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By Hsun Hu, R. S. Cline

The formation of annealing textures during the course of recrystallization in 2 pct Al-Fe crystals rolled in the (111) [112], (112) [111], and (112) [Till orientations has hem studied in detail. When the rolling texture is composed of both (111) [121] and (001)[110] components, the annealing texture consists of mainly (110) [001] and (113) [332] components. As the (001) [110] component diminishes from the surface to the interior of the rolled crystal, the relative concentration of the (113) [332] component in the annealing texture decreases accordingly, whereas that of the (110)[001] component increases with the (111)[112] component in the rolling texture. Such dependence of the annealing texture on the composition of the rolling texture is in accmdance with the oriented growth mechanism. Grain-growth characteristics during recrystallization, hence the annealing texture, can he considerablv different in (112) [111]-type crystals depending sensitively on the initial orientation of the crystal. In a previous publication,' the formation of rolling textures in 2 pct A1-Fe single crystals with initial orientations of approximately (1ll)[112], (112)[111], and (112)[111] was studied in detail. The deformation texture of these crystals consisted of either a single (111)[112] or a combination of (111)[112] and (001)[110] components in various concentrations. For the (lll)[112] crystal, the deformation texture was a single (lll)[112] up to 70 pct rolling reduction, but it became (lll)[112] plus (001)[110] after -90 pct reduction. For the (112)[113.]-type crystals, the relative concentration of the (111)[ 112] and (001)[110] components varied with the depth below the surface of the crystal, as well as with the amount of deformation. These series of specimens, having deformation textures with a range of concentration of the (111)[112] and (001)[110] components, could therefore be used for a thorough investigation of the effect of deformation-texture components on the formation of annealing textures. In a study of rolling and annealing textures in Si-Fe crystals, Dunn and Koh3 noted that the addition of a (001)[110] component to the (111)[112]-type deformation texture had practically no effect on the recrystallization texture.* According to the ori- ented growth mechanism for the formation of annealing textures, nuclei related to the deformation texture by approximately 30-deg rotation around a common [110] axis have the highest rate of growth and the resulting annealing textures generally have such an orientation relationship with respect to the deformation textures.314 It was reasoned by Dunn and Koh3 that if the oriented growth mechanism operated the recrystallization texture developed from a deformation texture containing both (111)[112] and (001)[110] components should be strongly centered around (113)[332], because (113)[332] is approximately midway between the (111)[112] and (001)[110], and is related to both of these two orientations by [110] rotations of 25 to 30 deg. Hence, nuclei of (113)[332] orientation should have a high rate of growth in the deformed matrix. However, their results were not in accord with this prediction. It was felt by the writers that a detailed study was needed to clarify the effect of deformation-texture components on annealing-texture formation. For this reason, the present investigation was conducted. EXPERIMENTAL PROCEDURE Specimens used for the present investigation were taken from the crystals rolled previously for deformation-texture studies.' In order to follow the progress of annealing-texture formation during the course of recrystallization, a single specimen was taken from each rolled crystal and its textural changes examined after successive anneals until recrystallization was complete. The specimen was carefully cut from the rolled strip with a jeweler's saw. Prior to annealing, the sawed edges were etched to remove distorted metal, while both faces of the specimen were protected from the etching solution by acid-proof plastic tape. After annealing, the specimen was etched from the "bottom" face only (the reference or "top" face of the specimen was protected by plastic tape) to one half of its original thickness, so that the texture at the surface and at the central section of the strip could be determined by the reflection technique. The

Jan 1, 1965

By I. R. Kramer

The stress associated with the high-dislocation layer at the surface of deformed aluminum crystals was measured by progressively polishing the specimen and determining the change in the initial flow stress when the specimen was reloaded. This surface stress increased linearly with strain in the Stage II and Stage III region. The depth to which the high-dislocation layer extends was found to be 0.0025 in. The influence of the surface layer on Stage I is discussed and it is shown that Stage I ends when, on the secondary slip system, the difference between the applied stress and the opposing stress due to the surface layer is equal to the critical resolved shear stress. In previous papers'-3 it was shown that the surface exerts a pronounced effect on the plastic-flow characteristics of metals. For fcc metals it was possible to increase the extent and decrease the slope of Stages I and II and decrease the work-hardening coefficient of Stage II by removing the surface of the specimen continuously during the deformation process.2,3 More recently,L it was shown that the activation energy for plastic deformation and the activated volume were also influenced by the surface. These changes were related to the existence of a high concentration of dislocations in the region near the surface of the deformed specimen and it was concluded' that the effective stress, T, acting on a dislocation was T = Ta-Ti-Ts [1] where 7, is the applied shear stress, Tj is the internal stress, and TS is the stress associated with the surface region containing the high concentration of dislocations. From Eq. [I] it is seen that the effective stress, 7, acting on a dislocation is a function of 7,. Therefore 7, becomes important in any description of the work-hardened state. In this paper the value of 7, as a function of strain and its variation with depth are reported for aluminum single crystals. In particular, it will be shown that the end of Stage I occurs when the net stress, 7, on the secondary slip system is equal to the critical resolved shear stress. To measure Ts, single crystals of aluminum were deformed in tension to various strains, whereupon the load was removed and a known amount of metal was removed by electrolytic polishing. The differ- ence between the final flow stress before the specimen was unloaded and the initial flow stress upon reloading is designated as ?Tp and is the decrease in the stress due to the removal of the surface layer in whole or in part. The value for Tp is taken equal to -Ts. EXPERIMENT PROCEDURE The details of the tensile apparatus, method of electrolytic polishing, and crystal preparation were the same as those used previously,1"3 The single crystals were 1/8 by 1/8 in. in cross section with a 3-in. gage length. The initial purity of the aluminum was 99.997 pet. The specimens were held in vacuo at temperatures 50°C below their melting points for 16 hr and furnace-cooled. Just prior to the application of the tensile stress the specimens were electrolytically polished to remove 0.004 in. from the thickness. This latter operation was conducted after the specimen was placed in the tensile apparatus. The tensile tests were conducted at a strain rate, i, of 10"5 sec-' and a temperature of 3°C. The aluminum crystals used for the determination of 7, are designated A1-3-12 and A1-116. The orientation of the various crystals used throughout the investigation is shown in Fig. 1. The ?Tp values for specimens A1-3-12 as a function of Ax were determined mainly at four strain levels, i.e., ? = 0.0217, 0.0381, 0.0593, and 0.075, where Ax is one half of the total reduction of the thickness after polishing and ? is the re-

