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By D. C. Hilty, W. Crafts

J. Chipman—It has been my privilege to discuss this work with the authors on several occasions and to observe at first hand the experimental methods employed. I wish, therefore, to emphasize certain points which they have mentioned only briefly with regard to the experimental techniques. The rotating induction furnace as here employed interposes liquid metal between slag and refractory thus preventing the two nonmetallic parts of the system from reaching equilibrium with one another. It is therefore impossible for the metallic phase to be completely in equilibrium with both the slag and the crucible. The metal also acts as a partially permeable membrane allowing certain components, including oxygen, to diffuse from slag to crucible. This transfer results in building up on the face of the crucible a layer of material whose composition is in part dependent on that of the bath. Reactions between the layer and the solid refractory are slow, as evidenced by the rather good life of the crucible. Hence it seems probable that the layer is more nearly in equilibrium with the metal than with the underlying crucible material and that, once it is established under a bath of a given composition, its further reactions with that bath are slow. Additions to slag or bath may be followed by changes in the layer; and time must be allowed for virtual completion of such changes, before it can be assumed that slag and metal are in equilibrium. We may judge from the results reported that, in general, this was the case and that the data represent at least quite close approximations to slag-metal equilibrium. Data on deoxidation and on oxygen solubility are no better than the analytical methods employed. The vacuum fusion method as used by the authors seems entirely adequate for the samples analyzed. I have had frequent occasion to compare results with their laboratory, always with very satisfactory agreement. The determination of aluminum at very low concentrations is perhaps an even more difficult procedure. Here also the colorimetric method used has been worked out with great care and is undoubtedly the most dependable method available. The discrepancy between observed and calculated deoxidation or solubility lines is not to be explained as the result of experimental errors, either in the sampling or analysis of the metal. Nor is it to be blamed upon inaccuracies in the several kinds of indirect data upon which the calculated results were based. It is true that both the observed and the calculated lines admit of some uncertainty as to their exact locations, but the uncertainties are small compared to the wide gap which separates the two lines. The authors have pointed out the real cause of the discrepancy. In all of their experiments the solid phase was not Al2O3 but a mixed oxide containing iron and aluminum. This suggests an extension of the calculated values to include equilibrium with the spinel FeO . A12O3. The free energies of FeO and A12O3 are known, that of the spinel is not. However, it cannot differ greatly from that of its component oxides for even in the more stable spinel, chromite, the free energy of formation from the oxides is less than 10,000 cal. For purposes of calculation we shall call this free energy X and solve for values of X lying between zero and 10,000 cal. The other data required are taken from the forthcoming revision of "Basic Open Hearth Steelmaking" and are given in the following equations in which underlined symbols indicate elements dissolved in liquid steel and the standard concentrations are 1 pct. ?F° at 1600°C, cal ?LA = 2 Al + 3 O; + 107,200 FeO = Fe + 0; + 5,460 FeO + A12O3 = Fe + 2A1 + 4 0; + 112,660 — X The corresponding equilibrium concentrations are shown in fig. 21. The line marked A12O3 corresponds to the first equation, those marked FeO . AL2O3 correspond to the last, with X = 0, 5000 and 10,000 cal, respectively. The two upper lines represent the data of Hilty and Crafts and of Wentrup and Hieber. The points are the observations of Hilty and Crafts in the presence of 0.50 pct Mn.

Jan 1, 1951

By Maxwell Gensamer

Jan 1, 1960

By E. T. Turkdogan

In this theoretical paper, a transport-reaction mechanism is suggested for the enhancement of the rate of vaporization of metals, or other materials, brought about by the process of convection and condensation. Based on theoretical reasoning it is predicted that, when there is a temperature gradient surrounding the heated object, a slight increase in the rate of vaporization brought about by natural convection is enhanced further as a result of condensation of the vapor close to the surface of the object. In order to derive the effective vapor-concentration profile, consideration is given to the super saturation of the vapor necessary for the homogeneous nucleation of the condensed phase from the vapor. For the formulation of the rate equation based on this mechanism, adequate information should be available on the transport properties of gases and vapors at elevated temperatures and the method of calculating nucleation pressures of the vapor. The methods of deriving such data are discussed in the paper and a rate equation is calculated for the vaporization of iron in helium for various temperature gradients in the boundary layer. Considerations are also given to the effect of oxygen on rates of vaporization of metals under isother ma1 and nonisotherma1 conditions. THE study of the methods of enhancement or retardation of basically transport-controlled vaporization reactions is of theoretical interest with possible practical implications. There are several ways of bringing about such effects. For example, Turk-dogan, Grieveson, and Darken1 demonstrated that the rates of vaporization of metals under isothermal conditions were increased by several orders of magnitude, up to the maximum rate attainable in vacuo, by introducing some reacting gas into the inert atmosphere surrounding the metal. Such an effect is brought about by the interaction of the counter-diffusing reacting gas and metal vapor in close proximity of the metal-gas interface. Another case which is often experienced in practice is that of vaporization affected by natural convection. Although several theoretical and experimental studies of this problem have already been made, no detailed consideration has been given to the possible effects of condensation of the vapor in the boundary layer on vaporization rates, which constitutes the subject matter of this paper. BASIC CONCEPT OF ENHANCED DIFFUSION-LIMITED VAPORIZATION When a heated object, for example a metal sphere, is submerged in a fluid medium, heat is transferred from the surface of the object to its surroundings by four simultaneously occurring transfer processes: i) free-molecular conduction at the gas-solid interface over the distance equal to the mean free path of the gas, ii) conduction and convection through the fluid-dynamic boundary layer, iii) latent heat of mass transferred, and it!) radiation. The free-molecular conduction becomes pronounced only when the total pressure in the system is very low, e.g., below 1 mm Hg. Therefore, this term may be neglected for ordinary pressures. At low mass-transfer rates, due to vaporization of the object, the contribution of process iii) to the heat transfer can also be neglected. Finally, since the temperature profile is not affected by radiation, the latter need not be considered. The natural convection is brought about by gravitational body forces arising from a decrease in the

