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By J. S. Aronofsky, J. P. Heller

This paper presents a mathematical analysis of the fluid mixing which occurs during flow through porous media. The analysis is based on the well-known diffusion equation with mass transfer term. It is pointed out that the use of this equation is justified by a single general assumption which does not specify any particular mechanism for the mixing process. Formulas are given for tracer fluid concentrations for two different boundary and initial conditions. Calculated numerical values compare closely with some published results of experiments in which no viscosity or density difference existed between displaced and displacing fluids. INTRODUCTION A phenomenological theory of the mixing and diffusion process is presented for the flow in a porous medium of two miscible liquids of equal viscosity and density. This is based on the classical diffusion equation which has been used to explain such processes as Brownian motion and heat conduction. More recently, this same differential equation has been derived (in a manner analogous to the work in this paper) for the problem of heat transfer during fluid flow in porous media.' The purpose of this paper is to show that the available experimental evidence justifies the use of this simple diffusion equation. The recent data of Koch and Slobod' and of von Rosenberg' are used to test this diffusion model by comparing concentration curve shapes and calculating "effective diffusion coefficients". The same differential equation for miscible displacement, as well as some experimental confirmation, has been published in Japan by K. Yuhara,4 and recently in this country by Day.5 Yuhara arrives at his con-clusions through analogy with turbulent diffusion, de- scribing the microscopic velocities in terms of "eddy motion" — although unlike the ordinary eddies of hydraulics. Day proceeds directly from Scheidegger's6 concept of the dispersion of velocities. After a very clear description of Scheidegger's theory, he applies it to calculate the motion first of a drop and then of a thin layer of brine into a bed of sand. For the latter case, Day derives and solves the same differential equation as Eq. 1. In our presentation no detailed assumptions are made as to the mechanism of displacement. In fact, several microscopic processes may well be involved—the only general assumption made is that their cumulative microscopic effect may be described by the addition of a second-order term to the differentirl equation of continuity. DERIVATION OF EQUATIONS Let us consider the displacement in one spatial dimension of Liquid A from a sample of porous media by Liquid B. A and B are assumed completely miscible and of the same viscosity and density. Both fluids are also assumed to be incompressible and it is specified that the total flow is the same for any cross section. It is evident that the rate at which Liquid B would be carried across such a section would be given by the product of the fluid velocity, u, and the concentration, C, of B in the fluid mixture assuming the constancy of u and C over the cross section. Since the volume of Fluid B is conserved, this leads to the one-way wave equation - u ?C/?x = ? ?C/?l where x increases in the direction of u—the "Darcy velocity", Q/A (or velocity flux per unit area), and 9 is the fractional porosity. Consider the case where fluid B is displacing Fluid A and the concentration distribution is represented by a step funcLon (with a vertical discontinuity). The solution of Eq. 1 predicts no mixing

Jan 1, 1958

The Sub-committee on Safety of the Industrial Organization Com-mittee of the Institute has been asked to cooperate with the National Safety Council, and has made certain recommendations to the Board of Directors of the Institute regarding ways and means of bringing about this cooperation. The National Safety Council has been in existence seven years. Its inception was at a meeting of the American Iron and Steel Electrical Engineers held in Milwaukee in 1912. The first annual congress was held in New York City in October, 1913, at which time the Council was definitely organized. Its membership now consists of nearly four thousand members, representing industrial plants, railroads, public utility companies, insurance companies, state labor commissions, Chambers of Commerce, manufacturers' organizations, etc. These members are in all states of the Union and in eleven foreign countries, and through them the National Safety Council reaches more than six million workers.

Jan 7, 1919

CONTENTS SECTION I Page Page War Notice v Personal xv St. Louis Meeting vi Employment : : xvii Nominations for Officers ix Local Section News xviii Burr A. Robinson x Meetings of Societies :.: xxiv New Collective Index of Transac- Library xxv tions xi Membership : xxxii Alabama Technical Association... xi Institute Committees xlix Proceedings, Meeting of Board of Officers and Directors lvi Directors xi Members of the Institute in Mili- tary Service xiii