Jan 1, 1965

By E. P. Miesch, P. B. Crawford

A study was made of the effect of permeable and impermeable lenses in a reservoir on the production capacity of a well. Both steady-state and unsteady-state data were obtained. An electrical resistivity model was used to obtain the steady-state data and thermal models. were constructed to obtain the unsteady-state data. The productivity of a well is affected very greatly only when the lenses are close to the well. The effect of circular lenses on the productivity ratio can be correlated with the distance from the center of the lens to the center of the well divided by the radius of the lens. When this dimensionless distance is equal to six or greater, the effect of the lenses on production capacity will be negligible. The pseudo steady-state productivity of a heterogeneous reservoir can be predicted using steady-state data. INTRODUCTION Many analytical solutions of reservoir behavior assume that reservoir rock is uniform and homogeneous. Although this assumption is used, all of the data from core analyses and well logging indicate that the reservoirs are heterogeneous. Very little work has been done on the performance of heterogeneous reservoirs. The work of Landrum,l et al. showed that transient phenomena in oil reservoirs could be studied with thermal models. Pickering and Cotman2 used thermal models to study flow in stratified reservoirs and investigated the effect of inhomo-geneities in oil reservoirs on transient flow performance. Loucks3 made a mathematical study of the pressure build-up in a system composed of two concentric regions of different permeability. Root, Silberberg and Pirson4 studied the effect of the growth of the flooded region on water influx predictions using a thermal model consisting of three concentric cylindrical regions of different thermal properties which simulated the aquifer, the flooded region and the unflooded portion of the original hydrocarbon region. Tomme, et a1.5 made a mathematical study of vertical fractures. The object of this investigation was to study the effect of highly permeable and impermeable lenses in the vicinity of the wellbore on the pressure depletion history of the well. Steady-state data were obtained for both conductive and nonconductive lenses that completely penetrated the formation. The lenses were symmetrically located at various distances from the wellbore. The unsteady-state data were obtained on seven thermal models. EXPERIMENTAL EQUIPMENT AND PROCEDURE STEADY-STATE DATA The steady-state data were obtained from an electrical resistivity model 30 in. in diameter and approximately 11/2 in. deep. The outside of the model was lined with a 30-in. diameter copper strip, which served as the outer boundary of the reservoir. The bottom was covered with a sheet of plexiglass so that it would be nonconductive. The model was filled with a slightly saline solution. The well size was varied from an 0.064-in. diameter copper wire to a 10-in. diameter copper cylinder. Readings were taken with an impedance bridge using AC current to prevent polarization at the contacts. Copper and wax lenses were used to represent infinitely conductive and nonconductive lenses, respectively. The resistance was first measured for each well diameter with no lenses in the reservoir. Then the conductive and nonconductive lenses were spaced symmetrically at various distances from the well and the resistance read from each lens location. The diameters of the conductive lenses were 3, 1.022 and 0.624 in., and those of the nonconductive lenses were 3, 2.25 and 1.563 in. The ratio of each resistance reading to the resistance reading with no lenses in the reservoir

Jan 1, 1965

By T. S. Lundy, R. E. Pawel, F. R. Winslow, C. J. McHargue

The volume-diffusion coefficients of Nb-95 and Ta-182 in niobium have been measured over the temperature range 878° to 2400°C. High-temperature specimens (T 21500°C) were sectioned by conventional lathe and grinding techniques while low-temperature specimens were sectioned by an anodizing and stripping technique previously described. Over a range of more than ten orders of magnitude in diffusivity, the self-diffusion data is well-represented by the equation: D = (1.1+ 0.2) exp [- (96,000 * 900)/RT ] cm2/sec Upward deviations from this line are explained by short-circuit diffusion in combination with the loss of resolution of the sectioning techniques. Oxygen contamination within the range 100 to 450 ppm was found to have little or no effect on the self-diffusivitj 01 niobium. In a limited number of measurements, the diffusivity of Ta-182 in niobium was found to be about half that of Nb-95 in niobium. These data may be described by D = (I.0+0.90.5)exp [- (99,300 * 2400) /RT ] PREVIOUSLY reported studies of self-diffusion in niobium were by Resnick and Castleman1 and Peart, Graham, and Tomlin.2 The data of Resnick and Castleman over a temperature range 1585" to 2120°C show considerable scatter but. can be represented by D = (12.4 *0.8) exp [-(105,000+3OOO)/RT] cm2/sec The limited data of Peart, Graham, and Tomlin follow the equation D = 1.3 exp (-95,00O/RT) cm2/sec In view of recent diffusion data for ß zirconium3 and 0 titanium4 in which Arrhenius-type plots do not yield straight lines and of the potential high- temperature uses of niobium and its alloys, we thought it important to investigate the diffusion behavior of this bcc refractory metal over a large temperature range. This has recently been done for molybdenum,5 chromium,6 vanadium,"" and tantalum.9 Niobium was a particularly suitable material for this study largely because of the development of an anodizing and stripping sectioning technique which enables diffusivities as small as l0-19' sq cm per sec to be determined accurately.10 In addition to self-diffusion data, data were obtained for the diffusion of Ta-182 in niobium and for the effect of varying oxygen content on self-diffusion. I) EXPERIMENTAL PROCEDURE Materials. The niobium was obtained from three sources: 1) melting stock from Shieldalloy Corp., 2) electron-beam melted single crystals, 1/2 in. diameter, from Semi-Elements, Inc., and 3) oxygen-doped, electron-beam melted single crystals from Materials Research Corp. The melting stock was electron-beam melted and specimens 5/8 in. diameter by 1/2 in. long were machined from the center of the bar. The analysis supplied by the vendor and an interstitial analysis of one of the specimens are given in Table I. The single crystals (type 2 above) were cut with a jeweler's saw to specimens about 3/8 in. long. The interstitial analysis of this material is given in Table 11. This material was used

