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By Nicholas J. Grant, Yoichi Ishida, Arthur W. Mullendore

An inert particle -marker technique was developed to provide a direct measurement of grain boundary sliding during creep in tile interior of aluminum specimens. Groin boundary sliding in the interior as measured by this technique was found to be nearly the same or slightly lower than that measured on the surface. These data disagree with those obtained by the grain-counting technique developed by W. A. Rachinger. In tests where both techniques were used, the grain-counting technique gave large and variable values of grain boundary sliding. It is shown that the grain-counting technique gines erroneozcs results because of a preferred direction of grain growth during creep. A question which has long plagued those who study grain boundary creep is whether or not surface measurements yield a true representation of the deformation in the interior of a specimen. The first attempt to measure grain boundary sliding in the interior of a creep specimen was made by Rachinger.1 His technique is based on the measurement of average grain diameters, both parallel and perpendicular to the tension axis, followed by a calculation of the grain elongation from these measurements. The difference between total elongation, Et, and the calculated grain elongation, Eg, is considered to be the result of grain boundary sliding, Egb. Surprisingly large values of Egb/ Et (90 pct) came out of creep tests of pure aluminum at temperatures above 250°C (480°F), utilizing the Rachinger technique. This value is very much larger than the values of 8 to 15 pct measured by numerous investigators on the surface of a specimen. Values obtained on the surface by Rachinger, however, were consistent with those measured by the displacement of reference scratches. Chaudhuri and Grant2 repeated the Rachinger method for A1-10 pct Zn, and found the same large values of Egb/Et inside the specimen. However, from purely geometrical considerations, grain boundaries cannot slide without grain deformation; therefore, they questioned the validity of Rachinger's grain-counting method. Several authors2,3 have suggested that grain boundary migration during high-temperature deforma- tion may tend to restore the equiaxed grain shape in order to minimize interfacial energy. Rachinger4 tested this hypothesis and found that it did not hold. Grains elongated by rapid extension retained their elongated shape during a subsequent slow creep test. It appears that some other factor was responsible for the abnormally high values of .Egb/El. McLean and Gifkins5 made a survey of the effect of grain size on the ratio Egb/ Et, and proposed that the high values were the consequence of a small grain size. They failed to explain the low value of Egb/Et which Rachinger observed on the surface of the small grain size specimens, and suggested that the surface effect on the value of Egb/Et does not always occur. Many of the disagreements arising from Rachinger' s work stem from the fact that there was only one method of estimating grain boundary sliding in the interior of a specimen, and that method was of an indirect nature. If a marker line of some sort could be introduced inside of the specimen, one could make measurements just as clearly as on the surface. In the present investigation, the technique utilizes a layer of finely dispersed oxide particles inside the specimen introduced by hot press-bonding of two pieces of aluminum. Rachinger attempted a similar technique but with the oxide distribution he obtained there was so much interference with grain boundary motion that quantitative measurements were not attempted. MATERIALS AND EXPERIMENTAL PROCEDURE A) Materials Preparation. Two pure aluminum rods (impurity content in percent: Si, 0.002; Cu, 0.004; Fe, 0.002; Mg, 0.000: Zn, 0.000; V. 0.001) 1 in. diameter by 2 in. high were jacketed end to end in a 4-in.-diam cylinder of commercial-purity aluminum, 4 in, high, which had a l-in.-diam hole. The l-in.-diam mating surfaces of the two pure aluminum rods had been electropolished initially. This interface provided the oxide-film internal -marker plane after the hot press-bonding process, see Fig. 2. The composite was annealed for 1 hr at 900 F and hot upset more than 50 pct reduction in height in one step. The resulting slab was then rolled to 1/2 in. thickness; the pure aluminum test material was cut out and annealed at 900°F for 1 hr and cold cross-rolled to 1/8 in. thickness. The sheet was machined into specimens with a 1/8-in.-square cross section and a 1/2-in. gage length. The following heat treatment was given the specimens: Specimen 5A series: annealed at 1000°F for 5 min for grain-size control and then cooled to 700°F and held for 15 hr for stabilization.

