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By F. C. Langenberg, R. W. Lindsay

COPPER sometimes is added to steel and cast iron as an alloying element to improve or impart specific properties. However, in some steels it exerts an impurity effect in impairing response to fabrication by hot working and deep drawing. The resid-

Jan 1, 1955

By H. C. Vacher, C. J. Newton

EXTENSIVE investigations in the field of residual strain measurement by X-ray diffraction have been made by Bollenrath, Hauk, and Osswald,1 by Smith and Wood,2'3 by Greenough; by Rosenthal and Norton." and many others. Since X-ray strain measuremeits apply only to those crystals of the test body which are of the proper condition and orientation to diffract and since the residual strains revealed may be accompanied by either body or tex-tural stresses, there has been considerable disagreement among investigators with respect to the validity of conclusions in this field. Although the experi-mentors have employed a variety of loading schemes, surface preparations, and X-ray wave lengths, the observations almost invariably have been made only on the outer surfaces of the specimens. The present note is not to be construed as an exposition of a new method of stress analysis by X-ray strain measurements on sections but as a presentation of some results which point to interesting possibilities for further experiments with sections. The two test rods used in this study were of ingot iron annealed at 910°C. The initial length of the gage section was 2 in. and the diameter was 0.415 in. Cross-sections were cut from the ends of the annealed rods to provide strain-free material. The tensile rod was axially loaded the desired amount in a commercial testing machine. A 1 in. portion of the gage length was cut from the other rod and was subjected to compression in the same machine. Details of this plastic straining of each rod are given in the upper half of Table I. A half-cylinder piece about 1/4 in. long was obtained by making a short longitudinal plane cut containing the axis of the rod near the center of the gage length. From adjacent material a disk about 1/8 in. thick was cut to provide the cross-section specimen. Later another section was cut from this same region with an angle of 30" between the normal to its surface and the axis of the test rod. A cross-section and a longitudinal section were cut from the compression rod in a similar manner. All of these as well as the strain-free cross-sections were mounted in Bakelite and used as specimens for the following X-ray strain measurements. During the course of the study, it became apparent that the condition of the surface of a specimen was a highly critical factor. One of the annealed strain-free specimens as a control was subjected to about 24 hr of polishing with fine alumina, interrupted about every 2 hr for etching with 1 pct nital. Its lattice parameter was determined at intervals from measurements on back-reflection X-ray diffraction patterns, which were calibrated with diffraction from tungsten powder. The parameter gradually approached the value found in the literature for strain-free iron and remained there, within the limits of the experimental error. This determined a long polishing and etching procedure which was adopted for all the specimens and which gave X-ray results from the surfaces believed to be representative of each specimen as a whole. A large number of back-reflection patterns were made with cobalt and chromium radiation, all at normal incidence. Except for some preliminary stationary exposures made to monitor the removal of cold work from the surfaces, each exposure was made with the specimen slowly translating and the film slowly rotating. In appropriate cases a thin layer of a standard metal powder, tungsten with cobalt radiation and silver with chromium, was dusted over a film of vaseline on the surface of the specimen to serve to calibrate the X-ray patterns. After the preliminary work, four films were made,

