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By R. W. Heckel, R. A. Tanzilli

Treatment of the finite, diffusion-controlled, two-phase, moving-interface homogenization problem has been carried out by numerical methods for a wide range of input parameters. Solutions have been obtained for planar, cylindrical, and spherical diffusion geometries. The effects of parameters such as the interdiffusion coefficients (concentration-independent) of- both phases, the concentrations (time-independent) of each phase at the interlace, mean composition, initial size of the dissolving- phase, and initial composition of- the two phases are considered. The results are displayed to show both the position of the interjace and the degree of homogenization (expressed in terms of concentration at the matrix phase symmetry boundary) as a function of diffusion time. Typical exaw~ples to which the results may be applied are discussed. A limited number of exact, closed-form solutions to the multiphase, diffusion-controlled, moving-interface problem exists in the literature, e.g., Refs. 1 to 7. The exact, closed-form solutions generally consider the outermost phases to be infinite in extent and also assume an interfacial velocity function. It is through use of such boundary conditions that closed-form solutions are readily obtained. An extensive literature also exists on numerical solutions to the mathematically analogous solidification problem, e.g., Refs. 8 to 12. In addition, a numerical solution involving mass transfer with spherical interfaces and infinite boundaries has recently been carried out.13 A practically important class of diffusion problems exists, however, in which the boundaries of each phase away from the interface are finite. For example the finite boundary condition arises when one sets up a model for analyzing the homogenization behavior of two-component powder compacts in two-phase systems or for studying the solution behavior of precipitates. Although exact, closed-form solutions have as yet not been found to this class of problems, solutions are possible using numerical methods. The purpose of this paper is twofold: 1) to describe a numerical method for treating the two-phase, diffusion-controlled, moving-interface problem involving finite boundaries with planar, cylindrical, and spherical interfaces; 2) to present the results of a parametric study which identifies the role played by each variable appearing in the analytical model. R. A. TANZlLLI,Student MemberAIME,onleaveofabsence from the General Electric Co., Re-entry Systems Department and A. W. HECKEL, Member AIME, are Graduate Student in Materials Engineering, and Professor, Department of Metallurgical Engineering, respectively, Drexel Institute of Technology, Philadelphia, Pa. Manuscript submitted May 6. 1968. IMD MATHEMATICAL MODEL The three geometries analyzed are shown in Fig. 1. For each configuration a symmetry element is shown, across whose boundaries the mass transfer is zero. Mean composition, C, and the characteristic solute-rich phase half-thickness (or radius), 1/2, are the independent variables while the characteristic symmetry element half-thickness, L/2 (measured from solute-rich phase center to the matrix phase plane of zero mass transfer), is a dependent variable. The symmetry element for a planar interface accurately represents a real diffusion situation involving the stacking of symmetry elements of constant size. Because cylindrical and spherical symmetry elements of constant size cannot be stacked to fill space, the meaning of the dimension, L/2, for these situations may be considered in terms of the following approximations: and where NA is the number of parallel cylindrical elements per unit area on a surface normal to the cylinder axes and Nv is the number of spherical elements per unit volume. The model consists of a solute-rich phase matrix phase composite of limited mutual solubility. The concentrations at the interface are assumed constant with time; no assumption of local equilibrium at the interface is necessary except for the case where the

Jan 1, 1969

By George A. Roberts

The development of an alloy system, high-speed steel, is used as an example of the progress of physical metallurgy. Tracing the history of men and their thoughts as they studied and invented and modified these materials, the story of high-speed steel since the 1890's is seen to be a long, slow, but steady progression of achievements. Today's multiplicity of high-speed steels are the result. Data are presented on quantitative metallography of carbides in high-speed steel with high vanadium content using the QTM instrument. Grindability as well as mechanical properties are related to the content of excess MC and M6C carbides in a series of high-speed steels and the newer matrix steels. These emphasize the present state of knowledge and show the current stages of thought that may affect the development in succeeding years. It is a great thrill for me, an ex-research metallurgist and ex-practicing metallurgical engineer, to speak to an audience currently engaged in both pursuits on the occasion of the 43rd Howe Memorial Lecture before the Iron and Steel Division of the AIME. I shall not review Henry Marion Howe's distinguished career, so adequately reviewed in Maxwell Gensamer's contribution in the 1965 AIME History of Metallurgy, except to point out that, while leading the life of an intellectual, he worked as a practicing research metallurgist and a practicing metallurgical engineer for significant periods of time and contributed greatly in both areas. For those of you who believe, as I do, that in the intellectual activity of metallurgy we are blessed with an intimate mixture of science and engineering (see Mehl's 1960 Howe Lecture), we might recall that Howe, while pursuing a life of writing and teaching in later years, served as the first Chairman of the Division of Engineering of the National Academy of Sciences. That metallurgists were called upon then to lead an engineering recognition movement is perhaps related to the strong part played by the AIME and its members in the recent establishment of a National Academy of Engineering and to the fact that a metallurgist is its head, 47 years after Howe served. I stress these engineering aspects for I wish to talk about a metallurgical engineering subject today. Alloy systems, physical metallurgy, and steel blended with an historical perspective and a report on new techniques to improve the old will, I trust, be of sufficient interest to bring these lectures back to the physical-metallurgy banner from which they have departed for 4 years. Those process metallurgists, open-hearth fiends, and physical chemists among you will just have to be patient. The development of an alloy system is the engineering application of scientific thought and fact. There are many interesting alloy systems, developed to a high degree of technology and sophistication over the past 40 to 70 years. These systems are bound together and related by a similar set of characteristics. For example, stainless steels are a system in which the members are related by a high chromium content which gives a corrosion-resistant characteristic. A subfamily in this system would be austenitic steels

