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By Ira B. Jorafemon

In the interesting Institute symposium of the preservation of peace by force, through mineral control, one important aspect of the question was not presented. This is the responsibility the United Nations, and particularly the United States, will incur the through limitation of the economic activities of nations that are now friendly to us, as well as of nations that are enemies or are under the control of enemies. After the war all nations, friends as well as enemies will be poor. Hunger and bankruptcy will, will like the sword of Damocles, hang over the heads of all of us on this blundering planet. When the actual fighting is over, there will be a universal attempt to squirm out from under the sword by resuming production of peacetime goods, for trade as well as immediate consumption.

Jan 1, 1944

By R. J. S. Brown, B. W. Ganison

A new logging method has been developed, based on measurement of the nuclear magnetism of formation fluids. The nuclear magnetism log (NML) is the only log that responds solely to formation fluids. It operates equally well in both oil-base and water-base muds and in empty holes, and can be used in all kinds of formations except strongly magnetic ones. Two separate NML measurements can be made, one of which provides a continuous formation fluid curve. This fluid curve is called the free fluid log (FFL) and is believed to indicate a minimum effective porosity in most formations. The FFL not only delineates fluid-containing zones, but provides an excellent correlation curve that can be obtained under conditions where conventional correlation logs are ineffective. Preliminary tests indicate that the second kind of NML measurement may help distinguish oil and water zones and provide information concerning permeability and wettability. (The FFL itself appears to provide some information on permeability.) The second kind of NML measurement requires stopping the logging tool for a short time opposite a zone of interest and taking more extensive NML data that can be displayed as nuclear magnetic relaxation curves. In some instances, oil and water saturations for the region immediately adjacent to the borehole can be read from these relaxation curves. INTRODUCTION In 1946, Bloch, Hansen and Packard and Purcell, Torrey and Pound3 independently announced the successful demonstration of the phenomenon of nuclear magnetic resonance. During the past 13 years, there have been many applications of nuclear magnetic resonance, including applications to the study of chemical structure and to the measurement of magnetic field strengths. Preliminary experiments on the feasibility of using nuclear magnetism measurements in well logging were made independently by California Research Corp. and Varian Assoc., the Varian work being sponsored by the Byron Jackson Tools, Inc. Since then a cooperative research program on nuclear magnetism logging has been carried out by the Byron Jackson Div. and Research Center of Borg-Warner Corp., and California Research Corp., subsidiary of Standard Oil Co. of California. The use of nuclear magnetism in well logging is of special interest because it offers a way of making direct measurements on the hydrogen in the formation fluids and not on the rock matrix. Within the past 1 1/2 years, successful measurements have been made with a research model logging tool in wells in California, Tex as, Utah, Louisiana and Wyoming. NUCLEAR MAGNETISM SIGNALS Polarization, Relaxation and Precession Many atomic nuclei possess magnetic moments and spins; that is, they are similar in some respects to bar-magnet and gyroscope combinations. Molecules and their nuclei are subject to thermal motion, which has a scrambling effect, tending to leave as many nuclear spins oriented in any one direction as in any other. However, if a magnetic field is applied, the magnetic nuclei tend to align in the direction of the field. The scrambling and aligning forces compete with each other, with the result that a few more spins are oriented parallel to the field than in other directions. This gives a net magnetization, or polarization, which is directly proportional to the strength of the applied magnetic field (aligning influence) and inversely proportional to the absolute temperature (scrambling influence). When the magnetic field in, or temperature of, a liquid sample containing protons is changed, the new equilibrium value of proton polarization is not established immediately but requires an amount of time which depends on the nature of the hydrogen-containing materials. The process of approaching the equilibrium value of polarization is called relaxation.'.' Polarization is a vector quantity, and the components parallel to and perpendicular to the magnetic field must be considered separately. Relaxation of the component parallel to the field is called "thermal relaxation", or "longitudinal relaxation", and the corresponding time for this component of non-equilibrium polarization to decay by a factor of e (natural log base) is denoted T. The relaxation of the perpendicular component is called "transverse relaxation", and the corresponding relaxation time is denoted T,. The potential energy of a magnet in a uniform field depends on the angle the magnet makes with the field; therefore, a change of the component of net polarization parallel to the magnetic field involves an exchange of energy between the spin system and the thermal motion of the molecules, leading to the term thermal relaxation for the relaxation of this component. Suppose we subject a sample to a strong magnetic field at right angles to the earth's field for a time greater than TI. A polarization, thus, is established at right an-

By J. Chipman, N. J. Grant, H. L. Bishop, H. N. Lander

Data of several studies on the equilibrium between molten iron and open hearth-type slags have been combined to determine some of the chemical reactions involved in steel-making. Effects of slag composition and temperature on the iron oxide activity, distribution of sulfur between slag and metal, and the carbon content of the metal are discussed. Also, an overall reaction for the equilibrium between sulfur and oxygen is presented. DURING the past 15 years, a number of significant equilibrium studies have been carried out between liquid iron and simple basic and acid slags in an effort to throw light on the chemical reactions involved in steelmaking. This paper is a summary of the experimental reports on investigations which have been conducted at the Massachusetts Institute of Technology, and of related work in other laboratories. The investigations summarized in this paper include the works of Fetters and Chipman1 and Taylor and Chipman,' which dealt with simple slags that are similar to those found in the open hearth. The sulfur determinations of the slag-metal tests of Fetters and Chipman as reported by Grant and Chip-man" are included. Also, the investigations by Win-kler and Chipman' and Grant and ChipmanQ f more complex slag systems are included in this summary. The experimental procedure is described in detail in each of these papers and will not be discussed. Since the previous reports have been somewhat independent, it is desirable to review and combine the data of the various investigations to determine, as accurately as possible, the reactions in the slag-metal systems of the open hearth. It is the object of this report to present the combined data in such a way as to enhance their utility and applicability. Oxidizing Power of Slags of the System (CaO+MgO)-Si0,-FeO in Equilibrium with Carbon-Free lron The slags selected to determine the iron oxide activity in equilibrium with pure liquid iron were those containing less than 2 pct each of P,O,, MnO, or A1,0, on a weight percentage basis. The method used to calculate activities of iron oxide in liquid slags was that developed by Taylor and Chipman.' The solubility of oxygen in molten carbon-free iron under pure iron oxide slags can be expressed by the following eauation —6320 log (pctO)-------------— + 2.734 [1] where T is the absolute temperature. The oxygen solubility values as determined from Eq. 1 were used throughout this study to calculate the iron oxide activity. The iron oxide activities of slags of various iron oxide contents are plotted in Fig. 1 as a function of the basicity, which is defined as the ratio (pct CaO + pct MgO)/pct SiO,, and are based on molecular percentage values of the components. The percent (FeO), is the total iron content in the slag calculated to FeO. Fig. 1 shows that as the basicity increases at constant mol pct (FeO),, the iron oxide activity increases rapidly and reaches a plateau which extends on the basicity scale from about 1.3 to 2.3; the iron oxide activity then decreases rapidly until a basicity of about 3.0 is reached, where it tends to level off. The solid portions of the curves represent the experimental data of Fetters and Chipman and Win-kler and Chipman. Their experimental heats were made in magnesia crucibles, and hence the slags were saturated with magnesia. The broken lines on the left represent the experimental data of Taylor and Chipman, who used a rotating crucible. In general, these slags contained less than 3 pct MgO. The absence of data for slags containing less than about 40 mol pct (FeO), and basicity ratios greater than about 2.5 made it necessary to calculate curves using ionic concepts of slags. The broken lines on the right, which disregard the solubility limits of di and tricalcium silicate and lime, were obtained by following the treatment of Flood and Grjotheim,"