Jan 8, 1917

By R. Taggart, D. H. Polonis, J. C. McMillan

Thin foil electron microscopy techniques have been used to study the micros tructure of a Ti- 7.5 wt pct vanadium alloy in the quenched and aged cond_itions. Selected area diffraction has identified a (1011) twinning mode accompanying the martens ite t9.an.sfo?rn~ation. Precipitation of the 0 phase during the aging of quenched alloys has been obsevced to occuv in the form of plates and needles with preferential growth along the (1120) direction in the a' matrix. In the present work, the micro structures of quenched and aged alloys of the 0 isomorphous Ti-V system have been investigated by means of thin-foil electron-microscopy techniques. Most of the previous studies of martensitic phases in titanium-base alloys have utilized optical microscopy and X-ray diffraction techniques. The application of transmission electron microscopy is more recent, and only a few such studies have been reported.1-5 This paper is concerned particularly with the crystallographic nature of substructures formed in the martensitic a' plates. The early stages of aging or tempering have also been examined to determine the modes of precipitation from the martensitic solid solutions. Such information is essential in studying strengthening mechanisms and in determining the feasibility of high-strength rnartensitic alloys based on titanium. Liu and Margolin6 reported several types of substructures within the martensitic plates of quenched Ti-Mn alloys. It was later suggested by Liu7 that the structure of martensitic plates might be very complex and not single crystals as normally assumed. The sub-markings could not be identified with the two possible habit-plane orientations {334}ß and {344}ß, and it was not positively determined whether they are associated with mechanical twinning. The recent studies by Armitage5 on titanium martensites in a variety of commercial alloys have indicated that twinning does not generally accompany the transformation. This observation is in accordance with the Mackenzie and Bowles model for the transformation in pure titanium8 which suggests that twinning is not to be expected. However, a number of other recent investigators have reported twinlike substructures in the martensitic plates of several titanium systems including commercia1 titanium,2,3 Ti-Cu,5,9 Ti-Ta,1 and the commercial alloy Ti-8A1-1Mo-1V. Blackburn* has reported that the structure of quenched Ti-8A1-1Mo-1V depends on the prior solution temperature. He identified two types of martensitic structures, one of which is described as a heavily faulted hcp or twinned fcc structure and the other an hcp structure with a high internal dislocation density. The latter type exhibited some twinning with a (1011) twin plane. EXPERIMENTAL PROCEDURES AND RESULTS The alloy used in the present work was a 7.5 wt pct V alloy that was prepared by conventional arc-melting techniques. This alloy composition was selected

Jan 1, 1968

By N. J. Grant, Hans Brunner

ThE materials used in this investigation were furnished by the Aluminum Co. of America and consisted of high-purity alurhinum (99.995 pct) and two aluminum-magnesium alloys containing approximately 2 and 5 pct Mg. The compositions of these alloys are listed in Table I. The materials were received as hot rolled 3/8-in. diam rods and were made from the same heats as the materials which were previously used in this laboratory.'j3 The rods were cold swaged to 1/4-in. diam by 1 in. long, and then had two parallel flats machined over the gage length 0.085 in. apart. The test bars were annealed for 10 min at 700° F, and strained 1 pct in tension at room temperature. They were electropolished (80 pct acetic acid; 20 pct perchloric acid, 70 pct concentration) at a temperature of 60°F at approximately 20 v. A grid, transverse or square, spaced 0.2 mm apart, was impressed by rolling a fine threaded screw (128 threads per in.) across the flat surfaces. The depth of the grooves was less than 5 p. For final annealing and grain size control the specimens were enclosed in aluminum foil and sealed in Vycor tubes. Annealing conditions varied from 1 hr at 700° F to 5 days at 1050° F, depending on the alloy content, to give for most of the specimens a final grain size of about 1 mm. This treatment was followed by electropol-ishing as described above. For the test series presented in Figs. 4 and 5 round specimens were used instead of flat ones, and fine machining marks served as marker lines instead of the impressed grid lines. Electropolishing was omitted. The major advantage is that the spacing of the machining marks is only about 1 u as compared to the 200 u of the impressed grid lines, permitting higher precision in strain measurements. Unfortunately the strain annealing necessary for grain size control also resulted in some preferred orientation of the grains. The preferred orientation of three arbitrary specimens was measured by X-ray diffraction methods and the averaged results are shown in Fig. 1. The possible effects of the preferred orientation on the test results will be discussed later. The testing temperatures were 410°, 515", 725", and 940° F, with one exception in the case of the 5.1 pct Mg alloy. Since the solubility limit of this alloy is 520°F, a test temperature of 545°F was cho-se sen instead of 515°F. The selection of the test temperature was based on two considerations: 1) at 900°F and above, extensive grain boundary migration made it more difficult to measure grain boundary sliding; 2) at 400°F and below, there was so little grain boundary sliding that it was again difficult to make precise measurements. The stress was chosen to give a creep rate of approximately 2.7 pct per hr in connection with Figs. 2