Jan 1, 1967

By H. W. Mead, C. E. Birchenall

The rates of growth of graphite nodules in cast irons are calculated for a model of a growing graphite sphere surrounded by a shell of austenite through which carbon and iron are diffusing. The carbon is supplied by a cementite-austenite mixture at the outer edge of the shell. The calculated rates from carbon diffusion agree fairly well with the measured values, but the rates based on iron self-diffusion are much too low. Because the iron must be removed for the process to continue, o plastic deformation mechanism is suggested. THERE has been an unfortunate tendency in the literature of growth and dissolution reactions to identify the slope of a plot of the logarithm of the growth or dissolution rate vs reciprocal of temperature with the activation energies determined by diffusion measurements in chemically similar systems. If the solubility limits at the growing or dissolving phase interfaces change appreciably with temperature, such procedures may lead to serious errors in specifying the mechanisms controlling the rates of these processes. A reaction involving the simultaneous growth of graphite from and dissolution of cementite in austenite will be discussed here to show that substantial oversimplifications have been made in earlier studies of this process. From a dilatometric study of the overall y-range graphitization process, Bunin and Danil'chenko' found an apparent activation energy of 90 kcal per g-atom. They concluded that, since this value was much nearer the approximately 68 kcal per g-atom observed for self-diffusion in pure iron than it was to 32 kcal per g-atom for diffusion of carbon in iron, the rate-controlling process must be the diffusion of iron away from the growth interface to provide space for graphite to grow. Bunin and Salli' bolstered this agreement with the observation that graphite forms preferentially at surfaces, cracks, and pores where free volume is present initially. Ziegler, Meinhart, and DeaconQ ad found an apparent activation energy for graphitization of 98 kcal per g-atom. This value, like that of Bunin and Danil'chenko, applies to nucleation and growth occurring simultaneously. It is not generally assumed that nucleation is entirely diffusion-controlled. Treatments such as prior cold-working and prequenching, which strongly affect the rate of graphitization, would be expected to have little effect on diffusion processes occurring at the graphitization temperature. In any case 90 kcal per g-atom is not particularly close to the 54 kcal or lower to be expected for diffusion of iron which is carbon-saturated.' The presence of silicon in iron is said to reduce the activation energy for diffusion,' so its presence in cast irons would be expected to have a similar effect. The growth rates of nearly spherical graphite nodules have been studied by Brown and Hawkes." The initial rate of growth before impingement of adjacent carbon-depleted areas was found to be parabolic, and rate constants were measured at several temperatures. Their apparent activation energy for the growth process only was roughly 45 kcal per mol. Burke and Owen' made growth-rate measurements on several alloys, recording appreciable induction periods, initial nucleation rates, and average radial growth rates based on an assumed linear rate of radial growth. They found that increased silicon content increases the ovel-all reaction rate and the initial rate of nucleation, and decreases the induction period. Assuming 1) spherical nodules. 2) constant volume rate of nucleation, 3) austenite in equilibrium with cementite at positions where the cementite is not depleted, and 4) a constant diffusion distance during the growth of a nodule, they calculated an apparent overall activation energy of 68 kcal per mol, which was related to an activation energy for nucleation of 79 kcal per mol and activation energy

Jan 1, 1957

By C. A. Siebert, O. S. Duffendack, A. W. Herbenar

IN metallurgical problems involving the study of equilibrium in binary systems, the ,existence of an additional vapor phase, due to the presence of a volatile component in the alloy, has often been neglected. This is well indicated by the modified form of the phase rule, usually accepted in condensed systems in which pressure is not considered as a degree of freedom. In many cases the vapor pressure of the volatile component is exceedingly small and for all purposes can be considered negligible, in which case this form of the phase rule is applicable. However, alloys containing Hg, Cd, Zn, or Mg, tend to show very marked equilibrium vapor pressure, even in the solid state, and therefore present cases where the modified form of the phase rule no longer holds true. A quantitative determination of the vapor pressure of zinc in alpha brasses is not only of practical interest because of the loss of zinc in the processing of these alloys, but also of theoretical interest in that such measurements provide a means of applying the principles of theoretical physics and physical chemistry to problems of applied metallurgy. A number of investigators have reported vapor pressure measurements of zinc in alpha brasses. Hargreaves1 made extensive measurements which were used by Birchenall and Mehl² and Guttman³ for the determination of activity coefficients of zinc in alpha brasses. Hargreaves1 used a differentially heated quartz tube and measured the condensation temperature at one end corresponding to the temperature of the heated brass at the other end. Birchenall and Cheng outlined the condensation method of obtaining vapor pressure of zinc and Cd over some of their silver alloys." The primary object of the present investigation was to increase the range and accuracy of the vapor pressure data for the alpha brasses. Preparation of Alloys: Six alloys were prepared from Bunkerhill zinc and O.F.H.C. copper, both of 99.99 pct purity. The cast ingots were annealed for 24 hr at 550°C, scalped, cold rolled 40 pct and annealed for 50 hr at 550°C. The annealed bars were then surface ground and degasified for 30 min at approximately 550°C in an induction heated vacuum furnace. The surface of the bars was removed before milling the bars into relatively fine chips for chemical analysis and samples for the equilibrium cell. The analyses of the six alloys are given in table I. Experimental Method: The vapor pressure of zinc over the various alloys at a number of temperatures was determined from absorption spectra data. The spark source was produced by means of a high tension discharge between two electrodes of pure zinc. The design of the absorption vessel is shown in fig. 1. The vessel was constructed of transparent quartz which transmits the whole of the visible spectrum and the ultraviolet down to a wave length of 2000 A. The thickness of the vapor space was set at 0.8 mm so as to permit a relatively wide range of measurements without altering the vapor space, and thereby necessitating recalibration of the vessel. The furnace used for heating the absorption vessel consisted of a split wound furnace as shown in fig. 2. The spectrograph used in obtaining the transmitted zinc spectra was a double prism type especially designed for a region of 2500-3500 A. A step diaphragm used in conjunction with a tungsten filament provided the necessary intensity patterns required for calibration of the photographic plates.