Jan 1, 1957

By Giovanni Barla, Stefan H. Boshkov

This paper examines the application of gelatin mixture models to the study of factors such as gravity effects, tectonic and residual stresses, anisotropy, physical nonlinearity, time-dependent behavior of the rock mass and connectedness of the geologic space. The technique of calibrating gelatin mixtures proposed by Richards and Mark in 1966 is applied to the particular problem considered. Similitude relationships between model and prototype are discussed with reference to the constitutive equations describing the physical behavior of the rock mass. The interaction between two openings in a linearly elastic medium, under conditions of plane strain, is used as an illustrative example with the view to describing the history of stress and deformation changes on the rock medium and lining around a slusher drift while undercuts are made in block caving. The prediction of the displacement, stress field and mode of fracture associated with a given rock structure, its initial stress field, and its physical properties is essential to rock mechanics and ground control. The basic approach is to assume the rock mass to behave as a continuous, homogeneous, and isotropic medium. The classical theory of elasticity is the simplest theory based on such a concept. Specification of the elastic constants, the initial state of stress in the ground, and the boundary conditions on stress and displacement allows one to predict stress and displacement within the body. Subsequently, provided that a criterion which governs rock fracture under various stress conditions has been established, a stability analysis of the rock structure can be performed. A natural extension of the present knowledge consists of removing some of the simplifying assumptions which characterize the analytical solutions based on the classical theory of elasticity. Complex geometry, the significance of tectonic and residual stresses, anisotropy, physical nonlinearity, time-dependent behavior of the rock mass and connectedness of the geologic space are some of the important factors which are neglected in the classical approach. A better insight into the real problem can be attained with either the finite element method of stress analysis or an experimental technique. The former has already been applied with success on several occasion 1-4 and is destined to render great service in the field of rock mechanics and ground control. The latter, which will be considered in this paper, has been used extensively in applications too numerous to be enumerated. Experimental technique involves either prototype testing, if the area to be studied is accessible, or model testing. Two- and three-dimensional photo-elastic analyses are very convenient means of obtaining the stress distribution in models of complex geometry. In general, such analyses are confined to studies of stress fields around openings which are sufficiently far removed from the surface boundary so that the stresses in their neighborhood are practically equal to those produced by an initial uniform stress field; i.e., so that gravitational effects are negligible. There are, however, many rock structures where these effects must be taken into account to attain a more realistic representation of the problem. Surface and near surface rock structures, systems of openings interacting with one another, and structural components loaded only by their own weight are some of the obvious examples. This paper was written to show how factors neglected in the usual analysis based on the classical theory of elasticity, can be taken into account when gelatin mixture models are used inconjunction with photoelastic methods. The interaction between two openings in a linearly elastic medium, under conditions of plane strain, is used as an illustrative example, with a view to describing the history of stress and deformation changes on the rock medium and lining around a slusher drift while undercuts are made in block caving. The birefringence of gelatin mixtures has been known for some time. A series of experiments were carried out by Rossi in 1910,5 but after that very

Jan 1, 1970

By W. J. Slatosky

As a means of effecting better control of endpoint temperatirres at the Jones & Laughlin basic oxygen furnace plant, a set of mathematical equations has been developed. The eqlutions are the product of a themlochemical anaysis of the process and aye designed to calculate the required scrap, lime, and hot metal additions in terms of a number of independent variables. Results of test heats have warranted adoption of this technique by the Prodrrction Department. BECAUSE of the autogeneous nature of the basic oxygen steel-making process, bath temperature can be controlled without an external fuel supply by charging the furnace with additions that are thermally balanced. The thermal requirements of the charge materials are such that, during the refining process, they throttle the heat generated by the metallurgical reactions in a manner designed to result in a speci-fied temperature at the completion of the heat. In the past, operating personnel at the basic oxygen furnace plant of Jones & Laughlin's Aliquippa Works relied on their experience and technical knowledge of the process to determine the quantities of charge additions needed to result in a finishing temperature in the range 2880"to 2920" F. (The charge consists primarily of 93 tons of scrap and hot metal plus an amount of lime sufficient to maintain a basicity ratio of 2.8 to 3.2). Estimates of these materials are based on a consideration of the effects on finishing temperature of 1) iron silicon content, having a variation of 0.8 to 1.8 pct; 2) iron temperature, ranging from 2250°to 2600°F; and 3)any excessive cooling of the furnace due to a production delay. The end temperature of the preceding heat also serves as a guide in that, if a heat was within the specified temperature range, the succeeding heat could be charged with materials of nearly the same proportions, provided the hot metal used in each of the two charges was of approximately the same temperature and composition. On the other hand, if a heat was outside the specified tapping range, or if the hot metal used in that heat was of different analysis and temperature from that of the iron to be charged, an adjustment in the proportion of additions is in order for the following heat. Due to the complex thermochemical behavior of the process and to the inexact and subjective nature of the described method of determining charge additions, consistently accurate temperature control was not to be expected. Therefore, those heats out- side the specified tapping range necessitated subsequent adjustments by either reblowing the cold heats for a suitable length of time so as to elevate the bath temperature to the desired level, or cooling hot heats with a proper amount of scrap. Because extra time is required to make these adjustments, production is delayed. In an attempt to devise a method for improving temperature control, an analysis of the thermochemistry of the process was undertaken. This, in turn, led to the development of a set of mathematical equations which enable the calculation of the quantities of scrap, lime, and hot metal needed to result in any specified tapping temperature range. The analysis was not intended to be a repetition of work done by others such as McMulkinl or ~hilbrook.' It was meant to be an extension of their work so that charge additions could be calculated not in terms of silicon alone but, rather, as a function of all independent variables. This paper presents the derivation of these relationships, their effectiveness in controlling bath temperatures, and a method of utilizing them on an operational basis. The Heat Balance—The first step undertaken in the analysis of the problem was the enumeration of the pertinent variables. A list is presented in Table I where it is noticed that these quantities have been separated into the following three categories: important variables, variables considered as constants, and variables to be neglected. The breakdown was an arbitrary one designed to facilitate the analysis; otherwise, the mathematical treatment would have been exceedingly cumbersome and complex. Fortunately, experience has shown that these simplifying assumptions do not seriously impair the accuracy of the calculations. These variables along with the limiting assumptions listed in Table n were then used to write a heat balance of the process by applying the equation of continuity, Rate of Rate of Rate of Increase = Income - Outgo PI ] of Heat of Heat of Heat.

Jan 1, 1962

By G. L. Tufford, R. L. Bleifuss

Low-grade manganiferous iron ores of Minnesota's Cuyuna Range, in general, do not respond to conventional mineral dressing techniques because of their fine-grained texture. Reducing these ores to magnetite with subsequent magnetic separation and flotation have not given satisfactory results because, in many instances, concentrate grade and manganese recovery are low. Metallization of iron and concurrent reduction of higher manganese oxides to MnO, as in the R-N process, followed by recovery of iron by magnetic separation and manganese by leaching, seems to be a technically feasible process. High-temperature x-ray diffraction studies show that solid-state reactions between iron and manganese, with the formation of intermediate iron-manganese oxides, occur during reduction and affect recovery of both iron and manganese from the final product. Solid state reactions also occur between FeO, MnO, and SiO, at temperatures as low as 900°C. The kinetics of these reactions are such that they become an important factor in the treatment of ores by the R-N process. These investigations suggest a temperature and gas composition cycle that would maximize both iron and manganese recovery. During the past ten years, iron ore shipments from the Cuyuna Range of Minnesota have decreased sharp1y. Because of adverse grade, structure, and cost, many Cuyuna ores are no longer competitive with high-grade foreign ores and domestic pellets. The low-grade manganiferous iron ores from the Cuyuna Range, in general, do not respond to conventional mineral dressing techniques because of their fine-grained texture. Reducing these ores to magnetite for subsequent magnetic separation and flotation has not given satisfactory results because concentrate grade and manganese recovery are often low. However, a technically feasible process appears to be metallization of the iron and concurrent reduction of manganese oxides to MnO with recovery of metallic iron by magnetic separation and extraction of manganese from the tailings by leaching. In 1962 the R-N Corp., with a grant from the Area Redevelopment Administration, conducted an amenability study of the metallization of manganiferous iron ore from the Cuyuna Range. The results of this preliminary investigation were sufficient to interest the Economic Development Administration in sponsoring further studies of the process with emphasis on secondary recovery of manganese from the nonmagnetic tailings. Inasmuch as the metallization process has considerable influence on the final form of the manganese - its texture and distribution between the magnetic concentrate and nonmagnetic tailings-the investigation included a study of metallization of the ore as well. Therefore, the investigation conducted at the Mines Experiment Station covered three interrelated phases: (1) laboratory R-N roasting studies and magnetic separation tests, (2) laboratory chemical extraction experiments of the nonmagnetic tailings, and (3) a mineralogical study of the crude ores and their various roast products. High-temperature x-ray diffraction investigation of the Fe-Mn-Si0,-0, system is the main topic of this paper and an extension of the mineralogical work. GENERAL GEOLOGY The Cuyuna Range is known for its complicated geologic structure, complex orebodies, and generally indifferent response to attempts at conventional beneficiation. Several geologists have made intensive studies of the Cuyuna Range, including Leithl (1907), ~darns' (1910), Zapffe3 (1925), Grout and Wolff4 (1955), and schmidt5 (1963), whose study was the most comprehensive of all. The Range is covered with glacial deposits - till, out-wash, and lake sediments -up to 250 ft thick. Bedrock stratigraphic units of the Cuyuna Range consist of three tightly folded Precambrian sedimentary formations. The lower unit is the Mahnomen formation, composed of 2000 or more feet of argillite, slate, siltstone, and quartzite. The middle unit is the Trommald formation, which varies from 45 to 500 ft in thickness and comprises the major iron-bearing formation. The upper unit is the Rabbit Lake formation, consisting of over 2000 it of argillite, slate, and interbedded lenses of lean iron formation. In the central part of the Cuyuna Range, the units have been folded into a series of