Jan 1, 1956

By B. L. Averba

THE determination of retained austenite by X-ray diffraction uses the following relationship:"" Pa = constant . RVaA (8) [1] where: P is the diffracted power from phase a; R, the calculated intensity factor; A, the absorption correction; 8, the diffraction angle; and Va, the irradiated volume of phase a For a flat sample making a glancing angle + with the incident beam the absorption correction is calculated as: * 1 sin (28 - 4) A .= 1 [2] µ sin, (28 — 4) + sin 4 where µ is the linear absorption coefficient. Beu3 has proposed that the computed absorption correction be combined with the constant and that the experimental observation of the absorption correction used in the original method be eliminated. This procedure is permissible only if: 1—There is no preferred orientation in the sample, and 2—The geometric requirements have been met precisely. If these conditions are not met the validity of the determination is questionable. Unfortunately the necessary conditions must be tested experimentally for each determination, and this is done most easily by observing whether the apparent absorption has the form of Eq. 2. In practice it may be convenient to plot P/R vs the parameter sin (2? — )[sin (28 — +) + sin +] to obtain straight lines for the ap- parent absorption correction. Deviations from straight lines indicate either that the sample has not been positioned correctly or that the relative intensities are incorrect. Geiger counter spectrometer methods also have been used successfully for retained austenite determinations. In the usual spectrometer arrangement the sample makes equal angles with the incident and diffracted beams (8 = ); thus the absorption correction is simply 1/2µ and independent of 8. The retained austenite is then easily calculated from integrated intensity measurements on austenite and martensite lines. If the austenite content is not too low and if excessive fluorescence is not encountered it is possible to use filtered radiation and a recording spectrometer. The integrated intensities are then proportional to the areas of the diffraction peaks. For lower austenite contents the following technique was used: A bent quartz monochromator and a Geiger counter spectrometer are employed. The monochromatic radiation is focused on the front slit, and the counter slit is made broad enough to include the entire line. A series of readings are taken in the vicinity of the diffraction peak. The highest reading includes the diffraction line plus background. The background is obtained from the average of several readings on each side of the peak. The integrated intensity is obtained by subtraction. CrK, and FeKa have been used for such determinations. This technique has been found to be as sensitive and as accurate as the photographic methods. In the spectrometer methods the ratio austenite/ martensite may be obtained from readings on austenite and martensite lines and the application of Eq. 1. It is also possible to use external standards and to obtain the austenite contents from measurements on the austenite lines alone. The small correction for carbides then becomes unnecessary. The best standards are probably samples with known

Jan 1, 1954

By E. S. Machlin

THE function of this paper is to present certain results based on the fact that the strain energy arising from the solution of out-of-size solute atoms into the solid matrix is free energy and not internal energy, and that this strain energy is almost wholly shear strain energy as Zener1 pointed out. One natural consequence of this fact is an expression for the excess entropy of mixing due to the strain energy. Also, a derivation of the integral molar free energy of mixing partitioned to strain energy will be made using the model of Lawson2 and thermodynamics. This derivation has the advantage of showing in a simple way the assumptions involved in Lawson's treatment. The excess entropy of mixing partitioned to strain energy can be derived in two ways. The first way makes use of the fact that the strain energy is almost wholly in the form of shear strain energy. In this case, as Zener1 pointed out, the change in entropy due to the addition of shear strain energy is to a first approximation given by ?S/?? p,T = - ?lnµ/?T p,? Hence, the excess entropy of mixing partitioned to strain energy will be given by Sx ? = ?S/?? p,T Gx ? = - ?lnµ/?T p,? Gx ? where, Gx ? is the relative integral molar free en- ergy partitioned to strain energy; S is the entropy; is the shear strain energy; µ is the shear modulus; T is the absolute temperature; p is the pressure; and ? is the shear strain. Zener,1 as well as others, has pointed out that the shear strain energy stored in a compressible isotropic solid due to the insertion of an off-size incompres-sible sphere into a spherical hole in the solid, is approximately given by 2/3 µ/O (O°I - O)2 where a is the volume of spherical hole and no , is the volume of sphere. If we now consider the introduction of one mol of such spheres into an infinite volume of solid, then the relative partial molar free energy excess due to strain energy alone is GM ? = 2/3 µ/v (v ° 1 - v)2 where v is the molar volume of solvent and v°1, is the molar volume of pure solute type 1. Let us consider that these spheres are the two types of atoms in a binary solution, then there will be a similar relation for solute 2. The total relative integral molar free energy excess due to strain is then, to the approximations stated above GM ? = GM ? x1 + GM2 ? x2 = 2/3 µ/v [(v ° 1 - v)2 x1 + (v ° 1 - v)2 x2]. Lawson's relation for the strain energy can be de-