Jan 1, 1964

By K. C. Mills, E. T. Turkdogan

The results on the rates of vaporization of Fe-Ni alloys, levitated by an electromagnetic field in a stagnant atmosphere of helium, are shown to be in close agreement with those predicted theoretically. AS shown in Part I of this series of papers, the rates of vaporization of metals enhanced by convection currents are increased further by the process of condensation of metal vapor when there is a steep temperature gradient in the boundary layer. At the time this theoretical work was completed one of the authors (K. C. Mills) had already carried out some experimental work on the rates of vaporization of molten Fe-Ni alloys. The experimental work was done under conditions which make it possible to compare the experimental rate data with those predicted on theoretical grounds. EXPERIMENTAL The object of the experiments was to evaluate the activities in a number of binary metal systems. The details of the experimental technique are given in another paper by Mills, Kinoshita, and Grieveson,2 and, for the present purpose, a brief mention of the relevant features of the experimental method will be adequate. Using an induction coil, the metal weighing about 1 to 1.5 g was levitated by the electromagnetic field in a stagnant atmosphere of pure helium. The helium was freed from oxygen and water vapor in the usual manner, and its pressure in the vaporization chamber was maintained at 1 atm through a bleeder device. The vaporization chamber consisted of a pyrex tube, 2.8 cm diam, with a side arm connected to the helium bleeder. The bottom of the tube, shaped conical, was surrounded by the induction coil, and the top was sealed with an optical flat for the purpose of measuring the melt temperature with a two-color optical pyrometer. By suitable adjustment of the high-frequency power input, the metal was brought to the desired temperature in about 30 sec of levitation. After a specified vaporization time, e.g., 3 to 4 min, the alloy was quenched by switching off the power. The amount of metal vaporized was determined from the difference between the initial and final weights of the sample. During the vaporization time, temperature fluctuations of about ±10°C were observed. COMPARISON OF EXPERIMENTAL DATA WITH THEORETICAL VALUES The experimental results are given in Table I. As already mentioned, the attainment of the vaporization temperature took about 30 sec from the moment of levitation. Therefore, the times recorded in Table I are 30 sec less than the total time; this is considered to be a reasonable estimate of actual vaporization times.

Jan 1, 1964

By Philip D. Anderson, Ralph Hultgren

Heat contents of extremely pure iron were measured over the range 300"to 1433"K, using a diphenyl ether calorimeter. Results from three samples containing widely differing impurities agreed with one another and with Previously reported results at higher temperatures (1184 ° to 1809°K) by Olette and Ferrier. From these data a table of heat contents of iron has been Prepared which is believed to be more accurate than those previously available. CP values have been derived which are consistent with these heat contents, with the best experimental Cp data, and with the thermodynamic conditions of equilibrium between bcc and fcc iron. The opinion is expressed that low-temperature extrapolations of presently known Cp values for y-Fe are not reliable. It would seem that the thermodynamic properties of iron, which is by far our most important metal, should have been well established long ago. This is not the case, however. As discussed by Olette and Ferrier,' there is objection to every earlier heat content measurement. While the best true Cp determinations agree well at temperatures below the Curie point, there is wide divergence at higher temperatures. Several investigators have examined available data and attempted to calculate thermodynamic functions for iron that are consistent with the two equilibrium temperatures of bcc and fcc iron. The two primary efforts were those of Austin' in 1930 and Darken and smith3 in 1948. The recommended values differ considerably; integration of Austin's Cp values leads to a heat content at 1100°K which is 300 cal per g-atom higher than the value recommended by Darken and Smith. The compilation of Fisher4 in 1949 was based on the selection of Austin. In 1956, Weiss and Tauer obtained yet another set of values by resolving Cp values into components due to dilation, lattice vibration, electronic excitation, and magnetism. The magnitude of contribution by each component and its dependence on temperature was estimated by semiempirical means. Their values are not self-consistent in that they do not form smooth curves when plotted vs temperature; moreover, their calculations cannot easily be repeated since they do not give the values of some of the parameters used. Clearly, experimental values for iron were in a most unsatisfactory state. The presently described measurements of the heat content of iron were therefore undertaken, covering temperatures as high as 1433°K. While the work was in progress, the high-temperature (1193" to 1789"K) heat content measurements of Olette and Ferrier' were published; in the region of temperature overlap the present results agree with Olette and Ferrier well within experimental accuracy. It is believed that the present results, combined with those of Olette and Ferrier, provide for the first time a reliable set of heat contents of iron from room temperature to the melting point. From these data, guided by available Cp measurements, it proved possible to derive Cp, entropy, and free energy function values for @-iron from room temperature to the melting point, and for y- iron in the temperature region of its stability. Exhaustive study led to the conclusion that extrapolations of y-iron functions to room temperature were not reliable enough to be useful; hence these have been omitted from the tables. EXPERIMENTAL Materials. Three samples of extremely high purity iron from different sources, containing widely different impurities, were measured. The first of these, designated "Chipman", was kindly supplied by Dr. K. K. Kelley of the U. S. Bureau of Mines from a lot which was made many years ago by Dr. John Chipman of the Massachusetts Institute of Technology. The second, designated6'Teddington", was supplied by the National Physical Laboratory, Teddington, England, from a lot zone-refined by them. The third sample, designated "Irsid", was supplied by the Institute de Recherches de la

