Search Documents

By P. Chiotti, J. T. Mason

Thermal, X-ray, metallographic, and resistivity data were obtained to establish the phase diagram for the Yb-Zn system. Six intermetallic compounds and five eutectics have been identified. The compounds position at 695°C. No evidence for the compound YbZn,, was observed. Whether this compound is stabilized or inhibited by small amounts of impurities is uncertain. SEVERAL aspects of the Yb-Zn system have been reported in the literature. Much of this work deals with the crystallographic identification of some of the compounds. The YbZn compound has been reported by Iandelli and palenzonal and the YbZn, structure and thermal data for the composition range between YbZn and Yb3Znll have been reported by Michel et al. A compound of uncertain stoichiometry in the range 60 to 68 wt pct Zn with a cubic structure has been reported by Kuz'ma et aL4 The YbzZn17, YbZn,,, and YbZn13 compounds have been reported by both Kuz'ma et a1 and Iandelli and Palenzona.' YbnZn17 has also been identified by Laube. This investigation was undertaken to establish the phase diagram of this system. Ytterbium in many respects behaves as an alkaline earth rather than a rare earth metal6 and it is of interest to note the resemblance between the Yb-Zn system, the Ca-Zn,' and typical rare earth-zinc systems.g'10 MATERIALS AND EXPERIMENTAL PROCEDURES The materials used in this investigation were Ames Laboratory ytterbium and Bunker-Hill slab zinc, 99.99 pct pure. Analyses of the ytterbium showed 38 ppm Ta, 82 ppm 0, and 15 ppm N with Ca, Cu, C, Mg, Al, Si, Cr, Fe, Ni, Sc, Y, Er, Tm, and Lu all less than 50 ppm. The ytterbium was dehydrogenated by heating in tantalum under vacuum for 8 hr at 900°C. The metal was kept under argon except when being cut with shears and when being weighed. Tantalum was found to be a suitable container for alloys in the composition range between ytterbium and Yb2Zn17. With higher zinc concentrations the tantalum was penetrated by the alloy and failed after several days at temperatures of 600" to 700°C. Approximately 20 g of zinc and ytterbium metal were sealed under argon in *-in.-diam tantalum cruci- bles equipped with thermocouple wells. The crucibles were in turn sealed in stainless-steel jackets. The alloys were equilibrated in an oscillating furnace and given various heat treatments in a soaking furnace. The steel jackets were removed and differential thermal analysis data were obtained under an atmosphere of argon. The thermal analysis apparatus was calibrated against the melting points of pure zinc, aluminum, silver, and copper and found to give thermal arrests within 1°C of the accepted melting temperatures for these elements. The thermal analysis apparatus has been described in an earlier paper.g Alloys were further heat-treated as necessary and subjected to metallographic examination and X-ray diffraction analysis. Most alloys were etched with Nital (0.5 to 10 pct nitric acid in alcohol). EXPERIMENTAL RESULTS The results of the thermal analysis are summarized by the points on the phase diagram, Fig. 1. Six compounds and five eutectics were observed. The eutectic temperature and compositions in weight percent zinc are 491°C and 12 pct, 645°C and 32 pct, 687°C and 54 pct, 742°C and 67 pct, and 750°C and 77 pct. The compounds YbZn, YbZn2, Yb2Zng, Yb2Zn17, and YbZnll melt congruently at 650°, 751°, 75Z°, 754", and 755"C, respectively. The compound Yb3Znll undergoes a peritectic decomposition at 695°C. The transformation and melting temperatures for the ytterbium were observed to be 797" and 817°C. re-

Jan 1, 1969

By R. E. Maringer, B. A. Wilcox, A. H. Clauer, J. H. Sovik

Internal friction measurements from 25° to 1100°C have been made on specimens machined from TD nickel bar. The use of miniature torsional pendulum specimens alloived damping measurements to be made on specimens whose axes were parallel to the original bar axis, at 45 deg to the bar axis, and at 90 deg to the bar axis. There was a marked difference in damping with varying specimen orientation, and this was related to the pronounced micro structural anisotropy of this material. Varying the microstructure by cold working plus re crystallization annealing also greatly affected the damping behavior. Recrystallization essentially removed the broad peak found at 400° to 650°C in as-received TD nickel, and in addition greatly lowered the background damping. DlSPERSION hardened metals such as SAP-type alloys (Al + AI2O3) and TD nickel (Ni + 2 pet ThO2) have been developed primarily to improve high temperature strength properties. There have been numerous damping studies on SAP-type alloys,1"9 and one of these6 showed that the damping capacity was greater than that of 99.5 pet pure Al from 25° to 600°C. Several preliminary observations on TD nickel10 and an experimental Ni-ThO2 alloy11 indicated that here, too, the damping capacity was quite high. A high damping capacity in TD nickel, combined with its relatively good high temperature creep strength, could provide an additional benefit for some high temperature structural applications. This work was undertaken to study the internal friction behavior of TD nickel bar over the temperature range 25° to 1100°C. In Ni-ThO2 and Ni-Cr-ThOz alloys, other properties such as steady-state creep rate,12 creep rupture life,12'13 modulus of elasticity,14 and ultimate tensile strength,14 are sensitive to orientation with respect to the primary working direction. Thus, in order to examine anisotropy effects in damping, studies were made on specimens machined with their axes parallel, at 45 deg, and transverse to the original bar axis. MATERIAL DESCRIPTION AND EXPERIMENTAL PROCEDURES The material used in this investigation was from the same £ in. diam TD nickel bar that has been studied previously.13'15 The structure typical of the as-received TD nickel is shown in Fig. 1, and additional details of the structure can be found in Refs. 13 and 15. Elongated grains are parallel to the bar axis and are about 10 to 15 u long and about 1 u in diam. This structure is very stable, since no recrys-tallization or grain growth occurred after annealing for 3 hr at 1300°C.13 The total ThO2 content was 2.3 vol pct and the particles ranged in diameter from 100 to 1000. The average particle diameter was 370Å and the mean planar center-to-center particle spacing was 2340Å. To examine the influence of grain and subgrain structure on damping, a section of TD nickel bar was swaged and drawn at room temperature from 1/2 in. diam bar to 0.040 in. diam wire (99.3 pct re-duction in area). The structure in Fig. 2 resulted after the wire was annealed for 3 hr at 1250°C. The recrystallized grains were much larger than the grains in as-received bar, but still showed considerable elongation in the direction of working. A high

