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By L. S. Darken

The manufacture and treatment of metals comprises operations whose effectiveness depends in large measure upon diffusion phenomena. The significance of such phenomena has, for a few simple cases, long been understood, but in more complex cases it has not been adequately recognized. This paper presents a mathematical analysis of some of the cases in which diffusion leads to the formation of a new phase within the metal, and this analysis provides a basis for interpreting quantitatively many apparently diverse experimental observations recorded in the literature, some of which are outlined in the following pages. OBservt1ons Recorded in Literature An outstanding instance is the general type of phenomenon in which diffusion of an element into an alloy is followed by a phase change, which most frequently is a reaction (precipitation) of the diffusing element with one or more components of the alloy to form a compound. Thus in certain alloys heated in contact with oxygen not only the usual oxide scale appears but, in addition, beneath the surface, a well-defined zone in which free oxide particles are dispersed with notabIe uniformity. This zone, commonly referred to as the subscale or zone of internal oxidation, is remarkable in that the visible boundary between it and the unaltered metal is usually sharp. Such a subscale, which appears to have been recognized first in oxidized copper alloys, has been described and studied by C. S. Smith,l by Rhines,2 and by Rhines, Johnson and Anderson;3 but it appears also in other alloys when they are exposed to conditions that bring about the precipitation of some compound, not necessarily an oxide. Another clear case of this same kind is the diffusion of carbon into a steel containing an element such as molybdenum, chromium, vanadium or tungsten, whose carbide is less soluble in iron than iron carbide, the result being that some part of that element is precipitated as a dispersed carbide. A similar phenomenon may occur on the welding of two alloys each of which contains one of a pair of elements that react to form a compound or a new phase of any sort. But in addition to the precipitation of a compound formed from the diffusing element, other effects may result merely from the presence of the diffusing element. For instance, if homogeneous austenite, nearly saturated with respect to carbon, is heated in contact with silicon in the absence of oxygen, one would expect to find, behind the several iron-silicon phases analogous to a scale, a zone of austenite containing dispersed carbide, because of the fact that silicon decreases the solubility of carbon in iron. As still another example, oxidation of an alloy may result in diffusion toward the surface of one or more of the constituents; for instance, during oxidation of a steel containing an element such as "copper, which is less prone to oxidation than iron, there is a notable enrichment of copper just beneath the scale-metal interface. AS an example of a yet more

Jan 1, 1942

By L. S. Darken

The manufacture and treatment of metals comprises operations whose effectiveness depends in large measure upon diffusion phenomena. The significance of such phenomena has, for a few simple cases, long been understood, but in more complex cases it has not been adequately recognized. This paper presents a mathematical analysis of some of the cases in which diffusion leads to the formation of a new phase within the metal, and this analysis provides a basis for interpreting quantitatively many apparently diverse experimental observations recorded in the literature, some of which are outlined in the following pages. OBservt1ons Recorded in Literature An outstanding instance is the general type of phenomenon in which diffusion of an element into an alloy is followed by a phase change, which most frequently is a reaction (precipitation) of the diffusing element with one or more components of the alloy to form a compound. Thus in certain alloys heated in contact with oxygen not only the usual oxide scale appears but, in addition, beneath the surface, a well-defined zone in which free oxide particles are dispersed with notabIe uniformity. This zone, commonly referred to as the subscale or zone of internal oxidation, is remarkable in that the visible boundary between it and the unaltered metal is usually sharp. Such a subscale, which appears to have been recognized first in oxidized copper alloys, has been described and studied by C. S. Smith,l by Rhines,2 and by Rhines, Johnson and Anderson;3 but it appears also in other alloys when they are exposed to conditions that bring about the precipitation of some compound, not necessarily an oxide. Another clear case of this same kind is the diffusion of carbon into a steel containing an element such as molybdenum, chromium, vanadium or tungsten, whose carbide is less soluble in iron than iron carbide, the result being that some part of that element is precipitated as a dispersed carbide. A similar phenomenon may occur on the welding of two alloys each of which contains one of a pair of elements that react to form a compound or a new phase of any sort. But in addition to the precipitation of a compound formed from the diffusing element, other effects may result merely from the presence of the diffusing element. For instance, if homogeneous austenite, nearly saturated with respect to carbon, is heated in contact with silicon in the absence of oxygen, one would expect to find, behind the several iron-silicon phases analogous to a scale, a zone of austenite containing dispersed carbide, because of the fact that silicon decreases the solubility of carbon in iron. As still another example, oxidation of an alloy may result in diffusion toward the surface of one or more of the constituents; for instance, during oxidation of a steel containing an element such as "copper, which is less prone to oxidation than iron, there is a notable enrichment of copper just beneath the scale-metal interface. AS an example of a yet more