Jan 1, 1961

By R. Silverman, H. Blumenthal

It was found that despite the similarity of chemical analyses of different titanium carbides used as base materials for cermets, the physical properties, especially transverse-rupture strengths, of test bars were different. Hence this metallographic study attempts to link physical properties to micro-structures. It is shown that microstructure, grain shape, and grain growth are functions of three interrelated factors: 1—powder production procedure, 2—surface conditioning of the particles, and 3—impurities either contained in the original powder or acquired during ball milling. An explanation is offered for the "coring effect," long observed, but heretofore of unknown origin. The explanation is based on assumption of an oxide film and on chemical analyses which substantiate these findings. TITANIUM carbide has become in recent years a material of great interest in the high temperature field. Consequently, many manufacturers in the United States and Europe are producing titanium carbide for cermet applications as well as for additions to the well known tungsten carbide tools. All present commercial processes of titanium carbide production utilize the chemical reaction of titanium dioxide and carbon to form as nearly as possible stoichiometric Tic. This reaction is carried out in three ways: 1—in a menstruum of molten metal,' 2—in the solid state, either in a protective atmosphere2 or in vacuum;" or 3—in an are-melting operation. In spite of the fact that the pure carbides obtained in these operations are almost identical chemically, the physical properties vary considerably when they are combined with a binder (Ni, Co) to form cermets. This fact led the authors to examine metal-lographically nickel-bonded titanium carbide in order to find the possible reasons for this behavior. Materials and Methods Five different titanium carbides were used in this investigation. They are identified in Table I. The first four materials were used in the as-received condition. Material E, received in lumps, was crushed to —100 mesh and carried through a flotation process in order to bring its graphite content in line with the other products. A Galagher flotation cell was used with pine oil as frothing agent. The chemical analyses of the investigated materials are given in Table 11. The binder used was carbonyl nickel of 9 to 14 microns particle size, supplied by A. D. Mackay. The materials were ball milled at a ball to charge ratio of 6:1 using procedures described under "Experiments and Results." All particle sizes mentioned are averages determined with a Fisher Sub-sieve Sizer. Test bars (lx0.40x0.16 in.) were prepared by 1—hot pressing to 85 to 95 pct of theoretical density at pressures between 1 and 1½ tsi and temperatures from 1600" to 1800°C, 2-—-cold presssing after 3 pct camphor had been added, or 3—wet pressing, both 2 and 3 at pressures between 5 and 10 tsi. All pressed bars were sintered in a vacuum of 105 to 10-6 mm Hg for 2 hr at 1350 °C. Transverse-rupture strengths were determined by breaking on a Baldwin Universal Testing Machine over a 9/16 in. span. Densities were measured by water displacement. The preparation of the specimens for micrographs was done according to Silverman and Doshna Luscz." All magnifications are at X1000. A sodium picrate electrolytic etch was used. Experiments and Results The influence of ball-milling procedure, ball-milling medium, pressing procedure, and sintering procedure on the microstructure of 80/20 — TiC/Ni were investigated. Ball Milling of Materials A, B, and C in a Steel Mill: Figs. 1 and 2 show microstructures of hot-pressed and vacuum-sintered test bars of materials A and B after the respective materials had been ball milled to 2.1 microns particle size in a steel mill and mixed with 20 pct Ni binder. Material A (Fig. 1) shows considerable grain growth. Also evident is a tendency of the carbide grains to coalesce. The density is 98 pct and the low transverse-rupture strength of 111,000 psi is probably caused by many large grains and an unfavorable packing factor. Almost all grains show a slight indication of "coring." Material B (Fig. 2), although showing grain growth, still has many small particles and a better distribution of binder and carbide due to the relative absence of the coalescing tendency. "Coring" can be observed in almost all grains. The high transverse-rupture strength of 179,000 psi and the density of 100 pct are believed to be due to the many small grains completely surrounded by the binder phase. There is also a preference to form spherical grains with material A, while most grains of material B preserve their angular shapes. Material C, of which no picture is given, stays between A and B in every respect. Rounding of some grains can be observed as well as coring, but the latter to a lesser degree than with material B. Its densification is good and the transverse-rupture strength obtained is 142,000 psi. Ball Milling of Materials A, B, C, and E in a WC Mill: When the Tic powders were ball milled to 2 microns particle size in a we mill, then ball-mill mixed with 20 pct Ni binder, hot pressed, and vacuum