Jan 1, 1965

By H. A. Domian, H. Biloni, G. F. Bolling

Jan 1, 1965

By L. B. Pankratz

Heat contents, measured above 298.15° K, and derived entropy increments are presented in tabular and equation form for the two crystalline forms of zinc sulfide (sphalerite and wurtzite) and for four solid solutions of iron and zinc sulfides having the compositions Zno.,,6Fe0.302S, Zno.750Fe0.250S, Zno.650Fe0.3505, and Zno.498Feo.502S.

Jan 1, 1965

By James D. Brown

The Bureau of Mines has written a computer program in FORTRAN to facilitate the calculation of concentrations from X-ray intensities in electron probe microanalysis. Philibert's absorption and Castaing's secondary fluorescence corrections are used; no atomic number correction is included. Background and dead time corrections are applied to the data before calculating the relative intensities. Data from any type of electron probe microanalyzer can be used with the program.

Jan 1, 1965

By J. B. Gayle

The Bureau of Mines studied the effects of air oxidation on the recovery of float coal. Both batch-and continuous-type tests were made on six bituminous coals, representing the range in rank of coals now commercially used for carbonization, and on one anthracite coal. The effects on flotation recovery of oxidation at 1000 C for periods up to 50 days were investigated using an alcohol-type frother and a kerosine-pine oil reagent. Two series of release analysis tests were made, using one medium-volatile bituminous coal. Float coal recovery was adversely affected by oxidation in all tests where the alcohol-type frother was used. Conversely, a small degree of oxidation improved recovery with kerosine-pine oil frother for some of the coals in continuous tests. Prolonged oxidation (beyond about 14 days) adversely affected float coal recovery for all coals, the effect being more pronounced for batch-type tests and for tests using alcohol-type frother. Reagent selectivity for the rejection of both ash forming and sulfur bearing minerals was reduced by oxidation. Severe reduction of reagent selectivity required only about 3 days' oxidation for alcohol-type frother but more than 10 days' oxidation when the kerosene-pine oil reagent was used.

Jan 1, 1965

By B. W. Howlett, M. B. Bever, Somnath Misra

The heats oj- formation at 0°C of the compounds AuSn,, AuSn2, AuSn, and the £ phase were measured in a metal -solution calorimeter with liquid tin or a liquid Sn-Bi alloy as solvent. The melting point, heat of fusion, and heat capacities near the melting point of- the compound AuSn in the solid and liquid state were measured in a constant temperature gradient calorimeter. The free energy and entropy of formation of the compound AuSn at its melting point and at 298 °K were calculated from the experimental results and published data. The heats of formation are discussed in relation to the nature of the compounds. The heat capacity below the melting point, heat of fusion, and entropy of fusion of AuSn are interpreted in terms of processes oc-curring before melting. The atomic arrangement in liquid Au-Sn alloys and the bonding in the intermediate phases of. the Au-Sn system are discussed in the light of the measured thermodynamic properties. THE available thermodynamic information on the intermediate phases in the Au-Sn system consists of the heats of formation of the compounds AuSn4, AuSn2, and AuSnly2 and of one composition of the < phase2 besides values of the heat content of the compound AuSn from 0" to 635".&apos; However, the heats of formation refer to different temperatures ringing from 90" to 450°C. Also, the reported error limits of some of the values are large and several inconsistencies are apparent. In the investigation reported here the heats of formation of the compounds AuS-, AuSnz, and AuSn and of three compositions of the < phase were determined for a single reference temperature of 0°C by liquid metal-solution calorimetry. The compound AuSn, which is the only congruently melting intermediate phase in this system, was further investigated in a constant temperature gradient calorimeter by measuring its heat of fusion, melting point, and heat capacity in the solid and liquid states near the melting point. From these data and published free energies of the liquid of composition Au~n,&apos; the free energies of formation of the compound AuSn at the melting point and at 298°K were calculated. The results shed light on the solid-liquid transition of AuSn and on the atomic bonding and state of association of gold and tin in the solid and liquid phases. 1) EXPERIMENTAL PROCEDURES 1.1) Preparation of Samples. Stoichiometric amounts of gold and tin, each 99.99+ pct pure, were melted in evacuated Vycor capsules (12 mm ID). The melts were maintained approximately 150°C above the liquidus for about 12 hr and shaken repeatedly. Samples of the compound AuSn were cooled slowly to room temperature. Melts of the other phases, all of which solidify by peritectic reactions, were transferred to the narrow end (5 mm ID) of the capsule, which was then quenched into iced brine. The solidified samples were annealed in the unopened capsules for 10 days at 30" to 50° C below the respective solidus temperatures. The absence of microsegregation and second phases was confirmed by metallographic examination. At least two batches of each composition were prepared. 1.2) Solution Calorimetry. The heats of formation were determined by liquid metal-solution calorimetry. In this technique, the difference between the heat effects on dissolution in a liquid metal, or alloy bath, of the compound and a mechanical mixture of its annealed components, adjusted for changes in composition of the bath, is the heat of formation of the compound at the temperature from which the samples are added. Details of the equipment and technique have been described."&apos; A tin bath at 300" or 350°C was used with the compounds AuSn,, AuSnz, and AuSn. The high gold content of the £ phase would have caused it to dissolve with an appreciable exothermic heat effect. In order to achieve thermal compensation, the samples were added from 0°C to a bath at 350°C consisting of 66.2 wt pct Bi (99.999+ pct pure), balance Sn (99.99+ pct pure). This solvent gives thermal compensation because gold dissolves exothermically in tin and endothermically in bismuth. The calorimeter was calibrated by adding from 0°C approximately 0.015 g-atom of the solvent.

