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By T. S. Fuller

Various phases of the embrittlement of solid copper containing oxygen by the action of reducing gases at high temperatures are familiar to readers of metallurgical literature through the work of many experimenters. In 1900, Heynl recorded observations of copper being heated in hydrogen with the development of fine cracks, the result of the formation of steam within the metal through the action of hydrogen on the copper oxide usually found in copper. Archbutt,2 in 1905, published the results of experiments, showing that all oxygen can be removed from copper by heating to redness, for several hours, in hydrogen. Intercrystalline cracks and extreme brittle-ness developed. Archbutt attributed the brittleness to the reduction of oxides present in the copper. Bengough and Hil1,3 in 1910, encountered the now well-known embrittlement at the outset of their investigation and stated in their paper: It soon became evident that the effect of any heat treatment depended largely on the presence or absence of reducing gases in the atmosphere of the furnace, as well as on its temperature. Hence it became necessary to adopt a somewhat elaborate scheme of heat treatment. The authors found embrittlement in separate experiments due to both hydrogen and carbon monoxide and concluded that: "The gases ruin the alloys after being heated to about 650" C. in their presence." Ruder,4 in 1916, reported the results of a series of experiments made by heating commercial and deoxidized copper in hydrogen, carbon monoxide, carbon dioxide, and steam. In agreement with other writers, he found that copper containing oxygen was made brittle by reducing gases, while the deoxidized metal remained unaffected. In the case of

Jan 1, 1926

By Paul Merica

THOSE of you who, like myself, have had the privilege of hearing previous Howe Memorial Lectures will note, and I hope without too much disaffection, that for the first time in this series of lectures iron has been chosen as the subject. I feel sure that the predominant choice by previous lecturers of subjects relating to steel has been principally in deference to the well-known interest this subject held for Professor Howe, and that their choice has not reflected any lack of respect for the material, iron. Nevertheless, in the face of this record, I feel some diffidence in introducing this "Cinderella" of materials into the circle of distinguished subjects hitherto treated by Howe lecturers, which is relieved only by the fact that I hope to be able to present some evidence that this Cinderella has at last undergone some of those magical trans-formations which render her acceptable even in the society of her dis-tinguished sister, steel. Fortunately I can cite the old master himself in support of my choice of subject and recall to you that Professor Howe by no means overlooked or neglected cast iron in the long course of his metallurgical meditations. Indeed his attention was early arrested by a metallurgical aspect of cast iron which he believed and we still recognize as of the most funda-mental importance-namely, the genesis of graphite in gray iron and the means for the control of its quantity and distribution. He made some comments over 20 years ago regarding the nature of J. E. Johnson's oxygenated iron which indicate that even then his thoughts were taking directions which today we are finding it useful to explore in connection with the theory of high-strength iron. Had we had in the subsequent years the continuing benefit of Professor Howe's illuminating consider-ation of this important subject, our progress in the improvement of cast iron would undoubtedly have been even more rapid.

Jan 1, 1937

By J. D. Defilippi, E. M. Gilbert, K. G. Brickner

FCC chromium-manganese-nitrogen (Cr-Mn-N) steels differ from most other fcc materials in that these steels undergo a ductile-to-brittle transition. Transformation to martensite is considered to be responsible for this behavior in some metastable Cr-Mn-N steels. However, very stable Cr-Mn-N steels also exhibit a ductile-to-brittle transition. The results of this study indicate that deformation faulting is the probable cause of the brittle behavior of stable Cr-Mn-N steels. Deformation faulting accounts for the ductile behavior of these steels in a tension test at -320°F and brittle behavior in an impact test at -320°F. Deformation faulting also accounts for the toPological features observed on the fracture surfaces of impact specimens of these steels. FACE- centered- cubic chromium-manganese-nitrogen (Cr-Mn-N) steels differ from most other fcc materials in that these steels undergo a ductile-to-brittle transition. Many Cr-Mn-N steels transform to martensite during deformation,l-5 and several investigatorsl-3 have suggested that the brittle behavior of these steels is caused by martensite formation. However, very stable Cr-Mn-N steels also exhibit brittle behavior. Schaller and Zackeyl reported that a very stable Cr-Mn-N steel (less than 3 pct martensite formed at -320°F) exhibited a transition temperature higher than that for steels in which large volume fractions of martensite formed during testing. The explanation given by Schaller and Zackey for this observation was that in the very stable steel the martensite, because of its higher interstitial content, was more brittle than that formed in their other steels. This explanation was questioned by Tisinai and samans4 and Baldwin.6 Moreover, because the toughness of stainless martensite at cryogenic temperatures is generally very low, this explanation does not account for Thompson's7 observation that small additions of nickel (1 to 3 pct) greatly improve the toughness of high nitrogen (0.35 pct) Cr-Mn-N steels. The present paper summarizes the results of an investigation of the low-temperature brittleness in very stable Cr-Mn-N steels. The importance of the mode of deformation on the toughness of these steels is discussed. Table I. Compositions of the Steels Invertigated, Pet Steel C Mn P S Si Ni Cr N - A 0.09 14.70 0.018 0.011 0.47 0.22 18.40 0.54 B 0.12 14.90 0.001 0.008 0.48 0.14 17.80 0.38 C 0.12 14.95 0.004 0.005 0.62 3.95 18.43 0.38 MATERIALS AND EXPERIMENTAL WORK The compositions of the steels investigated are shown in Table I. Steels A and B had compositions within the limits of a proprietary Cr-Mn-N stainless steel,* whereas Steel C was similar in composition to the proprietary steel except for its 3.95 pct Ni content. All steels were hot-rolled to 1/2-in. thick plate. The plates were subsequently annealed for 1 hr at 2000°F and water-quenched. Standard longitudinal and transverse Charpy V-notch impact specimens were machined from the annealed plates. Duplicate longitudinal and transverse impact specimens were tested at 212", 80°, 32", 0°, -100°,-160°,-200°,-256", and -320°F. Longitudinal tension-test specimens were also machined from the plates and tested at a crosshead speed of 0.05 in. per min at the aforementioned temperatures. The fractured impact and tension-test specimens of all three steels were examined to determine whether martensite had formed during testing. Magnetic, X-ray, electron-diffraction, and electron-microscopy techniques were used to detect the presence of martensite in the highly deformed areas of these specimens. Metallographic examination of highly deformed areas of impact and tension-test specimens revealed the presence of dark-etching bands, such as those shown in Fig. 1. These bands were observed only in deformed samples and were thought to be associated with the low-temperature brittleness of the Cr-Mn-N steels. Accordingly, a sample 1 in. wide by 3 in. long was cut from the 1/2-in.-thick plate of Steel C. This sample was surface-ground to a in. and then cold-rolled 60 pct at -320°F. Thin foils were prepared from the cold-rolled sample and examined in a JEM electron microscope. Brightfield, dark-field, and selected-area diffraction techniques were used to determine the cause of the dark-etching bands. Fractographic experiments were also performed. Impact specimens Of Steels A, B, and C were broken at -320oF, and the fracture surfaces of these specimens were immediately shadowed with carbon. The carbon replicas were examined in a Siemens electron microscope, and attempts were made to correlate the topological features of the fracture surfaces with the deformation mechanisms that could be occurring during an impact test of these steels.