Jan 1, 1955

By C. G. Dunn, M. Sharp

HE orientations of 137 crystals of copper pro-T duced by secondary recrystallization in a cube texture matrix have recently been obtained. Although the crystals were not prepared for the purpose of determining a secondary recrystallization texture, the orientations obtained proved to be rather interesting, as they confirmed, in part, published results and also disclosed additional preferred orientations in the texture. The investigation of Dahl and Pawlek,&apos; Bowles and Boas,&apos; and Kronberg and Wilson3 showed respectively that the orientations of secondary grains growing in a cube texture matrix were related to those of the primary grains by a rotation of approximately 30" about [001], the rolling direction, by 30" about a <111> direction, and by either 22" or 38" about a <111> direction. Kronberg and Wilson also obtained a component of the texture similar to that of Dahl and Pawlek except the angle of rotation about [001] was 19". When the cube texture matrix was deformed a small amount, Kronberg and Wilson also obtained large grains on subsequent annealing corresponding to a rotation of 15" about the normal to the sheet, but these grains should not be classified as secondary recrystallization grains since they were produced subsequent to mechanical straining. The particular texture obtained, of course, depends on the composition of the copper and the processing schedule employed, since these factors markedly affect the primary recrystallization texture and the sharpness of any cube texture produced. In the present investigation, pieces of OFHC copper in the form of M in. round bars were cold forged to a thickness of about 0.40 in., annealed 1 hr at 350°C in an atmosphere of hydrogen, and cold rolled crosswise to a thickness of 0.200 in. These pieces were given a penultimate anneal of 1 hr at 350°C in hydrogen and a 90 pct cold-rolling reduction lengthwise to a thickness of 0.020 in. Indentations generally were put in one end of the as-cold-rolled strips to promote earlier formation of secondary grains.

Jan 1, 1953

By Gordon W. Hodgson, Edward Tipman

INT&apos;RODUCTION An appreciable number of the oil fields in Western Canada are accumulations of heavy black oils in more or less unconsolidated sandstones. When the crude oils are produced by conventional means, they are frequently contaminated with both sand and oilfield water. The water is usually present as emulsified water, and the sand and other solid materials are suspended in the emulsions. The presence of the solid material in the crude oils is troublesome and, in general, little is known about the behavior of suspended solid particles in emulsions. The Stokes equation describes the behavior of suspended particles in homogeneous fluids in terms of particle size, density differential, and fluid viscosity. In the case of an emulsion, particle size and density differential introduce no difficulties, but considerable doubt centers around the viscosity term. It has been reported1 that the viscosity of an emulsion is related to the viscosity of the continuous phase by an expression of the type: n = a, (1 + a C) where n is the viscosity of the emulsion, n,, is the viscosity of the continuous phase, a is a constant, C&apos; is the volume concentration of the disperse phase. The value of 17, the coefficient of the concentration term, has been determined for various systems, and has been found to vary from a value of 1 to 4.75. The value of 2.5 has been found to be applicable to a large number of systems, and this is the value that is widely used in the equation which then becomes the Einstein equation for the viscosity of emuls~ons. It is of considerable significance that neither the particle size nor the viscosity of the disperse phase enters the expression; the expression for the viscosity of the enlulsion is based solely upon the viscosity of the continuous phase and the concentration of the disperse phase. For crude oil emulsions the Simha equation and the data presented by Fukushima and lchimurai show a non-linear dependence of the viscosity ratio on the water concentration. While it is undoubtedly reasonable to use these data for predicting the viscosity of a specific emulsion, and while it is equally reasonable to expect the calculated viscosity to predict the settling rate of a solid spherical particle in the emulsion by means of Stokes equation, there seems to be no direct evidence that this calculation is indeed sound for describing the settling rates of solid particles in emulsions of water in crude oils. PROCEDURE A direct approach to the problem was thus indicated. Laboratory equipment was designed and built for the direct determination of the rate-of-fall characteristics of solid particles in emulsions of water in oil. Although the apparatus incorporated the basic design of conventional falling-ball viscometers, the study was concerned directly with the rate-of-fall characteristics of particles in emulsions, rather than with the viscosity of the emulsions as such. The crude oil used in this study was a very heavy black crude oil—the McMurray oil obtained from oil-soaked sands outcropping on the Athabasca River in northeastern Alberta. It was produced from the sands by strip mining followed by hot-water separation of the oil in the separation plant of the Alberta Government at Bitumount&apos;. The primary plant product was a wet crude oil containing about 5 per cent solids and 35 per cent water. The final plant product was only slightly different from the native oil, having lost only about 4 per cent of its bulk as light ends during dehydration distillations. In the present investigation two kerosene dilutions of the McMurray oil were used in addition to the dry plant product. The McMurray oil contained 1.92 per cent solids. Analysis of the solids by X-ray diffraction showed the presence of kaolinite, pyrite, and illite as major constituents. with lesser amounts of quartz. Particle size of the pyrite and quartz was less than 10

