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By J. D. Alexander, W. L. Martin, J. N. Dew

This paper presents data obtained using a flood-pot technique to determine the fuel available and the corresponding theoretical air requirements for in situ combustion of crude oils. Since the technique is relatively quick and easy, it is a practical and convenient tool for evaluating reservoirs as fireflood prospects. It is also a research tool which facilitates systematic study of the variables affecting fuel availability and corresponding air requirements. The understanding of these variables is of prime importance to those concerned with the technical and economic development of in situ combustion as an oil-recovery process. The experimental results show conclusively that the fuel available for in situ combustion is not a constant but, rather, varies with crude-oil characteristics, porous-medium type, oil saturation, air flux and time-temperature relationships. Thus, the fuel availability for specified field applications should be determined using actual reservoir crude and core material and the process conditions expected during in situ combustion in the reservoir. INTRODUCTION In situ combustion is a thermal process for recovering crude oil from reservoirs. The thermal energy released during the combustion of a small amount of the oil in place aids in the displacement of the remaining oil. Numerous articles have been published describing the in situ combustion process giving detailed results of laboratory and field experiments.10 In order to engineer an in situ combustion project, a number of important factors must be considered and determined. These factors include: (1) the amount of fuel consumed per unit of reservoir volume swept by the combustion zone, (2) the composition of the fuel consumed, (3) the amount of air required to consume this fuel, (4) the portion of the reservoir swept by the combustion zone, (5) the appropriate air-injection rates and pressures, (6) the amount of oil that will be recovered, (7) the rate of oil production and (8) the operating costs. Nelson and McNiell1 recently have described a procedure which utilizes laboratory combustion-tube data as a basis for the calculation of some of these design factors. Various authors have attempted to describe the in situ combustion process mathematically, and considerable progress has been made. Analytical solutions to the problem of heat transfer from a moving combustion front have been obtained for linear and radial systems."-' All of the published results involve the assumptions that: (1) fuel concentration is constant throughout the reservoir, or that fuel concentration is inversely proportional to the velocity of the front for a given rate of oxygen consumption; and (2) the fuel reacts instantaneously with injected oxygen, while liberating a constant amount of heat per unit weight of fuel at all temperatures. It seems both desirable and reasonable to test the validity of these assumptions experimentally. This paper presents laboratory data which were obtained by means of a "fire flood-pot" method for determining fuel availability and composition, and the corresponding theoretical air requirements for in situ combustion of crude oils under variable conditions. The mechanics of the method are similar to a conventional tube-run experiment.' The important differences involve the size of the reservoir model used and the method for providing the experimental environment. The new method subjects conventionally-sized core samples or unconsolidated sands to a programmed environmental sequence similar to that experienced by a similar volume of rock during the approach and passage of a combustion front in a long tube or in an oil reservoir undergoing in situ combustion. Restored-state samples can also be used. The small samples and relatively simple techniques involved allow an experiment to be set up, run and calculated in about three 8-hour days. This is a considerable improvement over long-combustion-tube techniques which can require several days to run and several more work days to set up and calculate. All the runs presented were run at 40-psig injection pressure. Pressure was not considered as a variable for these experiments, since we previously had found that it had only a small effect on fuel availability up to 600 psig.APPARATUS AND MATERIALS APPARATUS The fire flood-pot apparatus consists of a consolidated

By E. T. Turkdogan, J. H. Swisher

The solubility of oxygen in zone-refined iron was determined in the temperature range.from 881" to 1350°C. The solubility in a iron at 881°C ms found to be about 2 to 3 ppm; in y iron, the solubility was found to increase from about 2 to 3 ppm at 950°C to about 25 ppm at 1350°C. The permeability of oxygen in an iron -0.1 pct Al alloy was determined in the y iron range, using an internal oxidation technique. By combining the permeability and solubility data, the diffzisivity of oxygen in y and a iron was calculated. The oxygen diffusivity in solid iron may be s~immarized as follows: 8820 For 6 iron and IN a recent paper, Hepworth, Smith, and Turkdogan1 reported on the solubility, permeability, and diffusivity of oxygen in 6 iron, together with permeability data for oxygen in a iron. In the present investigation, similar measurements were made in the ? phase region. In addition, a solubility measurement was performed in the a phase region to permit calculation of the diffusivity of oxygen in a, iron. References to early work on this subject are given in the previous publication.' EXPERIMENTAL Solubility Measurements. The oxygen solubility was determined by equilibrating cylindrical samples 0.3 in. diam by 14 in. long of zone-refined iron in water vapor-hydrogen gas mixtures. The zone-refined iron was prepared by B. F. Oliver of this laboratory, using an apparatus and technique described elsewhere.2'3 Six zone-melting passes were used to achieve a total impurity level of about 30 ppm. Of this 30 ppm, the combined nickel and cobalt content was about 20 ppm, oxygen was 4 ppm, and all oxidizable impurities less than 1 pprn each. A vertical resistance furnace wound with molybdenum wire was used for the experiments. The temperature was measured before and after each experiment with a Pt/Pt-10 pct Rh thermocouple. In the gas train, flow rates of hydrogen and argon were measured with capillary flow meters, and the resulting mixtures were passed through a column containing 90 pct oxalic acid dihydrate and 10 pct anhydrous oxalic acid to obtain predetermined ratios of H2O to H2. The vapor pressure of H2O above this mixture as a function of temperature is well-known.4 The exit gas was ana- lyzed periodically for H2O, and good agreement (+3 pct) with the calculated composition was obtained. The zone-refined iron specimens were held in the furnace for a sufficient length of time for equilibration, e.g., 18 hr at 1350°C and 1 week at 881°C, then quenched in a brine solution. After removing the surface oxide from the samples by machining, duplicate analyses were obtained by a combined vacuum fusion-infrared method; oxygen analysis was reproducible within 2 ppm. Permeability Measurements. The permeability of oxygen in alloys containing about 0.1 pct A1 was determined by internal oxidation and measurement of the subscale thickness as a function of time. The experimental alloys were prepared by adding aluminum to electrolytic iron (grade 104A plastiron) that had previously been vacuum-carbon deoxidized. The resulting ingots contained about 20 ppm O, 100 pprn C, 40 pprn Si, 50 ppm Mo, 20 ppm P, 20 ppm S, and 20 pprn Zr as the principal impurities. After hot rolling the ingots to 1-in.-thick slabs, specimens were machined from the stock in the form of rectangular plates, 4 by 5 by 2 in. The general procedure for the permeability experiments was the same as those for the solubility measurements. The specimens were cooled in a reducing atmosphere rather than quenched, however, in order to maintain a clean surface for measurement of the sub-scale thickness. This measurement was made on a polished cross section of each specimen, using a microscope with a micrometer stage. The inclusions formed at the lowest temperature 1033°C were too small to be seen with an optical microscope. An electron micrograph showing the size and shape of individual particles is shown in Fig. 1. The dark band in the picture is a boundary between two subgrains. The subscale thickness in these samples was measured with an optical microscope after heavily etching in 2 pct nital, which gave contrast between the subscale and the unoxidized zone.

Jan 1, 1968

By W. S. Row

This mine is operated at 4000 to 4500 tons daily through a single shaft, with one rock hoist and one senice hoist. Latest shaft construction is concrete with wooden dividers. Economics of drifters and air-leg drills are compared, as well as costs of shrinkage and sub-level stoping. Economy of large haulage equipment and underground crushing is shown. THE property of Kerr-Addison Gold Mines is located in the Larder Lake district of Ontario about 3 miles from the Quebec boundary on the highway between Kirkland Lake and Noranda. It is roughly 320 miles due north of Toronto and 365 miles north of Buffalo, N. Y. The property was staked in 1906 and after several development efforts finally came into continuous production at 500 tons per day in 1937. In 1939 the daily tonnage -was increased to 1200 and in 1941 to 2100 tons. At the end of the war, because of the shortage of labor, tonnage was down to 1100 tons per day, rising to 2200 in February 1947. A further plant expansion inaugurated in 1946 was completed by December 1948, bringing the capacity of the mine and mill to a production rate of 4000 tons per day. Current production, with 880 men employed, is 4400 tons per day. Changes in mining methods and equipment, required by the recently completed expansion program, have yielded interesting comparative results, some of which are described in this paper. Hoisting of ore and waste from the mine, as well as all service facilities for handling men and supplies underground, are provided for in a single vertical five-compartment shaft. Ore and waste are hoisted in 12½-ton skips in balance by a 14-ft diam hoist with drums 115 in. wide, grooved for 2?-in. wire ropes. This hoist, with a total rope pull of 85,000 lb, was designed to operate at a speed of 2600 ft per min to a depth of 4000 ft, hoisting 15 tons of ore in each skip. It is amplidyne-controlled and powered with dual drive dc motors of 2250-hp each, through flexible couplings to two pinion shafts, one on each side of the main gear. Each motor has a peak load rating of 4500-hp at point of greatest duty. Direct current power to the hoist motors is supplied from a motor generator set consisting of a 5000-hp synchronous motor driving two 1750-kw dc generators. The loading pockets used so far are at depths of 1500 and 2725 ft respectively. Consequently the present hoisting speed is 2000 ft per min and the skips capacity only 12½ tons. Now that the shaft has been deepened the new pockets at 3934 ft will be increasingly used so that the speed and the skip size will be increased up to original specifications as required. Some difficulty in meeting the required hoisting cycle is expected because of the shape of the skips. As now in use the cross-sectional dimensions of the inside of the skip are 4 ft 6 in. x 3 ft 8 in. To hold 121/2 tons, therefore, they are 14 ft 10 in. deep. Since the skips are the conventional overturning or Kim-berley type, considerable hoisting time is lost in retardation in entering the headframe dump and in acceleration when leaving. It is expected that to obtain the specified tonnage from this hoist when the skip size is increased to 15 tons it may be necessary to resort to bottom dump skips. This type of skip could reduce considerably the present excessive acceleration and retardation times. Analyses of the skip-hoisting operation are made monthly, and every effort is made to reduce controllable delays. For a nine-month period in 1951 such an analysis shows that the hoist was in operation 92.5 pct of the available time, which was allotted as shown in Table I. Overall hoisting costs, cage and skip, for the year 1951, averaged $0.168 per ton of ore milled. The mine is serviced entirely by means of a single cage, capacity 35 men or 15,700 lb, operating in con-