Jan 1, 1970

By H. E. Stauss, J. Hino

INTEREST in silicon has arisen again in the past decade as a result of improvements in crystal rectifiers.' Although the preparation of silicon was first reported by Berzelius in 1880, the early product was of relatively low purity, and only the need for rectifiers in World War II led to the production of a 99.9+ pct pure powder. This material in crystalline form was consolidated into massive silicon for use, and the method developed was to melt it with selected added constituents as "doping" agents. Melting techniques, therefore, are of great importance. There are two basic problems in producing silicon ingots free of doping additions; one is the prevention of spitting and the other is prevention of cracking of the ingot during freezing. The most satisfactory arrangement yet developed for producing massive silicon is to melt and freeze in a cylindrical quartz crucible surrounded by a concentric heating element and concentric radiation shields or insulation. For example, use can be made of a tubular heater with a high frequency generator as the source of power and reflecting shields of alundum cylinders. The spitting of silicon is related to gas evolution, and the gas comes from two primary causes—adsorbed gas and the reaction products of silicon and the crucible. Gas is also released from bubbles contained in the quartz crucible walls. Improved removal of adsorbed gas can be achieved by means of controlled melting and freezing. The seriousness of the problem in vacuo is reduced with an electrically operated mechanical movement of the high frequency power coil. The upper portion of the powder charge is melted first and the high frequency coil lowered until the powder is completely molten. During cooling the high frequency coil is raised slowly. These means also reduce the final nonviolent extrusion of large beads of metal through the ingot top during freezing. Better control of spitting and bead extrusion is obtained when melting is done under helium at. atmospheric pressure instead of in vacuo. The problem of reaction between silicon charge and crucible in practice is confined to the reaction between silicon and quartz. This2 apparently is: Si + SiO2 + 2SiO The part that this reaction plays in spitting has not been isolated for separate study. SiO is a volatile vapor at the melting point; of silicon and is released freely during melting in vacuo, but hardly at all in helium at atmospheric pressure. The cracking of ingots is a major difficulty in melting silicon, and its prevention requires special melting techniques or the addition of "toughening" agents such as aluminum or beryllium.' The cracking of the ingots has been explained as being the result of the expansion that occurs upon freezing; although direct observation of freezing ingots reveals visible cracks on the surface only after a red heat has been reached, suggesting that cracking is the result of differential contraction of silicon and quartz. Silicon wets quartz, and the ingot adheres tightly to the crucible. Therefore as ingot and crucible cool, the two either have to pull apart, or at least one must crack. Surprisingly, in spite of the relative thinness of the quartz and the thickness of the ingot, the ingot and the crucible both crack. Microscopic and X-ray4 studies fail to show any plastic flow other than twinning in the ingots. Slow cooling fails to prevent cracking. Another possible solution to cracking is to weaken the crucible. Use of thin-walled crucibles finally led to success with fused quartz crucibles with a wall thickness of 0.25 to 0.50 mm. With such thin-walled fused quartz crucibles consistently uniform success is secured in producing sound ingots 30 mm in diam from the purest available grade of silicon (99.9+) without the use of any type of addition. Melts are made in the size range of 50 to 100 g. Omission of a deliberately added doping agent is not sufficient to insure pure ingots. The reaction of silicon with crucibles and the resultant solution of impurities in the silicon is well-established." In this laboratory, the presence of Al, Be, and Zr has been found spectroscopically in ingots melted in contact with alumina, beryllia, and zircon. The best crucible materials reported in the literature are MgO and SiO2. Use of MgO in this laboratory has resulted in a heavy deposit of magnesium on the furnace walls, showing that a reduction of the magnesia occurred and the resulting magnesium removed from the melt by volatilization. In the case of quartz, the silica is reduced and SiO liberated to deposit on the equipment walls. There probably is real danger that oxygen is dissolved in the ingot when either magnesia or silica is used as the crucible material. Preliminary analyses by Dean Walter in his vacuum unit in this laboratory6 indicate the presence of oxygen in undoped silicon melted in quartz.

Jan 1, 1953

By G. W. Brownell, H. T. F. Lundberg, R. W. Pringle, K. I. Roulston

The rapid improvement of the airborne scintillometer and the perfection of its efficiency for counting low energy gamma radiation has made it possible to work out a technique to map in great detail the radiation pattern at the earth's surface. On such maps low radiation over certain areas appears to indicate the existence of oil accumulations, forming a pattern similar to that obtained by the geo-chemists. RADIOACTIVE analyses of samples from the surface of oil fields were carried out more than 10 years ago in Alberta by the alpha particle ioniza-tion chamber technique,' but large enough tracts could not be covered in these investigations to make possible any evaluation of the method as a means of oil exploration. Considerable interest has recently been revived, however, as a result of certain striking advances which have been made in the instrumentation available -for the measurement of radioactivity. It is the object of this paper to indicate the nature of these improvements in radiation technology and then to describe the attempts that have been made to interpret the radioactive patterns obtained in the course of airborne recordings with the new instruments. Since the survey can be carried out from the air and records can be accumulated over vast areas in a short time, the result may easily lend itself to statistical treatment. Areas have been surveyed in Alberta, British Columbia, Saskatchewan, Quebec, Texas, New Mexico, Nebraska, Colorado, Utah, and Montana. Producing fields in Alberta and West Texas have been flown over several times in different directions, Fig. 1. The operations were then extended into unknown territory and drill holes were put down on the anomalies which looked promising. The results from these drillings were encouraging and have given hopes for the development of an entirely new method of oil exploration. Any large scale method for the survey of radioactive anomalies must be based on the measurement of gamma rays, as beta and alpha rays have much too short a range to be of any significance. Thus the essential improvement which has made the present stage of this work attainable is the development of new highly sensitive detectors for gamma radiation. In the past the only detectors of any consequence that were available were the ionization chamber and the geiger counter, but both of these suffer from the defect that only a small proportion of the gamma rays passing through the counter are detected, possibly 0.1 to 0.2 pct. The recent development of the scintillation counter2,3 has completely transformed the situation and has had a considerable impact on many branches of nuclear technology. The detection of alpha particles in zinc sulphide screens by visual observation of the individual scintillations which these particles produce dates back to the early spinthariscope of Rutherford and Crookes, but the combined use of an appropriate scintillating phosphor and photomultiplier tube had to await the technical development of the latter many years later. With this development came the modern era of the scintillation counter and a knowledge of phosphors which have a large light output under the bombarding action of gamma radiation. Some of these phosphors are relatively dense and are capable of stopping a large proportion of the incident gamma radiation. As the sensitive region is the whole volume of the crystal, a very high detection efficiency, 50 pct or more, can be obtained for medium energy gamma rays. Scintillation counters for geological purposes were first developed in 19494-6 in an attempt to utilize this remarkable improvement in efficiency, which has the attractive consequence that only a small portion of the normal background of the counter is due to cosmic radiation. In 1949 tests were made in northern Saskatchewan by Lundberg Explorations Ltd. with portable scintillation counters which gave excellent results in the search for uranium and served to indicate unknown uranium deposits in areas previously closely surveyed with geiger counters. Portable scintillometers (registered in Canada) are now commercially available and in regular use,' and the adaptation of the instrument to radioactivity oil well logging has also been very successful.8 Initial attempts to measure radioactivity from aircraft with scintillation counters were made during this period in the same area and yielded most encouraging results. It would be appropriate to consider some specific requirements for airborne investigations. The essential problem to be met in the detection of any radioactive source is the necessity of obtaining a signal greater than the statistical fluctuations of the background counting rate for the instrument. It is possible to show that Nt>2k2 is the condition for detectability of a signal where N = average background counting rate for the detection. t = time constant of the counting rate meter, used to determine the average number of counts arriving in a certain predetermined time interval. N' = average source counting rate at the detector. k = N/N', and N>>N'. Sample values are given in Table I. Assume that the aircraft carrying the equipment is travelling at 120 mph, in which case it will cover 176 ft in 1 sec. Assume also, as a first approximation, that a point source target is in range when the air-

