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By J. P. Hirth, A. H. Clauer

A simple graphical method is presented for the determination of climb forces on dislocations exerted by uniaxial stresses. In conjunction with standard stereographic projections, the technique is applicable for any crystal system. Climb forces on glide dislocations in bcc crystals are determined as an application. In connection with a study1 of elevated temperature creep of molybdenum single crystals, a detailed analysis of the climb force on a dislocation was necessary. In general, such forces can be calculated for an arbitrary dislocation segment from the Peach-Koehler equation2 (or one of its variants3"6) where Fk are the components of the force per unit length of dislocation line, ?i of the unit sense vector tangent to the line, ojl of the stress tensor, bl of the dislocation Burgers vector, and is the Einstein permutation operator with components ?123 = ?231 = ?321 = —?132 = — ?321 = —?—213 = unity, and all other components zero. It is understood in the suffix notation of Eq. [I.] that repeated indices are to be summed over 1, 2, and 3. For the most general coordinate system, the matrix manipulations required to solve Eq. [I] are fairly complex. However, a simplification can be achieved by specifying a coordinate system based on the dislocation in question. The pertinent system involves cartesian coordinates xi, x;, xi, with attendant unit vectors e'i; ei being parallel to the Burgers vector b, and e'3; being parallel to the climb directions (b x ?), i.e., normal to the slip plane. In this coordnate system b = (bi, 0, 0) and ? = (?'1,?'2, 0). Hence, Eq. [I] yields for the climb force per unit length F3 = ?'2s'11b'1—?'1s'12b'1 [2] The first term on the right side of Eq. [2] is the climb force on the edge component of the dislocation, while the second is the (cross-slip) force normal to the glide plane acting on the screw component. Thus, the problem of determining the climb force reduces to that of resolving the stress components —il and s'12 in the xi coordinate system. Several authors7- l0 have shown, for the glide case, that such stress resolution can be performed most readily by graphical methods. Therefore, we present a similar method for the climb case. Of the suggested methods, we follow that of Hartley and Hirth,9 which can be performed directly with a standard stereographic projection for the crystal system in question. We treat the case of simple tension, or compression, this being the most common creep test in which climb is important. A set of cartesian coordinates (x1, x2, x3) is fixed with x3 parallel to the specimen axis. This set is connected to the x'i set by the factors defined in Table I. A perspective view of the coordinate systems relating them to the glide ellipse, is given in Fig. 1, while a stereographic projection of the coordinate systems is presented in Fig. 2. The transformation matrix connecting the xi and xi coordinates is x'i =aijXj [3] where an a11 a13 aij = a21 a22 a23 a31 a23 [4] s The corresponding transformation for the stresses is i [5] The only nonzero component of okl for the simple tension case is s33,. Hence, using Eqs. [4] and 151, we find that Eq. [2] becomes F3 = b'1s33 sin2 cos ?[cos ? sin a - sin ? cos a] [6] = m1b'1s033 sin a- rn2b's33 cos a where sin a = 5: and cos a = ?i, with a the angle measured from b to ?, i.e., a polar angle in the x1, x2 plane. The same equation with a sign change applies for compression. A graphical plot of the "Schmid" factor m1, relating to the climb force on the edge component, is presented in the stereographic projection of Fig. 3. In this projection the glide plane normal points toward the top of the page and the glide direction points normal to the plane of the page. To use the graph, one

Jan 1, 1970

The Mineral Industry, Published by McGraw-Hill Book Co, New York, N Y. The Mineral Industry is an annual review of the mineral industry It is a standard and complete reference on the mineral industry for the year covered Through the cooperation of the A I M E its publication in 1933 was made possible Mineral Industry for 1930 contains sections devoted to the production, consumption, trade, market, uses and technology of the following headings: Abrasives, aluminum and bauxite, antimony, arsenic, asbestos (b), asphalt, barium and strontium, chromium (b), coal and coke, cobalt (b), copper, diatomite, fluorspar, gold and silver, graphite, gypsum, iron and steel (b), lead, magnesite, manganese, mica, molybdenum, nickel, petroleum and petroleum products, phosphate rock (b), platinum group metals (b), potash, precious and semiprecious stones (b), quicksilver, radium (b), uranium and vanadium, slate (b), sodium salts, sulfur, pyrite, sulfuric acid, talc and soapstone, tin, titanium and zirconium, tungsten (b), zinc, minor metals, minor nonmetals, ore dressing and coal washing (b). Sections marked (b) have appended a bibliography of recent literature on the subject. Each section is written by an acknowledged expert. Other volumes contain similar material Prices -The Mineral Industry, 1892-1930, vols. 1 to 39. Complete sets of this work, uniformly bound, except vols 25 and 26,

