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By P. E. Rider, K. A. Gschneidner, O. D. McMasters

The solid solubilities for thirteen rare-earth metals in gold were determined by using the X-ray parametric method. Solubilities ranged from 0.1 at. pct for lanthanum in gold up to 8.8 at. pct for scandium in gold. The solubilities from lanthanum to gadolinium were very small and essentially constant, but a sharp increase occurred from gadolinium to scandium. The large solubilities for the heavy rare-earth metals were not expected because of the large size and electrochemical differences between rare-earth atoms and the gold atom. Contributions from first- and second-order elasticity theory plus an electronic contribution were found to reasonably account for a more favorable size factor. Electron transfer from the rare-earth metal to the gold Is thought to occur such that the resultant rare-earth and gold electronegativities are favorable for solid-solution formation. It was also found that this mutual adjustment of size and electronegutivity does not occur if the pure-metal size factors are greater than a critical value of 25 pet. The eutectic temperatures for ten systems were determined and these remained fairly constant at approximately 809 "C for the lighter lanthanide metal-gold systems until the Er-Au system was reached, at which Point the eutectic temperature successively increased reaching a maximum of 1040°C in the Sc-Au system. This rise was correlated to the size factor becoming more favorable for solid-solution formation at erbium. The valence state of ytterbium was found to change from two in the pure metal to three when ytterbium is dissolved in the gold matrix. RECENT results1 reported concerning the solubility of holmium in copper, silver, and gold, showed that the solubility of holmium in gold was quite large, 4.0 at. pct, compared with 1.6 in silver and 0.02 in copper. The small solubilities of holmium in silver and copper are quite reasonable in view of the large size difference (22.2 and 38.2 pct, respectively), large electronegativity difference (0.59 for both systems), and possible unfavorable valency factor (assuming one for silver and copper and three for holmium). The large solubility in gold, however, is unexpected because these same factors are also unfavorable for holmium and gold (22.5 pct size difference and 0.69 electronegativity difference), and because the light rare-earth metals, lanthanum, cerium, and praseodymium, have negligible solid solubilities in gold.2 In view of this unexpected behavior, it was felt that a study of the solid solubilities of most of the rare-earth metals in gold would be desirable to better understand the factors involved in the formation of solid solutions. Of the rare-earth metals added to gold in this study, only ytterbium is divalent in the pure metallic state (the other rare-earth metals are all trivalent) and many of its physical properties (such as the metallic radius, electronegativity, and so forth) are much different from those of the normal trivalent rare-earth metals.' The properties of ytterbium are such that one would expect solid-solution formation to be less favorable for ytterbium in gold than for any of the normal trivalent rare-earth metals. But chemically ytterbium is known to possess a stable trivalent state, and it is quite possible that ytterbium may alloy as a trivalent metal under certain conditions rather than as a divalent metal. Because of the dual valency nature and because so little is known about the alloying behavior of ytterbium, the gold-rich ytterbium-gold alloys are of special interest. EXPERIMENTAL PROCEDURE Materials. The gold used in this investigation had a purity of 99.99 pct with respect to nongaseous impurities. In general the rare-earth metals were prepared by reduction of the corresponding fluoride by calcium metal.3 The impurity contents of the metals used in this study are given in Table I. Preparation of Alloys. Two- or 3-g alloy samples were prepared by arc melting. The samples, with the exception of some of the Er-Au alloys, had weight losses of 0.5 pct or less. All alloy concentrations noted in this paper are nominal compositions. After arc melting, the alloys were wrapped in tantalum foil, sealed off in quartz tubing under a partial atmosphere of argon, homogenized for approximately 200 hr at 780°C, and then quenched in cold water. X-Ray Methods. The X-ray parametric method was used in determining the solubility of the rare-earth metals in gold. filings were sealed in small tantalum tubes by welding under a helium atmosphere. The tantalum tubes were then sealed in quartz tubing under a partial argon atmosphere, and annealed for times ranging from 1/2 to 3 hr (the length of time was inversely proportional to the an-

Jan 1, 1965

By T. A. Wilson, S. L. Hoyt

THE plastic deformation of slender single crystals of zinc has been described in some detail in the paper by Mark, Polanyi and Schmid,1 which has become a classic, and also by one of the present authors in a somewhat shorter account.' The study of single-crystal zinc is termed classical because zinc single crystals offer, perhaps, the best material yet available for the study of atomic behavior during deformation and the effect known as "strengthening" in metals. A considerable amount of additional work has also been done on single-crystal zinc, but as it is not closely related to the present paper it will not be considered. Throughout all the former work, the mechanism of plastic deformation first described by Mark, Polanyi and Schmid has been assumed to hold. This may be said to offer the strongest confirmation of its correctness. Even so, the picture of the process has never been as completely portrayed as is desirable. The first object of the present paper is to describe work that has been done in this field, and which is even yet being carried on, in the hope that a more complete picture may be obtained. Mathewson and Phillips' have recently described a new mechanism of the deformation of zinc based on their study of large rectangular crystals. One of their conclusions was that deformation produced twinning with a rotation of some of the basal planes into positions 94° removed from their original position; a position almost the same as that of the prismatic planes before twinning. A second conclusion was that fracture occurred along these basal planes in their new position, and, therefore that fractures previously regarded as prismatic were in reality basal. Such findings are of great significance and they raise a question as to the generality of such behavior. Professor Mathewson's opinion is that even the slender cylindrical single crystals behave in the same manner as his large rectangular crystals when strained by simple tension.

Jan 1, 1928

By S. S. Marsden, S. A. Khan

Externally generated foam was injected continuously into short porous media. Both flow rate and pressure drop were measured. Liquid saturation was determined by electrical conductivity. Foam yuality I, expressed as the ratio of gas volume to total volume, was varied from 0.70 to 0.96. As measured with a modified fann VG Meter, apparent viscosity of this foam µa decreases with increasing shear rate but usually falls within the range of 50 to 500 cp. At a given shear rate, µa increases almost linearly with I-. When measured with a Bendix Ultraviscoson, kinematic pa is independent of V but absolute pa increases with T from about 3 to 8 cp. The effective permeability -apparent viscosity ratio ke/µa decreases almost linearly with V for porous media of high permeability, but the rate of decrease becomes less for tighter ones. The relative permeability-apparent viscosity ratio kr/µa us V data does not fall on a single line. The kr/µa ratio increases with liquid saturation in the porous medium and with surfactant concentration. Estimates of pa for foam in porous media vary from 30 to 100 cp. INTRODUCTION Although research on the development of a foam-drive, oil recovery process has been going on for almost a decade, most of the significant publications have appeared within the last several years. This illustrates well the rate at which interest in this process is accelerating. Bond and Holbrook 1 were the first to describe the use of foam to improve oil recovery in their patent of 1958. They proposed that an aqueous foaming agent slug be injected into the formation and that this be followed by gas to produce a foam in situ. Fried 2 studied the injection of foam into porous media which had already been subjected to conventional gas or water drives and found that gas could be used to drive a foam bank which would, in turn, displace additional oil in the form of an oil bank. He attributed the increased oil recovery to the high effective viscosity of foam flowing in porous media. His microscopic observations showed the importance of foam generation and regeneration within the porous medium. By injecting both air and aqueous surfactant solution, Bernard3 generated foams within the porous medium in which oil displacement was being studied. In a separate empirical test, he also measured the dynamic foaming characteristics of the same surfactants in water and/or oil. With some exceptions and for the seyen surfactants studied, there seems to be a qualitative relationship between the efficiency of liquid rlisplacrment and the dynamic foaming testtsed. This relationship was not consistent enough to eliminate the necessity of actual foam flood tests in porous media for surfactant selection. In a study basic to gas storage in aquifers, Bennett4 described the displacement of brine by foam in consolidated porous media. Among other things, he stated that the ability of a surfactant solution to foam is more important than the stability of its foam. The presence of a foam bank between the displacing air and the displaced brine improved both breakthrough and ultimate recovery. In a continuation of this work Kolb5 attributed the great reduction in surfactant solution production rate as displacement by air progressed to a decrease in relative permeability to gas. These several effects reported by both Bennett and Kolb can all be attributed to the high apparent viscosity of foam which was obviously flowing in the porous media. Bernard and Holm6 observed that gas permeability in the presence of foam was much less than in the absence of foam when both were measured at the same gas saturations. This reduction in permeability was proportionately greater for more permeable sands and sandstones than for the less permeable. Viscosities of the surfactant solution and air were used for their calculations rather than apparent foam viscosities. The foam stability increased with decreasing permeability, which was probably due to the natural regenerative properties of porous media, and the permeability reduction increased