Jan 1, 1954

By P. R. Sahm, T. V. Pruss, D. A. Gandolfo

Cb 3 Sn powders were hot-pressed to estahlish densi-fication conditions and assess the possible use of such compacts in multiphase structures with ceramic or magnetic inclusions. Superconducting transition temperatures, Tc, were measured as a function of powder particle size, pressing temperature, and second-phase admixtures. The highest transition temperatures were found in coarse powder (5 to 500 u) compacts and were only weakly depended on pressing temperatures up to 1200°C. Fine powders (below 5 p), however, both single-phase CbsSn and Cb3 Sn-composites, showed a stronger dependence on hot-pressing temperatures. While Al2 O3 phase admixtures did not affect T, much more, a Pronounced T, degradation was observed upon the addition of ferrimagnetic Fe2 Mno. 5 Zno.5 O4 powders. Likewise, critical current densities, Jc, at 4.2° K were lowered appreciably in the ferrite doped samples, whereas the neutral A1203 inclusiow gave slightly improved Jc values. MULTIPHASE structures in electronically active materials have recently gained in interest as pointed out by Galasso in a review article.' In superconductors the most widely reported group are eutectic alloys which have been mostly investigated with respect to the proximity effect.2"4 In addition, "artificial eu-tectics", for example in the form of mercury-vycor glass sponge5 or fine niobium wires imbedded in a copper matrix,= have been prepared to attain higher critical fields and critical current densities. The idea was to enhance flux pinning phenomena by second-phase inclusions or ho1es. 7 Flux pinning should also be possible by the introduction of insulator inclusions into a superconducting matrix. Ceramic-metal combinations are most easily produced by hot pressing (= pressure sintering), as it permits an almost unlimited selection of material combinations. Cb 3 Sn has been prepared by vapor phase growths or in the form of thin films. Large compacts must be sintered,1° however, and normally present difficulties. At temperatures below 1350°C insufficient densities are obtained and at higher temperatures the loss of tin due to dissociation upsets the stoichiometry. Hot pressing is a natural approach to circumvent the problems, since one can obtain satisfactory densities despite low sintering temperatures. This work was mostly concerned with establishing conditions to hot press Cb3 Sn and Cb3 Sn multiphase structures (= composites), because no data are presently available, and to evaluate these with respect to their transition temperatures. However, a few measurements on critical current densities were also carried out, in particular to assess the value of ferrimagnetic inclusions. I) EXPERIMENTAL PROCEDURE The experimental procedure involved the preparation of feed material and powders, hot pressing, and evaluation of the resulting ingots. As no attempts were made to synthesize Cb3Sn from the elements during hot pressing, feed material had to be produced. For this purpose, a stoichiometric Cb-Sn powder mixture was compacted into a 3-cm-diam ingot (80,000 psi) and then inserted into a quartz tube and evacuated. Rf heating was employed. Above the tin melting point (230°C) liquid tin was forced out of the ingot, but was pulled back by capillary action after approximately 0.5 hr of continuous pumping at 700°C. Thus, it appears that evacuation at this temperature caused desorption of impurity gas creating wetting surfaces which, later on, favored alloying at relatively low temperatures. After a presintering period of 17 hr at 800°C, the quartz tube was tipped off and sealed into another such larger-diameter tube which, in turn, was connected to a pump system. This configuration permitted a temperature treatment at 1400°C, carried out for 65 hr, without collapsing of the glass walls or unfavorable chemical interaction of Cb3Sn with the quartz. The resulting material was

Jan 1, 1969

By C. E. Lundin

The Ce-H system was investigated in the temperature range, 573° to 1023°K, and the pressure range, 10-3 to 630 Torr, as a function of 'composition up to 72 at. pct H. Families of isothermal arid isopleth curves were plotted from the pressure-terr~perature-composition relationships. From these curves the solubility relationships were determined for the system. The isopleths are analytically represented by equilibrium dissociation pressure equations. The relative partial molal enthalpzes and entropies of solution of hydvogen in the systerrz were calculated fronz the dissociation pressure equulions and are tabulated. The integral free energies, enthalpies, and entropies of mixing in the Ce-H system were determined from the relative partial quantities and are also tabulated. The standard free energy, enthelpy, and entvopy of reaction of the dihydride phase at kcal per kcal per mole H2, and ?S° = -34. 1 cal per deg mole H2, respectively. The equilibrium dissociation pressure equation in the two-phase region is: UNTIL recently very little was known of the detailed solubility and thermodynamic relationships of the Ce-H system. Two previous investigations1,2 are noteworthy. However, significant discrepancies and omissions exist on analyzing them. The work of Mulford and Holley1 on cerium did not clearly delineate the boundaries of the two-phase region, Cess - CeH2-x. The plateau partial pressures were not thoroughly defined and were considerably displaced in pressure compared to those from the work of Warf and Korst.2 These latter authors concentrated their studies primarily from 823° to 1023°K in the pressure range of 1 to 760 Torr. No data were determined to outline the regions of primary solid solubility and the hydride phase. Also the establishment of the plateau partial pressures was rather limited in scope. In neither work was a treatment conducted of the relative partial molal enthalpies and entropies of solution of hydrogen in the single-phase regions and the integral thermodynamic quantities of mixing throughout the system. Therefore, it was the objective of this research to determine the complete equilibrium solubility relationships and thermodynamic data for the system by pressure-temperature-composition studies. EXPERIMENTAL PROCEDURE The cerium metal for this study was donated by the Reno Metallurgy Research Center of the Bureau of Mines. Total impurity content was 0.13 pct with only 60 ppm O. The metal was checked metallographically and contained only minor amounts of second phase compared to cerium from other sources. Specimen preparation was done in a dry box flushed with argon gas. The surface of a small rectangular piece of cerium (about 0.2 g) was filed with a clean, mill file. Final weighing was done in a tared enclosed vial containing argon gas. The specimen was then loaded quickly into the reaction chamber which was purged several times with high-purity hydrogen gas and then allowed to pump to about 10-6 Torr. The furnace was heated to the reaction temperature and the run started. The equipment used to conduct the hydriding was a Sievert's-type apparatus. Basically it consisted of a source for pure hydrogen, a precision gas-measuring burette, a heated reaction chamber, a McLeod gage, and a mercury manometer. Pure hydrogen was supplied by the thermal decomposition of uranium hydride. The 100-ml precision gas burette was graduated to 0.1-ml divisions and was used to measure the quantity of gas and admit it to the chamber. The reaction chamber was a quartz tube. Prior to each run, the cerium specimen was wrapped in a tungsten foil capsule to prevent reaction of the cerium with the quartz. Control of the temperature was achieved within ±1°K. Pressures in the manometer range were measured to ±0.5 Torr and in the McLeod range (10-3 to 5 Torr) to ±3 pct. The compositions of hydrogen in cerium were calculated in terms of hydrogen to cerium atomic ratio. These compositions were estimated to be ±0.01 H/Ce ratio. The technique used to study the equilibrium pressure-temperature-composition relationships of the Ce-H system was to develop experimentally a family of isothermal curves of composition vs pressure. The range of pressure through which each isotherm was developed was from 10-9 to about 630 Torr in the temperature interval, 573° to 1023°K. RESULTS AND DISCUSSION The hydriding characteristics of cerium are iso-morphous with those of the elements of the light-rare-earth group (lanthanum, cerium, praseodymium, and neodymium) wherein the region from the dihydride to trihydride is continuously single phase.' The structure of this phase is fcc.3 The heavy rare earths form a trihydride,2 which is hcp, separated by a two-phase region from the fcc dihydride phase. The Ce-H system is represented by the family of experimental isotherms in Fig. 1. Due to the small scale required to draw the curves, the experimental points are omitted; however, a total of 240 experimental data points were taken to prepare these curves. The solubility relationships can be deduced therefrom. Three distinct regions of partial pressure and composition can be seen. The region of cerium solid solution is represented by the rapidly rising isotherms in the dilute composition range. In accordance with Gibbs Phase Rule only one solid phase, the cerium solid so-