Jan 1, 1954

By R. J. Quigg, G. S. Doble

Commercial stress -relieved TD Nickel bar was shown to retain room- and elevated-temperature tensile strength after exposure up to 2501°F. Cold swaging increased both room -temperature and 2000°F tensile strength. After annealing at 2500°F the strengthening due to swaging was retained at 2000°F hilt eliminated at room temperature. Annealing produced changes in hardness and X-ray half peak width indicating the presence of recovery processes as 1071° as 1000°F but no recrystallization of swaged material was noted at any temperature. In contrast to swaging, rolling induced a recrystal-lized structure after annealing. The tensile strength of this recrystallized structure was comparable to the cold-worked condition. High-temperature tensile properties of as -received bar were highly anisotropic with the transverse tensile strength being one fifth the longitudinal value. The aniso-/ropy is affected by working direction and may he partially reversed by changing the direction of metal flow. The divergence in tensile strength, beginning above 550°F or- approximate one third the absolute melting point, is strain-rate dependent. T D Nickel is a commercial dispersion-hardened alloy containing 2 vol pct thoria. The dispersion, consisting of spherical particles 0.030 to 0.050 in diameter with an interparticle spacing of less than 1 is reported to maintain stable properties up to 2400°F.1 This stability of second phase results in maintenance of elevated-temperature strength at higher temperatures and longer times than normal nickel-base superalloys.2 The purpose of this paper is to describe the effect of various mechanical working operations on the strength and microstructural stability of TD Nickel bar. MATERIAL AND PROCEDURES All material used in this study was commercial TD Nickel bar. This material is produced by a chemical process which results in a nickel powder containing a dispersion of thoria particles. The powder is then pressed, sintered, extruded, and subsequently worked to bar stock. Three starting materials from three separate lots were used: as-extruded bar. 1-in.-diam stress-relieved bar, and 1/2-in.-diam stress-relieved bar. Since TD Nickel bar stock is cold-worked without a recrystalliza-tion anneal, the accumulated deformation or degree of cold work in these materials increases as the bar diameter decreases. Some of the 1/2-in.-diam bar was swaged to 1/4 in. diameter at room temperature in order to produce an as-worked condition for comparison with the stress-relieved stock. Tensile testing was performed on an Instron Tensile Tester at a constant crosshead speed of 0.020 in. per min. The 0.2 pct offset yield strength was measured from the load-crosshead movement plot. Specimen gage dimensions were 0.080 in. in diameter by 0.40 in. in length, producing a strain rate of approximately 0.050 min-1. Specimens were tested in air and heated within a resistance-wound furnace controlled to ±5°F. A 15-min soak at temperature was employed before testing. Samples were heat-treated in air and specimens machined after exposure with sufficient material removed to eliminate any surface contamination. X-ray line breadth was determined from a diffractometer scan of a transverse face of a bar using copper K, radiation. Metallographic preparation utilized standard mechanical polishing with Carapella's etch. Specimens for electron microscopy were electropolished in a 1:7 sulfuric/methaol solution and chromium-shadowed collodion replicas prepared. RESULTS AND DISCUSSION I) Effect of Elevated-Temperature Exposure on the properties of TD Nickel. The effect of various elevated-temperature exposures on the room-temperature tensile strength of TD Nickel is shown in Table I. In the unexposed condition the tensile strength, reduction in area, and hardness all increase with increasing accumulated deformation while the elongation decreases. After exposure at 2500°F the strength of all three materials decreases to about 65,000 psi and the elongations increase slightly. The apparent increase in strength of the 1-in. bar after a 2000°F treatment is probably experimental scatter. These results indicate that the room-temperature strengthening due to additional deformation is annealed out upon elevated-temperature exposure. In contrast to the room-temperature data, the 2000°F tensile strengths increase in order of increasing deformation even after exposure. Although some loss of strength occurs after exposure, much of the effect of working is still maintained at 2000°F. The room-temperature hardness after various

Jan 1, 1965

By D. W. White

The kinetics of isothermal transformation of ß-to-u uranium have been studied over a broad temperature range in alloys containing from 0.3 to 4.0 atomic pct Cr. Two modes of transformation are indicated by the existence of two C-curves in the TTT diagram. The upper temperature mode is regarded as a nucleation and growth mechanism, whose rate is controlled by diffusion of chromium in the ß phase matrix. The lower temperature mode is martensitic in nature. The M, temperature increases with decreasing chromium content, suggesting that the two transformation processes become synonymous in unalloyed uranium. URANIUM metal undergoes two allotropic transformations in the solid state. The a phase, orthorhombic in crystal structure,' is stable from room temperature up to about 665°C. The ß phase, characterized by a complex tetragonal structure,' prevails from 665" to about 770°C. The y phase is body-centered-cubic3 and is the stable modification from 770°C up to the melting point (about 1130"). In uranium of reasonable purity, neither of the two high temperature phases can be retained by quenching. However, the addition of certain alloying elements to uranium makes it possible to retain either the y-uranium phase or the ß-uranium phase at room temperature. Chromium alloyed in small amounts with uranium will permit retention of the ß-uranium phase in a metastable state at room temperature upon quenching from a ß-phase temperature.' From available information' on the equilibrium phase diagram for the U-Cr alloy system (Fig. I), it is to be expected that, however sluggish in its rate, the ß phase in such alloys should decompose eutectoidally to a phase and elemental chromium. It was the aim of this investigation to measure the rate and study the nature of this decomposition as a function of temperature and of chromium content. The investigation was reported in classified literature about five years ago and has recently been declassified for publication. In the meantime, there have appeared the papers of Holden,5 Mott and Haines,".' and Butcher and Rowe8 ealing with the metallography and the crystallography of the ß-to-a transformation in U-Cr alloys. These investigators have confirmed several of the phenomenological observations that will be described in the present paper and have examined in considerable detail certain aspects of the transformation and its mechanism. Although all of these investigations have concerned themselves experimentally with U-Cr alloys for the most part, an important consequence has been a clearer understanding of the nature of the ß-to-a transformation in uranium metal itself. Experimental Procedure This investigation dealt with a series of uranium alloys varying in chromium content from 0.3 to 4.0 atomic pct (0.066 to 0.90 weight pct). On five of the alloys, rates of isothermal transformation from the ß to the a phase were measured over a wide temperature range, leading to the development of TTT (time-temperature-transformation) diagrams. Transformation rates were measured over certain narrow temperature ranges on additional alloys. The alloys were prepared by vacuum melting and casting, using zircon or magnesia crucibles and graphite molds. Electrolytic chromium was used as the alloying addition, and the uranium was Mallin-ckrodt biscuit metal that had been vacuum remelted and cropped to remove many of the nonmetallic impurities that had floated to the top of the ingot. The ingots, 3/4 or 1 in. diam, were reduced in size by swaging. Alloys containing less than about 2 atomic pct Cr were swaged at 250° to 275°C, with initial and intermediate anneals at 550°C after every 75 pct reduction in area. Alloys with higher amounts of chromium were swaged at 550" to 600°C, although at the smaller sizes some of them were reduced by the procedure used on the more dilute alloys. Before use as test specimens, the swaged rods were annealed at 700" to 720°C for several hours, followed by slow furnace-cooling. The purpose of the anneal was to achieve the maximum amount of solution of the available chromium into the ß phase, as well as to remove extensive preferred orientation. The isothermal transformation rates were measured dilatometrically, using a quenching dilatometer and an experimental technique similar to those employed by Davenport and Bain in their original work on the transformation kinetics of austenite in

