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By S. G. Epstein

Electromigration has been measured in dilute liquid alloys of lead in antimony and antimony in lead. In these alloys antimony migrates with the electron current; lead migrates in the opposite direction. These results, which contradict the mass criterion, were predicted by the electron drag model for electromigration in liquid alloys. The existing experimental data are shown to correlate with the difference in electrical resistivities of the alloy components. FOR many years investigators have attempted to relate observed electromigration phenomena in liquid alloys to the physical properties of the alloy components. The most successful correlation was found by Angus et' al.,1 who in 1959 proposed an empirical criterion for predicting the relative direction of motion of the components of a liquid alloy in an electric field: the component with the smallest atomic mass concentrates at the cathode. While this criterion is obeyed in nearly all the alloy systems which had been investigated, the physical basis for such an effect was not understood. It was also disturbing that the mass criterion predicted the wrong sign for the Haeffner effect; observations with pure liquid metals revealed that in every instance the lighter isotope was transported to the anode.2 Klemm3 explained these isotopic separations by suggesting that the lighter isotopes were more mobile and more easily carried to the anode with the electron stream. Additionally, several deviations from the mass criterion have been found in liquid alloys, notably involving transition metals such as chromium, nickel, palladium, and zirconium, which migrate to the anode in liquid bismuth.4'5 Recently, a model has been proposed6 in which electromigration in liquid alloys is attributed primarily to the interaction between the electron stream and the metal ions. In essence, this model predicts that the component with the greater electron-ion scattering cross section will be preferentially transported to the anode, displacing the other component to the cathode. The electrical resistivity of each pure component at its melting point is taken as the measure of its scattering cross section. This model was developed from the results of systematic studies with various solutes in liquid mercury,7'8 bismuth,9 and sodium.10 In every alloy, the component with the greater resistivity has centrates at the anode. Coincidentally, in every instance the component with the greater resistivity has also the greater mass, apparently satisfying the mass criterion. In order to differentiate between electron-ion coupling and atomic mass as the relevant physical prop- erty influencing electromigration, measurements were made with Pb-Sb alloys. Lead has an atomic mass nearly twice that of antimony, but lead has an electrical resistivity of 91 microhm-cm while antimony has a value of 113.5 microhm-cm at their respective melting points. The mass criterion predicts that in an alloy of the two antimony will concentrate at the cathode; the electron drag model predicts that antimony will concentrate at the anode. EXPERIMENTAL To conclusively determine the relative motion of lead and antimony in each other, solute electromigration was measured in dilute liquid alloys of antimony in lead and lead in antimony. Both starting materials were 99.999+ pct pure. The measurements were made with the same capillary-reservoir technique previously used for measuring electromigration in liquid bismuth alloys.11 Several changes in the experimental apparatus were necessary, however, to accommodate liquid antimony, which has a higher melting point than bismuth. The modified apparatus is depicted in Fig. 1. In each experiment four quartz capillaries were filled with the molten alloy. A direct current was passed through two of the capillaries; the electrode in one of these capillaries was made the cathode, and the electrode in the other was made the anode. The remaining two capillaries sampled the alloy in the reser-

Jan 1, 1969

By L. M. Yokum

Tremendous strides have been made in front end loaders in the last 15 years. Fifteen years ago a 21/4-cu-yd front end loader was the largest standard machine you could purchase. Today there are two commercially available 15-yd front end loaders and many 10-yd loaders. The estimated total worldwide market for all front end loaders over 1 cu yd has increased to over 30,000 units yearly. The trend for front end loaders, in general, and for the mining market, in particular, is to larger and larger loaders. Today there are 18 and 24-cu-yd front end loaders in prototype form. It is not inconceivable that within another 15 years there will be front end loaders in the 50-cu-yd class with design features quite different from today's. These larger loaders are being designed at the demand of the mining industry, and the design criteria are being directed at this market area. The costs of these larger loaders may be greater per unit of capacity, but it is the intent of the various manufacturers that they will be more reliable, be easier to service, give greater availability, live longer, and cost less to maintain, than previous loaders. It is also the intent of the manufacturers to compete directly with the large mining shovel as the front end loaders become appropriately larger and more reliable. There has been some trend in this direction in the past with smaller shovels and loaders. In Table 1 are data for U.S. production of front end loaders (5 to 6-cu-yd class and 10-cu-yd class) and U.S. production of cable-operated, crawler-mounted power shovels, draglines, and cranes (11/z to 5-cu-yd class) for the years 1965 and 1970 (Source: Bureau of Census, U.S. Department of Commerce). Many believe that the decline in shovel production, in particular, is due at least in part to the acceptance of the front end loader as a primary production tool. However, the foregoing comparison is for a smaller shovel class than for front end loaders. It has generally been a rule of thumb that a front end loader is competitive on a cost and production basis with a shovel when it is approximately twice as large as the shovel. This same relationship may not hold true with the larger 10 to 15-cu-yd electric shovels, but at some point, direct competition will probably occur. Current Trends There are many trends today that are significant. One major usage trend in large front end loaders involves load and carry operations. This application is defined as "performing the functions of loading, hauling and dumping with one machine over distances within its economical limits." Many people are using front end loaders to transport material as well as load it. It is estimated that nearly half of all 10-cu-yd front end loaders sold in 1970 went into primary load and carry work. Many times, significant savings result from using the load and carry system, instead of small truck and shovel operations, for distances in excess of 1000 ft. Strip mining in coal utilizes great numbers of front end loaders in this manner. In-pit crushing of limestone is developing on an ever-increasing level, especially in Europe, and this stimulates interest in load and carry operations. In Table 2 is a cost example for 10-cu-yd front end loader in a limestone quarry. More than likely, load and carry use will continue to increase over the next few years. While some types of mining do not lend themselves to load and carry in the pit, such areas as surge piles are applicable and should be studied. In the area of machine operating cost reduction, there

Jan 1, 1974

By D. H. Shaffer, W. F. Harris, W. M. Hickam, M. H. Loeffler

Experiments have been performed on the quantitative addition to niobium of enriched isotopes 018 and 017 at the 0.1 - 40 micro-gram level and their subsequent recovery. A measured quantity of molecular oxygen of known isotopic concentration is added to niobium metal by oxidation. Recovery of the enriched isotopes as carbon monoxide is by the vacuum fusion technique. Quantitative determinations of the enriched isotopes are made in standard volumes at constant temperature using accurately calibrated micromanometers and the mass spectrometer as pressure measuring instruments. THE presence of low concentrations of nonmetallic impurities in metals can often adversely affect the physical properties of the metal. The increase in hardness and the embrittlement of refractory metals due to oxygen is well known. In metallurgical studies dealing with the diffusion rates or the effect of oxygen on the physical properties of refractory metals, it is often necessary to add small quantities of oxygen to the metal and later recover the total quantity present. It is desirable, therefore, to establish the accuracy with which microgram quantities of oxygen can be added to niobium and recovered by vacuum fusion. The successful addition of microgram quantities of oxygen to metals by the usual manometric techniques and the subsequent recovery by vacuum fusion is difficult because of the uncertainty in the accurate determination of the quantity of oxygen originally present in the metal and because of the chance of contamination by atmospheric oxygen. In order to minimize these uncertainties earlier workers have added quantities of O16 at levels much higher than the oxygen concentrations that are of interest.'-3 In order to eliminate the uncertainty associated with the O16 additions to metals at low microgram levels, experiments have been performed on the quantitative addition of oxygen highly enriched in O17 and O18 at the 0.1 to 40 pg level to niobium and the subsequent quantitative recovery of the isotopes by vacuum fusion. Since the natural abundance of O17 is 0.04 pct and of 0" is 0.2 pct this enriched oxygen provides a uniqueness from interference not achieved in earlier work.'-= A measured quantity of molecular oxygen of known isotopic concentration is diffused into the metal. Recovery of the isotopes in the form of carbon monoxide is by vacuum fusion. The total quantity of gas is determined in standard volumes at constant tempera- ture using accurately calibrated Consolidated Electrodynamics micromanometers and the mass spectrometer for pressure measurements. The molecular and isotopic composition is determined mass spectrometrically. APPARATUS A schematic of the oxygen addition apparatus is shown in Fig. 1. Take-offs are provided for the attachment of the isotope container and for sample bulbs which are used to transfer samples to the mass spectrometer. Metal valves are used throughout the system including the sample bulbs in order to achieve a vacuum of 10"6 mm Hg. Evacuation is accomplished with a 3-stage oil-diffusion pump backed by a mechanical pump. A liquid nitrogen trap is used to remove condensables and to prevent oil vapor from entering the system. A micromano-meter is used for pressure measurements. The furnace assembly is shown in Fig. 2. It consists of a quartz tube joined to the apparatus through a 40/W joint with Apiezon W low-pressure wax. The furnace cap, also a 40/W pyrex joint, is provided with a pyrex hook. The sample is suspended from this hook with a platinum wire. The total volume of the furnace section is 435 ml. All volumes were determined by expanding a known volume of gas at a known pressure into the evacuated system and re-measuring the pressure. Both the micromanometer used on the oxygen addition system and the micromanometer used on the mass spectrometer were compared to a precision

