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By A. Kelly, S. Sato

Tensile tests have been performed on aluminum single crystals of 99.99 pct purity at 196°K. The resolved shear stress when the stress-strain curve becomes concave to the strain axis depends on orientation, being always higher for crystals with an initial orientation close to the sides of the unit triangle. Observations have been made, with the optical microscope, of the appearance of slip lines on polished surfaces of the crystals. Particular attention has been paid to the first appearance of cross-slip. It is confirmed that marked cross-slip is first seen when the stress-strain curve becomes concave to the strain axis. Measurements are reported of the lengths of the slip lines observed on top and side faces of the crystals at various stages of the deformation. The lengths of the slip lines vary inversely as the flow stress for all crystals, independent of crystal orientation. From measurements of the lengths and separations of the slip traces it is possible to estimate the number of dislocations which are annihilated at each cross-slip site. It is concluded that the annihilation of screw dislocations of opposite sign is the most important cross-slip process occurring. FRIEDEL1 recently pointed out that the stress-strain curve of many pure metals of face-centered-cubic structure can be considered as composed of three stages. Plastic flow commences with a region showing a small rate of hardening which is approximately linear. This has been called "easy glide*. It is followed by a region of more rapid hardening in which the slope of the curve is again approximately constant and this, in turn, is superseded by a final part of the curve which is concave to the strain axis. Following Diehl2 we may designate these regions as stages I, II, and III respectively. The onset of stage 111 occurs at lower stresses at higher temperatures. The appearance of the slip lines formed during these various stages has been described by a number of workers?-5* The object of the present work was to make detailed observations of the lengths and separations of slip lines for a number of crystals of different orientations deformed at the same temperature and strain rate. Although much previous work has been published on the deformation of aluminum single crystals the importance of measurements of these quantities has only recently been realized—they are essential for experimental tests of recent theories of work hardening.' 9 In aluminum, deformed at room temperature, stage 11 of the stress-strain curve is very weakly marked, as the stress for the onset of stage 111 is attained soon after the end of easy glide. In the present experiments it was decided to use a temperature lower than room temperature so that stage II of the curve was better developed. However, at temperatures as low as 90°K slip lines are not measured easily with the optical microscope.5 For this reason 1960k was chosen as a suitable temperature. Even at 1960k however, stage III of the curve commences at glide strains of 6 to 10 pct and hence

Jan 1, 1960

By R. R. Klimpel Discussion by C. C. Harris, L. G. Austin

C. C. Harris (Columbia University) — The authors ' have presented relationships for the random division of a magnitude into r + l parts taking account of the order of selection. Interpreting their model in comminution terms, their Eqs. 7, 9 and 11 refer to the one-dimensional case; that is, to the subdivision of a long thin rod at random. It is assumed that the fragments may be indefinitely small. Real materials, however, are limited in the degree of subdivision which can be attained through the intervention of practical restrictions. One in fine grinding is the depletion of microflaws as material becomes finer. Another is the

Jan 1, 1969

E. T. Turkdogan (British Iron & Steel Research Assoc., London, England)—I would like to suggest a different method for the treatment of the authors' data on the Si-0 equilibrium in liquid iron. Because the activity coefficient of silicon dissolved in iron is influenced by the concentration of silicon as well as that of oxygen, the equilibrium constant K2 of reaction 2 becomes a function of metal composition, and, as shown in Fig. 1, a plot of log KP1 at 1600°C against the weight percent of silicon gives a smooth curve. A similar curve is obtained when log Kzl is plotted against the oxygen content of iron. Before