Jan 1, 1970

By L. C. Graton

Although marked by numerous well-known attributes of its own, gold does not possess a kind and range of physical, chemical and geological characteristics wholly different and apart from those of other metals. Instead, it is merely one of the family of metals, with its individual and distinctive traits subordinate to the underlying family relationships and resemblances. The geologist concerned with pure science will pursue, therefore, the same general course and will examine the same broad kinds of facts and interrelations when studying the occurrence of gold as when studying that of copper or cadmium, or any other metal. But when we come to consider the use and economics of the metals, we discover that gold differs strikingly from all the others. Gold, in short, is unique, not by virtue of its inherent characteristics, but because of a peculiar and concerted psychological regard in which it is held. It will be evident, therefore, that the geologist who would deal with gold supply must give far greater weight to economic considerations than is required in his contacts with any other metal. If the geologist be called the scientist of occurrence, and the economist the scientist of use, the economic geologist stands as the necessary link between them. Perhaps it is in part because the economic geologist has made himself more familiar with the science of occurrence than with the science of use and has thus in some degree failed to bridge effectively the gap between the two fields, especially with regard to gold, that the usen1 of gold now appear to be in a state of general concern and even of alarm for the security and adequacy of future supplies. In the case of no other mineral commodity do the users, as a rule, trouble themselves greatly about the adequacy of supply except in so far as that may affect the price which they shall have to pay for the commodity. Oversupply, with resulting low price, they regard as a gift of good fortune. As to long-term undersupply, they are generally content to go ahead on faith, leaving the producer to discover as best he may the means for meeting their requirements or the inventor to find a substitute. But history has shown that for gold a different situation exists. While

Jan 1, 1931

By P. E. Rider, K. A. Gschneidner, O. D. McMasters

The solid solubilities for thirteen rare-earth metals in gold were determined by using the X-ray parametric method. Solubilities ranged from 0.1 at. pct for lanthanum in gold up to 8.8 at. pct for scandium in gold. The solubilities from lanthanum to gadolinium were very small and essentially constant, but a sharp increase occurred from gadolinium to scandium. The large solubilities for the heavy rare-earth metals were not expected because of the large size and electrochemical differences between rare-earth atoms and the gold atom. Contributions from first- and second-order elasticity theory plus an electronic contribution were found to reasonably account for a more favorable size factor. Electron transfer from the rare-earth metal to the gold Is thought to occur such that the resultant rare-earth and gold electronegativities are favorable for solid-solution formation. It was also found that this mutual adjustment of size and electronegutivity does not occur if the pure-metal size factors are greater than a critical value of 25 pet. The eutectic temperatures for ten systems were determined and these remained fairly constant at approximately 809 "C for the lighter lanthanide metal-gold systems until the Er-Au system was reached, at which Point the eutectic temperature successively increased reaching a maximum of 1040°C in the Sc-Au system. This rise was correlated to the size factor becoming more favorable for solid-solution formation at erbium. The valence state of ytterbium was found to change from two in the pure metal to three when ytterbium is dissolved in the gold matrix. RECENT results1 reported concerning the solubility of holmium in copper, silver, and gold, showed that the solubility of holmium in gold was quite large, 4.0 at. pct, compared with 1.6 in silver and 0.02 in copper. The small solubilities of holmium in silver and copper are quite reasonable in view of the large size difference (22.2 and 38.2 pct, respectively), large electronegativity difference (0.59 for both systems), and possible unfavorable valency factor (assuming one for silver and copper and three for holmium). The large solubility in gold, however, is unexpected because these same factors are also unfavorable for holmium and gold (22.5 pct size difference and 0.69 electronegativity difference), and because the light rare-earth metals, lanthanum, cerium, and praseodymium, have negligible solid solubilities in gold.2 In view of this unexpected behavior, it was felt that a study of the solid solubilities of most of the rare-earth metals in gold would be desirable to better understand the factors involved in the formation of solid solutions. Of the rare-earth metals added to gold in this study, only ytterbium is divalent in the pure metallic state (the other rare-earth metals are all trivalent) and many of its physical properties (such as the metallic radius, electronegativity, and so forth) are much different from those of the normal trivalent rare-earth metals.' The properties of ytterbium are such that one would expect solid-solution formation to be less favorable for ytterbium in gold than for any of the normal trivalent rare-earth metals. But chemically ytterbium is known to possess a stable trivalent state, and it is quite possible that ytterbium may alloy as a trivalent metal under certain conditions rather than as a divalent metal. Because of the dual valency nature and because so little is known about the alloying behavior of ytterbium, the gold-rich ytterbium-gold alloys are of special interest. EXPERIMENTAL PROCEDURE Materials. The gold used in this investigation had a purity of 99.99 pct with respect to nongaseous impurities. In general the rare-earth metals were prepared by reduction of the corresponding fluoride by calcium metal.3 The impurity contents of the metals used in this study are given in Table I. Preparation of Alloys. Two- or 3-g alloy samples were prepared by arc melting. The samples, with the exception of some of the Er-Au alloys, had weight losses of 0.5 pct or less. All alloy concentrations noted in this paper are nominal compositions. After arc melting, the alloys were wrapped in tantalum foil, sealed off in quartz tubing under a partial atmosphere of argon, homogenized for approximately 200 hr at 780°C, and then quenched in cold water. X-Ray Methods. The X-ray parametric method was used in determining the solubility of the rare-earth metals in gold. filings were sealed in small tantalum tubes by welding under a helium atmosphere. The tantalum tubes were then sealed in quartz tubing under a partial argon atmosphere, and annealed for times ranging from 1/2 to 3 hr (the length of time was inversely proportional to the an-

