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By J. P. Givry

The bath and the liquid metal in the aluw~inuw~ electrolytic cells are moving under the action of the Laplace forces. Consequently there are differences in level at the interface of the liquid. This phenomena is studied by means of a computer; the characteristics of the mathematical model used are presented with the results corresponding to two typical cases. This study gives a new and origi~zal interpretation of magnetic ej-jects; their action depends very closely on the hydraulic phenomenon which explain the sensibility of the cells to the slope and thickness of solid bath frozen around the pot. MAGNETIC effects produced in the electrolytic cells used for the production of aluminum are known to exist, a factor whose importance is well-known by producers through its influence on cell operation and output. In particular, these effects bring about movements in both the bath and metal as well as interface variations in level that are detrimental to sound electrolysis . A direct study of these effects by means of an experimental device would raise a number of problems particularly difficult not to say impossible to solve in the present state of techniques. It is for this reason that we had recourse to an electronic computer for working out the speed and pressure distribution within the liquid in the cells. We have assumed that all other possible causes for movement, such as thermal convection and evolution of gas at the anode, are acting without any connection with magnetic effects, and that consequently we may study each of these causes separately. A basic cause for magnetic effects lies in the presence of Laplace forces within the bath and metal. Electric current and magnetic field distribution have been calculated with the help of an electronic computer, and two communications about it have already been made to AIME.* 1) PRESENTATION OF THE MATHEMATICAL PATTERN In order to solve this problem, it was essential to assume a number of simplifying hypotheses with regard to both the geometry of the actual cells and the phenomena themselves. A first simplification consisted in assuming that the movements of the conducting liquid modify neither the electric currents nor the magnetic fields. In consideration of the magnitude of the values involved this assumption seemed accep-tible. 1.1) Finding the Equation of the Problem. The problem raised consisted in determining the flow of two viscous immiscible liquids with different densities subjected in a complex environment to gravity and Laplace forces. As a matter of fact, the sum of the external forces acting on the liquids is: F = JAB +pg where F = volume energy, B = magnetic field, J = current density, p = specific gravity, g = gravity. In the case of a laminar flow and assuming that the liquids are Newtonian and incompressible liquids, the equations governing movements are the following: 1) Navier Stokes' equation written in vectorial form: In fact one tries to find a steady-state solution, so aVx/at = 0; besides, one assumes that the movements are slow enough for quadratic terms such as Vy(a Vx/ay) (of round about the square of speed) to be neglected in front of the viscosity term: pAV, so

Jan 1, 1968

By Reynold Q. Shotts

INTRODUCTION THE small domestic underfeed stoker as now designed is unusually sensitive to the coking and plastic properties of coals, and when the attempt is made to burn the high rank coking and caking coals of the Appalachian fields, serious trouble may occur. Part of the trouble may be caused by the ash content and clinkering characteristics of the particular coal in use, but more often it is the result of an excessive accumulation of coke in the form of "trees" or masses in the fuel bed. Often the zone of burning becomes so restricted that the fire goes out, and in extreme cases the fire may be lifted completely out of the fuel bed and away from the air ports. Even if the fire is preserved, excessive coking may cause response to subsequent heat demand to be slow and irregular. Coke trees seem to grow. most readily during periods of hold-fire operation, so that in order to preserve the fire in mild weather it is often necessary to set the timer for such a long operating period each hour that much unneeded and unwanted heat is developed, causing discomfort. During demand periods the fire may pick up so slowly that the intense burning which develops just before stoker cut-off causes a serious overshooting of the thermostat. Stoker coal performance tests which have been made in a number of laboratories 1, 2, 3, 4, 5 are one method of approach to the problem of selecting stoker coals. As yet these tests have not been standardized and they are expensive and time-consuming. The value of the results probably increases with the length of the test. Sherman and co-workers at Battelle Memorial Institute believe that even a one-week test is not too reliable a trial2 and it is quite likely that others will agree. A great advantage of such tests is that characteristics of coals, other than the tendency to form coke masses, may be evaluated from them. The selection of stoker coals would be greatly facilitated if there existed some simple measure of the tendency of a coal to form coke in a fuel bed. Although possessing all of the disadvantages of any small-scale laboratory test, the test for the free-swelling index of coal has been found useful for evaluating the probable effects of swelling properties upon combustion. 7 Ostborg, Limbacher and Sherman, have shown that the test can predict, roughly, the tendency of coke to accumulate in the fuel bed of a domestic stoker. They also gave instances of its value in predicting combustion behavior in some large installations. The use of the test for free-swelling index has become well established and has been adopted as a standard by the American Society for Testing Materials.8 When domestic stoker coal investigations began at the State Mine Experiment Station in the summer of 1944, it was decided

Jan 1, 1948

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

Hypoeutectoid Ti-Cu alloys are responsive to heat treatment, and considerable variation of mechanical properties may be produced by transformation of the ß phase. Control of cooling rate, isothermal transformation, or quench tempering determine the transformation structure and properties. The transformation products are similar to those of carbon steel. THE equilibrium diagram for the Ti-Cu system has been studied by various investigators, and the most recent diagram is that determined by Jou-kainen, Grant, and Floe.' The titanium-rich portion of this diagram is reproduced in Fig. 1. The alloy compositions and annealing temperatures used in this work are shown. The Ti-Cu alloys containing up to 17 wt pct Cu are representative of an active eutectoid alloy system. Joukainen et a1.l have stated that ß phase cannot be retained on quenching and this has been confirmed in the present work. The similarity between the Ti-Cu system and the Fe-C system is evident and, as will be shown later, many of the transformation products appear to have similar microstructures. Heat treatments in this program were designed to produce the structures of primary interest for study and determination of mechanical properties. Experimental Procedures Preparation of Alloys: Five ½ lb ingots, ranging in composition from 0.8 to 6.83 pct Cu, were prepared by double arc melting in an atmosphere of high purity argon. Titanium melting stock was obtained from high purity iodide titanium, and copper additions were made from copper wire clippings. Segregation was reduced by inversion melting, in which the once-melted ingots were inverted in the crucible and remelted. The double-melted ingots were forged at 1600°F to ¾ in. diam rods, with both heating and forging operations being carried out in air. Surface scale was removed by grit blasting and grinding, after which the forgings were vacuum annealed at 900°C. The alloys then were swaged to ¾ in. diam rod at 750°C and test specimens were cut from this material. The vacuum annealing operation was to remove dissolved hydrogen, which is commonly present in the iodide titanium as-received. Although vacuum fusion analyses were not obtained for all these alloys, past experience indicates that the 6 hr treatment with a limiting pressure of 10- to 10-5 mm of Hg is sufficient to reduce the hydrogen level to 10 to 30 ppm. Vacuum fusion analysis of the 0.8 pct Cu alloy showed 19 ppm of hydrogen. In addition to the five hypoeutectoid alloys, three 15 g ingots were prepared with nominal copper additions of 9, 10, and 11 pct. Fabrication procedures were similar, except that these alloys were rolled to 0.040 in. sheet. Microstructure specimens only were obtained. Table I shows analyzed compositions and fabrication temperatures for these alloys. Heat Treatments: All heat treatments were made in potentiometer-controlled, resistance-wound tube

