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MINING ENGINEERING presents the annual membership report of the Society of Mining Engineers; see page 109.

Jan 7, 1963

By I. R. Kramer

The stress associated with the high-dislocation layer at the surface of deformed aluminum crystals was measured by progressively polishing the specimen and determining the change in the initial flow stress when the specimen was reloaded. This surface stress increased linearly with strain in the Stage II and Stage III region. The depth to which the high-dislocation layer extends was found to be 0.0025 in. The influence of the surface layer on Stage I is discussed and it is shown that Stage I ends when, on the secondary slip system, the difference between the applied stress and the opposing stress due to the surface layer is equal to the critical resolved shear stress. In previous papers'-3 it was shown that the surface exerts a pronounced effect on the plastic-flow characteristics of metals. For fcc metals it was possible to increase the extent and decrease the slope of Stages I and II and decrease the work-hardening coefficient of Stage II by removing the surface of the specimen continuously during the deformation process.2,3 More recently,L it was shown that the activation energy for plastic deformation and the activated volume were also influenced by the surface. These changes were related to the existence of a high concentration of dislocations in the region near the surface of the deformed specimen and it was concluded' that the effective stress, T, acting on a dislocation was T = Ta-Ti-Ts [1] where 7, is the applied shear stress, Tj is the internal stress, and TS is the stress associated with the surface region containing the high concentration of dislocations. From Eq. [I] it is seen that the effective stress, 7, acting on a dislocation is a function of 7,. Therefore 7, becomes important in any description of the work-hardened state. In this paper the value of 7, as a function of strain and its variation with depth are reported for aluminum single crystals. In particular, it will be shown that the end of Stage I occurs when the net stress, 7, on the secondary slip system is equal to the critical resolved shear stress. To measure Ts, single crystals of aluminum were deformed in tension to various strains, whereupon the load was removed and a known amount of metal was removed by electrolytic polishing. The differ- ence between the final flow stress before the specimen was unloaded and the initial flow stress upon reloading is designated as ?Tp and is the decrease in the stress due to the removal of the surface layer in whole or in part. The value for Tp is taken equal to -Ts. EXPERIMENT PROCEDURE The details of the tensile apparatus, method of electrolytic polishing, and crystal preparation were the same as those used previously,1"3 The single crystals were 1/8 by 1/8 in. in cross section with a 3-in. gage length. The initial purity of the aluminum was 99.997 pet. The specimens were held in vacuo at temperatures 50°C below their melting points for 16 hr and furnace-cooled. Just prior to the application of the tensile stress the specimens were electrolytically polished to remove 0.004 in. from the thickness. This latter operation was conducted after the specimen was placed in the tensile apparatus. The tensile tests were conducted at a strain rate, i, of 10"5 sec-' and a temperature of 3°C. The aluminum crystals used for the determination of 7, are designated A1-3-12 and A1-116. The orientation of the various crystals used throughout the investigation is shown in Fig. 1. The ?Tp values for specimens A1-3-12 as a function of Ax were determined mainly at four strain levels, i.e., ? = 0.0217, 0.0381, 0.0593, and 0.075, where Ax is one half of the total reduction of the thickness after polishing and ? is the re-

Jan 1, 1965

By Paul Soros

Terminal facilities were recently completed at Conneaut, Ohio, on Lake Erie, for the Bessemer and Erie Railroad Co. (a wholly-owned subsidiary of U.S. Steel Corp.) which may become the blue- print for all future coal shipping terminals. Design and engineering of the new facility was by Soros Associates, New York, N. Y. Unlike terminals of conventional design, for example, those at Toledo and Newport News, which load coal directly from the railroad car to the vessel, the new installation passes the coal into temporary storage, loads the vessel from temporary storage and provides alternative reclaiming systems in case of major system failure.

Jan 1, 1966

By F. E. Jaumot, R. L. Smith

Self-diffusion in zinc at temperatures below 200°C has been studied using both single crystal and polycrystal samples. Anomalous results were obtained for single crystal samples, the data indicating that in some cases grain boundary diffusion predominated. These anomalous results are presumed to be due to low angle lineage boundaries in the single crystals. When volume diffusion occurred in either single or polycrystal samples, the values for the diffusion coefficient were as much as several orders of magnitude larger than would be expected from high temperature data. ONSIDERABLE work has been done on self-^-*diffusion at temperatures in the neighborhood of two thirds of the melting temperature (in OK) and higher, but very little has been done at lower temperatures. This is particularly true of self-diffusion in single crystals. This paper reports work on self-diffusion in zinc at temperatures below 200 °C where both polycrystalline and single crystal samples have been used. The measurements were made using both the sectioning and absorption techniques. The experiments on diffusion at low temperatures were initiated primarily for three reasons: to obtain data from single crystal diffusion covering a wide range of temperatures, to obtain values of the activation energy for grain boundary diffusion, and to obtain, if possible, a lower limit to the temperatures at which the absorption technique may be used. It is possible to determine whether volume or grain boundary diffusion predominates at low temperatures by analyzing the manner in which the concentration of the diffusing atoms varies with the depth of penetration. The analysis is possible only for the sectioning technique. For volume diffusion and for the boundary conditions of the present experiment, the curve of the logarithm of the concentration, C, vs the square of the penetration depth, x, is a straight line with the slope proportional to — 1/D. If grain boundary diffusion predominates, Fisher' has shown that a curve of In C vs the first power of the penetration depth should be a straight line. This linear dependence of concentration on depth has been observed experimentally by several investigators. (See, for example, refs. 3 and 4.) Following Fisher's analysis, the grain boundary diffusion coefficient can be written as where 8 is the grain boundary width, D, is the volume diffusion coefficient at the temperature involved, t is the time of diffusion, C is the concentration of diffusing material, and x is the depth of penetration. A more general analysis employing the same model as Fisher's but with fewer assumptions has been given by Whipple.' In contrast to Fisher's analysis the more general analysis of Whipple does not always yield a straight line relation between In C and x. Recently Turnbull and Hoffman have discussed both analyses and have applied the Fisher-Whipple model to a more refined dislocation model of the grain boundary. They have also discussed the possibility of a large effect of grain boundary direction on diffusion. In the case of the absorption technique, for which results are also given, one simply gets a value for the diffusion coefficient with no indication of the predominating mechanism. Experimental Techniques Single crystals of 99.99+ pct Zn were grown using a modified Bridgman method. Polycrystal samples were prepared in three grain sizes (small, about 4 mm2; medium, about 9 mm'; and large, about 25 mmz) by quenching, air cooling, and furnace cooling. The grains of the polycrystalline samples tended to be columnar, with some preferred texture such that the c-axis was inclined at about 20" to 25" from the normal to the diffusion face, particularly in the medium and large grain size samples. The samples were cut from the rod, polished, and heavily etched, and faces cut accurately parallel using a jeweler's lathe. They were again etched to remove the lathe smear and annealed for 3 hr at 250" to 300°C. After annealing, they were etched, examined, and the orientation determined by Laue back reflection photographs. They were then electroplated with Zn. The plated surfaces were examined for uniformity; nonuniform coatings were removed by etching and the samples replated without additional preparation. For the diffusion anneals, the samples were placed in pairs, with active faces together, in evacuated Pyrex tubes. Constant temperature baths were used, and the variation in temperature did not exceed ±l°C, Diffusion runs were made at l00°,

