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By Amitava Gangulee, Michael B. Bever

The effects of changes in short-range order on some thermodynamic, electrical, and mechanical properties of the silver-rich Ag-Mg solid solutions have been investigated. The heats of formation at 273°K of several alloys after two different thermal treatments were measured by liquid metal solution calorimetry. Their electrical resistivities were measured at temperatures ranging from 4° to 773°k. Tensile tests and microhard-ness measurements were carried out at room temperature. An effective short-range order parameter and an effective interaction energy are defined. The measured changes in the properties are interpreted in terms of these quantities. The short-range order parameter is evaluated separately from calorimetric and X-ray data; the results are in fair agreement. Increasing short-range order lowers the resistivity of- the silver-rich Ag-Mg alloys but does not measurably affect the temperature dependence of the resistivity. Short-range order increases the yield stress of these alloys but does not affect the ultimate tensile stress. Changes in the effective short-range order parameter independently obtained from measured changes in the heat of formation, resistivity, and yield stress are in fair agreement. THE thermodynamic, electrical, and mechanical properties of solid solutions have been investigated as functions of composition in many alloy systems, but the effects of configurational variables, such as short-range or long-range order, on these properties have received much less attention. The silver-rich terminal solid solutions in the system Ag-Mg are well-suited for the investigation of the effects of order. The composition of these solid solutions may be varied over a range extending to about 27 at. pct Mg.1 Appreciable short-range ordering is likely to take place in these solid solutions; the degree of short-range order can be varied by suitable thermal treatments. In the alloy Ag3Mg long-range ordering is possible.2 This paper is primarily concerned with the effects of short-range order on some thermodynamic, electrical, and mechanical properties of the silver-rich Ag-Mg solid solutions.-The long-range ordering transition is the subject of a concurrent paper.3 1) EXPERIMENTAL PROCEDURES 1.1) Preparation of Specimens. Ag-Mg alloys containing up to 26.4 at. pct Mg were prepared by melting 99.99 pct pure Ag (obtained from Baker Chemical Co.) and 99.99 pct pure Mg (obtained from Eastman Chemi- cal Co. or Johnson Mathey & Co.) in graphite crucibles under molten potassium chloride. The solidified ingots were homogenized at 823°K for 10 days in evacuated Vycor capsules. A surface layer 6 in. thick was then removed by machining. The ingots were swaged into rods (2.5 mm diam) which were drawn into wires (1.0 mm diam). The wire specimens were annealed at 773°K for 24 hr in vacuum and either quenched into iced brine or cooled to room temperature over a period of 15 days. The average grain diameter (obtained from the linear intercepts) was about 0.1 mm. 1.2) Calorimetry. The heats of formation of the alloys were measured in a tin solution calorimeter as the difference in the heat effects of alternate additions of samples of an alloy and the mechanical mixture of its component elements. The additions were made from 273°K to the bath at about 623°K. The heat effect on addition of the alloys was approximately 5.5 kcal per g-atom. The procedure and the method of calculation have been described.4 1.3) X-Ray Diffraction. Short-range order parameters of two alloys were calculated from diffuse scattering intensities,' obtained with briquettes made from powdered specimens. A GE-XRD 5 diffractometer with filtered copper radiation was used. The absolute intensities were based on calibrations with paraffin. 1.4) Resistivity Measurements. The electrical resistivities were measured by a potentiometric method in which the potential drop across the specimen was compared with that across a standard resistance. For measurements below room temperature, the specimens were immersed in liquid helium (4°K), liquid nitrogen (78°K), dry ice and trichloroethylene (195°K), or ice and water (273°K). Measurements above room temperature were made on specimens held in a furnace under helium or in vacuum. The resistivity measurements were reproducible to ±0.5 pct or less. 1.5) Mechanical Tests. Tensile tests were carried out at room temperature with a Tinius-Olsen XY elec-tromatic Universal testing machine. Wire specimens (nominal gage length 1 in.) were used. The strain was measured with an extensometer, which had a sensitivity of 4 x 10-5; the strain rate was 10-3 min-1. Microhard-ness measurements were made with a square-pyramid indenter and a 100-g load.11 2) RESULTS AND DISCUSSION All measurements were made on two parallel sets of specimens, one quenched and the other slowly cooled from 773°K. The reported values are the averages of at least three measurements. In the range of magnesium concentration substantially below that of the composition Ag3Mg, quenched alloys have less short-range order than slowly cooled alloys. As the magnesium concentration approaches that of Ag3Mg, slow cooling develops long-range order. Quenching sup-