Jan 1, 1961

By S. R. Mitchell, M. C. Fuerstenau, A. M. Gaudin

The two principal attributes of a thickener pulp are its settling rate and the ultimate pulp density of the thickened mud. Testing for evaluation of thickening attributes of a pulp has usually been done batch-wise by placing the pulp in a one-liter glass graduated cylinder and noting the position of the boundary between clear liquor and mud as a function of time. Refinements in testing have included repulping a thickened mud to various dilutions and evaluating the settling rate on these various repulped muds. This is considered to make possible an estimate of the settling rate as a function of pulp density and therefore to pinpoint the slowest settling pulp which ought to be critical from the standpoint of thickener plant design. Finally, tests are sometimes made with model-size continuous thickeners of arbitrary size. In batch tests it is generally accepted that the behavior of a pulp is described by a curve such as the one shown in Fig. 1, in which the position of the boundary between clear liquor and mud (the mudline) is plotted against time. It has also been assumed that the initial settling rate (the slope of the line segment AB) is descriptive of the pulp and independent of the size and shape of the container. Where the settling rate is slower and clearly a function of time (portion CD of the settling curve), it has been assumed that the data are not of much use because of the intrusion of compacting phenomena. The next important datum is the height. PE, which is a measure of the so-called ultimate pulp density. This quantity is assumed to be characteristic of the pulp and independent of the container. When actual data are recorded, results are rarely exactly according to this theory and numerous deviations may be noted. For example, some pulps seem to require an appreciable delay before beginning to settle, as in line AF. This is spoken of as representing the need for an induction time for flocculation. It has seemed desirable to explore thickener data with a more sensitive charting tool than is afforded by the coordinates of Fig. 1. Instead of relating the position of the mudline to time, it has seemed desirable to relate the rate of descent of the mudline to time. This, in effect, amounts to charting the slope of the line in Fig. 1, or the derivative of its ordinates, against the same abscissas. Fig. 2 shows the new chart for the curve ABCDE of Fig. 1. When this new tool was applied to data obtained, for example, with sized clay pulps, astonishing differences appeared. Apparently the traditional tool conceals differences instead of revealing them, whereas the new method emphasizes them. It seems, also, that both charting methods have their uses. In this article attention is focused on the effects of pulp density and container height as they affect the settling behavior of flocculated suspensions of a sized kaolin. The thesis by M. C. Fuerstenau' gives more details than this summary, as well as some information about the effect of other variables. Sized fractions of kaolin were used, supplied through the courtesy of S. C. Lyons of the Georgia Kaolin Co. Large batches were made by agitation in a flotation machine and in a glass jar equipped with a mixer. The settling vessels were 2, 4, and 6-in. diam glass cylinders of various heights. Pulp Dilution: The effects of pulp dilution on sedimentation behavior are shown in Figs. 3, 4, and 5. Fig. 3 shows data on pulps ranging from 2.44 to 16.7 pct solids initial pulp density, flocculated with Separan and charted in the traditional manner. At least two of the lines appear nearly straight in their early sections, but neither of the others does. Each of the curves in this figure includes a region labeled

Jan 1, 1960

By R. E. Reed-Hill, W. H. Hartt, W. A. Slippy

An unusual form of double kinking has been observed at the ends of {1121} twins in deformed zirconium. These kinks lie partly outside of the twin and partly inside. While they are undoubtedly closely associated with accommodating the twinning shear into the matrix, they are apparently closely related to other important aspects of twin growth. A mechanism is proposed for {1121} twin growth involving interactions between 1/3 (1120) dislocations in the bend planes and twinning dislocations. It is also shown that boundaries without long range strain fields develop at the tapered ends of the twins. The {1121} twins can, therefore, grow without forming high-energy noncoherent twin boundaries containing large numbers of closely spaced twinning dislocations. NUMEROUS investigators have indicated that slip is often closely associated with deformation twinning. An example is twin accommodation kinking,1-3 where dislocations form bend planes and permit accommodation of a twinning shear within the parent crystal. Another is the incorporation of slip dislocations into twins, as proposed by Sleeswyk and verbraak4 and Ishii and Kiho5 for iron and ß-tin, respectively, and observed in hcp metals by Price.6 In addition, it has been shown that shear discontinuities exist at the points of twin intersections in zinc,7 magnesium,8 titanium,9 ß-tin,10 and bismuth," where the continuity conditions for twin intersections, originally proposed by cahn,12 are not satisfied. A similar situation occurs for zig-zag (1121) twins in zirconium13 and ?-phase silver-aluminum alloys,14 where the twinning shears of the two component twins are not parallel. In all these latter cases additional deformation by slip is believed to accommodate the twinning shear discontinuity. The present paper is concerned with a newly observed aspect of the slip and twinning interrelation, in which two kinks, one inside the twin and the other external to the twin, are formed. These kinks, observed in conjunction with (1121) twinning in zirconium, form to accommodate the twinning shear. A model has been constructed explaining the growth and accommodation of (1121) twins in terms of these kinks. This mechanism may be significant since it is concerned with an important twin mode, which occurs not only in zirconium but also in titanium and hafnium. The practical significance of (1121) twinning has been adequately demonstrated. At 77° K the high ductility of zirconium containing a large number of grains unfavorably oriented for slip is primarily due to (1121) twinning.'5 Also, (1121) twins nucleated at 77°K may grow during further deformation at room temperature. This growth can greatly increase the transverse ductility15 as well as produce large mechanical hysteresis effects.= EXPERIMENTAL PROCEDURE Arc-melted, sponge zirconium plate previously described17 was prestrained 0.65 pct at 77° K by cold-rolling to introduce {1121} twins into the structure. Tensile specimens were cut with axes normal to the plate rolling direction. These specimens were pulled in tension to near the point of failure in an Instron machine at room temperature at a cross-head speed of 2 x10-2 in. per min. This additional deformation caused growth of the twins nucleated by prestrain. Deformed specimens were then prepared for metallo-graphic examination. This included an anodizing treatment18 that made the surfaces sensitive to polarized light, permitting small lattice rotations to be revealed. EXPERIMENTAL RESULTS Nature of the Twin-Kink Band Structure. Fig. 1 is a photomicrograph of a typical specimen after prestrain at 77° K. The structure is characterized primarily by long, narrow, parallel sided (1121) twins which norma1ly traverse the entire grain. Fig. 2 shows several (1121) twins after additional straining at room temperature. These lie near the center of the polarized light photomicrograph and are inclined upward to the right. It is evident that this latter deformation has resulted in appreciable twin growth. The dark regions extending from the ends of these twins are accommodation kinks. The difference in reflected light intensity indicates the

