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By Morris Muskat

TEe method of R. W. Moore' for determining subsurface interfacial depths by means of integrated curves of apparent resistivity has been analyzed theoretically. It is found that the only unique tangents that can be drawn to such curves are the asymptotes at infinite electrode spacing and the tangents through the origin at vanishing electrode spacing. Explicit expressions have been derived for the relationship between the electrode spacing at the points of intersection of these tangents and the thickness of the surface strata as a function of the conductivity parameters for the two-layer and three-layer earths. It is found that in all cases the electrode spacing at the points of intersection will exceed % of the thickness of the surface layer, and may even become indefinitely large as the resistivity of the deepest layers increases as compared with that of the surface layer. These results do not agree with the empirical findings of Moore that the intersection of the tangent lines fall at an electrode spacing very approxirnately equal to the thickness of the surface layer. Introduction In a recent paper, R. W. Moore1 proposed a new method for the analysis and interpretation of earth-resistivity measurements. This consists essentially in plotting against the electrode separation of a Gish-Rooney system the integral of the apparent resistivity with respect to the electrode spacing, and observing the breaks in the integral curves. Specifically, tangents are drawn to the various segments of the integral curves, which show appreciably different slopes, and the intersections of these tangents are used as indications of the depths of the various underlying strata. By numerous examples Moore has shown that the electrode separation at the first intersection so found agrees very closely with the depth of the bottom of the surface layer. Moreover, in a number of instances the intersections for greater electrode spacings seemed to correspond to the depths of deeper beds. From a strictly empirical point of view, the procedure proposed and demonstrated by Moore appears to be particularly interesting because of its simplicity as well as its apparent accuracy, Moreover, such a simple method would be especially valuable in view of the well-known difliculties heretofore encountered in the quantitative interpretation of resistivity data. It therefore seems appropriate to attempt a mathematical analysis of the problem to see whether the integral method of Moore has a sound basis. Such an analysis is presented here. Even on cursory consideration, it is clear that the remarkable successes observed by Moore in the application of his method are indeed surprising. For it depends upon the determination and choice of the slopes of smooth and continuous curves, which by their nature must show even more gradual- variations than the original apparent-resistivity plots that are already so difficult to interpret quantitatively. It is well established, of course,

Jan 1, 1946

By T. Egleston

circumstances, would prefer the steel with which they are now familiar, to a specimen that Mr. Sandberg has described as having broken into seventeen pieces under the wheels. After blowing such low manganese steel, it may be coaxed into a rail, but it is a wonder that it holds together so long as it does, with so great a nornber of minute flaws. I would not in any way depreciate chemistry, but I think it should be kept in its proper sphere. Let the chemist look after the quality of pig metal, and apply common sense in the avoiding of extremes, then the most fastidious railroad cannot find fault with the result. PROFESSOR EGLESTON, New YORK City : It is not my place as an engineer to apologize for the chemists, but as no one seems disposed to do so, and as they have had more than their share of criticism, 1 am glad to say that I believe there are chemists in this Institute whose work and word are just as reliable, arid perhaps even more so, than that of the average engineer. But we ought to make a distinction; there are chemists and chemists. With the ordinary commercial chemist, who looks upon the science as so much merohandise, I have not a particle of sympathy; but with the chemist who looks upon his profession as engineers do upon theirs, I have every sympathy. When matiufactorers and engineers go to a chemist and ask him to make an investigation, and scretv him dowu to the lowest point, turning the equivalent of his brains into cents and mills, they ustially get an exact equivalent in poor work for miserable pay, and no one has or should have any sympathy with them, and the under these conditions has no right to ask for any, and no reason to criticise any work that he may get under such circumstances. But I am disposed to think that the chemists who have been replwented and discussed at this meeting do their work conscientiously, and that it is as reliable as that of almost any profession. I believe, however, that this problem of steel rails is being investigated in a wrong direction. I said so at the Pittsburgh meeting, and I think the discussion of this meeting will prove it to all those who have heard it. I think the chemigt is incapable of solving this problem unlees he goes very far into the domain of physical chemistry, so far that it becomes physics and not chemistry; and that the physicist will be the one on whom we must rely in the future for the elucidation of the subject. The chemist may aid the physicist, but it is my decided opinion that we are looking in the wrong place to get the explanation of the phenomena.

Jan 1, 1881

By Glen R. Neighbors, Sylvan Cromer

HIGH subsurface temperatures and pressures are making cementing operations more difficult as deeper producing horizons are being sought. Recorded bottom-hole temperatures above 200°F. and pressures in excess of 12,000 Ib. per sq. in., obtained by combining hydrostatic and pump pressures, are not uncommon. Insufficient time is available for proper placement of standard Portland cement, because of the shortened setting time produced by these excessive temperatures and pressures, therefore special types of cements have been developed to overcome these difficulties. From the standpoint of placement, the ideal slurry would be one that would remain fluid long enough to be placed, then harden rapidly, so that there would be a limited amount of contamination and the well could be placed on production in a minimum of time. It is highly desirable, therefore, that some method be devised to measure accurately the time that any slurry will remain in a fluid state while being pumped into the well. To study the effect of elevated temperature and pressure on fluidity, the authors have developed the pressure-type consistometer (Figs. I and 2) described below, and are presenting data obtained with it, using slurries of both quick-setting and slow-setting cements. Studies were made over a temperature range from 110° to 270°F., and a pressure range from atmospheric to 3000 lb. per sq. inch. APPARATUS The fluidity of cement slurries at atmospheric pressure is usually determined with the Halliburton consistometer1 or the Thickening Time Tester.2 These instruments are similar, in many respects, to an ordinary ice-cream freezer. The slurry to be tested is placed in a container that is rotated at a constant speed with an electric motor. Constant temperature is maintained by surrounding the container with a thermostatically controlled bath. The torque on the paddles, which is proportional to the force needed to shear the slurry, is indicated on a scale. The Halliburton instrument is calibrated from 0 to 100 poises against fluids of known viscosity. To permit direct correlation of observed elevated pressure data with those published at atmospheric pressure, the authors' designs of the slurry container, paddle, and torque indicator closely resemble those used on the Halliburton instrument. Duplicate results may be obtained at atmospheric pressure in either instrument. Instead of the atmospheric constant-temperature bath, one was built from a high-pressure steel bull plug. A Uni-Bolt union equipped with a blanking plug serves as the top, permiting the instrument to be opened or closed in less than one minute. The slurry container is built from Shelby steel tubing. A wrench socket welded to the bottom of the container engages a hexagonal nut on the top of the steel shaft that rotates it. This acts as a universal

