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By C. K. Eilerts

Finite difference equations were programmed and used to integrate the second-order, second-degree, partial differential equation with variable coefficients that represents the transient linear flow of gas-condensate fluids. Effect was given to the change with pressure of the compressibility factor, the viscosity, and the effective permeability and to change of the absolute permeability with distance. Integrations used as illustrations include recovery of fluid from a reservoir at a constant production rate followed by recovery at a declining rate calculated to maintain a constant pressure at the producing boundary. The time required to attain such a limiting pressure and the fraction of the reserve recovered in that time vary markedly with properties of the fluid represented by the coefficients. Fluid also is returned to the reservoir at a constant rate, until initial formation pressure is attained at the input boundary, and then at a calculated rate that will maintain but not exceed the limiting pressure. The computing programs were used to calculate the results that would be obtained in a series of back-pressure tests made at selected intervals of reservoir depletion. If effect is given to the variations in properties of the fluid that actually occur, then a series of back- pressure curves — one for each stage of reserve depletion — is required to indicate open-flow capacity and related flow characteristics dependably. The isochronal performnce method for determining flow characteristics of a well was simulated by computation. INTRODUCTION The back-pressure test procedurel is based on a derivation of the equation for steady-state radial flow of a gas, the properties of which are of necessity assumed to remain unchanged in applying the test results. The properties of most natural gases being recovered from reservoirs change as the reserve is depleted and pressures decline, and the results of an early back-pressure test may not be dependable for estimating the future delivery capacity of a well. The compressibility factor of a fluid under an initial pressure of 10,000 psia can change 45 per cent and the viscosity can change 70 per cent during the productive life of the reservoir. There are indications that the effective permeability to the flowing fluid can become 50 per cent of the original absolute permeability before enough liquid collects in the structure about a well as pressure declines to permit flow of liquid into the well. The advent of programmed electronic computing made practicable the integration of nonlinear, second-order, partial differentia1 equations2.3 pertaining to flow in reservoirs. Aronofsky and Porter4 represented the compressibility factor and the viscosity by a linear relationship, and integrated the equation for radial flow of gas for pressures up to 1,200 psi. Bruce, Peaceman, Rachford and Rice5 integrated the partial differential equations for both linear and radial unsteady-state flow of ideal gas in porous media. Their published results were a substantial guide in this study of integration of the partial differential equation of linear flow with coefficients of the equation variable. The computing program was developed to treat effective permeability as being both distance-dependent and pressure-dependent. In this study all examples of effective permeability are assumptions designed primarily to aid in developing programs for giving effect to this and other variable coefficients. The accumulation of data for expressing the pressure dependency of the effective permeability is the objective of a concurrent investigation. FUNDAMENTAL DIFFERENTIAL EQUATIONS DIFFERENTIAL EQUATION OF FLOW Linear transient fluid flow is represented by the partial differential equation,

Jan 1, 1965

By Lincoln F. Elkins

The Spraberry Trend Field of West Texas was discovered in January, 1949. Drilling of 2.234 wells and production of some 45 million bbl of oil by January, 1953, indicated this to be an important field which will ultimately cover more than 400,000 acres. In addition to being the world's largest field in areal extent, the Spraberry has presented many problems in well completion and operation and has demonstrated unique reservoir performance characteristics. The pay section consists primarily of a few fine grained sandstone or siltstone members in a thousand-ft thick section of shale, limestone. and siltstone. Since porosity averages only 10 per cent and nearly all permeabilities are less than 1 md, conventional core analysis does not delineate the "pay" section. Mercury injection was used as a capillary pressure test adaptable to rapid routine use to select those intervals having low enough connate water saturation to contain commercially significant oil saturation. In the central area of the field this "pay" amounts to 16 ft of Upper Spraberry and 15 ft of Lower Spraberry sands. An interconnected system of vertical fractures, observed in cores, provides the flow channels for oil to drain into the wells hut most of the oil is stored in the matrix since the void volume of fractures is estimated to be less than 1 per cent of that in the sand. Initial potentials of wells range up to 1.000 B/D after fracture treatment which should be compared with estimated capacity of 5 to 10 B/D if oil had to flow into the wells through the sand itself. Without exception initial pressures of later drilled wells were significantly lower than initial pressures of earlier drilled nearby wells in a large area some 6 miles long. This means the earlier drilled wells had drained fluids from areas much greater than their 40-acre proration units. Since most of this performance occurred while the reservoir pressure was above the. saturation pressure it was analyzed by the compressible fluid flow theory. This analysis gave calculated initial presrilres which agreed within 30 psi of measured pressures of 60 per cent of wells in the area using 16-md permeabilitv corresponding to a fracture system substantially that indicated by cores and using combined compressibility of rock and its contained oil and water corresponding to the core analysis data. The most important feature of this analysis was the very close agreement between effective compressibility of the rock and its contained oil and water from the field performance and that from the core tests, because it meant there are no "islands" of low permeability reservoir rock left untapped in the inter-well area and thus no additional wells are necessary to insure that at least one well penetrates each "reservoir." Twenty-five of forty-four 40-acre spaced wells on three contiguous sections were wed in a four-month inteference test. Six shut-in well. were tested monthly for oil production. productivity index. gas-oil ratio and pressure buildup, and seven shut-in wells were tested for decline in reservoir pressure. Tests on 12 regularly producing wells gave comparative data for interpretation of shut-in test wells. Reduction in reservoir pressure, decline in productivity index. and increase in gas-oil ratio were found to be substantially the same in the shut-in test wells as those in the comparative regularly producing wells, meaning that the producing wells were depleting the

Jan 1, 1953

By C. S. Smith, W. M. Williams

THE quantitative study of grain shape in three dimensions has been a difficult one from the practical standpoint. Experiments on grain shape have usually been based on indirect observations of two-dimensional metallographic samples or on grains separated by intergranular corrosion or fracture. The latter method was used in particular by Deschl in 1919 in observing the shapes of ß-brass grains which had been separated with mercury. The similarity in detail of shape and packing that exists between bubbles in a soap froth and metal grains was noted by Desch who remarks that: "Surface tension has an. important share in determining the form of the crystal grains in a solidifying metal and such grains have a tendency to assume the shape of foam cells." More recently the relation between grain shape and grain growth has been studied by Harker and Parker.' The importance of surface tension forces in determining microstructure has been discussed by Smith," and an analysis of the topologi-cal rules that apply to such structures has been made by the same author.' Biologists have made valuable contributions to the general problem of shape and form in an assembly of space-filling cells subject to surface tension forces. Particular mention must be made of the extensive researches of Lewis5,8 on botanical and anatomical tissues, and Matzke and Nestler,7,8 who have made painstaking studies of bubble shapes in different kinds of foam. The present paper introduces a new method of studying individual grains in particular alloys—a method which may well find use in other metallurgical researches, and which seems also to be applicable in biological problems. Metal Grains in Three Dimensions The individual grains in a piece of metal or the bubbles in a soap froth must satisfy two conditions —they must be in juxtaposition so as to fill space and their interfaces must conform to the laws of surface tension. If a further restriction is imposed, namely, that only one type of polyhedron be used, then the sole possibility is an assembly of "minimal" tetrakaidecahedra," each polyhedron having eight doubly-curved hexagonal faces and six plane quadrilateral faces, the angles between adjacent faces being 120". Such cells could be stacked on a body-centered cubic lattice and would be quite stable. For many years it was believed that soap bubbles actually possessed the shape of this ideal body, and the hypothesis was the starting point for several investigations on the shapes of soap bubbles, biological cells, and metal grains. These investigations have shown, what might have been obvious in the beginning, that if the condition of symmetry is relaxed the tetrakaidecahedron is almost never found. If we retain only the rule that all contacts should be in local surface tension equilibrium and that the assembly should fill space, metal grains may then take a nearly infinite variety of shapes and no single one may be regarded as an archetype. These two conditions, which are fully discussed in one of the previously mentioned papers,' lead us to think of a typical grain in an annealed metal as having the following characteristics: 1—A grain may have any number of faces, but usually between nine and eighteen. The faces (each of which is, of course, shared by two grains in the assembly) may have any number of edges, but usually between four and six. Pentagons are by far the most frequent. 2—In the assembly of grains each edge is shared by three faces and by three grains. Each vertex is a point shared by four grains, six faces, and four

