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By Wallace W. Wilson

This DaoerAA calls to attention for the first time, to the writer's knowledge, a purported recovery of oil by substantially horizontal gas cycling that is considerably in excess of 50 per cent of the oil originally in place. The average angle of dip along the path of travel of the gas is less than one degree of arc. The best recovery by gas cycling previously brought to the writer's attention1 occurred in the case of the Mile Six Field in Peru, where about 68 per cent of the original oil in place has so far been recovered. In this case, however. the recovery was greatly aided 1)y the high dip angle of about 17.5". An approximate estimate of recovery was made by the method developed by the writer' for the case of the Cook Ranch Field, using an average relative permeability ratio function dictated by past experience with a number of good quality sandstones. A result of about 40 per cent recovery of the original oil in place wa* obtained after the 8.5 pore volumes of cumulative gas cycling undergone by the Cook Ranch Field. Tile writer desires to emphasize what appears to him as the sound engineering practiced at Cook Ranch, and also the care attending the taking of data and the high quality of the calculations made. It is impossible to take issue on factual grounds with any of the conclusions drawn in the paper. It is, however, desired to point out the difficulty of explaining the unexpectedly favorable oil recovery on ordinary theoretical grounds. It would be of interest to know whether relative permeability ratios have been measured on the Cook sand. The operator is inclined to attribute some of the excess benefit to settling of the oil across the bedding planes into the lower part of the sand. It is difficult for the writer to appreciate the importance of such an effect, inasmuch as the concomitant opening of excessive vacated pore space in the upper part of the sand would he expected to cause excessive bypassing of the gas. REFERENCE 1. Welge. H. J.: "A Simplified Method for Computing Oil Recovery by (Gas or Water Drive." Trans. AIME, (1952), 195, 91. AUTHOR'S REPLY TO MR. WELGE Welge has poined out clearly the difficulty of applying material-balance procedures in calculating the Performance of low-pressure, dispersed gas injection operations. There can be no argument that even with the most favorable assumptions of K,/K,, and with cumulative gas cycling in excess of normal expectations, the calculated oil recovery will be considerably less than the 72.5 per cent recovery realized from this project to Jan. 1, 1951. There probably are at least two reasons for the unusually high recovery from this reservoir, the effects of which would be difficult or impossible to calculate by known methods: 1. The operator did not use the same injection wells for the entire operation, and exercised considerable control over producing GOR by changing the locations of injection wells whenever well performance indicated excessive bypassing. Fifty-six wells were used for injection, not over 29 of which were in use simultaneously. This procedure resulted in frequent shifting of the fluid movement patterns in the reservoir and undoubtedly increased the ultimate recovery. The writer knows of no satisfactory procedure for calculating the effect of this practice. 2. Vertical movement of oil across the bedding planes of the reservoir rock hy gravity drainage tended to maintain a relatively high oil saturation, and hence a favorable K,/K, ratio, in the lower sections of the reservoir. As pointed out by Welge, this condition has aggravated the tendency for high producing GOR, but at the same time it has resulted in increased oil recovery. As may be seen from the performance charts for the various battery areas, operating (GOR'S have been quite high for the last several years of reported history.