Jan 1, 1941

By A. G. H. Andersen, A. W. Kingsbury

SILICON bronzes containing iron are used to a considerable extent in industry, under the trade name of P.M.G. alloys. Various classes of wrought alloys fall in the composition range 1.5 to 3.5 per cent silicon, and 0.5 to 2.5 per cent iron. Castings may contain as much as 6 per cent silicon and 3 per cent iron at present. The constitutional diagrams of these alloys are thus of considerable practical importance. Copper-silicon-binary alloys have been thoroughly investigated by a number of workers, the latest reports being those of C. S. Smith' and of A. G. H. Andersen .2 Although much work has been done on iron-copper alloys,3 recorded investigations on the copper-rich copper-iron binary constitutional diagram are not numerous. Tammann and Oelsen4 determined the solubility limits of iron in copper by means of magnetic measurements, and found that the solubility of iron in copper amounts to a fraction of one per cent at 400°C., increasing slowly to one per cent at 800°C. From 800°C., the solubility increases rapidly and attains 4 per cent at 1100°C. Hanson and Ford," using electrical resistivity measurements and the microscope, determined a somewhat different solubility limit. Of earlier X-ray works on the copper-iron system, very little has been published. The work by Bradley and Goldschmidt6 on copper-iron-aluminum alloys includes some information on the copper-iron binary. These investigators conclude that substitution of iron in the copper lattice decreases the spacings, which is contrary to the evidence of the present work. Hanson and West7 have investigated the ternary alloys of copper with iron and silicon. Although their diagrams are valuable contributions to the understanding of these alloys, they did not recognize the kappa phase,1,2,7,8 and their diagrams do not everywhere conform to the phase rule. The present work contains a check by means of X-rays of the solid solubility limit of iron in copper, and an X-ray investigation of the ternary-phase diagram, which, owing to present conditions, it became necessary to curtail considerably. PREPARATION OF SAMPLES Castings weighing about 75 grams were melted under vacuum. The charges were made up of ingot iron, copper cathodes from Laurel Hill, and refined silicon supplied by the Electrometallurgical Co. Alundum crucibles were generally used. The exceptions were alloys 77 and 78, which were melted in graphite crucibles. The ingots were annealed at 800°C. for one week, then samples were cut for chemical analysis. Longitudinal sections of the binary alloy ingots were hammered into plates h in. thick. Wherever possible, these plates were homogenized at temperatures ensuring

Jan 1, 1942

By R. P. Carreker, J. G. Leschen, J. H. Hollomon

The external appearance of a crystal which has undergone plastic flow suggests that adjacent blocks of the crystal have glided bodily past one another along the slip planes. However, the great discrepancy between the shear stresses calculated to effect such a movement and those actually observed has for many years stimulated searches for more satisfactory interpretations of the slip process. Appreciable success in these efforts has been realized by assuming the presence in the crystal of various sorts of imperfections and by considering the consequences of the presence of these flaws when stress is externally applied. The theory that has received the most attention recently—that of dislocations—postulates the occurrence of small, mobile imperfections or dislocations which move through the crystal along the slip direction, each dislocation being attended by a local shear displacement of one interatomic distance. Thus only that portion of the crystal through which the dislocation has passed may be said to have slipped. Since each dislocation produces a displacement of only one interatomic distance, an avalanche or train of many dislocations would be necessary to account for the observed displacements of several hundred or thousand interatomic distances. The salient point of the theory of dislocations is the concept that a slip band does not suddenly appear in its entirety. On the contrary, it grows progressively across the slip plane as the individual dislocations successively appear and advance in a train through the crystal. However, the concept of growth is not intrinsic only to the theory of dislocations, since atomistic mechanisms other than that postulated by the dislocation theory can quite probably also describe the growth of a slip band. For instance, a slip band might resemble a disc-like interface that appeared and then grew continuously from a small size, producing a displacement that increased with the size of the disc. Whatever the precise mechanism, the concept of growth is in itself consistent both with the observed low values of critical shear stress and with the experimental observation that slip bands frequently do not traverse the entire crystal. The likelihood that slip bands grow implies that they must first be nucleated and that the initiation of slip can therefore be analyzed in terms of the general concepts of nucleation. Indeed, this suggestion was advanced1 several years ago, but the matter does not appear to have been further pursued. Recent advances in the theory of nucleation 2,3,4 have encouraged such a treatment of the slip process. As will presently be demonstrated, this approach to the problem not only accounts successfully for the incubation periods that have been observed 5,6 to precede slip but also predicts certain transient effects in the deformation process. The existence of these transients apparently has not hitherto