Jan 1, 1951

By W. C. Krumbein

GEOLOGICAL problems are approached from a geometrical (space relations) viewpoint, a kinematical (time sequence) viewpoint, or a dynamical viewpoint. The first two require sound training in conventional geology and in field methods. The third approach requires a solid foundation of chemistry, physics, and mathematics. Modern training for geologists should include close integration of basic sciences with geological principles. INTRODUCTION Our knowledge of the earth has increased tremendously during the last half century. We know more about its surface configuration, the distribution of its natural resources, the procession of living forms that inhabited it in the past, the chemical composition of its oceans, the areal distribution of its surface rocks, the movements of its atmosphere, and so on. Not only do we know more facts about the earth, but we have a better understanding of the processes that take place on and within it, such as the nature of earthquakes, the thermodynamics of the atmosphere, the chemical equilibria involved in the formation of igneous rocks, the mechanics of stream flow, the dynamics of the earth's origin, and so on. Many sciences contributed to the sum total of this knowledge, including such established disciplines as geology, geography, physics, chemistry, astronomy, biology. Out of this accumulation of new knowledge grew also a group of new sciences, such as seismology, oceanography, meteorology, volcanology, hydrology. Collectively these latter are known as the geophysical and geochemical sciences, and to a large extent they began as branches of geology. Until the turn of the century, for example, the study of earthquakes (seismology) was a part of geology, although as early as 1846 Mallet, a physicist, had suggested that the subject could be investigated by elastic-wave theory. Comparatively little progress was made along these lines until the seismograph was developed near the turn of the century; since then, additional earthquake data have accumulated rapidly, but more important, the interpretation of these data essentially has kept pace with their accumulation. In similar fashion, meteorology was generally considered a branch of geology as recently as one or two decades ago. Considerable progress had been made in such aspects as weather forecasting, but the science dates its recent rapid rise from the year 1911, when Bjerknes first applied the principles of dynamics to the analysis of air masses. The rapid development of such disciplines as oceanography, volcanology and hydrology was due in part to the application of principles of chemical equilibrium, of dynamics, and of thermodynamics to earth problems, by men who were essentially physicists or chemists by training. The last half century, therefore, and particularly the last two decades, saw the influx of numerous chemists and physicists into the realm of the earth sciences. In the meantime the main body of geology itself showed a marked growth, and

Jan 1, 1941

1-Coal and Coal Products HOWARD N EAVENSON, Chairman C. T. HAYDEN, Vice-chairman, Bituminous Coal Production CHARLES DORRANCE, Vice-chairman, Anthracite Coal Production HOWARD P. ZELLER, Vice-chairman, Evaluation of Coal for Coke Making W H. FULWEILER, Vice-chairman, Gas and Its Manufacture J. B. MORROW, Vice-chairman, Coal Preparation Bituminous Coal Production C. T. HAYDEN, Chairman R L ADAMS EUGENE MCAULIFFE HAROLD J ROSE WILLIAM H BLAUVELT H E NOLD D. A RUSSELL GEORGE W EVANS JAMES W PAUL CECIL W. SMITH JOHN A GARCIA GEORGE S RICE SAMUEL A TAYLOR H. S GEISMER W F RITTMAN F G TRYON FRANK HAAS J D ROGERS FRANCIS R WADLEIGH CHESTER M LINGLE