Jan 1, 1953

By R. G. Davies, R. H. Richman

Several techniques, X-ray diffraction, transmission electron microscopy, conventional, metallography, and mechanical property measurements are combined to investigate decomposition in the suPersaturated solid solution Fe-27 at. pct Be. The following sequence of structures for aging temperatures below 400°C is established: massive short-range order, pseudo-FeBe (L2o) order, Fe3Be (DU3) order, sinusoidal modulation of composition, general or continuous precipitation, and discontinuous or cellular precipitation. In addition to this sequence itself, several features of the individual stages are noteworthy; for example, when coherent modulations occur, their development is parallel to (100) everywhere in the specimen apparently without incubation, and both the wavelength and the composition amplitude of the modulations increase with aging time. Two types of discontinuous reaction are observed, depending upon the aging temperature. At low temperatures (<550°C) the boundary-nucleated variety of discontinuous precipitate predominates; but at higher temperatures (>600°C) the crystallographic variety occurs instead. Hardness and flow-stress measurements clearly reflect the quoted structure sequence. Some qualitative aspects of the structure changes and of the relationship between mechanical properties and structure are discussed. BERYLLIUM in solid solution markedly strengthens iron.&apos;" A recent study demonstrated that not only were supersaturated single crystals of Fe-27 at. pct Be very strong, but they deformed primarily by mechanical twinning.3 Such behavior, coupled with the decrease in solid solubility of beryllium in a Fe from about 33 at. pct at 1165°C to about 10 at. pct at 500°C4 as shown in Fig. 1, leads naturally to questions about property changes with aging in this system. In 1929 roll,1 and later Seljesater and Rogers,5 reported that useful increases in strength could be obtained by aging quenched Fe-Be alloys, but it was not until quite recently that any of the details of precipitation in these alloys were studied. Richman6 observed that both an Fe3Be superlattice (with a DO3 crystal structure the same as Fe3A1, illustrated in Fig. 2) and a modulated structure preceded the appearance of a discrete second phase in the 20 at. pct Be composition. Here, a modulated structure refers to a periodic composition fluctuation within one crystal, while its lattice remains coherent. Subsequent work on a Fe-Be alloys by Heubner7 and von Heimendahl and Heubner8 confirmed the existence of the modulated structure, although only an FeBe (L20) ordered structure was detected (also shown in Fig. 2). Both Rich-man and Heubner corroborated the large increases in hardness during aging reported earlier, but other mechanical properties were not examined. Since modulated systems are encountered relatively infrequently, the influence of coherent modulation upon mechanical properties is not well-known. With the accumulation of information about age-hardening systems, it has become clear that many precipitation reactions cannot always be described by the concept of heterogeneous nucleation at some lattice discontinuity followed by diffusional growth. Rather, complex sequences involving prior "preparation" of the matrix are quite common; that is, a transition structure occurs in the parent phase, instead of in some "nucleus" form. Delineation of such subtle sequences appears to be a worthwhile step toward the understanding of solid-state precipitation. Since not many structural progressions of comparable nature have been reported, the objectives of the present survey are to identify and elucidate the various

Jan 1, 1967

By M. E. V. Plummer, F. E. Beamish, J. C. Hole, J. M. Kavanagh

Prior researches have shown that the iron-copper-nickel content of platinum concentrates may be reduced by carbon to form a collecting alloy for the platinum metals in a manner exactly analogous to the formation of the lead fire assay button. The nature of the iron-copper-nickel alloys with the platinum metals has been investigated. Palladium and probably some of the other platinum metals form solid solutions with this alloy. ONE of the greatest known reserves of the platinum metals is to be found in the nickel, copper, iron sulphide deposits of Northern Ontario. The very large tonnage of copper-nickel ore processed makes the Sudbury district a significant world source of the platinum metals, the latter being recovered as byproducts in the electrolytic refining process for copper and nickel. Chalcopyrite, pentlandite, and pyrrhotite are carriers of the platinum metals;&apos; these minerals contain from 0.03 to 2.0 ppm of the noble metals. The analysis of the above ores for the platinum metals necessitates an initial concentration of the minute quantities present in the ore. The method usually employed involves the extraction of the noble metals by molten lead with or without small proportions of silver. The lead is then separated from the precious metals by cupellation, a process which involves absorption by the cupel and volatilization of lead oxide, leaving the precious metals collected in a silver bead on the surface of the cupel. The collection by lead is probably achieved by a process of dissolution followed by some degree of segregation in the lead alloy since the cold button is seldom uniform in composition. With silver-lead alloys this process of liquation has been used to re- cover pure lead since, during the cooling period, crystals of pure lead separate and silver becomes concentrated toward the center of the solid.&apos; Platinum and gold liquate in a manner similar to silver which may account for the successful recovery of platinum by fire assay even though it is considered insoluble in a solid lead medium. 3 In the case of iridium the liquation process may be a disadvantage in that the iridium may appear in the outer areas of the button and thus be lost mechanically during the handling processes. In any case the deficient alloying characteristics of lead for the platinum metals encouraged attempts to find an improved collecting alloy, and by analogy with aqueous extractions, preferably one in which solid solutions would be readily formed. Since, beyond a certain minimum solute to solvent ratio, the formation of a solid solution is accompanied by a lattice distortion, one would expect some relationship between the atomic diameters of any two metals and their tendency to form a solid solution. In one survey5 the hypothesis was put forward that when the atomic diameter of the solute differs by more than about 15 pct from the solvent, the "size factor" is unfavorable and the formation of a solid solution is restricted. On the other hand, when the atomic diameters are within this limit the size factor is favorable and solid solutions are readily formed, e.g. the transition metals of Group VIII having similar radii form solid solutions over wide ranges of composition.6 Even with a favorable size factor, elements having different crystal structures cannot form a continuous series of solid solutions. Cell dimensions alter as the concentration of the solute increases, causing a