Jan 1, 1949

By Donald W. Scott

GENERALLY speaking, there is nothing very difficult about taking good micrographs of photogenic thin sections or grains with a petrographic micro-scopecamera setup. However, sometimes it is desired to show some detail that cannot be illustrated satisfactorily by the usual micrographs taken with parallel polarized light, with crossed nicols, or even with two micrographs. A simple procedure giving good results has been used at Battelle Memorial Institute for subjects falling into this classification, and it is believed to be of interest, especially to research people who must sell a point to executives through the medium of well-illustrated reports. The following problem illustrates a typical application: It is desired to photograph a thin section of an iron ore to illustrate the character and association of the iron oxides and the individual quartz crystals. A magnification of 75 dia. is acceptable. A micrograph of the field in question (Fig. I[a]) was taken with parallel polarized light. Due precaution was taken to provide critical illumination, correct exposure, a sharp focus, a good darkroom technique, and other essential conditions. It illustrates correctly the iron oxides, but it fails to show the individual quartz crystals. A micrograph of the identical field (Fig. I[b]) was taken under the same precise conditions, but with crossed nicols. It gives a better idea of the character of the individual quartz crystals but is likely to be misinterpreted unless accompanied by a lengthy descriptive note. This micrograph suggests that the centrally located, large black area is composed entirely of iron oxides. That this is an incorrect interpretation is evident by reexamining the micrograph of Fig. I[a]. The correct interpretation is that the dark area contains quartz crystals oriented with their optical directions parallel to, or nearly parallel to, the vibration directions of the polarizer and analyzer of the microscope. Thus, the executive, or anyone who had not done the work personally, would get no more than a fair interpretation, even if two micrographs were included; and in the interests of both brevity and clarity, one micrograph usually is more desirable. Exactly how many quartz crystals occur in this region cannot be told from the two micrographs, and a printing of the two negatives in register would likewise not show the detail desired. Thus, it is evident that some subjects cannot be satisfactorily illustrated by the usual procedures. In photographing Fig. is the light was subdued and, during the entire exposure of 75 sec., the analyzer nicol was rotated uniformly in its mounting from a crossed position to 45° uncrossed position to introduce the desired amount of contrast in the various individual quartz crystals. The true reproduction of the character and association of the iron oxides, and the additional structure and detail in the quartz areas, is apparent. It might be

Jan 1, 1946

By R. W. Fenn, H. A. Lepper, W. R. Hibbard

THIS paper reports the results of static tension and torsion tests made on single crystals of alpha brass for the purpose of determining its elastic coefficients. 70-30 alpha brass was chosen because it has been used extensively in the study of the plastic deformation and because it has the following desirable characteristics: (1) face-centered cubic structure, (2) marked elastic anistropy, (3) low elastic modulus. In 1928 Masima and Sachs' using static methods reported the following values for the elastic coefficients of 72-28 pct alpha brass: S11 = 19.4 X 10-13' cm2 per dyne S12 = —8.35 X 10"' cm2 per dyne S44 = 13.9 X 10-13= cm2 per dyne These values were obtained from the measurements shown in fig. 1. The experimental points for both tension and torsion lie consistently below the lines drawn to represent them. Fig. 2 shows the stress-strain curves for their specimens. Only a few points in the elastic range of these curves were available to obtain their values for Young's modulus. Therefore, it was considered that a re-evaluation of these data was desirable. In addition a variation of from 1.13 to 1.485 kg per mm2 was found in the values of the critical resolved shear stress for 70-30 alpha brass reported by Burghoff,² Treuting and Brick: Martin,4 Maddin, Mathewson and Hibbard5,6 and von Goler and Sachs.' Therefore, it was desired to evaluate the conclusion of Boas and Schmid8 that a constant resolved shear stress and not a constant elastic shear initiates plastic deformation. Theoretical Considerations*: The elastic deformation of cubic crystals may be defined by three elastic coefficients (S11, S12, S44,) or three elastic parameters (C,,, C,, C,,). These coefficients or parameters are sufficient to define the stress and strain relations for cubic crystals in the generalized form of Hooke's law referred to Cartesian coordinates. Elastic parameters and coefficients in the cubic system are related by the expressions: C11 —S11+S12/(S11-S12)(S11+2 S12) C12=-S12/(S11-S12)(S11+ 2 S12) (S11 — S12) (S11 + 2 S12) [2] C44 =1/S44 PI It is possible to determine all the elastic coefficients for a cubic metal by measuring two of the three elastic constants: Young's modulus (E), torsion modulus (G), or compressibility (S). The following relations exist between crystallographic orientation and E, G and S for cylindrical crystals of the cubic system: 1/E = S11 — 2 [(S11 - S12) — Su] (?1² ?2² + ?2²?83 + ?3² ?1²) [4]

Jan 1, 1951

By H. E. Hostetter

GROSSMANN'S method1 for calculating the hardenability of steel from the composition and grain size has gained wide acceptance, and when properly used, has been well proved in practical application, both for estimating the hardenability of known compositions and for selecting compositions to meet known hardenability requirements. The Grossmann method uses as the criterion of hardenability the "ideal critical diameter," DI, which is the size round that will just harden to a structure of 50 per cent martensite at the center when given the theoretically fastest quench, or "ideal quench." The DI can be related to actual quenching practice if the severity of quench is known; or the DI can be correlated with hardenability as determined by the Jominy end-quench method.2 The effect on hardenability of each element present in a steel can be represented by a multiplying factor, the value of which depends on the amount of the element present and the degree of effectiveness of the particular element. (The value of the factor for a given carbon content varies with the grain size.) When the factors for all elements present in a steel have been determined from charts, they are multiplied, and the resultant product is the D, of the steel. The validity of Grossmann's scheme of multiplying factors has been confirmed in a number of other investigations.3 -6 It can be appreciated that a certain desired level of hardenability can be obtained by adding chromium, molybdenum, nickel and vanadium to a base composition containing carbon, manganese, silicon and the usual impurities. Many of the ranges of hardenability used commercially can be obtained by any of the foregoing alloying elements used singly in the base composition. The same hardenability levels also can be obtained through use of any of a great number of multiple element combinations of these alloying elements. In this report a method will be presented for determining what one combination is the most efficient (based on hardenability and cost of added alloy) for a given level of hardenability. It should not be assumed from the emphasis given to hardenability, that hardenability is the only criterion for the selection of an alloy composition. Such properties as the hot-working characteristics, machinability, carburizing characteristics, amount of distortion during quenching and the retention of austenite may be considerations of importance in many applications. However, hardenability is one of the most important properties of an alloy steel and one that must be considered in almost all cases involving heat-treatment by quenching. Therefore, a method for determining the lowest-cost alloy combination should be of considerable value. DETERMINATION OF MOST EFFICIENT COMBINATIONS For comparing the alloying elements on standards of cost and hardenability, it