Jan 1, 1969

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

SELF-DIFFUSION in pure gold has been studied by Sagrubsky,1 McKay,2 Gatos and coworkers,3,4 and Okkerse.5 Sagrubsky used a sectioning technique but reported results far lower than any of the others. The work seems to be carefully done, and it appears that a factor of 60 must have been omitted in his calculations or the units misstated by an equivalent amount. McKay used a surface activity method, and Gatos and Kurtz, following Gatos and Azzam, applied autoradiography to the measurement of activity on an oblique section through the diffusion zone. These two investigations agree well with each other but give results below those reported here. Okkerse employed a very careful sectioning technique. Chemical interdiffusion in Au-Ag alloys has been measured under several concentration conditions. Average values of the diffusion coefficient for the range of 0 to 18 atomic pct Au were obtained by Braune.6 since the diffusion coefficient probably varies markedly over this range, the values may not be too useful. Also, a plot of these data suggests that grain boundary contributions may have been appreciable at the lowest temperature employed. Ebert and Trommsdorf7 give average values for 0 to 9 atomic pct Ag, and Johnson8 reports average values for 45 to 55 atomic pct Au. Johnson also measured silver and gold self-diffusion coefficients in 49.2 atomic pct Au alloys, and self-diffusion in pure silver. The self-diffusion of gold in pure silver has been determined by Jaumot and Sawatsky.10 Other measurements which do not cover a range of temperature or are of low precision are not mentioned in this account since a review by Kubaschewski is available." This contribution reports diffusion coefficients for self-diffusion in gold, self-diffusion of gold in Au-Ag alloys, and chemical diffusion in Au-Ag alloys. Although it had been intended to obtain silver self-diffusion data in the alloys it now appears unlikely that these measurements can be done soon, so a table has been worked out for a self-consistent scheme of diffusion coefficients which should not be too far from the true values. Experimental Details Experiments on pure metals were conducted using fine gold of 99.99+ pct Au and silver of the same purity. Alloys were prepared by melting the two metals together in a graphite crucible in vacuo and allowing the slug to solidify in the crucible. After machining to a cylinder about 0.85 in. diam each slug formed one half of a diffusion couple. Compositions were determined later by analyzing chips taken from the extremities of the diffusion zones. The gold used in the preparation of alloys was sometimes pure gold but was normally either in the form of clean pickled alloy from previous experiments or gold recovered by oxalic acid precipitation from warm aqueous solution. Chips from the various stages of experimentation were dissolved in aqua regia and the solution taken to low bulk, diluted with water, and again taken to low bulk before diluting for the precipitation. This precipitated gold contained a small amount of silver as the only impurity detectable by spectrographic analysis. Disks for use in diffusion couples had opposite plane faces abraded on emery paper as far as zero grit, were annealed for 12 hr at 900°C in argon, and had one face of each disk polished to 000 emery paper. Radioactive gold was plated at about 2 ma per sq cm from a small volume of cyanide solution containing 1 mg of inactive gold as a carrier. Specimens , were freshly abraded on 4/0 emery paper immediately prior to plating. In the case of the active couples disks of a similarly prepared but unplated alloy or pure metal were placed on top and welded to the active disk. With the concentration couples disks of different compositions were welded. Welding was performed after a pressure of 5,000 lb had been applied at

Jan 1, 1958

By R. S. Kinasevich, D. D. Crabtree, D. W. Fuerstenau, T. P. Meloy, A. L. Mular

This paper presents details of the concept that size reduction in comminution machines takes place by three mechanisms; namely impact, abrasion, and chipping grinding. Experimental evidence is presented to show that each of these comminution mechanisms produces particles of a characteristic size distribution. The actual product from a comminution device has been postulated to be the result of a composite of these three types of mechanisms. Composite curves are demonstrated for a material following the Gaudin-Schuhmann, Gaudin-Meloy, and Rosin-Rammler size distributions. About forty years ago, Gaudin1 showed that grinding may be considered a combination of impact and attrition. Since that time, major efforts have been devoted to studies, both experimental and theoretical, of impact and compression fracture, while attrition has been almost wholly neglected, at least quantitatively. A significant attempt to distinguish between attrition and impact grinding is the work of Tanaka2 in Japan. By means of an instrumented abrasion grinder and a drop weight device, he determined coefficients relating the increase in surface area of various materials to the energy expended by the two methods of comminution. He showed that physical properties of a material determine its response to attrition and impact grinding. By extending his ideas to ball milling, he concluded that to a large extent the basic comminution process in a ball mill is due to the impact of falling media. Because Tanaka used a mass of particles in his drop weight device, however, he did not obtain pure impact size reduction. The purpose of this paper is to define basic mechanisms of size reduction, to verify that each has a characteristic and meaningful distribution curve, and to show how a combination of these mechanisms results in a size distribution very like that produced by grinding mills. DEFINITION OF COMMINUTION MECHANISMS The product from a grinding device will be considered to be the sum of the contributions resulting from the action of three basic mechanisms of size reduction which operate in a ball and rod mill. These are impact grinding and two forms of attrition, namely abrasion grinding and chipping grinding. Each is defined below. Impact Grinding: If a straight line is obtained when the cumulative weight fraction finer than a given size is plotted on log-log paper as a function of that size, the slope of the line is defined as the distribution modulus. A number of investigators 3,4,5 have shown that impact fracture of single specimens of different composition and shape results in a distribution of daughter particles that exhibit a distribution modulus of unity. This has also been true for materials broken in slow compression. Moreover, under slow compression or impact fracture conditions, theoretical distribution equations6*' which approximate the Gaudin-Schuhmann distribution when the distribution modulus is close to unity agree reasonably well with the experimentally obtained products. If one now considers a comminution process where many impact or compression fracture events are taking place, then any rational summation of the individual events yields, in the finer size range, a Gaudin-Schuhmann distribution whose distribution modulus is also unity. If the size distribution of the product from a mill has a distribution modulus of unity, it is implied that particles are fractured in a manner which results in a comminution event having a distribution like that obtained for the breakage of single specimens. These impact events would occur when a particle is smashed between balls or between a ball and the mill liner. Attrition, on the other hand, is that form of grinding which cannot be called impact grinding, and comprises both abrasion and chipping grinding. Abrasion Grinding: Abrasion is a form of surface wear resulting when particles rub against each other or against balls or the mill liner of a tumbling mill, somewhat like a piece of wood being rubbed over a piece of sandpaper. The surface wears at a more or