Jan 1, 1952

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 R. D. Vaughn

The analysis of laminar flow of power-law non-Newtonian fluids in narrow, eccentric annuli is employed in this paper to discuss the problems of lubricant flow in journa! bearings and of errors introduced by eccentricity in experimental studies with concentric annuli on extruders and wellbore annuli. The velocity profile and pressure loss-flow rate equations are developed for the laminar flow region. In addition, the expected error in flow rate and pressure-loss measurements for concentric annuli as a result of eccentricity is determined. For example, a 10 per cent displacement of the core of an almost concentric annul us would cause a 1.8 per cent decrease in the observed pressure loss for a fluid with a power-law exponent n of 0.25. The corresponding increase in the observed volumetric flow rate would be 7. 5 per cent. INTRODUCTION Non-Newtonianism and eccentricity occur simultaneously in two engineering problems: (1) flow of lubricants in journal-bearings and pressure-reducing bushings, and (2) flow of non-Newtonian fluids in plastic extruders and wellbore annuli. The lubricants used for moving parts are often non-Newtonian in character — often they are plastic in behavior. A solution to the problem of flow of non-Newtonian fluids in narrow eccentric annuli is particularly pertinent to this problem. In all experimental studies of laminar flow of fluids in concentric annuli, such as in extruders and well casings, the error due to eccentricity must be estimated or studied. A number of publicationsl-4,6,7 have dealt with this problem for Newtonian fluids; however, I am not aware of work for non-Newtonian fluids. This work is directed to the non-Newtonian problem. Before the solution to the problem is given, the pertinent conclusions from the work on Newtonian fluids will be reviewed. Heyda 1 and Redberger and Charles 2 have published general solutions to the problem of the laminar flow of Newtonian fluids in eccentric annuli, apparently without knowing of the earlier work of Ca ld well 3 and Bairstow and Berry,4 which is reported by Dryden, et al. 5 Although several mathematical routes are encompassed by the work of these authors, the results appear to be equivalent. Redberger and Charles2 show that the error caused by eccentricity in concentric annuli is negligible for small diameter ratios (k < 0.5); however, for large diameter ratios (k + l), the error in the predicted flow rate can be as great as 100 per cent or more. Partial solutions to the problem are available from the work of Dryden,5 Tao and Donovan6 and Piercy, et a1.7 Tao and Donovan examined the case of flow in narrow, eccentric annuli (k + 1) with and without rotation of the annular core. These authors also reviewed previous work on this subject and verified their approach with experimental data. Dryden gives the solution for the limiting case of complete eccentricity or tangency. Piercy, et a l. published an early solution to the problem of narrow eccentric annular flow. The conclusions of Redberger and Charles2 and the experimental proof of Tao and Donovan6 both suggest that the region of large diameter ratios (k + 1) is of main interest and that the parallel planes approximation to the solution in this region is satisfactory. This method will now be extended to the laminar flow of non-Newtonian fluids in narrow eccentric annuli. THEORETICAL SOLUTION The geometrical aspects of the problem are illustrated in Fig. 1. To represent the non-Newtonian fluid the power-law model was selected. This model has many disadvantages which have been pointed out; nevertheless, its simplicity, its frequent and wide applicability justify its use in this work. Fredrickson and Bird8 and Savins9 have used it as a basis for a theoretical study of laminar flow of non-Newtonian fluids in concentric annuli.

Jan 1, 1966

By D. H. Polonis, Gary A. Dreyer

This investigation involved a study of the reactions occurring during aging of supersaturated a phase in a CIL-Si alloy. The aging processes at temperatures below 552°C were studied by means of metallography, microhardness, and electrical resistivity measurements. During the initial stage of aging in the temperature range 275o to 525oC an anisotropic phase, which is visible in the form of striations in the micro-structure formed prior to the appearance of the -phase. This transition phase has been designated k&apos; due to its structural similarity to the k phase. The rate of K&apos; formation during aging increased with aging temperature. At 450o and 525°C the reaction appeared to reach completion before significant amounts of precipitation were observed. The overall precipitation reaction in this system involved four stages: formation of formation of at a grain boundaries, growth of particles in 7-egions, and coagulation of into large particles. The relative role of each of these processes is dependent on the temperature of aging. The formation of phase from supersaturated a during aging increases the electrical resistivity and slightly increases the hardness of a 4.9 pct silicon alloy. The formation of during aging decreases the electrical resistivity and increases the hardness until coalescence of particles begins during the final stages of aging. The coalescence of results in a decrease of both electvical resistivity and hardness. THE available literature does not record a detailed analysis of the aging processes in Cu-Si alloys. Such an analysis has been difficult due to both the limited data available and misleading microstructural observations which have been reported. Previous work suggests that a rather complicated series of processes may be involved in the aging of supersaturated a. The present investigation is concerned with an analysis of the sequence of these aging processes in a 4.9 pct Si alloy. The currently accepted version of the Cu-Si equilibrium diagram, Fig. 1, was published by C. S. Smith in 1940.&apos; This diagram shows a eutectoid at 5.2 pct Si with the high temperature phase, having its composition range entirely to the right of this value. By quenching alloys in the composition range 4.6 to 5.2 pct Si from the region, Smith was able to retain the phase. However, this phase exhibited a striated microstructure which was anisotropic to polarized light. These striations were suggested by Smith to be duplex twins. Using an oscillating crystal X-ray method Barrett2 studied alloys containing 4.0 to 5.4 pct Si quenched from the and regions. The striations observed in quenched specimens were attributed by Barrett to quenching stresses. He found that striations could also be formed by deformation after quenching and identified them as stacking faults in alloys containing 4.0 to 5.0 pct Si. Barrett related the striations in alloys containing 5.0 to 5.4 pct Si both to stacking faults and to a metastable phase which he called The striated structure reported by smith&apos; was also obtained by Hoffmann, et al. 3 By deeply etching their specimens the anisotropic phase on the surface was removed, leaving a structure which was microscopically similar to pure copper. By means of X-ray analysis before and after deformation at room temperature it was concluded that the anisotropic phase was metastable This conclusion has been questioned by Barrett who attributes the discrepancy to superposition of k and lines on the powder patterns of Hoffmann, et alm3 The decomposition of supersaturated according to smith&apos; and Anderson,4 is very sluggish. However, Nony and Dreyer,5 and Hoffmann, et al.&apos; found that deformation increases the rate of decomposition. X-ray studies by Hoffmann, et al on