Jan 1, 1933

By A. T. Aldred, K. M. Myles

The vapor pressure of chromium over solid V-Cr alloys has been measured by the torsion-effusion method in the temperature range 1450" to 1650°K. The chemical activities as well as the free energies, entropies, and enthalpies of formation of the alloys have hem computed from the vapor-pressure data. The activities of both chromium and vanadium exhibit fairly small negative deviations from Raoult's law over the entire composition range. The values of the excess entropies and the enthalpies of formation found at 1550°K are considered in terms of the changes in the clzaracteristic properties of vanadium and chromium that occur upon alloying. RECENT interest in the theory and properties of transition-metal alloys has shown the need for relevant thermodynamic data. The present investigation of the V-Cr system was undertaken as part of a more general study of thermodynamic properties of transition-metal alloys. The system was chosen because of the reported complete solid solubility of the components at all temperatures1 and because the difference in magnitude of the vapor pressures of vanadium and chromium allowed a simple effusion technique to be used. The torsion-effusion method was employed to minimize compositional changes in the alloys during the experiments. EXPERIMENTAL Equipment. The torsion-effusion apparatus, shown diagrammatic ally in Fig. 1, consists of a torsion system suspended inside a vertical vacuum chamber whose lower end is surrounded by a high-temperature vacuum furnace. An auxiliary optical lever and screen are used to determine the angle of rotation of the effusion cell. The torsion fiber is an annealed, high-purity, tungsten wire usually between 0.003 and 0.007 cm in diameter and about 43 cm long. The wire supports a concave mirror and a rigid tantalum connector tube. The effusion cell is fastened to the lower end of the connector tube by a dovetailed yoke and har- ness arrangement. The cells, which are 1.27 cm in diameter and 4.4 cm long, were made by electron-beam welding tantalum endcaps onto a 0.025-cm-wall tantalum tube. The two orifices, formed by drilling, have similar areas ranging from 0.011 to 0.031 sq cm. The noninductive sheath-type furnace consists of a single-phase tantalum heating element 6.35 cm in diameter, 15 cm high, and 0.013 cm thick; the element is completely surrounded by radiation shields in an evacuated chamber. The power system includes a 17-kva self-saturating saturable core reactor with an integral magnetic amplifier and a water-cooled, 15-kva, step-down power transformer with a multitap secondary. Temperatures are controlled to within ±1/2o at 1600°K by means of a unit that includes a reference voltage source, a dc electronic null detector, a current-adjusting proportional band relay, and the self - saturating reactor. At 1650°K the temperature variation within the cell, vertically and horizontally, is 3/4oK. Unwanted motions of the torsion system are damped by the movement of an aluminum vane, which is mounted on the connector tube, between the poles of an electromagnet. When not in use the magnet is withdrawn and rotated 90 deg to prevent its interaction with the rotation of the system. Measurements. The vapor pressure, p, is re-

Jan 1, 1964

By R. L. Fleischer, R. S. Davis

BICRYSTAL specimens grown from the melt have been used extensively for investigations of the influence of grain boundaries on plastic deformation. The bicrystals are usually of predetermined orientation prepared by seeded growth from the melt in milled graphite boats. This technique has been described in detail by Chalmers.' Since the direction that the grain boundary follows during growth is affected by both thermal conditions and crystallography, a difficulty arises in maintaining the grain boundary position constant along the length of the specimen. This problem is particularly

Jan 1, 1960

By R. Clare Coffin

The production of oil in the Rocky Mountain district, including southeastern New Mexico, increased from 33,048,630 bbl. in 1930 to 34,325,163 bbl. in 1931. This increase was due to production in New Mexico, which exceeded the 1930 figure by approximately 5,000,000 barrels. Total production by fields is given in Table 1. Exploration during 1931 resulted in the discovery of a new oil-producing horizon in the Big Muddy field in Natrona County, Wyoming, and ' the discovery of a new gas pool in the Powder Wash structure, Moffat County, northwestern Colorado. Gas was discovered also in the Frontier sands of the Bunker Hill dome, Carbon County, Wyoming, but no test has yet been made by which to determine the significance of this discovery. All other exploration which resulted in increasing the known reserves of oil and gas in the district was confined to drilling in partly outlined fields where known limits of production were extended. During the year two major gas pipe lines were completed in western Montana, and one in southwestern New Mexico was extended into Arizona. One new project involving the marketing of natural gas from Wyoming fields included the conversion of an existing oil line to a gas line to serve towns in southeastern Wyoming and western Nebraska. Colorado The decline of 132,501 bbl. in the production of oil in the Colorado fields during 1931 from the figure of 1930 is due to the natural decline of existing wells, partly offset by the increased production in the Greasewood area. New exploration was limited largely to northeastern Colorado, where attempts were made to find oil in areas adjacent to the Grease-wood field. Powder Wash, Moffat County.—The Ohio Oil Co. is to be credited with the discovery of a gas field in the Power Wash structure in Moffat County, Colorado. The initial well drilled in sec. 5-11-97 encountered a sand at a depth of 2152 ft. which produced 34,188,000 cu. ft. of gas on an open-flow test. The rock pressure was reported as 630 Ib.

