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

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

Jan 1, 1970

By J. B. Cohen

EARLY investigators1-4 reported that additions of beryllium to silver caused embrittlement. The in-termetallic phases which are now known to exist5,' were not known at the time. Solidification appeared to occur by a simple eutectic reation.4,7 (The primary beryllium-rich phase appeared globular, when the liquidus temperature was near the melting point of pure beryllium, and angular when the liquidus was much lower; in discussion of Sloman's work,4 it was suggested that this difference was due to an intermetallic compound which was not revealed by the polishing technique.) In the investigation reported here, it was found that if the compounds now known to exist were avoided, certain beryllium-silver alloys containing large amounts of the primary beryllium phase possessed sufficient ductility to be cold formed. Alloys containing 14 and 20 at. pct Ag were prepared from vacuum-cast beryllium containing 1.0 to 1.2 pct impurities and silver, 99.99+ pct pure. The elements were melted together by induction in beryllia or alumina crucibles under argon at less than 1 atm pressure. The cooling rate was adjusted by regulating the temperature of the melt and by reducing the power to zero without stopping the water flow in the induction coils, which were in contact with the crucible. Ingots were about 0.75 in. in diam with a grain size of 0.12 to 0.25 in. Microscopic investigation of transverse or longitudinal sections of an ingot cast from a temperature well above its melting point showed that, in general, the compounds did not form, presumably because of rapid cooling; the alloys consisted of beryllium-rich particles in a silver-rich matrix as shown in Fig. 1. A eutectic structure was not observed, probably .due to the low beryllium concentration of the eutectic composition and eutectic divorcement. Within a given grain, the small globules of the primary phase were all oriented in the same direction, as indicated by examination under polarized light; the orientation varied from grain to grain. This suggested that the globules were branches of the same dendrites. If cooling was too slow, a third constituent was observed in the microstructure; because it formed around the primary beryllium-rich globules it was Fig. 1—Ag-Be alloy, 18.6 at. pct Ag, as-cast. Bright field illumination. Etched with an aqueous solution of NH,OH and H2O2. X500. Reduced approximately 21 pct for reproduction. probably the 6 compound. A thin ring around an ingot often contained this constituent. When this compound was present in large quantities, or the silver segregated so that large regions occurred with the beryllium-rich globules in contact, sections from the ingot were brittle. When the compound was initially absent, it was possible to carry out reductions in thickness of 50 pct by cold rolling with only limited edge cracking; failure did not occur until reductions of 80 pct. A typical cross section after cold rolling is shown in Fig. 2. After simple bend tests, microcracks were found; these apparently were difficult to propagate in the two-phase structure, as the specimens continued to behave in a ductile manner after the cracks appeared. Similar cracks would probably be closed during rolling. It is apparent in Fig. 2 however, that the primary beryllium particles undergo extensive plastic deformation. Hardness values of the alloys indicated that some work-hardening occurred during cold working. Fig. 2—Ag-Be alloy, 18.6 at. pct Ag, reduced 83 pct in thickness by cold rolling. Bright field illumination. Etched with an aqueous solution of NH,OH and H2O2. X500. Reduced approximately 21 pct for reproduction.