Jan 1, 1969

By T. G. Digges, C. L. Vold, M. R. Achter

A study was made of the effect of the growth conditions on the perfection of single crystals of niobium (columbium). Dislocation densities, determined by means of double-crystal diffractometer measurements , were not greatly affected by the method of crystal preparation but could be reduced by annealing treatments. However, the size, sharpness, and tilt angles of the substructures, observed with X-ray reflection macrograph, were sensitive to variations in growth procedures as well as to subsequent thermal treatments. Although the dislocation density was the same in both types, there were more low-angle bound-aries in crystals grown by zone melting than in those prepared by strain anneal. Mechanisms to account for these observations are discussed in terms of dislocation movements. A planned study of the structure-sensitive properties of refractory metals required the use of single crystals of a high degree of structural perfection and, for ease of handling, of large cross section. It appeared that the strain-anneal technique could satisfy both of these requirements. First, crystals grown in the solid state have been reported to be more perfect than those obtained from the melt.' Second, the diameters of rods which may be produced by zone melting should have a theoretical limit determined by specific gravity, thermal conductivity, and surface tension, while the diameter of strain-annealed rods is limited only by practical considerations. Previously it was shown that niobium (columbium) single crystals of 1 in. diam2 may be grown by strain anneal, compared to the 0.5 in. maximum diameter achieved by zone melting, as reported for molybdenum by Belk.3 The current research was undertaken to investigate and optimize the effect of various process variables on the perfection of 1/4 and 1/2-in.-diam niobium single crystals grown by strain annealing and to compare their perfection to those grown by zone melting. Characterization of these crystals was more conveniently accomplished by means of X-ray than by metallo-graphic techniques. EXPERIMENTAL PROCEDURE Specimen Preparation. Zone-melted crystals of 1/4 in. diam were produced by the standard electron-beam zone-melting technique. The swaged and cleaned rods were outgassed, in the solid state at a temperature near its melting point, at a rate of 12 in. per hr, and single crystals were grown by making two molten passes at 2 in. per hr. By maintaining a zone length of 4 to % in., very uniform single crystals several inches long were obtained. For the strain-annealed crystals, an induction heater was used, in preference to other types of heating, to take advantage of the good penetration of large sections. A five-turn coil, 1 in. long, operating at 10 kc and powered by a motor generator, was contained in a vacuum chamber. The rod, suspended from the upper end, was raised through the coil for both recrystallization and crystal growth. In preliminary work single crystals of the same material were also grown with single and multiturn coils powered by a 450-kc generator. A vacuum of 2 X 10-6 Torr was maintained at temperatures up to 2400°C. Starting with electron-beam-melted ingots of 21/2 in. diam, the analysis for which is given in Table I, the material was cold-swaged to the desired cross section of 1/4 and 1/2 in. diam and then recrystallized. The rods were then strained in a tensile machine and converted to single crystals by passing through the induction coil. As with zone melting, control of orientation is possible by the use of special procedures. Other investigators, see for example Williamson and smallman,4 have reported that orientation control may be achieved by a bending technique. In the present work the strained rod is partially lowered through the coil to start the growth of the crystal. Then it is removed and bent at a point in the poly crystalline portion. Finally, it is returned to the chamber and growth is continued "around the corner". This procedure has certain limitations. If the bending operation exceeds the critical strain, recrystallization may take place. Also, the amount of bending which can be imparted to the rod is limited by coil geometry, and up to now has been 10 deg. However, by repeating the bending and growing operations it should be possible to attain any desired orientation. In preparation for X-ray examination, single crystals were sectioned and planed by means of the spark-erosion technique. To obtain the maximum reflected intensity, the (110) plane was exposed for examination. They were then etched 3 to 5 min in a mixture of con-

Jan 1, 1967

By W. A. Backofen, D. L. Holt

Push-pull fatigue tests have been carried out at 4.2°K, 77oK, and room temperature on two poly crystalline materials of widely different stacking-fault energy (?): pure copper (? - 70 ergs per sq cm) and the Cu-8 wt pct A1 alloy (? - 2.8 ergs per sq cm). Constant stress-amplilude was imposed and measurement was made of the plastic-strain amplitude (ep) at saturation. Lives extended from 104 to 106 cycles. Designating lives at the various temperatures by NRT, N77, and N4.2. the ratios N77/NNT and N4.2/N77 ranged from 3.5 to 18 under the condition of common Ep . Metallo-graphic examination revealed different crack morphology in Cu-8 Al fatigued at room temperature, and at 77" and 4.2oK. At room temperature, cracks lay in or near grain and lain boundavies; at 77o and 4.2oK. cvacks were transcrystalline. Tests on single crystals of Cu-8 A1 showed that such a change in the cracking mode in polycrystallitle material accounted for a factor of- about 3.25 in N77/NRT . The longer life at lower tewperatztre (conslant cp) has heels attributed to two deuelopinents: a reduced production of the dislocation tangles and subgrain boundaries which serve as paths of rapid cracking, and suppression of oxygen chetni-sorption at the crack tip It was concluded that in both materials the luller accounted for an extension of the life at 4.2oK beyond that at room temperature by a factor of 15. XV ECENT experiments on the fatigue of Cu-A1 alloys in the so-called high-cycle range (greater than lo4 cycles) have emphasized the importance of stacking-fault energy (y) as a quantity affecting crack propagation rate and fatigue life.1,2 It was found in comparisons at essentially fixed plastic-strain amplitude that crack growth rate decreased by a factor of about 5 over the composition range from copper (? - 70 ergs per sq cm) to Cu-8 wt pct Al (? - 2.8 ergs per sq cm). The argument was made that, when stacking-fault energy is high, cross slip and climb are favored, so that dislocation tangles and/or subgrain boundaries form more readily under cyclic loading. Since the boundaries and tangles act as paths of rapid crack propagation ,3, 4 life is shortened as a result. However, when stacking-fault energy is reduced (as by alloying), cross slip and climb become more difficult, with the result that substructure formation is retarded and growth rate is also reduced. A purpose of the present work was to investigate the substructure effect in relation to temperature. As temperature is lowered, ? is varied only slightly (if at all), but decreased thermal activation can interfere with cross slip and climb. Thus substructure formation could be curtailed and life increased. Fatigue life in the high-cycle range is also known to be strongly influenced by environment. Working with copper, Wadsworth and Hutchings observed that life in a vacuum of 10-8 mm Hg exceeded life in air by a factor of 20.5 They isolated oxygen as the agent that furthered cracking. While the details are still unclear, a requirement in any mechanism of oxygen-accelerated cracking is that there be chemisorption at the crack tip. That could prevent welding on the compression half cycle,= interfere with reversal of slip,1, 6 or aid in breaking metal-metal bonds at the crack tip.5'7 In the work being reported here, temperature was lowered by immersion in liquid nitrogen and helium, which also served to reduce both the oxygen concentration and chemisorption rate. A possible effect upon life, i.e., a lengthening, had to be recognized. Several researchers have determined fatigue lives at low temperatures presenting their results in the form of stress amplitude (S) vs cycles in life (N) curves.8-11 Such curves reflect, primarily, the fact that metal is strengthened by lowering temperature; effects of substructure and changing environment tend to be masked. The difficulty can be overcome by comparisons based on identical plastic-strain amplitudes, and in the present work the dependence of life on both plastic strain and stress amplitude was established. EXPERIMENTAL Materials. The principal materials were polycrystal-line copper (? - 70 ergs per sq cm)" and the Cu-8 wt pct Al alloy (? - 2.8 ergs per sq cm),I3 the latter being near the limit of solubility of aluminum in copper and having, therefore, the lowest stacking-fault energy in the CU-Al system. Specimens were machined from 0.118-in.-diam cold-swaged rods of high-purity (99.999 pct) copper and the Cu-8 Al alloy, the latter produced initially in a graphite boat by induction vacuum melting a mixture of 99.999 pct Cu and 99.99 pct Al. The machined specimens were annealed to produce mean grain diameters of about 0.070 mm in copper and 0.190 mm in the alloy. Specimen dimensions are given in Fig. 1. Values of the tensile yield stress, ultimate strength, uniform strain (determined by the Considgre construction), and reduction of area, for both materials at 4.2oK, 77oK, and room temperature, are listed in Table I. The tensile apparatus in which these results were obtained has already been described.14 Apparatus. Specimens were fatigued in push-pull with a machine that is illustrated schematically in Fig. 2. The specimen is first soldered into the top grip (1) with Woods metal, and the grip is then screwed into the inner tube (2) which is connected to the drive rod of the Goodmans vibration genera-

