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By E. F. Johnson, F. H. Brinkman, H. J. Welge, S. P. Ewing

This paper presents a method for predicting the manrler in which oil will be displaced from a porous body by enriched gas. The calculations apply to a gas rich enough to give a partially, but not a completely, misci-ble displacement. The method — a three-component, two-phase analysis — takes into account condensation of some of the intermediate hydrocarbons from the injected gas into the oil, as well as enhanced volatility of heavier hydrocarbons at elevated pressures and temperatures. The condensation swells the oil and decreases its viscosity, thus aiding in its recovery. The calculations have been extended to apply to actual crude oil-natural gas systems by arranging the components into three groups according to their volatility. As an approximation, each group is then treated as a single component in the analysis. The influence of an angle of dip for an inclined displacement is also taken into account. The recovery predictions are corroborated by experiments which used both consolidated sand cores and un-consolidated glass beads. In some of these tests, actual live crude oil was displaced by a multicomponent gas typical of enriched gases used in oil fields. INTRODUCTION This paper presents a method for predicting the amount of oil that can be displaced from a homogeneous, linear, porous body at various stages during the injection of enriched, or "wet", gas. The porous body can be in either a horizontal or an inclined position. 'This type of displacement is sometimes known as condensing gas drive The method is developed especially for the case in which the injected gas is enriched enough to be partially, but not completely, miscible with the reservoir oil. The need for a calcula-tive procedure for this type of operation is emphasized by the number of field projects where completely miscible drives are not practical, but where near-miscible conditions are feasible. The factors taken into account in the predictive calculations include: (1) the condensation of gas components into the oil, with a resulting increase in oil volume; (2) the lowering of oil viscosity by the addition of lighter ends from the gas; (3) the increase in oil volatility at high temperatures and pressures; and (4) the physical displacement of the oil by the gas. The techniques developed in the paper can be extended to other nonequilibrium displacement processes. Other such processes that we have analyzed include a displacement by lean gas which stripped intermediates from the oil, and a water flood in which the water con. tained in solution a substance somewhat soluble in the oil. ANALYSIS OF ENRICHED-GAS DRIVE GENERAL PRINCIPLES Our method for predicting the amount of oil that can be displaced by an enriched gas uses an analogy between a three-component and a multicomponent system.' The predictive method is based on these assumptions: (1) constant, or nearly constant, pressure; (2) complete equilibrium by diffusion perpendicular to the main direction of flow, but no significant mixing along the direction of flow; (3) constant injection velocity; and (4) flow in a linear porous body. The composition of a liquid or a vapor with respect to three components can be plotted on a three-component, or ternary, diagram like that in Fig. 1. Let Point A represent the composition of the oil originally in place. In this case, Oil A is undersaturated with gas. If Point A lay on the equilibrium Curve BF, the oil would be saturated. In the extreme case where the original oil contained no intermediates or dissolved gas, Point A would lie at the lower left-hand corner of the ternary diagram. In a displacement of Oil A by Gas D, there will be a progressive change in the composition of the oil phase as more and more gas is brought into equilibrium with the oil. The end result of this progressive change is an oil having the composition represented by Point F. This oil is richer in intermediate hydrocarbon and methane than the original oil and, therefore, has a greater forma-

By P. E. Busby, C. Wells, M. E. Warga

Fundamental data on the rate of diffusion of boron in austenite and solubility of boron in the a and y phases of iron and steel have been obtained from deboronizing experiments and provide partial explanations for some of the phenomena observed in boron steels. The rate of diffusion of boron is about the same as carbon in austenite. The solubility of boron in austenite at normal heat-treating temperatures is less than 0.001 pct. A partial tentative Fe-B phase diagram in the important low boron concentration ranges and an equation representing the diffusion of boron in austenite are presented. A LTHOUGH a search of the literature revealed ALTHOUGHthat boron diffusion had not been studied quantitatively and systematically prior to 1948, a few qualitative observations which were made by following the diffusion of boron into iron packed in ferro-boron1-3 suggest that boron obeys normal diffusion laws and that the rate of diffusion increases with increasing temperature. The claim of Cornelius and Bollenrath1 that boron does not appear to influence the rate of carbon diffusion has recently been substantiated by Wells, Batz, and Mehl.4 Calculations based on data from the paper by Campbell and Fayv indicated that the diffusion coefficient (D) for boron in iron at 900°C is approximately 3x10 sq cm per sec; a value of 2x10-7 sq cm per sec at 1038°C has been reported by Digges et al in connection with decarburizing experiments on a commercial boron steel containing 0.43 pct C. During the period 1948 to 1950 several diffusivity constant (D) values for the diffusion of boron in the y phase of iron and steel and a number of solubility values for boron in both a and y phases were reported. It was concluded tentatively as a result of Metals Research Laboratory studies that D values for boron in y and a phases are about the same as for carbon in the comparable phasesa and that carbon up to 0.4 pct did not affect the rate of diffusion of boron in y iron above 1000°C within the limits of experimental error. Whether saturation of the y or a phases with carbon would significantly affect rates of diffusion of boron through them was then and still remains in doubt. The best estimate of Q (activation energy) was reported to be about 25,000 cal, somewhat lower than that for carbon in y iron. The solubility of boron in y iron at 1000°C was thought to be higher than 0.004 pct B but not as high as a more recent analysis of available data shows it to be. The solubility of boron in a iron at 700°C was reported to be 0.0004 pct B, but it would not have surprised the authors if the true solubility value is actually lower than this. Breaks in diffusion curves which were not understood when first obtained prior to 1950 have now been recognized as indicating solubility limits, and these are included in the present paper. Experimental Procedure Two methods were employed in an effort to determine diffusion coefficients (D) for boron in austenite. Early experiments involved the use of welded couples prepared in accordance with the procedure of Wells and Mehl,' but when the results of these experiments proved to be unsatisfactory for calculating D values, studies were continued by means of deboronizing experiments. In both cases, boron analyses following the diffusion anneal were carried out spectrographically and all D values were computed using the Grube solution of Fick's law. The precision of the spectrographic method used proved to be about equal to that reported by Corliss and Scribner" —average deviation from the mean about 5 pct of the amount present when the boron content is 0.003 pct. Concentration-penetration curves obtained from spectrographic analyses of welded couples generally indicated that practically no boron was transported across the weld interface during the diffusion anneal. Furthermore the concentration-penetration

Jan 1, 1954

By W. A. Hockings, M. E. Volin, A. L. Mular

Batch grinding tests at short times were made in a laboratory rod mill with 10 x 14 mesh quartzite in corn syrup-water mixtures of varying viscosity. The weight fraction broken and size modulus were found to be independent of viscosity up to 20 cp, but at higher viscosities breakage of the feed decreased while the size modulus increased. The mechanisms of the effect of viscosity are discussed on the basis of particle dynamics. The effect of viscosity of the suspending medium on grinding has not been accorded much attention, although both wet and dry grinding are used in bene-ficiation processes and the viscosities of water and air differ greatly. schweyerl investigated the rates of grinding of quartzite in a pebble mill with air, water and glycerol as the suspending media and found the rate in terms of new surface developed per thousand revolutions of the mill to be constant and dependent on viscosity up to 20,000 rev, but to decrease and become independent of viscosity for longer grinding times. Based on considerations of the drag forces exerted on suspended particles and on the grinding media under turbulent and laminar flow conditions, viscosity can be expected to inhibit the rate of grinding in a given system as it changes the flow conditions from turbulent to laminar. The objective of this study was to determine the effect of viscosity of the suspending fluid in the batch grinding of a homogeneous feed of uniform size for short residence times, a region of more practical interest than the long times investigated by Schweyer. In actual grinding operations, the viscosity of the fluid does not change, but the consistency (apparent viscosity) of the pulp increases with additions of fines. In this study the consistency of the pulp was not measured because it was thought that the grinding times were too short to alter the apparent viscosity appreciably.* *Minus 200 mesh quartz at 65% solids has an apparent viscosity of about 25 cp as measured by a simple consistometer. Personal communication from D. F. Kelsall to A. L. Mular. For the purposes of this study, the effect of viscosity on grinding can be shown sufficiently well on the basis of the cumulative weight fraction finer than the feed size at any time, and the size modulus, ku, of the finer than feed sizes. The parameter, ku, is obtained from a form of the Gaudin-Schuhmann equation. METHOD AND MATERIAL The grinding tests were accomplished in a laboratory rod mill 10-1/2 in. long and 8 in. bore with a 20-lb rod charge consisting of two 1-in., eight 3/4-in., eight 1/2-in., and eight 1/4-in. diam rods. The mill speed was 43.2 rpm. Charges of 400 g 10 x 14 mesh Wisconsin quartzite** were ground for times of 60, **Courtesy of Minnesota Mining and Mfg. Co. 120, 180 and 240 sec in 500 cc of fluid made up of corn syrup and water in measured proportions. The temperature of the pulp was measured immediately upon completion of grinding, and the size distribution of the quartzite was determined by a wash-wet-dry screening technique. Corn syrup was chosen because of its high viscosity and ideal viscous behavior, and also because its density is not greatly different from that of water. The viscosity of each fluid mixture was measured with an Ostwald viscometer at 25 C. and a correction was made for the temperature of the pulp according to tabulated values for sucrose solutions. The density differences were so small that they probably did not significantly affect breakage. RESULTS AND DISCUSSION The conditions of the grinding tests, computed viscosities, weight fractions finer than the feed size and values of a and ku are listed in Table I. The values of a and ku were taken from the linear portions of the log-log plots of cumulative weight fraction finer vs size for the various grinding times. The plots for tests in fluids of average viscosity 8.6 cp are shown in Fig. 1. In general all of the sets of curves were linear throughout most of the size