Jan 1, 1923

By W. C. Krumbein

GEOLOGICAL problems are approached from a geometrical (space relations) viewpoint, a kinematical (time sequence) viewpoint, or a dynamical viewpoint. The first two require sound training in conventional geology and in field methods. The third approach requires a solid foundation of chemistry, physics, and mathematics. Modern training for geologists should include close integration of basic sciences with geological principles. INTRODUCTION Our knowledge of the earth has increased tremendously during the last half century. We know more about its surface configuration, the distribution of its natural resources, the procession of living forms that inhabited it in the past, the chemical composition of its oceans, the areal distribution of its surface rocks, the movements of its atmosphere, and so on. Not only do we know more facts about the earth, but we have a better understanding of the processes that take place on and within it, such as the nature of earthquakes, the thermodynamics of the atmosphere, the chemical equilibria involved in the formation of igneous rocks, the mechanics of stream flow, the dynamics of the earth's origin, and so on. Many sciences contributed to the sum total of this knowledge, including such established disciplines as geology, geography, physics, chemistry, astronomy, biology. Out of this accumulation of new knowledge grew also a group of new sciences, such as seismology, oceanography, meteorology, volcanology, hydrology. Collectively these latter are known as the geophysical and geochemical sciences, and to a large extent they began as branches of geology. Until the turn of the century, for example, the study of earthquakes (seismology) was a part of geology, although as early as 1846 Mallet, a physicist, had suggested that the subject could be investigated by elastic-wave theory. Comparatively little progress was made along these lines until the seismograph was developed near the turn of the century; since then, additional earthquake data have accumulated rapidly, but more important, the interpretation of these data essentially has kept pace with their accumulation. In similar fashion, meteorology, was generally considered a branch of geology as recently as one or two decades ago. Considerable progress had been made in such aspects as weather forecasting, but the science dates its recent rapid rise from the year 1911, when Bjerknes first applied the principles of dynamics to the analysis of air masses. The rapid development of such disciplines as oceanography, volcanology and hydrology was due in part to the application of principles of chemical equilibrium, of dynamics, and of thermodynamics to earth problems, by men who were essentially physicists or chemists by training. The last half century, therefore, and particularly the last two decades, saw the influx of numerous chemists and physicists into the realm of the earth sciences. In the meantime the main body of geology itself showed a marked growth, and

Jan 1, 1941

By W. C. Krumbein

GEOLOGICAL problems are approached from a geometrical (space relations) viewpoint, a kinematical (time sequence) viewpoint, or a dynamical viewpoint. The first two require sound training in conventional geology and in field methods. The third approach requires a solid foundation of chemistry, physics, and mathematics. Modern training for geologists should include close integration of basic sciences with geological principles. INTRODUCTION Our knowledge of the earth has increased tremendously during the last half century. We know more about its surface configuration, the distribution of its natural resources, the procession of living forms that inhabited it in the past, the chemical composition of its oceans, the areal distribution of its surface rocks, the movements of its atmosphere, and so on. Not only do we know more facts about the earth, but we have a better understanding of the processes that take place on and within it, such as the nature of earthquakes, the thermodynamics of the atmosphere, the chemical equilibria involved in the formation of igneous rocks, the mechanics of stream flow, the dynamics of the earth's origin, and so on. Many sciences contributed to the sum total of this knowledge, including such established disciplines as geology, geography, physics, chemistry, astronomy, biology. Out of this accumulation of new knowledge grew also a group of new sciences, such as seismology, oceanography, meteorology, volcanology, hydrology. Collectively these latter are known as the geophysical and geochemical sciences, and to a large extent they began as branches of geology. Until the turn of the century, for example, the study of earthquakes (seismology) was a part of geology, although as early as 1846 Mallet, a physicist, had suggested that the subject could be investigated by elastic-wave theory. Comparatively little progress was made along these lines until the seismograph was developed near the turn of the century; since then, additional earthquake data have accumulated rapidly, but more important, the interpretation of these data essentially has kept pace with their accumulation. In similar fashion, meteorology, was generally considered a branch of geology as recently as one or two decades ago. Considerable progress had been made in such aspects as weather forecasting, but the science dates its recent rapid rise from the year 1911, when Bjerknes first applied the principles of dynamics to the analysis of air masses. The rapid development of such disciplines as oceanography, volcanology and hydrology was due in part to the application of principles of chemical equilibrium, of dynamics, and of thermodynamics to earth problems, by men who were essentially physicists or chemists by training. The last half century, therefore, and particularly the last two decades, saw the influx of numerous chemists and physicists into the realm of the earth sciences. In the meantime the main body of geology itself showed a marked growth, and

Jan 1, 1941

By R. H. Frazier, C. H. Lorig, F. W. Boulger

THERE are both advantages and disadvantages in using semikilled steels in place of killed steels. One advantage of semikilled steels is they provide a higher ingot-to-product yield. This is especially important to shipbuilders in the time of national emergency. By using semikilled steel for hull plates, a greater number of ships can be built from the same ingot tonnage. Consequently, if semikilled steel plates are adequate for the service, the advantage of the higher product yield is of considerable importance. The performance of hull plates is closely associated with the ductile-to-brittle transition temperature, and this, in turn, is strongly dependent on the composition of the steel. A low transition temperature is desirable because it indicates that the steel is less likely to fail at low ambient temperatures. Killed steels are known to have lower transition temperatures than semikilled steels. It is believed that the better qualities of killed steels in this respect are due mainly to the low oxygen contents of the steel. The principal deoxidizers, aluminum, silicon, and manganese, lower the oxygen content. Fundamental studies1-0 have shown that the oxygen content remaining after the addition of one of these three elements is influenced by the residual amounts of the other two present. In the current study, therefore, various amounts of silicon and aluminum were added to steels containing different manganese contents for the purpose of studying the influence of silicon and aluminum on the notched-bar properties of hot-rolled steels. Eleven types of steels were studied. The temperature at which the plates were finish-rolled was care- fully controlled at 1850°F. All plates were rolled to ¾-in. thickness, and tested in the as-rolled condition. The total number of steels prepared in the laboratory for this study was 95. The charge consisting of ingot iron and ferrosilicon equivalent to 0.10 pct Si was melted in a 200-lb induction furnace under an atmosphere of argon to insure low, uniform nitrogen contents. After the charge was melted and the desired temperature was obtained, the melt was partly deoxidized with either silicomanganese or aluminum. Aluminum was used for this purpose in only those steels with very low silicon contents, where the finished steel was to contain some aluminum. This initial deoxidizing addition was made to obtain consistent recoveries of subsequent additions of ferro-manganese, ferrosilicon, and aluminum. Carbon, in the form of graphite, was added, either just prior to tap or to the final aluminum addition. The entire heat of 200 lb was poured directly into a 6x6-in. big-end-up mold. The ingots of semikilled steel were capped with a steel plate. The killed steels, on the other hand, were poured with a hot-top containing 14 pct of the total volume of the ingot. The ingots were processed by heating to 2250°F, followed by forging to slabs 1¾ in. thick and 6 in. wide. After reheating to 2250°F, the slabs were rolled to 0.9-in. gage, using reductions of approximately 1/6 in. per pass. The 0.9-in. thick plates were immediately recharged in a furnace held at 1850°F. After 30 min in the furnace at 1850°F, the plates were rolled to ¾ in. in one pass. Following the final pass, the plates were stacked on edge on a brick floor, with a brick separating one from another, where they were allowed to cool in air. Drillings for chemical analysis were taken from the plates at locations corresponding to the top and bottom of each ingot. Carbon, manganese, silicon, phosphorus, sulfur, and nitrogen contents of each sample were determined. The analysis of each steel was carefully controlled so that the contents of

