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By G. M. Gay, R. L. Perrine

This paper describes a method of numerical computation for three-dimensional, unstable, miscible displacement behavior useful for heterogeneous systems, as well as for more ideal conditions. In the method, flow equations are first linearized by a perturbation approach. The basic flow process is separated and a solution for its behavior readily obtained. The remaining problem of deviations from the basic flow caused by non-ideal conditions is then subjected to numerical analysis. Results obtained from use of the method are also presented. Although conditions assumed in the test cal-culations were severe, results show the type of dispersing flow expected and appear quite satisfactory. The method has eliminated or reduced in importance problems of oscillating values near steep fronts, excessive computer smoothing, etc. A unique advantage of the method is that the source of variations from ideal behavior can be observed. ,The one serious drawback results from the algebraic complexity of the perturbation approach, and the need for second-order terms to be retained in calculations of interest. Fewer array points are available and more computer time is required than would be desired. However, these difficulties are also experienced with other approaches to the solution of three-dimensional dispIacement problems. INTRODUCTION Prediction of behavior of the miscible displacement process within a porous medium for any system of engineering importance is plagued by a number of difficulties. With typical fluid properties the displacing fluid has the lower viscosity, and there is a natural tendency toward flow instability. The problem of predicting instability is compounded by the fact that every real system is heterogeneous. Permeability will vary from point to point — not entirely systematically, and yet not in a random fashion leading to a readily defined average. Furthermore, permeability is unlikely to be isotropic. These permeability properties, which are characteristic of any real porous medium, accentuate the effects of flow instability. Another factor to be considered is that flow dispersion accompanies the displacement process in a porous medium. Mechanistically, dispersion is due to the fact that flow between any two points in the medium follows multiple tortuous paths, each characterized by slightly different flow properties. The fact that the coefficient characterizing dispersive properties of the real medium JS a tensor with variable elements complicates matters. Further difficulties arise because the parabolic influence, while not negligible, is small. Thus, there is a tendency toward steep and uneven displacement fronts along which dispersion smoothing must be represented accurately. Yet frequently used numerical analysis schemes may tend toward either instability, oscillation or excessive smoothing, none of which gives the desired accurate picture of flow behavior. Thus, while many experimental and analytical studies of the process have been made, predictions of actual performance are still subject to considerable uncertainty and possible improvement. This paper reports on part of a study which attempts to develop improved methods for solution of the flow equations describing the miscible displacement process. Of necessity, the calculations were performed on a large digital computer. A three-dimensional system is represented, and the coefficients defining dispersion and permeability can be varied in a manner representative of a real system. Because the differential equations are nonlinear, a first step is to linearize them using a perturbation approach. Objective of this approach has been to separate the basic flow which would occur in an ideal system and for which predictions are readily made. Then the numerical analysis, which is necessarily complex, is directed toward solution of the perturbation equations. These equations state how the basic flow is modified

Jan 1, 1967

By E. H. Bunce, E. C. Handwerk

The inherent difficulties of zinc smelting arise from the fact that metallic zinc is volatilized at the reducing temperature of zinc oxide and thus is liberated in the form of a vapor. This vapor must be subsequently condensed to obtain metallic zinc, first in molten and eventually in solid form. Zinc vapor is sensitive to oxidation not only by air but by combustion gases containing carbon dioxide. It is, therefore, necessary to carry out both the reduction and the condensation operations in a closed system consisting of an externally heated muffle with attached condenser from which extcrnal oxidizing agencies are excluded. However, the reoxidation of zinc vapor cannot be entirely prevented by excluding external sources of oxidation. Internal sources of oxidation are necessarily present when oxidic zinc ores are reduced by a carbonaceous reducing agent. The reduction reactions themselves involve, first, the production of carbon monoxide in an amount at least equal in volume to the zinc vapor produced in the reaction, and, second, the formation of carbon dioxide. Not all of the carbon dioxide is reduced again to carbon monoxide by the excess carbon in the time available, and the slightly oxidizing condition, which results, seriously affects the efficiency of the condensation of the zinc vapor to the metallic state. In the past the difficulties arising from these causes have limited practical zinc smelting on an industrial scale to the use of small retorts equipped with small condensers. The retorts had to be small, because a closed refractory container capable of excluding oxidizing gases from the heating chamber surrounding the retort could not be built in large dimensions. The size was also limited because ordinary refractories when thin enough to conduct heat readily are not capable of sustaining a heavy load of charge at high temperature. Moreover, a loose charge of zinc ore and carbonaceous reducing material such as fine anthracite coal or coke breeze is a poor conductor of heat, thus limiting the cross section of the retort. The operation of these small retorts requires arduous

