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By William Klement

KNELLER' has recently reported that extensive metastable solid solutions may be obtained in Cu-Fe alloys by simultaneous vapor deposition. This note reports that solid solutions, apparently single -phase, can be obtained for Cu-Fe alloys containing 0 to 20 and 85 to 100 at. pct Fe by rapid quenching from the melt; the inability to extend the solid solubilities further is related to the liquid miscibility gap, Fig. 1, as for Cu-Co alloys.2'3 Accurate lattice spacings of the copper-rich fcc and iron-rich bcc solid solutions have been obtained. Homogeneous alloys were prepared by casting4'5 and sintering2 from elements of 99.9+ pct purity. The quenching techniques were as before,' except the iron-rich alloys were liberally covered with argon while at elevated temperatures. Flakes about 1 sq mm in area were obtained and investigated with the Debye-Scherrer technique, as previously described.2,4 All X-ray work was done at 25° 2°C using filtered copper and cobalt K radiation. Relative visual intensities of the diffraction lines for the phases in the quenched alloys are shown in Table I. The lattice spacings of the fcc structure for alloys containing up to 80 at. pct Fe are plotted in Fig. 2. The variation of these lattice parameters with composition is in good agreement with the re- of cementite spots usually present (all hkl reflections are allowed) and the ease of confusing them with ferrite or martensite reflections. Copies of the report can be obtained by writing to the Materials Research Department, Rocketdyne. 6633 Canoga Avenue, Canoga Park, Calif., 91304. A copy is also available at the Engineering Societies Library, 2nd floor, 345 East 47th Street, New York, N.Y., 10017. Photocopies, either full-size or microfilm, may be purchased from the Engineering Societies Library. sults6 of Andersen and Kingsbury, Fig. 2, although there is some disagreement in absolute value. This discrepancy may be due to the different temperatures at which the X-ray measurements were carried out and perhaps to the different extrapolation procedures. Also, Andersen and Kingsbury6 state that their lattice spacings were computed relative to the wavelengths given by Siegbahn in 1933; this reference has not been found and it is assumed that the well-known 1931 wavelengths were used, the lattice spacings then being in kx units which are converted into angstroms by the factor 1.00202. There is no support for the contention that solution of iron decreases the lattice parameter of copper, as con-

Jan 1, 1965

By K. A. Johnson, F. H. Ellinger, C. C. Land

The Pu-In phase diagram has been determined by thevmal, filtvation, micrographic, and X-ray diffraction methods. This alloy system is characterized by 1) limited solubility of indium (-2 at. pet) in 6 and e plutonium, 2) one eutectic, and 3) fizte intermediate phases. Of the latter, PuIn and PuIn3 melt con-gruently, and Pu31n, Pu31n5, and the high-temperatuve 7 solid solution are formed peritectically. The n phase decomposes eutectoidally into Pu3In and PuIn at 865°C. Although the 6 phase can readily be retained to room temperature, it is not thermo-dynamically stable below 300°C. The Pu-In system has been investigated at Los Alamos as part of a study of the alloys of plutonium with the group 111-B elements. Constitutional studies of the Pu-A1 and Pu-Ga systems have been reported earlier.'9' To date, published information on the constitution of Pu-In alloys covers only the identification of the intermediate phases Pu3In and PuIn3.3,4 EXPERIMENTAL The alloys were prepared from five different lots of plutonium and three different lots of indium. The principal impurities in the plutonium differed from lot to lot within the following limits (in ppm): iron, 30 to 80; nickel, 30 to 60; aluminum, 15 to 30; silicon, 20 to 145: thorium, 50 to 300; carbon, 75 to 335; and oxygen, 20 to 135. Spectroanalysis of the indium showed that two of the lots were 99.9 wt pct pure, and the third was 99.98 wt pct pure. The alloys, in the form of about 5-g buttons, were prepared by arc melting in conventional equipment. The components for each alloy were weighed to the nearest 0.1 mg. In most instances the weight losses during melting were negligible; therefore confirmatory chemical analyses were usually not made. A few results are given in Table I. Density measurements of the arc-cast buttons were made by the liquid displacement of bromoben-zene. Heat treating was done in muffle furnaces controlled to +2°C. The alloy buttons were wrapped in tantalum foil before being enclosed in evacuated clear silica capsules. As a precaution against breakage, each capsule was in turn placed in a silica tube closed with a refractory wool plug prior to being charged into the furnace. For a moderately fast quench of the alloys, the outer protection tubes containing the capsules were plunged into cold water. Differential thermal analyses (DTA) in racuo were performed at heating and cooling rates of about 1.5°C per min. Tantalum crucibles having inverted thermocouple wells were used for most of the analyses. It was found micrographically, however, that the liquid alloys containing more than about 35 at. pct In reacted with the tantalum, resulting in contamination of the surface of the alloy. A search for a more satisfactory crucible material was not successful: tungsten and yttria behaved comparably to tantalum; thoria, vitrified magnesia, and vitrified alumina severely contaminated the alloys. So as to minimize the contamination by the crucible mater-

