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By A. G. Crocker

The positions of twin reflections in electron-dijjcraction patterns obtained from thin metal foils may he calculated for any twin in any crystal structure by means of an elementary application of vector algebra, General equations for the four classical orientation relationships are presented using the superscript and subscript notation of the tensor calculus, which is briefly described. As an example of the application of these expressions, the case of twinned rhomhohedral crystals, and hence as a special cased twinned cubic crystals, is examined. CONSIDERABLE interest has recently been shown in the interpretation of electron-diffraction patterns obtained from twinned regions of thin metal foils. In the present paper, it is shown that the necessary information may be obtained directly for all twins in any crystal structure by means of a very elementary application of vector algebra. The equations involved are most conveniently presented by making use of the very powerful superscript and subscript notation of the tensor calculus. The use of this notation will first be described and then applied to the problem of calculating diffraction patterns for any twinned crystal. Finally, as an example of the application of the method, the specific case of twinned rhombohedra1 crystals will be considered.

Jan 1, 1965

By H. C. Boynton, Albert Sauveur

In the course of some experiments conducted in the Metallographical Laboratory of Harvard University, some interesting facts were brought to light which appear to be worth recording in advance of a more elaborate and exhaustive paper which the authors hope to present to the Institute in the near future. Fig. 1 shows, under a magnification of 100 diameters, the microstructure of the cross-section of a steel bar 1/2-inch square, containing 0.52 per cent. carbon, heated to 1100 degrees C. and cooled slowly with the furnace. Fig. 2 illustrates the structure of the same steel, heated to the same temperature but cooled more rapidly in the air. Both samples were cut from the same bar and heated side by side in the furnace. When a temperature of 1100 degrees C. had been reached, one sample was taken out of the furnace and allowed to cool in the air, while the other was cooled with the furnace. The only difference, therefore, in the treatment of both samples will be found in their respective rate of cooling. This variation in the rate of cooling resulted, as shown

Jan 1, 1904

By S. E. Haszko

Fused alumina or silica crucibles were used as the containing vessel. X-ray powder photographs were taken with CrKa radiation and the use of Straumanis type Norelco cameras of 114.6 mm diam. Crystallographic data for these compounds are shown in Table I. These results are in agreement with others of this series reported previousiy by Wernick and Geller.l The abnormally large atomic volume of Eu and Yb metal3 is manifested in EuA12 and YbAl2, when one compares them with the compounds reported in Ref. 1. However, the behavior of Yb in the Ni compound is the same as that observed in Ni5Yb having the Cu5Ca structure.4 Thus, it appears that Yb has a valence closer to 3 only in the Ni compounds; i.e.. the 2s and Id electrons are lost to the conduction band. 1,4 Europium in EuAl2, appears to have a valence closer to 2. In previous work.' X-ray patterns of ingots of NdCo2 indicated a multiphase material with faint indication of the presence of a phase having the MgCu2 structure. It was thought that NdCo2 formed peri-tectically from the melt, resulting in a multiphase system when cooled under nonequilibrium conditions. An X-ray pattern of a sample from a melt cooled more slowly than in past work showed that the major phase was NdCo2. The lattice constant, Table 1, is in excellent agreement with the value one can predict from the data of Ref 1. One of the other phases was identified as Co,Nd. The author wishes to thank J. H. Wernick for his guidance in this work, and D. Dorsi for the preparation of these compounds. 'J. H. Wernick and S. Geller: AIME Trans., in press. 'J. H. Wernick and S. E. Haszko: to be published. 'F. H. Spedding and A. II. Daane: Progress in Nuclear Energy, Series 5, Eds.: H. M. Finniston and J. P. Howe, McGraw-Hill Book Co., 1956. 'S. E. Haszko: to be published. 'J. H. Wernick and S. Geller: unpublished work. 6J. 11. Wernick and S. Geller: Acla Cryst., 1959, vol. 12, p. '162. The Influence of Hydrogen on the Lattice Parameters of Ti-Sn Alloys A. Coucoulas and H. Margolin A reinvestigation of the lattice parameters of Ti-Sn alloys by the present authors has revealed consistently higher c and a values than those obtained by Worrier. The difference is most pronounced in the c-parameters which are, therefore, used as a basis of comparison. This discrepancy was not due to air contamination, since precautions were taken to exclude this possibility. Specimens for Debye-Scherrer photograms were prepared by arc-melting 15-g buttons of Bureau of Mines titanium and 99.99 pct Sn, with compositions of 6, 8, 10, and 12 at. pct Sn. These buttons were forged under an oxygen-acetylene torch to 1/8-in. sq rods to produce relatively fine grained material. Scale and some surface were ground off, and the rods, after wrapping in molybdenum and titanium sheet, were vacuum annealed 15 min at 800 °C to remove hydrogen. Heat treatment of one of the samples at 875°C to produce ß and reveal a at the surface showed no surface contamination. Following the vacuum treatment, the specimens were wrapped in molybdenum and annealed for 1week at 800°C under two atmospheres of argon. After water-quenching, the rods were ground so that the thickness tapered to 0.1 mm at the tips. The ground specimens were then recapsuled as previously and reannealed 1 hr at 800°C to remove cold work. The