Jan 1, 1962

By Robert E. Green

Experiments were performed in order to investigate the influence of magnitude of driving force, recouery, and previous heat treatment on grain boundary migration in deformed aluminum crystals. The frequency of occurrence of strain-free grains possessing Preferred crystallographic orientations was studied both as a function of heat treatment and as a function of amount of deformation of the matrix crystal. Aluminum of such composition as to exhibit precipitation-hardening behavior was used. CONSIDERABLE work has been devoted to the factors influencing grain boundary migration in metals.1&apos;52 Aust and Rutterl-9 have studied grain boundary migration into matrix crystals containing a striation substructure, which provided a thermally stable driving force during the course of the migration experiments. These authors state that, while variations in the striation pattern were sometimes observed, it was possible to obtain reasonably uniform and reproducible striation structure by careful control of the solidification conditions. Admittedly, this source of driving force is a unique one and has served well in numerous experiments. However, although the striation substructure provides a thermally stable driving force, the subject of its reproducibility from crystal to crystal is questionable. In fact, Aust and Rutter3 attribute the scatter shown in some of their experimental points and several anomalies in boundary migration rates to variations in the substructure driving force along a single specimen. A further limitation on striation-induced driving force is that the driving force cannot be varied over wide ranges in a controlled manner. More often used as a source of driving force is the strain energy stored in a crystal during plastic deformation. This type of driving force has the disadvantage that it is not thermally stable due to recovery taking place simultaneously with the grain boundary mobility measurements. On the other hand, this strain-induced driving force is very reproducible from crystal to crystal since it is very easy to grow single crystals possessing the same purity and crystallographic orientation and then to strain them identically. In order to measure grain boundary migration rates two different methods are primarily used. Most often the technique employed is the heat-cool-etch method1&apos; which involves thermal cycling, while the other technique, developed by Graham and Cahn11 using an X-ray diffractometer and goniometer furnace, involves continuous heating only. Thus the influence of thermal cycling vs continuous heating is a factor to be considered in grain boundary migration rate measurements, particularly in cases where the source of driving force is the strain energy stored in the deformed matrix, and recovery is likely to occur. Numerous recent investigations have shown that extremely small impurity additions to zone-refined metals exert a marked effect on grain boundary migration rates1-5, 9, 12-27 and a few have considered the effect of the distribution of impurities.28-35 The concentration of impurities and their distribution as influenced by heat treatment must also be taken into account in migration-rate studies. In the present article consideration is given to the influence of the magnitude of driving force, recovery, and previous heat treatment on grain boundary migration rates. In order to vary the driving force over a large range it was necessary to use as a source of driving force the energy stored in the matrix crystal during plastic deformation. A majority of the investigations were performed on aluminum specimens which were of such compositions as to exhibit precipitation-hardening behavior.

Jan 1, 1965

By A. T. Chatas

A description of the geometrical characteristics of spherical reservoir systems, a discussion of unsteady-state flow of such systems and examples of engineering applications are presented as backgmund material. The fundamental differential equation, a description of average spherical permeability and the introduction of the Laplace transformation serve as theoretical foundations. Engineering concepts are investigated to indicate particular solutions of interest, which are analytically obtained with the aid of the Laplace transform. These are numerically evaluated by computer, and presented in tabular form. INTRODUCTION A tractable mathematical analysis of unsteady fluid flow through porous media generally requires incorporation of a geometrical symmetry. The simplest forms include the linear, cylindrical (radial) and spherical. Most analytical endeavors have concentrated on cylindrical symmetry because it occurs more often in petroleum reservoirs. Nevertheless, some reservoir systems do exist that are better approximated by spherical geometry. Review of technical literature revealed but a single reference to unsteady spherical flow in petroleum reservoirs.l The motive and purpose of the present work was to remove this gap in technical information, and to provide the practicing engineer with some useful analytical tools. The mathematical details associated with the particular solutions of interest involved use of the Laplace transformation. Hurst and van Everdingen previously demonstrated the efficacy of this operational technique, and in many respects the present treatment was patterned after their earlier work.2 PRELIMINARY CONSIDERATIONS GEOMETRICAL CHARACTERISTICS Geometrically, a spherical reservoir system is defined at any instant of time by two concentric hemispheres whose physical properties of interest vary only with the radial distance. Every physical property is thus restricted to be a space function of only one variable: the distance along a radius vector emanating from the center. Such a system is composed of an outer region and an inner region, separated by a defined internal boundary. The inner region simply extends inward from this boundary, whereas the outer region extends outward from it to an external boundary. The position of the internal boundary is presumed fixed, so that the size of the inner region remains constant. On the other hand, the position of the external boundary at any given instant of time is determined by the distance into the system that a sensible pressure reaction has occurred, Thus, the external boundary may change position with time. It initially emerges from the inner region and advances outward to its ultimate position. When this ultimate position coincides with a geometric limit, the reservoir system is said to be limited. When it coincides with points subject to pressure gradients furthest removed from the internal boundary, yet short of a geometric limit, the system is said to be unlimited. In this investigation two different boundary conditions are imposed at the ultimate boundaries of limited systems. The first requires that no fluid flow occur across this boundary; the second that the pressure remain fixed at this boundary.3-5 UNSTEADY-STATE FLOW In a strict sense virtually all flow phenomena associated with a reservoir system are unsteady-state. The transient behavior of these phenomena requires accounting, however, only when time must be introduced as an explicit variable. Otherwise, steady-state mechanics may be used. Analytically, steady-state conditions prevail in a reservoir system only over that portion of its history when this relation is satisfied:

Jan 1, 1967

By B. Ramaswami, U. F. Kocks, B. Chalmers

This paper describes the tempetrature, solute (gold), and orientalion dependence of the plastic rleforlirnlion of silver single crystals. The virgin flow stress, To, and its temperatutre dependence incrense with increase in solute concentration. el decreases with decrease in temperature below room teiirperature and with increase in solute coucentralion. The dependence of 011 on temperature arid solute sontenl is due to the dependence of Ts on the two variables. An increase in ts, due to either the temperature or the solute conlent, results in a decrease of e11 in crystals of single-slip orientation and an increase of 011 in crystals of&apos; (100) find (111) orientation. is orientation-dependent and at all the temperatures and in all the materials studied. The Leveling off of the engineering stress-strain curve in crystals of (100) 07-ientotion at a stress tl, is associated with extensive cross slib. The temperature and strain -rate dependence of tl are similar to those of indicating that a rate process is the cause 01 this phenomenon. The plastic deformation of silrer crystals of (110) orientation is multiple to that of crystals of single-slip orientation. THE work hardening of fcc crystals has been the subject of intensive investigations in the past 15 years. The effect of orientation, deformation temperature, solutes, second phase or precipitates, strain rate, etc., has been studied in a number of fcc metals.&apos;-5 In spite of the considerable amount of work reported on the dependence of work hardening on the orientation, temperature, and solute concentration, certain aspects of the plastic deformation of fcc crystals have not been clarified. For instance, with the exception of a few investigations,6-8 where crystals of multiple-slip orientations have been studied, almost all the studies have been on crystals of single-slip orientations. Hence, a major portion of this study has been devoted to the dependence of plastic deformation on the multiplicity of slip systems and the enhanced possibility of dislocation interactions resulting from such multiplicity. Further, the abnormally low rate of work hardening observed at large strains at certain temperatures in crystals of the (100) orienta-tion 6-8has not been explained satisfactorily. It is the aim of this study to clarify this aspect of the orientation and temperature dependence of the plastic deformation of fcc single crystals. The work-hardening characteristics of single crystals of aluminum of ( 110) orientation have been studied at room temperatur "&apos;12 and above." They have not been studied at temperatures where the virgin flow stress is dependent on temperature or where, in Seeger&apos;s terminology is important. The work hardening of single crystals of (110) orientation is of interest for another reason. As shown in Table I, the dislocation reactions that are possible in the (110) orientation are similar in certain respects to those that are possible in the (100) orientation. Hence, the deformation of single crystals of silver of (110) orientation was studied in the temperature range 100° to 900°K at intervals of 200°K. The effect of solute concentration on the plastic deformation of fcc single crystals of single-slip orientation has been studied by several investiaators.> In all of these investigations—with the exception of Ref. 20—single crystals of identical orientation have not been used, with the result that the orientation dependence of plastic deformation is superimposed on the effect of the solute. In addition, the effect of the solute on the work-hardening characteristics of single crystals of multiple-slip orientations has not been studied by the previous