Jan 1, 1955

By E. R. Brownscombe, Francis Collins

The pressure distribution in a reservoir producing an incompressible fluid by radial flow in a horizontal structure is a simple logarithmic function' used daily by reservoir engineers. The assumption of an incompressible liquid is equivalent to assuming that pressure is maintained constant at the well radius and at some external "radius of drainage," or, in other words, that the entire flow into the well passes across the external radius. In most cases a well is surrounded by other wells draining adjoining areas so that the "radius of drainage" is not a line of constant pressure with flow equal to the flow into the well but rather a contour of zero pressure gradient across which no flow occurs, production being due to the expansion of the liquid within the area. The radial flow steady state pressure distribution for this case does not seem to be extensively used despite the fact that the mathematical analysis has been given in detail' and the results are simple and generally applicable. 'The object of this discussion is to develop this result from a physical rather than a mathematical viewpoint, thereby aiding intuition in judging circumstances to which it may be applicable. If the production rate at a well in an unsaturated reservoir is maintained constant while no flow occurs across the outer radius a steady state will soon be reached in which the flow rate or pressure gradient is constant with time at all points in the reservoir. To preserve such a condition it is necessary that the pressure decline at the same rate at all points in the reservoir, that is, the curves of pressure versus radial distance at successive times are all parallel. Then each unit volume of oil is expanding at the same rate and contributing an equal share to the production. The rate of flow q across any circle r is thus proportional to the volume of the reservoir between r and the external radius re, or q = qw (I-r2/r2e) ......(1) where q, is the production from the well and it is assumed that rw is very small compared with re. This equation can be combined with the differential form of Darcy's law for radial flow, 2phkr dp q =—— ........(2) aµß dr ( where q is not a constant as in the incompressible flow case but is a function of r given by Equation (1). If Equation (1) is substituted in Equation (2) the variables p and r can be separated and the result integrated to obtain the pressure distribution p = pw +--------In------------- 2pkh[ rw 2re2] ......(3) This equation differs from the incompressible case only in the addition of the term proportional to the square of the radius

Jan 1, 1950

By K. D. Hester, A. C. Anderson

The Elliot Lake uranium deposits are contained in a pebble conglomerate which is similar throughout the basin. This paper compares the solid-liquid separation circuits of two nominal 3000 T/d acid leach uranium concentrates treating Elliot Lake ore. One concentrator employed rotary vacuum drum filtration for solids removal and washing, the .other used counter current decantation in torque arm thickeners. Capital and operating costs, operation and maintenance, and metallurgical performance of the two solution recovery methods are compared and contrasted. A recent development, removal of the sand fraction ahead of C.C.D. and separate sand washing in hydraulic cyclones, is also discussed.

Jan 1, 1973

By R. B. Falk, F. E. Luborsky

Small iron particles in mercury pow by diffusion of iron atoms through the mercury. Iron particles, with diameters about 200Å, have been stopped from gvowing in size, even up to the boiling point of mercury, by the addition of a third metal. The metal additives were classified according to whether they produced 1) negligible inhibition, 2) some inhibition, or 3) marked inhibition of the growth rate. Metal additives which resulted in a marked inhibition of iron-particle growth form a stable monolayer on the iron particles. Only those metals which may form compounds with iron showed this pronounced effect. The one exception was manganese. Metal additives which resulted in no inhibition of growth, showed no evidence for adsorption and could not form compounds with iron. None of the added metals, even those which strongly inhibited particle gvowth and thus had adsorbed on the particle surface, actually formed any compounds with iron at room temperature at the concentrations required for complete inhibition of growth. ThE stabilization of the size and shape of metallic particles dispersed in liquid metals has important technological implications in "homogeneous" nuclear reactor systems and in elongated particle magnets and is directly related to the problem of corrosion by liquid metals. Growth in these par-ticulate systems may occur by diffusion of atoms from surfaces of high energy, corresponding to a small radius of curvature, to surfaces of low energy or large radius of curvature. Thus, small particles dissolve and large particles grow to increase the average diameter of the particles. reenwood' has analyzed this diffusional growth of a system of particles containing a distribution of sizes and has obtained reasonable agreement with data on the growth of uranium particles in liquid sodium and UPb3 particles in liquid lead. Greenwood concluded from his analysis that the chief factors promoting stability of dispersed particles growing by a diffusion mechanism are large mean radius, high density, and low molecular weight with low values of the solute diffusion coefficient, the solubility, and the interfacial tension. In the case of elongated particle magnets the system of interest is that of iron particles dis- persed in mercury. Previous work,2 concerned with "spherical" particles in mercury, has indicated a diffusional growth mechanism similar to that discussed by Greenwood. It has also been shown3'4 that the addition of certain metals to Fe-Hg dispersions results in the formation of a monatomic layer of adsorbed atoms on the iron particles. In this paper we will show that this adsorbed layer provides the decrease in the iron-atom flux through the mercury necessary for size stabilization. The general features of the stabilization of the iron particles in mercury through the formation of this "coating", with many different metals, will be described. EXPERIMENTAL RESULTS Iron particles in mercury were prepared by elec-trodeposition,2, 4 and measurements2, 4 of coercive force HCi) and saturation induction (Is) were used to follow changes in size and composition during thermal aging in the mercury in the presence of relatively small amounts of an added metal. In Fig. 1 is plotted the aging behavior of spherical particle samples in the presence of some of the added metals to be discussed. The iron particles have an initial average diameter of 180Å. Each sample was aged for 20 min at each temperature in succession in the presence of a twofold to threefold excess of added metal over that required to form a monolayer on the iron particles. These are the same samples used previously3 to study the adsorp-