Jan 1, 1957

By Lawrence Adler

MINE hoist ropes have hitherto been selected by successive approximation, a process both tedious and inexact. The proposed expression is a readily solved synthesis of existing data and the following standard equation:&apos; [ W + Wr + (W + Wr) -a 9 (W + W)f + b] n=T [1] For convenience, a glossary of all terms appears on page 564. Since rope weight (W,) and bending load (B) are functions of unit rope weight (Wv), which in turn is a function of rope strength (T), W, and B can be expressed in terms of T. W, as a Function of T: A study of the curve in Fig. 1, unit rope weight vs strength, yields Eq. 2: W. = -f- [2] Therefore Wr = WvL = T. [3] iv B as a Function of T: From Fig. 2, unit rope weight vs diameter, Eq. 4 is obtained: W, = 1.6d2 [4] B is related2 to d and D, and d has been expressed in terms of W, by Eq. 4, so the curve B vs W, (Fig. 3) gives Eq. 5: 177,000 177,000 This may readily be checked from the expression3 for a 6x19 rope, i.e., d3 B = 288,000D Since d2 = 0.625 W, and N = substituting d into the above expression gives Ea. 6: 180,000 180,000 B T, which will be used. [6] Into Eq. 1 substitute Eq. 3 and Eq. 6, noting that f=0.02: W + T 1.02+=T. [7]

Jan 1, 1958

By F. S. Buffington, Morris Cohen

THERE is little quantitative information available concerning the effect of applied stress, in both the elastic and plastic ranges, on diffusion kinetics. Accordingly, a program has been undertaken to determine the rate of self-diffusion in high purity iron, with the specimens subjected to stress during the course of diffusion. Results are reported here for body-centered cubic iron at a diffusion temperature of 890°C. The iron used was 99.97 pct Fe, the principal impurities being 0.002 pct C, 0.008 pct 0, and 0.02 pct Si. The surface-decrease method of self-diffusion analysis was employed, and Fe55 Mn x-radiation, 2.9 years half-life) was the tracer element. Details of specimen preparation and equipment are given elsewhere.&apos; Disks of the high purity iron, % in. diam x 1/4 in. thick, were annealed at 890°C for 18 hr in dry hydrogen to produce large grains of a ferrite. The faces of the disks were then surface ground, and possible grinding stresses were relieved by annealing at 890 °C for 45 min in vacuum. A layer of radioactive iron 0.00186 cm thick was electroplated on one face of each disk. The self-diffusion coefficient was calculated from the ratio of the radiation intensities emanating from each of these faces, as measured before and after diffusion.&apos; The heating was carried out in a vacuum furnace (10-5 mm Hg) controlled to ±1.5°C. The specimens were loaded in compression between two quartz disks during the diffusion runs by means of a lever system operating through a vacuum seal. Thus one quartz disk was pressed directly against the radioactive face of the specimen, minimizing the vapor loss of radioactive iron. Steady-state creep occurred in all instances where permanent deformation could be detected, but the specimens did not exhibit appreciable transverse barreling until natural strains of 0.2 to 0.3 were attained. Essentially, the diffusion took place under uniaxial stress. The plastic strain in each case was obtained at the diffusion zone by measuring the diameter d there before and after the run: e = 2 In — do Let Du equal the self-diffusion coefficient which would have prevailed at the given temperature if no stress had been applied. This was calculated from the temperature-dependence equation which had been previously determined: —59,800 D, = 6.2 exp ( I sq cm per sec* [I]