Jan 1, 1965

By R. Fawley, M. A. Quader, R. A. Dodd

Stacking fault energies and annealing twin frequencies have been measured for austenitic stainless steels having a) constant 20 wt pct Cr and varying nickel contents, and b) constant 20 wt pct Ni and varying chromium contents. The effect of nitrogen has also been studied and, to a lesser extent, so has the effect of carbon. All measured stacking fault energies plot linearly against the corresponding annealing twin frequencies, suggesting that, for constant prior deformation and grain size, twinning frequency can be used to estimate stacking fault energy. Compositions low in nickel possess the lowest fault energy, while the maximum fault energy within the investigated composition range occurs mound 20 pct Cr-20 pct Ni. Nitrogen has practically no effect on stacking fault energy when increased from 0.005 to 0.05 wt pct, although Planar dislocation glide is associated with higher nitrogen contents; this may be a short-range order effect. Carbon may raise the stacking fault energy a little, and causes pronounced dislocation tangling in deformed alloys. The basically different dislocation structures promoted by nitrogen and carbon, respectively, are not associated with large variations in stacking fault energy, and the reason for the difference remains unknown. INTEREST in the dislocation configurations developed in plastically deformed alloys arises principally from a desire for an understanding of mechanisms of plastic deformation and fracture. Comparatively little basic work has been concerned with austenitic stainless steels, although considerable interest has developed in the fundamental aspects of deformation of these alloys since the suggestion that those compositions deforming essentially by planar glide are particularly prone to transgranular stress corrosion cracking.' Certain facts are well-established. An 18 Cr-8 Ni steel (type 304) has a low stacking fault energy which is increased by higher nickel contents, and the structure of these steels when moderately plastically deformed changes concomitantly from planar to less planar to distinctly tangled dislocation configurations. These changes are thought to relate to changes in stacking fault energy, and considerable effort has been expended in measuring stacking fault energies of austenitic stainless steels through the determination of node curvatures2"4 even though the method has limitations due to formula approximations,5 an upper limit of measurement of 50 erg cm-2 at the most,5 and the necessity of an extremely meticulous experimental technique. Therefore, it is not surprising that only qualitative agreement between different investigators is generally to be found.'-' At high energies where node radius measurements are inappropriate, some use has been made of annealing twin frequencies to estimate relative stacking fault energies, although a recent critical evaluation of the method suggests that it should be used cautionsly with due regard to effects of grain size and prior deformation.6 Finally, there is a question as to whether the structures of some deformed steels are due to ordering effects. In particular, the role of nitrogen in promoting planar dislocation motion has been suggested to be due to ordering,' but similar suggestions have been made for steels having low interstitial contents.4 EXPERIMENTAL Small ingots of austenitic stainless steels (-50 g) were prepared from components exceeding 99.99 pct purity, the nickel and chromium being Johnson Matthey "Specpure" metals. Carbon was added as pure graphite, and nitrogen as CrN. The components were accurately weighed, and it was assumed that the final composition was the same as the nominal composition

Jan 1, 1969

By Thomas J. Pike, Keith G. Kirk, Mark F. Weider, Lawrence E. Welborn

As part of the mine permitting process as delegated by the Surface Mining Reclamation and Control Act of 1977 the regulatory authority must assess the probable hydrologic consequences and cumulative hydrologic impacts of surf ace mining. The U.S. Office of Surface Mining (OSM), in conjunction with Energy & Minerals Technology Assessment and ENCORE Systems Inc., has developed a user friendly groundwater model that is capable of predicting the effects of surface mining on groundwater quality and quantity. The model is a variation of the Prickett-Lonnquist model which has been modified to be specifically applicable to surface mine applications. This model is presently being used by OSM, the states, and industry to determine mining impacts on groundwater resources. The model is designed for use by the hydrologist with minimal computer training. The model accounts for multiple pumping wells, injection wells, multiple mine pits, and mine pit movement through time. This paper presents an example of how the model may be used in permit application review and how the model can be used by industry to simplify permit preparation.

Jan 1, 1983

By Elmer A. Jones

Like the caboose on the end of a long freight train L made up of mineral and metal processing and consuming industries, the mining industry progresses according to the movement of the train to which it is coupled. Sometimes the caboose rolls smoothly; occasionally it bumps along on the ties; almost always it is under criticism from someone for being too small, too large, too expensive, foolishly progressive, or hopelessly out of date. We who ride in the caboose are used to the rough by now, but it is nice now and then to have a bit of the smooth. Last year the train of industrial production rolled ahead swiftly and smoothly, and, except for a hot-box caused by strikes in copper mines, so did the caboose. As is brought out elsewhere in this issue, the outlook for 1956 is for more of the same.

Feb 1, 1956

By G. V. Jere, V. Krishnan, C. C. Patel

Standard free energy and standard enthalpy changes as a function of temperature have been calculated for the chlorination reactions of different oxides constituting columbite and tantalite. The tallies of standard lee-energy change (F) indicate the possibility of pvefeential chlorination of different oxides but the ease 0.f chlorination of columbium pentoxide at about 250°C and the chlorinating tendency of columbium pentachloride in promoting the chlorination of tantalum and other metal oxides, p7-evetzt the separation of columbiu?n and tantalum from other oxides and pom each othel.. It is likely that low temperatuves of chlorination and continuous 1err2oval of columbium pentachloride from the ..eaction zone may help partial separation of columbium from tantalum as well as from titanium. The standavd enthaply change (AH?) values shotr that 1ou.-temperature chlorination around 300" to 500°C is likely to sustain the chlorination , without external heating. COLUMBIUM (niobium) and tantalum metals, their alloys and interstitial compounds are finding extensive uses in nuclear reactors and high-temperature equipment.la-3 These metals also find uses in chemical process plants, electrical rectifiers and capacitors and as "getters" in electronic tubes.la With the development of Kroll process of reduction of volatilized titanium tetrachloride by magnesium for the production of titanium metal, chlorine metallurgy is receiving greater attention. Chlorine metallurgy has several advantages, the foremost amongst them are: the ease of chloride formation, separation of the different constituents of minerals by selective chlorination, and the reduction of the chlorides in vapor phase to the respective metals. Recently, Si-bert, Kolk, and Steinberg4 have considered a number of methods for the preparation of columbium metal and the most promising is found to be the halide reduction. Since the minerals columbite and tantalite are comparatively abundant in nature, the future of the metallurgical processes depends on the utilization of these minerals for the production of columbium and tantalum chlorides by chlorination. In this paper, an attempt has been made to interpret thermodynamically the chlorination of individual oxides constituting columbite and tantalite, with the help of the recent thermodynamic data.5-8 For this purpose, standard free energy and standard enthalpy changes of the chlorination reactions of the oxides with chlorine, both in absence and presence of carbon as the reductant, have been calculated as a function of temperature and represented graphically. Similar calculations for the reactions employing carbon tetrachloride and carbonyl chloride as chlorinating agents have also been incorporated in this paper. REPORTED WORK ON CHLORINATION Cuvelliezg has patented a process for the separation of columbium and tantalum from their concentrate, wherein 75 pct Cb05 is claimed to be chlorinated at 1050°C in the course of 7 hr using chlorine or chlorine containing nonreducing gases, the products of reaction being CbC1, or CbOC1,. At this temperature, Ta,05 is claimed to remain unaffected. It is further claimed1° that at higher temperatures, the proportion of Ta205 chlorinated increases while that of Cb205 diminishes. During the studies on the action of chlorine on individual metal oxides, Kangro and Jahn" have observed that Ta,05 is not chlorinated even at 1200" in the stream of chlorine, while 75 pct of Cb,05 is converted into CbOC1, around 900 to 1100°C. The chlorination of Cb205 by chlorine in the presence of carbon, investigated by Lind and Ingle,' and