Jan 1, 1965

By John Dasher

Getting spodumene to float quickly and cleanly can be a problem. The author has presented an excellent account of a valid and useful approach to the scale-up of such problem floats. This indicated advantages for doubling retention time, i.e., buying another set of flotation cells. The author states that 21 pct of the spodumene floated in 2 min in the laboratory cell, that the grade of the rougher was about 75 pct spodumene, and that the final tailing contained 4 to 12 pct spodumene in different sizes with the present cells and 1 to 9 pct spodumene with twice as many cells.

Jan 6, 1959

MINING AND METALLURGICAL SOCIETY OF AMERICA San Francisco Section The San Francisco Section of the Mining and Metallurgical Society of America held a joint meeting with the local section of the American Institute of Mining Engineers at the Engineers' Club, San Francisco, on Tuesday, Apr. 16, 1918. The meeting was preceded by a dinner. Letters from the parent body in NewYork asking for the consideration of the proposed bill before Congress, and an expression of opinion relative to the appointment of a Federal Administrator of Mines justified the joint meeting of the local sections of the two mining societies, in that a more representative opinion of the engineers of California could he obtained. The meeting was called to order at 7:15 P.M. by Mr. Frank H. Probert acting as Chairman. About thirty engineers were present. Mr. Probert read a letter of March 14, from Secretary Huntoon, asking that the meeting be called. He read excerpts from Bulletin 117 of February 28, 1918, of the Mining and Metallurgical Society containing a copy of the proposed bill, so that all present might be advised of its essential contents. He briefly commented on the urgent need of such legislation and invited discussion of the subject. After long and thorough discussion on the part of the members present, Professor Lawson made the following motion: I move that a resolution expressing the sense of the joint meeting of the local sections of the American Institute of Mining Engineers and Mining and Metallurgical Society of America be forwarded to the secretaries of the two societies to the effect that we heartily approve of the purpose and intention of the bill designed to promote and stimulate the production of minerals necessary for the successful prosecution of the war; and that we suggest prices should be fixed for the period of the war and two years thereafter, and that these prices, guaranteed by the Government, should apply at the nearest shipping point to place of production of the minerals. This motion was carried. The meeting then adjourned, and a telegram was sent by Mr. Probert, the Chairman, to Mr. Huntoon, notifying him of the motion that had been carried at the meeting.

Jan 7, 1918

By Harold Linke

THE following article presents notes and data compiled and computed by the writer for use in the determination of: size and slope of mill launders, details of junction boxes and downspouts, and distribution of pulp. It also includes pulp formulas, volume of discharge through bushings, paths of discharging streams, banking of turns and curves. In the design of a concentrating mill, the draftsman usually considers launders to the extent of providing ample "head" for transmission of pulp from one department of the mill to another. The superintendent of construction aims to build his launders wide and deep, and on a slope steep enough to ensure positive flow. So launders are laid generally on too steep a slope, with the result that the repair gang works to maintain launder bottoms and sides against the erosive action of the conveyed pulp. To this end many kinds of liners have been devised: concrete, mastic, white iron, glass, rubber. True, the reduction of slope to the point where a pulp will flow with minimum wear, will minimize labor and expense; but when the desired slope is not predetermined, the millman hesitates to readjust his launder slopes by cut-and-try methods. To the end that the desired size and slope may be found readily, the writer has: (1) conducted experiments with pulps of different specific gravity, screen analysis and dilution; (2) gathered a few graphic data from standard reference works (such as Peele's Mining Engineer's Hand-book and Taggart's Handbook of Ore Dressing); (3) computed several tables; and compiled results that have proved dependable for Utah Copper ore. It is quite possible that the following tables and graphs may not be applicable to all ores, but it is hoped that they may prove helpful, even in slight degree, in alleviating a portion of the trouble and migraine of some other millman.