Jan 1, 1962

By P. L. Raffo, T. E. Mitchell

Single crystals of Ta-Re alloys have been deformed in tension and compression as a function of solute concentration and temperature. The temperature dependence of the yield stress is decreased by alloying. At low temperatures there is a minimum in the yield stress (at about 2 at. pct) as a function of concentration. Three-stage hardening was not observed in the alloys. Linear hardening rates, where observed, were characteristic of stage II in pure tantalum. At low temperatures and high concentrations, work softening was often prominent at high strains. Electron microscopy revealed that dislocations are mostly of screw orientation, although heavily jogged and cusped, and often occurring in dipole pairs. The alloys become more prone to cleavage with increasing rhenium content, due mostly to an increasing yield stress rather than a change in cleavage strength. Alloying apparently decreases the Peierls stress of bcc metals at low temperatures by facilitating kink nucleation at solule atoms on screw dislocations. Higher solute concentrations further increase the yield stress. Quantitative calculations and comparisons with other bcc alloy systems are made to show that the predominant hardening mechanism is due to the interaction of dislocations with misfitting solute atoms close to their slip planes. The interaction is so localized that the core dilatation of dislocations could be important. CONSIDERABLE interest has arisen in recent years concerning the mechanical properties of unalloyed bcc metal single crystals.&apos;-7 These and similar studies on polycrystalline materials have resulted in a considerable understanding of the macroscopic yielding characteristics8, 9 and the process of work hardening.&apos;&apos; This latter advance is due in a large part to the increased use of transmission electron microscopy in P I RAFFO junior Membar AlMF is Metallyureist Iewis such studies and the general observance of three stages of work hardening in the shear stress-shear strain curves. The properties of substitutional alloy single crystals of bcc metals have not been determined in as much detail as in the pure metals. Insufficient systematic studies have been made on the effect of alloying on the magnitude and temperature dependence of the yield stress or the stress-strain curves. The alloy systems which have been studied to some extent have been Ta-W,11, 12 Ta-Mo," Ta-Nb,12&apos;14 Mo-Re,15 W-Re,16 and alloys of iron with nickel,17 platinum,17 vanadium,18 and aluminum.18 A large body of data exists on Fe-Si alloys, but these have mainly been a result of the experimental convenience of using this material in place of unalloyed iron, rather than a comprehensive study of the mechanical properties of the alloy system per se. The present authors have previously reported additional data on the properties of Ta-Re, Ta-W, and Ta-Mo alloy single crystals.1g Some of the data on Ta-Re alloys will be described later in this paper. Briefly, single crystals of Ta-Re (1.2 to 10.6 pct), Ta-W (6.2 and 10.2 pct), and Ta-Mo (2.9 and 9.0 pct) were grown by the floating zone method in vacuum. Compression tests were performed in the temperature range 77" to 623°K. Slip was found to occur in Ta-Re alloys at 77&apos; and 298°K on the (~ll)[lil] system and slip lines were coarser and straighter than in unalloyed tantalum. No three-stage hardening was observed in any of the alloy systems and the curves were nearly parabolic. At temperatures above 175°K the yield stress* increased monotonically with in- creasing composition while at 77" and 175°K the yield stress initially passed through a minimum after which it began to increase again for concentrations greater than about 2 pct Re. Similar minima were observed in Ta-Mo alloys and to a lesser extent in Ta-W alloys. The minimum was interpreted as being a result of a

Jan 1, 1969

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.&apos; 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&apos;s3 equation for nonabsorbing thin films. In Lucy&apos;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.&apos; 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 R. L. Pober, L. Kaufman, E. V. Clougherty