Jan 1, 1967

By Robert K. Steunenberg, Irving Johnson, James B. Knighton

The activity coefficient of plutonium in liquid magnesium, over the temperature range 650° to 800°C, was obtained from measurements of the distribution of plutoninm between a 50 mole pct MgC12-30 mole pct NaCl-20 mole pct KC1 molten-salt mixture and liquid Zn-Mg alloys. For dilute solutions (0.08 at. pct Pu) the activity coefficient of plutonium was found to vary from 10.1 at 650°C to 12.2 at 800°C. The activity coefficients of plutonium in dilute liquid solutions of plutonium in uranium, silver, lanthanum. cerium, and calcium were estimated to be. The distribution data indicate a value of about 0.1 at 800°C for the activity coefficient of PuCl3 dissolved in the above ternary salt mixture. LIQUID magnesium and several liquid alloys of magnesium with metals such as zinc and cadmium have been shown to be useful solvents in pyrochemical processes for the recovery of uranium and plutonium from discharged nuclear fuels,' and for the separation of transuranium elements.' The present study was undertaken to determine the activity coefficient of plutonium in liquid Pu-Mg alloys in support of process-development work. The activity coefficient of plutonium in liquid magnesium was determined from experimental data on the distribution of plutonium between a liquid ternary MgC12-NaC1-KC1 salt mixture and various liquid Zn-Mg alloys. The distribution data were used to calculate the ratio of the activity coefficients of plutonium in liquid zinc and in liquid magnesium. The activity coefficient of plutonium in liquid magnesium was then computed from the known activity coefficient of plutonium in liquid zinc. It was not necessary to know the thermodynamic properties of the molten-salt system explicitly. The major features of the Pu-Mg system have been reported by Schonfeld.3 At the temperatures of interest in the present study, i.e., above about 600°C, the phase diagram indicates the existence of a wide liquid-miscibility gap, with the plutonium-rich liquid containing about 8 at. pct Mg and the magnesium-rich liquid containing about 10 at. pct Pu at the intersection with the solidus regions. Additional data on the compositions of the two equilibrium liquid phases obtained in this laboratory4 have defined the miscibility gap up to the consolute temperature (at about 1040°C). EXPERIMENTAL PROCEDURE AND RESULTS Materials. The 50 mole pct MgC12-30 mole pct NaC1-20 mole pct KC1 salt mixture was prepared by melting the required proportions of reagent-grade NaCl and KC1 with anhydrous MgC12. The molten salt was then purified by contacting it with liquid Cd-30 wt pct Mg alloy (at 450°C) to reduce oxidizing impurities, followed by filtration through a stainless-steel frit (pore size, 65 µ) to remove solid MgO formed during the reduction. The purity specifications of the zinc, magnesium, and plutonium were 99.999, 99.8, and 99.85 pct, respectively. Apparatus. The liquid salt and metal were contained in a tantalum crucible inside a graphite secondary vessel. The crucible assembly was located inside a resistance-heated stainless-steel furnace tube. The furnace tube was closed by means of a stainless-steel cover, which was attached by bolts, with a neoprene O-ring serving as a gas-tight seal. The top of the furnace tube was water-cooled to protect the O-ring. The furnace-tube cover was provided with a tantalum thermowell, a tantalum stirrer, and a port through which sampling tubes could be inserted and materials could be added to the melt without admitting air to the furnace tube. Vacuum and an argon atmosphere were available through a side-arm on the furnace tube. The furnace temperature was regulated by a proportional controller that was actuated by a chromel-alumel thermocouple between the furnace tube and the heating elements of the furnace. The melt temperature was measured by means of a chromel-alumel thermocouple in the tantalum thermowell. The accuracy of temperature measurement was ±3°C. The salt and metal phases were intermixed by a motor-driven tantalum paddle positioned at the liquid interface. The tantalum crucible was provided with four baffles to increase the turbulence. The sampling tubes consisted of 1/4-in.-OD tantalum tubing that terminated in a tantalum frit (Kawecki Chemical Co.; average pore size, 30 µ). Procedure. The zinc, magnesium, plutonium, and salt were charged to the tantalum crucible; then the system was evacuated and filled with argon. The melt was brought to the desired temperature, and agitated for 1 to 2 hr. After allowing the salt and metal to separate, both phases were sampled. Filtered samples were obtained by immersing the end of the sampling tube in the liquid and increasing the argon pressure sufficiently to force the liquid salt or metal through the frit into the tantalum tube. The sample was then partially withdrawn into the cooler portion of the furnace tube and permitted to solidify before being removed. The temperature sequence for sampling at each magnesium concentration was 800°, 700°, 600°, 650°, and 750°C. The composition of the liquid-metal phase was varied by incremental additions of magnesium in a series of experiments at low magnesium

Jan 1, 1967

By T. E. Eagan, W. R. McCrackin

IN dealing with segregation in babbitt, and its effect on the final cast structure, which is a bearing, it is obviously impossible to cover all of the compositions manufactured. Each composition, of course, will exhibit certain specific types of segregation. However, as examples,, two compositions of babbitt are presented: one a tin-base of well-known analysis and the other a lead-base, which in the past few years has found wide usage. Bearings usually are cast either statically or centrifugally; therefore the effect of these two methods on segregation is presented. EXPERIMENTAL PROCEDURE A slab of babbitt 1/2 in. thick by 5 in. wide and 17 in. long was cast, using a book mold with the long edge vertical. An A.S.T.M. grade 2 babbitt was used (3.5 per cent copper, 7.5 per cent antimony, remainder tin), to which 0.10 per cent tellurium had been added. Unfortunately, no metal without tellurium was available. The mold to hold the babbitt was heated to approximately 300°F., the temperature being judged by the babbitter. The pouring temperature of the babbitt was 875°F. (470°C.). One slab was made by allowing the babbitt to cool without stirring. The other slab was stirred during the entire cooling cycle. This stirring consisted of a vigorous churning or puddling into the mold until complete solidification had taken place. Three samples were removed from these slabs. One was taken at the extreme bottom, another half way to the top, and another at the extreme top, all at the center of the width. Chemical, macroscopic and microscopic examination was made of all samples. Table I shows the chemical analyses obtained at the described positions [ ] in the slab. The analyses show no serious amount of gravity segregation. Microscopic examination from edge to edge of the slab showed little change in structure. From top to bottom there was a progressive coarsening of the grain size in the stirred slab but little change in the slab that was not stirred (Fig. I). No definite exhibit of segregation could be detected. In line with our experimental study on the tin-base babbitts, we cast an almost duplicate slab using A.S.T.M. Alloy No. 15, containing 0.9 to 1.25 per cent tin, 14.75 to 15.5. per cent antimony, 0.80 to 1.25 per cent arsenic and 0.4 per cent copper. The slab was 16 in. long and 3/8 in. thick, cast with the long side vertical. One slab was allowed to cool normally and the other was stirred continually during cooling. The pouring temperature of the babbitt was

Jan 1, 1944

By Raymond Ward

IN the past few years several papers have appeared dealing with different aspects of the oxidation of dilute alloys, especially with respect to the formation of internal oxides or subscales. Subscale has been defined1 as that layer or zone of oxide particles precipitated in a matrix of metallic metal in which the oxide particles are dispersed uniformly and occur by diffusion of the oxygen inward from the metal surface. Alloys composed of a solvent metal more noble than the alloying elements are subject to subscaling or internal oxidation. In these alloys the solute must be present in such quantities that if the alloy is exposed to an oxidizing atmosphere at elevated temperatures, the rate of diffusion of the oxygen into the metal will be greater than the rate of diffusion of the solute outward. There is a composition range of the iron-silicon system that falls into this classification. Knowledge of the nature and rates of oxidation of iron-silicon alloys is of great commercial importance, but very little information of this nature is available. Darken2 recently has made calculations to show the limits of concentration of silicon for which subscales are produced in iron-silicon alloys; however, the main thesis of his paper was to analyze and to explain the already existing data. The purpose of this paper is to present the effect of com position, temperature, time, and atmosphere on the type of scale-metal layer obtained and to give some qualitative indication of the effect of these variables on the rates of oxidation. Since this paper is a study of silicon steels that are available commercially, extremely low-silicon and high-silicon alloys are not included. EXPERIMENTAL PROCEDURE The alloys used in the experiment were taken from heats of silicon steel that ranged in analysis from 0.70 to 5.8 per cent silicon. This composition range takes in most of the commercial silicon steels. In Table I are listed the compositions of alloys used. Other than iron and silicon, the alloys normally contained approximately the following impurities: carbon, 0.03 per cent; manganese, 0.07; phosphorus, 0.008; sulphur, 0.02; copper, 0.07; tin, 0.01, and from nil to a trace of chromium, nickel and copper. All of the alloys used were melted in open-hearth furnaces, except where otherwise noted, and were hot-rolled to 0.100-in. plate. Samples approximately 1/2 in. square were then cut from these materials. So that the surface conditions of the samples used for oxidation would be standardized, each sample was ground through 000 emery paper immediately before oxidation. Two different techniques were employed in carrying out the oxidizing treatments. One consisted simply of heating the samples with free access to air. In this treatment the samples were set on edge on a refrac-