Jan 1, 1961

By S. R. Rao, J. Leja, K. S. Moon

A prolonged grinding of sulphide ores in steel mills appears harmful to flotation recovery and selectivity whenever xanthates are used as collectors. Particles finer than about 10µm show a pronounced decrease in floatability. A supposition was made that the cause of the reduction in floatability of ground sulphides is the presence of metallic iron abraded during grinding and deposited on the ground particles. Electro- chemical measurements were made of mixed potentials developed by different sulphide-mineral electrodes (galena, chalcopyrite, pyrite, marmatite, pyrrhotite) in xanthate solutions, without a direct con- tact or in contact with a metallic iron electrode. These measurements showed that without a galvanic contact between the sulphide and the iron, the values of mixed potentials were in the vicinity of the xanthate/dixanthogen redox potential. When contact with iron was established, the mixed potentials shifted towards the more negative reducing or cathodic values. The shift was greater the higher was the ratio of the surface areas: iron electrode to sulphide electrode. Further, the shift in mixed potentials was greater the more reducing were the conditions on the sulphide electrode. Chemical analysis of reaction products produced on the surfaces of sulphides and in the bulk solution showed that less thiosulphate was formed in all of the sulphide-xanthate systems and that more elemental sulphur was detectable on the pyrite and marmatite surfaces. Adsorption of xanthate parallels the amount of thiosulphate formed with which xanthate is exchanged by metathesis. If the supply of oxygen is limited, the demand for oxygen by the abraded metallic iron competes with that by the valuable sulphide, resulting ultimately in poorer hydrophobicity. If excessive amounts of pyrite or pyrrhotite are present as well, the conditions are so reducing that there is little adsorption of xanthate ions on the valuable sulphides to make them hydrophobic and floatable. The presence of increased quantities of sulphur on pyrite or marmatite is responsible for a non-selective flotation. Flotation tests on synthetic mixtures with and without metallic iron powder in the feed confirmed the above conclusions from electrochemical and chemical measurements.

Jan 1, 1976

By R. Neilson Clark

THE coal-beds of Canyon City are situated six miles below the town, upon the Arkansas River. At this point the Rocky Mountains have thrown out from their main ridge two spurs. The one to the north, containing Pike's Peak and Cheyenne Mountain, is known as part of the "Rim Range;" the one to the west and south is known as the "Greenhorn Range." Against these syenitic mountains, the later rocks are piled and uplifted ; at right angles to the direction of this main uplift is the axis of a lesser plication. On the north, west, and south, the pitch is steep, gradually flattening as it approaches the centre of the basin and rising again to the east at a pitch of about 5", thus forming a perfect basin, the centre of which is only three miles east of the base of the Greenhorn Range.

By H. Brandhorst, C. G. Dunn

THE main purpose of the present note is to provide further information on the effect of orientation on strain-induced grain boundary migration in sheet material. A secondary purpose is to draw attention to the presence of a possible (hkl) dependent surface energy driving force, when the two grains of a bicrystal specimen have different (hk2) planes at the gas-metal interface, and to suggest means of eliminating this effect from the strain effect. If two grains A and B of a bicrystal have specific surface energies ? A and ? B respectively, there exists a driving force for grain boundary migration equal to 2(? B - ? A)/t, where t is the thickness of the specimen.' When t is quite small and the residual strain energy densities €A and €B of grains A and B, respectively, adjacent to the boundary are nearly equal, it is possible that the surface effect may be larger than the strain effect. he difference € B - € A gives a driving force per unit area of grain boundary due to an applied strain.)2 However, with increasing t the surface effect decreases while the strain effect presumably remains constant. Therefore, at some sufficiently large value of t, it is possible to ignore surface energy driving forces.* On the other hand, the surface effect is eliminated for all value of t when both grains have the same (hkl) orientation or have identical values of surface energy. Although the previous study provided information on the effect of orientation on strain-induced erain boundary migration,' no orientations with the (100) plane in the plane of the sheet were included. The present paper provides information of this kind. A seed crystal reorientation technique4 was used to prepare a large bicrystal of silicon iron (3 1/4 pct Si) consisting of two (100) grains in the (100) [001] and (100) [Oil] orientations. After a cold rolling strain (7 pct reduction to 3/4 mm final thickness), small specimens were prepared as before2 and then annealed in hydrogen. The boundary migration was such that the grain in the (100) [011] orientation always grew. After overnight anneals at 1100° or 1000°C, none of the initial (100) [001] grain remained. An anneal of 30 min at 950°c, however, provided information on the start of boundary migration. Fig. 1 shows both the initial position (lower line) and the final position (upper curved line) of part of the boundary, as revealed by thermal grooves. In a different area, part of the final boundary was not revealed by thermal grooves; the rate of boundary migration presumably was too high for the growth front to be defined by the time dependent thermal grooving process. In another area there was a vacated intermediate position connected to the initial position of the grain boundary. This indicates that only part of the boundary