Jan 1, 1932

By Emil Gathmann

STEEL as it is poured, or teemed, into the mold for forming the ingot may be broadly separated into two divisions; i.e., effervescing or gassy steel, also termed evolution steel, and non-effervescing or killed steel, also termed solution steel. Between these primary divisions there are various types having the characteristics of both divisions but really not belonging to either; such steels are termed semi-piping, rising, or wild, as the type may be. True unkilled, or effervescing, steel should contain large volumes of gases, which are evolved while the metal is being teemed, or cast from the ladle nozzle into the mold, and while the temperature of the steel is being reduced prior to the solidification or freezing of the steel, the upper portion, or top, of the ingot remaining liquid due to the evolution of gases until an ingot skin of considerable thickness has been formed. These gases consist principally of hydrogen, carbon monoxide, nitrogen, and ammonia. It is generally understood that nitrogen gases are the first evolved and form the skin blowholes, at times troublesome, in the forming solidifying ingot. Ingots made of effervescing steel will always contain a large number of blowholes. Such blowholes are not deemed objectionable in various products if they occur well within the interior of the ingot where they will not be subject to oxidation upon the ingot's cooling and subsequent re-heating and rolling or forging. Very little top or bottom discard is taken from this type of ingot as pipes, or large shrinkage cavities, at the upper portion of the ingot do not usually occur, the difference in volume between the liquid and the solid steel (6 to 10 per cent.) being compensated for by the innumerable blowholes distributed throughout the body of the , ingot. Of the 40,000,000 tons of steel made in the United States during the year 1919, at least 35,000,000 tons of ingots were made of gassy or semi-gassy steel. Killed, or solution, steel is termed true piping steel from the characteristic pipe or shrinkage cavity that usually occurs in the uppermost central portion of the ingot.

Jan 8, 1920

By R. W. Regehr, R. A. Burmeister

Epitaxial growth of GaAs 1-xPx on germanium substrates was achieved using an open tube vapor transport system. The compositional range of 0.3 < x < 0.4 was examined. The best results were obtained with (311) orientation of the germanium substrate. The physical and chemical properties of the resulting layers were investigated using several techniques. Spectrographic analyses of the layers indicate substantial incorporation of germanium into the GaAs t-X Px layer. Evidence is presented which indicates that this incorporation occurs via a vapor phase transport process rather than by solid phase dijfu-sion. Electrical measurements suggest that the germanium thus incorporated behaves predominantly as a deep donor in the compositional range of 0.33 < x * 0.40 and has a deleterious effect upon the luminescent properties of GaAs1-x Px. The increasing technological importance of GaAs1-xPx for use in light-emitting devices has led to an evaluation of several aspects of existing growth processes. The method most commonly used to prepare GaAs1-xPx for electroluminescent device applications is vapor phase epitaxial growth on GaAs substrates.&apos;-4 In a typical electroluminescent diode structure the active region of the diode is entirely within the epitaxial layer and thus the electrical properties of the substrate are relatively unimportant since it is effectively a simple series resistance (assuming hetero-junction effects to be negligible). The use of germanium rather than GaAs as the substrate material is of interest for several reasons. First, GaAs of reasonable structural quality has been epitaxially grown on germanium4-2 and it is reasonable to expect that GaAs1-xPx could subsequently be deposited on the GaAs layer. Second, germanium substrates are readily available with both lower dislocation densities and larger areas than GaAs. Finally, single crystals of germanium are more economical than GaAs single crystals. The principal objective of the present investigation was to test the feasibility of growing GaAs1-xPx epi-taxially on germanium substrates, and to evaluate the properties of such layers with regard to electroluminescent device requirements. The approach used was to a) demonstrate epitaxial growth of GaAs1-xPx on germanium, and b) characterize the relevant structural, electrical, and optical properties of the GaAs1-xPx layers. The possibility of germanium incorporation into the grown layers was of special interest since there was some indication of this in previous studies of GaAs growth on germanium.5&apos;11,12 Although a study of the electrical properties of germanium in GaAs1-xPx was not an intent of this investigation, several features of the electrical properties of the layers grown in the present study which appear to be due to germanium are described. EXPERIMENTAL PROCEDURE The open-tube vapor transport system used for the epitaxial growth of GaAs1-xPx is illustrated in Fig. 1. This system utilizes the GaC1-GaC13 transport reaction and is similar in most respects to the larger system described elsewhere.&apos; The germanium substrates were n-type, with a resistivity of 40 ohm-cm (Eagle-Picher Co.). These were cut to the orientations of {100), {111), and (3111, and were mechanically polished and chemically etched in CP-4 (5 min at 0°C) prior to growth. In some cases, a GaAs substrate was employed in addition to the germanium. The orientation of the latter was {loo}, and they were also mechanically polished and chemically etched prior to growth. The initial composition of the deposited layer was pure GaAs. After approximately 10 microns of GaAs was deposited on the germanium substrate, the phosphorus content of the layer was gradually increased over a distance of approximately 15 microns to the desired concentration and maintained at this value throughout the remainder of the growth. Typical operating parameters used during growth are given in Table I. Selenium was used as a n-type dopant in several runs to facilitate comparison of the electrical properties of the layers grown on germanium with those of layers grown on GaAs substrates, which are usually doped with selenium. The concentration of H2Se in the gas phase was adjusted to a value which would normally yield a carrier density of 1 to 5 x 101 7 at room temperature in layers grown on GaAs substrates. The terminal surfaces of the epitaxial layers were examined by optical microscopy for structural characteristics. Laue back-reflection photographs (Cu radi-ation) were also made on the terminal surface to verify the epitaxial nature of the deposit. After these steps