Jan 1, 1953

By D. S. Bloom

RECENTLY a report has been published on an investigation of the MO-RU system by E. Raub.&apos; In this report it is stated that below approximately 1200°C the system consists of two terminal solid-solution phases and the intervening two-phase field; at 1200°C and above, an intermetallic compound labeled Mo,Ru, makes an appearance. Along with some other little known systems in which it was considered possible for a u phase to form, the Mo-Ru system had been under investigation in this laboratory. Since molybdenum and ruthenium have very high melting points and also since ruthenium is expensive, the investigation was confined to X-ray diffraction by sintered powder compacts. The compositions which were studied were (in atomic percentages): 75 Mo-25 Ru, 67 Mo-33 Ru, 50 Mo-50 Ru, and 25 Mo-75 Ru. All compacts were made from the pure powders, and no chemical analyses were attempted. Each compact weighed about 5 g. All annealing was done in evacuated Vycor capsules, and even though the capsules completely collapsed at 1250°C, they still admitted no air. The results of this investigation in general corroborate the work of Raub. Up to 1150°C the two terminal solutions and the intervening two-phase field were found, and at 1200°C and above an intermetallic compound was found. However, the composition limits of the compound were estimated to lie close to 70 atomic pct Mo rather than 62.5 atomic pct Mo as Raub had reported. At least the X-ray diffraction results indicated that the 75 atomic pct Mo specimen consisted of the molybdenum solid solution plus the compound, while the 67 atomic pct Mo specimen consisted of the ruthenium solid solution plus the compound and the equiatomic composition contained only very little of the compound. The most interesting observation, however, was that the diffraction pattern of the compound was similar to that of the well known u phases, except that unusually large lattice constants were indicated. The d-values, or interplanar spacings, of the diffraction lines (as produced by filtered copper KCX radiation) of the compound are given in Table I, as determined from specimens annealed at 1250°C for 9 hr and then quenched in water. Also shown are the lines of the Mn-Mo u phase as given by Decker, Waterstrat, and Kasper,&apos; the lines of the Fe-Mo a as given by Goldschmidt," and the lines of the Mo-Ru phase multiplied by constants in order to make comparison with the Mn-Mo and Fe-Mo patterns easier. These results indicate that the compound in the Mo-Ru system is apparently isomorphous with the other o- compounds. The rather large lattice constants of the Mo-Ru a phase are acceptable in view of the comparatively large size of the constituent atoms. The data in Table I for the Mo-Ru compound check quite well with those given by Raub, not shown here, though there are some discrepancies between the two sets of data in the estimated intensities of a few lines. Although very little is known at present about this u phase, there are some things which may be pointed out, mainly in comparison with other better known u phases. Even though molybdenum and ruthenium are in the same columns in the Table of Elements as chromium and iron, respectively, the Mo-Ru u phase contains much more molybdenum than ruthenium, while the Cr-Fe u phase centers around or very nearly around the equiatomic composition; furthermore, the Mo-Ru u is stable only above approximately 1200°C, but the Cr-Fe u is stable only below about 825 °C. With respect to its being unstable below 1200°C, the Mo-Ru u is similar to the other binary molybdenum u phases in the Co-Mo and Fe-Mo systems. Similar to the latter two systems, the Mo-Ru u apparently exists over a rather narrow composition range, whereas the Cr-Fe u at lower temperatures is stable over a much wider composition range. The Mo-Ru u thus is closer to the other molybdenum u phases than to the Cr-Fe cr phase. The most striking feature of the Mo-Ru u phase, however, is the absence of any of the transition elements of the First Long Period.

Jan 1, 1956

By J. W. Downey, M. V. Nevitt

DURING the course of the present investigation of alloy phases involving transition metals, phases were found in the systems Os-Ta, Os-W, and Ir-Ta. The (Os, W) phase was also recently reported by Raub.1 Pertinent information is given in Table 1. The approximate composition range of sta- bility was determined metallographically on arc-melted buttons that were annealed 72 hr at 1200°C and water quenched. X-ray powder patterns were obtained with a 114.6 mm diam powder camera using filtered copper radiation. The composition for (Os, W) given by Raub (66 atomic pct W) is in agreement with the composition range reported here. However, the lattice constants reported by Raub are: a0= 9.913±0.007, c/a= 0.515. The reason for the discrepancy between the lattice constants reported by Raub and those given here is not known. Acknowledgments The authors wish to thank M. H. Mueller and H. W. Knott for assistance with the X-ray diffraction work, and R. A. Morris for the preparation of the alloys. This paper is based upon work performed at the Argonne National Laboratory under the auspices of the Atomic Energy Commission.