Jan 1, 1956

By Pierre I. Desré, Donald T. Hawkins, Ralph Hultgren

The torsion effusion method has been used to measure the vapor pressure of thallium over pure thallium in the temperature range 931" to 996'k The resulting 100 cal per g-atom is in excellent agreement with previous values. Vapor pressures of T1 above seven Ag-Tl alloys ranging from 33 to 90 at. pct T1 were measured at 979K. Calculated silver activities show a positive deviation from Raoult's law, approaching ideality near the liquidus. Measured thallium activities scatter less than previous measurements using the electromotive force technique. Values for the silver component were calculated by Gibbs-Duhem integration. This paper reports the results of a study of the liquid Ag-T1 system by the torsion effusion method. The method has been discussed in detail previously1 and will be only briefly summarized here. The sample is contained in a cell which is suspended on a torsion wire. Vapors effusing from orifices on opposite sides of the cell exert a torque on the wire. The torque is related to the vapor pressure by the following relation: where D is the torsion constant of the wire, 4 the angle of torque, fl and f2 the correction factors determined by Freeman and seamy2 to account for orifice length, a1 and a2 the areas of the orifices, and ql and q2 the distances of the orifices from the axis of rotation. By using the same cell for pure thallium and the alloy, it follows that: so that most systematic errors are eliminated in determining the activities. EXPERIMENTAL 99.999+ pct T1 was obtained from the American Smelting and Refining Co. and 99.999 pct Ag was obtained from Cominco American, Inc. Seven Ag-T1 alloys, ranging in composition from x^\ = 0.33 to 0.90, were prepared by melting together weighed amounts of the pure metals in sealed, evacuated Vycor tubes and quenching the melts in water. The apparatus and graphite cells were the same as those used by Hawkins and Hultgren3 in their study of the Pb-Sn system. RESULTS Ten measurements were made on pure thallium in the temperature range 931" to 996K, and the results are presented in Table I. Values of were calculated using tabulated Gibbs (free) energy functions.4 No dependence of on temperature or orifice size was found, indicating that equilibrium was attained. Data for the Ag-T1 alloys are shown in Table 11. Values were smoothed with respect to composition by a plot of where . DISCUSSION The value = 43,520 * 100 cal per g-atom for pure thallium (95 pct uncertainty limit) is in excellent agreement with previous investigations.4 In the Ag-T1 system, this study shows positive deviations from Raoult's law at all compositions. Fig. l gives the phase diagram according to Hansen, and Fig. 2 presents the activity values measured in this study as well as those from electromotive force measurements at 950°K by Terpilowski, Kundys, and slaby.'

Jan 1, 1969

By P. Shahinian, J. Weertman

Minimum creep rates of nickel samples were measured in the stress region of 2.5x107 to 2.8xl0 dyne per sq cm and the temperature region of 400° to 1100°C. The creep rate seems to be proportional to (stress) at stresses below 7x10H dyne per sq cm. The activation energy of creep is approximately 65,000 cal per mol. IN a recent theory' of steady-state creep which is based on Mott's dislocation climb mechanism, the following creep equation was derived for creep in polycrystalline metals (if where K is creep rate, Q the activation energy of self-diffusion, S the entropy of activation of self-diffusion, L' the grain size, L the subgrain size, b the length of the Burgers' vector of a dislocation, u the shear modulus, u the stress, a the critical shear stress, M the density of active Frank-Read sources, v the vibrational frequency of a vacancy, and kT has its usual meaning. This equation predicts a creep rate which depends on the stress through a power law at low stresses. At high stresses the creep rate increases much more rapidly with stress. The theory breaks down for stresses great enough that the inequality holds true. It was the purpose of the present in-