Jan 1, 1956

By T. B. Massalski, H. W. King

An hcp phase may be induced by cold working the ß&apos; phase of the Ag-Zn system. This phase reverts to ß&apos; on subsequent aging. No phase change occurs on cold working the o phase, but ß&apos; is formed when the deformed alloy is subsequently aged at room temperature. It is concluded that for alloys near 50 at pct Zn the ordered bcc ß&apos; phase is the equilibrium structure at room temperature. WhEN the disordered bcc ß phase of the Ag-Zn system is cooled to temperatures below 258o to 274oC, it transforms to a complex hexagonal phase <o.1,2 The nature of the o ß=o transformation has been the subject of some discussion,2&apos;3 and the structure of o has been described in detail.&apos; The latter phase appears to be stable on aging at room temperature but decomposes following cold work. When alloys containing approximately 50 at. pct Zn are rapidly quenched from the 0 phase field, the ß ? o transformation may be suppressed; but the ß phase undergoes an ordering reaction (ß ? ß&apos;). The ß&apos; structure may also be obtained as a result of cold working and aging at room temperature.4 Kitchingman, Hall, and Buckley4 have suggested that the decomposition of (o following cold work proceeds in two stages, (o ? ß followed by ß ? ß&apos;, but did not confirm this by experiment. When the ordered &apos; phases in the systems Cu-Zn5 and Ag-Cd6 are cold worked, they become unstable and transform to a close-packed hexagonal phase (( ) indicating that when order is destroyed in a ß&apos; structure the close-packed hexagonal phase may in many cases be more stable. It thus became of interest to study more closely the effect of cold work and annealing on the stability of both the ß&apos; and o phases in a Ag-50 at. pct Zn alloy. Predetermined weights of spectroscopically-pure Ag and Zn, supplied by Johnson and Matthey, were melted and cast under 1/2 atm of He in transparent vycor tubing. The ingot was homogenized for 1 week at 630°C and quenched into iced brine. Since mechanical polishing was found to induce a phase change, sections were first polished at room temperature, sealed in tubes under 1/2 atm of He, reannealed for several days at 630o or 200°C and then quenched into iced brine. Sections of the alloy thus prepared were found to be homogeneous when examined under the microscope. The sample quenched from 630°C (ß -phase region) was pink in color, whereas the sample quenched from 200°C (o-phase region) was silver. The latter sample showed the characteristic hexagonal anisotropy when examined under polarized light. Filings of the alloy were examined at room temperature, after various heat treatments, using an RCA-Siemens Crystalloflex IV diffractometer with filtered CuKa radiation. The X-ray reflections from flat powder specimens quenched from 630o and 200°C and sieved through 230 mesh were recorded graphically at a scanning speed of 1/2 deg per min. The resultant patterns are shown in Figs. 1(a) and 1(b) and may be identified as those of the 8&apos; and <02 structures respectively. The lattice parameter of the ß&apos; phase was determined as 3.1566Å.* This value compares very well withthatto be expected for a 50 at. pct Zn alloy from the data of Owen and Edmunds? and indicates that no loss of Zn occurred during casting. In order to study the effect of cold work upon the ß&apos; and o phases, filings made at room temperature and sieved through 230 mesh were mounted immediately in the diffractometer-i.e., without a strain-relief anneal. Changes in structure on subsequent aging were followed by scanning repeatedly over the regions of the low index reflections of the ß&apos; and o structures-i.e. , 28 from 35 to 44 deg. Immediately after filing the 8&apos; specimen, additional diffraction peaks were observed in the low-index region of the pattern, as shown in Fig. 1(c). These additional peaks do not coincide with those of the o structure, Fig. l(b), but may be indexed as the (10.0), (00.2), and (10.1) reflections of an hcp phase (<) with nearly ideal axial ratio. However, this hexagonal phase appears to be very unstable since within a very short time at room temperature it reverts back to the ordered ß&apos; phase, the reversion being complete within seven hours. The 5 ? ß&apos; reversion reaction is, therefore, very similar to those already reported in Cu-Zn5 and Ag-Cd6 7&apos;alloys. The action of filing caused the deformed surface of the originally pink ingot to become silver in color, indi-cating that the ( phase possesses similar reflecting properties to the o phase. Hence, the subsequent

Jan 1, 1962

By W. J. Moore, E. M. Swiggard, H. Shenker

Beryllium is the most soluble of the double-acceptor impurities in germanium; the solubility is at least 1 x 10 19 atoms cm3. Photoconductive, optical, and electrical measurements were made on a set of Ge:Be samples grown without other intentionally added imp~ivities. The excited-states spectrum of beryllium in germanium was determined both in zero field and in magnetic fields up to 30 kc. It was found that the absorption 0-f lines in the vicinity of the G line increased markedly with increasing magnetic field. The ioniza-tion energy of neutral beryllium in germanium was determined to be 24.3 * 0.1 mez: using the excited-states spectrum. An infrared detector using a Ge:Be element was found to have a normalized detectivity D* (50 p, 1000 cps, 1 cps) of 9 X ldO cm-~ps"~-w-&apos;. The Ge:Be sambles exhibited low-field breakdown and inibzirity band conduction effects at low temperatures. WHILE the properties of most dopants in germanium have been thoroughly investigated, the properties of beryllium in germanium have had relatively little attention. Much of the work that has been done&apos; has been concerned with the properties of singly ionized beryllium in germanium. The purpose of the present work was to determine the photoconductive and electrical properties of beryllium-doped germanium (Ge:~e) with a small concentration of other electrically active impurities. Ge:Be is of special interest since beryllium is the most soluble of the known double-acceptor impurities in germanium. MATERIALS PREPARATION A set of &:Be crystals with beryllium concentrations between 5 x 1013 and 1x 10&apos;&apos; cmm3 and without other intentionally added impurities was grown in a hydrogen atmosphere by the horizontal zone-refining techniques described by Swiggard and Shenker.2 The segregation coefficient of beryllium in germanium was found to be about 0.07 and its maximum solubility was found to be greater than 1 x 10&apos;&apos; atoms cm-3 which is in agreement with previous results.&apos; Most of the crystals were found to have a small net concentration of shallow acceptors; for example, a crystal having a beryllium concentration of 1.1 X 1016 cm-3 was found to have a net concentration of shallow acceptors of less than 1.5 X 1013 cm-3. Ingots designed to have a beryllium concentration of 1 x 1017 cm-3 or less exhibited a loss of electrically active beryllium. That is, the beryllium concentration was lower than expected and the decrease of the beryllium concentration along the length of the ingot was much larger than expected. It is hypothesized that this effect is due to the oxidation of the beryllium by the residual oxygen in the system. This effect is similar to but not as severe as the effect observed with boron in germani~m.3, 4 OPTICAL ABSORPTION SPECTRUM The excited-states spectrum of neutral beryllium atoms in germanium was studied by measuring the infrared optical absorption spectrum. A typical spectrum is shown in Fig. 1; the labeling of the absorption lines follows that of Fisher and Fan.* The spacings between the observed lines and the D line are nearly equal to the corresponding spacings for the other ac -ceptors in germanium.5-7 By the use of the theoretical result67&apos; that the neutral impurity ionization energy is 2.53 mev larger than the energy of the D line, the ionization energy of neutral beryllium in germanium was determined to be 24.3 * 0.1 mev at 4.2"K. This method yields a more precise value of the impurity ionization energy than the usual Hall effect method.&apos; The absorption spectrum of Ge:Be was also measured as a function of magnetic field using a magnetic field parallel to the incident radiation and using unpolarized radiation. A typical spectrum taken at 30 kG is shown in Fig. 2. An unexpected observation is that the absorption of the lines in the vicinity of the G line (there is a strong possibility that some of these lines may be associated with lines other than the G line) increases with magnetic field. RESISTIVITY AND HALL DATA Measurements of Hall voltage vs temperature were made on several of the samples. The thermal activa-