Jan 1, 1967

By J. E. Miller, W. E. DeVaney, L. Stroud

During a recent phase study of a natural gas, two stable equilibrium liquid phases were observed at temperatures below —200°F and pressures above 200 psi. This paper reviews the published literature on the occurrence of multiple equilibrium liquid phases and presents analytical data for the vapor and two equilibrium liquid phases of the liquefied natural gas at five experimental conditions. In addition, data for 30 conditions of two-phase equilibria are included. INTRODUCTION The low-temperature phase behavior of gases, most of which contained helium, has been investigated in the laboratories of the Helium Activity for many years. Since 1952, experimental studies of these systems have been continuous as part of the research program at Amarillo, Tex. Because of their value to private industries interested in participating in the Helium Conservation Program, several "Open File" reports containing phase equilibria data for heliurn-bearing natural gases have already been released by the Helium Activity. A paper containing information on the general phase behavior, operating criteria and extensive vapor-liquid data for two helium-containing systems was recently published.2 Additional publications presenting experimental data on the phase relationships of various gas systems are now in process and will be available in the near future. PREVIOUS EXPERIMENTAL WORK Although the formation of multiple liquids has been reported for various systems, to our knowledge this paper is the only substantiated evidence of a vapor-liquid-liquid equilibria in a naturally occurring gas. In 1940, Vink, Ames, and others13 reported the presence of two liquid phases in a hydrocarbon system consisting of mixtures of crude oils, solvents and natural gas. Eilerts and co-workers; published data on the recombined fluids from a gas-condensate well. This condensed gas, containing approximately 76 per cent methane and 24 per cent ethane-plus, exhibited two distinct liquid phases. Weinaug and Bradley 14 observed "unusual" phase behavior in a reservoir mixture. These workers postulated that the anomalous phase behavior was due to the "imminent formation of a second liquid phase". Botkin, Reamer, Sage and Lacey 1 studied two California crude oils that exhibited multiple phases. Kohn and Kuratal0 recently reported two equilibrium liquid phases in the methane-hydrogen sulfide system. Roof and Crawfordl1 and Eakin, et a16 also have reported experiments with binary systems that formed two stable equilibrium liquid phases. APPARATUS AND PROCEDURE A U. S. Bureau of Mines Phase Equilibrium Apparatus was used in conducting this study. The apparatus and procedures employed in its operation have been previously described3 and will not be repeated in detail ill this report. Briefly, the apparatus consists of a windowed cell which can be maintained within ±0.5°F for temperatures between room temperature arid -320°F. Pressure within the cell can be maintained within 0.1 per cent of gauge reading up to 800 psig. Equilibrium vapor and liquid samples are obtained in special containers4 for analysis by a mass spectrometer. Although the accuracy of the analyzer is about ±0.1 mol per cent, the reproducibility of the phase-equilibrium apparatus is considered relatively poor. Values reported from methane and nitrogen are considered accurate to ±l.0 and ±0.6 mol per cent. Data for ethane-plus in the vapor are accurate within 0.2 mol per cent; liquid-phase data for this aggregate compolnent are accurate within 1.5 mol per cent. For helium in the vapor phase, the analytical data are accurate within 0.2 mol per cent; liquid-phase analyses for this component were obtained by the charcoal adsorption method described by Frost8 and are accurate within 0.006 mol per cent. All of these references to the accuracy of reported values are conservative estimates based upon a statistical treatment of reproducibility data obtained with the apparatus.