Jan 1, 1965

By Yoshinao Nakada

In many experiments involving electropolishing such as electropolishing during deformation and electrothinning of deformed metals for electron microscopy, it is usually assumed that the specimen temperature is the same as the temperature of the polishing bath. In order to test this assumption, the interior temperature of aluminum single and polycrystals was measured while they were being electropolished. Specimens were 1/4 by 1/4 by 6 in. and were of 99.99 pct purity. A small hole 1 in. deep was drilled axially at one end of the specimen so that a copper-constantan thermocouple could be inserted. The electropolishing solution was 4 parts methanol (reagent grade) and 1 part perchloric acid (70 pct). The electropolishing was performed using an apparatus shown in Fig. 1. The electropolishing solution was stirred by a motor-driven stirrer and was cooled to —5°C with a mixture of methanol and dry ice. Electrolyte temperature was measured and remained at -5°C during the electropolishing. Current density of 0.3 amp per sq. cm was used. When the current was turned on, after about a 5-sec delay, the temperature began to rise rapidly until it reached 65°C. In order to determine whether the temperature measured was localized, the thermal expansion of the specimen was meas-

Jan 1, 1965

By N. Albon, J. F. Miller, R. W. Coutant

The deposition of nickel from nickel carbonyl onto amorphous substrates has been studied, with attention being paid to the specific effects of the physical and chemical nature of the substrate and to the effect of oxygen on the crystal morphology. With substrates having microscratches or etch lines, nu-cleation was observed to occur preferentially at these surface features. Flame polishing of the substrate surfaces was found to remove any regularity in preferred nucleation sites. Nucleation was observed to occur less readily on substrates having relatively low surface energies, e.g., Teflon and carbon, than on materials having relatively high surface energies such as fused silica. At low oxygen concentrations [Ni(CO)4/O2 > 54 x 1031, apparently pure and well-formed nickel crystals were observed to nucleate and grow irrespective of the presence of oxygen. At higher concentrations of oxygen, a secondary growth process, dependent upon oxygen concentration and resulting in a gradual change in crystal morphology, was observed. It is concluded that the influence of oxygen on the nucleation and growth of nickel is determined by the relative kinetics of the various possible reactions, and that under the experimental conditions employed the 0-Ni interaction occurs at some nucleation or prenuclea-tion stage. THE purpose of the research on crystal nucleation in chemical vapor deposition as described in this paper has been twofold: 1) to examine some effects arising from the use of amorphous substrates, and 2) to study the specific effects of oxygen on the nucleation and growth of nickel in a nickel carbonyl-carbon monoxide system. The nickel-nickel carbonyl system was chosen for study for several reasons: 1) nickel films are of potential interest in electronic technology, and 2) the deposition can be carried out at moderate temperatures, thus making possible detailed study of the processes occurring and the use of a variety of substrate materials (including some which melt at relatively low temperatures). Fairly well-characterized chemical kinetics and a broad background of information are available on the py-rolysis reactions and on the mechanisms of Ni-O interactions. NUCLEATION AND GROWTH THEORY The theoretical background for the analysis of nucleation and growth by vapor deposition for a one-component system (physical vapor deposition) and the problems encountered therein have been reviewed by Hirth and pound.' More recently Mande12 has indicated the difficulties of applying such theory to chemical systems. One of the major problems involved is the possible multiplicity of chemical reactions and deposition routes. For example, those reactions which are probably of significance in a discussion of the pyrolytic deposition of nickel from nickel carbonyl under the conditions of the present experimental work are illustrated in Fig. 1. As is true with most cases of chemical deposition, many of the quantitative data necessary for a complete analysis of the system are either not available or not directly measurable. However, with the present system, sufficient data are available for a discussion of nucleation and growth on a qualitative basis. Classically, the rate of nucleation of a monatomic species being deposited from a vapor phase is given by