Jan 1, 1957

By S. C. Schaeker, A. W. Schlechten, A. H. Larson

PARRAVANO and Malquori' studied the equilibrium of H2S-Hz with molybdenum and its lowest sulfide which they believed to be MoS2. Mc Cabe' has shown that its composition is actually Mo2S3 and determined its dissociation pressure by means of Knud-sen effusion measurements. Stubbles and Richard- son3 have recently studied the equilibrium of gas mixtures of H2S-HZ with the two-phase solid mixtures of Mo-MozS3 and Mo2S3-MoS2. The latter investigators found that M02s3 deviated slightly from the stoichiometric composition, but they did not determine the homogeneous region of the disulfide phase. Morimoto and Kullerud, studied the Mo-S system by quenching, microscope, and X-ray methods and concluded that the disulfide is stoichiometric. The present investigation was concerned with the measurement of the sulfur vapor pressure variation with composition at 1100°C in the homogeneous region of "MoS2". These measurements were made by reacting: 1) molybdenum powder (99.97 pct Moj with sulfur vapor, and 2) MoS1.g9 (formed by reaction of Mo + H2S) with sulfur vapor in a quartz capsule. Conditions were controlled to form an equilibrated phase within the homogeneous region of the disulfide. The quartz capsule was sealed off initially under a vacuum and the residual gases were gettered by titanium powder contained in one end of the capsule. A mixture of Mo + S or MOS,., + S was in the other end. The section containing the titanium powder was heated for 24 hr at 700°C and then removed by flame sealing. The end of the capsule containing the charge was then heated to 1100°C. The other end of the capsule was maintained at a temperature which would produce the desired sulfur pressure in the capsule (liquid sulfur distilled from the charge mixture was retained in this end). After equilibration, the capsule was removed from the heating assembly and rapidly air-cooled. It is assumed that equality existed between the total sulfur pressures (PT) in the two ends of the capsule and not between the partial pressures of the different molecular species (S, SZ, Three separately controlled heating elements were used to maintain the proper temperature gradient over the length (approximately 12 in.) of the capsule. A thermocouple-Wheelco "Capacitrol" system was used for temperature control of the two end heating elements within 2"C. The center heating element was controlled directly by a " Power -stat". Separate controlling and measuring thermocouples were used for both end heating elements. Pt-Pt(l0 pct Rh) thermocouples were used for 1100°C and Chromel-Alumel thermocouples were used for lower-temperature control and measurement of the assembly. Silver foil was wrapped around the end of the capsule containing the liquid sulfur to insure a constant temperature zone. The thermal gradient over the entire length of the capsule was measured to: 1) ascertain that the length of the constant temperature zone of the liquid-sulfur end and the sulfide end was sufficient, and 2) ascertain that the liquid-sulfur zone was the zone of lowest temperature. The data obtained in this investigation are shown in Fig. 1 and Table I. The total sulfur pressure (PT) and p(S2) were calculated from the data of Braune et UZ.~ The compositions of the equilibrated disul-

