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By B. C. Allen

Grain-boundary gvoocing was studied irz chronziu?n. molybdenum, tungsten, and the solid-solution alloys, Cr-35Re. Mo-33Re, and W-25Re at 0.6 to 0.9 of the absolute liquidus temperature under an inevt atmosphere , foveign nzetal zlapor, and liquid metal. The controlling mechanism of matter transport was deduced frolr groove size and shape. kinetics of growth, and cotnparisoz with theoretical relatiotzships derived by Mullins. Grooves in chowzizon formed prittzarily by volume diffusion tkrongk kelium or argon at 1 atm pressure and by e1)apovation-condensatiotz in a static vacuum. Groozles in the other nzetals and alloys forrned priniarily by sirface diffusion, the coefficients of which were calculated. Carbon was found to decrease the acti7:ation energy for surface diffusion on molybdenun. Sitrface diffusizities weve sinzilav for iWo-0.0ZC and Mo-33Re. The presence of about 1 -?nm pressure of silver or tin vapor did not affect the neckanis)n of grooz;e formation. In liquid titz or silz:er, pain bolindary gvooves formed by zolume diffusion in the liquid. BASED on theories of ullins," the mechanisms of grain-boundary grooving have been determined for low-melting metals such as copper in an inert atmospheres or in liquid lead.4 The purpose of this investigation was to study grain-boundary grooving in the refractory Group VI-A metals, chromium, molybdenum, and tungsten, and the bcc solid-solution alloys, r-35e, 0-33e,= and -25e,' at 0.6 to 0.9 of included to see whether Mullins' theories were applicable to them as well. EXPERIMENTAL WORK The materials chromium, molybdenum, tungsten, Cr-35Re, Mo-33Re, and W-25Re were in the form of 0.050-cm-thick sheet assaying 99.98 pct or better. The nominal carbon level was generally 30 ppm. The oxygen + nitrogen + hydrogen content was -50 ppm. Mo-33Re and W-25Re were prepared by powder-metallurgy methods and supplied by Chase Brass and Copper Co. The remaining materials were arc-cast. Chromium and Cr-35Re were prepared at Battelle by arc melting, extruding, swaging, and rolling. Mo-0.003C was supplied by Climax Molybdenum Co., and Mo-0.02C and tungsten by Universal Cyclops Corp. As a source of liquid metals, tin and silver granules assaying 99.98 pct were used. Spectrographic analyses indicated the presence of -100 ppm each of iron and silicon. Vacuum melting reduced the combined gas content to c5 ppm (2.60,, 0.9N2, 0.4H2 in tin and l.602, 0.7N2, and c0.04H2 in silver). Specimens were prepared for grain-boundary grooving. Coupons 0.5 by 1.5 cm with a small hole in one end, or substrates 1.5 by 1.5 cm, were cut from sheet. The specimens were annealed in containers of the same material to provide a vapor-solid equilibrium as well as to protect them from gaseous impurities. Outgassing was done at 2 x 10"5 mm for 15 to 30 min at 1150°C for chromium and Cr-35Re, 1750°C for molybdenum and Mo-33Re, and 2600°C for tungsten and W-25Re. Then recrystallization to a stable grain size of about 0.5 mm was accomplished by annealing at least 1 hr at 1600°C for chromium, 1800°C for Cr-35Re, 2350°C for molybdenum, and 2300°C for Mo-33Re in a rhenium-element resistance furnace under 1 atm of static argon or helium. The atmosphere was gettered by tantalum radiation shielding. Tungsten and

Jan 1, 1967

By A. R. Elsea, E. E. Fletcher

Cast X-40 alloy with the lowest nitrogen content studied had a 100-hr rupture stress at 1500°F about equal to the reported value for the commercial alloy. Increases in nitrogen content progressively decreased the rupture strength, and with about 0.1 to 0.2 pct N a minimum strength was reached, but there was no accompanying change in microstructure. Further increases in nitrogen resulted in the fomzation of progressively increasing amounts of a lamellar, pearlitic-type structure at the grain boundaries, with accompanying increases in rupture strength, and above about 0.25 to 0.33 pct N, the rupture strength exceeded the normally reported values. Two series of melts representing different melting stocks exhibited minimum rupture strengths at different nitrogen contents. This suggests that some unidentwed trace element not removed by vacuum melting has a strong influence on the response of this alloy to variations in nitrogen content. In a series of melts with manganese contents ranging from 0.6 to 3.2 pct, the material with the lowest manganese content had the highest 100-hr rupture strength at 1500°F. The manganese variations had no appreciable effect on the microstructure. CAST cobalt-base alloys such as X-40* exhibit high strengths at elevated temperatures (1500°F and above), but they also show considerable scatter in high-temperature properties. Since the design of parts for critical applications must be based on the minimum expected properties, this broad scatter appreciably lowers the design strength of the alloy. If the relatively poor properties exhibited by a few test parts from any given group could be improved, the spread in properties would be narrowed, and the design stress could more closely approach the average expected properties. The purpose of this research investigation was to learn what were the causes of these erratic properties and, if possible, to find methods for eliminating them. Earlier unpublished work showed that vacuum melting markedly influenced the high-temperature strength of cast X-40 alloy. There were indications that this behavior may have been the result of changes in the nitrogen or manganese content of the castings. Consequently, in the current investigation, the influence of variations in nitrogen and manganese content on the structure and high-temperature properties of cast X-40 alloy was studied. In this program, X-40 melting stock was vacuum melted to produce a base material that was very low in nitrogen content and in volatile trace elements. Additions were then made to this base material to produce alloys of the desired composition. The metal was cast into investment molds producing coupons which were machined into stress-rupture bars. These bars were subjected to stress-rupture tests and me-tallographic study to determine the influence of changes in analyses (nitrogen and manganese content) on the structure and properties. Material—The melting stock used for these experi-ments was in the form of shot from two master heats of commercial X-40 alloy. Only one master heat was used in a given series of melts. Thus, any differences in structure or properties that showed up in the specimens from a given series would be the result only of the intended variations in composition. The certified analyses of the master heats were as follows: C Mn Si Cr Ni Lot No. 2 0.50 0.71 0.66 25.44 10.53 Lot No. 3 0.54 0.73 0.70 25.95 10.00 W Fe Co P S Lot No. 2 7.45 1.34 Bal. 0.011 0.013 Lot No. 3 7.58 1.53 Bal. 0.005 0.016

Jan 1, 1960

By L. S. Birks

The bainite transformation in a 3.5 pct Ni-1.25 pct Cr steel was studied under various conditions of cooling and stress. Several characteristics may be specified: 1) transformation in the bainite region (925° to 575°F) is very little affected by the manner of cooling from the austenitizing temperature at 1600°F to 575°F)tothe upper limit of bainite transformation at 925°F; 2) starting time for the bainite transformation is the same order of magnitude for either isothermal transformation or continuous cooling, but the rate of transformation is somewhat greater for isothermal transformation; 3) tensile stress accelerates both isothermal and continuous cooling transformation, and 32,000 psi stress changes the form of the isothermal transformation diagram to correspond in appearance to the continuous cooling diagram; 4) transformation for nonlinear, continuous cooling may not be determined directly from the linear, continuous cooling transformation diagram, but may be predicted by assuming first that the fractional amount of austenite transformed in a given small temperature interval depends on the approximate linear cooling rate during that temperature interval and then by summing stepwise over the whole temperature range. IN a previous publication' an X-ray spectrometer was described with which the X-ray diffraction from a specimen could be observed continuously under controlled temperature and tensile stress. This instrument has now been applied to a study of the austenite-bainite transformation in a Ni-Cr steel for both isothermal and continuous cooling conditions, with and without stress. Certain characteristics of the transformation lead to a method of predicting the amount of transformation to be expected at a given temperature for any type of cooling curve. Material and Specimen Preparation The steel chosen for the investigation was a Ni-Cr steel having the composition in the following percentages: 0.30 C, 0.27 Mn, 0.019 P and S, 3.50 Ni, and 1.25 Cr. In order to fabricate specimens suitable for the X-ray spectrometer, a 1/4 in. plate was ground down to 0.060 in. and then cold rolled to about 0.035 in. Next it was heat treated by quenching in oil from 1650°F and tempering at 1200°F for 1 hr. Then it was etched in dilute nitric acid to reduce its thickness to 0.014 in. and cut into blanks in the shape of flat tensile specimens 3 1/4 Vi in. long, 7/16 in. wide, with a notch % in. long and 7/32 in. wide; see Fig. 1. X-Ray Technique Since the X-ray spectrometer has been described in detail elsewhere,' only a brief outline of the principles will be repeated here. A focusing, pow- der-diffraction arrangement' was used, as shown schematically in Fig. 1, and the specimen was mounted vertically in a vacuum furnace (not shown in the figure). The X-rays, moving in a horizontal plane, enter and leave the furnace through beryllium windows. As shown in the figure, X-rays diverging from the line source A are diffracted by the specimen B and converge at the detector slit C. The detector D and the slit C may be set at the proper angle in the horizontal plane to receive X-rays diffracted by either the face-centered phase (austenite) or the body-centered form (ferrite, bainite, martensite). The specimen is heated by electrical conduction between connectors E, and E,, and a Pt—Pt-10 pct Rh thermocouple spot-welded to the center of the notched region on the side away from the X-ray beam indicates the temperature continuously on a Brown recorder. Temperature control is exercised manually with a variable transformer on the input to E,-E,. Any desired time-temperature relationship is easily obtained by first drawing the desired curve on the temperature recorder chart and then adjusting the variable transformer during the run so that the thermocouple