Jan 1, 1956

By F. H. Callaway, W. O. Keller

The various theories as to the well spacing-recovery relationship are reviewed in considerable detail and these theories analyzed in terms of their consistency with modern reservoir engineering concepts. It is concluded that the well spacing problem must be analyzed in terms of recovery efficiency and that a positive answer to the relation between well density and recovery efficiency is not available from direct comparisons of the production histories of wells and fields. The results of an engineering analysis designed to permit approximate calculation of recovery efficiencies as a function of well spacing in a depletion type reservoir from basic reservoir data is presented. Results of this type analysis indicate that the effect of well spacing on recovery efficiency in depletion type reservoirs can be expected to be very small. Limitations of this approach are pointed out, particularly with respect to its application in lenticular reservoirs. Testing techniques are outlined which should indicate whether or not a reservoir is continuous between wells and whether or not satisfactory drainage is being obtained with present spacings. A mass of data of this type indicates continuity to exist in most fields. INTRODUCTION The purpose of this paper is to review critically the engineering aspects of the well spacing problem, both from the standpoint of certain concepts and from the standpoint of reservoir mechanics. The well spacing problem is primarily an economic problem in which the optimum well density for a particular field is that density which will yield the greatest oil recovery consistent with justifiable development costs. The well spacing answer in terms of economic conditions, however, is extremely sensitive to the variation in recovery efficiency with well density. The variation in recovery efficiency with 'References given at end of paper. Manuscript received at the office of the Petroleum Branch October 2, 1949. Paper presented at the Petroleum Branch Meeting in San Antonio. Texas, October 5-7. 1949. well density is properly an engineering problem. Different opinions as to the correct answer to this engineering problem is the basis for most of the wide difference in opinion among various members of the industry as to optimum well spacing. This paper will be confined to the engineering problem of the relation between well density and ultimate oil recovery; economic considerations necessary for the evaluation of optimum well density for any particular field will not be discussed. The paper can be logically divided into two parts. The first part deals with a critical examination of the background and logic of the Cutler Rule and of similar studies by other authors and of related well spacing concepts. It is indicated that the variations in recoveries with well density* observed by Cutler and. others can be logically attributed to regional migration. Theoretical justification of the Cutler type relation wherein observed variations in recovery with well density in the same field is attributed to variations in recovery effiiency, in terms of energy relations, is refuted. The second part consists of a review of concepts of reservoir mechanics with regard to the well density-recovery relation. It is indicated that little variation of recovery efficiency with well density can be expected in a depletion type reservoir, unless lenticular conditions prevent communication between wells. The significance of field test data with regard to the existence or non-existence of lenticular conditions is pointed out. THE CUTLER RULE The first published article concerning the engineering aspects of the well spacing problem to receive wide attention was the work of W. W. Cutler' of the U. S. Bureau of Mines, published in 1924. In a study of decline curves from a large *The expression "well density" as utilized herein refers to the number of acres attributed to each well in a uniform well pattern, and is expressed in acres per well. The term "well spacing" Is utilized to denote the average distance between adjacent wells in a uniform well pattern. †Although the Cutler rule is treated critically in this discussion the authors intend no personal criticism of W. W. Cutler or of his hark The currently accepted concepts of reservoir mechanics were no": existent at the time of Cutler's work, as were even the moat basic tools (such as the bottom hole pressure bomb) for observing reservoir behavior.

Jan 1, 1950

By L. D. Lash, J. R. Ross

Discovery of scandium in the Vitro solvent extraction plant for uranium led to commercial recovery of the byproduct. Micro amounts of scandium were extracted with uranium by dodecyl phosphoric acid, but failed to follow ura-niuminto the hydrochloric acid strip solution and were eventually concentrated in the organic extractant. A fluoride strip system was developed to recover scandium from the solvent in concentrated form. High purity scandium oxide was then prepared in multi-pound lots by chemical separation techniques. The plant recovery operation, final product purification, and analytical procedures are described. Scandium is a pseudo-rare earth which is truly rare and expensive. It has special properties which may make it desirable even at the present price of $2750 per lb. Recently the price was lowered from $5000 per Ib which had prevailed since 1952, and it is anticipated that usage will be stimulated because of the lowered price. This metallic element is distributed widely in trace amounts in the rocks of the earth's crust. In addition to micro-amounts found in most uranium ores, concentrations of 50 to 100 ppm have been found in Colorado ferberite ore, lateritic nickel ore, heavy sandstone from Utah, Wyoming, and New Mexico, and various zircon sands and monazites from the western part of the U. S. Scandium has been found as an essential constituent of very few minerals, the most important being thortveitite, a scandium silicate. At the present time, this mineral commands a price more than twice that of gold. Chemically, scandium is in group 3A of the periodic table. It is closely associated with yttrium and the rare earths which it strongly resembles in its reactions. It has a valence of three and will form an insoluble hydroxide, fluoride, or oxalate under proper conditions, similar to the rare earths. Eight years before its discovery, scandium was predicted by Mendeleef who ascribed his eka-boron with properties nearly identical to the actual properties of scandium. Its position as the element with Atomic No. 21 and Atomic Weight 44.96 places it between calcium and titanium in Period 4 of the chart. The successful commercial application of scandium must depend on unique properties to justify use of this high cost substance. Greater consumption would allow additional price reductions, but scan- dium will remain a relatively high-priced commodity because of its inherent scarcity. Research reportedly has been oriented toward use of scandium as an agent to achieve high-temperature, low-density alloys with magnesium and tantalum.' Also, the U.S. Air Force sponsored a project for production of research amounts of pure scandium metal.' The oxide has been used experimentally in electronics, ceramics, and metallurgy. The various aspects of scandium are well covered in recent publications.s-5 CONCENTRATE RECOVERY Small amounts of scandium exist in uranium ores and are dissolved during an acid leach yielding up to 0.001 gpl Sc2O9. When Vitro converted their uranium plant from phosphate precipitation to solvent extraction: scandium was found to follow the uranium into the dodecyl phosphoric acid solvent (DDPA). However, scandium did not strip with uranium from the DDPA in hydrochloric acid, but remained in the solvent. Therefore, a concentration of scandium built up in the organic phase. Residues from the solvent were spectrographed by the U.S. Bureau of Mines and found to contain scandium. As a result of this discovery, provisions were made in the plant for recovery of scandium-bearing concentrates. Solvent extraction of uranium was added to a conventional acid leach process in a typical installation? The ore was crushed and ground, and then leached with dilute sulfuric acid. Addition of an oxidant such as sodium chlorate insured conversion of uranium minerals to a soluble form. At this point, the slurry was chemically reduced by a sulfide, such as sodium hydrosulfide, to remove substances such as ferric iron and molybdenum which were partially extracted by the solvent. The solids-liquid separation was accomplished by a four-stage counter cur rent decantation (CCD) thickener circuit. The uranium was extracted from pregnant liquor with 0.1M DDPA in kerosene and stripped with ION

