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By Charles L. Mantell, Kurt Straler

The hydrogen reduction of Cr2O3 to chromium metal was found to be feasible at very low water-vapor concentrations, corresponding to dew points of -38° to -24°C, over a temperature range of 1130" to 1490°C. Hydrogen reduction under these conditions was predicted by the calculated equilibrium curves which also indicated that CrzOs is reduced directly to chromium without forming the intermediate oxide, CrO. This reduction path was confirmed by X-ray diffraction analysis. The percent reduction of Cr2O3 at each reaction temperature was constant with time, suggesting an inhibiting effect of water vapor. A small increase in the residual water-vapor concentration of a single temperature, 1490°C, strongly retarded the rate of reduction This effect was expressed by an empim'cal equation which indicated a direct relationship between "distance from equilibrium" and the rate of reduction. me effect of temperature over the range of 1130" to 1490°C was expressed in an Arvhenius plot of log rate vs reciprocal absolute temperature. From this curve the apparent enthalpy of activation was found to be 29,600 cal. Based on the hypothesis that the rate of reductiun is contvolled at the oxide-metal interface, an over-all rate equation consistent with the experimental data and the thery of absolute reaction rates was formulated. A simplification of this expression to an Arrhenius equation was justified by the overriding effect of temperature on the rate of reaction for the minimum water-vapor concentration range. MOST of the metals in Subgroup V1 of the periodic table can be prepared commercially by direct reduction of their oxides by hydrogen or carbon monoxide, at temperatures considerably below the melting points of both the metals and their oxides. Chromium is an exception, being generally reduced from its ore, Cr2O3 . FeO, by silicon in an electric arc furnace which operates above the melting point of the Fe-Cr alloy or above the melting point of chro- mium if a chromium oxide be the starting material. In reduction of chromium oxide by hydrogen, either reduction does not occur at all or the rate of reduction is extremely slow. Theoretical considerations based on the high, exothermic, free energy of formation of Cr2O3 compared to the oxides of the other Subgroup VI metals, molybdenum, tungsten, and uranium, would also suggest a slow rate of reaction and a high activation energy. Interest in the direct gaseous reduction of fine-powdered ores in fluidized beds was considered justification for examination of this reaction. In order to develop a basis for a continuing study of the commercial feasibility of the direct gaseous reduction of chromite, a study of the kinetics of the reduction of Cr2O3 with hydrogen was undertaken. To the authors' knowledge no accurate kinetic data for this reaction have been obtained. Neither has an activation energy been determined nor has an attempt been made to establish a mechanism of reaction. LITERATURE Maier10 compared the data of I. Y. Granaat,6 H. von Wartenburg and S. Aoyama, and G. Grube and M. Flad7 with that derived from calorimetric and ther-modynamic properties for the equilibria for the reduction of Cr2O3 with hydrogen. These results, plotted as the log of the equilibrium constant vs absolute temperature for the reduction of Cr2O3 and the intermediate oxide, CrO, to chromium, show agreement between the differently derived data. In both cases the equilibrium constants were extremely low. Maier showed that, over a temperature range of 1000° to 2000°K, Cr2O3 is more readily reducible than CrO. Granat assumed that CrO was preferentially formed from Cr2o3 above 1100°C. Grube and Flad's analysis of their reaction products in the 895" to 1000°C range indicated the coexistence of only Cr2O3 and chromium. The hydrogen reduction of the other Subgroup VI metals, molybdenum, tungsten, and uranium, shows that reduction of the higher oxide proceeds through all of the intermediate oxides before being reduced to the metal. Since evidence pointed to an anomaly in the reduction behavior of Cr2O3, the authors investigated the reduction path of Cr2Os.to chromium. This was done theoretically with more recently available free-energy data and experimentally by X-ray diffraction analysis. This work reinforces Maier's conclusion.