Jan 1, 1945

By B. G. Agnew

In evaluating fracture treatments, the need to answer such questions as "What zone or zones were actually treated?" and "What was the vertical extent of the treatment" is necessary, since determining effectiveness of the fracture treatwrent depends on knowledge of the reservoir portions stimulated and the vertical extent of the fracture system or systems. Injection of hot or cold fluids during fracturing operations will transfer heat to the surrounding formations and fracture faces mainly by heat conduction. Once injection ceases, temperature anomalies will develop opposite the zone fractured because the rate of temperature decay is less than that opposite zones heated or cooled by flow inside the wellbore or along the cement sheath. Thus, temperature surveys can he used to determine where fractures were generated outside the wellbore and to reasonahly estimate the vertical extent of the fractrires. This technique has been used successfully to evaluate over 344 fracture treatments at depths ranging from 1,500 to 15,700 ft. Examples of actual temperature surveys are presented to show how this method of fracture treatment evaluation can be used effectively and beneficially. INTRODUCTION Stimulation of producing or injection wells by fracturing is commonplace in the industry today. In evaluating these treatments, two basic questions which arise are "What zone or zones were actually stimulated?" and "What was the vertical extent of the treatment?". Knowledge of the reservoir portions stimulated and vertical extent of the fracture system or systems is vital to effect efficient and economical well completions and to assure maximum recovery from reservoirs. Not all fracture treatments are successful and many times the desired or anticipated results are not achieved. When this occurs, it is in most cases the engineer's job to determine why. The answer to this problem forms the primary basis for deciding whether to spend more money for development drilling and/or completion attempts or to forego additional expenditures to improve the particular zone. Also, knowledge of the reservoir portion actually stimulated is invaluable in planning future workovers. This is especially true in wells producing from reservoirs containing multiple porosity stringers or zones. For various reasons, all zones within a reservoir may not be perforated on initial completion with the thought of developing remaining zones through future workover operations. Because particular zones are perforated and fracturing fluid pumped down the wellbore, it cannot be assumed that all perforated zones are stimulated, and in turn drained. Occasionally, unperforated zones which are planned for future development are actually stimulated on initial completion. eliminating the need for future recompletion attempts or all zones perforated initially are not stimulated, thus requiring additional completion work to insure that these zones are adequately drained. In most cases, it is costly. if not impossible, to determine with assurance why a fracture treatment is unsuccessful after the job has been completed and the results tested. Further, unpredictable upper and lower fracture barriers. as well as possible borehole communications (cement channels), do not permit it to be taken for granted that the formation opposite the perforations is the only zone receiving the fracture treatment. Thus. evaluation of fracture treatments is necessary for efficient and prudent well completion practices and should be done simultaneously with the fracture job. Several methods have been used to locate fractured zones, all of which are based on detection of radioactive tracer materials added to either the fracturing fluid or the propping agent. These methods have been helpful in increasing knowledge of fracturing operations; however, they are seriously limited because of cost and inability to detect accurately radioactive tracer material more than a few inches away from the borehole. To develop a better diagnostic tool to pinpoint which zone or zones had actually been fractured, temperature surveys were run after fracturing with heated and cooled fluids. Significant temperature anomalies were found to exist opposite zones suspected of receiving the fracture treatment. From the analysis and examples to be shown, it can be seen that temperature surveys run in a stabilized wellbore several hours after a fracture treatment using hot or cold fluid will yield temperature anomalies which show the actual reservoir portion stimulated, the vertical extent of the fracture system or systems and a qualitative indication of the portion of fracture-fluid volume entering a given depth interval. The experience and illustrations used in this paper are based on evaluation of over 344 fracture treatments during the past three years using this diagnostic tool at depths ranging from 1.500 to 15,700 ft and fracture volumes ranging from 2.000 to 110.000 gal. Based on analyses of these temperature surveys, analyses of fracture gradients and evaluation of several open-hole packer impressions in the West Texas area,' vertical fracturing is the predominant mechanism and horizontal fractures occurred frequently, if at all.

Jan 1, 1967

By William Fink

SINCE so many different curves have been published for the solid solubility of zinc in aluminum, it seems desirable to definitely establish the correct curve by two or more independent methods. The curve published in part I1 was based entirely upon X-ray measurements because the other methods employed at that time were not satisfactory. The present paper (the seventeenth of this series on high-purity aluminum alloys) describes the determination of the solid solubility of zinc in aluminum by the measurement of electrical resistivity at temperature and by microscopic examination. Since the publication of our part I in 1932, an investigation of the solubility relations in the aluminum-zinc system has been reported by Schmid and Wassermann2, who obtained their solubility results from lattice-parameter measurements on heat-treated and quenched speci-mens. The diagram that they published is shown in Fig. 1. In this investigation they also found by X-ray measurements that the parameter of the gamma phase changed continuously with zinc content and at such a rate that it would be identical with that of the beta phase at 60 atomic per cent zinc. It was concluded therefore that the beta and gamma phases, from the point of view of structural relationship, are one single phase. They also suggested a gap of immiscibility between 270° and 350° C. The complete boundary in this region could not be deter-mined satisfactorily by the method employed and therefore was not shown in their diagram.

Jan 1, 1936

By M. Duclos, A. Sawatzky

A simple model has been developed which describes the steady-state solute distribution in Ti-H type systems above the eutectoid temperature in the presence of a temperature gradient. The solute distribution is dependent on the shape of the phase boundaries. An interesting result, and one that is not observed at steady state in thermal diffusion below the eutectoid temperature, is the existence of a two-phase region. The heat of transport for hydrogen in a titanium, Q*a, over the temperature range 275" to 650.C is determined to be 4500 * 230 cal per mole. The heat of transport for hydrogen in B titanium, QB* over the temperature range 320" to 590.C is found to be 630 ± 200 cal per mole. It is also shown that thermal diffusion provides a method by which phase bounduries above the eutectoid may be determined in Ti-H type systems. IN modern technology materials are being used at constantly increasing temperatures under greater temperature gradients. Thus atomic migration in metal alloys due to a temperature gradient (thermal diffusion) may in some cases occur to an observable extent. The thermal diffusion of hydrogen in zirconium has in recent years received considerable attention1-' because of the use of zirconium alloys in nuclear power reactors. The thermal diffusion kinetics below the eutectoid (547°C) are fairly well understood. At steady state the solid solution, a, and hydride, 6, phases are completely separated with the hydride precipitating at the lower temperatures. No experimental work has been carried out in the a + B region although Droege4 suggested that a complete separation of the two phases, as observed at temperatures below the eutectoid, might not always occur. In the present investigation a simple model has been used to determine the steady-state solute distribution under a temperature gradient in Zr-H type systems heated above the eutectoid temperature. The solute distribution is shown to be dependent on the shape of the phase boundaries in the constitutional diagrams and several typical cases are discussed. The model has been applied to Ti-H. This system was chosen in preference to Zr-H because of its much lower eutectoid temperature (-300°C as compared with 547.C), thereby reducing experimental errors due to oxidation and hydriding. The heats of transport for hydrogen in the a and B phases of titanium also have been determined since they were required to compare the proposed thermal diffusion model with experiment. THEORY In the presence of a temperature gradient the atomic flux in a single-phase region of a two-com-ponent system of which the atoms of only one component are diffusing is given by:' J = - U\dx + RT3 dx) which can be written as: j-D(dn/dt +Q*n/RT2)dt/dx [11 J - -D\dT + RT2)dx [1] where D = diffusion coefficient, n = solute concentration, T = absolute temperature, R = gas constant, dT/dx = temperature gradient, and Q* = heat of transport. At steady state (J = 0) Eq. [I] leads to the solute distribution: n = noexp Q*/RT where no = a constant depending on total solute content. The heat of transport Q* can be experimentally determined from the steady-state distribution. In the present paper we shall determine the solute distribution in systems having the constitutional diagram exemplified by Ti-H shown in Fig. l.' As shown, N,(T) and NB(T) are the equilibrium solute concentrations in the a and 0 phases at temperature T. Lines AA' and CC' define the region of interest to us. The following assumptions are made: 1) Steady-state conditions prevail. 2) In a single-phase region all points on an isotherm have the same thermodynamic potential so that the composition over an isotherm is uniform. If a two-phase region exists, thermodynamic equilibrium is found only at phase interfaces. However, we assume the component of the concentration gradient along an isotherm to be small so that the composition in each phase is approximately the same as at the interface and is given by the constitutional diagram, Fig. 1. 3) There is appreciable diffusion of only one component. 4) We shall consider only the case where Qa*, QB*, and Qg*, the heats of transport for solute diffusion in the a, B, and 6 phases, respectively, are positive. This has been observed for the thermal diffusion of hydrogen in zirconium3 and titanium.10 We will show that the steady-state solute distribution above the eutectoid is primarily determined by the heats of transport and the temperature dependence of Na(T) and Np(T). It may be quite different from the steady-state distribution below the eutectoid. For example, we will see that, under certain conditions,