Jan 1, 1965

By A. L. Labbe, J. J. Donoso

Hard-won experience in the operation of smelting plants has pointed the way to the most efficient design and economical operation of a baghouse system for recovery of metallurgical fumes. This paper treats of the principles governing bag filtration and the factors most directly affecting bag life. Methods for temperature conditioning of smoke previous to filtering are described and the evolution of bag shaking mechanisms is brought up to date. THE history of the bag filter process, as applied to the recovery of metallurgical fumes, goes back to 1876, when the Lone Elms Works of Joplin, Missouri, erected a two-section baghouse for filtering fumes from Scotch Hearth lead smelting furnaces. By modern standards this installation was crude, but the basic operating principles remain essentially the same today. Great progress, however, has been made in the mechanization of the process by the use of devices for mechanically and automatically cleaning bags of adhering fumes, in the use of instruments for recording and controlling the variables affecting baghouse operation, and in the conditioning of the smoke previous to filtering. The principles governing bag filtration of fumes were investigated in 1929 by A. J. Seitz of American Smelting and Refining Co., and he arrived at the following conclusions: 1. Pressure on Bags at Constant Volume: The rate at which the pressure builds up in a bag with constant volume is directly proportional to the time, with the same kind of smoke and dust burden (fig. 1). 2. Pressure on Bags for Change in Volume: With equivalent smoke and dust burden, the bag pressure increases with the square of the increase in volume. The rapid increase in pressure is due to (1) increase in volume, (2) increase in amount of dust on the bag, and (3) more intense packing of the dust at higher velocity (fig. 2). 3. Effect of Intensive Filtering on Pressure: Since the pressure builds up directly as the square of the volume, with the same smoke and dust burden, it is necessary to shake the bags in that increased ratio, and vigorously, to keep the pores of the bag open and pressure down. This increases the wear on the bags and the dust losses. 4. Effect of Shaking on Dust Losses: The losses are in direct proportion to the frequency of shaking because the loss takes place immediately after shaking, before the bag seals itself. Tests show that with hand shaking the last 20 pct of the removable dust requires seven times more shaking per unit weight of dust than the first 80 pct. 5. Effect of Fineness of Dust on Losses: The fineness of the dust particle increases the loss in two ways: (1) When the bag is clean a greater percentage of it will pass through before the bag seals itself; (2) fine material penetrates farther into the bag pores, building up pressure faster and necessitating more shaking, thereby increasing the loss. The physical principle of operation of the bag filter is simply the separation of solids from a gaseous carrier through a porous medium, and is analogous to the filtration of solids from liquid carriers. Basically, the mechanics of the process are as follows: Fume-laden gases drawn from the operating fur-

Jan 1, 1951

By Allen F. Agnew

Detailed stratigraphic studies in the Wisconsin-Illinois-Iowa district have made it possible to map the folds and faults that controlled the deposition of the zinc-lead ore. Prospecting on the basis of this mapping and prospecting in lower zones that are potentially ore-bearing have led to discoveries of ore. GEOLOGIC studies for the Federal and State governments in the Wisconsin-Illinois-Iowa zinc-lead district were begun in 1835, and subsequent surveys were made in the three states at intervals until 1916, see Table I. The current study of the district, Fig. 1, by the U. S. Geological Survey was begun in 1942 in the hope that a systematic investigation would help increase production of zinc and lead, then in extremely short supply. Major emphasis of the USGS program was on detailed mapping of the geologic structure and ore deposits. Preliminary maps and reports covering localities of intensive mining activity have been published during the course of this study, Fig. 2. By 1950 the objectives of the study by the USGS were revised; 71/2-min quadrangles of relatively unprospected localities as well as intensively mined localities are now being mapped in Wisconsin. Since 1945 the investigation in Wisconsin has been made in cooperation with the Wisconsin Geological and Natural History Survey, and since 1951 the geologic mapping of areas of particular interest in Iowa has been performed in cooperation with the Iowa Geological Survey. At intervals since 1943 the Illinois State Geological Survey has mapped the geologic structure and ore deposits of localities in the Illinois part of the mining district, see Fig. 2. Geology was applied by mining company personnel as early as 1853, but only sporadically, with periods of greater application between 1890 and 1925. Much of the so-called geologic work was in reality mining engineering. Since 1946 the major mining companies in the district have employed geologists who have successfully applied geologic techniques in the search for ore. History of Mining Occurrence of galena in the district was known as early as 1658 or 1659, when French explorers heard of lead mines that were apparently in the vicinity of Dubuque, Iowa. In 1690 a trading post was established near Dubuque to obtain galena. The first significant attempt at mining by white men took place in 1788 when the Indians granted to Julien Dubuque mining rights for 20 miles along the west side of the Mississippi River, including the vicinity of Dubuque, Iowa. By 1805 lead was being mined near Galena, Ill. In 1819 permanent settlement of the region was begun, and most of the important lead-producing areas had been found by 1830, see Fig. 3. Lead production in the Wisconsin-Illinois-Iowa district between 1830 and 1871 far exceeded that of any other district in the U. S.&apos; Smithsonite was first mined in 1859, and sphalerite was mined as early as 1867. After 1873 the production of sphalerite exceeded that of smithsonite. In 1873 annual zinc production from the district first equaled lead production, and from then until 1893 production of zinc and lead was roughly the same. Since 1893 the ratio of zinc to lead mined has generally ranged between 5:l and 20:l. In 1942 the Wisconsin-Illinois-Iowa zinc-lead district ranked 14th among zinc-producing districts of the U. S. From 1946 until February 1953 the dis-