Jan 1, 1964

By R. Ebeling, M. F. Ashby

The paper is in two parts. The first develops the formulae and method needed to calculate the size, nu)nber, spacing, and volume fraction of hard or inert particles in the interior of a specimen from measurernents made on an extraction replica; throughout, the spread of- particle sizes in a single specimen is taken into account, and the extraction efficiency of the replica is considered. A method for testing whether the particles are randotnly distributed in space is described, and the spacing of randomly distributed particles is discussed. The second Part describes the application of the method to copper containing spherical particles of silica; the description includes an estimate of the errors involved, and a comparison of this with alternative methods. All parameters except uolume fraction can be determined satisfactorily, and the method offers advantages over other electron-,rzicroscopic techniques when dealing with hard particles in a softer matrix, or inert particles in a chem-ically less inert matrix. 1 HE experimental measurement of sizes and numbers of discrete particles of a second phase embedded in a matrix material from opaque, plane sections has been considered by many authors, notably by Fullman.' It is assumed that, when the specimen is sectioned, the particles are also sectioned, so that the diameters of the circles of intersection of particles with the plane of the cross section ("surface diameters") are measured. It is difficult to derive the distribution of true particle diameters ("volume diameters") from measurements of the distribution of "surface diameters" on a plane section. The measurement of size and numbers of small second-phase particles by transmission electron microscopy through thin foils of matrix containing the particles has been described by Cahn and ~uttin~' and by ~illiard.~ Because of overlap and the fact that particles which intersect the foil surface may be sectioned whereas those in the bulk of the foil are not, it is again difficult to measure the true distribution of particle sizes. The use of replicas for this sort of measurement has not been analyzed in detail. A replica made from an opaque cross section, thus replicating the circles of intersection of particles with the plane of section, is analyzed by Fullman's method and suffers from the same difficulties. Under certain circumstances, however, extraction replicas can be used, and offer a special advantage in that they make the determination of the true distribution of particle diameters particularly simple. It is the purpose of this paper to describe this extraction replica method. Consider the example of an alloy consisting of SiOz particles, whose mean diameter is about 1000A, dispersed in a copper matrix. When the alloy is sectioned and mechanically polished, the particles are not sectioned, because they are much harder than the matrix, and so will be either left in the surface or pulled out whole, and because the particle size is smaller than the abrasive size of even the finest abrasive. The particles are chemically inert in solutions which chemically etch or electropolish the matrix, so that chemical treatments do not section the particles either. (Experimental measurements of particle shape in this alloy confirm this—truncated particles are never seen.) Small, hard or inert, particles are therefore not sectioned when the specimen is sectioned and polished. An extraction replica taken from this polished surface shows the true "volume" diameter of each extracted particle; the distribution of diameters seen on the replica is the surface distribution of true "volume" diameters, and the volume distribution of true "volume" diameters is easily derived from it. The extraction replica method is not subject to the difficulties associated with sectioning of particles, and avoids the problem of overlap from which the transmission method suffers. The method is well-suited for studying hard particles in a soft matrix. Examples are provided by internally oxidized alloys, oxide-dispersion strengthened metals like T.D. Nickel, and carbides, nitrides, and strong intermetallic compounds in metals. It should be possible to adapt polishing techniques in alloys containing softer but inert particles to avoid sectioning the particles (say by electropolishing or etching). The method is tested and illustrated in Sections 8 and 9 by applying it to a dispersion of spherical SiO2 particles in a copper matrix. I) SYMBOLS Symbols are defined where they first appear in the text. Volume fractions of particles are denoted by the symbol f, particle diameters by x, center-to-center particle spacings by D, and numbers of particles by N. Mean particle diameters and standard deviations about these means are denoted by x and a. Both arithmetic (subscript A) and geometric (subscript G) means are employed. In this paper we measure the distribution of true diameters of particles which touch or pass through a random-plane section of the specimen. We may want to know the distribution of particle diameters in the

Jan 1, 1967

By B. D. Cullity, S. S. Hsu

The stress distribution at the surface of a twisted cylinder is analyzed along the boundary of a slip plane of arbitrary orientation and this analysis is applied to the torsion of cylindrical crystals of magnesium. A criterion for slip is developed and the critical resolved shear stress of magnesium in torsion is found to be 0.038 kg per sq mm. The mechanism of torsional deformation in magnesium and aluminum is described, as well as the relaxation of a twisted crystal at elevated temperatures. THERE has been considerable fundamental study A of the mechanism of slip occurring during deformation in tension and compression but comparatively little attention has been paid to the mechanism of torsional deformation. This paper is concerned with the way in which a single crystal deforms in static torsion and with the phenomenon of untwisting which a twisted crystal undergoes during annealing. Particular attention is paid to the application of the critical resolved shear stress law to torsional deformation. Probably the most likely mode of torsional deformation that can be imagined consists of rotation of one part of the crystal relative to another on the active slip plane. Here the most interesting feature is the slip direction. If a cylindrical single crystal is twisted about its axis and if, to consider the simplest case, the active slip plane is normal to the specimen axis, then the direction of gross slip at any point must always be at right angles to the radius drawn to that point. It follows that the crystallographic direction of slip must be continually changing, in sharp contrast to slip in tension which occurs in a crystallographically constant direction. Extensive investigations of slip in torsion have been made by Gough and his associates.' They made torsional fatigue tests on metal single crystals belonging to a number of different crystal systems and observed, with a microscope, the appearance of slip lines on the surface and of strain markings on the transverse cross section of cylindrical specimens. They concluded that the critical resolved shear stress law was just as valid in torsion as in tension, in the sense that slip occurred on that plane and in that direction in which the resolved shear stress was a maximum. They also established that the operative slip planes and directions were the same as in tension. They did not, however, measure the critical resolved shear stress in torsion nor, in fact, did they establish that a critical value of the resolved shear stress was necessary for the initiation of slip. Their investigations were, moreover, restricted to torsional fatigue tests which necessarily involve small strain amplitudes. Wilman,' studying crystal growth and the abraded surfaces of crystals, observed crystal fragments