Composite structure of hafnium, zirconium, and titanium diboride with additions of metals and/or compound phases were prepared by reactive high-pressure hot pvessing and evaluated in air and in mixtures of oxygen and helium at temperatures up to 2400°K and at linear flow rates of 0.1 to 0.2 ft per sec stp. Oxidation characteristics, principally depth of conversion of diboride to dioxide, were determined by a gas analysis method and by postoxidation metallo-graphic analyses. The best oxidation resistance was observed for hafnium diboride-silicon carbide composite which exhibited a 6-mil conversion to dioxide for a 1-hv oxidation in air at 2200°K compared to a 20-mil recession for hafnium diboride with no additive. Analogous improvements in oxidation resistance were observed for the addition of silicon carbide to zirconium. EARLIER investigationof the oxidation behavior of the diborides of the transition elements of Groups IVA and VA in flowing gas mixtures have produced a ranking of these compounds according to which HfB2 is the most oxidation-resistant followed in turn by ZrB2 > TiB2 > TaBz > NbB2. Other ~tudies~-~ have examined the physical, thermal, and thermodynamic properties of these diborides to provide a sound basis for the more detailed and specialized investigations which are required to generate the information needed to assess the usefulness of such materials in high-temperature oxidizing environments. Recent oxidation studies7 have examined the effect of variations of metal and boron content on the oxidation characteristics of zirconium and hafnium diboride in flowing gas mixtures including air and helium plus oxygen. Results obtained in the latter investigation confirmed the superior oxidation resistance of HfB2 over ZrB2. Moreover, metal-rich compositions of hafnium diboride showed improved oxidation resistance over boron-rich compositions at temperatures up to 2000°K; at higher temperatures the differences are not distinguishable. In particular HfBI.7 exhibited a diboride to dioxide conversion depth of 4 mils in 1 hr at 2000°K; HfB2. 2 exhibited a conversion depth of 16 mils for the same exposure.~ Specimens for the study of metal and boron stoichiometry on the oxidation characteristics of HfB2 and ZrB2 were prepared by high-pressure hot pressing, a specialized type of fabrication which produced dense crack-free bodies of the desired compositions with no significant impurity introductions. The purpose of the present investigation was to explore the possibility of further improving the oxidation resistance of the metal-rich ZrB, and HfB2. The plan to accomplish this objective was based in the formulation of several diboride compositions containing other compounds and phases which are generally known to have good oxidation resistance in one or more types of test environment. Ideally, such additives would also enhance or at least not diminish other boride property values principally mechanical strength and those parameters related to thermal stress resistance. The additions selected for HfBz included zirconium, aluminum, and (Ta + TaB2) designed to produce ternary metal diborides, hafnium to form a discrete HfB phase, chromium to provide a metal skeletal phase, (Hf + Si) to form a discrete hafnium silicide phase, and Sic to provide a discrete second phase. Additions to ZrB2 included A1 + B designed to produce a ternary metal diboride, Zr + Si to form a discrete zirconium silicide phase, and Sic to provide a discrete second phase. All the specimens were prepared by high-pressure hot pressing which was used to advantage to fabricate billets of the variety of compositions desired and suitable for oxidation testing. The present investigation also included the evaluation of high-pressure hot-pressed TiB2and TiB2-20 vol pct Sic, conventionally hot-pressed Boride 2,&apos; and KT silicon carbide. Boride

Jan 1, 1969

By R. E. Reed-Hill, W. H. Hartt, W. A. Slippy

An unusual form of double kinking has been observed at the ends of {1121} twins in deformed zirconium. These kinks lie partly outside of the twin and partly inside. While they are undoubtedly closely associated with accommodating the twinning shear into the matrix, they are apparently closely related to other important aspects of twin growth. A mechanism is proposed for {1121} twin growth involving interactions between 1/3 (1120) dislocations in the bend planes and twinning dislocations. It is also shown that boundaries without long range strain fields develop at the tapered ends of the twins. The {1121} twins can, therefore, grow without forming high-energy noncoherent twin boundaries containing large numbers of closely spaced twinning dislocations. NUMEROUS investigators have indicated that slip is often closely associated with deformation twinning. An example is twin accommodation kinking,1-3 where dislocations form bend planes and permit accommodation of a twinning shear within the parent crystal. Another is the incorporation of slip dislocations into twins, as proposed by Sleeswyk and verbraak4 and Ishii and Kiho5 for iron and ß-tin, respectively, and observed in hcp metals by Price.6 In addition, it has been shown that shear discontinuities exist at the points of twin intersections in zinc,7 magnesium,8 titanium,9 ß-tin,10 and bismuth," where the continuity conditions for twin intersections, originally proposed by cahn,12 are not satisfied. A similar situation occurs for zig-zag (1121) twins in zirconium13 and ?-phase silver-aluminum alloys,14 where the twinning shears of the two component twins are not parallel. In all these latter cases additional deformation by slip is believed to accommodate the twinning shear discontinuity. The present paper is concerned with a newly observed aspect of the slip and twinning interrelation, in which two kinks, one inside the twin and the other external to the twin, are formed. These kinks, observed in conjunction with (1121) twinning in zirconium, form to accommodate the twinning shear. A model has been constructed explaining the growth and accommodation of (1121) twins in terms of these kinks. This mechanism may be significant since it is concerned with an important twin mode, which occurs not only in zirconium but also in titanium and hafnium. The practical significance of (1121) twinning has been adequately demonstrated. At 77° K the high ductility of zirconium containing a large number of grains unfavorably oriented for slip is primarily due to (1121) twinning.&apos;5 Also, (1121) twins nucleated at 77°K may grow during further deformation at room temperature. This growth can greatly increase the transverse ductility15 as well as produce large mechanical hysteresis effects.= EXPERIMENTAL PROCEDURE Arc-melted, sponge zirconium plate previously described17 was prestrained 0.65 pct at 77° K by cold-rolling to introduce {1121} twins into the structure. Tensile specimens were cut with axes normal to the plate rolling direction. These specimens were pulled in tension to near the point of failure in an Instron machine at room temperature at a cross-head speed of 2 x10-2 in. per min. This additional deformation caused growth of the twins nucleated by prestrain. Deformed specimens were then prepared for metallo-graphic examination. This included an anodizing treatment18 that made the surfaces sensitive to polarized light, permitting small lattice rotations to be revealed. EXPERIMENTAL RESULTS Nature of the Twin-Kink Band Structure. Fig. 1 is a photomicrograph of a typical specimen after prestrain at 77° K. The structure is characterized primarily by long, narrow, parallel sided (1121) twins which norma1ly traverse the entire grain. Fig. 2 shows several (1121) twins after additional straining at room temperature. These lie near the center of the polarized light photomicrograph and are inclined upward to the right. It is evident that this latter deformation has resulted in appreciable twin growth. The dark regions extending from the ends of these twins are accommodation kinks. The difference in reflected light intensity indicates the