Jan 1, 1970

Discussion of the paper of E. L. deGolyer, to be presented at the Colorado meeting, September, 1918, and printed in Bulletin No. 137, May, 1918, pp. 987 to1000. J. A. UDDEN,* Austin, Tex. (written discussiont).-I have read Mr. E. L. deGolyer&apos;s paper on The Theory of Volcanic Origin of Salt. Domes, with a great deal of interest. It seems to me a very able summary and discussion of the various theories set forth to account for the origin of our salt domes on the coast. It has always appeared to me that what we need is more observations on the facts involved and I regret very much that so far we have not been able to devote much time to the study of our salt-dome fields on the coast in this State. One feature that I do not find mentioned in Mr. deGolyer&apos;s paper is the so-called "cap. rock" overlying the salt. The nature of this rock seems to vary from a coarsely crystalline limestone to a fine-grained limestone containing sand and in which the limestone seems to be intersticially introduced material. We should be prepared to accept, if necessary, "more than one theory. To my mind, the igneous theory and the artesian theory, if I may so call it, may very well both be true. The "squeeze" theory and the artesian .theory may,, it seems tome also, jointly explain the phenomena. Neither the volcanic nor the salt "squeeze" theory explains the presence of the cap rock. The latter certainly does not explain the extensive sulphur deposits which occur in association with the cap rock. Whichever additional theory will be found best to explain the salt-dome structures, when we shall know them better, it seems to me that the theory first advanced by R. T. Hill and later elaborated by G. D. Harris, is not likely to be entirely replaced. Whatever cause has first set into action an upward circulation of gases and liquids in our salt domes, it seems to me that to a gentle circulation of the kind postulated by their theory is to be ascribed the uppermost and the later phenomena in our salt domes on the coast, with which we are most familiar; such as the cap rock, the sulphur, and the gypsum and anhydrite deposits.

Jan 7, 1918

By Pol Duwez, Spencer R. Baen

A LTHOUGH the practical importance of Fe-Cr--iV Mo alloys has long been recognized, constitution studies have been limited to a few alloys within rather narrow ranges of composition. The purpose of the present study was to establish the phase boundaries in the ternary diagram at a temperature of 1200°F (650°C).* The identification of phases and the determination of phase boundaries were based primarily on X-ray diffraction measurements and occasionally on microscopic observation. The methods used for locating the phase boundaries were essentially those described in detail by Andersen and Jette,&apos; and by others.&apos;, The compositions of 180 alloys, prepared by powder metallurgy techniques, are shown in Fig. 1. The chemical analysis and mesh size of the powders which were used for the preparation of the alloys are given in Table I. The powders were mixed for 48 hr or longer, then compacted under 80,000 psi in a %-in. diam steel die. Each specimen weighed approximately 5 g. The compacts were sintered for 4 hr at 2500°F (1371°C) in an atmosphere of pure dry hydrogen (dew point near the temperature of liquid nitrogen). An open tray of chromium powder was placed upstream of the compacts to act as a "getter" for the last traces of oxygen or water vapor. In many cases this chromium powder was bright after sintering. Occasionally the upstream side of the powder was slightly greenish, but in all cases the downstream side was metallic. Some of the alloys contracted during sintering and some expanded as much as 20 pct. The latter alloys, which in all cases were brittle, were crushed in a tool steel mortar, repressed, and resintered for 4 hr at 2500°F. After sintering, the alloys were aged for ten days at 1200°F (650°C) in evacuated (105 mm Hg or better) fused silica tubes and were cooled rapidly to room temperature following the aging treatment. The use of the powder metallurgy technique in preparing alloys for structural investigation offers a simple method &apos;of avoiding contamination or non-homogeniety which could result from a melting operation. It is very often possible to dispense with chemical analysis of the alloys which have been prepared by the powder metallurgy method. In lieu of chemical analysis, it is necessary to determine the weight of the compact before and after sintering. The chemical composition of the alloy may be considered as that of the green compact, within the limits of accuracy determined by the loss of weight during sintering. In phase-diagram studies it is important to achieve homogeniety in structure, whether the alloys are prepared by powder metallurgy or by melting. Homogeniety means complete diffusion during the sintering of the alloys which are prepared by powder metallurgy. It has been found from experience that the best criterion for establishing the completeness of diffusion is the sharpness of the X-ray diffraction patterns. This criterion has been used throughout the present study. The X-ray diffraction data were obtained using powder cameras of either 214.86 or 71.62 mm diam. Copper, cobalt, or chromium Ka. radiation was used, the choice being based on the alloy composition. The powder samples were obtained by filing or crushing, depending on whether the alloy was ductile or brittle. In some cases, the powder was annealed for 4 to 6 hr at 1200°F in vacuum. The measurements were corrected for film shrinkage and absorption. The large camera, in which the film is mounted