Jan 1, 1957

By A. M. Gaudin, T. P. Meloy

This paper presents the theoretical derivation of the distribution equation for single fracture. The equation is shown to accord with experiment. Several empirical size-distribution equations have been proposed to describe the size of broken materials. Among them are the Gaudin-Schuhmann equation and the Rosin-Rammler equation.3*4 The Gaudin-Schuhmann equation relates the relative fraction of undersize to relative size —. In this relationship Mo is the total weight of crushed sample, M(x) the weight of undersize contained, x the size considered, K a quantity called the size modulus, which together with the slope parameter, m, characterizes the product. The slope parameter is usually close to unity. The Rosin-Rammler equation relates the same relative fraction of undersize to the relative size modulus by an equation of different form In this relationship, e is the base of natural logarithms. In the fine size-range when m is unity both equations give Gilvarry and Berstrom have sought a size distribution equation having a sound theoretical basis. They have come to an equation taking into account the effect of volume, surface and edge flaws in fragmentation. If the effect of the volume and surface flaws is neglected, the equation taking only edge flaws into account has the form of the Rosin-Rammler equation. In the present paper, a theoretical size-distribution

Jan 1, 1962

By Albert D. Brokaw

The accompanying charts are presented to extend and improve a chart published under the title "A Chart to Provide Approximate Correction for Temperature and Deviation from Boyle's Law."' The applicability of this earlier chart was limited by the fact that it was based on the work of Burke and Keyes² and Kvalnes and Gaddy3 whose experiments were conducted with pure methane, the adjustments suggested for natural gases of higher specific gravity were unsatisfactory except within limited ranges of temperatures and pressures, and precise interpolation was difficult. The extensive work of G. G. Brown, D. L. Katz and their associates on the heavier natural gases has provided better bases for the needed corrections, and the present charts. which are based largely on their work, are intended to simplify the computations involved. The design of the charts has been changed by plotting temperatures as a function of pressure and correction factor, on a semilogarithmic or "ratio" grid, which gives fairly even spacing of the graphs and simplifies interpolation. Charts have been prepared for natural gas with specific gravities of .60, .65, .70, .75 and .80. The standard computation for use in estimating the quantity of gas in a reservoir may be expressed as follows: _ PA X 520 X VR ZT where: Q is the volume of gas at 60°F and one atmosphere pressure PA is the absolute formation pressure in atmospheres

Jan 1, 1949

By Albert D. Brokaw

The accompanying charts are presented to extend and improve a chart published under the title "A Chart to Provide Approximate Correction for Temperature and Deviation from Boyle's Law."' The applicability of this earlier chart was limited by the fact that it was based on the work of Burke and Keyes² and Kvalnes and Gaddy3 whose experiments were conducted with pure methane, the adjustments suggested for natural gases of higher specific gravity were unsatisfactory except within limited ranges of temperatures and pressures, and precise interpolation was difficult. The extensive work of G. G. Brown, D. L. Katz and their associates on the heavier natural gases has provided better bases for the needed corrections, and the present charts. which are based largely on their work, are intended to simplify the computations involved. The design of the charts has been changed by plotting temperatures as a function of pressure and correction factor, on a semilogarithmic or "ratio" grid, which gives fairly even spacing of the graphs and simplifies interpolation. Charts have been prepared for natural gas with specific gravities of .60, .65, .70, .75 and .80. The standard computation for use in estimating the quantity of gas in a reservoir may be expressed as follows: _ PA X 520 X VR ZT where: Q is the volume of gas at 60°F and one atmosphere pressure PA is the absolute formation pressure in atmospheres

Jan 1, 1949

By B. Kopelman, C. C. Gregg

THE reduction of tungstic oxide to tungsten metal powder by hydrogen is a process by which one might expect the resultant metal powder to he porous. In- deed, sponge iron, prepared by rcduction of the oxide in a reducing gas, is generally accepted as quite porous. with pores large enough to be seen readily under the optical microscope at relatively low magnifications. However, any pores that may exist in tungsten metal powder are not resolved by the optical microscope, and apparently, not even by the electron microscope. Fig r shows commercial tungsten powder magni- fied at I0,000 X by the electron microscope,' both etched and unetched. In an earlier paper by one of the authors,* the existence of ports in tungsten powder was required to explain adequately the particle size changes occurring during the reduction of tungstic oxide. The inability to detect these pores under the electron microscope at 10,000 X implies that these {pores} are of a size of 100 A units or less. (This in itself is by no means proof that pores above 100 A would not exist, since polishing effects on the specimen might smear up holes of such small magnitude). If, then, these pores are less than IOO A. and of the order of molecular size, then the density of the metal powder should be