Jan 1, 1965

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

The second order, {1011}-{1012} twin bands observed in critically deformed magnesium are often accompanied by an unusual form of kinking. These kinks, which lie adjacent to and run more or less parallel to the twin band habit, allow plastic deformation that occurs inside the twins to be accommodated into the matrix. The bend planes of these kinks cannot be explained using slip dislocations with Burgers vectors lying in the basal plane. A mechanism involving a single set of {1012)(1011) dislocations is proposed to account for the kink band habit, in good agreement with the experimental observations. It has been shown that second order, {101l)-{1012} twinning is an important phenomenon for magnesium deformed in the ambient temperature range. A detailed study of these twins has recently led to a better understanding of their irrational habit plane1 and their relation to fracture in magnesium.' This paper is concerned with a third aspect of these twins; this being the kink bands, originally referred to as shear accommodation kinks,3'4 that are often induced in the adjacent matrix. A twin band and its shear accommodation kink usually appear as a single macroscopic deformation, as seen in Fig. 1. The complex nature of these deformed regions is easily revealed, however, with the aid of a suitable microscope. It has been proposed374 that the primary function of these kinks is to accommodate the nonhomogeneous deformation that normally occurs in the second order twins. The twins tend to form as small discrete lamellae lined up approximately one in front of the other.''' Very large plastic deformations varying in magnitude from one twin to the next, may occur inside these lamellae. The kinks serve both to pass this strain into the matrix and to accommodate strain variations between twins. Deformation within the kinks, subsequent to their formation, has also been observed;3,4 and it is thought that this contributes to the strain accommodation process. The bend planes of the kinks have a habit near that of the twin band itself, which lies about 56 deg from the matrix basal plane. This orientation does not bisect the angle formed between the basal plane to either side of the bend plane and therefore differs markedly from the kink structure usually observed in hcp metals.'-' The present paper reports the results of a study of shear accommodation kinks and proposes a possible solution to the problem of the orientation of the bend plane. EXPERIMENTAL PROCEDURE Rectangular cross-section tensile specimens with axes parallel to (1010) and faces to (1210) and (0001) were cut and acid machined from a high-purity magnesium single crystal. After straining on an Instron machine the specimens were examined by both optical and replica electron microscopy. The basic procedures have been previously reported."' EXPERIMENTAL RESULTS AND DISCUSSION Structure of Shear Accommodation Kinks. A typical, large (101l)-{1012) twin band with its associated shear accommodation kink is shown running diagonally from upper left to lower right in Fig. 1. In this optical micrograph the twin band, consisting of a row of small, highly deformed twin lamellae, is visible as a narrow dark band along the left hand edge of the structure in question. The kink lies to the right of the twins, is approximately three times as wide, and is lighter in contrast. The horizontal slip lines visible on the general specimen surface correspond to matrix basal slip and are parallel to the tensile axis. Note that on the right-hand side of the band these slip lines can be followed from the matrix into the kink. At the kink band boundary the slip lines suffer a clockwise rotation of about 25 deg. Rotations of this magnitude are not uncommon. When a surface such as that in Fig. 1 is given an etch1 making it sensitive to polarized light, it has been observed that the slip traces in the kink are parallel to the basal plane trace in this region. This is in excellent agreement with the assumption that these regions are indeed kinks. Fig. 2 is an electron micrograph of this same twin band and kink. Note that a row of small supplimation pits has formed

Jan 1, 1969

By Gearge C. Wallick

This paper describes experimental procedures for the calibration of capillary tubes to be employed as comparison standards in gas flow-rate measurements and considers several types of flow which were observed in the calibration of seven capillaries of varying diameter. It is shown that under certain experimental conditions deviations from Poiseuille flow are observed which may not be attributed to turbulence, and that this flow behavior may be described empirically by introducing the classical kinetic energy correction into the Poiseuille equation. INTRODUCTION Techniques have been developed for the measurement of the volume rate of flow of nitrogen through glass capillary tubes as a function both of the differential pressure applied and of the absolute gas pressure. Capillary tubes thus calibrated are frequently used to determine the rate of gas flow through a porous sample in the measurement of slip-corrected permeability. The purpose of this note is to describe the calibration procedure and to discuss some observed deviations from the ideal flow behavior predicted by the Poiseuille equation. EXPERIMENTAL PROCEDURE The volume flow rate of nitrogen as a function of the differential pressure was determined experimentally for a series of seven glass capillary tubes of varying diameter. As is shown in Table 1, the capillary radii in the series ranged from 0.004 cm for K1 to 0.07 cm for K7. The capillary tubes were cut from capillary tubing purchased on special order from several manufacturers and the bore radii were determined by microscopic measurement. The gas volume flow rate was measured for each capillary tube at a series of differential pressures in the range from 0 to 3 cm of mercury and at average absolute pressures of 1.0, 2.5, 4.0, and 6.0 atm. Experimental Procedure for Small Capillaries A schematic diagram of the apparatus used to calibrate the three smallest capillaries, Kl, K2, and K3, is shown in Fig. 1. By means of a standard Ruska Instrument Corp. volumetric pump (equipped with a synchronous motor drive, two stages of gear reduction, and a quick-change lathe gear box), nitrogen was displaced by mercury from a metal cell immersed in a constant-temperature bath. The pump, the line to the cell, and a part of the cell were filled with mercury. As mercury was forced into the cell, it displaced nitrogen which passed through the capillary tube being calibrated and into a large container with a volume of approximately 30 liters. Since the volume of this container was very large compared to the total volume change of the gas resulting from the action of the displacement pump, the absolute pressure of the system was essentially constant throughout any one run. Prior to any determination this pressure could be set at any desired level by means of an auxiliary nitrogen cylinder. The differential pressure across the capillary was measured with a Meriam Red Oil manometer and recorded together with the corresponding pump displacement rate which was equal to the gas flow rate. By repeating this process for a series of different displacement rates at each of the absolute pressures of interest, the data necessary for plotting the calibration curves for capillaries K1, K2, and K3 were obtained. All calibration measurements were made in a constant temperature room to minimize errors due to temperature fluctuations. In each run. the flow was maintained until equilibrium was established. Experimental Procedures for Large Capillaries The flow rates through Capillaries K4, K5, K6, and K7 required to obtain the pressure drops desired were larger than could be obtained from available constant displacement pumps, and it was thus necessary to employ an alternative calibration procedure. The arrangement of apparatus used in calibrating these capillaries at an average pressure of one atmosphere is shown in Fig. 2. Each capillary was calibrated by flowing nitrogen through the capillary and recording the differential pressure as a function of the flow rate. 'The differential pressure was measured with a Meriam Red Oil manometer and the flow rate was determined by collecting the effluent gas over water at constant pressure and recording the increase in volume per unit time after an equilibrium had been established. Appropriate corrections were made for the