Jan 1, 1964

By G. W. White

Over the past several years, the steady progress of gas lift from a mysterious art into a developing science has been traceable through the many fine papers that have appeared in Journal of Petroleum Technology. Consequently, this magazine has rightly become a standard for the serious students of gas lift all over the world. The following discussion is offered in a sincere attempt to accurately present certain topics covered in the subject paper in the light of acknowledged state of the art procedures. INSTALLATION DESIGN The first point to be questioned is the author's installation design, beginning with Eq. 6. The use of 1,200 psi in the spacing equation instead of the 1,275 psi noted as available seems, at first glance, to be a simple arithmetic error. Upon further examination, it appears evident that both this 75 psi plus the 100-psi safety factor must be subtracted from available kickoff pressure because of conditions imposed by the characteristics of the ASC valve (see Fig. B-1). Pressure-charged valve design is incorrectly penalized by spacing the first valve using only 1,100 psi. The use of such a high back-pressure makes it appear that a typical ASC installation would require no more valves than a comparable conventional valve installation. Using a value of 100-psi tree pressure, the well could be valved to 11,000 ft very conservatively with seven pressure-operated valves, but would still require 11 ASC valves. The use of 400-B/D spacing gradient for a 140-B/D rate is not an accepted practice using precharged valves. The author would have done well to note the advantages to be gained by reducing the 500-psi tree pressure, which is clearly explained by Beadle, Harlan and Brown.' In Step 1 of Part III of the continuous flow discussion, the author incorrectly applies the Poettmann and Carpenter curves.2 Item 2 is an incorrect statement. An excellent reference on this point is the paper by Baxen-dell and Thomas.' VALVE MECHANICS The next topic relates to the mechanics of precharged valves. Eq. 2 for the ASC valve can be used to describe the condition of equilibrium, wherein the valve is closed with opening pending. When this equation is used to determine relative values of casing, dome and tubing pressure with conditions approaching the transition value, some strange results are obtained. The following uses the author's symbols and values given on page 689. Fig. B-1 shows the condition that exists at the moment an ASC valve has been uncovered during the unloading process (Condition I). The obvious result is a locked condition. The basis for the curve is shown on the figure which includes 1,000 psig casing pressure to uncover the valve. If injection gas is not bled off the casing until the pressure is decreased by an amount exceeding the stabilizer discharging valve pressure, upward adjustment of the casing pressure is mandatory for the valve to open and unloading operations to continue. In Condition I the dome pressure exceeds the casing pressure by 20 psi, and the tubing pressure required to open the valve is 1,212 psig. This tubing pressure would not exist under the assumed conditions. In Condition I1 the casing pressure is increased to the dome pressure, and the tubing pressure required to open the valve is 1,102 psig. It is apparent that the casing pressure must be increased to a value exceeding the dome pressure before unloading operations could continue. In Condition I11 a maximum casing pressure of 100 psi (stabilizer charging valve set pressure) above the dome pressure is reached, and the tubing pressure required to open the valve is 549 psig. The author's statement after Eq. 5 that "the minimum tubing pressure required to open an ASC valve is equal to the casing pressure at depth less the transition pressure of the valve" is incorrect except for Condition I11 only. Otherwise, the equation is invalid.

Jan 1, 1965

By N. K. Chen, R. Maddin

Columbium single crystals were deformed in tension and compression. Reorientation by X-rays and stereographic projections of slip traces indicate that plane of slip may be considered as (110). The plastic behavior is shown to be quite similar to the deformation of molybdenum single crystals. STUDIES on the crystallography of the deformation process in body-centered cubic metals have been renewed recently with investigations of iron single crystals1-" and molybdenum single crystals.4 It is now apparent that too many exceptions to the rationalization based upon the ratio of absolute testing temperature to absolute melting point by Andrade5 exist to permit more serious discussion of this type of analysis. The considerations of resolved shear stress utilizing only planes of the type {ll0}, {112), and {123)³,6 permit analysis of the deformation only on the basis of those three types of planes. The suggestions made by Elam7 and by Greninger8 in which the slip process is envisioned as a composite slip on two nonparallel {110) planes can be illustrated schematically in Fig. 1. It may be seen that an unresolved trace on any plane containing a <111> direction may be accomplished by varying the number of atoms participating in the composite process. By further varying the number of atoms in each plane but keeping the ratio of participating atoms constant, jogs could be obtained in the traces and hence wavy slip lines could be produced. Vogel and Brick&apos; studied the behavior of a iron single crystals in which they suggest that the plane of glide is "non-crystallographic" and may be predicted from the intersection between the great circle joining the slip direction and specimen axis with the great circle whose zone axis is the slip direction. In a more recent investigation on iron single crystals, Steijn and Brick" suggest that the slip mechanism may be considered as made up of a type of composite slip occurring on {110} and {112} planes. Evidence for a possible composite nature of the slip process has been presented for the case of molybdenum in the form of analysis of asterism and specimen axis rotation." Definite proof of a composite slip process must, however, await good electron microscopic resolution of the individual traces making up the unresolved optical trace used in determining the acting slip plane. The present investigation was undertaken to study the behavior of columbium single crystals not only in tension but also in compression since the specimen axis migration should indicate the plane or planes of glide in the same manner that the specimen axis migration in tension indicates the direction of glide. The orientations of eleven crystals investigated are shown in Fig. 2. Specific orientations are missing (those in the vicinity of [Ill] and [001] and consequently the effect of orientation on the crystallography of deformation could not be considered. Experimental Procedure The 1/8 in. rods (7 in. long) were subjected to an axial tension in vacuo while at temperatures in the vicinity of 2000°C for 2 to 4 hr. This treatment resulted in large cylindrical grains (about ½ in. long) occupying the entire cross section. A number of these rods were used for the tension studies by observing the behavior of the individual grains. For the compression studies, single crystals approximately % in. long by 1/8 in. in diameter were cut from the rods; the ends were ground parallel. All specimens were polished electrolytically in a solution of 15 cc HF(48 pct) and 85 cc H2SO4 (concentrated) using a platinum cathode, a current density of 0.04 amp per sq cm and a temperature between 25" and 60°C.10 Orientations were obtained using a Laue back-reflection method (3 cm film to specimen distance) with a ½ mm collimator 9 cm long. For the compression specimens, a reference mark was scratched on one of the compression sur-

Jan 1, 1954

By Paul B. Crawford, Bobby L. Landrum

Electrical model studies have been made of the effect of drainhole drilling on production capacity. Drain holes are those lateral holes which are sometimes drilled to assist in increasing the oil drainage into the main wellbore. The studies indicate that if the drainhole length i.r near 0.2 of the drainage radius, the increase in production capacity may be approximately 1.8, 2.08, trnd 2.33 for the case of one, two and four drain holes, respectively. If multiple drain holes are drilled, shorter holes are required to achieve a specific increase in production capacity than if one or two holes are drilled. To achieve increases in production capacities by factors near three it is shown that the drainhole lengths divided by the drainage radii must be approximately 0.64, 0.48, cnd 0.37 for the case of one, two and four drain holes, respectively. IN T RO DUCTION Kecent developments in drilling techniques have permitted the drilling of lateral or horizontal holes to increase the rate of production. The number of these drain holes may vary from 1 to 10, and they have been drilled laterally as much as 100 ft. Drainhole drilling at substantial depths is of recent origin but has been used in the Spraberry field of West Texas, the La Pas field in Western Venezuela, and certain fields in California. The diameter of the drain holes has been approximately 6 in. In drilling drain holes it is desired to know how much increase in production capacity may be expected, what additional benefit may be gained by drilling more than one drain hole, and what increase in production capacity may be brought about by lengthening the existing drain holes. In realization of the importance of lateral drilling, electrical model studies were made to provide quantitative estimates on the effect of drain holes on production capacity. ANALYSIS An electrical model was used in studying this problem. A wooden circular reservoir approximately 30 in. in diameter and 2 in. deep was filled with a dilute salt solution to a depth of 1 in. A copper band formed the periphery of the tank, and a copper wire was inserted in the center of the tank to represent the well. The drainage radius divided by the well radius was equal to 500. A diagram of this type model is shown in the inset of Fig. 1. An electrical potential was applied to the wire well and copper band at the periphery to determine the flow of current. Following this measurement copper wires of various length were soldered to the vertical wire well in such a manner as to simulate lateral wells drilled into the reservoir. Multiple lateral holes of various lengths were studied by varying the number and length of copper wires soldered to the vertical wire well. All multiple lateral wells were located symmetrically about the vertical well. The effect on production capacity by drilling an infinite number of lateral holes was studied by replacing the lateral hole with a copper disk. For each condition the flow of current was measured and compared with the flow of the vertical well only. The model which is thus described provides the steady state increases in production capacity which may be expected in some cases. The data conform to those which would be observed for a uniform homogeneous reservoir. The data may have primary application to those reservoirs producing above the bubble point. It is realized that few lateral holes are drilled in reservoirs of this type, but the data may be of some value in guiding future work or aiding to explain observed phenomena.