Jan 1, 1965

By Gordon H. Geiger, J. Bruce Wagner

Electrical conductavity and therrnoelectvic nzeasuretnents on synthetic hematite slabs with 0.01 to 0.90 at. pet Ti and with 0.30 at. pet Ca were made. Additions of titanium and of calcium both increased the electronic conductivity with titanium yielding greater n-type behavior and calciurn p-type behavior. Reduction studies of hematite to magnetite in CO-CO2 atmospheres between 600° and 900°C initially exhibited linear kinetics. These linear rates were increased by additions of titanium and decreased by calcium. IN recent years many studies have been reported in the literature on the kinetics of the reduction of hematite and magnetite to iron. In addition, Hansen and Josephl and Schenck and Schultz2 have reported studies on the reduction of hematite to magnetite, the first step in total reduction to iron. In order to evaluate the results of the studies of over-all reduction in terms of the actual mechanism of the reaction and to define further the important factors in the rate- controlling mechanism of the magnetic roasting reaction, the following experiments were undertaken. Specimens of undoped hematite and hematite containing titanium or calcium in solution as doping agents were reduced to magnetite in CO-CO2 mixtures. In addition, electrical-conductivity measurements were correlated with the reduction kinetics using concepts of defect solid-state chemistry. EXPERIMENTAL Fisher certified Fe2O3 powder was used to make specimens for both the electrical and kinetic studies (see Table I for analysis). Doping with titanium and calcium was accomplished by adding TiO2 and CaO powders to the Fe2O3 powder. The powders were mixed in a Waring blender for minimum times of 1/2 hr. Satisfactory blending was achieved based on comparison of analyses of individual specimens af- ter reduction. The specimens were formed in a steel die using opposed punches with a rectangular opening 10.0 by 40.0 mm. The Fe2O3-TiO, platelets were pressed cold at 16,000 psi. They were sintered for approximately 16 hr at 1075°C in air, in accordance with information in the literature3, 4 on the time and temperature needed to obtain solution of the titanium in the hematite. The Fe2O3-CaO mixtures were first cold-pressed at 20,000 psi and sintered for 3 hr at 1225°C to insure solution of CaO. This material was then ground to -325 mesh in a 6-in. ball mill and the resulting powder was used to make platelets in the same manner as above. The sintered platelets were usually between 1/16 and 1/8 in. thick. They were ground on a carborundum wheel and polished on 2/0 paper. Typical dimensions of the kinetic-study specimens were 1.6 by 0.8 by 0.05 cm, and a typical weight was 0.3 g. Conductivity and thermoelectric specimens were approximately the same size, but were subjected to further sintering in order to ensure maximum densification. Finally, all specimens were measured to the nearest 0.0005 in. and weighed on a Mettler H-15 balance to the nearest 0.0001 g and the density calculated. The average density of the specimens used for the reduction studies was 4.87 g per cc, or 7.1 pet total porosity. The standard deviation ranged from 0.14 to 0.063 g per cc within a composition group. In the present study, the apparent surface area as measured with a micrometer was taken as the true surface area. The chemical analyses for calcium and for titanium within a group showed maximum variations of 50.04 pet from the average values used in Figs. 9 and 11. In order to suspend the specimen from the balance for the kinetic studies, a hole, 0.03 in. in

Jan 1, 1965

By J. W. Spretnak, G. W. Powell, J. H. Bucher

Tlze room-temperature tensile fracture oj smooth, round specitnens of three ultrnhigh- strength steels tempered to a wide range of strength levels was studied by means by light and electron-microscopic examination of the fracture surfaces. The fracture of AISI 4340 and 300 M at all the strength levels studied, and H-11, except after tempering at 1200° and 1300°F, occurs in three stages. The initiation of fracture is internal (except in some lightly tcmpeved specimers in which fracture is initiated at surface flaws), and is nucleated largely by separation at metal-second phase intevjaces. TIze voids grow and, coalesce to form a crack. When the crack has reached a sufficienl size, rapid propngutio~z ensues. Failure in this stage of fracture usually occurs by dimpled rupture of inicroshear stefis. In the case of H-11 tempered in the 1125° to 1300°F range, fracture in the shear steps is predominantly by concentrated deformation without void formation. The termination of fracture is usually occomplished by the formation of a shear lib in which fracture occurs by shear dimpled rupture. In the case of H-11 tempered at 1200° and 1300°F, no shear lip was obserued, and the radial elelments extend to the surface—a true termination slage does not exist. ThE tensile fracture of several metals and alloys has been investigated.2-4 In the case of polycrystal-line materials, cup-cone fracture usually results. The mechanism of cup-cone fracture may be summarized as follows.5 Cavities are formed in the necked region of the specimen. They usually are initiated by inclusions or second-phase particles. The cavities extend outwards by means of internal necking, and a crack lying about perpendicular to the length of the specimen is formed in the necked region. Subsequent crack growth occurs by the spread of bands of concentrated plastic deformation inclined at an angle of 30 to 40 deg to the tensile axis. Cavities are formed in the bands of concentrated deformation. The deformation bands zigzag across the bar with the net result that mac-roscopically the crack extends about perpendicular to the specimen axis. The final separation, or cone formation, appears to occur by continued crack propagation along one of the deformation bands out to the surface of the specimen. The micromechanics of the tensile fracture of ultrahigh-strength steels have not been thoroughly investigated. Larson and carr6,7 studied the tensile-fracture surfaces of AISI 4340 with a low-power microscope and reported that three stages of fracture could be observed in general. A centrally located region characterized by circumferential ridges, an annular region characterized by radial surface striations, and a peripheral shear lip were found. It was first pointed out by 1rwin8 that the central region is very probably one of fracture initiation and slow growth, and that the annular, radially striated region is one of rapid crack growth. Presumably the crack grows slowly, assuming roughly a lenticular shape, until it is large enough for the initiation of rapid propagation. In this investigation, it was attempted to determine the fine-scale aspects of the room-temperature tensile fracture of some ultrahigh-strength steels, and to relate the variation in fracture mode with microstructure. The steels studied were AISI 4340, 300M, and H-11 tempered to a wide range of strength levels. I) EXPERIMENTAL PROCEDURE The compositions of the steels studied are given in Table I. The steel was received in the form of hot-rolled bar stock 5/8 to 1 in. in diameter from which oversized specimens were machined and heat-treated. The heat treatments employed are given in Table 11. Subsequent to heat treatment, the specimens were ground to the final dimensions and stress-relieved by heating for 1 hr at 350°F (with the exception of the as-quenched steel). Standard smooth round specimens of 0.252-in. diameter and 1-in. gage length were tested in a Tinius Olsen Universal Testing Machine using a cross-head speed of 0.025 in. per min. The relatively coarse aspects of the fracture topography were determined by light-microscopic examination of sections through the fracture surface of nickel-plated specimens. A direct carbon-replication technique9 was used in the electron-microscopic study of the fracture surfaces. The replicas were examined in the electron microscope, and stereo pairs of electron micrographs were taken. The stereo pairs were then examined using a Wild ST4 Mirror Stereoscope. Carbide and inclusion particles extracted in the replicas were analyzed by selected-area electron diffraction. II) EXPERIMENTAL RESULTS The mechanical testing data are summarized in Table 111. The values reported are the average of