Jan 1, 1969

By C. G. Rhodes, D. Kramer

The kinetics of precipitation of transient a phase during the transformation in U-16 wt pct Mo between 400° and 550°C were studied using quantitative metallography and electrica1 resistiuity measurements. The volume percent of a phase goes through a maximum in time, corresponding to a critical degree of progress of y' formation. prior to its re-solution after prolonged annealing. The fastest rate of a precipitation oc-cuvs at 500°C with a concomittant lowest peak of 9.5 vol pct a. At 450°C, 14 vol pct a, greatest fov any temperature, was observed after 24 hr witlz an associated slowest rate of formation. a precipitation at 400°C ceases after approximately 160 hr and the amount of a present remains unchanged after long times at temperature; no y' was observed metallographically at this temperature. IN the U-Mo system at 16 wt pct Mo, an ordering reaction takes place below 600°C, see Fig. 1, whereupon the random bcc solid solution, y, transforms to the ordered bct phase, y'."2 The new unit cell is constructed of three old unit cells somewhat distorted. While attempting to study the kinetics of this transformation it was observed that an unexpected phase was precipitating out early during the transformation anneal reaching appreciable amounts before disappearing after long times. The y' appeared in the presence of this new phase and after long times constituted the whole sample. Owing to the high optical activity of this unexpected phase under polarized light, it was suspected to be the a phase. Subsequent X-ray powder pictures confirmed this belief. The kinetics of a phase formation and disappearance is the subject of this paper. EXPERIMENTAL PROCEDURE A) Alloy Preparation. Alloys for this study were prepared by vacuum induction melting normal reactor grade uranium and 99.5 wt pct Mo pellets in thoria crucibles. Two ingots were prepared, and sections of the top and bottom of each ingot were chemically analyzed for uranium and molybdenum content. The results of the analyses appear in Table I. B) Metallography. Samples of 16M were wrapped in tantalum foil, sealed in evacuated (5 X 10"6 mm of Hg) quartz capisules, and annealed at 1110"C prior to being transferred directly to the transformation temperature. They were examined metallographically after increasing times to determine the progress of the transformation at 400°, 450°, 500°, and 550°C. The samples were prepared for metallographic examination by mechanical polishing with diamond paste and electrolytic polishing with a solution of glacial acetic acid and chromic acid. Since the y' phase is tetragonal, its presence can be detected by viewing the sample in polarized light. To increase the contrast between y' plates, the samples were electro-etched in a 10 pct oxalic acid solution. To reveal a phase in bright field (it can be seen in polarized light in the "as-polished" state), the samples were electro-etched in a solution of citric acid and nitric acid. To determine the vol pct a phase, a variation of the one dimensional systematic point count method as described by Hilliard and cahn3 was used. The

Jan 1, 1962

By P. C. Hodges

WHILE there is very little romance connected with the operation of a stone quarry, yet to those who have participated in the growth and development of a business that has been a pioneer in its field and that FIG. 1.-LOCATION OF PROPERTY OF MARBLE CLIFF QUARRIES COMPANY. has been in continual operation two-thirds of a century there is bound to be a background of experience, which if properly capitalized, brings progress as well as satisfaction in its accomplishment.

Jan 1, 1936

By Carl Henrich

In the planning and erection of smelting-works, especially of such as contain the modern large water-jacketed blast-furnaces, we are often confronted with an insufficiency in the watersupply. It may be impossible to find in the immediate neighborhood of the selected site a sufficient supply to furnish the jackets with cold water. Or there may be enough water for this purpose, but it may be highly charged with scale-forming minerals held in solution. Or, the main water-supply, if pumped from the workings of a mine, may carry iron- or copper-salts, or even some free acid in solution, all of these substances being derivable from the oxidation of sulphuret-ores in the mine. Moreover, such mine-waters sometimes contaminate the waters of the creeks, so that these become unavailable, and we have to fall back on an inadequate supply of pure water furnished by some spring or springs, entirely too small in