Jan 1, 1955

By Paul D. Merica, O. B. J. Fraser

PROBABLY the first metallic objects used by man were nickel alloys. In search for flints suitable for the fashioning of their rude tools, our paleolithic ancestors, some 25,000 years ago, quite likely may have come upon some of those heavy, metallic fragments that we now know as meteorites, which consist of an alloy of nickel and iron containing usually from 5 to 15 pct of nickel. Whether paleolithic man ever did discover and use meteoritic fragments, his sketchy records do not actually disclose. We do know, however, that such fragments have been found and used by peoples, particularly the North American Eskimos, for weapons and implements in just the same manner as stones, and prior to any knowledge by those peoples of the reduction of metals from ores. Meteoritic showers were recorded frequently in earliest times and the meteorites often were found and fashioned into useful objects. The ancient Arabic and other myths of "invincible swords fallen from heaven" seem thus to have had a very definite basis in fact, and such weapons, of meteoritic material, have actually been re- covered from archeological excavations. It thus seems probable that meteoric nickel-iron was found and used long before iron was recovered by smelting iron ores (perhaps about 1200 B.C.) and probably even before there was knowledge and use of bronze and gold. Although many centuries were to pass before nickel was first isolated, in 1751, from Swedish ores and recognized as an elemental

Jan 1, 1953

By G. Y. Chin, M. T. Dolan, W. L. Mammel

In the case of plastic deformation by slip, von Mises&apos; showed that an arbitrary shape change of a crystal generally requires the activation of five independent slip systems. The selection of the five active systems was worked out by Taylor ,&apos; who hypothesized that, among all combinations of equivalent slip systems which are capable of accommodating a given imposed strain, the active combination is that one for which the sum of the absolute values of the glide shears is a minimum. Taylor analyzed the case of {lll}( 110) slip for fcc metals and applied the analysis to crystals undergoing axisymmetric flow, which approximates the shape change of an embedded grain in a polycrystalline aggregate deformed in tension (or compression). For the twelve equivalent (111) (110) slip systems, there are 384 independent combinations of five slip systems that satisfy the imposed strain.&apos; Taylor laboriously calculated the value of M = ZjIyj /E for each combination (although some were missed) and obtained the minimum M, hence the active combination, for a number of axial orientations distributed throughout the stereographic triangle. (yj is shear from slip on the th system and e is the tensile strain). Detailed contours of constant minimum M were recently obtained by Hosford and Backofen using a simplified but equivalent Bishop and ill&apos; analysis. Due to the numerous combinations of slip systems involved in the calculations, however, the full potential of the powerful Taylor analysis has not been exploited. For this reason, we have recently utilized techniques of linear programming to obtain solutions of the Taylor analysis for axisymmetric flow, for slip on {110)(< 111), {112)(111), and {123)(111) systems as well as mixed slip composed of these three systems. These slip modes are of obvious importance in the deformation of bcc crystals. Some of the salient results are summarized below. 1) Stress-Strain Data for Polycrystal. The value of M averaged over all axial orientations is the ratio of the tensile flow strength of a randomly oriented aggregate to the critical resolved shear stress for slip. This value enters importantly in theoretical deductions of the polycrystalline stress-strain curve from single-crystal data.2&apos;3&apos;5 Table I lists the values of Ma,, for the several cases of slip, as obtained by the present computer work. 2) Texture Hardening. Since the value of M depends on the axial orientation, the (tensile) flow strength of a specimen may be increased through texture control.&apos; An example of the computer results is shown in Fig. 1, where contours of minimum M have been computer-plotted for the case of mixed slip on {110}(111), {112)(111),and {123}(11 1) systems. It may be seen that, under axisymmetric flow, wires of (111) and (110) axial orientations are 50 pct stronger than those oriented at (100) .