Jan 1, 1962

TWO recent developments in open hearth steelmaking have had a substantial impact on metallurgical practices and operating procedures. These are: (1) the use of oxygen roof lances for accelerating the refining reactions, and (2) the use of a spring-arch, basic roof for prolonging the life of the furnace. Although these practices can be used separately, they are generally used to complement each other in an effort to obtain minimum heat time consistent with an acceptable rate of wear of the refractory roof, walls and port ends. DECARBONIZATION BY OXYGEN INJECTION The use of oxygen to speed carbon elimination was perceived by Sir Henry Bessmer but its practical use in steelmaking could not be realized until processes were developed for the manufacture of low cost, tonnage oxygen. However, as early as 1922 Bigge1 obtained a patent covering the use of gaseous oxygen to speed decarbonization of a molten steel bath. At that time, oxygen was available only in bottles and at a cost of $240 per net ton. At the end of World War II the price of oxygen had dropped to $80 per net ton, and as a result, metallurgical oxygen (99.5 per cent began to come into widespread experimental use for decarbonization in open hearth and electric furnace shops.2-8 Even this price prevented oxygen's routine use for other than decarbonizing the bath in shops producing substantial quantities of steels containing less than 0.40 per cent carbon. Today, tonnage metallurgical oxygen can be manufactured for less than $15 per net ton, and commercial purity oxygen (95 per cent is reported to cost less than $5 per ton. Thus, it is not at all surprising to find many open hearth shops effectively using large quantities of oxygen to accelerate decarbonization. Equipment for Oxygen Injection. The oxygen may be injected by a lance pipe inserted through the wicket hole and pushed several inches into the steel bath, or by a water-cooled jet inserted through the back- wall, endwall, or roof, and immersed in the slag or set just a few inches above the slag. Oxygen at approximately 100 psi is piped directly to control stations adjacent to each furnace. The installations should include adequate safety devices such as fire checks and emergency valves,

Jan 1, 1964

By J. L. Huitt, S. R. Darin

The use of a partial monolayer of propping agent to obtain a high flow capacity for a hydraulically induced fracture is discussed. From the results of laboratory work it was shown that a modified form of the Kozeny-Carman relation could be used to describe the flow in the partial monolayer propped fracture. With equations presented in the paper, the density pattern of the propping agent (number of particles per unit of fracture surface) that results in the maximum flow capacity for the fracture can be determined. The maxitnum flow capacity obtained with a partial monolayer is often an order of magnitude greater than the flow capacity obtained in greater width fractures containing multilayers of the propping agent. INTRODUCTION One of the predominant factors controlling the success of a hydraulic fracturing operation is the propping of the fracture. The trend in hydraulic fracturing recently has been an increase in the ratio of propping agent-to-fluid. The primary purpose of this increased ratio is to sustain a propped fracture of greater width. It was shown in a recent study' that for some formations low concentrations of propping agent would result in "closing" or "healing" of the fracture. In some cases, in an effort to insure sufficient propping agent concentration, the fracturing operation is designed to obtain a pack of the propping agent in the fracture. The placing of a pack of propping agent in the fracture provides a fracture of maximum width; however, the width alone does not control the flow capacity of the fracture. The flow capacity is dependent on the permeability of the fracture, as well as the fracture width. Thus, increasing the permeability to obtain larger flow capacities is as important as obtaining a greater width fracture. By increasing the concentration and particle diameter of the propping agent, fractures of sufficient flow capacities are obtainable for effective well stimulation in a number of formations. However, in some of the recovery techniques, the fracture capacity obtained by commonly used practices in fracturing is inadequate. One such recovery technique is gravity drainage via a horizontal fracture placed near the base of the productive zone. For this recovery technique, the fracture capacity desired is usually one to two orders of magnitude greater than the fracture capacity normally obtained in fractures propped with the size of sand commonly used (20-40 mesh). By the use of particles of larger diameter, the permeability of a pack2 is increased; however, even a multilayer pack results in a fracture flow capacity lower than that desired for some formations. For example, a fracture of 1/4-in. width, packed with 8-12 mesh sand of about 2,000 darcies permeability, would result in a fracture flow capacity (permeability X fracture width) of only 40,000 md-ft. If the fracture flow capacity needed is an order of magnitude greater than that cited in the example, an approach different from the formation of a pack in the fracture is needed. One approach is a partial monolayer of large-diameter propping agent. In working with this type of fracture system, it was found that the flow problems were unique to the system; therefore, the study discussed in this paper was made. THEORY AND RELATED STUDIES Previous studies, although related to that described in this paper, have not pertained directly to the flow in a fracture propped with a partial monolayer of propping agent. However, studies such as flow between parallel plates,' flow in packed columns,' fracture flow capacity' and flow in simulated fractures reduce the scope of this flow problem considerably. A fracture propped with a partial monolayer of dropping agent may be considered to be between two extremes — between an open fracture and a bed of particles packed In a conduit of fracture geometry. Thus, it seems appropriate to review the extreme cases.