Jan 1, 1953

By John D. Price

COAL blending, in the preparation of coal before coke making, is so commonly practiced as to be almost universal. But the reasons underlying this practice, the benefits resulting from it, and the materials used in blending vary widely. This paper will outline the various phases of the subject and present information which may be correlated with work that has been done elsewhere. It will deal entirely with work done on the high-volatile coking coals of the western part of the United States, special emphasis being given to the coals of Colorado and Utah. A surveyL of the 86 coke plants in active operation in the United States during 1949 indicates that only 9 plants, or 10.5 pct of the total, charged one single rank of coal into their ovens, while the remaining 89.5 pcl made use of blending in some form. This report indicated that of these total plants 5 used straight high-volatile coal, 4 used straight medium-volatile coal, 47 used blends of high and low-vola-tile coals, 25 used blends of high, medium, and low-volatile coals, 2 used blends of high and medium-volatile coals, 3 used blends of medium and low-volatile coals. The fact that certain plants operated on a single kind of coal should not be interpreted to mean that no blending was practiced there, for invariably such plants secure their coal from more than one source and in the interest of uniformity do blend the coals as received. The general term coal blending covers two fields, the first of which is the mechanical mixing of a number of coals to secure uniformity. Often it is found necessary to secure coal for coke production from a number of different mines; these coals, though of the same general type or rank, may differ in their chemical composition or in the physical qualities they impart to coke made from them. Again, it is not unusual to find that coal from different sections of the same mine may show variations in quality. Under such conditions it may be necessary, in the interest of a uniform final product, to introduce a system of blending bins, a bedding yard, or other mechanical methods of securing a uniform mixture. Unfortunately this form of blending has received very little attention up to the present time; it has not received the consideration its value merits. The second type of blending, while also for the purpose of coke improvement, deals more particularly with the use of a blending agent differing in character from the base coal: it is this form of blending that will be discussed here. To consider only the western coals, for blending may be found necessary for other reasons with other coals, blending has been practiced experimentally or commercially under the following conditions: 1—When a single coal or mixture of coals of the same rank does not produce a satisfactory coke. For example, a high-volatile coal when used alone is likely to contract when coked so that a comparatively weak coke is formed. Or, if of very low rank, the coal may be deficient in the necessary bitumens required for good coke production. 2—When a product of some special quality is required, for example, when a plant ordinarily producing blast furnace coke must operate at slow coking rate to produce a high-grade foundry coke. Under this condition the reduced daily production of all products which accompanies slow coking time may be undesirable, and the use of some blending agent to increase the size of coke made at faster coking rates may be necessary. 3—When greater yield of coke or its coproducts is needed. Depending upon economic values of the products it may be found desirable to increase the yield of one or the other. 4—When supply of a particular coal must be used, either to protect reserves of high quality coking coal or to utilize a surplus or inferior product not otherwise usable. Many materials have been used for blending purposes, the exact agent to be used depending both upon the condition to be corrected and the nature of the base coal. No universal blending agent that can

Jan 1, 1954

By R. F. Mehl, C. E. Birchenall

SINCE Maxwell1 first considered the self-diffusion process in 1872 its importance in the kinetic theory of matter has been recognized. Until the discovery of isotopes in 1913, a direct measurement of this quantity seemed impossible. The only information that could be gathered indirectly was for gaseous systems for which the kinetic theory was well developed. When methods of direct observation be-came available, investigations on self-diffusion were carried out in condensed phases. In metals these data are presumably of potential importance in the study of recovery, recrystallization, creep, sintering, and related phenomena. Following the pioneer work of Von Hevesy2 and his collaborators, who determined the rate of self-diffusion in lead with the naturally occurring thorium B isotope, several metals have been investigated. Pb, Ag³, Au.6,5, and Cu6,7,8,9 are examples of isotropic crystals existing in only one phase modification. Anisotropy of diffusion has been demonstrated in Bil6 and Znll. This paper is a study of a single metal in two allotropic forms and also of self-diffusion in a body-centered cubic lattice. Despite the fact that the measurements in each of the papers cited on self-diffusion in copper seem to be internally consistent to about 10 to 15 pet, the curves reported by different authors differ by factors of 2 to 4 at the same temperatures. This uncertainty may account, in part, for the failure to establish a successful correlation between the self-diffusion rates and other physical characteristics of the metals. No satisfactory theory of metallic self- diffusion has as yet been proposed to account for all the existing data and to permit estimation in other metals. Experimental Part: Two units of radioactive iron were used in these experiments, each a mixture of Fe53 and Fe59 (12). Fe53 decays by K electron capture and the emission of an X ray with a half life of about 4 years. Fe59 emits two beta spectra, one with a maximum energy of 0.26 Mev, the other 0.46 Mev, and gamma rays of 1.1 and 1.3 Mev, with a half life of about 44 days. They were present in nearly equal concentration initially. The composite half life started at about 50 days and increased as the Fe59 decayed, leaving Fe55 relatively more abundant. After aging a year, the half life was too long to measure significant decay in a month. The absorption properties also changed with time. Because of the importance of the absorption coefficient in the diffusion calculations, it was necessary to determine this quantity frequently over the period during which these experiments were carried out. This correction was unsuspected at the time of publication of notesl3 on this work and accounts for the discrepancy in alpha iron and for part of the discrepancy in gamma iron.* * The data in the present paper supersede those given in the notes entirely. In one note the scale of log D was inadvertently reversed. In addition to the correction for the drift in absorption coefficient, the D values for gamma iron at low temperatures were high owing to insuficient correction for diffusion occurring during heating and cooling through the high temperature part of the alpha range at a rate much slower than that employed in the runs reported here. The high temperature alpha rates are much higher than the low temperature gamma rates and correspond to large equivalent times at these temperatures. These experiments were discarded and new measurements taken. Independent experiments with the same activity units indicated a radioactive contaminant in the iron, but exhaustive attempts to isolate and identify it chemically failed. These experiments? indicate † These experiments will be discussed in a later publication from this laboratory. that the contaminant represented only a trace of little importance in the diffusion results. The active iron was plated from an iron chloride solution. Enough of the solution was dropped on a 1% in. square of filter paper to wet it thoroughly.

Jan 1, 1951

By Z. Moser, W. Ptak

The experiments were carried out by the method of measuring the electromotive force of concentration cells having zinc as a reference electrode, the second electrode being the liquid alloy Zn-Sn-Cd-Pb. The electrolyte consisted of liquid chlorides and had zinc ions. The measurements were made for seventy -five alloys of different mole fractions within the temperature range of 714° to 877°K. The experimental results enabled the calculation of the activity of zinc in tested solutions. The activities of zinc were calculated by means of Krupkowski's formulas.3 In addition, the formulas for coefficients of activity of zinc, tin, cadmium. and lead as the function of composition and temperature were given. Activity of zinc was compared with the values obtained from experimental results, and good agreement has been observed. On this basis it can be stated that the theoretical formulas are suitable for determining the thermodynamic properties of liquid quaternary metal solutions. IN the metallurgical processes being carried out at present multicomponent liquid metal solutions take part. For the thermodynamic analysis of these processes it is necessary to know the thermodynamic properties of these solutions. Therefore, many experimental and theoretical papers deal with this problem. The theoretical papers are generally based on the assumption that the structure of liquid metals is similar to their structure in the solid state. In this manner the model of liquid solution, consequently described by means of statistical thermodynamics, has been accepted. This method is being lately developed, especially for solid solutions. Statistical thermodynamics was applied among others by Guggenheim 1 for describing the thermodynamic properties. Unfortunately, the formulas of statistical thermodynamics are often not suitable for the interpretation of experimental results. Attention should be drawn to the relations obtained by means of formulas of phenomenological thermodynamics which always have constants derived with the aid of experimental methods. In the case of the multi-component solutions which contain some additions of impurities besides the basic metal, wagner2 introduced interaction parameters. Equations for the relationship between the activity coefficients and composition were also given by Krupkowski." he application of these formulas requires a good knowledge of the thermodynamic properties of the corresponding binary systems. In these formulas, as in Wagner's, there appear constants which should be determined from ex- perimental data. Nowadays, different experimental methods are applied for evaluating the thermodynamic functions of solutions, for instance: vapor pressure measurements, calorimetric methods, and the measurements of electromotive force of concentration cells. In the present paper this last method for evaluating the thermodynamic properties of four-component systems, Zn-Sn-Cd-Pb, was applied. For instance in the case of Zn-Sn solutions Alabyshev and Landratov, 4 Fiorani and Valenti, 5 and ptak6 performed the investigations. The Zn-Pb system was worked out by Kleppa 7 and Cd-Pb and Cd-Sn by Elliot and chipman.' This method was also applied for determining the activity of zinc in ternary solutions. 1) EXPERIMENTAL METHOD The experimental arrangement with detailed description is given in Fig. 1. It consists of resistance furnaces, one serving for melting samples and the other containing the flat-bottomed, measuring quartz tube with the liquid electrolyte. Liquid metals and alloys are in glass supremax tubes, which have an opening in their lower part above the metal level. This opening allows the filling of the tubes by the electrolyte. In these tubes tungsten wires are placed which by means of suitable conductors are connected with a potentiometer. It is assumed that tungsten dissolves Fig. 1—Schematic diagram of the experimental arrangement for the investigation of the thermodynamic properties of liquid metal solutions: 1, resistance furnaces; 2, autotransfor-mers; 3, galvanometers; 4, regulator of temperature; 5, gas purifier with concentrated H2SOP; 6, U-tube with P2O5; 7, thermostats; 8, steel block for thermostating; 9, supremax tubes for alloys; 10, tungsten electrodes; 11, inlet and outlet of argon; 12, measuring quartz tube; 13, tube for melting samples; 14, tube for thermocouple; 15, cover of quartz tube; 16, rubber seal; 17, bottom cover; 18, outlet of electrodes to potentiometer; 19, outlet of thermocouples to potentiometer; 20, upper view of the quartz tube cover; 21, orifices for cover screws; 22, orifice for argon inlet; 23, orifice for thermocouple; 24, orifices for tubes containing liquid metals; 25, inlet for water-cooling system.