Jan 1, 1956

By C. van der Poel

When oil is displaced from a horizontal formation by another fluid of lower density, the latter tends to override the former in the shape of a tongue owing to gravity segregation. This gravity tongue has an adverse influence on the oil recovery. If the fluids are miscible, diffusion (mixing) takes place at the interfacial boundary of the gravity tongue. This mixing should have a favorable effect on oil recovery. The report describes a laboratory study of the magnitude of the mixing zone under various conditions, so as to assess the effect of diffusion on oil recovery both in laboratory experiments and under actual field conditions. The technique used enables visual observation and measurement of the size of the mixing zone in transparent glass-powder packs. The results show that in experiments in small models and cores the width of the mixing zone may well be of the same order of magnitude as the height of the model. In such cases oil recovery is favorably affected by mixing. It can further be concluded that, under conditions prevailing in the field, mixing of the injected fluid with reservoir oil is equal to that caused by molecular diffusion alone, eddy-mixing not taking place to any appreciable extent. A simple calculation, then, shows that molecular diffusion is too small for a beneficial effect to be expected from the injection of miscible fluids in horizontal or nearly horizontal reservoirs unless pay zones are thin. INTRODUCTION This paper gives results of experiments made on the mixing which occurs when a miscible displacement is carried out in a horizontal reservoir. This mixing takes place at the interfacial boundary of the gravity tongue formed when the lighter injected fluid overrides the oil present in the reservoir. The object of the experiments was to simulate the field case where, for example, propane with a viscosity of 0.075 cp under reservoir conditions displaces an oil of viscosity 0.6 cp. In the experiments the lighter fluid had a viscosity of about 1 cp and the heavier one a viscosity of about 8 cp, so as to obtain the same viscosity ratio. In order to enable the results to be compared with those published in the literature, a set of experiments with viscosity ratio equal to one was also performed. EXPERIMENTAL TECHNIQUE The technique developed for the purpose enables the width of the mixing zone to be studied as a function of time and place. A glass-powder pack is saturated with a water-glycerine mixture of suitable viscosity, which represents the reservoir fluid. The pack is then rendered transparent by dissolving sufficient ammonium thiocyanate in the mixture to obtain a solution with a refractive index matching that of the glass powder. Alkaline water to which phenol-phthalein has been added is used as the lighter and less-viscous displacing fluid. In those places where mixing or diffusion of the two liquids occurs, the slightly acidic ammonium-thiocyanate solution neutralizes the alkali in the water, and the glass pack shows up white against the red-colored invading water. If a black cloth is hung over the back of the apparatus, the transparent part of the glass pack appears black. In this way the position of the two phases and the transition zone between them is clearly visible, as shown in Fig. 1 (where the red-colored invading water is the grey-shaded zone lying uppermost). In all experiments the amount of alkali in the water was chosen such that the upper contour corresponded to a concentration of 5 per cent of the dense liquid. The lower contour is determined by the size of the glass grains and the thickness of the pack and, consequently, varies from experiment to experiment. Corresponding concentrations of the dense liquid range from about 97 per cent for packs of small grain size (permeability = 1 darcy) to about 95 per cent for those with large grains

By C. J. Rosa, W. C. Hagel

An attempt is made to determine the diffusion coefficients of oxygen ions in hypostoichiometric zirconium oxide. A phenomenological theory is developed for three-phase, unidirectional volume diffusion of a gaseous species from a planar source. Knowledge about oxygen diffusion in a and ß zirconium and experimentally measured rates of movements of interfaces permit the evaluation of oxygen ion diffusivi-ties in ZrO2-x. The results conform to the relationship: sq cm per sec, for the temperature range of 875" to 1050° C. DIFFUSION coefficients of oxygen ions in stoichio-metric oxides have been studied by many investigators. The obtained results not only supplement the knowledge about the lattice-defect structures of oxides and conduction mechanisms but also provide information of technological importance. Rate processes such as oxide sintering, high-temperature creep deformation, and oxidation of metals and their alloys are directly dependent on diffusion phenomena. Unfortunately, diffusion coefficients obtained from studies on stoichio-metric oxides cannot be treated without restraints when applied to oxidation kinetics, if precise evaluations of oxidation rates are desired. Oxides formed on metals are usually nonstoichiometric and exhibit nonuniform distribution of either cation or anion vacancies across their thicknesses. Debuigne and Lehr1 extended Danckwerts&apos;2 mathematical analyses and furnished a semitheoretical treatment for evaluating oxygen diffusion coefficients in zirconium oxide in terms of weight gain measurements during oxidation of zirconium in the temperature range 400° to 850°C. Their calculations are based on theoretical partitioning3 of the total amount of oxygen between a zirconium and its oxide phase. An inherent discrepancy appears to continue throughout their calculations. The amount of oxygen confined to the oxide phase should be corrected by multiplying the calculated oxide thickness by the inverse of Pilling-Bedworth ratio, if expansion of zirconium dioxide is taken into account. The purpose of the present investigation is to provide a new semitheoretical treatment for evaluating diffusion coefficients of moving species in hypostoichiometric oxide. The analyses are relevant to unidirectional volume diffusion. Although the presented method is quite general, its applicability will be discussed in terms of kinetic measurements from oxidation of zirconium at temperatures above the a/ß transition, for reasons stated in the later part of this paper. EXPERIMENTAL Pure, 99.93 wt pct, zirconium samples of approximately 2 by 1 by 0.35 cm were exposed to oxygen for various times at four temperature levels: 875°, 950°, 1000°, and 1050°C. High-purity, better than 99.9 vol pct oxygen was passed through a cold trap and columns containing anhydrous CaSO4 to remove residual water vapor. Before exposing to oxygen at a pressure of 500 Torr, specimens were subjected to wet abrasion on 200- through 600-grit Sic papers and polished with 1—p diamond dust. Prior to oxidizing, all zirconium samples were vacuum-annealed at 10-6 mm Hg for about 15 min at the test temperature. The temperature variation across the uniform heat zone was ±2°C from the preset value. Final polishing, for phase thicknesses measurements, was performed by using 8- and 1-p diamond dust and followed by vibrator polishing with 0.05-µ ? Al2O3 solution. Measurements of phase thicknesses were made by projection on a metallographic viewing screen. Conventional powder X-ray analyses for the oxide were employed. RESULTS Fig. 1 is an example of the cross section of oxidized zirconium. Designations of phases given below this figure are the same as those used in the three-phase diffusion system represented by Fig. 5 in the following section. Zirconium oxidized for longer exposure times showed two types of oxides: white oxide at the surface and an underlaying layer of gray oxide. X-ray powder patterns of these oxides at room tern-