Jan 1, 1961

By L. D. Mullins, W. R. Bartlett, R. H. Barham, W. L. Wahl

This paper describes an electrical model and its applicution to the analysis of four reservoirs in Saudi Arabia. The model has 2,501 mesh points and represents 35,000 sq miles of the Arab-D member. Details of modeling such as mesh size, control problems and standards of performance in matching reservoir history are discussed. The particular performance match achieved for the Arab-D rnember is presented. Details such as permeability barriers, aquifer depletion and iwerference between oil fields are given. The performance match realized in the Abqaiq pool is presented in detail. INTRODUCTION The resistor-capacitor network and associated control equipment described in this paper comprise an electrical analog of a reservoir system. Similar equipment has been used to study the transient response of reservoirs for many years. The unique feature of the model and application to be described is the extremely large size of the model and reservoir system, and the detail observed in simulating the reservoir with the model. The Arabian American Oil Co. first became interested in analog computers for simulation of oil reservoirs in 1949. Since that time, several models have been developed, each more elaborate and refined so that the reservoir system might be more closely simulated. The current model is the latest in a series designed, built and operated by the Field Research Laboratory of Socony Mobil Oil Co. in collaboration with Aramco. It has been and continues to be used to study the regional performance of the Arab-D member limestone reservoir. The Arab-D member is one of the Middle East's most prolific producing horizons.. THE MODEL The theory of simulating a reservoir system with an electrical system has been presented in the literature.1-5 Therefore, this paper will not discuss the theoretical aspect of the problem except to point out the correspondence between the fluid system and electrical system, as shown in Table 1. In general, the complete model is made up of input devices, output devices, central control and a resistance-capacitance (RC) network. At times, the RC network alone is referred to as the "model". However, it should be evident from the text which meaning is attached to the word "model". A discussion of the equipment follows. THE RESISTANCE-CAPACITANCE NETWORK The RC network consists of 2,501 capacitance decades interconnected through 4,900 resistance decades. The components are arranged to form a rectangular network of 2,501 mesh points in a 41- X 61-mesh array. Imposing the mesh grid system on the continuous reservoir system divides the reservoir into discrete areal segments. These discrete segments may be of various sizes. More precisely, the mesh size need not be uniform throughout the model. The RC network is fabricated in two sections which are connected at the top. An inside view of the "tunnel" formed by the two sections is shown in Fig. 1. The height and width of the tunnel are shown in the figure. Numerals appear along the bottom and along the back opening of the tunnel. These numbers denote the x and y co-ordinate positions of mesh points. Fig. 2 presents a rear view of one-half the model. The length dimensions of the model, as well as a rear view of the capacitor decades, are shown in this figure. The control dials used in adjusting the resistance and capacitance values on the model can be seen in the enlarged portion of the model shown in Fig. 3. The electrical capacity at any mesh point can range from 0 to 1.0 microfarads set to the nearest tenth of a microfarad. The electric resistance connecting any two mesh points can range from 0 to 9,990,000 ohms set to the nearest 1,000 ohms. External capacitors may be added to any or all mesh points if the need arises. The values of electrical resistance and capacitance are adjusted manually by manipulating the two types of decade units. INPUT EQUIPMENT A considerable quantity of equipment is used to control the input to the RC network. These input devices are

By F. D. Rosi

The plastic properties of extended silver and copper crystals of varying purity were studied as a function of crystal orientation in the early stages of flow. Variations in the gross shape of the shear stress-shear diagram and in the properties of critical Variationsshear stress and shear-hardening coefficient were correlated with changes in slip-band developments. The phenomenon of work hardening is discussed in terms of the existing dislocation theory. IT appears certain from the early studies on the deformation characteristics in metal crystals1-3 that plastic flow takes place in a preferred crystallo-graphic slip system which is determined by the geometry of the crystal (law of maximum shear stress), and that the value of shear stress for this system is independent of crystal orientation (law of critical shear stress). Experimentally, it has been demonstrated further that the law of critical shear stress can be extended to include extensive plastic flow.&apos; Thus, the shear-hardening coefficient, which is defined as the slope of the shear stress-shear curve, also is considered to be independent of orientation. It is noteworthy that deviations from this empirical shear-hardening law have been reported in cubic crystals whose initial orientation favors slip on more than two systems.&apos; Moreover, this law appears to have been derived from stress-strain data relating to relatively high values of shear strain (0.5 to 4), where widespread slip and complex distortions can be expected, regardless of crystal orientation. Since existing data indicate that the strain inhomogeneity in a crystal is manifested particularly in the early stages of flow, it would appear that a more exacting test as to the fundamental nature of the shear-hardening law would be to investigate systematically the shape of the stress-strain curve as a function of crystal orientation in the earlier stages of deformation. With regard to the general form of the shear stress-shear curve for cubic crystals, early studies show a parabolic hardening law, where the shear 1 stress is proportional to the square root of the shear-strain. Since this law was predicted theoretically by Taylor" in his original dislocation model for hard- ening, it has been accepted widely as a fundamental flow characteristic of cubic metals. However, it was recently pointed out by Masing6 hat the parabolic law is not the elementary form of hardening in cubic crystals, but instead is a consequence of complexities in the flow process (e. g., deformation bands and unpredicted secondary slip). Thus, in the very early stages of deformation (< 2 pct extension) where the occurrence of such complexities is unlikely, a different strain-hardening behavior might be anticipated. This view is supported by the recent work of Rosi and Mathewson7 on high purity aluminum where a linear law was obtained for extensions up to 2 pct. A linear hardening over a wider range of deformation also was reported by Rohm and Kochendorfer8 ho deformed aluminum crystals under conditions approximating pure shear. Even more pertinent is the recent evidence of Masing and Raffelsieper9 on high purity aluminum crystals. It was found that for crystals having initial orientations near a <l00> or <1ll> axis, a high hardening was obtained, whereas crystals with a <110> orientation exhibited a low and linear hardening curve followed by a region of more rapid hardening. Since much still remains obscure concerning the details of strain hardening as well as slip-band formation in face-centered-cubic crystals in the early stages of deformation, the present study was undertaken to evaluate the effect of crystal orientation on these two important manifestations of glide. It is important to note here that at the time of this study, Lucke and Lange11 presented information on the orientation-dependence of the shape of the strain-hardening curve in aluminum of various purities. Their work, which essentially represents an extension of that of Masing and Raffelsieper, in many respects is parallel to that of the present study. Experimental Procedure Production of Single Crystals: Single crystals of silver and copper of varying purity were used in

Jan 1, 1955

By C. E. Lundin, D. T. Klodt

The binary alloy systems, Y-Ti, Y-Zr, and Y-Hf, have been investigated throughout their entire composition regions. There is no compound formation in any of the systems, and each system is characterized by a single eutectic reaction. The eutectic compositions and temperatures are as follows: A eutectoid reaction pct Y and 870°C occurs in the Y-Ti system, whereas a peritectoid reaction,: pct Y and 880°C occurs in the Y-Zr system. Peri-tectic-type reactions at temperatures above the eutectic levels are postulated for the yttrium and hafnium transfovmations. The development of the technology of yttrium has been given considerable attention during the past few years, and studies of binary phase equilibria have, of course, taken a prominent position in this development. In many respects yttrium, in the third group of metals of the periodic table, is similar to the adjacent group of metals, titanium, zirconium, and hafnium, and the knowledge of the phase relationships of yttrium with these metals is basic to their technology. MATERIALS AND EXPERIMENTAL PROCEDURES Materials. The metals for this investigation were supplied by the General Electric Co., Aircraft Nuclear Propulsion Department. The yttrium was in the form of an arc-melted ingot, and the other metals were in the form of high-purity, iodide-Process crystal bar. Table I lists the purities of these materials. Alloy Preparation. Melting was done by conventional techniques in a nonconsumable electrode arc furnace in an atmosphere of purified argon. Melting conditions for each binary system were the same. Each alloy button was inverted and remelted several times to assure homogeneity. Accurate weights of the charges and resultant alloy buttons were obtained to indicate deviations from intended compositions. No chemical analyses were obtained since melting weight losses were consistently in the range of 0.1 to 0.2 pct of the total weight. 10- or 20-g buttons for each 5.0 wt pct composition increment were melted to survey the three individual alloy systems. Additional alloys differing in composition by 1.0 or 0.1 wt pct increments were also melted to study selected regions of the systems. Metallograpllic Techniques. Standard metallo-graphic techniques were followed for mounting and rough grinding. Preliminary polishing was accomplished using 6-u diamond paste as an abrasive on a Metcloth Lap. Final polishing was done on a Microcloth-covered wheel using 1-u diamond abrasive paste. Purified kerosene was used as a lubricant for both polishing stages. • sothermal- Annealing. Alloys were sectioned for as-cast structlure examinations and then homogenized in preparation for isothermal-annealing treatments. Homo{:enization was accomplished by cold pressing the alloy buttons followed by 72-hr anneals at 1100c. The alloys were encapsulated in Vycor or quartz for the homogenization treatments or for isothermal anneals. Resistance-wound or resistance-element tube furnaces were used for the annealing treatments. The homogenized alloy buttons were cold rolled until cracking occurred or until a -in. specimen thickness was obtained. Small -in. square) specimens for the isothermal anneals were then sawed from the alloys. Each specimen was wrapped in tantalum foil before being sealed in the capsule. Temperatures during the anneals were controlled The time at temperature necessary to equilibrate the structures during the anneals was determined for each alloy system by holding triplicate specimens of alloys at a constant temperature for three different periotls. The specimens were quenched and examined microscopically to determine the number and amounts of phases present in the micro-structure as a function of time. Melting Studies. Eutectic temperatures of the three alloy systems were established from the results of incipient-melting studies conducted on as-cast alloys. Specimens to be melted were suspended on a tungsten wire inside a graphite cylinder placed in a glass vacuum chamber. An optical pyrometer was used to follow the temperature of the specimen as it was inductively heated in a high vacuum. The temperatures were corrected for emissivity losses by standardizing the pyrometer with known-melting-point metals. Accuracy of the temperature measurements is estimated to be + 10°C. The melting point of the yttrium was determined to be 1550°C by this technique. The invariant-temperature levels were also checked by an anneal-quench technique. This technique consists of annealing a series of