Jan 1, 1969

By W. Rostoker

Single isothermal sections were constructed for the titonium-rich corners of the systems Ti-Fe-O, Ti-Cr-O, and Ti-Ni-0 with a view to locating the shape and disposition of the ternary intermediate-phase fields for the compounds isomorphous with Fe3W3C. IN a previous note,' it was reported that a group of ternary intermediate phases existed which occurred in the general composition range Ti,X,O-Ti&O where X was one of the following elements: copper, nickel, cobalt, iron, or manganese. In two instances, binary intermediate phases occurred (Ti²Cu and Ti²Ni) which appeared to be isomorphous. The X-ray diffraction patterns of the phases could be indexed on a cubic lattice whose cell edge was of the order of 11 kX. Karlsson2 stated that the line extinctions and line intensities indicated that these phases were isomorphous with Fe³W³C and therefore belonged to the space group Oh. This author also noted that no unique phase of this type occurred at the composition Ti,Cr,O. This latter statement was accepted as true at the time the previous technical note was written.' However, work continued along these lines and that reported here has shown that a phase isomorphous with Fe³W³C does exist in the vicinity of the composition Ti³Cr³O but not at or near Ti4 Cr²O. The lattice parameter of this phase was found to be 13.01 kX. Metallographic examination of both as-cast and annealed specimens of these supposed ternary oxide phases disclosed structures which were far from single phase in many instances. It was considered a point of some interest to locate more positively the composition coordinates of the single-phase fields. To this end, single isothermal sections for the systems Ti-Fe-O (1000°C), Ti-Cr-0 (1000°C), and Ti-Ni-0 (900"C) were constructed. Phase relationships were studied by both X-ray diffraction and metallotrra~hic methods. Allovs were prepared as 10 g buttons by melting in a noncon-sumable electrode, water-cooled copper crucible arc-melting furnace using a helium atmosphere. Oxygen was introduced quantitatively by the use of weighed amounts of TiO² or TiO. Iodide titanium and the purest available alloying metals were used. All results are discussed in terms of the nominal composition of the melts. Previous experience with making oxygen-rich alloys had shown that oxygen losses were not significant if a homogeneous melt was produced. Weight-loss measurements were used to check loss in metallics during melting. Anneals were conducted in evacuated Vycor bulbs, and annealing times ranged from 24 hr at 1000 °C to 48 hr at 900°C. To achieve equilibrium in certain sluggish alloys, seven-day anneals were used. Debye-Scherrer powder patterns were taken in a 14 cm diam camera using filtered CuK radiation (K² = 1.541232 kX; K., = 1.53739 kX). Specimens were prepared by crushing and screening previously annealed buttons. In general, the X-ray diffraction results were used to identify the major phases, while the metallographic examinations were more useful in indicating the number of phases present. By the use of the combined results and general fundamental rules governing ternary equilibrium, it was possible to construct isothermal sections in good detail. In some instances where auxiliary lattice-parameter data were available, it was possible to lay down tie lines and to locate more positively corners of three-phase fields. Isothermal Section of the System Ti-Fe-O at 1000°C The binary systems Ti-O³ and Ti-Fe4 have been published. Binary phases, TiO, TiFe, and TiFe2, are likely to be encountered in the titanium-rich corner of the system. The structures are NaCl (Bl), CsCl (B2), and MgZn, (C14) types, respectively. Although preliminary X-ray diffraction studies indicated the presence of a ternary phase in the composition range Ti,Fe,O-TiJ?e,O, metallographic examination of two specimens at these compositions revealed the presence of other phases. Thirty-eight alloys were used to delineate the phase boundaries of the isothermal section illustrated in Fig. 1. The five almost single-phase ter-

Jan 1, 1956

By D. L. Sikarskie, B. Paul

A theory is presented for the static penetration of a single rigid wedge into brittle material. The material considered is one which exhibits both crushing and chipping phases in the penetration process. If the wedge angle and three parameters are specified, the theory predicts forces and associated penetrations during both the crushing and chipping phases. For certain ranges of the parameters agreement with the limited experimental data available is promising, except for the initial phase of the penetration process where refinements on the proposed theory are required. The theory also predicts that for certain values of the wedge angle and other known parameters, the chipping process does not occur and penetration is due entirely to crushing. When viewed in detail, the drilling of rock by percussive means involves, among other things, system dynamics, actuating forces, dynamic stress levels and the actual penetration mechanism of the bit into rock. If rock drills are to be significantly improved, a thorough understanding of the entire system would be highly desirable. In this paper, one aspect of the system, namely the mechanism of penetration of the bit, will be studied in detail. It has been found1 that for the velocities encountered in percussive drilling (of the order of 20 fps) a static analysis adequately describes the penetration process, at least for some rocks. Hence, we will only be concerned with describing analytically the static penetration of a single wedge shaped tool. It will further be assumed that the wedge is long enough to permit a two-dimensional analysis. Numerous authors have studied the static penetration of a wedge into rock. The following papers give some of this work and provide additional references to other work. Cheatham2,3 has assumed the rock to behave plastically and has obtained force-penetration equations for both Coulomb-Mohr and parabolic yield criteria. Evans and Murrell4 have studied the penetration of two types of coal and have found equations relating the penetration characteristic (P/dSc) to wedge angle for the various strength coals tested. race' attempted to find a correlation between hardness as determined by indenting the material and other mechanical properties and concluded that the results of such a test are generally inconclusive. His paper however contains a very extensive bibliography on the indenting of many different materials. Gnirk6 also has a fairly complete literature review on the static penetration of rock, of which he makes use in his indexing studies. A wide range of behavior is found in the wedge penetration of different rocks under different external conditions. For example, a rock that is essentially elastic-brittle at standard pressure may become elastic-plastic at a high confining pressure.7 It has also been observed4. " that some rocks will merely be crushed and indented by a wedge, whereas others will crack and form chips, furthermore the existence or non-existence of chips depends in great measure on the geometry of the indentor, type of rock and the depth of penetration. Hence, to attempt a theory which embraces all possible behavior is not practical at present. We, therefore, confine our attention to predicting the force-penetration characteristic and volume removal behavior for a type of rock which exhibits both crushing and chipping phases in the penetration process. Such behavior is characteristic of the harder rocks such as granites and represents a more difficult problem than the behavior of softer rocks such as coal and certain sandstones. In this preliminary study an attempt will be made to describe only the essential features of this complex penetration process. A qualitative description of these essential features is obtained with the aid of Fig. 1.1, where a wedge of vertex angle 28 is shown at some intermediate stage of the penetration process. As the wedge advances, the rock is fragmented (i.e. crushed) in some local region surrounding the wedge, the shape of this region being unknown. Simultaneous with the fragmentation in this local region, essentially elastic stresses are assumed to be building up in the surrounding rock. When a certain penetration level, di+1, is reached, the stresses along some surface are sufficient to cause failure and a chip is thus formed. The process now repeats, i.e., a crushing phase followed by the formation of a chip.