Jan 1, 1942

By John Philip Zannaras

John Philip Zannaras (Registered Professional Engineer, Congress, Ariz.)- The authors show in their [Fig. 4] the cumulative results of grinding with two sizes of bails, one 30 mm and the other 20 mm. The Gaudin-Meloy probability for breakage for a single fall used by the authors in their paper is given by their [Eq. 6]. Another form of [Eq. 6] is given by Gaudin-Meloy in their paper as follows: [ ] From the definition of A given by Gaudin-Meloy it is obvious that A30 is greater than A., it therefore follows from the foregoing equation that according to the Gaudin-Meloy formula the probability of breakage for a single fall of all the balls in the 20-mm experiment was more than 2.25 times the probability of breakage in a single fall of all the 30-mm balls which is contradicted by the authors' experimental evidence in [Fig. 4] in which is shown that much more grinding took place with the 30-mm balls. In fact the authors present convincing evidence that the Gaudin-Meloy work is erroneous because their work is based only on a geometric configuration and on ambiguous and uncertain definition of A and disregards the fact that the distribution of fracture depends on other important and indispensable factors including the intensity of stress caused on the feed grain by the balls. That there is an immense and chaotic variation of stresses caused on the feed grains by the balls is shown by a formula, derived by this writer and published in 1955. The derivation of this formula is given in the Appendix of this discussion; it contains the variables in the operation of ball mills and is based on the science of mechanics-not on probabilities. [ ] where T is the unit stress in pounds per square inch produced by the moving load, h is the height in feet through which P has fallen, E is the modulus of elasticity of the rock, P is weight of one ball, and L is the size of the grain (assumed to be a cube of side L). It will be shown by this writer's formula that when a 30-mm ball strikes any size of feed grain it will cause 1.837 times higher stress than the 20-mm ball when striking the same size grain. It will be shown that when the 30-mm ball or the 20-mm ball strikes a feed grain of 0.1 mm it will cause 90 times more stress on the grain than when it strikes a 2-mm grain.

Jan 1, 1974

APPLICATIONS for loan contracts for the exploration, development and mining of strategic and critical metals and minerals are now being accepted by the Department of the Interior. The RFC is authorized and directed by Executive Order 10161 to make such loans but the Secretary of the Interior must pass on the necessity for the loan. Applications should be addressed to James Boyd, acting deputy administrator, Defense Minerals Administration, Department of the Interior, Washington, D.C. rather than to the Field Offices of the Bureau of Mines as was first planned. Application forms are not yet available but it has been learned that data accompanying the application should include the known quantity and grade of reserves, the anticipated rate of production, the equipment, supplies, and man power required for the additional production, etc.