Jan 1, 1957

By A. J. de Witte

It has been observed that upon invasion of a sand containing oil or gas and connate water by mud filtrate the hydrocarbons are more rapidly flushed by the filtrate than is the connate water.' In time, it appears that the following displacement pattern emerges: oil (or gas) is being swept ahead by connate water which, in turn, is pushed by invading fluid. Eventually the connate water may have "banked up" sufficiently to form a zone of appreciable thickness leading the invading front. In the extreme case, Fig. 1 shows how the situation will develop.' Immediately adjacent to the borehole (radius r) there is a zone, the invaded zone proper, where the connate water has been flushed out completely and which contains only residual oil or gas and mud filtrate. This zone (extending out to a radius ri) grades more or less abruptly into the next (thickness A), which contains only residual hydrocarbon and connate water. Beyond it, again more or less sharply bounded, extends the virgin formation with the original interstitial water saturation Sw. The various saturations are indicated in Fig. 1. The three zones generally will be marked by resistivity contrasts owing to their different fluid contents. As the connate water is usually more saline than the invading fluid, the second zone having a high connate water saturation forms a concentric cylindrical ring or annulus of low resistivity R, around the borehole.',' It will be referred to as the "low zone." Fig. 1 shows schematically the resistivity profile. It is clear that the phenomenon of a low zone could not occur in invaded water sands. The presence of a low zone, therefore, would be a qualitative indication of a hydrocarbon-bearing formation. Granted that the phenomenon is real, if it were pronounced enough to be detected, one might thereby have a means of locating oil or gas in the ground. This is the aim of the "displacement logging" method.' In any case, the presence of a low resistivity zone will affect the reading of electric logs. Using conventional log interpretation techniques, one must be aware of this and, if necessary, correct for it. Whether correction or detection should be the goal will depend primarily on the magnitude of the effect. The type of log which is likely to be affected most is the induction log. The current pattern of an induction log is concentric with the borehole. Any concentric ring of low resistivity, therefore, will tend to become crowded by current lines. This zone of maximum current density will obscure the relative contributions to the current conduction by other portions of a bed making, for instance, the contribution of the virgin formation less significant and thus detracting from the value or the induction log as an R, reading device. The present note is intended to ascertain the maximum possible effect of a low zone in the extreme case portrayed by Fig. 1 on three commercially available types of induction logs, sc., 5 FF 27, 5 FF 40 and 3 F 60. Type 5 FF 27 or 5 PF 40 is currently run in conjunction with a 16 in. normal and SP log. This combination is gradually replacing the regular electric survey (two normals and one lateral) as a standard log in many areas. On the basis of the scheme of Fig. 1 (sharp boundaries between successive zones), the thickness of the low zone may be computed for various amounts of infiltration measured by the ratio of invaded zone diameter to hole diameter D,/d. Referring to Fig. 1, we can set up a material balance for the water displaced from the invaded zone proper and the water present in the low zone. The volume of connate water displaced from invaded zone upon flushing by mud filtrate is: V1 = e p (r2 - r2) ? Sw . where c = bed thickness ? = porosity Su, = original connate water satu-ration. The volume of water finally accu-mulated in the low zone is: Vz = e p [(r1 -?)2 - r2 4] ? Sw . where SW1 = 1 — Sor = "water" saturation in the invaded and low zones both. The volume of water originally present in the low zone is:

Jan 1, 1958

C. A. ROSE, New York, N. Y. (written discussion *).-Without doubt the excellent results obtained at Ajo will cause surprise among metallurgists; 75 per cent. average capacity and 80 per cent. extraction during the first year of operation of a plant using a new metallurgical process are figures that speak for themselves. It is obvious that the most troublesome feature of the process is the fouling of solutions. The effects of this are most evident in the electrolytic tank house; but apparently the solutions are so heavily loaded with salts that their dissolving power is also impaired. This is indicated by the fact that copper comes into solution during washing after the leaching of the ore is completed, as shown by the decreasing ratio of acid to copper in the various washes tabulated in Table 4, and also by the fact that 4.9 per cent. of the total copper in the ore remains in the tailings in a soluble form. Even though the extraction in leaching and the ampere efficiency in electrolysis would be benefited by keeping the salts in solution at a lower concentration, it is doubtful whether it would pay to decrease these salts by discarding more electrolyte without other changes in the, process, since this would increase the amount of cement copper produced, which is already very large. If, however, it would not disturb the process otherwise, this object could be accomplished by increasing the range of electrolysis, so that solution going to the tank house would contain, say, 4 per cent. copper and 1 per cent. acid, and the solution returned to the leaching plant 1 1/2 per cent. copper and 4.8 per cent. acid, and by increasing the volume of solution to be discarded, this to be taken from the electrolyzed solution returned to the leaching plant. By this arrangement, more salts will be removed from the system per ton of cement copper produced; and if sufficient solution is discarded to keep the iron content down to 1 1/2 per cent. it would he feasible to recover the copper from

Jan 4, 1919

By M. Yoshinuga, S. Watanabe

Some iron ores, sinters and pellets occasionally show abnormal behavior during reduction which makes them undesirable as blast furnace burden. These may be divided into the following three types: (1) decrepitation of iron ore, (2) swelling of iron ore and pellet, (3) size degradation of sinter. In this paper reduction experiments and microscopic examinations were made to clarify the mechanisms and causes of these abnormal phenomena. Decrepitation occurs mainly when compact hematite ores containing small amounts of limonite are heated to about 500°C. Abnormal swelling of ores and pellets is caused by the rapid growth of fibrous metallic iron from the surface of wustite grains during rapid reduction and is fundamentally related to their original microstructure. Size degradation of sinter occurs through the development of cracks in the reduction stage from hematite to magnetite. About 80% of the iron ore used in Japan's blast furnaces comes from abroad, and the iron and steel industry must import this raw material from distant overseas places at high freight rates. The blast furnace operators, therefore, have made strong efforts to cut costs under these restrictive raw materials conditions by increasing productivity and simultaneously decreasing coke consumption. If, however, a high proportion of the ore burden consists of unsuitable materials furnace irregularities often result, establishing the need for detailed investigations of the basic natures of the ore constituents and their reactions during the reduction process. Recent investigations '-' of various ore burdens suggest that some iron ores, sinters and pellets are occasionally abnormal in appearance and behavior during reduction studies and may prove to be undesirable for use in the blast furnace. In the present study reduction experiments and microscopic observations were made to clarify the causes and the mechanisms of the abnormal behavior observed in some constituents of the burden and their effect on blast furnace performance. REDUCING APPARATUS The four kinds of reducing apparatus used in this investigation were the following: 1. The JIS* (Modified Gakushin') apparatus shown in Fig. la is most commonly used in Japan to evaluate the reducibility of ores under static conditions. It consists of a stainless steel tube of 60 mm inside diam suspended from a balance. 2. Linder's Reduction Test apparatus (Fig. lc) has a reducing barrel 130 mm diam and 200 mm long which rotates at 30 rpm. Some modifications were made in test procedures. 3. Gakushin Standard Test apparatus for determining the reducibility of granular ores (Fig. Id) consists of a horizontal silica tube 32 mm diam, 370 mm long and a movable electric furnace which enables rapid heating and cooling of the specimens. 4. The test apparatus for reduction under load (Fig. lb) gives a comprehensive evaluation of the behavior of ores under conditions simulating the static loading and the chemical reduction conditions encountered in. a blast furnace stack. A stainless steel tube of 50 mm diam and a carbon rod of 35 mm diam were used as the sample container and the support for the weight, respectively. In each investigation care was taken to select the most suitable method and apparatus to distinguish the abnormal nature of the ore in question. SIZE DEGRADATION OF SINTER DURING REDUCTION Sinter makes up the major portion of the blast furnace burden and its behavior during reduction should bear a close relationship to the iron productivity. Recently, some of the sinter was found to show serious size degradation during reduction at a relatively low temperature range. Because this phenomenon was thought to be a possible source of furnace irregularities, tests were made to clarify the phenom-

Jan 1, 1969

By J. Fred, Johnson

THIS TALK is a digest of some of the information contained in tables, one on practices and one on costs of shaft sinking, in Bulletin 357 of the U. S. Bureau of Mines written by E. D. Gardner, Supervising Engineer of the Bureau at Tucson, and myself. The table of practices contains information on 43 shafts and the table of costs contains information on 25 shafts. These various shafts were sunk between 1917 and 1930 so they may be termed modern practice with costs applicable in the United States, Canada and Mexico. In the compilation of this material the statistics on shafts which were concreted have been eliminated, as these figures were entirely out of line with corresponding figures for timbered shafts. It is my experience that where costs are divided between sinking and concreting the tendency is to load the costs onto the larger item of concreting. Thus a shifting of costs making an addition of 10 per cent in concreting costs may suffice to make a deduction of 40 per cent in sinking costs. Fine work is done (on the books) and everybody is happy. Most shafts are sunk with three shifts of men per day. Each shift consists of men who are miners, muckers, or timbermen, as chance may call for during their shift. Where pumping or high fixed costs do not necessitate three shifts it is cheaper to sink on two shifts. It is desirable for speed and economy in any case to work out a cycle of operations for each 24 hours. In this way men are hired for their ability as machinemen, muckers, or timbermen; they know exactly what to do and there is no passing the buck to the next shift.