Jan 1, 1937

By E. T. Turkdogan

This paper deals with an analysis of the conditions leading to the formation of blowholes and surface and subsurface defects in cast low-carbon steels. The theoretical analysis of the problem is based on the concept of the occurrence of deoxidation reactions during cooling of liquid steel and during its solidification. The reaction equilibrium data are given on deoxidation of steel by carbon, silicon, and manganese. The details of the calculations are given on the simultaneous deoxidation of steel by silico-manganese additions to produce a desired level of deoxidation at certain residual concentrations. Based on an idealized model, an attempt is made to calculate the enrichment of solutes in the solidifying liquid entrapped within the interdendritic cells which are known to be less than 200 µ thick. Formulae are derived for the calculation of the change in the residual oxygen content of the enriched liquid steel, controlled by Si/Mn deoxidation. It is shown that for every particular initial silicon, manganese, and oxygen concentration in steel (as residuals in liquid solution at the beginning of solidification) there is a particular carbon concentration below which carbon monoxide, leading to blowholes or pinholes, is not expected to form. There are a number of independent variables which have a decisive influence on the formation of blowholes. For example, it is shown that the position of the curve depicting the critical relation between initial silicon and carbon content for suppression of the evolution of carbon monoxide) can be shifted to lower silicon or higher carbon levels by: increasing manganese content; decreasing oxygen, hydrogen, or nitrogen content; or increasing external pressure on the solidifying mass. FOR the production of sound castings it is essential to prevent the formation of interdendritic worm-holes or pinholes brought about by gas evolution during solidification. Another major problem encountered in solidification of ingots is the formation of surface defects. These problems are thought to be closely associated with the deoxidation reaction occurring in liquid steel during cooling and subsequent solidification. As the liquid becomes richer in impurities during dendritic solidification of steel, a series of reactions may occur in the liquid phase trapped within the branches of growing dendrite platelets. Because of the strong interaction between dissolved oxygen and impurities in liquid steel, the reactions most likely to occur are of the deoxidation type. However, inherent to the extreme complexity of the problem in question, numerous simplifying assump-

Jan 1, 1965

By C. W. MacGregor

THE observation of the flow layers, or Lüders' lines, produced in mild steel when it is stressed into the plastic range often provides considerable useful information for the study of the fundamental mechanism of the plastic flow of metals. It is a commonly observed fact that as soon as the upper yield point in a mild-steel tensile-test bar is passed, an unstable condition develops in the equilibrium, the load on the testing machine drops and if the surface of the bar contains a thin mill scale, the latter begins to flake off rapidly along certain "lines." These "lines" are in reality traces of wedge-shaped flow layers and are formed by the intersection of the surface of slip and the surface of the bar. The average plane of the flow layer itself has been found by various experimenters to be inclined at an angle of approximately 45° to the axis of the test bar. In a body of more complicated shape stressed in possibly a different man-ner, the tangent planes to the flow layers at each point seem in many cases to be inclined at an angle of about 45° to the principal stress direc-tions at the point. As examples of the latter may be mentioned the logarithmic spirals obtained when a rivet hole is punched in a thin plate, or when a tube is subjected to internal pressure only, etc. Hence if the flow layers are observed from an experiment, the shear-stress trajectories -the curves indicating the directions of the maximum shearing stresses in the body-may then be approximately determined. Since the latter curves form an orthogonal family inclined at 45° to the principal stress directions, the family of principal stress trajectories, or the curves indicating the directions of the principal stresses, may be thus obtained. Although the discontinuous type of stress-strain curve at the yield point is commonly observed with test bars of mild steel, more recent experiments have shown that this is by no means the only material exhibiting this interesting phenomenon. A similar effect has been observed in zinc and cadmium crystals, by Becker and Orowan;1 in duralumin and other aluminum alloys, by Dawidenkow,2 Elam,3 Fell, and others; in copper and copper-alloy crystals, by Elam;5 in brass by Elam;5 in brass wires by deForest;6 in higher carbon steels, tungsten steel, and