By C. Chu

An investigation has been made of the radial heat-wave process using a mathematical model in two-dimensional cylindrical coordinates. This model considers combustion, convection and conduction inside the reservoir, but only conduction in the bounding formations. From a study of the general features of the process, an important phenomenon has been revealed, namely, the feedback of heat into the reservoir on the trailing edge of the heat wave. The effects of various process variables on the performance characteristics of the process have also been investigated. It was found that up to the time when the combustion front reaches a given point, the per cent heat loss, provided it is not higher than 40 per cent, is approximately directly proportional to the square root of thermal conductivity arid fuel content, but inversely proportional to the square root of gas-injection rate and oxygen concentration. The effecr of reservoir thickness is more pronounced, since halving the thickness doubles the per cent heat loss. The most decisive factor in determining the center-plane peak temperature is the fuel content of the reservoir. Within the temperature range investigated, doubling the fuel content doubles the peak temperature in the early stage, but the rate of decline of the peak temperature is high. Reservoir thickness is also a very influential factor. The peak temperature is lowered when the thickness is reduced; however, the effect of thickness becomes less pronounced when the thickness is high. Reduction of oxygen concentration increases the peak temperature in the early stage but lowers it afterwards because of the higher rate of decline of the peak temperature. Increase in gas injection rate or decredse in thermal conductivity geives a higher peak temperature which stays high for a longer period. The propagation range of the heat wave is chiefly governed by the fuel content of the reservoir. An increase of 0.2 1b/cu ft in the fuel content increases the propagation range by 100 per cent. The propagation range is more than doubled by doubling the gas injection rate, or reservoir thickness, or by reducing the thermal conductivity by 50 per cent. Comparatively, oxygen concentration has less effect on the propagation range. INTRODUCTION Several investigators have conducted theoretical studies of a radial heat wave. Vogel and Krueger1 studied a system with a moving cylindrical heat source of constant temper- ature, considering conduction in the radial direction only. Ramey2 included conduction in the vertical direction in his studies. Bailey and Larkin2 attacked a more general problem where initial well heating, vertical heat losses and arbitrary frontal velocities were included. In all these studies, however, conduction was considered to be the only means of heat transfer. Bailey and Larkin in a later paper included the effects of convection in a study involving both linear and radial geometries. Vertical heat losses were neglected in the radial case. Katz5 studied a similar problem in a one-dimensional radial model, using a heat-loss coefficient to account for vertical heat losses. Selig and Couch6 mployed a cylindrical model and investigated two limiting cases. In one case they considered no heat loss from the reservoir whereas in the other they assumed a constant temperature at the interface between the reservoir and its bounding formations. Thomas' studied a more general case but assumed a permeable bounding formation so that the convection effect is not confined to the reservoir. In the present work a more realistic and more generalized model is used. It involves a two-dimensional cylindrical system with combustion, convection and conduction inside the reservoir, but only conduction in the bounding formations. The purpose is to establish the temperature distribution both inside and outside the reservoir, to study the general features of the radial heat wave process, and to investigate the effects of various process variables on the performance characteristics of the process. THEORY We fist consider a circular porous reservoir of thickness H extending vertically from y = — H/2 to y = + H/2. The reservoir extends from a well bore radius r, to an external radius re. A stream of oxygen-containing gas is introduced into the reservoir through the wellbore. The oxygen-containing gas reacts with the fuel contained in the reservoir and forms a combustion front wherever the prevailing temperature can support the combustion. It is here assumed that this combustion front constitutes a cylindrical surface source of heat having an infinitesimal thickness in the radial direction and extending vertically throughout the whole thickness H. This is designated as Region I. We next consider a Region II corresponding to the upper and lower formations bounding the reservoir, extending from y = — - to y = — H/2 and from y = + H/2 to y = + m. Since r, is very small, we may assume that the two bounding formations have the same dimensions, symmetric with respect to the center plane of the reservoir. In this way, we may take the upper half of the system alone into consideration. In contrast with

By J. D. Mote, J. E. Dorn

This investigation was undertaken to study the effects of piledup arrays of dislocations on inducing slip, twinning, and fracturing in magnesium bicrystals. A series of variously oriented bicrystals of magnesium having a vertical grain boundary were prepared and tested in tension. It was found that piled-up arrays of dislocations at the grain boundary could, under appropriate conditions, induce slip, twinning- and cracking. The results that were obtained substantiate, at least qualitatively, the general dislocation mechanism for transmission of strain across grain boundaries and the Petch-Stroh concept of fracturing. WHEREAS single crystals of magnesium generally exhibit extensive deformation, coarse-grained poly-crystalline magnesium at subatmospheric temperatures fractures after a few percent elongation.' Although a small amount of ductility is obtained, several features of this fracturing are characteristic of typical brittle behavior. Over a rather broad temperature range the fracture stress is insensitive to the test temperature and the fracture stress increases linearly with the reciprocal of the square root of the mean grain diameter. The course of fracturing is predominantly intergranular, but small fragments of adjacent grains frequently adhere to the fractured surface.2 The brittle behavior of polycrystalline magnesium is attributable to the limited number of facile deformation mechanisms it exhibits at low temperatures. For a general deformation of a randomly oriented polycrystalline aggregate, each grain must exhibit at least five independent mechanisms of deformation to permit accommodation of the imposed deformation from grain to grain.= Although minor amounts of prismatic slip occur in corners of grains where stress concentrations are known to be high, glide in polycrystalline magnesium at low temperatures takes place almost exclusively by basal slip.' The common type of twinning, which takes place on the (1012) pyramidal planes, can under the most favorable orientations, lead to a. strain of only 6.9 pet; the contribution of twinning to the tensile strain would indeed be much less than this in a randomly oriented polycrystalline aggregate of magnesium. Since the three mechanisms of basal slip are coplanar, they are equivalent to only two independent mechanisms, a number insufficient for a general deformation. Consequently, once the permissible twinning has taken place in conjunction with basal slip, no further plastic deformation is possible because of interference to slip at the boundaries of dissimilarly oriented grains. At this stage brittle fracturing takes place due to high stress concentrations at the juncture of slip bands with the grain boundaries; the predominance of intergranular fracturing in magnesium, in preference to transcrystalline fracturing which is prevalent in zinc, has not yet been rationalized. A more atomistic description of the plastic behavior and fracture characteristics of magnesium follows from the analyses made by stroh4 on the stresses induced by piledup arrays of dislocations. Slip first takes place by dislocation motion in the most favorably oriented grains. As the dislocations approach the boundary of a dissimilarly oriented adjacent grain they begin to form an array of dislocations with its attendant stress field. Piledup arrays of screw and edge dislocations introduce high localized shear stresses at the spur of the array; piledup arrays of edge dislocations also induce high tensile stresses localized in the vicinity of the grain boundary. Whereas the shear stresses can induce slip to take place, the tensile stresses, if sufficiently high, can cause fracturing. The localized shear stress will be relieved if sufficient numbers of mechanisms of deformation become operative in the original and the adjacent grain to permit accommodation of the dislocations in the grain boundary. In this event a ductile behavior will be obtained. But if the number of deformation mechanisms is insufficient for complete migration of dislocation arrays into the grain boundary, the tensile stresses due to the edge components of piledup dislocation arrays will continue to increase with increasing applied stress until fracturing takes place. Whereas face-centered-cubic metals have a sufficient number of mechanisms of slip for accommodation of dislocations in their grain boundaries to exhibit ductile behavior, hexagonal-close-packed metals, in general, do not. Consequently, hexagonal-close-packed metals are usually brittle except when conditions such as alloying or temperature permit facile slip by a number of mechanisms. The arguments presented above suggest that the mechanical behavior of magnesium depends on whether or not dislocation arrays in adjacent grains can enter the grain boundary. When such accommodation is possible, ductile behavior is expected; but when such accommodation is impossible, fracturing will ensue. To further test the validity of these arguments it was considered advisable to study the