Jan 1, 1945

By Walter W. Bradley

(Three, papers included, in this discussion are classified as Mining Geology and also as one of the following-A, Metal Mining: B, Milling and Concentration: L, Geophysics. These papers are TP 2255, TP 2092 and TP 2038.) CONTENTS [PAGE Review of Fluorescence as Applied to Minerals, with Special Reference to Scheelite. (TP 1967 by J. W. VANDERWILT, Min. Tech., March 1946. Discussion by WALTER W. BRADLEY) I Geologic Interpretation of Magnetic Exploration on the Mesabi Range, Minnesota. (TP 2038 by R. B. H. JONES, Min. Tech., July 1946. Discussion by ROBERT B. SOSMAN) I A Technique for Photographing Difficult Subjects through a Petrographic Microscope. (TP 2092 by DONALD W. SCOTT, Min. Tech., Nov. 1946. Discussion by HORACE WINCHELL) 2 The Search for Concealed Deposits-a Reorientation of Philosophy. (TP 2146 by SAMUEL G. LASKY, Min. Tech., May 1947. Discussion by T. M. BRODERICK)3 Occurrence of Lead-zinc Ore at Iron King Mine, Prescott, Arizona. (TP 21 go by H. F. MILLS, Min. Tech., July 1947. Discussion by HUGH M. ROBERTS)3 Geologic Relations and New Ore Bodies of the Republic District, Washington. (TP 2197 by LAWRENCE B. WRIGHT, Min. Tech., July 1947. Discussion by AUGUSTUS LOCKE and J. A. RICHARDSON) 4 San Manuel Prospect. (TP 2255 by H. J. STEELE and G. R. RUBLY, Min. Tech., Sept. 1947. Discussion by L. KENNETH WILSON, ELDRED D. WILSON and the author) 5] Review of Fluorescence as Applied to Minerals, with Special Reference to Scheelite WALTER W. BRADLEY*-AS I recall, the first portable units for ultra-violet light of practical use with scheelite were developed at the Nevada-Massachusetts Tungsten Mine at Mill City, Nevada, and were used underground. Ultra-violet lamps are also installed there in the mill, above the gravity-concentration tables, for control observations. Geologic Interpretation of Magnetic Exploration on the Mesabi Range, Minnesota ROBERT B. SOSMAN*-When artificial precipitated magnetite is oxidized at a temperature in the vicinity of 100°C, the oxide is converted into a chocolate brown ferric oxide of the formula Fe2O3, free from ferrous iron, yet possessing the same magnetic susceptibility as the original Fe3O4. This form of Fe2O3 is variously called "ferromagnetic ferric oxide," " maghemite," or "gamma ferric oxide," and has been found as a natural mineral. If a body of magnetite in the Biwabik were to oxidize to this form, the oxidized and leached ore body might successfully conceal itself from Mr. Jones' survey by this ferromagnetic pretense. So far, gamma ferric oxide has not been found on the Minnesota iron ranges. I thought I had found some in the Hibbing pit in 1940, in a strongly magnetic specimen of soft ore differing in color from the prevailing hematite

Jan 1, 1947

ON Oct. 5, 1926, the day before the general ses-sions of the fall meeting of the American Insti-tute of Mining and Metallurgical Engineers at Pittsburgh, a round table conference on the combus-tibility and testing of coke was held at the Bureau of Mines Experiment Station. There were about fifty present, with A. C. Fieldner, chief chemist of the Bureau of Mines, as chairman. The following organi-zations were represented: American Institute of Min-ing and Metallurgical Engineers, American Society for Testing Materials, American Gas Association, Eastern States Blast Furnace and Coke Oven Association, Gas and Fuel Division of, American Chemical Society, and Southern Ohio Pig Iron and Coke Association. In opening the proceedings, Mr. Fieldner explained that the meeting had been called at the suggestion of several members of the Institute and members of other organizations. The subject is of interest to the pro-ducer and the user of coke whether it be in a blast furnace, cupola furnace, house-heating furnace, open grate, gas producer, or in a water-gas generator. There has been much confusion on this subject largely because there is no common definition of combustibility. Does the blast-furnace superintendent, the coke-oven operator, and the fuel engineer have the same under-standing of the term "combustibility"? If a common understanding can be reached, many differences of opinion will disappear. COMBUSTIBILITY OF COKE R. H. Sweetser of Columbus, Ohio, disagreed with the statement of P. H. Royster, T. L. Joseph, and S. P. Kinney in Reports of Investigations, Serial No. 2524, of the Bureau of Mines, in which it was stated that the coke-oven op-erator cannot change coke combustibility by modifying oven practice. Mr. Sweetser held that the coke-oven man can change the combustibility of coke. Blast-furnace men know that coke that will burn easily with low pressure and will. come down in the regular way in the furnace can be pro-duced from a given mixture of coal. His idea of the combustibility of coke is the rate of flow through the com-bustion zone of the blast furnace. If the coke does not pass through in normal manner it is highly incombustible. H. J. Rose of the Koppers Co., Pittsburgh, objected to being pinned down so closely on this phase of the com-bustibility and incombustibility of coke. Coke-oven men are frequently obliged to change oven conditions to make a coke which gives blast-furnace men what they want. The size of the coke and the screening have an important bear-ing on combustibility, and there are many cases on record where by simply changing the different sizes of the coke, everything worked smoothly, and that is a much more combustible coke.