Jan 1, 1968

By Joseph B. Story, John T. Clarke

A modification, of the Kelvin bridge using an inductor was used to measure the conductivities of molten sodium chloride, calcium chloride, and mixtures thereof. A capillary-type four-lead fused quartz dipping cell was constructed. The effect of a small amount of potassium chloride on the conductivity of the melt was determined. IN the electrowinning of sodium and chlorine from sodium chloride in Downs cells, calcium chloride is added to the sodium chloride in an approximately equimolar amount to permit cell operation at a lower temperature. This lower temperature improves current efficiency and ease of operation, but decreases voltage efficiency by decreasing the electrical conductivity of the melt. A knowledge of the electrical conductivity of the Downs cell melt is necessary to the understanding of Downs cell operation, for the IR voltage drop across the melt is responsible for a significant part of the electrical power consumed by the cell. The work of previous investigators on fused sodium chloride-calcium chloride mixtures was reviewed from the standpoint of consistency with the results of others on the conductivities of the pure constituents. The electrical conductivity of pure fused sodium chloride has been established with accuracy by Van Artsdalen and Yaffe,1 by Edwards, Taylor, Russell, and Maranville,2 and by Lee and Pearson.3 It has also been studied by a number of other investigators.4-13 The best values for calcium chloride are believed to be those of Lee and Pearson,3 since the sodium chloride and potassium chloride conductivity values given by them check the best literature values. A number of other investigators have also reported values for calcium chloride.&apos;-"."&apos; Electrical conductivity data for fused sodium chloride-calcium chloride mixtures have been reported by Sandonnini,12 Vereshchetina and Luz-hnaya,18 Ryschkewitsch,11 Barzakovskii,5 and Alaby-shev and Kulakovskaya.15 Sandonnini reports no data at temperatures lower than 850°C. The conductivity values reported by Vereshchetina and Luz-hnaya, by Ryschkewitsch, and by Barzakovskii for pure sodium chloride and for pure calcium chlor- ide vary somewhat from the literature values believed to be best and the sodium chloride-calcium mixture data of these authors and of Alabyshev and Kulakovskaya (who give no data for the pure compounds) show significant variations. In view of these facts, it seemed that an investigation of the electrical conductivities of fused sodium chloride-calcium mixtures would be worthwhile. Apparatus Bridge System—The bridge used,in this investigation is diagrammed in Fig. 1. In general, the elaborations of this bridge over the simple Wheatstone bridge were for the purposes of a) eliminating lead resistances or making them accurately measurable, and b) eliminating major capacitative and inductive effects or balancing them against each other. Lead resistances in the lower arms of the bridge were kept as low as possible by making the leads short and of low resistance wire. This could not be done in the cell arm of the bridge because of the remoteness of the cell from the other bridge components and because of the high-resistance nickel or chrome1 wires used in the cell. Since maximum sensitivity is attained when the resistances of the four arms of the bridge are equal, 50-O resistors were used in the lower arms of the bridge when fused salt conductivities were being measured, and 1000-O resistors were used when the cell was being calibrated with normal aqueous KCl solution. The cell resistance was of the order of 50 ohms with fused salts and of the order of 1000 ohms with normal aqueous KC1 solution. The resistors used were non-inductive and accurate to 50.05 pct (General Radio Co. Types 500-C and 500-H). The lead resistance between point A in the cell and point E at the measuring resistor was eliminated by using the kelvin bridge principle; that is, the voltape drop across the lead from point A to point E was divided between the cell arm of the bridge and the measuring arm of the bridge in proporation to the resistaxes in the lower arms of the bridge.

Jan 1, 1958

By John D. Sullivan, Edwin J. Rogers, Chester R. Austin

THE problem of making a building unit combining the necessary physical and mechanical properties and good thermal insulation has been foremost in the minds of architects and ceramic and construction engineers for many years. This paper presents the results of studies on thermally expanding shales or clays to produce light-weight cellular products suitable for making building units. An expanded clay block suitable for building purposes should be large enough so that substantial savings may be effected in labor costs in laying the wall. The permeability should be low and it should have sufficiently good "dry-wall" characteristics to permit exposing the exterior surface to the elements, and to permit plastering directly the inside wall surface. The thermal conductivity should be low and the mechanical properties should be adequate. Obviously, a unit possessing satisfactory qualities for constructing an outside wall would be satisfactory for interior walls and for back-up purposes. The results of studies on bloating various shales or clays† and the properties of the expanded products are reported. In another paper1 basic factors involved in bloating of clays are discussed. Manufacturers of ceramic products, particularly structural clay, may encounter bloating of the ware during burning, and precautions must be followed to avoid this phenomenon. About 1927 the C. F. Burgess Laboratories, Madison, Wis., while carrying on an investigation for the American Face Brick Research Corporation, conceived the idea of intentionally bloating clay while holding it in a restrained condition, with the hope of producing a unitary cellular mass. Work was carried on until about 1931, when studies were terminated because of business conditions. These studies were continued later by The Western Brick Co., Danville, Ill., which developed a process of "inwardly expansive bloating." The major purpose of the latter investigation was to produce back-up tile to compete with concrete blocks made from Haydite or cinder aggregate. Haydite is a light-weight aggregate formed by heating certain clays or shales rapidly in a rotary kiln. While the investigations at the C. F. Burgess Laboratories or at Western Brick Co. were not carried far enough to lead to the commercial production of material for the construction of walls, particularly outside walls, they showed that certain clays could be thermally expanded and that it was possible to produce a material of low permeability with a large percentage of the total voids or cells closed. Commencing in 1939, the Ozark Chemical Co. sponsored a research program at Battelle Memorial Institute for the purpose of determining whether it is technically feasible to make thermally expanded building units, and specifically to get answers to the following questions:

Jan 1, 1942

By R. N. Upadhyay, M. Maleki, I. Fatt

Conventional laboratory core analysis tests on samples of two limestone reservoir rocks indicate that about 20 per cent of PV is in dead-end pores. These tests (electric logging formation factor, mercury injection capillary pressure and miscible displacement) were carried out on 1/4-in. diameter test plugs. Test results show a clear dilference between these samples and sandstone or homogeneous limestone reservoir rock. Although the amount of dead-end pore space can be only roughly estimated, the presence of such pore space seems clearly indicated. Pressure transient studies also show presence of deadend PV. Although they do not give quantitative results, pressure transient data yield a reasonable estimate of the size of the neck connecting dead-end pores to the main flow channels. INTRODUCTION Equations conventionally used to describe reservoir flow behavior contain the implicit assumption that all connected pore spaces contributed to both porosity and permeability. Several authors3-7 have pointed out the changes in pressure transient behavior and in electric log interpretation that may result if this assumption is incorrect and, instead, dead-end or cul-de-sac pores are present. There is a need for laboratory tests that can detect presence of dead-end pores in core samples. With such information on hand the petroleum engineer can make more rational use of the mathematical tools now available for analysis of reservoir flow behavior. This paper describes laboratory studies designed to detect and, if possible, give a quantitative measure of dead-end PV in laboratory-size core plugs. Three reservoir rocks were used, two of which were limestones suspected of having deadend pore spaces and a well-known sandstone, used as a comparison standard, in which there is believed to be little or no dead-end pore space. All the studies were designed to measure the natural dead-end PV; i.e., the pore space which is dead-ended because of rock structure. During multiphase flow in a rock without dead-end pores, some parts of one of the phases can become surrounded by the other, thereby giving (for certain flow behavior) an effective dead-end pV8,9. Such behavior will not be described here.

Jan 1, 1967

By C. S. Barrett, D. B. Masson

Martensitic transformations have been found in AgCd both upon cold-working at room temperature and cooling to lower temperatures. The crystal structures of the transformation products were found to be close-packed hexagonal in the first case and or-thorhombic in the latter. The transformation characteristics also were studied. Similar treatment of AuZn alloys failed to yield any transformation. THE literature on martensitic transformations of body-centered cubic metals and alloys indicates widespread instability of this structure at low temperatures, a tendency which merits further study. The body-centered cubic ß-phase of CuZn, for example, when it contained less than 42 wt pct Zn, was found by Greninger and Mooradian&apos; and others&apos; to transform on cooling to subzero temperatures to a phase that was tentatively considered to be tetragonal. Further work by Massalski and Barrett" demonstrated that cold work at low temperatures causes a partial transformation of ß CuZn of higher Zn content. The structures of the strain-induced transformation products were found to be different from those induced by simple cooling. Another well-known martensitic transformation among body-centered cubic phases is that of ß AuCd, first studied with X-rays by Olander,&apos; then very thoroughly by Chang and Read.5,6 Here again transformation was found to occur both as a result of cooling and of strain. The alkali metals Li and Na, as well as certain Li-Mg alloys, also undergo transformation from their normal body-centered cubic structure, both on cooling and on cold-working. The phase AgCd, the subject of the present report, should be expected to behave quite similarly to CuZn for a number of reasons. It is the chemical analogue of CuZn, silver being directly below copper and cadmium directly below zinc in the periodic table. The size factors (percent difference in size) of the atoms, possibly a consideration in the stability of the ß-phases, are +3.1 in AgCd and + 4.2 in CuZn. Likewise the relative electronegativities of the two pairs of metals are about the same, CuZn possessing an electronegativity difference of 1.0 and AgCd one of 0.8. These values are from a table of electronegativities given by Darken and Gurry." The phase diagrams of the two systems around 50 atomic percent are similar, both possessing a disordered body-centered cubic phase, ß, at high temperatures and an ordered bcc phase, ß, at room temperature; however, the ß and ß&apos; phases of AgCd are separated by a hexagonal phase, [, stable in the range 220-440oC, which has no analogue in CuZn. There has been confusion in the literature as to the structures of the ß&apos; and [-phases. The phase diagram in the ASM handbook&apos;" has the structures of the two phases interchanged; however, Hansen" reports the correct relative positions and Muldawer" verified that ß&apos;, the low-temperature phase, is body-centered cubic. Work by the present authors also