Jan 1, 1961

By W. Bonfield

A study has been made of the dislocation substructures produced in hot-pressed beryllium specimens strained to various levels in the range from 800 x 10-6 In. pev in. to fracture. A number of distinctive dislocation configurations were observed in this region which had not been noted at lower levels of strain. These included dislocation-dislocation interactions to form networks, dislocation "walls", subgrain boundaries and complex arrays, interactions between dislocations and large beryllium oxide particles, and the generation of dislocations from certain particles. The nature of these differences in substructure and their relation to the stress-strain characteristics of polycrystalline beryllium are discussed. In a previous study1 of the plasticity of commercial-purity, hot-pressed beryllium a transition was found in the deformation characteristics in the mi-crostrain region. The initial plastic deformation could be represented by a parabolic stress-strain equation, but above a critical stress there was a complete departure from this relation and a reduction in the strain-hardening rate. The dislocation configurations produced by various levels of micro-strain in this region were examined by transmission electron microscopy and a general correlation was established between the observed transition in deformation characteristics and the dislocation structure of the material. The two stages in the micro-strain region distinguished in these experiments were designated as Stage A' and Stage B'. Stage A' type deformation generally was noted up to a plastic strain of -80 x 10"6 in. per in. and Stage B' type from -80 x 10-6 to -800 x 10'6 in. per in. The discovery of two stages in the microstrain region naturally posed pertinent questions as to the existence of any further distinct stages in the subsequent plastic deformation. The purpose of this paper is to present a study of the dislocation configurations produced in similar beryllium specimens strained to various levels in the range from -800 x 10 in. per in. to fracture and to discuss the relation between substructure and the stress-strain characteristics. It is concluded that this region of strain can be considered as a distinct stage in the plastic deformation of polycrystalline beryllium. Tensile specimens of gage length 1 in. and cross section 0.18 by 0.06 in. were prepared from commercial-purity, hot-pressed QMV beryllium and then annealed at 1100°C for 2 hr. 2 followed by a careful chemical polishing procedure.3 The specimens were strained at a constant rate to various levels of strain in the range from -800 x 10-6 in. per in. to fracture (at 0.5 to 2 pct elongation), using the Tuckerman strain-gage technique1 to measure plastic and total strain. Thin foils were obtained from the strained and fractured specimens by chemical polishing3 and were examined using an RCA-EMU 3 electron microscope. Considerable care waS taken to avoid both accidental deformation during the preparation of the thin foils and excessive heating during their examination. Selected-area diffraction patterns were determined for each micrograph. Tilting experiments were also performed whenever appropriate to establish the dislocation zero-contrast position and hence determine the Burgers vector. This operation was sometimes not possible due to the rapid contamination of the foils which occurred in the electron microscope. RESULTS AND DISCUSSION To enable the distinctions between the dislocation arrays at high and low strain levels to be adequately made, the main characteristics of Stage A' and Stage B' deformation are briefly reviewed. 1) Stage A'. In the annealed starting condition there was a variable density (5 x 107 to 3 x 10' cm per cu cm) of isolated dislocations within a grain. The initial deformation in a tensile specimen was heterogeneous, with the dislocation density increasing in a few grains to 5 x 10g to 1.5 x 101° cm per cu cm. The deformation occurred exclusively on the basal plane by the movement of one or more 1/3 (1130) type dislocation systems. The dislocations were long and regular in form and nearly all the intersections exhibited a simple four-point node configuration. No interactions between glide dislocations and beryllium oxide particles were observed. 2) Stage B. In Stage B' there was a large increase in the number of grains exhibiting dislocation movement and also a change in the nature of the deformation, in which jogged dislocations and elongated loops became the characteristic feature. The splitting up of the elongated loops into smaller loops and the possibility of source action from the re-

Jan 1, 1965

By R. H. Edsal, G. Horvay

The transient one-dimensional heat-conduction equation is solved for two semi-infinite media, at different initial temperatures, brought into (poor) thermal contact. It is shown that the two interface temperatures gradually approach the well-known, instantaneously assumed, common interface temperature of the case of zero contact resistance. The present analysis, with slight modifications, may be used in fair approximation also for the class of problems involving a change of phase. One particular application of the boundary value problem solved in this paper concerns the determination of the temerature distribution in metal castings and molds.P This problem has been treated extensively by analytical methods (see e.g., the literature listed in Refs. 1 to 4) by electrical analogs (see e.g., Refs. 11 to 14) and also by experimental methods (see the literature listed in Refs. 4, 5), but prior to the work of Pellini and Ruddle the experimental results were rather unreliable. Immediate motivation for the work described in this paper was to better understand the results of Pellini,' which are typified by the curves of Fig. 1. Pellini cast 20-in. high, 7-in. sq steel ingots into cast-iron molds of various thicknesses. He measured the temperatures at mid-height, at a number of stations in the casting and the mold, and obtained the cooling curves shown in Fig. 1. The most conspicuous thing about Fig. 1 is the large temperature discontinuity at the interface between casting and mold, due presumably to the shrinking away of the casting from the wall and the attendant creation of an airgap, as the casting cools. Such a contact resistance slows down the anticipated freezing rate; an analytical prediction of this is of much interest in foundry practice. The determination of the effect of contact resistance in the presence of a change of phase will be dealt with, by an approximate method, in a separate paper.' In the present paper the much simpler problem is considered in which there is contact resistance but no change of phase. This problem frequently arises in the analysis of aircraft structures.+ It can initial temperature, and may be regarded as semi-infinite. We suppose the thermal properties in the two media to be time, temperature, and space independent; there are no sources or sinks within the media. In Fig. 2(a) we illustrate, schematically, the case of no contact resistance. The semi-infinite media "0" and "2:' initially at temperatures 8 (- m) and 8(+ -), respectively, are brought into contact at time t =0. A common interface temperature 8,i = is instantaneously established, and thereafter remains constant. Temperature curves are drawn for three instants of time. When there is contact resistance between the two media, the temperature equalization occurs as sketched in Fig. 2(b). Fig. 2(c) illustrates a temperature curve, using the dimension-less notation Barber-Weiner-Boley6 have stated the equations [23a, b] given below, which govern the heat transfer in the two media, and solved them for a rather complicated special case. In their example both media "O" and "2" are finite, are insulated at their far ends, and there is steady heat input into medium 2. In Eq. [27] we give the general solution of the most important special case, where the two media are semi-infinite and there are no sources or sinks. In this case the results may be stated in simple closed form. In Fig. 3, to be discussed in the next section, we illustrate the variation of the interface temperature when steel at 2760" is brought into contact with iron at 100". This example, if we disregard the effect of the heat of fusion, is comparable to Pellini's experimental results, Fig. 1. (Unfortunately, however, experimental determination of the interface temperatures was difficult to carry out, and hence Fig. 1 is not very accurate near the interface.) In Figs. 4 and 5 of the following section, we similarly compare Pellini's sandcasting tests with analytical results for the case where steel at 2760" is brought into contact with sand at 100". It will be pointed out that, insofar as the interface temperatures are concerned, heat of fusion has a minor effect, and so the present approximation, with small modifications, may be