Jan 1, 1968

By John G. Tate, George W. Nicolson, James L. Bruce

FOR more than 25 years modern mining has been carried on in the Island of Cyprus, Mediterranean Sea, by the Cyprus Mines Corp. of Los Angeles, Calif. The general features of these operations have been described.1 From 1935 to June 30, 1940, top slicing in the Mavrovouni mine produced in excess of 2,000,000 long tons. The rate for the last part of this period was approximately 50,000 tons per month. DESCRIPTION OF ORE BODIES The shape of the ore body now being top sliced in the Mavrovouni mine is an inclined irregular pyritic pipe or chimney of large dimensions, extending from unknown depths below the bottom level at elevation 250 ft below sea level, to the highest level at elevation 400 ft above sea level. The present surface above the ore body lies between 550 and 650 ft elevation. Undoubtedly the ore body extended to surface and was mined by the ancients by opencast and underground methods. The old pits were gradually filled up by erosion until now they show as slight depressions in the topography. The largest area of the ore body is at elevation 170 ft below sea level, where the horizontal section is almost elliptical, with a width of 600 ft and a length of 1000 ft. Below this elevation the shape of the ore body continues to be elliptical but with reduced dimensions. Above this elevation it rises flatly towards the south with a substantial depression in the upperside of the chimney and irregular ridges or wings rising on each side. It gradually grows smaller as it rises. The ore body is a pyritic replacement of andesitic extrusives which occur as flows and pillow lavas. With the exception of the upper portions of one or two small offshoots rising from the main ore body, all ore is completely surrounded by andesite. Most of the andesite lying above the ore body is covered by marl and clay sedimentaries of Miocene and later age. The Miocene is presumed to be older than the ore mineralization. That portion of the andesites which lies between the sedimentaries and the ore body has been broken by slumpage, and weathered, and iron-stained by the descending meteoric waters. It is a mass of crushed material that caves and follows downward readily as the top-slice stopes retreat. The main ore body is a heavy cupreous pyrites mass assaying on the average about 4.0 pct Cu; 48.0, S; and 42.0, Fe. In places the copper drops below 1.0 pct. On the borders of this heavy sulphide ore body lie disseminated cupreous pyrites ore deposits of large dimensions. Some portions of these appear to be closely related to the heavy sulphide ore, as the ratio of copper to pyrite is about the same. The greater part of the disseminated ore, most of which lies immediately to the east of the main ore body, contains less than 0.10 pct Cu and about 25.0 to 30.0 pct S. This probably can

Jan 1, 1947

By Gregory M. Dexter

Recent litigation in Pennsylvania between three coal-mining companies and a private water company resulted in the payment by the coal companies of the equivalent of about $500,000 to buy a new water supply to replace that which had been damaged by acid drainage from strip mining. An investigation of the relevant facts indicates that the water could have been treated by spending about $40,000 on equipment and $15,000 yearly for chemicals, labor, and power until the contarnination could be reduced about 80 pct. The water company&apos;s supply, furthermore, had deteriorated largely by reason of dry weather before stripping was begun by the coal companies. Payment to the water company should not have exceeded $300,000 and could have been as low as $100,000. Strip mining of coal is common in Pennsylvania. The most important objection to it in Pennsylvania is generally acid pollution of runoff water. An outline of the methods, therefore, that could be used to reduce such pollution, to compare acid-contaminated waters. and to treat such waters to make them satisfactory for public and industrial use is worth-while. The watershed of the West Penn Water Co. covers about 4.5 square miles, 20 miles west of Pittsburgh, and has two 90,000,000 gal reservoirs supplying about 1,300,000 gal daily for public and industrial use of which 450,000 gal daily are for two railroads. The pollution arises from weathered derivatives of typical&apos;" Coal Measures"&apos; rocks, the principal source being pyrite (and marcasite) in Pittsburgh and Rooster coals. Springs and seeps on hillsides issue from sandstone and limestone formations intersecting shale or clay land surfaces, or from perched water tables. The two reservoirs create an artificial permanent water table. Soap-hardness tests on three seepage samples taken in a dry summer ranged from 150 to 500 ppm. Water sampled came from aquifers above Pittsburgh and Rooster coals, obviating the possibility of contact with pyrite-containing coal. Since acid contamination of mine waters is the result of chemical reactions of oxygen and water with pyrite, it will be reduced by the exclusion of either air or water. The Sunnyhill Coal Co. has applied this principle in its "contouring" method of strip mining by burying contaminated coal-waste material under a compact, smoothed-up surface of top-soil, gravel, clay, and sand at a cost