Jan 1, 1962

By D. J. Carney, J. Chipman, N. J. Grant

SINCE the beginning of this century it has been known that hydrogen contributes to the porosity of steel and that it is harmful to its mechanical properties. The evidence for this has been largely qualitative. Steel to which hydrogen was purposely added. in sufficient .amounts was shown to be either porous or brittle or both, whereas similar steel of low hydrogen content was shown to be free of porosity and to possess normal physical properties. There have been a considerable number of qualitative experiments of this type. Also, early in this century, a few attempts were made to measure the amount of hydrogen normally dissolved in commercial steels. This was usually done by placing the sample under an inverted liquid column such as mercury and collecting the evolved gas. These attempts, while not successful in measuring actual amounts of dissolved hydrogen gas, were able to prove that this gas will diffuse out of steel at room temperature, and that the amount of hydrogen dissolved is normally very small. On the basis of such qualitative evidence, hydrogen has been and still is blamed for a great number of the troubles encountered in the steel industry. In recent years, partial solutions for many steel-working problems have been obtained. These have led to increased interest in accurate quantitative work on hydrogen in steel, with the expectation that the results might possibly answer a few of the remaining unsolved problems. Commercially, two of the obvious questions which are in need of an answer are: (1) what are the most important sources of hydrogen, and (2) what quantity of hydrogen can be tolerated in various steels? There are many other unanswered questions. To begin to find the answers it seemed logical to start at the beginning of steel production with the liquid metal. Further, it seemed almost imperative to solve first the problems of analysis and sampling of the metal for hydrogen. Once these problems have been solved, it would be possible to answer more of the important commercial problems mentioned above. As a consequence, it was decided to design an analytical apparatus and, upon satisfactory completion of this, to develop an accurate method of sampling liquid metal for hydrogen.

Jan 1, 1951

By D. J. Carney, J. Chipman, N. J. Grant

G. A. Moore—The tin-fusion method has been a very favorable possibility for many years. The authors apparently have settled the question that delayed the method for a long time by showing that no hydrogen is absorbed in the tin. This, of course, is very important. I want to make a few remarks concerning the absolute accuracy of analysis, which must be the final basis for deciding among the various methods. From the figures in the paper, there seems to be some remaining slight discrepancy on the actual amount of hydrogen present in various samples which may be presumed essentially identical. (This is of the order of the precision of individual analyses but appears in averaged results.) From the analyst's viewpoint, the tally of hydrogen content can be regarded as occurring in three portions. First is a large portion which comes off easily and automatically during sample storage and later on heating in the apparatus. This is fairly easily analyzed. Second is an item which may be either positive or negative in the tally sheet. In warm or hot evolution, this is a portion which, in practice, can never be re-

Jan 1, 1951

By W. O. Philbrook. K M Goldman, M. M. Helzel

RADIOACTIVE calcium has been used to learn whether calcium can be detected in iron saturated with carbon after it has been melted under CaO- A12O3- SiO2 slags similar to those used in the iron blast furnace. It was hoped that the radioactive tracer technique might make possible a general study of steelmaking reactions in which calcium or calcium oxide are involved. No calcium could be found in the metal under conditions which were favorable for the reduction of calcium, and it has been concluded that the calcium content of the iron was less than 6 x 10 - pct. Some of the problems encountered have been instructive with regard to pitfalls and limitations of tracer methods. Calcium oxide occurs in almost all iron- and steelmaking slags, and it is essential to the success of all commercial basic steelmaking processes. Calcium alloys are sometimes used in the deoxidation of steel and for the innoculation of gray iron. The element calcium is therefore almost as ubiquitous in the steel industry as are carbon and oxygen, but calcium has been thought to be completely immiscible with iron in both the liquid and the solid states.' It does not seem entirely unreasonable to Suppose, however, that some low concentration of calcium might exist in liquid iron under a basic slag with other conditions being favorable, just as silicon and other elements can be introduced into iron by reduction of their oxides from slags under appropriate circumstances. The radioactive tracer technique offered a more sensitive method than chemical analysis of testing this supposition. The reasons for interest in this investigation were strong enough to justify a recognized risk of failure. On the theoretical side, information on the distribution of calcium between liquid iron and a slag and the rate at which the equilibrium distribution is approached would contribute strongly to the general theory of slag-metal interface reactions. Furthermore, any evidence on the presence of calcium in liquid iron might provide a vital clue to the mechanism of the desulphurization of iron by slags. All of the reactions which have been proposed to explain desulphurization postulate that the sulphur ultimately becomes fixed in the slag as calcium sulphide, but the mechanism by which sulphur