Jan 1, 1958

By Bernt Ellingsaeter, Terkel Rosenqvist

IN the silicothermic reduction of magnesia, burned dolomite is treated with high grade ferrosilicon in an evacuated steel retort at temperatures between 1150° and 1200°C. The following reaction is assumed to occur MgO + CaO + 1/2 Si (Fe) - Mg(g) +- & Ca,SiO, + Fe with the equilibrium constant on the basis of thermodynamic data for the substances involved and assuming unit activity for all solid constituents, Kubaschewski and Evans&apos; calculated the magnesium pressure as a function of temperature logp,, (mmHg) = 15.06-1.61 T- log T- 13,16O/T. Pidgeon and King," who measured the magnesium pressure by means of a flow method, found values about three times the calculated ones. This may be caused by uncertainties in the thermodynamic data, but may also be caused by the formation of other reaction products, such as Ca,SiO,, which is known to be the stable silicate in equilibrium with lime. Whatever the exact reaction may be, it is evident that as long as all other factors are maintained constant the magnesium pressure will vary with the silicon activity, viz: p,, = &,. (p,,) ", where (p,,)" is the magnesium pressure by the reduction with silicon of unit activity. In the present investigation, p,,, was therefore measured for various grades of ferrosilicon and their silicon activities were calculated. The experimental method was similar to that used by Pidgeon and King. Briquettes of burned dolomite and Fe-Si alloys were placed in a 1 in. heat resistant steel tube and were heated to 1200°C. By means of a flow of purified hydrogen, the magnesium vapor was swept into a condenser filled with steel wool. From the amounts of hydrogen used and magnesium condensed the magnesium partial pressure was calculated. First a tube of 28 pct Cr steel, and later a tube of Kanthal D (a ferrous alloy with 22.6 pct Cr, 2 pct Co, and 4.5 pct Al), was used as a heat resistant tube. The latter tube showed the best heat resistance. The dolomite used had the following composition: 43.6 pct MgO, 55.5 pct CaO, 0.2 pct K,O + NalO, 0.2 pct Fe,O,, and 0.3 pct insoluble. The ferrosilicons were prepared from 98 pct Si of technical grade (0.7 pct Al, 0.3 pct Ca, and 1 pct Fe) by melting with various amounts of electrolytic iron of high purity. The alloys thus obtained were analyzed on their iron and silicon contents, which added up to between 99 and 100 pct. The amounts of reactants were chosen so that there would always be an excess of the oxides, and the average decrease in silicon content during the experiments would be about 1 pct. Most of the reaction occurred in the part of the reaction mixture facing the gas flow. The change in the silicon concentration in the part facing the condenser was, therefore, negligible. To facilitate the reaction, about 1 pct fluorspar was added to the briquette mixture. Fluorspar does not enter the reaction, but is known to act as a

Jan 1, 1957

By R. P. Carreker, R. L. Fullman, J. C. Fisher

CREEP tests are usually constant load tests. As deformation occurs, the cross section of the specimen changes so as to maintain approximately constant volume. Until necking starts, A _ l0 A0 - 1 where A is the cross-sectional area, 1 is the specimen length, and the subscript o indicates initial values. Thus, during a tensile creep test under constant load, the stress increases in proportion to the elongation. A A, 1, where S is the stress and F the load applied to the specimen.

Jan 1, 1954

By K. S. Milliken

NORMAN W. Lord&apos; has shown that the resultant impurity distribution after n zone passes is given by in the ingot section OSa<N—n, where a is the displacement in zone lengths, N is the ingot length in zone lengths, C,, is the initial uniform impurity concentration, k is the segregation constant = Ceoll C,,,,,,,, at equilibrium, and The foregoing expression is formidable in respect to computational labor. However, the triple sum can be reduced as follows is better if computing for only a single value of n. For k<l, it can be shown that this last equation is equivalent to The infinite series is useful only when k is small enough to force rapid convergence. In such cases, the absence of subtraction from unity has the definite advantage of preserving accuracy. Acknowledgments It is a pleasure to acknowledge stimulating correspondence with Dr. Howard Reiss of Bell Telephone Laboratories Inc. This note is published by permis-sion of the Deputy Minister, Dept. of Mines and Technical Surveys, Ottawa, Ont., Canada.