Jan 1, 1939

By Zay Jeffries

Tungsten has the highest melting point of all the known metals, namely 3350 C.; it is one of the hardest of the metals; it has the highest equiaxing or recrystallization temperature after strain hardening, of any pure metal known. It is particularly distinguished because, when composed of small equiaxed grains, it is extremely brittle and fragile at room temperature, and when possessing a fibrous structure it may be ductile and pliable at room temperature. The common ductile metals act in exactly the opposite manner in this respect. The present paper will include a brief note regarding the manufacture of wrought and ductile tungsten. The metallography of wrought and ductile tungsten in the various stages of manufacture will be considered more or less in detail. The general relationships between the properties of tungsten and other metals will also be considered. A discussion will be given explaining why fibrous tungsten is ductile at room temperature, even though past experience with other metals would indicate that it should be brittle. Finally, a brief note regarding some new fundamental metallographic propositions relating to all metals will be given. Manufacture of Wrought and Ductile Tungsten Up to about 10 years ago, it had not been possible to work tungsten mechanically. About the year 1908, Dr. William D. Coolidge, of the General Electrie Go., produced ductile tungsten from what was then supposed to be an inherently brittle metal and which, in fact, was inherently brittle in its normal state, that is, when composed of equiaxed grains. Since that time many products, chief among which are the filaments for electric incandescent lamps, have been made from wrought and ductile tungsten. Tungsten is produced chiefly from the minerals wolframite and scheelite.1-8 The ores may be reduced in many ways. For example, the ore may be fused with alkali carbonates and the fusion dissolved in water; sodium tungstate is formed, which is soluble in water. This

Jan 1, 1919

By C. W. Nicolson

THE Tri-State zinc and lead-mining district is in the northeast corner of Oklahoma, the southeast corner of Kansas and the southwest corner of Missouri. The area throughout which active mining has been conducted is about 45 miles long and about 5 miles wide, extending northeasterly from Commerce, Okla., to Alba, Missouri. Although the lead ores were mined on a very small scale in the vicinity of Joplin, Mo., as early as 1848, nothing of any importance was done in the district until 1870, since when both mining and smelting have been prosecuted with considerable vigor. In the beginning the lead ores only were exploited, but within a few years extensive deposits of zinc ores were found and since that time the production of zinc ore has far exceeded that of lead. Both the surface and mineral rights in Missouri and Kansas were under individual ownership by the time ore was discovered. Although some of these rights were purchased by mining companies, most of the mining has been done under leases covering small areas, usually 40 acres, although in the past many leases were given on much smaller tracts. In Oklahoma most of the mineral land had been alloted by the Government to various Indian tribes and although the title to some of these lands had been acquired by various white men before the discovery of the rich Picher field, the title to most of the land has remained with the Indian tribes and the leasing of the mineral rights has been done by the Federal Government for the benefit of the Indians. The Indian allotments were of 200 acres each and some of the mining leases covered entire allotments, although many leases were granted for only 40 acres or even less.

Jan 1, 1938

By N. D. Shutler

This paper describes a numerical mathematical model of the steamflood process that depends on fewer restrictive assumptions than models previously reported. The solution, however, is obtained economically. Example calculations are presented that, on comparison with experimental results, tend to validate the model. Results that expose certain process mechanics are discussed. The model describes the simultaneous flow of three phases — oil, water and gas — in one dimension. It includes the effects of three-phase relative permeabilities, capillary pressure, and temperature- and pressure - dependent fluid properties. Interphase mass transfer of water-steam is allowed, but the oil is assumed nonvolatile and the hydrocarbon gas insoluble in the liquid phases. The model allows heat convection in one dimension and two-dimensional heat conduction in a vertical cross-section spanning the oil sand and adjacent strata. The hydrocarbon-steam gas composition is tracked, but the effect of gas composition on water-steam phase behavior is neglected. The model is solved numerically in three separate stages. The three-phase mass balances are solved simultaneously using Newtonian iteration on nonlinearities occurring in the accumulation terms. The energy balance is solved separately by noniterative application of the alternating-direction implicit procedure. Separate solution of the composition balance is accomplished by straightforward solution of the finite difference equations. The method of effecting nonsimultaneous, stable solution of the mass and energy balances is the key to the success of the model. INTRODUCTION Mathematical tools as well as laboratory and field experiments are necessary to help us understand the complex steamflood process. A mathematical model can expose process mechanics and show the relative importance of process variables, but this ability is often limited by restrictive assumptions. Most known models of steam processes,l-5 with the exception of the model of Gottfried,6 are "simplified" in that they involve analytic approximations and require many restrictive assumptions. The primary utility of these methods lies in the routine use as an aid in engineering design. By contrast, the comprehensive model presented here is numerical and requires far fewer restrictive assumptions. It finds its primary utility as a research tool. It serves as an aid in understanding the nature of the process, in interpreting laboratory experiments and in evaluating and developing simpler mathematical models for engineering design. The major reason why previously presented models have been confined to the "simplified" class is evidenced by the one published exception. In 1965, Gottfried6 presented a numerical model for the combustion process of which the steam process is a subset. The result is a comprehensive tool (though it neglects capillarity and two-dimensional heat conduction) that is troubled with convergence problems and that requires 2 to 3 hours of IBM 7094 time to complete a calculation. Though our present model does not simulate combustion, it does consider capillarity and two-dimensional heat conduction and it overcomes the convergence and computer-time problems. MATHEMATICAL DESCRIPTION OF STEAMFLOODING FLUID FLOW The equations employed to describe three-phase fluid flow are of a familiar form. Darcy's. law provides expressions for the velocities of the three phases (oil, water and gas), which, when combined with oil, water and gas mass balances, give the partial differential equations governing flow of the