Jan 1, 1939

By William B. Plank

STATISTICS just released by the American Society for Engineering Education and given in the table, show that the total current enrollment of 200,227 in the 220 engineering schools of the U. S. and Canada represents a gain of 9.8 pct over a year ago, while the mineral engineering enrollment in the U. S. of 9826 shows a gain of only 4 pct in that field. The spurt in the mineral group shown last year is thus slowed down to less than one half of that in the whole engineering student body. Last year, it was growing more rapidly than the whole engineering group.

Jan 5, 1954

By V. W. Buys, R. E. Havener

11.3-1. Basic Principles. Communications systems available for application to surface mining operations can be divided into basic categories. These are: 1. Wired systems requiring some type of metallic conductor 2. Nonwired systems, or those commonly referred to as space-radio systems. Under the heading of wired systems, telephones of the ringer type utilizing magnetos were used in the early pit operations. These are still being used in underground mining operations where calling is accomplished by ringing a code made up of short and long rings. While the standard Bell Telephone Systems have not been applied extensively in underground mining, they have been used in open pit operations but have the disadvantage of using multiple pair cables which must be installed and maintained as the mining operations proceed. They have the advantage however, that when a Bell System is installed in a surface mining operation, communication is available not only within the operation but to any point in the world through the facilities of the world-wide Bell Systems. A second type of communication available is the audio system or public address system requiring the use of a special audio cable made up of shielded pairs for the loudspeaker and microphone circuits. Audio systems have one outstanding advantage over most telephone systems in that, with a high-powered amplifier, a paging call can be heard over and above the high ambient noise conditions usually found at a surface mining operation. However, they have the disadvantage of requiring special cable which must be installed and maintained. Another type of wired communication system available for surface mining is that of carrier frequency equipment similar to that used in underground mining operations. In this system, transmission is accomplished by means of a frequency modulated carrier that travels over the underground trolley wire, the rail on which locomotives travel, and adjacent telephone wires.

Jan 1, 1968

By AIME

WILLIAM WALLACE MEIN, known to his intimates as "Will" or "Billy", is a mining engineer who has taken the fundamentals of successful mining--operating, engineering, and financial-and applied them to the founding of new industries. Born in Nevada City, Calif., in 1873, Will Mein grew up in an atmosphere of mining, and began to develop his sound judgment in a practical way before starting his formal technical education. As a young man he supplemented his early observations by helping his father, Captain "Tom" Mein, on mining work in California and Alaska. He then went with his father to the Rand, and after a period of milling experience as operator and shift boss he became, in 1894, manager of the chlorination of gold ores at the Robinson mine.

Jan 1, 1947

By George Rice

WITH so tremendous a subject, an attempted review of the coal situation of the world in a short talk must necessarily be of a sketchy character. It is hardly necessary to tell a body of engineers that had it not been for nature's gift of coal the material side of modern civilization would never have reached its present status. On the other side, it is regrettable that it was a byproduct of coal, T. N. T., which made possible Germany's initial success in this war, because that country had an enor-mous development of manufacturing plants that could be immediately utilized to make this destructive agent. One sometimes hears the casual remark that when the coal of the world is exhausted we shall use electricity; but, of course, electricity is ordinarily only a means of transforming and transmitting energy derived from fuel or water power, and chiefly from coal. It is true, we have much undeveloped water power, but it is more or less remote from the centers of industry; and when all shall have been developed it will not begin to supply the power requirements of the world. It is, however, reasonable to expect that before the world's supply of coal shall be exhausted, methods will have been discovered of harnessing other forces of nature, such as the tides, or the energy emanating from the sun. Petroleum and natural gas naturally come to mind, but the days of both, as fuel, appear to be numbered, although the products of petroleum, if economically used, doubtless will be available for internal-combustion engines, automobiles, trucks, and boats. for a long time, provided the reckless use of crude petroleum as an ordinary fuel is stopped. The products of petroleum are too valuable to mankind for such waste to be permitted. The civilization of the world, therefore, appears to rest, and, so far as can be seen, will indefinitely continue to rest, upon coal.