By A. K. Mukherjee, John E. Dorn

The effects of strain rate and temperature on the critical resolved shear stress for (321)[111] slip were determined for the silver-rich CsCl type of intermetallic compound AgMg. The flow stress increased only slightly as the test temperature was first decreased below room temperature; a rapid increase in the flow stress was obtained with yet further decrease in temperature from about 250' to 4OK. The effect of both the temperature and strain rate on the flow stress over the low-temperature range could be rationalized satisfactorily in terms of the Peiwls mechanism when the deformation was controlled by rate of nucleation of pairs of kinks. IN spite of the well-documented interest of metallurgists and engineers concerning the mechanical behavior of intermediate phases and intermetallic compounds, very little definitive information is available on this important subject. As recently summarized by westbrook,1 only limited and modest progress has been made thus far in elucidating the details of the mechanism of plastic deformation for the intermetallic compounds; the available information largely concerns phenom-enological descriptions of empirical observations and experimental facts, principally with reference to poly crystalline aggregates. The present report on the elucidation of the rate-controlling mechanism for slip in the bcc structure of AgMg is part of the comprehensive program of a systematic investigation on the mechanical behavior of intermetallic compounds. The intermetallic compound AgMg has a CsCl type of lattice structureZ and is completely ordered up to its melting point of 820c3 This material was selected for our present investigation because of its simple crystal structure, moderate and congruent melting point, ordered structure persisting up to the melting point, and some solubilities of the constituent elements, which could be expected to help in the growing of single-crystal specimens. Whereas previous investigations on the properties of AgMg include hardness,*"6 slip systems,7 tensile flow stress of polycrystalline specimens,' and electrical resistivity,4 the current investigation will be directed principally at elucidating the rate-controlling dislocation mechanism responsible for slip in single crystals at low temperatures. It will be shown that the strain rate is consistent with a model involving the rate of nucleation of pairs of kinks by the Peierls mechanism for plastic deformation. EXPERIMENTAL TECHNIQUES Single-crystal specimens of the AgMg intermetallic compound were prepared and tested as follows: 1) A master alloy ingot of AgMg was produced by melting and chill casting the high-purity silver (99.995 wt pct) and high-purity magnesium (99.997 wt pct) in an induction furnace under a helium atmosphere. 2) Sections of the above-mentioned ingot were placed in a graphite mold containing a spherical cavity in which a single-crystal sphere of 1 in. diam was grown under helium by the Bridgman technique. 3) The operative slip systems were investigated at room temperature on a singlecrystal of AgMg, from measurements of the angles made by the slip traces on the two surfaces of the specimen, which were at 90 deg to each other. The investigation confirmed that the AgMg compound undergoes slip primarily in the (321) plane and in the [Ill] direction, but a small amount of secondary slip was also noticed in the (112) (111) system. No slip was observed in the (110) planes. 4) The single-crystal sphere, mentioned earlier, was oriented in a graphite mold containing a cylindrical cavity of 3/8 in. diam above the spherical receptable to give the angle xo = 45 deg between the axis of the cylindrical bar and the normal to the slip plane (321), and the angle AO = 45 deg between the slip direction [Ill] and the axis of the bar. Oriented single-crystal bar seeds were produced by melting, under a helium atmosphere, a polycrystalline bar in the cylindrical cavity above the oriented spherical seed and by growing an oriented single-crystal bar from the seed. 5) Finally, oriented single-crystal specimens were grown from these cylindrical seeds. 6) The cylindrical specimens were machined in a High-Tension Spark Cutting unit to give a 2-in. gage length. The spark-machined gage section was elec-tropolished in a bath containing 200 ml of H3PO4,

Jan 1, 1964

By P. C. Johnson, B. A. Stein

This paper describes a study of the effects of combined heat treatment and explosive loading on the mechanical properties of high-strength steels. nis program investigated two distinct areas: 1) the effect of shock waves, without gross irreversible defmmution, on a 3-Cr steel at various stages of heat treatment; and 2) the effect of rapid deformation (explosive forming) on H-11 and D6-AC steels in the metastable austenitic state. The mechanical properties of these steels were improved, in some cases markedly, as a result of these treatments. ,AUSFORMWG, which requires the plastic deformation of metastable austenite, is a process which can appreciably improve the properties of selected alloy stee1s.l,2 The Ausform process significantly increases the strength of these steels without decreasing their ductility. The properties at high temperatures are also improved through a change in the response of the steels to tempering. Although the mechanism by which ausforming alters the properties of these steels is not fully understood, it appears that the dislocation arrays produced by deformation of the metastable austenite influence the structure of the martensite on subsequent transformation. This, in turn, affects the strength, ductility, and tempering response of the martensite. This research used chemical explosives to deform steels at various stages in their heat treatment in order to improve the properties of these steels. The explosive energy is used in two ways; 1) high-pressure shock waves are propagated through the steel to produce extensive microscopic shear strain without causing a large irreversible change in shape, and 2) explosive energy is used to cause extensive macroscopic plastic strain in the metastable austenitic state (explosive forming). I) AUSFORMING WITH INTENSE SHOCK WAVES The steel used in this phase of the research was an alloy having a nominal composition 0.43 pct C, 3.0 pct Cr, 1.5 pct Ni, and 1.5 pct Si. The steel was subjected to intense shock waves in three conditions: 1) in the metastable austenitic state, 2) in the tempered mar tens itic state, and 3) in the tempered martensitic state after ausforming by conventional techniques. The specimens were in the form of disks 2.75 in. in diam and 5/16 in. thick. These were incorporated into a specimen assembly consisting of two disks pressed into a 5 by 5 by 1 in. block of stainless steel, Fig. 1. Spalling (or scabbing) is confined to the front disk. The specimen is protected from oxidation and decarburization by the surrounding metal. The temperature of the assembly is monitored by a thermocouple inserted into one side of the stainless steel block. The assembly is positioned over an oil reservoir which serves both as a means of catching the disks and as quenching medium for the disks shocked under ausforming conditions. Plane shock waves are introduced into the assembly by a metal driver plate impacting the top surface of the block. The driver plate is accelerated by a chemical explosive sheet supplied by E. I. du Pont de Nemours & Co. All the specimens were subjected to plane shock waves having a peak pressure of approximately 430 kbar. The pressure is that quoted by G. E. Dieter for the plane wave generator used in this work.' The driver plate used was 1/4 in. thick, so that the initial pulse was essentially a l/2-in.-wide square wave. The attenuation of the peak pressure during the subsequent 1/4 in. is estimated to be less than 5 pct. The shock front induces a temperature rise, a portion of which is irreversible. Rough estimates (+25 pct) of this temperature rise have been made for iron shocked at room temperature.4 For a 500-kbar shock wave, the temperature rise in the shock front is about 700°F, and is held for a time of the order of microseconds. The irreversible temperature rise, which remains after the shock wave passes, is about 450°F.4 The disks are quenched to room temperature within a few seconds of the shock treatment. It should be emphasized that the temperature rises given above are estimates for pure iron at room temperature, and are not necessarily true for the tests made in this work. The disks shocked at temperatures in the metastable austenitic range were austenitized in the stainless steel assembly in a furnace protected from the firing area. The assembly was removed from the furnace and placed over the recovery reservoir. The plane wave generator was then positioned and