Jan 1, 1950

By E. M. Tory, P. T. Shannon

An analysis of batch and continuous thickening in terms of the movement of planes of constant concentration (i.e. continuity waves) is presented. Use of solids flux as a primary variable greatly facilitates the analysis and clarifies the relationship between batch and continuous thickening. An "ideal" slurry is defined as one whose settling rate is a function only of the local solids concentration. An analysis of continuous thickening of this ideal slurry in an ideal thickener explains many aspects of the steady — and unsteady — state behavior of real slurries, such as the main features of a thickener&apos;s "solids profile" (including the break attributed to rake action), the sudden appearance at abnormally high feed rates of a zone of constant concentration and the velocity with which it rises, and the effect of detention time at constant weight of sludge per unit area. Where deviations exist, they are explained in terms of the batch settling behavior of real slurries. The purpose of this paper is to interpret continuous thickening phenomena in terms of batch settling behavior. Both types of thickening may be considered as the process of propagating concentration changes, due to the downward movement of the solids, from the bottom of the settling vessel upward through the slurry.&apos; These concentration changes may be either finite or infinitesimal as in the case of the propagation of a continuous concentration gradient. The slurry itself may be moving downward as in the case of continuous thickening. The downward velocity of the slurry may be such that the concentration changes being propagated up from below remain stationary relative to the thickener walls. This is the case for steady-state thickening. It seems appropriate to analyze continuous thickening in terms of the movement of planes of constant concentration. This has already been done for batch settling."3 Although our main interest is in real slurries, there are certain aspects of both types of settling which can be deduced from a theoretical analysis of highly idealized systems. To this end, an "ideal slurry" is defined as one for which the dimensionless settling rate at any point is a function only of the local solids concentration.1,2 An "ideal thickener" is one in which there is no radial variation in either the solids concentration or in the downward component of slurry velocity. The underflow outlet is a point sink. It is to be expected that the behavior of non-ideal systems will deviate in some measure from theoretical results. However, the same characteristics which cause deviations in continuous thickening should be evident in batch settling, permitting a rational explanation of the former in terms of the latter. PREDICTED RESULTS FOR AN IDEAL SLURRY IN AN IDEAL CONTINUOUS THICKENER General Theory: In continuous thickening, the downward solids flux (mass/area-time) relative to the thickener, G, results from two different

Jan 1, 1967

By D. H. Henley, F. F. Craig, W. W. Owens

The oil recovery performance of systems producing entirely by bottom-water encroachment has been experimentally determined in a series of scaled laboratory-model tests. The effects of well spacing, fluid mobilities, rate of production, capillary and gravity forces, well penetration and well completion techniques on the oil recovery performance have been investigated. The laboratory tests were performed using two uniform, un-consolidated sand-pack models. The models have ratios of the interwell distance to the formation thickness of 12 and 2, respectively. Tests at constant total fluid production rate were performed simulating a range of uniform reservoir characteristics and operating conditions encountered in field operations. The performance was determined by material balance and by observation of the encroachment of dyed fluids into the models. The results of the model tests agreed with those obtained mathematically when the conditions previously considered in theoretical studies were simulated, that is, when the oil and water are of equal density and no capillary forces exist. The model study of bottom-water drive indicated that certain variables can aoect the oil recovery performance to a greater degree than can be predicted by present analytical methods. In one comparison, the oil recovery at a water-oil ratio of 20 (obtained at a wide well spacing) varied as much as threefold, depending upon the system&apos;s properties and the production rate. Lesser effect of mobility ratio and no eflect of capillary forces over the range studied were observed. The test &apos;results also showed that the deeper the well penetration into the oil column, the greater the total water production to a producing WOR of 20. However, the ultimate sweep efficiency, and so the oil recovery to this level of WOR, did not vary significantly with well penetration. Horizontal fractures at the top of the formation did not significantly change the sweep characteristics of the reservoir models when values of radius and fracture capacity encountered in actual reservoirs were used. Impermeable pancakes at the bottom of the well moderately increased the oil recovery efficiency both at water breakthrough and at high water-oil ratios. A method is outlined by which the oil recovery performance of other uniform bottom-water drive systems can be estimated from the information obtained in these model tests. INTRODUCTION When oil is produced from a well which partially penetrates an oil zone completely underlain by water, the water rises directly beneath the well in a symmetrical cone when the system is uniform. Two different flow mechanisms can cause the water cone to form—coning and bottom-water drive. In coning, the aquifer is relatively inactive and the cone is formed beneath the well by the pressure gradients associated with the oil flow to the well. The oil can be produced by a solution-gas drive, an edge-water drive or other driving forces in the interwell area. In a bottom-water drive, the driving force for oil production comes from an upward encroachment of the underlying active aquifer. Two papers have analyzed the theoretical performance characteristics of bottom-water drive reservoirs. In the initial mathematical investigation, Muskat&apos; established the equations which determine the pressure distribution in this type of reservoir and solved these equations for certain conditions. Specifically, it was assumed that the water and oil had equal mobilities and equal densities, there were no capillary forces, the pressure throughout the oil zone remained above the bubble-point pressure, a constant pressure existed at the initial water-oil contact and the oil was completely displaced by the encroaching water. These assumptions were used in obtaining analytical solutions. In general, Muskat found that the sweep efficiency to initial water breakthrough to the well was larger for the thicker oil zones, the closer well spacings, the lower ratios of vertical to horizontal permeabilities, the smaller the penetration of the well into the oil zone and the smaller the bore size of the well. The production history after water breakthrough was expressed as a volumetric sweep efficiency at a given producing water-oil ratio. The results indicated that cumulative oil production at producing water-oil ratios of 10 is less affected by the well spacing than is the water-free production history. Muskat studied well spacing which today would be regarded as close. The maximum value of his dimensionless well spacing (ratio of interwell distance to formation thickness) was 4.3. This would require the development of a 50-ft-thick oil sand on less than 10-acre spacing if the vertical and horizontal permeabilities were equal, with