Jan 1, 1918

By D. J. Schmatz, H. I. Aaronson, H. A. Domian

Diffusion kinetics in disordered hcp Cd-Mg alloys have been investigated by means of the Kirkendall effect and concentration-penetration curves determined with an electron-microprobe analyzer. Self-diffusion coefficients of both species were determined at the three marker compositions obtained, averaging 27.6, 46. 7, and 78.1 at. pct Mg, by means of the Darken analysis. These coefficients were then corrected for the unequal and concentration-dependent partial molar volumes of the two elements with the Balluffi analysis, and for the vacancy flux effect by the Manning analysis. The latter correction reduced the Balluffi correction produced larger changes in the self-diffusiv-ities; neither, however, produced statistically significant changes in the Do's or the H'S. The most striking result of this investigation is that at all three compositions and at all temperatures studied both the uncorrected and corrected self-difjusivities of magnesium are higher than those of cadmium. The Cd-Mg system is the first one found in which the higher melting, lower vapor pressure element diffuses more rapidly. Both an empirical correlation due to Toth and Searcy and considerations of the atomic mechanism of diffusion indicate that this anomaly is probably due to a comparatively low value of the activation energy required for a magnesium atom and a vacancy to exchange sites, perhaps occasioned by the higher compressibility of magnesium atoms. KIRKENDALL effect studies have been previously reported for only two hcp solid solutions: the E phase of the Zn-Cu system1 and the a phase of the Cd-Hg system.' In neither investigation were the marker-movement studies supplemented with the concentration-penetration curve determinations necessary to evaluate self-diffusivities by means of the atano and the Darken analyses. The present program was undertaken to obtain both types of data on a hexagonal solid solution in order to provide more detailed information relevant to the mechanism of diffusion in this type of lattice. The Cd-Mg system was chosen for this study because the disordered solid solution extends across the entire phase diagram at temperatures above 253"c5 and the substantial difference in the melting points of the component pure metals promised that marker movements would occur at reasonably rapid rates should the diffusivities of the two species be as unequal as might be anticipated. The experimental convenience of the relatively low melting points of cad-miun and magnesium and the availability of extensive and accurate activity data6 (required for application of the Darken analysis) were additional reasons for selecting this alloy system. Since the anisotropy of diffusion is not large in either pure cadmium7 or pure magnesium,' the diffusion couples were prepared from polycrystalline components. The presence of a well-defined texture in the couples—the c axis of individual crystals tended to be normal to the diffusion direction— however, provides a fair degree of crystallographic definition to the data obtained. The principal (and entirely unexpected) finding of this investigation, that magnesium, the high-melting low-vapor pressure element, diffuses more rapidly than cadmium, in contradiction to a broad range of results in fcc and bcc alloys, as well as in the previously studied hcp alloys,172 makes the self-diffusivity determinations of immediate interest in understanding the origin of this anomalous result. EXPERIMENTAL PROCEDURE The cadmium (Belmont Smelting and Refining Co.) and magnesium (Dow Chemical Co.) used in this study were both of 99.99 pct purity. Alloys containing 51.0 and 65.6 at. pct Mg were prepared from these materials by melting under a MgC12-base flux in a high-purity graphite crucible. These alloys were subsequently hot-worked and then homogenized in a helium atmosphere at temperatures close to their solidus points. Sandwich-type diffusion couples of the type g/d/g were prepared from the pure metals by solid-state diffusion. Two-piece alloy couples of Mg/65.5 at. pct Mg (Mg/gCd) and Cd/51.0 at. pct Mg (Cd/CdMg) were welded by a liquation technique. The individual components of both types of couple were initially cylinders 1.27 cm in diam and in length; the ends of these cylinders were machined accurately flat and parallel. For both welding techniques, the pure cadmium cylinders and the alloys were chemically polished in a mixture of 40 pct ethyl alcohol, 40 pct hydrogen peroxide (30 pct conc), and 20 pct nitric acid,g while those of pure magnesium were polished in a solution of 10 pct nitric acid in ethyl alcohol.' Immediately afterwards, both metals were rinsed in freshly distilled acetone, and then in similarly purified methanol.' The Mg/Cd/g couples were assembled in a carefully cleaned stainless-steel welding fixture, in which a screw operating through a self-centering arrangement permitted a controlled pressure to be exerted upon a couple prior to welding.'' Tungsten marker wires 0.005 cm in diam were placed at the d:g interfaces of some of these couples, and imbedded in the couples during the application of pressure. As soon as a couple had been assembled, the welding fixture was inserted into a Pyrex capsule containing a packet of zirconium chips at each end. The capsule