Jan 1, 1968

By P. F. Gnirk, J. B. Cheatham

Single bit-tooth penetration experiments under static load were conducted on six rocks at confining pressures of O to 5,000 psi using sharp wedge-shaped teeth with included angles ranging from 30 to 120° In general, the force-displacement curves for all rocks exhibit an increasingly nonlinear and discontinuous behavior with decreasing confining pressure. The confining pressure at which a rock exhibits a macroscopic transition from predominantly ductile to predominantly brittle behavior during penetration vmies from about 500 to 1,000 psi for the limestones to greater than 5,000 psi for dolomite. The correlation between calculated values of force per unit penetration based on plasticity theory and experimental values is quite encouraging, even at confining pressures as low as 1,000 psi A qualitative correlation between volume of fragmented rock per unit energy input for a single bit-tooth and drilling rate for microbits appears to exist over a confining pressure range of 0 to 5,000 psi. INTRODUCTION Laboratory experiments utilizing a small-scale drilling apparatus have demonstrated that penetration rates are reduced considerably as a result of increasing the confining pressure from atmospheric to a few thousand psi?-3 This undesirable situation can, in general, be attributed to a combination of decreased efficiency of chip removal at the bottom of the borehole, increased rock-failure strength, and a possible change in the mechanism of chip generation and rock fragmentation with increasing confining pressure. To more fully understand the principles underlying the last circumstance, it is the purpose of this investigation to experimentally study the mechanism of single bit-tooth penetration into dry rock at low confining pressures and, in particular, to establish the confining pressure at which the penetration mechanism may undergo a brittle to ductile transition for various rock types commonly encountered in drilling. Confining pressure as used here refers to the differential pressure between the borehole fluid pressure and the formation-pore fluid pressure. EXPERIMENTAL PROCEDURE Using an experimental apparatus previously described: a single, sharp wedge-shaped tool was forced under a "statically" applied load into an effectively semi-in finite dry rock sample subjected to a prescribed confining pressure. To prevent the invasion of the con fining-pressure fluid into the pores of the rock sample during penetration, the exposed surface of the rock was jacketed with a layer of silicon putty.* Electrical instrumentation incorporated into the apparatus yielded a graphical plot of force on the tool as a function of penetration or displacement of the tool into the rock during an experiment. During the course of the experimentation the following conditions were maintained constant: (1) pore pressure — atmospheric (i.e., the rock was dry); (2) temperature — 75F; (3) rate of loading — essentially static (approximately 0.002 in./sec); (4) bit tooth — a sharp wedge-shaped tool loaded normal to the rock surface; (5) rock surface — smooth and flat; (6) drilling fluid — hydraulic oil; and (7) maximum depth of penetration — approximateiy 0.1 in. In addition, each experiment was performed on a different rock sample so the rock surface is free of a layer of cuttings and of any previous indentation craters. The influence of the corners of a borehole was neglected, since each rock sample was cemented inta a section of aLuminum tubing to simulate a semi-infinite body. Indentation experiments were made on a sandstone, two limestones, a marble, a dolomite and a schist with a 60' bit-tooth over a range of confining pressures from atmospheric to 5,000 psi and at a constant confining pressure of 1,000 psi for a variety of bit-teeth with angles ranging from 30 to

Jan 1, 1966

By K. E. Gray, M. S. Seth

Equations of elasticity for transversely isotropic, axisymmetric, homogeneous, porous media exhibiting pore fluid pressure were formulated. Using an analogy between thermal and porous body stresses, it was shown that the solution for a transversely isotropic porous body may be obtained by incorporating body forces and the stresses due to a boundary load into the corresponding solution for the thermal stress problem. Equations of elasticity ad the thermal analogy method were used to determine transient horizontal, tangential, and vertical stresses and radial displacement in a semi-infinite cylindrical region when either a constant pressure or a constant rate of flow is maintained at the wellbore. The vertical and tangential displacements are zero from the conditions of the problem. A numerical analysis was made of the solutions obtained by using a digital computer to determine the relative influence of each system variable. Considering rock as a porous body with internal fluid pressure generally gives results significantly different than considering the rock to be nonporous; the directional character of rocks leads to significant differences as compared to results based upon the common assumption of isotropy. Stress gradients are high near the wellbore but die out away from the well. Radial stresses are compressive or neutral, whereas tangential stresses are tensile, neutral or compressive, depending upon the boundary conditions and physical properties of the system Vertical stresses are compressive for an unbounded system. For constant wellbore injection rate, the vertical stress is proportional to the rate of fluid injection and decreases with time, whereas the radial and tangential stresses increase with time. At a given location, the radial displacement generally is very dependent upon time. INTRODUCTION A realistic appraisal of the state of stress in subsurface rock formations would be of considerable interest and use to the petroleum industry. For example, knowing the state of stress in proximity to a wellbore would be of fundamental importance in designing a fracturing operation or, more important, of clearly understanding the conditions necessary to produce rock failure of desired dimensions and geometry. Understanding conditions necessary for rock failure at the wellbore would also be of utility in a preventive sense. For example, borehole stability is an important consideration for many rock formations, and knowledge of the stress state at and near the wellbore under conditions of substantial pressure gradient due to fluid flow would be of great value. When fluid flows through a porous body which is initially at some uniform stress level, the following forces generate stresses at any point in the body. (1) Forces due to nonuniform pressure distribution. With increasing pressure the elements of a body are compressed. Such compression cannot proceed freely in a continuum when the pressure is not uniform throughout, and thus, stresses due to flow of fluid are set up. (2) Pore fluid pressure. This gives rise to normal stresses whose value at any point is the product of areal porosity and the fluid pressure. Although the fluid exerts uniform pressure, the stresses it creates in an anisotropic body may not be the same in all directions since the areal porosity in an anisotropic porous body is a direction-dependent quantity. This consideration leads to the concept of directional porosity. (3) Body Forces. The flow of the moving fluid imparts a force to the rock matrix, the magnitude of which depends upon the pressure

