to dissociate the oxide into its component atoms.' Data are available for computation of this energy, at least approximately, for the oxides of slags and glasses. In general those oxides from which it is most difficult to remove the positive atom are the strong acids while those in which it is most loosely held are the strong bases. It is in the latter, of course, that formation of oxide ion occurs most readily as, for example, in CaO which in solution ionizes to form the weak acid Ca++ and the strong base O—. The order of arrangement found by Sun is shown in the first column of Table 1, to which have been added the data for

Jan 1, 1950

By Lo-Ching Chang, J. Chipman

C. B. POST*—Just what are you showing that has not been shown by fixing the attention on molecular species and choosing the molecular species to give you a perfect solution? J. CHIPMAN (authors' reply)—In general a fairly satisfactory thermody-uamic treatment of slag-metal equilibria can be worked out on the basis of assumed molecular species in the slag. This has been the method used by Shenck and more recently by White. Winkler and I also used it in studying dephosphoriza-tion. Darken and Gurry found that it did not fit satisfactorily in the case of their data on iron oxides. The ionic formulas used here conform to the data much better and probably correspond somewhat more closely with the actual structure of the slags. C. B. POST—It does seem to be similar to you? J. CHIPMAN—It is alternative, and may lead to a more complete understanding. C. B. POST—Have you had a chance to talk to glass technologists on this? Have they been using this type of set-up for glass solutions? J. CHIPMAN—Yes, and the ionic formulas have given them a little better understanding of what liquid glass is like. C. B. POST—Nelson Taylor always said we were going- about slag reactions from the wrong viewpoint when using molecular species. Evidently the glass technologists use ionic species exclusively when dealing with liquid glass reactions. J. CHIPMAN—I agree that it seems more rational and more accurate to use ionic rather than molecular formulas. We should be cautious, however, and not suppose that we really understand the structure of a slag just because we are able to fit its reactions by ionic equations.

Jan 1, 1950

By J. Chipman, J. B. Gero, T. B. Winkler

IN the basic open hearth process the reaction of manganese in the bath with iron oxide in the slag attains a condition very closely approximating true equilibrium, and the distribution of manganese between slag and metal during the refining period is determined by the factors which control this equilibrium condition. For this reason a number of investigators have studied this reaction both in the laboratory and under various conditions of furnace operation. The principle reaction and its equilibrium constant are: FeO (in slag) + Mn = MnO (in slag) + Fe (liq.) [1] (MnO) .= (FeO),[%Mn] The symbols in parentheses represent activities of the two oxides in the slag which, in the simple slags consisting almost wholly of the two oxides, may be assumed equal to the respective mol fractions. The symbol (FeO)r is used to denote the total iron oxide computed as FeO; or it is the sum of the mol fraction of FeO plus twice that of Fe2O3. Early attempts to obtain laboratory data on this reaction suffered from failure to appreciate the great speed of the reaction. When slag and metal are cooled slowly together, the equilibrium shifts with temperature and the final compositions correspond to equilibrium at the freezing point rather than at bath temperature. The early work of Oberhoffer and Schenck¹ and of Tammann and Oelsen² apparently suffered from this source of error. In most of the other published laboratory investigationsa. '.' this error was not present but other uncertainties have existed, notably dependence upon optical temperature measurements and exposure to atmospheric oxidation.

Jan 1, 1951

By J. Chipman, J. B. Gero, T. B. Winkler

D. C. Hilty—This paper is a useful and timely addition to our store of quantitative data relating to manganese distribution between slag and metal in steel-making processes. For some time, many of us have suspected that the values of Kmn derived by Körber and Oelsen might be too low, and this paper now appears to confirm that suspicion. Application of the new constant to openhearth data should prove interesting. The manganese deoxidation curves of fig. 4 agree fairly well with direct measurements of isothermal solubilities of oxygen in liquid iron containing manganese that have recently been made at the Union Carbide and Carbon Research Labs., Inc. According to the solubility data just mentioned, however, the curves for 1550" and 1600°C lie much closer to each other than the authors have indicated. In other words, the solubility measurements suggest that the logarithm of the oxygen solubility is not a linear function of the reciprocal of the absolute temperature, as the authors have assumed for their calculations. It seems possible that this discrepancy may be due in part to the authors' use of the distribution coefficient, L,,, obtained from Taylor and Chipman's curve for the solubility of oxygen in iron as shown in fig. 2. Taylor and Chipman gave the equation of this curve as —6320 Log % 0 - ---T + 2.734 Their data, however, can be fitted equally well by a curve having the equation: 13.23 x104 1.18x10" Log % O = 36.350 -13.23x10 Moreover, this curve also fits the authors' oxygen distribution data somewhat better than does the linear curve of Taylor and Chipman. Its use in the derivation of Lo for calculation of the deoxidation curves by the authors' eq 15 causes the effect of temperature on the calculated curves of fig. 4 to agree quite well with the temperature effect that has been observed. An experimental determination of the temperature coefficient of the manganese reaction appears to be desirable. J. E. Stukel—Because the authors have done such an excellent job, my comments will be confined to additional information. Very shortly Professor T. L. Joseph and I will publish the results of a study of the reaction between molten manganese and silica. It was found that electrolytic manganese, melted in silica crucibles, reacted with the silica to form a silico-manganese alloy containing 18 pct silicon (1500°C) and a silica saturated MnO-SiO, slag. Therefore, the presence of silicon and its oxides in the Fe-Mn-0 system will affect the equilibrium. Carbon is also an important factor. The higher the carbon content of the iron the less ability manganese has to reduce silica. As a matter of interest, recently a study of the manganese equilibrium in carbon saturated iron and blast furnace slags was completed at Carnegie Institute of Technology. As a comparison to the present study, 2 to 5 hr were required to reach equilibrium and temperature was a much more important factor than slag composition in determining the (Mn)/(MnO) ratio. These results will also be published in the near future. It can be seen, therefore, that the results of this paper cannot be applied directly to openhearth studies without a degree of flexibility. J. Chipman (authors' reply)—With regard to the effect of silicon on the manganese constant, this effect is, of course, known. Much more data is needed in order to establish it accurately, and I hope we can look forward to having some accurate data on that. Mr. Hilty suggests that a three-term expression for the Taylor-Chipman solubility of oxygen in liquid iron might fit a little better than the two-term equation. I think that it would be too great a compliment to the precision of the data to employ a three-term equation, and I would still recommend the simple, two-term expression.