Jan 1, 1956

By William R. Barton

Iron and steel slag represent man&apos;s most successful attempt to date to profitably utilize a solid waste. Its consumption represents a solution to a solid waste problem and also represents tonnage of natural aggregates that will not have to be mined with concomitant disturbance of the land. Slag has been produced as long as iron has been made; but until a little more than 50 years ago, it was mostly a waste product to be disposed of with as little effort and cost as possible. Huge piles of waste slag were generated over the years of iron and steelmaking. Sporadic use was found for small amounts starting with slag (from Catalan forges) used for road bases by the Roman Empire. The first recorded sustained commercial use was, as is often the case in man&apos;s history, for making war. Some profit- conscious munitions maker in the 16th century realized that he could make cannon balls of slag instead of the more precious iron. Other small-volume uses gradually developed: cast building blocks, slag-lime mortars and cements, slag wool, ballast, road base, and, finally, in concrete. But it was not until after World War II that the true potential of blast-furnace slag as a construction aggregate was really recognized. Now nearly all blast-furnace slag produced is used, and much of the earlier stock- piles in the U. S. have been reduced or entirely consumed. Steel slag for aggregate use has been in commerce for only the past 10 years, and use has increased rapidly (10-50% per year) during the past 5 years as blast-furnace slag supplies became depleted. However, much remains to be accomplished in determining character and optimum conditions of use for various types of steel slags before such slags will realize their full use potential. Although slag represents only 2% of construction aggregate materials used in the U.S., its production involves certain features that make its production record far more important than national tonnage figures would indicate. Its source is in iron and steel production and concomitantly slag availability is restricted to those areas where iron or steel is produced. In such areas, it often represents one of the principal aggregates marketed and, because of special properties that make slag a selected aggregate for certain uses, the tonnage imbalance may be overcome by the importance of its contribution to quality or special characteristics of end products. The location and number (Fig. 1) of slag plants handling this annual production is governed by the geographic makeup of the iron producing industry. Prior to the period marked by World War 11, most blast furnaces were in the Great Lakes area-Pittsburgh, Cleveland, Chicago, Gary, Buffalo, Detroit, Youngstown, and Toledo, with exceptions at Baltimore, Bethlehem, and Birmingham. Since that time, iron and steel facilities have been established in Texas, Utah, and California. Today 85 slag plants in 15 states provide employment for almost 2000 persons. The slag plants also recover almost 4 million tons of slag-encrusted iron each year for return to the blast furnaces. Much of the success in developing uses for slag can be attributed to the efforts of the National Slag Association founded in 1918. Since then, it has conducted numerous field and laboratory investigations to demonstrate the properties and uses for slag and slag products. These investigations have resulted in total recognition of blast-furnace slag as a construction material of consequence. The American Society for Testing & Materials Designation C125 recognizes blast-furnace slag as "the nonmetallic product consisting essentially of silicates and aluminosilicates of

Jan 1, 1975

By A. W. Bethune, L. M. Pidgeon

The equilibrium vapor pressure of zinc has been determined over the systems: ZnS(s) + Fe(s) = FeS(s) + Zn (vapor) and ZnS(s) + 2Cu(s) = Cu2S(s) + Zn (vapor) by reacting the components in an evacuated tube containing a thin copper fiber, and allowing equilibrium to be established with respect to the brass formed and the zinc in the vapor phase. The composition of the brass formed was determined and equilibrium vapor pressure values obtained from existing data. Between 850&apos; and 1000°C, values for the first reaction ranged from 8 to 58 mm Hg; for the second reaction from 1.8 to 22 mm Hg. THE direct reduction of metallic sulphides may be indicated by an equation of the form MS + X = XS + M [1] where X is some suitable reducing agent. In the case where M is a metal of relatively high volatility, the use of vacuum will displace the equilibrium to the right at comparatively low temperatures in the face of the usually unfavorable thermochemistry. For this technique to be feasible, MS, X, and XS, must of course be nonvolatile compared to M. In this regard, zinc becomes an obvious metal both from the point of view of its volatility and the fact that most commercial ore deposits of this metal occur as the sulphide, and its direct reduction would avoid the expensive roasting process necessary prior to present day reduction methods. Two reducing agents are of interest, namely copper and iron, with the former having the added attraction of being relatively easily regenerated by oxidation in the copper converter. The possibility of these reactions has been considered before. Imbert1 patented a process whereby zinc sulphide was reduced by either copper or iron. The process as described took place at atmospheric pressure and, at the high temperatures required, the system was molten, resulting in the formation of a matte with the consequent reduction in the activities of the reactants. Peterson2 did further experimental work on these reactions and, although promising results were obtained on a small scale, attempts to increase the size of the furnace led to excessive "blue powder" formation. The early workers failed to realize the large reduction in temperature afforded by the use of vacuum and its desirable results. More recently, the direct reduction of zinc sulphide by iron has been the subject of a thermody-namic investigation by Kelley,3 and Gross and War-rington&apos; have studied the kinetics of the reaction in the temperature range 900" to 1000°C, their experiments being conducted using vacuum and indicating that the reaction would proceed practically to completion in 1 to 3 hr, depending on the temperature. A qualitative examination of the system ZnS-Cu carried out at this University indicated that 98 pct of the theoretical zinc in the charge could be recovered in 1 hr at 1000°C when operating under reduced pressure. The purpose of this research program was to study the equilibrium of the two reactions. During the investigation, reference to the experimental work of Schenk5 was found but, due to lack of detail in the report, it was felt that it would be desirable to continue the equilibrium measurements. Selection of Method The measurement of vapor pressure of metals presents obvious problems resulting from the high temperatures which must be employed. In the present case, the production of the "reaction pressure" introduces a further difficulty since a chemical reaction must proceed before any metal vapor pressure is produced, resulting in depletion of the re-

Jan 1, 1954

By E. Hein, R. A. Dodd

The fatigue softening of prior strain-hardened poly crystalline copper has been determined by measuring changes inflow stress resulting from fatigue treatments. Tensile fatigue does not soften the metal, while the softening due to reversed stress fatigue depends on the extent to which fully reversed stressing is approached. True tensile fatigue is shown to be possible only in the case of long wire specimens. Annealing following fatiguing of strain-hardened metal shows that tensile fatigue is very effective in modifying normal recovery and recrys-tallization. OBSERVATIONS by Ludwik and Scheu,&apos; Kenyon,&apos; Polakowski and Palchoudhuri, Kemsley, and Broom and Ham,596 have shown beyond doubt that strain-hardened metals are softened by reversed-stress fatigue. To some extent the softening might be associated with a rearrangement of dislocations, but the results of Broom and Ham5 on the temperature dependency of the fatigue hardening of annealed copper, and those of McCammon and Rosenberg7 on the partial recovery at 100&apos;C of fatigue-hardened copper suggest that point defects may be involved. Since lattice vacancies are the only species of point defect present in appreciable quantities in thermody-namic equilibrium, most attention has been accorded them in the various theories advanced to explain hardening and softening effects resulting from fatigue. Precise mechanisms remain uncertain, and while some effects may be due to single vacancies, defects arising from vacancy clusters may also contribute to the changes in properties. All types of plastic deformation result in point-defect formation, one frequently invoked formation mechanism involving the nonconservative motion of jogs formed by the intersection of, for example, mixed dislocations. But since fatigue deformation is thought to be a particularly effective way of forming point defects, additional mechanisms peculiar to fatigue must be sought. One possibility is that jogged loops contract during the unloading cycle to give rows of vacancies. A local high-vacancy concentration could conceivably promote polygonization and recovery by climb, and, therefore, could explain the fatigue softening of strain-hardened metals under appropriate conditions of temperature. Conversely, the experiments by Broom and Ham6 on the fatigue hardening of copper single crystals involving subsequent tensile testing of previously fatigued specimens, resulted in the observation of distinctly lowered yield points. This could be due to vacancy atmospheres associated with dislocations, possibly augmented by jogs on dislocations. In addition to the yield-point phenomenon, a post-yield hardening was observed, with a temperature-dependence resembling the friction-hardening of irradiated metals,9 this again suggesting a point-defect mechanism. An important development in this field has been the observation,10 by transmission electron microscopy, of high concentrations of prismatic loops in fatigued aluminum. By analogy with quenched aluminum filmso11 it seems certain that these loops originate in the collapse of vacancy clusters formed during deformation. Metals, such as copper, having a relatively low-stacking fault energy would tend to produce Frank sessile loops (in practice tetrahedral defects with stacking faults on all (111) planes) rather than the glissile prismatic loops observed in aluminum. The manner in which these various defects affect the different aspects of fatigue behavior has not yet been fully investigated. The present work was designed principally to indicate whether tensile fatigue gives rise to hardening and softening effects similar to those associated with reversed stress fatigue, and with the hope of providing additional information on the contribution of point defects to fatigue deformation. Despite the uncertain ty often associated with the interpretation of resistivity data, i.e., the relative contribution of stacking faults and other defects, such measurements are conveniently employed to study point defect pheno-