Jan 1, 1969

By Ursula E. Wolff

The precipitation of carbides from an alloy containing 33 pct Ni, 21 pct Cr, balance iron, was investigated electron microscopically by means of extraction replicas and thinned metal foils. Annealing temperatures ranged from 565°to 870°C and up to several thousand hours. M23C6 precipitated in pain boundaries, incoherent and coherent twin boundaries in that sequence. The orientation relationship between carbides and austenite matrix was determined and correlated with the morphology of the carbides and with the type of boundary in which precipitation occurred. In large-angle grain boundaries, as well as in coherent twin boundaries, the carbides had the same orientation as one of the adjacent pains. These carbides formed sheets of individual flakes with shapes related to the orientation of the boundary. In incoherent twin boundaries carbides precipitated in ribbons composed of pavallel rods. An unidentified subcarbide was found to precede precipitation of M23C6 in these boundaries. The M 23 C6 rods had a kind of fiber texture with (110) parallel to the long dimension of the rods and ribbon, and with orientations of both of the adjacent twin-related austenite crystals Predominant in the texture of the carbide. A hard sphere crystal model has been used to discuss orientation and morphology of the carbides in terms of free volume and vacancies available in the boundaries. A number of papers have dealt with the morphology of chromium carbide (M23 C6) precipitated in austenitic stainless steels.1"7 In all these investigations, the carbides were examined in the electron microscope by means of extraction replicas. With this technique, the carbides retain the spatial distribution they had in the bulk sample. However, since the matrix is dissolved in the process, the particles can turn in an unpredictable way; and the orientation relationship between matrix and carbides cannot be established. In this paper the results of studies on extraction replicas and on thinned metal foils are reported. These studies were undertaken to determine the matrix-to-car bide orientation relationship, and to correlate the orientation of the carbides with their morphology. PROCEDURE The material used was an austenitic alloy with 33 pct Ni, 21 pct Cr, balance iron, containing approximately 0.05 pct C. Coupons of 1.25-mm sheet were first solution-annealed at 1050°C for 15 min and air-cooled. Then, to precipitate the carbides, samples were isothermally annealed in the range from 565" to 870°C for times up to several thousand hours. All further specimen-preparation procedures were carried out after the final anneal. Carbon extraction replicas from polished and etched surfaces were made with 10 pct bromine in methyl alcohol.' Thin foils were prepared from punched-out 3-mm-diam disksg which fit into the electron-microscope holder. The disks were prethinned by grinding to approximately 0.5 mm thickness, and then electro-polished in a polytetrafluoroethylene holder1' with a solution containing 5 pct perchloric acid in acetic acid to which 10 g per 1 Cro3 and 5 g per 1 nickel chloride were added (etchant modified from that of Briers et al."). This solution dissolves neither the carbides nor the austenite around the carbides preferentially. By using extraction replicas, electron micrographs and selected-area electron-diffraction patterns were taken from the same carbide arrays. By using thin foils, electron micrographs were made from a grain boundary area containing carbides. Electron-diffraction patterns were then taken from the same area and from each of the adjacent grains separately. In this manner, the orientation of each grain could be determined without interference by the carbide pattern. A peculiarity of extraction replicas should be pointed out. After the matrix is etched away, the carbide arrays float freely in the etching and washing solutions, and are held in place only at the anchoring points in the carbon replica. When the replica is picked up with a screen the carbide arrays tend to flip to one side. Thus, while the surface features are preserved, the original arrangement of the carbides may severely and unpredictably be disturbed whenever the specimen contains large amounts of interconnected carbides. Nevertheless, it is possible to correlate the different morphologies of the carbides with the type of boundary in which they have precipitated. RESULTS 1) Extraction Replicas. Fig. 1 shows that the grain boundaries usually are curved, multicornered surfaces of random orientation. The coherent twin boundaries (which are (111) planes) cut a grain into parallel slices. Incoherent twin boundaries occur at the ends and on the steps of twins and are often narrow, parallel-sided strips which are much longer than they are wide. Different morphologies can clearly be distinguished for the M23Ce carbides precipitated in each of these types of boundaries, and agree well with those observed by kinzel.2 The kinetics of this precipitation has been investigated." The first carbides precipitate in junctions of three grain boundaries and fan out from there into the adjoining boundary surfaces, Fig. 2(a). These carbides are oriented randomly, Fig. 2(b), and become coarser and thicker as annealing time increases. The large-angle grain boundaries are next to fill

Jan 1, 1967

By K. A. Jackson, J. D. Hunt

A new classification of eutectics is proposed, based on tlze entvopies of wzelting of the tuio eutectic phases. The clnssification was used to predict suitable tvansparent analogs of the metallic systems. Experimental confir?nation loas obtained for the theovetical shape of the lamellar solid-liquid interface, fov the fault mechanisms of lanzellar spacing changes, and for the development of low-energy solid-solid boundaries between the lamellae. An explanation is presented to account jov the irvegular and coinplex regular structures zrhich are found in some eritectic systems. FrOM experimental observations, single-phase materials can be divided into two groups according to their solidification characteristics, those that grow as faceted crystals and those that do not. acksonl' showed from thermodynamic reasoning that the type of growth depended on a factor a which was almost thg entropy of melting. Most nonmetals have high entropies of melting (a greater than 2) and grow with crystalline facets. Most metals have low entropies of melting (CY less than 2) and grow almost isotropically with no facets. The authors propose that eutectics may be classified in a similar manner. There are three groups of eutectics, those in which both phases have low entropies of melting, those in which one phase has a high and the other phase has a low entropy of melting, and those in which both phases have high entropies of melting. Lamellar or rodlike structures are formed in systems in which both phases have low entropies of melting. In these alloys dendrites of either phase may be formed, when the alloy is rich in the relevant component. Examples are Pb-Sn, Sn-Cd, Pb-Cd, Sn-Zn, Al-Zn. Irregular, Fig. 14((), or complex regular, Fig. 14(b), structures are formed in alloys in which one phase has a high entropy of melting and the other has a low entropy of melting. Examples are A1-Si, Zn-MgzZnll, Pb-Bi, Sn-Bi. When the alloys are rich in the low entropy of melting phase, dendrites are formed; when the alloys are rich in the high entropy of melting phase, faceted primary crystals are produced. These crystals are sometimes called hoppers or pseudodendrites. In this work the term dendrite will only be used to describe nonfaceted primary crystals. Dendrites are not formed during solidification in high entropy of melting single-phase materials. The third group of eutectics includes alloys in which both phases have high entropies of melting. Each phase grows with a faceted solid-liquid interface. Since most metals do not have high entropies of melting, metallic examples in this eutectic group are rare. However they may occur between some intermetallics and semiconductors or semimetals such as silicon, germanium, and bismuth. Attempts have been made to study eutectic solidification visually by watching the growth process.374 Since metals are not transparent, the observations had to be made on external surfaces. This difficulty can be overcome by using transparent analogs of the metallic systems. As was mentioned earlier, most single-phase compounds have entropies of melting greater than 2 and so grow as faceted crystals. Recently organic materials with entropies of melting less than 2 were investigated.' These materials grow in exactly the same way as the low entropy of melting metals. When the materials are pure, they grow with a solid-liquid interface parallel to an isotherm; when they are impure, cells or dendrites are formed. Since these materials are transparent, have low melting points, and even have cubic structures, they should be ideal for making up transparent analogs of the metallic eutectics. The purpose of the present work was to investigate these organic eutectics and to see whether this quite different series of eutectics could be classified in the same way as the metallic systems. The observations made on the organic alloys are also discussed with reference to the current theories of lamellar growth. Explanations are proposed to account for the structures formed in the other eutectic groups. EXPERIMENTAL Thin cells containing the organic alloys were uni-direction ally solidified on a specially constructed microscope stage.' Uniform growth rates were obtained by moving the cells, with a motor drive, through a fixed temperature gradient, so that the solid-liquid interface remained stationary with respect to the microscope objective lens. The cells were made by fusing two microscope cover slides 7/8 by 7/8 by 1/100 in. together on three sides, leaving a gap of 1 to 3 mils between the slides, and these were filled by surface tension. A preliminary investigation of the phase diagram between two components could be made very rapidly. One side of the cell was filled with component A and the other side with component B. Since only a small amount of mixing could occur every composition from pure A to pure B was present in the cell. When the cell was placed in the temperature gradient a pictorial representation of the phase diagram was obtained. Eutectics, peritectics, "interorganics", and solid -solid transformations could be readily detected. Fig. 1 shows part of a eutectic phase diagram. The Sample was first grown slowly then stopped. The two