Jan 1, 1967

THE CHAIRMAN (A. F. LUCAS, Washington, D. C.).-The activities of the Petroleum and Gas Committee for the half year have brought gratifying results, as exemplified by 14 technical papers, brim full of novel and attractive issues in which we are all keenly interested. I beg to extend my hearty thanks to all members and authors who have responded to my appeal, and to all those who have endeavored to meet the growing demand which has resulted in the augmented production of this commodity which is so essential for the Nation's welfare, comfort and safety. As you well know, within the last few years, petroleum and its products have been used for numerous and novel purposes, so that we have become accustomed to their use in thousands of activities, and pleasures as well, but we should also note that we have been wasting and misusing these wonderful products, apparently believing that their sources are inexhaustible.

Jan 1, 1918

By C. L. Colburn

Discovery is the first step in the location of the claim. The provision of the Revised Statutes (2320) is, " No location of a mining claim shall be made until the discovery of the vein or lode within the limits of the claim located." Strictly speaking, discovery may be defined as the finding of ore or metalliferous rock in place in a well-defined vein. This definition was too strict, so discovery extended later to cover such indications of the pregence of ore, within rock in place, as would justify an experienced miner in spending his time and money with a reasonable expectation of finding ore in paying quantities. According to Colorado statutes a discovery must show a well-defined crevice; in Arizona, a lode, deposit, or mineral in place; in Montana, a well-defined crevice or valuable depositi; in Nevada, a lode or deposit of mineral in place. It is wrong to require a discovery. An honest prospector, wishing to obey the law, finds himself compelled, in most cases, to evade this point. In Clear Creek district, Colorado, a quartz seam will constitute a discovery; in Butte, a red capping; in Leadville or Ely, it is any place where a man can find a piece of vacant ground big enough upon which to sink a . 10-ft. hole. If the vein or deposit outcrops a man can show a discovery, but if it does not outcrop it is foolish to compel him to show one; and this point has been gently side-stepped. Any hole 10 ft. deep now constitutes a discovery. It is no use having laws that the people cannot consistently ob_ey. No sane man will dig unless he expects to find mineral, and he should be protected while digging. He should be required to show that he has mineral ground only when he comes to patent.