Jan 1, 1957

By Donald L. Johnson

REVIEWS on the applications of optical ellipsometry to the study of polycrystalline metal surfaces and oxidation-corrosion processes have been presented by Kruger and Hayfield, and white.' In view of the ability of this method to measure differences in film thicknesses to below 10A, ellipsometry was used to study nitrogen chromium surface reactions during the early stages of growth. Chromium specimens in the form of a vapor-deposited film on glass substrate were exposed to purified nitrogen for selected time increments at 700°F. This temperature was selected because it gave the best combination of exposure time and thickness change. Ellipsometer readings were taken immediately after exposure to determine polarizer and analyzer angles using monochromatic light at 5000A.2 After each set of readings was obtained, the specimens were exposed for an additional increment of time in nitrogen and a new set of readings taken. Film thickness was computed from LUCy's3 equation for nonabsorbing thin films. In Lucy's derivation, two equations for computing thickness were obtained. Peterson and Bashara4 have discussed the validity for using one of these equations when an independent value of the refractive index is used. The film was assumed to be Cr2N (Ref. 5) and was determined to be optically isotropic. Optical isotropy was determined by rotating the films about the surface normal and noting that the azimuth and phase difference did not change. Since Cr2N is reported to be hexagonal, it is assumed that optical isotropy results from randomly oriented grains of very small size. The thickness was computed using refractive indexes varying from 1.6 to 2.0. The maximum variation in computed thickness over this range for a given exposure was 20 pct. The data reported are based on a refractive index of 1.8. Reference readings on the metal surface were taken just prior to nitrogen exposure. No attempt was made to deoxidize or denitride the metal surface after vapor deposition, although specimens were observed to gain approximately 2A per day in air at room temperature. Twelve experimental exposures were made on a single sample over a total accumulative time of 132 min. Additional experiments over longer time intervals were made to determine the effect of heat up and cool down during and after exposure. As a result of these experiments, the thickness computed for each exposure was increased by 4A. Time profiles based on the linear law are similar to the oxidation profiles for many metals.' The rate of accumulation of the nitride film is rapid at first and slows down as the film thickness increases. The parabolic law x2 =k1t +k2 [11 gives a straight line in Fig. 1; therefore, it is concluded that the kinetic behavior is parabolic. Sey-bolt and Haman5 reported similar results for CrlN on chromium at 1000°C although the order of the thickness was much greater (10-3 cm). Analysis of thickness data based on other values of refractive index shows that the curves are shifted vertically but retain the same shape. According to Mott,7 it is expected that for thin films k2 is zero in Eq. [I]. Since the plot in Fig. 1 is linear through the origin, k2 is zero and the parabolic nature of the film growth is further indicated. The parabolic rate constant, calculated from the slope in Fig. 1, is 4.4 x 10-16 sq cm per sec. The corresponding work (+) required to bring an electron from the metal into the oxide is estimated to be 1.5 ev.7 The author thanks professor N. M. Bashara and D. W. Peterson, Electrical Materials Laboratory, University of Nebraska, for making the ellipsometer available and providing technical assistance. The Electrical Materials Laboratory is supported by the office of Naval Research, NONR 3718 (01). This work was partially supported by the Engineering Experiment Station and the Mechanical Engineering Department, University of Nebraska.

Jan 1, 1967

By S. J. Matas, R. F. Hehemann, R. H. Goodenow

The hot-stage metallographic method has been employed to determine radial growth rates of upper and lower bainite. Lower bainite appears to grow as individual plates that increase in both length and thickness while upper bainite grows as sheaves of closely spaced plates or needles. A discontinuity in the temperature dependence of the growth rate appears to be associated with the transition from upper to lower bainite and stepped quenching experiments suggest that lower bainite will not continue to grow when the temperature is raised to the upper range. Thus, a single process does not appear to control the growth of both upper and lower bainite. A tentative model based on the forces acting on a dislocation interface is proposed to account for the slow growth of bainite. It has been recognized since the early studies of Davenport and Bain that a close relationship exists between the martensite and bainite transformations in steels. However, diffusion of carbon during the transformation has lead to considerable controversy concerning the reaction mechanism.1-7 Many studies4,5,7-9 have emphasized the structura and kinetic aspects of the bainite reaction and, in particular, the difference observed between the two forms of bainite—frequently termed upper and lower bainite. A kinetic difference between the two types of bainite has been revealed in the activation energy determined from the overall reaction;4,5 however, many difficulties arise in an interpretation of these activation energies since a number of temperature dependent factors contribute to the kinetics of the overall reaction. The displacive surface relief10 accompanying the bainite reaction permits a separation of the nuclea-tion and growth contributions to the reaction and allows the kinetics of the growth process to be examined. Several investigations of this type have been conducted; however, they have been restricted to the low temperature range.3'6'11 Here, bainite plates are observed to grow slowly in both length and width. The present investigation extends such studies to include the upper bainite range. MATERIALS AND PROCEDURE Materials. The composition of the steels studied in this investigation are presented in Table I. The range of composition permitted a study of the effect of carbon content on the growth rate of upper bainite in the 9 pct Ni steels and consideration of both upper and lower bainite in the higher carbon steels. These steels were received as hot-rolled rounds and were forged to approximately 1/2 in. thick plates for preparation of metallographic specimens. In order to produce an essentially zero carbon steel, Steel A was decarburized in wet hydrogen at 1550°F for 15 days with the result tabulated as Steel AD. Experimental Procedure. In order to study the slow growth of the displacive transformation product, a commercially available Leitz hot stage was modified to permit heating of the specimen by its own resistance in a manner similar to that employed by other investigators.6 The furnace chamber was maintained at a pressure of 2 to 3 X 10-5 mm Hg prior to austenitizing at 2000° ± 12° F for 5 min. Samples could be cooled from the austenitizing to the transformation temperature in approximately 15 sec and the progress of transformation was recorded with a 9 cm by 12 cm single frame camera or a 16 mm movie camera. RESULTS AND DISCUSSION Growth Characteristics. The general growth characteristics observed in this investigation were analogous to those reported previously.3,6,11 Typical growth sequences for the high temperature and low temperature forms are illustrated in Figs. 1 to 5. In both temperature ranges, bainite plates increase in length at slow, temperature dependent rates until interrupted by a grain boundary, another plate, or