Jan 1, 1896

By J. J. Gilman

IT is well established that dislocations exist in crystals and account for crystal plasticity.' However, the origins of the dislocations are not clear. Among the means by which dislocations might originate are: a) through crystal growth accidents, b) by the collapse of condensed sheets of vacancies, or c) by stress-induced nucleation. Theoretical calculations' have indicated that the last means should require very high stresses in order to operate. The purpose of this paper is to show that the stresses around the tips of cracks are large enough to nucleate large numbers of dislocation loops. Specifically, it will be shown that (100) cleavage cracks in LiF crystals nucleate dislocations in regions of the crystals where dislocations did not exist previously. It is believed that the use of LiF for this investigation does not restrict the significance of the 1 results. In fact, it is believed that this complements and extends previous papers by the same author which dealt with metal crystals.10,14 The dislocations were detected by means of the etching techniques that were described in a previous paper by Gilman and Johnston.3 In that paper it

Jan 1, 1958

Discussion of the paper of Edward Keller, presented at the Butte meeting, August, 1913, and printed in Bulletin No. 80, August, 1913, pp. 2093 to 2115. GEORGE L. HEATH, Hubbell, Mich.:-In the admirable paper quoted, is mentioned the date when the 5-g. assay was first proposed is a standard for refined metal. The author omitted, however, to mention a later paper,1 which contains a proposal for the use of a single " stock solution " of mixed acids, which has been adopted by the American Brass Co. and others. The suggestion is made that such a scheme would save time and manipulation with converter metal. Unless the low current of 0.5 ampere and the large excess of nitric acid, recommended by Mr. Keller, have been proved necessary to hold up antimony-and selenium, the use of the mixed solution which we have adopted will permit the use of 1 ampere of current per square decimeter of cathode surface, until the solutions have become colorless. At this point, we wash the covers and reduce to 0.5 ampere to prevent oxidation or contamination. The ordinary split electrodes have been used. With strong current, at least, the use of an excess of nitric acid tends to the neutralization of the solution before the end of the period, from the formation of too much ammonia., and this is detrimental. Antimony deposits more easily than arsenic, and tends to drag the latter dorm with it. There must, be some such explanation for the fact. that we have made hundreds of deposits of pure cathodes from Lake material containing no antimony, but as. high as 0.5 per cent. of arsenic. By placing an assay beaker in the Frary solenoid, or rotary device, a cathode deposit with less than 0.01 per cent. of impurity is easily obtained in one operation from 3 g. of whitneyite, carrying from 7 to 10 per cent. of arsenic. In such a case, it is necessary to test several times for end point and remove the plate as soon as no brown tint appears (at once) when hydrogen sulphide water is added to the test portion on the spot plate. Edward Keller's proportion,, of solvent figure out as 14 cc. of strong nitric to 11.4 cc. of sulphuric acid (1.84).

Jan 11, 1913

By C. J. Bauer

WHEN the pipe lines from the Middle East to the Mediterranean are completed, the Middle East supplies will relieve the strain on Western Hemisphere petroleum resources, part of which are now shipped for Eastern Hemisphere use. A sketch of the world petroleum situation as it appears today and in the immediate future will help in understanding the future place of Middle East oil supplies. Anticipated 1951 world demand is slightly under four billion barrels. To meet this requirement, crude output and refinery runs throughout the world (including Russia) must be increased about two million barrels per day above the average of 1947. This increment, together with pipe lines, tankers, and other facilities, will require in excess of ten billion dollars of new capital in the next four years. We are, therefore, looking forward to the greatest expansion program in the history of the industry.

Jan 1, 1948

R. Trimble, Pittsburg, Pa (communication to the Secretary) : There are in the proposed specifications only two points on which I wish to comment at this time.

Jan 1, 1902

By E. V. Daveler, Frank L. Antisell

CERTAIN physical and chemical properties of copper are so intimately related that a change in variation of the physical properties indicates a certain chemical change. The standard specifications of copper of the American Society for Testing Materials are based upon physical characteristics with one exception, namely, the copper contents. Certain phenomena of the surface indicate the adaptability of the metal for forging or rolling. The writer believes that it is much simpler to produce shapes that are metallurgically correct than those that are mechanically satisfactory. The appearance of the surface of the copper when cooled is considered as to its "pitch," or the general contour of the surface, and the "set," or the decail appearance of the surface of the shape. The set of the copper is, in a very large measure, directly related to the pitch; and so intimately are these characteristics connected that they are often used as synonymous terms by the refiner when he is speaking of well-refined copper. Oxygen is often spoken of as a medicine for copper, it being used to regulate the pitch.