Jan 1, 1969

By John Chipman

THE equilibrium between titanium in liquid iron and titanium oxides has been studied by Hadley and Derge.&apos; They have shown that a minimum occurs in the oxygen content of the metal between 0.1 and 1.0 pct Ti, but its exact level was not fixed. The oxide phase in this minimum range was principally TiO, containing some iron oxide. On the other hand, for concentrations above 5 pct Ti the oxide phase was TiO and the oxygen content of the metal increased rapidly with increasing titanium content. From their observations and the free energy of Ti0 and TiOz reported by Kelley and ah,&apos; it is possible to derive approximate values for the activity coefficients of titanium and oxygen in liquid iron-titanium alloys and the conditions for equilibrium in steel deoxidation. Neglecting possible departures from the stoichio-metric composition, the condition of equilibrium with Ti0 may be expressed as follows: TiO= Ti_ + C) log K = log NTl + log [% O] + log yTi + log fQ Here as a matter of convenience the titanium concentration is expressed in mol fraction while that of oxygen is in weight percent. The activity coefficients are yTi and fo. The value of log fo approaches zero as the concentration of titanium approaches zero, while that of log yTi approaches a limiting value of In Fig. 1 the sum of log NTi + log [% 0] is plotted for mol fractions of titanium between 0.05 and 0.50. The smooth extrapolation gives a value of —4.15 which corresponds to log K — log y:i . We therefore have the equation: According to the data of Kelley and Mah,&apos; the free energy of formation of Ti0 at 1900°K is -82,400 cal. The free energy of solution of half a mol of oxygen in iron, taking 1 pct 0 as the standard state, is -29,300 cal. From these we write: From these equations the activity coefficient of titanium at infinite dilution in iron is found to have a value of 0.011 or log y°. = -1.96. This is only an approximate value but is certainly better than the estimated 0.05 in Basic Open Hearth Steelmaking To obtain approximate values for the activity coefficient at intermediate concentrations, it is as- sumed that log yTi(l is constant and equal to -1.96. This corresponds to a value of E;: = 3 In yTi/aNTi = 9.0 which is not unreasonable We now have the value for the activity of titanium and the percentage of oxygen in equilibrium with TiO. It is therefore a simple matter to calculate the activity coefficient of oxygen which is shown in Fig. 2. The effect of titanium is rather large, being comparable to that of vanadium, but not so large as has been reported for aluminum. The slope of the line at low concentrations corresponds to E: = aln yo/ aNTi=-0.37. At concentrations below 1 pct Ti the deoxidation constant and oxygen content for equilibrium with TiO, can be calculated from the foregoing data and the free energy of formation of TiO,, which according to Kelley and Mah is -144,600 cal at 1900°K. The free energy of solution of oxygen has been given; that of Ti to form a dilute solution with 1 pct Ti as the standard state is RT ln (0.5585 y:i/47.9) = -34,800 cal. From these data we find (for concentrations in wt pct): TiO, = Ti + 2 -0; hFTgO0= + 51,200 cal log if =-5.89 The interaction coefficients, concentrations being expressed as wt pct, are e;: = alogfTi/a[% Ti] = +0.048 and e:&apos; = a logfo,/a[ojTi] = -0.187. The calculation gives the following results which, in view of the impurity of the oxide phase, must be regarded as approximate:

Jan 1, 1961

By David V. Ragone, James A. Craig, Richard E. Balzhiser

The Gibbs free energies of formation of UC2 and UC were measured by equilibrating two-phase mixtures of UC2 + C and UC, + UC with liquid bismuth. The measured equilibrium concentrations of uranium in the bismuth combined with available activity coefficient information yielded uranium activities in these two-phase regions. Measurements on UC2 were performed over the range 1015 to 1160 K and on UC over the range 1115° to 1165°K. The values obtained for UC2 are in excellent agveement with values determined using combustton calorimetry and low-temperature heat capacity measurements. The UC values are in fair agreement with the calorimetric values, differing by about 10 pct from the calorimetric determination. MUCH interest has been shown in the uranium carbides in recent years because of their potential as nuclear fuels. As nuclear reactor operating temperatures have been raised to increase thermal efficiency, new fuels have been required. The uranium carbides are of interest because of their high melting points, >2000°C, high thermal conductivity, and resistance to irradiation damage. The manufacture and use of uranium carbides are aided by a knowledge of their stability and reactivity under various conditions. In this regard the thermo-chemical properties of the carbides, i.e., heat capacity, heat of formation, free energy of formation, and so forth, are particularly important. A great amount of work has recently been done on the thermodynamics of the U-C system. Unfortunately, however, there has not been good agreement among the various investigations. This study of the free energies of formation of uranium monocarbide and uranium di-carbide in the temperature region 1100°-1200° K was undertaken to help clarify the situation. It should be noted that in the temperature range of this investigation, 1100°- 1200° K, the thermodynam-ically stable phase in equilibrium with graphite is U2C3, not UC2, Fig. 1. However, U2C3 is reported to be stable only under extremely low oxygen and nitrogen pressure. Although UC2 is metastable below 150O°C, it exists under most experimental conditions. It should also be noted that "UC," never exists as UC2 but with compositions near UC1.9. However, "UC2" will be used to designate the dicarbide phase except when the stoi-chiometry is necessary for clarity. METHOD The approach taken in this study of the free energies of formation of UC and UC2 was to determine the thermo- dynamic activities of uranium in the two-phase regions UC, + C and UC + UC, by equilibrating the two-phase mixtures with the liquid bismuth. When a mixture of solid UC2 + C is brought to equilibrium with liquid bismuth, the reaction that occurs is: Neither carbon nor UC, could be detected as dissolved material in the bismuth. The standard free energy for this reaction may be written: In the two-phase region UC, + C, Fig. 1, the thermo-dynamic activities of UC2 and carbon are unity. The activity of uranium in this region was determined by measuring the concentration of uranium in a liquid bismuth melt in equilibrium with the two-phase mixture. This concentration was then used in conjunction with the activity coefficient data of uranium in bismuth reported by Tien et al.&apos; to determine the activity of uranium in the two-phase region, UC, + C. All of the quantities in Eq. [2] were then known, and the AG; (uc,) was evaluated. UC + UC2. For the studies involving UC + UC,, the reaction taking place when the two-phase mixture is brought to equilibrium with liquid bismuth is: The standard free-energy change for this reaction is given by:

Jan 1, 1969

By Herman Dykstra, Irving Fatt

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.&apos; Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George&apos; showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille&apos;s Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell&apos;s equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille&apos;s Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy&apos;s Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy&apos;s Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI&apos; By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By Irving Fatt, Herman Dykstra

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.&apos; Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George&apos; showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille&apos;s Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell&apos;s equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille&apos;s Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy&apos;s Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy&apos;s Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI&apos; By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By John Griffen

THEORY HYDRAULIC classification as explained by Rittinger and others was largely restricted to conditions wherein the free-falling velocities of the particles were conceived as governing the separations effected (see chapter 9). The laws governing classification under free-falling conditions have been summarized by Chapman and Mott as fo1lows:l Nomenclature r represents, in a particle of irregular shape, the round-hole screen through which the particle would pass, or some other linear dimension of the particle equivalent to d, the diameter of a sphere. s, the specific gravity of the particle. 1, the specific gravity of the water used as a medium. K, a constant. W, the velocity of the water. In an Upward Current of water 1. A particle will move upward if [V > K dr(s - 1)] and, by suit- ably regulating the speed of the water current, the larger and heavier particles may be made to fall downward against the current, leaving the smaller, lighter particles in suspension in the current. 2. Particles such that [- = -] cannot be separated in an upward- current classifier with any one velocity of current. Coal particles having a specific gravity of 1.35 cannot be separated from refuse particles of [2.5 - 1 2.5 sp. gr.] unless the ratio of diameters is less than [ 4.3 to 1, 1.35 – 1] and the raw coal must be screened to size limits within this ratio if they are to be separated. Cone-shaped vessels or vessels of other shapes that allow the use of different velocities of current at different points in the flow are used to modify this limitation.