Jan 1, 1970

By W. E. Ruder

It has been pointed out by Stead1 that grains of considerable coarseness may be developed in steels containing from 3 to 5 per cent. of silicon, and in a previous paper2 the present author has shown that under the proper conditions of annealing single grains having an area of 50 sq. cm. may be obtained. It is the purpose of this paper to discuss in more detail the conditions promoting the growth of these grains, in the hope that the experiments described may throw some additional light upon the general problem of grain growth in metals. These silicon steels lend themselves particularly' well to such experiments because of the ease with which the change in structure may be followed and because of the fact that the effect of the carbon present is largely obliterated by the high percentage of silicon. This forms a solid solution with the iron, which acts very much like a pure metal. This alloy has been found to have but one critical point, viz., Ar2. This point, determined by Roberts-Austen for Hadfield's 4 per cent. Si alloy, was found to lie at 703" C. Vigouroux3, in working with pure Fe-Si alloys, finds this point to rise from 750" C. for 0.5 per cent. Si to 860" for 6 per cent. alloy, with a flat region in the curve from 3 to 4 per cent. Si. No accurate determination of this point has been undertaken by the present author, but it has been roughly determined to lie between 730" and 750:. In the preliminary experiments, some of which have been described in a previous paper, it was found that practically all of these steels, when annealed to 1,200" C. or higher, showed grains of comparatively large size. These grains varied in size, however, from about 4 sq. mm. to 50 sq. cm. (see Figs. 1 and 2) under the same conditions of anneal, and it was for the purpose of determining the cause of this difference in size that the experiments herein described were undertaken. From a preliminary study of the chemical composition of the specimens

Jan 1, 1914

By T. F. Bower, M. C. Flemings

Results are reported of a study of surface dendrilic structure of an Al- Cu alloy solidified against a chill wall. Most primary and secondary "arms " in the surface dendritic structure are arranged orthogonally, giving the impression of strong preferred orientalion on the surface. However, no such preferred orientation exists and it is therefore evident the arms do not represent (100) directions. The primary arms are shown to be interseclions of a (100) plane wilh the chill plane, or, equally often. the projeclion of a (100) direction on the chill plane. Secondary dendrite arms are usually within a few degrees of 90 deg to the primary arm, independent of grain orientalion. Prirary, secondary, and higher-order surface dendrite arms almost always represenl intersections of (100) platzes with the chill surace, or pvojections of (100) direclions. Growlh of secondary arms is favored on the side of the primary arm where a (100) direclion points toward the chill surfAce a1 a Lou, angle. Surface dendrile arms are often observed to be bent. In these cases, the crystal lallice changes orientation; bending is concave to the chill surface. In a previous paper,' a technique was discussed whereby large grains can be obtained at a chill surface. The technique used involves quickly drawing superheated liquid A1-4.5 pct Cu alloy into a thin copper mold, so that the mold is full well before solidification begins. The chill surfaces employed are polished copper blocks coated with amorphous carbon. Shrinkage during solidification between dendrite arms and grains delineates both, without the need for polishing or etching of the cast surface. The grain structure of the chill surface was discussed in a previous paper;' in this paper, the dendrite arms within each grain are examined. Previous work on surface dendrites includes that of Edmunds, who studied the development of preferred orientation in zinc, cadmium, and magnesium.' In zinc and cadmium, he found that the surface region has a (0001) texture (parallel to the chill surface). Walton and Chalmers reasoned that, since the fast growth (1010) directions are in the basal plane, nuclei which have this plane parallel to the mold wall would produce larger grains than nuclei with other orientations. Hence, the texture observed is as expected.3 The same authors, in measurements on aluminum ingots, found no preferred orientation at the mold wall. However, the X-ray technique they used measured the preferred orientation in terms of grain numbers, not grain areas; larger grains were weighted equally with small ones. No preferred orientation is expected on this basis at the chill surface. In a later paper,' Edmunds stated that experiments show a random grain orientation at the surface in die cast aluminum; his technique, also used in his earlier paper, takes account of grain area. Little work has been published on the dendritic structure of metal chill grains. Recent work of Biloni and Chalmers on "predendritic growth" shows the change in morphology from spherical to dendritic during the initial stages of freezing, 5 but this work did not include detailed examination of the fully developed dendrites. Other pertinent work includes that of Lin-denmeyer, who investigated the growth of ice dendrites. 6 When growth was on a substrate, the dendrite axes were bent. The bend corresponded to a change in orientation of the crystal lattice and occurred in such a way as to align the basal plane to the substrate. DENDRITE STRUCTURE Fig. 1 shows the chill surface of a typical casting poured above the critical temperature necessary to produce coarse grains. A cursory examination of these grains shows that the surface dendrite arms within most of the grains are oriented roughly perpendicular to each other. One is tempted to assume that these are (100) directions and that, therefore, marked preferred orientation exists at the chill face. This, however, is not the case. Each of the grains in the casting of Fig. 1 was separately identified, Fig. 2, and its orientation determined by the Laue back-reflect ion method. Results are given in Fig. 3 and it is seen there that no preferred orientation exists. Even when grain area is accounted for, there is no significant preferred orientation. The relationship between surface grain structure and crystal orientation was then obtained by assigning X and Y axes to the casting surface, Fig. 1, and assigning the same axes to the stereographic projections of each grain. Thus, the visible surface structure could be compared readily with grain orientation. This was done for fifty-five of the grains of Fig. 1. Results of this study on three typical grains are described below, and some general observations given subsequently. Fig. 4 shows the structure and stereographic projection of a grain which lies near the (100) zone (with respect to the casting surface). The X and Y directions are marked on the projection, and the photomicrograph mounted with the same orientation. Poles of the stereographic projection represent crys-tallographic directions in the grain which point out of the casting, toward the chill. Two (100) directions are shown in Fig. 4. A line joining the center of the projection and a pole represents the projection of the pole onto the X-Y plane (chill surface). Two such lines are shown in Fig. 4 (solid lines). A line joining the intersection of a great circle with the circumference of the projection gives the trace of a crystallo-graphic plane in the chill surface; two such traces are shown (dashed lines).