Jan 1, 1963

By J. E. Neal, C. T. Naber, O&apos

Silicon thin films were deposited by electron beam evaporation in an ultrahigh vacuum onto (0001) and (1102) sapphire substrates. Attempts were made to correlate the structural properties of the deposited silicon films with the following: 1) substrate orientation, 2) substrate surface condition, 3) substrate temperature, and 4) deposition rate. The substrate temperatures were varied between 500° and 1000°C and the deposition rates were varied between approximately 50 and 700A per min. The following sapphire surface treatments were investigated: 1) annealing in the ultrahigh vacuum at 1200° C; 2) heating in a hydrogen atmosphere at about 1350°C; and 3) etching with silicon by evaporating silicon onto sapphire substrates heated to 1200° or 1300°C. Twinned silicon films were occasionally formed at substrate temperatures between the 800° and 1000°C on unprocessed mechanically polished substrates; however, the reproducibility and crystallinity of these films were generally poor. Single-crystal and twinned silicon films were formed at substrate temperatures between 700° and 1000°C on substrates which were silicon-etched at 1300°C prior to deposition. Fiber texture films were formed at substrate temperatures between 500° and 700°C. The (111) lattice plane of the silicon single-crystal films was parallel to the (0001) sapphire plane and the (100) silicon plane was parallel to the (1102) sapphire plane. TECHNIQUES are well-established for growing single-crystal silicon thin films on sapphire by chemical methods.'-* Vacuum epitaxial techniques have a number of advantages over chemical epitaxial techniques in the fabrication of thin film microcircuits.5 One of the most significant is that vacuum techniques are compatible with well-established procedures for forming vacuum-deposited thin-film resistors, capacitors, and interconnections. Salatna, Tucker, and young6 recently reported the formation of relatively poor crystalline-quality silicon films on sapphire by electron beam evaporation in a vacuum of about 7 x 10-7 Torr. The purpose of the investigation described here is to determine the relationships between the structural properties of silicon thin films deposited on sapphire substrates by electron beam evaporation in an ultra-high vacuum and the following: 1) substrate orientation; 2) substrate surface condition; 3) substrate temperature; and 4) deposition rate. The substrate temperatures were varied between 500° and 1000° C and the deposition rates were varied between approximately 50 and 700A per min. Two orientations of sapphire were used: (0001) and (1102). The thick-nesses of the films were between 8000 and 16,000A. The morphology and crystallinity of the deposited films and substrate surfaces were investigated by optical microscopy, electron microscopy, and electron diffraction. APPARATUS AND PROCEDURE A cross section of the ultrahigh-vacuum thin-film evaporator is shown in Fig. 1. The bell jar is stainless steel and copper gaskets are utilized at all seals. High vacuum is attained by a 6001iter per sec ion pump and a titanium sublimation pump. Sorption pumps are used to rough the system to a pressure of about 10 µ prior to starting the ion pump. Vacuums in the 10- 10 Torr range were attained after baking the system at about 250°C for 8 hr. Vacuums in the 10-8 to 10-9 Torr range were maintained during silicon evaporation. The silicon charges, which were cut from p-type single-crystal boules which had resistivities between 2000 and 4500 ohm-cm, were placed in the water-cooled copper crucible of a 180 deg bent-beam 5-kw electron beam evaporator. During evaporation, a molten zone was formed in the top center of the silicon charge, and the portion of the silicon charge in contact with the water-cooled crucible remained solid. The substrate heater, which has been described

Jan 1, 1969

By R. S. Shoemaker, D. L. Harris

PST investigations into the possibility of concentrating the low-grade iron ores of the Gogebic Range in Wisconsin have been hampered by the complex association of the constituent minerals. In part the problem arises from the fact that the iron occurs essentially as two minerals, hematite and goethite, having nearly the same chemical composition but exhibiting different physical properties. Individual grains of these minerals are usually so small that the ore must be ground to a size finer than 325 mesh if substantial liberation of the minerals is to be secured. Appraisal of beneficiation tests on this iron ore requires, therefore, some method of determining quantitatively the contents of constituent minerals in the various products of the beneficiation. Because of the chemical similarity of the two iron minerals, chemical analyses do not provide a means of differentiation. Although the minerals are different physically, they are both opaque and friable, and as the ore must be ground to a very fine size for liberation to be secured, quantitative microscopic methods of analysis are extremely difficult at best. In an effort to overcome these analytical problems, a quantitative X-ray diffraction analysis method has been developed at the University of Wisconsin for the research program on iron ore beneficiation. The X-ray diffraction analysis of chemical compounds of crystalline form has proved of inestimable value for structure studies and rapid qualitative analytical purposes in a number of fields.' In some cases X-ray diffraction analysis has been found suitable for quantitative determinations. H. P. Klug2 found that quantitative procedures for quartz powders when mixed with calcium fluoride were reproducible within ±1.0 pct. Talvenheimo and White3 reported quantitative analyses of clay minerals to be accurate within 10 pct and also detected 1 pct of bentonite in 99 pct illite. In other investigations,'" powders of quartz and mica have been analyzed quantitatively with accuracies from 1 to 5 pct. A powder of tungsten carbide was analyzed similarly by Redmond7 and Rooksby8 reported the determination of small amounts (0.11 pct) of calcium oxide in magnesium oxide. In the most generally practiced use of X-ray diffraction, traces of the diffracted beam are recorded as lines on a film much as lines of elements are recorded on an optical spectrograph film. As with the spectrograph, the darkness of the lines denotes the amount of the constituent in the sample. If the film is replaced by a Geiger tube assembly and a graphic recorder or a scaling unit, the intensity of the diffracted beam can be registered as a peak on a chart or energy impulses per unit of time on the scaler. Several methods of quantitative measurement have been investigated and reported in literature. Klug2 used manual operation of the goniometer and a counting technique to determine the difference in counting rates at the diffracted angle and for the background. In another case3 the area under the recorded diffracted peak was the basis for the determination. In other instances the height of the recorded diffraction peak above background, measured while the goniometer was moving, has been the basis for the measurement. The sizes of particles most suitable for diffraction techniques are reported in the literature as follows: for tungsten carbide a maximum of 40 microns7 and for quartz a maximum of 5 microns.' Very fine sizes of crystals are known to cause a broadening of the diffused beams; hence some workers have set a lower limit of 0.1 micron for quantitative results. Guinier10 has indicated that broadening of the diffracted X-ray beam is not appreciable for crystallites larger than 0.02 to 0.03

Jan 1, 1956

By W. B. Gogarty

With the use of polymer solutions in secondary recovery operations, the need has developed to understand the mobility control mechanism. This study investigated mobility control by considering both permeability and rheological effects. Experiments used a high molecular weight, partially hydrolyzed polyacrylamide polymer. Flow studies took place in reservoir and Berea cores having zero oil saturation. Effective size of the polymer flow unit was inferred from Nuclepore filter tests. Clay studies indicated the particle size capable of decreasing the core permeability. Flushed permeabilities measured the approximate core permeabilities with flowing polymer solutions. These permeabilities were considerably lower than original values. With mobility data and the flushed permeability, maximum effective viscosities were determined for polymer solution flow in a core. Effective viscosities showed that rheological properties play an important part in mobility control with polymer solutions. The study showed that permeabilities decrease and stabilize with polymer flow. At the lower permeabilities, high shear rates exist in the cores. Because of the pseudoplastic character of the polymer solution, the high shear rates caused low effective viscosities. This condition pointed to the inefficient use of the potentially high viscosity of the polymer solution at low shear rates. INTRODUCTION In the oil industry, a great deal of interest is being shown in the use of polymer solutions for secondary recovery and a number of polymer floods are being performed in the United States.1 Some of these floods have become commercial while others have been reported as failures. A number of floods are still in progress and remain to be evaluated. With the advent of polymer flooding, the need developed to understand the mobility control mechanism in porous media. Rheologically, the polymer solutions behave as pseudoplastic fluids. Investigators have studied the rheology for this type of non-Newtonian fluid in porous media?-6 Results have also been reported on the ability of polymer solutions to decrease mobility.7-10 Some investigators indicated that polymer solutions show a different rheological behavior in cores than on the viscometer.7,8 This study is representative of an initiatory investigation on mobility control with polymer solutions. Some effects are considered on a qualitative basis. Mobility control is considered from the standpoint of both permeability and rheology and, to the extent possible, permeability and rheological effects are considered separately. Results show that mobility control occurs from a reduced permeability caused by polymer retention and an effective viscosity determined by the average shear rate in the core. In this respect, rheological behavior is as important in mobility control as permeability. PROCEDURES A high molecular weight, partially hydrolyzed, polyacrylamide polymer was used in the investigation. Solutions of various concentrations were made with this polymer in different types of water. Some solutions used distilled water and others used tap water. The tap water contained approximately 500 ppm dissolved solids. As used in this paper, concentrations in ppm refer to parts by weight solute to one million parts by weight of solvent. In the tap water, calcium and magnesium accounted for from 60 to 80 ppm of the solids, the remainder being mostly sodium chloride. All solutions contained a bactericide, and anti-oxidants and antiprecipitants were added to the tap water. Capillary and concentric-cylinder* viscometers determined the rheological properties of solutions. The capillary viscometer is described elsewhere.6 Berea and reservoir sandstone were used as core materials for this investigation. Cores were 1 in. in diameter by approximately 2 to 3 in. long. Prior to mounting, the Berea cores were heat-treated for 3 hours at 850F. This treatment decreased the water-sensitivity of the clays in the cores. The reservoir cores were cleaned with solvent and

