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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' due to its structural similarity to the k phase. The rate of K' 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.' 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' 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' and Anderson,4 is very sluggish. However, Nony and Dreyer,5 and Hoffmann, et al.' 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.'-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.'' 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,12'14 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' 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.' 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 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,' 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.'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.' 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,' 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,' 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:' = 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.' 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.' 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' 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'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'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'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'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'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' 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.' 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' 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'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'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'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'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'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' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

During the latter part of 1937 consideration was given to the construction of a; local smelting plant for producing blister copper. Previously copper concentrates had been shipped to the United States of America. The proposition had the advantages of a saving in cost of realization, quicker financial return and reduced dependence on overseas shipping.The smelter was designed by the existing staff, who had difficulty in obtaining data on small plants, particularly on the reverberatory furnace. Construction was started in March, 1938, and the reverberatory was blown in on January 16th, 1939. One roaster had been operating for several weeks prior to this date.While results and operating technique on this new departure in small-scale smelting are barely beyond the experimental stage, it is felt that the experience gained to this time should be recorded to help fill the obvious gap in published information covering plants of this type.At present there are three copper smelters operating in Australia; the other two plants are equipped with blast furnaces.LOCATIONThe new smelter is situated in a position convenient to the concentrator and to the power plant. The site is traversed on two sides by a brick flue, from an old smelter plant, which connects with a 250-ft. stack. This stack and portion of the old flue are used in connection with the...

Jan 1, 1939

By George A. Savanick

The objective of this research is to develop a method for measuring the tensile strength at the interface between minerals in rock. These measurements reflect the strength of the attractive forces operating at crystalline interfaces in rock. Since these forces act in opposition to the forces set up in various rock fragmentation processes, measuring their strength may help in designing more efficient methods of rock fragmentation. The method developed for measuring the strength of intergranular adhesion in rock involves separating a bicrystal from the rock and determining the tensile strength at its solid-solid interface. This technique has been successfully applied to the study of quartz-feldspar interfaces separated from massive pegmatites, graphic granite, and the Rockville granite, yielding average tensile strengths of 5.86, 8.62, and 10.65 meganewtons per meter squared (MN/m2) (850, 1,250, and 1,524 psi, respectively). The data this technique provides indicate that the members of these bicrystals are strongly adherent. Examirtation of bicrystals broken at the crystalline interfaces indicates that the bonds responsible for this adhesion operate over only a portion of the interfacial area. This work conclusively demonstrates that tensile strength tests can be conducted on small selected areas; for example, grain boundaries in rock. The small-scale zones of strength or weakness determined in this way can be related to the overall strength of the rock.

Jan 1, 1972

By F. J. Sotillo

Mining in Peru is mainly concentrated on metallic and polymetallic ores of gold, copper, lead, zinc, silver, tin, iron, etc. However, little has been done to develop extensive and rich non-metallic or Industrial Minerals deposits with the exception of some silica and phosphate deposits. This paper presents the characterization and metallurgical studies for the development of a feldspar deposit. These studies showed that the special characteristics of the ore, such as high porosity, high Al2O3 content, low clays content, and sized material allowed us to obtain commercial products applying relatively simple and low cost concentrating unit operations. The characterization studies showed that the feldspar products contained no quartz and about 90% of albite (NaAlSi3O8). The 14x40-mesh size fraction product analyzed 5.91% Na2O, 22.56% Al2O3, 65.73% SiO2, 0.65% K2O, 6.50% CaO, and 0.40% Fe2O3; whereas, the 40x150-mesh size fraction product analyzed 6.22% Na2O, 24.30% Al2O3, 60.80% SiO2, 0.91% K2O, 7.06% CaO, and 0.54% Fe2O3. These products could be used for manufacturing glass, ceramics, refractory, and filters in different applications. In addition, Middlings, could be used as insulation material due to its porosity (bulk density of 0.828 Kg/dm3), analyzing 4.46% Na2O, 15.7% Al2O3, 67.2% SiO2, 2.57% K2O, 3.94% CaO, and 4.24% Fe2O3. The material showed a sphericity of 0.77, a roundness of 0.68, and acid solubility of 13.3025% on only washed and 2.72% effective for clean material suitable for use in these applications. No selective accumulation of the valuable mineral was observed at any specific size fraction. However, iron and titanium bearing impurities trended to concentrate in fine fractions (minus 70 mesh -212 µm-). Metallurgical studies demonstrated that this feldspar ore required sizing at 14x40 mesh and 40x150 mesh to render commercial products. In the case of the 14x40-mesh size fraction, the process involved magnetic separation, gravity separation, and flotation for feldspar (direct flotation) using a blend of primary and condensate amines. However, the reverse flotation for mica-biotite and iron bearing minerals was also possible using petroleum sulfonate. The metallurgical process for the 40x150-mesh size fraction required magnetic separation and reverse flotation of iron and titanium bearing minerals, the feldspar being reported in the sink material. Commercial products from this feldspar deposit for glass, ceramics, refractory, and filtration; and for the manufacturing of insulation material were obtained.