Jan 1, 1951

By T. L. Joseph, G. Bitsianes

THE layered structure of partially reduced iron ore was described in a previous paper.' Reduction by hydrogen was found to take place at well-defined interfaces between layers of the solid phases. In the present investigation, a detailed study was made of the wiistite phase that had formed during the partial reduction of a cylindrical compact of chemically pure hematite. An unusually wide band of wiistite permitted a rather detailed study of this phase. The specimen was made from Baker's C.P. hematite in the form of a cylinder 1.5 cm in diameter and 1.8 cm long. A dense ore structure with about 6 pct porosity was attained by heating the specimen in air at 1100°C for 3 hr. To confine reduction to the top surface, a ceramic coating was applied to the bottom and sides of the cylindrical compact. The specimen was then partially reduced in hydrogen at 850°C and subjected to a coordinated sequence of macro-, micro-, and X-ray examinations. A section of the partially reduced cylinder is shown in the macrograph, Fig. 1. Four layers consisting of metallic iron, wustite, magnetite, and unreduced hematite are clearly shown. The effort to force reduction to proceed downward in topochemi-cal fashion was only partly successful, as some reduction occurred along one side and bottom of the cylinder. A rather wide layer of dark wustite phase had formed, however, and permitted sampling for X-ray studies as indicated. To supplement previous work and to study the wustite layer in more detail, ten separate layers were removed for X-ray examination. Broad and diffuse patterns were obtained with the as-filed powders, especially with those of iron and wiistite, and the condition indicated a cold-working and variable composition effect within the respective layers. This condition was corrected by annealing the entire series of powders at an appropriate temperature. For the annealing treatment, the ten powder samples were wrapped in silver foil, sealed under vacuum in small quartz tubes, and heated at 750°C for 16 hr. The specimens were then drastically quenched in cold water to preserve the annealed condition. These annealed specimens were X-rayed in turn and the compiled patterns are shown in Fig. 2. The standard patterns for iron and its oxides have been interjected at appropriate positions for purposes of comparison and phase identification. All of the patterns obtained were clearcut and concise so that positive identifications could be made for all of the phases. The outermost layers A, B, and C were composed almost entirely of iron with a small amount of wiistite being detectable at the X-ray limit of phase detection. Layer D from the iron-wustite interface showed both of these phases. The next four layers E, F, G, and H were all in the dark phase band which had been tentatively identified as wustite by the macroexamination, Fig. 1. The diffraction data with their single-phase patterns of wiistite for these layers checked the visual evidence. Continuing the X-ray analyses after layer H, the macrograph (Fig. 1) shows that layer I came largely from the magnetite zone but included some fringes of the wiistite-magnetite interface. The diffraction pattern for the sample confirmed this observation. Layer J came from the unreduced core of the specimen and its diffraction pattern indicated a preponderance of hematite phase. The reduction behavior of synthetic compacts has thus been found to be similar to natural dense iron ore. The previous results were supplemented with measurements of the diffraction films and calculations of the respective unit parameters. These X-ray data are summarized in Table I and offer some interesting correlations as to the compositions of the various phases undergoing reduction. The iron layers that were analyzed gave lattice parameters close to that of pure iron at 2.8664A. Evidently this iron was present in layers A through D as a pure phase with little or no oxygen dissolved in its lattice. With the wiistite layers an entirely different situation prevailed in that there was a definite and

Jan 1, 1955

By W. O. Philbrook, H. E. Burner, F. S. Manning

The equation of continuity for the hydrogen reduction of hematite in a fixed bed of closely-sized particles is solved assuming a flat velocity profile, negligible temperature gradients, md negligible axial diffusion. A kinetic expression from the literature is used which assumes the reduction process is controlled at the oxide-metal interface. The integral fractional conversion is computed, and the importance of particle diameter, flow mte, temperature, bulk axial diffusion, and inter- and intra-particle mass trarnsfer is predicted. Comparison with experimental data suggests one or more additional undefined variable(s) is significant. Equipment modifications are suggested for fidture experimentcll work. WITH the increasing desire to "design" the ore feed of a blast furnace, it has become necessary to define more quantitatively the process variables and to evaluate the extent of their control upon the reduction process. The bulk of the work reported in the literature has centered about the reduction of single particles; however, the blast furnace process more closely resembles reduction of a fixed bed than that of single particles. To simplify this analysis, the isothermal reduction by hydrogen of a natural hematite in a fixed bed of closely-sized particles is examined. With appropriate modifications in the kinetic and flow rate expressions, the approach employed should be extensible to mixtures of carbon monoxide, hydrogen, and inert nitrogen, and to adi-abatic conditions, thus approaching the blast furnace process more closely. The fixed bed variables which are investigated in this study are particle diameter, flow rate, temperature, and bulk axial diffusion, as well as inter-and intra-particle mass transfer. Of particular interest is the effect of particle size upon fractional conversion for a bed operating under constant pressure drop. The constant pressure drop concept bears a close resemblance to the blast furnace process, where regions of larger particles may provide a greater permeability to divert most of the reducing gas flow from the regions of smaller ore particles. Under such conditions one would expect qualitatively that, for sufficiently small particle sizes where the flow rate is small and the total surface area is large, the reduction rate would be limited by the gas flow rate. Initially the gas entering the bed reacts very rapidly and the composition approaches the equilibrium conversion value a short distance from the reactor inlet. This concentration "wave-front" then moves up the bed as the flow of reducing gas is continued, leaving in its wake an ever increasing layer of reduced particles. Providing that the reducing gas leaves the bed at equilibrium concentrations, conversion is expected to increase with an increase in flow rate, and hence with an increase in particle diemater. Conversely, for sufficiently large particles the flow rate will be high but the surface area available for reaction will limit the reduction rate. Since the total surface area decreases with an increase in particle size, conversion, in this case, is expected to decrease as the particle diameter is increased. It is clear then that between these two extremes an optimum particle diameter must exist. THEORETICAL DEVELOPMENT Above the temperature where wiistite is stable (about 560°C) the reduction of hematite proceeds through the series Fe2O3/Fe3O4/FeO/Fe. On the basis of microstructural studies and earlier work, Edström1 has postulated a mechanism for the reduction of an ideal hematite lattice: 1) Iron phase formation at the boundary between wiistite, iron, and gas (for sufficiently porous iron). 2) Diffusion of iron across a wustite layer. 3) Phase boundary reaction of Fe3O4 to FeO. 4) Diffusion across a dense magnetite layer. 5) Phase-boundary reaction of Fe2O3 to Fe3O4. According to the mechanism postulated, gaseous reaction product has to be removed only at the boundaries between wüstite and iron or gas, the only possible exception being enveloped Fe3O4 specks. On this basis McKewan2,3 has proposed that one may consider the hematite reduction process as a simple two-phase system of oxide/metal. If, for FeO and Fe3O4 layers of negligible thickness, the hypothesis is made that the rate of formation of a