Jan 1, 1920

By A. W. Adamson

A model for transport processes in liquid mixtures is discussed which supposes that the elementary act involves a position exchange between two species and that the exchange is so confined by the solvent cage as to occur nearly isosterically. The rate-determining step, thus, is likened to a bi-molecular reaction and is so treated, using absolute rate theory. The cage model has been applied to diffusion, thermal diffusion, sedimentation and viscosity, but only the first and last of these phenomena are emphasized in the present paper. The model leads to semi-empirical relationships between the absolute value for a digusion coefficient and the activation energy for diffusion, between mutual and self-diffusion coefficients and for the variation of the viscosity of a binary mixture with composition. These are discussed in relation to experimental data for various systems, including hydrocarbon mixtures. It is shown that the proposed viscosity equation and seven other commonly used ones all may be regarded as special cases of a single general relationship; a brief critical analysis is made of the basis of selection of one or the other for data fitting or interpolation. INTRODUCTION AND GENERAL THEORY The present paper covers a brief discussion of a cage model for transport processes in liquid mixtures and how this model may be useful in treating the diffusional behavior and the viscosity of such systems. Since diffusion requires the more detailed treatment, it will be taken up first, and the model then applied to viscosity. There are two types of diffusion coefficients that may be measured experimentally, apart from thermal diffusion quantities. The first is the mutual or binary diffusion coefficient, D which may be defined in terms of Fick's first law. This states that the permeation, or flux P, is proportional to the concentration gradient. In the usual experiment, P is measured relative to a frame of reference fixed with respect to the medium (e.g., the diaphragm in a diffusion cell); as a consequence, the same value of D is obtained regardless of whether P and C refer to Component 1 or to Component 2; i.e., there is only one independent mutual diffusion coefficient for a binary system. In addition to D there will be various self-diffusion coefficients. defined in terms of the gradient in labelled species i and its permeation in an otherwise uniform medium. The thermodynamic approach to mutual diffusion supposes that the actual driving force is the gradient of the chemical potential, i.e., that In the case of a dilute solution of solute, Eqs. 1 and 3 lead to the Einstein equation, If the solution is ideal and the friction coefficient is taken to be then the familiar Stokes- Einstein equation results. Mutual and self-diffusion coefficients can not be related on general thermodynamic grounds; it is necessary to invoke some additional assumptions, i.e., a model; several such have been proposed. Hartley and Crank' supposed the existence of separate, intrinsic diffusion coefficients (Dl and D2) for each component, essentially corresponding to the two self-diffusion coefficients. The two flows can not be independent, however, but must be coupled through the usual restriction that there be no net volume flow. For an ideal solution. one then obtains' Glasstone, et al' treated diffusion in terms of absolute rate theory, but their approach otherwise resembled the previously mentioned one in that each species was considered to move with respect to the general medium in a manner determined by its individual jump distance and specific rate constant. For other than dilute solutions, a coupling of flows leading to an equation such as Eq. 6 would again be present. However, as required by Eq. 6, one does expect that the self-diffusion coefficient for the solute and the mutual-diffusion coefficient for the system become identical at infinite dilution. Lamm4 recognized that there should be three distinctive interactions in a two-component system-1-1, 1-2 and 2-2 — and, therefore, proposed three rather than two fundamental friction coefficients. Mutual diffusion resulted from 1-2 interactions only, and self-diffusion resulted from 1-2 plus either 1-1 or 2-2 interactions. Again, a collective coupling between all motions was imposed to meet the condition of no net volume flow. Laity' has shown how to convert the Onsager equations to a form very similar to Lamm's. Cage Model For Diffusion Work in this laboratory on diffusion in aqueous sucrose solutions made it apparent that three, rather than two, interactions were indeed needed," but considera-