Feb 23, 2014

By Yuanyuan Zhang, Patrick J. Masset

"The reduction of FexO in slag is one of the fundamental reactions in iron and steelmaking technology, including the blast furnace process (BF). Experiments on the reduction reaction of iron oxide using CaO-SiO2-Al2O3-FexO-C mixtures were carried out using thermogravimetric analysis (TGA) under reducing conditions at temperatures up to 1100°C. The composition of the primary slag was chosen so that the FexO concentration varied between 0 and 75 wt % and the CaO/SiO2 ratio being kept constant to 0.90. From the TGA curves recorded isothermally at different temperatures the kinetic parameters of the iron oxide reduction were determined.IntroductionIn blast furnace the iron ores and coke are charged in layers from the top. The reduction of iron oxide by coke is one of the fundamental reactions in the blast furnace process. Although a great amount of work has been done on the topic of reduction of composites [1, 2, 3], gasification of carbon [4, 5] and reduction of iron oxides by CO [4, 5, 6], the mechanism of reduction in iron oxide - carbon powder mixtures is not fully understood. Fruehan [1] and Rao [2] studied the reaction rate of the reduction of iron oxide by different types of carbon and concluded that the reaction mechanism is controlled by the oxidation of carbon at temperatures up to 1200°C. Rao [2] studied the reaction of hematite with graphite as carbon source up to 1080°C. An activation energy close to 300 kJ/mol was calculated within the temperature range of 950°C to 1087°C. In his study, Fruehan [1] determined the rate of reduction of Fe2O3 and FeO by coal, coke and coconut charcoal as carbon sources within the 900°C to 1200°C temperature range. He found that the reduction of Fe2O3 by carbon occurs in two stages and that the reduction of Fe2O3 to FeO is faster than that of FeO to Fe. This is due to the fact that the CO2/CO equilibrium ratio is higher, and hence, the rate of oxidation of carbon is faster. Fortini and Fruehan [3] have studied the reduction reaction of wustite by graphite and wood charcoal. They found that the wustite reduction can have a significant effect on the overall rate of reduction in composites at high temperatures or in the presence of a large excess of carbon. The calculated activation energy of the reduction reaction by wood charcoal was close to 368 kJ/mol, while the activation energy of the reduction reaction by graphite was 444 kJ/mol."