By J. W. Matousek, C. S. Samis

me thermodynamic properties of the components in the Cu-Ni-S ternary system have been studied by measuring the H2S/H2 ratios in a gas phase equilibrated with the molten matte at 1200°C. The measured sulficr potentials have been extended by extrapolation and combtned with previously published data to permit the thermodynamic analysis of the ternary system by integration techniques. A simplifying assumption of ideality in the Ni3Sz-CuS pseudobinary has been made. SINCE copper and nickel metals were first extracted from their sulfide ores the interaction between the two metals and sulfur has been of industrial and theoretical interest. The processes developed to extract copper and nickel have been reported periodically in the literature. The theoretical studies on the Cu-Ni-S ternary have been restricted to problems directly associated with production. It is only within recent years that the binary systems related to this ternary have been analyzed thermodynamically and mathematical devices developed to permit a corresponding treatment of the ternary system. In 1910 an investigation of the role of nickel in Cu-Ni-Fe-S mattes was reported,&apos; It was concluded from this work that nickel is not an element replacing iron in mattes, but rather that Cu-Ni alloys behave as a single metal during the matte converting operation. The laws which govern the converting of Cu-Ni alloys were found to be the same laws as those that govern the conventional converting of copper alone. Although considerable information has been reported on the theoretical aspects of copper smelting, little data is available on the smelting of Cu-Ni ores except for phase diagrams and process descriptions. The available information on the Cu-Fe-S ternary and related systems prior to 1953 has been summarized by Ruddle.2 Since Ruddle&apos;s publication, Rosenqvist and coworkers have completed phase equilibria investigations of the Fe-S, Co-S, and Ni-S binaries,3 the Fe-S-O ternary,4 and the Cu-Fe-S-O quaternary.4 An extensive investigation of the Cu-Fe-S ternary system at smelting temperatures has been made by Krivsky and Schuhmann.5 At these temperatures, the Cu-Fe-S system is very similar to the Cu-Ni-S ternary with respect to the location of the single-phase and two-phase liquid matte regions. In the former, however, the area of immiscibility is more extensive and the region of liquid matte-liquid metal-solid metal equilibria is much more extensive. Krivsky and Schumann observed that the Cu2S-FeS pseudobinary system is, for practical purposes, an ideal mixture. This investigation has served as a valuable guide in analyzing the Cu-Ni-S ternary. EXPERIMENTAL The experimental procedure employed in this investigation was the conventional technique of equilibration of the sulfide matte with gaseous mixtures of hydrogen and hydrogen sulfide at 1200°C. The thermodynamic properties of sulfur (S2) in the gas phase are determined by means of Eq. [I] and the activity of sulfur in the matte by Eq. [2].

Jan 1, 1963

By Robert E. Green

Formulae are given for calculating the modes of wave propagation in a single-crystdl specimen possessing a given crystallographic orientation. Such calculations lead to determination of the orientation factor appearing in the Granato-Lucke theory for the attenuation of these waves due to dislocation damping. A detailed treatment is given for the case of an aluminum crystal possessing the orientation having a maximum Schmid fac -tor of 0.5. FOR a number of years the attenuation of ultrasonic waves propagating in metals has been used to investigate various phenomena causing internal friction.Most of the experiments were performed on polycrystalline test specimens and the waves were assumed to be propagating in an isotopic medium. However Alers 6 in 1955 and more recently Hikata et at. Chiao and Gordon,8 and Swanson and Green 10 have used measurements of attenuation of ultrasonic waves to study internal-friction changes in single crystals. These authors were concerned with the energy losses experienced by the ultrasonic waves due to dislocation motion induced by plastic deformation of the crystals. Alers measured the attenuation of 7 mc per sec ultrasonic pulses propagating in zinc single crystals before, during, and after plastic deformation. Simultaneously he measured the time-dependent plastic strain at constant stress in order to study the correlation between this strain and attenuation. The crystals were oriented in such a way that the applied stress provided a direct shear on the slip plane, thus causing the deformation to proceed by slip on this plane. At the same time the high-frequency sound pulses were sent through the crystal perpendicular to the slip plane. He found that the attenuation of transverse waves, the stress vectors of which lie in the slip plane, was very sensitive to the deformation. The polarization of the particle displacements, associated with these waves, relative to the applied static shear stress, and hence the direction of slip, had no obvious effect on the results. The attenuation of longitudinal waves was affected by the deformation only when the slip plane was not perpendicular to the propagation direction. This indicated that the attenuation was caused by dislocations introduced by the deformation and moving only in the slip plane. Hikata et al. made simultaneous measurements of attenuation, velocity changes, and stress-strain relations on aluminum single crystals deformed in tension. Both longitudinal and shear waves were used, at frequencies of 10 and 13 mc per sec. They placed emphasis on the choice of propagation modes and polarization of the ultrasonic waves, such that interactions between these waves and dislocations on selected slip systems could be investigated. They also selected specimens possessing specific crys-tallographic orientations, which allowed investigation as a function of the number of equally favored slip systems under the applied stress. They found that, for symmetrical orientations, the change of attenuation decreases with the increasing number of equally favored slip systems, i.e., in the order

Jan 1, 1964

By T. E. Tietz, J. E. Dorn

Activation energies for creep of copper at intermediate temperatures, where crystal recovery was negligible, were determined by the simple technique of rapidly alternating the test temperature between and T2 (T2 = TI + about 10°K) throughout a constant stress creep test. The activation energy for creep H was found to be 37,000± 3,000 cal per mol, independent of stress and strain. The same creep laws as have been previously established for high temperature creep were found to be valid for creep at intermediate temperatures. But the AH was found to be lower than that for self-diffusion in the intermediate temperature range whereas it is known to be equal to that for self-diffusion at high temperatures. IT is now well established that creep at high temperatures can be correlated by the functional relationship&apos;-" e = f(?) s = constant [I] where E is the total plastic strain, f is the function that depends on the stress, ? = f e -- dt, t is the duration of test, e is the base of natural logarithms, AH is the activation energy for creep, R is the gas constant,T is the absolute temperature, and s is the stress. Thus, identical values of are achieved during creep under a given stress at two alternate temperatures at the same total strain. At the same strain therefore where subscripts refer to the two alternate temperature conditions of test. Consequently, the activation energy for high temperature creep is readily obtained with the aid of Eq. 2. Activation energies so obtained have been observed to be insensitive to the creep strain at which they are evaluated, the applied stress, grain size, minor alloying additions,&apos;-&apos; cold worked state, and the presence of thermally stable dispersions of intermetallic compounds in an a solid solution matrix Furthermore, the activation energy for high temperature creep is very nearly equal to that for self-diffusion in all cases where adequate data are available for comparison." " The apparent identity of the activation energies for high temperature creep and self-diffusion strongly suggest that high temperature creep arises from a dislocation climb process. This hypothesis is further strengthened by the fact that the energy of activation for high temperature creep is insensitive to the applied stress," and by the observations that the correlation suggested by Eq. 1 cannot be ex- tended to temperatures below those for rapid crystal recovery. When using the activation energy for self-diffusion, Eq. 1 fails to give the required correlations between creep curves at various intermediate temperatures.&apos; This suggests that the dislocation climb mechanism for creep might be superseded by some alternate mechanism in the intermediate range of temperatures. This investigation was initiated in a preliminary attempt to ascertain the type of creep law that might be valid in the intermediate range of temperatures. Special consideration, however, was given to the determination of the activation energy for creep in this range because the Becker-Orowan&apos;, " and the Mott-Nabarro10 theories for transient creep suggest that the activation energy should increase

