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By C. Dalton, H. L. McGill

The purpose of this study was to develop a method for predicting the time delay created by metering a fluid through an annular restriction with translational motion of the boundaries. This time delay is utilized to control the opening of valves in various down-hole oilfield tools and forms the basis for the "hydraulic jar". The hydraulic jar is used to give upward impact forces to tubing or other tools that become lodged down-hole. The design of these jars has primarily been by trial and error; varying the clearances, fluid viscosities and dimensions of the jar until a satisfactory time delay was achieved. Obviously, a better understanding of the fluid flow characteristics is required to produce designs that are satisfactory and to eliminate the trial-and-error approach. Previous studies of flow in annular spaces were based on constant length of the annular restriction. Any motion of the boundaries of the annular space was confined to a rotational motion, like that encountered in journal bearing design. Consideration of the effect of translational motion of one boundary with respect to the other was necessary in applying this previous work to a time delay device. A prediction method was developed that takes into account this relative translational motion. Equations were developed to predict the relative velocity, the flow rate, and the time delay in a concentric annular space. The effect of eccentricity also was included. Experimental data were obtained and closely correlated with the prediction method. This correlation is presented graphically in terms of predicted and actual relative velocities for various annular clearances and pressure drops. This extension provides design equations which predict the performance of the hydraulic jar, thereby eliminating trial-and-error solutions and reducing the development time required for satisfactory designs. INTRODUCTION The design of down-hole oilfield tools which use hydraulic delay systems based on flow through annular orifices with relative motion of the boundaries is usually a trial-and-error process. The annular clearances, fluid viscosities and dimensions of the mechanisms were varied until satisfactory delay times were obtained. The development of these tools has been expensive, and a better understanding of the characteristics of annular flow with relative motion of the boundaries could result in superior and less expensive designs. The purpose of this investigation was to provide a method of predicting the performance of down-hole tools which use annular flow and, in particular, the performance of a down-hole tool known as the "hydraulic jar". The hydraulic jar is used to free pipe, packers and other tools that become lodged down-hole. The jar, located in the tubing string between the surface and the object which is stuck, releases the object though the repeated application of upward impact blows. The jar is basically a slip joint that is restrained in a collapsed condition until the desired tubing tension has been developed. The slip joint is then released and accelerates rapidly until it shoulders, delivering an impact blow or jar to the object. The delay obtained by metering the fluid through the annulus formed by the jar valve and housing provides the time delay necessary to stretch and apply tension to the tubing or pipe. Fig. 1A gives a schematic diagram of the hydraulic jar and brief details of its operation. The metering of the hydraulic jar begins when the tension force being applied to the jar by the pipe creates a pressure differential across the valve that is approximately equal to the force divided by the displacement area of the valve. This pressure differential induces flow through the annular restriction formed between the valve and housing. The valve moves with respect to the housing as the

Jan 1, 1969

By H. W. Mead, C. E. Birchenall

The rates of growth of graphite nodules in cast irons are calculated for a model of a growing graphite sphere surrounded by a shell of austenite through which carbon and iron are diffusing. The carbon is supplied by a cementite-austenite mixture at the outer edge of the shell. The calculated rates from carbon diffusion agree fairly well with the measured values, but the rates based on iron self-diffusion are much too low. Because the iron must be removed for the process to continue, o plastic deformation mechanism is suggested. THERE has been an unfortunate tendency in the literature of growth and dissolution reactions to identify the slope of a plot of the logarithm of the growth or dissolution rate vs reciprocal of temperature with the activation energies determined by diffusion measurements in chemically similar systems. If the solubility limits at the growing or dissolving phase interfaces change appreciably with temperature, such procedures may lead to serious errors in specifying the mechanisms controlling the rates of these processes. A reaction involving the simultaneous growth of graphite from and dissolution of cementite in austenite will be discussed here to show that substantial oversimplifications have been made in earlier studies of this process. From a dilatometric study of the overall y-range graphitization process, Bunin and Danil'chenko' found an apparent activation energy of 90 kcal per g-atom. They concluded that, since this value was much nearer the approximately 68 kcal per g-atom observed for self-diffusion in pure iron than it was to 32 kcal per g-atom for diffusion of carbon in iron, the rate-controlling process must be the diffusion of iron away from the growth interface to provide space for graphite to grow. Bunin and Salli' bolstered this agreement with the observation that graphite forms preferentially at surfaces, cracks, and pores where free volume is present initially. Ziegler, Meinhart, and DeaconQ ad found an apparent activation energy for graphitization of 98 kcal per g-atom. This value, like that of Bunin and Danil'chenko, applies to nucleation and growth occurring simultaneously. It is not generally assumed that nucleation is entirely diffusion-controlled. Treatments such as prior cold-working and prequenching, which strongly affect the rate of graphitization, would be expected to have little effect on diffusion processes occurring at the graphitization temperature. In any case 90 kcal per g-atom is not particularly close to the 54 kcal or lower to be expected for diffusion of iron which is carbon-saturated.' The presence of silicon in iron is said to reduce the activation energy for diffusion,' so its presence in cast irons would be expected to have a similar effect. The growth rates of nearly spherical graphite nodules have been studied by Brown and Hawkes." The initial rate of growth before impingement of adjacent carbon-depleted areas was found to be parabolic, and rate constants were measured at several temperatures. Their apparent activation energy for the growth process only was roughly 45 kcal per mol. Burke and Owen' made growth-rate measurements on several alloys, recording appreciable induction periods, initial nucleation rates, and average radial growth rates based on an assumed linear rate of radial growth. They found that increased silicon content increases the ovel-all reaction rate and the initial rate of nucleation, and decreases the induction period. Assuming 1) spherical nodules. 2) constant volume rate of nucleation, 3) austenite in equilibrium with cementite at positions where the cementite is not depleted, and 4) a constant diffusion distance during the growth of a nodule, they calculated an apparent overall activation energy of 68 kcal per mol, which was related to an activation energy for nucleation of 79 kcal per mol and activation energy

Jan 1, 1957

By Klaus Schwerdtfeger

In order to test the performance of ZrO, (CaO) and Tho,(Yz03) electrolytes in the electrochemical determination of oxygen activities in liquid metals at steel-rrzakitng temperatures , electromotive force measurements have been made with the following cells: The oxygen-- activities are calculated from the electmrnotive forces for the investigated systems. The standard free energy of- formation of MnO and the activity of manganese in Fe-Mn melts are derived. Indications are that the Zr 0z(Ca0) electrolyte exhibits little electronic conductivity at oxygen pressures as low as 10'a atnz at 1600°C; however, the partial electronic conductivity may become noticeable at lower oxygen activities. The Tho,(Yz03) electrolyte is found to be an ionic conductor at the oxygen pressure as low as that for the Mn + MnO equilibrium, but exhibits partial electronic conductivity at oxygen pressures higher than 10"1 atm (1500°C). fi. better control of oxidation and deoxidation reactions in steelmaking may be facilitated if the oxygen activity in the steel is known during various stages of the process. In the present work oxygen activities have been measured in liquid iron, manganese, and iron alloys with galvanic cells using ZrOz(CaO) and s solid electrolytes with the object of establishing the range of oxygen pressure in which these materials can be used as electrolytes at steelmaking temperatures. Calcia-stabilized zirconia and Tho2-Y203 solid solutions are oxygen ion conductors. Such electrolytes were first used by Kiukkola and Wagner1 and Peters and ~ann' in galvanic cells for the determination of thermodynamicquantities of oxide systems in the temperature range 700" to 1200°C. At these moderate temperatures calcia-stabilized zirconia has been found to exhibit predominantly ionic conductivity at oxygen pressures as low as those for the Cr + Crz03 equilibrium,394 but at lower oxygen pressures elec- tronic contribution to conductivity becomes significants4 The Th02-Y203 solid solutions are ionic conductors at oxygen pressures lower than those applicable to zirconia base electrolytes.5'6 At high oxygen pressures Thoz base electrolytes exhibit significant p-type semiconduction. At the time the present experiments were carried out several papers1'-* were published on the electrochemical determination of oxygen activities in liquid iron using the ZrOz(CaO) electrolyte. The results of different authors do not agree well. For instance, according to Fischer and ~ckermann" stabilized zirconia can be used to measure oxygen contents in liquid iron larger than 0.02 wt pct, but according to Baker and west1' ZrOz(CaO) cannot be used for the determination of oxygen content in liquid iron because of high electronic contribution to the conductivity. Fig. 1 is a schematic diagram of the apparatus used. About 500 g of liquid metal is contained in a crucible into which a stabilized zirconia or Th02(Y203) tube is immersed. A platinum contact wire is pressed (with a spring mechanism) against the inside bottom wall of the electrolyte tube. The tube is flushed continuously with a stream of air, CO-CO, (or Hz-C02) (at 0.96 atm and at a rate of about 300 cu cm per min), via an alumina tube inserted inside the electrolyte tube. This alumina tube also contains the Pt-Pt/10 pct Rh thermocouple. A capillary alumina tube shielding the other contact wire is immersed in the melt. The molybdenum contact wires were used mostly; in some cases platinum wire was employed. Molybdenum has the advantage that it dissolves more slowly in the melt than platinum. The whole cell was contained in the alumina reaction tube of a resistance furnace with molybdenum winding. The reaction tube was closed gas tight at both ends and flushed continuously with argon. Because of the poor thermal shock resistance of the electrolyte tubes the cell had to be assembled in the cold furnace. The electrolyte tube and alumina sheath