Jan 1, 1964

By G. N. Goldberg, Robert A. Rapp

The steady-state kinetics and microstructures of simultaneous internal oxidation and external scale formation were investigated for the oxidation of Cb-Zr and Ch-Zr-Re alloys in pure oxygen at 1000°C. For each binary alloy, a constant rate of scale formation was observed at steady state; the internal oxidatton zone reached a steady-state, time-independent thickness. The dependence of the scaling rate on zirconium content exhibited a maximum at a low zirconium colttent; more concentrated alloys oxidized at a slower rate than pure columbium. This composition dependence of the scaling rate may be partially attributed to the effect of the internal oxidation process as an intenla1 sink for oxygen, with the formation of voluminous, and relatively impermeable ZrO2 precipitates. However, the morphologies of the ZrO2 internal oxide precipitates also affected the scaling rate. The internal oxide precipitates were distributed uniformly in the external scale. The steady-state thicknesses of the internal oxidation zones were not in agreement with those predicted theoretically from an idealized simple model. However, in this particular alloy systen1 the ideal model is not satisfied experitmentally. For ternary Cb- Zr - Re alloys with Nr10e = 0.02 or 0.05, the steady-state thicknesses of the internal oxidation zones were less than those for the corresponding binary Cb-Zr alloys. For ternary alloys with NRe(0) - 0.05, a more adherent and much less porous external scale was formed, and a reduction in the kinetics of scale formation was observed. A number of authors'-7 have reported linear oxidation kinetics for the reaction of pure columbium at 1000°C in air or in oxygen of about 1 atm pressure. A thin and tightly adherent oxide layer is found at the metal/oxide interface beneath a porous external layer of scale. Although the suboxides CbO and CbO2 represent thermodynamically stable phases at 100O°C, generally only Cb2O5* is identified as a reaction product in quenched specimens. Studies at 1000°C at lower oxygen pressures8,10 (Po2 - 10-4 Torr) show that both CbO and CbO2 do form and that CbO2 is a protective oxide. The growth of CbO2 results in parabolic kinetics until Cb2O5 is nucleated and grows. Apparently because of the large volume change associated with its formation, Cb2O5 is porous and does not serve as a diffusion barrier; linear kinetics prevail after the surface is covered with Cb2o5. On the basis of these observations, several authors5,9,10 have suggested that the linear oxidation of pure columbium at 1000°C in air or oxygen of 1 atm is limited by a Loriers-type mechanism,11 whereby the total rate or reaction is controlled by ionic diffusion through a thin layer of CbO2 which is maintained at a constant thickness throughout the linear oxidation. However, the concept of a Loriers model for a three-phase CbOlCbO2 Cb2O5 scale, with the only oxygen activity gradient across the NbO2 phase, is not self-consistent. Further, the suboxides CbO and CbO2 were not observed in the high-temperature X-ray diffraction study of columbium oxidation by Goldschmidt.8 From investigations in which the large PO2, dependence of the linear scaling rate was demonstrated, the importance of an oxygen adsorption or dissolution step has been suggested.4,5,7,10,12 Thus the mechanism for the linear oxidation of pure columbium remains quite controversial. Since further insight into the oxidation mechanism of pure columbium is not provided by this investigation, the authors wish to emphasize at the outset that their experimental results are not interpreted in terms of a particular rate controlling step for the oxidation of pure columbium. Previous investigations13-18 of the oxidation of Cb-Zr solid-solution alloys in air or oxygen at 1000°C suggest a remarkable dependence upon zirconium content. For an alloy of bulk zirconium mole fraction, N2r(0) equal to 0.05 or 0.10, the oxygen uptake is reported to be as high as four times greater than that for pure columbium;13,14 for alloys with NZr(0) 0.05 or 0.10 the oxygen uptake is reported to decrease with increasing NZr(0); to a minimum uptake of about one quarter that for pure columbium at NZr(0): = 0.50.13-15Since zirconium forms a more stable oxide (ZrO2) than the lowest columbium oxide (CbO), and since columbium exhibits a high solubility19,20 and diffusivity21,23 for oxygen, the internal oxidation of the zirconium component to ZrO2 is expected at a reaction front ahead of the advancing metal/scale interface. The external scale is then formed at the metal/scale interface by the inward migration of oxygen through the scale, probably through a series combination of molecular and ionic diffusion. Internal oxidation in conjunction with external scale formation has been investigated by Maak24 for the oxidation of dilute Cu-Be alloys in pure oxygen at 850°C. For cu-Be and many other binary alloys,24-27 very small, essentially uniaxial internal oxide particles are formed in the most dilute compositions; for somewhat more concentrated alloys. the internal oxide particles precipitate as platelets or needles. From pertinent solutions to the diffusion equation, Maak28

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 E. T. Turkdogan

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

Jan 1, 1965

By R. P. Agarwala, M. S. Anand

Using residual activity technique, the diffusion of palladium, silver, cadmium, indium, and tin in alunzinum has been studied in the temperature range of 400" to 630°C. The diffusivities (in units of square centimeters per second) have been expressed as: IMPURITY diffusion in aluminum,1-9 silverand lead5 for cases of low solid solubility of the impurity in the host metal has yielded frequency factors in the range of l0-6 to l0-9 sq cm per sec whereas the activation energy is practically half the self-diffusion activation energy value. From the observed values of frequency factor, activation energy, and entropy of activation, it has been suggested' that these solutes are not diffusing by vacancy or interstitial mechanisms but by a mechanism which should be consistent with such low values of the diffusion parameters (Do and Q). However in spite of extensive work on these types of systems, the mechanism of diffusion is still not well understood. The present investigation on the diffusion of palladium, silver, cadmium, indium, and tin in aluminum has been carried out to throw further light on the diffusion mechanism in systems, where the solid solubility is very low (except for the case of silver). The results are discussed on the basis of solid solubility and the structural changes involved owing to the presence of the solutes in aluminum solid solution. An attempt has also been made to apply the existing theories of charge5-8 and size8 difference between the solute and the solvent. EXPERIMENTAL PROCEDURE Specimens (1/2 in. diam by 3/8 in. high) were machined out of pure aluminum (99.995 wt pct) rod obtained from Johnson Mattheys. They were sealed under vacuum in quartz tubes and annealed at 620° C for several hours; the grains thus developed were sufficiently large to eliminate the possibility of diffusion along the grain boundaries. The flat ends were prepared carefully after polishing as described previously,10 Radioactive nitrates of cadmium, indium, and tin and chloride of palladium containing, respectively, cd115, 1n114, sn113, and pd103 were dissolved in distilled water and mixed with 30 pct acetone. By means of a micropipet a drop of this solution was placed on a smoothly polished and lightly etched surface of the specimen. Due care was taken to see that the solution spread uniformly on the surface of specimen without trickling down its sides. Radioactive silver was elec-trodeposited using a AgCN-KCN bath. The amount of sample deposited in all the cases was not more than 0.1 µ thick. The samples were then sealed in quartz tubes in vacuum. The cadmium samples were sealed in a purified argon atmosphere to avoid evaporation. The samples were then diffusion-annealed. The temperature of annealing varied between 400° and 630°C and was controlled to ±5°C. On heating to -400°C,the deposits of cadmium, indium, and tin, which were of the order of 0.1 p in thickness, were converted to their respective oxides. The contribution of oxygen present in the lattice of aluminum due to these oxides has been calculated and found to be less than 10 ppm in all cases. Oxide method has already been used by other workers11'12 in diffusion studies without any controversy on the issue. However, in some of these investigations, metallic deposition was also tried. The diffusivities calculated from these measurements were found to agree very well with the diffusivities obtained by using the oxide method. Thus it is assumed that the measured diffusivities represent true diffusion coefficients. Since palladous chloride decomposes at about 500°C, the deposited samples which were to be diffusion-annealed below 500°C were heated in vacuum for a very short time at 500°C to allow the decomposition of palladous chloride to palladium metal. Time taken in decomposition of nitrates to oxides and chloride to metal was negligibly small as compared to the period of the diffusion anneals. The residual activity technique13 was used to study the diffusion profiles where thin layers from the specimen surface were removed by grinding it parallel to a flat surface on a 600-grade carborundum paper. The specimen was washed, dried, and weighed, the differ -ence of the weight being the measure of the thickness of the layer removed. After each such abrasion and weighing, the total residual activity on the surface of the specimens was measured by counting 0.656, 0.94,