Jan 1, 1957

By R. V. McAfee

The fundamentals of vertical-lift performance are examined with the aid of computer-calculated flowing gradient charts. Flowing and gas-lift well performance characteristics are determined from available well test data. The effect of tubing size, gas-liquid ratio and wellhead pressure is discussed for both flowing and gas-lift wells. The effect of gas-injection pressure, formation gas, bottom-hole pressure and valve spacing is also discussed for gas lift wells. From these studies conclusions may be reached for improving or prolonging natural flow, obtaining optimum lift efficiency when natural flow ceases and improving existing gas-lift systems. The techniques perfected satisfy the requirement that the time involved to conduct an evaluation be practical for operating personnel. INTRODUCTION Flowing pressure gradients furnish the key to successful evaluation of vertical-lift performance in producing wells. Command of multiphase flow gradients in some readily usable form is a necessity before operating personnel can competently include vertical-lift performance evaluation of both flowing and artificial-lift wells in their over-all consideration of production efficiency. A readily usable form cannot be overemphasized since most of the decisions which confront the production engineer with a problem well must be made quickly. In moving a barrel of oil from the reservoir to the stock tank, the major portion of energy generally is expended in the vertical-lift phase. This may or may not be of concern during the flowing life of a well, depending upon the production requirements. It becomes of some concern when the flow performance of the well becomes erratic, and a conscious effort must be made to maintain natural flow. It is at this time that the first steps may be taken to modify existing conditions to relieve unnecessary limitations to proper flow. When natural flow ceases and some form of artificial lift must be installed, the amount of energy expended in lifting liquids becomes quite obvious. It is at this time, if no other, that lifting efficiency becomes important because that part which must be supplied from an outside source is now related directly as a cost per barrel of oil produced. Ten years ago, the majority of gas-lift wells were produced with gas-well gas. Today, the majority are produced by closed rotative gas-lift systems. This permits a direct evaluation of well performance in terms of horsepower requirements and has resulted in mixed conclusions as to the success of gas lift based upon the relative efficiency of a particular system. An increased awareness of the need to resolve vertical-lift performance on a readily usable, scientific basis was inevitable. An indication of the need for better applied science in this field is the often-asked question of whether or not gas-lift can efficiently deplete a given well or reservoir. This question cannot possibly be answered without first evaluating reservoir, surface and vertical-lift performance both as encountered today and as anticipated throughout the life of the well or wells. The technique presented in this paper was originally developed to upgrade gas-lift installation design from an applied art to an applied science. It has since been successfully used not only for this purpose, but also for the whole field of vertical-lift performance in its broadest sense. Lift efficiency should be considered important while the well is still flowing, as well as after natural flow ceases. Correct interpretation and proper modification of the vertical-lift performance of a producing well can provide dramatic improvement in production performance and/or efficiency. STATEMENT OF THEORY AND DEFINITIONS Fig. 1 illustrates the three divisions of production which will be used in this paper. The terms are a modified version of those presented in the very fine paper by Gilbert.&apos; The fields of reservoir and surface performance both have been greatly improved over the years. A study of those writings which may be found indicates that the field of vertical-lift performance has not progressed as well. There are two possible reasons for this lack of progress. 1. It has not been recognized as a scientific field in itself by the oil companies, as has reservoir engineering. 2. The equipment companies have confined their efforts to mechanical design research rather than the more basic study of vertical-lift performance of producing wells. Both organizations must have an economic stimulus for doing research in this field, and most of the results obtained in past work has been so erratic as to arouse little enthusiasm. The basic purpose of interpreting vertical-lift performance is to predict operating conditions below the surface of the ground from available data. The success of the interpretation depends upon the accuracy with

By F. L. Fayers, J. W. Sheldon

It has been a matter of concern to the petroleum industry to determine what effect the capillary term has on saturation profiles, since these profiles determine ultimate economic oil recovery. In their original solution of the non-capillary two-phase flow problem, Buckley and Leverett&apos; showed that solutions of the two-phase flow equations became multiple-valued in saturation. Since it is physically unrealistic for saturation to have more than one value at a given position, Buckley and Leverett resolved this difficulty by introducing a saturation discontinuity or "shock". They evaluated the strength and position of the shock from material balance considerations. Recently Sheldon, Zondek and Cardwell&apos; have demonstrated that the method of characteristics can be used to solve this and related problems. Owing to capillarity it is physically unlikely that saturation shocks occur in an oil reservoir. Buckley and Leverett suggested that the effects of interfacial tensions should be included in the fluid flow equations, if the solutions are to give continuous single-valued saturation distributions. An analogy to this problem is encountered in the theory of wpersonic compressible flow where the introduction of the viscous term eliminates shock behavior. However, the mathematical form of the capillary term in the porous medium fluid flow equations differs from the viscosity term in the Navier-Stokes equation. This paper demons~rates that capillarity does eliminate the triple-valued behavior and indicates the magnitude of capillary and gravity effects on the saturation profile for a variety of systems. DERIVATION OF LAGRANGIAN AND EULERIAN FORMS OF THE DISPLACEMENT EQUATION The equations representing capillary, two-phase flow are given by applying Darcy&apos;s law and a material balance condition for each phase. The familiar Darcy and material balance equations are as follows. ^U*^0......<3, ^^r=°......c« S is the saturation of the water phase, and B the inclination of the porous medium. Pressures in the oil and water phases differ by the capillary pressure associated with the interfacial tensions, P.-P.=pAS)..........(5) where p, is determined experimentally. The porous medium is said to be oil-wet if P, > Po and water-wet if P, < Po. If the fluids are incompressible and the total volumetric flow rate, q, is constant, then v, f v,, = q...........(6) By eliminating P.. /»,, and v, from Eqs. 1, 2, 5 and 6 it follows that It is convenient to normalize the variables in the problem after the manner of Handy and Hadley% so that Eqs. 3 and 7 become where j,, = —, the fractional flow of water; (F, is a capillary pressure normalizing constant.) Substitution of Eq. 9 into Eq. 8 gives In this partial differential equation for an initial value