Jan 1, 2011

By Christopher J. Pacitto

This paper presents a case history of an engineered, monitored, and tested program that provided an effective and satisfactory basis for the completion of pile foundations for Twin Dolphins 1 at La Peninsula Condominiums located in the Isles of Capri in southwest Florida, U.S.A. An 8-story building (withl-story parking underneath) along with recreational facilities (such as a swimming pool and tennis courts) had been planned for final construction. Following an evaluation of various foundation alternatives, a precast prestressed concrete (PPC) pile-supported system was selected. The building foundations were designed for pile capacities of 445kN (50 tons) and 890kN (100 tons) in compression and 133kN (15 tons) in uplift. A test pile program was performed to provide site-specific pile driving data, verify design assumptions, determine production pile lengths, and evaluate pile driving criteria. A total of 24, 356 mm (14-in.) square, 19.8 m (65 ft) PPC concrete piles were driven and dynamically load tested utilizing a Pile Driving Analyzer (PDA) within the building limits. Dynamic monitoring during probe pile installation and restriking was performed to estimate the ultimate capacity of the piles and to evaluate driving stresses during installation. CAPWAP analyses were preformed on PDA data to better estimate pile capacity, resistance distribution, and predict pile freeze (increase in pile resistance with time) and thus optimized the production pile lengths. Upon completion of probe pile installation, 12 of the probe piles were tested using the Pile Echo Tester (PET) function of the Pile Integrity Sonic Analyzer (PISA). PET testing was performed to evaluate the integrity of piles which had exhibited high driving stresses during PDA testing. Information gathered during the probe pile driving program was effectively utilized as part of the overall quality control program to install a total of 539 PPC piles (including 24 probe piles) within the building limits at the project site to depths ranging from 9.1 to 19.8 m (30 to 65 ft) below the existing ground elevation as part of the foundation support system. Prior to installation of probe or production piles, a termination criterion was established using 1-dimensional wave equation analyses in addition to the design pile embedment requirement. The predicted pile capacities compared very well with the capacities from the CAPWAP analysis for probe piles. Use of geotechnical instrumentation and PDA assisted technology enabled each foundation support element to be constructed to its optimum capacity and at optimum cost. Furthermore, by using PDA the consultant was able to quantify a difficult to measure geotechnical phenomenon termed "pile freeze" which eliminated costly overdriving and unnecessary splicing of piles.

Jan 1, 2002

By D. A. Rhys

"The Red Bluff porphyry is a tabular 2 km long north-west trending Early Jurassic quartz diorite to monzodiorite body that intrudes a folded Triassic greywacke sequence in the lskut River area, northwestern British Columbia. The porphyry is 500 m to 800 m northeast of the Snip orebody, which is a southwest-dipping shear-vein, termed the Twin zone that contains approximately 35 tonnes of gold.The intrusion associated with the mineralization is characterized by 0.3 cm to 4 cm phenocrysts of K-feldspar in a mediumgrained plagioclase porphyritic matrix. It is overprinted by pervasive sericite + quartz ± K-feldspar ± biotite (potassic) alteration characterized by intense stockworking of quartz veins containing magnetite--hematite bands. This assemblage is cut successively by quartz veins with minor iron-oxides and pyrite, and by younger pyrite veins with phyllic envelopes. The system is gold-rich but copper-poor, with typical grades between 0.25 g/t and 0.6 g/t Au, and 0.1% and 0.2% Cu. All styles of alteration and veining have similar abundances of these metals. Where southwest- and north-east dipping shear zones are developed in the porphyry, veins of all types are sheeted and foliation parallel. These sheeted zones are interpreted to be syntectonic. Asymmetric phenocrysts, folded veins and oblique foliations developed in the 130 haulageway of the Snip mine imply oblique normally-directed shear on the southwest-dipping foliation.The adjacent Twin zone is a high-grade auriferous shear-vein system that is internally banded with: (1) carbonate-chlorite-biotite veins, with textures indicating formation at least partially by wallrock replacement, and (2) dilatant quartz-sulphide veins. Veins commonly have potassic alteration envelopes that contain biotite ± calcite ± K-feldspar. The zone is highly deformed and schistose, with numerous kinematic indicators including shear bands, asymmetric folds, rotated porphyroclasts and oblique foliations that indicate a normally-directed shear sense which is parallel to that indicated by fabrics within the porphyry.Precious and base metal veins within 2 km or 3 km of the Red Bluff porphyry are zoned. Veins and shear-veins proximal to the intrusion, such as the Twin zone, are typically enriched in gold, copper and molybdenum, and have potassic alteration envelopes dominated by biotite. Distal veins usually contain relatively abundant zinc and lead and have sericitic alteration envelopes. Structures of both types have an Early Jurassic galena Pb-Pb isotope signature.The similarities in structural fabrics and alteration histories in both the Twin zone and the porphyry, the zoning of the vein systems in the area, and the apparently concordant Early Jurassic zircon U-Pb age from the porphyry and galena Pb-Pb dates from the Twin zone and surrounding vein systems suggest that intrusion, semi-brittle deformation and a large mineralizing hydrothermal system were closely related temporally and genetically."