Jan 1, 1965

By S. J. Gasior

A method for destroying the caking properties of bituminous coal was developed by the Bureau of Mines. Coal is treated in a fixed bed by heating through its plastic range under controlled temperatures in mildly oxidative atmospheres composed of inert gas and/or steam containing about 1 volume-percent oxygen. High-volatile A (hvab) and high-volatile B (hvbb) and low-volatile bituminous (lvb) coals in the size range 1/8 to 1-1/2 inches were successfully treated at 0 (atmospheric pressure) to 300 psig in static beds 6 to 18 inches deep. Conditions of treatment depended on the coal and ranged from 80 to 200 minutes at 350° to 510° C. Char produced in this manner from hvab coal was gasified with steam at 800° C and 100 psig in a fixed bed in one series of tests and in other tests was exposed to hydrogen in a dilute co current free-falling-bed system at 750° C and 3,000 psig without agglomerating.

Jan 1, 1965

By George R. Schottler

The objective of this research is to find the extent of the range of applicability of previously developed statistical methods for determining grade and tonnage of ore to bedded uranium deposits. Uranium assays obtained from gamma-ray logs of exploratory drill holes are used to compute grade and tonnage of ore in the deposit by a standard polygonal method and by statistical analysis. The results obtained by the two methods are compared. The uranium-assay frequency distributions are shown to be lognormal and a simple transformation permits the use of standard normal curve statistics. The effects on the assay frequency distributions of stratified sampling, a required minimum mining thickness, and increased assay-interval length are investigated. The addition of low-grade mineralization to make up the required minimum mining thickness results in a distinct change in the skewness of the assay frequency distribution. Any statistical inference regarding grade-tonnage relationships that will be produced, using the minimum mining thickness, should be made on the basis of this "revised" assay frequency distribution.