Jan 1, 1951

By B. B. L. Seth, H. U. Ross

A generalized rate equation for the reduction of iron oxide was derived from which two particular equations were obtained: one for rate controlled by the transportation of gas, the other for rate controlled by the phase-boundary reaction. Pellets of pure ferric oxide having diameters of 8.5 to 17.5 mm and a density of 4.8 g per cm3 were prepared and reduced by hydrogen at 750° to 900°C. From the analysis of data obtairzed, it was observed that neither the phase-houndarv reaction nor the transportation of gas controlled entirely the rate of redziction. Rather, the mechanism of reduction can he divided into three stages. In the beginning, the process seems to depend predominantly on the surJrce reaction, hut after a layer of iron is formed the diffusion of gas becomes the controlling factor. Towards the end, however, the rate falls sharply due to a decrease in porosity. The times predicted by the generalized equation for a certain degree of reduction showed an excellent agreement with those obtained experinmentally for pellets of varying sizes. WIDE interest in iron oxide reduction has resulted in many valuable studies pertaining to thermody-namical properties, equilibrium diagrams, and chemical kinetics. Although the thermodynamical properties and equilibrium diagrams are now known with a fair degree of accuracy, the mechanism and rate-controlling step in the reduction of iron oxides presents a problem to research workers which is still unsolved. This is because the field of chemical kinetics is so highly complex. Besides the chemical reaction between oxide and reducing gas, several other processes are occurring simultaneously such as solid-state diffusion of iron through intermediate oxides (FeO and Fe3O4), the diffusion of reducing gas inwards and of product gas outwards, and the sintering of iron if reduction is carried out above the sintering temperature of iron. Furthermore, there is a large number of variables, including the nature and flow rate of the reducing gas, the chemical composition and physical properties of the ore, the temperature of reaction, particle size, and so forth, all of which can affect both the mechanism and the kinetics of reduction. Despite the controversy and diversity of opinion about the mechanism of iron oxide reduction, three main schools of thought have emerged. According to the first, the rate is controlled by the diffusion of gas through the boundary layer of stagnant gas; the second claims that the rate is proportional to the area of the metal-oxide interface, while the third believes the transportation of reducing gas from the main stream to the metal-oxide interface and of product gas from the metal-oxide interface to the main stream to be the rate-controlling step. 1) The boundary-layer theory is true mainly for packed beds where the flow of gas through the bed is important. For a single particle, the boundary layer may be prevented from being the rate-controlling step if a gas flow rate of reducing gas above the critical flow rate is used. 2) Several workers have reported a linear advance of the Fe/FeO interface which provides excellent support for the belief that reduction is controlled by the surface area. McKewanl has given formal shape to this concept with mathematical derivation and has shown it to be valid for reduction of several iron ores, hematite, and magnetite, both by H2 and H2, H2O, N2 mixtures. Some other investigators, however, do not find this theory to be entirely valid. Deviations have been observed2 and further confirmedS3 Hansen4 also agrees that deviations do occur, at least in the latter stages of reduction, while from the data of several investigators summarized by Themelis and Gauvin,5 it is clear that the theory is not always applicable and further that, when it is applicable, it does not hold in the final stages of reduction. 3) Among those who claim the transportation of gas to be the rate-controlling step are Udy and Lorig,6 Bogdandy and Janke,7 and Kawasaki el a1.8 The validity of the theory has also been acknowledged indirectly by other research workers who show that the sintering and recrystallization of iron cause a decrease in reduction rate, for it is only if the transportation of gas is important that this sintering has any bearing. However, the theory has been rejected by some because they have failed to obtain