Jan 1, 1968

By R. P. Alger, M. P. Tixier, D. R. Tanguy

In the combination induction-electrical log used at present in the field, the induction logging tool is appropriate for the investigation of moderately invaded formations. A new induction sonde with a radius and investigation about twice as large has been developed recently for the case of deep invasion. It has very nearly the same vertical resolution as the present sonde so that thin beds are defined as accurately as before. The characteristics of the new tool are described, the corresponding interpretation charts are given and field examples are discussed. The design of the sonic logging tool has been modified to improve the calibration and the reliability. The fact that porosity can be accurately recorded by means of the sonic log has prompted new interpretation procedures for saturation estimation, wherein the data concerning the various permeable beds in a given well are correlated. One approach consists of plotting transit time vs true resistivity, with an appropriate scale. With this approach, saturations can be estimated conveniently even in cases where formation water resistivity is not well known. In another approach, a comparison is made of the values of the formation waters computed from the re- sistivity and sonic logs. Using the concept of continuity, this procedure makes possible a quick determination of zones of saturation in shaly sands and/or in case of appreciable variations of formation salinities with depth. It has been found that the comparison of porosity from the sonic log with the apparent porosity computed from a short-investigation resistivity log may reveal, in many cases, the presence of residual oil and thus detect potentially productive formations; this procedure is valuable when the true formation resistivity and the resistivity of the formation water are in doubt. INTRODUCTION During the past year, the efficiency of log interpretation has been vastly improved. The improvements have largely resulted from the introduction of a deep-investigation induction device and from the application of new interpretation techniques that utilize sonic vs resistivity readings. Since the new interpretation techniques depend, in part, upon good values of true formation resistivity, the new induction log will be discussed under Part I. The sonic interpretation techniques will be studied under Part 11. Early in 1959, the 6FF40 induction equipment was introduced in the field. This device was designed for a better approach to true formation resistivities in deeply invaded zones. The greatly improved radial investigation of the 6FF40 equipment has been achieved without sacrificing vertical resolution. The first combination induction-electrical log, the 5FF40, was introduced as a standard tool in 1956 for the logging of wells drilled with fresh muds. The tool has received wide industry acceptance in the United States. 'The 5FF40 induction log has a radial investigation sufficient to overcome average depths of mud filtrate invasion. At 5d invasion, for example, the 5FF40 induction log will read about 1.4 R. in a water sand where R., = 10R,. At 10d invasion, such induction log would read 2.45 R. in the same water sand. In either case, the effects of invasion would not be sufficiently great to cause a water sand to be mistaken for a shale-free oil- or gas-producing zone. Some formations, however, invade deeply — in excess of 10d. Such water zones could be mistaken for oil-or gas-saturated sands unless the porosity balance' can clearly make the distinction. It is for these deeply invaded formations that the 6FF40 was developed. CHARACTERISTICS OF THE 6FF40 Radial Investigation Characteristics To describe the comparative responses of the 5FF40

By R. G. Garlick, H. B. Probst

Tungsten single-crystal specimens of various orientations were deformed in tension at room temperature. Slip traces indicated both (112)(111) and (110) (111) slip; however, about 10 pct plastic dejormation was required bejore these traces could he seen. Resolzled shear-stress considerations indicated that at least some of the particular systems observed were not those on which slip initiated hut were secondary systems. This is highly probable, considering the high plastic strains involved. Analysis of the stress data with respect to possible slip systems indicated that slip must have been initiated at stresses below the proportional-limit stresses measured. ALTHOUGH there is general agreement that slip deformation in fcc and hep metals takes place on the plane of close packing and in the direction of close packing, there is no such agreement for slip in bcc metals. It is generally agreed that the close-packed direction (111) is the slip direction, but investigations have led to conflicting descriptions of the slip plane. As Hoke and Maddin1 point out, there are essentially four points of view. 1) Deformation in bcc metals is composite shear on (112) and (110) planes or on nonparallel (110) planes, and any apparent slip on other planes can be accounted for completely by slip on these planes. Chen and Maddin have reported this to be the possible case for molybdenum." 2) Slip occurs in the (111) direction and is limited to {110), {112), and (123) planes (the three closest packed planes of the lattice). 3) Slip occurs in a (111) direction, but not necessarily on planes of close packing (banal slip). 4) Slip occurs in those directions and on those planes for which ß, the ratio of Burgers vector to interplanar spacing, is a minimum. The slip systems of the bcc metal tungsten have never been fully determined, although several investigators have reported pertinent results.3"7 The present work was initiated to determine the active slip systems in tungsten at room temperature, the critical resolved shear stresses associ- ated with these systems, and the orientation dependency of operative systems. These features of tungsten deformation at room temperature have never been reported in the literature. The authors find this somewhat surprising, particularly in view of the availability of tungsten single crystals since the advent of electron-beam zone-melting techniques and the widespread interest in refractory metals. It would seem apparent that such work has been attempted but the results have not been reported, possibly due to the conflict with deformation theory. The results of the present work conflict with any straightforward description of deformation based on the proposed explanations of slip in bcc metals. Although these conflicts have not been resolved, a presentation of the problem seems in order and should be of value to others working in this field. MATERIALS AND PROCEDURE Single-crystal tungsten rods of 1/8-in. diameter were grown from undoped commercial rod by one-pass electron-beam zone melting in apparatus previously described by witzke.8 Representative analyses of the rod before and after melting are given in Table I. There was no detectable zoning of impurities during melting. Buttonhead tensile specimens, as shown in Fig. 1, were machined from single crystals. Two flats 90 deg apart were ground in the gage length of each specimen. These flat surfaces facilitated the analysis of slip traces. No attempt was made to position these flats with respect to the crystal orientation. The worked surface layer of the machined specimens was removed by electrolytic polishing in a NaOH solution. Tensile-axis orientations were determined by standard Laue back-reflection techniques. The sharpness of the Laue spots indicated that the crystals were free of strain.

