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Open Pit Porphyry Copper Mine-Block Inventory Update For Production PlanningPURPOSE OF UPDATED ESTIMATE FOR MINERAL INVENTORY BLOCKS During the production stage of an open pit porphyry copper mine it was observed that the expected production grade, as determined from the block inventory estimates, often differed greatly from the head grade of ore delivered to the mill. It was determined that, for purposes of production scheduling and monthly forecasting, better in situ grade estimates for mining blocks were necessary. Because all of the bench blastholes were being sampled, and periodic holes were being drilled into the next underlying bench, much more sample data existed than was being used for estimating the grade of nearby mining blocks. It was reasoned that, by periodically updating the mineral inventory block file over the benches scheduled for mining in the next time period using all existing data, better estimates and forecasts for production grade could be made. BLASTHOLE SAMPLE DATA MANAGEMENT The collars of all blastholes in each mined bench were surveyed and assays run on the cuttings representing the full 12-m (40-ft) bench height. The blastholes range from about 5 to 6 m (16 to 19 ft) apart along the front of the bench as well as perpendicular to the front. Overbreakage often left larger spacings between successive blasts. Fig. 17-1 is a plan map of blastholes on a typical mine bench. All blasthole data were keypunched to a format resembling that of the 12-m (40-ft) composite assay data file as follows: [Collar Coordinates Compite Assoy Hole ID Northing East Elewotion Total Copper Oxide Copper] Because of the many blasthole samples available, and in order not to use excessive computer time for running kriged estimates for 30.5 X 30.5 X 12-m (100 X 100 X 40 ft) blocks adjacent to and beneath the mined area, the decision was made to average all the blastholes falling with each 15.2 X 15.2-m (50 X 50-ft) mined block, and use the mean value of the samples as a regionalized variable for purposes of assigning kriged estimates and estimation variance to adjacent unmined blocks. In other words, instead of using individual blasthole samples for making kriged estimates, the holes were grouped by blocks and assay values were averaged and assigned to the centroid of the holes within the block, which was then treated as a single regional variable for purposes of kriging. See Fig. 17-2. VARIOGRAM COMPUTATIONS AND KRlGlNG RESULTS With the many blasthole samples it was possible to compute directional and vertical experimental variograms for both sulfide and nonsulfide copper assays falling within the enriched mineral zone for the full 12-m (40-ft) sample support. Due to the close spaced drilling, excellent definition of the experimental variograms was possible, and the spherical model exhibited good fits. A three-dimensional kriging program was then run over the two or three mine benches involved in the inventory update, and estimated grades reassigned to all mining blocks falling within the range of the new blasthole assay data according to the anisotropisms of the deposit. Better confidence limits could then be assigned to scheduled mining blocks and better short- range forecasts made. An interactive kriging computer program was also applied for the purpose of determining the kriging variance or estimation of error for larger, irregular mining blocks representing the monthly production from a particular bench. The interactive program permitted the operator to enter the limits of the irregular block onto the screen of a cathode ray tube (CRT) as a series of points around the perimeter of individual gridded blocks making up the larger irregular block. The computer then was programmed to calculate the kriging variance of the larger block using all samples fall- ing within range. Thus the limits of estimated grade could be established at any confidence level. Fig. 17-3 illustrates the output from the interactive kriging program showing the sample points entering into the grade and kriging variance computations, and also the kriging coefficient assigned by the computer to each sample.
Jan 1, 1980
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Geophysics - Significance of Geochemical Distribution Trends in SoilBy D. H. Yardley
GEOCHEMICAL investigation of trace elements in surface materials was begun near Ely, Minn., in 1953 along the basal contact of Duluth gabbro with Giants Range granite (Fig. 1). This article presents data on the distribution of copper and nickel in till and in stream sediments in the area and proposes an explanation for the types of distribution found. The Duluth gabbro, one of the world's largest basic intrusives, intrudes rocks which range in age from Keewatin to middle Keweenawan. Within the test area the gabbro is in contact with granite except for short sections where it is in contact with remnants of iron formation. Sulfide mineralization occurs within the gabbro, near and parallel to the basal contact for a distance of several miles. Schwartz and Davidson' have described the geologic setting of the mineralization. The sulfides, believed to be syngenetic, include chalcopyrite, cubanite, pentlandite, pyrrhotite, and minor amounts of bornite. They occur disseminated in the silicates and as small interstitial masses. The ratio of copper to nickel is about 3.8:1, based on 66 chemical analyses of rock samples from various outcrops (Ref. 1, p. 702, and Ref. 2). Test Procedures: With specified exceptions, all nickel and copper tests were made by the chromo-graph method,:' which measures the intensity of a colored spot formed by a reaction between the metal being determined and special reagent paper. The intensity is then compared to the intensity of spots prepared from samples of known metal content. Details of the test procedure are outlined in another article (Ref. 4, pp. 77,78). All soil samples tested in this investigation to date have been weighed on an analytical balance. However, a volumetric scoop designed to provide about 0.1 g of soil adds to the speed and ease of testing and has been found to give satisfactory results (Ref. 5, p. 531, and Ref. 19). The size of the samples used for the tests was 0.1 g. Whenever such small samples are used there is some question as to whether they are representative of the several grams in the field sample. Many repeat tests of the samples used in this investigation demonstrated that results can be reproduced within the limits of accuracy of the method without formal mixing beyond that inherent in screening the soil fractions. Furthermore, the 0.1 g is probably as representative of the field sample as the field sample is of its area of influence. Hawkes and Lakin (Ref. 6, p. 291), who considered the general problem, compared ground and quartered bulk samples of 500 g with 5-g grab samples. They concluded that "there is no significant loss in accuracy of data by substituting grab samples for bulk samples." The term soil implies somewhat different things to the geologist, engineer, and soil scientist.' For convenience the term as used in this article refers to unconsolidated material (the mantle) overlying bed rock. Sampling Procedure: Samples were taken at 100-ft intervals along north-south traverse lines across the gabbro-granite contact. The soil (till) samples were taken at an average depth of 1 ft, which was below the high-humus surface layer and into clean till. Samples taken at 1-ft intervals down to ledge showed as high a metal content at 1 ft below the air-surface as at greater depths and in two instances were slightly higher. The till at 1-ft depth did not appear to differ from material at greater depths. Total depth to bedrock has been tested at only a few points and where measured varied from 1 to 10 ft. Aerial Distribution Contours and Profiles: Plotting of copper, nickel, and cobalt content in contour form (Fig. 2) shows that anomalous amounts of these metal ions occur in till over and closely adjacent to mineralized areas of the gabbro. Contouring nickel content alone, or the copper content, outlines the same target area. Contours of the copper content provide a more distinct anomaly than nickel because of the higher copper concentration. The traverses are rather widely spread for interpolation; however, drilling has confirmed the target area essentially as shown.
Jan 1, 1959
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Institute of Metals Division - Creep-Rupture Characteristics of Al-Mg Solid-Solution AlloysBy N. J. Grant, A. W. Mullendore
Three aluminum alloys of 0.94, 1.92, and 5.10 pct Mg, prepared from very high purity metals, were tested at 500°, 700°, and 900°F in creep rupture. The degree of strengthening through solid-solu-tion alloying and the effects on the deformation characteristics and fracture were examined. The ductility of the alloys as a function of stress and temperature was closely followed. STUDIES of the creep process in pure metals in recent years have done much to expand the understanding of the fundamental deformation and recovery processes that contribute to overall creep behavior. In order that this knowledge may be applied to commercial alloys, it is necessary to know the principles governing the effect of alloying on the mechanisms of creep. A limited amount of work has been performed in this field, but few investigators have attempted to follow the changes in particular creep mechanisms with alloying. Recently, studies of the effects of solid-solution alloying on the plastic properties of aluminum have been conducted by Dorn, Pietrokowsky, and Tietz,1 Sherby, Anderson, and Dorn,2 and Sherby and Dorn.3 This paper presents the results of an investigation of the effect of solid-solution alloying of high purity aluminum with magnesium on the creep-rupture properties, and correlates these observations with changes in the creep mechanisms. This work is thus an extension of the creep-rupture observations of Servi and Grant4,5 and the deformation studies of Chang and Grant.6,7 Experimental Procedure Three alloys of aluminum containing approximately 1, 2, and 5 pct Mg were tested. These alloying additions are all within the solid-solubility limit at the testing temperatures.' The analysis of the materials is presented in Table I. The tests fall into two categories: l—creep-rup-ture tests at 500°, 700°, and 900°F, and 2—structure study tests performed primarily at 700°F. Speci-mens of 0.160 in. diameter with milled flats for metallographic observations" ' were utilized for the structure studies. All specimens were annealed in one step to give the desired grain size for the tests. Table II presents the annealing data and final grain sizes. The specimens were polished electrolytically before testing with Jacquet solution (2/3 acetic anhydride, 1/3 perchloric acid) at 25" to 30°C, and 15 to 20 v. Creep-rupture testing was performed under constant load with the apparatus previously described." Results and Discussion Creep-Rupture Properties: The log-log plots of creep-rupture data are presented in Figs. 1 and 2. For these very pure single-phase alloys, the minimum creep rate and the rupture life both exhibit straight-line dependence on stress in this method of plotting as they have for commercial alloys0,10 and for pure aluminum." Curve breaks, based on the use of straight-line segments, at 500°F have been found by metallographic study to correspond to a transition from low to high temperature behavior and so represent zones of equicohesion. Specimens on the high creep-rate side of the break showed normal granular deformation processes whereas those on the low creep-rate side showed rapidly increasing grain-boundary sliding and migration with extensive evidence of intercrystalline cracking at 500°F. Two micrographs of the 0.94 pct Mg alloy, Fig. 3, show the increased participation of the grain boundary in the deformation process at 500°F with decreasing stress. In Fig. 3a is shown the structure of a specimen which exhibits little deformation along the grain boundaries and failed transgranularly; in Fig. 3b is shown the increased deformation along the grain boundaries at a lower stress for a specimen which showed appreciable intercrystalline cracking. The severity of intercrystalline cracking increased with increasing magnesium content at 500°F. Intercrystalline cracking disappeared in most of the specimens at 700°F and persisted only in the 5 pct Mg alloy at high creep rates. At 900°F all of the specimens deformed with extensive grain-boundary participation, including extensive grain-boundary migration. None of the alloys at 900°F showed intercrystalline cracking.