Jan 1, 1965

By F. F. Skiba, J. E. Warren

An idealized miscible displacement process in a three-dimensional, heterogeneous porous medium has been studied via experimental computation based on a "Monte Carlo"' model. The macroscopic dispersion which results solely from variations in the permeability of the porous system is related to the scale of the heterogeneity as well as the distribution function for the permeabilities. The interpretation of laboratory data is often subjective and may bt? misleading since ambiguities are not always recognized. Furthermore, an experiment performed on a conventional oil-field core does not yield a valid measure of Macroscopic dispersion for reservoir engineering purposes since the scale of heterogeneity that is significant in the laboratory is not significant in the reservoir. The analysis of field-performance data is discussed and it is shown that a unique characterization of the reservoir can not be obtained from this information alone. A possible method based on a minimum of data, for estimating the spatial distribution of permeabilities in a reservoir is postulated INTRODUCTION Many studies concerned with diffusion and dispersion in porous media have been undertaken because of the potential importance of miscible displacement processes for increasing the recovery of oil. The results from a large number of these studies have been published; in a recent paper Perkins and Johnstonl presented a comprehensive survey of the pertinent literature and excellent appraisal of the "state of the art". In this investigation, dispersion resulting from macroscopic variations in the properties of the porous medium is of primary interest. Dispersion, in this sense, is caused by fluctuations in the velocities of the individual fluid elements as they move through the porous system. This phenomenon is the result of inhomogeneities in the permeability and/or porosity, but it can be amplified by differences in the characteristics of the fluids involved. The objectives of this study are the following: (1) to determine the qualitative manner in which macroscopic rock properties affect the observed dispersion coefficient; (2) to evaluate the possible influence of macroscopic dispersion on laboratory experiments; and (3) to appraise the significance of macroscopic dispersion with regard to reservoir performance. Investigations of this type are essential since many miscible displacement processes, while seemingly understood from a mechanistic point of view, do not behave in a predictable manner under field conditions. Although a plausible explanation is that the process is dominated by the environment, little serious effort has been devoted either to describing the reservoir itself or to determining the probable effect of the reservoir properties on the process. This study is intended to be exploratory in nature; however, it is hoped that it will provide additional insight into the physical problem and that it will suggest areas suitable for further investigation. EXPERIMENTAL COMPUTATION MODEL To limit the observed dispersion to that which results solely from variations in the properties of the porous medium, an idealized process in which one incompressible fluid displaces another identical fluid is simulated. This simulation is achieved by means of a modified Monte Carlo method — by tracking a number of mathematical particles (tracer) through the system according to the steady-state, single-phase velocity distribution. Then the system is characterized by the distribution of the residence times of the particles. Since any number of particles can be injected simultaneously (a true delta-function distribution) and only pressure conditions are imposed on the boundaries, the model is completely determinate. Furthermore molecular diffusion, microscopic dispersion, adsorption and/or reaction are automatically precluded from the model. The heterogeneous medium is represented by a rectangular, three-dimensional array of uniform, homogeneous porous blocks which are randomly arranged; it is assumed that any two opposing faces of the system are held at fixed potentials

Jan 1, 1965

By H. Biloni

A metallographic study of solute segregation produced during controlled solidification of Sn-Pb alloys has previously been reported.' It was found that the growth conditions which produced well-developed cellular substructures led to severe segregation, and even at solute concentrations of 0.2 wt pct Pb regions of a lead-rich phase were formed at the junctions of cell boundaries (nodes). Similar sample preparation and etching techniques have now been applied to several tin alloys at more dilute concentrations. The crystals were solidified uni-directionally under less-severe growth conditions so that the predominant interface structure was composed of two-dimensional cells.* Binary alloys with lead, using 9.999 pct Sn as a solvent, and ternary alloys with lead and bismuth or lead and antimony, using zone-refined tin as a solvent, were examined. The liquid was decanted from the growing crystals in all cases to reveal the interface structure and ensure that two-dimensional cells were being formed. However, since interference may arise from a liquid layer that clings to the interface during decanting,3 an examination of the segregation pattern was always made behind the interface. In all cases, the structure within the bulk of a crystal at greater than 1 cm behind the decanted interface was substantially the same as that nearer the interface. Representative photomicrographs of the dilute Sn-Pb alloy are shown in Figs. 1, 2, and 3. Most observations are similar to those of the previous investigation. For example, the solute concentration at the cell walls is higher than in the intercellular regions; where cell boundaries meet, the segregation is enhanced; the macromosaic or stria-tion substructure and grain boundaries show enhanced segregation; there is also a depletion of solute at cell walls near a striation boundary, as Spittle et a1.4 have observed at decanted interfaces. Not all these observations can be seen in the photos shown since attention has been focused on a special feature; as evident in the photomicrographs, cer-