By Larry Kaufman

A useful method for estimating the entropy of NaCl type compounds has been developed by combining the Debye theory of specific heat with the Lindemann formula. This method pemnits calculation of the entropy from a knowledge of the atomic weight, atomic volume, and melting point of the compound. Comparison of the calculated and observed entropies of 35 NaCl type compounds over a wide temperature range yields good agreement thus establishing the usefulness of the method. Application of the method to other crystal types is also discussed. KUBASCHEWSKI~ has suggested a useful method of estimating the enthalpy of formation of inter-metallic compounds from a knowledge of the crystal structure, lattice parameter, and heats of sublimation of the component elements. This method is quite valuable in predicting the tendency for compound formation in a given system and is of particular value in considering systems for which no experimental data are available. In order to supplement the enthalpy calculation afforded by Kubschewski's method, it would be of value to be able to estimate the entropy of compounds so that the entropy and free energy of formation could be evaluated. Although a considerable body of such data determined by calorimetric and equilibration techniques exists at present, the difficulty of making such measurements (particularly at high temperatures) and the ever increasing number of new compounds which are of interest make the desirability of such a computational method clear. This paper deals with a method for calculating the entropy of a compound from a knowledge of the atomic weight, atomic volume, and melting point. Since these data are generally easier to determine and therefore more readily available than thermo-dynamic data, they should provide an additional tool in estimating the stability and reactivity of compounds at high temperatures. I) THE ENTROPY OF PURE METALS As a first approximation, the specific heat of a pure metal can be represented by a sum of terms where C,($/tI is the vibrational specific heat calculated on the basis of the Debye theory, lo4 TC, (0/T) is an approximation to the Cp - C, correction. T is the electronic specific heat, and Cp (p) is the magnetic specific heat. Although the Debye theory does not provide a complete description of the vibrational specific heat, i.e., the Debye temperature 0 is not a constant, it does provide a good approximation when used properly. Blackman6'7 has written several reviews on this subject discussing the different values of 0 determined by various methods (specific heat, X-rays, elastic constants, electrical resistivity, and so forth), as well as the observed temperature dependence of 0 with T. In the present case the 0 in Eq. [I] naturally refers to the specific heat 0. The variation of Debye 0 (as determined from specific heat measurements) with temperature is observed to exhibit its most radical behavior at very low temperatures. At higher temperatures the 8 values are observed to become more nearly constant. Blackman6'7 has presented the variation of 0 with temperature for several metals. His tabulation is reproduced in Table I. Reference to Table I shows that above a certain temperature level, 0 remains fairly constant. The value of 0 which is most useful in computing the specific heat, and hence the entropy, is the value of 0 in the range 0/6 « T « 0. In 1910, Lindemann' suggested a relation for estimating Debye 0 values. According to this formula, where V is the atomic volume, T is the melting point in 'K, M is the atomic weight, and CL is a constant. Mott and Jones9 present this formula and state that there is at present no satisfactory theoretical explanation, but that it does have an empirical basis. By using the valuesof 0 in Table I along with known1' values of M, T, and the molar volume VM, where the Lindemann constant can be evaluated. This

Jan 1, 1962

By William C. Hagel

Oxygen-18 exchange between gaseous oxygen, held at a pressure of 125 mm Hg in a PL-IORh chamber, and splzeres of a Fe2O3 containing three or less grains was determined from 9000 to 1250°C. Isotope equilibrum on crystal surfaces appears to be quickly established, and the rate-determining factor is self-difiusion confbvrning to the relation D = 2.04 esp(- 77,900/RT) sq cin sec-'. Changing sphere diameters caused no detectable variation in diffusion coefficients. Oxygen ions diffuse faster than cations at low temperatures, but a crossover may occur at about 1150°C. INVESTIGATIONS by Davies et al.' and Himmel et al2 have suggested that the mechanism of iron oxidation above 600°C involves a predominance of cation migration in the wüstite (FeO) and magnetite (Fe301) layers and oxygen-ion migration in the hematite (a Fe2O3) layer. Evidence for little cation migration during hematite growth consists of: 1) the disappearance of radioactive-silver markers, presumed to vaporize from the oxide-gas interface, and 2) a large discrepancy between parabolic rate constants for magnetite oxidation and those calculated from Lindner's3 data for cation self-diffusion, D:, using Wagner's theory.4 Reversing the calculations gave anticipated self-diffusion coefficients, D:, for oxygen ions of 3.6 x 10-9 sq cm sec-1 at 1100°C and 5.9 x 10-10 sq cm sec-1 at 1000°C. Since then Kingery et a1.5 reported three values for oxygen-ion diffusion in polycrystalline, sintered hematite. These were obtained near 1200°C, at an oxygen pressure of approximately 150 mm Hg, and could be represented by the Arrhenius expression, Dg = 1 x 10 11 exp(-146,000/RT) sq cm sec-1. Extrapolation to temperatures below 1100°C infers that oxygen ions are less mobile than cations. This contradicts the aforementioned oxidation evidence and also coble7s study of the initial sintering of hematite. From the latter, apparent diffusion coefficients for the slowest rate-controlling species could be calculated, and fair agreement was found with an extension of Lindner's data for cation diffusion. Fig. 1 depicts such comparisons graphically. Three points have been included for the determinations of Himmel et al. on cation diffusion in large, natural hematite crystals surrounded by pure oxygen at atmospheric pressure. No dependence on crystal log raphic direction was noted. Since the value of 10-l4 sq cm sec-' at 1000°C actually represents an upper limit, one might interpret that there is a small decrease in D: when single crystals are employed. On the whole, however, cation diffusion appears relatively well-defined,* while the few results tension to lower temperatures. After having gained experience measuring oxygen-ion diffusion in certain glasses7 and in the corundum oxide, a Cr2O3, the purpose of this work was to determine D; values for hematite and thus possibly assist a mechanistic understanding of the kinetics of the oxidation and reduction of solid iron oxides. I) EXPERIMENTAL PROCEDURE A) Material. Hematite powder of moderately high purity was received from the Columbian Carbon Co. An accompanying lot analysis listed 0.03 H2O, 0.008 weight percents, with the remainder Fe2O3. Subsequent treatments were ball milling, drying, prepressing, and hot-pressing for 60 min at 1350°C under 5000 psi. Since graphite dies coated with a slurry of alumina were used for hot-pressing, the surrounding atmosphere at temperature was sufficiently reducing to form some magnetite on the outer surface of each cylinder. After removing any attached alumina, a stabilizing anneal of 50 hr at 1300°C in oxygen was added. The final product was nonmagnetic and exceeded 97 pct of the density (5.24 g cm-3) usually given for FezO3. On polishing cylindrical ends, counts were made of the number of grain boundary intercepts per