Jan 1, 1965

By W. O. Philbrook, K. M. Goldman, G. Derge

EQUILIBRIUM conditions for steelmaking reactions have been studied extensively over the past two decades by a .number of investigators, with gratifying results. Equilibrium data are essential to the understanding of any process, and such knowledge has the practical utility of placing a limit beyond which control measures cannot succeed. When, however, the driving rate of an industrial process is so fast that there is not time for reactions to reach equilibrium, it then becomes necessary that the factors which control the rates of reaction be known in order to establish full control of the process. The desulphurization of molten pig iron by slags within the iron blast furnace is one such process in which the actual degree of sulphur absorption by the slag does not approach the equilibrium distribution obtained for similar slag-metal systems in the laboratory.' A study of the rate-controlling factors governing the desulphurization of iron by slags is becoming increasingly important as the sulphur content of raw materials increases with depletion of higher grade ores and coal. Following up an initial study on kinetics,' this paper reports some results of a continuing laboratory investigation on the mechanism of sulphur transfer between molten iron saturated with carbon and slags of the CaO-SiO,-A12O3 system. Laboratory experiments cannot reproduce in detail the conditions which prevail in the hearth of a blast furnace, but they will contribute to an understanding of the smelting reactions and perhaps will explain some apparent inconsistencies in the factors controlling the equilibrium distribution of sulphur between iron and slags under reducing compared with oxidizing conditions. The mechanism of a reaction—that is, the individual steps and the sequence in which they occur to produce the overall reaction which is ordinarily observed—must be elucidated to learn which steps are the slow ones, or "bottlenecks," that fix the pace of the process as a whole. In the desulphurization reaction, for example, the overall rate might, in principle, depend upon the rate of diffusion of sulphur in the metal or in the slag, upon the speed of some homogeneous reaction taking place entirely within one of the phases, or upon some heterogeneous reaction taking place across the slag-metal interface. Even some side reaction or the back reaction might have some influence. Evidence on all of these points will be presented in this paper. The rate of diffusion of sulphur in both iron and slag is so slow that it seems necessary to assume that convection provides the mechanism of carrying

Jan 1, 1951

By W. O. Philbrook, K. M. Goldman, G. Derge

T. Rosenqvist—The most interesting point in this paper is the observed transfer of iron into the slag in the initial stage of the desulphurization process, after which the iron again is reduced to the metallic state. The authors interpret this observation as showing that the sulphur enters the slag as an iron-sulphur compound which subsequently is decomposed by the slag. The present writer has previously suggested the following equation for the desulphurization process: S + O2- ? S2- + O For equilibrium in the blast furnace the oxygen potential is defined by equilibrium with graphite and CO of 1 atm pressure: C + O ? CO [2] During the desulphurization process the reactions proceed in the direction of the arrows. If one assumes eq 2 to be significantly slower than eq 1, the transfer of sulphur into the slag, in accordance with eq 1, will build up a local oxygen potential at the metal-slag interface very much higher than that corresponding to the value defined by eq 2. This is possible because the equilibrium oxygen potential in eq 1 is high as long as the sulphur content in the slag is low. This oxygen potential will again be able to oxidize some iron: Fe + O ? Fe2+ + O2- and an increase in the iron content of the slag will be observed. Adding up eqs 1 and 3 one obtains: S + Fe ? S2- + Fe2+ The net effect is thus in harmony with the experimental observation but is obtained without assuming any close ties between the sulphur and iron atoms during the process. Furthermore, it follows from eqs 1 and 2 that when the sulphur content in the slag increases, and equilibrium with C and CO is finally approached, the local oxygen potential at the metal-slag interface will decrease, and the iron in the slag will be reduced back into its metallic state. C. E. Sims-—The data and conclusions presented in this paper are thoroughly convincing in establishing the mechanism of sulphur transfer from iron to slag as in a blast furnace. The evolution of gaseous CO in step 3 of the reactions given on p. 1112 makes the process virtually irreversible. Assuming that the process is similar in slag-metal systems other than in the blast furnace, it is readily seen why free CaO and re-ducing conditions so greatly favor desulphurization. On the other hand, the very effective desulphurization obtained in oxidizing slags when strongly basic, must be attributed to the relatively high stability of CaS as compared to FeS. The ease and simplicity with which the reactions of classic chemistry agree with the experimental data and explain the mechanism is noteworthy. The concept of molecules of FeS, soluble in both phases (metallic iron is not soluble in the slag), migrating from the iron to the slag and there reacting with CaO, which is soluble only in the slag phase, is clear and uncomplicated. This is likewise true for step 3. Those who would deny the existence of molecules or molecular-type combinations in liquid iron, must strain to provide a mechanism so lucid. In the absence of molecules, the Fe and S exhibit a remarkable collusion. L. S. Darken—The investigation and interpretation of rate phenomena in the range of steelmaking temperatures is a difficult task. Most of the laboratory investigations of steelmaking reactions have been concerned with equilibrium. Having determined the equilibrium, our attention naturally focuses next on the mechanism and rate of approach to equilibrium. The authors seem to have contributed substantially to our understanding of these factors for the case of sulphur transfer. I should like to ask the authors whether they consider that the sulphur transfer reaction is diffusion controlled as many high-temperature reactions seem to be. If so, it would seem reasonable to suppose that the slow diffusion step of the process is the transfer across a pseudo-static layer or film similar to that considered in heat flow problems. As the diffusivity and fluidity are smaller for the slag than for the metal, it may tentatively be assumed that the sulphur gradient exists in a thin layer in the slag adjacent to the slag-metal interface and that the metal and the main mass of slag are each maintained uniform by convection. On this basis the amount of sulphur transferred across unit area per unit time is D p (?S%)/100 ?1, where D is the diffusivity, p the density, (?S%) the difference in percent sulphur on the two sides of the layer, and ?l is the layer thickness. At the beginning of the experiment the main body of the slag and hence one side of the layer contains no sulphur; therefore (?S%) may be replaced by (S%), the sulphur content of the slag at the slag-metal interface, which in turn is equal to L[S%] where [S%] is the sulphur content of the metal and L is the distribution coefficient. The rate of transfer thus becomes DpL[S%]/100 ?l, which the authors designate K[S%]. Equating these two quantities and setting D = 10-6 cm2 per sec, p = 3 g per cm3, L = 40, and K = lo-+ g cm-2 sec-1, it is found that ?l, the film thickness, is about 0.01 cm—a value of the order of magnitude of that found in heat transfer problems in liquids. The uncertainty of the numerical values used leaves much to be desired, but at least it can be said that this calculation tends to support the proposed model involving diffusion through a film. Although this does not seem to affect the general argument, I should like to call attention to the fact that the diffusivity3 of sulphur in hot metal is found (on conversion of units) to be about 10-4 cm2 per sec rather than 104 cm2 per sec as stated by the authors. The three equations written by the authors to express the steps in the overall process of sulphur transfer may alternatively be written ionically as only two Fe + S = Fe++ + S-- Fe++ + O-- + C (graphite or metal) = CO (gas) + Fe where the underscore is used to designate the metallic phase; ionic species are slag constituents. After the authors have so neatly demonstrated that iron and sulphur transfer together (at least initially), this fact seems almost self evident; from eq 4 it is seen that if sulphur acquires a negative charge during transfer