Jan 1, 1962

By Samuel Lasky

FAULTING at Kennecott, with its attendant fracturing, is unusual, complex, and important. As study. and knowledge of the various fault systems have progressed, appreciation of that importance has helped in the selection of proper horizons for exploration and in the avoidance of useless crosscutting and drifting. During the study of this faulting and fracturing, a suggestion concerning the formation of the ore-bearing fissures occurred to me. Further study in the available portions of the approximately 45 miles of workings in the Kennecott mines for the purpose of checking up the the suggestion led to the hypothesis which this paper will attempt to present. Briefly, the hypothesis may be stated as follows: The formation of transverse faults that stop against a main, system is connected with changes in the strike or dip of the main fault, and such cross faults or fractures lie in the moving block of the main fault system and indicate a change in strike or dip of the main fault. It has been found that each kind of change tends to produce definite effects and that careful study of the evidence can often suggest the exact type of change.

Jan 1, 1928

By T. M. Chance

THE first bituminous coal cleaning-plant to use the sand-flotation process1 was placed in operation on Oct. 1, 1925, at the tipple of the East Broad Top Railroad & Coal Co., at Mt. Union, Pa. The general principles governing the design of plants of this type and typical operating results of anthracite sand-flotation units have been previously outlined.2 I will, therefore, confine myself to a description of this particular plant and to some of the elements of design it incorporates. THE ORIGINAL MT. UNION TIPPLE The plant was installed to transfer coal from steel narrow-gage cars of 60,000 and 70,000 lbs. capacity to standard-gage equipment. The coal was hauled some 30 miles from the East Broad Top field. This coal, mined by the Rockhill Coal & Iron Co. and other operators, is a low-volatile slow-coking coal with- ash of high-fusion point. It is normally a high-grade coal that does not contain an excessive amount of free impurities, but it requires careful handling to secure a fair domestic yield, and, naturally, the need for narrow-gage transshipment increases the difficulty of the problem. The narrow-gage cars were discharged into an 8-car track hopper equipped with two feeders passing the coal to two 42-in. apron intake conveyors. Twin units were installed throughout in this original plant, two lump-and-egg shaking screens, two lump picking-tables, two egg picking-tables and two stoker conveyors. The stoker coal was loaded without cleaning. The loading tracks and booms were in duplicate and with the layout as originally installed either unit could be run independently, each unit shipping a different class of coal or both units making the same product.

