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By J. M. Uys, T. B. King

WalSH, Chipman, King, and rant' have measured the water content (as hydrogen) of actual steel-making slags. An average water content of 290 ppm was found for basic open-hearth tapping slags and 114 ppm for acid open-hearth slags. Upon equilibration of these slags at 1550°C with a 25 pct H20-75 pct Nz atmosphere, the water content increased to about 410 and 300 ppm for the basic and acid slags, respectively. Walsh et al. concluded that an acid slag was thus relatively far removed from equilibrium, and that basic slags showed a closer approach to equilibrium, with the water vapor in the furnace atmosphere. Herasymenko2 contended that these conclusions were unjustified, as the oxygen pressure used in the equilibration experiments, ;bout 5 x X atm, was quite different from that found in the furnace. Consequently, during the experiments the slag composition would have changed due to oxidation of ferrous iron. As an extension of Walsh's work and to attempt to clarify this matter, the solubility of water in a basic open-hearth slag was measured as a function of oxygen pressure. Similar measurements were also made on synthetic silicates in the "Fe0"-Fe203-SiO, system. The experimental technique has been described previously by Walsh et a1.l and Uys and King.3 Samples of the basic open-hearth finishing slag, contained in 10-cc platinum crucibles, were equilibrated at 1550°C with atmospheres of different oxygen pressure but constant water-vapor pressure, Ph~o = 0.192 atm. Calculations, as well as measurements, indicate that this figure approximates the water pressure of the combustion gases in a steam-atomized, oil-fired open hearth. Oxygen pressures in the open hearth can vary from 10"2 atm in the combustion gases to between l0-' and 10" atm in the steel bath. The former figure depends on the combustion practice and the latter on the carbon content and temperature of the bath. The oxygen pressure of the slag should lie somewhere between these extremes and is expected to be closer to that of the steel bath than that of the combustion gases. Oxygen pressures were therefore varied between 10" and 6 x l0 atm. At the lowest pressure the slag "puffed up" when quenched (indicating possible loss of water) so experiments were not conducted at lower oxygen pressures. The results are shown in Fig. 1, which includes the water content of the slag "as sampled". The results show that the water content of the slag increased appreciably on equilibration with water vapor at 0.192 atm pressure and that the water solubility apparently decreases with increased oxygen pressure. The solubilities found are comparable to those of the Li20-Ca0-Si02 system.3 Work with synthetic slags in the "Fe0"-Fe203-SiOz system was performed at 1500" C, with Ph20 = 0.192 atrn and for oxygen pressures varying between 10"2 and 10-lo atm. Samples for chemical analysis were prepared as described by Larson.4 The results are shown in Fig. 2. Some low-silica melts tested at low oxygen pressures "puffed up" when quenched and analyzed less than 100 ppm water; these results are not included in Fig. 2. The melts containing 40 mol pct silica also showed a tendency to "puff up" during the quench, when they were tested at the lowest oxygen pressure. These results indicate that, at constant silica content, the solubility of water decreases somewhat with increased oxygen pressure. The effect is, however, small considering the wide range of oxygen pressures studied. Also, at constant oxygen pressure (above about lom5 atm) the solubility increases

Jan 1, 1963

By Nicholas J. Grant, Rolf Nordheim, Thomas B. King

Constant-load creep-rupture tests were conducted in an argon atmosphere at temperatures of 1600 to 2200°F on two heats of iron containing about 0.06 and 0.09 pct P in solid solution. The tests were conducted in the as-cast condition. Stresses were selected to give strain rates approaching those encountered in the hot working of steel, and within the limits of the creep-rupture test apparatus, namely. from about 0.001 to 50 pct per sec. FOR generations, rolling and forging practices have been developed largely by empirical methods, based on prior experience. While largely successful, difficulties are frequently encountered when new or different alloy compositions are tried for the first time. There is need to know the relationships which exist among temperature, strain rate, composition, and other variables on the deformation and fracture characteristics of steels. It has been shown for aluminum and several high-temperature alloys that the deformation and fracture characteristics follow rather well-defined laws and patterns which are closely related to the effects of strain rate, temperature, and composition.1"3 As the melting temperature of aluminum or its alloys was approached, it was possible to study the interplay of work-hardening factors and recovery or recrystal-lization, the latter resulting in improved ductility and increased resistance to intercrystalline fracture. In particular, the effects of composition are very poorly known. Within the meaning of "composition" should be included impurity elements, such as sulfur, phosphorous, lead, copper, and many others, as well as those elements which are added for alloying purposes in iron. The role of multiphase structures, in contrast to solid solutions, should also be studied in much greater detail. high strain rate creep-rupture tests would provide information regarding the deformation and fracture characteristics of metals at hot-working temperatures. It was also desired to establish the stresses which are necessary to accomplish the desired deformation, and to relate these to the strain rate and temperature. Secondly, it was the purpose of this particular study to determine the effects of phosphorus, within solid solution limits, on the deformation and fracture characteristics of iron at hot-working temperatures. EXPERIMENTAL PROCEDURE Two phosphorus levels were selected, one corresponding to the upper limit normally found for commercial steels, and one substantially higher than this, but within the region of solid solubility at the test temperatures chosen for this investigation. Twenty-pound heats were prepared by induction melting electrolytic iron in air in a magnesia lined furnace. After deoxidation with about 0.2 pct Al, ferro-phosphorus was added, and the heats were then poured into prefired silica molds. The purpose of using silica molds was to obtain a slow cooling rate during solidification to produce a relatively coarse grain size, producing a structure subject to some segregation and therefore more nearly characteristic of ingot structures. The major part of the casting assembly provided a large shrinkage head in order to produce sound castings and to promote slow cooling of the specimens. The primary austenitic grain size varied from ASTM No. 2 to No. 00. The composition of the heats, including a low phorphorus melt, used for comparison purposes, is shown in Table I. It will be noted that the oxygen content of the phosphorus containing heats is relatively high, in spite of the deoxidation practice, a condition which is difficult to control in small melts. Creep-rupture tests were nevertheless undertaken when it was noted that this quantity of oxygen did not appear to give results any different from those from a heat containing 0.01 pct 0, low phosphorus and comparable carbon Content;4 see Table 11.