Jan 1, 1969

By A. W. Schlechten, C. M. Hsiao

The apparent vapor pressures of a number of metal sulphides were determined by measuring their rate of weight loss when they were heated under vacuum. The calculated pressures are due in some instances to the volatility of the sulphide and in others to the decomposition pressure. FIE direct reduction of metallic sulphides, as in the precipitation method for lead or antimony, is not a widely used process today. However, it might be employed for the production of a number of metals if the operation were carried out under reduced pressures. Two general procedures are possible; the reducing agent could form a stable nonvolatile sulphide from which the valuable metal could be removed by volatilization or liquation. The other approach would be to choose a reducing agent which would form a sulphide that could be volatilized away from the valuable metal. A vacuum operation would serve to protect the sulphides and metals from oxidation and would increase the evaporation rates. A related process is the separation of metallic sulphides by selective volatilization either at atmospheric pressure or under vacuum. This procedure is already used commercially for the elimination of lead and cadmium as PbS and CdS from zinc calcines; it might well have other applications. To predict such processes it is necessary to know the relative volatilities of the metallic sulphides and to know whether they volatilize as sulphides or whether the predominant weight loss is due to decomposition. Such data would also be of value in studying problems such as the use of sulphides for refractories, as described by Brewer,] or in the evaluation of the theory of ore deposition from the vapor state, as proposed by Brown.&apos; Qualitative statements concerning the volatility of metallic sulphides can be found frequently in the literature and are well summarized by Mellor, but accurate determinations of rates of evaporation or vapor pressures are very scarce. Kelly" lists vapor pressure data only for PbS; his reference being to the work of Schenck and Albers,4 who measured the vapor pressure of PbS by a dynamic method between 850" and 995°C. More recently Veselovskii5 has determined the vapor pressures of the sulphides of antimony, lead, cadmium, and zinc at temperatures ranging from 360" to 1000°C using Knudsen&apos;s method. A second Russian worker, Pogorelyi,6 determined the vapor pressures of CdS and ZnS at temperatures from 900" to 1250°C. The results obtained by these workers are shown in subsequent graphs in comparison with the data of this paper. Brewer and coworkers1 have studied some of the metallic sulphides to determine their suitability as refractories in vacuum. Veselovskii&apos;s determinations on PbS checked well with those of Schenck and Albers, and his determinations of CdS check almost exactly with Pogo-relyi. For the vapor pressure of ZnS the data of Veselovskii and that of Pogorelyi are in fair agreement, as shown in Fig. 1, but it should be pointed out that Lumsden7 has discovered that the equation given by Veselovskii for the vapor pressure of ZnS: - 14,200 log P9.495 is in error by a factor of ten when compared to the experimental data. In contrast with the scarcity of data on vapor pressures, the decomposition pressures of many metal sulphides have been determined and are summarized by Smithells.8 Theoretical Considerations The experiments described in this paper consisted of determinations of the rate of weight loss of certain metallic sulphides under very low pressures at different temperatures. These data plus observation and analyses of the products reveal the mechanism of the weight loss and also provide a basis for the calculation of the vapor pressure or apparent vapor pressures of the sulphides.

Jan 1, 1953

By Wayne L. Worrell

Thermodynamic data for the stable carbides and oxides of chromium, molybdenum, and tungsten have been critically eualuuted and are used to determine the stable condensed phases at 1 atm total pressure in each metal-carbon-oxygen system. Pourbaix-Ellingham diagrams have been constructed and are used to estimate the minimum temperatures neces.see)*y to oblain these metals by corbolhermic redlrction under reduced pressures. USING recently reported data for the carbides and oxides of chromium, molybdenum, and tungsten, the stable phases in the Group VI metal-carbon-oxygen systems at specific temperatures and pressures can be determined. The thermodynamically stable regions in each metal-carbon-oxygen system can be completely pictured using a Pourbaix-Ellingham diagram in which the two coordinates are oxygen potential (-RT In Po2) and temperature. Worrell and chipman&apos; have described and constructed such diagrams for the metal-carbon-oxygen systems of vanadium, columbium, and tantalum. Downing2 has used similar diagrams to provide a description of the reactions in submerged arc furnaces. One of the examples which he cited was the Cr-C-O system; however, an improved diagram is presented in this paper using recently obtained data for the carbides of chromium. Although some of the oxides and carbides of the Group VI metals exist over slight ranges of composition,3 all solid phases are represented as stoi-chiometric compounds in the subsequent diagrams. Any error introduced into the calculated equilibria by neglecting the compositional variation of these phases is less than the uncertainty in the thermodynamic data. In a Pourbaix-Ellingham diagram for a three-component system, the phase rule requires that at equilibrium four condensed phases specify a point, three condensed phases determine a line, and two condensed phases define an area. To obtain a well-defined area at high oxygen potentials and teniperatures, the initial carbon to oxygen mole ratio is specified to be more than sufficient to reduce the oxide but not enough to convert all the metal to carbide. Thus, the lowest regions in the subse- quent Pourbaix-Ellingham diagrams represent areas in which the metal and its carbide are the stable condensed phases. Cr-C-O SYSTEM A) Thermodynamic Data. To simplify the subsequent calculations, all thermodynamic data are presented in the form of linear Gibbs-energy-of-formation* equations which were derived for the temperature range 505° to 2000°K and are reasonably accurate over the entire temperature ranges of the diagrams. The thermodynamic data for the compounds occurring in the Cr-C-O system are summarized in Table I. Several volatile chromium oxides have been reported,4 but their influence is negligible in the Cr-C-O system. Thermodynamic data for CO and CO2 were taken from the compilation of Coughlin.5 The only solid chromium oxide sufficiently stable to exist below 1800°K in the Cr-C-O system is Cr2Os.11 The Gibbs-energy-of-formation equation for Cr2O3 was obtained by revising the data tabulated in Coughlin,5 using the heat of formation of ah&apos; and the high-temperature thermal data for chromium.7 In 1953 Richardson8 re-evaluated the original work of Kelley and coworkers,9 who measured the thermodynamic properties of the chromium carbides. However, the high-temperature equilibrium results of Boericke9 yield values for ?G°f of Cr2O3 which are 2 kcal more positive than the accepted data. His results for the chromium carbides are based on the same questionable equilibria. Gleiser10 recently determined the Gibbs energy of formation of Cr3C2 and the equation in Table I was calculated from her data and the thermal data of Kelley and coworkers.9 Thermodynamic data for the Cr7C3 and Cr23C6 carbides were obtained by combining the Cr3C2 data

Jan 1, 1965

By B. H. Caudle, R. L. Slobod, E. R. Brownscombe

An earlier publication has discussed three methods lor obtaining relative permeability data on small core sample-: and the apparatus and technique for the capillary pressure displacement method. This paper describes the apparatus and technique for the solution gas and the dynamic displacement methods and presents a routine procedure for obtaining oil-gas and water-oil relative permeability data. Theoretical and experimental considerations are presented to show that the end effect commonly associated with the dynamic flow mechanism is extremely small where constant rates are employed in the flowing phase. An effect of flow rate on relative permeabilities obtained by the dynamic system is found only when gas is one of the flowing phases and this effect is ascribed to a form of channeling in the capillary system. The apparatus and procedure* used to obtain relative permeability data with three phases flowing are described and some preliminary results of the use of this method are shown. INTRODUCTION In a previous publication from this laboratory there appeared a brief discussion of the concepts behind three basic methods for obtaining relative permeability data.&apos; These three methods were called the capillary pressure displacement method. the solution gas displacement method, and the dy. namic displacement method — the names being suggestive of the type of process used for obtaining the desired saturation prior to making the permeability measurements. In the same publication, the apparatus and technique for the capillary pressure displacement method were described and some typical results obtained by this method were presented. This paper will present: 1. The routine procedure used to obtain complete relative permeabilitv data (In small core samples with two phasec flowing; 2. The experimental techniques for the solution gas and dynamic displacement methods for obtaining relative permeability data; 3. The results of some studies on the mechanism of fluid flow through consolidated porous media; and, 4. The preliminary results on the determination of relative permeability for a system in which three phases are flowing. TECHNIQUE AND APPARATUS FOR THE DETERMINATION OF RELATIVE PERMEABILITY WITH TWO PHASES FLOWING In order to obtain relative permeability data on a small core sample which will describe the various phases of reservoir depletion. it is necessary that the methods used duplicate, as closely as possible, the various mechanisms involved in rescbrvoir depletion. It is important that. in any type of relative permedbility determination. the core be originally at virgin reservoir conditions with respect to the fluids within the pore *paces. (for example. oil used to displace water from core until connate water saturation estahlished). and that the subsequent saturation changes in the core be analagous to tile reservoir depletion mechanism for which the data are to he used. PROCEDURE OF DETERMINING RELATIVE PERMEABILITY DATA WITH TWO PHASES FLOWING A standardized procedure has been set up for obtaining relative permeability data and other information on small core samples. This procedure essentially consists of 11 steps as shown below: 1. Determination of tile capillary pressure curve.&apos;! This information is used to help select samples for relative permeability determinations and to charactrrize. in general. the pore size distribution of the sample. 2. Determination of the specific permeabilities to air, oil. and water. These values are those on which the relative pern~eahility calculations are based. 3. Reduction of the core to connate water by an oil drive using the high speed centrifuge. 1. Determination of the critical gas saturation value and the associated relative permeability to oil by the solution gas drive method. 5. Determination of the relative permeabilities to oil and gab in the region where both phases are flowing by the capillary presqure method. 6. Reduction of the sample to residual oil in the centrifuge by an air drive. and the determination of the relative permeability to gas at this point.