Jan 1, 1965

By Malcolm T. Hepworth

RECENT interest in thermoelectric devices has been directed toward studies of the properties of thermoelectric materials of semiconducting solid compounds with little attention given to ionic and semiconducting liquids such as aqueous solutions, fused salts, and mattes. One type of thermoelectric system is the thermocell: a nonisothermal galvanic cell with two identical electrodes at different temperatures connected by an electrolyte bridge. An electromotive force, v, is generated which is a function of the electrode reactions and the properties of the electrolyte according to the Eastman&apos; equation: where S* is the entropy change of the system arising from the electrode reactions and by heat transferred by ion migration and by thermal conduction. The quantity nF is the product of equivalents passed and Faraday&apos;s constant. A value of S* of 23.06 cal per "C is equivalent to 1 mv-Faraday per "C. The symbol, a, is used for dV/dT in analog to the See-beck coefficient of solid-state thermoelements. de Bethune2 has calculated the temperature coefficients of the electromotive force of a large number of nonisothermal aqueous cells from measurements on the nonisothermal temperature coefficients of the standard hydrogen electrode, combined with data on the isothermal temperature coefficients of half-cells tabulated in the literature. Values of these coefficients (a) in de Bethune&apos;s compilation ranged up to 3 mv per C. In particular he reported a value of +2.059 mv per "C at 25&apos;C for the cell: Fe (aqueous, unit activity) (aqueous, unit activity) written for the hot-electrode reaction. The positive sign indicates that the hot electrode is positive (an "n-type thermocell"). In analog to a solid-state p-n system, it would be possible to couple two thermocells together to form a system in which the figure of merit could be calculated by adding the temperature coefficients according to the relationship described by offee:&apos; where a is the Seebeck coefficient in volts per "C, p is the specific resistivity in ohm-cm, and K is the thermal conductivity in watts per cm "C. Even though ionic systems have rather high electrical resistivities compared with semiconducting and metallic systems, it was felt that a preliminary study of one ionic system should be made to establish some basis for evaluating the possibility of a p-n thermocell for energy conversion. Accordingly the Fe", Fe"&apos; system was studied as a possible component for a p-n system. A glass system was constructed consisting of two vertical water-jacketed tubes connected by a horizontal tube, Fig. 1. Platinum-black electrodes 1 cm by 1 cm in dimension were inserted in each vertical tube with thermometers to register the electrode-compartment temperatures. The temperature of the electrode compartments was controlled by circulating water from thermostatted baths around the electrode compartments. The electromotive force of the cell was then read by a potentiometer for zero current as a function of the temperature of the hotter electrode. Current output of the cell for varying external loads was also measured. The cell resistance was measured by means of a bridge circuit with 10,000 cps signal and oscilloscope. Resistance measurements were converted to specific resistivity by calibrating the cell with a solution of known conductivity.

Jan 1, 1965

By J M. Gibbs

Craigmont Mines Limited mine 50,000 tons of ore and waste per day from the open pit at Merritt, British Columbia. An electric-powered "down-the-hole" drill, a diesel-powered rotary drill and two electric-powered rotary drills have been used. All primary drilling, as a result of cost and operating experience, is now performed with two electric-powered rotary drills. Trials with various loading techniques have increased the amount of AN-FO and decreased the amount of commercially prepared slurries used for primary blasting. Approximately 95 per cent of the primary blasting is accomplished with AN -FO, mixed at the hole. Introduction THE Craigmont mine is located near the village of Merritt, B.C., 240 miles northeast of Vancouver. The concentrator has been in production since September of 1961. Craigmont is a combined open-pit and underground operation. To date, slightly more than 95 per cent of the mill feed has been mined from the open pit. As underground development proceeds, the ore requirements from the open pit will decrease. The average milling rate from September, 1961, to April, 1964, was approximately 4,900 tons per day.

Jan 1, 1965

A drive, 3,500 ft long, was planned to explore mineralization exposed by diamond drilling. A rate of advance of 150 ft per fortnight, approximately double previous Broken Hill rates, was required. Subsequent to the completion of this drive its extension for a further 6,200 ft was planned to provide a main haulage way along which ore could be transported from a newly acquired lease back to the main hoisting shaft, a total distance of 13,500 ft.This paper describes the working conditions, relationships, manning and costs, and gives details of the cycle and equipment used to achieve rates up to 170 ft per fortnight.OBJECTIVEDiamond drilling from the 1,000 ft level at the Delprat Shaft section had indicated that the zone of mineralization, about 150 ft wide, which had been explored on the 1,000 ft level for a length of 2,600 ft, continued downwards with a westerly dip. The drilling results showed that within this wide zone there were arrower lenses of mineralization of possibly payable grade (see composite plan, Fig. 1).Diamond drill holes of 2,000 ft and over, particularly through heavily sheared areas of sericite schist, had been found to be costly, slow, and inadequate in testing the potential and trends of these smaller concentrations of mineralization.It was therefore decided that an exploratory drive should be advanced from the northern limit of the 1,480 ft level into the western mineralization, and that from this drive diamond drill holes should be drilled at dose intervals to outline the ore.The 1,480 ft level was chosen for the following reasons.1. It had the greatest northerly reach of the accessible levels at No. 7 Shaft section below the 1,000 ft horizon and therefore would enable the test to be made most quickly.