Jan 1, 1964

By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally. Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan," show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used' for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan's pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision, using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.' However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,' has been deduced for these frequencies: 3_____________________ fB = 9.20.vV.vn. (n-1).(n+2)/8 [I] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts as the order of the harmonic. As an example, Spedden and Hannan's published motion picture of a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsym-metric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system of one degree of freedom can be applied: fP = -1/2-vE/m [2] Here fp is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: t, = 2/f = nvm/E [3] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson7 1831) P = /4 D2-pL-g-h + D.y sin a [4] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, PL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of the liquid in cm, y the surface tension in dynes per cm and a the supporting angles or the one required to insure equilibrium, a being smaller than the contact angle 0. Although demonstrated by Poisson, it has not

Jan 1, 1953

By P. A. Laxen, H. R. Spedden

WHEN a mineral particle is fractured, bonds between the atoms are broken. The unsatisfied forces that appear at the newly formed surface are considered to be responsible for the adsorption of ions at the mineral surface. A knowledge of the mechanism and extent of ion sorption from solution onto a mineral surface is of interest in the development of the theory of flotation.'*' Study of the adsorption of sodium from an aqueous solution oftheon quartz offers a simple approach to this complicated problem. The availability of a radioisotope as a tracer element meant that accurate data could be obtained."." Three main factors which appeared likely to affect the adsorption of sodium are: l—concentration of sodium in the solution, 2—concentration of onotherof cations in the solution, and 3—anions present in the solution. Hydrogen and hydroxyl ions are always present in an aqueous solution. By controlling the pH, the concentration of these two ions was kept constant. The variation in thesethe amount of sodium adsorbed with variation in sodium concentration was then determined under conditions standardized in regard to hydrogen ion. The effect of concentration of hydrogen ions and of other cations was also measured. A few experiments were made to get a preliminary idea on the effect of anions. The active isotope of sodium was available as sodium nitrate. Standard sodium nitrate solutions were used throughout these experiments except when the effects of other anions were studied. It was found that sodium adsorption increased with sodium-ion concentration, but less rapidly than in proportion to it. Increasing hydrogen-ion concentration, or conversely decreasing hydroxyl-ion, brings about a comparatively slight decrease in sodium-ion adsorption. Increasing the concentration of cations other than hydrogen or sodium decreases somewhat the adsorption of sodium ion. It would appear as if the kind of anion is a secondary factor in guiding the amount of sodium ion that is adsorbed. Materials and Methods Quartz The quartz was prepared as in previous work in the Robert H. Richards Mineral Engineering Laboratory' except for the refinement of using de-ionized distilled water for the final washing of the sized quartz, prior to drying." To minimize the laborious preparation of quartz, experiments were made to determine .whether the sodium-covered quartz could be washed free of sodium and re-used. The experiments were successful as indicated by lack of Na" activity on the repurified material and by its characteristic sodium adsorption. Table I gives the spectrographic analyses of the quartz used. The quartz ranged from 16 to 40 microns in size, averaging about 23 microns (microscope measurement), and had a surface of 1850 sq cm per g (lot I), 2210 (lot 11) and 2000 (lot 111) as determined by the Bloecher method." Radioactive Sodium Method of Beta Counting for Adsorbed Sodium: Na22, the radioisotope of sodium, possesses convenient properties.' It has a half-life of 3 years, thus requiring no allowance for decay during an experiment. On decay it emits a 0.575 mev ß+ radiation and a 1.30 mev r radiation. The decay scheme is illustrated in the following equation: ß+ NaR-------'8'77NeZ2 3 years The /3 radiation is sufficiently strong to penetrate an end-window type of Geiger-Mueller counting tube. This, in turn, makes it possible to use external counting, a great advantage in technique. Furthermore, it permits the assaying of solids arranged in infinite thickness, while assaying evaporated liquors on standardized planchets. The equipment used was standard and similar to that employed by Chang.R The original active material was 1 ml of solution containing 1 millicurie of Na" as nitrate. This active solution was diluted to 1000 ml. Five milliliters of this diluted active solution was found to give a quartz sample a sufficiently high activity for accurate evaluation of the sodium partition in the adsorption measurements. Also, 1 ml of final solution gave a sufficiently high count for precision on the liquor analyses. The sodium concentration of the diluted active solution was 1.2 mg per liter, so that 6 mg of sodium for 60 ml of test solution and 12 g of quartz was the minimum amount used. The active solution was stored in a Saftepak bottle. Procedure for Adsorption Tests: The method consisted of agitating 12 g of quartz with 60 ml of solution of known sodium concentration for enough time to establish equilibrium between the solution and the quartz surface. The quartz was separated as completely as possible from the solution by filtering and centrifuging. The activity on the quartz and in the equilibrium solution was measured and the partition of the sodium was calculated from the resulting data. The detailed procedure for the adsorption test is set forth in a thesis by Laxen." In brief, it included the following steps: 1—Ascertainment of linearity between concentration of Na" and activity measured. 2—Evaluation of factor to translate activity on solid of infinite thickness in terms of activity on an evaporated active film of minute thickness, on the various shelves of the counter shield. 3—Taking precautions to avoid evaporation of water during centrifuging

Jan 1, 1953

By P. A. Laxen, H. R. Spedden

WHEN a mineral particle is fractured, bonds between the atoms are broken. The unsatisfied forces that appear at the newly formed surface are considered to be responsible for the adsorption of ions at the mineral surface. A knowledge of the mechanism and extent of ion sorption from solution onto a mineral surface is of interest in the development of the theory of flotation.'*' Study of the adsorption of sodium from an aqueous solution oftheon quartz offers a simple approach to this complicated problem. The availability of a radioisotope as a tracer element meant that accurate data could be obtained."." Three main factors which appeared likely to affect the adsorption of sodium are: l—concentration of sodium in the solution, 2—concentration of onotherof cations in the solution, and 3—anions present in the solution. Hydrogen and hydroxyl ions are always present in an aqueous solution. By controlling the pH, the concentration of these two ions was kept constant. The variation in thesethe amount of sodium adsorbed with variation in sodium concentration was then determined under conditions standardized in regard to hydrogen ion. The effect of concentration of hydrogen ions and of other cations was also measured. A few experiments were made to get a preliminary idea on the effect of anions. The active isotope of sodium was available as sodium nitrate. Standard sodium nitrate solutions were used throughout these experiments except when the effects of other anions were studied. It was found that sodium adsorption increased with sodium-ion concentration, but less rapidly than in proportion to it. Increasing hydrogen-ion concentration, or conversely decreasing hydroxyl-ion, brings about a comparatively slight decrease in sodium-ion adsorption. Increasing the concentration of cations other than hydrogen or sodium decreases somewhat the adsorption of sodium ion. It would appear as if the kind of anion is a secondary factor in guiding the amount of sodium ion that is adsorbed. Materials and Methods Quartz The quartz was prepared as in previous work in the Robert H. Richards Mineral Engineering Laboratory' except for the refinement of using de-ionized distilled water for the final washing of the sized quartz, prior to drying." To minimize the laborious preparation of quartz, experiments were made to determine .whether the sodium-covered quartz could be washed free of sodium and re-used. The experiments were successful as indicated by lack of Na" activity on the repurified material and by its characteristic sodium adsorption. Table I gives the spectrographic analyses of the quartz used. The quartz ranged from 16 to 40 microns in size, averaging about 23 microns (microscope measurement), and had a surface of 1850 sq cm per g (lot I), 2210 (lot 11) and 2000 (lot 111) as determined by the Bloecher method." Radioactive Sodium Method of Beta Counting for Adsorbed Sodium: Na22, the radioisotope of sodium, possesses convenient properties.' It has a half-life of 3 years, thus requiring no allowance for decay during an experiment. On decay it emits a 0.575 mev ß+ radiation and a 1.30 mev r radiation. The decay scheme is illustrated in the following equation: ß+ NaR-------'8'77NeZ2 3 years The /3 radiation is sufficiently strong to penetrate an end-window type of Geiger-Mueller counting tube. This, in turn, makes it possible to use external counting, a great advantage in technique. Furthermore, it permits the assaying of solids arranged in infinite thickness, while assaying evaporated liquors on standardized planchets. The equipment used was standard and similar to that employed by Chang.R The original active material was 1 ml of solution containing 1 millicurie of Na" as nitrate. This active solution was diluted to 1000 ml. Five milliliters of this diluted active solution was found to give a quartz sample a sufficiently high activity for accurate evaluation of the sodium partition in the adsorption measurements. Also, 1 ml of final solution gave a sufficiently high count for precision on the liquor analyses. The sodium concentration of the diluted active solution was 1.2 mg per liter, so that 6 mg of sodium for 60 ml of test solution and 12 g of quartz was the minimum amount used. The active solution was stored in a Saftepak bottle. Procedure for Adsorption Tests: The method consisted of agitating 12 g of quartz with 60 ml of solution of known sodium concentration for enough time to establish equilibrium between the solution and the quartz surface. The quartz was separated as completely as possible from the solution by filtering and centrifuging. The activity on the quartz and in the equilibrium solution was measured and the partition of the sodium was calculated from the resulting data. The detailed procedure for the adsorption test is set forth in a thesis by Laxen." In brief, it included the following steps: 1—Ascertainment of linearity between concentration of Na" and activity measured. 2—Evaluation of factor to translate activity on solid of infinite thickness in terms of activity on an evaporated active film of minute thickness, on the various shelves of the counter shield. 3—Taking precautions to avoid evaporation of water during centrifuging