Jan 1, 1952

By W. J. Sharwood

In the cyanide process, gold and silver are dissolved from crushed ore as double alkali-metal cyanides, from which they may be precipitated by such positive metals as sodium (amalgam), aluminum, or zinc, or by electrolysis. Two extreme conditions may be noted. Some works, especially slime plants practising decantation, use a relatively large volume of solution—possibly 4 or 5 tons per ton of ore—nearly all of which may require precipitation, so that the solutions handled are of much lower value per ton than the ore. On the other hand, in some leaching plants it is possible to extract with very little solution, and to percolate some of this more than once through the charge before precipitation, so that the solution to be precipitated may be much less than half the weight of ore, and proportionally richer. Solution intended for further use need not have all its precious metal removed, but any that has to be thrown away should be impoverished as far as is economically possible. In spite of certain advantages possessed by other precipitants, zinc in some form has been almost universally used.. In some of the first attempts to utilize cyanides as gold solvents, a "piece or plate of zinc" was suggested as a precipitant, but extension of surface was early recognized as a desideratum. . Macarthur and the Forrests adopted a "metallurgical filter" of zinc shaving, turned from disks or rolled sheets. They had previously experimented on other forms of zinc, ax! Mscarthur records having tried zinc dust, which had of course been long known as a general reducing agent. It had also been known and used as a precipitant of precious metal from plating and photographic solutions, and comminuted zinc had been patented for recovering copper, etc., from ore leaches. Other inventors proposed the virtual making of zinc powder by the attrition of balls of zinc, and by similar means, during the passage of a stream of gold-bearing solution. Sulman claimed the use of zinc dust, or fume, in a special apparatus, effecting a more or less regular feed of dust and solution by means of intermittent siphons; the mixture or "emulsion" (as it is still called) rising with diminishing velocity through an inverted cone in which it

Jan 1, 1918

By Wallace W. Wilson

This DaoerAA calls to attention for the first time, to the writer&apos;s knowledge, a purported recovery of oil by substantially horizontal gas cycling that is considerably in excess of 50 per cent of the oil originally in place. The average angle of dip along the path of travel of the gas is less than one degree of arc. The best recovery by gas cycling previously brought to the writer&apos;s attention1 occurred in the case of the Mile Six Field in Peru, where about 68 per cent of the original oil in place has so far been recovered. In this case, however. the recovery was greatly aided 1)y the high dip angle of about 17.5". An approximate estimate of recovery was made by the method developed by the writer&apos; for the case of the Cook Ranch Field, using an average relative permeability ratio function dictated by past experience with a number of good quality sandstones. A result of about 40 per cent recovery of the original oil in place wa* obtained after the 8.5 pore volumes of cumulative gas cycling undergone by the Cook Ranch Field. Tile writer desires to emphasize what appears to him as the sound engineering practiced at Cook Ranch, and also the care attending the taking of data and the high quality of the calculations made. It is impossible to take issue on factual grounds with any of the conclusions drawn in the paper. It is, however, desired to point out the difficulty of explaining the unexpectedly favorable oil recovery on ordinary theoretical grounds. It would be of interest to know whether relative permeability ratios have been measured on the Cook sand. The operator is inclined to attribute some of the excess benefit to settling of the oil across the bedding planes into the lower part of the sand. It is difficult for the writer to appreciate the importance of such an effect, inasmuch as the concomitant opening of excessive vacated pore space in the upper part of the sand would he expected to cause excessive bypassing of the gas. REFERENCE 1. Welge. H. J.: "A Simplified Method for Computing Oil Recovery by (Gas or Water Drive." Trans. AIME, (1952), 195, 91. AUTHOR&apos;S REPLY TO MR. WELGE Welge has poined out clearly the difficulty of applying material-balance procedures in calculating the Performance of low-pressure, dispersed gas injection operations. There can be no argument that even with the most favorable assumptions of K,/K,, and with cumulative gas cycling in excess of normal expectations, the calculated oil recovery will be considerably less than the 72.5 per cent recovery realized from this project to Jan. 1, 1951. There probably are at least two reasons for the unusually high recovery from this reservoir, the effects of which would be difficult or impossible to calculate by known methods: 1. The operator did not use the same injection wells for the entire operation, and exercised considerable control over producing GOR by changing the locations of injection wells whenever well performance indicated excessive bypassing. Fifty-six wells were used for injection, not over 29 of which were in use simultaneously. This procedure resulted in frequent shifting of the fluid movement patterns in the reservoir and undoubtedly increased the ultimate recovery. The writer knows of no satisfactory procedure for calculating the effect of this practice. 2. Vertical movement of oil across the bedding planes of the reservoir rock hy gravity drainage tended to maintain a relatively high oil saturation, and hence a favorable K,/K, ratio, in the lower sections of the reservoir. As pointed out by Welge, this condition has aggravated the tendency for high producing GOR, but at the same time it has resulted in increased oil recovery. As may be seen from the performance charts for the various battery areas, operating (GOR&apos;S have been quite high for the last several years of reported history.