Jan 1, 1949

By Y. C. Liu, G. A. Alers, S. S. Choi

In searching for an explanation for the obvious difference between the copper and the brass type of rolling texture, it is common practice to look for correlations with other properties. For example, there are obvious differences between copper and brass in the critical resolved shear stress, the extent of easy glide or stage I, and the amount of "overshooting)) during single-crystal deformation.' Also, the slip lines in copper are fine and wavy while those in brass are more coarse and better described as slip bands.' Since neutron irradiation is known to make these properties in copper change in such a way as to resemble brass,2'3 an excellent test for these possible correlations is to see whether neutron irradiation produces a corresponding change in the texture, i.e., whether irradiated copper develops a brass-type rolling texture. The experiment would also answer the more important question of whether or not lattice defects like those introduced by neutron irradiation have any effect on the development of rolling textures in fcc metals. Experimental studies using conventional X-ray pole figure techniques are inconvenient because the X-ray detection system must be modified to discriminate against the radioactivity which is induced in the specimen by the necessarily long exposure to neutrons. Nevertheless, some texture determinations have been

Jan 1, 1968

By M. H. Richman, L. M. Markowitz

MUCH of the available information on which the heat treatments of a particular steel are based is found in the isothermal-transformation diagram. Such is the case despite the fact that the usual thermal treatments involve continuous transformations, i.e., transformations which occur on cooling, rather than isothermal transformations. This rather unusual practice is continued because of the abundance of published isothermal-transformation diagrams1, 2 which are relatively easy to determine experimentally as compared to continuous-transformation diagrams.3, 4 However, this can easily lead to the production of improper micro-structures and may not allow full advantage to be taken of the inherent hardenability of a steel. A mathematical method of estimating the continuous-transformation diagram from the available isothermal data was developed by Grange and Kiefer;5 but, due to the mathematical approximations required in the calculations, the computation of continuous-transformation diagrams has been limited to individual cases and no large-scale compilation of these diagrams is available. With the present availability of high-speed digital computers, the problem of time-consuming approximations may be minimized and continuous-transformation diagrams may be constructed with the insertion of isothermal data into a basic program. It is the purpose of this report to announce the availability of such a program and compare the computed and experimental continuous-transformation diagrams for two different steels. Let us first review the method of Grange and Kiefer5 and then compare the results of the machine calculations with the experimentally determined diagrams. In order to apply this method, one requires the isothermal-transformation diagram and a set of curves representing cooling at constant rates. A section of an isothermal-transformation diagram is shown in Fig. 1 together with a cooling curve of M0F per sec. The cooling curve is constructed to start from the A1 (eutectoid) temperature if the transformation product is the eutectoid microconstituent (i.e., pearlite or bainite), from the A3 temperature if the product is primary ferrite, or from the 4, if it is proeutec-toid cementite. The cooling curve in Fig. 1 intersects the curve representing the start of isothermal transformation at a point A' corresponding to a temperature TX and a time fX. An arbitrary lower temperature To (on the

Jan 1, 1968

By P. Crowther, G. J. Lamprecht

The solubilities of silver, zinc, and cerium in liquid sodium, in the temperature ranges 100 to 270°C, 190° to 550°C, and 120" to 460°C, respectively, have been determined. From the solubility data the heat the entropy the partial molal enthalpy of mixing the excess entropy and the partial molal free energy of solution for the systems Nu-Ag and Na-Zn have been calculated. For the system Na-Ce the observed negative is discussed in terms of the solubility of the oxide Ce2O3. In an earlier publication the results obtained in the study of the solubility of tin' in liquid sodium are presented, as well as the detailed analytical procedures used. 1) REAGENTS Spectroscopically pure metals as supplied by Johnson Matthey and Co, were used to produce the following tracers: 253-day Ag110, 245-day zn65, and 325-day ce141. The tracers were prepared by irradiation in a thermal neutron flux of 4 x 10 13 neutrons cm-2 sek-1. To obtain a uniform amount of the required specific activity, needed for each solubility experiment, the radioactive metal was diluted with the corresponding inactive metal, by melting them together in an inert atmosphere. The liquid sodium used contained 11 ±2 ppm of O,1 determined by the vacuum distillation method.' The oxygen was assumed to be present as the oxide NaD. 2) THE SYSTEMS: SODIUM-SILVER AND SODIUM-ZINC Plots were made of the log of the mole fraction of silver, Fig. 1, and of zinc, Fig. 2, dissolved in the liquid sodium vs reciprocal absolute temperature. The equations for the solubilities, based on the least-squares fit to each plot, are: where Xi is the mole fraction metal dissolved in sodium, T is the absolute temperature, and s is the standard deviation in the value of log Xi. The heats and the entropies lution were calculated from the solubility data by In neither of the two cases was any intermetallic compound formed between sodium and the solute metal as was the case for tin.' Thus, for the silver and zinc systems the pure metal was taken as the reference phase. Since the solids in equilibrium with the liquid sodium were the pure metals, one can calculate the partial molal enthalpy of mixing and