Jan 1, 1967

By T. O. King, Y. P. Gupta

The self-diffusion of sodium in two sodium silicate liquids was measured in the temperature range 850" to 1500°C by the capillary-reservoir technique. Radioactive Na 22 was used as the tracer. The total count and autoradiographic methods were used for determination of the total Na 22 depletion and diffusion profiles of the dqy-used specimens. The diffusion coefficients obtained by the autoradiographic technique are slightly smaller than those obtained by a total count method. Error analysis of the two methods suggests that more confidence be placed in the results of the total count method. The experimental results were analyzed in terms of the existing activated rate process theory. The activation energy for diffusion was shown to decrease markedly as the temperature increased. This was attributed to a variation in the heat of activation with temperature, probably related to a change in the distribution of anions associated wilh the cation. In terms of a model, suggested for diffusion in liquid silicates, differences in the aclivation energies for diffusion and electrical conduction may arise from the effect of the electric field applied in conduction measurements. It is generally accepted that liquid silicates consist of cations and an equilibrium distribution of complex anions determined by temperature and composition. Transport properties in molten silicates are of interest, not merely because of their relevance to the kinetics of pyrometallurgical reactions and glassmak-ing processes, but also because they are useful to development of the theory of such ionic liquids. Self-diffusion is one such transport process that may, if studied for liquid silicates of widely varying compositions, indicate structural changes through changes in the activation energy for diffusion. The self-diffusion of calcium, silicon,' sulfur: aluminum, 4 and oxygenS in lime-alumina-silica melts and of iron6 in molten iron silicates have been measured. Unfortunately, the errors in some of the reported activation energies for diffusion are too large to allow firm conclusions concerning structure and the mechanism of the diffusion process to be drawn. The research reported here was a study of the self-diffusion of sodium in liquid sodium silicates. The soda-silica system was chosen since: i) a reasonable composition range can be covered in the binary system at moderate temperatures; ii) suitable isotopes of sodium (radioactive Na 22 and NaZ4) can be obtained; iii) data on the electrical conductivity and viscosity of sodium silicate liquids are available. However, the range of composition actually used in diffusion experiments was limited, to 20 to 35 wt pct soda, by the relatively high viscosity of silica-rich compositions and by evaporation of soda from basic melts. EXPERIMENTAL PROCEDURE The capillary-reservoir technique was used, wherein a radioactive tracer, Na 22, incorporated in the capillary melt, was allowed to diffuse out of the platinum capillary tube into a large reservoir of silicate liquid containing a chemically identical melt, but without radioactive tracer. After a specific diffusion time, both the total depletion in the tracer concentration and concentration-distance profiles of the diffused samples were measured by procedures to be described later. The diffusion cell assembly was similar to that used by Koros and King.' The temperature of the diffusion cell was measured with a calibrated Pt, Pt-10 pct Rh thermocouple located at the center of the liquid reservoir. The same thermocouple was used to obtain the temperature profile in the reservoir. The temperature at the top of the reservoir was slightly higher (2°C) than that at the bottom, to minimize convection in the capillary tubes, which were placed, open end up, in the reservoir. Convection was not expected to be a problem since the length-to-diameter ratio of the tubes was about 12:1 and the maximum capillary diameter was 1 mm. The diffusion cell was heated in a molybdenum-wire resistance furnace, previously used by Koros and King, but somewhat modified. A Pt, Pt-10 pct Rh thermocouple enclosed in an alumina tube and located near the furnace winding was used in conjunction with a preamplifier and Micromax proportional controller for temperature control, within 4°C, at temperatures near 1500°C. Before starting a diffusion run, the furnace was heated to the desired temperature and an alumina guide assembly for the capillaries was slowly lowered to within 2 cm of the liquid reservoir. The capillaries were thus heated to about the temperature of the bath. The run was started by lowering the assembly till the open ends of the capillaries were about 1 cm below the surface of the liquid. The run was ended by raising the assembly to about 15 cm above the liquid bath. Later, the sample assembly was slowly withdrawn from the furnace. Six diffusion samples were usually run at the same time. Three runs made with the open ends of the capillaries down were discarded because in the majority of these samples air bubbles trapped at the open end were observed. Some glass adhered to the outside of the capillary on withdrawal. This was carefully removed and used to check that the Na 22 activity in the sink remained at a low level. Materials. Nonradioactive sodium silicates were prepared by melting, in a platinum crucible, weighed quantities of sodium carbonate and powdered silica. To prepare radioactive sodium silicates, Na2 obtained in HC1 solution, was first checked for radioactive impurities by obtaining a y-ray energy spectrum, then the chloride ions were removed by anion-ex-

Jan 1, 1968

By K. T. Koone, R. J. Blackwell

One of the more important problems to be solved in designing a miscible flood is related to the size of the solvent bank used. Size of the bank may be critical to economic success. Too large a bank loses money; too small a bank may deteriorate and fail to maintain the miscibility needed for high recovery. An important factor in deterioration of a small bank is permeability channeling. In a highly stratified reservoir, solvent speeds ahead in the more permeable zones and mixes laterally with fluids bypassed in adjacent, low-permeability strata. Numerical solutions have been obtained .for the differential equations that describe the movement of a slug through a two-layer system in which mixing occurs both in the direction of flow and transversely. The solvent slug is assumed to have the same density and viscosity as the resident fluid and the pushing fluid. These solutions have been verified by comparing them with similar concentration profiles obtained in the laboratory in a 36-ft stratified model packed with glass beads. The theoretical study revealed that when the dominant mechanism causing a bank to fail is lateral mixing the bank size needed for a given recovery may increase with length rather than decreasing as the square root of reservoir length, as suggested by one-dimensional mixing theory. From a comprehensive examination of the variables, a generalized correlation is developed that relates strata thicknesses, bank size, fluid velocity, mixing coefficients, system length and simple solvent-resident fluid phase behavior to the area miscibly swept. INTRODUCTION Miscible displacement, or solvent flooding, continues to receive widespread attention as a method for increasing oil recovery over that possible in conventional gas-drive or waterdrive projects. A basic economic requirement in the application of such processes is the use of as little solvent as possible. A basic physical requirement is that enough solvent be used to maintain miscibility. Economics places an upper limit on the size of a solvent slug, and physical considerations establish a lower limit. Consequently, the practicality of any given miscible process requires that the economic limit be greater than the lower limit imposed by physical requirements. Procedures exist for determining the economic limit; however, procedures for determining realistic minimum bank sizes exist for only special reservoir situations. In the past, bank size has usually been selected on the assumption of a piston-like displacement for which only longitudinal mixing is important. This assumption leads to the favorable conclusion that bank size, expressed as per cent of pore volume, is inversely proportional to the square root of length. Collins considered the problem of transverse mixing of solvent with fluids in bypassed zones with the assumptions that no forward mixing occurs and that the concentration is uniform in the permeable stratum of interest. 1 Lauwerier considered a mathematically similar problem in thermal recovery operations.2 Their work suggests the much less favorable conclusion that bank size could be directly proportional to the length or even higher powers of the length. This paper considers the physical behavior of a small solvent bank as it moves through a real reservoir, without imposing many of the restrictive assumptions of past treatments. To facilitate mathematical description, an idealized, two-layer model that permits mixing both laterally and in the direction of flow will be considered. A calculation procedure for solving the descriptive equations will be developed for a displacement involving fluids of equal density and viscosity. In addition, laboratory experiments designed to check the computational results will be described, and the coincidence of calculated and observed results will be discussed. The use of many solutions for a variety of bank sizes, strata thicknesses and characteristic system lengths to develop a usable correlation between