Jan 1, 1965

By R. T. Hukki, P. Voutilainen

This paper describes a new apparatus for continuous wet fine-screening. Its preferred size range seems to be from 0.1 to 1 mm. The supercritical trommel screen is a short cylindrical trommel of wedge-bar type construction operated at a speed greater than the calculated theoretical critical speed and at a speed lower than the speed at which particles introduced into it will centrifuge. The paper describes results obtained with the prototype supercritical trommel screen in pilot plant scale. The results point to a high capacity and simultaneously to a high sharpness of screening. Finally, an analysis is presented of the forces acting in screening on a supercritical trommel screen. In the era of high speed, high capacity processing of raw materials the conventional slowly rotating trommel screen is often considered a relic from the times passed. A typical trommel screen is the cylindrical trommel rotated about a horizontal or slanting axis at a relatively low speed. Its screening characteristics are well known. Trommel screens of various types of construction, methods of operation, performances and other characteristics have been described in detail by Taggart.1 The theoretical critical speed of a trommel screen is defined by the same well known equation as that applied for grinding mills: where ncritical = the numerical value of the theoretical critical speed in rpm, D 1 = the inside diameter of the trommel in feet, and D2 = the inside diameter of the trommel in meters. ncritical corresponds also to the centrifuging speed provided that the coefficient of friction f between the trommel surface and the outer layer of the charge is = 1.0. In a general case: From Eq. 2 it is seen that in all cases where f < 1.0 the centrifuging speed of the trommel is greater than the theoretical critical speed. The supercritical trommel screen concerns screening operations within that speed range which is between the theoretical critical speed defined by Eq. 1 and the centrifuging speed defined by Eq. 2, under conditions such that the coefficient of friction f<1.0. It is reported by Taggartl that the optimum speed of a conventional cylindrical trommel screen 36 in. in diam was experimentally found to be about 16 rpm. From Eq. 1, the critical speed of this trommel is 44.2 tpm. The indicated optimum speed corresponds to (16/44.2) x 100% = 36.2% of the theoretical critical speed. The optimum speed range based on information available seems to vary from 33% up to 45% of the theoretical critical value. The trommel screen operated at a supercritical speed: operates at a speed greater than the calculated theoretical critical speed; operates at a speed lower than the speed at which the charge introduced into it will centrifuge; operates within the supercritical speed range in such a way that the coarse fraction of the charge must slide in respect to the inside surface of the trommel; the outer layer of the said fraction next to the screen tends to proceed in the same direction as any selected point on the trommel surface, but now at a lower speed, and indeed at a subcritical speed; allows to a certain degree adjustment of the maximum determining particle size x of the fine product simply by a variation of the speed of the trommel within the supercritical speed range. With increasing trommel speed, finer and finer material only will get the opportunity to find its way into the fine product while the screen opening remains constant. In conventional practice, the low speed trommel is generally used for sizing of coarse and medium coarse material, but seldom for fine screening. The characteristic feature of the product passed through the conventional trommel is that the determining size x of the biggest particle is barely smaller than the nominal size of screen opening. The supercritical trommel screen, on the other hand, is best suited for sizing of relatively fine material. Furthermore, the characteristic determining size x of the biggest particle in the fine product can be substantially smaller than the nominal width of the screen opening or slot. In the trommel screen best suited for the applications

Jan 1, 1965

By T. A. El-Bassyouni, Paul Gordon

Grain-gvowth data in zone-refined aluminum and in dilute alloys of copper with this aluminum have been obtained. The amounts of copper added were from 4 to 400 at. ppm. It was found that in both the unalloyed aluminum and the alloys grain growth was characterized by a high value of n in the isothermal growth equation 6n = Kt The inadvertent presence of 1 at. ppm Fe in the alloys was found to he more potent in slowing growth than the purposely added copper. Possible rationalizations of these observations and their general relevance to the theoretical use of gvain-grozvth data have been discussed. Grain growth data of Winegard and his co-workers&apos; on zone-refined tin and dilute tin alloys were analyzed with some success2 in terms of approximate theoretical equations for boundary migration.2-4 In view of this success, experiments were carried out in an effort to obtain similar data on zone-refined aluminum and on dilute copper-in-aluminum alloys. The results obtained were anomalous in several respects and could not be used to test theory. A discussion of these anomalies is presented here; they have been attributed to impurity effects and serve to emphasize the sensitivity of grain growth in general—and the particularly high sensitivity in aluminum—to impurities. The resulting difficulties in the theoretical use of grain-growth data are also discussed. EXPERIMENTAL DETAILS An aluminum bar was zone-refined and leveled by methods similar to those described previously.&apos; The degree of purity obtained is indicated in Table The data in Table I were determined by mass-spectrographic methods through the courtesy of Mr. Thomas A. Johnson of AIAG Metals, Inc.* Three dilute copper alloys with this aluminum were prepared also by methods described previously.&apos; The alloys contained nominally 4, 40, and 400 at. ppm of Cu, respectively (0.001, 0.01, and 0.1 wt pct). Each material was fabricated by swaging and rolling into a round bar about 1/4 in. in diameter with an annealed penultimate grain size of approximately 0.003 to 0.007 cm. In order to minimize preferred orientation the fabrication was carried out in several steps, each consisting of a reduction of about 40 pct followed by a recrystallization anneal. Annealing temperatures for the grain-growth studies were attained by the use of boiling liquids up to 213°C and molten metal baths at higher temperatures. Temperatures were controlled to within 1°C. Samples for measurements were cylinders about 3/4 in. long and 1/4 in. in diameter cut from the fabricated rods. In the interests of sample economy a single sample was used for the grain-growth measurements at each temperature. Each sample was, thus, annealed for several successive periods of time, the grain size being measured at each annealing period on a transverse surface exposed by

Jan 1, 1965

By Jean Howard

THERE are two mechanisms by which secondary crystals can develop in bcc alloys, namely 1) impurity inhibition and 2) strip-thickness inhibition. This paper reports some studies of each mechanism; the alloys were Si-Fe, A1-Fe, Cr-Fe, Mo-Fe, and Ge-Fe, as well as iron itself. All the alloys, which were of interest as part of a program of work on soft magnetic materials, were made by a powder-metallurgy process, using carbonyl iron (Grade MCP) as the starting material. Earlier phases of the work have already been published. Work described previously1 shows how the oxygen content of the sintering. atmosphere can be used to produce silica in the material which acts as a grain-growth inhibitor. Since then it has been found more convenient to make use of the oxide in the iron powder to control the silica content of the material. The compacts are sintered in vacuum which allows a direct reaction to take place between the iron oxide and the silicon. Details are given elsewhere.4 By this method, and by suitable adjustment of the rolling schedule, material with cube-on-edge secondary crystals has been produced in thicknesses from 0.1 to 0.001 in. in iron containing from 2-1/2 to 4-1/2 pct Si. It was also found possible to process 6-1/2 pct Si-Fe to 0.001 in. This was achieved by refinement of the sintered-compact grain size by using fine-particle silicon (i.e., <200 mesh). The brittleness of the material necessitated hot rolling to 0.020 in., from which thickness cold rolling was possible. If the conditions of sintering and the cold-rolling schedule were correct (i.e., as given elsewhere4 for 3-1/4 pct Si-Fe) secondary crystals of (110) [001.] orientation could be developed. The size of the secondary" crvstals" could not be