Jan 1, 1951

By Lawrence H. Van Vlack, Otto K. Riegger, Gerald I. Madden

The microstructural variations of periclase (MgO) in the presence of oxide liquids are examined under the steelmaking variables of: 1) temperature, 2) liquid composition, and 3) FeO additions under different oxidation levels. Attention is given to the distribution of the phases, both liquid and solid, and to the growth of individual crystalline grains. Silicate liquids penetrate more extensively between individual periclase grains than do liquids containing high percentages of Fe2O3 Higher MgO solubilities in the liquid and lower MgO contents of the solid favor more rapid grain growth. The presence of a second solid phase reduces the periclase grain growth rate and increases the amount of the solid-to-solid contact within the oxide microstructures at high temperatures. The service suitability of a refractory depends on many factors. Two are of major importance and include 1) the thermal resistance to melting, and 2) the mechanical resistance to loads at service temperatures. Neither is a simple consequence of the service temperatures because service conditions will alter compositions, produce partial melting, and induee phase changes. Consequently, the equilibrium phase relationships have been rather thoroughly studied and give a knowledge of the thermal resistance to melting, but do not give full information about the mechanical properties because two refractories with the same types and quantities of phase may have different microstructures. Although variations of microstructures with time, temperature, and composition have been subjects for extensive investigation in metals, only a limited amount of comparable microstructural work has been performed for refractory materials.' This study was an attempt to evaluate some of the consequences of service parameters upon the microstructures of refractories so that bases may be established for the analyzing of high temperature mechanical properties. Periclase (MgO) was chosen as the refractory oxide; variables included those which are encountered under steelmaking conditions such as 1) temperature, 2) liquid composition, and 3) FeO additions under various oxidation levels. Specific attention was given to the distribution of the phases, both liquid and solid, and to the growth of individual crystalline grains. The most closely related work on microstructures of polyphase materials is that of Van Vlack and Rieg-ger2 on the microstructure of magnesiowüstite [(Mg,Fe)O] in the presence of silica. In that work which pertained to solid solutions with less than 40 pct MgO, most of the quantitative work was performed on FeO microstructures. The chief conclusions concerning these relatively low-melting oxide solids were as follows: 1) the rate of crystalline grain growth is inversely proportional to the grain diameter, 2) grain growth proceeds more rapidly at higher temperatures but is slightly retarded by additional liquid content, and 3) a Silicate-containing liquid penetrates as a film between the individual magnesiowüstite grains independent of time, temperature, amount of liquid, or the MgO/ FeO ratio. The above observations are in contrast to prior work3 on the microstructure of silica in the presence of iron oxide-containing liquids where the liquid does not penetrate as a complete film between solid grains. The phase relationships for the compositions of the present work are shown in Fig. 1 which is a summary of the work of several investigators.4 Of importance is the fact that CaO forms a more stable structure with SiO2 and Al2O3 than do either MgO or FeO. The oxygen potential has little effect on periclase unless iron oxide is also present. The iron oxide is ferrous at moderately low oxygen levels, changing to ferric as the Oxygen potential is increased so the spinels, magnetite, and magesioferrite are formed.5 These two phases are relatively stable in air at steelmaking temperatures. I) EXPERIMENTAL PROCEDURE ractory were made with reagent grade Oxides. The magnesium oxide used was 99 pct MgO after ignition, and the iron oxide raw material had a minimum content of 99 pet Fe2O3. The CaO, SiO2, and A12O3 were also reagent grade raw materials. After mixing, the required compositions were pressed into pellets at a minimum pressure of 5000 psi to insure compaction of the raw materials and prevent excess void content. A silicon carbide element tube furnace was used with thermocouple control for sin-