Jan 2, 1926

By J. P. Neumann, L. Raymond

At temperatures near 1000°C, only the (112) (111) slip systems are operatire in tungsten. Therefore, the substructure introduced into the billet upon rleforming a single crystal by rolling at 1000 "C can be controlled by proper selection 01. processing ral'iubles. Using a reduction of 10 pct pel- pass, the (001)[110] and the (110)[001] crystals will deform by duplex slip rip to a 50 pet reduction in thickuess. These rolled single-crystal sheels are characlerized by anisotropic hardening, retention of ductility with warm working, lattice bending which is related to the conlacl (angle, and macroscopic dimensional changecs in the length bid not the width of the billet. When several slip systems become operative, a greater degree of work hardening is itztvoducetl into the crystal. This rolling- condition is characlerized by isotropic hardening, loss of ductilily with warm working, complex lattice distortions, and macro-scopic dimensional changes in both the length rind Width of the billel. IN tungsten, the {1 10}(111) slip systems are operative below room temperature,' while above 700°C only the {112{ (111) slip systems are observed.2,3 In the transition region, i.e., room temperature. both systems appear. It is the purpose of this investigation to show that tungsten single crystals deformed by rolling at a temperature where only one slip system is operative generate dislocation substructure which depends on the crystal orientation. For a specific crystal orientation. the resulting dislocation substructure can be further influenced by modifying the rolling procedure. Crystals oriented for multiple slip display less substructural sensi- tivity to modifications in processing techniques than do single crystals oriented for duplex slip. Under simple slip modes of deformation, very little work hardening is introduced into a rolled single-crystal sheet. Mechanical properties such as room-temperature strength. ductility, and hardness are used to confirm the existence of the different work-hardened conditions generated within the crystal by modified warm-rolling techniques. EXPERIMENTAL PROCEDURE Material. Single-crystal billets of four different crystal orientations. grown by the Arc-Verneuil technique. were ground to a size of 0.25 by 0.375 by 3 in. In terms of their rolling plane and rolling direction, the billets had the following orientations: (1101 [001 ] (110) [110] (001) [110] (001) [100] The actual orientation of all crystals was within 5 deg of the ideal orientations. The typical impurity content of the crystals is given in Table I. Polishing and Etching. Polishing was done elec-trolytically in a 20 g per liter aqueous solution of NaOH at approximately 10 v. It was established by the Laue back-reflection X-ray technique that the surface damage due to grinding and cutting operations with a diamond wheel did not exceed 0.001 in. Therefore after each cutting or grinding operation at least 0.002 in. was removed electrolytically from the surface in order to eliminate surface effects. By lowering the voltage to 3 v, subgrain boundaries and individual dislocations are identified in agreement with Berlec 4 where the etch-pit traces on a cubic plane form a square. The etching time was about 5 sec at room temperature. Rolling. Rolling was carried out on a Loma 2-high mill (Model 600). The peripheral velocity of the 6-in.-diameter rolls was 500 in. per min, with the surface temperature of the rolls about 400° to 450° C The billets were heated before each pass for 30 min in argon to 1000 C. Oxidation of the crystals during rolling in air resulted in a thin layer of greenish-yellow WO 3 This oxide was removed after each pass by immersing the crystals for a few minutes in a boiling NaOH solution. Prior to the initial rolling pass, a surface layer of 0.001 in. was removed by polishing. The crystals were then annealed in vacuum (10-4 torr) at 2400 C for 30 min. All crystals were rolled in the same direction; i.e., the same end was always introduced into the rolls. The rolling program was conducted in

Jan 1, 1965

By A. E. Bellis

ROBERT J. ANDERSON, Cleveland, Ohio (communication to the Secretary *).-The paper by Messrs. Bellis and Hardy was interesting to me and has led me to make a few remarks concerning some of the points brought out. The question of employing correct hardening temperatures is one that is sadly neglected, particularly in many large plants that forge and treat their machine tools for private use. As is most aptly remarked in this paper, "The custom of using one, high-speed temperature for all tools is very poor practice;" still, such practice is more common than otherwise. An instance came to my attention some time ago, in connection with some work with the standardization of high-speed steels for machine tools, where there were no less than six different brands of alloy steels being used for machine tools such as lathe, shaper, planer, boring mill and cutters of like nature. All of these different steels received identical heat and forging treatment-or at least that was the aim of the tool hardener. That the results were highly unsatisfactory goes without saying. That the hardening department of many plants is conducted on a rule-of-thumb fashion is the reason for a great deal of the trouble and disappointment which seems to be the lot of many tool-steel users. Exceedingly crude execution is the rule rather than the exception, and it is no small wonder that the results are as good as they sometimes happen to be. It would seem that at the present price of alloy steels the subject should receive a closer scrutiny by purchasers than it does. One not familiar with the workings of souse plants that disdain to lend an ear to scientific heat treatment would scarcely give credence to some of the methods employed, not only in the treatment of the steel but also in its selection and purchase. Heating for hardening should be conducted under close pyrometric control only after the correct hardening temperature has been determined.