Jan 1, 1955
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Part IX – September 1969 – Papers - Effect of Crystallographic Orientation on the Surface Free Energy and Surface Self-Diffusion of Solid MolybdenumBy B. C. Allen
Surface free energy and surface self-diffusion of solid molybdenum were studied in the temperature range 1600" to 2400°C using pressure-sintered bi-crystals. Comparison of groove angles formed in various surfaces perpendicular to the grain boundary indicate a maximum of 1 pct variation in surface free energy with crystallographic mientation. This anisotropy tends to decrease with increasing temperature. The surface diffusion of the bicrystals is equivalent to that of sheet with a mild (100) Preferred orientation. Anomalously low values found for bi-crystals with surface orientations of (OOl), (012), and (011) are rationalized in terms of anisotropy in surface free energy. THE effect of crystallographic orientation on surface free energy1,' and surface self-diffusion3,4 has been primarily studied in fcc metals. The object of this work was to study the effect of orientation on surface diffusion and surface free energy of bcc molybdenum using pressure-sintered bicrystals. EXPERIMENTAL WORK Materials and Crystal Preparation. Arc-melted molybdenum rod was obtained commercially and electron beam zone refined at 50 cm per hr at 10- 5 torr to form single crystals about 8 cm long and 0.65 cm diam. Three crystals were prepared with axial orientations about 1 deg from [001.], [011], and. [111]. To reduce the carbon content, the crystals were annealed 2 hr in 1.4 atm flowing wet hydrogen at 2050°C. Then the oxygen content was reduced by annealing for 2 hr in -30°C dewpoint hydrogen at 2020°C. The resulting impurity analysis is given in Table I. Bicrystal Preparation. The single crystal rods were cut into transverse slices with a thin silicon carbide abrasive wheel to produce specimens about 0.6 cm long. They were mounted in epoxy and surrounded by stainless steel washers. Cutting in half was done longitudinally at various angles to known crystallographic planes containing the cylinder axis according to Fig. 1. To reduce surface deformation resulting from the cutoff wheel and thus reduce parasitic grain boundary formation on subsequent annealing, about 0.003 cm was manually ground off each cut surface with 600 grit paper. Care was taken to keep the surface flat. After removal from the mounts, one half was generally ro-tated 180 deg with respect to the other to give a po- tential symmetrical tilt grain boundary between the two halves. In the other cases when low misorienta-tion angles were desired, the crystals were not rotated. On the basis of symmetry, sufficient bicrystals were prepared to cover the entire range of misorientations for symmetrical tilt boundaries. The misorientations, +, ranged from 0 to 45, 0 to 90, and 0 to 60 deg for [001], [011], and [111] bicrystals, respectively. One [Ill] twist bicrystal was prepared from 2 single crystal discs rotated 17 deg relative to each other. Each specimen consisted of two pieces which were placed in a cylindrical tantalum can. Sharp edges were rounded and the fit was made as snug as possible to reduce subsequent deformation during bonding. The assembly and crystals generally were vicuum outgassed at 900" or 1700°C and then electron beam welded in the can at l x 10-4 torr. After being leak checked, the samples were placed in an autoclave and hydrostatically gas-pressure bonded5 in four batches under helium at 10,000 to 18,000 psi at 1650°C for 3 hr. Satisfactory bonds were obtained in many cases, and most of the crystals bonded after two exposures. The results did not appear to be affected by the various pressures used, preannealing conditions, crystal orientation, or time-pressure-temperature route taken to the final bonding condition. After bonding, the tantalum cans were selectively removed in cold concentrated HF. Measurements indicated overall deformation was under 1 pct. The bicrystals were metallographically ground and polished flat and perpendicular to the axis. Examination showed the boundaries were straight and almost free of parasitic grains caused by extraneous local deformation. Annealing. In preparation for thermal grooving, the bicrystals were cleaned and annealed by outgassing at 10-5 torr at 1900°C and heating at 2300°C under 1 atm 99.996 Ar for 0.5 hr. The crystals were held in a closed 4-deck box made of molybdenum sheet, and were heated in a Ta-1OW resistance furnace. The ar-
Jan 1, 1970
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Institute of Metals Division - Ignition Temperatures of Magnesium and Magnesium Alloys - DiscussionBy Leonard B. Gulbransen, John R. Lewis, W. Martin Fassell, J. Hugh Hamilton
T. E. Leontis (The Dow Chemical Co., Midland, Mich.)—This paper is of particular interest to me because of my own work with F. N. Rhines on the oxidation of magnesium and magnesium alloys a few years ago. The authors are to be complimented on their development of an accurate and reproducible technique for measuring ignition temperatures and on their comprehensive study of the many variables that affect the ignition temperature of magnesium. It is indeed gratifying to see that they have obtained a good correlation between ignition temperatures and the oxidation rates reported by us. The correlation is valid not only with composition within one alloy system but also between alloy systems; that is, alloying elements which effect the greatest increase in oxidation rate also produce the greatest decrease in ignition temperature. There are a few points upon which I would like to comment. In attempting to correlate ignition-temperature data, one must be sure that the same definition of this quantity is used by all investigators. It does not appear to me that such is the case in the authors' comparison of their data with the theoretically calculated values of Eyring and Zwolinski. The equation derived by these investigators defines the ignition temperature, To, as the temperature at the gadoxide interface, whereas the present authors use the metal temperature as the criterion for ignition. The contradiction in the effect of oxide-scale thickness on ignition temperature between the predictions of the Eyring-Zwolinski equation and the observations reported in this paper indicate that some variable has not been taken into consideration. Could that be the geometry and size of the specimen? There is a marked difference in the type of specimen used in this investigation and that used in our work which formed the basis of Eyring and Zwol-inski's theoretical treatment. Another factor which plays an important role in ignition is the vapor pressure or the rate of vaporization. Combustion can safely be assumed to take place in the vapor phase by the reaction between vaporized magnesium and oxygen. Thus, a more accurate theoretical analysis may be made on the basis of the rate of vaporization which may be the controlling rate of the process. The effect of a large number of alloying elements on the ignition temperature has been reported in this paper, but beryllium was not included. Practical experience dictates that beryllium markedly decreases the burning tendency of magnesium. I was wondering if the authors plan to study the effect of beryllium in their future work. The authors predict that concentrations of sulphur dioxide in the furnace atmosphere greater than 5.8 pct would be expected to increase the ignition temperature to values still higher than those they measured. I would like to mention that large concentrations of sulphur dioxide markedly increase the rate of combustion of magnesium once ignition has started. Although it has been shown in the paper that the ignition temperature of magnesium in oxygen increases with increasing sulphur dioxide content up to about 1 to 2 pct, in practice relatively low-melting commercial cast alloys (AZ63A and AZ92A) are being continuously heat treated at temperatures just below the melting point in air containing 0.5 to 0.75 pct SO*. In regard to the change in color of the oxide scale observed on magnesium and magnesium alloys just prior to ignition, I would like to mention that in our work alloying elements were found to color the usually white magnesium oxide even though ignition did not occur. For example, the oxide formed on Mg-A1 alloys was gray, increasing in intensity with aluminum content in the alloy. Finally, I might suggest that the authors indicate their source of the value of 0.8 g per cc for the density of MgO as it is formed on magnesium upon oxidation at elevated temperatures. W. M. Fassell, Jr. (authors' reply)—The comments by Dr. Leontis are very excellent ones and I will attempt to answer them in order. First, the problem of ignition of magnesium is a rather difficult one since many factors are involved. Concerning the comparison of the To in the Eyring-Zwolinski equation, eq 4, with the experimentally determined values, it will be noted that the calculated and experimental values of the ignition temperature in Table I are not self-consistent. In the case of the 1.78 pct A1-Mg alloy the calculated value is 49°C below the experimental value; for the 3.81 pct A1-Mg alloy, 122°C below the experimental value; for Mg with 5x10-' cm film, 19°C above the experimental value; for Mg with 2x10-I cm film, 28 °C below the experimental value. Thus, if it were merely a matter of difference of location of temperature measurement the calculated ignition temperature would always be below the experimental value, the difference being due to the thermal gradient through the oxide film. The possibility of a thermal gradient in the magnesium metal must be considered. From Carslaw and Jaeger,'Y t can be shown that the maximum temperature gradient that could exist between the oxide-metal interface and the center of the sample is of the order of O.Ol°C. The geometry and size of the specimen could certainly have some effect on the ignition temperature. The equation for ignition that has been proposed in reference 14 is of the following type containing terms to account for this and other factors: M dT AHv(T) =Cp--------------\-J(.T—TB) + ZAHl-M A dx where AH is the heat of reaction, v(T) is the velocity of the reaction at temperature, Cp is the heat capacity of sample, M is the mass of sample, A is the area of sample, t is time, J is the total coefficient of heat transfer outward from the reaction zone, TR is the temperature of the bath or furnace, and AH,, is the heat associated with any phase change involved. Prior to the instant of ignition, the vapor pressure of magnesium is of no special significance. After ignition, neither eq 4 nor the above equation is applicable. The actual combination of magnesium cannot safely be assumed to take place in the vapor phase. While experimental data is lacking to support a hypothesis that ignition does or does not occur in the vapor phase, some observation on the pressure ignition experiments may be of interest. At high oxygen pressures, once ignition has occurred, the reaction of magnesium with oxygen approaches near explosive violence, the entire sample being consumed in probably less than 1 sec. At atmospheric pressure it usually requires 15 to 20 sec. Thus it appears that the oxygen concentration becomes the rate determining factor. Further, if burning magnesium is observed through darkened glass (Lincoln Super-visibility Shade No. 12) the magnesium sample is very much hotter than the "smoke" and the outline of the sample is retained perfectly. No "flame" is visible above the metal. No work was done on Mg-Be alloys. We do, however, intend to study this problem in the near future.