Jan 1, 1968

By W. D. Forgeng, R. L. Folkman, D. C. Hilty

The solubility of oxygen in molten Fe-Cr alloys has been determined at 1550° , 1600°, and 1650°C for alloys containing up to alloyshasbeenabout 50 pct Cr and found to decrease as chromium increases to 6 pet and then to increase gradually. Phase relations in the Fe-Cr-0 system at steelmaking temperatures have been evaluated and two previously unreported oxides have been identified. OPERATIONS in the melting and refining of chromium steels are dependent to a major degree on the reactions of chromium and iron with oxygen and are primarily directed toward controlling and modifying these reactions to secure maximum advantage in the utilization of chromium. Although fairly effective practices have been developed empirically, understanding of the specific reactions is limited. Moreover, the ability of molten steel to dissolve oxygen that subsequently precipitates as oxide inclusions during solidification is well known, so that clarification of the effect of chromium on the nature and mechanism of formation of these inclusions is desirable. Study of the problem indicated that increased knowledge of the fundamental Fe-Cr-0 system is essential to further technical and economic improvement. Consequently, an investigation of the influence of chromium on the solubility of oxygen in molten iron and of phases and phase relations in the Fe-Cr-0 system was undertaken at the Metals Research Laboratories of the Electro Metallurgical Co. as part of a general program on the effective utilization of chromium in chromium steel production. Experimental Procedure All of the experimental runs made during this investigation were carried out in the rotating crucible induction furnace which has been described in detail in a previous publication.' In review, the principle underlying this furnace is that rotational forces in the crucible cause the molten metal to assume a concave shape in such a manner that the slag is contained in the molten metal cup, thereby minimizing slag/crucible contact and subsequent reaction. Practically all of the heats were melted in commercial-quality magnesia crucibles of the type usually furnished for laboratory induction furnaces. All of the runs were made under an argon atmosphere after the furnace chamber had been degassed. Bath temperatures were controlled by Pt—Pt-10 pct Rh thermocouples. The basic furnace charge consisted of a premelted 12 to 15 lb electrolytic iron slug which had been cast to a shape convenient for fitting into the rotating furnace crucible. A typical analysis of the electrolytic iron slugs is given in Table I. For certain runs, it was desirable to melt down charges containing high initial chromium contents. In these cases the chromium was added to the electrolytic iron during the premelting operations. Chromium was added to the rotating furnace bath in the form of electrolytic chromium of the analysis given in Table 11. In all of the constant temperature runs, the standard procedure was to melt down the electrolytic iron or alloy slug under vacuum, admit argon to slightly greater than atmospheric pressure, and adjust rotational speed to develop a well formed "cup" on the bath surface. The melt was then saturated with oxygen by an addition of ferric oxide and the temperature of the bath adjusted to within +5°C of the desired level. At this point the heat was permitted to come to equilibrium prior to sampling or further addition. This time interval was varied from 15 min to 2 hr but generally was about 20 min. After sampling, the desired chromium addition was made and the bath again equilibrated prior to subsequent sampling. This cycle of addition and sampling continued for the duration of the run which lasted from 4 to 8 hr. At the end of this period, power was shut off and the bath allowed to solidify in the furnace. Quenched metal samples were taken from the equilibrated melts by means of the "Taylor sampler" which has been described by Taylor and Chipman.' Before being submitted to chemical analysis, all samples were carefully examined for surface slag occlusions and cold shuts. Later in the study, each sample was radiographed and examined metal-lographically in cross-section to determine the presence of internal defects. On the basis of these examinations, sound and apparently clean specimens were selected from the Taylor samples for chemical analysis.

Jan 1, 1956

By Norman Pilling

The effects of lead and tin up to maximum contents of about 0.1 per cent. each, in the presence of oxygen between 0.04 and 0.30 per cent., have been studied. Tin is retained efficiently in the oxidized condition, whereas lead is not. An approximate relation between the lead-oxygen and tin-oxygen contents is deduced which, if observed, permits the presence of these elements without detrimental effect. Excess of lead beyond this limit affects ductility and rolling properties adversely and an excess of tin correspondingly diminishes the conductivity. It is shown that copper carrying a combined lead and tin content of several hundredths per cent., yet fully equal in quality to electrolytic wirebar, may be produced under commercial conditions. TIN is not normally found in more than bare traces in current grades of American electrolytic copper, and lead is rarely found to more than a few thousandths per cent. In the electrolytic refining of copper these metals do not present great difficulty in separation and their presence in any considerable amount in copper that has been refined by this method need not be tolerated. On the other hand, the effect of these elements is not entirely academic, as a considerable tonnage of scrap copper liberally contaminated with them has been reclaimed by the fire-refining process into metal with a residual lead and tin content of several hundredths per cent., yet having excellent working properties and fully equal in quality to current grades of electrolytic wirebar. Such copper has been found entirely suitable for use in the manufacture of electrical apparatus. In the absence of oxygen, tin is known to depress the conductivity rapidly, and lead to impair ductility and the rolling properties, yet the effects of these metals on commercial grades of copper-i. e., copper containing from 0.03 to 0.10 per cent. of oxygen-apparently has not received systematic attention. Occasional reference is made to the fact that in the presence of oxygen lead may be tolerated, yet Addicks says,1 in regard to overpoling: "The unstable condition can be controlled by adding certain substances, notably lead, in small quantities, but as mere

Jan 2, 1926

By T. G. Nilan

Steels containing 0.4 and 0.8 pet C have been transformed isothermally at pressures up to 34 kbuv. Decomposilion mechanisms are so intimately related to phase equilibvia that, as the equilibria shift under high pressure, the microstruclures of the decomposition producls change, maintaining at pressure the same correspondence between a given phase equilibrium and a given microstructure as a1 1 atm. A bainitic unicvo-structure occurs in these steels at high pressure that IS observed only at 1 aim abole 1.4 pct C. This strrrcl111,e 1s ruliorzalized in terms of the effect of pressure on the transformation to lower bainite. The pressuve depetlderlce of the kinetics of pearlile formation is descrihed by an absolute rule theory amalysis. The activation volume for the transformation is 7 cu cm per mlole, which is indicative of a phase-interface transformation-rate cotntrol mechanism. This fortmulation, when expressed in terms of known solule effects on the energelics of tvansformation, gives promise of explaining the effects of alloying elemenls on hnrden-abilily, particularly that of 'coball. KINETIC processes in solids are functions of the primary thermodynamic variables of state: composition, temperature, and pressure. Until the development of high-pressure techniques' that permitted the generation of sustained high pressure at high temperatures, metallurgical studies of such reactions were largely limited to isobaric conditions at atmospheric pressure. The data so obtained, and theoretical deductions based on these data, were necessarily incomplete For the particular case of austenite decomposition, a knowledge of the phenomenology of the reaction in terms of all the state variables should lead to a clarification of the process. This deeper understanding should facilitate a decision between conflicting theories that have been proposed to rationalize these phe- nomena. An analysis, derived from an understanding of the transformation mechanisms, may aid in the optimization of alloy steel development. The first studies of the effect of pressure on transformations in steel were made by Kulin et al. in 1952.' In a study of the influence of applied stress on mar-tensite formation in a 30 pct Ni steel, they found that the martensite start (M,) was depressed 8°C per kbar* by hydrostatic pressure. Jellinghaus and Friedewold3 were apparently the first to investigate the effect of pressure on isothermal transformations above the Ms. They found that the bainite transformation rate in a 1.2 pct C, 3.8 pct Mn steel was reduced by a factor of 3 by a hydrostatic pressure of 4 kbar. In both of these investigations,2,3 the M, of the steels studied was below room temperature. Austenitizing and quenching were done at atmospheric pressure, followed by the decomposition of the metastable austenite under pressure. The maximum temperature at pressure in the bainite study3 was 350°C. Until the advent of the present high-pressure devices, it was not possible to conduct isobaric high-pressure heat treatments from austenitizing through isothermal decomposition and quenching. The exploitation of high pressure as a variable in metallurgical studies was greatly advanced by the apparatus and techniques developed by Hall4 and co-workers. Utilizing these techniques, Radcliffe et a1.5 and Hilliard6 etermined the pressure dependence of phase equilibria in the Fe-C system. Hilliard and cahn7 examined the pearlite transformation rate in an AISI 1080 steel and also in a high-purity 0.92 C Fe-C alloy at 1 atm and at 34 kbar and found a 700-fold reduction in rate at pressure in the 1080 steel but only a fivefold reduction in the high-purity alloy. In agreement with the shift of phase equilibria under pressure, the microstructures were hypereutectoid at 34 kbar pressure, whereas they are eutectoid at 1 atm. Determination of the effect of pressure on carbon diffu-