Jan 1, 1963

By V. F. Hollister

The Queen Charlotte gold deposit (also known as the Specogna, Babe, or Cinola) was discovered in late 1970 by Efrem Specogna and Johnny Trico. They were prospecting along the trace of the Sandspit fault, and they sampled jarositic material that included veins from the fault zone. Their assays included some good gold values. They located the Babe Claims in 1971 and optioned them to Kennco Explorations Ltd. Kennco conducted stream sediment and soil geochem studies, geological mapping and drilling of 55.2 m (181 ft) in two drill holes. Kennco withdrew from the property, and by 1977, Cominco, Placer Development, Silver Standard, and Quintana Minerals had each successively worked on the deposit. Consolidated Cinola Mines bought the claims in 1977 and completed exploration of the deposit ultimately in a joint venture arrangement with Energy Reserves. Energy Reserves entered in late 1979, and by 1983, a total of 200 surface and 12 underground drill holes had been completed, totaling 28 600 m (93,832 ft). In addition, a 461.9 m (1515 ft) adit was driven in the ore body. Reserves published by Cinola aggregate 34 Mt (37 million st) of 1.7 g (0.060 oz) Au per tonne. All industry geologists working in the area agree that the Queen Charlotte gold is an epithermal gold deposit in porous volcaniclastic and clastic rocks that is genetically related to a Miocene-Pliocene rhyolite plug. The geologic description here follows the oral presentation made by G. G. Richards, J. S. Christie, and M. R. Wolfhard at a 1976 CIM meeting. Additional comments by the late C. S. Ney of Kennco Explorations are included with the Richards, Christie, and Wolfhard data to complete the geologic set- ting. The attached reprint by Champigny and Sinclair (1 980) provides additional data on the deposit. The Queen Charlotte (Babe, Specogna, or Cinola) gold deposit is located on Graham Island in the northern Charlotte Islands, at the fault boundary of the Skidegate plateau and the Charlotte lowlands. The Sandspit fault marks the physiographic boundary, and it is intruded by rhyolite porphyry at the deposit. Because displaced geochem anomalies, drain- age patterns, and topography suggest dextral and east side down movement for the fault, exposed east block rocks are younger than rocks west of the fault. The east block, which included the ore deposit, is a lowland largely masked by unconsolidated Pleistocene and Recent clastic rocks. Rocks west of the rhyolite plug, on the Skidegate plateau, are Cretaceous carbonaceous and calcareous shale unconformably overlain by a thin veneer of rhyolite tuff. The deposit is about 100 m (328 ft) above sea level. GEOLOGIC SETTING At the ore deposit, the Sandspit fault is a complex structure. However, lithologies on either side of the fault-controlled rhyolite porphyry plug are distinct. West of the rhyolite, the upper member of the Cretaceous Haida formation shale is the most common rock type. The member is composed of dark grey to black, poorly consolidated, and thinly bedded carbonaceous and calcareous shale. The sequence is silicified to an argillite or a hornfels near the rhyolite. West of the rhyolite porphyry plug, but not importantly involved in the mineralization, is a thin masking cover of rhyolite tuff. The tuff unconformably succeeds the cretaceous shale, but it is largely eroded in the mine area. East of the fault-controlled rhyolite porphyry plug is a thick section of conglomerate and sandstone of the Miocene- Pliocene Skonun formation. The ore body occurs within the coarse clastics, the rhyolite intrusive as the western boundary. Ore is entirely contained within the clastics. Original permeability of the clastic rocks was a major control for ore deposition and alteration, and for that reason, the Skonun formation is described in greater detail. The Skonun formation clastics unconformably overlie Haida shale. The Skonun is at least 300 m (984 ft) thick in the mine area, where it trends northerly and dips easterly 15º to 25º. The sequence is about 62 percent conglomerate, 3 1 percent coarse arkosic sandstone, and 7 percent interbedded siltstone and sandstone. Contacts between adjacent beds are generally sharp. Stratigraphic correlations between drill

Jan 1, 1985

By D. Turnbull, J. H. Hollomon, J. C. Fisher

Application of the concepts of nu-cleation and growth to the analysis of experimental transformation data has led to valuable descriptions of phase transformations, an outstanding example being the transformation austenite —* pearlite which has been examined with particular care by Mehl and co-workers.&apos;-5 In addition to the pearlite transformation, the proeutectoid fer-rite and proeutectoid carbide transformations are known to proceed by nucleation and growth. Martensite, on the contrary, until recently was thought to form by a mechanism involving neither nucleation nor growth; however, extension of standard nucleation theory6 suggests that martensite, bain-ite, and the other products of austenite decomposition all grow from nuclei in the parent phase. The theory that martensite forms by nucleation and growth is strongly supported by recent experimental work of Kurdjumov and Maksimova.7 The concepts of nucleatioli and growth have been fruitful also in providing a sound basis for quantitative theoretical treatments of the kinetics of phase transformations. For example, Volmer and Weber8 and Becker and Döring9 developed the theory of nucleation from fundamental considerations to a point where excellent agreement was obtained with the results of experiments on the condensation of supercooled vapors. As a result of their analysis, the kinetics of vapor-liquid transformations now can be predicted. It seems probable that application of the theories of nucleation and growth to a quantitative study of austenite decomposition similarly will clarify the nature of the individual transfor: mations involved, and will enable the calculation of austenite transformation kinetics. In the present paper, the theories of nucleation and growth are applied to the austenite ? martensite transformation in steels. The analysis begins with a discussion of nucleation in single component systems. Martensite appears to be coherent with the parent austenite, hence the nucleation theory is modified to include the effects of elastic distortion. Nucleation in the two component iron-carbon system then is discussed, for most steels are primarily alloys of these two elements. Finally, M. temperatures and martensite transformation curves are calculated for each of several alloy steels of varying carbon and chromium content, and are compared with those determined experimentally by Lyman and Troiano10 and Harris and Cohen.11 Nucleation Theory NUCLEATION IN SINGLE COMPONENT SYSTEMS6,12-14 The work required for reversible formation of a region of phase within the parent a phase is expressed conveniently as the sum of two terms: W1 = Aa, the product of the area of the interface and the interfacial free energy, and W2 = VAf, the product of the volume of the region and the free energy increase per unit volume associated with the transformation. The total work is therefore W = Aa + VAf. When a is more stable than ß, Af is positive and W increases without limit as the volume increases. The transformation a ?ß does not occur. It is nevertheless true that small regions of phase ß enjoy temporary existence here and there in the a. The equilibrium number of ß regions of given size is proportional to exp(— W/kT) per unit volume of a, assuring that larger (ß regions occur with diminishing probability. When a is less stable than ß, Af is negative and W passes through a maximum as V increases. Assuming for simplicity that regions of ß are spherical, as is true when the interfacial tension is isotropic and there are no elastic strains, W = 4r2a + (4/3)*r3Af The maximum value of W is W* = 16iro3/3Af2 [1] for regions with radius r* = -2o/Af. [2] For single component condensed systems it has been shown14 that the steady rate of nucleation of 0 per unit volume of untransformed a is nearly proportional to exp[- (W* + Q)/kT] where Q is the activation energy for the unit processes of adding or removing one atom from an embryo or nucleus. If To is the temperature at which a and ß are in equilibrium, the rate of nucleation is a maximum at a temperature 0 < T < To where (W* + Q)/kT is a minimum. P regions smaller than critical size are called embryos; they tend to grow smaller and disappear, only exceptionally growing larger. Regions equal to or larger than critical size are called nuclei. A critical size nucleus may grow indefinitely large or may shrink back to a, either process decreasing the free energy of the region.