Jan 1, 1967

By Keith R. Bock, Norman Parlee, Albert M. Barloga

Coils of pure iron and iron-carbon alloy wire (0.05 to 0.80 pct C) and sufficient sulfur to saturate the solid phase were equilibrated in evacuated or argon filled tubes. After rapid cooling, and removal of the outside nonmetallic layer, the wires were analyzed for carbon and sulfur and the data used to construct an Fe-S binary and isotherms of the Fe-C-S ternary in the range 1149° to 1427°C. THE solid solubility of sulfur in steel is of interest in connection with such phenomena as hot shortness, burning, and so forth. "Burning," the more or less permanent damage that some steels suffer when heated for forging or rolling, has been shown to be related closely to the behavior of sulfur and less closely to carbon and oxygen.' Attempts to interpret burning phenomena in steels fail because of lack of data on the Fe-C-S and the more complex systems in this family. Rosenqvist and Dunicz 2 and Turkdogan, Ignatowicz, and pearson3 have largely elucidated the Fe-S diagram in the region of interest but no information on the Fe-C-S diagram in this region appears to be available in the literature. This paper deals with the elucidation of the Fe-C-S diagram in these interesting ranges. The method employed is different from those used by previous workers2'3 on the Fe-S system. EXPERIMENTAL METHOD Pure iron wires (Ferrovac E) or iron carbon alloy wires of 1 mm in diam were cleaned with acid and acetone, coiled, and placed in silica tubes (7 mm OD and 5 mm ID) previously closed at one end. Enough sulfur was added to assure saturation of the solid iron phase. The filled tubes were either simply evacuated and sealed, or filled with argon at a reduced pressure and sealed. The argon was required at the higher temperatures to prevent collapse of the tubes. The filled and sealed tubes were placed in the middle uniform temperature zone of a Globar tube furnace and equilibrated at temperatures ranging from 2100°F (1149°C) to 2720°F (1493°C). After equilibration the tubes were removed from the furnace and quenched in air or water, the form of quenching being found to have no effect on the results. The tubes were broken open and the coils were placed in a 1 : 1 HC1 solution to remove the sulfide-rich layer. The coils were then cut into small pieces and analyzed for sulfur and carbon. In the early stages of the investigation different equilibration times ranging up to 17 hr were tried and the cores of the wires were analyzed to test for saturation. One hour appeared to be sufficient to reach maximum sulfur content at 1454°C and 2 hr sufficient at 1149°C. The practice adopted was to use at least 3 hr at the higher temperatures and at least 5 hr at the lower temperatures. The iron-carbon alloy wires used were made by carburizing pure iron wire with carbon monoxide gas in a one inch diameter ceramic tube at about 1204°C. Differing carbon contents were obtained by allowing fairly large coils to react with the gas for varying lengths of time at a flow rate of 800 cc per min. The reacting times ranged from 15 min to 4 hr depending upon the amount of carbon desired. The furnaces used were controlled by means of Leeds and Northrup Speedomax Type H instruments with D.A.T. Control attachment. Thermocouples were calibrated against the melting points of gold and copper. The temperatures recorded appear to be accurate within i2.7OC. Starting with run No. 85 and continuing with the

Jan 1, 1962

By E. R. Macgregor, J. Halpern

The kinetics of the reduction of cupric salts in aqueous solution by molecular hydrogen to metallic copper are described. The rate of reduction appears to be homogeneously determined and shows a marked inverse dependence on the hydrogen-ion concentration. Precipitation of copper is more rapid and complete in sulfate than in per-chlorate solution. A mechanism is proposed which accounts for this behavior. IN recent years a number of important hydro-metallurgical processes have been developed in which metallic salts in aqueous solution are reduced by gaseous hydrogen, usually at elevated temperatures and pressures, and thereby precipitated either in metallic form (e.g. Ni, Co, Cu) or as an oxide or salt of lower valence (e.g. VO, and VA).1 ; In connection with applications such as these, most of which involve heterogeneously catalyzed reactions, recent demonstrations"-" that salts of certain metals, e.g., Cu", Ag' , Hg" , and Hg,+ can activate molecular hydrogen homogeneously and thus catalyze hydrogenation reactions in aqueous solution, are of considerable interest. For example, cupric salts catalyze the otherwise slow homogeneous reduction of dichromate and ceric salts by hydrogen, i.e. Cr,O; + 3HL. + 8H1 ? 2Cr'- -- 7H,O [1] 2Ce ' ! H.. ? 2Ce" | 2H . [2] In perchloric-acid solution, where Cu" is not appreciably complexed, the kinetics have been found" " to be of the form -d [H,] _- k,[HJ [CU"]' dt -LCu+' l+ (k ,/k,) [H] [3] where, K = 1x10"' exp [—26,600/RT] 1, mole-' min-' ... [4] and (k ,/k,) - 0.25 at 110°C. This kinetic behavior suggests that the reaction proceeds by a mechanism involving the following sequence of steps kt Cu" +H1CuH' 4-HA [51 k., CUH + CU" ? + 2Cu f H' [GI 6Cu'+ Cr,07 + 14H'+ 2Cr- (¦ 7H,O + 6Cu" ['i] fast The catalytic activities of the undissociated cupric-sulphate and cupric-acetate complexes are somewhat greater (by factors of 6.5 and 120, respectively) than that of the simple hydrated Cu" ion.'" These considerations suggest that, in contrast to the other hydrometallurgical hydrogenation reactions, referred to previously, reduction of cupric salts in aqueous solutions by molecular hydrogen, should proceed homogeneously, and in the absence of an extraneous catalyst. This has already been demonstrated" for acetate-buffered solutions where the product of the reaction is a precipitate of cuprous oxide (Cu,O). In the present paper, an investigation of the reduction of cupric salts in perchloric-acid and sulphuric-acid solutions, leading to the precipitation of metallic copper, is described. Some results for the sulphate system, which is of considerable hydrometallurgical interest, have been reported previously by Ipatieff",' " and by Schaufel-berger' but these do not give a quantitative account, of the kinetics and mechanism of the reaction. Experimental The reduction experiments were conducted in the 1-gal, titanium-lined autoclave described in connection with earlier related investigations," " and using a similar procedure. The solutions were made up by dissolving known amounts of CP grade Cu(ClO,), and HC10, (or CuSO, and HISO,) in dis-tilled water. While in the autoclave, the solution was stirred and maintained at a constant temperature (±loc) and under a constant partial pressure of hydrogen gas. It was ascertained that the agitation (provided by two 3-in., four-bladed stirrers, rotating at 900 rpm) was adequate so that at no time was the rate of reaction limited by solution of hydrogen. During each experiment, samples of the solution were withdrawn periodically, allowed to cool, and the concentration of copper remaining in solution was then determined electrolytically. Some Cu' is formed during the reaction, but undergoes disproportionation when the solution is cooled to room temperature. For purposes of kinetic calcula-