Jan 1, 1943

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 Donald L. Katz

The equilibrium constants developed by Souders, Selheimer and Brown1&apos; have been very useful tools in predicting vapor-liquid equilibria during the past five years. Their equilibrium constants were computed by assuming ideal solutions and recognizing the deviations of vapors from ideal gas laws. The same fundamental concepts were used by Lewis and co-workers8 for predicting vaporization phenomena by means of fugacities. The equilibrium constant is defined by equation 1: y\x =K [1] in which K = equilibrium constant, y = mol fraction of a constituent in the vapor phase, x = mol fraction of the constituent in the equilibrium liquid phase. The equilibrium constants are a function of temperature and pressure and might be considered as replacing the ratio of the vapor pressure to the total pressure of Raoult&apos;s law. They may be used to compute the vapor or saturation pressure of a liquid or the dew point of a vapor for any pressure or temperature from the analysis of the mixture much as Raoult&apos;s law is used. Likewise, the quantity of a mixture that will vaporize at any equilibrium temperature and pressure and the composition of the vapor and liquid may be calculated. The purpose of this paper is to review the available equilibrium data of interest in petroleum production, to discuss the auxiliary physical properties of the hydrocarbons, and to present typical uses of the equilibrium constants. The particular applications chosen are the computation of the results of stage separation of crude oil and natural gas, the calcula: tion of a pressure-volume curve of a crude oil-natural gas mixture, and information gleaned from a consideration of reservoir equilibria.

Jan 1, 1938

By K. G. Black, B. P. Faulkner

Laboratory batch flotation rests are used for comparison of the floatability of ores and for comparison of the effect of various treatments on ore floatability. Although it is difficult to predict exact recoveries for continuous flotation on the basis of batch tests, considerable quantitative information can be obtained through their use. A simple method is presented which provides a convenient means of quantitatively evaluating results from laboratory batch tests. The information obtained is in the form of a discrete flotation rate distribution, which, if desired, can be used directly in a simulation of continuous flotation. Equation of Batch Flotation The validity for batch flotation of the first-order kinetic equation is accepted: [ ] where k is flotation rate of a class of articles and W (t) is weight of particles of the class in cell at time t. Thus, at time t, the fraction of the original amount of the class of particles still remaining in the cell is [ ] where W (0) is weight of class of particles in cell at time zero. If there are several classes of particles in the cell, each with its own flotation rate, k4, the fraction of the particles remaining is [ ] where W (t) is now the total weight of n classes, a, being the original fraction of W (0) belonging to the ith class. Accordingly, [ ] [Fig. 1] shows the result of a typical batch test. Such result can be characterized by a set of particle classes, each set described by a flotation rate, [ki,] and a corresponding fractional magnitude, [ai.] [ ] Multiple Regression Equation Eqs. 3 and 4 may be combined to give

Jan 1, 1973

Z. W. Bartlett, J. C. Carrington, H. C. Petersen and K. T. Price were elected vice-presidents of the Freeport Sulphur Co. Blandford C. Burgess was transferred on January 1 to the new Defense Materials Procurement Agency as strategic materials specialist. In May the Region III headquarters of this organization was moved to London. L. C. Campbell was elected president of National Coal Assn. Mr. Campbell, who has been a member of the National&apos;s Board of Directors and Executive Committee for many years, is vice-president of the Coal Div. of the Eastern Gas & Fuel Associates and in charge of their extensive mining operations in West Virginia, Pennsylvania and Kentucky. Vern H. Christoph has been transferred to Panama Canal Co., Marine Bureau, Navigation Division, Port Captains Office, as an admeasurer at Cristobal, Canal Zone. Eugene Cline, recently graduated from the University of Kentucky, has been employed by Pond Creek Pocahontas Coal Co., at Evanston, Ky. Sanford S. Cole, assistant manager of research at the Titanium div. of National Lead Co., received the Alumni Citation from his alma mater, Alfred University, Alfred, N. Y. This was in recognition of outstanding achievements and services in the field of ceramics which have brought honor to the institution. U. K. Custred, recently graduated from University of Kentucky, and may be reached now at Box 87, Monterey, Tenn. Robert E. Dwyer, executive vice-president of Anaconda since 1940, was recently elected president of this company and its subsidiaries, Chile Copper Co., Chile Exploration Co., and Andes Copper Mining Co. As president, Mr. Dwyer succeeds the late William H. Hoover who died in Butte, Mont.