Jan 1, 1956

By G. W. Tracy

The material balance equation has been used for many years by engineers to determine reservoir performance. The use of this equation in general has been twofold: first, to determine the oil-in-place in a reservoir; and second, to predict the future performance. The Schilthuis form of the material balance equation, or one equivalent to it, has been used by many of the engineers. The use of the Schilthuis form in predicting future performance has proved to be laborious in that one generally must make several estimates at each step of the trial and error calculation before arriving at a check of the oil-in-place. A method is presented for expediting the calculations. The Schilthuis form of the material balance has been rearranged into a more useable form. In using the material balance to predict the future performance of a reservoir, it has become common practice to estimate the incremental oil production for each step of the calculation which corresponds to a given pressure reduction. Instead of estimating the incremental oil production, the method outlined in this paper better lends itself to estimating the instantaneous gas-oil ratio. A check of oil-in-place is more easily accomplished by estimating gas-oil ratio since it is less sensitive to small inaccuracies. This method incorporates the same self-checking feature inherent in the Schilthius form. DEVELOPMENT OF SIMPLIFlED EQUATION In the development of the simplified equation, the Schilthuis form of the material balance equation will he used. Substituting in Equation 1 for and rearranging terms In Equation 2, the cumulative oil production (n) is multiplied by a factor which is uniquely a function of pressure. Also, the cumulative gas production (G) and net water influx are also multiplied by factors which are a function of pressure alone. These factors are called and are defined as follows: Using these factors, Equation 2 becomes The equation in this form is easier to manipulate mathematically than any of the previous forms which, have been used. Sources of data for the pressure factors are a bottom-hole fluid analysis and the ratio of initial gas cap volume to oil volume in the reservoir. AID IN DETERMlNING THE ORIGINAL OIL-IN-PLACE Each of the curves and +, have a similar shape. Each is infinite at the bubble point pressure. As lhe pressure is reduced below the bubble point, the

Jan 1, 1956

By N. L. Ananthanarayanan, J. F. Libsch

A LITERATURE survey1-&apos; of sintering metal pow-A ders and powder compacts indicates that studies have so far been confined primarily to the latter stages of sintering in relatively coarse powders. Presumably this is due to the difficult techniques associated with studies of the early stages of sintering. Recent experimental and theoretical investigationsL-" on the preparation and the magnetic properties of ultrafine ferromagnetic powders suggest the possi- bility of following the sintering process from a very much earlier stage than has previously been considered. It is now well-known that ferromagnetic powder particles which are below a critical size behave as single domains and exhibit permanent magnet qualities characterized by a very high coercive force. When the same particles are fully sintered, the coercive force decreases to very low values corresponding to those of the solid metal. Thus the coercive force appears as a sensitive parameter which may be measured to study the early stages of sintering. To determine the feasibility of this technique, experi-

Jan 1, 1954

By D. W. Fuerstenau

In 1940 Schuhmann1 showed that the size distribution of a comminuted material can be expressed by the following empirical relationship: y = 100 (|f [i] where y is the cumulative percentage of material finer than size x, k is a size modulus, and a is a distribution modulus which is constant for a given material and machine. During the past few years, considerable emphasis has been given to the investigation of the extent of size reduction resulting from the expenditure of mechanical energy in crushing and grinding. Recently Schuhmann&apos; presented a derivation of the energy-size reduction relationship by postulating that comminution in a device such as a ball mill can be considered to be the summation of many single comminution events, each of which yields a size distribution of particles following the Schuhmann size distribution equation. By grinding

Jan 1, 1961

By N. J. Grant, I. S. Servi, A. Chaudhuri

IN a recent paper by Servi and Grant,&apos; it was illustrated that the slip band spacing and stress based on creep test data were related by the equation: d =1/ where d is the spacing in millimeters and v is the stress in psi, based on a more complete equation proposed by Orowan. It was shown further,&apos; that for a. given grain size, the slip band spacing became larger with decreasing stress (and was independent of temperature), until such time that the slip band spacing becomes greater than about one-half the grain diam- eter. When this occurred, the mechanism of deformation in creep of 2s aluminum at high temperature changed from slip to grain boundary deformation (sliding). Additional metallographic evidence is now available which confirms this in a most interesting fashion.