Jan 1, 1953

By L. D. Hall, D. R. Mash

The paper presents the results of experiments on the anelastic. behavior of gold, as manifested by grain boundary relaxation. Two grain boundary internal friction peaks are found for 99.9998 pct Au. It is found that the peaks are associated with primary and secondary recrystallization. However, the existence of two discrete peaks cannot be explained on the basis of grain size and shape alone. It is suggested that grain boundary stability, as determined by orientation, plays a role in the observed effects. EVIDENCE for the viscous behavior of grain boundaries in metals has been presented in recent years by several investigators, based upon studies of various anelastic effects, especially internal friction. KG1 has contributed greatly to this field, having put forward a coherent body of evidence for stress relaxation by the viscous intercrystalline flow mechanism. In this connection, he has made extensive use of pure aluminum (99.991 pct) as the test material, although he has also studied other metals and alloys, including pure iron (Puron).² Rotherham, Smith, and Greenough³ have studied the internal friction of pure tin, interpreting their results in a manner similar to that of KG. In view of the importance of such studies in shedding light upon the fundamental structure and behavior of the grain boundaries in pure metals, it appears that the use of a very pure test material which is inert to its environment should provide useful information on anelastic properties and the source of such behavior in pure metals. The present work was carried out on spectrograph-ically pure, 99.9998 pct Au, free of all impurities except for a trace of silver, estimated to be present to the extent of about 0.0002 pct. The term "pure gold" will hereafter refer to this very pure material. Gold of commercial purity, 99.98 pct, was also studied to observe the effects of small amounts of impurities. A pure gold "single crystal" specimen was also tested for comparison. The variation of the internal friction and rigidity modulus as a function of temperature was determined by means of a torsion pendulum apparatus employing extremely low stress amplitudes and a frequency of vibration of the order of 1 cycle per sec. A 12 in. length of 0.031 in. (20 gage) gold wire formed the suspension element. The apparatus was similar to that described by Ke.l The test procedure and the basic requirements to be met for obtaining useful experimental data by this method have been given elsewhere.1,2 It should be made clear that in all of the experiments to be described, the internal friction and rigidity were independent of the amplitude of torsional vibration. The semilog plot of amplitude of vibration vs ordinal number of vibration was a straight line. This was carefully verified for each internal friction measurement. The linear variation shows that the internal friction was independent of stress; i.e., that the specimens were not being cold-worked during testing. The reproducibility of the internal friction curves, which were obtained by cyclic heating and cooling, indicates that the gold was unaffected by its environment during the tests. The measure of internal friction adopted in the present study is the conventional "logarithmic decrement," defined as follows: log. dec. = l/n In A0/An [I] where n is the number of cycles or vibrations; A,, the initial amplitude of vibration; and An, the amplitude after the nth cycle. When the logarithmic decrement is small, the shear modulus, G, of the wire is proportional to the square of the frequency of vibration provided the length and radius of the wire are kept constant. A plot of frequency squared vs temperature gives the following ratio:' This expresses the fraction of the stress which has not been relaxed at a given temperature. Gr and Gv are the relaxed and unrelaxed moduli, respectively. The frequency of vibration in the polycrys-talline specimen is fp, and the frequency of vibration of a single crystal is f8. This latter quantity is obtained simply by extrapolating the linear, low temperature portion of the curve of frequency squared vs temperature for the polycrystalline specimens. The theory of viscous grain boundary stress relaxation as demonstrated by the anelastic behavior of metals has been discussed in detail by Zener4 and need not be reproduced here. Experimental Results Initial measurements of the internal friction of pure gold were carried out on specimens which had been drawn with no intermediate annealing, resulting in a material which had undergone approximately 99 pct reduction of area in final processing. Annealing was then carried out at successively higher temperatures starting at 400°F for 1 hr and proceeding in this manner to as high as 1600°F in 100°F intervals. After each annealing treatment an internal friction and rigidity vs temperature curve was obtained over the range from room temperature to the particular annealing temperature. The resulting internal friction curves did not exhibit well defined maxima (peaks), but rather several fairly flat

Jan 1, 1954

By E. Miller, K. Komarek, W. Johnson

The activity of aluminum in solid Cr-A1 alloys has been measured by an isopiestic technique between Cr-A1890' and 1126" and 13 and 80 at. pct Al. The integral free energy of mixing has a minimum value of —5600 cal per g-atom at 59 at. pct Al. The maximum solid solubility of aluminum in chromium was determined to be 43 at. pct Al, and the composition limits of the compounds CrA14, Cr4A19, and Cr5Al, at 1000"~ were found to be 79 to 80, 66 to 70, and 59 to 63 at. pct Al, respectively. The thermodynamic properties of the Cr-A1 system have been investigated as part of a thermodynamic study of aluminum-transition metal systems.172 Little information is available on the equilibrium properties of the Cr-A1 system. The heats of formation of solid Cr-A1 alloys have been determined by Kubaschewski and Haymer at 600" and low-temperature specific heat data have also been obtained.~ More extensive work has been performed on the phase diagram, and a compilation has been provided by Hansen and Anderko,~ their phase diagram at elevated temperatures being essentially based on the work of Bradley and LU.~ The high-temperature portion of the phase diagram shows an intermediate phase CrA14 decomposing peritectically at 1018°C and existing at 82 at. pct A1 at 1000°C. They also identified the compounds with solubility limits of 72 to 75 at. pct A1 at 1000°C, and Cr5A1,, existing at 61 at. pct A1 at 1000°C. The maximum solid solubility of aluminum in chromium at 1000°C was found to be 46 at. pct Al. These elevated-temperature data were obtained by examination of quenched samples and were considered as less precise than the lower-temperature data. Koester, Wachtel, and Grube7 have revised the phase diagram as a result of their magnetic susceptibility and X-ray study. The results of this work differ appreciably from those of Bradley and Lu at temperatures above 800°C. The CrA1, compound is given as existing between 79 and 81 at. pct A1 at 1000°C, and they do not indicate the presence of a CrA13 phase reported by Bradley and Lu. They also report the compound Cr4Alg as having solubility limits of 66 to 70 at. pct A1 at 1000°C, while Bradley and Lu show this compound stable only up to 870°C. Koester et al. state that the high-temperature modification of the compound Cr5A18 is stable down to 1125"C, and not 980°C as stated by Bradley and Lu, and that the low-temperature modification of Cr5Al, has a range of homogeneity of 58 to 63 at. pct A1 at 1000°C. They also report that the maximum solid solubility of aluminum in chromium is 43 at. pct A1 at 1000°C. APPARATUS AND EXPERIMENTAL PROCEDURE An isopiestic method was employed which has been successfully applied to the determination of aluminum activities in solid ~e-All and Ni-Al alloys. Alloy specimens were held at different positions in a temperature gradient and were equilibrated with aluminum vapor from an aluminum reservoir kept at the temperature minimum of an impressed thermal gradient in a closed alumina system. Diffusion of aluminum into the specimens occurred until equilibrium was reached, at which the partial pressure of aluminum in each of the specimens was given by the vapor pressure of the pure aluminum reservoir. The activity of aluminum referred to liquid aluminum as the standard state in a given equilibrated sample at temperature T could therefore be expressed by: vapor pressure of pure aluminum at _ the temperature of the reservoir Vapor pressure of pure liquid aluminum, at specimen temperature T Since both the temperature of the aluminum reservoir and the specimen temperatures were determined experimentally, and the vapor pressure of pure aluminum is known as a function of temperature,' the activity of aluminum in a given aluminum alloy of known composition could be calculated. Initial runs were made with samples consisting of pure chromium chips placed in alumina crucibles. These runs exhibited large inconsistencies, indicating that equilibrium was not attained. High aluminum content Cr-A1 alloy powders were therefore substituted for the pure chromium specimens. The starting composition of the alloys was adjusted through experimentation until the concentration change necessary to attain equilibrium was small. In this manner, consistent results were obtained in reasonable times. SPECIMEN PREPARATION Alloy specimens were prepared from chromium of 99.997 pct minimum metallic purity: with 0.028 to 0.038 pct H, 0.0002 pct N, and 0.27 to 0.46 pct 0 (Aviquipo, Inc.). The aluminum had a purity of 99.99+ pct and the following impurities: 0.003 pct Cu; 0.002 pct S; 0.002 pct Fe; 0.001 pct Pb; 0.001 pct Ga (Aluminum Corp. of America). Alloy powders were prepared from weighed mixtures of chromium and aluminum by double-arc melt-