Jan 1, 1962

By C. G. Dunn, F. W. Daniels

IN recent publications1-5 the existence and behavior of subgrain boundaries in high-purity metals has been clearly brought to light. Lacombe and Beaujardl by means of special etching methods disclosed in polycrystalline sheets of aluminum the existence of substructures differing in orientation by small amounts (about 1/4"). Boundaries of these structures at relatively high temperatures had the remarkable property&apos; of moving about while the ordinary boundaries remained stationary. Cahn2 also observed substructures in bent and annealed single crystals of aluminum, zinc, magnesium, and rock salt. The position of subboundaries could be explained in terms of a dislocation mechanism of polygonization in which dislocations move into lines at right angles to the bent glide planes thereby relieving elastic stresses in these planes. Guinier and Tennevin8,6 disclosed the further interesting feature that polygonized structures coarsened significantly upon prolonged annealing. Somewhat similar subgrain phenomena have been observed in silicon iron of commercial purity. Although some evidence for the development of macro-mosaic structures in silicon iron already has been reported by one of the authors6,7 under the phenom-enological term "crystal recovery," much better evidence recently has been obtained due to improved etching techniques. In addition, phenomena regarding structural changes have been uncovered. The present investigation is divided into three parts: (1) The phenomenon of Laue spot sharpening on annealing cold-rolled crystals, (2) the phenomena of polygonization and subgrain coarsening The material used in the present investigation was high-grade commercial silicon iron sheet of nominal composition, 3.3 pct Si, 0.004 C, 0.011 P, 0.010 S, 0.04 Mn, 0.01 Al, 0.04 Cu, 0.01 Sn. Large single crystals of this material Were prepared for cold-rolling or bending as scheduled. Cold-rolling of 12 pct was carried out on a laboratory 8-in, diam rolling mill. The bending deformations were performed by pressing the crystals between a solid Fig. 2—lllustrative foue patterns to show Laue spot sharpening. a (Left)—Specimen as cold rolled, b (right)—After 48 hr at 1400°C. round bar and a mating half cylinder, both heavily greased. Individual specimens were cut from the deformed crystals, and the cut edges were deeply etched prior to annealing. Laue photographs were made using 40-kv tungsten radiation. The technique used to disclose the various subboundaries was an electropolish and electroetch in a bath of chrome-acetic acid.&apos; The anodic polishing done at 22 v was immediately followed by etching at a reduced voltage, which was dependent upon the nature of the subboundaries. Phenomenon of Laue Spot Sharpening on Annealing Cold-Rolled Crystals Fig. 1 gives the initial and final orientations of the specimens cold-rolled 12 pct. Each specimen was annealed at a temperature and for a time which caused significant structural changes as evidenced by alterations in Laue patterns. Representative Laue patterns and micrographs showing the essential changes are given in Figs. 2, 3, and 4. The essential points to be derived from these illustrations follow: 1. Annealing at 950°C clearly develops a substructure with the orientation of the cold-rolled specimen. 2. The subboundaries formed obviously separate regions of nearly the same orientation. Some of the subboundaries appear as a sequence of dots similar to those observed in aluminum by Lacombe and Beaujard,&apos; but whether this is due to extremely small differences in orientation is not known at present. 3. The substructure coarsens upon prolonged annealing. 4. Prolonged annealing also causes a decrease in orientation spread according to Laue spot sharpening&apos;

Jan 1, 1952

By D. L. Albright, R. W. Kraft

Solidification experiments were conducted with the objective of testing the theory of eutectic colony formation. Appropriate control of variables in tests on a series of high-purity aluminum-copper specimens of eutectic composition resulted in the observation of three types of eutectic microstructures, these being a unique structure consisting of lamellae essentially parallel to one another, a banded structure, and the colony structure. Lamellar faults, which are morphologically similar in many respects to edge dislocation models in crystals, produced a complex substructure in these specimens. SOLUTE rejection at the advancing solid-liquid interface of a unidirectionally solidified single-phase metal can cause the liquid immediately in front of the interface to become constitutionally super-cooled below the equilibrium liquidus temperature. Constitutional super-cooling occurs if the solidification rate, R, is too rapid, or if the thermal gradient in the liquid at the interface, G, is too low. 1 This constitutionally supercooled layer in turn stabilizes a cellular rather than a planar interface.&apos; A similar cellular interface has been observed when lamellar and other types of eutectics were unidirectionally solidified, and it has been shown that the cellular interface led to the formation of eutectic colonies.&apos; The lamellar structure is fan-shaped at the edges of colonies (which correspond to valleys or grooves in the cellular interface) because the lamellae grow normal to the local interface. One of the possible mechanisms which might cause the formation of the cellular interface, in the case of solidifying eutectic alloys, is constitutional supercooling of the liquid with respect to a third component rejected by both phases of the eutectic.3,4 On the basis of the analogy between the solidification of single-phase metals and binary eutectics, a eutectic alloy should solidify with a planar interface if the ratio of G/R is sufficiently high to compensate for any impurity which might be present and causing constitutional supercooling. The fan-like microstruc-ture of eutectic colonies should not occur under these conditions and the lamellae should be parallel to one another and to the solidification direction for extended distances. The experiments conducted in this investigation were designed to test these ideas. Following a resume of the experimental procedure, the various microstructures observed during the study are described, and their relationship to the growth conditions which produced them is discussed. EXPERIMENTAL PROCEDURE The eutectic between an aluminum solid solution and 0 phase (approximate composition CuA12) was chosen for this work for the following reasons: it was known that a lamellar structure forms, the eutectic temperature is low enough to facilitate experimental work, and the components can be procured commercially in a very pure form. High-purity copper (est. 99.999 pct Cu, obtained from National Research Corp.) and spectrographic aluminum rods, having impurities other than copper estimated to be Zn-15 ppm, Mg-10 ppm, Fe-3 ppm, Na-2 ppm, Cd-1 ppm, and Mn < 1 ppm, were melted in a stabilized zirconia crucible in a vacuum induction furnace at a pressure of 10 pof Hg. The melt was superheated to about 1000°C to assure mixing, cooled to 780°C and cast into an investment mold which yielded sixteen cylindrical specimen blanks 1/2 in. in diam and 5 1/2 in. long. The casting was allowed to solidify under vacuum. This master heat had an analysis of 32.6 wt pct Cu and 67.4 wt pct A1 by difference. The cylindrical specimen blanks were remelted and solidified unidirectionally in an apparatus illustrated schematically in Fig. 1. An RF induction coil heated