Jan 12, 1950

By J. S. Diller

In 1827, chromite was discovered near Baltimore by Isaac Tyson, Jr., who initiated the mining of chrome ore an:! later (1845) .the manufacture of chromium compounds in this country. From 1828 to about 1860 the United States, supplanting Russia, supplied chromite for most of the world. Chrome deposits were found also in California, and the Tyson Company shipped ore to Philadelphia by way of Cape Horn. In 1848, J. Lawrence Smith, an American in the employ of the Porte, discovered large bodies of chromite in Asia Minor. They were developed in 1865 and became the chief source of the world's supply for a number of years. The discovery of the large high-grade bodies in New Caledonia, and later in Rhodesia, with other foreign sources, gives at present an abundant supply for all demands. For a number of years before the great war, the United States produced only a few hundred tons of chromite annually, for local use, but during the war the demand for domestic ore resulted in a production of more than 82,000 long tons of crude ore in 1918, and it was demonstrated that the United States has reserve deposits equal to a war demand of several years' duration. Now that the war is over, the country is conserving its domestic supplies by employing higher-grade but cheaper ore from foreign countries. ChromiUm-bearing Minerals Oxides: Chromite-—chromic iron ore................ FeO.Cr2O3 Picotite—chromic iron ore................. (MgFe)O.(Al,Cr) Chromates: Crocoite—lead chromate................... PbCrO4 Phoenicochroite—basic lead ohromite........ 3PbO.2CrO3 Vauquelinite—phospho-chromate of lead..... 2(PbCu)CrOd.(PbCu)3P2O8 Sulfates: Redingtonite—hydrous chromium sulfate.... Knoxvillitel—hydrous basic sulfate of chromium.............................. Daubreelite-—iron-chromium sulfide (known in meteorites only)...................... FeS.Cr2S3

Jan 1, 1920

T. S. FULLER, Chairman C. H. MATHEWSON, Past-chairman W. A. SCHEUCH, Vice-chairman J. L. CHRISTIE, Vice-chairman E. M. WISE, Secretary International Nickel Co., Bayonne, N. J. W. M. CORSE, Treasurer Executive Committee H. A. BEDWORTH W. M. PEIRCE D. K. CRAMPTON A. J. PHILLIPS E. H. Dix JR. GUY C. RIDDELL R. F. MEHL J. WALTER SCOTT JEROME STRAUSS Finance Committee C. H. MATHEWSON, Chairman W. M. CORSE H. S. RAWDON ZAY JEFFRIES SAM TOUR Data Sheet Committee R. S. ARCHER Chairman N. B. PILLING Vice-chairman L. W. KEMPF JEROME STRAUSS A. J. PHILLIPS F. L. WOLF'

Jan 1, 1932

By A. Matsubara

Jan 1, 1922

By A. Matsubara

Jan 1, 1922

By C. P. Gazzara and

The modulus of elasticity and yield strength of commercially pure, annealed titanium sheet was investigated at room temperature as a function of strain rate and direction of loading. The value of E varied with direction of measuremeni in the sheet but was unaffected by strain rate in the range 0.04 x 10-to 10-2min-1. The yield strength increased with increase it2 strain rate and varied with specimen orientation. VALUES of the modulus of elasticity, E, in tension for commercially pure titanium have been reported at from 14 to 20Xl06 psi.' Reasons suggested for this variation have been a) composition, b) strain rate, c) texturing, and d) creep. For example, alloys of titanium with aluminum, manganese, and nitrogen have yielded modulus values of from 12.5 to 16.8 x lo6 psi at room temperature.' It was shown by Klier that the modulus in titanium plate was sensi-tive to strain rate. while Dotson and kattus meas- ured variations in E as the strain rate was increased from 3X to 60 min-l. For RC-7OA, 0.040-in. titanium sheet at room temperature Dotson and Kattus found that the average values of E, for specimens in the rolling direction, increased from 14.7 to 16.0 X lo6 psi as the strain rate increased. Simultaneously, the 0.2 pct yield strength increased from 74,700 to 95,700 psi for the same specimens. Differences in yield strength and E have been reported as a function of directionality in titanium sheet.= Dotson and Kattus report such an effect, and Feola6 found in annealed titanium sheet marked anisotropy in tensile strength, yield strength, reduction in area and elongation at room temperature, with