Jan 3, 1917

By H. H. Rachford

This work presents a first-order analysis of the instability underlying viscous fingering in adverse viscosity-ratio water floods. It extends previous analyses of frontal instabilities, which were carried out with equations for parallel plate models, by including effects of the saturation transition zone observed behind the front in water floods in water wet systems. This zone tends to insulate incipient fingers from the high-mobility watet;. thus conditions for the onset of fingering differ from those in the parallel plate theory. Finite-difference solutions of the two-dimensional equations of displacement in porous media exhibited the predicted stability characteristics in six hypothetical field- and laboratory-scale floods in rectangular reservoirs. In contrast to results with parallel plate systems, this paper concludes that for waterwet reservoirs, laboratory models scaled by the usual criteria are also correctly scaled for frontal instability. Further, fingering in the systems studied can occur in any saturation range behind the front, and may occur at an intermediate saturation even though stability obtains both at the saturation corresponding to the Buckley-Leverett front and near residual oil saturation. Other points of contrast are that the likelihood of occurrence of fingering may not increase as flow rate or viscosity difference increases, but my be sensitive to changes in he relative permealdlity and capillary pressure functions. INTRODUCTION The recovery of oil by water flooding frequently involves displacing the oil by water of a lower viscosity. Displacement of a fluid by a less viscous one may lead to gross channeling or fingering like that observed in solvent floods, in which it severely lowers recovery efficiency.1 In addition to adverse effects on recovery, it has been suggested that the unstable move- ment causing fingering may interfere with interpretation of scaled model studies of proposed water floods, since the instability in the model might not be faithfully scaled to that in the reservoir prototype. In view of the serious implications of this possible breakdown of widely used scaled model techniques4-6 it is the purpose of this paper to examine the question further. Instabilities in the solutions of systems of differential equations imply a loss of smooth dependence on initial and boundary conditions. Thus, the possibility exists that in using models whose scaling is based on the differential system there may arise size- and rate-dependent factors which are not properly scaled. This possibility was examined in detail by Chouke et al., who analyzed the instability of frontal advance in a related problem, water-oil displacement in parallel plate models,2 in which a moving interface separates two regions of constant, unequal mobilities. First-order perturbation theory predicts the existence of a critical wave length for the growth of perturbations: and a wave length of maximum instability of A, = The interpretation is that wave lengths in a perturbation which are longer than A, will grow. Thus, if the width of a two-dimensional channel is greater than A,, fingers will grow, and the spacing of the fingers which grow at the maximum rate will be approximately It is important that the higher the velocity and/or the difference in flow resistance, the lower is A,, and thus the greater the number of fingers that can grow in a given model. In applying these conclusions to porous media, a pseudo-interfacial tension, , was assumed for the invasion front. Since this would not necessarily be equal to the liquid-liquid interfacial tension, an unknown constant was substituted for the foregoing expression for A, This was determined

Jan 1, 1965

By Courtenay de Kalb

So far as the writer is aware, no detailed investigation into the behavior of ores or rocks when subjected to crushing under digerent conditions has yet been made. He cannot himself claim to have carried such investigations very far; but the results of some studies which he has been pursuing for a couple of years, as opportunity permitted, seem sufficiently interesting and suggestive to warrant a brief statement of them, preliminary to nildertaking a more exhaustive course of experiments. Criticisms and suggestions are earnestly invited, with a view to making these studies as instructive as possible. As a part of the examination of ores, preparatory to concentration, my students have been required to take lots of 100 pounds each, and crush them. These are then screened through a series of hand-sieves, 15 inches in diameter. The products remaining on each screen are weighed, and from the results is plotted a curve, called the sizing-curve. It was assumed at first that different ores would yield, under like conditions of crushing, curves showing unlike characteristics as to the quantities remaining on the various sieves. After a number of such curves had been obtained it became evident, as often happens, that this a priori reasoning was faulty. The curves presented practically identical characteristics, and only by varying the crushing-conditions were variations in the curves obtainable. Another peculiarity, which was as little anticipated, appeared by inspection of these results, namely, that successive crushing to smaller sizes did not greatly augment the quantities of the filler products, so long as the machines employed applied the crushing-force to the ore-particles in the same manner. In these experiments the fines were not eliminated between successive crushings. I believe it will be readily admitted that rock can be crushed

Jan 1, 1899

By Woolsey McA. Johnson

In metallurgical circles it is known widely, but somewhat vaguely, that the ease of reduction of metallic oxides depends largely on the way they hare been prepared. It is likewise known that different forms of carbon have different and greatly varying reducing powers. It is the purpose of this paper to show somewhat more definitely and scientifically these facts. Some years ago the writer published an account of pyrometric determinations of the reduction temperature of zinc oxides variously prepared and of several kinds.' In said paper it was shown that the temperature at which zinc oxide evolves zinc according to the equa-tion ZnO + C = Zn + CO depends upon the nature of the two reacting bodies. The determina-tions had a range of accuracy of from 2° to 6°C., whereas differences were found to amount to an extreme of 90' C. So the differences are real ones and must have a definite cause. The equation of boiling water, (H2O)4 D 4 (H2O) has a fixed temperature for equilibrium of 100° C. at 760 mm. pressure. In general, all equations reacting in the liquid or the gaseous phase have well-defined constant physical conditions which govern the equilibrium point and reaction velocities. In a reaction where we have one or more solid phases, the tempera ture conditions requisite for the unbalancing of the stable system are found to vary. These variations are due to the fact that in a solid there is a very complex molecule and it is not a question solely of the tearing away of two interlocked atoms, but also of the destruction of a complex molecule containing hundreds, or possibly thousands, of smaller molecules. In other words, there are two forces to be overcome: a certain