Jan 1, 1961

By Lo-Ching Chang, K. M. Goldman

The kinetics and mechanism of transfer of a constituent across a slag-metal interface are fundamentally important because many metallurgical processes involve the existence of a slag phase and a metal phase. Industrial processes seldom proceed to equilibrium, and information of the rates and modes of reactions are therefore often of greater practical importance than equilibrium data. A study of the kinetics of sulphur transfer across a slag-metal interface under reducing conditions will contribute a great deal toward a better understanding of desulphurization in the blast furnace process. The general principles existing in the transfer of a constituent, such as sulphur, across a slag-metal interface can be extended to similar transfer phenomena in other metallurgical processes. The present paper will demonstrate how such studies will lead to fruitful results from both the practical and theoretical standpoints. EXPERIMENTAL METHOD The apparatus used was, simple. A graphite crucible 15/8-in. id, a wall 1/8-in. thick, and a depth of 4 in., was packed in an outer fused silica tube with powdered magnesia. The crucible assembly was rotated at a speed of 235 rpm inside an in- duction coil. A charge of 250 g of Armco ingot iron was introduced into the graphite crucible and melted by induction heating. The melt was held at a desired temperature for 3-5 "'in., aftcr which 7.5 g of granular ferrous sulphide was added and the bath was held for another 3-5 mi11. A metal sample was then taken by means of a fused silica tube and a rubber suction bulb. Immediately after the metal sample was taken, 30 g of a prefused and crushed slag were introduced. The slag reached the ternperature of the furnace in 1 to 1 1/2 min. Slag

Jan 1, 1949

By K. M. Goldman, Lo-Ching Chang

The kinetics and mechanism of transfer of a constituent across a slag-metal interface are fundamentally important because many metallurgical processes involve the existence of a slag phase and a metal phase. Industrial processes seldom proceed to equilibrium, and information of the rates and modes of reactions are therefore often of greater practical importance than equilibrium data. A study of the kinetics of sulphur transfer across a slag-metal interface under reducing conditions will contribute a great deal toward a better understanding of desulphurization in the blast furnace process. The general principles existing in the transfer of a constituent, such as sulphur, across a slag-metal interface can be extended to similar transfer phenomena in other metallurgical processes. The present paper will demonstrate how such studies will lead to fruitful results from both the practical and theoretical standpoints. EXPERIMENTAL METHOD The apparatus used was, simple. A graphite crucible 15/8-in. id, a wall 1/8-in. thick, and a depth of 4 in., was packed in an outer fused silica tube with powdered magnesia. The crucible assembly was rotated at a speed of 235 rpm inside an in- duction coil. A charge of 250 g of Armco ingot iron was introduced into the graphite crucible and melted by induction heating. The melt was held at a desired temperature for 3-5 "'in., aftcr which 7.5 g of granular ferrous sulphide was added and the bath was held for another 3-5 mi11. A metal sample was then taken by means of a fused silica tube and a rubber suction bulb. Immediately after the metal sample was taken, 30 g of a prefused and crushed slag were introduced. The slag reached the ternperature of the furnace in 1 to 1 1/2 min. Slag