Jan 1, 1962

By T. E. Leontis

Data are presented in this paper to show that addition of zirconium to sand-cast Mg-Th alloys effects a marked decrease in the grain size of these alloys which is accompanied by a significant increase in the mechanical properties over the entire range of thorium content investigated. The beneficial effect of zirconium on the strength properties is maintained at elevated temperatures up to 700°F. In addition the alloys exhibit exceptionally high creep resistance at temperatures up to 600°F. Zirconium does not greatly improve the strength or creep characteristics of extruded Mg-&apos;Th alloys. Cerium is not a desirable addition to Mg-Th-Zr alloys. IN a previous paper,&apos; it was shown that addition of thorium to magnesium imparts exceptionally high resistance to creep at elevated temperatures both in the sand-cast and in the extruded states. The large grain size of the sand-cast alloys, however, renders them of questionable value as engineering materials. Sauerwald² showed that the grain size can be reduced effectively by the addition of zirconium. Results of a detailed study of the properties of Mg-Th-Zr alloys over a wide range of thorium content are presented in this paper. In accordance with the preliminary findings of Sauerwald,² it is shown here that Mg-Th-Zr alloys possess the unusual combination of fine grain size and a high level of strength and creep resistance at elevated temperatures. Some information on the effect of cerium on the properties of Mg-Th-Zr alloys is presented also. Effect of Th on Solubility of Zr in Molten Mg Sand-cast test bars and 3 in. diam extrusion billets of Mg-Th-Zr and Mg-Th-Ce-Zr alloys* were pre- pared according to the procedures described in the previous paper.&apos; The zirconium was added in the form of sponge metal as supplied by the Bureau of Mines.&apos; The maximum amount of zirconium that usually can be introduced into magnesium at the customary alloying temperature of 1350° F is about 0.7 pct. The analyses in Table I clearly show that thorium in- creases the solubility of zirconium in liquid magnesium. The tabulated zirconium contents are designated as "acid soluble;" this serves to distinguish these values from the small amount of zirconium that is not dissolved when the alloy is subjected to the action of a dilute acid solution. The "acid-insoluble" zirconium is believed to be ineffective as an alloying ingredient. The acid-insoluble zirconium contents ranged between 0.03 and 0.16 pct in the present alloys, the tendency was toward higher values in alloys with higher thorium content. In contrast to the effect of thorium, cerium decreases the solubility of zirconium in magnesium. This is shown by the three Mg-Th-Ce-Zr alloyst in- cluded in Table I and stands in agreement with the observations of Nelson and Stricter".&apos; on Mg-misch-metal-Zr alloys. Effect of Zr on Grain Size of Mg-Th Alloys The potent effect of zirconium as a grain refiner has been demonstrated for many types of magnesium alloys.3-8 Of greatest importance to date are Mg-Zn-Zr alloys5,6,8 and Mg-mischmetal-Zr alloys.3,4,7 Zirconium has also been found to exert a marked grain-refining action on Mg-Th alloys. All the Mg-Th-Zr alloys cast in the form of ½ in. diam test bars have an exceedingly fine grain size (Table I). Reference to the previous paper&apos; will show that binary Mg-Th alloys containing up to 6 pct Th are almost completely columnar even in the M in. diam reduced section of a test bar, and that 10 to 50 pct Th alloys have an equiaxed grain structure of 0.03 to 0.08 in. The data in Table I also show that addition of cerium to Mg-Th-Zr alloys has no effect on the grain size. In addition to increasing the strength properties, the fine grain size of Mg-Th-Zr alloys

Jan 1, 1953

By W. M. Robertson

The kinetics of grain boundary groove formation on copper surfaces immersed in liquid lead have been studied over the temperature range of 400° to 900°C. The groove widths were Proportional to the cube root of the annealing time, indicating that the diffusion of copper through the saturated liquid-lead solution is the mechanism by which grooves form. The rate constant for the process can be calculated by a theory due to Mullins. Using published data for the solubility of copper in liquid lead, for the interfacial energy of the solid copper-liquid lead interface, and for the diffusion coefficient of copper in liquid lead, the calculated rate constants almost exactly reproduce the measured values over the entire temperature range. The decay of scratches placed on copper surfaces has also been studied. The rate constant for scratch decay agrees with that for grain boundary groove growth, though scratch decay is sensitive to convection currents in the liquid. The interaction of solid and liquid metals has been studied extensively and has been found to be rather complex. Many of the studies have been complicated by a host of competing effects, including temperature gradients, concentration gradients, the formation of one or more intermetallic phases, natural or forced convection, and the presence in both the solid and liquid of considerable amounts of impurities and alloying elements. Recently theories have been developed of changes in surface profiles driven by capillary forces,&apos; which allow the interaction of the solid and liquid to be analyzed quite directly. The present paper reports a study of the formation of grain boundary grooves on pure copper immersed in liquid lead, which allows the theory to be checked quantitatively. The Cu-Pb equilibrium diagram is quite simple: there are no intermetallic compounds, copper is just slightly soluble in liquid lead, and lead is almost completely insoluble in solid copper.2 The Cu-Pb system has been studied extensively,3-9 and all of the quantities—interfacial energy, diffusion coefficients, and equilibrium solubilities-necessary to calculate the rate of groove growth by a volume-diffusion mechanism are known. The kinetics of grain boundary grooving and scratch smoothing have been studied on the noble metals and the iron group metals in a reducing atmosphere or in vacuum.10 The main interest of these studies has been the determination of surface-diffusion coefficients at metal-gas interfaces using the theories developed by Mullins.1 The present paper uses similar methods for the study of diffusion processes at the interface between two condensed phases. There has been one previous study" of the kinetics of groove growth in a solid-liquid system, which, however, was troubled by the fact that neither interface energies nor diffusion coefficients were known in the Ni-S system studied. THEORY The theory of grain boundary groove growth has been developed by Mullins for the cases of volume diffusion," surface diffusion," and a combination of the two processes.14 He has also analyzed the kinetics of the flattening of a scratched surface by these processes.l5,l6 Several assumptions and approximations were used in the derivations of the surface profile shapes. The applicability of these assumptions and approximations to the present system will be considered in the discussion. At the intersection of a grain boundary with an initially flat interface the equilibrium between the interfacial energy and the grain boundary energy establishes an equilibrium groove angle. This induces curvatures in the interface. The chemical potential of material at a curved interface is higher than at a flat interface, so that material moves away from the region of the grain boundary. Mullins&apos; calculations indicated that the groove profile would be similar to that shown schematically in Fig. 1. Small humps form above the level of the original flat surface. For a volume-diffusion mechanism the separation, w, of these humps at a time, t, is given by and where co is the equilibrium concentration of the solid in the liquid, y, the solid-liquid interfacial free energy, O the volume occupied by a solute atom in the liquid, D the diffusion coefficient of the solid in the liquid, and kT has its usual meaning. For a surface-diffusion mechanism the groove width is proportional to the fourth root of the time. For grooves forming by a combined surface and volume-diffusion mechanism the exponent of the