Jan 1, 1965

By G. Sachs, C. C. Chow, L. J. Klingler

Most structural parts which are heat treated are designed using strength properties which have been determined in the principal direction of the wrought material. For example, for rolled or drawn materials, properties are given for the rolling or drawing direction. The structures, however, may be loaded so that the critical stress is in some direction other than that for which the properties of the material are known. Investigations of forged products,123 have shown that while the yield strength and tensile strength of carbon steel billets and bars vary little with the direction of the test specimen in relation to the fiber, the contraction in area in tension tests and the impact strength in notched bar impact tests decrease in the transverse direction. The contraction in area and, consequently, the fracture stress of hard aluminum and magnesium alloy forg-ings have also been found to be lower in the transverse direction. An investigation on aluminum alloy plate4 likewise has shown the dependence of the fracturing characteristics upon the direction* of the test specimens, the longitudinal direction being considerably stronger than the transverse direction and the normal direction, with the normal direction being the least strong. The variation of properties with direction has been explained by a type of anisotropy called mechanical anisot-ropy. This anisotropy results from the elongation, in the direction of the principal strain, of certain phases, inclusions, and/or cavities in the metal during working. A mechanical fibering is thus produced which seems to persist through annealing and heat treatment. This investigation was initiated to determine the flow stress and fracture stress, at high hardness levels, at 90° to the rolling direction in a round steel bar. It is this direction which receives the critical stress in drawing dies machined from round bars. Preliminary tests showed a large difference in properties between the 0° and 90° directions. Consequently, it was felt that a more complete investigation, utilizing several types of tests, was warranted to determine the flow and fracture characteristics of a steel at various orientations, for a number of hardness levels. This investigation was conducted on an air hardening nondeform-ing die steel. Material and Procedure The distribution of properties was made on a 3-in. round bar of annealed high-carbon, high chromium steel of the following analysis: Pct Carbon................... 1.53 Manganese................ 0.39 Silicon.................... 0.27 Chromium................ 11.76 Vanadium................. 0.25 Molybdenum.............. 0.81 The 3-in. bar was produced from an 8-in. ingot, which was annealed and forged to a 4-in. square billet. The billet was annealed and rolled to a 3-in. round which was then annealed and straightened. This steel is an air hardening die steel which has very good dimensional stability on hardening; therefore, the residual stresses resulting from hardening would be expected to be low. A hardness survey across the diameter of the annealed bar showed no difference in hardness from the center to the outside. However, the test sections of all the specimens were taken approximately half way between the center of the bar and the surface to avoid any surface effect or possible porosity at the center. Tension, compression and bend tests were made on specimens hardened and tempered at six different temperatures. The tension test specimens, Fig 1, were machined from the bar at orientations of 0, 22.5, 45, 67.5 and 90° from the axis of the steel bar. The specimens were rough machined, heat treated and then ground to size. The test section on each specimen was lapped in a direction parallel to the axis of the specimen to remove any transverse scratches which might act as stress raisers. The specimens were tested in fixtures which insured concentricity of loading of less than 0.001 in.5 The transverse strains were measured with a radial strain gauge,5 the least count of which was 0.0001 in. change in diam. The compression specimens, Fig 1, were machined from the bar at ori-

Jan 1, 1950

By H. N. Treaftis, J. W. Cahn

THE previous determinations of the solvus of tin in solid lead disagree with one another by as much as 40°C or almost 10 at. pct. Even determinations that appear to be careful differ considerably in both the solubility and its temperature coefficient. Recent kinetic workl -3 on the rate of precipitation of tin from lead-tin alloys and thermodynamic work4 on the heat of solution of tin in lead have given some insight into the time necessary to reach equilibrium in this system. As this time is longer than that used in almost all previous determinations of the solvus, these determinations are questionable. Since the interpretation of recent kinetic results requires accurate values of the equilibrium solubility the present work was undertaken. DISCUSSION OF PREVIOUS RESULTS The methods used in previous studies may be placed into three classes: 1) Several alloys covering a range of compositions are allowed to reach "equilibrium" at a certain temperature.5-7 Some property, such as the X-ray lattice parameter of the lead-rich phase or the re- sistivity of the alloy, is then measured as a function of composition. The solubility limit for that temperature is taken to be that composition at which a discontinuity in the property occurs. However, the recent kinetic work has shown that tin precipitates in two stages. The first stage is rapid but leaves the lead still supersaturated. The second stage is very slow, and it seems from the equilibration times quoted by the investigators of the solvus that the end of the first stage of precipitation was usually mistaken for equilibrium. This is especially true at temperatures below 100°C where the first reaction is still quite rapid (from minutes to months), but where the second stage is so slow that very long holding times are required to reach equilibrium. Alternatively micrographic work8 on several alloys of different compositions seems to have given good results if done carefully. 2) The beginning of precipitation in a homogenized alloy is measured as it cools slowly8-10. Since reactions in solids undercool easily, such determinations will always give too low a temperature for the solvus. 3) Some property of an alloy is measured as a function of temperature while the alloy is above the solvus.5,9,11 The range of temperature can usually be extended slightly into the two phase region. Then the alloy is precipitated at a much lower temperature and slowly reheated. The solvus is taken to be the lowest temperature where the property of the reheated alloy is equal to that previously determined for the homogeneous alloy. Usually one also expects a discontinuity at the solvus in the temperature variation of the property for the reheated alloy. The difficulty in this method is the sluggishness of the dissolution process, and this method may give too high a solvus temperature. EXPERIMENTAL The phase boundary or solvus temperature was determined by a modification of method 3 for a series of chemically analyzed high-purity alloys, ranging from 5.1 to 26.4 at. pct Sn. The resistance, as a function of temperature, of a sample of homogenized alloy (which could easily be undercooled) was compared with the equilibrium resistance which that alloy sample attained after precipitation at room temperature followed by long isothermal anneals at various temperatures. Before each anneal the sample was rehomogenized and reprecipitated. The solvus temperature could be located to within 1°C as the intersection of the resistance vs temperature curves for the homogenized and equilibrium alloys. No attempt was made to locate the phase boundary more accurately since the limiting factor was the precision with which the alloys could be analyzed. This precision was ±0.1 wt pct Sn and corresponds to an error of 1 deg in temperature. This use of isothermal anneals differs from some of the previous investigations in which method 3 was used with baths of slowly rising temperatures. It was found early in the investigation that solvus temperatures tended to be high if the latter method was used even at extremely slow heating rates. For example a

Jan 1, 1961

By W. J. Houk, F. C. Hull

To clarify interpretations of grain structures and to assist in calculations of spatial grain size distributions, plane distribution curves have been determined for random sections through four regular polyhedrons approximating the shapes of metal grains. The characteristics of the distribution curve for the average metal grain are predicted. IT was realized early in the history of metallurgy that metals are polycrystalline aggregates and that the size and shape of crystals affects the properties of the material. Reaumur1 in 1722 employed the microscope to examine the fractured surfaces of steel and of white and gray cast iron and suggested a polyhedral arrangement of the crystals. The first extensive investigation of the form of crystal grains was carried out by Desch.2 He examined the disintegrated grains from a ß brass sample and noted that the number of faces per grain ranged from eleven to twenty and that the number of edges per face varied from three to eight and the maximum occurred at five. While it has been found practical to examine isolated grains only in exceptional cases, it is always possible to make a plane section through the metal and examine the shape of the grain sections on the plane of polish. Desch2 tried to determine the relation between the form of a polyhedron and that of its plane sections for comparison with distribution curves of numbers of sides per grain section of actual metal samples. The polyhedrons investigated were the rhombic and pentagonal dodecahedrons and the orthic tetrakaidecahedron. However, the frequency distributions of the number of sides of plane intersections were not sufficiently characteristic to decide which polyhedron most closely approximated the average grain in a metal. Determination of Statistical Shape of Grain in Space Scheil3 was interested in the problem of calculating the distribution of grain sizes in space from the easily measured distribution of grain section sizes on the plane of polish. Assuming that the grains were spheres and using the plane distribution curve for a sphere shown in Fig. 1, he employed a successive subtraction method to calculate the spatial distribution. In order to evaluate the accuracy of these calculations, Scheil and Wurst4 determined the actual distribution of grain sizes in space in their sample of ingot iron by polishing off successive layers and following every individual grain in a series of micrographs. From curves of mean radius of intersection of a given grain vs thickness of metal removed in polishing, Scheil and Wurst attempted to derive the statistical shape of a grain in space. Their calculated plane distribution curve for this shape is compared with the distribution curve for a sphere in Fig. 1. A table of values based on this curve was prepared for calculating spatial distributions of grains. The calculated and measured spatial distributions of their sample then agreed much better than when a spherical shape had been assumed. In the present paper, an attempt has been made to learn something about the average metal grain by studying in detail the effect of the shape of regular polyhedrons on the plane distribution of areas and shapes of areas produced by random sections through them. From the data presented below, it can be concluded that the plane distribution curve for the average metal grain differs in three fundamental respects from the curve derived by Scheil and Wurst. Polyhedrons Selected for Study The polyhedrons selected for the statistical study are illustrated in Fig. 2 and consisted of a cube, a figure formed by cutting off the corners of a cube at the midpoints of the original edges, a tetrakaidecahedron, and a pentagonal dodecahedron. The length of edge on any one figure is a constant. For the above models the edge lengths were 3.50, 4.00, 2.00, and 2.08 in., respectively. A cube was selected for one of the polyhedrons because of its simple geometry, because it is a form that by repetition can completely fill space, and because it represents a convenient degree of departure from compactness beyond which the shape of