Jan 1, 1949

By J. R. Mihalisin, J. S. Iwanski

The response of Inconel "700" to heat treatment has been studied by light and electron microscopy combined with X-ray and electron diffraction techniques. A heat treatment which vesults in low ductility for this alloy appears to be associated with the formation of MC carbide in a Widmanstdtten distribution. This type of precipitation can be suppressed by suitable heat treatment with concurrent increase in ductility. Various other phases precipitated in this alloy are also identified. RECENT studies of commercial nickel base su peralloys have demonstrated the importance of the morphology of carbide phases upon physical properties.' For example, empirical heat treatment studies applied to Nimonic "80" and Inconel "X" have resulted in prescribing double aging treatments for optimum physical properties. These treatments have subsequently been related micro-structurally to grain boundary carbide morphology.2 The purpose of this study was to obtain information about the morphology and identity of some of the phases precipitated in Inconel "700" after heat treatment. It was hoped that some correlation could be made of micro structure with heat treatment similar to that observed with Inconel "X" and Nimonic "80." EXPERIMENTAL PROCEDURE Specimens were obtained from a hot-rolled bar of Inconel "700" of the following composition: C Mn Fe S Si 0.10 0707 0.42 0.007 0.12 Cu Cr -A1 -Ti- Co Mo Ni 0.02 -14.90 TM 2.22 27.61 2.92-- Bal. Specimens were prepared in the following heat-treated conditions: (A) 2275°F for 2 hr WQ (B) 2275°F for 2 hr WQ + 2000°F for 1 hr (C) 2275°F for 2 hr WQ + 1600°F for 48 hr. (D) 2275°F for 2 hr WQ + 2000°F for 1 hr + 1600°F for 48 hr. Empirical stress-rupture studies had shown that treatment (D) resulted in optimum stress-rupture life and ductility. Treatment (C), although giving a good aging response, resulted in low ductility. Treatments (A) and (B), respresenting individual. steps in treatments (C) and (D) were added here for microstructural comparison studies. The procedure was to make an optical and electron microscopic investigation supplemented by X-ray diffraction analysis of electrolytically extracted residues. Electron diffraction studies were made utilizing selected area diffraction techniques with extraction

Jan 1, 1960

By John V. Beall

HEAVY-DENSITY separation processes, a commercial application of the sink-float test used in mineralogical laboratories for the separation of mineral particles by their difference in specific gravity, are the biggest development in mineral dressing since flotation, which was at about the same stage of development thirty years ago. The scope of their application has broadened and, though still in the development stage, they are being accepted in a constantly increasing number of commercial installations. This progress in mineral beneficiation is especially satisfying when we realize that our high-grade ore deposits are fast disappearing and a big factor in determining whether a hole in the ground is being sat upon by a liar or an honest citizen is how economically the ore dressers can concentrate comparatively low-grade ores. As early as the middle of the nineteenth century attempts were made to use aqueous salt solutions in a heavy-liquid separation for cleaning coal. But the original and recovery costs of these liquids were high and further, the fact that they were corrosive, unstable, and toxic added to the difficulty in using them.

Jan 1, 1948

By John V. Beall

Thai means free. Historically accurate, as the country has never been subjugated by foreign occupation, the name "The Land of the Free" also seems to fit the attitude of the people. At the Bangkok airport, without so much as a kopkhun (thank you), travelers are found behind, beside and in front of ticket counters. A pretty Thai face on TV calls flights in English and Thai. Baggage disappears with alarming rapidity and your reporter and spouse despaired of ever being reunited with it. But at the entrance, all the parts came together and there was even a limousine from our hotel, The Oriental. Driving downtown English style, we noted that there were four lanes of traffic occupying the space we would allow for three lanes. Motorcycles and enclosed three-wheel motorcycle taxis were much in evidence, but the occasional water buffalo held up the slow lane. In the city, men wore European-type slacks and shirts but the women were colorful in traditional ankle-length wraparound skirts.