By Werner Langguth

SINCE the introduction of the improved method of precipitating gold from chlorine solution by SO2 and H2S at the Golden Reward chlorination-works, Deadwood, S. D.,* this modern method has been further adopted in the chlorination-works of the Portland Consolidated Company at Deadwood, and in those of the Black Hills Milling and Smelting Company at Rapid City, S. D. It has proved practically most successful in the handling of large quantities of gold solution, and constitutes up to date, with Mr. John E. Rothwell's most important improvement, namely, barrel-leaching under hydraulic pressure, the principal progress made in gold chlorination. The method of refining the gold sulphides which result from this method of precipitation, was introduced by me in 1890 at the Golden Reward works, and in 1892 at those of the Black Hills Company. It has not suffered any changes during the last three years, and is substantially as described below:

Jan 1, 1895

By V. Koump, R. H. Tien, W. J. Kim

This paper presents an approximate solution of the problem of freezing of a binary alloy. he alloy is in the form of a one-dimensional slab of finite thickness. The surface temperature of the slab is assumed to be constant and lower than the solidus (or eutectic) temperature. The densities of the liquid and the solid are assumed to be equal. For a given binary alloy system, initial concentration of solute and surface temperature, the solution yields a) the temperature distribution in the solid skin, b) the temperature, concentration, and solid fraction distribution within the solid-liquid region, and c) the positions of the liquidus and the solidus (or eutectic) fronts as a function of time. The results of calculation for Fe-C and Fe-P systems are presented. In this investigation we are considering the problem of solidification of a binary alloy. The alloy is in the form of a one-dimensional slab of finite thickness. The molten alloy is initially at liquidus temperature. At time zero the surface of the slab is reduced to a temperature T, < Te,, where Te, is the solidus (or eutectic) temperature and T, is a constant. The densities of solid and liquid alloys are assumed to be equal and independent of temperature and composition. A qualitative picture of solidification of an alloy, under these conditions, is illustrated in Fig. 1. During the initial stage of solidification, before liquidus front reaches the center of the slab, freezing proceeds by propagation of two isothermal fronts, the liquidus front and the solidus (or eutectic) front. The fraction of solid at the liquidus front is zero; the fraction of solid at the solidus front is unity, The solid fraction and the temperature distribution between the two fronts and the width of the solid-liquid region change with time. During the later stage of freezing, after the liquidus front reaches the center of the slab, the liquidus front disappears. The solid fraction and the temperature at the center of the slab, as well as throughout the solid-liquid region, are now changing with time. The solidification is completed when the fraction of solid at the center of the slab reaches unity. In solution of this problem we seek to determine a) the temperature distribution in the solid, b) temperature, concentration,

Jan 1, 1968

By R. L. Templin

THE increasing use of aluminum and its alloys in commercial fields has demanded a better understanding of their machining properties. This fact is exemplified by problems that have arisen in the automotive and airplane industries, but many in other fields might be cited. As pure aluminum and its alloys in their various commercial conditions show appreciable differences in their machining properties, it is not surprising that quite divergent solutions have been offered for the machining problems encountered. However, if the fundamental requirements of the most suitable cutting tools for these metals are understood, these machining problems lend themselves more readily to satisfactory solutions. Since the machining of free cutting brass and mild steel is understood by most persons accustomed to working these metals, it may serve our purpose better to first make a general comparison of the tools more commonly used in machining these metals with the tools most suitable for machining aluminum, then proceed to a more specific discussion of the individual stools.

Jan 1, 1927

By Arthur Phillips

THE progress made in recent years in the art of dispersion-hardening has naturally led to an intensive study of alloy systems capable of yield-ing supersaturated solid solutions at ordinary temperatures. In general, the investigations have been confined to rather precise determinations of solubility limits and to experimental approaches designed to furnish more complete information regarding the rate and nature of precipitation under appropriate thermal conditions. Efforts are being made to focus more sharply on the atomic changes that are a direct consequence of the instability of the supersaturated solution. Here precision X-ray methods have come to be of considerable importance because lattice parameter measurements indicate very precisely the concentration of solute atoms in the solvent lattice. In spite of the general acceptance of parameter values as a criterion for the placing of solubility limits, it may be suggested that no thorough appraisal has been made of the several factors that conceivably may affect such measurements. More specifically, little attention has been devoted to the significance of surface energy conditions, specimen size and method of preparation, with par-ticular regard to the genesis of the grains and the surface concentration changes as a consequence of heat treatment and etching. Stenzel and Weerts1 recently published the results of a detailed study of precipitation reactions in aluminum-rich copper alloys. They found that, although copper lowers the lattice constant of aluminum, a 5 per cent copper alloy quenched from 150° and 225° C. had parameter values unquestionably higher than that of pure aluminum. Their results seem to substantiate, at least qualitatively, the earlier work of von Göler