Jan 1, 1969

By O. N. Carlson, S. A. Bradford

Discontinuous yielding in tensile tests was observed in V-O alloys in the temperature ranges of 150° to 175°C and also 350° to 400°C. The magnitude and intensity of the serrations were found to vary considerably with oxygen content. Maxima were observed in tensile and yield strengths and in the strain-hardening coefficient at the higher temperature only. The strain rate sensitivity was observed to be negative between 150° and 400°C. THIS investigation was undertaken to study the effect of oxygen on the tensile properties of iodide vanadium in the temperature range of 25o to 450°C. Brown1 observed an increase in strength between room temperature and 400°C in vanadium metal, and found that oxygen and nitrogen had a rather pronounced effect on the strength and ductility. A maximum in the tensile strength was observed by Rostoker et al.2 near 300oC and by Pugh3 around 450°C for calcium-reduced vanadium. Pugh also found a maximum in the yield strength and in the strain-hardening exponent, and minima in the elongation and strain rate sensitivity at the same temperature. Eustice and Carlson4 reported the appearance of serrations in the stress-strain curves between 140° and 180°C in iodide vanadium containing 600 ppm O. These anomalies in the mechanical properties indicate that strain aging occurs in vanadium, but the impurity or impurities responsible for the above-mentioned effects have not been identified. The phenomenon of strain aging is usually characterized by the return of the yield point after interruption of a strength test. In the temperature range where strain aging occurs, the yield and tensile strengths attain maximum values, elongation and strain rate sensitivity exhibit minima, and discontinuous yielding is generally observed in the stress-strain curve. Cottrell5, 6 has postulated that strain aging is due to the migration of solute atoms to dislocation sites to produce locking after the dislocations have broken free from their impurity atmospheres during the initial yielding. At the strain-aging temperature the process is a dynamic one in which the solute impurity atoms diffuse to the vicinity of the moving disloca- tion producing "locking" which gives rise to maxima in the tensile strength and serrations in the elongation curves. Cottrel17 has noted that discontinuous yielding in iron occurs when the diffusion coefficient of nitrogen, D, and the strain rate, i, are related by D = 10-9 €. EXPERTMENTAL PROCEDURE The vanadium metal employed in this study was prepared by the iodide refining process as described by Carlson and owen.8 A representative analysis of the vanadium used in this investigation was: 150 ppm O, <5 ppm N, <1 ppm H, 150 ppm C, 150 ppm Fe, 70 ppm Cr, <50 ppm Si, 30ppm Cu, 20 ppm Ni, <20 ppm Ca, <20 ppm Mg and <20 ppm Ti. Alloys containing from 200 to 1800 ppm O, all of which lie in the solid solution range of the V-O system, were prepared by arc melting vanadium together with portions of a high-oxygen master alloy. The master alloy was prepared by tamping pure V2O5 into holes drilled in a vanadium ingot and arc melting this five or six times in an inert gas atmosphere, inverting the button between each melting step. The oxygen content of the master alloy was then determined by vacuum fusion analysis. Vanadium containing less than 150 ppm O was prepared in the following manner. A bar of iodide vanadium was deoxidized by sealing it in a tantalum crucible with a few grams of high-purity calcium. This was held at 1100°C for 4 days to allow time for the oxygen to diffuse to the surface and to react with the calcium vapors. The calcium oxide product was later dissolved from the surface of the bar with dilute acetic acid. In this way vanadium containing from 20 to 50 ppm O was prepared. Sample Preparation. The are-melted ingots were cold swaged into 3/16-in. diam rods and these were machined into cylindrical tensile specimens with a reduced section of 1.00-in. length and 0.120-in. diam. The test specimens were annealed for 4 hr at 900°C in a dynamic vacuum of mm of Hg to remove hydrogen from the metal. This recrystal-lization treatment produced a uniformly fine-grained structure with a mean grain size of approximately 0.06-mm diam. The oxygen contents reported in this paper were determined by a vacuum fusion analysis of the tensile specimens after testing. Analyses for other interstitial or metallic impurities showed no significant changes from that of the original material. Tension Tests. Tension tests were performed on a screw-driven tensile machine at a constant cross-head speed of 0.01 in. per min. Tests at elevated temperatures were carried out by heating the

Jan 1, 1962

By H. C. Brown

SINCE 1934 the steel industry has been utilizing the spectrograph for supplementing wet chemical analysis in the production control of electric and open hearth furnaces. This means of control made great strides during the war years because of the general acceptance of the spectrograph and the increased emphasis that was placed on rapid control methods. However, in the post war era, with the demand still on increased production, it became apparent that a still more rapid and economical means of production control was needed. Since the spectrograph had been used mostly in the analysis of low alloying and residual elements, it also became apparent that equipment was needed to extend the spectrographic technique to the analysis of the high alloying elements in stainless steel. For these reasons, companies manufacturing spectrographic equipment were prompted to start development work on direct reading instruments. In June 1949, the Applied Research Laboratories of Glendale, Calif., announced that a direct method of spectrochemical analysis for stainless type steels had been developed. This paper will describe the use of the Applied Research Laboratories Production Control Quantometer in the quantitative control of stainless, silicon, and plain carbon steels being made at the Butler Pennsylvania Div. of the Armco Steel Corp. The Armco Butler Div. has one 70-ton electric furnace and six 150-ton open hearth furnaces. The electric furnace is employed in the making of all types of stainless steel and the open hearth furnaces are used for the production of silicon, wheel, and plain carbon steels. The ARL quantometer was purchased primarily for the purpose of controlling the steelmaking in the electric furnace, but its use has been extended for the analysis of final tests (ladle tests) on a number of different types of stainless, silicon, and plain carbon steels. Because of this additional work by the quantometer, substantial savings in manpower and time have been realized by the laboratory. In the analysis of a set of preliminary tests from the stainless steel furnace, approximately 40 min in laboratory time are saved due to quantometric analyses. Despite the fact that more specialty grades of stainless steel are being made in the electric furnace, the average tons per hour have been increased since the quantometer was put into operation. Specialty grades require more furnace time than regular commodity grades of stainless steel. The installation of the ARL production control quantometer was completed on March 13, 1952. By May 1, 1952, the instrument was calibrated for nickel, chromium, manganese, silicon, and molybdenum, which are the elements necessary for the production control of the stainless steel furnace. Within the following month, training of personnel on the quantometer was achieved and a study of the accuracy of the instrument showed that the results obtained were sufficiently accurate for control purposes. Therefore, on June 11, 1952, the quantometer was placed on production control for all types of stainless steels. Starting September 11, 1952, the instrument was gradually placed on ladle analysis (final tests) as the analytical curves were refined and additional curves were drawn. The quantometer has been relatively free of breakdowns since placing it on production control. The samples from only one stainless steel heat have had to be analyzed by wet chemistry because of instrument trouble. The previously existing heat-time record was also bettered by 15 min on a commodity grade of 18-8 stainless steel. Scope of Control In general, the quantometer determines all elements necessary for the production control of all types of stainless steel heats and for the ladle analysis of various types of stainless steel heats. It is also used in reporting final results for silicon, manganese, chromium, nickel, molybdenum, tin, copper, and aluminum on all silicon steel grades and manganese, chromium, nickel, molybdenum, tin, and copper on several plain carbon steel grades. Table I shows the elements and the concentration ranges of these elements in the various types of stainless, silicon, and plain carbon steel that are determined on the quantometer. A study of the results obtained on ladle test samples of stainless steel types 410, 430, 430 Ti, 446, 301, 302, 304, 304L, 305, and 17-7 PH will be discussed. Also included in the study are the results obtained on ladle test samples of a number of silicon steels. Apparatus In order to take full advantage of the potentials of the production control quantometer, the unit has been placed in an air-conditioned room with relative humidity control. The temperature is maintained at 73&apos;22°F and the humidity at 45&5 pct. The air conditioning serves as a precaution to minimize the amount of adjustment and calibration needed during operation. It also reduces contaminating fumes and dust and thereby lessens the necessity for maintenance on the equipment. The quantometer is composed of three units: the high precision multisource unit, the 1.5 meter vertical spectrometer, and the console. The source unit supplies excitation conditions varying from spark-like discharges to arc-like discharges. The voltage to the source unit is supplied by a motor-generator