Jan 1, 1970

THE first session, on alloys, took place on Feb. 20, Mr. Hibbard presiding in Mr. Campbell's absence. The session covered papers on manganese, chrom-ium, and silicon-iron systems. The paper by Mr. Wohr-man was presented by title. This paper showed that manganese produced many of the effects generally at-tributed to carbon and indicated that our ideas on manganese-bearing carbon steels will have to be modi-fied. Mr. Krivobok discussed this paper at length, the gist of the discussion being that Mr. Wohrman had not taken sufficient precautions in carrying out some of his work, particularly as to the effect of silicon content. Mr. O'Neill's paper was also submitted by title and no discussion was presented. Mr. Kinzel showed an accu-rate determination of .the carbon-free chromium-iron loop obtained by means of a specially constructed tele-scopic dilatometer. The loop ends at 12.2 per cent chromium and the A-3 line at 900° is unaffected by chromium content. The A-4 line runs from 1400° to 900° at 12.2 per cent chromium as an oblique hyperbola. Mr. Armstrong noted that the brittleness in high chromium alloys is often attributed to the gamma trans-formation and, according to Mr. Kinzel's diagram, this was impossible, as the alloys contain a great deal more than 12 per cent chromium. Mr. Kinzel pointed out that the presence of carbon in the commercial alloys caused the elongation of the loop and made possible local austenite transformation. Mr. Styri discussed the relations of the coefficients of expansion as shown in Mr. Kinzel's diagram. Mr. Corson presented the iron-silicon diagram as he has worked it out, showing a pre-viously unknown intermetallic compound, Fe3Si, to-gether with characteristic martensitic microstructure varying with the heat treatment. This compound formation is the real cause of brittleness in certain re-gions of the iron silicon system. Dr. Hoyt believed some of the evidence presented by Mr. Corson to be in contradiction to the phase rule. Mr. Corson, however, explained that true equilibrium does not exist under the conditions at hand so that the diagram was accurate in spite of the discrepancies. The meetings of the subcommittee on the physical chemistry of steel making were interspersed through-out the day. Mr. Feild presided and a program of future activities was outlined. This includes plans for a symposium at the next annual meeting and methods for interesting physical chemists, particularly those in the universities, in the steel man's problems. This committee has been newly formed and bids fair to be especially active. The Iron and Steel Committee met at lunch at the Engineers' Club at noon, with Dr. Mathews presiding. After disposing of the food the report of the Nominat-ing Committee was called for, and the following were elected as officers for 1928: R. H. Sweetser, chairman; F. C. Langenberg and W. J. Priestley, vice-chairmen; and T. T. Read, secretary. The report of the commit-tee appointed at the last meeting to consider publica-tion and general policy for the committee was then called for and freely discussed, after which it was unanimously voted to instruct the new chairman to se-cure from the Board of Directors the necessary author-ization for the Committee to recognize as a Division. This action was reported to the Board at its meeting the following night and the authority granted.

Jan 3, 1928

By Max Mason

In 1923 a Western mining company was experimenting with the device of an inventor designed to locate buried ores by radio. Because the progress was slow and the results were confusing, the company began to doubt the usefulness of the method and invited me to review the whole question of the application of physics to ore detection. I was fortunate in securing the cooperation of several physicists who had worked with me during the war on the problem of submarine detection. This group has been increased and has been studying the problem of physical exploration for ores since that time. It was evident that the problem is a big one, with many angles of approach. Its general features may be set down, in rough outline, as follows: The soils, rocks and ores hidden beneath the surface differ one from another in many respects. These differences may be made to furnish a clew for the physicists working from the surface. To bring these differences into action the physicist creates some kind of an effect which penetrates into the ground and is distorted and reflected when it meets boundaries between different sorts of underground structure. In other words, he sends a message down, and the rocks and ore send back signals in reply. In picturing this process, we should not regard the ground as dense and impenetrable. The kind of messages used pass through the earth about as readily as a sound wave travels the air. If, then, the fundamental procedure is to shout down questions in the hope that an orebody will hear and answer back to us, it is clear that a large part of the expert's study must relate to the kind of questions best suited to the temperament and intelligence of orebodies. It will be easier for the ore to reply to some of our questions than to others, and it is for us to find the right questions. In certain cases, we are spared the necessity of using a messenger, because nature has already provided one. For example, we already have a terrestrial magnetic field which automatically and continually conveys messages from underneath. We also have available the earth's gravitational field which furnishes us

Jan 1, 1929

By Maxwell Gensamer, Vsevolod N. Krivobok

It is generally recognized that "low temperatures" have a definite effect on the properties of metals and alloys. Furthermore, it is also generally understood that the effect is decidedly adverse. The possibility that the same low-temperature treatment might be employed for the purpose of improving certain properties of the alloys has received less attention until recently, and the experimental and theoretical knowledge consequently is meager. The effect of low temperatures may be studied in two ways: by studying such properties as tensile strength, hardpess, impact resistance, etc., at low temperature, and by studying the properties of alloys at room temperature after these alloys have been subjected to a low-temperature treatment. Even in the latter case, certain properties will differ materially from the same properties obtained on identical material but without cold treatment. In other words, subjecting alloys to cold treatment results in an irreversible change in mechanical properties. Changes of this character are usually indications of the appearance of a new phase or phases, and would be likely to occur in alloys which, either by virtue of their composition or by heat treatment, are retained at room temperature in a metastable condition. Consequently, studies of the effect of low temperatures logically should be conducted from the physicochemical point of view, since the results of such studies not only would furnish metallurgists with interesting theoretical data but would clearly indicate the classes of alloys that would hold promise of improvement, and, possibly, of new applications. As the present investmigation deals with chromium and chromium-nickel alloys of iron of the stainless variety, it has been thought desirable to present the data concerning low-temperature properties of these alloys, available from the most recent and most comprehensive work of H. S. Russell.l A summary of these data is given in Table 1. The data are confined to a limited number of alloys of the type dealt with in the present