Jan 1, 1965

By Sofoulis J

In the Archaean of the Kalgoorlie-Norseman area, the layered rocks have been subdivided into two sequences, both containing basic igneous rocks and sediments. The lower sequence is distinguished by the presence of acid volcanic flows and large acid sills. The upper sequence is unconformable on the lower one.In some areas, clastic sediments become coarser and pass into conglomerates. Th:s passage is accompanied by thinning of the beds.These features and their distribution suggest a basin of subsidence flanked by areas of shore-line conditions.Repeated igneous activity, including vulcanism, has occurred along the flanks of this basin. These different igneous and sedimentary environments have played an important part in the primary distribution of metals.A chronology of all basic and acid igneous activity, as well as sedimentat:on, has been established for the Precambrian of this area.INTRODUCTIONThe subdivision of Archaean rocks into those of basic igneous or of sedimentary origin has formed the basis for the nomenclature appearing in past literature. These subdivisions were distinguished as greenstones (predominantly basic igneous rocks) and whitestones (predominantly sediments), and it was generally accepted that the greenstones were stratigraphically lower in the sequence than the whitestones.Recent studies show that, between Kalgoorlie and Norseman, basic igneous rocks interfinger with and pass laterally to sediments, and that basic volcanic rocks occur at different stratigraphic levels. Younger Precambrian. units are also...

Jan 1, 1965

J. H. Lord (Geological Survey of Western Australia): During the last few days in Kalgoorlie here we have heard on various occasions of the great job the mining engineers have done persisting against rising costs and increasing salaries without a rise in the price of gold. I think it has been somewhat overlooked that it has been difficult to find additional ore as well. I consider that geologists also should be commended on their action in persisting to search for more orebodies. This goes on in any mining community, but in Kalgoorlie in particular, I believe, over the last few years that it has been more difficult all the time to find additional orebodies and the Companies are calling for higher grades to offset the economic condition. I feel that this paper by Mr. Finucane shows that the geologists have persevered on an idea and discovered that they can find additional orebodies in the calc schist where previously it was thought that these did not occur. This has added many tons to the ore reserves, and although it is not very significant at the moment, the significance will probably improve as more work is done.The whole thing has shown us the importance of economic geology. Mr Finucane has had many years of experience here and he has given us a very able exposition of the economics of ore finding, and there are not many questions that one could pose to him, because most of the information he presented is obviously fact borne out by drilling, underground development and lining up the ore channels. He did briefly touch on ore shoots-the Oroya shoot and several others. It would be very good if we could, and I feel sure...

Jan 1, 1965

By T. S. Lundy, J. Askill

J. Askill and T. S. Lundy (Oak Ridge National Laboratory)—Moore has proposed a simple correlation between the activation energy for solute diffusion in fee metals and the atomic volume of the diffusing species using both tracer and chemical-diffusion data. The first point we wish to make is that it is wrong to attempt such correlations without separating the two types of data. Activation energies obtained using tracer techniques cannot, in general, be directly compared with those obtained from chemical-diffusion experiments. A knowledge of the variations of chemical potentials with composition is necessary and chemical-diffusion data must be corrected for such variations, even for dilute alloys, before a comparison is possible. Secondly, for nickel, iron, aluminum, and lead, Moore neglected a number of recently published works, e.g., Al26 and Mn54 in aluminum,46 cr51 in nickel,47 and Fe55 in iron.48 These and others should have been used. If one considers only the tracer diffusion data, there is left no simple correlation of the type proposed by Moore. For example, in the case of solute diffusion in aluminum the only reliable tracer data listed by Moore are for zinc and aluminum. The nickel, cobalt, and iron data of Agarwala49 are representative of near-surface diffusion-not bulk diffusion. In conclusion we suggest that for tracer diffusion data in these fee metals there is no justification for proposing any simple correlation of activation energy with atomic volume using the limited data that are presently available. R. H. Moore (author&apos;s reply)—The writer has proposed a simple correlation which is useful in estimating the internal consistency of diffusion data. The accuracy of the correlation is, of course, a function of the number of data available. Lundy and Askill take issue with the writer&apos;s decision to include data for the systems: nickel, iron, aluminum, and lead, taking the view that the data are insufficient to establish the correlation. The writer agrees that the data are insufficient and has cau- tioned the reader that the correlation is tentative in these instances. Inclusion of these systems is justified by the interesting trends the correlation reveals. For example, the distinction between interstitial and substitutional diffusion may be clearly established, Figs. 4 and 6, and the behavior of transition elements and nontransition elements is indicated to parallel the behavior illustrated by the silver and copper systems. Lundy and Askill have singled out the aluminum system for special criticism. The writer chose to discuss the data for diffusion of iron, nickel, and cobalt in aluminum in the terms used by the original authors9 and has included the comments of Balluffi.l0 The writer did not intend the reader to conclude that data for these elements should correlate with data for the nontransition elements as Lundy and Askill have evidently assumed. Iron, nickel, and cobalt form intermetallic compounds with aluminum, so the activity coefficients of these elements may be expected to deviate markedly from unity. This may account for the low frequency factors observed by Hirano.9 The nontransition elements, on the other hand, yield relatively simple phase diagrams with no evidence for intermetallic compound formation as in the case of iron, nickel, and cobalt. In dilute solution, Henry&apos;s law should be closely obeyed, the activity coefficients should not deviate markedly from unity, and the effect on the activation energy should not be large. The accuracy of the correlation applied to these systems will improve as the data is extended. It does not seem unreasonable to conclude that its extension should be encouraged.