Jan 1, 1995

By Laszlo Imreh, Pierre Trudel, André C. Tessier

"The Siscoe gold mine is ranked as the fourth largest mine in the history of the Val d' Or mining district with a total production of 27.4 tAufrom1929 to 1949. Most of the gold mineralization occurred in quartz veins, hosted in a small (.69 km2) intrusion of altered quartz gabbro known as the Siscoe stock. The southern contact of the Siscoe stock is crosscut by a major shear zone (the ""K"" zone) trending 295/80 NE and from which gold mineralization was also exploited within the limits of the stock. Field and petrographic observations of the Siscoe stock combined with chemical analyses of major, trace and rare earth elements of the stock and its volcanic host rocks (Dubuisson Formation) suggest that:The Siscoe stock comprises four alteration facies formed from a homogeneous precursor: 1) the actinolite - Mg-chlorite facies, characterized by low FeOt,Na2O andTiO2 , and highAlp3 and MgO; 2) the albite- Fe-chlorite facies, containing high concentrations of FeOt and Nap; 3) the Mg + Fe-chloritefacies, which is transitional between the actinolite- Mg-chlorite and albite- Fe-chloritefacies; 4) the carbonate-chlorite facies, which consists of rocks that were subjected to extreme hydrothermal alteration, is spatially associated with mineralized veins and part of the K-zone. The first three facies are depleted in SiO 2, CaO and Au, and enriched in MgO, relative to fresh rocks of the Siscoe stock and the equivalent rocks of the Dubuisson Formation.Hydrothermal fluids introduced mainly along the K-zone ""channelway"" induced three types of element remobilization, resulting in the various alteration facies: 1) redistribution of elements within the stock from one facies to another (e .g., FeOt, Nap, Ti02 migrated from the actinolite- Mg-chlorite facies to the albite- F e-chlorite and Mg + Fe-chlorite facies); 2) remobilization of elements from the intrusive rocks into veins (e.g ., SiO 2 and CaO ); 3) introduction of elements by hydrothermal fluids in rocks of the Siscoe stock (e .g., Al2O3, MgO, H2O, CO2 and FeOt).The Siscoe stock and the Dubuisson Formation form part of the same tholeiitic suite. Similarly, the Bourlamaque batholith and the Val d'Or Formation belong to a single calc-alkaline suite. In view of this relationship, dissimilarities between the petrochemistry of the Siscoe stock and the Bourlamaque batholith suggest that the two intrusions are not co-magmatic.Finally, gold may have been leached from rocks of the Siscoe stock and remobilized into the quartz-carbonate mineralized veins. In order to account for the total production at the Siscoe mine, approximately 1.2 km3 of the Siscoe stock is thought to have been partially leached of its gold."

Jan 1, 1990

By Tao Zeng, Jianchao Li, Chang Jie, Jieyu Zhang, Jifang Xu, Kuochih Chou

"The densities of the selected quaternary Ca0-5%Mg0-Alz03-Si02 slag with low silica were measured by the Archimedean method in a wide temperature range from l 723K to 1823K. Slag compositions were chosen based on five different levels of Si02 content between 0.00 pct and 11.40 pct. The MgO content was equaled to 5.00 pct. The mass ratio of CaO/Alz03 was varied from 0.67 to 2.14. The effects of temperature, Ca0/Alz03 ratio and optical basicity were studied. It is shown that density decrease approximately linearly with an increase in temperature. With the same Si02 content, the density decreases with increasing of CaO/Alz03 ratio and optical basicity. Based on the experimental data as the boundary of the homogenous phase region predicated by F ACTSAGE software, the mass triangle model is used to calculate the density of selected limited homogenous phase region. The results showed that the mass triangle model is working well.IntroductionIt is of great importance to measure density of slag melt not only to the theory research for melt, which that is directly amenable to the structure correlations of molten slags, but also to the industrial application. Many metallurgy phenomena such as inclusion formation in molten melt and its removing, slag foaming, slag-metal reaction are closely related to the density of slag. Density is also required to estimate other fundamental properties, like surface tension, viscosity, and thermal conductivity from thermal diffusivity so that a relatively complete picture in regard to the behavior of high-temperature molten oxides could be made."