Jan 1, 1954

By Richard A. Queeney, Lance G. Peterson

ESTIMATES of the stacking fault free energy of copper reported in the literature show an extensive divergence of results. Based on measurements of dislocation node radii, Thornton et al.7 find the lower limit of stacking fault energy to be 60 ergs per sq cm: Jossang and coworkers4 estimate the same value should be less than 40 ergs per sq cm. Assuming stacking fault free energy to be twice the coherent twin boundary free energy, Valenzuela8 reports 72 ergs per cm, while Inman and Khan2 cite a value of 24 ergs per sq cm. which can no doubt be accounted for by almost complete absence of interstitials in solution. However, the minute concentration was sufficient to permit observable recovery of dislocation damping. Assuming a dislocation density of 1010 CM -2 and an average loop length of 0.5 , a concentration of interstitials as low as 0.01 at. ppm is sufficient to reduce dislocation damping by more than a factor of ten. The concentration of interstitial solute atoms in Ferrovac E-0.15 pct Ti was thus estimated at 0.01 at. ppm < (C + N) < 2 at. ppm. The absence at elevated temperature of strengthening due to interstitials, Fig. 1, was therefore anticipated in the titanium alloy. The temperature dependence of the flow stress below 300°K was unaffected by addition of either titanium&apos; or zirconium.&apos; Observed, however, was an initial difference in the absolute value of the flow stress below 320oK, Fig. 1. Grain size may account for the difference; the grain diameter of Ferrovac E was 30 to 45 µ and that of Ferrovac E-0.15 pct Ti 65 to 90 µ. Although second phase particles in the form of titanium carbides and nitrides precipitated in the Ferrovac E-0.15 pct Ti alloy, the spacing was too large to produce any strengthening effect. The mechanical properties measured, therefore, were inherent to the bcc lattice. 1W. C. Leslie and R. J. Sober: Trans. ASm, 1967, vol. 60, pp. 99-111. 2 H. Conrad: Journal of Metals, 1964, vol. 16, pp. 582-88. 3 A. S. Keh and W. C. Leslie: Materials Science Research. H. H. Stadelmaier and W.W.Austin, eds., vol. 1.pp. 208.50, Plenum Press, New York, 1963. 4A. S. Keh, Y. Nakada, and W. C. Leslie: Dislocation Dymmics, Rosenfield, Hahn, Bement, Jr., and Jaffe, eds., pp. 381-406, McCraw-Hill Book Co., New York, 1968. &apos;W. J. Bratina, J. T. McCrath, and H. E. Rosinger: Can. Met. Quart., in press. 6 W. J. Bratina, J. T. McGrath, and D. Mills: Suppl. Trans. Japan Inst. Metals. 1968, vol. 9, pp. 436-43. &apos;H. E. Rosinger and C. B. Craig: Can. Met. Quart., In press. %. Mills. J. T. McGrath. and W. J. Bratina: ScriptaMet,, 1968, vol. 2, pp. 311-13. The purpose of this note is to present the results of a direct measurement of the stacking fault free energy in copper. The present method avoids both the question of interaction forces of nodal dislocations and the assumption that the coherent twin boundary free energy is one-half that of a stacking fault. Fig. 1 shows a transmission electron micrograph of a stacking fault intersecting a high angle grain boundary in copper: Fig. 2 is a schematic representation of the intersecting interfaces. To produce the specimen, pure copper was rolled to 0.002 in. thickness and annealed for several hours at 875°C. These foils were strained in tension to l04 µ in. per in., and rean-nealed to 8 min. Recrystallization and/or grain growth were not observed during the second anneal, indicating that intersections such as Fig. 1 are equilibrium configurations. Many such stacking faults were observed, but few were noted as intersecting grain boundaries in well-illuminated areas. The intersection of Fig. 1 was well away from the specimen edge. Since similar defects have not been observed in fully recrystal-lized and annealed copper, it is felt that this defect is due to the tensile straining. Electron transmission

Jan 1, 1970

By R. M. S. B. Horta, W. T. Roberts, D. V. Wilson

Evaluation of results obtained by the Harris method for inverse pole figures is discussed. Two existing analyses and a new approach are compared. In the most frequently used analysis, different reflections are accorded equal weight. A second method involves area-weighting of reflections, mainly to take account of nonuniformity of Pole distribution. In the new method, reflections are weighted according to their multiplicity factors. Intensity ratios obtained from a sample of steel sheet by the three methods are compared. INVERSE pole figures offer a convenient method of depicting the proportions of material with various orientations referred to a unique specimen axis. The technique was first applied to fiber textures, but it is now frequently used as a description of texture in sheet metal, the unique axis in this case usually being the sheet normal. The Harris method&apos; for the determination of inverse pole figures has the great merit of simplicity. It suffers certain intrinsic limitations, but provided that these are borne in mind, the results allow useful conclusions to be drawn regarding the effects of texture components on certain mechanical properties. Much thought has been given to alternative methods of texture description, aimed at eliminating the ambiguity in the simpler methods.2"6 Refinements in the method of description are obtained at the price of increasing complexity, and it seems clear that a simple method, such as that of Harris, will continue to find application. The original derivation by Harris1 has been corrected by Morris7 and later by Mueller, Chernock, and Beck.2 Since the latter reference is more accessible, it is referred to more frequently than the work of Morris. Most users of the inverse pole figure method present their results on the basis of the treatment by Mueller et al., and it is the purpose of the present communication to comment on this treatment and to suggest a simple modification to the method of presentation which enhances the meaningfulness of the results. It will be convenient first to summarize the Mueller analysis as follows: The intensity Ihkl of a hkl reflection from a textured specimen is: Ihkl=CI0AL\Fhkl\2NhklPhkl [1] where C is a constant for a given sample I, is the intensity of the incident beam A is an absorption factor. With usual diffrac-tometer geometry and a flat specimen, A is inversely proportional to the density of the specimen. L is the Lorenz polarization factor Fhkl is the structure factor for the hkl reflection Nhkl is the multiplicity factor phkl is the fraction of crystals in the polycrystal-line aggregate with any particular (nkl) plane parallel to the surface. The corresponding equation for a specimen with randomly oriented grains is lR,hkl=CRl°ARL\fnkl\2Nnklk [2] the subscripts R indicating the factors that are different for the random sample, which will, in general, have a density different from that of the textured one. The intensity ratio is hkl , c A Phkl [3] IR,hkl CR AR PR The constants are eliminated by summing over all the measured reflections ^iRMi °R AR PR ljPkkl and from Eqs. [3] and [4] T IR,hkl The only unknown in Eq. [5] is Yj phkl and before this can be evaluated, it is necessary to adopt some form of normalizing procedure. Mueller et al. assume that when a large number, n, of reflections is used, the average value of p as defined by Eq. [6] below will be unity ? = £j**l3l [6] and the final result of their analysis follows: hkl Pkkl = i I&Jf~ [7] ±y* Ihkl ^ in,hki The normalizing procedure used by Mueller et al. involves an unrealistic assumption since it gives equal weight to each of the hkl reflections. Other normalizing procedures can now be examined with a view to selecting a more appropriate one. For an infinite number of reflections, the function p can be averaged over a continuous range of orientations covering the complete solid angle 4p by the integral relation: p =1 jp(a)dQ = l [8] This is the only exact procedure, but in practice a