Jan 1, 1959

By R. W. Armstrong, D. H. Feisel

Self-diffusion in pure crystalline solids has been described through extension of the Cohen and Tum-hull volume -fluctuation model originally proposed for diffusion in simple liquids. It is shown, for a number of crystalline solids, that the self-diffusion coefficient, D, obeys the relationship where a is the lattice spacing, v the Debye frequency, Z' the lattice-volume fluctuation per atom required for a diffusion jump, and (?V/Vo) the relative increase in the lattice volume resulting from thermal expansion between O°K and the temperature under consideration. The calculated value of Z' is dependent upon the difiusion mechanism and the lattice geometry. ThE need for an increased understanding of mass-transport processes in crystalline solids has resulted in much research to determine rates of self-diffusion.' For several metals (e.g., copper, silver, and iron), the experimental values of the self-diffusion coefficient, D, have been determined over a large interval of temperature and the accuracy of D has been investigated through repeated experiments. Also, a number of empirical and theoretical diffusion studies have established a rational basis for understanding the D values for the different elements.2"6 The empirical diffusion analysis by Sherby and simnad6 supplied the main stimulus for the present study. Sherby and Simnad, reviewing the self-diffusion data for a substantial number of pure crystalline solids, suggested that sufficient data were available to establish with some certainty the apparent intrinsic material properties which influence D. Without explicit regard for any mechanism of diffusion, these investigators obtained an empirical relationship for D which correlated the self- diffusion coefficient for each element with the melting temperature, crystal structure, and valence of the particular element. Their analysis is only unsatisfactory in that the effect on D of crystal structure is not very clear and the valence to be assigned to an element is not always straightforward. The present study is an attempt, from a very different viewpoint from that of Sherby and Simnad, to establish a basis for understanding the self-diffusion coefficients for crystalline solids. This analysis was undertaken for the purpose of developing a general expression for D which would explicitly depend on the mechanism of diffusion. The main result of the study is that diffusion in crystalline solids may be described in terms of a volume-fluctuation model which was originally proposed by Cohen and Turnbull7 to describe diffusion in simple liquids. The model appears to be useful for predicting self-diffusion coefficients in crystals. The following sections describe the volume-fluctuation model for diffusion, the application of this model to crystals, and the resultant agreement with experimental data. 1) THE VOLUME-FLUCTUATION MODEL FOR DIFFUSION Cohen and Turnbull7'8 developed their model for liquid self-diffusivity for the purpose of describing certain properties of liquids, glasses, and the liquid-glass transition. A hard-sphere model for the liquid structure is used. In this model, the size of a spherical molecule or atom is fixed for all temperatures by the interatomic spacing at the absolute zero of temperature. At any temperature above O°K, the atom is viewed as being contained within a larger spherical cage defined by the interatomic spacing of the atoms at that temperature. A random distribution of varying cage sizes is assumed to exist in the liquid. An individual diffusion jump occurs when the free volume of an atom (the volume of the cage containing the atom minus the volume of the atom) is large enough for the atom to jump out of its cage. With this physical picture of diffusion in liquids, Cohen and Turnbull derive the following equation for self-diffusivity: D=Doe-yv*/vf [1] where Do is the product of three factors which are the diffusion-path geometry, the diffusion-jump distance, and the velocity of the diffusing atom, v*

Jan 1, 1964

By T. M. Kegley, J. H. Frye, D. L. McElroy, M. L. Picklesimer, E. E. Stansbury

Measurements of rate of growth, thermodymmic quantities, and partitioning of Mn are reported for high-purity eutectoid Fe-C and Fe-C-Mn steels for the auistenite-pearlite reaction. Evaluztion of the cotnstants of a derived-rate equation with these data indicate that Mn additions cause the decrease observed by increasivg the activation energy and apparent activation entropy or the movenment of complexes at the interface. A diffusion-controlled mechanism is not required. Appreciable partitioning of Mn to cementite occurs entirely behind the austenite-pearlite interface for more than 30°C of subcooling. ThE growth of pearlite from austenite has been extensively studied over a period of years. but the rate-controlling step in the process is not known nor is the mechanisrn of the effect of alloying elements understood. A comprehensive review of the subject has been given by Mehl and Hagel. The present study has been concerned with further considerations of the effects of alloying elements on the rate of growth of pearlite. Analytical relatioriships for the rate of growth of pearlite have been considered by Zener.2 Turnbull,3 Machlin,4 Cahn.5 Frye,6 and Frye et a1.7 The derived expressions in each case involve the free energy of the transformation. the interlamellar spacing. and some rate term of the nature of the diffusion coefficient. mobility or frequency of occurrence of some rate-determining step. The treatments. of course. differ in detail. Further consideration is given in the present paper to the equation of Frye, Stansbury. and McElroy which was derived from modified absolute rate theory without in any way specifying the mechanism of the reaction. This equation is r=c ? T ? F exp -?E*/RT [1] where r = rate of growth in mm/sec c = a constant AT = equilibrium transformation temperature minus actual transformation temperature "C ?F = free energy per mol of austenite minus that of pearlite ?E* = activation energy R= gas constant ?F in Eq. [1] is computed from the following: ?F=?H?T/To - ?T' dT' ?T' ?CdT"/T" [2] To To where AH is the enthalpy per mol of austenite minus that of pearlite at the equilibrium temperature, To, and AC is the difference in specific heat between austenite and pearlite per mol. Subsequently, Darken, Fisher, and Galligan8 have reported that a layer of ferrite separates pearlite from austenite at the growing interface (i,e., the advancing face of Fe3C is in contact with ferrite, not austenite) and the ratio of the thickness of this layer to the spacing of the pearlite has not been found to vary with alloy content or transformation temperature. This observation does not require any alteration in the above equation: however, it may require that a different significance be attached to the factor, AT. The AT term appears in Eq. [I] as a consequence of a factor for the amount of growth per complex transformed at the interface.* It is based *This is not the sole reason for expecting such a relationship. See Ref. 7._______________________________________________________ on a l/2 ?T dependence of the interlamellar spacing. Zener2 has developed a theory which leads to Soa 1/?V where So = the pearlite interlamellar spacing. This relation is as consistent with the data on interlamellar spacing as other relationships, although, as pointed out by Mehl and Hagel,1 the data are not sufficiently precise to consider the relationship as confirmed. The work of Darken, Fisher, and Galligan8 requires that the above be written where f = the thickness of ferrite layer between austenite and pearlite. The present paper is concerned with iron-carbon-manganese eutectoid alloys and reports experimental measurements of the following kinds: 1) the effect of

Jan 1, 1961

By H. F. Webster, C. G. Dunn

Rolling md annealing procedures are described for developing the (110) preferred orientation in tantalum for use as a thermionic-emission materinl where electrodes of a uniform high work function are needed. The development of a (110) [001] annealing texture is also reported. A preferential growth process due to low (110) gas-metal surface energy is considered in explanation of the observed growth of (110) grains. ThE growth of (110)-oriented grains in thin strips of rolled zone-refined tantalum, previously discussed briefly,' is reported together with more recent information on the formation of a (110)[001.] annealing texture, i.e., one where the [001] direction of each grain lies close to the rolling direction. The development of tantalum sheet with a (110) preferred orientation (position of [001 ] directions unspecified) is of importance as a thermionic-emission material in thermionic-energy converters. Since therm ionic-emission properties of cesium-coated crystals vary over a wide range depending on (hkl) a2-7 a single (hkl) preferred orientation is more useful than either several preferred orientations or none. Furthermore, the (110) preferred orientation yields the highest thermionic-emission density for a cesium coverage of less than a monolayer.5-7 A consideration of the stability of the grain structure needed at high operating temperatures suggests that the preferred orientation itself should be produced by annealing processes. Information on annealing textures in tantalum, however, is rather limited. Pugh and Hibbard 8 obtained (111)[112] and (lll)[112] components in a 1400°C recrystallization texture in 95 pct cold-rolled foil; these components were enhanced on annealing at 2500°C. Muller9 rolled 99.97 Ta to 90 pct reduction in thickness in the final stage and noted only a slight sharpening of the rolling texture, with some intensification of the (111)[112] component upon annealing at 1200°C. The experimental procedure followed in the present work stemmed from the idea of using possible differences in (hkl) surface energies to provide a small driving force for growth of grains having the lowest (hkl) surface energy.l0* This would mean using high-purity tantalum processed into thin sheet form and annealed at high temperatures either in a noncontaminating atmosphere or in one producing additional sample purification. EXPERIMENTAL Zone-Refined Tantalum. National Research Corp. tantalum in the form of 1/8-in.-diam rod and of 99.98 purity (53 ppm 0, 15 ppm N, and 8 ppm C) was zone-melted four times. The traversing speed was 4 mm per min. Such treatment increased the resistance ratio, R293k/R20K , where R293K is the resistance of the specimen at 20°C and R20K the re-resistance at liquid-hydrogen temperature, from a value of 25 for the initial rod to 175 for the zone-refined rod (the increase in the resistance ratio provides a measure of purification11,12). Part of a zone-refined rod was rolled unidirec-tionally to a strip 0.003 in. thick and 0.28 in. wide. Samples were given anneals in the range 1300" to 2100°C using ac conduction heating in an oil-free vacuum system. Recrystallization to small grains appeared to be complete at 1300°C. Large grains were formed at higher temperatures, but these were not entirely strain-free, some grains showing asterism in Laue X-ray patterns and some displaying a range in orientation. Part of the difficulty was caused by thermal expansion of the tantalum strip as it was held between fixed supports. However, in a different arrangement with the tantalum freely suspended in a tantalum can, high-frequency induction heating in vacuo at about l0-6 Torr produced