Jan 1, 1959

By H. A. Lesser, H. L. Stone, G. H. Bruce

ESSO PRODUCTION RESEARCH CO., HOUSTON, TEX. A mathematical model that represents the conduction heating of a rock formation of limited permeability is formulated. Heat is introduced by the injection of a hot condensing gas into horizontal fractures through the formation. The fractures are assumed to be equally spaced; the flow of fluid is linear. The model consists of three coupled partial differential equations and two functional relationships. Temperature histories for both fractures and formation are obtained by numerical procedures. Application of the model in predicting in situ heating of oil shale is illustrated with four sample cases. Influences of shale thermal diffusivity, fluid pressure in the fracture and fracture spacing upon heating rate are demonstrated. In all cases considered, several years were required to heat all the formation to 700F with 1,000F steam. Less than 32 per cent of the injected heat was utilized for heating the shale. To facilitate extensive calculations of this type, a set of seven dimension-less quantities are derived. With this dimensionless system, the effect of controllable parameters on economics can be explored. INTRODUCTION Vast deposits of hydrocarbons are contained in oil shale formations in the western United States and in other countries. These hydrocarbons, known as kerogen, are difficult to recover because they are immobile solids and because the rock formations in which they are found have very limited permeability. The kerogen can be converted through pyrolysis to recoverable liquids and gases if the formation temperature is elevated to the range 600 to 800F. To accomplish this heating, the formation might be artificially fractured and a hot fluid injected into the fractures. If the injection and production wells are vertical and the fractures horizontal, interwell communication will be established and the hot fluid will flow from an injection well to a production well. In this process, some of the heat in the fluid will be given up and conducted into the formation. Products of pyrolysis will flow from the heated rock matrix into the fractures and be produced, commingled with the injected fluid. The practicality of such a process is strongly influenced by the rate at which heat can be transferred from the hot fluids to the formation. An analysis of this heat conduction problem is the subject of this paper. Linear flow of a condensing gas through a set of horizontal, equally spaced fractures is considered. Temperature histories for both fractures and formation are obtained from numerical procedures. The analysis also applies to formations containing streaks of natural permeability instead of fractures. Heat flow problems similar to the one treated here have been studied by other workers. Thomas1 has solved a radial problem in which he considers the injection of a noncondensing gas into a single, horizontal fracture and approximates the temperature profile in the fracture by a step function. The solutions to other problems, which are less similar to the present problem than the one treated by Thomas, have been reviewed by Spillette.2 In addition to these mathematical studies, a field test of an in situ shale oil recovery process using hot natural gas as the injected fluid has been reported.3 The first part of this paper is concerned with the mathematical development of the problem. The differential equations, boundary conditions and functional relationships which describe the physical model are formulated and the equations are cast into finite difference form. The method of solution of the difference equations is discussed (Appendix B). The second part of this paper presents results computed for a typical oil shale formation for which steam at 1,000F is the injected fluid. Fracture spacing, horizontal and vertical thermal diffusivities

Jan 1, 1967

By Francis F. Lucas

A microscope objective of given numerical aperture, when used with light of given wave length, has some fixed limit of resolution. This may be expressed as potential resolving ability—the ability to resolve is inherent in the lens but whether this limit is achieved in practice is quite another matter. Nearly 50 years ago Abbe evolved theoretical considerations which indicated that the ability of a lens to resolve detail is directly proportional to twice the numerical aperture of the objective and inversely proportional to the wave length of the light used. It is true, unquestionably, that as the numerical aperture of the objective is increased the potential resolving ability of the lens is increased and likewise when the wave length of the light used is decreased, the degree of resolution is increased. Whether Abbe&apos;s formula expresses the exact relationship is not a matter of great concern. It suffices to know that to improve resolution, other things being equal, two avenues of approach are available. Either the numerical aperture of the objective may be increased or the wave length of the light decreased. With the apochromatic system it is possible to employ successfully wave lengths from 400 to 500 uu and still secure reasonably short exposures. The present limit for numerical aperture is 1.40 N. A. although objectives of 1.60 N. A. are now an experimental possibility for metallurgical work. Thus certain well defined limits are set for those who work within the range of the visible spectrum. In order to take advantage of the increase in resolving power which accompanies a decrease in the wave length of light employed, Dr. A. Kohler and Dr. M. Von Rohr of the Zeiss Scientific Staff developed the "monochromats." These are quartz objectives corrected for the single wave length 275 uu which lies in the ultra-violet region of the spectrum. They also developed a series of quartz oculars and a complete photo-micrographic equipment with which to use the quartz optics. Quartz must be used for the optical parts because glass absorbs ultra-violet light almost completely. Thus there was made available about 20 years

Jan 1, 1926

By D. A. J. Swinkels

The problem of determining oxygen levels in liquid steel to aid in deoxidation control has received general attention for a number of years. Work in this direction started at the B.H.P. Central Research Laboratories early in 1967 with an evaluation of sampling techniques followed by vacuum fusion analysis to determine the oxygen content of the samples (1). It was found that these techniques had a number of drawbacks if they were to be used for deoxidation control. The method of analysis was rather too slow to allow effective control and measured total oxygen level rather than dissolved oxygen. Furthermore, the results were found to be very variable due to slag entrainment in the samples. Attention therefore turned to the galvanic cell method using a solid oxygen ion conductive electrolyte such as cubic stabilised zirconia. The ionic conductivity properties of electrolytes such as (ZrO2) 85 (CaO).15 had been studied by a number of investigators and had already been applied to the measurement of oxygen activity in gases, in lower melting metals such as copper, lead, tin, silver, alkali metals and indeed the first studies in steel had been made (2,3). Since then the results of a number of studies in the development of an expendable oxygen probe for steel have been reported (4-9).