Jan 1, 1955

By R. T. Hukki

John F. Myers (Consulting Engineer, Greenwich, Corm.)—Since the art of comminution has lain practically dormant for many years, it is very interesting that R. T. Hukki approaches the subject with a new concept. One is reminded of the research carried on by A. W. Fahrenwald of Moscow, Idaho, a few years ago. Fahrenwald mounted a steel bowl on a vertical shaft. The balls and ore placed in the bowl were rotated at fast speeds, thus simulating the supercritical speeds used by Hukki. The rolling action of the balls against the smooth shell liner has pretty much the same effect. The action is horizontal in one case and vertical in the other. Both researchers report good grinding activity. It is also constructive that such able investigators give to the students of comminution their interpretation of their laboratory results in terms of large-scale operation. History shows that it takes a lot of time for such radically new ideas to be absorbed by the industry. Typical of this is the present-day activity of cyclone classification in primary grinding circuits. The idea of cyclone classification has been kicking around for 30 or 40 years. Certainly we all suspect that the ponderous grinding mills of today, and their accessory apparatus, large buildings, etc., will ultimately give way to small fast units, just as this has occurred in other industries over the past 50 years. At the moment there is no evidence that ball and liner wear is prohibitively high. In fact, at the time Fahrenwald was demonstrating his high-speed horizontal machine at the meeting of the American Mining Congress, several years ago, he assured this writer that the balls retained their shape much longer than they do in conventional tumbling mills. Rods and balls that slide (as some operators in uranium plants are experiencing) get flat. Apparently the balls have a rolling action. Mr. Hukki&apos;s references to the processing capacity of the Tennessee Copper Co. mills is adequate. Those studying this subject will be greatly interested in the paper presented by Richard Smith of the Cleveland-Cliffs Iron Co. at the annual meeting of the Canadian Institute of Mining and Metallurgy in Vancouver April 24, 1958. This paper will be published during the latter part of 1958 in the Canadian Institute of Mining and Metallurgy Bulletin. Hukki&apos;s pioneering spirit is to be commended. R. T. Hukki (author&apos;s reply)—It has been heartening to read the objective discussion by J. F. Myers. The sincerity of his opinions is further strengthened by the fact that the article he has discussed contradicts in a major way the parallel achievements of his life work. Myers is right in his opinion that in general it takes a long time before new ideas are accepted by the industry. On the other hand, revolutions usually take place at supercritical speeds. There are many indications at present that both the unit operation of grinding and the related subject of size control are now just about ripe for a revolution. In grinding, brute force must ultimately give way to science. Rapid progress can be anticipated in the following fields: 1) Autogenous fine grinding at supercritical speeds will be the first advance and the one that will gain recognition most easily on industrial scale. At this moment, little Finland appears to be leading the world. Crocker recently made a statement that in nine cases out of ten, your own ore can be used as grinding medium more effectively and far more economically than steel balls. This is true. The present author would like to introduce a supplementary idea: In eight cases out of the nine cited above, it can be done at the highest overall efficiency in the supercritical speed range. Fine grinding must be based on attrition, not impact. The path of attrition may be vertical, horizontal, even inclined. 2) In coarse grinding, the conventional use of rods is sound practice. However, even the rods can be replaced by autogenous chunks large enough to offer the same impact momentum as the rods. To obtain the momentum, the chunks must be provided with a free fall through a sufficient height in horizontal mills operated at supercritical speeds. Coarse grinding must be based on impact. Detailed analysis of the subject may be found in a paper entitled "All-autogenous Grinding at Supercritical Speeds" in Mine and Quarry Engineering, July 1958. 3) All conventional methods of classification, including wet and dry cyclones, are inefficient in sharpness of separation. Continuous return of huge tonnages of finished material to the grinding unit with the circulating load is senseless practice. In the near future the present methods will be either replaced or supplemented by precision sizing. These three fields are also the ones to which J. F. Myers has so admirably contributed in the past. Fine Grinding at Supercritical Speeds. By R. T. Hukki (Mining EnGineERInG, May 1958). Eq. 9, page 588, should be as follows: T , c, (a — 6&apos;) n D Ltph On page 584 of the article the captions for Figs. 4 and 5 have been placed under the wrong illustrations and should be interchanged.