Jan 1, 1964

By Robert D. Pehlke, Weldon L. Daines

The reduction of manganese oxide from a basic slag by silicon dissolved in liquid iron at steelmaking temperatures was studied to determine the rate-controlling step for the process. The experiments were carried out under an argon atmosphere in a resistance-heated vertical-tube furnace. The two liquid phases, slag and metal, were held in zirconia crucibles. Sampling and chemical analysis of the slag phase led to time-concentration curves for the system. Results obtained by varying parameters such as temperature, stirring rate, concentration, and melt geometry defined the limiting reaction mechanism. The reduction of manganese oxide by silicon is a fast reaction and reached equilibrium within 90 min. The rate of stirring has a marked effect on the reaction rate, while, on the other hand, the effect of temperature is very small. This identifies the rate-controlling step as diffusion rather than interfaciul chemical reaction. The variation of other parameters revealed that a) diffusion of manganese in the iron phase is the slow step, b) the value of D/6 for manganese in iron at 1550°C is 7x 10-4 cm per sec, c) the energy of activation for the apparent rate constant is 7 kcal per mole, and d) increasing the amount of silicon in the iron decreases the diffusion coefficient of manganese. THE equilibrium relations pertinent to the reduction of manganese oxide from a steelmaking slag by silicon dissolved in liquid iron have been studied, but little is known about the mechanisms that control the rate of the process. The purpose of the present investigation was to study the rate of reduction by silicon and to determine the rate-limiting step. The effects of stirring rate, temperature, composition, and melt geometry were investigated as a means of identifying the controlling step. On the laboratory scale, relatively little work has been done in the area of slag-metal kinetics, primarily because of the problems confronted in attempting to contain liquid slags and metals in laboratory crucibles at steelmaking temperatures. Since graphite is an ideal material for a crucible, several investigations have been carried out on the reduction of various oxides from a slag by carbon in graphite-saturated iron and on the transfer of sulfur between a slag and graphite-saturated iron. Most of this work has been performed in induction furnaces. Studies where the container was not graphite are extremely limited. A single kinetic study of manganese transfer between molten iron and basic slags was carried out by Sano, Shiomi, and Matsushita.' These investigators prepared calcium oxide and titanium oxide crucibles to contain the two-phase system. Only a few experiments were carried out and the results had to be treated qualitatively. Despite the paucity of kinetic data, a large quantity of information is available in the literature concerning the thermodynamics2-12 and physical properties'3-21 of the slags containing manganese oxide and the dilute liquid iron alloys containing manganese and silicon which were involved in this research program. EXPERIMENTAL METHOD A vertical-tube resistance-heated furnace was used in this investigation to study the slag-metal reaction Although most previous slag-metal studies were carried out in induction furnaces, a resistance furnace has several advantages including better control of temperature and stirring rate. Hence, a resistance furnace was selected for this study, and its design is shown schematically in Fig. 1. Slip-cast, fine-grained, low-porosity, lime-stabilized cubic zirconia crucibles were used for the kinetic experiments. The crucibles were 4 1/2 in. high and 2 1/8 in. OD with a 1/16-in. wall. The crucibles were only slightly

Jan 1, 1969

By C. N. J. Wagner, E. N. Aqua

Dilute Fe-Si alloys (0 to 5 wt pet Si) were cold-worked by making filings at room temperatuve. The analysis of the broadening of the X-vay powdev pattern peaks yields anisotropic particle sizes normal to the (110), (100), and (112) planes which are a consequence of deformation faults (probability a) and twin faults (probability p). The combined fault probability (1.5a +ß) increases from 0.01 in pure iron to 0.02 in Fe-5 pct Si. The root mean square stvains vary with crystallographic ovientation due to elastic anisotropy of the alloys, and increase from about 0.0035 in pure iron to 0.005 in Fe-5 pct Si measured in the [100] direction. Assuming that deformation and twin faults occur with equal probability, the X-ray data would imply that the stacking-fault energy does not change upon alloying. THE crystallographic aspects of the plastic deformation of dilute Fe-Si alloys has been studied many times since the observation of glide band structures by Barrett et a1.l These glide bands were much straighter than the wavy bands observed by Gough2 in unalloyed iron nearly 40 years ago. This difference in the morphology of the slip band structure has been verified many times, most recently by replication electron microscopy3 and dislocation etch-pitting methods.4,5 These observed differences in deformation behavior have been considered to result from the degree of cross slip that occurs in pure iron and in the Si-Fe alloys. The lowered tendency for cross slip would result from a lowering of the stacking-fault energy of iron by the silicon alloying addition. Experimental evidence for this lowered stacking-fault energy in the Si-Fe alloys, obtained with transmission electron microscopy, is the observation of dissociated dislocations in Fe-6 pct si6 and Fe-3 pct Si alloys,7 and the observation of sharply defined cellular substructures in Fe-3 pct si6,7 compared to the more diffuse substructure in zone-refined iron.' The activation energy for recovery of cold work is greater in the Si-Fe alloys than it is in pure iron, indicating that cross slip has become a more difficult process.9 The purpose of this investigation is to determine the change in stacking-fault probability from the broadening of powder pattern peaks in dilute silicon-in-iron solid solutions, when cold-worked at room temperature. The knowledge of the stacking-fault probability and the dislocation density, both of which can be deduced from line-broadening analysis of two orders of reflections from (110), (200), and (112) planes, will permit us to calculate the change in stacking-fault energy upon alloying silicon into iron. Previous X-ray investigation of cold-rolled Fe-5 wt pct Si (100)[001 ] single crystals did not reveal any line broadening, whereas cold-rolled Fe-3.1 wt pct Si (001) [110] and (001)[100] single crystals10 showed line bro2dening as a consequence of small particle sizes (-200A) and root mean square strains (-0.25 pct), which are comparable to those found in cold-worked iron filings.11 EXPERIMENTAL PROCEDURE A series of five Fe-Si alloys containing nominally 1 to 5 wt pct Si and pure iron were cold-worked by making filings at room temperature. The actual silicon content deviated at the most by +0.1 pct which is of no significance in the present study. The carbon contents of these materials were less than 0.02 pct. The X-ray diffraction patterns were measured with molybdenum, cobalt, and iron radiation using a GE and a Philips diffractometer. The (110)-(220), (200)-(400), and (112)-(224) pairs of reflections were