Jan 1, 1952
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Part IV – April 1969 - Communications - Study of X-ray Line Breadths in Some Fcc Metals Quenched from the MeltBy P. Ramachandrarao, T. R. Anantharaman
EVER since the technique of quenching metals and alloys from the melt (splat cooling) was perfected a decade ago, it has been recognized that the grain size of products solidified by this technique may be extremely small.' The further observation that fcc metals quenched from the liquid state contain very few dislocations has led to the inference2 that metals are subjected to negligible or no stresses during the rapid solidification characteristic of the "gun" or "piston-and-anvil" technique. Evidence for the incidence of appreciable densities of stacking faults has, however, been obtained in case of some splat-cooled fcc and hcp alloys,3 although not for pure metals. In the light of these earlier observations it was considered desirable to study X-ray line-broadening effects, if any, in fcc metals rapidly cooled from the melt. In the present work pure silver (>99.99 pct), aluminum (>99.99 pct) and lead (>99.9 pct) were quenched from the liquid state from temperatures about 50°C above the melting point by the "gun technique" and the resulting foils were subjected to X-ray examination in a Philips Diffractometer. The quenched foils (up to -10 u thick) did not generally stick to the substrate surface and could be easily transferred to the Diffractometer without introducing any plastic deformation. The profiles of the first five reflections from the foils were recorded in each case with Cu Ka, radiation at the slowest available scanning speed of 1/8 deg per min. To correct for instrumental broadening, profiles were also recorded from the metals annealed in vacuo at suitable temperatures. The integral breadths of the X-ray reflections were arrived at by a procedure described earlier.' There was a distinct suggestion of preferred orientation in the recorded intensities of reflections from aluminum and lead foils. Such an effect was not observed in case of silver. In addition, the integral breadths of X-ray reflections from splat-cooled aluminum and lead were not significantly different from those recorded for the annealed metals. The analysis was therefore continued only for silver where the X-ray line broadening was appreciable. The pure diffraction broadening, B, was evaluated for each X-ray reflection (hkl) from silver from the observed, B, and instrumental, b, breadths with the aid of each of the three equations due to Scherrer,5 Anantharaman and Christian,6 and Warren and Biscoe,7 respectively: Bs= B-b BAC=B- b2/B Table I gives the values of particle size, 71, the lattice strain, E, arrived at by the use of the following well-known relations and on the assumption that all observed diffraction broadening could be attributed to lattice strain or particle size, respectively: E = 1/4 cos ? n= B cos ? where A is the wavelength of X-radiation and 0 is the Bragg angle. As no significant peak shifts or asymmetry could be detected in the profiles from the foils, the possibility of any significant contribution due to twins or stacking faults was ruled out. The absence of faults is by no means surprising since pure silver is known to develop stacking faults only on severe deformation and the stacking fault densities recorded so far for even silver filings have been extremely low.' The very low values for percentage mean deviation from the mean value for the particle size in Table I strongly suggest that all observed broadening in splat-cooled silver can be attributed only to small particle size. This conclusion receives further support from the lowest mean deviation recorded for data computed from the Scherrer equation based on Cauchy profiles that are considered characteristic of particle size broadening. Further analysis for separation of particle size and lattice strain effects was considered unnecessary in view of the very large mean deviations obtained for strain values and also the earlier results suggesting absence of even detectable strain in metals and alloys quenched from the melt. It is to be stressed in this connection that the particles are actually grains and not cells formed by walls of high dislocation density usually encountered in deformed samples. As such, the absence of strains is not surprising. The present results are probably the first to record X-ray line broadening due only to small particle
Jan 1, 1970
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Institute of Metals Division - Production of Submicron Metal Powders by Ball-Milling with Grinding AidsBy Charles Smeal, Robert J. Schafer, Max Quantinetz
Normally metal powders cannot be ground to sub-micron sizes because of welding and agglomeration phenomena. Through the use of selected grinding aids and grinding fluids, nickel and other metal powders have been ball-milled as fine as 0.1 It was found that certain inorganic salts are more effective grinding aids for metal powders than conventionally used surfactants. METAL and alloy powders are used to produce reagents, pigments, coatings, solders, brazes, and parts for industry by powder metallurgy techniques. They are also combined with refractory compounds to produce cermets and dispersion-hardened products. One of the interests at the Lewis Research Center has been to explore the potentialities of the dispersion strengthening process. Since the work of Ir-mann, many investigators have shown that the strength of dispersion-hardened products may increase with decreasing interparticle spacing.24 One approach to achieving small interparticle spacing is to combine fine refractory compounds and metal powders, preferably below 1 in size. In attempting to obtain fine metal powders, it was found that until very recently the best that could be obtained from commercial suppliers, particularly of ductile metals, was about 1.0 . Interest was therefore developed in providing finer metal powders for dispersion-hardening studies. Information obtained from the literature, from others working in the field, and from prior experimental work performed at NASA, led to a consideration of ball-milling as a technique to produce the desired materials. Some of the variables associated with ball-milling are the size, material, and nature of construction of the grinding container; the nature and amount of the grinding material and material to be ground; and the nature and amount of the grinding liquid and grinding aid, if employed, and the grinding time. In all ball-milling, welding and agglomeration can oc- cur as well as grinding. Because of the tendency of ductile metals to weld together, they are difficult to grind.5 The ultimate particle size obtained on grinding is generally the one at which the rate of grinding becomes equal to the rate of welding. To help delay welding and thus obtain smaller particle sizes, grinding aids are often employed. The principal objective of this investigation was to produce submicron metal powders by ball-milling the powders with selected grinding aids and grinding fluids. A secondary objective has been to attempt to explain the variations observed in grinding behavior by considering possible grinding mechanisms and correlating various parameters with grinding effectiveness. Three groups of ball-milling experiments were run; one in which the grinding aid was varied, a second in which the grinding fluid was varied, and a third in which the material being ground was varied MATERIALS, APPARATUS, AND PROCEDURE In the first group of experiments in which the grinding aid was varied Inco Carbonyl Grade B nickel powder initially 2.5 (all sizes refer to average particle size as measured by Fisher Sub -sieve Sizer) was used as the material being ground and 200-proof ethyl-alcohol as the grinding fluid. Surfactants, representative of typical organic structures, were selected as grinding aids. Inorganic salts used as grinding aids were chosen on the basis of the size and valence of their ions. Water soluble salts were used in order to facilitate their removal from the slurry after grinding. In the second set of experiments, grinding of the 2.5- Ni powder was tried in four different grinding liquids; water, cyclohexane, n -heptane, and methy-lene chloride. In this study seven grinding aids selected from those tried in the first group of experiments were employed. In the third group of experiments 200-proof ethyl alcohol was again used as the grinding fluid to mill Cu, Cr, Fe, Ag, and Ni powders of various initial particle sizes' All mill charges contained 300 ml of grinding liquid and 3000 g of 1/2 in. stainless steel balls. When inorganic salts were used as the grinding aid, 70 g of salt and 210 g of metal powder were employed, and with surfactants 6 g of grinding aid and 300 g of
Jan 1, 1962
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Industrial Minerals - Chromite and Other Mineral Occurrences in the Tastepe District of Eskisehir, TurkeyBy Ferid Kromer
Geography: The Tagtepe district of the Vilayet of Eskigehir is about 20 miles northeast of the city of Eskigehir (approximately midway between Ankara and Istanbul) in western Anatolia. The area is a mountainous one, the highest peak being Tagtepe Mountain (5200 ft) which is approximately in the center of the district. The mountains drop off to the deep valley of the Sakarya River on the north and to the plain of Eskigehir on the south. FERID KROMER, Junior Member AZME, is a Consulting Mining Engineer and General Manager, Bagtag Turk Maadin Ltd., Istanbul, Turkey. New York Meeting, February 1950. TP 2629 H. Discussion of this paper (2 copies) may be sent to Transactions AIME before Feb. 28, 1950. Manuscript received Dec. 29, 1948. For the most part, the watershed is on the northern side of the mountain barrier, draining into the Sakarya River, which in turn empties into the Black Sea midway between Zonguldak and the mouth of the Bosphorus. The approximate area covered by the Tagtepe district is shown in fig. 1. Transportation to shipping points is available via the Istanbul-Ankara railroad. The station on this line nearest the mining district is Alpikoy station, about 20 miles by road southwest of Tagtepe Mountain. Interior roads within the district are poor. Being of dirt, the winter rains and snows render them almost impassable for trucks from about the middle of December until the end of March, thus presenting a considerable transportation problem. However, the roads from the Bagoren and Tagtepe chromite mines to the railroad shipping point at Alpikoy station have recently been repaired and will be maintained for all-weather truck transportation. Detailed climatic data are not available. However, in general the spring, summer, and early autumn months are dry, and good weather may be expected from May until early November. Then the winter rains commence, and heavy snow is usual during January and February. Geology: The mountainous structure of Tagtepe belongs to basic rocks of serpentine (Variscan Orogeny) which is in contact with Paleozoic schists at west, and an Oligocene outcrop of red clays in Margi-Sepetci region (see fig. 1) at southeast. The northwest and southwest borders of Tagtepe district are, respectively, surrounded by Paleozoic schists and pebbly gray and yellow Neogene clays. More recent formations of alluviums overlay the plain of Eskigehir. Dark basic rocks of trachytes with hornblende are visible on Turkmenbaba Mountain, at the west of Tagtepe. Mineral Occurrences: Chromite: the most important mineral found in any quantity in the Tagtepe district. The alignment of the deposits of chromite is in general along the line Bagoren-Tagtepe (see fig. 1). The first mines in the area were those of Tagtepe and Bagoren, which were developed over 20 years ago with Swedish capital. Other deposits of chromite, more recently discovered and so far of less importance, are being worked at Kurucor, Komurcu, Gelinmezari, and Lacin (see fig. 1). Deposits average generally between 46 and 48 pct chromic oxide, with the exception of the Bagoren mine which averages 44 pct. However, a new lode, very recently plotted, in the Tagtepe mine averages 50 pct Cr,O,, 4.6 pct SOz, and 7 pct FeO. Geological character of the chromite occurrences in the Tagtepe mine may be considered typical of most chromite lodes in this area. The indications are that the formations of ore lenses are developed by the segregation of chromite crystals intruded into the serpentinized rock, and exposed later to tectonic movement within the zone of crystallization. All lenticular masses are more or less regular in shape and follow each other in southeast-northwest direction and dip generally 70" NE. Ore lenses do not seem to persist in depth, average depth of two lenses is 60 ft below surface. Three lodes .have been mined as open-pit. The average dimensions of individual lenses are as follows: pitch length, 100 ft; breadth, 27 ft; and width, 20 ft. The lenses and their enclosing rocks are broken by parallel fractures in approximately east-west direction. These joints are filled, except in one lode, with cementing material, which gives to the ore a