Jan 1, 1961

By M. R. Tek, R. L. Nielsen

The scaling laws as formulated by Rapoport relate dynamically similar flow systems in porous media each involving two immiscible, incompressible fluids. A two-dimensional numerical technique for solving the differential equations describing systems of this type has been employed to assess the practical value of the scaling laws in light of the virtually unscalable nature of relative permeability and capillary pressure curves and boundary conditions. Two hypothetical systems — a gas reservoir subject to water drive and the laboratory scaled model of that reservoir — were investigated with emphasis placed on water coning near a production well. Comparison of the computed behavior of these par ticular systems shows that water coning in the reservoir would be more severe than one would expect from an experimental study of a laboratory model scaled within practical limits to the reservoir system. This paper also presents modifications of the scaling laws which are available for systems that can be described adequately in two-dimensional Cartesian coordinates. INTRODUCTION Present day digital computing equipment and methods of numerical analysis allow realistic and quantitative studies to be carried out for many two-phase flow systems in porous media. Before these tools became available the anticipated behavior of systems of this type could be inferred only from analytical solutions of simplified mathematical models or from experimental studies performed on laboratory models. To reproduce the behavior of a reservoir system on the laboratory scale, certain relationships must be satisfied between physical and geometric properties of the reservoir and laboratory systems. Where the reservoir fluids may be considered as two immiscible and incompressible phases, the necessary relationships have been formulated by Rapoportl and others.2-5 Rapoport's scaling laws follow from inspectional analysis of the differential equation describing phase saturation distribution in such systems. It will be recalled that these scaling laws presuppose three conditions: (1) the relative permeability curves must be identical for the model and prototype; (2) the capillary pressure curve (function of phase saturation) for the model must be linearly related to that of the prototype; and (3) boundary conditions imposed on the model must duplicate those existing at the boundaries of the prototype. These three requirements seldom if ever can be satisfied in scaling an actual reservoir to the laboratory system because: (1) The laboratory medium normally will be unconsolidated (glass beads or sand) while the reservoir usually is consolidated. Relative permeability and capillary pressure curves are usually quite different for consolidated and unconsolidated porous media. (2) The reservoir usually will be surrounded by a large aquifer which could be simulated in the laboratory only to a limited extent. (3) Wells present in the reservoir would scale to microscopic dimensions in the laboratory if geometric similarity is to be maintained. In view of these considerations, rigorous scaling of even a totally defined reservoir probably would never be possible. The purpose of this paper is to assess the practical value of the scaling laws in the light of the unscalable variables. This has been done by carrying out numerical solutions in two dimensions to the differential equations describing the flow of two immiscible, incompressible fluids in porous media for a field scale reservoir and a laboratory model of that reservoir. While both the reservoir and the laboratory model were purely fictional, each has been made as realistic and representative as possible. The field problem selected as the basis for the investigation was an inhomogeneous, layered gas reservoir initially at capillary gravitational equilibrium and subsequently produced in the presence of water drive. The laboratory model of this reservoir was designed to utilize oil and water in a glass bead pack. The numerical treatment employed was similar to that of Douglas, Peaceman and Rachford6 and it included both capillary and gravitational forces as

By J. S. Brown, A. G. Guy

With the exception of the work of Tammann and Hartmann,1 no published information has been found on the structural changes produced in eutectic structures as the result of heating following plastic deformation. In part this lack of information may be due to the fact that many eutectic structures contain an intermetallic compound as a prominent phase, and as a consequence have been considered to be unworkable. For example, Tammann and Hartmann were able to obtain useful data only on those alloys that they could greatly reduce in thickness by cold rolling. This restriction placed on the investigation of alloys containing intermetallic compounds has been largely removed by the work of Savitskii2 which showed that large deformations of such alloys can be produced by relatively slow compression at temperatures near the melting range. It was possible, therefore, to carry out the present work on a range of binary eutectics including one composed of two intermetallic compounds. The essential results obtained on the alloy systems studied are illustrated by the Pb-Mg eutectic containing 33.2 pct Mg, Fig 1. The cast structure, Fig la, was obtained by melting together magnesium of 99.8 pct purity and chemically pure test lead, casting into a heated, small steel mold, and furnace cooling in the mold from about the eutectic temperature. The fairly coarse eutectic structure thus obtained was too brittle to work at room temperature without cracking. Fig 16 shows the worked structure obtained by compressing a 1/2-in. cube 70 pct in about 15 sec at 550°F and then water quenching. The pronounced changes in the distribution of the two phases produced by heating the worked alloy at 850°F for 1 hr are shown in Fig lc. Recrystallization of both phases appears to have taken place, and the mechanical properties of the cast alloy must have been significantly changed by the working and heat treatment. Similar results were obtained with the Mg-59.5 pet Bi, Mg-36.4 pet Sn, Mg-65.4 pet Cu, and Bi-40 pet Cd eutectics, only the last of which could be worked at room temperature. Tammann and Hartmann reported a thickening and shortening of the needles of the eutectics which they heated about 10°C below the melting range for 1 hr after drastic cold rolling. They found the following eutectics, given the indicated amounts of reduc- tion, to have a granular structure after heat treatment: Sn-9 pet Zn (98 pet); Cd-82.5 pet Pb (60 pet); and Bi-43.5 pet Pb (90 pet). On the other hand the alloy Al-11.7 pet Si (60 pet) showed no change after heating. Tammann and Hartmann observed a distinct shrinking of the needles in unworked eutectics subjected to heat-treatment. In the present work inappreciable change in the eutectic structure was found on heating undeformed alloys. In summary, it appears that eutectic structures can be recrystallized into a "spheroidized" condition by heating near the eutectic temperature after severe deformation. If the eutectic contains one or more brittle phases the necessary deformation can be accomplished by pressing at high temperatures. It is reasonable to expect that this tendency towards equiaxed grains from the plate- or needle-like eutectic structure should be general since the energy relations and mode of growth in recrystallization are so different from those that hold for eutectic crystallization. References 1. G. Tammann and H. Hartmann: Ztsch. Melallkunde (1937) 29, 141-144. 2. E. M. Savitskii: Doklady Akad. Nauk S.S.S.R. (1940) 62, 349-351. Abstr. in Melal Prog. (July, 1949) 56, 126, 128.