Jan 1, 1963

By J. Chipman, N. J. Grant, B. M. Shields

The vacuum tin-fusion method of analysis for hydrogen, developed by Carney, Chipman, and Grant, has been modified to permit the analysis of the evolved gases for hydrogen by means of a thermal conductivity cell. A properly prepared sample can be analyzed in 10 min with a probable error of ±0.12 ppm. A study of various methods for storage of hydrogen samples shows that samples can be safely held in a dry ice-acetone bath as long as six days. Storage in liquid nitrogen is necessary for samples to be held one week or more. HE vacuum tin-fusion method, as developed by I- Carney, Chipman and Grant,' is the only analytical procedure which has shown promise of being fast enough for use in the control of hydrogen during steelmaking. It was felt that further simplification and faster speed of operation could be effected by the use of thermal conductivity measurements for analysis of the gases evolved in the tin-fusion method. The application of conductivity measurements to the tin-fusion method is possible because: 1—the evolved gas is essentially a mixture of hydrogen, nitrogen and carbon monoxide with a hydrogen content usually over 50 pct, 2—the evolved gas is collected at a relatively low pressure, and 3— the thermal conductivities of CO and N2 are practically identical while that of hydrogen is very much greater. The major part of this research program was devoted to the construction and calibration of a vacuum tin-fusion apparatus which analyzes the evolved gases for hydrogen by means of a thermal conductivity cell. The second phase of the problem was associated with the development of a procedure for storage of samples prior to analysis. With the rapid quenching method for hydrogen sampling,' which seems to be the most practical for steel mill use, it is necessary that the samples be stored safely during the interval between sampling and analysis if the hydrogen content of the molten metal is to be maintained in the supersaturated solid samples. The thermal conductivity bridge has been used for a number of years in the analysis of certain gas mixtures. An elementary discussion of the theory and practice of gas analysis by thermal conductivity measurements is given by Minter.3 A more comprehensive discussion of the theory and of the various measuring circuits is presented by Daynes.' A complete knowledge of the theory and properties of the thermal conductivity of gases and gaseous mixtures can be gained by a study of the standard textbooks on the kinetic theory of gases."' The existing data on the thermal conductivity of single gases are reviewed by Hawkins: that for a number of binary gas mixtures by Daynes' and Lindsay." The thermal conductivity method may be applied to the determination of the composition of a binary mixture if: 1—the thermal conductivity of the mixture varies monotonically with composition, and 2— the two gases have measurably different thermal conductivities. The greater the difference between the two gases, the greater the sensitivity of the method.10 he method is applicable to the analysis of multicomponent mixtures when all of the gases in the mixture except one have nearly the same thermal conductivity. Fortunately, the mixture of hydrogen, nitrogen, and carbon monoxide evolved by the tin-fusion analysis' falls in this latter classification. The thermal conductivities of nitrogen and carbon monoxide are practically equal; and the thermal conductivity of hydrogen is approximately seven times that of the other two. Therefore, the thermal conductivity of a gaseous mixture of hydrogen, nitrogen, and carbon monoxide at known temperature and pressure can be related directly to the percentage of hydrogen in the mixture by suitable calibration. Usually the thermal conductivity of a mixture of gases is measured at atmospheric pressure where the thermal conductivity is independent of pressure over a wide pressure range. At very low pressures (below 1 mm Hg), the thermal conductivity of gases varies with the pressure. This phenomenon has been utilized in the Pirani vacuum gage for the measurement of pressures in the range of 10" to 10-0 mm of mercury.= Very little has been published concerning the variation of thermal conductivity with pressure at intermediate pressures between 1 mm Hg and 1 atm. However, preliminary measurements indicated that the thermal conductivities did vary with pressure over the range of pressures (up to 10 mm Hg) at which gases are delivered from the vacuum pump. Therefore, the calibration of the thermal conductivity cell had to be planned to include the effects of both gas composition and pressure. Such a calibration chart is shown in Fig. 4. Most industrial applications of the thermal conductivity method of gas analysis have used a compensated Wheatstone bridge circuit containing two