Jan 1, 1959

By John Henderson

FOR some time now the most commonly accepted description of liquid silicate structure has been the "discrete ion" theory, proposed originally by Bockris and owe.&apos; This theory is that when certain metal oxides and silica are melted together, the continuous three dimensional silica lattice is broken down into large anionic groups, such as sheets, chains, and rings, to form a liquid containing these complex anions and simple cations. Each composition is characterized by "an equilibrium mixture of two or more of the discrete ions",&apos; and increasing metal oxide content causes a decrease in ion size. The implication is, and this implication has received tacit approval from subsequent workers, that these anions are rigid structures and that once formed they are quite stable. The discrete ion theory has been found to fit the results of the great majority of structural studies, but in a few areas it is not entirely satisfactory. For example it does not explain clearly the effect of temperature on melt structure,3 nor does it allow for free oxygen ions over wide composition ranges, the occurrence of which has been postulated to explain sulfur4 and water5 solubility in liquid silicates. In lime-silica-alumina melts the discrete ion theory is even less satisfactory, and in particular the apparent difference in the mechanism of transport of calcium in electrical conduction8 and self-diffusion,&apos; and the mechanism of the self-diffusion of oxygen8 are very difficult to explain on this basis. By looking at melt structure in a slightly different way, however, a model emerges that does not pose these problems. It has been suggested5" that at each composition in a liquid silicate, there is a distribution of anion sizes; thus the dominant anionic species might be Si3,O9 but as well as these anions the melt may contain say sis0:i anions. Decreasing silica content and increasing temperature are said9 to reduce the size of the dominant species. Taking this concept further, it is now suggested that these complexes are not the rigid, stable entities originally envisaged, but rather that they exist on a time-average basis. In this way large groups are continually decaying to smaller groups and small groups reforming to larger groups. The most complete transport data 8-10 available are for a melt containing 40 wt pct CaO, 40 wt pct SiO2, and 20 wt pct Al2O3. Recalculating this composition in terms of ion fractions and bearing in mind the relative sizes of the constituent ions, Table I, it seems reasonable to regard this liquid as almost close packed oxygens, containing the other ions interstitially, in which regions of local order exist. On this basis, all oxygen positions are equivalent and, since an oxygen is always adjacent to other oxygens, its diffusion occurs by successive small movements, in a cooperative manner, in accord with modern liquid theories." Silicon diffusion is much less favorable, firstly because there are fewer positions into which it can move and secondly, because it has the rather rigid restriction that it always tends to be co-ordinated with four oxygens. Silicon self-diffusion is therefore probably best regarded as being effected by the decay and reformation of anionic groups or, in other words, by the redistribution of regions of local order. Calcium self-diffusion should occur more readily than silicon, because its co-ordination requirements are not as stringent, but not as readily as oxygen, because there are fewer positions into which it can move. There is the further restriction that electrical neutrality must be maintained, hence calcium diffusion should be regarded as the process providing for electrical neutrality in the redistribution of regions of local order. That is, silicon and calcium self-diffusion occur, basically, by the same process. Aluminum self-diffusivity should be somewhere between calcium and silicon because, for reasons discussed elsewhere,&apos; part of the aluminum is equivalent to calcium and part equivalent to silicon. Consider now self-diffusion as a rate process. The simplest equation is: D = Do exp (-E/RT) [I] This equation can be restated in much more explicit forms but neither the accuracy of the available data, nor the present state of knowledge of rate theory as applied to liquids justifies any degree of sophistication. Nevertheless the terms of Eq. [I] do have significance;12 Do is related, however loose this relationship may be, to the frequency with which reacting species are in favorable positions to diffuse, and E is an indication of the energy barrier that must be overcome to allow diffusion to proceed. For the 40 wt pct CaO, 40 wt pct SiO2, 20 wt pct Al2O3, melt, the apparent activation energies for self-diffusion of calcium, silicon, and aluminum are not significantly different from 70 kcal per mole of diffusate,&apos; in agreement with the postulate that these elements diffuse by the same process. For oxygen self-diffusion E is about 85 kcal per mole,&apos; again in agreement with the idea that oxygen is transported,

Jan 1, 1963

By P. E. Doherty, B. Chalmers

Subboundaries may be revealed in aluminum by the formation of pits on the surface during cooling from elevated temperatures. The pits do not form in the vicinity of high- or low-angle boundaries. They are attributed to the condensation of vacancies from a super saturation produced during coolirzg. Using the vacancy pit and Schulz X-ray techniques for observing low-angle boundaries, a study was made of the transition from the nearly perfect seed to the striated structuke characterist-ic of aluminum crystals grown from the melt. It was found that the individual striation boundaries develop by the coalescence of very small-angle boundaries, as well as by the addition of individual dislocations. Several mechanisms for the formation of striations are discussed. Evidence was found suggesting that a super-saturation of vacancies exists near a growing interface, and it is proposed that the resulting climb of existing dislocalions produces "half&apos;-loops" at the interface, which combine to form the low-angle striation boundaries. LINEAGE, or "striation" boundaries, have been studied in detail by Teghtsoonian and Chalmers 1,2 in crystals of tin grown from the melt, and by Atwater and Chalmers3 in lead. They found that single crystals grown from the melt consist of regions which are separated by subboundaries that lie roughly parallel to the growth direction. A difference in orientation of 0.5 to 3 deg exists between the striated regions; the misorientation is such that the lattice of one region could be brought into coincidence with the lattice of its neighbor by a rotation about an axis approximately parallel to the direction of growth of the crystal. They observed an incubation distance for the formation of striations which increased with decreasing growth rate. They also found that in any crystal, the sum of all rotations of the lattice in one sense, in going from one striation to the next, is very nearly equal to the sum of all the rotations in the opposite sense. A striation boundary, which is a low-angle grain boundary, can be described as an array of dislocations. If it is assumed that suitable dislocations are introduced into the crystal during solidification, the formation of striation boundaries can be explained as a result of the migration of the disloca- tions into arrays. The formation of arrays is energetically favorable since the energy of an assembly of dislocations can be reduced by the interaction of the stress fields when a suitable array is formed. This investigation presents and interprets new information concerning the nature and origin of striation boundaries in aluminum. EXPERIMENTAL TECHNIQUE Single crystals of high-purity aluminum (Alcoa 99.992 pct) were prepared by horizontal growth from the melt.&apos;&apos; The specimens were subsequently electropolished in a solution of 5 parts methanol to 1 part perchloric acid kept between -10° and 0°C in a bath of dry ice and alcohol. The current density was approximately 6 amps per sq in. Doherty and Davis9 have shown that in aluminum sub-boundaries with misorientations of not less than several seconds of arc may be revealed by the vacancy pit technique. During cooling from elevated temperatures pits form on electropolished surfaces of aluminum crystals as a result of the condensation of vacancies.11 Pits do not form in the vicinity of small- or large-angle grain boundaries, presumably because such boundaries act as sinks for vacancies. Boundaries of misorientations down to 3 sec of arc are revealed as pit-free regions, see Fig. 1. The Schulz X-ray technique12 was used to determine the angular misorientations of subboundaries. In this method, white radiation from a micro-focus X-ray tube is used to produce an image of a fairly large area of a single crystal surface. Subboundaries cause splitting in the diffracted image, see Fig. 2. Misorientations down to about 15 sec of arc may be observed with this technique. OBSERVATIONS AND DISCUSSION Figure 1 shows a striated aluminum crystal grown at 10 cm per hr etched by the vacancy pit technique. An incubation distance of about 1 cm is observed before the initiation of striation boundaries. Fig. 2 is a Schulz X-ray photograph of a striated crystal similar to that shown in Fig. 1. A large area of the crystal was studied by means of a series of photographs. Fig. 2, which is a reflection from the (100) plane, included about the first 4 cm of crystal to freeze. There is an incubation distance of about 1 cm, and a distance of about 2 cm over which the angle of misorientation builds up to its final value of approximately one degree. Some twist component can be seen in Fig. 2 at the right side of the photograph. From Fig. 2 it can be seen that the sum of all rotations of the lattice in one