Jan 1, 1954

By E. S. Greiner

THE hot working of chromium was first reported by Hunter and Jones; who used small pellets of the material obtained by the reduction of chromium chloride with sodium. Later, the working of chromium at 600° to 1100°C was reported by Marden and Rich,2 and at 1250°C by Kroll3 The hot rolled material3 had a Brinell hardness of about 150 (62.5 kg, 2.5 mm ball, 1 min) and was brittle at room temperature. Except for that associated with hardness indentations, no plastic flow in chromium at room temperature has been reported to the author&apos;s knowledge. Studies described here have shown slip markings in chromium after deformation at room temperature.

Jan 1, 1951

By C. S. Smith

The partial persistence of grain size and grain shape on melting and resolidifying crystalline substances, as well as the general effects of pre-solidifi-cation and of superheating on nuclea-tion rate, have been attributed to the presence in the liquid of crystalline impurities bearing some structural relation to the principal solid and hence capable of serving as nuclei for its crystallization. That such lattice matching does sometimes occur is well established, but it is surely improbable that a compound possessing both high-temperature stability and the requisite structural similarity should be naturally available in almost every system. It is now suggested that a mechanism for producing appropriate nuclei exists in the crystallization of all but absolutely pure substances. Impurities can he of many kinds. Some will give rise to compounds that are less soluble in the solid crystal than in the liquid. A . crystal forming from a melt or solution containing these will be supersaturated in some degree, and the foreign atoms will commence to segregate during or after solidification. They do not necessarily form pure, unstrained, crystals of the precipitating compound with its normal composition and structure. Generally—at least in the metallurgical examples that have been most studied —the first recognizable nuclei have lattice coherency with the surrounding matrix and have practically the same crystal structure and lattice spacing as the material in which they form, differ- ing only in composition. An extremely thin oxide layer formed under appropriate conditions on or in a solid metal will tend to be coherent with the metal lattice, and the first few atom layers of the oxide in contact with the metal will differ in both composition and structure from massive crystalliue oxide. It will resemble the metal more closely than the oxide. If it did not subsequently change on melting, such an oxide film would constitute an almost perfect "template" or two-dimensional matrix to hold a few atoms of the primary metal in the exact array needed to form a nucleus for solidification. Any precipitating material will adopt the correct spacing over a few atom diameters, and with appropriate substitution of other atoms of the correct sizes a precipitate can match the parent lattice over large areas of cohererlce without excessive strain. In metals, the componentsof a host of oxides, silicides, borides, nitrides, carbides, sulphides, and other compounds are always present in minute amounts. Some of these will be eliminated because of extreme insolubility in the liquid, while others will remain soluble in the solid; occasionally, however, particles will be formed in the solid by coherent precipitation—not of pure substances, but of whatever assortment of atoms best satisfies the joint requirements of availability, affinity, and appropriate average atom size. Of these, many will disappear on melting, but a few will persist unmelted as little rafts of complex composition, maintaining in the liquid a surface of the exact geometry needed to nucleate the solid on subsequent cooling. Their number and size distribution will determine the resulting grain size; the dimensions of the largest will determine the degree of undercooling that can occur before solidification commences. A similar process may operate in the case of phase transformations in solids. The coherent precipitation of supersaturated minor constituents in a low-temperature phase should facilitate the nucleation of this phase on subsequent cooling after transforming into another phase at higher temperatures. At first sight this hypothesis may seem little different from the older ones. It should therefore be emphasized that it does not depend on chance to provide the right compound to form a nucleus, but postulates that every crystal, containing minute amourlts of any of a wide range of impurities, automatically engenders particles having the correct surface structure to serve as nuclei for subsequent solidification. It could operate in any system, metallic, organic, or inorganic. The suggested mechanism is closely analogous to the production of antibodies from antigens in living organisms—indeed, it was a description of the matrix theory of this process that suggested to the writer its crystalline analogue.

Jan 1, 1950

By E. C. Burke

IN view of rather widespread use of calcium as an alloying addition to magnesium alloys, it is rather surprising to find that, although the general features of the Mg-Ca equilibrium diagram are known with a fair degree of certainty,&apos; ," considerable ambiguity concerning the solid solubility of calcium in magnesium exists. By using the disappearing phase technique in a metallographic study, Haughton&apos; found that 0.6 pct Ca was soluble at 300°C and 1.8 pct was soluble at 516°C, the eutectic temperature

Jan 1, 1956