Jan 1, 1965

By B. M. Larsen

Jan 1, 1965

By Caudle B. H., Cooper H. E. Jr., O. K. Kimbler

The results of studies of areal sweepout behavior in nine-spot injection patterns are presented in this paper. The ratio of the production rates of the two types of producing wells in a nine-spot pattern is considered in its effect on breakthrough. A model study was used to develop a method to predict the production histories of both side and corner wells and to develop the production history of the pattern or the field. INTRODUCTION The importance of areal sweepout behavior in injection operations has been recognized for a number of years. We now know that the fraction of a reservoir which will be reached by an injected fluid is a function of the geometric arrangement of the production and injection wells and of the mobility ratio of the fluids. Of these two, the mobility ratio (which is a measure of the relative ease with which the oil and the injected fluid can move through the reservoir) appears to have the greatest effect on recovery. The effect of mobility ratio on production history has been reported for most of the dispersed injection patterns (i. e., five-spot, staggered and straight-line drives).4-6 ere has been very little published on the nine-spot injection pattern. This may be because the two types of producing wells in the nine-spot pattern can—and sometimes should —be produced at different rates. This adds a second variable (the fist being mobility ratio) to be covered in a study of the nine-spot flooding network. Muskat1 has reported the sweep pattern efficiency at breakthrough for a mobility ratio of one at various ratios of producing rates for the two types of wells. For these conditions he found maximum oil production at breakthrough to occur when the corner well (the producing well farthest from the injection well) is produced 10.7 times as fast as the side well. Other investigatorsa2,3 have studied a few of the many possible operating conditions possible with this injection pattern. This paper presents the results of studies which are strictly applicable to a nine-spot injection pattern surrounded by other nine-spots in a homogeneous reservoir and which has no flowable gas present (no oil bank is formed). Although the full ranges of the variables mentioned above have not been covered, the results reported here should allow reasonable estimates of field operations to be made. EXPERIMENTAL The well spacing geometry of the nine-spot pattern is shown in Fig. 1. Here we see that each injection well is surrounded by eight production wells arranged in a square. Four of these producing wells are located at the corners of the square; the other four are in the midpoints of the four sides. These two types of producing wells are called "comer wells" and "side wells" respectively. It is the ratio of the producing rates of these two types of wells that affects the breakthrough recovery, as calculated by Muskat.&apos; This ratio is defined as the total producing rate of a corner well divided by the total producing rate of a side well. The model used in this study represented one-eighth of a nine-spot pattern, as shown in Fig. 1. It contained the equivalent of one-fourth of a side well, one-eighth of a comer well, and one-eighth of an injection well. Because of these proportions, the actual producing rate ratios in the model were one-half of the ratios of producing rates as

Jan 1, 1965

By E. Teghtsoonian, A. R. Causey

THE fact that the surface plays an important role in the plastic deformation of a single crystal has been demonstrated by several investigators. The surface conditions have been altered using oxide films,1&apos;2 alloyed metal layers,3, 4 deposited metal films,&apos; and polycrystalline layers.677° The resulting effects on the initiation and subsequent plastic deformation have been investigated extensively except for the case of a single crystal surrounded by a polycrystalline layer of the same material. The purpose of this paper is to describe an investigation of the effect of a polycrystalline surface layer on the yield stress, the critical resolved shear stress, and the work-hardening slope of tin single crystals. The tin single crystals used in this study were grown from the melt using material having an initial purity of approximately 99.999 + pet with lead and iron the major impurities. Fig. 1 shows the orientation of the (110)[001] slip system with respect to the crystal surfaces. The crystals had a 1/4 by 1/4 in. cross section and a gage length of 2 in. The polycrystalline surface layer was produced by abrading the single-crystal specimens with emery paper. Fig. 2 shows the broken Debye rings obtained from the deformed surface. The thickness of the layer was controlled by the number of passes on different grades of paper and was determined by electropolishing in dilute HC1, until the grains produced by the abrasion had all been removed. Metal-lographic examination showed that the grain size varied with depth, increasing from 10 µ right at the surface to 40 µ in the interior of the layer. The yield stress, critical resolved shear stress,

Jan 1, 1965

By B. D. Smith, K. H. Coats

Experiments in which calcium chloride displaced sodium chloride from four cores showed the extent of asymmetry in the resulting effluent concentration profiles. These results provided a check on how validly the mixing process is modeled by a differential (i.e., not finite-stage) capacitance mathematical model. The effluent concentration profile from two consolidated cores exhibited considerable asymmetry, while two unconsolidated cores yielded nearly symmetrical profiles. All runs resulted in breakthrough of the 50 per cent concentration significantly before one pore volume was injected. In addition, velocity appreciably affected the effluent concentration profile from a Torpedo sandstone core. The differential capacitance model matched the data significantly better than a simple diffusion model. The capacitance model allows determination of the amount of dead-end pore space in a porous matrix and the effect of velocity on the rate of diffusion into this space. An experimental program yielding insight into the physical validity of the capacitance effect is described. INTRODUCTION Axial dispersion — the mixing accompanying the flow of miscible fluids through porous media — has been the subject of many relativeiy recent studiesl-13 and a comprehensive review of the topic has been given by Perkins and Johnston.14 This dispersion is of practical interest in studies of the miscible displacement process, fixed-bed chemical reactors, and the adsorption of solutes from a flowing stream onto the surface of a porous medium. In the latter case, the effect of dispersion must be considered when adsorption parameters are determined from the nature of concentration profiles. In general, early studies of dispersion assumed applicability of a simple diffusion equation and were concerned with correlation of the experimentallv determined "effective" diffusion coefficient with system properties over a large range of the latter. Recent have been concerned with the deviations between the asymmetrical effluent concentration profiles observed and the symmetrical ones predicted by the diffusion model. In the present study, effluent concentration profiles were obtained from consolidated and unconsolidated cores. These profiles were compared with those predicted by a differential (i.e., not finite-stage) capacitance model. Solutions to the simple diffusion model, for three sets of boundary conditions, were compared with one another and with the experimental profiles. SUMMARY OF PREVIOUS WORK The reader is referred to Perkins and johnston14 for an extensive review of studies of dispersion in porous media. Many investigators have employed the simple diffusion model characterized by Eq. 1 below: The dispersion coefficient D for unconsolidated systems is correlated by u is interstitial velocity and dp is particle diameter. Since heterogeneity of the sand pack affects the mixing, this equation is also expressed as where a is proportional to the degree of heterogeneity and is about 3.5 for random packs of unconsolidated sand.l4 Eq. 3 holds for 2 For a Do homogeneous (regular) type of packing, should be 1 or less.6 Aris and Amundson6 and Carberry and Bretton consider o to be the number of particle lengths per mixing cell in the finite-stage model. Data from consolidated cores indicate dp to be about 0.36 cm for outcrop rocks, Torpedo sandstone having a reported value of 0.17 cm.15 For v /Do less than about 2, the effect of molecular diffusion must be considered and the total dispersion coeffi-