Jan 1, 1968

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

A general theory for the growth of lamellar and rod eutectics is presented. These modes of growth depend on the interplay between the diffusion required for phase separation and the formation of interphase boundaries. The present analysis of these factors provides a justification for earlier approximate theovies. The conditions for stability of rod and Lanlellar structures are consitleved in terms of the mechanisms by which the structure can change. The mechanisms considered include both small adjustments to the lnnzellar spacing due to the motion of lamellar faults, and catastrophic changes due to instabilities. It is concluded that stable growth occurs at or near the minimum interface undevcooling for a gizierz growth rate. The conseqrlences of the existence of a diffusion boundary layer at the interface are discussed. The experimental results for the variation of growth rate, undercooling, and Lanzellar spacing are cornpared with the theory. We believe that the theory presented in this paper provides an adequate basis for understanding the complex phenomena of lanzellar and rod eutectic growth. The growth of lamellar eutectics has been the subject of several theoretical and many experimental studies. The foundations for the theoretical work were laid by zenerl and Brandt2 in their analyses of the growth of pearlite. Zener estimated the effect cf diffusion, and took into account the surface energy of the lamellar structure. He found that the lamellar structure could grow in a range of growth rates at a given undercooling provided the lamellar spacing was appropriate for the growth rate. Since pearlite grows with only one growth rate and one lamellar spacing at a given undercooling, there is clearly an ambiguity in the theory. Zener removed this ambiguity by postulating that the growth rate was the maximum possible at the given undercooling. He predicted then that the product of the growth velocity v and the square of the lamellar spacing A should be constant, i.e., A2v = const. Brandt2 started out by assuming that the interface between the lamellae and austenite was sinusoidal. Because of this, the ambiguity encountered by Zener did not arise. Brandt was able to obtain an approximate solution to the diffusion equation, but, since he did not take into account the surface energy, his considerations are incomplete. Tiller3 applied some of these ideas to the growth of eutectics, and proposed a minimum undercooling condition to replace the maximum velocity condition used by Zener. These conditions are formally identical. Hillert4 extended the work of Zener. He found a solution to the diffusion equation assuming the interface to be plane. Taking surface energy into account, and applying Zener's maximum condition, he was able to calculate an approximate shape of the interface. Jackson et al.5 used an iterative method employing an electric analog to the diffusion problem to refine the calculation of interface shape. It was found that the interface shape calculated from a plane-interface solution to the diffusion equation was negligibly different from the exact solution. The method provided an analog only for eutectics for which the volumes of the two phases are equal, growing from a melt of exactly eu-tectic composition. There has also been considerable experimental work on eutectics, Several experimenters8-10 found that A2v is constant as predicted by Zener.1 Hunt and chilton10 demonstrated that ?T/v1/2 is also a constant for the Pb-Sn system as predicted. Lemkey et al.11have recently found A2v to be constant for a rod eutectic. In the present paper, we present the steady-state solution for the diffusion equation for a lamellar eutectic growing with a plane interface, for the general case, that is, with no restriction on the relative volumes of the two phases, and with the melt on or off eutectic composition. A similar solution is also found for a rod-type eutectic. Expressions are obtained for the average composition at the interface and the average curvature of the interface. These equations for the average composition and curvature are similar in form to those derived by Zener1 and Tiller,3 and provide a justification for some of the approximations made by these authors. The mechanisms by which the spacing in a lamellar structure can change are considered. The important mechanism for small changes in lamellar spacing involves a lamellar fault. Examination of the stability of lamellar faults leads to the conclusion that the growth occurs at or near the extremum.* The insta- bilities which can develop in a rodlike structure are also discussed, resulting in the conclusion that this structure also grows at or near the extremum. Comparison of the conditions for rod and lamellar growth permits a prediction of the surface-energy anisotropy required to produce rods or lamellae for various volume-fraction ratios. The diffusion equation predicts the existence of a diffusion boundary layer at the eutectic interface unless the eutectic has 0.5 volume fraction of each phase and is growing into a liquid of eutectic composition. This boundary layer is such as to make the composition in the liquid at the interface approximately equal to the eutectic composition. This boundary layer permits changes in composition during the zone refining of eutectics. Photographs of the eutectic interface of a growing transparent organic eutectic system have been made. Both the components of this eutectic are transparent organic compounds that freeze as metals do.12 The in-