Jan 1, 1965

By N. J. Grant, B. C. Giessen, Paul Predecki

ALLOYS of gold, silver, and aluminum with elements of the groups BII, BIII, BIV, and BV were prepared by a rapid quenching technique (splat) and were examined by X-ray diffraction. Five new intermediate phases were found and will be described briefly herein. For the gold and silver systems, the concentration ranges having an electron/atom ratio e/a of 1.4 to 1.5 ("3/2 Hume-Rothery phases") were studied primarily. Master alloys were prepared from high-purity metals (99.9+ pct or better) by melting either in evacuated fused silica capsules or by nonconsum-able-electrode arc melting in an argon atmosphere. Small pieces, 20 to 50 mg, of each alloy were blast-atomized to form a splat, by a technique similar to that described by Duwez and Willens.1 The technique used for this study is described in detail in Ref. 2; it utilizes a resistance-heated graphite crucible with a small hole at the bottom, directed toward a metal substrate or quenching plate. The prepared alloy rests over the fine hole, through which it is expelled by an explosion shock wave in the form of fine droplets (1 to 50 µ) of molten metal onto a copper or silver substrate, which is maintained at about -190°C. The resulting very high cooling rates (see Ref. 2 for quantitative measurements) can prevent the process of nuclea-tion and growth in many instances, resulting in the formation of metastable phases. The splat particles were transferred to a GE-XRD5 diffractometer and maintained at -190°C, where they were examined with CuKa radiation. The samples were then allowed to warm to room temperature or were heated to higher temperatures until the equilibrium structures formed. Of fifteen alloy systems considered, nonequi-librium structures were encountered in six; these are described below and summarized in Table I. In the system Au-Sb a metastable £ phase (A3 type, hcp, a = 2.898 + 0.002A; c = 4.731 * 0.004A; c/a = 1.633) was found in the concentration range Au + 13 to 15 at. pct Sb. This phase is isomorphous with the stable phases in the systems Au-Cd, Au-In, and Au-Sn, all at an average e/a ratio of 1.4 to 1.5. The concentration range of one-phase metastable was deduced from the small amounts of supersaturated gold solid-solution phase present in the splat product. It was found that ? could also be retained by splatting onto a substrate held at room temperature: however, decomposed into the equilibrium phases Au + AuSb2 after heating to 200°C for 1/2 hr, or on holding the powdered splatted alloy at 20°C for several months. Calorimetric measurements will be made in an attempt to decide the question whether ? is metastable at all temperatures or whether it is a stable phase at low temperatures. There is evidence that another phase, possibly also close-packed but with a different stacking sequence, can be obtained by rapid quenching of alloys with a different antimony content. Klement, Willens, and Duwez3 reported the existence of an amorphous phase on quenching Au-Si alloys (25 at. pct Si) to - 196°C. They found that on heating to room temperature another phase of unknown crystal structure was formed. This was confirmed (see Table I); however, the new crystalline phase, designated as ?, could also be formed simply by rapid quenching to room temperature, and even was found to exist already in the as-cast Au + 20 at. pct Si alloy. It was found that ? decomposed into Au + Si on the specimen surface at room temperature. This behavior, and the question whether or not there is an equilibrium-temperature region for ?, have not yet been resolved. It is probable that ? (Au + 20 to 21 at. pct Si) is cubic of the -brass type (D81-3) with a = 9.60, + 0.01A and N = 52 atoms per cell [compare 6 (CU-Sn)4]. Except for two very weak lines, the powder pattern of about thirty lines could be indexed on this basis; however, a determination of the atom positions has not yet been attempted. For Au-Ge the C phase was observed at about 21 at. pct Ge as reported by Luo et at.5 Lattice parameters a = 2.876A, c = 4.73,A, c/a = 1.64 were found. In the Au-Pb system, formation of a ? phase was not observed, but in the lead-rich region at 75 at. pct Pb, broad peaks belonging to an amorphous phase were found. The maximum diffracted intensity occurred at 28 = 32.4 deg which is about 1 deg larger than the position of the (111) line of lead (Cuka). For Ag-Pb, an amorphous phase analogous to the one found in the Au-Pb system was observed; this metastable phase exists probably at about 75 at. pct Pb. Since no lead-rich alloys were tested, all alloys consisted of silver + amorphous phase at -190°C. In A1-Ge alloys, line-rich and complex powder patterns were obtained at about 30 at. pct Ge; they bear similarities to those of aluminum and germanium, but are of lower symmetry; the existence of more than one intermediate phase is possible. The authors are grateful to the Kennecott Copper Corp. for Fellowship support, and ARPA (Contract

Jan 1, 1965

Jan 1, 1965

By D. C. Shelton, C. S. Ek

Corneille S. Ek (Assistant Professor in Ore Dressing, University of Liege, Liege, Belgium) — This is a very valuable paper, in that it shows how it is possible to take care of a multitude of laboratory routine tests, and derive from them successful modifications of flowsheets or of operating methods. The author and the Company appear to be test-minded and this is best seen through the case histories described. There are however some corrections to be made, and questions arise when one studies the paper. If all the equations are to be homogenous, one obviously has to write Eq. 4 On the other hand, it is difficult to accept the definition put on Eq. 7, for that equation, which represents the factor of transformation from tpd of solids to cu ft per min of pulp in Eq. 6, has nothing to do with conditioning. It is evidently assumed here that conditioning means, as Gaudin calls it,' modulation of collection. One would prefer, for Eq. 7, the appel-ation "pulp conversion factor". Eq. 8 and 9, giving the amount of reagent to be fed

Jan 1, 1965

Jan 1, 1965

By T. P. Papazoglou, N. A. D. Parlee, W. C. Phelps

HE high vapor pressures of metals such as lead, calcium, lithium, bismuth, and magnesium at steel-making temperatures present experimental problems which have thus far rendered it almost impossible to obtain really reliable data for their solubilities in liquid iron. Many investigators have attempted to equilibrate liquid iron in the same crucible with the undissolved liquid phase of such volatile metals. The published results,l-6 although useful, are often questionable on the grounds of not being obtained under true equilibrium conditions. Such information is not always of practical value in any case since the equilibrium vapor pressure is often several atmospheres and steel is not currently made at these pressures. Solubility measurements at lower partial pressures (< 1 atm) appeared to be more practical and easier to make. These data could be used to calculate solubilities at other pressures where Henry&apos;s Law is obeyed, and to estimate solubilities under other conditions of temperature and pressure with useful accuracy. This note outlines the development of a general technique for the measurement of solubilities in systems of this kind. The method involves equilibration of the high-boiling metal at known temperatures with the vapors of a low-boiling metal at known partial pressures. Analyses of quenched samples provide vapor pressure-solubility data and make calculations of alloy thermodynamics possible. The principle involved is similar to the closed-system diffusion-transport method which is difficult to apply with most high-melting liquid metals like iron, due to closure problems. A two-zone horizontal (molybdenum wire element) tube furnace, Fig. 1, provides two constant-temperature zones in a reaction tuve (3/4 in. ID by 1 in. OD by 36 in.). A high-boiling metal sample, 9, introduced in the higher-temperature zone, is maintained at temperature T1, and a volatile metal sample, 7, in the lower-temperature zone, is held at T2. A stream of argon with 10 pct hydrogen is passed via flowmeters, 1, and mixing-drying towers, 2 and 3. through the reaction tube at a favorable flowrate and acts as a carrier gas which entrains vapor from the volatile liquid metal at a specific constant partial pressure. The gas mixture passes through a system of constrictions, 6 and 8, to the higher-temperature zone, establishes intimate contact with the high-boiling liquid sample, 9, and exits through a small condenser tube. The entire system is at (nearly) atmospheric pressure and the volume of carrier gas passed is measured with a wet gas meter. When the high-boiling sample attains equilibrium with the vapor phase, both samples are removed and quenched. Analysis of the high-boiling sample for solute content reveals its solubility for the low-boiling metal at a vapor pressure calculated from carrier-gas volume and either a) weight loss of volatile metal or 6) weight gain of high-boiling sample plus condenser (which collects the undissolved vapors). To test the capabilities of the method, liquid silver at 1403&apos;C was equilibrated with lead vapor at various partial pressures. The relatively simple Pb-Ag system was particularly suitable for uncovering experimental problems and providing the first step toward investigations with more volatile metals and more difficult combinations.