Jan 1, 1968

By C. J. McHargue, J. C. Ogle

Lightly deformed columbiun single crystals which contained only parallel hoins or purullel and intersecting trains were annealed at 1000' and 1600"C. No re-crystallizntion occurred in specimens hawing only parallel twins. Only noncoherent twin boundaries nzipated at 1000°C but both coherent and noncoherent ones moved al 1600°C. Recrystallization occurred within a few minutes at twin intersections at 1000°C. The orientation 01 the recrystallized grains differed front that of both the matrix and deformation twins, but could he derired by (110) and/or(112) rotations. ALTHOUGH twinning in metals has been extensively studied, there have been no definitive studies of the annealing behavior of crystals containing deformation twins. Some effects observed after annealing deformation twins have been summarized by Cahn1 and Hall2. Any or all of these phenomena are observed: 1) The twins may contract so that the sharp edges of the lens become blunted, and eventually the twin may disappear entirely. 2) The twins may balloon out at an edge, giving rise to a large grain having the same orientation as the twin. 3) The specimen may recrystallize; i.e., new grains are nucleated and grow at the expense of the twins and the crystal immediately adjoining the twin. Such grains have orientations which are not present before. Contraction has been observed in iron,3 titanium,3, 4 beryllium,5 zinc,8, 7 Fe-A1 alloy,' and uranium.9 Long anneals at high temperatures are required to have any appreciable effect in these metals and only thin twins are absorbed. Lens-shaped twins are absorbed from the edges: the thin, almost parallel-sided twins are usually punctured in several places and each piece contracts independently. Absorption is very gradual and no sudden cooperative jumps have been observed. The expansion of a twin into a larger grain of identical orientation is unusual, but such growth has been observed in iron,"'" zinc,6 and uranium." Crystals which have been deformed simultaneously by slip and twinning recrystallize first in the area adjacent to the twin. New grains appear faster where the twins intersect: but isolated twins, especially if thick, can also give rise to new grains. This type of recrystallization occurs in zinc.6, 7, 12, 13 and beryllium.14 Reed-Hill noted, in a single crystal of magnesium, the nucleation of a recrystallized grain at a twin intersection which had the same orientation as the second-order twin and which grew into the highly strained matrix.15 Short-time annealing has been reported to cause no change in the deformation twins in vanadium,16 columbium, 17, 18 tantalum,19 tungsten,'' and zinc.7 The purpose of this investigation was to note the effects of annealing on the coherent and noncoherent boundaries of deformation twins in columbium and to locate the nucleating sites for recrystallization. The orientation relationships, which the new recrystallized grains have with the parent crystal and the deformation twins, were also determined. EXPERIMENTAL PROCEDURE Single crystals of columbium were obtained by cutting large grains from electron-beam-melted buttons which contained 10 to 50 ppm C, 10 to 100 ppm O,, 1 to 10 ppm H2, and 10 to 15 ppm N2. The crystals were hand-ground and chemically polished until all grain boundaries were removed. The specimens were mounted in an epoxy resin and a face of each crystal was mechanically polished on a Syntron polisher using Linde A and then Linde B polishing compounds. After all faces were mechanically polished, the crystal was electrolytically polished to remove all distortion due to cutting and grinding. Laue photographs were taken of all faces of the crystals to determine the quality and orientation of each crystal. The crystals were compressed about 10 pct at -196 C in a specially constructed compression cage with an Instron tensile machine. Each crystal was separated from the top and bottom anvils by teflon films which acted as a lubricant. With the specimen crystal in position, the entire cage was cooled to -196°C by being submerged in a Dewar containing liquid nitrogen. The crystals were compressed at a rate of 0.02 in. per min and the load was recorded on a strip-chart recorder. After deformation the crystals were mechanically polished on 600-grit paper and Pellon cloth with Linde A and Linde B polishing compounds. The crystal faces were chemically polished and then etched. The twin planes were identified metallographically from an analysis of the twin traces on two surfaces. Annealing was carried out by placing each crystal in a columbium bucket made from the same electron-beam-melted material as the crystal itself and suspending the bucket by a tantalum wire in a quartz tube. After a vacuum of 10-7 Torr was attained, a furnace at 1000" or 1600 C was raised into position and the crystals held for various lengths of time. The crystals were repolished and etched after annealing to remove any surface contamination. Approximately 0.010 in. was removed during this process. The resulting surface was examined metallographically for microstructural changes due to annealing. A microbeam Laue camera mounted on a Hilger Micro-focus X-ray unit was used to determine the Orientstions of the recrystallized grains. This X-ray micro-beam camera had a 0.002-in.-diam collimator and incorporated the ideas of both and and chisWik21 and Cahn.22

Jan 1, 1967

By C. G. Bieber, J. R. Mihalisin, R. T. Grant

A growing demand for longer service life of gas turbines has placed increasingly rigorous requiret~rents upon superalloys employed for that application. Long-titne testing at high temperature has revealed that phase transformations occur in all superalloys. A common one of particular interest is o formation. Presented here are studies made to identify a and to characterize its formation and effect on properties in three cast nickel-base superalloys—IN 100 alloy, alloy 713C, and alloy 713LC. Methods are discussed by which o can be eliminated or inhibited in IN 100 alloy and alloy 713C. Evidence was obtained to indicate that some types of o may be more detrimental than others. Limitations in the electron vacancy approach to o prevention are pointed out, and it is shown how alternative approaches, such as reducing a complex superalloy matrix to the form of a pseudo-ternary system permitting equilibrium diagram treatment, lead to additional insights into the formation of in these alloys. AROUND 1960. Beiber1 developed IN 100 alloy, which still remains one of the strongest commercially available nickel-base superalloys. The principle used in the design of this alloy was to produce large quantities of y' phase in a y matrix through the use of copious amounts of aluminum and titanium. In 1963, ROSS' showed that when certain heats of this alloy were held for a long time at 1650°F they formed an acicular phase, subsequently identified as a.3 a is a hard and brittle phase first discovered in the Fe-Cr system by Bain and Griffiths.4 They termed it the "B" constituent. Subsequently this same phase was found in other systems, primarily those of the transition elements, and acquired the name "a" by which it is now known. The crystal structure of the a phase was first determined in the Fe-Cr system in 1950.5 It was shown to be tetragonal with a c/a ratio of about 0.52. as is the case with a found in other systems. This characteristic crystal structure is now the means by which a is identified. In superalloys, such as IN 100 alloy. large amounts of o impair the high-temperature creep strength and drastically reduce room-temperature tensile ductility. Discovery of o phase in some heats of IN 100 alloy quickly led to investigations of other superalloys for similar transformations. It was found that many of the stronger, more highly alloyed. super-alloys were indeed susceptible to o formation. This investigation has been concentrated on three commercial alloys: IN 100 alloy, alloy 713C, and alloy 713LC. J.R.MIHALISIN,MemberAIME, and C.G.BIEBER are with The International Nickel Co., Inc., Paul D. Merica Research Laboratory, Sterling Forest, Suffern, N. Y. R. T. GRANT, Member AIME, is with The International Nickel Co., Inc., Pittsburgh, Pa. Manuscript submitted May 22. 1968. IMD A detailed study has been made of the phase transformations and their relation to a formation along with a consideration of electron vacancy approaches for predicting a-forming propensity in these alloys. EXPERIMENTAL PROCEDURE Phase transformations were studied by light and electron microscopy, electron diffraction, microprobe investigations, and X-ray diffraction. Specimens for light micrographic examination were prepared by conventional grinding and polishing followed by etching with glyceregia (2:l HC1/HNO3 + 3 glycerine by volume). Photomicrographs of stress-rupture specimens were taken adjacent to the fracture unless otherwise noted in the text. Negative replicas for electron microscopy were taken from surfaces electropolished with a solution of 15 pct H2SO4 in methanol. For carbon extraction replication, a solution of 10 pct HC1 in methanol was used. A Siemens Elmiskop I was used for all electron microscopy. Selected-area diffraction studies were made at 80 kv using evaporated aluminum for standardizing the patterns. A nondispersive electron microprobe attachment was used to analyze the extracted precipitates chemically. The fluorescent X-rays were recorded using a flow counter containing P10 gas (90 pct Ar-10 pct methane) with a beryllium window and a single-channel pulse-height analyzer. The pulses from the analyzer were passed to a scaler-ratemeter and differential curves of counting rate vs pulse amplitude were obtained. The base line of the analyzer was driven with a synchronous motor at 0.5 v per min and a channel width of 0.5 v. The time for 105 counts was printed out for each 0.5-v increment. The microscope was operated at 80 kv with beam currents of 1 to 20 pa. This equipment detects elements from atomic number 13 to 40. X-ray diffraction studies were usually made on residues electrolytically extracted in 10 pct HC1 in H2O, although in one case a pattern was obtained from an etched surface of a metallographic specimen. A Siemens Crystalloflex IV was used with iron-filtered CoKa radiation. X-ray patterns were recorded using a goniometer speed of : deg per min. The scintillation counter and pulse-height analyzer operated at a channel height of 10 v and a channel width of 12 v. The equipment was calibrated with a powdered gold standard. The residues usually contained a number of phases. several of which could not be found in the ASTM card file. In addition, as is shown for the case of a phase in IN 100 alloy, other phases had a somewhat different lattice parameter from that reported in the ASTM card file, making it difficult to separate and identify constituents by comparison with ASTM d spacings. For these reasons, phases were identified on the basis of the lattice parameter obtained by indexing the ob-