Jan 1, 1933

CONTENTS PAGE ANDERSON, ROBERT J., and ENOS, GEORGE M.-Corrosion of Brass as Affected by Grain Size. Discussed by Henry S. Rawdon, Robert J. Anderson, Francis B. Coyle, William B. Price, and W. R. Webster 1 RAWDON, HENRYS., and MUTCHLER, WILLARD H.-Effect of Severe Cold Working on Scratch and Brinell Hardness. Discussed by W. H. Bassett, John Livermore Christie, John R. Freeman, Jr., W. R. Webster, William B. Price, Norman B. Pilling, D. J. McAdam, Jr., F. G. Smith, Zay Jeffries, F. E. Carter 3 WILLIAMS, ROBERT S., and HOMERBERG, VICTOR 0.-Relation of Heat Treatment to the Microstructure of 60-40 Brass. Discussed by 0. W. Ellis 14 Corrosion of Brass as Affected by Grain Size Discussion of the paper of ROBERT J. ANDERSON and GEORGE M. ENOS, presented at the New York Meeting, February, 1924, and issued as Paper No. 1282, with MINING AND METALLURGY, December, 1923. HENRY S. RAWDON,* Washington, D. C. (written discussion).-So numerous and so varied are the factors that affect the corrosion of metals that particular care is necessary in corrosion tests to eliminate so far as possible all extraneous factors. It appears to the writer that the question may well be asked as to whether all the necessary precautions have been observed in this investigation. It may be that the points to be mentioned were considered by the authors and found to be insignificant; however, there is nothing in the report to show this.

Jan 5, 1924

Edward Halse, Puerto Berrio, Colombia, S. A. (communication to the Secretary): I have read with much pleasure the interesting and valuable paper by Mr. Kunz, and hope that the following brief notes, gathered a few years ago, while a resident in Mexico City, may help to elucidate the subjcct: Turquoise.—This was known to the Aztecs as Xihuitl. Santiago Ramirez states that they found it in the Cerro Xicohtzonc, close to Atzcapatzalco, a suburb of the City of Mexico (compare page 59). Opal.—This was known to the ancient Mexicans, for they named it mezcuitlatt (compare page 63). Jade.—Under this was iucluded a third mineral, prehnite, not mentioned by Mr. Kunz. According to James D. Dana, part of the "jade " of China is prehnite; and Humboldt informs us, in his work on New Spain, that the same species of jade is known in some parts of Mexico as mahagua (majagua ?). The same writer says, in his Views of the Cordilleras, that the Aztec name Tecpatl included flint, hornstone, and green jade; and finally, in his Travels in South America," he discusses the nature of the ancient amazon-stones, and declares them to have been made out of a jade resembling " compact feldspar," one of the constituents of the gabbro verde di Corsica. IIence those stones were probably composed of nephrite. According to Humboldt, the form given to them most frequently is that of the Babylomian cylinder, longitudinally perforated, and loaded with inscriptions and figures. They were also cut by the natives into very thin plates, perforated at the center, suspended by a thread, and worn as amulets. According to the historian Clavijero, the specific name given by the Aztecs to the nephritic stone (jadeite) was Quitzalitztli,

Jan 1, 1902

By B. K. Parekh, W. M. Goldberger

A novel process is proposed for continuous removal of ash and unreacted solids which become suspended in the oils obtained during coal liquefaction. The proposed method uses water in direct contact with the oil under conditions which cause the suspended residue solids to transfer from the oil to the water phase. Separation of the phases yields a product oil essentially free of suspended solids. The water is cooled, clarified or filtered by conventional low-cost systems, and recirculated. The paper describes experimental work leading to development of the novel concept and includes the result of batch experiments that establish the feasibility of the process.

Jan 1, 1980

INTRODUCTION Mineral explorationists range throughout the world looking for mineral deposits which can subsequently be made into mines. Mines are not found! Mines are made, usually at great cost and not often without significant risk. The process of making a mineral deposit into a mine involves a great deal more than a complete appraisal of the deposit. The making of a mine demands detailed feasibility studies of many factors, any one of which, if shown to be negative, could prevent the deposit from becoming a successful mine. Total feasibility analysis involves at least three major fields of study: (1) economic analysis, (2) financial analysis, and (3) political and environmental analysis. Economic analysis is essential for proper decision making at many stages in the evaluation of a mineral deposit. It is the yardstick by which the proposed mining project and alter- native investment opportunities are measured. Economic analysis is concerned with costs and potential profits and can be applied at various stages in the evaluation of a mineral deposit to determine if the project merits the additional funds necessary to bring about each succeeding stage. The nearer any deposit approaches to becoming a mine, the more carefully the economic analysis should be made. Financial analysis has reference to how, where, and at what cost the investment funds can be obtained to finance the proposed mine project. Political and environmental analysis has reference to the many intangible factors that can affect the making of a successful mine. These factors loom larger today than ever before, due to the profusion of government regulations and various environmental constraints now imposed upon the mineral industry both by law and by the weight of public opinion. Ultimately, many of these intangible factors can be resolved back into the economic analysis as an added cost to mine development, but more and more often they have become insurmountable obstacles to any development of certain deposits. The role of financial analysis and the analysis of intangible factors must never be underestimated when making a feasibility study upon which to base investment decisions; however, the emphasis of this text will be upon economic factors. THE PARAMETERS OF MINERAL ECONOMIC ANALYSIS The two major elements of economic analysis are: 1) The potential earnings or annual generated cash flow of the project. 2) The investment costs necessary to realize such earnings. If the difference between the two elements is large enough, i.e., if the return on investment from the cash flow is high enough to attract investors, the project can be said to be financially feasible. The mineral economic analysis must take into consideration many parameters, some of which are known or knowable within certain limits, and others of which are unknown or unpredictable within certain limits and for which estimates must be made. Because both known and estimated parameters enter into the same analytical computations, it is important for the analyst to realize the nature of each when considering the results of an analysis. Some parameters such as the grade of mining block, although estimated, are said to be known within mathematically defined limits. Other parameters, such as the future price for minerals produced, etc., can only be estimated or "guestimated" within reasonable limits for which no precision can be assigned. Known or Knowable Mineral Economic Parameters Known or knowable parameters are: 1) Tonnage and grade of valuable minerals for the total mineral body and for individual mining blocks. 2) Metallurgical recovery of valuable mineral. 3) Minimum operating life of mineral de- posit at any specified production rate. 4) Royalty schedule, property payments, etc. 5) Sales-purchasing agreements, smelter schedules, marketing contracts, etc.