Jan 1, 1927

By A. G. H. Anderson, A. W. Kingsbury

Silicon bronzes containing ken are used to a considerable extent in industry, under the trade name of P.M.G. alloys. Various classes of wrought alloys fall in the composition range 1.5 to 3.5 per cent silicon, and 0.5 to 2.5 per cent iron. Castings may contain as much as 6 per cent silicon and 3 per cent iron at present. The constitutional diagrams of these alloys are thus of considerable practical importance. Copper-silicon-binary alloys have been thoroughly investigated by a number of workers, the latest reports being those of C. S. Smith1 and of A. G. H. Andersen.2 Although much work has been done on iron-copper alloys,3 recorded investigations on the copper-rich copper-iron binary constitutional diagram are not numerous. Tammann and Oelsen4 etermined the solubility limits of iron in copper by means of magnetic measurements, and found that the solubility of iron in copper amounts to a fraction of one per cent at 400°C., increasing slowly to one per cent at 800°C. From 800°C., the solubility increases rapidly and attains 4 per cent at iioo°C. Hanson and Ford,5 using electrical resistivity measurements and the microscope, determined a somewhat different solubility limit. of earlier X-ray works on the copper-iron system, very little has been published. The work by Bradley and Goldschmidt6 on copper-iron-aluminum alloys includes some information on the copper-iron binary. These investigators conclude that substitution of iron in the copper lattice decreases the spacings, which is contrary to the evidence of the present work. Hanson and West? have investigated the ternary alloys of copper with iron and silicon. Although their diagrams are valuable contributions to the understanding of these alloys, they did not recognize the kappa phase,l,2,7,8 and their diagrams do not everywhere conform to the phase rule. The present work contains a check by means of X-rays of the solid solubility limit of iron in copper, and an X-ray investigation of the ternary-phase diagram, which, owing to present conditions, it became necessary to curtail considerably. Preparation of Samples Castings weighing about 75 grams were melted under vacuum. The charges were made up of ingot iron, copper cathodes from Laurel Hill, and refined silicon supplied by the Electrometallurgical Co. Alundum crucibles were generally used. The exceptions were alloys 77 and 78, which were melted in graphite crucibles. The ingots were annealed at 800°C. for one week, then samples were cut for chemical analysis. Longitudinal sections of the binary alloy ingots were hammered into plates 1/8 in. thick. Wherever possible, these plates were homogenized at temperatures ensuring

Jan 1, 1943

By Morris Muskat

TEe method of R. W. Moore' for determining subsurface interfacial depths by means of integrated curves of apparent resistivity has been analyzed theoretically. It is found that the only unique tangents that can be drawn to such curves are the asymptotes at infinite electrode spacing and the tangents through the origin at vanishing electrode spacing. Explicit expressions have been derived for the relationship between the electrode spacing at the points of intersection of these tangents and the thickness of the surface strata as a function of the conductivity parameters for the two-layer and three-layer earths. It is found that in all cases the electrode spacing at the points of intersection will exceed % of the thickness of the surface layer, and may even become indefinitely large as the resistivity of the deepest layers increases as compared with that of the surface layer. These results do not agree with the empirical findings of Moore that the intersection of the tangent lines fall at an electrode spacing very approxirnately equal to the thickness of the surface layer. Introduction In a recent paper, R. W. Moore1 proposed a new method for the analysis and interpretation of earth-resistivity measurements. This consists essentially in plotting against the electrode separation of a Gish-Rooney system the integral of the apparent resistivity with respect to the electrode spacing, and observing the breaks in the integral curves. Specifically, tangents are drawn to the various segments of the integral curves, which show appreciably different slopes, and the intersections of these tangents are used as indications of the depths of the various underlying strata. By numerous examples Moore has shown that the electrode separation at the first intersection so found agrees very closely with the depth of the bottom of the surface layer. Moreover, in a number of instances the intersections for greater electrode spacings seemed to correspond to the depths of deeper beds. From a strictly empirical point of view, the procedure proposed and demonstrated by Moore appears to be particularly interesting because of its simplicity as well as its apparent accuracy, Moreover, such a simple method would be especially valuable in view of the well-known difliculties heretofore encountered in the quantitative interpretation of resistivity data. It therefore seems appropriate to attempt a mathematical analysis of the problem to see whether the integral method of Moore has a sound basis. Such an analysis is presented here. Even on cursory consideration, it is clear that the remarkable successes observed by Moore in the application of his method are indeed surprising. For it depends upon the determination and choice of the slopes of smooth and continuous curves, which by their nature must show even more gradual- variations than the original apparent-resistivity plots that are already so difficult to interpret quantitatively. It is well established, of course,