Jan 1, 1969

By J. E. Cannaday, R. J. Austin, R. K. Saxer

PREVIOUS investigators have determined activation energies and have postulated various controlling mechanisms for creep.'-' Recently Barrett et 01.I5 have suggested, as the result of their work with cadmium, that the apparent activation energies for creep (AHc) above 0.5 T, could be correlated by means of activation energies for self-diffusion (AHSD) and modulus of elasticity functions: AHC = AHSD - (5RT/E) dE/dT. The wide disparity of apparent activation energies previously obtained with nickel compared to those reported for other fcc metals and the desire to test the postulate of Barrett el al. prompted this study. The as-received 17.5-mil nickel wire used during this work assayed 99.87 pct pure, Table I. X-ray analysis indicated that the wire was in a stress-re- lieved state and metallographic examination revealed an equiaxed grain size of approximately 0.01 mm. Specimens degreased in acetone and cut to 1-1/2 in. lengths were tested in a cam-mechanized constant-stress creep machine. A vacuum of at least lo-5 mm Hg was maintained during all tests. Stresses were applied when thermal equilibrium was established. When a measurable (at least 0.5 pct) secondary creep was observed, the temperature was pulsed to a higher temperature. Pulsing time varied from 30 sec at 480°C to 2 min at 1300'C and above. Slopes of creep curves were determined after the initial acceleration in the strain rate had subsided and steady-state creep was achieved. To confirm the results obtained, additional tests were performed incorporating a temperature pulsing method suggested by sherby. In this method the load was removed during temperature pulsing and reapplied after thermal expansion had occurred. No appreciable differences in results were obtained. Tests were performed over a wide range of temperature (470" to 1310°C) and stresses (250 to 17,000 psi). The expression was used to calculate activation energies. In this expression T1 and T2 are the initial and final temperatures, and el and i2 are the creep rates at T, and T2. The variation of the apparent activation energies with the mean test temperature calculated by means of Eq. [I] are shown in Fig. 1. The mean test temperature (Tmean) was calculated from the relationship

Jan 1, 1967

By Olav Klomstadlien

The lean, but extensive iron ore deposits of the Dunderland Valley north of Mo i Rana, Norway, are the raw material base for Rana Mines, a division of the state-owned A/S Norsk Jernverk steel mill. The iron bearing minerals are magnetite and specular hematite. The magnetite/hematite ratio varies considerably both within each deposit and from one deposit to another. The ore bodies that lend themselves to mining have generally a thickness of 30-60 m grading 30-35% Fe and 0.15-0.25% P. The grain size varies from 0.05 to 2.5 mm. The fine grained ores are hard while the coarse grained ores are soft and easy to grind. The A/S Norsk Jernverk steel mill operates both a sinter and a pellet plant, and this necessitates production of two types of concentrates. The present flowsheet is shown in [Fig. 1]. The crude ore from the pits is crushed in a 1.07-m gyratory crusher with an open side setting of 12.7 cm. The crusher product is transported by rail to the concentrator located 25 km from the mines. The ore is fed by twelve 1.22 X 1.83 m vibratory feeders onto conveyor belts which carry the ore to a surge bin ahead of the autogenous mills. The feed rate is automatically adjusted to maintain a set power load at a level suitable for the ore type being processed. The mills operate in closed circuit with twelve dual-drum screens equipped with a 0.8-mm screen cloth. Oversize is returned by gravity to the mill feed while undersize flows to the gravity separation section which consists of Humphrey spirals in three stages. The ores are very heterogenous and analysis may vary quite considerably. The quantitative need for concentrate in the steel mill may also change rapidly. The process in the concentrator must therefore be easily changed, and consequently alternative process lines have been established. This is indicated with the dotted lines in the flowsheet. Apatite is removed by flotation by fatty acids to give a final sinter concentrate of 63% Fe and 0.020% P or less. Pellet concentrate contains about 65% Fe and less than 0.020% P. The fineness is about 1500 Blain.