Jan 1, 1980

By Eckley B. Coxe

I DES~RE to call the attention of the Institute to two deep vertical shafts, which are now being sunk in Schuylkill County, Pennsylvania, about miles north of Pottsville. These shafts are of interest to the mining engineer, not only on account of the novelty of the method of sinking adopted, which promises to produce a revolution in that branch of mining engineering, but also as examples of the manner in which such work should be undertaken. GEOLOGICAL SKETCH OF THE TERRITORY TO BE WORKED BY THE SHAFTS AND REASON FOR SINKING THEM. The Mammoth or E Vein of the anthracite coal-measures in that part of the Schuylkill region near and north of the town of Pottsville lies at a great depth below the surface, and has, in consequence, never been worked in that locality.

THE papers by G. F. Loughlin and I. A. Ettlinger discussed the distribution of formations and ore-bodies in two of the main mining districts of the Southwest. The convergence of the deeper orebodies at Cripple Creek points to their common hypogene ori-gin, as do the occurrences of the copper ores of, central Arizona. E. L. Bruce described the areas in southwestern On-tario around Red Lake and Woman Lake, another prom-ising gold district. Of special interest was a series of lantern slides showing the use of power-driven boats and of hydroplanes as means of transportation. Within a few years, no doubt; such devices will revolutionize the mining industry and reconnaissance mapping in these relatively inaccessible areas. Much interest was evinced in the paper by J. W. Finch on "Sedimentary Metalliferous Deposits of the Red Beds." It was written as a caution to people at-tempting to mine these deposits. The discussion of the chemical equations presented in the paper brought out the fact that a large amount of study of such ores is necessary before we shall be able to write equations to explain their formation. Especially pertinent were the discussions by David White as to the relation of decay-ing plant tissue to metalliferous deposits and the color of sediments; also the point brought out by T. S. Lover-ing that chemical compounds produced by bacteria may greatly affect the deposition and reorganization of sedi-mentary metalliferous deposits.

Jan 3, 1928

By R. Rocca, M. B. Bever

THE adiabatic elastic deformation of a body is accompanied by a change in temperature. This phenomenon is known as the thermoelastic effect. Under adiabatic conditions the temperature of a metal bar is decreased by an elastic elongation and is increased by an elastic compression. All materials which elongate on heating behave in this manner. The sign of the thermoelastic temperature change is reversed for the few materials which have a negative coefficient of thermal expansion. The following equation for the thermoelastic effect can be derived from fundamental thermody-namic theorems, as shown in the Appendix: dT8 =-a1/cs T dss [1] Cs In this equation, T is the absolute temperature, S is the entropy, a, is the coefficient of linear thermal expansion, cs' is the heat capacity per unit volume at constant stress and s is the stress (positive in tension). Eq 1 can be applied to small, but finite changes in stress in the following form: ?Ts =- a1/cs T?ss [2] The sign of the temperature change AT is opposite to that of the change in stress s for materials which have a positive coefficient of thermal expansion. Eq 2 has been verified for many different materials and stresses at room temperature. No previous publication appears to have been devoted to an in- vestigation of the thermoelastic effect over a range of temperatures. Review of Literature Lord Kelvin (W. Thomson) presented a general theory of the thermoelastic effect in 1851' and later applied it to a solid, subject to an arbitrary system of stresses'. His analysis was based on a cycle of isothermal and constant-strain transformations and led to Eq 2 above. Even today, one of the clearest expositions of the thermoelastic effect is found in Lord Kelvin's article on elasticity in the Ninth Edition of the Encyclopedia Britannica (1878). R. ROCCA, Junior Member, and M. B. BEVER, Member AIME, are Research Assistant in Metallurgy and Associate Professor of Metallurgy, respectiuely, Massachusetts Institute of Technology, Cambridge, Mass. AIME New York Meeting, Feb. 1950. TP 2760 E. Discussion (2 copies) may be sent to Transactions AIME before APT. 1, 1950, and is scheduled for publication Nov. 1950. Manuscript received Oct. 15, 1949.

Jan 1, 1951