Jan 1, 1951

By R. L. Slobod, B. H. Caudle, E. R. Brownscombe

An earlier publication has discussed three methods lor obtaining relative permeability data on small core sample-: and the apparatus and technique for the capillary pressure displacement method. This paper describes the apparatus and technique for the solution gas and the dynamic displacement methods and presents a routine procedure for obtaining oil-gas and water-oil relative permeability data. Theoretical and experimental considerations are presented to show that the end effect commonly associated with the dynamic flow mechanism is extremely small where constant rates are employed in the flowing phase. An effect of flow rate on relative permeabilities obtained by the dynamic system is found only when gas is one of the flowing phases and this effect is ascribed to a form of channeling in the capillary system. The apparatus and procedure* used to obtain relative permeability data with three phases flowing are described and some preliminary results of the use of this method are shown. INTRODUCTION In a previous publication from this laboratory there appeared a brief discussion of the concepts behind three basic methods for obtaining relative permeability data.&apos; These three methods were called the capillary pressure displacement method. the solution gas displacement method, and the dy. namic displacement method — the names being suggestive of the type of process used for obtaining the desired saturation prior to making the permeability measurements. In the same publication, the apparatus and technique for the capillary pressure displacement method were described and some typical results obtained by this method were presented. This paper will present: 1. The routine procedure used to obtain complete relative permeabilitv data (In small core samples with two phasec flowing; 2. The experimental techniques for the solution gas and dynamic displacement methods for obtaining relative permeability data; 3. The results of some studies on the mechanism of fluid flow through consolidated porous media; and, 4. The preliminary results on the determination of relative permeability for a system in which three phases are flowing. TECHNIQUE AND APPARATUS FOR THE DETERMINATION OF RELATIVE PERMEABILITY WITH TWO PHASES FLOWING In order to obtain relative permeability data on a small core sample which will describe the various phases of reservoir depletion. it is necessary that the methods used duplicate, as closely as possible, the various mechanisms involved in rescbrvoir depletion. It is important that. in any type of relative permedbility determination. the core be originally at virgin reservoir conditions with respect to the fluids within the pore *paces. (for example. oil used to displace water from core until connate water saturation estahlished). and that the subsequent saturation changes in the core be analagous to tile reservoir depletion mechanism for which the data are to he used. PROCEDURE OF DETERMINING RELATIVE PERMEABILITY DATA WITH TWO PHASES FLOWING A standardized procedure has been set up for obtaining relative permeability data and other information on small core samples. This procedure essentially consists of 11 steps as shown below: 1. Determination of tile capillary pressure curve.&apos;! This information is used to help select samples for relative permeability determinations and to charactrrize. in general. the pore size distribution of the sample. 2. Determination of the specific permeabilities to air, oil. and water. These values are those on which the relative pern~eahility calculations are based. 3. Reduction of the core to connate water by an oil drive using the high speed centrifuge. 1. Determination of the critical gas saturation value and the associated relative permeability to oil by the solution gas drive method. 5. Determination of the relative permeabilities to oil and gab in the region where both phases are flowing by the capillary presqure method. 6. Reduction of the sample to residual oil in the centrifuge by an air drive. and the determination of the relative permeability to gas at this point.

Jan 1, 1951

By B. H. Bergstrom, J. J. Gilvarry

Previously the authors showed that the Gilvarry equation correctly describes the distribution of fragment size in single fracture, provided the exoclastic particles showing original surface of the specimen are removed from the distribution. In the present work this conclusion has been strengthened in two respects. First, it has been shown that the existence of two peaks in the differential distribution for the endoclastic particles, corresponding to the effect of surface and volume flaws in the interior of the specimen, can be demonstrated from the average of data for a large number of specimens. Second, it has been shown by means of a Coulter counter that data obtained from specimens fractured in gelatin display the behavior at fragment sizes approaching 1 p which is demanded by the limiting form of the Gilvarry equation in this case. In previous work, a rigorous derivation of the proper distribution function for fragment size in single fracture of a brittle solid has been given by Gilvarry,&apos; based on a closely defined physical model and deduced strictly by the laws of probability. Experimental work has been reported by Gilvarry and Berg-str~m,~ confirming the theory in its broad outlines. Subsequently, Gilvarry and Bergstrom extended the theoretical discussion to include comminution and presented experimental data bearing on this point. They have described further experimental results for the case of single fracture recently. The experimental evidence regarding single fracture was rather convincing. However, it was based on only five specimens for which fragment sizes were determined by sieve analyses and three for which measurements in the finer sizes were made on a Coulter counter. The purpose of the present paper is to extend the experimental results as obtained by means of both sieve analyses and the Coulter technique. In the former case, sufficient specimens are included so that the average data should vield ac- curately the detailed behavior of the distribution function for the coarser fragment sizes. In the latter case, measurements for the finer sizes are reported which correspond to single fracture more closely than prior results and fill a lacuna left in the experimental verification. In addition, an extension of the theory given recently bGilvarry for the case of fracture of a two-dimensional solid will be outlined, and experimental results obtained by him will be discussed.6 THREE-DIMENSIONAL CASE Gilvarry&apos; has shown that the Schuhmann size modulus is a measure, in a sense specified later, of the number of activated edge flaws in a specimen undergoing single fracture. Single fracture is defined as that resulting from a single instantaneous application of energy, such as the blow of a hammer whose motion is halted when fracture begins. Plural fracture consists of a short sequence of single fractures, as in a jaw or gyratory crusher; multiple fracture obtains when many applications of energy are made, as in a ball mill. The Griffith flaws associated with fracture of a specimen are flaws occurring within the volume of the body, on the new surfaces created within its interior and on the new edges (intersections of two surfaces) within the body. Fracture proceeds by activation of flaws in the volume of the specimen, in the fracture surfaces throughout its interior, and in the edges produced by intersection of fracture surfaces. If all the flaws and all groups of flaws are distributed at random, independently of other flaws or groups thereof, it has been shown by Gilvarry that the distribution function for fragment size has the form of a Poisson distribution. The fraction y, by weight or volume, passing a sieve of mesh size x is given by where k is an average spacing of activated edge flaws, j2 is an average amount of surface containing one activated surface flaw and i3 is an average volume corresponding to an activated volume flaw. The averages in question are referred to the mean dimension x of a fragment. On the basis of the theoretical