Jan 1, 1965

By P. G. Shewmon

Radioactive MgZA has been used to study the rate of self-diffusion in oriented single crystals of magnesium in the temperature range 468O to 635OC. The diffusion coefficients parallel and perpendicular to the c-axis are: Dl, = 1.0 exp (—32,200IRT) cm2 per sec and Dl = 1.5 exp (—32,500IR T) cm Qer sec. The ratio Dl/Dll was found to vary from 1.13 at 468 to 1.24 at 575 C. Assuming a vacancy mechanism, an explanation of this aniso-tropy of diffusion follows from a consideration of the difference in the saddle points for diffusion in and out of the basal plane. RECENT discovery of radioactive Mg2"&apos;-&apos; has made possible the study of self-diffusion in magnesium. The experimental procedure and the results of a study of diffusion in polycrystalline magnesium have been described in an earlier paper.V he present work is an application of the same techniques to the study of self-diffusion in oriented single crystals of magnesium. In the general diffusion problem the diffusion coefficient is a second order tensor relating the two vectors, the diffusion flux, and the concentration gradient. In a hexagonal lattice, such as magnesium, the complete determination of the diffusion coefficient D as a function of direction in the lattice requires a knowledge of D,, and D,, i.e., the diffusion coefficients parallel and perpendicular to the c-axis, respectively. It can be proven quite generally that in a hexagonal lattice D is independent of direction in the basal plane, and that out of the basal plane it varies with 0, the angle between the c-axis and the direction of diffusion, according to the equation D(B) = D,,cos2B + D,sin2B. [I] The proof of Eq. 1 depends only upon the symmetry elements of the hexagonal lattice and upon the transformation properties of a second order tensor." Therefore, Eq. 1 holds for any mechanism of diffusion and any c/a ratio. Experimental Procedure The experimental procedure used with polycrystalline specimens can be briefly outlined as follows. Radioactive Mg" was produced by bombarding a NaCl crystal with 350 mev protons and was chemically separated from the target as MgO. The Mg" was then vapor deposited on a specially cleaned magnesium specimen by heating the MgO on a tantalum ribbon in a vacuum. During the diffusion treatment, oxidation and vapor loss of the radioactive material were minimized by annealing the samples in pairs with the active faces in contact, each pair being inside a magnesium container, which was in turn surrounded by an argon atmosphere in a sealed Pyrex tube. The distance-activity profiles were obtained by measuring the activity of thin sections cut parallel to the original interface with a lathe. The only technique which was peculiar to this work was the preparation and orientation of the single crystal specimens. The single crystals used in this work were grown by E. C. Burke of the Dow Chemical Co., using a modified Bridgman method, in which the furnace and specimen were stationary while the temperature gradient moved.&apos; In growing these crystals the starting material was distilled magnesium, the crucibles were machined from Acheson electrode graphite, and the furnace atmosphere was tank argon. The crystals were grown from sublimed magnesium with the following analysis: 0.0002 pct Al, 0.0017 pct Fe, 0.0009 pct Mn, 0.0001 pct Ni, 0.0006 pct Pb, and less than 0.01 pct Ca, 0.0001 pct Cu, 0.001 pct Si, 0.001 pct Sn, and 0.02 pct Zn. The two crystals used were roughly lh in. diam and eight in. long. The c-axis made angles of about 7" and 78", respectively, with the specimen axes. If the values of D obtained by the use of these two crystals are taken equal to D,, and D,, respectively, the error introduced by this assumption is less than 1 pct. This can be shown by combining Eq. 1, the identity sin% + cos&apos;8 = 1, and the experimental fact that DJDn in magnesium was always less than 1.25.

Jan 1, 1957

By R. M. N. Pelloux

This study of aluminum-copper alloys had two aims: 1) To determine the effect of the amount and distribution of a second phase, CuAl2, on the creep-rupture strength, ductility, and fracture characteristics of the alloys. The work of Gemmell and grant&apos; on single-phase aluminum-copper alloys provided a basis for the present study. 2) To attempt to provide a relation between the microstructure and strength of two-phase alloys deformed at comparatively high temperatures (greater than 0.45 T,). The creep behavior of the two-phase magnesium alloys Mg;Ce and Mg-A1, has been treated by Roberts. 9 In work reported by Sully and Hardy4 and by Underwood, Marsh, and Manning~ on A1-Cu two-phase alloys, and also in a portion of the work of Gemmell and grant,&apos; aging took place during the creep tests. &apos;In the present work, overaged aluminum-copper alloys were subjected to creep deformation at two temperatures, 500 and 700OF. The overaging treatments to produce the precipitate dispersions were performed prior to the test, at temperatures which were the same as the ultimate respective test temperatures. Hence, the present study is concerned with the creep behavior of stable (in contrast to "underaged") two-phase A1-Cu alloys, i.e., alloys in which no depletion of the solid-solution matrix occurred during: creep. MATERIALS AND PROCEDURE A 2 and a 3 pct Cu alloy, supplied by Alcoa, were studied; Table I shows the compositions. The grain size of the specimens, 0.9 to 1.0 mm, was achieved by annealing the machined test bars for 2 hr at 1000°F, followed by furnace-cooling to 900°F, and homogenizing for 4 hr. Both compositions are in the single-phase condition at 900°F. Two types of overaged dispersions, termed "over-aged I" and "overaged 11" were prepared after the grain size and the homogenization anneals. The overaged I alloys were prepared by quenching to room temperature after homogenization, aging at either 500&apos; or 700°F for 72 hr, and air-cooling to room temperature. The overaged I1 alloys were prepared by furnace-cooling after homogenization, to either 500&apos; or 700°F, and holding at the necessary temperature for 72 hr. The times for furnace-cooling from 900°F to 700° and 500°F were, respectively, about 2 and 3.5 hr. The structures of the A1-2 pct Cu alloys are shown in Fig. 1 (overaged I) and in Fig. 2 (overaged 11). A comparison of Figs. 1 and 2 shows that in the overaged I alloys the precipitate particles along the grain boundaries are much more closely spaced and the grain boundaries are straighter than they are in the overaged I1 alloys. Further, the particle size and spacing in the grains are smaller than in the overaged I1 alloys. Microstructures of the A1-3 pct Cu alloys have not been shown; the structures of these alloys differed from those of the A1-2 pct Cu alloys only in that the distribution density of the particles was greater. The creep specimens had a gage section 1 in. long with a diameter of 0.155 to 0.195 in. Before testing, specimens were electropolished in a solution of 100 cc glacial acetic acid, and 30 cc of 60 pct perchloric acid, at 40&apos; to 50°F, at 24 v. The specimens were kept refrigerated prior to testing to avoid precipitation at room temperature. Constant stress creep tests were conducted; the load was applied 75 min after heating of the specimens to test temperature had begun. EXPERIMENTAL RESULTS Creep-Rupture—Fig. 3 shows the log stress-log rupture life plotfor the overaged alloys studied, and also for the underaged A1-2 pct Cu alloy.&apos; At 700°F, the stress-rupture life relationship is nearly independent of both the amount of precipitate (i.e., composition) and of the type of overaging treatment (i.e., precipitate dispersion). At 500°F it is apparent that the increase in rupture life that was ex-

Jan 1, 1960

By H. M. Otte, A. L. Esquivel

A new leasl-squares method is Presented for determining lattice parameters of hexagonal or tetragonul structures. The method is adapted for use on electronic computers and involves a reiterative procedure. The correction factor employed raries linearly with the lattice parameter, a (determined from the Brag, angle). In contrast, Cohen&apos;s method and recent modifications of it use a correction factor that varies incersely as the squure of the lattice paramneter, a. While the recent modifications attempt to improve the precision of the extrapolated lattice parameter, a, (or-cu). by stressing the importance of the weighting factor. the present approach emphasizes the need for choosing the correct extrapolation function. A comparison between the present method (the Linear method) and Cohen&apos;s method indicates that the Linear method may be more appropriale in certain cases. through a priori no critertion appears to he available for making a chorce between the methods. The size of hexagonal and tetragonal crystal lattices is determined by two parameters, a, and c,. Although in principle the two lattice parameters can be determined independently from reflections for which h - k = 0 and 1 = 0, respectively, in practice this may be inconvenient (because of the angular positions at which these reflections may occur) or not easily possible (because of low intensity). Furthermore, if a high precision or accuracy is required, the limited number of reflections of this type available, particularly in the high-angle region, is not sufficient for the necessary corrections (mainly due to absorption) to be determined with accuracy. Several methods1-7,11-13 have been proposed employing all reflections, to obtain the optimum values, a. and co, either by a trial and error procedure or a least-squares fit. Of the latter method, cohen&apos;s5 is the best known one since it provides explicit expressions for the optimum a. and c,. However, Cohen&apos;s method is only strictly valid if an extrapolation function is used that varies linearly with l/a2 or lie2 (see Section 3), a requirement that does not appear to be generally appreciated. On the other hand, all the better known and more widely used A recent trial and error method was proposed by Massalski and King8,7 who computed extensive auxiliary tables of axial ratios vs the functions A = [(4/3)(h2 + hk +k2) + l2+(a/c)2] and C = A(c/a)2 used in computing a and c values from the observed Bragg angles. These values of a and c were then plotted against a function which permitted linear extrapolation. As a criteria; for the "optimum" values, Massalski and King rely upon a visual fitting of the line through points representing reflections of low 1-index points to compute the extrapolated value of ao and high 1-index reflections to obtain CO. The successive computations and graphical plotting required to reach the "optimum" value are quite lengthy and tedious even on a desk calculator and no quantitative assurance is obtained of having in fact selected the optimum value.* If the method of Massalski and King is used on an electronic computer, then their published tables become redundant and a least-squares fit becomes a natural selection for the choice of optimum values. Such an approach will be called the Linear method. For work now in progress on the effect of certain physical variables on the lattice parameters of hexagonal crystals, it has become essential to determine the confidence limits of small changes in the lattice parameters. Since extrapolation functions that varied linearly with a and c actually also appeared to vary linearly with l/a2 or l/c2 when tested against published as well as our data, a comparison of Cohen&apos;s method and the Linear method was considered desirable (Sections 3 and 4). For the latter method an electronic computer was required since a reiterative procedure to obtain the optimum ao and co values had to be employed. The purpose of this paper is to describe the principles of the Linear method, illustrate its application, and compare it with Cohen&apos;s method. 1) THE LINEAR METHOD The standard practice in obtaining the lattice parameters in the Debye-Scherrer method is to