Jan 1, 1962

By R. I. Jaffee, F. C. Holden, H. R. Ogden

Ti-Mn alloys were studied in order to determine the factors affecting the mechanical properties of &stabilized titanium alloys. The principal compositional factors have been found to be solid-solution strengthening, the martensitic transformation, and instability of the P phase. Structural factors, such as grain size and shape, were found to have more influence on ductility and toughness than on strength. THE alloys of titanium with the &stabilizing elements offer the chief hope for developing useful heat treatments. Conversely, the heat-treatment response possible with the p-stabilizing elements causes difficulties such as weld embrittlement and thermal instability during service at elevated temperature. Therefore, it is of considerable technical importance to understand the factors that govern the heat-treatment responses in these alloys, so as to be able to soften the alloys if they are embrittled by an adventitious heat treatment, to render them stable in service, or to harden them while maintaining adequate ductility and toughness. The Ti-Mn system is a good example with which to demonstrate the factors that govern strength and heat-treatment response in. a P-stabilized system. The region of the a-j3 transformation, after the work of Maykuth, Ogden, and Jaffee,&apos; is shown in Fig. 1. The a solubilities are low. This means that, in the two-phase a-p field, partition of manganese between the two phases occurs practically only to the P phase. The solid-solution effects are therefore chiefly the result of solution in the ,8 phase. The eutectoid occurs at 20 pct Mn and 550°C, and proceeds very sluggishly. It can be ignored in heat treatments in hypo-eutectoid alloys, except for long-time storage at low temperatures below the eutectoid temperature. Even here, there is some question that diffusion proceeds far enough to involve eutectoid decomposition. Three compositional factors bear on the mechanical properties and structure of titanium a-P alloys. These are: 1—solid-solution strengthening, 2—mar-tensite transformation, and 3—P instability. Combined with the purely structural factors of grain size and shape, these govern the properties of the alloys. Perhaps the most important factor is solid-solution strengthening. The facts that manganese dissolves in a titanium to a maximum of only 0.5 pct and most of the manganese partitions to the p phase dominate the structure and properties of the a-/3 alloys. Because of the overwhelming preference of manganese for the ,3 phase, the P phase is harder and the a phase is softer. The relative amounts of both phases may be modified by heat treatment in the a-P field as application of the lever rule in the two-phase field clearly shows. A critical temperature in the Ti-Mn diagram is 800°C. This is the P transus temperature of the 6.4 pct Mn alloy, which has the lowest manganese content which will form all retained-P phase on quenching to room temperature. Any quench performed from below 800°C will produce a structure consisting of only a, a plus retained P, or retained p, for alloys of the compositions used in this work. For alloys containing less than 6.4 pct Mn, any quench from above 800°C will always result in structures

Jan 1, 1955

By L. J. Kashar

By means of a continuum-mechanics approach, the following equation for calculuting the pressure for axisymmetric cold forging has been derived: where P is the extrusion pressure; K and n are the strength coefficient and the strain-hardening exponent of the steel, respectively; a and b are strain factors, primarily dependent on the die design; and R is the extrusion ratio. Data from compression and backward-extrusion tests performed at a crosshead speed of 0.5 in. per min on a nonwork-hardening material pure lead) and on a work-hardening material (1018 steel) indicate that the predicted extrusion pressures obtained from the derived equation agree very closely with the actual extrusion pressures. Therefore, the equation can be used to predict backward-extrusion pressures from standard mechanical-test data. The decision to cold-forge a part is based on several considerations, most of them related to economics. However, the production feasibility is usually determined by the pressure needed to extrude the part and the availability of tooling that can repeatedly sustain this pressure for over several hundred thousand cycles. A major contribution to the cold forging of steel would result from the development of steels that could be forged at reduced pressures and from the development of techniques that permit the accurate prediction of the pressure necessary to cold-forge the part. The ability to predict extrusion pressures is necessary to properly design the tooling required for the cold-forging process. Attempts to theoretically predict the cold-forging pressure, especially for work-hardening materials, have been unsuccessful in previous investigations of the cold-forging process.1-3 Many empirical relations have, therefore, been proposed relating the extrusion pressure to the chemical composition,&apos; the extrusion ratio,2 the tensile strength,273 and hard- ness, 2 and the yield strength3 of the material being extruded. However, these empirical relations are valid only for the specific conditions used in their development, and, in some cases, the empirical relations had a scatter band greater than * 10 pct. A study of the extrusion process was undertaken with the objective of developing predictor equations for extrusion pressure by using a continuum-mechanics approach to the problem of metal flow. The derivation of such an equation is summarized in this paper, and data are presented that confirm the validity of the derived equation. DERIVATION OF THE EXTRUSION EQUATION If the extrusion of a material through a die is considered in terms of a work balance, it has been shown that it is possible to derive an equation relating the work necessary to move the material through the die to the deformation work undergone by the material. The work done, W, in moving the material is given by where F is the extrusion force, I, is the distance the material was moved, A, is the original cross-sectional area of the material, P is the extrusion pressure acting on A,, Ap is the cross-sectional area of the extrusion punch, and Pp is the punch pressure acting on Ap. The deformation work, WD, is given by where V is the volume of metal deformed, ay is the flow stress of the metal, and E is the total strain undergone in the extrusion. If there are no frictional losses, the work done, W, is equal to the deformation work, WD; therefore, Since the volume of a metal does not change during deformation,

Jan 1, 1968

By T. F. Bower, M. C. Flemings, H. D. Brody

A series of experiments are reported which show thai reasonable assumptions for analysis of solute redistribution in solidification of castings and ingols illclr(de: negligible undercooling before nuclcation of solid phases, negligible increase of solute in advance of the tips of growing dendrites, complete diffusion within the Liquid oer distances the order, of dentrite arm spacings, platelike dentrite t/o?$holog?.. Qzmli/ali,e and periment is obtained JOY Al-Cu alloys front measurements of amount of nonequilibrium second phase, minimum solute content at the centers dentrites arms (after solidification), and 3) change in minimum solute content in dentrite arms during solidification. In a previous paper&apos; analyses were given describing solute redistribution in dendritic solidification. The analyses were undertaken primarily to permit prediction of "severity of microsegregation" in a casting or ingot after solidification and cooling to room temperature, but can also be used to predict "local fraction solid&apos; as a function of temperature in the solidifying alloy. Numerical results were given for Al-Cu alloys. The aims of this paper are to examine the validity of some of the assumptions of that analysis, and to compare predictions of the theory with experiments. All experiments reported are on Al-Cu alloys, the bulk on Al-4.5 pct Cu alloy. EXPERIMENTS Experiments conducted were on small ingots, 41/2 in. in diam by about 10 in. high. solidified in a controlled thermal environment (i.e., in a resistance-heated, re-circulating air furnace, whose temperature could be controlled to 1°C). In one series of experiments, the ingots were solidified very slowly (solidification time was varied from 8 to 1000 hr) and at constant rate of heat extraction. In a second series of experiments the ingots were solidified ( &apos;unidirectionally". Fig. 1 is a sketch of the method of making the two different types of ingots. The unidirectionally solidified ingots were fully columnar, and the slowly solidified ingots had equiaxed structures, Fig. 2. In making the slowly solidified ingots, the mold employed was carbon steel, coated with inert refractory. Typically the mold and its environment were heated to 700°C. The molten alloy was then poured into the mold and the temperature of the system equilibrated above the liquidus. The environment of the mold was next cooled with a controller responding to a differential thermocouple that measured the difference between the temperature of the melt and the temperature of the mold environment. The differential thermocouple consisted of one chromel-alumel junction in the melt connected in opposition with a second junction in the furnace. The potential across the differential thermocouple was input to the controller which acted to keep this potential at a set. constant value; hence the temperature difference between the two junctions was maintained nearly constant. Major resistance to heat flow in the above apparatus was between the metal surface and the furnace atmosphere, not in the metal itself. By maintaining a constant temperature difference between the metal and the furnace atmosphere, the controller maintained an essentially constant rate of heat extraction during solidification, regardless of amount of heat released by the metal per unit temperature change. When the metal temperature dropped just below the eutectic temperature. the ingot was removed from the furnace and water-quenched. The unidirectionally solidified ingots were cast in a similar mold to the foregoing except that provision was made to extract heat through the bottom face of the mold by passing air or water through the mold base, Fig. 1. For these experiments, metal and mold temperature were again equilibrated above the liquidus. Temperature of the mold environment was then held