Jan 1, 1965

By J. J. Kramer, K. Foster

The orientation distribution of surface-energy -induced secondary recrystallized grains was determined. This work was conducted on thin sheets of a 3 pct Si-Fe alloy annealed under environmental conditions that furor grouth of grains with a (100) plane in the surface of the sheet. The texture was found to be extremely sharp and almost independent of sheet thickness. The distribution varied exponentially with the angular deviation from the {100} plane. It was possible to relate the distribution to the nu-cleation rate of the secondary rains as influenced by the surface-energy difference. THE role of surface energy in the secondary grain growth of cube-oriented grains (grains with a (100) plane in the plane of the sheet) in thin Si-Fe sheets has been previously discussed.1-4 In high-purity sheet material normal grain growth usually occurs until the grains have extended through the sheet. Further grain growth is inhibited by the thermal grooving of the boundaries at the sheet surface. However, additional growth of cube grains can occur by a secondary grain growth process under conditions where the (100) plane has a lower surface energy than other orientations. Apparently for these alloys, cusps exist in the polar plot5 of surface free energy with the lowest cusp energy occurring at the (100) orientations. This has been reported to be the result of preferential adsorption of sulfur on the (100) planes.6 As a result of this process, a distribution of orientations could arise from two possible mechanisms. First, when a cusp is present in the polar plot of surface free energy, there are orientations inside the cusp that have a lower surface energy than elsewhere on the polar plot. Also, at sufficiently high temperatures, flat surfaces whose orientations are inside or just outside the cusp (depending on its shape) can often thermally etch, yielding a microscopically stepped surface of even lower surface energy. As a result, grains oriented close to cube would also have a lower surface free energy, either because of the cusp shape or by thermal etching, and could possibly grow as secondary grains by the surface-energy phenomenon. One should thus observe a distribution in the surface orientation of the cube grains comprising the secondary structure. It is the purpose of this paper to investigate this orientation distribution experimentally and to discuss the factors involved in its formation. For this purpose, the surface orientations of a large number of secondary grains in various sheet thickness were determined by means of the Laue back-reflection X-ray technique. PROCEDURE A vacuum-melted 3 pct Si-Fe alloy containing a nominal impurity content of 0.005 wt pct was processed into strip. A single cold-rolling step of 90 pct reduction was used for each strip regardless of the final sheet thickness. Final strip thicknesses of 0.60, 0.30, 0.15, and 0.075 mm were used. Care was taken to insure that the final strip surface was smooth and flat. All strips of a given thickness were annealed together at 1200°C in dry hydrogen (dew point -70°C) to develop the desired secondary structure and to insure identical environmental annealing conditions. The annealing time was selected to develop a complete secondary structure in the thinner sheets but to permit the thicker sheets (0.60 mm) to have residual primary grains remaining. This was necessary to determine whether growth impingement could lead to one secondary grain consuming another at a greater angular deviation. For the X-ray determination of the surface orientation of the secondary grains, a special specimen holder was used. The camera and holder arrangement could be aligned by X-raying a grain in three positions rotated 180 deg to each other. Thus, with a small beam X-ray focus (1 mm), the surface orientation of any grain could be determined to within one-half a degree. The surface orientations of one hundred cube secondary grains were determined for each sheet thickness. The criteria of a secondary grain were its size relative to the sheet thickness and the number of sides of the grain observed in the sheet surface. (A primary recrystallized grain extending through a sheet will generally have six edges visible in the plane of the sheet, whereas a secondary grain will have many more when growing entirely into primary grains.) Grains were selected as randomly as possible by X-raying every secondary grain found along a line drawn on the strip. No attempt was made to determine the exact orientation of the planes of the surface, as many strips from randomly selected sheets were used. On1y the angular deviation of the surface plane from {100} was measured. In order to assess the volume distribution in the