Jan 1, 2013

By J. C. Huyhua

The effect or various oxidants on gold and silver dissolution in thiourea solutions (0.05 M in H2SO4) was studied using the rotating disc technique, a.t 2s c and 600 rpm. These studies were carried out at constant (4:1) initial molar ratio or thiourea to oxidant concentrations, to produce 50 % thiourea. oxidation. The initial dissolution rate of gold was approximately four times higher in the presence. of ferric sulfate (5.37 x 10-3mg cm-2 s-1) than in the presence of hydrogen peroxide (H2O2), potassium persultate (K2S2O3), or monopersulfa.te (KHS06). The dissolution rates for silver were considerably lower than gold for the same oxidants. Oxidation of thiourea in the presence of peroxygen and persulta.te compounds is a. fast reaction and it is completed in less than ten minutes. On the other hand, the oxidation or thiourea with? ferric.sulfate is slow, yielding a second-order reaction rate constant k = 6.09 I mol-1 h-1. Sulfur formation in the ferric thiourea system begins when ferric ion reduction approaches to completion. With hydrogen peroxide, sulfur is observed at lower thiourea concentration than ferric. Suifate. The presence of a large excess or free thiourea i.e., s to 20 % thiourea oxidation) retards sulfur formation and maintains favorable dissolution rates. Finally, carbon-in-leach experiments indicate that thiourea solutions a.re stable for several days, with ferric sulfate or hydrogen peroxide. The dissolution rates of gold and silver doubles in the presence or activated carbon when hydrogen peroxide is used as oxidant.

Jan 1, 1989

In flotation, particulate materials are separated by controlling the hydrophobicity of the particles using appropriate collectors. In this regard, contact angle (?) is the most important process variable. However, the flotation models used in industry today do not include ? as a parameter. As result, flotation circuits are designed based on the first-order flotation rate constants (k) determined from laboratory experiments. A problem with this approach is that laboratory experiments usually give substantially higher k values than achievable in full-scale operations, which makes it difficult to use the model for plant design. In the present work, we have developed a model from first principles using both surface chemistry and hydrodynamic parameters, such as ?, ?-potentials, surface tension (?), particle size, energy dissipation rate, etc. The basic approach is similar to the one developed previously for bubble-particle interactions under laminar flow conditions (Yoon and Mao, J. Colloid and Interface Science, 181, 61, 1996) except that the model parameters have been modified by considering the turbulence in a flotation cell. In addition, the model describes the recovery processes in froth phase, including bubble-coarsening due to coalescence. Based on this model, we have developed a computer simulator (FlotSim) that can be used to design flotation circuits from the mineralogical (or liberation) data on the feed and the hydrodynamic characteristics of a flotation machine. Since the model is dynamic, it can also be used for process control. Further, the simulator has predictive capacity as it is based on a first-principles model. The model-based simulator has been validated in a carefully controlled bench-scale flotation experiments. Keywords: flotation kinetics, flotation model, contact angle,?-potential, size-by-size recovery, liberation, DLVO theory

Sep 1, 2012

By Ragnhild E. Aune, Mark William Kennedy, Shahid Akhtar, Jon Arne Bakken

"To determine the heating rate of billets using ‘short coils’, an appropriate correction factor must be applied to the theoretical relationship. In 1945, Vaughan and Williamson published a semi-empirically modified Nagaoka coefficient applicable for moderate frequency induction heating processes (10 kHz). Recently it was demonstrated that the method of Vaughan and Williamson gives <10% error in the estimated power when heating aluminum billets at 50 Hz.In the present study, experiments have been conducted on aluminum billets in order to verify an empirical frequency corrected ‘short coil’ equation. Measurements of electrical conductivity (<± 0.5%), current (± 1%), heat (± 1-3%), and magnetic flux density (± 1-2%) have been performed. The results are compared with 1D analytical calculations, and 2D axial symmetric FEM modeling using COMSOL 4.2®. The frequency corrected equation has proven to provide accurate predictions of power (<4% error) within the frequency range 50 Hz to 500 kHz.IntroductionInduction heating is commonly applied to the re-heating of billets before forging or extrusion processes. The resistive heating produced by eddy currents in the solid or semi-solid work piece during this procedure, is driven by the time varying magnetic flux density in the air-gap between the work piece and the coil. The flux in the air-gap is created by the current flowing in the induction coil, i.e. the magneto-motive force. In Figure 1 it can be seen that the currents present in the work piece are concentrated in the outer ‘shell’, or the first electromagnetic penetration depth (dw), and flow in a direction which opposes the magnetic field produced by the induction coil."

Jan 1, 2012