Jan 1, 1965

By A. G. Rozner

TRANSVERSE rupture tests have been commonly used in mechanical investigations of brittle materials. The specimens are simple, easy to prepare, and loading presents no difficulty. Owing to the complexity of stress distribution in bending1 one can determine stresses rigorously only for the elastic range. The bend-test results, however, are at times converted into tensile-strength data, determined as maximum fiber stress. The assumption is made that for small plastic deformations the linear stress-strain relation applies. This problem was experimentally investigated by Bach3 who tested cast iron in bending and in tension and found that the maximum fiber strength obtained in bending exceeded the experimental tensile strength by a factor depending on the geometry of the tested piece. The factor varied from 1.57 for a rectangular cross section to 2.12 for a circular cross section of the tested beam. Since this work was carried out 60 years ago, the cast iron used could be expected to have been highly brittle, thus the extent of plastic deformation prior to fracture very small. We have therefore carried out a number of tests on magnesium-modified cast iron with an average elongation of -5 pct. It was hoped that the data obtained from the tests would serve as a guideline for comparing data obtained in tension and bending for brittle materials. Mechanical properties were measured at room temperature on an Instron tensile machine at a crosshead speed of 0.05 in. per min. The three-point bend test employed cylindrical bars 0.20 in. in diameter with a 1.0-in. span. For the tensile test, cylindrical tensile specimens with a gage length of 0.85 in. and a diameter of 0.160 in. were used. Results are summarized in Table I. From Table I one can see that fracture strength

Jan 1, 1965

By Craig R. Barrett, Oleg D. Sherby

The creep characteristics of four pure metals with widely Varying stacking-fault energies (silver, copper, nickel, and aluminum) were evaluated above 0.5Tm. Creep tests were performed under conditions of constant atomic diffusivity and constant stress over the elaslic modulus. The sleady-state creep rate, Es, was found to he a funclion of the THE most common empirical representation of the steady-state creep rate, Es, at high temperatures and intermediate stresses is of the form where a is the applied stress, E is an elastic constant, A and n are constants (n is typically stacking-fault energ, y, such that Es is proportional to y3,5. In addition, it was uncovered that the primary creep strain and the strain to fracture increased with increasing y, and that the ratio of initial to steady-state creep rate decreased with increasing y. about 5), Q is the activation energy for creep (usually equal to that for self-diffusion), and kT has its usual meaning. sherbyl and McLean and ale&apos; have used this expression to correlate creep data for a number of pure metals. An interesting aspect of Eq. [I] is the absence of any dependence on the stacking-fault energy. While most creep data seem to obey the stress and temperature dependence predicted by Eq. [I], when data for several metals are put on a master plot they do not fall on a common line but form a band. The width of this band corresponds to a variation in Es of 102 to l03. sherbyl attempted to explain this band by assuming that a grain-size effect was present which led to the observed variation. On the other hand, Felt-

Jan 1, 1965

By James R. Boyle

The mining methods and practices used at the Young zinc mine, American Zinc Co. of Tennessee, have resulted in a low-cost, high-yield operation. Zinc ore (sphalerite) occurs in limestone-dolomite beds of the Kingsport Formation and is mined by modified room and pillar method. Utilizing trackless mining equipment which incorporates a high degree of flexibility, this operation has had a steady increase in productivity.