Jan 1, 1967

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

It) an attempt to ulLcoce.lP the operative strain-rate-contl-olliy: dislocation nieclzanistns, specially oviented sizgle clystals of the intel-nzediate 1zexagonal phase containing Ag plus 33 at. pct A1 were tested in tension over a wide range of temperatures. Slip was observed to take place by the {0001} <1120> {l100} mechani fracture took place across the(i100) plane and winning occurred by the (i01Z) ?lechanisn. Basal slip exhibited a strong yield point over the -alzge from 77 to 450°K, the upper ,esolved shear st]-ess having the exceptionally high value of 10,500 psi over this entire ?-a?zge of tenzpei,atuves. The critical 9-esolved shear stress for prismatic slip decreased f7-om 48,000 psi at 4.3"K to 23,000 psi at 170°K (Region 1) follozcirg zt:lzich it decl>eased sloz&ly to 21,500 psi at 475°K (Res&apos;on II); from 475" to 575°K (Regioz III), the c7-itical esolced shear stress dec&apos;-eased precipitously to 2000 psi; and from 575" to 750°K (Region IV) it decreased less afi&apos;dly to a low value of about 500 psi. Pvistintic slip in Region I was pobably controlled by the tliel-nally activated riecharzisui of nucleation and g,-ozcth of kinks in dislocations lying in Peierls potential troughs. In Region II for prismatic slip the critical 1-esolved shear stress was slzocn to be deteemined by sh0l.t-range 01-dering, Overall the forgiorz fo basal slip, 7.c.lre1-e a Strong yield-point phenorlienu ia7as observed, the critical vesolved slzea?-stress was shoztn to be determined by n conibirzation 0-f Szizuki locking and short-range-order Izavderzizg, The precipitous decrease in the critical resolved shear stress with increase in ter,/pe7-atrir-e over Region HI was tentatively ascribed to a decrease in the degree of slort-)ange 07-del;iqq (0)- clusteing) and also the effect of fluctuations the degree of o?der, It is at pgreser2t zrtzce)taitz as to 1t1hethe1- these or other possi1)le effects are also ,esponsible. fo- the data obsel-ved 172 Region IV. 1NTEREST in inter metallic compounds stems not only from their role in dispersion hardening of polyphase alloy ystems but equally from their potentialities for high strength, hardness, and stability not only at atmospheric temperatures but especially at elevated temperatures. As summarized in a re- cent symposium of the Electrochemical Society on "Mechanical Properties of Inter metallic Compound", most of the experimental evidence regarding the mechanical behavior of intermetallic compounds centers about the effect of temperature on the hardness and ductility of polycrystalline specimens. The available data reveal that the plastic behavior of intermetallic compounds might be rationalized in terms of the usual dislocation mechanisms appropriate to a solid solutions providing the additional complexities arising from crystal structure, long-range ordering, short-range ordering, and defect lattices are taken into consideration. It is apparent, however, in terms of the history on a solid solutions, that a complete detailed mechanistic rationalization of dislocation processes may not be possible until the deformation processes are studied in single crystals of intermetallic compounds. The present paper contains a preliminary report on the plastic behavior of single crystals of the hexagonal Ag-A1 intermetallic phase over a wide range of temperatures. The results confirm the thesis that single crystal data provide a most effective method of identifying operative dislocation mechanisms in intermetallic compounds. EXPERIMENTAL TECHNIQUES Several factors prompted the selection of the hexagonal Ag-A1 intermetallic phase for this preliminar investigation on the plastic properties of single crystals of intermetallic compounds: 1) This phase has a wide solubility range5 which would permit future investigations on the effect of composition and axial ratios on slip mechanisms. 2) Although it undoubtedly exhibits short-range ordering (or clustering) this intermetallic phase is free from complexities arising from long-range ordering.6 3) Since the atomic radii of aluminum and silver are practically identical, the possible complications due to Cottrell locking are minimized. 4)Whereas the dislocations on the basal planes are expected to dissociate into Shockley partials and are thus susceptible to Suzuki locking, those on the prismatic planes probably remain complete. 5) The axial ratio, being 1.61, is almost ideal, suggesting that short-range ordering may be almost spherically symmetrical. The present investigation was conducted exclusively with the hexagonal Ag-A1 alloy containing 33 at. pct Al. Preliminary investigations revealed that this alloy undergoes basal slip by the (0001)

Jan 1, 1962

By M. S. Burton, J. E. Ritter

The sessile-drop technique was employed to study the effect of atmosphere and alloy additions of titanium and chromium on the surface tension and contact angle of nickel on sapphire substrates at 1500oC. Shear tests were conducted on the solidified sessile drops. The liquid-gas surface tension of pure nickel on sapphire was found to be 1747 ergs per sq cm, with a contact angle of 109.6 deg. The surface tension and contact angle were not affected significantly by the four atmospheres, vacuum, impure argon, pure argon, and pure hydrogen. Small additions of titanium and chromium decreased the contact angle and for the same alloy content, contact angles were lower in pure argon than in pure hydrogen. On the basis of shear-test results , the most probable cause for adhesion in the Ni-Al2O system is the formation of NiO:Al2O3 spinel at the interface; in the titanium alloy-Al2O3 system adhesion is thought to be due to a mechanical interlocking effect; in the chromium alloy-Al2O3 system adhesion is believed to be the result of solid-solution formation involving Cr2O3 and Al2O3 at the interface. In the last few years there has been considerable interest in reinforcing metals with ceramic whiskers. It has been postulated that, by reinforcing nickel with sapphire whiskers, high-temperature strengths su- perior to those of the best current nickel alloys can be achieved.&apos; To fabricate a whisker-metal composite having optimum density and strength, understanding of wettability and adherence in the system is of prime importance. Although there has been some previous research in this a a need for further studies has been cited4-8 to understand better the effects of impurities, alloys additions, and atmosphere on the wetting and bonding of metals to metal oxides. The purpose of this research was to investigate the factors involved in the wetting and adherence of nickel/nickel alloys to sapphire (single-crystal a Al2O3). Sessile-drop experiments were conducted in vacuum, impure argon, pure argon, and pure hydrogen, to determine the effect of atmosphere on the contact angle of the metals on sapphire, and the liquid-gas surface tension of pure nickel. The solidified sessile drops were sheared from the sapphire substrate to measure the bond strength between the metal and ceramic. The alloy additions chosen were titanium and chromium since both enhance the wetting of nickel on sapphire.2, 3c Also, titanium is commonly used when brazing metal-to-ceramic seals to improve adherence. Since chromium forms an oxide that is completely soluble in sapphire, it was thought that the oxide could serve as a transition phase to promote bonding between the Ni-Cr alloy and sapphire. I) EXPERIMENTAL APPARATUS AND PROCEDURE The sessile-drop apparatus was a horizontal furnace, with an induction-heated, cylindrical molybdenum susceptor in a water-cooled Pyrex chamber. This apparatus was patterned after that of Williams and Nielsen.7 A flat Pyrex window at each end of the furnace allowed temperature measurements to be made at one

Jan 1, 1968

By A. J. Strauss

The solubilily of lead in PbS as a funclion of lemperature has been investigated by means of Hall coej&apos;icient (RH) measurentents OIL samples prepared by annealing and quenching Bridgman-grourz single crystals, which contain excess lead incorporated during /heir growth from the mell. For sufficiently long annealing times and sufficiently rapid quench rules, the samples obtained consist of n-lybe PbS snturated with In the semiconducting compounds PbS, PbSe, and PbTe, the point defects associated with the presence of lead in excess of the stoichio metric composition are shallow donors. The defects associated with the presence of excess nonmetal are shallow acceptors. lead at the annealing teuiperatiire, together luilh a dispersed second phase of lead microprecipitates. Due to the retrograde solubility of lead, the measured free carrier concentration (n = l/eR77) decreases with decreasing annealing tewperature (T) from- 2.4 X 10 em-3 for 1l85OK to 1.3 X 1018 cm-3 for 623°K. The dala are well-represented by the equation n =(1.08 x 102) exp[ - (0.37 ev.)/kT] cm-3 For most undoped samples of these compounds, the carrier concentration at room temperature and below is determined primarily by the stoichiometry, since the concentration of either excess lead or excess non-metal is large compared to the concentrations of intrinsic carriers and electrically active impurities. Therefore the dependence of composition in temperature and partial pressure can be investigated by means of Hall coefficient measurements, even though the deviations from stoichiometry do not exceed 0.03 at. Pct