Jan 1, 1934

By F. Valton

In the number of the Engineering and Mining Journal for April 7th, 1877, Mr. W. P. Ward, of Cartersville, Georgia, explains in a very interesting manner, the results he obtained in the manufacture of ferromanganese in the blast furnace. These results may be summed up as follows : Production in the blast furnace of an alloy containing 67.2 per cent. manganese and 3 per cent. of carbon at most, with a utilization of the manganese amounting to 58 per cent. With the exception of the indicated proportion of&apos; carbon, which should be almost doubled to express the true state of facts, we would have had no observations to make on Mr. Ward&apos;s paper had he taken into account the results obtained in the same line in other centres of production. Before 1870, spiegel with 8 or 10 per cent. manganese only was known among blast-furnace products. In a journey to Sweden, in 1871,I ascertained that the Schysshyttan works manufactured regolarly a spiegel with 18 per cent. manganese. Later, at the Vienna Exhibition, in 1873, the Sava and Jauerburg works, in Carniola, presented to the jury a ferromanganese, obtained in the blast fur-

Jan 1, 1879

By A. Eilers

In a former paper on Western Smelting Works, I mentioned the great difficulty of obtaining accurate information in regard to the economy of the processes in practice; and to-day, although nearly two years have elapsed since my former paper was written, I am sorry to say that very little improvement has taken place in the keeping of accounts, and in the direction of a more systematic management in the majority of these works. But I am quite certain that by this time even the most sanguine furnace managers must have become convinced, from the experience of the last year, that somewhere in their processes there are enormous losses. Rates for the purchase of ores in 1873 were not as high as they were in former years in certain parts of the country ; labor was no &apos;higher than formerly; the demand for unparted lead was good throughout the year, with the only exception of the time of the panic, in the fall of 1873; yet there are, of between 40 and 50 works, not more than two or three in Utah and Nevada to-day, that have paid a reasonable interest on the capital invested.

By A. Filers

IN a former paper on Western Smelting Works, I mentioned the great difficulty of obtaining accurate information in regard to the economy of the processes in practice ; and to-day, although nearly two years have elapsed since my former paper was written, I am sorry to say that very little improvement has taken place in the keeping of accounts, and in the direction of a more systematic management in the majority of these works. But I am quite certain that by this time even the most sanguine furnace managers must have become convinced, from the experience of the last year, that somewhere in their processes there are enormous losses. Rates for the purchase of ores in 1873 were not as high as they were in former years in certain parts of the country ; labor was no higher than formerly ; the demand for unparted lead was good throughout the year, with the only exception of the time of the panic, in the fall of 1873; yet there are, of between 40 and 50 works, not more than two or three in Utah and Nevada to-day, that have paid a reasonable interest on the capital invested.

Jan 1, 1875

By J. M. Dupouy, R. A. Rawe, M. B. Bever

The aging characteristics of a titanium alloy containing 13 pct V, I1 pct Cr, and 4 pct A1 have been investigated by hardness measurements, X-ray diffraction, and metallography. The P phase decomposes into 0 + a, and 0 + a, + TiCr, above about 1050°F; below this temperature a transition phase, believed to be w, precipitates first, followed by a, and TiCr,. The observed hardening is attributed to these reactions. Cold working of solution-treated specimens accelerates hardening and raises the hardness level attained. A TTT diagram is proposed. NEW titanium-base alloys, designated as "all-beta," have recently been developed. These alloys contain large amounts of P-stabilizing elements such as molybdenum, chromium, or vanadium. When cooled from the solution temperature, they consist only of P; in particular, the martensitic a,&apos; phase does not form.