Jan 1, 1952

By C. S. Matthews, H. C. Lefkovits

The performance of depletion-type reservoirs at the stage in which the gas is at such low pressure that gravity is essentially the sole driving force has been investigated both theoretically and by use of scaled models. A simple theory is developed which completely explains the scaled model experiments. It also agrees with some field data. When the range of production rates to be considered is less than 25, the theory predicts that the production rate decline curve for homogeneous reservoirs in which there is a free surface will be of the hyperbolic type with n = 2: The theory gives a physical significance to the parameter y. INTRODUCTION This investigation was undertaken to determine a method for prediction of performance of reservoirs where gravity is the sole driving agent. Depletion-type reservoirs fall into this category after the pressure has fallen to some low value. Some examples of this type are found at Healdton (&apos;Oklahoma), Oklahoma City (Oklahoma), Midway-Sunset (California), and East Coalinga (California). Generally the production rate per unit thickness is quite low in such reservoirs, with the conse- quence that this stage is sometimes called the stripper stage. However, per well production rates may be of the order of 50 B/D because of the considerable sand thickness open in some of the reservoirs. In the past, predictions of behavior of such reservoirs have been based on empirical extrapolation of the rate of production to the economic limit. Difficulties arise when new wells are drilled in the field or when production is artificially curtailed, since in such cases the decline rate of individual wells or leases changes and no clear trend can be detected. It was hoped that the present study would lead to improved methods for evaluation of such reservoirs. The study was initiated by building a scaled model for a particular field and by running a number of experiments on this model. Later a simple theory was developed which explained the laboratory results completely. The theory led, as shown below, to a hyperbolic-type decline equation which had been used previously&apos; in a completely empirical manner. THEORY The General Case The problem to be treated here is the following: We are given a homogeneous cylindrical porous reservoir with exterior radius r, wellbore radius r., and height h,, containing, from the bottom up to a height hit oil, some gas, and interstitial water (see Fig. 1 A). The portion of the reservoir between K, and h, is filled with gas at low pressure, with residual oil, and with interstitial water. If at a time t = 0, the level of the oil in the wellbore is lowered to a height h,, what is the production rate from the reservoir at a time to The configuration within the reservoir at some instant

Jan 1, 1957

By W. P. Sykes

ThiS investigation was undertaken primarily to establish the relations existing between temperature and mechanical properties in molybdenum, nickel, and an aluminum-copper alloy. Mlolybdenutn (m.p. 2500" C.) was chosen because it is partly similar to tungsten and partly similar to the common ductile metals. Also it is known to furnish, by proper treatment, a desirable material to use in studying relation of grain size and physical properties. The molybdenum used was of the quality that is drawn into wire 0.003 in. in diameter for use as filament supports in incandescent lamps; Chemical analysis shows less than 0.1 per cent. of impurities. Nickel belongs to the same class as iron. Its melting point is 1450" C. and an allotropic change at about 370" C. results in a loss of magnetism above that temperature. This feature made nickel doubly valuable for the purposes of these tests. The nickel used was obtained from the Driver-Harris Co. as 0.090 in. (2.3-mm.) wire, annealed; analysis showed 99.8 per cent. nickel and 0.150 per ccnt. iron. Aluminum is one of the low melting-point metals. Some tensile tests at clevated temperatures have been reported by Bengough but the possibility of learning more with the low temperature and sensitive apparatus available rccommendcd this metal. The samples marked A1 arc an aluminum-copper alloy that contains 3 per cent. copper, 0.42 per cent. iron, and 0.21 per cent. silicon. The presence of the copper somewhat coniplicates the analysis of the results; but the action of copper in aluminum has been studied so that its influence might have been foretold, in part at least. The material and analyses were furnished by the Aluminum Castings Co. The nickel wire, which was deformed at 400" C., was drawn under a bath of molten lead and through a die, which also was immersed in the bath. A thermocouple was suspended in the molten metal to indicate the temperature. Hot oil was uscd as the heating bath for drawing the

Jan 1, 1921

By W. E. Gaby

THE form of dip chart here presented for the use of the profession was devised by the author when he was confronted with a particularly heavy job of geological section making and. did not have any of the usual tables or charts at hand. This was at the property of the Teziutlan Copper Co. in Puebla, Mexico, where the orebodies are much faulted and lie conformably with a slightly inclined and. much folded schist. Because of the low dip and the folding of the orebodies, the engineering, and geological data respecting them were best represented on vertical cross-sections quite closely spaced. A less finished form of the chart was published in the Mining & Scientific Press of Aug. 6, 1921, with an explanation of its use. I have checked the new drawing for accuracy against the calculated table given, and constructed an explanatory diagram beneath. As some geologists are accustomed to using the table, I have included it, since no advantage is obtained by mere interpolations from the chart to get the required angle, except as it gives a mental picture of this angle. The chart gives a more rapid and much easier solution when cases multiply so that it becomes desirable to eliminate the tedious manipulations of a separate protractor. In fact, using the parallel ruler as des-cribed, it is not even necessary to make note of the angle sought. It is brought out graphically, leaving the mind free to note the correlations. The chart itself may be made more convenient by reproduction on celluloid with a slot running on the zero line of the protractor.