Jan 1, 1968

By Alfred Boyles

THE experiments described below are a continuation of work on the graphitization of cast iron conducted as part of the program of funda-mental research at Battelle Memorial Institute. In previous work it was found that melting in hydrogen increased the amount of eutectic and in others i produced al marked changes in the size of the graphite flakes. These effects seemed to be III sulphur and manganese present in the material studied. Iron-carbon- respond silicon alloys did same manner as mg cast iron and there was no evidence to show that hydrogen was able to stabilize the carbide in such alloys unless additions of sulphur were made. The two alloys examined contained about 2 per cent of FIG. 1.-APPARATUS FOR MELTING UNDER PRESSURE. silicon. The present paper is con- A, inlet for gas. cerned with alloys of lower silicon B, outlet for evacuation. content and describes the structural C, power lead. D thermocouple changes produced by melting in E, plug for access to furnace. various atmospheres at pressures F, crucible. ranging from a partial vacuum up to 300 lb. per sq. inch.

Jan 1, 1939

By D. Dever, E. S. Fisher

Measurements of the temperature dependence of the elastic moduli in single crystals of hep ruthenium, rhenium, cobalt, dysprosium, and erbium were carried out for various temperature ranges so as to investigate the correlation, suggested by prior work, between the shear anisotropy ratio, A = C44/C66, and the occurrence of the hcp — bee phase transformation. These measurements confirm the suggestion that A has a positive temperature dependence in that group of hcp metals that undergo thermally induced transfornzations to the bee structure and a negative or zero temperature dependence in the other hcp metals. It appears, from indirect evidence, that the hcp -fee transformation in cobalt is preceded by a highly negative temperature dependence of A. These results indicate that elastic anisotropy is an important factor in determining the temperatures at which martensitic phase transformations occur. Two possible roles for elastic anisotropy are proposed: 1) the shear-modulus ratio within the habit planes must be nearly similar for the two phases and 2) a large anisotropy decreases the stress necessary for the movement of the transfornzation dislocations. FUCHS&apos; calculations of the elastic moduli in the alkali metals have shown that the high shear-anisotropy ratios, c/c&apos;, in certain bee metals and alloys are the result of large negative contributions to c&apos; = (c11 - c12)/2 arising from the nearest-neighbor repulsive forces.&apos; On this basis, and following Zener,2 the association between high c/c&apos; ratios and the martensitic phase transformations that occur upon cooling certain bee metals is explained as a unique characteristic of the bee structure. Recent measurements of the elastic moduli in hcp titanium and zirconium show, however, that a high elastic anisotropy also exists in these hcp structures at the temperatures at which they transform to bee upon heating3. If there exists a direct and consistent correlation between the elastic anisotropy in close-packed structures and the occurrence of transformations to the bee phases then there is evidently a need to re-examine the conclusions of Zener theory. Elastic anisotropy may also be the result of the effects of temperature on the stability of the low-temperature close-packed structures or it may play an important role in the mech- anism of the martensitic transformations. The present measurements were aimed at establishing the phenomenological correlation between elastic shear anisotropy in hcp structures and the thermally induced hcp —bee transformations that occur in the majority of the twenty-three hcp metals, as shown in Table I. Prior to the present work the temperature dependence of the anisotropy ratio, A = c44/c66, was known at various temperatures for nine of the metals listed. The data showed a negative temperature dependence of A for cadmium, zinc, magnesium, and cobalt, which do not transform to bee, and a positive temperature dependence of A for thallium, zirconium, titanium, hafnium, and yttrium. The correlation was, however, ambiguous in that these two groups of metals are also separated with respect to the c/a ratios as noted in Table I. There remained the possibility that the temperature dependence of A is a function of c/a and not consistently associated with the transformation. The measurements of the elastic moduli in rhenium and ruthenium, in which hcp —bee transformations do not occur, were needed to help decide this question. The studies of dysprosium and erbium were undertaken to determine whether the correlation holds for the heavy rare earth metals.

Jan 1, 1968

By Elmars Ence, Harold Margolin

The partial isothermal section of the Ti-Cu-Zr system at 750°C has been studied. The crystal structure of Ti2Cu has been detevnlined as tetragonal and when expressed as face-centered tetragonal, a = 4.164, c = 3.611 A, and c/a = 0.867. TITANIUM systems in which ß-titanium decomposes eutectoidally into a and a compound rather readily are known as active eutectoid systems. Recently in active eutectoid alloys based on the Ti-Cu system, and containing additionally A1 and Zr, it has been found that zirconium may produce both moderate weakening and marked strengthening at elevated temperatures.&apos; In order to obtain some insight into the behavior of zirconium, an attempt was made to determine whether compounds of the type Tix Zr and TixZryCu exist. Only results of the Ti-Zr-Cu studies are reported here since data on Ti-Zr alloys will be presented in a separate publication. EXPERIMENTAL PROCEDURE Alloys were nonconsumably arc melted in argon atmosphere as 15-g buttons, prepared from materials of the following purities: Bureau of Mines electrolytic Ti — Bhn 63 OFHC copper Reactor Grade Zirconium Bhn .C 150 Prior to alloy preparation the electrolytic titanium was premelted to avoid excessive spattering of the charges during melting. The weight losses during melting did not exceed 1 pct of the total weight of the charge. The alloys prepared are listed in Table I together with analyzed compositions. in cases where they were determined. Specimens for heat treatment were wrapped in molybdenum sheet, annealed in argon-filled quartz capsules, and quenched by breaking the capsules under iced brine. About 1 to 2 sec are required to remove the capsule from the furnace, drop it into the iced brine and break it. Because of the insulation effect of the quartz, this delay in quenching should not produce a large drop in temperature. In many instances, no difference or little difference has been detected between the same specimen quartz capsule quenched or directly quenched in vacuum by an impinging stream of water.&apos; Ti-Cu-Zr alloys were homogenized for 48 hr at 825°C prior to annealing at 750°C. Annealing for 5 days at 750°C produced the same results as 11 days at temperature and it was therefore assumed that 5 days was sufficient to establish equilibrium. Titanium-copper alloys were homogenized for 40 hr at 900°C prior to heat treatment for 6 days at 750°C. Specimens for metallographic examination were electropolished and etched with the following solution:

Jan 1, 1962

By Robert Archer

THE proper material of construction for a given purpose is that material which meets the requirements satisfactorily at the lowest ultimate cost. It is consistent with this principle that most aluminum castings are made of an alloy containing about 8 per cent. copper. This alloy possesses mechanical properties satisfactory for general engineering purposes together with manufacturing characteristics leading to the production of finished castings at low cost. It is to the aluminum industry what gray iron is to the iron and steel industry. Just as some services require "semi-steel," malleable castings or steel castings instead of gray iron, there is a certain and growing demand for aluminum castings of superior strength or ductility, or both. Since the beginning of the industry producers and others have sought to develop alloys or processes by which such castings could be made. Out of these efforts have emerged many alloy compositions and special processes, of which only a few have had sufficient merit to survive. It is the purpose of this paper to describe those which seem to the authors to offer the greatest promise for the production on a commercial scale of aluminum castings of superior mechanical properties, with special reference to heat-treated castings. The suitability of an alloy or process for actual manufacture is affected by so many factors that the problem of appraisal is not a simple one. Since this is such an important part of the whole subject it is proposed to discuss briefly some of the requirements. The final verdict is of course the result of commercial trial and experience. It will therefore, perhaps, be profitable to employ a somewhat historical method of treatment in discussing the subject of alloy development.

Jan 9, 1926

By M. R. Lorenz

Efficient visible light emission from p-n junctions in semiconductors is currently achieved in the four materials, Sic, GaP, ]Ga1-xAs and GaAs1-x,. Recent advances in materials preparation and p-n junction formation are briefly reviewed. The radiative recombination processes in the different materials depend largely on the band structure and the impurity states of each material. The spectral distribution of the emission ranges from the blue in Sic, to green in Gap, yellow in Sic and red in Gap, Ga1-x AlxAs and GaAs1-x Px. The origin of the various processes are discussed. The conversion of the electrical power into optical power and the measurement of the conversion efficiency are reviewed. The currently maximum quantum efficiencies at 300°K are: 3 pct in GaP(red), 1 pct in SiC(yellow), 0.1 pct in GaP(green), 0.2 pct in Ga1-x AlxAs at 66001, and 0.1 pct in GaAs1-x Px at 6800. The brightness and the interplay of the quantum efficiency and the luminous efficiency are given detailed consideration. VISIBLE light generated by the application of a direct current to a semiconductor crystal was first observed by Lossev1 in 1923. Light emission came from naturally occurring junctions in Sic crystals but little was known then with regard to the mechanism of charge transport and light emission. Some nearly 30 years later and with a vastly increased understanding of semiconductors the phenomenon of electroluminescence was studied in more detail, for example in p-n junctions of germanium.2 In these early studies, the efficiency of converting the electron current into a photon current was very low and therefore aroused little interest toward practical application. More recently it became apparent that in certain materials, for instance GaAs, and under certain conditions, the conversion efficiency was not low at all.3 The subsequent discovery of the p-n junction laser4-6 provided the impetus for increased studies of electroluminescence. Light emitted from GaAs occurs in the infrared region of the electromagnetic spectrum and is not visible to the eye. At nearly the same time the use of GaAs1-xPx led to laser action at low temperatures which was visible to the eye.7 Later a red light emitting diode, made from Gap, was reportedS which emitted incoherent radiation at 300°K with an external quantum efficiency of about 1.5 pct. The fact that such efficient devices were obtainable led to a more concentrated effort in the search for highly efficient room-temperature semiconductor light sources. It is some of this later work on p-n junction luminescence with which we will be concerned here. Since our aim is centered on visible light, with hv =1.8 ev ( ?=7000?), only the wider band gap semiconductors are of interest, i.e., Eg 1 1.8 ev. Although many compounds meet this criterion, only a limited number of those are also good semiconductors, i.e. contain low resistance n and p regions. Some of the more promising candidates are listed in Table I. We will only be concerned with light generation from a p-n junction. This limitation excludes essentially the group II-VI binary compounds, although we will briefly review the case of ZnTe and the solid solution ZnTe1-xSex. As we will show they may contain a p-n junction but only of a special kind. Most of the discussion will deal with the four materials, Sic, Gap, Gal-xAlxAs, and GaAs1-xPx. These appear to be at the present time the best visible light emitting semiconductors. In the following sections we will briefly consider: 1) the electrical properties of p-n junctions; 2) some recent advances in materials preparation; 3) the formation of p-n junctions; and then in somewhat greater detail we will consider: 4) the various radiative recombination processes; 5) the measurement and observation of the external quantum efficiency; 6) the luminous efficiency; 7) the brightness of light emitting diodes (LED&apos;S). THE P-N JUNCTION The p-n junction in a semiconductor crystal is the interface between two differently doped regions. More specifically the p region is doped predominantly with acceptor impurities and the n region contains predominantly donor impurities. The energy band structure of a degenerate p-n junction at thermal equilibrium is shown in Fig. l(a). The excess electrons on the n side of the junction are confined to this region by the barrier potential Eg. Similarly the excess holes on the p-side of the junction are confined to the p-region by a similar potential barrier. If we now apply a dc voltage V such that the p region is made positive and the n region negative, the barrier potential EB is reduced by the applied voltage, V and the junction is said to be forward biased. With the barrier potential lowered, electrons and holes can drift toward the p region and n region, respectively, see Fig. l(b). The current voltage characteristics of p-n junctions in most wide band gap materials can be described by the relation: J = Joexp(eV/BkT) [1] where the functional form of Jo is determined by the recombination mechanism. Jo is generally a complicated parameter which depends on a number of different factors including temperature, junction width, bias voltage, and carrier lifetimes. The parameter B also depends on the recombination mechanism but