Jan 1, 1914

By Roshan B. Bhappu, Raul A. Deju

A method is proposed by which the chemical reactions between water and a silicate bed can be related to equations of flow. First the reaction mechanism is studied both theoretically and experimentally. Once the reaction mechanism is established, the equations of flow are solved, and a solution (under physically reasonable side conditions) is obtained. Experiments to substantiate the solution are also presented. The knowledge of surface reactions at the water-solid interface is of critical importance in extractive metallurgy. This is especially true in regard to the froth-flotation process of mineral concentration and all phases of hydro metallurgical recovery of metals. Similarly, the problem of ground-water contamination is one of growing concern, not only because of the increasing demands on our sources of supply but also because of the increasing necessity to find vehicles of waste disposal. The hydrochemistry of waste waters must be understood to exploit and develop such resources properly. To understand these problems, it is necessary to obtain a better insight into the reactions that take place between water and a solid packed bed. To do this, we will develop here in a theoretical model that predicts the fate of a chemical species in solution as it reacts with a silicate bed through which the liquid percolates. The treatment will be one-dimensional in nature and will not include dispersion. Experiments will also be presented to substantiate the theoretical model, using the silicate minerals listed in Table 1. This paper is preliminary in nature and is part of a larger study of the surface chemistry of the silicate-water interface. Mechanism of Surface Reactions In a previous paper,' the authors discussed the properties of various silicate minerals from a mineralogical standpoint. Now efforts will be made to study the reactions that occur when these minerals are put in contact with water. The reactions occur almost entirely in the surface layer of the mineralsa and are termed sorp-tion reactions. In this study sorption denotes the composite of all physical adsorption and chemical adsorption occurring between the silicate surface and the water in contact with it. A model of sorption as seen from a chemical-bond standpoint is presented below. On the basis of this model, the surface reactions between deionized water and a silicate mineral can be studied. Sorption Model: It is known that as the oxygen-silicon ratio increases from quartz to the olivines, a greater percentage of the oxygen bonding power is available for bonding to cations other than silicon. Hence, with an increasing oxygen-silicon ratio, the oxygen-to-metal bonding increases. Upon the fracturing of a silicate-mineral crystal, the oxygen-metal bond breaks more easily than the stronger oxygen-silicon bond, resulting in a negatively charged surface. Then, if the mineral is immersed in a liquid containing hydrogen ions, the negatively charged surface should tend to be neutralized by hydrogen ions from solution, resulting in a change of the solution pH. Thus, an increase in the degree of sorption of hydrogen ions must occur as the oxygen-silicon ratio in the crystal structure increases. Also in a previous paper,' the authors found that for a given silicate mineral the change of pH with time is given by

Jan 1, 1971

By J. Geertsma

In order to obtain a better insight into the pressure-volume relationship of reservoir rocks a theory of pore and rock bulk volume variations is presented. The theory is independent of the shape of the pores but is restricted to isotropic porous media built up of continuous homogeneous matrix material. The main conclusion obtained from this theory is that only three elastic constants and three viscous constants are required for describing pore and rock bulk volume variations if the porosity is explicitly introduced into the treatment. In addition, reasonable approximations are introduced for various types of reservoir rock, e.g., sandstones, limestones, and shales, which lead to further simplifications of the basic formulas. In consequence there is then a further reduction in the number of deformation constants which have to be determined experimentally. It is shown how measurements of these remaining deformation constants can be performed most conveniently. Finally the application of the theory to reservoir studies is discussed and the translation of experimental results obtained in the laboratory into reservoir behavior is considered. INTRODUCTION The decline of fluid pressure in connection with the withdrawal of fluid from an underground reservoir gives rise to a change in volume of both reservoir fluids and reservoir rock. The volume variation of the reservoir rock results in a decrease of both the pore volume and the total volume of the fluid-filled formation. Whereas the variation in volume of the reservoir fluids with pressure is usually known from PVT analysis, that in the volume of the porous medium is rarely measured, as it is considered of minor importance in reservoir engineering. Nevertheless, certain experimental results' suggest that in a number of cases the neglection of the variation in pore volume may introduce errors into material balance calculations of reservoirs producing above the bubble point. Only a few experimental results on the compressibility of porous rocks have been published. The compressibility of pure quartz and of calcite can be found in a paper by Adams and Williamson'. Botset and Reed' carried out some experiments on the compressibility of loose sands, while Carpenter and Spencer' measured the compressibility of a number of consolidated sandstones, which data were supplemented by Hughes and Cooke5. Hall' finally reported a number of experiments designed to study the influence of the porosity on the compressibility of oil-bearing formations, from which it appeared that, particularly in the low porosity range, the compressibility of the pore volume is important enough to be taken into account. Difficulties, however, arise in applying these experimental results to field cases. This is partly due to the fragmentary nature of the published data. Yet even if more complete data were available, the need for a theoretical background would be strongly felt. Such a background can be partially found in studies carried out by Biot,6,7 who published a theory of elastic deformations of porous materials and their influence on fluid displacement within the pores, by Lubinski8, who studied the stress distribution in an elastic porous medium neglecting pore compressibility, and by Gass-mann" who mathematically analysed the elasticity of packings of spheres. The contributions of Biot intro-duce a number of deformation constants which are impractical for reservoir rocks from an aspect of experi-mental determination. The theory developed by dass-mann is correct but difficult to read. It appeared, how-