Jan 1, 1970

By A. G. Spillette, R. L. Nielsen

The purpose of this paper is to further the understanding of reservoir response to hot-water injection by desuribing a two-dimensional, mathematical model of the process. Key assumptions are that no gas phase is present, and that the injected fluid reaches thermal equilibrium instantaneously with the reservoir fluids and sand. The resulting system of three partial differential equations is solved simultaneously through the use of a "leap-frog" application of standard alternating direction implicit methods for the solution of the mass-balance equations and the method of characteristics for solution of the energy-balance equation. The utility of the mathematical model is demonstrated by comparing numerical and analytic temperature distributions for hot-water bank injection and by comparing calculated with observed field behavior. Additional calculations show that hot waterfioding can recover significantly more oil than cold waterflooding, and that a hot-water bank recovers, with less energy input, nearly as much oil us continuous injection. Introduction Consistent field success with hot fluid injection processes requires good reservoir description and a thorough understanding of recovery mechanisms. The latter is fostered by a combination of well designed experimental studies and physically sound mathematical modeling. The purpose of this paper is to further the understanding of reservoir response to hot-water injection by describing a two-dimensional mathematical technique, indicating its validity, and demonstrating its utility for studying the effects of reservoir and operating parameters. Published experimental studies of hot fluid injection processes are few." Even if extensive data were available, two considerations discourage exclusive reliance on laboratory or field work. First, because of the severity of scaling requirements," laboratory results must be interpreted with care. Second, because of the one-shot nature of field experiments — injectivity/productivity tests and pilot floods—results seldom are available over the desired range of operating conditions. These factors emphasize the need for devoting attention to mathematical modeling to complement laboratory and field work. Through the use of mathematical models, scaling uncertainties can be bridged and response can be predicted for unique combinations of reservoir and operating conditions. Numerous mathematical models developed during recent years enable us to calculate temperature distributions, thermal efficiency (or conversely, fraction of heat lost), and oil recovery behavior for hot fluid injection. Ramey" and Spillette' recently have provided reviews of these methods. Most models have concentrated on predicting temperature distributions and thermal efficiency; few have been directed at predicting oil recovery.'."1° Although these techniques are useful for estimating effects of reservoir parameters and operating conditions on process performance, results are limited by the assumptions made and by the methods of coupling independently solved fluid-flow and energy-balance equations. A computer-based method is presented for predicting total reservoir response to hot-water injection that obviates most simplifying assumptions. The model simulates fluid flow and heat transfer in two dimensions within a vertical cross-section spanning the oil sand and adjacent unproductive strata. Known numerical procedures are used to solve the governing partial differential equations. The mathematical model handles the effects of reservoir heterogeneity, gravity, capillarity, relative permeability and temperature-dependent fluid properties. In addition, a wide range of operating conditions can be modeled, including hot-water followed by cold-water injection. Mathematical Description of Hot-Water Injection Key assumptions in the mathematical model for hot-water injection are that (1) no gas phase is present and (2) the injected fluid reaches thermal equilibrium instantaneously with the reservoir fluids and sand. Relative permeability and capillary pressure are assumed independent of temperature. Darcy's law for multiphase fluid flow relates the velocities of the oil and water phases to the phase pressure gradients by the following relations:

Jan 1, 1969

By H. J. Morel-Seytoux

Methods of predicting the influence of pattern geometry and mobility ratio on water flooding recovery predictions are discussed. Two methods of calculation are used separately or concurrently. The analytical method yields exact solutions in a convenient form for a unit mobility ratio piston-like displacement. A few typical pressure distributions, sweep efficiencies and oil recoveries are presented for various patterns. For non-unit mobility ratio, one may resort to a numerical method, such as that of Sheldon and Douherty. 1,2 Because the domains of applicability of the analytical and numerical techniques overlap, the exact solutions provide estimates of the errors in the numerical procedures. The advantages of the analytical and numerical methods can be combined. To develop a numerical technique as independent of geometry as possible, the physical space is transformed into a standard rectangle. The entire effect of geometry is rendered through one term, the "scale-factor", derived from mapping relations. The scale factor can be calcu-lated from the exact unit-mobility ratio solution for the particular pattern of interest. By this means recovery performances for arbitrary mobility ratio con be obtained for many patterns. A sample of tesults obtained in this manner is presented. INTRODUCTION Pattern geometry and mobility ratio are two major factors in making a waterflood recovery prediction. Because assisted recovery has become increasingly important to the oil industry, pattern configuration and mobility ratio also assume a greater significance in the assessment of the economic value of recovery projects. The influence of pattern geometry and mobility ratio in shaping a recovery curve and on the other quantities of interest to the reservoir engineer is the main subject of this paper. Much effort has already been spent on estimating quantitatively the influence of either pattern or mobility ratio or both on oil recovery. The literature reports many investigations of this nature. 3-9 However, many results or methods of recovery prediction presented in the literature cannot be considered fully satisfactory. Even for unit mobility ratio and piston-like displacement, where analytical solutions are available, the literature shows discrepancies. For non-unit mobility ratio, the divergence in the results is extreme. For infinite mobility ratio in a repeated five-spot, depending on the investigator, the sweep efficiency ranges from 0 per cent to 60 per cent. With respect to the influence of pattern on recovery, only the repeated five-spot has received much attention. Other confined patterns and pilot configurations have received very little attention. Two calculation methods are presented in this paper, either separately or concurrently: the analytical method of potential theory and the numerical method of finite-difference approximation. The analytical method is more restricted in scope than the finite-difference method, but it has the definite advantage of providing exact solutions within its range of applicability. If a unit-mobility ratio piston-like displacement is assumed, the analytical approach is possible. A few typical results are reported in this paper; the detailed description of the general method and of a great variety of results will be the subject of other articles. Fornon-unity mobility ratio, we must resort to a numerical scheme. The numerical technique is that which was described by Sheldon and Dougherty.l,2 It is not limited to piston-like displacement. However, mainly single interface results will be presented here. Because the respective domains of applicability of the analytical and the numerical method overlap, useful comparisons of exact and numerical solutions can be made for a variety of patterns. The advantages of the analytical and numerical approaches can be combined. The reason for the success of this analytical-numerical approach can be summarized in the following two points: 1. The numerical solution for arbitrary mobility ratio can be programmed most efficiently when the physical space in which the displacement actually takes place is transformed into a standard shape; and 2. This can be done with remarkable simplicity whenever an analytical expression for the pressure

Jan 1, 1966

By M. Cohen

THERE seems to be a natural urge for the human mind to wonder about the beginning of things. When an explosion occurs, we immediately inquire "what set it off?" If a person contracts a disease, we are likely to ask "how did it happen?" On a much loftier plane, when we reflect about the universe, there is the inevitable question "what, or rather Who, started it all?" In principle, these varied queries have at least one attribute in common: they are attempts, whether earnest or casual, to search out the origin of events in nature. Accordingly, they involve not only scientific, but philosophical and even re1igious matters of deep concern. It is evident that, in a broad sense, the phenomenon of nucleation is enmeshed in this enticing concept of "the beginning", but we must extract the scientific component of the problem for our present purposes. Nucleation, as in the case of phase transformations, is best regarded from the standpoint of kinetics. There are then two main steps, which may come in either order: (a) Experimentally, one attempts to measure the frequency with which transformation centers spring into existence; and (b) theoretically, one seeks a model that will account for this observed birth-rate. Temperature, composition, strain, and prior history are some of the important variables that must be considered both experimentally and theoretically when dealing with nucleation in the solid state. Such interaction of theory and observation is an integral part of science in general, but it is particularly significant in the nucleation problem because the very beginning of a phenomenon invariably occurs on too localized a scale in both space and time to be detected with available techniques. Thus, there is little hope of making direct measurements on the nucleus during its birth or to ascertain the exact nature of the process; one can only infer the details of nucleation from the model whose predicted behavior seems to harmonize best with the measured rate of nucleation and its dependence on known parameters. In the field of solid-state nucleation, both theory and experiment call for much ingenuity, but somehow the conceptual schemes have spawned faster than they can be tested by observation. This is not to say that there are many basically new ideas in modern nucleation theory; rather, as we shall see, it is because the required fine-scale measurements are of immense technical difficulty. Quite likely, some of the nucleation models existent today have survived only because of the latitude permitted by meager data. There is great need to bring theory and experiment into better balance in this important area of physical metallurgy. Although one can