Jan 1, 1915

By L. D. Mullins, E. B. Elfrink, W. L. Wahl

In the past few years several articles and papers presenting results of solution gas-drive depletion calculations have appeared in the lit-erature. Such calculations are of interest to the oil industry, for investment decisions must often be made before much is known about a reservoir. At other times, an estimate of the possible benefits to be realized from alternate production methods is desirable, and theoretical depletion calculations can serve as a floor or reference level from which to work. In any case, an estimate of ultimate oil recovery based upon engineering data is commonly required. An engineer confronted with the problem of obtaining, for a specific reservoir system, an estimate of ultimate oil recovery by solution gas-drive depletion usually will be forced to perform the calculations himself. This is despite the quantity of data in the literature. Rarely will either experience or the literature provide results from a reservoir system similar in all important respects to the one under consideration, and calculated results are not so plentiful that satisfactory interpolation procedures can be devised. Performing the calculations, however, is a tedious, time-consuming task unless an electronic computer is available, and, in practice, time and manpower are not always available for this purpose. A quick, simple, consistent method was needed for reducing the uncer- tainty in estimated oil recovery from solution gas-drive reservoirs when only minimum information about the reservoir system is available. PROCEDURE Method of Calculation The usual requisite assumptions were made so that the material balance equation could be used to calculate data for the charts. The following assumptions were made: (1) the reservoir is homogeneous and isotropic; (2) oil recovery is due entirely to solution gas drive and neither a gas cap nor a water drive nor gravity drainage is present; (3) the initial reservoir pressure is the bubble-point pressure of the reservoir fluid; (4) initial total liquid saturation is 100 per cent of pore space; (5) interstitial water saturation remains at the initial value as the reservoir pressure declines from the bubble-point pressure to atmospheric pressure; (6) equilibrium gas saturation is 5 per cent of pore space; and (7) oil and gas saturations are uniformly distributed throughout the reservoir at all times. There are no saturation gradients due to a wellbore, nor is the geometry of the reservoir system considered. The material balance equation was written in the form of a differential equation' which was integrated to determine the change in oil saturation for an assigned pressure drop. Formal integration was not possible, so recourse was made to the Runge-Kutta method' of numerical integration. All computations were performed on IBM equipment. Numerical integration yielded the change in oil saturation within the reservoir as the pressure. declined from the bubble-point pressure to atmospheric pressure. The initial oil saturation minus the change in oil saturation yielded the oil saturation at atmospheric pressure. The oil originally in place was obtained by dividing the initial oil saturation by the initial formation volume factor (differential liberation) while the oil in place at atmospheric pressure was obtained by dividing the final oil saturation by the formation volume factor at atmospheric pressure. U1timate oil recovery, expressed as a percentage of the initial oil in place, was obtained by dividing the difference between the oil initially in place and the oil in place at atmospheric pressure by the oil initially in place and multiplying by 100. PVT Data Charts were based upon 135 solutions to the material balance equation. PVT properties of the reservoir fluids were variables in this equation and had to be known as functions of pressure. The required PVT data might have been obtained from either actual reservoir fluid systems or correlated data. However, correlated PVT data were developed and employed in the calculations for the following reasons: (1) it is doubtful that 135 sets of PVT data could have been obtained for the values of variables investigated in this study, and (2) results of recovery calculations from randomly obtained PVT data could not be correlated as well as rssults from selected PVT data. The PVT data used to develop the