Jan 1, 1961

By R. W. Vieth, S. A. Bradford

THE orientations of tetragonal tin crystals are commonly examined by either the transmission Laue method or the back-reflection Laue method. The predominant planes and zone axes of the pattern are plotted on a Wulff net and indexed by measuring the angles between planes and directions. The problem of identifying the Laue spots has been approached in several different ways. Nicholas 1 tabulated interplanar angles for ten planes but did not relate the angles to permutation of indices or sign. A table of angles between adjacent planes and of angles between adjacent zones was published by Chandrasekhar and veal.&apos; These tables are very helpful, provided the film shows all the low-order zones that occur within about 20 deg of each other. Frounfelker and Hirthe&apos;s compilation3 of angles between the (001) plane and twenty-nine other planes is useful for the indexing, only if the (001) spot can be found on the film. For all but the simplest orientations, however, more information is needed to index the diffraction spots. Standard stereographic projections, such as those published by Bicelli, 4 provide part of the information required. By their nature, these projections show the positions of only a few zone axes. In the tetragonal system many low-order zone axes are not normal to the planes having the same indices. Consequently, planes and directions can have entirely different positions on a stereographic projection. For example, the [011] zone axis is 33 deg from the normal to the (011) plane. The crystallographic orientation usually has to be deduced from a combination of the predominant zone axes and a few low-order planes that appear on the film. In addition to a standard stereographic projection of the planes, a stereographic projection of the directions is needed. Such a projection can be constructed from the angles given in Table I. To provide more information about angles between planes and directions, we have calculated interplanar angles up to (332) and angles between planes and directions up to [332] on an IBM 1620 computer. The angles are differentiated according to permutations of sign and indices. Those doing research on tin single crystals are welcome to request a copy of these tables from the authors.

Jan 1, 1967

By J. S. Levine, M. Prats

Several methods are available for calculating the performance of solution-gas-drive reservoirs from the PVT properties of the oil and from the relative permeability and other properties of the formation. These methods require a number of simplifying assumptions. The present method of computation has made use of a high-speed computer to solve simultaneously the nonlinear partial differential equations that describe two-phase flow by solution-gas drive in order to calculate the performance of a reservoir. Some of the results obtained by the nonlinear partial differential equation solution are compared with those obtained with an approximate method, which has been called the semisteady-state solution. The pressure and saturation profiles from the wellbore to outer boundary calculated by the two methods are compared for one constant-terminal-rate case and two constant-teminal-pressure cases. The agreement in these profiles, as well as in the values of average reservoir pressure and cumulative recovery, leads to the conclusion that, for most engineering calculations, the semisteady-state method will give a reasonable approximation to the numerical solution of the differential equations describing solution-gas drive. An unfavorable (as regards ultimate oil production) set of relative permeability curves was used in the calculations in the belief that the effect of the parameters which were studied would be emphasized to a greater degree. Furthermore, the reservoir was assumed to be completely homogeneous, and these results should not be considered applicable to any other type of reservoir. Gravity effects are not considered. The absolute permeability was varied from 25 to 0.5 md. At an economic limit of 2 B/D, the recovery for a 25-md reservoir is about 1.8 times as great as that for a 0.5-md reservoir. The effect of permeability on the producing gas-oil ratio is minor. Once PVT properties of the oil and the relative penneability properties of the reservoir are fixed, the pro- during gas-oil ratio is found to be a function of the fraction of oil recovered. Well spacings of 10, 40 and 80 acres were considered. For the assumed homogeneous-reservoir properties, the effect of spacing on recovery at an economic limit of 2 B/D was very slight. Certain dimensionless groups can be used to extend the results to other fields having different penneabilities, spacings, reservoir thicknesses, well radii and porosities, so long as the PVT and relative permeability properties are similar to those used in this paper. INTRODUCTION An important aspect of reservoir engineering is the prediction of the performance of the reservoir based on the limited information normally available early in the life of a field. Usually, soon after a field has been discovered, it is necessary to decide upon the spacing to be employed and the production program to be used for most efficient utilization of reservoir energy. Where these decisions have not been dictated by legal or political considerations, they have frequently been based on experience factors which indicate that two fields with similar characteristics will probably have similar performances. To the extent that the industry has been successful in economically exploiting oil reservoirs, this rule-of-thumb method has been found to have merit. A large amount of theory has been developed with which it is possible to predict the performance of a reservoir by using certain known properties of the oil and the formation. Because of the difficulties of the mathematics involved for a drainage area having square or rectangular boundaries, the problem usually has been simplified and idealized by assuming each drainage area to have radial symmetry and the field to be represented by a number of these drainage areas. Muskatl was one of the first to formulate the theory for two-phase flow and to solve the equations for a few cases by numerical integration, using the relatively slow means of computing available at that time. His equations describing