Jan 1, 1972

By Stephen Krickovic

THERE is today no proven continuous mining machine that can be used under all the varying conditions found in most bituminous coal mines. During the last five years, however, both the machines and methods of using them have been improved. Coal operators can now exercise a fair degree of selectivity, except those who must struggle with thick and hard partings and operate in seams less than 40 in. thick. It must be realized, then, that more than one type of continuous miner may be used advantageously in the same coal mine. Although this appears to violate the standardization generally sought after, the gain can more than offset added maintenance and, to a lesser degree, operating problems. It is equally important to realize that most coal mines will require one or more conventional loader setups in the plan of total mechanization. Seam variations, adverse physical conditions, and special designs of main headings for haulage and ventilation, to name only three reasons, may render 100 pct use of continuous miners uneconomical. Of course, this situation may change. In one mine, prior to 1954, machines that ripped coal from the face achieved only average results, as compared to the impressive performance of boring-type units in another coal mine. A boring-type unit was therefore selected for the first mine in the belief that the chance of success would be greater if it were used in a combined cutting and wedging operation, cutting a full face in its forward movement. The miner was located in a part of the mine where a special projection could be readily developed, a solid area scheduled for mining according to the overall progress plan. All openings surrounding the particular area were carefully investigated for the presence of sulfur balls. Fig. 1 (opposite) shows the representative seam section, containing the several pyritic bands 1/4 to 1/2 in. thick; a characteristic Pittsburgh seam parting averaging 5 to 6 in. of slate, coal, and slate; and the occasional py-rite lenses 2 to 3 in. thick. Under normal conventional mining methods, the top 10 or 12 in. and the bottom 4 in. are left in place to offer roof protection

Jan 1, 1958

By George F. Comstock

It has been known for many years that the alloy containing 90 per cent. copper and 10 per cent. aluminum can be hardened, like steel, by quenching from a suitable temperature, and that the hardened alloy can be softened again by annealing or drawing the temper. It does not seem to be generally appreciated, however, that the effect of the first slight reheating after quenching is actually increased hardness, the softening effect not taking place until a certain temperature of "drawing" has been exceeded. This paper gives the results of a few experiments on various specimens of cast 10 per cent. aluminum bronze, quenched for maximum hardness, and subsequcntly annealed at different temperatures. The hardness measurements were made with both a scleroscope and a standard Swedish Brinell machine; some peculiarities of the scleroscope test on this material are described. The author is not aware of many previous investigations of the hardness of this alloy when quenched and drawn, but two important papers on the subject should be mentioned. The earliest was by Portevin and Arnou,1 in which it was stated that tempering quenched 10 per cent. aluminum bronze at 400" C. increased the hardness as compared with the quenched untempered alloy and that reheating above that temperature &apos; was necessary to obtain any softening effect. A later paper was by Seidell and Horvitz,2 who mentioned Portevin and Arnou&apos;s work, but did not report any increase in hardness obtained

Jan 1, 1925

By H. Reiss

The zone-melting process in which redistribution of solute in a solid bar is effected by the passage of a molten zone is considered mathematically. Simple approximate techniques are developed for computing the manner in which redistribution occurs as molten zones continue to pass. The introduction of the "zone-melting flux" provides valuable insight into the nature of the phenomenon, as well as a central mathematical theme in terms of which the process can be discussed. Curves are presented for typical and general cases. AN extremely efficient purification technique was described recently by Pfann.1 Known as zone refining, it consisted of the slow passage of a series of molten zones, produced by external heaters, through a long solid ingot of the substance to be purified. Equations were given for the maximum separation attainable, and a numerical computation method was described for obtaining the concentration in the ingot after a given number of zone passes. The present paper offers an interpretation of the physical nature of zone melting in terms of a transport process in which formal diffusive and convec-tive flows occur. This interpretation, in addition to providing insight into the physical nature of the process, also provides a basis for its mathematical treatment. From this basis, useful equations are developed for the solute concentration in the ingot as a function of the number of zone passes. These are applicable particularly where large numbers of passes are necessary and where numerical computational methods might be laborious. All considerations will deal with the limiting form of the process, described by Pfann,&apos; in which: 1—Diffusion in the solid is considered negligible. 2—Mixing in the liquid is supposed, complete. 3—The distribution coefficient, k, measuring the ratio (at equilibrium) of solute concentration in the solid to that in the liquid is supposed, independent of composition. In general, this paper will be concerned with a bar of uniform (actually unit) cross section, ex- tending in the x-direction from x = 0 to x = L, where L may be infinite. Zone melting is a transport process, and as such must admit of interpretation in terms of a flux of transported quantity. However, the progress of operation is not measured in units of time but in terms of the number of completed zone passes. Consequently, the zone-melting flux will be a rate, per unit pass, rather than per unit time. The description of this flux and the examination of its properties is given below. Zone-Melting Flux Fig. 1 represents an intermediate stage of the nth pass. Concentration C is plotted against distance, x. The molten zone with its back at the point x and front at x + I moves in the direction indicated by the arrow. As it moves, it leaves behind the nth