Jan 1, 1968

By T. Szaplonczay, D. E. Light

The auto-oxidation of sulfur dioxide to form sulfuric acid in commercially produced barren and recycle liquors, containing 1.66 and 4.56 gpl Fe respectively, from Elliot Lake was studied. A gas mixture, containing 3.5% SO2 and air was introduced into these liquors through a frit at a rate of 6.0g SO2 per hour per liter of solution. The barren and recycle were heated to 60°C. At the end of the first 24 hours of the process the concentrations of acid produced were 158 and 220 gpl H2SO4 for the barren and recycle respectively. Corresponding conversion efficiencies were 70 and 83%. In the period from 24 to 36 hours the rate of acid production decreased so that the H2SO4 concentrations at the end of 36 hours were 180 gpl for the barren and 260 gpl for the recycle; average conversions for the initial 36 hours were 55 and 68% respectively. Many investigators1'2'3 have considered the oxidation of sulfur dioxide to form sulfuric acid in aqueous solutions containing metallic ions. A summary of the work performed on this subject prior to 1946 has been presented by Keyes4 who described the auto-oxidation process as follows. Keyes also suggested that in this second reaction ferric ion serves as a catalyst for the conversion of sulfur dioxide to sulfuric acid. Neytzell-de Wilde and Taverner5 have reported on the use of auto-oxidation to produce a 4 to 5% sulfuric acid solution for use in a cyclic leach process at South African uranium plants. This paper describes investigations carried out to determine the feasibility of using the auto-oxidation process to produce sulfuric acid solutions of as high concentration as possible using commercially produced uranium plant barren and recycle liquors from the Elliot Lake region of Ontario. These liquors contained 1.66 and 4.56 gpl respectively of iron, chiefly in the ferrous state. This investigation is of particular interest to the uranium producers in Elliot Lake where the ores contain 3 to 4% sulfur, as sulfides. Flotation of these sulfides and roasting of same to produce SO, bearing gases have been successfully demonstrated using conventional methods.6'7 Barren and recycle solutions, as described previously, are also produced in large tonnages by these uranium producers. The experimental method and apparatus used to examine the auto-oxidation process will be described first. Then the tests carried out on laboratory prepared aqueous solutions containing ferric sulfate to determine optimum conditions will be presented. The next section will describe the tests using the commercial barren and recycle liquors. A final section will summarize the conclusions of the work. EXPERIMENTAL APPARATUS AND PROCEDURES Two types of solutions were used in the tests, a laboratory prepared aqueous solution containing definite amounts of ferric sulfate, and commercially produced iron bearing solution obtained from a uranium leaching plant in the Elliot Lake area. Two liters of a solution to be examined were placed in a 3 in. diam by 30 in. long glass cylinder with a cross-sectional area of 7 sq in. A mixture of air, and SO2 supplied from a lecture bottle for convenience, was introduced into the bottom of the vessel through a standard 30 mm glass frit, 700 sq mm in area. The temperature of the apparatus was controlled by a heating tape and variable transformer. Exhaust gases were vented to atmosphere. At the end of the test period the gas flow was shut off and the solution was analysed for H2SO4, Fe ++, and Fe +++, by conventional means. Four variables were examined using the laboratory prepared aqueous solution of ferric sulfate. First, the effect of SO2 concentration, from 1 to 1076, in the feed gas mixture was considered. Second, the temper-

Jan 1, 1964

By H. Herman, M. E. Fine

Kinetics of reversion and reformation of GP I were studied resistometrically in Al-1.7 at. pct Cu. The reversion process is over in roughly 1/2 minute at 205 "C irrespective of the amount of primary aging. After reversion the occurrence of an incubation time before reaging begins has been substantiated. The reaging kinetics is drastically accelerated by plastic deformation to the specimen. An incubation time is observed only if the specimen is aged before reversion. The incubation time and the effect of plastic deformation indicate that nucleation of GP I is heterogeneous. Simple clusters of copper atoms apparently do not act as nuclei for GP I. AFTER quenching aluminum-rich copper from the solid solution range, Guinier-Preston zones of the first kind, GP I, form very rapidly at room temperature. The rate, largely controlled by the concentration of vacancies, is initially most rapid1 (that is, at the time of the first measurement: 1/2 min) and decreases with time. The nucleation is thought to be athermal. If after aging for several days the GP I is dissolved by reversion at 205°C, according to measurement of Young's modulus an incubation period is observed before GP I begins to form on subsequent aging.2 Yet if the reversion is carried out immediately after quenching, both resistivity3 and modulus changes2 show no incubation effect. The zones which form after reversion have the same structure as those which form after the quench.4 Because of entropy considerations and also the short diffusion time, the solid solution after reversion, 2 min at 205°C, is probably more highly clustered than at the original solution treating temperature, 520" to 550°C. It appears most reasonable to associate with nucleation the incubation time observed on reaging after reversion. A simple cluster of copper atoms, many of which are presumed to be present after reversion, is then not a sufficient nucleus for GP I; a GP I nucleus must contain something in addition to a cluster of copper atoms. The purpose of the present note is to give some additional experimental information concerning the incubation time and rates of reaging after reversion. The existence of the incubation time has been verified by measurement of another property, the electrical resistivity. Acceleration of reaging after reversion by plastic deformation has also been investigated. In acl.dition, the kinetics of the reversion process itself was studied. EXPERIMENTAL Electrical resistance was measured by the poten-tiometric four probe method. The 1.7 at. pct Cu alloy was furnished by the Aluminum Co. of America in the form of 1/2 in. rod. The major impurities reported by Alcoa were Fe (0.002 wt pct), Si (0.003 wt pct), and Mg (0.001 wt pct). Specimens for measuremenl of resistance were prepared by rolling to 0.010 in., cutting 2 by 0.2 in. pieces, rolling the middle pclrtions of these to 0.005 in., and splitting the 0.010 in. sections up to the reduced central section to form current and potential leads. Aluminum extension wires insulated with ceramic tubes were spot welded to the leads. The specimen was supported by the lead wires. The whole specimen assembly was annealed at 500" C in an air furnace for more than 12 hr and then aged at room temperature. This was done to assure quick and complete resolution during subsequent solution treatments. These were carried out in Houghton's "430 Temper Salt" at 520'C for 1 hr. Unless otherwise specified, quenching was accomplished by quickly transferring the specimen from a salt pot to 25°C water. Aging was carried out in a 3 liter dewar of distilled water, rotated and stirred. The temperature was controlled to +0.01°C with a thermomercurial regulator in conjunction with a transistorized relay

Jan 1, 1962

By J. M. Smith, G. P. Willhite, J. S. Dranoff

Heat transfer rates were measured in sandstones with flow of gases perpendicular to the direction of energy transfer. Effective thermal conductivities ker ranged from 0.7 to 1.7 Btu/(br)(ft)(°F). The contribution of the solid phase appeared to be the most important in these consolidated materials, although the thermal conductivity of the gas had some effect. The velocity of the gas through the pores of the sandstones had no influence upon ker up to values of 168 lb/(br) (sq ft) in agreement with data obtained for unconsolidated beds of glass beads. The present results indicated that gas mixing, and hence heat transfer by convection in the pores, is less for perpendicular transfer of energy than when fluid flow and energy transfer are in the same direction. HEAT TRANSFER PERPENDICULAR TO FLUID FLOW IN POROUS ROCKS Heat transfer in porous media with pore sizes in the micron range depends upon the fluid in the pores and the geometry of the solid phase. The best characterized system is a bed of solid spherical particles. Heat transfer in this system has been studied extensive1y (Ref. 8 summarizes the literature up to 1959) when the pores contain stagnant fluid. When the fluid is in motion the directions of flow and energy transfer have an effect on the heat transfer rates, as demonstrated by comparing the work of Willhite, et al l3 for perpendicular flow and that of Kunii and Smith9 for parallel flow of energy and fluid. For perpendicular flow, no increase in effective thermal conductivity ke was noted up to mass velocities G of 77 lb/(hr) (sq ft). In contrast, for parallel flow ke, increased with G in the same range of flow rates. These higher values of ke in the direction of flow also have been observed3,4,10 in beds of larger particles, 0.1- to 0.5-in. diameter. For beds of consolidated materials, such as porous rocks, data are not available for these compar- isons, although Adivarahan1 reported results for the parallel case. Hence the primary objective of this work was to measure ke values for perpendicular flow of fluid and energy in porous rocks. Of interest also was the variation in effective conductivity with fluid velocity. APPARATUS AND PROCEDURE In the experimental method, a constant heat flux was applied to the inner surface of an annular section of the porous rock. By cooling the outer wall, a temperature gradient through the annular sample was established and measured with thermocouples placed within the sample at various radial positions, and at three elevations (A,B.C). The location of the 2-in. O.D., 3.75-in. long sample in the apparatus is shown in Fig. 1. Fluid entered the bottom (1) of the 3-in. I.D. (approximate) steel shell, flowed upwards through the sample and out at the top (3). pressure taps (2,4) were used to check the permeability of the sample. The energy flowed radially from the centrally-located electric heater through the sample and was absorbed in the water-cooled jacket. The samples studied were naturally occurring sandstones from different locations with the properties given in Table 1. These materials are identical with those used by Adivarahan 1 for the parallel flow of energy and fluid. Prior to use they were refluxed with toluene to remove hydrocarbons and leached with distilled water to remove soluble salts. Each sample was visually examined and discarded if large nonhomogeneities, such as cracks or stone particles, were noted. Eight copper-constantan thermocouples were inserted in holes drilled radially into the sample with