Jan 1, 1965

By G. S. Cole, G. F. Bolling

Recent experitnents on crystal growth have indicated that thermal convection in the liquid influences the conditions of solidification and subsequent crystal characteristics. However, the important columnar-equiaxed transition in castings has not been examined as a function of this free convection. An experiment is presented here to demonstrate a change in the transition as convection is suppressed. Lead- and tin-based alloys were cast in stainless-steel molds either without special procedures or with thin grids placed horizontally across the tnold diameter in portions of the castings. While the grids allowed some diffusion of heat and mass transport to occur during solidification, massive fluid flow was hindered in the vegiotz of the grids. A larger percentage of columnar grains appeared in the grid region than in other parts of the special castings or than in all regions of normal castings. This structural difference can be explained in terms of thermal convection. THERE is little information about the possible effects of natural convection which may occur during the solidification of a casting. Ruddlel-3 has stated that the movement of liquid metal produced by convection might assist in the transfer of heat, but in the absence of confirmatory evidence he suggested that this idea be treated with caution. chalmers4 considers, but does not assess, the importance of fluid motion in casting, while Tiller5 suggests that, in liquid metals which have extremely high thermal diffusivities, the effects of thermal convection may be negligible. In addition, throughout the literature, there are statements indicating the possible presence of thermal convection but without proofs or evaluations of its influence. Natural convection may be divided into two categories: thermal convection, where liquid flow is due to density differences caused by temperature gradients in the liquid (e.g., liquid near a cold wall falling with respect to hotter liquid further away from the wall); and solute convection, where flow is due to density differences as a result of concentration gradients, see Wagner.6 In most instances thermal convection predominates over solute convection. Nevertheless, even thermal convection has not been studied in any detail and is difficult to handle, since it can vary quantitatively from one experiment to another depending upon the exact positions of heat sources and sinks or the attitude of the container with respect to gravity. In spite of these difficulties it is possible to realize that a higher rate of heat transfer must result with convection than in any situation where conduction acts alone. Thus, the degree of increased heat transfer is the important undecided question in considerations of casting. It will be demonstrated here that a reduction in convective flow leads to a suppression of the columnar-equiaxed transition in a casting and that this suppression is related to a decrease in the degree of heat transfer. Fortunately it is possible to do this by comparative rather than quantitative measures. The insertion of horizontal plates or grids into a simple mold does not appreciably influence heat transfer per se, but in reducing the allowable height through which colder liquid may fall freely it reduces natural thermal convection. This leads to a reduced fluid velocity, a different flow pattern, and an altered heat transfer which can be measured. EXPERIMENTS The alloys were prepared from elements of 99.9 pct nominal purity and cast into an uncoated 2-in.-diameter stainless-steel mold insulated at the bottom with a suitable refractory so as to ensure predominantly radial heat flow during freezing. Casting was performed either in empty molds or in molds containing grids or plates in various configurations . The grids were constructed of aluminum screen (1/32 in. thick) which was cut to the desired shape, cleaned in aqua regia, and coated with a mixture of 2 parts aqua dag graphite -1 part Sauereisen cement mixture, thus supplying a hard, protective, and insulating layer approximately 0.006 in. thick. The

Jan 1, 1965

By Fred L. Morritz, Harold M. Manasevit, Richard Nolder, Arnold Miller

Experimental evidence is presented which confirnis the epitaxial relationship between the deposited silicon and the sapphire substrate. Four distinct modes of orientation relationships have been established. These have been shown to be Single-crystal gvowth retention as a function of surfaces oriented off ideal has been qualitatively indicated. Both full-circle goniometer X-ray techniques and replica electron microscopy have indicated varying amounts of microtwinning in the silicon. film, which may he caused by the mode of silicon formation. Parameters have been found where twin density is less than I pct. The early stages of&apos; epitaxy of silicon m sapphire have been examined by electron-microscope techniques... and mechanisms have been proposed. THE first report of the deposition of single-crystal silicon on sapphire (single-crystal aluminum oxide) was made at the American Physical Society Meeting in Canada&apos; by one of us and was subsequently published in the Journal of Applied physics.* This paper summarizes some of the work carried on in this area since that time, in addition to reviewing some of our earlier observations. The initial single-crystal deposits of silicon on sapphire reported were obtained on sapphire planes produced by cutting a sapphire rod perpendicular to its fastest growth direction, which is approximately 60 deg from the C axis. Direct correlations between the microstructure and X-ray data as to the single crystallinity as shown in Fig. 1 are evident. These deposits were identified as (111) silicon on the substrate oriented near the (1123) of sapphire. (Sapphire notations are designated according to the c over a ratio of 2.73.) It became evident that substrate quality and surface play an important part in successful epitaxy. For example, in Fig. 2 we observe an interesting

Jan 1, 1965

By D. L. Luffel

This paper presents two main developments: (1) a short, constantly accelerated centrifuge method of measuring drainage capillary pressure properties of cores, and (2) a new analytic method of treatment of centrifuge measurements to obtain saturation-capillary pressure relations. Toward the first objective, a clever experimental method is presented which is certainly more rapid than previous centrifuge methods. Toward the second objective, a new analytic method is derived to eliminate the approximate method of Hassler and runner. The derivation of this new analytic method, however, appears to be in error. The new analytic solution is developed as Eq. 5 in Appendix A. At the beginning of this derivation, the average wetting phase saturation of a core is expressed as, where is the centrifuge angular velocity. Eq. D1.2 makes explicit the dependence of S and S upon The second equation shown in Appendix A expresses the relation between the three variables Since for a given porous medium the saturation is uniquely related to capillary pressure, the functional dependence of S upon P is trivial, i.e., Pc.ri does not actually appear. Thus, the function 5 (r, ) may be expressed as a new function, S*, of PC, , alone The author transforms the variable of integration in Eq. Dl through use of Eq. D2 and writes

Jan 1, 1965

By I. L. Dillamore

A purely geomentrical analysis based on oriented-growth relationships is presented to derive annealing-texture orientations in bcc metals from their- known deformation textures. The analysis takes as its starting point a description of- the bcc deformation texture and follows previous work on fcc metals in considering pvobable nurleation sites for recrystallization and the textural limitations on grains growing into a deformed matrix. The analy-sis accounts for the prominent and the minor coinponents of the annealing textures formed from two the deformation textures and can account for the ob-sem:ed temperature dependence of the annealing texture of bcc metals. THERE have been a number of investigations of annealing textures in bcc metals but few attempts to relate these textures to the deformation textures. This has been largely due to the lack of definition of both annealing and deformation textures, neither of which shows sharply defined orientations. It is, however, necessary to get a better understanding of primary recrystallization textures in bcc metals in view of increasingly exacting demands upon the quality of steel sheet for drawing purposes and as a necessary step towards the control of textures through processing. An analysis is presented here which relates annealing textures to deformation texture, by a purely geometrical method. This takes as its basis the oriented-growth theory of recrystallization and makes some reasonable assumptions regarding the make-up of bcc deformation textures and the limitations on growth relationships in bcc metals. Detailed information on this latter point is not available at the present time, and the present analysis may need to be streamlined or extended when such information is at hand. It is felt, however, that despite these limitations the analysis provides useful results and a valuable aid towards understanding the effect of processing variables. 1) BCC ROLLING TEXTURES Different workers have used a variety of descriptions for the texture developed in bcc metals by rolling. For the present purpose it will be assumed that two different deformation textures can be obtained: 1) a texture containing a major (112)[li0] component and a minor (001)[1i0] component for which increasing deformation causes the (001)[li0] component to increase at the expense of the (112)[li0] component, as suggested by Dillamore and ~oberts&apos; (this is the texture predicted to arise starting from randomly oriented material); 2) a t~xture containing the above components and (111)[110] and (ii1)[112] components. This texture could arise from a material with an initial (110)[001] or (iil)[112] texture. It is well-known that the (ll0)[001] orientation rotates to (ii1)[112]that on roll-