Jan 1, 1955

Continued Discussion of the papers of Van Hise, Emmons, Weed and Lindgren, Bans., xxx., 27, 177, 424, 578. See also the papers of Vogt, Kemp, Rickard, Blake and Lindgren, at pp. 125, 169, 198, 220, 226, and also the final contribution of Prof. Van Hise, p. 284 of the present volume. All the foregoing, together with the discussion here following, are included in the special volume, "The Genesis of Ore-Deposits," issued this year by the Institute. H. Foster Bain, Des Moines, Iowa (communication to the Secretary):* The zinc- and lead-deposits of the Mississippi valley, which it has been my fortune to study, give particularly good examples of many of the principles of ore-deposition formulated by Prof. Van Hise. Perhaps there is nowhere clearer evidence supporting his fundamental tenet., that ore-bodies are to be regarded as a result, and as merely one of the phases, of the work of underground waters. The facts regarding the mines of the upper Mississippi valley have been given in some detail for Wisconsin by Prof. Chamberlint and, more recently, for the mines west. of the Mississippi by the Iowa Geological Survey.‡ Fortunately, also, the processes of underground water-circulation have been studied in some detail in connection with the investigation of artesian waters throughout the region.$ In Missouri and Arkansas the mines and ore-bodies have been much studied ; but the general problems of the circulation of underground waters have been neglected. During the season just closed the writer has been engaged in a re-study for the United States Geological Survey of the zinc- and lead-deposits of the Ozark region, with special reference to those of the . Joplin area; and his full report is now in preparation. It has been interesting to note how fully the statement that the orebodies result from the general action of underground waters is

Jan 1, 1902

By Alan Morris

SEASON cracking of brass has received wide attention and there is a wealth of technical literature on the subject. Its causes are fairly well understood and means for its prevention are inexpensive and effective, .so that the frequency of failures from this source has diminished of recent years. But its sister phenomenon, the failure of annealed brass by reason of applied tensile stress plus a certain type of corrosion, has received less attention, though it has been responsible for occasional more or less troublesome cases of cracking of brass in service. The work described in the following pages was undertaken about two years ago to determine the relative resistance of various commercial brass mixtures to stress-corrosion cracking, and to learn something of the controlling factors. By stress-corrosion cracking we mean the cracking of brass free- from internal stresses by reason of applied tensile stress and simultaneous attack by certain corrosive agents. Rogers,1 in discussing a paper by Hatfield and Thirkell, says : "He had also applied a solution of mercuric salt to tensile test pieces of brass whilst they were under stress in the testing machine. At very moderate stresses such test pieces cracked, and very readily broke." Moore, Beckinsale and Mallinson2 subjected test pieces to simultane-us corrosion and tensile stress. In order to determine the minimum stress detectable in brass by the mercurous nitrate test, tensile samples were placed under stress and treated with mercurous nitrate solution. They found that brass stressed below a minimum did not crack.

Jan 1, 1930

By C. G. Palagi, S. S. Stillar

The C. E. Weed concentrator treats 51,000 tons per day of 0.5% to 0.7% copper ore received from the Berkeley Pit, the Continental East Pit and the Butte underground mines. Improved operating techniques and conversion from semi-autogenous secondary grinding to ball milling have increased tonnage from an original design of 42,000 tpd. Separate treatment of sands and slimes, with recovery of soluble copper from the slimes, has increased total copper recovery. Concentrator tailings are pumped 600 vertical feet and 20,000 horizontal feet for disposal.

Jan 1, 1976

By R. A. Anderson, T. E. Tietz, J. E. Dorn

Recent investigations1,2,3,4 have conclusively shown that the strain hardened state of metals depends upon the temperature and strain rate of pre-straining as well as on the total plastic strain. A typical example of the effect of temperature of prestraining on the work hardening of metals is reproduced in Fig 1. When pure aluminum is strained at liquid nitrogen temperature the upper solid stress-strain curve (OFGH) is obtained. But when pure aluminum is prestrained to e2 = 0.153 at atmospheric temperature and the test is then completed at liquid nitrogen temperature, the curve OBCD results. Thus a prestrain E2 = 0.153 at atmospheric temperature gives a flow stress C when continued at liquid nitrogen temperature, whereas a higher flow stress G results when the specimen is strained exclusively at liquid nitrogen temperature to the same strain E2. Consequently the metal strain hardens more rapidly at the lower temperature. Obviously the strain alone is not a measure of the strain hardened state in metals. Inspection of Fig 1 reveals that the flow stress at C is identical with that at F. This fact suggests that a strain E2 = 0.153 at atmospheric temperature induces the same work hardened state as a strain E1 = 0.058 at liquid nitrogen temperature. But this concept of equivalent strains is also in error. If curve CD is shifted to the left so that point C falls on F, point D becomes D&apos;. Inspection of the curves reveals that the rate of increase of stress with strain at C is greater than the rate of increase of stress with strain at F even though the flow stresses are identical. Consequently C and F do not represent identical work hardened states. It therefore becomes important to ascer- tain how the strain hardened states at C and F might differ from each other. In a more recent report1 it was shown that straining at higher rates of strain increases the amount of strain hardening in a manner quite analogous to straining at lower temperatures. These observations suggested that the flow stress is not only a function of the strain but also a function of the strain rate-temperature history of straining, perhaps in accord with the Zener- ?H Hollomon parameter p = Ee /RT (where

Jan 1, 1950

By Paul Wilkinson

From the earliest times, the principal component of mallplaster has been ordinary lime. Plaster-of-Paris has also been known from early times, but never used to any extent in the actual base-work of plastering-materials; it is generally used for finishing over the brown coat and for ornamental work. As an illustration of the antiquity of the use of gypsum-plaster for mortar, I find that the analysis of the exterior covering of the pyramid of Cheops, as made by Dr. Wallace, is almost identical

Jan 1, 1898