Jan 1, 1931

By Robert B. McCormick

World War II has developed a use for the nonmetal mineral quartz crystal that was unknown in World War I. During the interim period of peace, experimental work in the radio field with the piezoelectric properties of quartz crystal resulted in the almost universal adoption of quartz-crystal radio oscillator plates to control frequency in radio broadcasting, police, commercial and amateur communications equipment. Telephone resonators and filters made from quartz crystal also were developed, which vastly improved the frequency control of long distance telephone circuits. Expansion of the Industry The sudden war demands of the armed services for radio equipment using quartz crystal for frequency control led to an unprecedented expansion of the manufacturing industry. It is estimated that the 1940 peacetime volume amounted to approximately $1,500,000, while today a vast new quartz-crystal industry supplies more than $150,000,000 worth of quartz oscillator plates to the Army and Navy each year. This demand has caused an enormous expansion not only of American manufacturing facilities but also of Brazilian mining output, virtually our only source of raw quartz crystal. Actual figures of imports and consumption cannot be cited, for security reasons, but certain comparisons have been made, which indicate the transformation of quartz crystal from a minor to a major nonmetal. Lundl has shown that the value of quartz-crystal exports from Brazil is now about equal to that of phosphate rock produced domestically in 1941 and actually exceeds the combined value of crude feldspar, gypsum and fluorspar production in the United States in the same year. This great expansion under wartime pressure was not accomplished without some anxious moments, but all the demands of industry have been met and the Government has been able also to accumulate a substantial stock pile of material against future contingencies. Inspection and Grading of Quartz Crystal The swift growth of the quartz-oscillator industry necessitated the simultaneous evolution of methods and criteria for inspecting and grading quartz crystal. It has been found that, generally speaking, it is economically feasible to cut only crystals that are at least 30 per cent by volume free from major defects such as optical and electrical twinning, cracks and fractures. Blue needles, bubbles, "chuva" and other minor imperfections can be tolerated in the usable portion unless present in great excess. The present marketing system in use in both Brazil and the United States, as far as quality is concerned, depends solely on the "usability" of a crystal, which is defined in the Brazilian-American agreement2

Jan 1, 1948

By Robert B. McCormick

World War II has developed a use for the nonmetal mineral quartz crystal that was unknown in World War I. During the interim period of peace, experimental work in the radio field with the piezoelectric properties of quartz crystal resulted in the almost universal adoption of quartz-crystal radio oscillator plates to control frequency in radio broadcasting, police, commercial and amateur communications equipment. Telephone resonators and filters made from quartz crystal also were developed, which vastly improved the frequency control of long distance telephone circuits. Expansion of the Industry The sudden war demands of the armed services for radio equipment using quartz crystal for frequency control led to an unprecedented expansion of the manufacturing industry. It is estimated that the 1940 peacetime volume amounted to approximately $1,500,000, while today a vast new quartz-crystal industry supplies more than $150,000,000 worth of quartz oscillator plates to the Army and Navy each year. This demand has caused an enormous expansion not only of American manufacturing facilities but also of Brazilian mining output, virtually our only source of raw quartz crystal. Actual figures of imports and consumption cannot be cited, for security reasons, but certain comparisons have been made, which indicate the transformation of quartz crystal from a minor to a major nonmetal. Lundl has shown that the value of quartz-crystal exports from Brazil is now about equal to that of phosphate rock produced domestically in 1941 and actually exceeds the combined value of crude feldspar, gypsum and fluorspar production in the United States in the same year. This great expansion under wartime pressure was not accomplished without some anxious moments, but all the demands of industry have been met and the Government has been able also to accumulate a substantial stock pile of material against future contingencies. Inspection and Grading of Quartz Crystal The swift growth of the quartz-oscillator industry necessitated the simultaneous evolution of methods and criteria for inspecting and grading quartz crystal. It has been found that, generally speaking, it is economically feasible to cut only crystals that are at least 30 per cent by volume free from major defects such as optical and electrical twinning, cracks and fractures. Blue needles, bubbles, "chuva" and other minor imperfections can be tolerated in the usable portion unless present in great excess. The present marketing system in use in both Brazil and the United States, as far as quality is concerned, depends solely on the "usability" of a crystal, which is defined in the Brazilian-American agreement2