Jan 1, 1963

By H. C. Chao, Y. E. Smith, L. H. Van Vlack

ThE phase relationships for the MnO-MnS system have been investigated only in the eutectic region. wentrupl reported a eutectic at 1280°C (2345°F) with approximately 50 wt pct of each component, as based on the earlier work of Andrew, Maddocks, and Fowler.2 More recently silverman3 corrected these figures to 2275° ±10°F (1246°C) with 63 wt pct MnS and 37 pct MnO. Neither Wentrup nor Silverman investigated the solid-solution limits in this system. However, Wentrup did suggest with his phase diagram sketch that the maximum solubility of MnS in MnO is 10 wt pct, and the solubility of MnO in MnS is nearer 20 wt pct, Fig. 1. These figures have been utilized in subsequent publications without further verification.4 There had been evidence found in this laboratory that the above solid-solution figures were high. An investigation was therefore conducted using the following procedure. Samples containing MnO and MnS were contained in platinum foil, heated just above the eutectic temperature in a purified nitrogen at- mosphere, and quenched into distilled water. The MnO had been prepared by calcining reagent grade MnCO3 in nitrogen at 1400°C. Only MnO was detected in subsequent X-ray diffraction analyses. The MnS had been prepared by sulfur deoxidation of reagent grade MnSO4 according to the reaction: MnSO4 + S2 ? MnS + 2SO2 The details of the sulfide preparation procedure, which utilized atmospheric sulfur pressures at 950°C, are discussed elsewhere.5 The sulfur content of the sulfide was determined to be 36.8 * 0.2 pct, which matches the stoichiometric value of 36.9 pct. No evidence of either MnO or MnSO4 was detected microscopically or by X-ray diffraction. The single-phase combinations of MnO and MnS at the eutectic temperature indicate the limit of solid solution as shown in Fig. 2(a) and (c), and the revised phase diagram is shown in Fig. 2(d). The melting temperature for MnO is that provided by Glasser.6 The eutectic temperature of 1232° ± 5°C and eutectic composition of 64 wt pct MnS are in close agreement with Silverman's correction of Wentrup's work. The maximum solubility of MnO in MnS was determined to be 1.7 ± 0.2 wt pct. The maximum solubility of MnS in MnO was determined to be 1.8 ± 0.2 wt pct. These figures represent the lower limit for the presence of liquid at 1260°C and are significantly lower than the earlier estimated solid-solution figures. The authors wish to acknowledge the support of U.S. Steel's Edgar C. Bain Laboratory for Fundamental Research. The comments and critical suggestions of Drs. A. S. Keh, R. Rickett, and R. B. Snow are appreciated.

Jan 1, 1963

By Clarence E. Sims

An effort has been made to give both a comprehensive and simplified picture of the origin, modes of formation, and characteristics of nonmetallic inclusions in steel. Exogenous inclusions, those formed by mechanical entrainment or heterogeneous reaction, have their principal source in ladle refractories. Mechanical emulsion is not considered a likely mechanism. Endogenous inclusions, resulting from homogeneous reactions, are formed mainly during cooling and freezing. They are principally oxides and sulfides but include some nitrides and carbides. Deoxidation affects both the quantity and character of such oxide inclusions and significantly affects the size and shape of sulfides. The importance of inclusions is largely in their effect on mechanical properties. It is fitting and proper that we should honor the memory of those technical giants who have left such a rich heritage to our profession. Today, according to annual custom, we pay tribute to such a man. To have been chosen to play a part in this observance prompts in me an inordinate pride while I am humble before the responsibilities of my task. The ranks are growing thin of those who had the good fortune to come under the personal influence of Professor Howe, but the number who continue to benefit from his legacy of technical wisdom con-stantly increases. I am among the latter. One has only to read his works to appreciate his unusual ability to take data and observations from many sources and give them a clear and comprehensive