Jan 1, 1961

By C. G. Goetzel

Until recently porous bronzes have found many applications for self-lubricating bearings in the automotive, electrical, household appliance and general machine industries. The bulk of an annual production of several million pounds of copper powder had gone into the manufacture of these articles, of which by now more than a billion are in service. However, the war has brought severe curtailment of these bearings because of the scarcity of the two main constituents, copper and tin. The development of substitute materials of equal or superior properties has led to a large-scale replacement by products made from iron powder. In spite of the diminished interest in powdered copper-tin alloys caused by this trend, it was believed worth while to investigate some mechanical properties of these materials as a reference base for substitutes. In addition, experiments using the hot-press method were incorporated to investigate possibilities of saving vital equipment or opening new fields of applications. It must be assumed that by this time the powder metallurgy process of making porous bronzes, a development that found its first industrial applications more than 10 years ago, is well known in engineering. The patent literature and bibliography is volu- minous, most publications referring to porous, self-lubricating bronzes, containing about 10 per cent tin and I to 5 per cent graphite, with porosities in the range of 25 to 35 per cent.l-7 The excellent antifriction properties of these bearings, caused by the uniform impregnation with oil, are dependent on the interconnection of the pores and the uniform distribution of the graphite inclusions. The sintering mechanism of porous bronze, with its structural changes during the transformation of the metal powder into the sintered bearing has been shown in colored photomicrographs by Hall.* Diffusion between copper and tin was found to begin within one minute, when tin-rich transitory phases were formed. After 25 min. a homogeneous matrix of alpha was reached for an alloy containing 9.5 per cent tin and 6 per cent graphite. Price, Williams and Garrand,9 studying certain metal powder combinations in which sintering is accompanied by the cementing action of a liquid phase, including a 90-10 bronze sintered at 925°C., have found that if the treatment is carried out within the liquidus and solidus temperature range of the system, a peculiar process of alternate solution and precipitation occurs. The particles of the major solid constituent are dissolved in the minor liquid phase, but thereafter are reprecipi-tated on certain nuclei, which develop into large grains, usually rounded.

Jan 1, 1945

C. N. FEnner, New York City (communication to the Secretary) : A possible explanation of some of the' phenomena of amalgamation cited by Mr. Bayliss and others has occurred to me. We know that if, to a quantity of mercury, gold and silver are added until a putty-like paste is formed, and if this mass is spread on a flat surface and pressure is applied, a more fluid portion of the mercury will be squeezed out from the rest, carrying gold and silver with it. The proportion of gold to silver will depend, I think, upon various causes and conditions—the relative chemical affinity which gold and silver have for mercury; the amount of pressure used; the presence of other metals:

Jan 1, 1898

By A. Rosenzweig, M. M. Karnowsky

The generalized binary diagram of the Au-Sn-Pb system is presented. The chief characteristic is the pseudobinary between lead and AuSn. On the high-gold side of the pseudobinary, four reaction isotherms were found at 363°, 274°, 225°, and 204°C. On the low-gold side of the pseudobinary, three reaction isotherms at 277°, 205°, and 176°C were found. A vertical section from the eutectic solder composition to gold was developed from the isothermal sections generated. METALLURGICAL problems arising from the intentional or accidental formation of Au-Sn-Pb alloys in soldering applications have indicated a need for information on the phase equilibria in this ternary system. The literature indicates that a complete diagram presenting this information has not been prepared. Even the recent excellent work by prince' entitled "The Au-Pb-Sn Ternary System" actually extends only to the AuSn or 50 at. pct Au range. There are more events in the 50 to 100 at. pct Au than in the less than 50 at. pct range. This article by Prince furnished much guidance in preparing this report. Initial efforts with the isopleth from the eutectic solder composition 61.9 wt pct Sn-38.1 wt pct Pb and 0 to 90 wt pct Au indicated that extensions of the work to the whole of the diagram (even if in less detail) were necessary to understand this system. In undertaking the construction of such a diagram, this study used differential thermal analyses (DTA) and metallography with verification and identification of phases by electron microprobe analyses. EXPERIMENTAL PROCEDURE The procedure began with the development of a cell which would be unreactive with lead, tin, and gold, retain its strength to 1100°C, exclude oxygen, and also furnish a suitable well for insertion and protection of a thermocouple to monitor temperature changes in the material. Such a cell would make it possible to reuse the sample should a repetition of determination be desired. Fig. 1 is a photograph of two such quartz cells as finally developed. The specimens have been run many times. The cell is made up of an inner sample bucket and an outer capsule with a thermocouple well which the sample surrounds. The DTA unit was an assembly devised from available instrumentation. The sample holder was a 3-in.-long cylinder of nickel, 2 1/2 in. in diam, fitted securely in a vertical tube furnace. Two holes 7/8 in. in diam were symmetrically located to receive the quartz cells. A dummy cell with nickel powder was used as the reference. The absolute temperature was recorded with a Pt/Pt 10-pct Rh thermocouple with an automatic Kaye ice bath compensator. (Calibration indicated the compensator to be accurate to better than ±0.5° over the 100° to 1000°C range.) The absolute temperature was measured in the sample and recorded on an L&N mul-tirange recorder with a full-scale display of 1 mv and automatic ranging of 99 mv. The differential signal between the sample temperature and the reference temperature was amplified with an L&N microvolt amplifier and recorded on an L&N Speedomax G recorder. Since two charts were obtained, the chart speeds were equalized and each event was noted on the differential chart, and the temperature at that time was obtained from the temperature record.