Jan 1, 1951
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Industrial Minerals - Chromite and Other Mineral Occurrences in the Tastepe District of Eskisehir, TurkeyBy Ferid Kromer
Geography: The Tagtepe district of the Vilayet of Eskigehir is about 20 miles northeast of the city of Eskigehir (approximately midway between Ankara and Istanbul) in western Anatolia. The area is a mountainous one, the highest peak being Tagtepe Mountain (5200 ft) which is approximately in the center of the district. The mountains drop off to the deep valley of the Sakarya River on the north and to the plain of Eskigehir on the south. FERID KROMER, Junior Member AZME, is a Consulting Mining Engineer and General Manager, Bagtag Turk Maadin Ltd., Istanbul, Turkey. New York Meeting, February 1950. TP 2629 H. Discussion of this paper (2 copies) may be sent to Transactions AIME before Feb. 28, 1950. Manuscript received Dec. 29, 1948. For the most part, the watershed is on the northern side of the mountain barrier, draining into the Sakarya River, which in turn empties into the Black Sea midway between Zonguldak and the mouth of the Bosphorus. The approximate area covered by the Tagtepe district is shown in fig. 1. Transportation to shipping points is available via the Istanbul-Ankara railroad. The station on this line nearest the mining district is Alpikoy station, about 20 miles by road southwest of Tagtepe Mountain. Interior roads within the district are poor. Being of dirt, the winter rains and snows render them almost impassable for trucks from about the middle of December until the end of March, thus presenting a considerable transportation problem. However, the roads from the Bagoren and Tagtepe chromite mines to the railroad shipping point at Alpikoy station have recently been repaired and will be maintained for all-weather truck transportation. Detailed climatic data are not available. However, in general the spring, summer, and early autumn months are dry, and good weather may be expected from May until early November. Then the winter rains commence, and heavy snow is usual during January and February. Geology: The mountainous structure of Tagtepe belongs to basic rocks of serpentine (Variscan Orogeny) which is in contact with Paleozoic schists at west, and an Oligocene outcrop of red clays in Margi-Sepetci region (see fig. 1) at southeast. The northwest and southwest borders of Tagtepe district are, respectively, surrounded by Paleozoic schists and pebbly gray and yellow Neogene clays. More recent formations of alluviums overlay the plain of Eskigehir. Dark basic rocks of trachytes with hornblende are visible on Turkmenbaba Mountain, at the west of Tagtepe. Mineral Occurrences: Chromite: the most important mineral found in any quantity in the Tagtepe district. The alignment of the deposits of chromite is in general along the line Bagoren-Tagtepe (see fig. 1). The first mines in the area were those of Tagtepe and Bagoren, which were developed over 20 years ago with Swedish capital. Other deposits of chromite, more recently discovered and so far of less importance, are being worked at Kurucor, Komurcu, Gelinmezari, and Lacin (see fig. 1). Deposits average generally between 46 and 48 pct chromic oxide, with the exception of the Bagoren mine which averages 44 pct. However, a new lode, very recently plotted, in the Tagtepe mine averages 50 pct Cr,O,, 4.6 pct SOz, and 7 pct FeO. Geological character of the chromite occurrences in the Tagtepe mine may be considered typical of most chromite lodes in this area. The indications are that the formations of ore lenses are developed by the segregation of chromite crystals intruded into the serpentinized rock, and exposed later to tectonic movement within the zone of crystallization. All lenticular masses are more or less regular in shape and follow each other in southeast-northwest direction and dip generally 70" NE. Ore lenses do not seem to persist in depth, average depth of two lenses is 60 ft below surface. Three lodes .have been mined as open-pit. The average dimensions of individual lenses are as follows: pitch length, 100 ft; breadth, 27 ft; and width, 20 ft. The lenses and their enclosing rocks are broken by parallel fractures in approximately east-west direction. These joints are filled, except in one lode, with cementing material, which gives to the ore a
Jan 1, 1951
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Industrial Minerals - Water Use in the Mineral IndustryBy A. Kaufman
More than 3 trillion gal of water are used annually by the mineral industry. Of this, approximately 21/2 trillion gal are recirculated, the rest constituting intake water. The major users are natural gas processing plants and phosphate rock, sand and gravel, and iron ore producers. Water was used by the mineral industry for mining (6%), processing (64%), cooling and condensing (27%), and miscellaneous uses such as boiler feed and sanitary purposes (3%). Whereas total water use is dependent on the quantity of material processed and on the particular process requirements of an industry, recirculation is dependent on processing, as well as cooling and condensing requirements, quality of new water intake, and the necessity for treating new and discharged water. Consumed water, on the other hand, is dependent on the quantity of water recirculated, and temperature and humidity in the area. Based on this analysis, an increase in water use by the mineral industry of 21/2 times by 1985 is forecast. Wster intake, however, will only rise 62%, because of a substantial increase in recirculation. In one report of a special series concerning the water resources of the United States, the Senate Select Committee on National Water Resources, 87th Congress, estimated that water demand would double by 1980 and triple by 2000.' In view of the possible water deficiencies that might result from such expanded usage and the need for research guidance, the Bureau of Mines organized and carried out a statistical canvass of water use in the mineral industry for calendar year 1962. The data used in this paper, unless otherwise noted, are derived from that canvass.' The efforts in this paper are devoted toward summarization of the canvass and analysis of the data. SOME DEFINITIONS Intake: Water introduced from an external source for the first time into a given mine or plant regardless of quality. Intake water is also called new water, water withdrawn, or makeup water. Fresh Water: Water suitable for cooking and drinking. Saline Water: Water containing more than 1000 parts per million of dissolved solids. Contaminated Water: Water not suitable for domestic use, but excluding saline water. Recirculated Water: Water reused to conserve intake water. Solutions that are recycled primarily because of fixed metallurgical practices, such as copper leaching solutions containing sulfuric acid, are excluded. Gross Water Used: Recirculated water plus intake water. Also called total water used. Consumed Water: Water that is lost by evaporation, as well as water lost in product. Seepage and transferred water are not considered consumed. The use of either intake or recirculated water may result in consumption. However, because of difficulties in measuring consulmption, consumed water is defined as the residual between intake and water discharged from the mine or plant. Mineral Industry: For the purposes of this paper, mineral industry includes all metal and nonmetal surface and underground mines and their associated processing plants, as well as custom mills, coal washing plants and associated mines, petroleum and natural gas well drillers, natural gas processing plants, and secondary recovery operations. WATER USE IN THE MINERAL INDUSTRY Water used by the mineral industry constitutes a relatively minor fraction of the water withdrawn by all users. Data compiled by the U.S. Geological Survey in 1960 indicate that water withdrawals, exclusive of that used to generate hydropower, approximate 99 trillion gal annually.3 Our data indicate that water withdrawals by the mineral industry comprise only 1% of this total, or 2% of the water withdrawn by industrial users. Use by Industry: Water used by various mineral industries is shown in Table I. The table indicates that close to one-half of the gross water used by the mineral industry in 1962 was used by natural gas processing plants, followed by sand and gravel, phosphate rock, and iron ore producers. The largest aggregate users of water are also the largest users per dollar of product. For example, Fig. 1 shows that the natural gas processing and phosphate rock industries are very large users of water per dollar of product. Their recirculation per
Jan 1, 1968
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Part XII - Papers - Characteristics of Beta - Alpha and Alpha - Beta Transformations in PlutoniumBy R. D. Nelson, J. C. Shyne
The ß and a ß transformations in plutonium were studied with particular emphasis on the transformation kinetics and microstructure. Significant observations are: 1) The kinetic data show conclusively that the ß — a transformation in high-purity plutonium can proceed isothermally with no athermal component. 2) Plastic deformation of the stable (3 phase retards the subsequent (3 — a transformation. 3) Plastic deformation of the stable a phase accelerates the a — ß transformation; the acceleration is attributed only to residual stresses. 4) The a and a?a volume changes occur anisotroPically in textured plutonium. 5) An apparent crystallogvaphic relationship exists between the parent and the product phases of the and (3 — a transformations. 6) Both applied uniaxial compressive stresses and uniaxial tensile stresses raise the starting temperature for the ß — a transformation. 