Jan 1, 1965

By S. Stopek, E. D. Hinkley, R. H. Rediker

Epitaxial heterojunctions have been prepared by melting the lower -melting-point semiconductor of the interface between two dijferent semiconductors. when the temperature is reduced, the melted material recrystallizes, having alloyed into the higher -melting-point semiconditctor. The electrical and elcctro-optical properties of such single-crystal heterojunctions between GaAs and Gash and between p-type InAs and n-type Gash are the subject of this paper. The forward current varies as exp (AV), where A is substantially independent of temperatuve. For Gds-Gash heterojunctions at temperatures above, 370°K, if the current-voltage relationship were to he expressed as exp (qV/nkT), then n would he less than unity. The injection luminescence associated with forward current is, for the most part, characteristic. of the lower bandgap semicondutctor. These results can he explained by carrier injection into the lower bandgap semiconductor by tunneling through a barrier at the interface. The photovoltaic effect measured for incident photons having energies in the range between the bandgaps of the two semiconductors is much smaller than that produced by higher-energy photon The smallness of this between -the-gap photovoltaic response can he explained by the low probability for penetration of the barrier by the carriers produced in the smaller -bandgap semiconductor. THE technique of interface alloying has been used to produce single-crystal junctions between dissimilar semiconductors.&apos; Oriented wafers are placed on a carbon heater strip, Fig. 1. so that semiconductor S1, which has the lower melting point, is supported by semiconductor S2. Electrical current passed through the heater strip produces a temperature gradient such that S2 is at a higher temperature than S1. As the temperature is raised the lower face of S1 begins to melt. Before the entire wafer can melt, however, the heater-strip current is turned off and, as illustrated in Fig. l. the melted portion recrystallizes, having alloyed into S2. Junctions have been fabricated by the above procedure between GaAs and germanium, between GaAs and GaSb, and between InAs and GaSb. Mroczkowski, Lavine. and Gatos have described the metallurgical and chemical aspects of the GaAs-Ge junction.2 The transition from GaAs to germanium is not monotonic and a portion of the recrystallized region consists of the GaAs-Ge eutectic. Since gallium is an acceptor and arsenic is a donor in germanium, since germanium dopes GaAs, and since the electrical properties of the GaAs-Ge eutectic have not been investigated, any interpretation of the electrical characteristics in terms of simple heterojunction theory would be incorrect. That the rectification of GaAs-Ge heterojunctions is not a property of the impurity doping of the GaAs or the germanium, but is most probably due to the impurity distribution in the recrystallized region, is clear from the fact that forward conduction occurred for all the GaAs-Ge interface-alloy junctions (whether they be n-n,n-p. p-n. or p-p) when the germanium was biased positively. The electrical characteristics of these GaAs-Ge heterojunctions will not be discussed further in this paper. Electron-beam microprobe analysis of GaAs-GaSb heterojunctions showed that the transition from arsenic to antimony atoms was without structure. and that the transition occurred within a 2 to 3 region.&apos; In this paper we will describe the electrical properties of the GaAs-GaSb heterojunctions as well as electrical and electro-optical properties of the InAs-GaSb heterojunctions. A band model for the junction will be proposed which can explain these properties. ELECTRICAL PROPERTIES OF GaAs-GaSb HETEROJUNCTIONS After interface alloying. in preparation for the electrical and electro-optical experiments, ohmic contacts were made by conventional means. For example. Kovar tabs clad with tin were alloyed to n-GaAs or similar tabs clad with Au-Zn were alloyed to p-GaAs. The units were mounted and then etched. All four combinations of conductivity types

Jan 1, 1965

By S. Atak, M. C. Fuerstenau

Clean quartz cannot be floated with a high molecular weight sulfonate as collector at any pH. Good flotation is achieved from pH 6 to 12 when Pb is added at low additions of sulfonate. The active species of lead responsible for flotation is shown to be Pb(OH), which in the presence of sulfonate forms precipitated lead-hydroxy-sulfonate, the apparent collector in these systems. The ratio of collector to metal ion addition is critical for flotation to be effected at a given value of pH. At low Pb++ additions, the constant, k, k = (hydroxyl activity)/(sulfonate addition)&apos;, must be equalled or exceeded for flotation to result. Similarly, at high additions of Pb ++, k1 = (hydroxyl activity)/(sulfonate addition) " must be exceeded. Previous work has shown that clean quartz cannot be floated at any pH with a high molecular weight sulfonate as collector.&apos;" Flotation can be effected, however, when a polyvalent metal ion is added to the system in a pH region in which the metal ion is hydrolyzing to its first hydroxide complex. Although the basic phenomenon responsible for activation is apparently metal ion hydrolysis, the amount of collector added in relation to the amount of metal ion is critical. In fact, Schuhmann and Prakash,3 and Gaudin and Rizo-Patron4 have demonstrated that this ratio of collector addition to metal ion addition determines whether any flotation is possible at a particular value of pH. The object of this paper is to explain and quantify the relationship between collector and activator additions as a function of pH. For this work, Pb++ was selected as activator, and a high molecular weight sulfonate was chosen as collector. EXPERIMENTAL MATERIALS AND METHODS Sodium alkyl aryl sulfonate (mol wt 450) was used as collector. Reagent grade n-amyl alcohol was added as frother, and pH adjustments were made with KOH. Lead was added to the systems as the chloride salt. Conductivity water, made by passing distilled water through an ion exchange column, was used in the investigation. Quartz was prepared by leaching the sized sample

Jan 1, 1965