Jan 1, 1970

By G. J. W. Kor, F. D. Richardson

The sulfide capacities a1 1500°C of slags in the systern CaO + CaF, +Al2O3 have been measured by bringing samples into equilibrium with gas mixtures made from CO + CO2 + SO, + N2. The capacities are negligzble both JOY CaF, and CaF, + Al2O3 melts but when lime is present even at 20 wt pct capacilies as high as 30 x lom3 can be obtained. The results have yielded information concerning the liquidus at 1500°C and fluoride-oxide melts in general. The slags used in electroslag refining contain substantial amounts of calcium fluoride. Robinson and Grainger&apos; report that good results can be obtained by using slags of the approximate composition 70 wt pct CaF2 + 30 pct Al2O3. It has also been reported2 that a mixture of 50 pct CaF2 + 30 pct A12O3 + 20 pct CaO makes a good slag for general use. In view of the fact that very low sulfur contents are claimed for ingots produced by the electroslag process. studies have been made of the sulfide capacities [c, = wt pct S (PO2/Ps2)1/2 at 1500°C. of slags consisting of pure calcium fluoride, and of its mixtures with lime and/or alumina. These studies have also provided information on the phase diagrams. The slags were brought into equilibrium with gas mixtures prepared from NZ + CO + CO2 + SO2. Because CaFz is volatile and also easily hydrolyzed. measurements were made of its loss in weight in various flowing gas mixtures. EXPERIMENTAL Procedure. The apparatus and procedure were the same as described previously. Both platinum and iridium crucibles were used (height and inner diameter about 1 cm), but those made from iridium were stronger and able to withstand a greater number of experiments. In each experiment two crucibles were set in an alumina support and 1 g of slag mixture was divided between them. The materials from each crucible were analyzed separately after being brought to equilibrium with the gas, and then quenched in the water-cooled end of the reaction tube. Materials. Alumina and lime were prepared as de-scribed previously.4 Calcium fluoride was obtained by igniting Analar calcium fluoride in a platinum boat at about 800°C in a stream of pure dry nitrogen: the product was cooled in a desiccator. The slags were produced from mixtures of the powdered constituents, these being melted together in the course of each equilibrium experiment. The sulfur analyses and the X-ray diffraction meas- urements on the solidified slags were made as described previously.4 From the latter it appears that the CaF2 contained less than 0.5 mol pct CaO. RESULTS Values of (ps2/po2) for the Gas Mixtures. The re-sults have been represented in terms of (ps, /Po,)"? for the various gas mixtures used. The va1;es of this function at 1500°C are listed in Table I: they were calculated from the data cited previously for calculations at 1350°C 4 Weight Losses with CaF, and CaF, + CaO. The re-sults of the weight loss measurements* at 1500°C for

Jan 1, 1970

By H. H. Rachford, J. Douglas, D. W. Peaceman

A numerical solution of equations describing two-phase flow in porous media shows promise in providing a technique for predicting the displacermet from satlds of oil by water or gas. The description includes the influence of relative permeability, fluid viscosities and densities, graviry, and capillary pressure, and, tholrgh tested ortly for two-dimensional cases, should be eqlmlly applicable in three-dimensional geometry. Two memorical methods ore presented: the first method is quite general in its applicability; the second method can be used only with certain types of boundary conditions but requires less computing. Comparisons of computed results with data from Inhoratory models are presented. These data were taken on a water flood of a strarified model and on water floods of a five-spot model for favorable and unfavorable mobility ratios. On the stratified model, excellent agreement with recovery at breakthrough was obtained; agreement with recovery after breakthrough was poor. In the five-spot model, good agreement was obtainecl with recovery at and after breakthrough. The purpose of this paper is twofold: first, to present a reservoir engineering method requiring knowledge only of rock geometry and the normally measured rock and fluid properties for calculating the multi-dimensional flow of water displacing oil from porous, water-wet rock containing connate water; and, second, to investigate the validity of the method by comparing results of calculations with previously observed displacements in laboratory models. The availability of such a verified technique of reservoir analysis would afford major advantages. First, it would demonstrate that the fundamental macroscopic concepts of two-phase fluid mechanics, i.e., relative permeability and capillary pressure, yield an adequate description of the physical process. Also, since most reservoir rocks appear to be water-wet and contain connate water along with oil, it would provide a method of technical and economic value for calculating the course of oil displacement by water directly from measured reservoir and fluid properties. It is important to emphasize that the calculation is subject only to the limitations of detail and precision of reservoir information, but not to limitations introduced by simplifying assumptions. Further, it would providc almost the only means of examining the influence of factors such as the size and extent of reservoir inhomogeneities and uncertainties in the basic reservoir data. Knowledge of this influence is essential in stating quantitatively the detail required to define a reservoir and in establishing the relation between the uncertainty in the definition of reservoir properties and the reliability of predicted performance. Moreover, in the process of solving a particular problem much detailed information would become available about the displacement process. For example, at each point in the reservoir for all stages of the displace ment. the calculations would yield not only the water and oil saturations but also the direction and magnitude of fluid velocities and the local fluid mobilities. Such dctail is potentially of great value in giving insight into the mechanics of particular displacements. The development of such a method has long been the goal of research in the application of numerical an-alysis to petroleum reservoir enginecrinz. The most complete treatment of the displacement process published to date is that of Douglas. Blair, and Wagner,&apos; which, however, was limited to flow in a single dimension. The method presented in the present work is hascd on the numerical solution of a finite difference analogue of the multi-dimensional differential system describing the displacement process. Although current work has considered only displacement of oil by water from water-wet sands, the differential system for other immiscible displacements, such as gas displacing oil with which it is in phase equilibrium, is quite similar. It should therefore be expected that the technique described will be applicable to displacement by gas as well. The description of the simultaneous flow of fluids through porous media in terms of relative perrncability and capillary pressure has been adequately discussed in the literature and standard textbooks. Sec, for exampje, Muskat. Chapter VII.&apos;