Jan 1, 1946

By D. B. Carson, D. L. Katz

Natural gases under pressure form crystalline hydrates with water. Experimental data are reported on four-phase equilibrium for the methane-propane-water, methanc-pentane-water, and methane-hexane-water systems. Temperatures and pressures for equilibrium between gas, water-rich liquid, hydrocarbon-rich liquid, and hydrate were measured, as well as the percentages of methane and propane in the hydrate. The data indicate that natural gas hydrate behaves as a solid solution and that pentanes and heavier hydrocarbons do not enter into the solid phase. Vapor-solid equilibrium constants are presented that permit the approximation of the conditions for hydrate formation, from the composition of a gas. Introduction Natural gas hydrates have been the object of considerable research in recent years, because of the trouble they have caused in the natural-gas and natural-gasoline industries. Natural gas hydrates are white crystalline compounds of water and gas, which, under pressure, exist at temperatures considerably above the freezing point of water. Because of the relatively high temperatures at which the hydrates exist, they become a nuisance in high-pressure gas operations where water is present, since their formation causes partial or complete plugging of valves and pipes. From a practical standpoint, the trouble incident to hydrate formation has been solved by dehydration of the gas before it enters the plant or pipe line, or by other remedial measures. Extensive work on gas hydrates in the latter part of the nineteenth century, by Villardl and others, gave data on methane hydrate and on ethane hydrate. Schroeder summarized these theoretical studies2 Hammerschmidt3 introduced the information on gas hydrates to the gas industry and Dcaton and Frost4-6 gathered a considerable number of data on the behavior of natural gas hydrates. Recent papers7,8 have extended both the data and the theory of these hydrates. At present, data are available on tem-peraturcs and pressures of hydrate forma. tion for pure methane, ethane, propane, n-butane, methane-ethane mixtures, meth-ane-propane mixtures, methane-butane mixtures, and some Is natural gases, all- in the Presence of excess water. However, up to the Present time no method has been available for predicting the temperature at given pressures or the pressure at given at at which natural gases will form hydrates if hydrates with water. 'This Paper Presents data on the methane-propane-water, methane-pentane-water and methane-hex-""e water systems in four phases, one of which is the hydrate. he application of the phase rule to the methane-~ro~ane-water data Proves that hydrates behave as solid solutions. The data of this paper and those in the literature were used to develop vapor-solid. equilibrium constants,8 which permit prediction of conditions of hydrate formation from the analysis of a natural gas.

Jan 1, 1942

By Don B. Carson, Donald L. Katz

NATURAL gases under pressure form crystal-line hydrates with water. Experimental data are reported on four-phase equilibrium for the methane-propane-water, methane-pentane-water, and methane-hexane-water systems. Temperatures and pressures for equilibrium between gas, water-rich liquid, hydrocarbonrich liquid, and hydrate were measured, as well as the percentages of methane and propane in the hydrate. The data indicate that natural gas hydrate behaves as a solid solution and that pentanes and heavier hydrocarbons do not enter into the solid phase. Vapor-solid equilibrium constants are presented that permit the approximation of the conditions for hydrate formation, from the composition of a gas. INTRODUCTION Natural gas hydrates have been the object of considerable research in recent years, because of the trouble they have caused in the natural-gas and natural gasoline industries. Natural gas hydrates are white crystalline compounds of water and gas, which, under pressure, exist at temperatures considerably above the freezing point of water. Because of the relatively high temperatures at which the hydrates exist, they become a nuisance in high-pressure gas operations where water is present, since their formation causes partial or complete plugging of valves and pipes. From a practical standpoint, the trouble incident to hydrate formation has been solved by dehydration of the gas before it enters the plant or pipe line, or by other remedial measures. Extensive work on gas hydrates in the latter part of the nineteenth century, by Villard1 and others, gave data on methane hydrate and on ethane hydrate. Schroeder summarized these theoretical studies.2 Hammerschmidt3 introduced the information on gas hydrates to the gas industry and Deaton and Frost4-6 gathered a considerable number of data on the behavior of natural gas hydrates. Recent papers7,8 have extended both the data and the theory of these hydrates. At present, data are available on temperatures and pressures of hydrate formation for pure methane, ethane, propane, n-butane, methane-ethane mixtures, methane-propane mixtures, methane-butane mixtures, and some 15 natural gases, all in the presence of excess water. However, up to the present time no method has been available for predicting the temperature at given pressures or the pressure at given temperatures at which natural gases will form hydrates if saturated with water. This paper pre¬sents data on the methane-propane-water, methane-pentane-water and methane-hexane water systems in four phases, one of which is the hydrate. The application of the phase rule to the methane-propane-water data proves that hydrates behave as solid solutions. The data of this paper and those in the literature were used to develop vapor-solid equilibrium constants,8 which permit prediction of conditions of hydrate formation from the analysis of a natural gas.

Jan 1, 1941

By A. G. H. Andersen, A. W. Kingsbury

SILICON bronzes containing iron are used to a considerable extent in industry, under the trade name of P.M.G. alloys. Various classes of wrought alloys fall in the composition range 1.5 to 3.5 per cent silicon, and 0.5 to 2.5 per cent iron. Castings may contain as much as 6 per cent silicon and 3 per cent iron at present. The constitutional diagrams of these alloys are thus of considerable practical importance. Copper-silicon-binary alloys have been thoroughly investigated by a number of workers, the latest reports being those of C. S. Smith1 and of A. G. H. Andersen.2 Although much work has been done on iron-copper alloys,3 recorded investigations on the copper-rich copper-iron binary constitutional diagram are not numerous. Tammann and Oelsen4 determined the solubility limits of iron in copper by means of magnetic measurements, and found that the solubility of iron in copper amounts to a fraction of one per cent at 400°C., increasing slowly to one per cent at 800°C. From 800°C., the solubility increases rapidly and attains 4 per cent at 1100°C. Hanson and Ford,5 using electrical resistivity measurements and the microscope, determined a somewhat different solubility limit. Of earlier X-ray works on the copper-iron system, very little has been published. The work by Bradley and Goldschmidt6 on copper-iron-aluminum alloys includes some information on the copper-iron binary. These investigators conclude that substitution of iron in the copper lattice decreases the spacings, which is contrary to the evidence of the present work. Hanson and West7 have investigated the ternary alloys of copper with iron and silicon. Although their diagrams are valuable contributions to the understanding of these alloys, they did not recognize the kappa phase,12, 7,8 and their diagrams do not everywhere conform to the phase rule. The present work contains a check by means of X-rays of the solid solubility limit of iron in copper, and an X-ray investigation of the ternary-phase diagram, which, owing to present conditions, it became necessary to curtail considerably. PREPARATION OF SAMPLES Castings weighing about 75 grams were melted under vacuum. The charges were made up of ingot iron, copper cathodes from Laurel Hill, and refined silicon supplied by the Electrometallurgical Co. Alundum crucibles were generally used. The exceptions were alloys 77 and 78, which were melted in graphite crucibles. The ingots were annealed at 800°C. for one week, then samples were cut for chemical analysis. Longitudinal sections of the binary alloy ingots were hammered into plates 3 in. thick. Wherever possible, these plates were homogenized at temperatures ensuring