Jan 1, 1965

By G. Rowan, M. W. Clegg

Approximate analytical solutions for non-Darcy radial gas flow are derived for bounded and infinite reservoirs producing at either constant rate or constant pressure. These analytical solutions are compared with published results for non-Darcy flow obtained on digital and analogue computers, and the agreement is show to be very good. Some observations on the interpretation of gas well tests are made. INTRODUCTION The flow of gases in porous media is a problem that has been the subject of much study in recent years [l - 71 , and many methods have been proposed for solving the non-linear equations associated with it. The assumption that the flow satisfies Darcy&apos;s Law It has been observed, however, that the linear relationship between the flow rate and pressure gradient is only approximately valid even at low flow rates, and that as the flow rate increases the deviations from linearity also increase. It has been suggested by a number of authors that Darcy&apos;s Law should be replaced by a quadratic flow law of the form This form of equation was first suggested by Forchheimer [9] and, later, Katz and Cornell [10], and Irmay [lll, developed a similar equation. Houpeurt [12] derived this form of equation using the concept of an idealised pore system in which each channel consists of sequences of truncated cones giving rise to successive restrictive orifices along the channel. This type of representation leads to a quadratic flow law of type [4], for all fluids, but it is found that the quadratic term is only significant in the case of gas flow. The methods of Houpeurt for solving gas flow problems will be discussed further in another section of this paper. Solutions of the non-linear equation for Darcy gas flow 121 may be classified as either computer (digital and analogue), or approximate analytical ones. The former include the well-known solutions of Bruce et al. [13], and Aronofsky and Jenkins [14] , but the latter solutions, apart from the simple linearisation of equation (2) to yield a diffusion equation in p2 , are not so well-known. Amongst these approximate analytical solutions should be mentioned the work of Barenblatt [IS], who has applied the techniques of dimensional analysis to obtain similarity solution to a large class of non-linear equations; also, a number of Russian authors, including Barenblatt [16] , Kim [17] and others, who have used the method of moments for obtain-

Jan 1, 1965

By E. L. Dougherty, J. W. Sheldon

Using the numerical techniques shown in this paper it is possible to compute the simultaneous dynamical behavior of multiple fluid-fluid interfaces in two dimensions. Hence, fluid-fluid inter face models of several oil recovery processes can be constructed which allow prediction of the effect of fluid flow in two dimensions on the behavior of these processes while taking into account various physical effects, such as saturation gradients, phase changes and thermal stimulation. Techniques for constructing fluid-fluid interface approximations for several oil recovery processes are reuiewed. The validity of these techniques is established by comparison to experimental results. The availability of a computer program for computing the behavior of multiple fluid-fluid interface problems makes the use of potentiometric models uneconomic. The results indicate the areal sweep efficiencies obtained from potentiometric model studies at high mobility ratios may be somewhat optimistic. The results also indicate that the areal sweep efficiency curves obtained at high viscosity ratios 2—4 using miscible fluids in porous media are misleading and that considerable care must be taken in defining the mobility ratio for a displacement process, especially for miscible fluids. INTRODUCTION Many of the methods used to estimate areal sweep efficiency assume that the oil recovery process can be represented by one or more fluid-fluid interfaces. When the mobilities of the displaced and displacing phases are assumed equal, this quantity can be computed using analytical mathematical methods.l.2 For non-unit mobility ratio, experimental methods based upon the fluid-fluid interface concept include potentiometric and electrolytic blotter models. Scaled models of porous media have also been used to study this problem. Fay and Prats3 and Aronofsky4 used numerical techniques to compute breakthrough sweep efficiency, but neither of these studies were extended beyond breakthrough. Numerical techniques which have been developed for solving a general fluid-fluid interface problem are presented in a companion paper.5 These techniques have been incorporated into a program for a large-scale digital computer which can treat simultaneously the dynamical behavior of as many as six fluid-fluid interfaces. Thus it is possible to simulate the behavior of several oil recovery processes taking into account such effects as saturation gradients. Techniques for representing several oil recovery processes by fluid-fluid interfaces are presented. Processes considered are conventional water flooding with and without a mobile gas phase, hot water flooding, miscible flooding and enriched gas drive. Other processes, whose effects could be studied by this technique, but are not considered in detail here, are underground combustion and steam injection processes and various slug processes such as gas-water injection and alcohol-solvent processes. Theoretical results obtained with single interfaces for mobility ratios of 0.25, 1, 2, 4, 8, 16, 32 and 64 in a repeated five-spot are compared to experimental results for this geometrical configuration obtained using miscible fluids and conductive analogs. Predicted recovery curves for water flooding in a repeated five-spot are compared to experimental results reported in the literature. Example calculations are shown for a conventional water flood in the presence of a free gas phase and for a hot-water flood. MATHEMATICAL PRELIMINARIES We assume that the rock matrix is homogeneous with constant thickness, absolute permeability and porosity. The fluids are incompressible. We also neglect the effects of gravity.