7) A given uniaxial tensile stress favors the a — ß transformation more than an equivalent applied uniaxial compressive stress opposes the transformation. These observations of the (ß —a and a — ß phase changes in plutonium are consistent with known mar-tensitic transformations. ThIS paper elucidates some of the characteristics of the a— ß and ß —a transformations in plutonium. Because considerable conjecture exists about the mechanisms by which the phase transformations occur in plutonium, experiments have been performed to provide indirect information concerning the mechanisms responsible for the a —ß and ß -a transformations. Indirect information is of particular value in the study of plutonium because of the experimental difficulties presented by the metal. Single crystals have not been produced in any of the allotropes. The large density results in high X-ray and electron-absorption factors and consequently complicating X-ray and electron diffraction. The kinetics of ß — a and a — ß transformations of plutonium and the behavior of the transformations under a variety of conditions have been investigated in detail. Information about the mechanisms of the allo-tropic transformations of plutonium was obtained indirectly from three sources: 1) the effect of plastic deformation of the stable parent phase upon the transformation kinetics; 2) the behavior of the metal transforming under applied stresses; and 3) the microstruc-tural and crystallographic features between parent and product phases. PHASE-TRANSFORMATION CHARACTERISTICS In characterizing solid-state phase transformations in metals and alloys, it is useful to define several types of transformations. An aim of the present work was to identify the low-temperature transformations in plutonium by type, i.e., as martensitic or nonmar-tensitic. Practical definitions for these terms follow. The terms commonly used to categorize phase transformations lack universally accepted definitions. This confusion arises doubtlessly because some terms specify crystallographic or morphological character while other words have a kinetic or a thermodynamic connotation. For example, martensitic specifies certain definite crystallographic restrictions. Unfortunately, martensitic is sometimes used in an ill-defined way to imply kinetic characteristics. Further confusion attends the use of such expressions as nucleation and growth, diffusional, and massive. From time to time new systems of phase-transformation nomenclature are suggested; unfortunately none of these has gained general acceptance.1,2 The authors of the present paper have no intention of entering the controversy. We recognize that some readers may object to the nomencliture used here. For exampie, the terms military and civilian have recently been used in much the same way as martensitic and non-martensitic are used in this paper. This paper is intended to describe several specific details of the low-temperature phase transformations in plutonium. The authors have found it useful to identify these transformations as martensitic; the term was chosen as the best available to describe the experimentally observed features of the transformations studied. A martensitic transformation is one that occurs by the cooperative movement of many atoms; the rearrangement of atoms from parent to product crystal structure occurs by the passage of a mobile semico-herent growth interface. The geometric features characteristic of a martensitic transformation are a specific orientation relationship between the product and parent phase lattices, a specific habit-plane orientation for the growth interface, and a shape change with a specifically oriented shear component. There is no alloy partition between the parent and product phases in a martensitic transformation. Martensitic transformations may display either athermal kinetic behavior or thermally activated isothermal kinetic behavior. Some martensitic transformations occur isothermally, although more commonly martensitic transformations are athermal. Isothermal martensitic transformations are suppressible by rapid cooling. In athermal martensitic transformations, nucleation and growth are not thermally activated and the transformations are essentially time-independent. Nucleation, growth, or both can be thermally activated in isothermal martensitic reactions. Transformation of the parent phase into a marten-
Jan 1, 1967
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Institute of Metals Division - Mercury-Induced Crack Formation and Propagation in Cu-4 Pct Ag AlloyBy Irving B. Cadoff, Ernest Levine
The crack formation and propagation in the single -phase Cu-4 pct Ag alloys were studied. The alloys were loaded in mercury to various stress levels, the mercury was removed, and the specimen examined for cracks. Cracks were found to develop below the fracture stress; the frequency of such cracks increased with increasing stress level. Some cracks were nmpropagative. Fracture in mercury was found to occur by the link-up of cracks formed at various stress levels rather than by the growth and propagation of a single crack. If the mercury environment is removed prior to a critical amount of crack formation, then continued loading results in ductile fracture. The appearance of the cracks at selected grain boundaries is related to the relative orientation of the boundaries, as are the propaga-tive characteristics of the crack. The mercury interaction appears to be one of lowering the strength of the metal-metal bonds in the high-stress area of the grain boundary. GRIFFITH'S microcrack theory1 proposed a critical crack size above which a crack in an elastic material grows with decreasing energy at a stress of From his theory it was proposed that the presence of a liquid tends to lower the surface energy of the microcrack faces2 leading to a decrease in the critical crack size necessary for spontaneous fracture propagation. stroh3 proposed that the stress concentration at a grain boundary due to pile-up may initiate a microcrack at the grain boundary. petch4 and Stroh5 evaluated the stress distribution at the head of a pile-up in a polycrystal-line material and deduced that the critical crack size and hence of is dependent on the grain size. Experimental verification of this dependence was found by petch6 for hydrogen embrittlement of steel. Studies in stress-corrosion cracking7 have provided a picture of fracture which shows that initial separations occur in a scattered, independent fashion in regions of high tensile stress. A minimum or threshold stress is necessary to produce a sufficient stress concentration to initiate frac- ture. These separations join up to form a crack. The extension of fracture is largely discontinuous and consists of a joining up of cracks. In recent worka evidence of this scattered crack network was found in a Cu-Ag alloy embrittled by mercury. For the Cu alloy-Hg couple, the crack path has also been found to be dependent on the orientation of adjacent grains, and with the addition of zinc to mercury a reduction in embrittlement along with a change in fracture morphology was found.9 In this present study, a mercury-dewetting method was used to observe crack initiation and fracture morphology when a Cu-4 pct Ag alloy is deformed in mercury and Hg-Zn solutions. PROCEDURE Specimens of Cu-4 pct Ag were prepared as in previous crack-path studies.' The specimens were heated at 770°C for 24 hr and water-quenched Tension tests using a table-model Instron were carried out in mercury and in various concentrations of Hg-Zn. Loading was in steps up to the fracture stress, with the load being removed and the specimen examined for surface cracks at each step. The specimens were dewetted after each load to permit examination of the surface structure and rewetted prior to continued loading. The specimens were wetted by electro polish ing in phosphoric acid, rinsing in alcohol, and then immersing in a pool of mercury. Dewetting was accomplished by flame heating the specimen for 30 sec in a vacuum. Some surface contamination was found, but not enough to obscure crack configurations and grain boundaries. RESULTS Fracture Characteristics in Mercury. Fig. 1 is a stress-strain curve showing the progressive step-wise loading of the specimen. As may be seen from the graph, the first position stopped at a is at a stress 5000 psi below the expected fracture stress of 25,000 psi. Examination of the specimen after removal of mercury showed only one crack. The appearance of this crack at a stress far below the fracture stress of this alloy in mercury did not affect the stress-strain curve in any manner. The specimen was then recoated with mercury and deformation was continued (curve b, Fig. 1) raising the stress by 4000 psi, and the same procedure re~eated. The initial crack was located and appeared as in Fig. 2 (crack lb). In this figure the crack is
Jan 1, 1964
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Institute of Metals Division - Recrystallization of a Silicon-Iron Crystal as Observed by Transmission Electron MicroscopyBy A. Szirmae, Hsun Hu
The early stages of recrystallization in a 70 pct cold-rolled Si-Fe crystal of the (110) (0011) orientation were studied with a Siemens electron microscope. Orientation studies based on electron-diffractzotz. patterns confirm the results of previous texture analysis. The driving energy for recrystallizatior and the critical radius for growth were calculated from the dislocation energy and the energy of the subgrain bourzdaries, and it was found consistent with the observed size of the recrystallized grains. The recrystallization characteristics of crystals with different initial orientations are discussed. The recrystallization of cold-rolled (110)[001] crystals of Si-Fe has been widely studied by various investigators.1-4 Their results on both deformation and annealing textures are in good agreement. The rolling texture after 70 pct reduction consists mainly of two crystallographically equivalent (111) [112] type textures and a minor component of the (100) [011] type. The latter is derived from the deformation twins, or Neumann bands, which are formed during the early stages of deformation and later rotate to the (100) [011] orientation upon further rolling reduction. Between the two main (111) [112] type textures, there is some orientation spread, because of which very low intensity areas appear in the pole figure. If these very low intensity areas are considered to be a very weak component in the texture, then a (110) [ 001 ] orientation may be assigned to them. When this rolled crystal is annealed at a sufficiently high temperature for recrystallization, the texture returns to a simple (110) [001]. The purpose of the present investigation was primarily to seek a better understanding of the recrystallization process by using the electron transmission technique. The (110) [0011 type of crystal was selected because orientation data for it are well known from previous studies with conventional techniques. Direct observations on the recrystallization of such a crystal have also been made by using a hot-stage inside the electron microscope, and the results will be reported in another paper. MATERIAL AND METHOD A single-crystal strip of the (110) [001] orientation was prepared from a commercial grade 3 pct Si-Fe alloy by the strain-anneal technique.= The strip was approximately 0.014 in. thick, and was rolled 70 pct at room temperature to a thickness of 0.004 in. Specimens were cut from the rolled strip and were annealed in a purified hydrogen or argon atmosphere. They were then electrolytically polished in a chromic-acetic acid solution to very thin foils. Best results were found by polishing first between two narrowly spaced flat cathodes with the specimen edges coated with acid-resisting paint, followed by polishing between two pointed electrodes until a hole appeared in the center as described by Bollmann.6 It was found that a thin transparent film always formed along the thin edges of the polished specimen. This film was then removed by rinsing the specimen very briefly in a solution of alcohol with a few drops of HF or HCl. RESULTS AND DISCUSSION 1) The Deformed Crystal. From the electron-diffraction patterns taken at various areas of an as-rolled specimen, the texture components as deduced - from ordinary pole-figure analysis were confirmed. Over most of the areas where orientation was examined, a (111) pattern with a [112] direction parallel to the rolling direction was obtained. This corresponds to the main deformation texture of the (111) [112] type. In a few areas the diffraction pattern was (100) [Oil], corresponding to the minor-texture component derived from the Neumann bands. The (110) [001] orientation, which corresponds to the very weak intensity area in the pole figure, was found infrequently. A typical example of the deformed matrix having the (111) type main texture is shown in Fig. 1, where (a) is the microstructure and (b) is the diffraction pattern taken from that area. It was also frequently observed that in other areas more or less continuous rings of weaker intensity were superimposed on the simple (111) diffraction pattern, suggesting the presence of a wide range of additional orientations. Other evidence indicated that the recrystallization characteristics are different in these two different types of areas. The hot-stage observations which provide this evidence will be discussed in another paper. AS shown in Fig. l(a), numerous dislocation-free areas of very small size are embedded in the "clouds" of high-dislocation density. This indicates that the deformation of a single crystal, even after a rolling reduction of 70 pct, is far from uniform on a micro-