Jan 1, 1958

By Wayne A. McCurdy

For the third consecutive year, predicted increases in coal production and consumption failed to materialize. Production of bituminous, sub-bituminous and lignite coal for 1961 was estimated by the U.S. Bureau of Mines at 400 million tons, a drop of 15,- 512,000 tons from the 1960 figure. Anthracite production for the year was 17.8 million tons compared to 18.8 million tons produced in 1960. Consumption figures are expected to show a proportionate decline. Of coal's major markets, only electric utilities showed an increase-and even here the increase of approximately 2% was smaller than had been expected. Major cause of relatively low consumption was a decrease of more than 20% in the use of metallurgical coal for making coke. Reductions of lesser importance were registered in general industrial, retail, and export markets.

Jan 2, 1962

By Y. Wang, M. M. Singh, H. L. Hartman

Knowledge of the state of stress at the bottom of a drillhole is of practical importance in rock drilling, since the induced stresses must exceed the strength of the rock in order to cause fracture. This note reports on a numerical method to determine the stress distribution at the bottom of a borehole induced by a static bit load and overburden and fluid pressures. The procedure adopted is similar to that for the plane-strain, discrete model employed by Harper and Ang.1,2 The rock medium is considered to be homogeneous, isotropic, and elastic-perfectly-plastic. METHOD OF ANALYSIS AND PROGRAMMING The discrete model adopted consists of two types of points: mass points and stress points. The configuration and numbering notation are depicted in

Jan 1, 1967

By R. J. Quigg, G. S. Doble

Commercial stress -relieved TD Nickel bar was shown to retain room- and elevated-temperature tensile strength after exposure up to 2501°F. Cold swaging increased both room -temperature and 2000°F tensile strength. After annealing at 2500°F the strengthening due to swaging was retained at 2000°F hilt eliminated at room temperature. Annealing produced changes in hardness and X-ray half peak width indicating the presence of recovery processes as 1071° as 1000°F but no recrystallization of swaged material was noted at any temperature. In contrast to swaging, rolling induced a recrystal-lized structure after annealing. The tensile strength of this recrystallized structure was comparable to the cold-worked condition. High-temperature tensile properties of as -received bar were highly anisotropic with the transverse tensile strength being one fifth the longitudinal value. The aniso-/ropy is affected by working direction and may he partially reversed by changing the direction of metal flow. The divergence in tensile strength, beginning above 550°F or- approximate one third the absolute melting point, is strain-rate dependent. T D Nickel is a commercial dispersion-hardened alloy containing 2 vol pct thoria. The dispersion, consisting of spherical particles 0.030 to 0.050 in diameter with an interparticle spacing of less than 1 is reported to maintain stable properties up to 2400°F.1 This stability of second phase results in maintenance of elevated-temperature strength at higher temperatures and longer times than normal nickel-base superalloys.2 The purpose of this paper is to describe the effect of various mechanical working operations on the strength and microstructural stability of TD Nickel bar. MATERIAL AND PROCEDURES All material used in this study was commercial TD Nickel bar. This material is produced by a chemical process which results in a nickel powder containing a dispersion of thoria particles. The powder is then pressed, sintered, extruded, and subsequently worked to bar stock. Three starting materials from three separate lots were used: as-extruded bar. 1-in.-diam stress-relieved bar, and 1/2-in.-diam stress-relieved bar. Since TD Nickel bar stock is cold-worked without a recrystalliza-tion anneal, the accumulated deformation or degree of cold work in these materials increases as the bar diameter decreases. Some of the 1/2-in.-diam bar was swaged to 1/4 in. diameter at room temperature in order to produce an as-worked condition for comparison with the stress-relieved stock. Tensile testing was performed on an Instron Tensile Tester at a constant crosshead speed of 0.020 in. per min. The 0.2 pct offset yield strength was measured from the load-crosshead movement plot. Specimen gage dimensions were 0.080 in. in diameter by 0.40 in. in length, producing a strain rate of approximately 0.050 min-1. Specimens were tested in air and heated within a resistance-wound furnace controlled to ±5°F. A 15-min soak at temperature was employed before testing. Samples were heat-treated in air and specimens machined after exposure with sufficient material removed to eliminate any surface contamination. X-ray line breadth was determined from a diffractometer scan of a transverse face of a bar using copper K, radiation. Metallographic preparation utilized standard mechanical polishing with Carapella's etch. Specimens for electron microscopy were electropolished in a 1:7 sulfuric/methaol solution and chromium-shadowed collodion replicas prepared. RESULTS AND DISCUSSION I) Effect of Elevated-Temperature Exposure on the properties of TD Nickel. The effect of various elevated-temperature exposures on the room-temperature tensile strength of TD Nickel is shown in Table I. In the unexposed condition the tensile strength, reduction in area, and hardness all increase with increasing accumulated deformation while the elongation decreases. After exposure at 2500°F the strength of all three materials decreases to about 65,000 psi and the elongations increase slightly. The apparent increase in strength of the 1-in. bar after a 2000°F treatment is probably experimental scatter. These results indicate that the room-temperature strengthening due to additional deformation is annealed out upon elevated-temperature exposure. In contrast to the room-temperature data, the 2000°F tensile strengths increase in order of increasing deformation even after exposure. Although some loss of strength occurs after exposure, much of the effect of working is still maintained at 2000°F. The room-temperature hardness after various