Jan 1, 1969

By G. J. Ballmer

Trucks Are Valuable Auxiliary Haulage Units in Rail Pits For: ( I ) Making railroad grades (2) Establishing benches (3) Making new dropcuts

Jan 10, 1951

By R. W. Fountain, W. D. Forgeng, G. M. Faulring

Precipitation of the phase Co3Ti (Cu3Au type) from a Co-5 pct Ti a11oy has been investigated using single-crystal X-ray diffraction techniques. Oscillation and transmission Laue patterns of specimens aged for short-time periods at 600" C indicate the formation of titanium-rich and titanium-poor zones coherent with the {100} matrix planes. Longer aging times at 600° C establish that the equilibrium phase also forms on the {100} matrix planes as platelets. These observations are corroborated by electron metallography; electron diffraction studies show the phase Co3Ti to be ordered. A probable sequence of the precipitation reaction is discussed. A previous publication by two of the present authors reported on the phase relations and precipitation in Co-Ti alloys containing up to 30 pct Ti.1 The results of this investigation established the existence of a new face-centered cubic inter metallic phase, ranging in composition from about 17.0 to 21.7 pct Ti at temperatures below 1000° C The decomposition of the fcc supersaturated solid solution was studied employing hardness and electrical resistivity measurements. The changes in hardness upon precipitation in alloys containing 3, 6, and 9 pct* Ti were found to be associated with an initial increase in hardness followed by a plateau and then a second, more pronounced hardness increase. Investigation of this behavior by electrical resistivity measurements suggested that two different kinetic processes were involved, which, when interpreted in terms of the kinetic relation,2-4 indicated that initial precipitation was in the form of thin plates. On continued aging, the plates impinged during the growth process. The general features of these findings have been confirmed by Bibring and Manenc,5 while, in addition, they report the phase to be ordered. The present investigation was undertaken to provide more definite information on the structural relationships between the precipitate and the matrix. EXPERIMENTAL PROCEDURE Single crystals of a (20-5 pct Ti alloy were prepared from the melt employing the Bridgman technique. Poly crystalline rod, 1/2 in. in diam, prepared from vacuum-melted material, was machined to 3/8- in. diam to remove any surface contamination that may have resulted from hot-working. The crystals were grown under a purified hydrogen atmosphere in high-purity alumina crucibles heated by induction. Considerable difficulty was encountered in attempting to grow monocrystals because of the high melting point of the alloy and the high solute concentration. However, one crystal about 6 in. long was obtained which was essentially a single crystal except for one or two very small grains around the periphery. The as-grown crystal was solution heat-treated for 24 hr at 1200°Cin a purified argon atmosphere and water-quenched. One-quarter-in. slices were taken from each end of the solution heat-treated crystal for chemical analyses, and the remainder of the crystal was mounted and oriented by the back reflection Laue Method. The chemical analysis of the crystal was as follows: Pct Ti Pct 0 Pct C Pct N Pct H Pet CO 5.29 0.08 0.004 0.002 0.0003 Balance By proper tilting of the crystal, it was possible to obtain slices 1/32 in. thick of [loo] and [110] orientation. The solution heat-treated crystal slices were sealed in silica capsules for the aging treatments, with titanium sponge placed at one end of the capsule to act as a getter. All slices were water-quenched from the aging temperatures, the capsules being broken under the water to ensure a rapid quench. Thinning of the slices for transmission X-ray studies was accomplished by a combination of mechanical and electrolytic techniques, the final thickness being about 0.1 mm. Laue patterns of the solution heat-treated crystal indicated that no strain was introduced by the thinning technique. ELECTRON METALLOGRAPHY After X-ray examination, the structural changes attending the precipitation were followed by examination of direct carbon replicas of polished and etched surfaces of the single-crystal slices and extracted phases. The earliest indication of significant structural change was observed after aging at 600°C The structure of a heavily etched, solution-treated crystal is shown in Fig. l(a). Aside from the etch pit pattern, no regularity of background structure is observed. On the other hand, in the background of the specimen heated for 500 hr at 600°C, the etching pattern shows a directionality indicating the influence of minute precipitate particles, Fig. l(b). On electrolytic dissolution of this specimen in 10 pct HC1 in alcohol, a large volume of very small, flattened cubes