By R. W. Guard, M. E. Fine

By treating the dislocation like a surface and ap-plying the usual thermodynamic treatment to the adsorption process a Gibbs adsorption equation for dislocations was derived. For extended dislocations in binary solutions the adsorbed concentration on the fault, X2a, may be computed from (jo/da2b) where a2b is the activity of the solute in the bulk material and s is the stacking-fault energy. Using the data of Howie and Swann for s the adsorption concentration goes through a maximum at 2 at. pct Al in Ag-Al, 10 at. pct Zn in Cu-Zn, and 8 at. pct A1 in Cu-Al. The pinning stress calculated from this concentration difference goes Ihrough a maximum at the same concentration us the peak in X2 a. The computed pinning stress thus does not vary with composition in the manner predicted by Suzuki, as was also pointed out by Hendrickson. The results are compared with the stress increment which can be attributed to Suzuki locking in Cu-Zn and Cu-Al stress-strain curves. They both agree in magnitude and in the location of the maximum. The predicted and observed maximum values for the Cu-Zn system (where activity data are available) are 700 g per sq mm (predicted) and 1000 g per sq mm (measured, laking into account the orientation factor of 2.2 to convert poly-crystalline to single-crystal data). CERTAIN simple internal surfaces may be regarded as dislocation grids. This fact suggested that it might be profitable to consider certain phenomena related to segregation of solute atoms at dislocations from the point of view of the thermodynamics of surfaces and surface adsorption. A general treatment of this type is given and then the results are applied to Suzuki segregation and pinning. Confirmation of the results is obtained from comparison of stress-strain behavior for copper and copper-base alloys. Two kinds of dislocations need be treated: perfect and extended dislocations. In either case the line tension of a dislocation, ?. the work which must be done to increase the length of dislocation by a unit length, is analogous to the surface tension. For an undissociated dislocation ? is the self-energy of a unit length of dislocation; for an extended dislocation where is the self-energy per unit length of a pair of partials far enough apart so that there is no interaction energy, is the interaction energy per unit length, is the stacking fault energy per unit area, and w is the equilibrium separation of the paired partials. In the absence of an applied stress the force pushing the dislocation partials apart in a close-packed structure is Gb2/12p where G is the shear modulus, b is the Burgers&apos; vector of the complete dislocation, and is the separation of the partials. At the equilibrium separation, w this force equals s. Thus

Jan 1, 1965

By I. R. Dunlap, R. F. Burdyn, F. D. Patchen

The composition and properties of a new type of cementing mixture are discussed. In these compositions, API Class A or C cements are added to n stable water-in-oil emulsion instead of the crsual water. The cement disperses in the oil phase and remains out of contact with the water under normal conditions of mixing and storage. At higher temperatcrres, such as those encountered down-hole during placement, the emulsion breaks and cement hydration can then proceed. An extremely low filtration rate is obtained; the major part of the filtrate is oil. Thickening times of the mixture may be increased to meet the 18,000-ft casing cementing schedule by varying the amount of emzilsifier. As in conventional Portland cement mixtures, high-temperature strength retrogression can be overcome by addition of silica flour. Results of several field app1ication.r show that mixing presents no diffculty if emulsion blenders are used and the emulsion is prepared beforehand. INTRODUCTION Water-in-oil emulsions., in which oil is the continuous or external phase and in which water exists as discrete droplets, have for some time been used successfully in drilling muds to reduce filtration loss.1,2 Applied to cement slurries, the same results are obtained; i. e., the fluid-loss is greatly reduced. In addition, thickening times may be extended, lower densities and strengths obtained, and water-base borehole fluids more easily displaced without contamination of the cement. A low filtration rate is often a desirable property in oil well cements since loss of fluid increases placement difficulties and may also cause damage to water-sensitive producing formations.&apos; In the casing cementing operation where the cement slurry is pumped into the narrow annulus between open hole and casing, rapid loss of fluid to a porous formation can cause the slurry to thicken and plug the annulus before the desired fill is obtained. Where a casing or a liner is cemented against a productive formation and the well completed through perforations, the fluid lost between the time the cement first contacts the formation and the time a set is obtained may invade the zone past the depth of the perforations. If the sand contains a material which will swell upon contact with cement filtrate, permanent damage may result. Previous methods for reducing the fluid-loss of cements have employed bentonite4 as an additive, usually with a lignosulfonate as a dispersant, or a derivative of some naturally occurring polymeric material such as cellulose ether." Oil emulsion cements have also been proposedv or fluid-loss reduction, but these have been of the oil-in-water type. Bentonite cements have been used most widely and have been successful in reducing incidence of premature setting of cement attributable to loss of water by filtration. It is the purpose of this paper to describe preparation and properties of a water-in-oil emulsion cement and to relate procedures followed and results obtained in several field applications. DESCRIPTION OF SYSTEM AND MECHANISMS A water-in-oil emulsion cement is prepared by adding an API Class A or C cement to a stable water-in-oil emulsion. Fig. 1 is a photomicrograph of this emulsion before addition of cement. Here the droplets are water and the surrounding medium is diesel oil. High emulsion stability is indicated by the small droplet size [1-5 microns], and by their uniformity.&apos; To form a stable water-in-oil emulsion as illustrated, several conditions must be met. A predominantly hydrophobic emulsifier must be present in sufficient concentration to produce a strong interfacial film; initially, the phase volume ratio (the water-to-oil ratio) must be low;

By David R. Mitchell

THIS paper is limited primarily to a description of dry coal-cleaning processes in which air currents are used to effectuate a separation between coal and refuse. Processes depending mainly on differences in the coefficient of friction, resilience and shape are not described unless the use of air is necessary for the proper functioning of the process. The air cleaning of coal is of primary importance to the coal industry of the United States. From figures presented in the 1941 edition Mechannual,1 it is estimated that at least 12 million tons of bituminous coal was cleaned in the United States during 1940 by machines using air as the separating medium. One of the current problems confronting the coal-preparation engineer is the dry cleaning of small sizes and slacks. Progress in machine development for the cleaning of small sizes has been slow in recent years in the United States of America; it has been much more rapid in Britain and on the European continent. This paper does not attempt an exhaustive survey of all these developments, and only machines and processes that have found considerable commercial application are cited. Further, no critical analysis has been made of the theory involved in the separation of coal from refuse by processes using air as the separating medium other than that necessary for an understanding of particular machine designs and applications. HISTORICAL SUMMARY The possibility of using air for the separation of coal from refuse was recognized early by mining men and many attempts were made to develop commercial machines. The ingenuity of the early experimenters is to be marveled at in view of their lack of knowledge of the theoretical principles involved. As in other arts, practice has largely preceded theory. Yet, science and practice play a game of leap frog, now one ahead, then the other; the careful experimenter governs his efforts along practical lines by adapting his experiments to the limits prescribed by scientific laws. By first studying developments and the theory involved, it is not only possible to adapt processes to new uses but also to reduce materially operating cost and to build larger units without costly failures. Although many inventors have applied for patents for separating minerals by the use of air currents, the literature in regard to coal is meager. Berrisford2 describes briefly some of the early attempts to clean coal without the use of water. Several of the examples cited by him are reproduced herein. Fig. I shows a machine used for grinding and sizing, in which rollers running in a pan with a perforated bottom and fan opening on the side crushed the coal, which was then carried by the air currents to a settling chamber. The heaviest particles dropped out first and the light ones farthest away, as shown. In the year 1864, a machine was made that could be used as a sizer or to separate dirt from coal with a sized feed (Fig. 2).