Jan 1, 1970

By J. E. Hanafee, G. J. London

MANY studies of the deformation behavior of materials under a superimposed hydrostatic pressure have shown that materials brittle at ambient pressure behave in a ductile manner under pressure. Thus, with a metal such as beryllium which possesses relatively low ductility, but otherwise exhibits quite useful physical and mechanical properties, hydrostatic pressure may be particularly useful for both forming beryllium shapes and studying its deformation behavior. In fact, it has been found1"4 that polycrystal-line beryllium in both ingot and powder form appears to behave in a more ductile manner on a macroscopic level in a hydrostatic pressure environment, and it has been suggested2 that this is due to activating a new slip mode. Furthermore, Andrews and Radcliffe5 have found pressure induced nonbasal dislocation activity in hot pressed beryllium. Recently6 it has been shown in "c-axis" compression tests under hydro-static pressures up to 28 kbars that the shear stress needed to cause slip with a Burgers vector out of the basal plane (pyramidal slip) does not change with increasing pressure in beryllium with a purity of some 99.5 pct. This material is equivalent or more pure than the beryllium used in the previous pressure studies. Thus, it appears, as suggested by Inoue et al.,3 that the hydrostatic pressure affects the fracture stress rather than the stress necessary to activate pyramidal slip in beryllium. However, in "c-axis" pressure tests on high purity 12 zone pass beryllium (˜50 ppm total impurities) the macroscopic compression stress needed to cause pyramidal slip was considerably lower than that at ambient pressure.6 It has further been shown that alloying beryllium with nickel and copper in the range 2-5 wt pct also favors the occurrence of pyramidal slip in "c-axis" compression tests,7&apos;8 while lower amounts of nickel and copper do not have significant effects. In the present study the combined effect of hydrostatic pressure and alloying high purity beryllium on the shear stress needed to cause pyramidal slip has been ascertained. A 2.5 wt pct Cu alloy was selected as the first alloy to study as this level of copper did favor pyramidal slip at room pressure. A high purity (12 zone pass) single crystal of beryllium 0.3 by 0.1 by 0.1 in. was cut and polished by an orientation and lapping technique8 so that the top and bottom compression surfaces were parallel and within 3 min of arc to the (0001) plane and the sides parallel to the {l010} and {ll20} planes. In these compression specimens, therefore, the resolved shear stress was nearly zero on both the basal and prism planes, and slip was restricted to pyramidal systems. Analysis of slip traces on the two lateral surfaces served to accurately identify the active slip planes.6&apos;9 The pressure unit was a modified piston-cylinder device fitted with a manganin transducer coil arrangement which continuously monitored and recorded the hydro-static pressure. The load on the specimen was measured by a strain gage load cell which operated entirely within the pressure chamber. This load cell was calibrated before and after each pressure cycle at room pressure in situ and the calibration did not vary more than ±1 pet. These techniques and devices have been previously described in more detail.6 Successively higher compressive stresses were applied to the single crystal under a superimposed hydrostatic pressure until fracture occurred. The strain rate was (4.5 ± 2.0) x 10-6 sec-1 and the average rate of pressure application and release was approximately 0.3 kbars per min. As the load on the specimen was applied by the piston which was used to increase the hydrostatic pressure, the pressure increased during the compression test. This increase ranged from 0.0 to 0.8 kbars, and the maximum hydrostatic pressures are quoted in Fig. 1. The lateral surfaces of the specimen were examined in a light microscope after each pressurization/stress cycle so that the stress at the onset of {1122} pyramidal slip could be ascertained. Post compression height measurements allowed the plastic strain in the specimen to be evaluated to within 0.03 pct. The resulting compression stress-plastic strain curve is shown in Fig. 1 with results of a "c-axis" test on a similar Be-2.5 wt pct Cu single

Jan 1, 1970

By R. L. Slobod, H. A. Blum

A semiquantitative method for measuring the wettability of reservoir rocks has been developed. These data are needed for reservoir analysis and for interpretation of laboratory displacement studies. The wettability of a core sample is measured by the contact angle for the system oil-water-solid. These contact angles are calculated from the displacement pressure (threshold pressure) obtained by use of the centrifuge, using first oil-water and second air-oil in the same core sample. This method is based on the assumption that the air-oil and oil-water interfaces occupy similar positions in the porous medium when desaturation of the wetting phase is initiated. The assumption is also made that the Contact angle for the air-oil-solid system which is close to zero in value does not change appreciably even when the contact angle for the oil-water-solid system experiences marked changes. "Apparent contact angles&apos;&apos; for five different solids ranging from 31" to 82" have been determined, and changes irr the "apparent contact angle" of a given sample with laboratory use from 33" to 53&apos; {lave been observed. INTRODUCTION Reservoir rocks vary in their wettability, 1,2,3,4 some being preferentially water wet while other are apparently preferentially oil wet. The degree of wettability, in theory, is measured quantitatively by the contact angle for the system solid-oil-water, hut in 1)practice this quantity is extremely difficult to determine." The need for obtaining some measure of this quantity has become obvious in recent years as a result of both laboratory. and field observations. Several reservoir.: such as the Bradford Sand in Pennsylvania and the Wilcox&apos; at Oklahoma City are reported to be oil wet. If these report:: correctly reflect the true nature of the surface of the rock in the ground, then these reservoirs probably will not perform as predicted on the basis of a water wet rock. In the laboratory many core samples have been Observed to be oil wet. These samples, while perhaps not correctly representing the reservoir, have markedly different properties from water wet rock. The location of the phases is different (oil is in contact with rock instead of water), and other quantities such as the connate water, the capillary pressure curve; residual oil. relative permeabilities. and the recovery of oil by water flooding are markedly affected by the value of the contact -4 A further complication observed in the laboratory is the chang-ing of the wettability of a rock specimen with use. such changes mean that repeat runs on the same core are not the duplicate tests desired, but represent new experiments on a more oil wet material. The changes in surface characteristics are sometimes so rapid that by the time an experiment requiring several days is completed, the results may not be representative of the core as originally described, The, rock material itself (Silica. carbonates. etc.), whell Clean and uncontaminated, is water wet. There seems b( : little evidence of the presence of oil wet minerals such as heavy metal sulfides. The oil wetness of reservoir samples, therefore, is believed to be caused by the accumulation of an adsorbed film in which the polar group of a large organic. molecule is adsorbed on the surface leaving the organic or hydrocarbon part of the molecule projecting out from the solid. Such a surface is much more readily wet 17" oil than by water. These considerations indicate the need for a method which will provide some measure of tile wettalbility (Contact(angle if possible) for reservoir rock ..samples) The method should be capable of (1.1 distinguishing between tile wettalility of dif. ferent formation,.. (2) detecting (change. ill wettalbility of a core with use. and (3) measuring the changes in Wettability which may be accomplished with cleaning operations. such as the use of sodium silicate for increasing water wrettalbility." A preliminary report on such a method is preseted below. not with the idea that this procedure alone will Solve the wettabil-ity problem. but rather that it may provide encouragement to

Jan 1, 1952

By J. Washburn, R. Drouard, E. R. Parker

Temperature dependence of the rate of recovery in zinc single crystals after a simple shear deformation at low temperature was investigated. Some tentative suggestions regarding the annealed and strain-hardened states of a crystal are discussed. RECOVERY may be defined as the gradual return of the mechanical and physical properties of strain-hardened metal to those characteristic of the annealed material; an increase in temperature increases the rate of recovery. The annealing process in strain-hardened polycrystalline metals is complicated by the inhomogeneity of strain which always exists in aggregates. Polygonization in bent regions of the crystals and growth of new almost strain-free grains starting at points of severe local distortion1-:&apos; make it almost impossible to isolate and study the recovery process. Homogeneously strained single crystals, however, do not polygonize or re-crystallize and hence they can be used advantageously to study recovery. In such crystals strain hardening is completely removed by recovery alone. Since recovery is a process whereby certain lattice disturbances introduced by plastic flow are gradually reduced, a knowledge of the rate and temperature dependence of this process for various conditions of prestrain might be helpful in formulating a model of the strain-hardened state. For simplicity it seemed desirable to limit the type of prestrain to the simplest obtainable, i.e., simple shear strain. In the experiments to be described, recovery was studied by observing changes in the stress-strain curve of prestrained zinc single crystals held for various times at temperatures above that employed for straining. Single crystals were grown from the melt by a modified Bridgeman technique from Horse Head Special zinc 99.99 pct pure, and from spectrographically pure zinc 99.999 pct pure. They were grown as 1 in. diameter spheres and acid-machined&apos; to the final specimen contour. The test section was a cylinder about 1/8 in. high and 3/4 in. in diameter. The conical sections adjacent to the test section were cemented into the grips so the load could be transmitted to the crystal as uniformly as possible. The specimens were oriented so that in testing the maximum shear stress was applied along one of the slip directions, [2110], in the (0001) plane. Details of the production and testing of such specimens have been presented.&apos; Each test was carried out according to the following schedule: 1—The crystal was strained at — 50°C until it reached a maximum shear stress, ,,,. The strain rate was approximately 5 pct per min in all cases. 2—After straining, the crystal was unloaded before the temperature was changed. Unloading required about 3 min. 3—The temperature of the specimen was then increased from — 50°C to the temperature, T, of recovery. This change in temperature was completed in a time of less than 2 min. The specimen remained at temperature, T, for a time, t, which differed for the various specimens. 4—Thereafter the temperature was again reduced to — 50 °C in approximately 3 min. 5—While at —50°C, the stress-strain curve after recovery was obtained. 6—The specimen was then unloaded and annealed for 1 hr at 375 °C in a helium atmosphere to bring about complete recovery. Cooling to room temperature after anneal required 90 min. 7—The same crystal could be re-used for another test because the plastic properties after annealing closely duplicated those of the original crystal. The specimen was immersed during the test in a bath of methyl alcohol which, through a system of tubes, could be pumped through either of two heat exchangers to regulate the temperature; this was accomplished by circulating the liquid through coils immersed in a bath of acetone and dry ice for cooling or in a bath of warm water for heating. Test temperatures were thus maintained constant within ±1°C. The — 50°C temperature was low enough so that no measurable recovery occurred during unloading and reloading. The stress-strain curve continued after recovery along a path below, but approximately parallel to, the path of a curve obtained in an uninterrupted test. Fig. 1 shows some of the results from a specimen of 99.999 pct Zn. The amount of downward displacement of the curve due to recovery was a