Jan 1, 1967

By M. E. Wadsworth, J. R. Lewis, J. M. Quets

Samples of snythetic magnetite were reduced in hydrogen at various partial pressures and temperatures. The reaction mas found to be surface controlled and directly proportional to hydrogen partial pressure over the temperature range studied (400° to 1000°C). A transition in the mechanism occurred at approxirnately 590°C. This has been attributed to a change in the slow step of the reduction reaction resulting from the presence of stable wüstite at higher temperatures. Below 590°C the heat of activation for the reduction was found to be 14,700 cal per mole and it was 3,200 cal per mole above 590°C. THE reduction of the oxides of iron has been a subject of study and interest for many years. Edstrom1 has reviewed the work up to 1953 and his findings provide much basic information concerning details of the reduction of hematite (Fe2O3 ) and magnetite (Fe3O4) with both H2 and CO. He concluded that below 600°C the reduction of both hematite and magnetite was essentially identical, since the rate was controlled by a surface reaction at a magnetite gas interface and the iron formed was very porous. The decrease in the reduction rate for both hematite and magnetite immediately above 600°C was attributed to the formation of a stable wüstite phase across which diffusion was very slow. The wide difference in reduction kinetics for hematite and magnetite above 600°C was explained in terms of the character of the wüstite formed. The rate of magnetite reduction increased slowly with temperature beyond the minimum immediately above 600°C and rates equivalent to those observed at 550°C were not obtained until the temperature was increased beyond 850oC. Edstrom and Bitsianes2 studied the solid-state reduction of magnetite, the reaction of which can be written (4x-3)Fe + Fe3O4—4 FexO [1] where x is between 0.83 and 0.95. The rate was found to be controlled by the kinetics of transport of iron ions through the wüstite phase. Bogdandy and Riecke3 studied the kinetics of reduction of small grains of iron oxide in hydrogen and qualitatively attributed the slow step in the reduction process to the diffusion of hydrogen and water vapor through pores. McKewan4 has analysed the data of Joseph,5 Stalhane and Malmburg,6 and Lewis7 and has demonstrated that the kinetics of reduction of both hematite and magnetite are controlled by surface reactions and also that the variation in surface area during reduction must be accounted for. McKewan was able to correlate the reduction data by the equation rodo[1-(1-R)1/3] = Kt [2] where ro is the initial particle radius, do is the density of the iron oxide, R is the fraction reduced at time t, and K is a rate constant. The applicability of Eq. [2] for temperatures above 600°C where a stable wüstite phase is present, indicates the slow step in the over-all kinetics does not result from diffusion unless diffusion occurs laterally along the oxide metal interface or through a wüstite layer of constant thickness. Diffusional control through a layer of wüstite is unlikely, however, in view of the pressure effects demonstrated by Tenenbaum and Joseph,&apos; Diepschlag,9 McKewan,10 and the results of the present study. McKewan has demonstrated a linear rate dependence on the hydrogen partial pressure over the temperature range 400" to 1050°C for the reduction of hematite.

Jan 1, 1961

By Joseph L. Gillson

BRAZIL has had an industry based on ocean beach deposits of heavy minerals containing monazite, zircon, rutile, and ilmenite for well over 40 years, but except at the very earliest period, prior to 1906, and again during World War 11, has this industry been at all comparable in size with similar operations in other countries. Limiting factors have been neither a lack of reserves nor lack of markets (except for zircon). Although poor local transportation and shipping facilities have handicapped the development in Brazil, these conditions were perhaps equally bad (when mining operations started) in the Indian State of Travancore, and in New South Wales and Queensland, Australia, in which states the principal production of beach deposits of heavy minerals has occurred. The outstanding restraints on the Brazilian industry have been the lower quality of the Brazilian minerals, the relative small size of individual deposits that were known until recently, the lack of interest of Brazilian investors in mining ventures, and the unfavorable climate for investment of foreign capital under Brazilian mining law. The lower quality of the minerals is indicated by the fact that the Brazilian monazite carries only 5 to 6 pct Tho2*, and the ilmenite 561/2 pct TiO2, whereas the corresponding Travancore minerals carry 9 pct Tho, and 60 pct TiO, respectively. The Brazilian zircon is a dirty brown color (which can be removed readily) as compared with the gleaming whiteness of the Australian zircon. An inadequate market for the abundant zircon that will be available in any operation in Brazil is certainly a heavy restraint, since otherwise it could be an important byproduct. The oxide of zirconia, baddeleyite, that has come from Brazil is from other sources.&apos; Since the Brazilian beach sands carry only a little rutile, that mineral has not been available as a valuable byproduct to help finance the operations. Substantial tonnages of rutile have been exported from Brazil. The sources of this mineral are stream placers and residual deposits over gneisses in the States of Goyaz, Minas Geraes, Ceara, etc. (Leonardos,&apos; and Chambers". With these handicaps, Brazilian production from beach sands has been marginal, and there has been only one consistent producer. This is a company, originally French, which was called Companie de Franco-BrazilliCne, but, with the downfall of France in 1940, became Brazilian under the name Monazita e Ilmenita do Brasil ("Mibra"). This company has operated several deposits in the vicinity of Guara-pary, in the State of Espirito Santo. Its office and plant has been at Guarapary. Recently a company called, "Fomil" (Fomento Monazita-Ilmenita) started operations. This company was organized by the Foote Mineral Co. of Philadelphia, and such share as a foreign company can hold under Brazilian law has now been acquired by the Lindsay Light and Chemical Co. of Chicago. When the writer went to Brazil in the fall of 1940, he found that no general survey of the beaches had been made except for a thorough study of part of the area by Abreu.4 The paper by Miranda6 had not then been written. The federal Geological Survey and Department of Mines knew only of the existence of the deposits in Espirito Santo south of Vitoria, and had a hazy idea that others might be found north of Vitoria. One deposit in Bala was known in Rio, but the larger one at Guaratiba was not known, although a Frenchman had prospected

Jan 1, 1951