Jan 1, 1965

By E. V. Kleber, V. F. Novy, R. C. Vickery

The constitutional diagram has been determined in part for the sgstem Gd-Fe. Seven intermetallic compounds have been found at compositions corresponding to the following Gd-Fe ratios; 2:3, 1.2, 1:3, 2:7, 1:4, 1:5, and 2:17. The GdFe, com-pound has a congruent melting point above 18000C, whereas all of the remaining compounds melt incongruently, A eutectic exists at 13 wt pct Fe at a temperature of 860°C. ALTHOUGH an increasing amount of information is becoming available on the metallurgy of pure rare earth metals, relatively few studies have been made on alloy systems of the rare earths with the transition metals; iron, nickel, and cobalt. Even less data are extant on gadolinium alloys although it could be expected that such alloys might possess interesting structural and magnetic properties. In this paper, we report investigation of the gadolinium-iron alloy system. Studies on systems containing nickel and cobalt will be presented in subsequent papers. Previous data on gadolinium-iron compounds have been reported by Endter and Klemm1 and Jep-son and Duwez.2 Both reports agree on the existence of the GdFe2 phase, which crystallizes with the C-15type structure (face-centered cubic). This is in accord with results of the present work. EXPERIMENTAL The gadolinium metal used was prepared by met-allothermic reduction of high purity gadolinium fluoride. A typical analysis of the metal thus produced indicated the principal impurities to be oxygen, 0.24 pct, and tantalum, 0.2 pct. The iron metal used for alloying was a reagent grade material. Alloys were prepared by arc melting mixtures of the respective metals. Appropriate quantities of the two component metals were carefully weighed, blended and compacted. The compacts were then melted in an arc furnace consisting of a water-cooled copper hearth plate and a water-cooled tungsten-tipped counter electrode contained in a brass vacuum chamber. The furnace was evacuated to an absolute pressure of less than 1 with the leak rate established as being less than 20 per min. The furnace was then back-filled to a pressure of 25 mm of Hg, with a 75 pct He-25 pct Ar mixture. Arc melting at 25 v and 300 amp was maintained for about 30 to 60 sec until the entire visible area of the sample became molten, by which time surface tension had drawn the molten metal pool into a large bead. After allowing the furnace to cool, the alloy button was inverted and the melting process repeated. A series of melts was made covering entire composition ranges from 100 pct Gd to 100 pct Fe. All samples were examined metallographically in the as-melted condition. As the phase diagram became rationalized, and differential thermal analysis had given indications of temperature arrests, annealing was carried out in vacuo or in argon. Generally, compositions containing more than about 60 pct Gd were heat treated at 750°C and alloys containing less than this quantity of gadolinium were annealed at 1000°C. Prolonged annealing times were of the order of 100 to 200 hr. Metallographic examination was repeated on the annealed materials. Although little material loss was noted during alloy preparation, chemical analyses were made on all specimens prepared. The following standard, analytical techniques were used. Samples were dissolved in hydrochloric acid; insoluble material was filtered off, ignited and fused with potassium pyro-sulfate. The cold melt was leached with dilute acid and the solution thus obtained added to the main sample solution. Gadolinium was always determined gravimetri-callv as oxide from oxalate ignition. Iron was removed from an aliquot sample by electrolysis on a mercury cathode at approximately six volts. Gadolinium in the iron-free electrolyte was then precipitated as oxalate which was subsequently ignited to oxide. Iron was determined volumetrically in an aliquot solution by reduction with stannous chloride fol-

Jan 1, 1962

By R. E. Zimmerman

Wide attention is being placed upon various methods for cleaning the fine sizes of bituminous coals. The author describes and analyzes the results achieved on wet concentrating tables of modern design on unclassified feeds of --1/2 in. particle sizes, including tests on high-sulphur coals.

Jan 9, 1950