Jan 1, 1942

By R. P. Carreker, J. G. Leschen, J. H. Hollomon

THE external appearance of a crystal which has undergone plastic flow suggests that adjacent blocks of the crystal have glided bodily past one another along the slip planes. However, the great discrepancy between the shear stresses calculated to effect such a movement and those actually observed has for many years stimulated searches for more satisfactory interpretations of the slip process. Appreciable success in these efforts has been realized by assuming the presence in the crystal of various sorts of imperfections and by considering the consequences of the presence of these flaws when stress is externally applied, The theory that has received the most attention recently-that of dislocations-postulates the occurrence of small, mobile imperfections or dislocations which move through the crystal along the slip direction, each dislocation being attended by a local shear displacement of one interatomic distance. Thus only that portion of the crystal through which the dislocation has passed may be said to have slipped, Since each dislocation produces a displacement of only one interatomic distance, an avalanche or train of many dislocations would be necessary to account for the observed displacements of several hundred or thousand interatomic distances. The salient point of the theory of dislocations is the concept that a slip band does not suddenly appear in its entirety. On the contrary, it grows progressively across the slip plane as the individual dislocations successively appear and advance in a train through the crystal. However, the concept of growth is not intrinsic only to the theory of dislocations, since atomistic mechanisms other than that postulated by the dislocation theory can quite probably also describe the growth of a slip band. For instance, a slip band might resemble a disc-like interface that appeared and then grew continuously from a small size, producing a displacement that increased with the size of the disc, Whatever the precise mechanism, the concept of growth is in itself consistent both with -the observed low values of critical shear stress and with the experimental observation that slip bands. frequently do not traverse the entire crystal. The likelihood that slip bands grow implies that they must first be nucleated and that the initiation of slip can therefore be analyzed in terms of the general concepts of nucleation. Indeed, this suggestion was advanced1 several years ago, but the matter does not appear to have been further pursued. Recent advances in the theory of nucleations2,3,4 have encouraged such a treatment of the slip process. As will presently be demonstrated, this approach to the problem not only accounts successfully for the incubation periods that have been observed5,6 to precede slip but also predicts certain transient effects in the deformation process, The existence of these transients apparently has not hitherto

Jan 1, 1948

By E. H. Kelton, R. D. Grissinger

In designing structural members of steel and some other materials the design engineer has available recognized values of elastic modulus and safe working stress that may be substituted in well-known engineering formulas to give him desired cross-sectional areas and deflections for a particular part. Zinc, on the other hand, has no generally recognized modulus. It flows under continuously applied loads. Therefore, the designer of structural members must use a range of working stresses depending on the continuous load and the amount of permissible distortion. The only method of obtaining these values is by creep testing. Creep testing of zinc has been carried on for some 20 years by this laboratory, covering a wide range of zinc and zinc alloys. Types of test included tension, compression, and simple and cantilever beams at temperatures ranging from o to I50°C. Specimen conditions ranged from as-cast or as-rolled to accelerated aged in steam or dry air. Effects of plating were investigated also. It is not the intention of this paper to expound all these factors but rather to present the final data on well-known zinc die-casting alloys and to suggest means of applying these data to engineering design. Early Work In the early work on creep testing of zinc, the direct-loading tension method was used. However, direct loading of die castings was unsatisfactory because of the high loads required. For instance, a standard die-cast tension bar having a cross-sectional area of about 0.049 sq. in. would require a direct load of about 1000 lb. for a unit stress of 20,000 lb. per sq. in. Also, tests were made at nominal room temperature, but normal variations caused fluctuations greater than those due to experimental error or other causes, so that control of this variable within ±1/2°C. seemed essential. These two factors led to the development of an apparatus described by J. Ruzicka,' in which the specimens were loaded by means of a lever and were held at constant temperature by means of an oil bath. While Ruzicka's apparatus yielded excellent check results, it seemed desirable to have some setup by which literally hundreds of die-cast specimens could be tested at the same time. This would permit the conducting of a number of low-load tests designed to run 10 years or longer and still leave capacity for current high-load work. Beam testing in a constant-temperature room was the answer. Test Method Preliminary work indicated that die-cast beams of various lengths and cross scctions yielded the same result within reasonable limits regardless of whether they were tested as simple beams, uniformly loaded beams, or cantilevers. Accordingly, the simplest type was adopted. This was a,