Jan 1, 1948

By E. van Walsum

Tunneling methods through rock have, since the successful development of explosives, relied almost solely on blasting. Over the last ten years, rock-tunneling machines (moles) have been developed and some major projects have been carried out successfully with the use of such machines, which rely on the destruction of rock by mechanical means rather than blasting. Various other basically new methods are presently under study, such as the use of laser beams, water jets, etc. For practical purposes, there are presently only two methods commercially available: 1) blasting or 2) tunneling by mole. A contractor would choose at present either one method or the other. Both methods have their advantages and disadvantages (Fig. 1). The thought has occurred that the next practical development in rock- tunneling technology might be a combination of the best features of the mole technique and those of the blasting technique. A preliminary evaluation of this approach indicated that there is definitely a good potential for fruitful developments along these lines. My purpose is to place on record some of the thinking and some of the ideas which were developed along these lines and to point out certain areas where development efforts are required. In trying to find an improved tunneling technique, we looked in particular for the following qualities: 1) safety, 2) continuity, 3) uniformity, 4) automation, and 5) flexibility. TUNNELING BY BLASTING Conventional tunneling by means of blasting proceeds generally in recurring sequences of events: 1) drilling, 2) loading, 3) firing, 4) mucking-out, and supplementary operations (such as scaling and lining). These four operations (drilling, loading, firing, mucking) proceed one after another.

Jan 1, 1970

By W. A. Backofen, B. B. Hundy

THE pole figure interpretation in a recent paper' on the torsion texture of copper was questioned in discussion,2 nd a simpler alternative interpretation was proposed. In the hope of reaching a positive decision in favor of one or the other, further studies were undertaken with 70-30 brass and Armco iron. This additional work has not answered all the questions about torsion textures, but the new pole figures do offer support for the original interpretation and show that the texture is more complicated than the alternative suggests. From the previous paper,' the appropriate method of describing the texture in a twisted bar is known to be a pole figure plotted on a plane tangent to the surface of the bar. The axes of the pole figure are chosen to coincide with directions in the tangent plane which are parallel and at right angles to the bar axis (the longitudinal direction, L.D., and the transverse direction, T.D.), for these directions define symmetry axes of the texture. Therefore any ideal orientation that might be selected to represent the texture gives the crystallographic plane parallel to the tangent plane and the crystallographic direction parallel to the axis of the torsion specimen. A unique texture was assumed in the original interpretation, and the four ideal orientations, (112) [111], (111) [112], (110) [001], and (112) [131], were used in its description. Of the four orientations, the first three provide possible slip directions along the direction labeled T.D. in the pole figure, which is one of maximum shear stress in a specimen being twisted. The alternative, however, simply considered the texture to be made up of two components, one a [Ill] alignment along the specimen axis with a random orientation about the axis as in the wire texture, and the other a superimposed orientation (110) [0011. Experimental evidence for this simpler interpretation was derived from two observations: 1—twisting did not alter the orientation of a single-crystal torsion specimen of a brass in which an octahedral plane was perpendicular (and a [Ill] direction parallel) to the axis, and 2—deformation bands with approximately the (110) [001] orientation were seen to develop in the crystal during the test. The new pole figures were obtained with a brass and an iron torsion specimen of 3/4 and 1 in. gage length diameter, respectively. After annealing, polishing, and twisting, seven rods, about 0.030 in. in diameter and with different orientations, were prepared from material near the surface of each specimen; these were required for the method of constructing pole figures by using a Geiger counter as developed by Norton.5 Since the shear strain gradient in plastic torsion is linear, it was readily computed that the material supplying the brass rods had been subjected to a shear strain of about 3.2, and that supplying the iron rods had received a shear strain of about 2. All details concerning specimen design, testing procedure, rod preparation, and use of the Norton technique can be found in ref. 1. Only this procedure was followed in working out the (111) and (100) pole figures for brass, Figs. 1 and 2. However, X-ray photograms were also involved in the construction of the (110) pole figure for Armco iron, Fig. 3. The photograms were made according to the conventional transmission diffraction technique using a small sheet taken parallel to the specimen surface and etched to a thickness of about 0.0025 in. They were especially important in locating the boundaries