Jan 1, 1962
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Institute of Metals Division - The Vapor- Liquid-Solid Mechanism of Crystal Growth and Its Application to SiliconBy R. S. Wagner, W. C. Ellis
A new mechanism of crystal growth involving oapor, liquid, crnd solid phases explains many observations of the effect of implurities in crystal growth from the vapor. The role of the impuuitq is to form a liquid Solution with the crystalline tnalerial to be grown from the vapor. Since the solution is n prefevred site for deposition firorti the uapor, the liquid becorrles supersaturated. Crystal growth occurs by precipitatzon from the supersaturated liquid crt tlie solid-liquid zntevfnce. A crystalline defect, such as a screw dislocation, is not essetztial for VLS (vapor -liquid-solid) growth. The concept of the VLS mechanism is discussed in detail with reference to tire controlled growth of silicon crystals using gold, platinum, palladium, nickel, silver, or copper as an implurity agent. RECENTLY a short communication' described a new concept of crystal growth from the vapor, the VLS mechanism. In this paper we present a detailed description of the process and its application to the growth of silicon crystals and we discuss its relevance to existing concepts of .'whisker" crystal growth. Crystal growth from the vapor is usually explained by a theory proposed by Frank2 and developed in detail by Burton, Cabrera, and Frank.3 In this theory a screw dislocation terminating at the growth surface provides a self-perpetuating step. Accommodation of atoms at the step is energetically favorable, and is possible of much lower supersatu-ration than required for two-dimensional nucleation. Crystals of a unique form resulting from aniso-tropic growth from the vapor are "whisker" or filamentary ones. Such crystals have a lengthwise dimension orders of magnitude larger than those of the cross section. For most filamentary crystals both the fast-growth direction and directions of lateral growth have small Miller indices. The special growth form for a whisker crystal implies that the tip surface of the crystal must be a preferred growth site. sears4 proposed that, according to the Frank theory. a whisker contains a screw dislocation emergent at the growing tip. Such an axial defect provides a preferred growth site and accounts for unidirectional growth. The hypothesis was extended by Price. Vermilyea. and Webb," still implying the presence of a dislocation at the whisker tip. They postulated that impurities arriving at the fast-growing tip face become buried while those arriving on the surface of slow-growing lateral faces accumulate and thereby hinder growth. These considerations led to a whisker morphology. There is increasing evidence that most whisker crystals grown from the vapor are dislocation-free. Webb and his coworkers6 searched for an Eshelby twist7 in zinc? cadmium, iron. copper, silver, and palladium whisker crystals. They found unequivocal evidence for an axial screw dislocation in only one element, palladium. However, not every palladium crystal examined contained a dislocation. Observations with the electron microscope have failed to show dislocations in whisker crystals of zinc, silicon.9 and one morphology of AlN.10 Since many whiskers are completely free of dislocations, an axial dislocation does not appear to be required for whisker growth of many substances. A significant advance in understanding whisker growth has been a recognition of the need for impurities. This requirement has been clearly demonstrated for copper,11 iron,13 and silicon9-1 whiskers. For silicon, detailed studies proved conclusively that certain impurities, for example, nickel or gold, are essential. Another pertinent phenomenon which has received little attention is the presence of a liquid layer or droplets on the surface of some crystals growing from the vapor. Crystals in which this has been observed include p-toluidine,14 MoO3,15 ferrites,16 and silicon carbide.'" The liquid layers or globules were considered to be metastable phases, molecular complexes, or intermediate polymers originating from condensation of the vapor phase. The possibility has been suggested that the halide being reduced is condensed at the tip18 or adsorbed on the surface11 of a growing metal whisker, for example copper. The literature on whiskers discloses illustrations of rounded terminations at the tips. These appear. for example, on crystals of A12O3,19,20 sic,21 and BeO.22 For BeO, Edwards and Happel suggested that during growth of the whisker the rounded termination consisted of molten beryllium enclosed in a solid shell of BeO. A recent paper9 on the growth of silicon whiskers contains many observations pertinent to an understanding of the mechanisnl of whisker growth. These observations are summarized as follows. 1) Silicon whiskers are dislocation-free. 2) Certain impurities are essential for whisker growth. Without such impurities the silicon deposit is in the form of a film or consists of discrete polyhedral crystals.
Jan 1, 1965
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Institute of Metals Division - A Constitution Diagram for the Molybdenum-Iridium SystemBy J. H. Brophy, S. J. Michalik
A constitution diagram for the system Mo-Ir has been determined. The maximum solubility of iridium in molybdenum is 16 at. pct at 2110ºC and decreases to less than 5 at. pct at 1500°C. The solubility of molybdenum in iridium is 22 at. pct. Three intermediate phases appear in the system: 8 MoJr, having the p-tungsten structure; a phase, a cornplex tetragonal structure; and the hcp ? phase. Metallography, melting point determinations, X-ray diffraction and fluorescence, and electron micro-probe unalyses were employed in establishing the diagram. PREVIOUS to the present investigation, the intermediate phases in the Mo-Ir system were identified, but no detailed account of the phase diagram has been reported in the literature. Raub1 investigated alloys of Mo-Ir over an extensive range of composition between the temperatures of 800º and 1600°C. The in-termetallic compound MosIr was found to exist with nearly pure molybdenum, as the solubility of iridium in molybdenum was not detectable parametrically in this temperature range. MO3Ir was found to be iso-morphic with a ß-tungsten type structure, having a parameter of 4.959Å. An intermediate hcp phase, designated as the ? phase, ranged in composition from 52 to 78.5 at. pct at 800ºC, and from 41 to 78.5 at. pct Ir at 1200°C. Parameters noted for the ? phase were as follows: at 42.7 at. pct Ir, a = 2.771i0, c = 4.4366, c/a = 1.601; at 78.5 at. pct Ir, a = 2.736A, c = 4.378A, c/a = 1.600. Molybdenum was found to be soluble in iridium up to 16.5 at. pct Mo (83.5 at. pct Irj, with the parameter of iridium increasing to 3.845A at the solubility limit. Knapton,2 who investigated alloys between 15 and 85 at. pct Ir, essentially agreed with Raub's data, but, in addition, found a a phase in as-melted alloys near 25 at. pcto Ir. The oaphase lattice parameters were a = 9.64Å, c = 4.96Å, c/a = 0.515. The a phase was replaced by the 8 -tungsten phase on annealing at 1600°C. Knapton concluded that the a was stable only at elevated temperatures, and placed the composition of the a phase at approximately 30 at. pct Ir. The intermetallic compound Mo3Ir, with a lattice parameter of 4.965A, was included among the 8-tungsten structures reported by ~eller.' Matthias and Corenzwit,4 and Bucke15 studied the superconducting nature of MosIr, and reported a superconducting transition temperature of 8.$K. The present investigation describes the phase relationships in the Mo-Ir alloy system determined by melting point measurements, X-ray diffraction and fluorescence, and metallography. EXPERIMENTAL PROCEDURES Alloys for the determination of the phase diagram were prepared from powders. Commercial 99.9 pct Mo from Fansteel Metallurgical Corp. and 99.9 pct Ir powder from J. Bishop and Co. Platinum Works were used. The powders were weighed to nominal compositions, mixed, and then pressed, without binder, into compacts weighing 4 to 6 g. These were presintered in uacuo between 1200' and 1400°C for 1 hr, to reduce the degree of spattering during subsequent arc-melting. The compacts were arc-melted in a nonconsumable tungsten electrode furnace six times on alternate sides on a water-cooled copper hearth in an atmosphere of zirconium-getter ed argon at 500 mm of mercury pressure. In almost all cases, this procedure yielded buttons of satisfactory homogeneity. The composition of all melted buttons were confirmed by X-ray fluorescent analysis using the experimentally determined ratio of the iridium La1 line intensity to that of the molybdenum Ka1 line as a function of composition. In this determination four alloys analyzed by wet chemical methods were used as standards. An uncertainty range of ±1 at. pct has been attributed to all indicated compositions. All heat treatments and solidus measurements were carried out in tantalum resistance heating elements in vacuum conditions of 10-4 to 10-5 mm of mercury. A detailed account of this procedure has been reported by Schwarzkopf and Brophy.8 In the heat treatment and solidus measurements of iridium-rich alloys (50 at. pct Ir or greater), a tungsten lining was inserted into the tantalum resistance heating element because of a eutectic reaction which occurs between iridium and tantalum at 1948ºc.7 Heat treatments and solidus measurements carried out at compositions less than 40 at. pct Ir both with and without tungsten linings within the resistance
Jan 1, 1963
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Technical Papers and Notes - Institute of Metals Division - Effect of Hydrogen on the Fatigue Properties of Titanium and Ti-8 Pct Mn AlloyBy W. S. Hyler, L. W. Berger, R. I. Jaffee