Jan 1, 1965

By Kung-Lee Wang

SUSTAINED growth characterized the U.S. economy in 1964. Many new peaks were achieved in production, sales, employment, employee earnings, and business profits. At the end of 1964, the economy had experienced 4 years of uninterrupted expansion, and the greatest net gains in output for all postwar cyclical advances had been registered. There were no indications of the various weaknesses which have previously characterized advanced stages of business expansion. Both gross national product (GNP) and national income were 6.7 percent higher than in 1963. In 1964 GNP totaled $628.7 billion, a gain of $39.2 billion over the 1963 figure. On an overall basis, prices rose 1.75 percent in 1964. The real volume of output of goods and services (GNP in constant dollars) increased by 5.0 percent ill 1964; this was more than the 3.8-percent gain in 1963 but less than the 6.6 percent gain in 1962. The 1964 output gain also exceeded the average 3.7 percent annual increase for the postwar period. Congress authorized a two-stage tax reduction designed to further stimulate economic growth and employment. The tax cut favorably affected the 1964 economy in the following ways: By helping to boost personal income, corporate profits, and industrial production; by accelerating the pace of consumer spending and business capital expansion; and by increasing employment, thereby reducing unemployment to 5 percent. Three major problems remained unsolved. These were unemployment of 3.7 million persons, poverty conditions among more

Jan 1, 1965

By R. V. Higgins

This paper presents a computer method to obtain the shape factors and equal cell volumes of the channels for any well spacing pattern from a potentiometric model. By using this program the authors have processed the data for the seven-spot, direct line-drive and the staggered line-drive patterns. The data for the five-spot pattern had been previously processed by a noncomputer method and are included for completeness. The shape factors and volumes for the channels are presented in tables for those who want to use them to process data using their own permeability relationships and viscosities of their reservoir oils. The authors have used the data and sets of representative permeability curves to process sample calculationr of waterflood performances. The comparison of the calculated results shows that the influence of well spacing is small. The permeabilities of the reservoir rock to oil and water had a greater influence on oil recovery for a given pore-volume throughput of water than the well spacing pattern. The more water-wet the reservoir rock, the better the possibility of permeabilities which are conducive to good recovery. The viscosity of the reservoir oil also influences the recovery more than the well spacing pattern. The reduction in the percentage recovery of oil with increase in viscosity of the reservoir oils is small when oil viscosities are in the range of 0.1 to 3. Above this range the reductions in recoveries are extensive. Sample comparisons of the time required for different patterns to recover the oil are presented. Results of an example calculation are given to show the effect of the permeability profile on recovery. INTRODUCTION The effect of well spacing pattern on the recovery of oil when flooding with either gas or water has been studied by many investigators. Muskat et al.1 presented an analysis using conductivity, sweep efficiency and unit mobility to the time of breakthrough. Dyes et al.2 used experimental techniques (X-ray shadowgraphs) and different mobility ratios. They presented quantitatively the relationship between mobility and sweep efficiency at and after breakthrough. Hauber3 presented a method to predict waterflood performance for arbitrary well spacing patterns and mobility ratios. Craig et al.,4 using techniques similar to Dyes et al. to determine sweep efficiency for a five-spot pattern, added the use of relative permeability curves at breakthrough and thereafter. Douglas et al.5 sed rela- tive permeabilities and continuously changing saturations throughout the entire five-spot flood pattern. In obtaining their solutions they used finite-difierence equations. Hig-gins and Leighton6,7 also used relative permeabilities and continuously changing saturations throughout the pattern before and after breakthrough. They employed techniques that process a flood-pattern calculation on the computer in about one minute. The methods of Douglas et al. and Higgins and Leighton both checked closely the laboratory results for a wide range of mobility ratios. This paper presents some sample performances calculated by the Higgins and Leighton method that show the effect on recovery of different permeabilities and viscosities using the seven-spot, the line-drive and the staggered line-drive, as well as the fivespot flood pattern. No previous paper has presented these data using different permeability curves and continuously changing saturations throughout the flood patterns. The paper also presents (1) the results and analyses of the flood-pattern prediction, (2) the computer techniques for determining the shape factors and volumes from the potentiometric models for the foregoing flood patterns, and (3) the shape factors and volumes of the channels of the flood pattern in the event reservoir engineers may like to process waterflood calculations using their own permeability curves and reservoir oils. DESCRIPTION OF METHOD VOLUMES AND SHAPE FACTORS The use of channels taken from a potentiometric model (see Fig. 1) to aid in calculating the performances of water floods of nonlinear patterns has been thoroughly explained in the literature.0,7 Therefore, very little theory, discussion, or proof regarding this phase will be repeated in this paper. The computer method presented in this paper to calculate the volumes and the shape factors of the channels of potentiometric models employs the trapezoidal rule for the volumes and the Pythagorean theorem (the hypotenuse equals the square root of the sum of the squares of the two sides of a right triangle) for the shape factors. In calculating the volume of a channel, the area of each cell in the channel is determined and then multiplied by the thickness to obtain the volume. In determining the areas of the cells, trapezoids are constructed whose vertical sides are spaced Ax apart, as shown in Fig. 2. The length of the sides is the difference between an ordinate cut off by the top and bottom of the cell — usually equipo-tentials. The coordinates of the points along an equipo-tential or streamline are obtained by Lagrange&apos;s8 equation of interpolation for which the constants are coordinate points at the intersections. Three intersections for con-