Jan 1, 1960

By D. I. Cameron

A graphical method has been developed and tested for separating the effects of grain boundary and lattice diffusion in polycrystalline materials. The method is based on the assumptions that for unidirectional diffusion from a plane source of radioactive material, the penetration of activity far into the specimen from the source is due solely to grain-boundary effects, and 2) pure grain-boundary penetration is described by a linear plot of log activity vs the perpendicular distance x from the source. The former is based on the fact that at any temperature the grain-boundary diffusion coefficient is always very large relative to the lattice diffusion coefficient; and the latter is based on the derivation of Fisher.1 Using these criteria along with appropriate penetration data (in this case, data for the diffusion of Cb95 in pressed and sintered UO2) one first plots the data as log activity vs x2 and as log activity vs x, as shown by curves 1 and 2, respectively, in Fig. 1. A tangent line to curve 2 for large x (curve 3) is then transferred to the x2 plot as curve 4. The subtraction of curve 4 from curve 1 yields curve 5 which represents only lattice diffusion and may therefore be related to the diffusion coefficient by using the appropriate solution to Fick's second law. It should be noted that the method has inherent inaccuracies for small and large values of x2 and only the subtraction at intermediate values can be used. For the illustrated specimen the calculated diffusion coefficient is 3.4 X 10-11 sq cm per sec at 1445°C while data using a single crystal of UO2 at the same temperature yielded a value of 2.9 x 10-11 sq cm per sec.2 The same method of subtracting grain-boundary diffusion effects to obtain lattice diffusion coefficients has been successfully used to determine self-diffusion coefficients of Th230 in polycrystal- line thoria.

Jan 1, 1962

By G. Derge, L. D. Kirkbride

In recent years the problem of sulfur elimination in iron and steel-making has been of increasing importance. This interest has been due to the increasing amounts of sulfur coming into the system via raw materials. As a result, many investigations have been directed at obtaining information pertaining to the rate and mechanism of sulfur removal in the blast furnace as well as measuring appropriate thermodynamic quantities. Chang and Goldmanl as well as others2'3 showed that the process of sulfur transfer from molten carbon-saturated iron to blast furnace-type slags could be considered as two opposing first-order chemical reactions. Recently, Ramachandran et al.4 have shown that during desulfurization electrical neutrality is preserved in both phases and iron and silicon are transferred into the slag concurrently with the evolution of carbon monoxide gas. They concluded that the reaction s + c-+ (0)=(S) + CO(g) does not express the stoichiometry of the sulfur transfer process. As in all previous investigations, these authors studied the process of a net transfer of sulfur from metal to slag across a slag-metal interface. However, no experimental data have previously been obtained for the process of sulfurization. It was the purpose of this study to investigate the sulfurization process, i.e., net transfer of sulfur from slag to metal. EXPERIMENTAL PROCEDURE Apparatus—The equipment used in this investiga-tion was typical of that used by others.1-3The furnace was a high-frequency induction unit powered by a 35 kw Hg spark gap converter. Fig. 1 shows a schematic diagram of the apparatus. A two-compartment crucible assembly was employed to melt the slag and metal charges; being similar to that used by Ramachandran,4 in size and design. The atmosphere was that produced by reaction of hot graphite with air. Temperature measurements were made by W-Mo thermocouples which were calibrated against a Bureau of Standards Pt - Pt 10 pct Rh couple. Temperature control was always good to * 5°C and in general was much better than this figure. Raw materials used in the experiments were C. P. reagent grade where possible. The silica used in the preparation of the slags was in the form of highly purified silica flour. Silicon and titanium additions

Jan 1, 1961

By Tasuku Fuwa, John Chipman, David H. Kirkwood

Fe-C-Si alloys in silica crucibles were held at 1600°C in a controlled atmosphere of CO and Co2 and the approach to equilibrium was obsertsed. Results were not of sufficient precision to establish the activity and interaction coefficients. Observations 012 the equilibrium provided an average value for the standard free-energy change which differed by + 1.1 kcal from the earlier accepted value. The C-SL relation at other temperatures is calculated and shown graphically. IN the refining of steel in an acid-lined furnace, it is well known that, unlike in basic refining, a very significant amount of silicon may remain dissolved in the metal even when the carbon content approaches a final endpoint. Further, it is known that the residual silicon increases with increasing temperature. The quantitative relation between silicon and carbon can be calculated for equilibrium conditions from data already available on the Fe-C-O and the Fe-Si-O systems. Such equilibrium calculations could show us approximately the limitations within which the reaction would be expected to operate in practice. In the oxidation of a bath containing both carbon and silicon it is well known that at low temperatures silicon is preferentially oxidized first. It can be shown by calculation that at high temperatures carbon will be oxidized preferentially. It is the purpose of this paper to record direct observations on the Si-C relation by means of experiments carried out in an atmosphere of carbon monoxide for Fe-C-Si alloys contained in silica crucibles. When such a system is brought into equilibrium, at a fixed temperature, the composition of the liquid metal is governed by the following equations: Both K1 and K2 are known with a fair degree of accuracy, and may be calculated from the tabulated In general the percentage of CO2 is extremely small compared to that of CO and in the experiments to be described the partial pressure of the latter was generally only slightly below 1 atm. EXPERIMENTAL METHOD The induction furnace employed was the same as that described by Rist and chipman' and by Fuwa and chipman.2 It was modified slightly in view of the change from alumina to silica crucibles. The small silica crucible was surrounded by a thin susceptor of molybdenum sheet which in turn rested inside a zirconia crucible. Since the zirconia was subject to breakage, it was supported inside an alumina crucible. The charge consisted of 30 to 35 g of electrolytic iron along with the required amounts of refined silicon and graphite to produce a melt of required composition. Purified carbon monoxide and carbon dioxide were passed into the furnace through carefully calibrated flow meters. Two separate and independent series of experiments were carried out. In Series I (D.H.K.) the melt was held in the furnace at 1600°C for periods of time up to 6 hr. Samples were taken at intervals in silica tubes and were analyzed for carbon and silicon. The results of the last one or two samples taken from each experiment and the direction in which equilibrium appeared to be approached are shown in Table I. In Series II (T.F.) the silica crucibles were of less satisfactory strength and the melts were held at 1600° C for periods of only 2 to 4 hr. In heats number 29 to 45 inclusive, the metal was cooled in the furnace and the ingot itself served as a sample for analysis. In heat 46 and all subsequent heats, samples were withdrawn in silica tubes at the termination of the heat, and these samples were analyzed. The results of all of these experiments in which equilibrium appeared to be approached are listed in Table II.