Jan 1, 1965

By J. P. Neumann, L. Raymond

At temperatures near 1000°C, only the (112) (111) slip systems are operatire in tungsten. Therefore, the substructure introduced into the billet upon rleforming a single crystal by rolling at 1000 "C can be controlled by proper selection 01. processing ral&apos;iubles. Using a reduction of 10 pct pel- pass, the (001)[110] and the (110)[001] crystals will deform by duplex slip rip to a 50 pet reduction in thickuess. These rolled single-crystal sheels are characlerized by anisotropic hardening, retention of ductility with warm working, lattice bending which is related to the conlacl (angle, and macroscopic dimensional changecs in the length bid not the width of the billet. When several slip systems become operative, a greater degree of work hardening is itztvoducetl into the crystal. This rolling- condition is characlerized by isotropic hardening, loss of ductilily with warm working, complex lattice distortions, and macro-scopic dimensional changes in both the length rind Width of the billel. IN tungsten, the {1 10}(111) slip systems are operative below room temperature,&apos; while above 700°C only the {112{ (111) slip systems are observed.2,3 In the transition region, i.e., room temperature. both systems appear. It is the purpose of this investigation to show that tungsten single crystals deformed by rolling at a temperature where only one slip system is operative generate dislocation substructure which depends on the crystal orientation. For a specific crystal orientation. the resulting dislocation substructure can be further influenced by modifying the rolling procedure. Crystals oriented for multiple slip display less substructural sensi- tivity to modifications in processing techniques than do single crystals oriented for duplex slip. Under simple slip modes of deformation, very little work hardening is introduced into a rolled single-crystal sheet. Mechanical properties such as room-temperature strength. ductility, and hardness are used to confirm the existence of the different work-hardened conditions generated within the crystal by modified warm-rolling techniques. EXPERIMENTAL PROCEDURE Material. Single-crystal billets of four different crystal orientations. grown by the Arc-Verneuil technique. were ground to a size of 0.25 by 0.375 by 3 in. In terms of their rolling plane and rolling direction, the billets had the following orientations: (1101 [001 ] (110) [110] (001) [110] (001) [100] The actual orientation of all crystals was within 5 deg of the ideal orientations. The typical impurity content of the crystals is given in Table I. Polishing and Etching. Polishing was done elec-trolytically in a 20 g per liter aqueous solution of NaOH at approximately 10 v. It was established by the Laue back-reflection X-ray technique that the surface damage due to grinding and cutting operations with a diamond wheel did not exceed 0.001 in. Therefore after each cutting or grinding operation at least 0.002 in. was removed electrolytically from the surface in order to eliminate surface effects. By lowering the voltage to 3 v, subgrain boundaries and individual dislocations are identified in agreement with Berlec 4 where the etch-pit traces on a cubic plane form a square. The etching time was about 5 sec at room temperature. Rolling. Rolling was carried out on a Loma 2-high mill (Model 600). The peripheral velocity of the 6-in.-diameter rolls was 500 in. per min, with the surface temperature of the rolls about 400° to 450° C The billets were heated before each pass for 30 min in argon to 1000 C. Oxidation of the crystals during rolling in air resulted in a thin layer of greenish-yellow WO 3 This oxide was removed after each pass by immersing the crystals for a few minutes in a boiling NaOH solution. Prior to the initial rolling pass, a surface layer of 0.001 in. was removed by polishing. The crystals were then annealed in vacuum (10-4 torr) at 2400 C for 30 min. All crystals were rolled in the same direction; i.e., the same end was always introduced into the rolls. The rolling program was conducted in

Jan 1, 1965

By H. R. Thresh

An oscillational vis cometer has been constructed to measure the viscosity of liquid metals and alloys to 800°C. An enclosed cylindrical interface surrounds the molten sample avoiding the free surface condition found in many previous measurements. Standardization of the apparatus with mercury has verified the use of Roscoe&apos;s formula in the calculation of the viscosity. Operation of the apparatus at higher temperatures was also checked using molten lead. Extensive measurements on five different samples of zinc, of not less than 99.99 pct purity, indicate i) impurities at this level do not influence the viscosity and ii) the apparatus is capable of giving reproducible data. The variation of the viscosity ? with absolute temperature T is adequately expressed by Andrade&apos;s exponential relationship ?V1/3 = AeC/VT , where A and C are constants and V is the specific volume of the liquid. The values of A and C are given as 2.485 x 10-3 and 20.78, 2.444 x 10-3 and 88.79, and 2.169 x 10-3 and 239.8, respectively, for mercury, lead, and zinc. The error of measurement is assessed to be about 1 pct. Prefreezing phenomena in the vicinity of the freezing point of the zinc samples were found to be absent. AS part of an over-all program of research on various phases of melting and casting nonferrous alloys, a systematic study of some physical properties of liquid metals and their alloys was undertaken in the laboratories of the Physical Metallurgy Division.1,2,3 The most recent phase of this work, on zinc and some zinc-base alloys, was carried out in cooperation with the Canadian Zinc and Lead Research Committee and the International Lead-Zinc Research Organization. One of the properties investigated was viscosity and the present paper gives results on pure zinc; the second part, on the viscosity of some zinc alloys, will be reported separately. Experimental interest in the viscosity of liquid metals has virtually been confined to the past 40 years. The capillary technique was already established as the primary method for the viscosity of fluids in the vicinity of room temperature; all relevant experimental corrections were known and an absolute accuracy of 1 to 2 pct was possible. Ap- plication of the capillary method to liquid metals creates a number of exacting requirements to manipulate a smooth flow of highly reactive liquid through a fine-bore tube. Consequently, the degree of precision usually achieved in the high-temperature field rarely compares with measurements on aqueous fluids near room temperature. However, the full potential of the capillary method has yet to be explored using modern experimental techniques. As an alternative, many investigators in this field have preferred to select the oscillational method. Unfortunately, the practical advantages are somewhat offset by the inability of the hydrodynamic theory to realize a rational working formula for the calculation of the viscosity. In attempting to overcome this restriction many investigators have employed calibrational procedures, even to the extent of selecting an arbitrary formula for use with a given shaped interface. However, where calibration cannot be founded on well-established techniques, the contribution of such experiments to the general field of viscometry is questionable. A critical appraisal of the viscosity data existing for pure liquid metals reveals a somewhat discordant situation where considerable effort is still required to establish reproducible and reliable values for the low-melting point metals. The means of rectifying this situation have gradually evolved in recent years. Here, the theory of the oscillational method has undergone major advances for both the spherical and cylindrical interfaces. The basic concepts of verschaffelt4 governing the oscillation of a solid sphere in an infinite liquid have been adequately expressed by Andrade and his coworkers.5,6 Employing a hollow spherical container and a formula, which had been extensively verified by experiments on water, absolute measurements on the liquid alkali metals were obtained. The extension of this approach to the more common liquid metals has been demonstrated by culpin7 and Rothwel18 where much ingenuity was used to surmount the problem of loading the sample into the delicate sphere. Because of the elegant technique required to construct a hollow sphere, the cylindrical interface holds recognition as virtually the ideal shape. On the other hand, loss of symmetry in one plane increases the complexity of deriving a calculation of the viscosity. The contributions of Hopkins and Toye9 and Roscoe10 have markedly improved the potential use of the cylindrical interface in liquid-metal viscometry. The relatively simple experi-