Jan 1, 1961

By Edward B. Dismukes, Walter R. Dickson

Measurements of current efficiency at an iron anode during the electrolysis of FeO-CaO-SiO2 melts contained in an iron crucible indicate that compositions of high SiO5 content conduct current almost entirely by ionic mechanisms. Hozueuer, compositions of high metal oxide content give euidence for considerable nonionic conduction that can be attributed to p-type semicon-duction. Measurements of transference numbers in a Hittorf-type cell show that both calcium and iron ions are important contributors to ionic conduction. ELECTROCHEMICAL properties such as conductance, transference numbers. and oxidation or reduction at an electrode have been studied as means of delineating the structure of simple silicate melts that are related to the more complex slags encountered ir steelmaking processes.' Measurement of these properties has strengthened the concept that molten silicates are constituted of metal ions and of silicate networks. Typically, the magnitude of electrical conductivity and the extent of agreement with Faraday's law have given evidence for ionic structures, and transference numbers have shown cations to be the exclusive carriers of electrical charge. However, melts containing oxides of iron, FeO in particular, have been found to exhibit nonionic conduction of curx,ent. The work by Inouye, Tomlinson, and chipman' demonstrated semiconduction, presumably of the p-type, in molten wüstite. Simnad, Derge, and George3 and Dukelow and Derge,4 in studying the electrolysis of FeO-SiO2 and FeO-MnO-SiO2 melts, concluded that p-type semi-conduction occurs in these systems, although ionic conduction is generally favored by increased percentages of MnO or SIO2. Previous research on the electrochemistry of

Jan 1, 1962

By Wei-Kao Lu

A general rate equation is derived for gas -solid reactions in metallurgical processes by considering the contributions of chemical reaction at inter-phase boundaries and diffusion through the solid product layer simultaneously. This equation takes care of the whole range continuously from purely diffusion control to purely chemical reaction control. The parabolic law,' McKewan's equationa derived with the assumption of interface area control and the equation derived by Kawasaki et al. with the assumption of purely diffusion control are found as the limiting cases of the corresponding forms of the general rate equation. Many metallurgical processes involving gas-solid reactions have been extensively studied. The common examples of these processes include the reduction of oxides to metallic products, the roasting of sulfides to oxides or chlorides and the oxidation of metals. Gas-solid reactions consist of at least two kinds of steps; one involves the transport of reactant and product to and from the reaction zone and the other is the chemical reaction taking place at the interphase boundaries. In the limiting cases one or the other of the above mentioned steps will be much slower than the other and is then rate controlling. For example, the oxidation of metals is diffusion controlled and obeys the parabolic law.' On the other hand, if the diffusion rate is much larger than the chemical reaction rate then it will be controlled by the chemical reaction rate. This latter case occurs for the reduction of iron oxides studied by McKewan. If the rate of diffusion and of the chemical reaction have the same order of magnitude, a more detailed analysis is necessary. Thus at the beginning of the reaction when the solid and gaseous reactants are in direct contact, the reaction should be chemical reaction rate controlled as no diffusion process is involved. At the other extreme as the reaction zone moves further into the solid, the diffusion distance becomes greater and the diffusion rate continuously decreases. Eventually, therefore, for a sufficiently large sample the rate must become diffusion controlled. As the transition from one controlling step to the other must be continuous, we cannot describe this transition period by either of the two limiting cases. In this paper the author attempts to derive a general rate equation for gas-solid reaction systems. This is effected by considering the rates of diffusion and chemical reaction simultaneously from the state of pure diffusion control to pure chemical reaction control. I) DERIVATION The system under consideration is made of at least three phases, namely the gaseous one, the solid reactant, and the solid product as shown in Fig. 1. The notations are listed at the end of the paper. The mass transfer process involves the diffusion of reactants and products across the solid product layer. It is reasonable to consider that no chemical reaction will take place in the solid product layer with respect to both gaseous reactant and product. For the characteristics of local equilibrium of the system, the diffusion process is really in a quasi-steady-state. It will be proved in the following paragraphs. Then we can invoke the law of conservation of mass valid for all chemical species passing through the layer. The solid reactant sphere has an initial radius, ro, after a fraction of completeness of the reaction, the unreacted core has a radius ri, where r, is in the solid product region. Let Cg be the activity of gaseous reactant in the