Hydrogen additions of 390 ppm to A-55 titanium and 368 ppm to Ti-8 pet Mn have no deleterious Hydrogenadditionseffect on the unnotched and notched rotating-beam fatigue properties of these materials. 'These amounts of hydrogen, however, are sufficient to cause severe notch-impact thesematerials.embrittlement in A-55 titanium and pronounced loss of tensile ductility in Ti-8 pet Mn. The lack of embrittling effect in fatigue in the latter alloy is consistent with the postulated strain-aging mechanism of hydrogen embrittlement in a-ß alloys. There is a significant strain-agingincrease in the unnotched endurance limit of A-55 titanium with the addition of hydrogen. This increase may be explained as the result of internal heating effects which would dissolve the hydride and cause solid-solution strengthening. TITANIUM and its alloys may be seriously embrittled by relatively small amounts of hydrogen. The form which this embrittlement takes has been shown to vary with alloy type. The a alloys, for example, suffer most strongly from loss of notch-bend impact toughness' when sufficient hydrogen is added, and this effect has generally been associated with the presence of hydride phase in the micro-structure. In a-ß alloys, on the other hand, hydrogen is most detrimental to tensile ductility in slow-speed tests,2-1 and the embrittlement may be detected in a most convincing manner by means of rupture tests at room temperature. This particular kind of embrittlement has not been associated with a change in microstructure, but has been classified rather generally as associated with a strain-aging type of mechanism.' In the present paper, the effect of an embrittling amount of hydrogen on the rotating-beam fatigue properties of both an a and an a-ß titanium alloy is covered. For this study, annealed commercially pure (A-55) titanium was chosen as an a alloy, and equilibrated and stabilized Ti-8 pet Mn as representative of a typical a-ß alloy. Nominal hydrogen levels of 20 and 400 ppm were evaluated, the latter amount having been shown previously to be severely detrimental to the impact toughness of commercially pure titanium and to cause pronounced strain-aging embrittlement in the Ti-8 pet Mn alloy. The only report of the effect of hydrogen on the fatigue properties of titanium is given by Anderson et al.,° in which a push-pull type of fatigue test was conducted on as-received commercial-purity titanium sheet. Much scatter was found in the results, but generally the presence of hydrides slightly decreased the fatigue strength of unnotched specimens in the longitudinal direction. The results of notched tests were masked too greatly by scatter to be significant. Experimental Procedure Preparation of Materials—Analyses of the A-55 titanium and the Ti-8 pet Mn alloy used in this investigation are given in Table I, which indicates the 8 pet Mn alloy to be more nearly a 6 pet Mn alloy. This alloy will be referred to as Ti-8 pet Mn, however, since this is the commercially designated composition. Both alloys were received in the form of5/8-in. diam rod and, after suitable surface preparation, 5-in. lengths were vacuum annealed at 820°C. Half of the rods for each material were then hydrogenated at 820°C to a nominal hydrogen content of 400 ppm. The hydrogenated and vacuum-annealed A-55 rods were hot swaged at 700°C from 5/8-in. diam to 1/4-in. diam, and then annealed 1 hr at 800°C and air cooled prior to preparation into test specimens. Fabrication of the Ti-8 pet Mn alloy was by hot swaging to 3/8-in. diam at 760" and then 1/4-in. diam at 704°C. This material was then annealed 1 hr at 704", followed by furnace cooling to 593"C, and finally air cooling to room temperature. Evaluation—In order to examine more completely the effects of hydrogen on the particular materials studied, slow-speed tensile and notch-bend impact properties were determined in addition to fatigue data. Tensile specimens were of the standard ASTM type with a reduced section of 1/8-in. diam and a gage length of 1/2 in. A subsize cylindrical Izod specimen was used for impact tests. These specimens had a 45" notch with a 0.005-in. radius and a 0.150-in. root diam, and the stress concentration factor of this notch in bending was Kr = 3. Both the ten-
Jan 1, 1959
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Institute of Metals Division - Hardness Anisotropy in Single Crystal and Polycrystalline MagnesiumBy M. Schwartz, S. K. Nash, R. Zeman
Knoop hardness in the rolling plane and in the longitudinal plane of hot-rolled and cold-rolled sheets of sublimed magnesiu?w was measured as a function of the angle between the long axis of the indenter and the rolling direction. These measurements were correlated with similar data taken on the (0001) and (1010) planes of a single crystal of magnesium where the hardness was measured as a function of the angle between the long axis of the indenter and the [1120] direction. The results were analyzed for compliance with the hypothesis of Daniels and Dunm to account for slip, and with a similar hypothesis to account for twinning. Some hardness anisotropy data are also presented for magnesium-indium and magnesium-lithium solid solution alloys. It is well known that the hardness of a crystalline specimen is different for its different surfaces, and also that the hardness is a function of direction within a single surface. Variations in hardness for single crystals have been found to be much larger than those for polycrystalline materials. Also, materials having low crystal symmetry were found to have a greater anisotropy of hardness than those of high symmetry. 0'Neill1 and Pfeil,2 using a 1-mm Brine11 ball, studied single crystals of aluminum and iron, respectively; and they found a variation of hardness of about 10 pct between readings taken along the principal crystallographic faces. Daniels and Dunn3 found that the Knoop hardness number varied about 25 pct as the long axis of the indenter rotated on the basal plane of a zinc single crystal. The variation on the (1450) plane was about 100 pct, and the average hardness on this plane was about twice that of the basal plane. They also studied the variation of hardness within the (loo), (110), and (111) faces of a single crystal of silicon ferrite and found variations of about 25 pct although the average values for these planes were almost identical. Single crystals of zinc were also studied by Meincke.4 He found that the Vickers hardness numbers varied about 30 pct depending on whether the axis of the indenter was parallel or perpendicular to the (1010) and (1110) planes. Mott and Ford,5 using a Knoop indenter, found a 25 pct variation in hardness on the basal plane of zinc. Crow and Hinsley6 studied heavily cold-rolled bronze, steel, brass, copper, and other metals. They found that the difference in hardness numbers based on the difference in the length of the diagonals of the Vickers indenter was from 5 to 12 pct. Some minerals and synthetic stones show a very large anisotropy of hardness. Robertson and Van Meter7 found the Vickers hardness of arsenopyrite to vary from 633 to 1148 kg per mm2. stern8 using the double-cone method on synthetic corundum found the hardness number to vary from 950 to 2070. And winchell9 reported a variation of hardness number from 184 to 1205 in kyanite. The variation of hardness as a function of direction in a given crystallographic plane in single crystals possesses a periodicity which is related to the symmetry of the lattice. Daniels and Dunn3 found a six-fold periodicity of hardness in the (0001) plane of zinc. They found that the hardness curves of silicon ferrite had a four-fold symmetry in the (100) plane, a two-fold symmetry in the (110) plane, and a six-fold symmetry in the (111) plane. Mott and Ford5 also reported a six-fold symmetry of hardness in the basal plane of zinc. And vacher10 found two-, four-, and six-fold periodicities of hardness in copper on the (110), (100), and (111) planes, respectively. The purpose of this paper is to report the results of an investigation on the anisotropy of hardness as a function of orientation in single crystals of mannes-ium, and samples of rolled magnesium, magnesium-indium, and magnesium-lithium solid solution alloys. The anisotropy of hardness of pure magnesium which had been hot rolled, and then cold rolled various amounts to fracture, was studied by means of Knoop indentation hardness numbers; and the results were correlated with the preferred orientation as determined by quantitative X-ray pole-figure data. A comparison was made of the hardness data obtained from the rolled sheets and those of single crystals of magnesium. In order to obtain a more fundamental understanding of the variation of hardness and of Knoop hardness testing, the data were analyzed by
Jan 1, 1962
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Logging and Log Interpretation - An Electrodeless System for Measuring Electric Logging Parameters on Core and Mud SamplesBy I. Fatt
A recently developed system for measuring electrical resistivity of liquids without use of electrodes offers some interesting possibilities in electric logging technology. The equipment as supplied by the manufacturer is satisfactory for continuous mud logging on a drilling rig or for measuring mud or filtrate resistivity in the laboratory. A simple modification of the commercially available instrument makes it suitable for measuring resistivity of core samples in the laboratory. The continuous measurement of mud resistivity on a drilling rig is a convenient means for detecting mixing of formation water with the drilling mud. Such information is useful to the geologist, the mud engineer and the logging engineer. However, continuous mud resistivity logging by conventional electrode-type resistivity cells is beset with difficulties. The mud, sand and rock chips abrade the electrodes, thereby changing the cell constant and eventually destroying the cell. Also, additives and crude oil in the mud may poison the electrodes by coating them with a nonconductive material. An electrode-type resistivity cell. therefore, may give erroneous readings under certain conditions. Electric logging companies circumvent the electrode poisoning problem by using a four-electrode resistivity cell for measurement of mud resistivity. In this cell, change in electrode area does not change the cell constant. However, the four-electrode cell is difficult to adapt for continuous reading and does not solve completely the problem of electrode abrasion by the sand and cuttings in the mud. The measurement of electric logging parameters on core samples in the laboratory encounters some of the same problems discussed in connection with mud logging. Ideally, the electrical resistivity of a core sample should be measured by placing platinum black electrodes in direct contact with the plane ends of a cylindrical or rectangular sample. Platinum black electrodes however, are much too fragile and easily abraded to be brought in contact with a rock sample. Also, oil or other constituents in the fluid contained in the sample will poison platinum black. In practice, gold-plated brass electrodes, in an AC bridge circuit operating at about 1,000 cps, are used for routine core analysis. For more precise work in research studies, a four-electrode scheme is used.',' Preparation of the samples for the four-electrode method is much too involved for routine core analysis. An apparatus for measuring resistivity of liquids without use of electrodes was described by Guthrie and Boys3 in 1879. They suspended a beaker, containing the electrolyte, by a torsion wire and rotated a set of permanent bar magnets around the vessel. The eddy currents induced in the electrolyte reacted against the rotating magnetic field to develop a torque, which was measured as a deflection of the torsion wire. In 1879 this method could not be made precise or convenient because of the lack of strong permanent magnets. The writer described a very greatly improved apparatus similar to that of Guthrie and Boys, but it was not suitable for continuous measurements or core samples.' Many electrodeless resistivity devices using radio frequency current are described in the literature.5, 6 These generally are suitable only for noting the end-point in a chemical titration. They do not measure resistivity, instead measuring a complex quantity which includes the dielectric constant and the magnetic permeability. The first description of the apparatus to be discussed in this paper was given by Relis.7 Improvements and modifications are described by Fielden,s Gupta and Hills,> and Eichholz and Bettens.10 DESCRIPTION OF APPARATUS The apparatus used in this study is based on the principle that the solution under measurement can form a loop coupling two transformer coils, as shown in Fig. 1. For a fixed AC voltage applied across Coil A, the voltage appearing across Coil B is a function of the resistance of the liquid-filled loop. The details of the voltage generating and measuring circuits are given in Refs. 7, 8, 9 and 10. A block diagram of the equipment is given in Fig. 7. Special features worth mentioning are the operating frequency of 18,000 cps and the automatic temperature compensation which results in the given resistivity readings being automatically correlated to 25°C. The liquid loop supplied by the manufacturer, shown in Figs. 1 and 2, was modified for use in core analysis (Fig. 3). The core sample under test is substituted for a section of the original loop. As shown in Fig. 3, the unit accepts only plastic-mounted cylindrical core specimens. A Hassler-type sleeve easily can be designed for the unit if unmounted cores are to be measured. EXPERIMENTAL PROCEDURE MUD LOGGING A simulated mud line was set up in the laboratory.