By R. C. Himes, K. Zanio, J. B. Wagner, J. W. Moody, J. F. Miller, W. Johnson

The recent research with which this paper deals has been concerned with the preparation of pure PbTe crystals suitable for control of radiative processes and othe.v electronic applications. The research has been directed toward the developrnent of methods for the preparation of puve, homogeneous, loul-ca,wier-density PbTe crystals suitable for use in the fabrication of optically pumped and electrically pumped diode lasers. Steps in the preparation of the crystals include 1) purification of the starting materials, 2) synthesis and purification of the PbTe, 3) growoth of PbTe crystals, and 4) adjustt~zertt of composition of the crystals This Paper describes the general preparation procedure employed and discusses some investigntiotzs of purification processes. THE as-received lead and tellurium are nominally 99.999 to 99.9999 pct pure. Assays furnished by the suppliers, obtained by emission spectrographic analysis, show only the presence of about 2 ppm Mg in the tellurium. Such analyses are not very informative, however, since they give no information on the concentrations of normally gaseous impurity elements such as oxygen. Both the lead and the tellurium in the as-received state usually contain appreciable concentrations of oxygen—primarily in the form of oxides on the surfaces of the material. To reduce the oxygen content, the lead is held in the molten state in hydrogen at -700°C for several hours. For this treatment, the lead is contained in a graphite boat which is rf-heated, and the hydrogen is passed through a liquid-nitrogen trap prior to use. Tellurium is subjected to multiple distillation in hydrogen to remove oxygen and other foreign impurities. If, in conducting the distillation, approximately the last 10 pct of the charge at each "stage" is left as the discard cut, purification of the tellurium proceeds as indicated in Fig. 1.l Tellurium used in this work has been distilled two or three times to reduce carrier concentration to about 10" per cu cm. The PbTe is prepared from the purified elements by reacting them in the molten state in sealed, evacuated, or hydrogen-filled silica ampoules. The charge is usually held above the melting point of PbTe (923°C) at 1000 C for 24 hr to ensure that it has been homogenized. Two methods have been employed for the growth of the required single crystals of PbTe: growth from the melt, which will be discussed first, and growth from the vapor phase. Large single crystals of p-type PbTe can be grown readily from the melt by the Bridgman method. For this method of crystal growth, the PbTe is synthesized in situ from proper proportions of the purified elements. Growth (dropping) rates in the range 1.3 to 6.5 mm per hr are employed. Material near the maximum melting composition (about 50.012 at. pct Te) is utilized to avoid composition change on freezing, and thus to obtain crystals of nearly uniform composition. Crystals prepared by use of procedures described up to this point were sufficiently pure and perfect that they could be used for the preparation of laser crystals in studies at Lincoln Laboratory.2-5 ADJUSTMENT OF COMPOSITION Good n-type crystals of PbTe cannot readily be grown from the melt. Further, growth from the melt of crystals of any compositions (n or p type) other than those near the maximum melting composition is difficult because of the large composition changes that must occur on freezing.'" However, melt-grown crystals can rapidly be brought to other desired compositions by isothermal equilibration through the vapor phase with a two-phase Pb-Te stock material, essentially as described by Brebrick and Allgaier.1 The work to be discussed has been concerned with the preparation of n-type crystals; thus, the two-phase stock which was employed contained excess lead, and all ensuing discussion is of the preparation and properties of n-type crystals. The equilibration was designed to the shift composition to the lead-rich limit of stability at the selected temperature. Initial treatment of the crystals at high temperature was employed to minimize the total time required for the equilibration. Final adjustments of the composition and state of the crystals were made by use of low-temperature heat treatment at temperatures in the range 200" to

Jan 1, 1968

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'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.' 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 J. Gross

G. H. Clevenger, Chairman of the Milling Methods Committee of the Institute, made the following introductory remarks: "Several years ago, a number of us felt that the time was ripe for a fundamental investigation of crushing and grinding. At the outset, it appeared that the first thing we needed was a yardstick whereby grinding efficiency could be measured. "The U. S. Bureau of Mines has been most generous in cooperating with the Milling Methods Committee in getting this work well under way. John Gross, who served the committee for a year as secretary, was placed in charge of the investigation and has been ably assisted by S. R. Zimmerley. "Messrs. Gross and Zimmerley will now present the Progress Report covering their work to date." PROGRESS REPORT J. Gross, Salt Lake City, Utah. -This has not been a simple problem, and when I tell you that we can give you a verbal report of what we have done during three years in five or ten minutes you will realize that we have necessarily done a great deal of work that does not appear in the final results. We have been in a virtually new field. Therefore, we have had to feel our way at each step so as to be fairly sure we were correct. The first thing that was realized in this problem was that unless we had some method of measuring what happened when we crushed an ore, we might as well quit and not go further. We realized that if we tried to measure the results of crushing or grinding by the ordinary sizing test we would not get anywhere. We could sieve down to say 200 mesh fairly accurately; we could even go one sieve size further with a little less accuracy, and then we were absolutely lost, unless we went into microscopic measurement. Even this latter method would not have been satisfactory. The question was: what were we going to measure? If we were going to measure size, we might measure one particular dimension of a particle and be off 200 per cent. or more. If we tried to measure surface, we would have something tangible; the surface of a particle, no matter how irregular, is something definite, far more definite than any linear dimension would be. Moreover, if we could measure surface, we would immediately have a method of checking the Rittinger law as to whether it was or was not correct. So the first thing that we sought was a method whereby we could measure surface on crushed particles or, we will say, on particles; it would not make any difference whether crushed or not. It then became a question of what kind of particles we were going to use in obtaining a method for surface measurement. We realized that it would be rather a com-

Jan 1, 1928