Jan 1, 1952

By J. J. Becker

BEAN1 has discussed the magnetic behavior of mixtures of small ferromagnetic particles on the order of 20 to l000A in diam. As he points out, there are three size categories with characteristic properties: 1) Particles large enough to contain many ferromagnetic domains magnetize initially by the motion of domain walls. The initial susceptibility of such particles, if domain-wall motion is assumed to be perfectly easy, depends only on their shape. It is equal to the reciprocal of the demagnetizing factor (and is thus 3/4 tt for a sphere) and is independent of temperature. 2) Smaller particles find it energetically undesirable to contain domain boundaries. They are always spontaneously saturated, and reverse their magnetization only by rotation of their entire magnetic moment. As assemblage of such particles has a remanence which is a large fraction of the saturation of the assemblage; its coercive force is on the order of 2K/1,, where K indicates magnetic aniso-tropy from any source, and I, is the saturation magnetization of the substance of which the particles are made. 3) Particles which are still smaller continue to be single-domain, but the direction of their magnetization fluctuates thermally, as first pointed out by Neel.&apos; They have no remanence and no coercive force and possess the temperature-dependent magnetization curve of a paramagnetic substance with a very large moment. Bean calls this superpara-magnetism. All of these kinds of behavior are observable in alloys consisting of a precipitate of ferromagnetic phase in a nonferromagnetic matrix. Fig. 1 shows a typical aging curve for the room temperature coercive force of a sample of 98 pct Cu-2 pct Co alloy

Jan 1, 1958

By AIME AIME

UNDER the auspices of the Institute&apos;s Committee on Industrial Preparedness, a symposium was arranged for the Annual Meeting on the subject "Ores, Metals, and the War," with many well-known Government men and industrialists participating. Wilfred Sykes, president of the Inland Steel Co., of Chicago, presided, with C. K. Leith and Clyde Williams as vice-chairmen, Mr. Williams presiding over the latter part of the meeting. On the Auditorium stage in the Engineering Societies Building was a formidable corps of "experts," with an audience of several hundred to hear what they had to say and to ask questions.

Jan 1, 1942

By F. W. Bowdish

A theoretical and experimental laboratory study has shown that the rate of breaking of oversized particles in a ball mill is proportional to 1) the concentration of such particles, and 2) the area of the balls, provided that the balls are larger than a certain size relative to the particles. If all undersized material were removed as formed, the rate of breaking would be almost independent of the quantity in the mill. Rate equations are given which are similar to those for zero, first, and second order reactions. Deviations of small balls from the equation for a second order phenomena are quantified by a factor called "nipping efficiency." Some data are correlated by a dimension-less equation, which is used to estimate nipping efficiencies from data not in the correlation. The investigation described here was undertaken after a literature survey revealed that little was known concerning the mechanism of breaking of particles within a ball mill and the effect of this mechanism upon grinding rates. One paper, by Roberts1 , offered a theory concerning the mechanism of breaking, and a rate equation for the breaking of particles larger than some size to particles smaller than that size. That paper provided the starting point for a theoretical and experimental investigation of grinding under carefully controlled conditions. THEORETICAL CONSIDERATIONS In his paper on the probability theory of ball mill grinding, Roberts theorized that "... a given expenditure of power leads either to a certain number of point to point blows per bp-hr or to a certain distance of line contact per hp-hr ..." He assumed that the balls touch each other during each blow or during moving contact. Then he said that a volume of pulp, dependent upon the size being considered, would be covered per minute within which all oversized particles would be crushed to particles smaller than that size. Naturally, the higher the concentration of oversized particles in the pulp, the higher the rate of which they would be broken. From this reasoning Roberts obtained the differential equation -dC/dt = k hp/ton C (1) where k is a constant for any size of particle, density of particle, and moisture content of pulp. C is the percentage of oversize in the material to be ground, t is the time, and hp/ton is the power input per ton of material in the mill. He then integrated the equation to log Co/Ct = k/2.3 hp/ton t , where Co and Ct are the percentage of oversize at time zero and t respectively. By always using the same quantity of material in a mill and assuming that it required constant power to run the mill, he was able to combine the horsepower per ton factor with the other constants to give an equation for a first order rate.

Jan 1, 1961