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Part XII – December 1968 – Papers - Evidence for the Importance of Crystallographic Slip During Superplastic Deformation of Eutectic Zinc-AluminumBy Charles M. Packer, Oleg D. Sherby, Roy H. Johnson
Originally round tensile specimens of a eutectic Zn-A1 alloy develop elliptical cross sections during superplastic deformation. This observation, coupled with a detailed study of the microstructure and preferred orieniation, suggests that crystallographic slip and continuous grain boundary migration or re-crystallization are important processes during super-plastic deformation. In spite of the extensive activity in superplasticity1-15 and the numerous explanations proposed, no single model has had universal acceptance. It has been established, however, that the general requirements for superplastic extension of two-phase alloys include an extremely fine, stabilized grain size of the order of a few microns, a temperature about equal to or greater than one-half the melting point, a critical range of strain rate, and a similarity in the mechanical strength of the major phases. The proposed models can perhaps best be characterized in terms of the important phenomena associated with them. These phenomena include: phase instability,1 diffusional creep by volume diffusion3 or grain boundary diffusion4,5 slip and continuous grain boundary migration or recrystalliza-tion,= grain boundary Sliding,7-9,13,14 and dislocation glide.'5 In this paper, experimental observations will be reported which support a model involving slip and continuous grain boundary migration or recrystalliza-tion. Specifically, a correlation will be made between this model and the development of elliptical cross sections as originally round specimens are superplas-tically deformed. For the most part, superplasticity studies have been conducted with eutectic or eutectoid alloys. Probably the most thoroughly studied material has been the monotectoid Zn-A1 alloy.1,2,6,12,13,15 No attention to the eutectic Zn-A1 alloy has previously been reported, and the results discussed in this paper represent part of a general study of the superplastic properties of this alloy. MATERIALS The alloys used in this investigation were prepared by melting appropriate quantities of 99.99+ pct A1 and 99.999 pct Zn in air, mixing, and pouring into a water- cooled stainless-steel mold. Wet-chemical analysis was conducted with each heat of alloy prepared, using the procedure of Fish and smith.16 The composition of the eutectic alloy was 95.1 wt pct Zn. Ingots about 2 in. thick were rolled to 0.4-in. plate at about 300°C with a reduction of 5 to 10 pct per pass. Specimens were machined from the plate with the tensile axis parallel to the rolling direction. The specimens were round, with 0.150-in.-diam, 1.25-in.-long gage length, and 0.25-in.-diam threaded grip sections. EXPERIMENTAL PROCEDURE Specimens were mounted inside a uniform-temperature quartz tube which was surrounded by a double elliptical radiant furnace with a 12-in.-long uniform-temperature hot zone and a low thermal capacity. The tube extended through the top and bottom of the furnace and permitted rapid quenching of the loaded specimens when quickly filled with cold water at the conclusion of the test. The quench precluded any effects on specimen microstructure from a normal, slow cool. Constant stress was applied to test specimens by suspending a load on a constant stress cam of the type described by Hopkin.17 The design of this cam permitted application of a constant stress for elongations up to 200 pct. For greater elongation, approximately constant stress conditions were maintained by systematically reducing the load manually. RESULTS As part of an investigation of the superplastic properties of the eutectic Zn-A1 alloy, evidence was obtained for the development of elliptically shaped cross sections as originally round specimens were extended. For example, after an elongation of about 100 pct, a round specimen with an initial diameter of 0.150 in. became elliptical with major and minor axis of 0.128 and 0.88 in., respectively. Photographs are presented to illustrate the ellipticity developed during superplastic deformation, Fig. 1. The specimen shown was deformed at a stress of 500 psi, at a temperature of 285°C, and a strain rate of 2.28 x 10-2 min-1. The strain-rate sensitivity exponent* was measured at *The strain-rate sensitivity exponent, m, is defined as d In o/d In c where o is the steady-state flow stress and E is the strain rate. this temperature and in the strain rate range 10"3 to 10-1 min-1 was found to be about 0.5. This value is typical of those observed with superplastic materials. The material studied exhibited negligible strain hardening during superplastic deformation, the creep rate remaining constant under constant stress and temper-
Jan 1, 1969
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Part IV – April 1969 - Papers - Studies in Vacuum Degassing Part I: Fluid Mechanics of Bubble Growth at Reduced PressuresBy J. Szekely, G. P. Martins
A formulation is given for describing the rate of expansion of spherical bubbles rising in liquids the freeboard of which is evacuated. The computer solution of the resultant differential equations has shown that, for low freeboard pressures (less than about 5 mm Hg), on approaching the free surface the bubbles expand much less rapidly than predictable from equilibrium considerations. In other words, in this region the pressure inside the bubbles will be significantly larger than the static pressure in the liquid corresponding to the position of the bubble. These theoretical predictions were confirmed by experimental work, using two-dimensional air bubbles rising in mercury. The important consequence of these findings is that the expansion of gas bubbles in vacuum degassing operations will be a great deal less than expected from hydrostatic considerations. This would lead to a significant reduction in the available interfacial area and may explain the apparent poor efficiency of many vacuum degassing units. VACUUM degassing as a treatment for liquid steel has gained widespread popularity in recent years; the number of known installations exceeds several hundred at the present time.' Although much information is available on both the thermodynamics of the system and the overall performance of various industrial units, much less is known about the fundamental aspects of the process kinetics.2-4 The basic physical situation common to virtually all vacuum degassing operations is the interaction between gas bubbles (swarms of bubbles) and the surrounding molten metal, held in a container, the freeborad of which is at a low absolute pressure. Once formed (or introduced from an external source) the bubbles will ascend, due to the buoyancy forces, and, during this ascent, a significant increase in their volume will occur. This progressive increase in the bubble volume is due to two factors: a) the continuous reduction in the static pressure acting on the bubble during its rise; and b) mass transfer into the bubble from the surrounding molten steel. In a recent paper Richardson and Bradshaw developed equations5 for describing mass transfer into gas bubbles from molten metals at reduced pressures. However, in deriving these expressions it was assumed that the pressure inside the bubble was identical to the static pressure in the adjacent liquid. In other words, the volume of the bubble was considered to be in equilibrium with the pressure of the fluid adjacent to it. This assumption, thus their analysis presented, was thought to be reasonably accurate for most of the bubble's ascent; however, it was unlikely to be valid in the immediate vicinity of the free surface, held at a low pressure. It was pointed out in the discussion6 that the region close to the surface may be of considerable importance as both the driving force and the interfacial area available for mass transfer are at their highest value here. The ' 'anomalous" behavior of gas bubbles when approaching a free surface at low pressures was recently confirmed in a preliminary investigation by Szekely and Martins. ?1 Here high-speed motion photography was used to study air bubbles rising in a column of n-tetradecane with a freeboard pressure of 0.1 mm Hg. It was found that significant distortion of the bubbles occurred on approaching the free surface; furthermore, the expansion observed was much less than what one could expect from hydrostatic considerations, i.e., factor a previously discussed. It follows from the foregoing that a detailed study of these phenomena would be justified both from fundamental considerations and because of their potential relevance to technology. The purpose of the paper is to present a more realistic formulation for the expansion of a gas bubble approaching a low-pressure region, together with a comparison of the theoretical prediction with experimental measurement. An inert bubble will be considered in the first instance; it is thought that the understanding of the fluid mechanics is an essential first step toward the realistic formulation of the mass transfer process. This latter problem will be the subject of a subsequent publication. FORMULATION The Physical Model. Consider a spherical bubble, of initial radius Ro, rising in a fluid, having a density pL. Initially let the bubble be at a distance H from the free surface, and at a pressure Pgo, as illustrated in Fig. 1. Pgo, the initial pressure in the bubble, is given by the following equation: pgo = Po = Ptp +pLgH [ la] where Po is the pressure in the liquid corresponding to the initial position of the bubble and Ptp is the pressure at the free surface. The fluid pressure at
Jan 1, 1970