Jan 1, 1962

By J. L. Carne

ORE control is a matter of planning and supervision based on a foreknowledge of the content and distribution of ore. The Inspiration orebody is predominately a copper-sulphide blanket, overlain by an oxidized zone of copper silicates, copper carbonates, and barren capping. Most of the ore is treated by leaching, and the optimum requirement of this method is the goal toward which the mining schedule is aimed. Both open-pit operations and underground mining are used. The problems of ore control at Inspiration are: I—maintenance of metallurgical balance, 2—conservation of oxide ore, and 3—mining out of the orebody at an average grade which parallels that of the reserve figure. Prior to the fall of 1926 all of the Inspiration division ores were treated by flotation, but the mixed ores of the Live Oak—Keystone section carried too large a proportion of copper in the form of chrysocolla for satisfactory flotation. For this type of mixed ore the leaching process now in use had been worked out, and the plant was put into operation in the fall of 1926. The process is known as the ferric sulphate leach, and the leaching solvents contain both ferric sulphate and free sulphuric acid. Sulphide copper in the form of chalcocite is leached by the ferric sulphate, and the oxidized copper minerals are dissolved by the sulphuric acid. From the beginning of operations to the present time the plant has treated some 67 thousand tons of ore having an average copper content of 1.142 pct, of which 0.605 pct has been in the form of oxidized copper minerals. The plant is currently being operated at the rate of 11,500 tons per day, 7 days per week. However, this tonnage is produced in 6 days of mine operation. The average current grade is approximately 1 pct copper, of which about 50 pct is present as oxidized or acid-soluble copper. Close control of metallurgical procedures is a vital factor in operation of the plant and is in turn dependent upon careful regulation of feed. An excess of sulphide copper requires the presence of more ferric sulphate in the leaching solvents. On the other hand, an excess of ferric sulphate in the presence of a low sulphide feed seriously reduces the efficiency of electrolytic precipitation in tank house operations. This condition must be avoided at all costs. An additional factor must be considered. It is known that the sulphide content is predominant in the ore which remains in the reserve. To maintain the necessary sulphide-oxide proportion, so that the entire reserve will mine out at both a grade and a sulphide-oxide ratio that will be permissible throughout the remaining life of the property, it is obvious that the oxide reserve must be currently preserved to as great an extent as possible. Fortunately much of the oxide reserve is found in the open-pit operation. This happy circumstance adds flexibility to the procedure and makes it possible to maintain the close regulation necessary to insure best overall results, both mining and metallurgical. The two ore streams from the pit and underground operations join at the coarse-crushing plant, and proper control must be exercised before the ore reaches this point. The open pit is currently providing about 55 pct of the ore and underground operations the balance of production. Both operations are under a single superintendent so that the closely interrelated problems may be more readily controlled. The least flexible of the two producing units is the underground mine, where the mining method is block caving. Although a block of ground may be undercut and developed, characteristics of the material determine its caving action. The ore in the chutes must be drawn. The area currently mined from underground is in a zone predominately sulphide and is generally

Jan 1, 1953

By J. L. Carne

ORE control is a matter of planning and supervision based on a foreknowledge of the content and distribution of ore. The Inspiration orebody is predominately a copper-sulphide blanket, overlain by an oxidized zone of copper silicates, copper carbonates, and barren capping. Most of the ore is treated by leaching, and the optimum requirement of this method is the goal toward which the mining schedule is aimed. Both open-pit operations and underground mining are used. The problems of ore control at Inspiration are: I—maintenance of metallurgical balance, 2—conservation of oxide ore, and 3—mining out of the orebody at an average grade which parallels that of the reserve figure. Prior to the fall of 1926 all of the Inspiration division ores were treated by flotation, but the mixed ores of the Live Oak—Keystone section carried too large a proportion of copper in the form of chrysocolla for satisfactory flotation. For this type of mixed ore the leaching process now in use had been worked out, and the plant was put into operation in the fall of 1926. The process is known as the ferric sulphate leach, and the leaching solvents contain both ferric sulphate and free sulphuric acid. Sulphide copper in the form of chalcocite is leached by the ferric sulphate, and the oxidized copper minerals are dissolved by the sulphuric acid. From the beginning of operations to the present time the plant has treated some 67 thousand tons of ore having an average copper content of 1.142 pct, of which 0.605 pct has been in the form of oxidized copper minerals. The plant is currently being operated at the rate of 11,500 tons per day, 7 days per week. However, this tonnage is produced in 6 days of mine operation. The average current grade is approximately 1 pct copper, of which about 50 pct is present as oxidized or acid-soluble copper. Close control of metallurgical procedures is a vital factor in operation of the plant and is in turn dependent upon careful regulation of feed. An excess of sulphide copper requires the presence of more ferric sulphate in the leaching solvents. On the other hand, an excess of ferric sulphate in the presence of a low sulphide feed seriously reduces the efficiency of electrolytic precipitation in tank house operations. This condition must be avoided at all costs. An additional factor must be considered. It is known that the sulphide content is predominant in the ore which remains in the reserve. To maintain the necessary sulphide-oxide proportion, so that the entire reserve will mine out at both a grade and a sulphide-oxide ratio that will be permissible throughout the remaining life of the property, it is obvious that the oxide reserve must be currently preserved to as great an extent as possible. Fortunately much of the oxide reserve is found in the open-pit operation. This happy circumstance adds flexibility to the procedure and makes it possible to maintain the close regulation necessary to insure best overall results, both mining and metallurgical. The two ore streams from the pit and underground operations join at the coarse-crushing plant, and proper control must be exercised before the ore reaches this point. The open pit is currently providing about 55 pct of the ore and underground operations the balance of production. Both operations are under a single superintendent so that the closely interrelated problems may be more readily controlled. The least flexible of the two producing units is the underground mine, where the mining method is block caving. Although a block of ground may be undercut and developed, characteristics of the material determine its caving action. The ore in the chutes must be drawn. The area currently mined from underground is in a zone predominately sulphide and is generally

Jan 1, 1953

By E. S. Machlin, C. W. Chen

RECENTLY Chen and Machlin&apos; proposed a mechanism for intercrystalline cracking in metals during high-temperature stressing. According to this mechanism the formation of voids at grain boundaries is primarily responsible for intercrystalline cracking. A model has been provided to demonstrate the initiation of submicroscopic cracks and voids at jogs of grain boundaries where grain boundary sliding is inhibited. Submicroscopic cracks can grow as a result of either further grain boundary sliding or localized tensile stress. In the former case, it is believed that grain boundary sliding produces more voids which link together to produce macroscopic cracks and which may lead to the eventual failure of the metal. Concurrently, Nield and Quarrell2 reported their interesting results obtained in a systematic investigation of intercrystalline cracking in two aluminum alloys under various creep conditions. Their observations are generally in agreement with the above mechanism, especially the conclusion that voids are formed as a direct consequence of grain boundary sliding. On the basis of the volume fraction occupied by voids, they could find no confirmation of vacancy condensation as the mechanism for void growth. Furthermore, an important feature of intercrystalline cracking has been likewise pointed out by them that the majority of cracks are not formed at grain corners. Nield and Quarrel1 meanwhile emphasized the importance of grain boundary migration by designating it as one of two main processes operative in the mechanism of crack formation during creep. The designation seems unnecessary because overemphasis of grain boundary migration only complicates the mechanism of void formation. There are two reasons which militate against the inclusion of grain boundary migration in the mechanism of void formation. In the first place, the formation of intercrystalline voids per se does not require grain boundary migration. Secondly, in addition to grain boundary migration, void formation may be minimized by any other process such as plastic deformation which is capable of relieving localized stresses around jogs. Chang and Grant3 have shown that intercrystalline cracking is prevented in aluminum by lattice bending in high stress regions. The influential role played by grain boundary migration in creep has also been realized in our studies. In several cases, voids did not appear at all in grain boundaries whenever grain boundary migration took place prominently during creep. The purpose of this paper is to discuss the effect of grain boundary migration on the formation of intercrystalline voids and other related rupture properties. Experimental evidence indicates that in an unstable grain structure void formation may be markedly modified by structural changes. The abnormally high ductility and the transcrystalline mode of fracture observed in copper at elevated temperatures reveals that effective grain boundary migration minimizes void formation. Grain boundary migration has long been known as a common high-temperature phenomenon in metals with the grain configuration in a nonequilibrium state. Its effect on ductility and mode of fracture has not been recognized until recently.4 Since the introduction of the term "Equicohesive Temperature," the conventional belief has been that below the equicohesive temperature the ductility of metals increases moderately with decreasing temperature until the ductile-to-brittle transition temperature of fracture is reached. In this temperature range, metals fracture in a ductile mode with a "cup-and-cone" fracture surface. Above the equicohesive temperature, ductility remains invariably low and decreases slightly with increasing temperature. The mode of fracture is strictly brittle and intercrystalline. Typical examples have been shown for a brass and copper in Fig. 1 and 9, respectively, in the paper by Greenwood, Miller, and Suiter.5 The observation in the upper temperature range that ductility of metals is low and insensitive to temperature may be explained in terms of void formation at grain boundaries. It is also in accordance with the findings of McLean6 and Fazen, Sherby, and Dorn7

Jan 1, 1961