Jan 1, 1965

By Harry C. Gatos, Frank J. Bachner, Mario D. Banus

The portion of the Nb-Sn phase diagram between 75 and 79 at. pct Nb at temperatures near the liquidus has been investigated by melting alloys of known composition and examining the microstmc-tzlres resulting when these melts were quenched. The Nb-Sn samples were contained in magnesia sleeves, and were mounted in a high-pressure apparatus. It was shown that Nb3Sn me1ts by a peri-tectic decomposition and that the composition of the compound Nb3Sn at the peritectic horizontal lies between 77 and 78 at. pct Nb. Analysis of the phases present in the samples was accomplished by anodic staining techniques and an electron-microbeam analyzer. DURING the past several years a great deal of work has been devoted to the Nb-Sn system, and the bulk of this work has been primarily concerned with the intermetallic phase Nb3Sn. However, the melting characteristics of Nb3Sn have not been investigated because of the difficulty in maintaining known compositions due to tin losses by vaporization, and the added difficulty of containing Nb-Sn alloys without sample-container reaction at the high temperatures involved. This paper reports on the development of a technique for containing Nb-Sn alloys under pressure high enough to prevent tin losses at temperatures in excess of the liquidus. Using this technique, melts of known composition were made and a phase diagram near the liquidus is proposed based on the microstructures resulting when these melts were quenched. EXPERIMENTAL The Nb-Sn alloys weighing 0.7 g each were prepared in the form of cylinders. Niobium powder, -200, +325 mesh, and tin shavings with a minute amount of tin powder for a binder were mixed in the desired proportions and cold-pressed at 50,000 psi in a 0.150-in. die. This cylinder was then enclosed as shown in Fig. 1, and the entire arrangement mounted in a 2.6-in. pyrophyllite tetrahedron.&apos; The desired temperatures (-2500°C) presented several problems in high-pressure container materials. Boron nitride, the usual sample holder, was found to react with niobium to form the nitride. However, MgO cans and plugs machined from refractory rods did not melt nor react with the sample. Thick tantalum contact disks were used to carry the large currents (~450 amps) to the graphite heater, since tantalum did not melt and had enough strength to prevent extrusion of the sample. It was further observed that the graphite heater and tantalum disks could not be in direct contact with the pyrophyllite because it melts and decomposes at these temperatures to kyanite and coesite (SiO2),2 the former reacting with graphite and the latter with tantalum to form the silicide. The use of a MgO outer sleeve

Jan 1, 1965