Jan 1, 1962

By O. D. Sherby

In 1938, Kanter' revealed that the steady-state creep rate of low-carbon iron alloys could be correlated by an activation energy expression, where the activation energy for creep, Qc, was found equal to about 90.0 kcal per mole for most of the alloys investigated. He suggested that creep at high temperatures might be controlled by some sort of solid self-diffusion process since the value of Qc was about equal to the known value for self-diffusion, Qd. Correlations were not further attempted along these lines until many years later, when new evidence2-8 was presented suggesting that Qc = Qd for many metals. This equality now appears to be established for ten metals (Al, Pb, Ni, Mg, Cd, In, a Fe, y Fe, Cu, and Au). This experimental fact prompted several investigators to postulate various mechanisms of dislocation motion which would yield an activation energy for creep equal to that for self-diffusion.7-9 Possibly the most accepted theory is that based on dislocation climb7 where a dislocation is envisioned to surmount a barrier by an atom-vacancy exchange process, thereby "climbing" from one slip plane to another. Such a model would suggest that the steady-state creep rate, i, should be directly proportional to the rate of self-diffusion, D, for a given creep stress. In order to more clearly reveal the relationship between creep and diffusion, and to eventually determine the correct model, it would be desirable to obtain data showing correlations between i and D, rather than with a comparison of the temperature coefficients, Q. It has been known for some time that the self-diffusivity of iron atoms is greatly decreased when body-centered-cubic (a) iron transforms to face-centered-cubic (y) iron. This has been ascribed to the more close-packed structure of y iron. The diffusivity ratio at the transition temperature is Da/Dy =350. Correlations of creep data for a and y iron5 reveal that the creep rates under a given stress at the transition temperature differ by about the same ratio (ea/ey 2 200). It would be difficult to reconcile these results on any other basis than that the diffusivity of atoms probably controls creep of iron in some very direct way. No other published data on other allotropic metals appear currently available for further checking such a possible correlation between i and D. Thallium transforms from a hexagonal close-packed (a) structure to a body-centered-cubic (ß) structure at 230°C (503°K) and the self-diffusivities of the two structures have been determined by shirn.10 His results are plotted in Fig. 1 where it will be noted that Dß/Da = 25 at the transition temperature. It would appear desirable, therefore, to determine the creep rates of polycrystalline a and ß thallium at the transition temperature, as well as determine