Jan 1, 1954

By Jean-Jacques Prompsy, J. S. Rinehart

Some time ago a study was initiated at the Colorado School of Mines in an effort to arrive at a better understanding of the stress fields developed within drill bits under dynamic loading and the influence that these stress fields could have on the failure of the bits. Particular emphasis has been given to the influence that bit shape has on the establishment of highly localized, potentially destructive stress inhomogeneities within the bit. The study has been divided into three phases involving three velocity regimes: impacts at very low velocities, 0 to 20 ft/sec, a velocity range in which dynamic effects are just beginning to be found; impacts at velocities ranging from 20 to several hundred ft/sec, a range commonly encountered in practical drilling operations; and impulsive loading through the detonation of explosives, a region in which the dynamic effects are greatly exaggerated and made more identifiable. The ultimate objective is to provide basic data which will enable the mitigation through judicious design of the frequency and severity of these transient concentrations of intense stress, thereby prolonging and increasing drill efficiency. This paper presents results of the third phase of this study — the development of a better understanding of the dynamics and mechanics of failures caused by transient stress-wave interactions. The impulsive loading or transient waves in these experiments were generated by detonating small explosive charges placed on the ends of Plexiglas cylindrical rods terminating in truncated cones. Under such intense loading, dynamic effects are greatly exaggerated and, hence, made more identifiable. The explosion generates a high-intensity transient stress disturbance which moves through the rod, reflects from surfaces which lie in its path, and establishes momentarily narrow regions of high concentrations of stress where failure of fracture may occur. The peregrinations of these waves, their interactions and their effects have already been described in the literature (see, for example, Refs. 1 and 2). The locations and extent of the regions quite apparently are strongly dependent on specimen shape, making it possible through judicious shaping of specimens to relocate the highly stressed regions, minimize their extent, or eliminate them entirely. These experiments were designed, first, to identify more clearly the vulnerable regions in geometries relevant to drill-bit design and, then, to modify these regions in a predictable way by changing specimen shape. Through this latter process, it is anticipated that better bit design might evolve. The specimens used in the experiments were cylindrical rods, 1 1/2 and 1 1/8 in. in diameter, ended by a truncated cone, with the cone angles ranging from 45° to 130°. Upper cone face diameters were 1/2, 3/4, or 1 in. A small plastic-covered electric blasting cap detonated on the axis of the specimen produced the spherical shock wave. The detonators used were Olin Mathieson No. 6, which induced into the rod a transient saw-toothed stress disturbance of about 3-microseconds duration, corresponding to a wave length of 0.3 in. in the Plexiglas. Five distinct systems of fracture were observed: (1) along the axis of the rod, a lower system of fractures, the cracks focusing around one point for specimens having cone angles of 80° and 90° and, as the cone angle was increased, spreading downward; (2) just above these fractures, an upper system of fractures composed of horizontal cracks observable in some specimens but not of any appreciable extent; (3) a third system of axial cracks still above the latter, observable in the small cone-angle specimens; (4) in the upper part of the specimen, a system of radial fractures extending from the blasting point; and (5) circular spalling due to reflection of the wave on the boundary of the cylinder. Only the first three systems, the axial fractures, are examined here. LOWER TENSILE FRACTURE SYSTEM The first, lower system of tensile fractures, shown in the photograph of Fig. 1, was observed in almost all of the specimens. It was due to the reflected tensile wave coming in from the boundary of the cylinder as shown in Fig. 2. The reflected wave was cylindrically convergent and focused

By A. G. Guy

Thermodynamic activity rather than chemical composition is basic to the analysis of diffusion. This is the essential conclusion reached by Darken1-3 and by Birchenall and Mehl.4 If so, it is reasonable to expect that diffusion calculations should be carried out using activities. This paper will illustrate a method of employing activities in analyzing interstitial diffusion. For interstitial diffusion (of carbon in iron and probably generally) the diffusion of the solvent atoms, volume changes, and other such complexities not explicitly provided for in the usual diffusion equations cause a negligible error of the order of 1 pct. Therefore it is relatively easy to test the validity of an analysis based on activities in the instance of interstitial diffusion. The mathematical treatment of the more complex substitutional diffusion could be simplified once the adequacy of the activity method had been established for substitutional diffusion. Thus the present work has the purpose not only of providing a superior analysis of interstitial diffusion but also of indicating a possible approach to the more important question of an adequate treatment of substitutional diffusion. Development of the Diffusion Equation Although activities are convenient quantities to determine experimentally, they are derived from the more fundamental fugacities.9 Possible confusion in using activities can be avoided by basing equations involving their use on the relationship, dP = -D1d/ax dt [I] where, dP = the number of grams of solute crossing one cm2 in the time dt sec. D, = the diffusion constant for use with fugacities; it is assumed to be constant at a given temperature, and has units of secs. f = the fugacity of the solute in the solid solution; the units are those of pressure, dynes per cm2. x = the distance in cm. Eq 1 can be considered to be the basic form of the first Fick Law for one-dimensional diffusion. In order to convert Eq 1 into an equation involving activities, a choice of a standard or reference fugacity, f°, must be made: then. a = f [2] where a is the activity corresponding to the fugacity f. However, the value of a is also determined by the relation, a = a\c [3] where a is the activity coefficient and c is the concentration. For a given value of a (such as a = 1) it is evident that the units used for expressing concentration will affect the numerical value of a corresponding to a given amount of carbon dissolved in y-iron. Since weight per cent concentration is so widely used, this unit will be adopted as the standard in this paper. When the value off given by Eq 2 is substituted in Eq 1, the first Fick Law becomes, dP= -D,f°dl [4] Since D,f° is constant (at a given temperature), the second form of Fick&apos;s Law can be obtained in the usual manner, -dt D&apos;f° dx [5] where c&apos; is the concentration in g per cm3. In terms of weight per cent concentration, c, Eq 5 becomes, dc _ 100 d2a Tt = T /f w [6] where p is the density of the solid solution and will be assumed to be constant. In order to simplify Eq6, it is necessary to consider the standard state, f°. Standard states are chosen for convenience. There appears to be one especially convenient choice for the analysis of interstitial diffusion. If the activity coefficient, a, is set equal to unity at infinite dilution of the solute, 100 then — 100D1fl° is approximately equal P to the usual diffusion constant in dilute solutions. This is true since the activity, a, in Eq 6 can be replaced by the concentration, c, with little error in an infinitely dilute solution.* Here f1° is the standard fugacity necessary to achieve this standard state. It is proposed that a diffusion constant Da&apos; be defined, Da1=100/pD1f1° [7] where A is the metal whose diffusion is * The second derivative of a is equal to the second derivative of c in dilute solution only if -da/dr- is. zero. Although theory does not require this condition, in the systems C in Fe, and Zn in Cu, dc is in fact found to be essentially zero.

Jan 1, 1950