Jan 1, 1965

By F. M. Smith, R. H. Moore, J. R. Morrey

Electrodiffusion in y cerium reported by Henrie has been confirmed and a Preliminary estimate made of the relative rates of electrodiffusion of iron, cobalt, and nickel. These diffuse to the anode at rates decreasing in that order. In addition, copper and manganese exhibit slow, but detectable, diffusion to the anode and molybdenum exhibits detectable diffusion to the cathode. The electrodiffusion of carbon, .zirconium, antimony, magnesium , and silicon in y cerium could not be detected. Iron and cobalt diffuse in y cerium at rates proportional to the current density and with no apparent dependence on temperature. Decreasing polarization of iron and cobalt with increasing temperature, which cancels the expected rate increase, would account for this behavior. The electrodiffusion rate of iron in y uranium and in E plutonium has been measured. Diffusion of iron is anode-directed. Tin was found to diffuse to the cathode, in y uranium, at an appreciable rate. In all of these solvent metals, negative ions diffuse to the anode and positive ions to the cathode. The potential field effect appears to account satisfactorily for these results. FROM early experimental work summarized by Jost1 and Seith,2 the driving force for electrodiffusion was attributed to the potential field acting on ions in a metal. More recently, Heuman,3 Wever,4 and Huntington5 have shown that momentum interchange between conduction electrons and mobile entities in the metal contributes to electrodiffusion. Electron momentum interchange is anodically directed and the direction of diffusion resulting from the field force is dependent upon the charge on the diffusing entity. These two effects may either reinforce or oppose each other. Glinchuk6 has pointed out that momentum transfer in defect conductors should be cathode-directed and this appears to be the case as demonstrated by wever&apos;s4 work on iron. Barnett&apos;s7 work, on the other hand, indicates that, even in defect conductors, electrons show a negative E/m ratio when accelerated with respect to the lattice and should lead to anode-directed momentum transfer. In discussing this problem, Wever and seith8 suggest that defect electrons interact preferentially with activated ions so as to allow a net movement toward the cathode while still maintaining an electron momentum transfer in the anode direction. Williams and Huffine9 and Henriel0 have demonstrated that electrodiffusion may be useful for purification of yttrium and cerium. In yttrium, Williams and Huffine note that movement of several metallic impurities toward the anode is in keeping with observations in most other metallic systems and indicates that yttrium remains a normal electronic conductor at least to 1230°C. Close inspection of their data shows, however, that oxygen, nitrogen, and the transition elements diffused toward the anode, while nontransition elements diffused toward the cathode. This suggests that potential field effects may have been appreciable. The present work was concerned with the applicability of electrodiffusion as a technique for purification of plutonium, but, because of the obvious hazard inherent in work with this metal, experiments to develop the technique were carried out using cerium and uranium. The results of electrodiffusion measurements on these metals and on plutonium are reported here. EXPERIMENTAL The metal specimens prepared for this work were 6 in. long, 1/4 to 1/2 in. wide, and 1/16 to 3/32 in. thick. The uranium specimens were machined from a bar which analyzed 310 ppm Fe and the electrodiffusion of iron was followed by spectrographic and by chemical analysis. Cerium and plutonium specimens were cut from sheet rolled from ingots obtained from molten salt-metal equilibrations during which radioactive tracers were introduced. The electrodiffusion of the tracers was subsequently determined by counting methods. The specimens were electrolyzed between nickel electrodes containing resistance heaters used to equalize the specimen and electrode temperatures, thereby reducing thermal gradients. The temperature of the electrodes adjacent to the ends of the specimen was measured with chromel-alumel thermocouples which were connected to the heater controls. The surface temperature of the specimen at a point midway between the electrodes was measured with a sapphire rod pyrometer, the output of which controlled the dc power supply. This assembly was enclosed within an evacuable chamber containing a quartz viewing window. The temperature of the specimen over its entire length could be scanned with a portable pyrometer through

Jan 1, 1965

By Y. C. Liu, G. A. Alers

Using X-ray pole-figure information and the single-crystal elastic constants, the angular variation of an elastic modulus in a polycrystal can be calculated and compared to measured clalues. This procedure has been used in the past to provide supporting ecidence for a particular choice of ideal orientations in the description o the X-ray pole figure. Since it is well-known that the absolute value oj an elastic modlus oj a poly crystal cannot be acczrralely calculated from the single-crystal elastic constants, there exists a serious question about the reliability oj this modulus method in the study of textures. This paper deriz-es sez3eral simple fornzulae for the ntzgular lariatiion of Young&apos;s modulus in the plane o a rolled sheet sing the same ssuinptions which lead to the lack oj detinztion of the absolute c&apos;alre OJ the elastic ,nodulus. The vesults show that, although the absolute isallre oj Young&apos;s modulus depends strongly on the assumptions made, the shape of the modulus vs angle curve is not very sensitive to the assumptions and thus can be used reliably in texture studies. Exatzples oj&apos; using this criteriotz are illustrated in the text. NeARLY all poly crystalline materials have some preferred orientation in the arrangement of their grains and hence exhibit anisotropy in their properties. This preferred orientation is usually measured and studied by X-rays which yield detailed information on the statistical distribution of grain orientations in the form of pole figures. The usefulness of these pole figures in theories of texture formation and in predictions of properties has come to depend almost entirely on the characterization of the pole figure by one or more ideal orientations. Unfortunately, this characterization is not unique and different authors often present different ideal orientations to characterize a given pole figure. In order to distinguish between these different choices of ideal orientations, it is necessary to go beyond X-rays and consider other physical properties which reflect the texture&apos; simply because any choice of ideal orientations must predict correctly the observed anisotropy in all physical properties. The most common example of this procedure has made use of the angular variation of Young&apos;s modulus with respect to the rolling direction in the plane of a rolled sheet.3 4 Here the anisotropy can be measured easily and it can also be calculated from the single-crystal elastic constants and the chosen ideal orientation. Unfortunately the methods used to calculate this anisotropy were chosen for their simplicity rather than for their mathematical rigor so that there exists a serious question as to the validity of conclusions reached by this modulus method. It is well-known5 that the absolute value of the Young&apos;s modulus of a polycrystalline aggregate cannot be calculated very accurately because different mathematical averages over the grains yield different results. It is one purpose of this paper to examine the effect of different averaging procedures on the calculated anisotropy of Young&apos;s modulus in the rolling plane of rolled sheets in order to see if this property can be used reliably in texture studies. This particular modulus and type of material were chosen because the modulus is easily measured and rolled sheet is technologically important. The results show that, although different averages yield different absolute values for Young&apos;s modulus, the shape of the modulus vs angle curve is not very sensitive to the averaging procedure and thus can be used as a criterion to check the various ideal orientations used to characterize the X-ray pole figure. Examples of this checking procedure are given in the final section. Another purpose of this paper is to examine the possibility of using the anisotropy of Young&apos;s modulus as an indicator of texture without reference to pole figures or ideal orientations. Such a use would require that different textures yield quite different shapes for the modulus vs angle curve so that the distinction between textures would be quite clear. The experimental results presented in the final section indicate that there is easily enough variation in shapes to allow modulus measurements to be useful texture indicators, par-