Jan 1, 1969

By A. J. Conelius, D. P. Sobocinski

This paper presents a correlation for predicting the behavior of a water cone as it builds from the static water-oil contact to breakthrough conditions. The correlation is partly empirical and involves dimensionless groups of reservoir and fluid properties and of production and well characteristics. The groups were deduced from the scaling criteria for the immiscible displacement of oil by water. The correlation is based on a limited amount of experimenfal data from a laboratory sand-packed model and on results from a computer program for a two-dimensional, incompressible system. Because the correlating groups are dimensionless, they can be used to estimate the performance of water coning cases not specifically considered in the correlation. However, despite its dimensionless nature, the correlation is not completely general and will not provide meaningful estimates of cone behavior in many situations. INTRODUCTION AND BACKGROUND The production of water from oil wells is a common occurrence which increases the cost of producing operations and may reduce the efficiency of the depletion mechanism and the recovery of reserves. We will deal with one cause of this water production, namely, coning. The coning of water into a producing well is caused by pressure gradients established around the wellbore by the production of fluids from the well. These pressure gradients can raise the water-oil contact near the well where gradients are most severe. Gravity forces that arise from fluid density differences counterbalance the flowing pressure gradients and tend to keep the water out of the oil zone. Therefore, at any given time, there is a balance between gravitational and viscous forces at points on and away from the completion interval. When the dynamic forces at the wellbore exceed gravitational forces, a cone of water will ultimately break into the well to produce water along with the oil. We can expand on this basic visualization of coning by introducing the concepts of stable cone, unstable cone and critical production rate. For instance, if a well is produced at a constant rate and the pressure gradients in the drainage system have become constant, a steady-state condition is reached. If, at this condition, the dynamic forces at the well are less than the gravity forces, then the water or gas cone that has formed will not extend to the well. Moreover, the cone will neither advance nor recede, thus establishing what is known as a stable cone. Conversely, if the pressure in the system is in an unsteady-state condition, then an unstable cone will continue to advance until steady-state conditions prevail. If the flowing pressure drop at the well is suffcient to overcome the gravity forces, the unstable cone will grow and ultimately break into the well. It is important to note that in a realistic sense, stable cones may only be "pseudostable" because the drainage system and pressure distribution generally change. For example, with reservoir depletion, the water-oil contact may advance toward the completion interval, thereby increasing chances for coning. As another example, reduced productivity due to well damage requires a corresponding increase in the flowing pressure drop LO maintain a given production rate. This increase in pressure drop may force an otherwise stable cone into a well. The critical production rate, well known in the literature, is the rate above which the flowing pressure gradient at the well causes water (or gas) to cone into the well. It is, therefore, the maximum rate of oil production without concurrent production of the displacing phase by coning. At the critical rate, a built-up cone is stable but is at a position of incipient breakthrough. Numerous papers have been published on critical rates. Some of the better known of these include the work of (1) Muskat and Wyckoff,' who first dealt with the coning problem; (2) Chaney, et al,' who developed expressions similar to those of Muskat but who presented results in a conven ient-to-use graphical form (the "Sun" method); and (3) Meyer and Garder,b hose analysis is based on radial-flow formulas. One assumption in critical production rate analyses is that the cone has built-up to just before its breakthrough into the well. But, these analyses reveal nothing directly about the time it takes for the cone to build up to this incipient breakthrough position. Thus, water-free oil can be produced from a well for prolonged periods at rates above the critical rate before the well reaches the condition to which the critical rate applies. The published literature contains little on the rate of growth of a cone. Experimentally, Meyer and Searcy studied the rate of rise of a cone in a Hele-Shaw model.' Additional related work on water breakthrough and produced water-oil ratios in water driven reservoirs was reported by Muskat," Hutchinson and Kemp," Henley, et al,' and Stevens, et a1.B Theoretically, the basic coning equations for a water-oil system can be developed by applying the conservation of mass to each of the phases, relating flow velocities with pressure by Darcy's law, and relating pressures across water-oil interfaces by capillary pressure. With the usual boundaries at the well and reservoir limits, the solution of the resulting equations for the time behavior of a water-oil interface constitutes a free-surface, boundary-value problem. The shape of the boundary depends on the internal potential distribution, while this

Jan 1, 1966

By C. A. Stickels

A heat of electrolytic iron, to whzch alunzinutn and nitrogen had been added, was hot-rolled, cold-rolled 90 pct, and recrystallized at temperatures from 500" to 700°C. Primary recrystallization textures appear to arise from competitive growth of two types of nuclei: 1) those having orientations belonging to the "usual" primary recrystallization texture found in riming steel, and 2) those with the {111} (110) ovientation. Development of a (111}(1 10) component in the primary recrystallization texture occurs only over a certain interval of isothermal recrystallizatzon temperatures when the material is supersaturated with respect to the precipitation of AlN. Lowering the degree of supersaturation depresses the temperature interval in which a (111)(110) component occurs. An elongated, 'pancake-shaped" recrystallized pain structure and a marked delay in the start of recrystallization were found in all specimens which were supersaturated with respect to A1N precipitation after cold work, regardless of their recrystallization texture. ONE of the consequences of killing low-carbon steel with aluminum is a significant change in recrystallization behavior. About 15 years ago, Solter and eatttiel showed that this behavior was largely controlled by aluminum and nitrogen in the steel. If complete precipitation of A1N was prevented before cold rolling, an increased "recrystallization temperature" was observed in subsequent. annealing, and the recrystal-lized grains were not equiaxed. Leslie et a1.2 studied this phenomenon in some detail and clearly demonstrated the relationship between A1N precipitation, recrystallization kinetics, and the development of "pancake-shaped" grains. It has also been known for some time that aluminum-killed steels, processed to produce elongated "pancake" grains, develop a (11 I}( 110) primary recrystallization texture. This texture has not been found in iron or low-carbon rimming steel as a primary texture4j5 but has been observed following grain growth in electrolytic iron.5 The present work was undertaken to study in more detail the effect of A1N supersaturation on recrystallization textures in iron. LITERATURE REVIEW The deformation texture in heavily rolled iron has been studied in detail by Bennewitz.~ The texture consists primarily of a partial fiber texture about a (110) axis in the rolling direction, designated here as fiber texture A. It includes the range of orienta- tions (111)[110] - (001)[ 110] - (11l)[110]. A weak secondary texture also is present.6 This is a duplex partial fiber texture about two (110) fiber axes located 60 deg from the rolling direction and 30 deg from the sheet normal. The range of this texture, designated here as fiber texture B, about the [101} fiber axis is (112)[110] - near (545)[252] - (211:1[011] *The range given here follows Bennewit~.~ A few pole figures from re-crystallized material indicate a broader range than this.' However, the components which are strongest in the recrystallization texture are in this range.'________________________________________________________ Primary recrystallization textures in unkilled steels can be accounted for by growth of members of fiber texture B present in the deformed metal.5 However, while members of fiber texture B dominate the primary texture, other orientations survive primary recrystallization as well. In particular, some {111}(110) members of fiber texture A must also grow during primary recrystallization, because a well-defined {1ll)( 110) texture develops during subsequent grain growth at 700°C.5 The unusual recrystallization behavior of deformed supersaturated solid solutions has been attributed to: 1) retention of the solute in solution,' 2) formation of coherent, preprecipitation solute clusters prior to and during re~r~stallization,~ and 3) formation of a precipitate prior to and concurrent with recrystallization.'~-'~ When aluminum is supersaturated with iron, the difference in grain boundary mobility between general high-angle boundaries and certain special coincidence site boundaries is apparently eliminated.' In aluminum-killed steels, precipitation of A1N can take place at ordinary subcritical recrystallization temperatures. The rate of precipitation increases with increasing aluminum or nitrogen contents.2'13 There is some doubt, however, as to whether true precipitates form during the time at temperature needed to complete recrystallization. Leslie ef a1.2 found that precipitation in one steel was complete after about 100 min at 700GC, or after about 1000 min at 650GC, as measured by chemical analysis for AlN. Aoki et a1.,13 using internal friction for dissolved nitrogen, showed that a large fraction of the dissolved nitrogen was removed from solution within a few minutes annealing time at temperatures from 400" to 800°C. However , the rate of formation of AlN, as detected bv chemical analvsis. was much slower than the apparent rate of nitrogen removal. Hasebe,'~~ using carbon extraction replicas, has identified A1N precipitates by electron diffraction in a 0.2 C steel, solution-treated at 1300°C and annealed 2 hr at 700°C. Borchers and kim,I6 also using a replication technique, observed precipitates after annealing treatments as short as 2 min at 640°C. However, Leslie et a1.' state that no A1N precipitate can be seen while recrystallization is being inhibited in aluminum-killed steel.