Jan 1, 1950

By John Fulton

The Menominee range is one of the four great mining belts that flank the western prongs of Lake Superior. It has received its name from its location along the north side of the Menominee river, which at this place flows between the States of Michigan and Wisconsin. The term "range" is derived from the elevated ridge, extending in a westward direction, and along the southern flank of which the iron-ore mines are located. This range is some 200 to 300 feet high above the general level of the adjacent country, and is made prominent by its surroundings of low, swampy lands. Its whole length is about 27 miles, and it is intersected, at intervals along its course, by gaps which are threaded by streams. The geology of the Menominee range is peculiarly interesting. It is composed of three distinct groups of Hurouian rocks. The supporting group consists of light-colored limestone beds of a crystalline, siliceous character, called the "Norway limestone belt." The map, Fig. 1, and the section, Fig. 2, will give a general notion of the position and structure of the range. The properties shaded in the map are those of the Penn Iron Mining Company, which is the Michigan representative of the Cambria Iron Company of Johnstown, Pennsylvania. This belt is at least 1200 feet thick. It outcrops boldly at many localities along the range, especially north of the Norway, Quinnesec and Chapin mines. At Quinnesec it can be studied readily. The next, or Banking group, which is estimated at a thickness of 1000 feet, is called the Quinnesec ore-formation. It consists, in the portion next to the limestone, of siliceons or jasper slates, largely impregnated with iron oxide. These are succeeded by argillaceous hydro-mica black and flesh-colored slates. This formation embraces the deposits of the iron-ores. The third group consists of a series of dark gray, slaty or schistose beds, with occasional quartzose bands, having a thickness of 2000 feet. It is called the Lake Hanbury slate group.

Jan 1, 1888

By James E. Howard

At the request of the Council of the Institute, I have the honor to submit the following remarks upon the Program of Tests under which the current work of the Watertown Arsenal Testing Laboratory is carried on, which comprises, among other items, the tests of steel ingot metal and derivative shapes. The intended scope of the tests may be illustrated by extracts from the descriptive part of the program as submitted by the Laboratory under date of April 17,1907, and subsequently approved by the Chief of Ordnance, U. S. A. Under Item 1, Ingot Metal—Open hearth, acid and basic; Bessemer, acid and basic; crucible; fluid compressed and uncompreesed—descriptive remarks were made as follon-s: "A thorough, fundamental inquiry into the physical properties of steel necessarily begins with the ingot metal. Investigations, having for their object the improvement of steels, should also begin with the ingot. A knowledge of the ingot structure is essential for judging of the subsequent behavior or appearance of the metal. Under ordinary conditions, so little information is obtained from the ingot in individual cases that practically none of importance is acquired. These remarks have particular reference to the state of physical and structural

Jan 1, 1909

By Donald W. Barnett

U.S. environmentalists have tended to oppose all new energy developments. Their efforts may be counterproductive because opposition to, say, offshore oil directly leads to the continued use of other energy sources that may have a higher social cost. Rather than attempting to eliminate all pollution from energy production, which would be prohibitively expensive, one should minimize the social cost of energy production for the given demand. Linear programming is used to rank various oils (California State and O.C.S., Gulf of Alaska, Prudhoe Bay, Athabasca tar sands, oil shale and certain foreign crudes) in terms of their social desirability. The objective is to minimize the cost of supplying the California market, subject to resource, sulphur and oil spill constraints. Social desirability is indicated by the inclusion of the oil in the optimal solution and the size of the associated shadow price. the larger the shadow price, the greater the benefits of increased production. The more negative, the greater the cost associated with forcing consumption of that fuel. The environmental shadow prices indicate the size of the trade-off between a particular environmental standard and minimum cost. The trade-offs can be surprisingly large. any reasonable spill standard can be achieved by changing the development pattern. Generally, the further offshore, the smaller is the environmental degradation, but the more expensive is the oil. Foreign oils can be economically and environmentally inferior to domestic oils. Crude from the California O.C.S., San Joaquin Valley end Prudhoe Bay appears a valuable resource, while the Gulf of Alaska, synthetic and foreign crudes appear marginal to submarginal.

Jan 1, 1977

By William Metcalf

IT is the object of this paper to oppose unnecessary changes, and the introduction of new and confusing terms. From the earliest times of which we have any record on the subject, iron has been divided into general classes. Whether iron was first known in the form of wrought iron or of steel, is a matter of no importance; but at the time when cast iron first became a prominent article of commerce, wrought iron and steel were old products¬steel, at that time, being generally made from wrought iron by the process of cementation. As steel was then properly defined as iron containing more carbon than wrought iron, so cast iron was appropriately defined as iron containing more carbon than steel. Until the year 1776, when Huntsman first began the manufacture of a new kind of iron by melting wrought iron and steel in crucibles, the above definitions were all that could be desired. At first, probably, owing to imperfect appliances, only a highly carburized iron was melted in crucibles, and this led to its being called cast steel. If our ancestors had found a name for this material not involving the use of the word steel, we would have been saved the trouble of the present discussion. As the arts developed, new uses were found for steel, and the products of the crucible were varied, until at the present day it is quite common to find steel containing no more carbon than average wrought iron, and other steel containing nearly or quite as much carbon as some cast iron. All of these various products of the crucible have retained, or received, the name cast steel, usually abbreviated to the simple word steel, without causing any confusion among producers or consumers in regard to terms or their meaning. In 1855, twenty-one years ago, the Bessemer process was introduced ; this was followed in a few years by the Siemens-Martin process, and the products of both were at once, and have ever since been, called steel, from the fact that they were identical in chemical and physical properties with crucible cast steel. At the present time, then, we have three subdivisions of cast steel, viz.: Crucible cast steel, Bessemer cast steel, and Siemens-Martin,