Jan 1, 1963

By David Schroeder, John Chipman

Jan 1, 1964

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

As a result of using copper-containing scrap in the steelmaking process, the copper content of steels has been steadily increasing for years. Consequently the possible role copper may play in the steelmaking process and in the finished product begins to attract the metallurgists' attention. Some time ago one of the present authors forwarded the idea—based on the results of the analysis of nonmetallic inclusions extracted electrolytically from steels—that sulphur in plain carbon steels is distributed mainly between copper and manganese, the amount of iron sulphide being very small; and that, consequently, the problem of copper and that of sulphur in steel cannot be treated separately.' At the time of the publication of the quoted paper little was known about the relative affinities of copper and manganese for sulphur at high temperatures except that at moderate temperatures (below 1000°C) the affinity of manganese for sulphur is much greater. To gather more experimental data on this subject, the present authors undertook the investigation of the equilibrium constants of the reactions: 2Mn(8 or 1) + S2(g) = 2MnS(s) 4Cu(s or 1) + S2(g) = 2Cu2S (S or I)* 2Fe(s) + S2(g) = 2FeS (s or 1) over a range of temperatures wide enough to establish the dependence of these equilibrium constants on temperature. From the equilibrium constants (K = l/Ps2) the free energy of formation (affinity) can be calculated from F° = -RTln 1/PSt (1) where the standard conditions chosen are: 1 atm of sulphur pressure and the activities of condensed components equal one. The decomposition pressure, Ps2, of sulphur over the respective sulphides is too small to be measured directly, but there is a way of eliminating this difficulty by measuring the equilibrium constant of the reaction between the sulphide and hydrogen. From the latter and from the equilibrium constant of the thermal dissociation of H2S we then calculate Ps2 for the respective sulphide. 2Mn + 2H2S = 2MnS + 2H, 2H2 + S2 = 2H2S_________ 2Mn + S2 = 2MnS The numerical values of the equilibrium constant of the thermal dissociation of H2S at different temperatures were taken from Kelley's paper, "The Thermodynamic Properties of Sulfur and its Inorganic Compounds."² In previous experimental work published by Jellinek and Zakowski3 and by Britzke and Kapustinsky4 the equilibrium constants of the reactions Metal sulphide + H2 = H2S + metal were determined by passing hydrogen, at different rates of flow, over the sulphide, analyzing the resulting H2S + H2 mixture and then extrapolating the H2S/H2 ratio (which is a function of the rate of flow) to the zero speed of flow, a method necessarily involving considerable uncertainty. In the present work the equilibrium ratio was actually measured instead of being extrapolated. The apparatus is shown in Fig 1. Experimental Procedure The sulphides were prepared by the following methods: FeS Powdered iron which had been reduced with hydrogen (ferrum reduc-tum) was mixed in stoichiometric ratio with sublimed sulphur and carefully ground. The mixture was put into an alundum crucible, covered with pure sulphur, and the reaction started by touching the mixture with a glowing iron rod. After the reaction was completed the product (still containing some metallic iron) was again ground with sulphur, put into a Rose crucible, covered with sulphur, and heated in a strong current of pure hydrogen. Analysis of the final product showed 62.46 pct Fe and 36.59 pct S. Theoretical for FeS: 63.53 pct Fe and 36.47 pct S. MnS Manganese sulphide (precipitated and carefully washed with distilled water containing H2S) was dried in a Rose crucible in an atmosphere of H2S and heated in a current of hydrogen for 2 hr at red heat. The product was then ground and ignited for several hours at 1000°C in a current of hydrogen sulphide. Analysis showed 64.53 pct Mn and 36.63 pct S. Theoretical: 63.15 pct Mn and 36.85 pct S. Some MnS samples were prepared from metallic manganese and sublimed sulphur by mixing and grinding them and then heating in a current of hydrogen sulphide in an alundum tube.

Jan 1, 1950

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