Jan 1, 1959

By A. F. Giamei, E. J. Freise

A discussion of the various factors affecting the accuracy of volume fraction determination by the direct comparison X-ray diffraction method is presented. To minimize errors introduced by nonrandomization effects such as preferred orientation and large grain size, as well as errors introduced by statistical effects, an iterative mathematical analysis is introduced. This analysis is applied to all observable diffractio~ spectra from a given specimen by means of computer techniques and is statistically superior to the standard direct comparison technique which utilizes only one or tm sets of intensity spectra. The computer program also presents a graphical interpretation of- the results which enables the investigator to visualize and readily assess the scatter in volume fraction estimates caused by deviations from randomness. Finally, the iterative analysis is applied to experimental data collected from a series of plain carbon steels in both the as-received and spheroidized conditions to determine the volume fraction of cemen-tite present in each case. The results show markedly good agreement with chemical analyses for all spheroidized specimens. In theory, quantitative X-ray diffraction is a power-ful analytical technique for precise determination of the volume fractions of various phases present in a multiphase poly crystalline aggregate. There are two generally used methods; both utilize the fact that the intensity of a diffraction line of a particular phase is a function of volume fraction of that phase present in the aggregate. The more common method is the so-called internal standard technique where a known amount of standard substance is mixed with the aggregate containing the unknown. The resulting ratio of the intensity of a particular diffraction line of the unknown to the intensity of a diffraction line from the standard is used to find the weight fraction of unknown material by reference to the intensity data obtained from a previously prepared set of standards containing the same amount of standard material. The details of this technique are outlined in standard works on X-ray diffraction.' The disadvantages of the technique are that it requires the use of powder specimens and that the powder mixture must be homogeneous near the surface to the maximum effective beam depth. The alternative technique is the direct comparison method in which the ratio of the intensity of a diffraction line of a phase in the aggregate to the intensity of a second-phase diffraction line yields the ratio of the volume fractions of each phase present. This method has been applied most extensively to the determination of the percentage of retained austenite in martensitic steels and to determining the amounts of hcp and fcc allotropic modifications in pure cobalt5 and the amounts of hexagonal and rhombohedra1 modifications in graphite.8 This method is applicable to bulk as well as powder aggregates and is the technique which will be considered in the following text. It is the purpose of the present communication to show that by combining the results of X-ray diffrac-tometry with the use of high-speed digital computers the results of the direct comparison quantitative X-ray analysis technique can be optimized by using all of the data available on a diffraction pattern. THEORETICAL DISCUSSION In optimizing any quantitative X-ray diffraction experiment, the problem of accuracy vs time to collect and analyze the experimental data arises. For any method to be practical, it is required that both experimental and analytical procedures are reasonably short. In most of the previous work performed by the direct comparison method, intensity data from only one or two sets of peaks were used to calculate the volume fraction of phases present in the aggregate. Consequently, rather long-time experimental measurements are required to assure that the intensity data are sufficiently accurate to justify the use of one or two sets of data. By using computer techniques to analyze the experimental data it becomes feasible to use all of the available data on a diffraction pattern. By so doing, the time spent in measuring any one diffraction maxima can be appreciably reduced. Although this results in poor counting statistics for any one maxima, the number of data points available for analysis is greatly increased. Based on the above discussion, it will be assumed that a continuous scanning counter-diffractometer technique will be used to collect intensity data from a two-phase mixture. The integrated intensity of the ith diffraction line from the a phase in the aggregate is given by:'" where is the volume fraction of the a phase, The various quantities in Eq. [la] are angular independent while those in [lb] depend on the hkl spectrum of a particular phase. The meaning of the individual quantities in Eqs. [la] and [lb] are given in Appendix 1. It is convenient at this point to outline briefly the factors which will affect the measured intensity of any one hkl spectrum. a) Extinction effects arise from two independent experimental conditions. Primary extinction arises from a high degree of crystal perfection and results in spectra having lower intensity than predicted by Eq. [I]. Any treatment, such as powdering, which reduces

Jan 1, 1968

By Henry Rawdon

THE METHOD of demonstrating the structure existing in a metal or alloy at high temperatures, by etching a polished sample after it has been heated to the desired temperature, is quite familiar to metallographists. The usual procedure1,2 is to heat the specimen, previously polished for microscopic examination, to the desired temperature, in a neutral atmosphere (hydrogen or nitrogen), then admit the etching gas. (chlorine, hydrochloric acid or similar gas) for. a few seconds, and finally, after flushing out the etching gas with the neutral one, cool the specimen in the neutral atmosphere. The pattern produced by etching at a definite temperature is usually taken as a record of the microstructure prevailing at that temperature. It has frequently been pointed out that changes in composition of the surface metal occur during the preliminary heating in the neutral atmosphere, so that the appearance produced' by the etching at high temperature may not exactly represent the condition of the interior of the specimen. To overcome this uncertainty, the heating has sometimes been done in vacuo,3 the etching gas being ad-mitted when the desired temperature was reached, then pumped out and the specimen cooled in vacuo.