Jan 1, 1945

By Donald W. Scott

Generally speaking, there is nothing very difficult about taking good microgrztphs of photogenic thin sections or grains with a petrographic microscope-camera setup. However, sometimes it is desired to show some detail that cannot be illustrated satisfactorily by the usual micrographs taken with parallel polarized light, with crossed nicols, or even with two micrographs. A simple procedure giving good results has been used at Battelle Memorial Institute for subjects falling into this classification, and it is believed to be of interest, especially to research people who must sell a point to executives through the medium of well-illustrated reports. The following problem illustrates a typical application: It is desired to photograph a thin section of an iron ore to illustrate the character and association of the iron oxides and the individual quartz crystals. A magnification of 75 dia. is acceptable. A micrograph of the field in question (Fig. Ia) was taken with parallel polarized light. Due precaution was taken to provide critical illumination, correct exposure, a sharp focus, a good darkroom technique, and other essential conditions. It illustrates correctly the iron oxides, but it fails to show the individual quartz crystals. A micrograph of the identical field (Fig. Ib) was taken under the same precise conditions, but with crossed nicols. It gives a better idea of the character of the individual quartz crystals but is likely to be misinterpreted unless accompanied by a lengthy descriptive note. This micrograph suggests that the centrally located, large black area is composed entirely of iron oxides. That this' is an incorrect interpretation is evident by reexamining the micrograph of Fig. Ia. The correct interpretation is that the dark area contains quartz crystals oriented with their optical directions parallel to, or nearly parallel to, the vibration directions of the polarizer and analyzer of the microscope. Thus, the executive, or anyone who had not done the work personally, would get no more than a fair interpretation, even if two micrographs were included; and in the interests of both brevity and clarity, one micrograph usually is more desirable. Exactly how many quartz crystals occur in this region cannot be told from the two micrographs, and a printing of the two negatives in register would likewise not show the detail desired. Thus, it is evident that some subjects cannot be satisfactorily illustrated by the usual procedures. In photographing Fig. Ic the light was subdued and, during the entire exposure of 75 sec., the analyzer nicol was rotated uniformly in its mounting from a crossed position to 45° uncrossed position to introduce the desired amount of contrast in the various individual quartz crystals. The true reproduction of the character and association of the iron oxides, and the additional structure and detail in the quartz areas, is apparent. It might be

Jan 1, 1949

By Richard H. Willey

Efficient handling of large tonnages in open-pit mining demands, primarily, an abundance of well fragmented rock. To accomplish this, a drilling and blasting department composed of a well-knit, versatile group of workers and supervisors must be established. Some costs will remain relatively on the same level over a period of years, while others can be greatly lowered as will be shown. 'The Utah Copper Division, Kennecott Copper Corp., Bingham Canyon, Utah, has been ever alert for improvements in operating methods and equipment to gain increased efficiency and lower costs. Bingham Canyon MIne The greatest dimension of the mine is 8000 ft northeast-southwest with a width of 5000 ft southeast-northwest. From the lowest level, at an elevation of 6040 ft above sea-level, the mountain rises in 27 benches on the west side to W level (elevation 7800 ft) and 21 benches on the east side to Q level (elevation 7460 ft). At the inception of open-pit mining in 1906, the overcapping of leached porphyry had to be removed to reach a commercial grade of sulphide ore. The overcapping or waste now remaining is quartzite with intercalated limestone beds. The limestones are usually soft in nature except in the south-middle portion of the mine where they have been meta-morphized along the contact zone. This area usually gives drilling and blasting operations a great deal of trouble. Here occurs the greatest amount of secondary blasting, as the well-established fracture planes cause the altered beds to break into large boulders. Several massive quartzite "ribs" occur in the overburden, and as a result, the uniform breakage is difficult to obtain. The major quartzite areas have been subjected to complex folding, fracturing and faulting because of the intrusion of the underlying stock. The monzonite porphyry, which carries the commercial values, presents no serious drilling problem because of its softness and extensive minute fracturing throughout the mass. A series of major slips or faults pass through the ore body which, although of considerable advantage to the drilling and blasting department, sometimes works to the disadvantage of the track department. Drilling an11 blasting of the porphyry apparently becomes easier as depth is attained. but highly siliceous streaks throughout the pit still present difficulties. At no place is the rock of such character as to allow excavation without preparations. On certain higher elevations or levels, old fill material can be dug by the shovels, but only at some risk to equipment because of bank slippage. Past Methods At the outset of shovel operations in 1906, drilling was done with the Ingersoll-Rand F-24 piston drill mounted on an un-

Jan 1, 1949

By H. E. Hostetter

Grossmann's method1 for calculating the hardenability of steel from the composition and grain size has gained wide acceptance, and when properly used, has been well proved in practical application, both for estimating the hardenability of known compositions and for selecting compositions to meet known hardenability requirements. The Grossmann method uses as the criterion of hardenadility the "ideal critical diameter," DI, which is the' size round that will just harden to a structure of 50 per cent martensite at the center when given the theoretically fastest quench, or "ideal quench." The DI can be related to actual quenching practice if the severity of quench is known; or the DI can be correlated with hardenability as determined by the Jominy end-quench method.2 The effect on hardenability of each element present in a steel can be represented by a multiplying factor, the value of which depends on the amount of the element present and the degree of effectiveness of the particular element. (The value of the factor for a given carbon content varies with the grain size.) When the factors for all elements present in a steel have been determined from charts, they are multiplied, and the resultant product is the DI of the steel. The validity of Grossmann's scheme of multiplying factors has been confirmed in a number of other investigations.3-6 It can be appreciated that a certain desired level of hardenability can be obtained by adding chromium, molybdenum, nickel and vanadium to a base composition containing carbon, manganese, silicon and the usual impurities. Many of the ranges of hardenability used commercially can be obtained by any of the foregoing alloying elements used singly in the base composition. The same hardenability levels also can be obtained through use of any of a great number of multiple element combinations of these alloying elements. In this report a method will be presented for determining what one combination is the most efficient (based on hardenability and cost of added alloy) for a given level of hardenability. It should not be assumed from the emphasis given to hardenability, that hardenability is the only criterion for the selection of an alloy composition. Such properties as the hot-working characteristics, machinability, carburizing characteristics, amount of distortion during quenching and the retention of austenite may be considerations of importance in many applications. However, hardenability is one of the most important properties of an alloy steel and one that must be considered in almost all cases involving heat-treatment by quenching. Therefore, a method for determining the lowest-cost alloy combination should be of considerable value. Determination of Most Efficient Combinations For comparing the alloying elements on standards of cost and hardenability, it

Jan 1, 1947