Jan 1, 1954

By Arthur R. MacPherson

The development of a simple method to predict the autogenous grinding possibilities of new ore deposits is attained. This method employs a 45-cm (18-in.) dry grinding Aerofall mill to grind small quantities of core or crushed samples in the top size range of 2 to 5 cm (1 to 2 in.). An extensive program has been carried out to correlate the data obtained in the 45-cm (18- in.) test mill with the actual results obtained in large commercial plants or autogenous test plants. Enough evidence now exists from these correlation programs that the 45-cm (18-in.) mill can be used to grind small samples from a new deposit and correctly predict the autogenous grinding mill requirements of a commercial plant to treat this ore.

Jan 1, 1978

By E. P. Abrahamson, S. L. Lopata

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deforlnation gradient matrix, F - [axi/aXj/ where X and x refer lo the initial and final positions of a particle. This matrix is readily evaluated in termas of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip systena. In the case of deforma tion from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Göler and Sachs.4 Taylor and Elam1 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, ! terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(aN as N — m while a — 0 in such a way that the Product Na = a finite conslant designatzng the accumulated amount of shear. It turns out that this limit is simply eafF1, where F, is the matrix whose elements are the coefficients of a in the F(a) twatrzx. Application is made of the present treatment to a fcc crystal of Permalloy compressed on the (110) plane and contrained to elongate in the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to (xl,xz,x3), both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By F. C. Newton

RefineRs of lead by the Parkes process have always been solicitous of recovering the zinc used in the desilverization, and justly so, as the loss in zinc constitutes one of the heavy costs in this method of refining. Part of this loss is due to the absorption of zinc by lead, and in the present state of knowledge is not recoverable as metallic zinc. The remainder of the zinc, which finds its way into the precious-metal-bearing crust, is recoverable and naturally engages the operators' most exacting attention. Careful elimination of the impurities in base bullion has enabled the refiner to produce a zinc crust better adapted to retorting, which reflects favorably in the zinc recovery;- and to produce a richer crust, thereby lowering the zineking cost, as the increased efficiency of the zinc results in less of it being in circulation. It is obvious that if the ratio of concentration be increased, a lessening of the amount of crust formed will ensue, throwing less work on the retorts and diminishing the amount of retort metal sent to the cupels, thus making an actual money saving in all these operations. In the effort to obtain a rich crust, the metallurgist has increased the heat to a considerable degree, upon the assumption that at the higher temperature the zinc-dver alloy could be squeezed free from the adhering lead. A further possibility for improvement suggested itself in the freezing-point curve of Prof. H. C. Carpenter, upon zinc and silver. Study of this curve disclosed the existence of a definite chemical compound, Zn3Ag2, with a freezing point of 665" C., a promising compound for practical application. In the experiment undertaken it was endeavored to force this compound into the crust, hoping thereby to obtain a higher concentration than formerly. It was recognized that in bringing a large kettle of lead to such a heat, more fuel would be used, the life of the kettle would perhaps be shorter, and other disadvantages would be experienced. AS a commercial operation, the project would have to stand on its own feet,

Jan 1, 1915

By Charles C. Goddard

Since discovery of silver-gold lode deposits in 1864, the Butte district has produced more than $2.25 billion worth of copper, zinc, manganese, silver, and gold, an unprecedented value in the mining world. Exhaustion of the gold placer deposits along Silver Bow Creek, southwest of Butte, forced the early-day placer miners to turn their attention to the bold out- crops of the many veins exposed on the hillsides above the placer diggings. These outcrops bore silver and gold, and enough so that many lode claims were located. Such famous silver mines as the Alice, Moulton, Magna Carta, Nettie, and Blue Bird were developed. These and many smaller operations contributed to making Montana the leading silver-producing state in the 1880's. As depth was gained in the silver mines in certain parts of the district, occurrence of zinc minerals became troublesome. Zinc was not recoverable at the time, and in the chloridizing, roasting, and amalgamation of the ores, silver and gold recovery was greatly reduced. A period of active silver mining continued until 1892, when a decline in the price of silver brought the silver mining period to a close. Elsewhere in the district it was discovered that while some of the veins contained silver ores in the oxidized portions, the predominant minerals that were deeper were copper-bearing. Marcus Daly exposed rich copper ore on the 300 level of the Anaconda mine in 1891, and mining in the district disclosed that copper was destined to be developed in abundance. Early copper ore shipments were made to Swansea, Wales.

Jan 3, 1959