Jan 1, 1966

By Richard R. Zupp, David A. Stevenson

An experimental method to determine the carbon activity in various solid solutions was developed. Samples of the solid solutions and an Fe-C reference sample were equilibrated with respect to carbon content by annealing them in a Hz-CHI gas mixture in a closed cell. The carbon content of each sample was determined, and the carbon activity was obtained from the carbon content of' the reference sample and well-established data for the dependence of the carbon activity on the carbon content in Fe-C alloys. The influence of vanadium on the activity of carbon in austenitic Fe-C-V alloys at 1000°C was determined by this technique. A general semiempirical correlation was developed to describe the dependence of the activity coefficient of- carbon on the composition of ternary austenitic iron-base alloys containing interstitial carbon and a substitutional solute. The correlation is particularly useful in predicting the partitioning of- carbon between various alloys. THE influence of substitutional solutes on the activity of interstitial solutes in metallic solid solutions is important in the theory of alloy phases. Solid solutions of particular interest are the fcc austenite phases of ternary Fe-C-Z systems, in which carbon is the interstitial solute and Z represents any substitutional solute. Carbon-activity data are also needed in these solid solutions to solve practical problems; the quantitative treatment of diffusion-controlled transformations' is an examvle. Experimental information is available for ternary austenitic solid solutions containing Mn,2 Si,2 and A16 as the substitutional solute. Because qualitative preliminary studies indicated that vanadium appreciably decreases the carbon activity,14 the present investigation was undertaken to determine the influence of vanadium on the activity of carbon in austenite. Although Flender and ever" measured carbon activity over a range of compositions in the Fe-C-V system, they were primarily interested in determining phase boundaries in the ternary system, so most of their measurements were outside the composition range for stability of single-phase austenite. Petrova and Shvartsman' also made limited measurements of the carbon activity in Fe-C-V alloys. The dependence of the carbon activity on the carbon content of an alloy may be determined by passing COCOz or H2-CH4 gas mixtures of carefully measured composition over the alloys, determining their equilibrium carbon content, and utilizing the relevant equilibrium relationships. smith16 used this technique with both CO-COZ and HZ-CH4 gas mixtures to determine the dependence of carbon activity on carbon content in pure Fe-C alloys. His data, which are in good agreement with those of some previous and subsequent investigators,6'17 but not with those of others,lfl'ao are usually considered to be the most reliable. Although the same method can be applied to Fe-C-Z alloys, it is difficult experimentally, because the appropriate gas mixtures are almost pure CO or Hz. A simpler technique is to simultaneously equilibrate the Fe-C-Z alloys and pure Fe-C alloys with the gas mixtures, and then use Smith's data to determine the carbon activity in the pure Fe-C alloy. A number of investigators have employed this technique. others Have used the partitioning of carbon at the interface of a diffusion couple prepared from an Fe-C alloy and a Fe-C-Z alloy. In the present study, a closed-cell method was developed by which carbon was selectively transferred via a gas medium between pure Fe-C alloys and Fe-C-V alloys which were not in physical contact. A similar method was developed independently by Heckler and winchel14 and used to study the Fe-C-Ni system. EXPERIMENTAL METHOD A schematic diagram of the experimental arrangement is shown in Fig. 1. In a typical experiment, a 5-g Fe-C sample was placed in one compartment of a quartz cell, and a 5-g Fe-V sample was placed in each of the other compartments. The cell was evacuated, outgassed, backfilled with approximately 125 Torr of hydrogen, and sealed. After being placed in a fur-

Jan 1, 1967

By Edward J. Felten

Binary Cr-A1 alloys containing from 2.5 to 30 wt pct Al and 0.7 wt pct Y were heated in oxygen, air, and nitrogen between 1000" and 1200°C. The reacLivity of the alloys was found to be dependent both on the alloy composition nnd the nature of t he atmosphere. In oxygen, nllojs containing up to 15 to 20 wt pct A1 reacted to produce an external scale of Crz03 and a subscale consisting Predominently of Al203. Alloys contazning 20 to 30 wt pct A1 react in oxygen to produce an A1203 external scale and little m no subscale. The latter alloys were markedly more oxidation resistant than those of low alurninum content. In air, the alloys on which an external Crz03 scale was formed were found to be permeable to nitrogen ns evidenced by the copious amomts of chromium and aluminum nilrides observed ns part of the subscale. The reactizities in nir (or nitrogen) of these alloys increase <m their aluminurn contents increase. However, alloys on which Al,O, us an external scale is formed were nol culnerable to nccelerated attack in air, and no eltldence of nitvide subscnles were observed. For all alloys, yttrium serwed pYimarily to improve oxide adhrence. THE role of chromium in the oxidation resistance of Fe-Cr alloys &apos;-&apos; and that of aluminum in Fe-Cr-A1 al10s&apos; has received considerable attention in recent years. This is understandable since many of these alloys have excellent oxidation resistance due to the formation of either a Cr203 or a-Ala03 film between the metal and the oxidizing atmosphere. Small additions of yttrium or other rare earth metals are effective in preventing spalling of the protective oxide from the metal substrate."" In contrast, little is known regarding the oxidation resistance of Cr-A1 alloys, although some work has been done by Tumarov et a1.&apos; The poor niechanical properties exhibited by Cr-A1 alloys make them undesirable for use as structural components, but their use as coatings cannot be disregarded. The use of chromium-rich aluminide coatings for refractory metal alloys is an example of the potential use of this type of sytem. The purpose of this work is to examine the oxidation behavior of Cr-A1 alloys containing 2.5 to 30 wt pct A1 and 0.7 wt pct Y. The effects of temperature, atmosphere, and thermal cycling have been determined. EXPERIMENTAL PROCEDURE The alloys used in this investigation can be divided into two groups. Those containing 2.5, 5, 7.5, and 10 wt pct A1 and 0.7 wt pct Y were extensively evaluated in the temperature range from 1000" to 1200°C. Alloys containing 15, 20, 25, and 30 wt pct A1 and 0.7 wt pct Y were tested only at 1200°C. All of the alloys were prepared by standard arc-melting techniques in the form of cylinders approximately 4 in. long and 19 in. in diam. Wafers were cut from the cylinders and subsequently subdivided into rectangular coupons. The alloys were brittle and therefore some cracks were found in almost all specimens. The coupons were prepared for oxidation by mechanically polishing through 600 grit Sic paper, and were thoroughly degreased just prior to testing. Two types of oxidation experiments were conducted, namely; cyclic tests in which the specimens were examined and weighed after each 2 hr exposure, and continuous thermal balance tests run in a controlled atmosphere (oxygen, air, or nitrogen) for 20 hr. In the former test the spalled oxide was not included when the specimens were weighed. The physical condition of a specimen was noted visually after each cycle and testing was continued either to failure or until the performance of the specimen was well characterized. Both Micro and Semi-Micro Thermal Balances (Ains-worth) were used in the continuous tests. The oxidized specimens were sectioned and prepared for metal log raphic examination. The specimens were polished through 600 grit Sic paper. After polishing through 6 and l p diamond, a final mechanical polish with Linde B-Alz03 was used. Specimens containing 2.5 pct A1 were etched electrolytically using a 10 pct oxalic acid solution at 4 v for about 2 sec. Selected specimens were examined in the electron microprobe analyzer. Oxide specimens were examined by standard X-ray diffraction techniques. EXPERIMENTAL RESULTS For convenience, the test results have been broken down according to the exposure temperature, and further subdivided according to the type of test and atmosphere employed. Because of the poor quality of the specimens a larger than normal amount of scatter was observed in the measured rate constants. Also, the evaluation of the weight gain data was done on a somewhat arbitrary basis and may not be truly representative. However, the results obtained do show a significant trend in behavior regarding both alloy composition and the nature of the oxidizing atmosphere. I) Oxidation Behavior at 1000°C. A) Continuous Oxidation estsin Oxygen. This series of experiments was run in the Ainsworth Micro-Thermal Balance using pure oxygen at a pressure of 76 mm Hg. Under these conditions all specimens oxidized in accordance with the parabolic rate law over a major portion of the exposure time; the rate constants appear in Table I. The oxide formed externally on all specimens was predominantly Cr,O,, which was generally adherent. In some cases a slight amount of spalling in the form of a fine powder was noted. a-A1203 was observed as a subscale, along with Yz03 in all alloys. Alloys containing up to 7.5 wt pct A1 oxidize more rapidly than the Cr-0.7Y alloy.