Jan 9, 1922

By R. E. Hook, H. J. Garrett, A. M. Adair

X-ray diffraction and metallographic techniques were employed to examine the impurity phases occurring in as-swaged and recrystallized chromium produced fvom high-purity iodide chromium crystals. Chromium oxides are found to form in a consistent manner associated with the temperature of recrystallization. Microscopically observable second phase particles of Cr203 are observed to form intergranulurly beginning at 1300T. Beginning at 1500°C. Cr30, is formed intergvanulurly, atzd at 1600°C and above Cr30, is also formed in association with migrating grain boundaries. Geometrical traces formed by particles of this high temperature oxide uithin the grains rez)eal the histmy of grain boundary motion. X-ray evidence is presented which suggests the existence of a high temperature form of Cr203. Other impurity phases in addition to the oxides of chromium are also present. THE partitioning Of impurity elements between grain boundary aid lattice sires, either as solutes in solution or as second phases, may exercise an important influence on the mechanical behavior of metals and alloy systems. This partitioning of impurities could have a direct bearing on the iecrys-

Jan 1, 1963

By J. J. Gilman, T. A. Read

S URFACE effects in the cleavage of brittle crystals have been known for some oftime,1, 2 but our knowledge of surface effects in the plastic deformation of crystals is of relatively recent origin. In 1936, Roscoe9 eported his observations comparing oxidized and clean cadmium crystals. He found that cadmium crystals 1/2 mm in diam when covered by an oxide film less than 1200 atoms thick had critical shear stresses about twice those for clean crystals. This effect is anomalous in that it cannot be caused by the inherent shear strength of a normal oxide film. Either an interaction between the film and the crystal causes the large increase in strength, or the oxide film has an abnormal mechanical strength. Several authors since Roscoe have studied surface effects in crystal plasticity. A complete review of the literature will not be presented, but most of the results may be summarized as follows: 1—The critical shear stress for slip is increased markedly by very thin oxide films on zinc4 and cadmium crystals;" &apos; also, the entire stress-strain curve is raised by an oxide coating;3,4 both effects increase with decreasing specimen radius. 2—Surface active substances such as oleic acid destroy the hardening effect of oxide films.4, 6-8 The time required for the reduction of the hardening effect to begin increases with the viscosity of the solvent4~ 3—There has been dispute in recent years about the effects of surface active substances themselves on plastic deformation. Rehbinder, Lichtmann, and Maslenikov9 state that surface active substances reduce the strength of metal monocrystals markedly and increase the number of slip lines per unit length at a given strain. The effect varies with orientation for tin crystals being smallest for x, = 0, largest for x, = 45", and intermediate as x, + 90°.10 Several workers claim to have disproved the results of Rehbinder&apos;)"." but Rehbinder and Lichtmann9 have defended themselves and Masing with his collaborators" has confirmed some of Rehbinder&apos;s results. 4—Immersion of metal specimens in electrolytes such as sodium chloride reduces their strength12,13&apos; and subsequent cathodic polarization increases the strength reduction. For noble metals, the strength reduction occurs for both anodic and cathodic polarization," increasing with increasing polarizing voltage. 5—Electroplated copper coatings effect the creep rates of zinc monocrystals. Poly crystals are not affected." 6—Immersion in dilute acid destroys the hardening effect of an hydroxide film. When an acid solution is applied to a steadily creeping crystal, the creep rate jumps to a very high value and then drops gradually to a steady value which is higher than the initial steady rate.*&apos; " If the hydroxide film to be removed is very thin (about 100A thick), the creep rate does not change measurably, but a small rapid strain-increment is observed when dilute acid is applied." 7—Crystal plasticity depends on specimen dimensions. This was observed by Lichtmann and Ven-stroml" for monocrystalline tin and by Andrade and Kennedy" for polycrystalline lead. 8—Immerson of copper crystals in mercury has no effect on their stress-strain curves.&apos;" 9—Bombardment of creeping cadmium crystals with a particles which penetrate the surface to only 0.005 mm may increase their creep rates as much as five times.&apos;&apos;&apos; The experiments which will be described in this paper pertain to: (a) the effect of a crystal&apos;s shape on its plastic deformation, and (b) the effect of metallic surface films on plastic deformation. For the work pertaining to (a), crystals of zinc, tin, and lead were grown which had various shapes. These were tested in simple tension. Macroscopic rotations about the tension axis which are unpredicted by the classical theory of slip were observed, and serrated edges were observed in tin crystals. For the work pertaining to (b), the effects of evaporated and electrodeposited films of copper, nickel, gold, and zinc on the mechanical properties of zinc, tin, and lead crystals were determined. The films influenced both slip and twinning of the crystals in creep and tensile tests. Experimental Details Chemically pure zinc, tin, and lead were used in this investigation. The zinc was 99.999t pct pure;