Jan 1, 1954

By R. G. Ward

The temperature gradient in the subhearth metal or "salamandern of the iron bhst furnace results in the establishment of gradients in the concentrations of silicon, manganese, carbon, and sulfur. The temperature and compositional variations observed in three blast furnaces are analyzed according to irreversible thermodynamics and the systems appear to be close to the steady state condition. Apparent heats of transport, Q, for silicon, manganese, carbon, and sulfur are found to be respectively -17.5, -5, -2.1, and+22k cal per g mol. In conclusion the significance of thermal diffusion in extraction metallurgy is briefly discussed. INCREASING interest has been shown in recent years in the application of irreversible thermodynamics to metallurgical problems. In particular studies have been made of the transport of matter in thermal gradients1-' and under chemical gradients imposed by a binary solvent However, no detailed example in extraction metallurgy has been reported although gradients are the essence of many extractive processes. The case of the distribution of elements in molten blast furnace iron under a thermal gradient is discussed here. DATA In blast furnace operation the hearth bottom is often extensively destroyed by molten metal, and the metal may penetrate perhaps 10 ft into the furnace foundations forming a "bear" or "salamander". Several hundred tons of molten metal may thus exist beneath the level of the conventional tap hole and remain relatively undisturbed for several years under a thermal gradient. This system is subject to little convective stirring because the temperature decreases from top to bottom, and mechanical stirring due to movements in the stack and to tapping operations is unlikely to penetrate far into the metal. The system may thus be regarded as static

Jan 1, 1963

By N. A. Gokcen, M. Ohtani

Thermodynamic intevaction pararnetevs of elements E2(2), for dilute binary solutions of a component "2" in liquid iron, i.e., E(22) = 9 In f2/?N2 where f2 is the activity coefficient and N2 the mole fraction, and E(3) 2 = In f2/ N3 dilute ternary solutions of "2" and "3," and the carbon saturation parameter sc(3) (In f c/ N3) N c/N Fe for N3 - 0, are critically examined and correlated. It has been found that the interaction parameters and the atomic numbers of alloying elements follow regular periodic putterns. PHYSICO-chemical behavior of alloying elements in molten iron have become the subject of numerous investigations during the past 25 years. Consequently, the mutual effects of elements in the iron-rich solutions Fe-C-X, Fe-N-X, Fe-H-X, Fe-O-X, and Fe-S-X where X represents an alloying element, have gradually become better understood. These effects for a given temperature and pressure may be expressed by the interaction parameter of Wagner1, 2 derived briefly in the following manner. The complete differential of the Gibbs free-energy equation at constant temperature and pressure is dF = Fl dn, + F2 dn, + F3 dn3+ . . . [ 1] where F is the free energy; F 1, the partial molar free energy of "I"; and n,, the number of moles of "i." Cross-differentiation of this expression* *Cross-differentials are obtained as follows: Since the order of differentiation of F with n2 and n3 is immaterial, the left sides of the second differentials are equal, hence the derivation of Eq. [2] is obtained. For a dilute solution of components 2 and 3 in solvent 1, with the substitution of RT In f i = Fi xs for Fi where fi is the activity coefficient, and Fixs is the excess partial molar free energy, Eq. [2] becomes O) [3] where N2 and N, are the mole fractions. The interaction parameters are defined by

Jan 1, 1961

By N. A. Gokcen, S. Fujishiro

The dissociation pressure of Cr3C2 has been measured in the range of 1908" to 2237°K by means of graphite Knudsen effusion cells. It has been found that Cr3C2 vaporizes according to the following reaction: 1/3 Cr3C2 (s or 1) = 2/3 C (graph.) + Cr (g). The equilibrizcm pressure, P, of Cr (g) is found to be log Ps=- - (21,194/T) + 6.525 over solid Cr3C2 and estimated as log P, = - (19,535/T) + 5.76 over liquid Cr3C2. CARBIDES of chromium are of great importance in alloy steels and cemented carbides. The published data on their therm odynamic properties at high temperatures, however, are meager. The heat capacity and change in entropy of Cr3C2 were determined calorimetrically by Kelley and Moore1 in the range of approximately 50" to 300°K, and by Oriani and Murphy2 from 297" to 1188°K. The standard entropy of Cr3C2at 298.15°K, obtained by Kelley.7 was later confirmed by DeSorbo.4 Equilibrium in the reaction was investigated by Boericke.5 A recent tabular summary

Jan 1, 1962

By N. A. Gokcen, S. Fujishiro

THE pressures of Mn(g) in equilibrium with Mn7C3 and graphite have been measured by McCabe and Hudson' and Butler, McCabe, and paxton2 by means of graphite, zirconia, and Ta-Mo Knudsen cells. The details of corrections in their measurements were somewhat different from those of the authors;3'4 hence, further independent results at higher temperatures seemed to be warranted. The stoichiom-etry of Mn7C3 in equilibrium with graphite and its stability up to the vicinity of 1373 °K have been satisfactorily established by Kuo and persson5 (See also Hansen and Anderko).' The method of investigation has been described elsewhere in detail.3'4 The carbide was prepared in the manner described by McCabe and Hudson. In order to avoid possible reactions with refractory oxides, only graphite cells were used for the effusion experiments. The authors' results are the runs M-1, M-2 and M-3 listed in Table I, together with those of McCabe and co-workers. The heat capacity, c;, of Mn7C3 is not known; therefore McCable et al. plotted their data as log P vs 1/T and the results were only expressed first' as, and later2 as logP=- -14220+6.06 without further thermodynamic calculations. However, it is possible to estimate closely the necessary heat capacity as follows: When H; - &98 of CrC, or MnO, is plotted vs x, corresponding to various compounds, with temperature as the parameter, it is seen that the relationship is represented by a line of very small curvature. This relationship is also followed by other compounds which do not exhibit solid state phase transformations. In view of the fact that chromium and manganese have the atomic numbers of 24 and 25 respectively, it is reasonable to assume that H; - H;ae vs x for MnC, follows the same type of lines as those for CrC, for which adequate data are available.7 Similar correlations appear to be valid for oxides of two neighboring metals for which reliable data are available. The procedure is thus to move the lines for CrC, vertically (parallel to the axis of HT - H298) until they coincide with the points for MnC1/3, the only carbide of manganese whose H; - HO298 has been