Jan 1, 1970

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 L. A. Geoffrion, R. H. Perkins, J. C. Biery

Densities of cerium metal and several lour-melting binary cerium alloys were measured over the range 25° to 800°C. A rolumeter, using NaK as working fluid, was used to obtain the data. The cerium, Ce-Co, Ce-Ni, and Ce-Cu alloys all exhibited an increase in density on melting, while a Ce-Mn alloy expanded on melting. FOR the proper design of a nuclear reactor, the change in density of the fuel with temperature must be known. This is especially important in a system utilizing molten fuel, such as LAMPRE (Los Alamos Molten Plutonium Reactor Experiment), since a relatively large change in density usually occurs during the solid-liquid transition. The fuel for LAMPRE is a Pu-2.5 wt pct Fe alloy with a melting temperature of 410°C. However, limitations in reactor design with this fuel have led to consideration of other plutonium-containing alloys for use in future generations of this type of reactor. Several ternary alloys containing plutonium and cerium as two components have satisfactorily low melting points. The system that at the present time appears to be most acceptable is Pu-Ce-Co; it exhibits little change in melting temperature with wide variation in plutonium concentration. Other alloys that have received some consideration contain nickel, copper, and manganese as the third constituent. The proposed fuel alloys are difficult to handle experimentally in the 25" to 800°C temperature range since they oxidize readily, react with many solvents, and contain a poisonous fissionable material. In addition, in this temperature range the alloys pass through the solid-liquid transition. Several techniques are available for measuring the densities and volume coefficients of expansion of solids or liquids. However, the only apparatus that appears suitable for measuring expansion coefficients over this temperature range and through the phase transition is a volumeter. In a volumeter, the indicating medium must be essentially inert to and insoluble in the material being studied. It must also possess a low vapor pressure over the operating temperature range, and its coefficient of expansion must be accurately known. One material that is satisfactory in nearly all of these respects is the alloy Na-78 wt pct K, which melts at -10°C and has a vapor pressure of 860 mm Hg at 800°C. This relatively high vapor pressure at 800°C requires an overpressure of an inert gas to prevent boiling. While a volumeter is capable of determining accurately the volume coefficients of expansion of materials, it cannot be used for absolute density measurements. Therefore, a density determination at a known temperature must be coupled with the volumeter measurements to give all the desired data. The weight-loss technique using immersion in bromobenzene at room temperature proved to be satisfactory. The preliminary work that was done on this experimental program involved developing and calibrating the equipment, and measuring the densities and volume coefficients of expansion of cerium and some low-melting binary cerium alloys. The complications that are caused with the introduction of plutonium into the system were avoided until the equipment was proved to be satisfactory and until experience was gained in its operation. It is this first phase of the experimental work that is described in this report. DESCRIPTION OF EQUIPMENT AND OPERATING PROCEDURE The NaK volumeter is shown schematically in Fig. 1. Basically, the equipment consists of two weld-sealed stainless-steel containers of nearly identical volume. One container holds a tantalum crucible and the specimen being measured; the other contains a tantalum crucible and a tantalum specimen used as a control reference material. To avoid temperature gradients, the bombs are located in a copper block inside the furnace. Stainless-steel capillaries of equal length and volume connect each stainless-steel container to a glass viewing capillary. The stainless-steel containers, stainless-steel capillaries, and a portion of the glass capillaries are filled with NaK (22 wt pct Na-78 wt pct K). The NaK/gas interface in the glass capillary is viewed with a cathetometer which is accurate to *0.5 mm. The cathetometer readings are used to calculate the volume changes of the samples during a run. This volumeter is basically the same as that described by F. Knight in Plutonium 1960. 2 However, changes in equipment design and operating procedure were made to eliminate some major operating difficulties. These changes are summarized below. 1) In filling the manometer with NaK, gas was frequently entrained in the system. Evacuation of the system before filling failed to eliminate the en-

Jan 1, 1965

By GUY C. RIDDELL, Donald M. Liddell

THE electronic arts today constitute the outstanding development in the field of rare metals, if not indeed in the arena of scientific progress at large. The year 1930 may become known as the year in which the electronic tube took hold of the wheels of industry; it is the year in which the tube&apos;s emancipation from the art of communication was proclaimed. The little tube which made a $500,000,000 industry out of a vacuum has now been applied to mining, manufacturing, transportation, chemistry, and other industries. Not many appreciate the extensive utility that e1ectroni.t tubes have already found in transportation, where they control the speed and security of express trains, as well as operate traffic lights on important highways-in the case of the Detroit-Windsor bridge counting the traffic and instantly turning the reports into the superintendent&apos;s office some distance away. In an Ohio steel mill, ten-ton ingnts &apos;rash back and forth through the rolls, reversed by their own shadows. The vacuum tube also starts, stops, and levels, fast passenger elevators.

Jan 1, 1931

By Eugene S. Machlin

A classical theory of solid solutions involving neavest-nergkbor intevactions with both central and linked-central forces between atoms has been developed. It has been found that the theory, where it can be checked quantitatively, is in ageement with experiment. The theory encompasses a description of many diverse pkenomena, such as antiphase shift structures, size effect, relative stabilities of various solutions, lattice para,neters, and order-disorder transitions. In particulav. a quantitative prediction not involving adjustable pavameters is made concevning the deviation of the Au-Cu interatonlic distance in long-range ordered (Ll,) Cu-Au I fronl the average distance based on the distances in pure gold and copper. This prediction, which is in agreement with expel-intent, has not been encompassed by any preuious theory. The theory of order-disorder is fragmentary. That is, no one theory exists that can explain the variety of qualitative phenomena observed. Further, many theories are not in good quantitative agreement with experiment. This subject has been reviewed by Muto and Takagi, Tuttman, and Oriani.3 There exists no doubt that the quasi-chemical approximation is not a complete description and that the inclusion of strain energy using macroscopic elasticity theory concepts leads to results in disagreement with experimenL4 The observation of antiphase domains and ordering systems such as Cu-Pt has led to Brillouin zone treat-ment of the order-disorder transition as opposed to the classical Ising model. The objective of this paper is to demonstrate that it is possible to develop a pairwise approximation model that can explain many of the observed order-disorder phenomena that have puzzled investigators in the past. This theory is based upon an empirical model due to ergmman&apos; for the elastic constants of metals. This model is generalized for multicomponent systems. As will be shown, the theory yields a short-range ordering energy for the disordered solution which differs from the ordering energy calculated from the differences in energy of disordered and long-range ordered solutions. It will be demonstrated that there is no necessary correlation between heats of formation and the tendency to order or between size effect and the tendency to order. Also, the existence of antiphase domains and iso-short-range-order systems that form superlattices (Cu-Pt) is predicted on the basis of the theory. Further, the relative stability of competing superlattices is calculable from the theory. If single-crystal elastic-moduli data are available for the pure components and one superlattice then there exists but one adjustable parameter in the calculation of lattice parameters for both the disordered and ordered solid solutions. In one special case, no adjustable parameters are required and a quantitative prediction is made. For the calculation of energies and partial order, there exists but one additional adjustable parameter, the pair-exchange energy V used in the quasi-chemical approximation (or the Ising model.) However, in these calculations, much more precise values are required for the single-crystal elastic moduli than available if the quantitative uncertainties in the predicted values of the energies are to be sufficiently small. THEORY ~er~man&apos; has developed a model with which he was able to obtain fair agreement with experiment for the relations between the elastic constants for metals. This model which we shall call Bergman&apos;s model is a linear combination of his models I and 11. In effect, Bergman, in this model, considers that each interatomic distortion is composed of two components: a classical central force distortion with an associated central force constant and what we shall call a linked-central force distortion with an associated linked central-force constant. The linked-central force distortion component obeys the constraint that the sum of such distortions over all the bonds equals zero. No constraint is imposed on the classical central force distortion component. Bergman&apos; derives the constraint on the linked-central force distortion on the basis of application of Pauling&apos;s relation between bond distortion and bond number to metals.ga This assumption is not logically necessary, however, and the Bergman model may be taken as a mathematical model for elastic constants, e.g., a purely empirical model without a physical basis. In the present work, the method of Bergman has been applied to two-component systems (solid solutions). In place of an external strain—which would allow a calculation of the elastic constants for the two-component system—it is considered that internal interatomic distortions exist as a consequence of having three potentially unequal distortion-free interatomic distances and but one "average" interatomic distance. It is assumed that the distortion-free interatomic distances between atoms of the same element are those found in the pure element having the same undistorted crystal structure as the solid solution. The distortion-free interatomic distance between unlike atoms is in general not measurable except in the probably nonexistent

Jan 1, 1967