Jan 1, 1962

By Willard L. Hunter

Four solvent extraction systems were studied to determine their efficiency jor extraction and separation of tantalum and columbium. Aqueous feed solutions of varying HF-HCl concentrations and metal content were contacted with equal volumes of cyclohexanone, 3-methyl-2-butanone, and 2-pentanone and solutions of varying HF-H2S04 concentrations were contacted with equal volumes of 2-pentanone. One multistage continuous test was made in a polyethylene pulse column using cy clohexanone as the organic phase. In each system studied, columbium and tantalum purities in excess of 95 pct with respect to each other were obtained in single-stage tests at low acidities in the feed solution. Separation factors ranging from 1700 to 2400 were obtained when rising HF-HCl mixtures in the aqueous phase. Best results were obtained when a solution of HF-H2S04 was used as the aqueous phase and 2-pentanone as the organic phase. A separation factor in excess of 6000 was obtained in one stage with aqueous solution concentrations of 2 _N HF and 2N H2S0,. When acid concentrations were increaszd to 52 HF and 10 _N H2S0,, 99.9 pct of the tantalum and 98.2 pct of the columbium initially present in the feed solution were transferred to the organic phase. The separation of columnbium and tantalum obtainable by means of the solvent extraction systems presented in this paper was found to corn -pare favorably with other systems, including the HF-H2SO4-methyl isobutyl ketone system currently used by most producers for the extraction and separation of these metals. TANTALUM and columbium are always found together in minerals of commercial significance, although the proportion of the two metals in ores varies within broad limits. Columbium is estimated to be 13 times more abundant than tantalum. Five methods generally employed for the separat:ion of these metals are: 1) fractional crystallization (the Marignac process),2 2) solvent separation, 3) fractional distillation of their chlorides, 4) ion exchange, and 5) selective reduction. Of these methods, the one currently used by industry to the greatest extent is that of solvent separation. One of the early technical developments in solvent separation of tantalum from columbium was reported by the Bureau of Mines: the HF-HC1-methyl isobutyl ketone system; data were presented for both laboratory and pilot-plant experimentation.3 Of twenty-eight organic solvents tested for their ability to extract tantalum from an HF-HC1 solution of columbium and tantalum, 3-pentanone (diethyl ke-tone), cyclohexanone, 2-pentanone, and 3-methyl-2-butanone were chosen for further study. Data on the HF-HC1-diethyl ketone system has been published4 and data describing the use of cy clohexanone, 2-pentanone, and 3-methyl-2-butanone as the organic phase are included in this report. RAW MATERIAL The source of tantalum and columbium oxides for this study was (&apos;Geomines" tin slag from the Manono Smelter, Cie Geomines, Gelges, S.A., Congo. In order to extract the valuable Ta-Cb content, the slags were carbided, chlorinated, and the sublimate from chlo-rination was hydrolized and washed free of chloride with water. The washed material was air-dried and stored in a stoppered container. Throughout the paper, "feed material" refers to this mixture of hydrated oxides which was employed because of its high solubility in aqueous solutions. Typical analysis of the hydrated oxides is shown in Table I. I) HF-HC1-CYCLOHEXANONE SYSTEM Batch Separation. Effect of Acid Concentration. To determine the effect of varying the acid concentration upon the transfer of tantalum and columbium, a series of tests was made in which approximately 2.5 g of feed material was added to 25 ml solutions of 2, 4, 6, 8, and 10 N HF and 0 through 5 N HC1. Tantalum pentoxide concentration of the solu%ons was approximately 21 g per liter and columbium pentoxide was 14 g per liter. These starting solutions were shaken with equal volumes of cyclohexanone in 100 ml polyethylene bottles for 30 min. The phases were carefully separated in 125 ml glass separatory funnels. The time of contact of the solutions with the separatory funnels was kept at a minimum to reduce silica contamination. The measured phases were separated into 400 ml polyethylene beakers and the metal contents of each were precipitated by addition of an excess of ammonium hydroxide. Precipitate from each phase was filtered on ashless filter paper, ignited at 800" to 1000°C for 45 min, weighed, and analyzed by X-ray fluorescence.5 Data tabulated in Table I1 and illustrated in Fig. 1, show that maximum separation of tantalum from columbium for each HF concentration was obtained with no HCl present. The purest tantalum product was obtained with some HCl present. The highest separation factor was obtained at 2 N HF and

Jan 1, 1970

By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally. Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan," show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used&apos; for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan&apos;s pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision, using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.&apos; However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,&apos; has been deduced for these frequencies: 3_____________________ fB = 9.20.vV.vn. (n-1).(n+2)/8 [I] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts as the order of the harmonic. As an example, Spedden and Hannan&apos;s published motion picture of a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsym-metric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system of one degree of freedom can be applied: fP = -1/2-vE/m [2] Here fp is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: t, = 2/f = nvm/E [3] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson7 1831) P = /4 D2-pL-g-h + D.y sin a [4] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, PL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of the liquid in cm, y the surface tension in dynes per cm and a the supporting angles or the one required to insure equilibrium, a being smaller than the contact angle 0. Although demonstrated by Poisson, it has not

Jan 1, 1953

By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally.&apos; Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan,3 show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used&apos; for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan&apos;s pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision; using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by, the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.5 However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,&apos; has been deduced for these frequencies: [3fB = 9.20•&apos;./V•Vn- (n-1) • (n+2) /8[1]] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts&apos; as the order of the harmonic. As an example, Spedden and Hannan&apos;s published motion picture of, a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsymmetric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat I than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system, of one degree of freedom can be applied: [1E/m[2] fP = 27] Here f, is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: [t~ = 2/f = 7r\/m/E[3]] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson&apos; 1831) [aP = 4 D2.pL•g•h +7rD•y sin a[4]] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, pL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of-the liquid in cm, y the surface tension in dynes per cm and a the supporting angle&apos; or the one required to insure equilibrium, a being smaller than the contact angle ?. Although demonstrated by Poisson, it has not

Jan 1, 1952

By A. H. Grobe, F. N. Rhines

AT elevated temperatures the oxide of silver is unstable in the air at atmospheric pressure, consequently no external oxide scale forms upon pure silver under conditions of high-temperature annealing. When small quantities of certain alloying elements are present in the silver, the formation of a thin external scale is possible&apos; and in addition there may form a subscale composed of the oxide of the solute element precipitated within the body of the silver. Norbury2 and Leroux and Raub3 have reported internal oxidation (subscale forma¬tion) in alloys of silver with 2, 7.5, and 30 per cent of copper. The presence of the subscale is believed to be responsible, at least in part, for the objectionable "fire mark" in Sterling silver.4 Several other alloys of silver, after oxidizing heat-treatments, are known to exhibit undesirable polishing characteristics that may be the result of internal oxidation. Except for the absence of an external scale of silver oxide, it is to be anticipated that silver alloys will prove to be very similar in their oxidation behavior to the alloys of copper, the oxidation characteristics of which have been studied in some detail5,6 The present research confirms this anticipation. The oxidation of a series of 20 dilute alloys of silver has been studied metallographically; some types of subscale not encountered among the copper alloys have been found. Instances of internal oxidation in alloys of most of the metals of the I-b and VIII groups of the periodic system are on record, but evidence of this type of oxidation in alloys of the metals of the intermediate groups is lacking. A number of the metals of the intermediate group, among them cadmium, lead, tin, and zinc, appear to provide the conditions essential to subscale formation; i.e., they form oxides with a relatively low negative free energy of formation, they dissolve other metals that form more stable oxides, and, presumably, oxygen will diffuse through them. In a study of 4o alloys of these white metals only a few cases of internal oxidation have been found. The probable reasons for this difference in behavior will be discussed presently. EXPERIMENTAL PROCEDURE Silver.-The silver alloys employed in the oxidation studies were prepared in heats of 30 grams each from high-purity silver (99.993 per cent Ag)* and the purest avail-

Jan 1, 1942

By A. H. Grobe, F. N. Rhines

AT elevated temperatures the oxide of silver is unstable in the air at atmospheric pressure, consequently no external oxide scale forms upon pure silver under conditions of high-temperature annealing When small quantities of certain alloying elements are present in the silver, the formation of a thin external scale is possible&apos; and in addition there may form a subscale composed of the oxide of the solute element precipitated within the body of the silver Norbury2 and Leroux and Raub3 have reported internal oxidation (subscale formation) in alloys of silver with 2, 7 5, and 30 per cent of copper The presence of the subscale is believed to be responsible, at least in part, for the objectionable "fire mark" in Sterling silver&apos; Several other alloys of silver, after oxidizing heat-treatments, are known to exhibit undesirable polishing characteristics that may be the result of internal oxidation Except for the absence of an external scale of silver oxide, it is to be anticipated that silver alloys will prove to be very similar in their oxidation behavior to the alloys of copper, the oxidation characteristics of which have been studied in some detail 5,6 The present research confirms this anticipation The oxidation of a series of 20 dilute alloys of silver has been studied metallographically, some types of subscale not encountered among the copper alloys have been found Instances of internal oxidation in alloys of most of the metals of the I-b and VIII groups of the periodic system are on record, but evidence of this type of oxidation in alloys of the metals of the intermediate groups is lacking A number of the metals of the intermediate group, among them cadmium, lead, tin, and zinc, appear to provide the conditions essential to subscale formation, i e , they form oxides with a relatively low negative free energy of formation, they dissolve other metals that form more stable oxides, and, presumably, oxygen will diffuse through them In a study of 4o alloys of these white metals only a few cases of internal oxidation have been found The probable reasons for this difference in behavior will be discussed presently EXPERIMENTAL PROCEDURE Silver -The silver alloys employed in the oxidation studies were prepared in heats of 30 grams each from high-purity silver (99 993 per cent Ag)* and the purest avail-

Jan 1, 1942