Jan 1, 1959

By Norman Goss

IT is generally agreed that cold-working mechanically refines the grains into smaller fragments and with continued working these are oriented with certain crystallographic directions bearing a relation to the direction in which the metal is worked. Some of the energy expended on the metal during plastic deformation appears in the form of heat, but a very small portion remains in the metal as stored energy. The entropy, specific heat capacity, temperature at which recrystallization will just begin, density, ductility, elasticity, tensile strength, and resistance to corrosion are affected. These properties have been studied extensively and some of the changes in the physical properties due to cold-working were attributed to lattice distortion.1-8 The broadening of the K. lines on the X-ray diffraction diagrams of plastically deformed metals is believed to indicate lattice distortion, and consequently the existence of internal stresses. The evidence supporting this theory rests solely upon the observed experimental fact that the dif-fraction lines are broadened and the K a doublets are completely diffused. Elam9 has reviewed the matter of lattice distortion in relationship to the hardening of metals by plastic deformation. The X-ray diagrams of plastically deformed metals differ in general from annealed metals. The hardening of a metal was believed due to lattice distortion.9 The resolu-tion of the doublet is lost when a metal is cold-worked and the Lane spots are elongated. At one time this elongation was thought to indicate the elastic bending of the crystal planes. However, more careful work showed that the asterism was due to new orientations developed within the fragmented grains during plastic deformation. Some theories attrib-uted the hardening to fragmentation of the grains into smaller units.

Jan 1, 1940

By Günter Petzow, Siegfried Steeb

DURING an investigation of the U-Co-A1, U-Ir-A1, and U-Ni-A1 ternary systems, three previously unknown phases have been identified which correspond to the phases UCoA1, UIrA1, and UNiA1, and which be- long to the C22 (Fe2P) type (P 6 2m). In the following the structure determination of the new ternary phases is reported. The alloys have been prepared in an arc furnace under purified argon from 99.97 wt pct U, 99.83 wt pct Co, 99.99 wt pct Al, 99.95 wt pct Ni, and 99.97 wt pct Ir. The pellets obtained were bright and brittle; chemical analyses agreed with the nominal compositions. To obtain equilibrium, the samples were annealed in evacuated quartz capsules at 950°C for 30 hr and then quenched in water. Guinier photographs were processed and evaluated according to a method already described previously.1,2 The hkl's, measured and calculated sin2 6 values, and in the case of UCoAl only calculated and estimated intensities, are given in Tables I to 111. Lattice parameters refined according to the least-squares method and the respective mean-square variations are presented in Table IV. Lattice parameters, especially the c/a ratio, lead to the assumption that the three phases are crystallizing in the C22-type structure. For the calculation of the intensities given in Table I, the atomic positions recently reported by wyckoff3 have been accepted for the C22 (Fe2P) type. The uranium atoms were assumed to be in phosphorus sites; furthermore the scattering amplitudes of the boron atoms have been averaged in the stoichiometric formula UB2 according to atomic percentages; i.e., for these atoms a statistical distribution on the iron sites was assumed. The two smallest distances between a uranium and

Jan 1, 1967

By W. P. Sykes

Seven years ago, Dr. S. L. Hoytl presented a masterful discussion of the hard metal carbides and cemented tungsten carbide. His lecture summarized most of the data then available in the field; many of the details relating to the production, properties and structure of cemented tungsten carbide had never been previously published, for, in fact, this information was only then being acquired. During the intervening years, the cemented carbides have assumed a place of real importance in the commercial field, with an ever widening variety of applications due to constant improvement in the control of production technique and the unremitting search for new compositions that might better the performance of the alloys in one or another type of service. The most recent summary of production methods, properties and guides for the successful application of the cemented carbides appears in the 1936 edition of the Metals Handbook. Of necessity, much detailed information relating to structures and physical properties is not included in such a summary, and it is with such details that the present discussion is concerned. Steps in Preparation While the past 25 years have contributed a valuable store of working knowledge in the field of powder metallurgy, many of the process controls are derived entirely from experience and are not as yet finally explained by a specific physical or chemical phenomenon. For most of the cemented carbides such difficulties are aggravated by our lack of knowledge not only of the complex alloy systems involved, but also by the possible changes in structure and even in composition which may accompany variations in temperature, heating time, and furnace atmospheres. The principal steps in the preparation of these cemented carbide alloys are fairly well known, but to supply a foundation for discussion these steps are briefly outlined as follows : 1. Formation of the metal carbide in the form of powder by heating a mixture of carbon and the metal powder or oxide for several