Jan 1, 1950

By Rex B. McLellan

A simple model for dilute interslitial solid solutions is set up which enables a solubility equation for the equilibrium between the solid solution and the gaseous solute to be deduced. This solubility equation is used to estimate the partial thermody -namic functions of Ag-O and Fe-N dilute interstitial solid solutions from the measured equilibrium between these solutions and the gas phase. It is shown that the partial excess entropy of the solute atom in solution is a vibrational entropy which is due Principally to the oscillation of the interstitial atom and does not arise from electronic or elastic interaction between the solute atoms and solvent matrix. In this work measurements of the equilibrium between dilute solid interstitial solutions and a gaseous phase are used to deduce the important thermody-namic functions of the solid solution with the aid of a theoretical solubility equation formulated from a knowledge of the thermodynamic functions of the gas and a simple model for the solid solution. The quantity of principal interest which is deduced from the equilibrium data is the change in vibrational entropy occurring when a solute atom (u) is placed in an interstial site in the solvent (u) lattice. This paper forms part of a more general study in which the properties of condensed phases are deduced from measurements of the equilibrium between the condensed phase and a gas. Previous investigations have dealt with the equilibrium between krypton and liquid metals,&apos; a pure metal and its vapor,&apos; and dilute substitutional alloys and the vapor,3 and the subject has been popularly reviewed by McLellan.4 In the latter investigation3 the vapor pressures of very dilute Cu-Ag and Cu-Au alloys were measured with a Knudsen cell technique over a large range of temperatures and the analysis of the vapor-pressure data showed that the relative partial excess entropies were large and positive [ds= -Sudk = 30 for Au-Ag alloys and 150 for Cu-Au alloys; these values should be compared to unity, the value assumed for these exponentials in the quasi-chemical theory of solutions]. For many interstitial solutions experimental data is available for the equilibrium between the solution and a gaseous phase, and this can be used to deduce the vibrational entropies of the solute atoms in solution. The general method employed is to calculate the chemical potential of the solute atoms in the gas and equate this to pi, the chemical potential of solute atoms in the solid, which is deduced from a simple model set up for the dilute interstitial solution (in which the solute atoms act as bound oscillators in interstitial sites). This enables a theoretical solubility equation to be set up. In the case of Ag-O and Fe-N solid solutions the solubility c, is found to vary with temperature according to a relation of the type, where PU2 is the pressure of the O2 or Np molecules. Essentially, the theoretical solubility equation enables the parameter A(T), which gives the vibration entropy, and the parameter AH, which gives the energy of solution of a solute atom, to be estimated from the measured variation of solubility with temperature. The solutions treated are dilute enough to enable solute-solute interactions to be neglected so that the partial energy and excess entropy of solution E, and GS are not functions of composition and the configurational entropy is that of a random solution. Large positive values have been found for sxSu this quantity has not been given sufficient consideration in recent work on interstitial solutions and it is felt that the partial thermodynamic quantities of very dilute solutions should be understood before the thermodynamics of concentrated solutions can be fully appreciated. EXPERIMENTAL DATA 1) The Silver-Oxygen System. The measurements of Steacie and Johnson,= using silver foils, indicate that there is a pronounced minimum in the solubility vs temperature curve for O-Ag solutions. Eichenauer and Miiller6 have recently redetermined the solubility of oxygen in silver using a method developed in the investigation of metal-hydrogen systems.7 The solubility determinations were carried out on compact specimens of differing shapes and sizes and the results indicate a much lower solubility than was obtained by Steacie and Johnson with no minimum at 400°C. Subsidiary experiments showed that the erroneous results of Steacie and

Jan 1, 1964

By W. N. Hiatt

The mathematical theory of the flow of two-phase, incompressible fluid through porous media is clarified, and the development of a general fluid displacement equation for two-phase, incompressible vertical flow through porous media is outlined. The relationship between the three components of the equation — the "fluid drive effect", the "gravity effect", and the "capillary effect&apos;&apos; — is discussed, as well as implications of the analysis in connection with the study of certain types of petroleum reservoirs. INTRODUCTION The purpose of this paper is to clarify and summarize the mathematical basis of the theory of two-phase incompressible fluid flow through porous media, particularly as it pertains to vertical flow, and to present a qualitative* exposition of the controlling factors involved in circumstances where this type of flow may exist. Although the generally accepted theory of heterogeneous fluid flow through porous media was developed a number of years ago by Muskat,1 and Buckley and Leverett2, 3 using the basic premise of Darcy, (and since then expounded upon by many others) there is a need for an over-all summary and clarification of this theory, especially regarding certain types of applications in connection with so-called "gravity-drainage-type reservoirs". The source and derivation is outlined for what is referred to here as the "General Fluid Displacement Equation for Incompressible Vertical Two-Phase Flow through Porous Media&apos;&apos;. This equation would apply under the condition where the pressure drop along the path of flow is negligible in comparison with the pressure level on the system, or where compressibility and solubility effects are negligible. These conditions exist ordinarily in gravity-drainage-type reservoirs. Specifically, it will be shown that this general equation may be developed directly from the basic equations, which, according to present theory, govern the general case of viscous heterogeneous flow through porous media. This general equation has appeared in the literature previously, but in most cases its development from basic theory is not indicated clearly, or the equation is presented in terms of groups of constants and variables involving reduced or dimensionless quantities. This presentation is expedient in cases of experimental or computer applications; but it may make it difficult for the practicing petroleum engineer to identify all the factors involved or to understand the relationships between them. Therefore, in the following development, only ordinary mathematical parlance will be used, and no terms involving groups of other equations or reduced or dimensionless quantities will be used. DERIVATION The following equations for two-phase oil and gas flow result from analogy with Muskat&apos;s general equations,** if solubility and compressibility effects are neglected, and if all volumes are considered in terms of reservoir conditions, and the water phase, if present, is considered to be immobile (or effectively a part of the porous medium.) In this case, the sum of the oil and gas saturations may be taken as unity, and the saturation of each phase is in terms of the total hydrocarbon saturation. Note that in Eqs. 1 and 2, and in the derivation following, z is taken as positive in the vertically downward direction,