Jan 1, 1942

By Samuel H. Dolbear

THE purpose of a technical report is to record facts, usually collected by investigation, and to interpret these facts in understandable language. The audience may range from a small shareholder without technical knowledge, to a highly trained engineer or geologist. If the client is a mining company with technically trained executives, the report writer&apos;s problem is relatively simple. The writer will then be appraised not only for his conclusions, but for clarity of language and organization of the report. If the writing is bad, the construction careless, and there is a failure to clearly convey to the reader the facts and the author&apos;s conclusions, the report is a failure and the writer may have damaged his professional character. Spoken words die quickly, written words may constitute a permanent record and if they are badly composed they may rise up to damn the author. "A good measure of an author&apos;s understanding of his subject is his ability to express it clearly in plain words." Good English Teachers in the fields of mineral technology have frequently complained that even in post-graduate groups there is an appalling indifference to their appeals for good English. Some have even noted a student&apos;s belief that the use of refined English is effeminate. If those with such immature beliefs could measure the pay-check damage arising from the use of "sloppy" language, they would realize that precision and refinement in English may be quite as important as technical accuracy. When the reader audience is without technical knowledge simplicity in treatment becomes especially important. If one is engaged in consulting work, in government service, or in any field where reports have public distribution, the language employed should be technically adequate but simple enough to be understood by non-technical readers. For example, one may use the term "visual" in place of "megascopic." Technical language can be so obscure that it cannot be understood even by highly-trained students. In the March-April (Vol. 47-No. 2) issue of Economic Geology, Nicholas Vanserg ridicules these extremes and quotes various paragraphs from published material, such for example: "However, lattice orientation unaccompanied by cognate dimensional orientation can never be attributable to growth from an isotropic blastetrix." "The temperature declines because of cessation of the exothermic chemical and mechanical equilibriopetal processes." These he calls "good geologese" and they are calculated not only to baffle the reader but to impress upon him the erudite character of the author. Revision In some cases, difficulty arises from the fact that the writer is too close to the subject and unconsciously assumes that his reader is equally familiar with the background of the report. It is difficult for the writer to regard his work objectively and to determine to what extent it is likely to be understood. Every important manuscript will gain in clarity if the author will have it reviewed by an informed reader. But the writer must not be oversensitive to criticism and should not treat his composition as perfect and beyond the possibility of improvement. The first draft of a report always requires revision, regardless of the care used or the ability of the writer. Three or four revisions are not uncommon. The first draft usually requires expansion in places, the deletion of non-essential material, and language changes to promote clarity of expression. This should be done by the author after a lapse of time, even if only overnight, in which his mind has been occupied on some other subject. Possible improvements are always more visible. The manuscript should be passed on to another reader for further suggestions. Organization of Material The engineer should study available reports and library references before going into the field. If the previous reports have been responsibly done and can be accepted as correct, then much field time can be saved. It is, of course, customary to make some on-the-ground checks to confirm earlier reports, particularly those relating to ore reserve which may have undergone changes. Report writing requires time and expense, but nevertheless, the basic reasons for conclusions should be presented even in the case of a worthless property, for it may prevent a duplication of the work. If the mine examined is obviously of no further interest, no useful purpose can be, served by preparing a report in detail. In one case an engineer travelled all the way to South America only to find that the mine had been grossly misrepresented and was valueless. His cabled report "Nonsense" is a case of over-simplification, but it served his company&apos;s purpose. The first step in report organization should be the selection of subjects. This should be done at the mine, and the data collected for each subject should be reviewed in considerable detail on the ground. Otherwise one may find that he has failed to collect some essential details not readily obtained after he has returned to headquarters. If the property to be described is undeveloped, then many of the subject titles are automatically eliminated. Usually no useful purpose is served by an attempt to calculate the cost of production under such circumstances, although the cost of exploration

Jan 1, 1952

By R. N. Thurston, E. A. Nesbitt, G. Y. Chin

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deformation gradient matrix, F - [axi/aXj1, where X and x refer to the initial and final positions of a particle. This matrix is readily evaluated in terms of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip system. In the case of deformation from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors&apos; knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Goler and Sachs.4 Taylor and Elam5 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(dN as N — m while a — 0 in such a way that the Product Na = 0, a ftnite conslant designatzng the accunzulated amount of shear. It turns out that this limit is simply , where F, is the matrix whose elements are the coefficients of a in the F(a) matix. Application is made of the present treatment to a fcc crystal of Perlrzalloy compressed on the (110) plane and contrained to elongate zn the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.&apos; Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By H. J. Snyder

Both the room-temperature and 600°F (315°C) primary solid-solution phase boundaries for the silver comer of the Ag-Cd-In temary system have been determined using X-ray diffraction and metallo-graphic techniques. Solid solubility of indium in silver at room temperature and 600°F (315°C) is shown to be between 20.3 and 21.7 wt pct, and corrects the previously extrapolated value of 18 wt pct appearing in the literature. The solid solubility of cadmium in silver at room temperature, not previously established, is shown to be between 34.9 and 41.3 wt pct. The solid solubility of cadmium in silver at 600°F (315°C) is confirmed as 43.2 wt pct. The shape of the primary phase boundary line for the subject temary system appears straight at room temperature and curves con-vexly towards the solvent (silver) comer at 600°F (315°C). THIS investigation was undertaken to initiate development of the Ag-Cd-In ternary diagram by establishing the primary solid-solution phase boundary in the silver corner of the diagram. At the present time, a diagram for this ternary system is not available, while this system appears to offer potential for a variety of uses. One alloy in the system has already proven to be useful as a control rod material in nuclear reactors.1"3 To encourage additional exploration of the potential of the system an understanding of its ternary diagram would be beneficial. It is towards this end that the present study is directed. LITERATURE SURVEY In undertaking this study, a comprehensive literature survey was first conducted to find information that would be useful for guidance. Useful knowledge did result from investigating the respective solubilities of indium and cadmium in silver as indicated in the binary constitutional diagrams of the systems Ag-In and Ag-Cd and also reviewing possible shapes of ternary primary phase boundaries. Weibke and Eggers~ used metallographic techniques to establish the system In-Ag as illustrated in Fig. Is This diagram shows that silver in the solid state is capable of dissolving approximately 18 wt pct In. This solid solubility of indium in silver holds true from room temperature up to 1276°F (691°C), then decreases continuously up to 1&apos;761°F (960.5"C), the melting point of the silver. The solid-solubility limit of indium in silver established by Weibke and Eggers has been confirmed by Hume-Rothery and Reyno1ds. G Durrant&apos; used a method which consisted of microscopic examination of quenched specimens to establish the Cd-Ag system as displayed in Fig. 2.&apos; The primary phase boundary of Fig. 2 proved to be in good agreement (ie., within 1 wt pct) with other studies*&apos;1&apos; of the Ag-Cd system made using X-rays and metallog-

Jan 1, 1968