Jan 1, 1877

By Eugene S. Meieran

The effects of methods of crystal growing, wafer sawing, polishing, routine handling, diffusion, and epitaxial growth on the defects in GaAs are reviewed and studied using reflection and transmission X-ray topographic techniques. In general, it was found that boat-grown crystals exhibited fewer defects than Czochralski crystals, although all crystals showed large numbers of precipitates visible when examined in the electron microscope. Mechanical surface treatments such as sawing and mechanical polishing introduce damage to a depth of about 5 µ, most of which can be removed by suitable chemical or chem-mechanical polishing. In addition, defects can be introduced through routine handling of wafers, for example with metallic tweezers. These defects can be quite severe, and have been observed 20 µ below the wafer surface. Defects can also be introduced through diffusion and epitaxial growth. These defects, which include precipitates, growth pyramids, stacking faults, dislocations, and so forth, can be detrimental to device fabrication. It is shown that wafers or films which appear defect-free optically can contain defects visible in the X-ray topographs. WHILE the use of GaAs in the semiconductor industry has increased very rapidly in the last few years, due mainly to the recent development of many important GaAs devices,1,2 the major limit to the production of commercial quantities of many GaAs devices remains a severe lack of suitable materials technology. This lack is apparent in two critical areas. First, production quantities of high-quality GaAs crystals, reproducibly doped and precipitate-free, simply are not available commercially, although some reasonable quality material is available on a limited first-come, first-serve basis. Second, in comparison to silicon technology, little is known about the effects of processing variables on the defects either present in as-grown GaAs or introduced through processing and handling of wafers. These areas are now receiving some attention from semiconductor device manufacturers, who are studying defects in GaAs in order to better understand how either to prevent their occurrence or to cope with their existence. Most investigations of the defects in GaAs have been made by optical microscopy3-5 or transmission electron microscopy techniques.'-' Recently, however, the imaging techniques of X-ray topography, electron mi-croprobe analysis, and scanning electron microscopy are being applied to the study of GaAs.9-14 In the case of X-ray topography, a one-to-one image is obtained that must be photographically enlarged. In compensa- tion, the defects within entire wafers may be imaged by simple scanning (Lang technique15) if the wafer is reasonably perfect, or by using the scan oscillation technique developed by Schwuttke16 if the wafer is warped or distorted. The purpose of this paper is to both review and extend the general application of X-ray topographic techniques to GaAs. Emphasis will be placed on the effects of growth and process variables on the quality and perfection of both bulk and epitaxial GaAs. Reference to optical or electron microscopy results will be made when useful. Since the effects on defects of a wide variety of processing variables such as crystal growing, sawing, polishing, diffusion, and epitaxial growth will be somewhat superficially reviewed, a fairly extensive bibliography of the most important recent results in these areas is included. However, for completeness, important defects will be illustrated here, although such defects have been previously shown by others. While this paper is concerned with defects rather than with the physics of X-ray scattering, the mechanisms of contrast formation in the topographs will of necessity be briefly mentioned. EXPERIMENTAL GaAs crystals, both boat-grown18 and Czochralski-grown,'8 containing a variety of dopants of various concentrations, were purchased from outside vendors. Wafers were sliced from the crystals using a Hamco ID saw and were mechanically polished using 1 µ diamond paste. Chem-mechanical polishing was done in bromine-methanol as described by Sullivan and Kolb.18 Chemical polishing was done using a modified sulfuric-peroxide solution, 11 parts H2SO4, 1 part 30 pct H2O2, 1 part DI water.5 Zinc diffusion was carried out in a closed tube, using a 10 pct Zn-In source at 825°C for 1 hr. Oxide masking techniques were used to select the area to be diffused. Epitaxial wafers were either purchased or prepared here. All epitaxial runs prepared here were carried out using a Ga-GaAs-AsC13 source in a closed tube at a substrate temperature of 750°C. Wafers were chem-mechanically polished and gas-etched prior to deposition. The X-ray topographs were taken on a Krystallos Lang camera, operating in the transmission scanning geometry (Lang technique15) or in the reflection scanning geometry (modified Berg-Barrett technique20,21). MoKa, radiation was used for all transmission topographs using a Jarrell-Ash 100-µ spot focus. CuKal radiation was used for all reflection topographs using a General Electric CA-7 1-mm spot focus X- ray tube. Topographs were printed from an intermediate contrast inversion film, so the contrast shown in all figures here is the same as that of the original 50-µ-thick emulsion L4 Iiford nuclear plate used to record the topograph.

Jan 1, 1969

By D. E. Coates, G. R. Purdy, S. V. Subramanian

The morphological stability of the planar solid-liquid interface in dilute ternary alloys, undergoing steady-state unidirectional solidification, is analyzed in terms of both the constitutional supercooling principle and the perturbation methods recently developed by Mullins and Sekerka. First, various steady-state solutions for the two solute distributions ahead of a planar interface are examined. The nature of the solutions depends on the size and concentration dependence of the off-diagonal diffusion coefficients. W~thin the framework of the constitutional supercooling principle, a cumulative contribution to instability frorn the two solutes is found to exist in the absence of diffusional interaction. It is shown that the latter can produce a further enhancement of instability or can have a stabilizing influence, depending on the form of the liquidus surface and on the sign of the solute-solute interaction. A perturbation analysis, which ignores diffusional interaction, verifies the cumulative influence of lhe solute fields and demonstrates that the Mullins-Sekerka stability criterion for binary systems (with capillarity accounted for) can be readily extended for application to ternary systems. SOME time ago, Tiller et al.' calculated the solute concentration distribution ahead of the planar solid-liquid interface of binary alloys undergoing steady-state unidirectional solidification. An earlier qualitative proposal that the transition from planar to nonplanar growth morphologies is associated solely with the onset of constitutional supercooling in the liquid layer ahead of the moving interface2 was used in conjunction with this calculation to put the now well-known constitutional supercooling (C-S) stability criterion into quantitative terms. Mullins and Sekerka,3 in a recent and very elegant analysis, established a more complete criterion (hereafter referred to as the M-S criterion). Interfacial stability was investigated by determining the time derivative of the amplitude of a sinusoidal perturbation of infinitesimal amplitude which had been introduced into the originally planar shape of the moving interface. Of particular importance is the fact that capillarity was included in the boundary conditions of their calculation. The purpose of the present paper is to extend all of this earlier work on dilute binary systems for application to dilute ternary alloy solidification. The analysis is divided into three sections. In the first the two solute distributions ahead of a moving planar interface are considered. Mathematical solutions are de- termined for situations in which: a) diffusional interaction is negligible, 6) diffusional interaction must be considered but circumstances permit use of constant diffusion coefficients, and c) the concentration dependence of off-diagonal diffusion coefficients can be described by first-order dilute solution approximations. In the next section, a stability criterion analogous to the C-S criterion is developed and the influence of diffusional interaction on interface stability is analyzed. Finally, the perturbation formalism of Mullins and Sekerka, with capillarity included in the boundary conditions, is extended for analysis of ternary systems in which diffusional interaction is negligible. The study of interface stability in binary systems usually commences with the assumption that the equilibrium distribution coefficient and the slope of the liquidus line are constant at values corresponding to infinite dilution. Similar assumptions have not been introduced into the present treatment; that is, we do not assume planar solidus and liquidus surfaces joined by tie lines which yield constant distribution coefficients. The latter involves the assumption of no ther-modynamic interaction between solute species in both the solid and liquid. We consider a ternary phase diagram for which the solidus and liquidus surfaces are, in general, nonplanar and of course pass through the corresponding binary solidus and liquidus lines. These lines are not assumed to have constant slope. In the dilute regions we are concerned with, the following assumptions are made: i) The solidus and liquidus surfaces are of a form such that both the solidus and liquidus temperatures are monotonically varying functions of each solute concentration. ii) The tie lines are such that the equilibrium distribution coefficient of a given solute is greater than unity for every point on the solidus (or liquidus) surface or it is less than unity for every point. STEADY-STATE SOLUTE DISTRIBUTIONS IN THE LIQUID As will be demonstrated in the next section, a knowledge of the steady-state solute profiles is not a necessary prerequisite for the formulation of a ternary C-S stability criterion. However, in that details, such as the complete description of the equilibrium liquidus temperature profile, require an evaluation of the solute distributions, the overall treatment is enhanced if these distributions are determined. Consider a ternary system (solvent plus solutes 1 and 2) for which a planar solid-liquid interface is in unidirectional motion at constant velocity V. At this stage it is unnecessary to limit ourselves to dilute solutions. For a stationary frame of reference the generalized forms of Fick's equations are:

Jan 1, 1969

Jan 1, 1940

Jan 1, 1940

Jan 1, 1941