Jan 2, 1920

By J. E. Crawshaw, Francis B. Foley

In the first report1 disks of steel of known composition and history were exposed, under carefully prescribed conditions, to impacts of explosion products resulting from the explosion of 50-gm. charges of explosives having well-determined rates of detonation, or to impacts of a weight of known mass, falling through measured distances. There were available at the Bureau of Mines Experiment Station five explosives, having rates of detonation of 5716, 4470, 3190, 2296, and 1523 meters per second. It being desired to continue this exposure downward, and no explosives with a lesser rate of detonation being at hand, resort was had to the impact of a falling weight, the differences in the velocity of impact being attained by varying the height from which the weight was allowed to fall. It was expected by this means to demonstrate experimentally that the development of Neumann bands was determined by the suddenness of the deformation of the metal in which they were produced. But while progressive deformations were obtained with the explosive charges, the falling-weight method failed because the tup was progressively deformed, also the disks were so flattened as to be unfit for metallographic examination. A return, therefore, has been made to the use of explosives as the source of energy, an air-gap being interposed between the charge of explosive and the disk, as the effect diminishes as the function of the distance between the charge and the object on which the products of its explosion, or the shock wave from its detonation, impinge. The details of the arrangement of the tests by the air-gap method were the same as those described by Foley and Howell,2 except that after the system had been set up and the desired apparent specific gravity for the explosive attained by tamping it, the small lead block, with the steel disk adhering

Jan 1, 1926

By E. M. Wise

IN a previous communications the improvement in strength, harden-ability and color, occasioned by replacing gold in a typical gold-silver-copper alloy by various amounts of platinum, or palladium, was discussed. In the present paper the results of further studies upon the constitution and the nature of the hardening transformation in these alloys are pre-sented. This research may be summarized as follows: 1. The liquidus and solidus have been determined for the alloys of the palladium and platinum series. Cooling curves were utilized for deter-mining the liquidus of the palladium alloys but this method proved unsuitable for the platinum alloys so that a, novel quenching method was utilized for the latter. Both the liquidus and solidus of the palladium alloys increase steadily with the palladium content. The liquidus of the platinum alloys increases rapidly with the platinum content, while the solidus temperature increases with the platinum content up to about 14 atomic per cent platinum, but suffers no further increase with additional increments of platinum up to 20 atomic per cent at least, owing to a peritectic reaction. 2. Palladium, and even more effectively platinum, reduces the rate of grain growth. Owing to this fact and to the increase in the solidus temperature, "overheating" does little or no damage to alloys containing reasonable quantities of these elements. This is confirmed both by tensile tests and metallographic examination. 3. The excess phase present in one of the high-platinum-content alloys has been isolated and chemically analyzed and was found to consist almost wholly of platinum, gold, and copper, evidently derived from the compound AuCu, by the partial replacement of gold by platinum.

Jan 1, 1933

By Nev A. Gokcen

DISCREPANCIES and scattering in the equilibrium data on the reactions of hydrogen, and CO with dissolved oxygen in liquid iron are un- duly large. Available experimental results on the reduction of liquid ferrous oxide, i.e., wüs-tite, with hydrogen and CO are questionable, as pointed Out by Darken and Gurry'l Direct determinations of the solubility of oxygen in liquid iron are subject to errors which cannot be easily reduced by further experimental refinements, and therefore an accurate but indirect method is highly desirable. The purpose of this investigation was, therefore, 1)

Jan 1, 1957

By Robert Mehl

A STUDY of the structures arising from the decomposition of the a solid solutions in the Cu-Zn and the Cu-Al systems is of peculiar interest in the study of the mechanism of precipitation from solid solutions. It is possible in these alloys, by varying the composition within the ß field, to precipitate from the same basic lattice phases having different lattice structures. It has been rather generally assumed heretofore that the type of structure originating from the decomposition of a solid solution-the Widmanstätten structure-is determined by the lattice structure of the parent solid solution alone. In the first paper of this series1 evidence was advanced which threw doubt upon this hypothesis; but definite proof of the correctness or incorrectness of the hypothesis should be forthcoming from a study of these alloys, for if the structures originating, for example, from the precipitation of the a phase from ß and of the -y phase from the ß in the Cu-Zn system should be shown to be crystallographically different, the hypothesis would necessarily be held as definitely disproved. Furthermore, the newer proposal enunciated in the first paper of this series-that the origin of the Widmanstätten structure lies in a cooperation between the lattice of the parent solid solution and that of the precipitate-which at present seems the only alternative hypothesis, would in such an event be given added weight. The work here reported shows that the Widmanstätten structures originating in the precipitation of the a phase from the a and in the precipitation of the -y phase from the ß in the Cu-Zn system are indeed crystallographically different; and incidentally presents some new descriptive information on the Widmanstätten structure from a more general point of view.