Jan 1, 1953

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

The "(3034) " twin lamellae in magnesium have been reexamined using electron microscope replicas. The double twinning sequence (1011)- (1012) for these lamellae has been reconfirmed. Evidence is presented showing that the irrational habit of these twins is probably the direct result of a need to accommodate the second-order twinning shear. This accommodation vesults in both an external shear in the matrix and an internal shear in the lamella. A model is presented which accounts for the experimental obseruations. HCP metals are generally characterized by strong textures in which the basal planes of the grains tend to be aligned parallel to the rolling direction in sheet or plate and to the axis of wires and rods. Since these directions are normally those in which finished products may be subjected to uniaxial tensile stress, these textures effectively place the crystals of magnesium objects in orientations unfavorable to both basal slip and {1012) twinning, the easily activated deformation systems of this metal. However, when magnesium crystals are deformed near room temperature by a tensile stress nearly parallel to the basal plane, another mode of deformation can occur.&apos;,2 This is _a double twin which forms first by twinning on {loll), followed by retwinning on (1012). The resulting twin lamellae are of considerable interest. First, they can be responsible for "brittle fracture&apos;&apos;; when a tensile stress axis lies in the basal plane, because the reoriented crystal structure of a lamella is well-aligned for slip while the parent crystal is not. Extensive internal deformation may thus occur while the matrix is still almost undeformed. This deformation can produce a ductile rupture running the length of the twin.3 Complete failure of the specimen may then oc-cure by the spreading of cracks from one twin lamella to another, or by the movement of a crack into a grain boundary and then along grain boundaries. Since the the volume fraction of these doubly twinned elements is normally very small, the fracture may be classed as brittle, although the fracture mechanism is, of itself, essentially ductile. It is quite probable that the ductility transition, normally observed4 in magnesium at or slightly Obove room temperature, is closely associated with these second-order twins. The detailed relationship of these twins to fracture in single crystals will be the topic of another paper. The present paper is concerned with a second important aspect: the irrational habit of these double twins that falls close to {3034), or approximately 7 deg away from the primary (10il) twin habit. There is good reason to believe that this habit results directly

Jan 1, 1968

By Junius D. Edwards

WHEN Charles Martin Hall invented the electrolytic process for the production of aluminum, one basic requirement was a supply of pure alumina. Now, more than 50 years later, the same requirement still holds, and there are no technical straws in the wind to indicate that this situation is likely to change. Long ago, Aluminum Company of America took a number of steps to see that this country should not face shortages of alumina and aluminum in time of emergency. As one step to this end, the Company developed and used a supply of bauxite in South America in order to conserve dwindling Arkansas reserves. Another, and more a program than a step, was to investigate every type of process that might bear the possibility of utilizing the low-grade ores of aluminum that are more plentiful than bauxite. It is a long story, but the investigation included electric-furnace processes, acid extraction processes and alkaline extraction processes, with or without preliminary furnace and sinter treatments. Some of the processes developed were operated in commercial production. This work has been continuous since the first World War. The turn of the wheel came sooner than was expected when, in 1942, bauxite shipments through the Caribbean became uncertain and hazardous through the operation of submarines. The tremendous requirements of aluminum for the war effort were consuming high-grade bauxite at an alarming rate and a national search for substitutes began. High-grade bauxites, for technical and economic reasons, have been defined as those containing about 7 per cent or less of silica. While bauxite of this grade was limited in amount in the United States, there was in sight a substantially greater volume of low-grade, high-silica bauxite not amenable to economic treatment by the Bayer process, but richer in alumina than the clays or other available low-grade ores. It was at this point, and after several years of intensive research on this particular phase of the problem, that Aluminum Research Laboratories brought to completion the invention of one of its research staff, which made practical the utilization of large reserves of low-grade bauxite in America. BAYER PROCESS The Bayer process has been almost universally used for the &apos;production of alumina from bauxite. This process, in outline, comprises the digestion of finely ground bauxite in a solution of caustic soda (NaOH) under pressure and at an elevated temperature. Alumina in the bauxite goes into solution as sodium aluminate and the impurities-oxides of iron, titanium and silicon-remain undissolved. The undissolved residue, known as "red mud," from its color, is separated and run to waste. Aluminum hydrate (A1202.3H20) is precipitated from the solution of sodium aluminate, and the liquor containing the caustic soda and some alumina is returned to the process for digesting more bauxite. The aluminum hydrate, after washing, is calcined at a high temperature to produce

Jan 1, 1945

By Walter S. Tower

IN making comparisons of steel industries, one country with another, the convenient common denominator is annual capacity to make raw steel in the form of ingots. It is always necessary, however, to remember that there are different methods of figuring such capacity. For most countries no official figures on capacity are available, and the only authentic data on production are now six or eight years old. But in spite of those limitations on the accuracy of statistical comparisons, any flaws in the figures are probably not serious enough to alter materially the larger conclusions which may be drawn from them.

Jan 1, 1944

•Mineral Development Corp. of Salt Lake City, Utah purchased the Somerset and Oliver coal mines from the Kaiser Steel Corp. The mines are located at Somerset, Colo., about 75 miles east of Grand Junction, Colo. Somerset Town, with housing for 600 persons was included in the transaction. The mines employ 115 miners and have a combined capacity of 1750 tons per day. The Minerals Development Corp. is headed by Claude P. Heiner and is controlled by Godfrey L. Cabot, Inc. of New York and Boston. The Cabot Company is a major producer of carbon black. • The Dept. of Interior has announced that the name of the Defense Minerals Administration will be changed to Defense Minerals Exploration Administration. The new name of this defense agency more nearly describes its duties, since the mineral programming, procurement and claimant functions of the former DMA have been transferred to the Defense Minerals Procurement Agency. C. O. Mittendorf, formerly acting administrator of DMA, is serving as acting administrator of the new DMEA.

Jan 1, 1952