Jan 1, 1967

By Akinobu Kasami, Keiji Maeda, Makoto Naito, Masaharu Toyama

Gap electroluminescent diodes have been prepared by the vapor phase diffusion of zinc into n-Gap crystals which were grown from a gallium solution (10 wt pct Gap) doped with tellurium and Ga203. A marked improvement in the efficiency of the red electrolumines -cence has been achieved by heat treatment after diffusion. External quantum efficiencies of diodes annealed under optimum conditions are 0.2 to 0.6 pct at room temperature, or about 200 times higher than the efficiencies of diodes quenched after diffusion. The optimum dopant concentrations in the gallium melt from which the crystals were grown are 3to6 x at. pct Te and 4 to 8 x 10-2 mol pct Ga203. The efficient diodes are characterized by linearly graded junctions with an i-layer 0.1 to 0.2u thick. Annealing increases the emission intensity by a factor of 20 to 50 and decreases the current density to 1/3 to 1/8 that of quenched diodes at a given bias. The decrease in current is attributed to an annihilation of deep recombination centers in the depletion layer. The increase in emission intensity is interpreted in terms of an increase in lifetime of minority carriers and an increase in the relative intensity of red-to-infrared emission. The dependence of these quantities on the tellurium and oxygen doping levels is also discussed. A number of studies have been made of the red light emission from for ward-biased Gap diodes.' At room temperature this emission band is centered at 7OOO? with a spectral width of nearly 1000?. Low-tempera-ture photoluminescence indicates that this emission is due to either the radiative annihilation of an exciton bound to a pair of zinc and oxygen atoms substituting on nearest neighbor lattice sites2,3 or the radiative recombination of an electron bound to this Zn-O pair with a hole bound to an isolated zinc shallow acceptor.3 An emission band is also observed with a spectral peak at 9800?. This infrared emission has been shown to be due to the recombination of an electron trapped at an isolated oxygen deep donor with a hole trapped at an isolated zinc acceptor.4 The red emission from Gap diodes is fairly efficient at room temperature because the nearest neighbor Zn-0 pair forms a deep electron trap at 0.3 to 0.4 ev below the edge of the conduction band.2'4 In diodes grown by liquid epitaxy an external quantum efficiency of 2.1 x 10-2 (photon/electron) has been attained by heat treatment at relatively low temperatures.5 This heat treatment was found to increase the efficiency by a factor of 3 to 6. However, no detailed studies have-been reported on the effects of heat treatment. We can only cite Onton and Lorenz's work6 on the change ; in the relative intensity of red-to-infrared emission. Heat treatment has also been tried on junctions built in during growth, but contrary to expectations the efficiency decreased. In-diffusion is a simple and controllable method of fabricating p-n junctions. For Gap, zinc is generally used to form a p-type layer on n-type crystals. The emission efficiencies of in-diffused diodes are, however, extremely low in comparison with liquid epitaxial diodes.' Although efficiencies as high as 2 x 1O-3 have been reported, values from 10-6 to 10-4 are generally obtained by typical diffusion techniques. Out-diffused diodes are known to be a little more efficient than in-diffused diodes. Nevertheless, the quantum efficiency is at most 7 x 10- 3 and ordinarily of the order of 10-4.8 NO results have been reported on heat treatment of either in-diffused or out-diffused diodes. This paper reports a marked improvement in the efficiency of the red emission observed for in-dif-fused diodes as a result of heat treatment after diffusion. The method described reproducibly yields diodes with external quantum efficiencies of 2 to 6 x 10-3. The observed dependence of efficiency on annealing time and on doping level will be discussed in terms of the lifetime of minority carriers and the formation of Zn-O complex pairs. EXPERIMENTAL A) Diode Fabrication. The n-Gap crystals used in this study were grown from a saturated gallium solution by a slow cooling method.8 The Gap content in the gallium melt was fixed to 10 wt pct corresponding to a growth temperature of about 1100 Tellurium was chosen as the n-type dopant and added to the melt in concentrations ranging from 0.001 to 0.06 at. pct. Oxygen was added in the form of Ga2O3, whose concentration was varied from 0.004 to 0.2 mol pct. The resulting crystals were platelets with well-developed (111) surfaces. Typical electrical properties were Hall mobilities of 130 to 30 sq cm per v-sec and carrier concentrations of 1016 to 10" cm-3 at room temperature. Diodes prepared from crystals with relatively low doping levels, in which u = 130 to 100 sq cm per v-sec and n = 0.6 to 6 x 1017 Cm-3, were examined in detail. The p-n junctions were produced in these n-Gap crystals by the diffusion of zinc from the vapor phase by the following procedure. The platelets were carefully lapped on both sides to a thickness of 150 to 200 u while maintaining the (111) orientation. After being etched in hot aqua regia, the crystals together with the zinc were sealed in an evacuated 12 mm ID quartz ampoule 20 cm long. The crystals and the zinc were then separated from each other at opposite ends

Jan 1, 1970

By Ravindra M. Nadkarni, Milton E. Wadsworth

The kinetics of cetnentation of copper with iron were observed to follow first-order kinetics and increase with speed of agitation to a limiting value. Maximum rates agree closely with theoretical values based upon a model of aqueous solution diffusion through a litniting boundary film. Back reaction kinetics are shown both theoretically and experimentally to be independent of ferrous iron concentration in solution. The inlportance of attnospheres of air, oxygen, nitrogen, and hydrogen was studied and the results have been correlated with several impovtant oxidation processes involving metallic iron and copper. The kinetics of the reaction of ferric ion with metallic iron were found to be slow in the absence of metallic copper and essentially proportional to the surface area of metallic copper present in the system. THE precipitation of copper on iron is classic as an example of a relatively ancient art applied successfully for centuries with little fundamental understanding of the important parameters involved. There is some indication that the process has been a commercial means to produce copper since the sixteenth century.' The amount of fundamental work on the cementation of copper with iron is not great. Wartman and Roberson2 carried out a series of detailed copper cementation experiments using natural and synthetic mine water. The following were presented as the three principal reactions: Reaction [I] is the desired cementation reaction and accordingly 0.88 lb of iron would produce 1 lb of copper. In actual practice iron consumption would more normally fall in the range of 1.5 to 2.5 lb per lb of copper. Wartman and Roberson attributed the excess consumption of iron to Reactions [2] and [3]. They found that Reactions [I] and [2] proceeded at approximately the same velocity while Reaction [3] was much slower and would be diminished by controlling the contact time. It was also pointed out that increased agitation is beneficial in removing hydrogen bubbles and barren layers of solution at the iron surface as well as removing contaminants resulting from the hydrolysis of iron. Episkoposyan3 and Episkoposyan and Kakovskii4 studied copper and silver cementation on rotating iron disks in chloride solutions. The kinetics based upon a diffusion model were first order and varied linearly with surface area and with angular velocity raised to the one-half power according to the Levich equation. The experimental activation energy for both copper and silver was approximately 3 kcal per per mole. Excess iron consumption was found to increase with temperature. The rate of cementation first increased with increasing acidity and then diminished at high acid concentrations. sutolov5 has presented an excellent review of the Leach-Precipitation-Flotation (LPF) process including a discussion of copper cementation from an electrochemical point of view although few experimental results were presented. From voltage considerations he predicted that cementation should not be influenced by the concentration of ferrous iron in solution. He considered several secondary reactions including Reactions [2] and [3] and pointed out the importance of oxidation of ferrous iron to ferric with oxygen. In addition it was suggested that Reaction [2] was enhanced by the dissolution of metallic copper by ferric iron which in turn consumed excess iron by the cementation reaction, Eq.[1]. Cementation of copper on metals other than iron has been studied by several investigators but, as in the case of iron, the amount of fundamental work is not extensive. Bashkova and kovalenko6 and Bashkova7 studied the cementation of copper on indium from copper and indium sulfate solutions. The rate was found to be first order and to increase with acidity. This was associated with a decrease in potential (EIn — ECu) and the simultaneous reduction of hydrogen ions at low pH. The rate of cementation also decreased with increasing indium concentrations which was postulated to be due to the decrease in the rate of diffusion of the ions in solution. Below 97°C the experimental activation energy was found to have the unusually low value of 2 kcal per mole and was attributed to diffusional control. Above 97°C the rate increased suddenly and was explained as a change in the rate-controlling step to a chemical reaction. In Part I of this study Nadkarni et a1 .1 have reported on preliminary results obtained in a laboratory study of the kinetics of the cementation process. The rate was found to be first order, proportional to the surface area of the iron, and to increase with speed of stirring until a maximum rate was observed. At low stirring speeds the deposit was spongy and adherent. At medium speeds the copper peeled off in bright strips and at high speeds finely divided copper was produced and continually removed from the surface. The amount of excess iron consumed increased with speed of stirring and with temperature. The average experimental activation energy combining results from several types of iron was 5.8 + 1.6 kcal per mole suggesting diffusional control through a limiting boundary film. Traditionally copper cementation has been carried out over the centuries in gravity-fed launders of various design containing scrap iron. More recently rotating drum precipitators and activated launders8'10 have been used. In the latter, copper-bearing solutions are

Jan 1, 1968