Jan 1, 1965

By John F. Elliott, John R. Rawling

The rate of reduction of silica to silicon by carbon at 1550° to 1700°C in iron blast-furnace type slag-metal systems has been investigated. In the tower portion of the temperature range oxygen transport in the metal boundary layer at the slag-tal interface is probably rate limiting. A second step, which apparently involves a chemical process in the slag at the slag-metal interface, appears to be rate limiting when the oxygen-transport limitation is avoided. Above 1650°C rate control of the reduction by carbon probably is mixed between the two steps. INVESTIGATIONS1.2 into the equilibrium distribution of silicon between graphite-saturated slags and metals typical of iron blast-furnace practice show that, under the experimental conditions specified, the reduction of silica to silicon is relatively slow compared with the rates of other slag-metal reactions under similar conditions. For this reason, the reduction of silica in blast-furnace slag-metal systems was considered to be an interesting subject for further study. Investigations of the kinetics of the reaction3-5 suggest that several possible steps may be rate controlling, and that the rate-controlling step depends not only on the physical state of the systems but also on the configuration of the apparatus. The main objects of the investigation reported here were to sug- gest plausible reaction paths for the reduction of silica under the experimental conditions chosen and to determine the step or steps which control the rate of reduction of silica. EXPERIMENTAL Two types of experiments involving the reduction of silica from the slag were carried out. In the first, the only reducing agent present was carbon (graphite), for which the over-all reaction is (SiO2) +2C(gr) —Si + 2Co(g) [l] The second type was a graphite-saturated ferro-silicon-iron concentration cell. In it silica in the slag could be reduced either by carbon according to Eq. [I], or by a reaction of electrochemical nature in which silicon was oxidized at the ferrosilicon-slag interface and silica was reduced at the slag-iron interface without the formation of CO. The two types of experiment are described below. Reduction of Silica with Carbon as the Only Available Reducing Agent. The reduction of silica was accomplished by allowing a liquid lime-alumina-silica slag and graphite-saturated iron to react in an induction-heated graphite crucible. The crucible was 2.25 in. diameter and 5 in. deep; it was fitted with a graphite stirrer which penetrated through the slag and into the metal, Fig. 1. The slag and metal charges weighed 350 g each. Pure carbon monoxide at a pressure of 1 atm was maintained above the melt by passing the purified gas through the crucible at a rate of 0.5 liter per min. The gas did not stir either the slag or metal. Temperature measurements were made by sighting an optical pyrometer down the hollow stirrer rod into a 1/4-in. hole drilled in the stirrer blade. The crucible temperature was maintained within *15"C of the required value by manual control of the power supply to the