Jan 1, 1969

By Herbert H. Kellogg

Graphs representing the standard free-energy of formation as a function of temperature for 21 fluorides are presented, along with estimated values for the standard free-energy of formation of 20 atedadditional fluorides. A few of the many possible uses of these data in metallurgical calculations are discussed, including the fluorination of oxides, sulphides, metallurgicaland chlorides, and the reduction of metal fluorides. RECENT papers which have presented free-energy data for oxides, sulphides, chlorides, carbonates, sulphates, and silicates in the form of free energy vs. temperature plots,1-5 have found important uses in teaching and metallurgical development work. This method of presentation of thermo-dynamic data serves to make available in readily usable form thermodynamic constants which are scattered throughout the literature, and to show by graphical means the stability relations which exist between the compounds of a given type. It is certainly desirable to have these free-energy-temperature diagrams for as many types of compounds as are of present or potential use in metallurgical processes. Thus, even though there are but few uses of metallic fluorides in extractive metallurgy today, the potential uses of fluorine processes are of great importance and serve as the principal justification of this paper. Recent developments in the production of fluoro-carbons have resulted in vastly improved methods for the production and handling of fluorine and corrosive fluorides, with consequent reduction in costs.".&apos; The extractive metallurgist should no longer overlook possible fluorine processes when development of a new process for a relatively high unit-price metal is being considered. In a previous paperv he author outlined in some detail the importance and use of free-energy data in metallurgical calculations and also discussed the properties of a standard free-energy vs. temperature diagram. The same method of presentation is adopted in this paper, and the reader is referred to the earlier work for explanations of the use of free-energy data. Thermodynamic Data This paper presents standard free-energy vs. temperature diagrams, Figs. 1 and 2, for those fluorides for which the major thermodynamic constants are known. In the calculations of the standard free-energy of formation (AGO), values of the enthalpy of formation at 298°K (?Ho,) were taken from "Selected Values of Thermodynamic Constants"8 most of the values of standard entropy at 298°K (S°298) were taken from "Selected Values"," but in a few cases the values given by Kelley9 ere preferred; data for the Phase changes came from "selected Values" and several of Kellley&apos;s publics- tions;0-12 and most of the specific-heat data were taken from Kelley.l0 The appendix gives a detailed list of the sources of the data. As explained in an earlier paper,6 he accuracy of some of the standard free-energy relationships is not high. An error of +1 kcal at 1000°C is expected in most of the curves of Figs. 1 and 2. The error may be as high as +3 kcal in some of the curves. Rather than attempt to estimate the reliability of each curve, the source of the data used is reported in the appendix, and the reader may compare these data with newer values as they become available. Figs. 1 and 2 fail to show values for the fluorides of many important metals. In most cases this is because the entropy of the metallic fluoride is unknown. For preliminary calculations it is often useful to have available the best estimate of an unknown datum, rather than no information at all. With this in mind, Table I lists estimated standard free-energy values for a number of important metallic fluorides not included in Figs. 1 and 2. The values reported in Table I were, calculated by Brewer et al.13 and are based on estimated entropy values. The estimated uncertainty of the values for each fluoride were calculated from the uncertainty values given by Brewer1&apos; for ?H°, and the entropy function.

Jan 1, 1952

By Thorp D. Sawyer

In June 1914, one week before I was to be awarded my sheepskin in upper New York State, I received a telegram from New York City which read "Can offer you position as engineer in Chile at $115 a month contract for one year. (signed) Chile Copper Co." That night, Friday, I took a sleeper to New York and arrived at the Guggenheim Brothers&apos; company office at 165 Broadway, just as it was opening up on Saturday morning. Saturday was no holiday in that era. Presenting the telegram at the office, I was ushered into a sub-executive&apos;s office and shown a mimeographed contract which 1) agreed to pay me $115 per month from the date of leaving New York until I returned, and with travelling expenses both ways, 2) fixed a charge of $46 per month for board and lodging in company quarters, and 3) stipulated a contract term of one year with the right to retain my services for another year if the company so elected. While a bit huffed at the year&apos;s "kicker" I nevertheless accepted. I was then told to prepare to leave the following Wednesday (June 17) on a United Fruit Co. steamer for Panama. Objecting that I still had to receive my degree on the 17th and had planned a vacation in Ohio for a week or so…

Jan 12, 1960

By B. Ball, D. W. Fuerstenau, P. C. Kapur

A two-phase distributed-parameter model of the flotation process has been extended to allow consideration of the important process parameter, concentrate grade. A simple expression is presented for the grade of concentrate in terms of the zeroth and first moments of the concentrate distribution. An example is given for a binary ore containing two pure minerals each having nondistributed rate constants. For extend-ing the model to the distributed rate constant case, a cubic polynomial zoas utilized to simulate the feed distribution. One particular example is considered and grade-recovery curves are generated to show the dependence of such curves on the initial feed distribution. Operating flotation plant engineers have traditionally evaluated plant performance in terms of the recovery of valuable mineral and the grade of the concentrate. In both operation and research, grade-recovery relationships have been used as a guide for selecting flotation conditions. Weissl illustrated the use of grade-recovery curves in plant operation and considered the grade-recovery relationship to be a metallurgical one. The extensive experimental work of Chi" using standard batch flotation tests on iron ores shows that, even with extensive statistical correlation of data, little insight can be gained into the basic fundamentals of these relations. Such relations must depend on the kinetic behavior of the various mineral species in the flotation circuit. In his flotation text book, Gaudin3 considered the relationship of recovery and of product grade to flotation kinetic indices, but he did not extend his calculations to yield grade-recovery relations. Although Gaudin used a simplistic model for his analysis, he did recognize that variations in flotation rates must result from variations in locking, surface heterogeneity, particle size and shape, among other things. In a recent paper,&apos; we presented a model of the flotation process that could be readily analyzed with an analog computer. This model combines the concept of a distributed set of rate constants"" with that of the two-phase flotation model,8" resulting in a model more powerful and flexible than previous ones. The purpose of the present paper is to show how this model can be used to generate grade-recovery curves and to determine the dependence of such curves on the various kinetic parameters. In this paper, the model will be limited to the semi-batch case, but extension to the continuous case is a straightforward step.

Jan 1, 1971