Jan 1, 1965

By R. L. Stegman, M. R. Achter

R. L. Stegman and M. R. Achter (U.S. Naval Research Laboratory)—In a study of the surface structures developed in the fatigue of nickel at low strains as a function of temperature, we have obtained similar results.3 As our apparatus permits fatigue tests to be conducted in vacuo, there was no masking of the surface at high temperatures by oxidation so that the structures there could be observed directly. The relatively few broad slip bands observed at room temperature gave way at 300°C to a large number of uniformly distributed and narrower slip bands. At 550°C deformation began to concentrate around the grain boundaries and progressively increased up to 800°C. In addition fatigue strength was observed initially to increase with increasing temperature up to about 600°C due to the effectively increased ductility caused by the dispersal of fatigue damage. The fatigue strength then decreased at higher temperatures as grain boundary cracking dominates. Maria Ronay, W. H. Reimann, and W. A. Wood (authors&apos; reply)— The authors are pleased to note that R. L. Stegman and M. R. Achter reach similar conclusions from their study of surface slip on nickel. However, they would emphasize that their own conclusions are based on what is shown by study of specimens that have been sectioned and that this study also shows that surface slip is not necessarily representative of what happens below the surface.

Jan 1, 1965

By R. E. Pray, M. C. Fuerstenau, J. D. Miller, B. F. Perinne

Quartz cannot be floated with potassium amyl xanthate as collector at any pH. Complete flotation is achieved with certain minimal additions of amyl xanthate and Pb from pH 5.8 to 8.5 and with amyl xanthate and Zn from pH 7.5 to 8.1. The active species of these metal ions responsible for activation are shown to be PbOH and ZnOH No flotation was effected when Cu and Mg were added as activators. Previous work1,2,3,4,5,6,7 has shown that quartz may be floated in the presence of sulfonate or soap when the following two criteria are met: 1) some portion of the added metal ion has hydro-lyzed to its first hydroxy complex, and 2) a precipitate of the metal-collector has formed. Since sulfonate and soap, two substantially different anionic collectors, conform to these criteria, this phenomenon may well be expected to be of a general nature. In this view then, it would appear that any anionic collector, including xanthates, should also float quartz when these two criteria are met. The object of this paper is to demonstrate the conditions under which quartz will respond to flotation in the presence of potassium amyl xanthate. EXPERIMENTAL MATERIALS AND TECHNIQUES Quartz was prepared by leaching the sized sample (48 x 150 mesh) with HC1 until no iron could be detected in the leach liquor. Conductivity water, made by passing distilled water through an ion exchange column, was used in the investigation. Potassium amyl xanthate was selected as collector. Purification of this reagent was effected with the following method: 1) a laboratory sample of potassium amyl xanthate was dissolved to saturation in hot ethyl alcohol and filtered several times while still hot, 2) the filtrate was cooled, during which time potassium amyl xanthate crystallized out of solution; the xanthate was then separated from the solution by filtration, 3) the amyl xanthate was dissolved in fresh hot ethyl alcohol and filtered, 4) step (2) was repeated, 5) the crystalline potassium amyl xanthate was washed with ethyl ether five times, and 6) the xanthate was dried for 24 hours under continuous vacuum. Inorganic impurities are insoluble in hot ethyl alcohol whereas dixanthogen is soluble in ethyl ether. Five-gram charges of 48x150 mesh quartz were conditioned for 3 min in 125 cc of solution containing the reagents and were floated with the small-scale cell and procedure described in previous papers.478 Reagent grade HCl and NaOH were used for pH adjustment, while reagent n-amyl alcohol was added as frother. Frother addition is necessary with this technique, but it should be mentioned that data, similar to those shown in Fig. 2 for 1 x10-4 mole per liter Pb++ and 1 X 10-4 mole per liter AX-, were also obtained with a Hallimond cell in the absence of frother. EXPERIMENTAL RESULTS Clean quartz could not be floated with amyl xanthate at any pH. Flotation was achieved under certain conditions, however, when various metal ions were added to the system. The activating ions used were lead, zinc, copper and magnesium, added as reagent grade chloride salts. Lead as Activator: The effect of Pb++ as activator was examined at five different additions of amyl xanthate (Fig. 1, 2 and 3). When 1x 10-5 mole per liter xanthate was added in the presence of 1 x 10"4 mole per liter Pb ++, no flotation was obtained at pH 6.5 or below, while a recovery of about 60% was effected at pH 7. When the pH was increased to 7.8, no flotation was again obtained, Complete depression was noted from pH 7.8 to about 10, at which point a recovery of about 30% was achieved. At about pH 11, the precipitate of lead amyl xanthate which was present below this pH dissolved and complete depression occurred. When 2.5x 10-5 mole per liter xanthate was added with the same lead addition, no flotation was obtained at pH 5.8 and below, whereas a recovery of