Jan 1, 1965

By W. O. Philbrook, A. E. El-Mehairy

The reduction by hydrogen of individual particles of dense hematite implanted in beds of inert spheres is controlled by single-particle kinetics. No evidence of reagent starvation was found down to low flow rates established by pressure gradients as low as 0.01 in. H2O per- in. of depth in beds of spheres as small as 3/16 in. diam. The optimum size for most rapid reduction of beds of homogeneous ores results from the effect on reducing potential of the gas of competing factors of supply and consumption. A recent publication1 presented the results of a study of the rate of reduction of iron ore in a fixed bed by hydrogen introduced at constant pressure differential. Under these conditions the reagent flow rate varied directly with the bed permeability, which was a function of particle size and shape and bed voidage, and inversely with the temperature-dependent viscosity of the gas. The present note adds data from supplementary experiments designed to reveal whether or not any partial reagent starvation arising from a flow-dependent transport resistance in the gas phase might have been operative. Kinetic studies were made of the reduction of individual spheres of iron oxide inserted into beds of inert spheres, so that the reagent flow rate and aerodynamic conditions were again determined by bed characteristics and temperature. The experimental techniques and apparatus were similar to those previously described.' The synthetic iron ore spheres were wet-rolled by hand from powdered, reagent-grade* Fe2O3 and subsequently dried and then fired in air at 1250°C. The indurated pellets has almost no porosity as indicated by their specific gravity of 5.10. The beds were made of dense alumina spheres, closely sized to the same dimension as the iron oxide spheres, in the following diameters: 3/16, 1/4, 5/16, and 3/8 in. Each bed was hand-packed of particles of a single size to a controlled voidage of 0.32 and depth of 3 in. within a capsule having an internal diameter at least 10 times the particle diameter. A few weighed iron oxide spheres were individually planted in the central plane of the bed of inert spheres at points away from the wall. Reduction was carried out at atmospheric pressure by purified hydrogen at 670°, 800°, and 985°c. The reagent was supplied at precisely controlled pressure differentials of 0.01, 0.02, and 0.03 in. of water per in. of bed depth. This gave a range of flow rates similar to that used in the study of beds of ore and comparable with blast-furnace practice in terms of mols of reducing gas per hr per sq ft of cross-section. Viscous flow prevailed in all beds under the experimental conditions of this study. The reduced particles were checked for loss in weight and then sectioned for metallographic examination. Occasional particles were found to have contained minute internal cracks that interfered with the concentricity of the reduction interfaces, and data for such particles were rejected. An experimental rate constant for the reduction of the imbedded Fe2O3 spheres was calculated on the assumption that the rate was proportional to the metal-oxide interface area by an equation that has been found by McKewan2 to describe the reduction of single spheres

Jan 1, 1962

By H. W. Hockin, D. r. Brandt, R. H. Walsh, P. L. Dietz, P. R. Girardot

New Jersey, Florida, and Canadian ilmenites were reduced with hydrogen or coke under various experimental conditions and the phase changes occurring in the ilmenite upon reduction have been studied by microscopic examination of polished sections and by X-ray diffraction. The products formed were dependent upon the type of ilmenite, temperature, time and reducing agent. Of the reducing agents, hydrogen was the more effective at lower temperatures. 1 HE possible utilization of ilmenite as a source of both iron and titanium has resulted in the development of a number of methods for the separation of the iron and titanium content. Slagging processes as currently used in Canada are typical of such methods. Somewhat less attention has been given industrially to the reduction of the iron content at less than the slagging temperature. Although references maybe found to such work, in general only one type of ilmenite, either natural or synthetic, has been studied by each author. We have attempted to draw some relationship between the results of experimental reduction and the type of deposit from which the ilmenite was derived, as evidenced by phases occurring in the ores and in the reduction products. Ilmenite ores having from 27 to 61 pct titanium dioxide were included in this study and in each case reduction was carried out at such temperatures that only limited coalescence of the particulate iron product occurred within the ilmenite grains. The history of the individual ilmenite samples and the temperature of reduction were found to determine the occurrence of various phases and the mode of distribution of the iron. REVIEW OF EARLIER WORK ON REDUCTION One of the earliest references to the reduction of ilmenite at less than the slagging temperature was made in 1917.' The metallic iron produced was_____ leached out by the action of dilute sulfuric or hydrochloric acid, to leave a product high in titanium dioxide. Subsequent to this, numerous patents2-'? and other references13"21 have appeared concerning reduction of ilmenite by carbon, hydrogen, carbon monoxide, methane, coal gas, water gas, or the like in the absence of fluxing agents. Mineragraphic examinations were not reported, and in the main, the only examinations made were chemical analyses. However, in two cases3,13, titanium suboxides were reported in the products and in one case2' rutile was reported, in addition to metallic iron. Both were identified by X-ray diffraction. While reductions in the absence of fluxing agents were generally followed by either a wet or dry chemical process for removal of the metallic iron, a Canadian source17 reported removal of the metallic iron by magnetic separation. By the addition of fluxing agents during reduction, the metallic iron has been coalesced into "pearls." Each reference to such a process23-28 has shown that the coalesced iron could be removed by magnetic or gravity means after the product was crushed. In the absence of fluxes, the coalescence did not generally occur. The major part of the present study has been limited to reductions without fluxing agents in order to determine the primary reactions of naturally occurring ilmenites. Titaniferous iron ores have also been studied,29-33 17, l9 their reduction having been used as the basis of a commercial process for beneficiation of such ores in Norway29 and more recently considered in the United States34,35. The ease of reduction of titaniferous iron ores relative to that of hematite or magnetite has been referred to,33 with the conclusion that the more

Jan 1, 1961

By Claude H. P. Lupis, John F. Elliott

IN the recent past, extensive use has been made of the interaction coefficient in treating the thermody-namic behavior of components in solutions at dilute concentrations. The development of this concept by wagner1 and chipman2,3 is sufficiently well-known so that its elucidation here is not necessary. The present discussion is focused on the relationship between E and e. The usual forms of the coefficients are:

Jan 1, 1965