Jan 1, 1931

By J. H. Craig

As a result of information that the Navy Department was questioning the advisability of raising the maximum allowable exposure temperature for zinc-coated steel parts from 500 to 750 F., it was decided to make a series of high temperature tension tests on several types of uncoated and zinc-coated steels. The objective was to determine at what temperature intergranular penetration of galvanized steel by zinc might take place under conditions of rapidly applied stress and temperature. Tests were conducted in the range from room temperature to 1400 F. In this range, low-carbon and high-carbon steels did not suffer any adverse effects due to zinc coatings. In fact, at 1400 F. the zinc coatings appeared to have a beneficial effect. In stainless steel, the coating had no effect up to 1000 F. Above this temperature, the zinc coating appeared to cause a marked loss in ductility and a less pronounced loss in strength. There was no visible evidence of zinc penetration of the stainless steel structure, but it was assumed that this was the cause of the adverse effect.

Jan 1, 1945

By Arthur Bell

(San Francisco Meeting, September, 1915) . PRIOR to 1908 the oil production in the State of California, had been almost entirely a heavy fuel, oil, with a high flash point, hut changed within a-short period to a large percentage of refining oil with a low flash, by reason of the coming in of the Santa Maria field, the Midway field, and the increased production of the Fullerton field. This is clearly shown in the following tabulation of California's production: Year Barrels . Below -20° Be, Above 20° Be,, Per Cent_ Per Cent. 1905 48,307,000 90 10 1910 77,698,000 SO 20 1912 90,075,000 6o 31 1914 10:3,600,000 47 53 The bringing in of these high percentage's of light oil with their dangerous low flash and the increasing demand for the refined products necessitated the devising of some cheap and efficient means of quickly separating the lighter elements either in the field or at the main distributing points; also it became necessary to remove the excessive percentage of water which many of the light oils carried in emulsion.

Jan 9, 1915

By Herbert Clark Hoover, Lou Henry Hoover

SINCE I have written of the varied work of pre- paring the ores, I will now write of the various methods of smelting them. Although those who bum, roast and calcinea the ore, take from it something which is mixed or combined with the metals ; and those who crush it with stamps take away much ; and those who wash, screen and sort it, take away still more; yet they cannot remove all which conceals the metal from the eye and renders it crude and unformed. Wherefore smelting is necessary, for by this means earths, solidified juices, and stones are separated from the metals so that they obtain their proper colour and become pure, and may be of great use to mankind in many ways. When the ore is smelted, those things which were mixed with the metal before it was melted are driven forth, because the metal is perfected by fire in this manner. Since metalliferous ores differ greatly amongst themselves, first as to the metals which they contain, then as to the quantity of the metal which is in them, and then by the fact that some are rapidly melted by fire and others slowly, there are, therefore, many methods of smelting. Constant practice has taught the

Jan 1, 1950

By B. S. Butler

PART I SUMMARY CERTAIN relations between the formation of ore deposits and other geological processes are pretty generally accepted, namely: that many ore deposits are closely associated with igneous activity; that ore deposits accompany certain types of intrusive bodies, notably batholiths and stocks, and that they are concentrated near the tops of such bodies; that igneous activity occurs in belts of strong folding and faulting; that folding and faulting are greatest in basins of extensive sedimentation and least in areas of erosion or slight sedimentation; that areas of erosion or slight sedimentation and of heavy sedimentation persist over long periods and exert a major control over structure, igneous activity, and ore deposition; that cycles of erosion, deposition, folding and faulting, igneous activity, and ore deposition, have been repeated through geologic time resulting in rather definite periods in which metal deposits have formed. In short, ore deposition is but one phase of a series of closely related geological events. It is attempted in this chapter to point out the relations of these interreacting geologic processes to the distribution of ore deposits in the western United States. Three great periods of mineralization are recognized; pre-Cambrian, post-Jurassic, and late Cretaceous-Tertiary. In distribution the deposits of the three periods, with certain exceptions, show a concentration about two large positive areas, the Colorado plateau and the Columbia plateau, which suggests a causal relation. The most general age divisions of the rocks of the Cordilleran region of the United States are (1) pre-Cambrian, and (2) Cambrian and later rocks. The pre-Cambrian rocks are exposed mainly through the Rocky Mountain belt from the Canadian boundary southward to Arizona and westward through Arizona to southern California. They have commonly

Jan 1, 1933