Jan 1, 1965

By W. F. Hosford

A series of aluminum single crystals was subjected to axially symmetric flow by drawing through dies. The orientation dependence of the drawing stress, which indicates the resistance to this type of flow, compares reasonably with predictions of Taylor and of Bishop and Hill. Measured lattice rotations likewise are generally consistent with theory. The most successful analyses of the plastic behavior of polycrystalline metal and its relationship to single crystal behavior are those of Taylor1-3 and of Bishop and Hill.4-6 The purpose of this paper is to provide a critical test of some of the basic assumptions involved in these theories. Both treatments apply to fcc metals and assume the shape change of each grain in a polycrystal to be the same as that of the polycrystal as a whole. Thus for a randomly oriented polycrystal extended under uni-axial tension each grain is assumed to undergo axially symmetric flow. dey = dez = -1/2dex, deyZ = dezx = dexy = 0 [l] where x, y, and z are a set of orthogonal axes, x being the tensile axis. Although [011.] oriented grains in bcc and fcc metals may depart markedly from this ideal behavior,7,8 the assumption is probably quite reasonable for most grains. Under a uniaxial tensile stress, ox, the work dW per unit volume expended in producing an increment of axial strain dex is, dW=oxdex [21 Since this work is expended in slip, dw =STi dyi 131 where Ti and yi are the shear stress and shear strain on the active slip systems. In both analyses Ti is taken to be the same on all slip systems, and dependent only on the total prior shear strain on all systems, so dw = Tdy [41 where t is the shear stress required for slip and y is the sum of the shear strain yi on all slip systems. Combining 121 and [4] and defining M = oX/T The ratio M is a generalized Schmid factor. It relates the tensile stress required for axially symmetric flow, ox, to the basic shear stress, 7, and it also expresses the ratio of crystallographic strain, y, to the tensile strain, Ex It depends only on the orientation of the crystal. Taylor evaluated M for various orientations by finding the least value of dy/dEx which could satisfy the shape change. Bishop and Hill, on the other hand, found M by considering the relative work (1/T)dW/dEx expended by stress states which could activate enough slip systems to produce the shape changes. The results of both methods appear to be equivalent, although certain omissions were made in Taylor&apos;s original work. The orientation dependence of M, calculated by the second method,9 is shown in Fig. 1. Taylor used the average 2= 3.06 for all possible orientations to predict the tensile stress-strain curve (oxvs Ex) for a random polycrystal from the shear stress-strain curve (t vs y) of a single crystal. Changes in M from lattice rotation were neglected so points on the ox vs ex curve were simply taken at ox = 3.06t and e = y/3.06 from corresponding points on the t vs y curve. Recent extension of the analyses of Taylor and of Bishop and Hill to crystallographically textured metals has been used to relate plastic anisotropy to textures, and to predict the potential texture hardening that could result from texture control.9 Unfortunately there have been relatively few experimental tests of the underlying theory. Taylor found that the tensile stress-strain curve of polycrystalline aluminum did agree reasonably well with that predicted from a single-crystal T-y curve. Had the single crystal undergone easy glide, how-

Jan 1, 1965

By B. A. Wilcox, A. H. Clauer

DURING the course of an investigation on the high-temperature creep behavior of TD Nickel* (Ni + 2) vol pct ThO2), it was observed that the creep fractures were similar in appearance to low-temperature ductile fibrous fractures and creep ruptures by cavitation. Microfractographs of fibrous ruptures are typically characterized by a dimpled appearance, with second-phase particles frequently found near the bottom of the dimples.&apos;-4 These somewhat resemble creep ruptures by cavitation, in that fracture occurs by void formation, with the subsequent growth and final merging of the voids to form a complete fracture.&apos; It is the purpose of this communication to describe the creep fracture of TD nickel and suggest a mechanism for the rupturing process. The discussion is relevant to material crept to fracture in vacuo at a constant stress of 18,000 psi, over the temperature range 900" to ll00°C. The material used in this investigation was 1/2-in.-diam bar stock supplied by Du Pont, contain- ing 2.3 vol pct Tho2. The final fabrication treatment consisted of -95 pct reduction by swaging followed by a 1-hr anneal at 1000°C. Transmission and replica electron microscopy revealed that the material had a fibered structure with a transverse grain size of -1 µ and a longitudinal grain size of 10 to 15 µ. Selected-area diffraction indicated that the fiber axis was parallel to (00l), in agreement with the results of Inman et a1.6 The thoria particle size varied from 80 to 1000Å, with an average size of 400Å, and the mean particle spacing was about 1200Å. The remarkable structural stability7 was confirmed by annealing for 6 hr at 1300°C (about &apos; 0.9 the absolute melting point). Transmission electron microscopy revealed that the only structural change was a slight decrease in dislocation density. Furthermore, recrystallization or grain growth during creep has not been observed. All specimens were annealed in vacuo at 1300°C for 3 hr prior to creep testing. The following times to rupture were obtained for vacuum creep tests at a constant stress of 18,000 psi: 900°C, 854 hr; 930°C,

Jan 1, 1965

By R. W. Lai, I. Iwasaki

Some physical as well as chemical aspects of the methods of dispersion of various corn starches and their derivatives are investigated and their effects as depressants in anionic silica flotation of iron ores ascertained. The adsorption behavior of starches on hematite and quartz is strongly affected by their molecular sizes as inferred from viscosity measurements. The implication of this behavior on flotation and flocculation is discussed. Mechanical treatment of causticized starch solutions is shown to reduce the starch requirements in flotation appreciably. Starches and starch products have been used as depressants for iron oxides both in amine flotation of siliceous gangue and in soap flotation of activated silica from iron ores. Cooke and his associates1,2,3,4 extensively studied the effects of certain starches and their derivatives in the amine flotation of iron ores at near-neutral pH and found that although most starches were good flocculants for hematite and de- pressed that mineral more or less selectively1,3 they did not flocculate quartz suspensions. Further, that replacement of active groups in corn starch modified its behavior as a flocculant for hematite or quartz suspensions1 and as an iron oxide depressant. Schulz and cooke2 showed that many starches and their derivatives, except aminoethyl starch, were abstracted more effectively by Brazilian hematite than by quartz and that the adsorption of a starch product was strongly dependent on pH and on the presence of calcium ion. In soap flotation of calcium-activated quartz, certain starches and their products have been used to depress iron oxides.5&apos;6 The behavior of these substances in flotation appears at times to be at variance with those previously reported and especially with results obtained in the Mines Experiment Station laboratories. This is attributed, at least in part, to differences in flotation procedure and flowsheets and in the method of preparing the depressant. Most of the investigators referred to above, solubilized the starch products by autoclaving at 120°C. Others have used acid,7 alkali8 or oxidizing agents.9 In view of the limited knowledge of the depressing action of starches and their derivatives in iron ore flotation, particularly in soap flotation of calcium-activated silica at high alkalinity, an extensive study

Jan 1, 1965