Jan 1, 1963

By Avnulf Muan, Egil Aukrust

The activity-composition curve for cobalt oxide in (Co,Fe)304 solid solutions with spinel-type stmcture has been determined experimentally by studying the equilibrium between the spinel phase and a coexisting cobaltowüstite phase, "(Co,Fe)O", at 1200°C. A large negative deviation from ideal behavior prevails in the spinel at low cobalt oxide concentrations and a positive deviation at high cobalt oxide concentrations. The activity-composition curve for iron oxide in the solid solution is determined from the above curve by integvation of the Gibbs-Duhem equation along the join Co3O4,-Fe3O4. The standard free energy of formation of cobalt ferrite, CoFe2O4, from the oxide components CoO and Fe2O3 is calculated to be -8.2 kcal. ThERMODYNAMIC properties of (CO,Mn)3O4 solid solutions with spinel-type structure have been presented recently.' The present paper deals with similar relations in another spinel solid-solution phase, that represented by the system Co3O4-Fe3O4. The principles involved in measurements and calculations of thermodynamic properties for the system Co3O4-Fe3O4 are analogous to those used and discussed in detail in the work on (CO,Mn)3O4. A (CO,Fe)3O4 solid solution coexists in equilibrium with a (Co.Fe)Ot solid solution over a considerable Here acOo1.33 and aao are the activities of cobalt oxide in the spinel and the oxide solid solutions, respectively, pO2, is the oxygen pressure of equilibration, and pb, is the oxygen pressure at which CoO and CosO4 coexist in equilibrium in the binary system Co-O at the same temperature. The activity-com position curve for cobalt oxide in the (Co,Fe)O solid solution in contact with metal has been determined in a previous investigation by the present authors.' The system shows a small positive deviation from linear behavior. Because of the large defect concentration in wiistite and in (Co,Fe)O solid solutions, one cannot assume that the activity-composition relations in the oxide phase coexisting with a spinel phase at relatively high oxygen pressures are the same as those prevailing in the oxide solid solution coexisting with metal. However, a Gibbs-Duhem integration over the ternary Co-Fe-0 solution can be used to determine activities of cobalt and iron, and hence of CoO and FeO, from a knowledge of the oxygen potentials. Several papers have dealt with the subject of application of the Gibbs-Duhem equation to multi-component systems. 3-6 In the present case, it was

Jan 1, 1964

By Avnulf Muan, Egil Aukrust

Activity-composition curves jor cobalt oxide and manganese oxide in solid solutions with spinel-type structure have been determined by studying the equilibrium between the spinel phase and a coexisting solid-solution phase in the tewzperature range 1100" to 1400"C. Within limits of experimental error, the system displays the behavior of a regular solution. The excess integral free energy of mixing is represented by the equation . The standard free energy of formation of cobalt manganite, CoMn,O,, from the oxide components COO mzd Mn2OS at 1200°C is calculated to be -8.6 kcal. AMONG the technologically and theoretically most important oxide phases are those which crystallize with the same structure type as the mineral MgO . A120,. Although the name spinel originally was used only for this mineral, the term is generally used today to designate the whole group of oxide phases with this same structure type. It is in this wider meaning that the term is being used in the present paper. The previous literature on spinels is very extensive. There are two aspects of spinels which have attracted particular attention: the structure, including the nature and distribution of the cations present, and the physical properties (electric, magnetic). The status of knowledge in these fields has been well-summarized in recent review articles.1'2 By contrast, thermodynamic properties of spinels are virtually unknown. Delineation of the activity-composition curve over the whole composition range of a solid-solution series with spinel-type structure is the objective of the present work. The system at elevated temperatures (>1000"C) constitutes such a series. The activity-composition curves for this system can be calculated from a study of the equilibrium between the above spinel solid solution and a solid solution (Co,Mn)O with sodium chloride-type structure. Data for the latter solid solution have become available recently.3 The system, in contact with metallic CO at 1200°C, obeys Raoult's law. The determination of the activity-composition curve for the spinel phase is based on the following relations. Consider the reduction-oxidation equilibrium for cobalt ions according to the equation: Because it is impossible in practice to measure single activities of electrically charged constituents, we will treat the equilibria in terms of electrically neutral components. Eq. [I] can then formally be written as follows: where and the activities of cobalt oxide in the (Co,Mn)O and the spinel solid-solution phases, respectively, K is a constant at constant temperature, and Pa is the oxygen pressure of the gas phase. The numerical value of K can be determined from a determination of the oxygen pressure P& for the equilibrium coexistence of Cos04 and COO in the binary system Co-0. Under these circumstances be set equal to 1, and hence K = [Po Eq. [3] can therefore be written