Jan 1, 1938

By W. P. Sykes

Seven years ago, Dr. S. L. Hoytl presented a masterful discussion of the hard metal carbides and cemented tungsten carbide. His lecture summarized most of the data then available in the field; many of the details relating to the production, properties and structure of cemented tungsten carbide had never been previously published, for, in fact, this information was only then being acquired. During the intervening years, the cemented carbides have assumed a place of real importance in the commercial field, with an ever widening variety of applications due to constant improvement in the control of production technique and the unremitting search for new compositions that might better the performance of the alloys in one or another type of service. The most recent summary of production methods, properties and guides for the successful application of the cemented carbides appears in the 1936 edition of the Metals Handbook. Of necessity, much detailed information relating to structures and physical properties is not included in such a summary, and it is with such details that the present discussion is concerned. Steps in Preparation While the past 25 years have contributed a valuable store of working knowledge in the field of powder metallurgy, many of the process controls are derived entirely from experience and are not as yet finally explained by a specific physical or chemical phenomenon. For most of the cemented carbides such difficulties are aggravated by our lack of knowledge not only of the complex alloy systems involved, but also by the possible changes in structure and even in composition which may accompany variations in temperature, heating time, and furnace atmospheres. The principal steps in the preparation of these cemented carbide alloys are fairly well known, but to supply a foundation for discussion these steps are briefly outlined as follows : 1. Formation of the metal carbide in the form of powder by heating a mixture of carbon and the metal powder or oxide for several

Jan 1, 1938

By H. S. Price, J. C. Cavendish, R. S. Varga

This paper presents a new technique for solving some of the partial differential equations that are commonly used in simulating reservoir performance. The results of applying this technique to a simple problem show that one obtains accurate pressure values near wells, as well as accurate pressure pdients, which can be explicitly calculated. The method is completely rigorous in that convergence of the discrete numerical solution to the continuous solution for both pressure and pressure gradient is established. High-order, piecewise-polynomial approximations are used near the wells where pressure gradients are steep, while low-order, piecewise-polynomial approximations are used elsewhere to reduce greatly the calculation time. This combination is shown to give a uniformly good approximation to the solution. These approximations, obtained by using a Galerkin process with suitable Hermite subspaces, are shown to be theoretically and numerically superior to the usual approximations obtained from standard finite-difference techniques. Not only are much greater accuracies obtained, but computer times are also greatly reduced. The application of this technique to multiphase flow problems (e.g., single well coning problems) would have considerable practical interest, but such extensions of this technique with full mathematical rigor have not been made as yet. However, the numerical methods presented here are general, and in principle extend to multidimensional, multiphase flow. Moreover, the preliminary results given in this paper are sufficiently encouraging that we feel the effort in attempting these extensions is justified. INTRODUCTION The problem of obtaining accurate pressure distributions and pressure gradients around wells is of considerable importance in the numerical simulation of reservoir performance. The most common approach to solving this problem is to use finite difference techniques (see McCarty and Barfield9 or Peaceman and Rachfordl0). This approach, however, has many disadvantages, the major one being that many grid points are generally necessary for accurately describing the pressure distribution and the pressure gradient around wells. This need for a fine grid results in large computer times and often in prohibitively high costs. Besides investigating the method of finite differences, some authors, such as Welge and weber17 and Roper, Merchant and Duvall,13 have considered a combination of analytical and numerical techniques with some success. These approaches, however, are all nonrigorous and quite often cannot even be applied. In this paper, we present a numerical formulation of high-order accuracy, based on the Galerkin method, for solving this problem. We treat here only the partial differential equation that describes steady-state, single-phase flow. However, the methods presented are general and in principle extend to multidimensional, multiphase flow. Specifically we treat special cases of the problem in two dimensions described by: where G is a rectangle (with sides parallel to the coordinate axis) with boundary ?G, ?/?n denotes the outward normal, and y and B are non-negative constants such that y + B > 0.

Jan 1, 1970