Jan 1, 1967

By T. W. Watson, D. R. Flynn

Measurements have been made of the thermal conductivity and electrical resistivity of two specimens of 0.005-cm (2-mil) Be-Cufoil over the temperature range -140° to +200°C. The thermal cmductivity of Be-Cu Alloy 125 was found to be significantly higher than that of Alloy 25, which had a higher impurity content. The thermal conductivity and electrical resistivity values obtained were in concordance with the Smith and Palmer relation for copper alloys which states that ? = 0.0239 (T/p) + 0.075 where A is thermal conductivity (W cm-&apos; deg-&apos;), p is electrical resistivity (microhm-cm), and T is absolute temperature (OK) , indicating that the Smith and Palmer relation can be used to predict the thermal conductivity of this type of Be-Cu alloy over the temperature range -140" to + 200°C to within an accuracy suitable for most engineering applications. THE National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, Md., requested the National Bureau of Standards to measure the thermal conductivity of 0.005-cm Be-Cu foil which was to be used to fabricate antennae for use in Radio Astronomy Explorer space craft. It was felt that measurements had to be made on the actual antenna material, rather than on a thick bar of similar material, since the cold-working and age-hardening properties of the alloy would make it very difficult, if not impossible, to place a thick bar in the same metallurgical state as the 0.005-cm material. As discussed in Section 111 of this paper, the thermal conductivity of many copper alloys can be computed rather accurately from electrical resistivity data using an empirical relation developed by Smith and palmer&apos; and further confirmed by owell.&apos; However, there has been very little work done on correlating thermal and electrical conductivities on Be-Cu alloys. We were reluctant to assume the validity of the Smith-Palmer relation on Be-Cu alloys because of the very large mass difference between beryllium and copper. As will be seen, however, our experimental results indicate that the Smith-Palmer relation is valid for the two alloys on which we made measurements. I) DESCRIPTION OF SAMPLES Samples of Be-Cu Alloy 25 and Be-Cu Alloy 125 were furnished to NBS in the form of rolled strip material, 0.005 cm thick by 5.08 cm wide. The Be-Cu Alloy 25 was purchased by NBS in the form of a continuous length of flat strip. The Be-Cu Alloy 125 was furnished to NBS by Goddard Space Flight Center in the form of two lengths of strip that had been formed into "tubing" of about 1.2 cm diam, with one side of the strip overlapping (but not connected to) the other side by about 90 deg. This "tubing" had been opened up to be flat and then rolled onto spools of about 3 cm diam. When unrolled, the strip would spring back into tubular form. Samples of both of the Be-Cu alloys were chemically analyzed by the NBS Analytical Chemistry Division. The beryllium content was determined quantitatively by the phosphate-gravimetric method to be 1.83 wt pct for Alloy 25 and 1.80 wt pct for Alloy 125. The two alloys were also examined by a general qualitative spectrochemical method for metallic elements. The Alloy 25 specimen contained between 0.1 and 1.0 wt pct Al, Co, Fe, and Si and between 0.01 and 0.1 pct Ni. The Alloy 125 specimen contained between 0.1 and 1.0 pct Co and between 0.01 and 0.1 pct Al, Fe, and Si. Other metallic elements present were in amounts less than 0.01 pct. The NBS Engineering Metallurgy Section measured the tensile strength, elongation, and Knoop hardness of both the Be-Cu Alloy 25 and the Be-Cu Alloy 125. These are given in Table I. The NBS Engineering Metallurgy Section also prepared photomicrographs of the two alloys; these are shown in Figs. 1 and 2.

Jan 1, 1969

By C. J. Leith

A study of the effect of rock composition, rock structure and degree of weathering on the stability of cut slopes is being sponsored jointly by the U.S. Bureau of Public Roads and the North Carolina Highway Commission. In 58 mountain and piedmont counties of North Carolina the percentage of failed cut slopes is greatest in micaceous metasediments, gneisses, and schists, and in saprolite and soil derived from these rock types. Soil slope failures outnumber rock slope failures by two to one. Joints and similar planes of separation exert a strong influence on size and shape of the sliding mass. They may or may not act as failure surfaces, depending on their orientation with respect to the active forces. Climatological data, though indicative of weathering conditions, do not correlate well with slope failure frequency. Because of the presence of joints and similar planes of weakness in soil and rock materials, conventional methods for analyzing slope stabilities are not directly applicable. Empirically derived modifications of these methods are being investigated. A study of the stability of highway cut slopes, sponsored by the U. S. Bureau of Public Roads and the North Carolina State Highway Commission, began in 1962 at North Carolina State of the University of North Carolina at Raleigh. As part of this study all slides, rockfalls and other types of cut slope failures on Federal and State highways in the 58 mountain and piedmont counties in North Carolina were located and described, and the data catalogued in a punched card file system. A major objective of the project is to relate slope failures to properties and physical conditions of the geological units in which the slopes were constructed, and to correlate soil type and/or geological unit with type and frequency of slope failure. The complexities of the problem of slope stability and the limitations which these complexities impose on methods for analyzing slopes have been recognized for many years. A great variety of factors and processes may lead to slides, often making it almost impossible to analyze theoretically the conditions required for stability of slopes. One of the principal factors determining maximum safe slopes is the shear strength of the material in which the slopes are cut, but unfortunately there are very few data available concerning shear strengths of residual soils. Vargasl tested clay derived from gneiss and granite in southern Brazil; the properties of decomposed granite occurring near Hong Kong were determined by Lumb.2 These data are being used, when applicable, to supplement the test data obtained in the present study by Yorke.3 The locations of the North Carolina slope failures, more than 400 in number, are shown on Fig. 1. This map, adapted from the Geological Map of North Carolina,4 suggests the possibility of a relationship between frequency of slide occurrence and rock type. However, the evaluation of this possibility requires consideration not only of the type of rock, but also of its large and small scale structural features, its susceptibility to and degree of weathering, and the composition and structure of the weathering products. Soil slope failures in thoroughly weathered soil material and saprolite outnumber rock slope failures two to one. INFLUENCE OF ROCK TYPE The agricultural soil type involved in each soil slope failure was identified and each failure was catalogued in terms of the parent material from which the soil was derived. These data indicate that most of the slope failures, whether in the rock or in the derived soil, are associated with metamorphic rocks (see Fig. 2a). The data may be skewed somewhat because of the relative sizes of the total areas underlain by the various rock types, but Leith and Gupton5 have demonstrated that the preponderance of failures in metamorphic rocks is of much greater magnitude than could be accounted for by the areal factor alone. The dominance of metamorphic rocks is emphasized when soil slope failures are considered in terms of the specific rock types from which the soils were derived (see Fig. 2b). In particular, mica schists and mica gneisses account for more slides

Jan 1, 1965

By P. J. Spencer, J. N. Pratt

The vapor pressure of manganese over liquid Mn-Sn alloys has been determined by a high-temperature torsion-effusion technique. Alloys containing from 8 to 100 at. pct Mn were investigated in the temperature range jrom 1280" to 1580" and the measured pressure values were used to calculate the partial and integral thermodynamic properties of the liquid alloys. The activities show small negative departures from ideality while the integral heats and excess entropies of mixing are asymmetric inform, changing from positive to negative with increasing manganese content. The possible contribution of various factors to the observed thermodynamic properties is discussed. COMPARATIVELY few thermodynamic data are available for manganese alloy systems.&apos; Therefore, as part of a continuing program of studies of the thermodynamic properties of transition metal alloys, measurements have been made on various binary alloys involving this element. In recent publications,2~3 investigations of liquid Mn-Cu alloys and of the Mn-Au system in both solid and liquid states have been reported. For the first-mentioned system the work suggested that magnetic interactions may be responsible for the observed form of the thermodynamic properties, while in the second the influence of the electrochemical factor appears to be dominant. The present paper describes a similar study of liquid Mn-Sn alloys. Again the thermodynamic properties have been obtained from vapor pressure measurements made by use of a high-temperature torsion-effusion technique.4 A detailed description of the apparatus and of the experimental procedures used in alloy preparation and pressure measurement may be found elsewhere.2&apos;4 EXPERIMENTAL RESULTS Sixteen alloys, ranging in composition from 8 to 100 at. pct Mn, were prepared from spectroscopically standardized manganese of 99.99 pct purity and tin of 99.999 pct purity, both supplied by Johnson-Matthey and Co., Ltd. One-gram samples of the alloys were obtained by carefully weighing appropriate amounts of the pure components into an effusion cell; this was then suspended in the apparatus and the metals melted together in situ by heating under vacuum to approximately 1550°K. After allowing sufficient time for a homogeneous liquid alloy to be formed, vapor pressure measurements were commenced. These were determined as rapidly as possible at a series of steady temperatures within the range of interest. The duration of experimental runs on individual samples was kept sufficiently short to ensure insignificant varia- tion of alloy composition during investigation. After completing pressure measurements, the alloys were rapidly cooled and their compositions checked by weighing or chemical analysis. All experiments were conducted using effusion cells machined entirely from boron nitride. Measurements were made using a variety of cells with orifice areas ranging from 0.0032 to 0.0075 sq cm and lengths of the order of 0.04 cm; the usual effusion correction factors for orifice geometry and molecular distribution were calculated using Freeman and Searcy&apos;s equation5 and had values between 0.6 and 0.75 for the orifices employed here. The vapor pressures of manganese over the alloys were measured at approximately 20°K intervals in the temperature range 1280" to 1580°K. In view of the close approximation of the measured pressures to Clausius-Clapeyron behavior in the experimental temperature range, the data for each alloy have been expressed by equations of the form: logp(atm) =-A/T + B A least-squares computer treatment was applied to the vapor pressure values in order to obtain the coefficients A and B with their associated error. The resulting equations are listed in Table I, together with the equation for pure solid manganese obtained from a previous study.4 To minimize the effect of possible apparatus calibration errors, the activities and partial free energies of manganese in the alloys were calculated by initial reference to the latter equation, obtained from identical torsion-effusion measurements. The immediately resulting thermodynamic quantities, based on a solid manganese reference state, were then converted to refer to the more appropriate supercooled pure liquid manganese standard; tabulated values of the free energies of solid and liquid manganese from Hultgren et al.&apos; were used for this purpose. Partial entropies of solution of manganese were calculated from the temperature coefficients of the free energies and partial heats from the Gibbs-Helmholtz relationship.

Jan 1, 1969