Jan 1, 1964

By C. W. Sherman, J. Chipman, H. I. Elvander

THE pronounced and usually deleterious effects of sulphur on all ferrous metals and the resultant necessity for its control in metallurgical processes have stimulated many investigations of the system iron-sulphur. The data required for thermodynamic study of the behavior of sulphur in molten iron and steel include the activity and free energy of the dissolved sulphur and its heat of solution. Such data are also of theoretical interest since there is all too little information available concerning solutions of nonmetallic solutes in metallic solvents. It was the purpose of this investigation to attack the problem very directly by a study of equilibrium at several temperatures in the reaction H2 (gas) + S = H2S (gas) [1] K1 = PH2S /PH2 as where the sulphur is present in the liquid iron in amounts up to several percent by weight. Such a method of attack is not new since several careful studies have already been reported. It is planned, however, to extend the study to other metallic solvents and particularly to determine the effects of the various alloying elements on the activity of sulphur in liquid iron. This paper presents the results on molten iron-sulphur alloys containing up to 4 pct sulphur in the temperature range 1530°-1730°C. Literature Review The significant researches on dilute molten solutions of sulphur in iron include those of Chipman

Jan 1, 1951

By C. W. Sherman, J. Chipman, H. I. Elvander

J. F. Elliott—This is an excellent piece of work and makes a chemical metallurgist more enthusiastic than ever about what can be done with multicomponent systems, if we have satisfactory data. I have a remark to make on the interpretation of fig. 5. First, I will comment on the problem of activities in solutions. The iron-sulphur system has in its phase diagram an intermediate solid phase FeS. The occurrence of an intermediate phase is normally associated with negative departures from Raoult's law over a portion of the activity curves in the liquid. (Perhaps it would be better to reserve the phrase "departure from ideality" to departures from Raoult's law line rather than to departures from Henry's law line). Fig. 5 indicates that the deviation of the sulphur activity curve from the Henry's law line is negative;

Jan 1, 1951

By H. F. Ramstad, F. D. Richardson

The equilibria (a) SiOz +Hz =SiO +H20 and (b) Si + SiO, = 2Si0 have beet1 studied at temperatures of 1425"to 1600°C ad 1310°to 1485°C respectively. The stattdard free energy changes for the tzrro reactions are given by the equatiotts Combination of the results for both equilibria leads to tiotz removes certain anomalies in existing high-terlzperature data for equilibria involving silica and silicon in iron. In many metallurgical processes and in many laboratory investigations silicon monoxide undoubtedly plays an important role. It is unfortunate therefore that wide differences exist between the results obtained by different investigators1-7 in their studies of such equilibria as In an attempt to put our knowledge of SiO on a surer basis, an exhaustive study has been made of equilibria [I] and [2] at temperatures ranging from 1300" to 1600°C. Reaction [I] was studied by measuring the amounts of silica which could be condensed from streams of Hz or Hz + HzO which had previously been brought into equilibrium with silica at temperatures ranging from 1425" to 1600°C. Reaction [2] was studied by measuring the material that could be condensed from streams of Hz or argon which had been brought into equilibrium with mixtures of silicon and silica at temperatures ranging from 1310" to 1485°C. EXPERIMENTAL Materials. The silicon was "superpure" grade and contained less than 0.1 pct impurities. The silica was prepared from pure mineral quartz; this was crushed and treated with concentrated hydrochloric acid to remove particles of iron, washed with water, and finally dried at 120°C. For the hydrogen + silica reaction, the silica was sized to —20+100 mesh. For the silicon + silica reaction, the two materials were ground to a fine powder in an agate mortar. The hydrogen and argon were commercial oxygen-free gases. The gas streams were controlled with capillary flow meters and the volumes were measured by wet gas meters. After passing through the meters, the gases were partially dried by silica gel. The hydrogen for the HZ + SiOz reaction was then passed through palladised asbestos at 300°C and dried with magnesium perchlorate. The efficiency of oxygen removal was checked throughout the experiments by passing the gas over an electrically heated strip of nichrome, used as an indicator as described by Rathman and de itt.' When mixtures of HZ + Hz0 were required, the partial pressures of water vapor (1.8 to 22 mm) were obtained by passing the hydrogen through oxalic acid dihydrateg' lo held at various controlled temperatures, O.l°C, by means of a water bath. The hydrogen for the Si + Si02 reaction was purified by passing it over a mixture of 3 parts of magnesium to 5 of lime heated to 600°."l1 u The argon for this reaction was passed through titanium powder (-3/16 in. + 100 mesh) heated to 900°C. The nitrogen used to prevent the reaction products escaping from the condenser (see later), was deoxidized by copper or iron at 600°C. All these gases were finally dried with magnesium perchlorate. Furnace, Temperature Contr01, and Measurement A molybdenum resistance furnace was used for both sets of experiments. The reactions were conducted inside a high-grade alumina tube, 36 in. long and 1 in. in diam as indicated in Fig. 1. With this arrangement an even temperature zone (2"C) 4 cm long was satisfactorily obtained. The temperatures were kept constant by means of a proportional controller actuated by a Pt-Pt 13 pct Rh thermocouple. This was placed between the two alumina tubes, so that the temperature at the junction was 1400" to 1450°C. Up to 1485"C, the temperatures were measured with Pt-Pt 13 pct Rh thermocouples. For higher temperatures an optical pyrometer was used, this being sighted (through the glass window 1 in Fig. 1) on the end of the alumina tube, that held the SiOz or Si +SiOz mixture, 10 in Fig. 1. The optical pyrometer was recalibrated whenever a change was made in any part of the apparatus situated in the hot zone. Successive readings with the optical pyrometer were reproducible to within 1"C. Equilibrium Apparatus and Procedure. Hydvogen and Silica Reaction. The apparatus is shown in Fig.

Jan 1, 1962