Jan 1, 1981

By B. G. Zambre, G. A. Parks, J. N. Roco

Automatic controls have long been a fact of technological life. Some understanding of control systems is rapidly becoming essential to the competence of mineral engineers. Students in undergraduate mineral engineering curricula, however, should not be expected to develop proficiency in the design and interpretation of control systems. They should be provided the opportunity to absorb some of the fundamental concepts and cant of such highly specialized peripheral fields as automatic controls. The present paper describes the components of a simple, flexible and relatively inexpensive control system designed primarily for the use of students in independent study projects. The control system is based on a continuous on-stream optical analyzer analogous to commercially available systems using X-Ray fluorescence analysis. The components can be easily adapted to control other separators and separations. As described here, they have been arranged to control the magnetic separation of a magnetite bearing specular hematite from quartz to produce a quartz product of fixed hematite content using a minimum of power. The control system consists of the magnetic separator* with a vibrating feeder, † a sampler, an optical scanner, a differential amplifier, a millivolt recorder ‡ and a motor driven, metered variable DC power supply for the separator electromagnet. An optional magnet current recorder is useful. The system as arranged for closed loop control is illustrated in Fig. 1. The elements of the loop are identified in automatic control jargon in Table I. The same components can be easily adapted for use in other control modes.§.1 * A Carpco Induced Roll High Intensity Magnetic Separator (Carpco Manufacturing, Inc., Jacksonville, Fla.); modified for external magnet power supply. A Jeffrey-Traylor Vibrating Feeder Type 1B (Jeffrey Manufacturing Co., Columbus, 0.). A Beckman Laboratory Potentiometric Recorder (Beckman Instruments, Inc., 619-A) fitted with adjustable limit switches for external circuit control (Beckman Instruments, Inc.. 71980). Terminology is taken from ref. 1. CLOSED LOOP OPERATION The separation is monitored through the optical reflectivity of the tailings stream which is proportional to the hematite content, THA. The difference, A, between the measured analysis (actually a proportional voltage) and a reference analysis (also a proportional voltage) is continuously recorded. The separation is controlled through changes in the electromagnet current, I, supplied from a motor driven variable source. The two primary variables, ? and I, are linked through adjustable limit switches on the

Jan 1, 1965

By G. Thomas, O. Johari

MEIERAN and Richman' have proposed a method for the determination of electron-diffraction patterns from twinned bcc crystals. It is the purpose of this note to present a general method capable of predicting the positions of all reflections from both matrix and twin regions for all possible orientations of cubic crystals. The method has been verified for twinning in explosively deformed copper, and is found to be a very useful tool when used in conjunction with stereographic projection, and dark-field electron microscopy. Let an isometric crystal be twinned in any (hkl) plane. The twinning can be considered either as a reflection in the twin plane or as a 180-deg rotation about the twin axis. In reciprocal space, the 180-deg rotation about the twin axis would place a given point p, q, Y to a new position P, Q,R, such that both will be equally inclined to the twin axis. This is represented in Fig. 1. If the coordinates of three such pairs of points are determined, the matrix of the transformation can be obtained.' It is also seen that such pairs would satisfy another condition, i.e., the vector [p,q,r] plus the vector [P,Q,R] will yield a multiple of hkl, i.e., the indices of the twin plane, because in isometric systems the axis [hkl] is perpendicular to the plane (hkl). This can be simplified by taking the points along the three axes. If a point h2 + k2 + 12, 0, 0 is taken along the x axis, it is seen that its new indices should be so as to yield a sum 2h2, 2hk, 2hl,i.e., 2h(h,k,1). (Also the points h2 - k2 - 12, 2hk, 2h1, and h2 + k2 + 12, 0, 0 are equidistant from the origin and both points make equal angles with the twin axis, i.e., cos-' h/dh2 + k2 + l2.) Similar operations for the points yield respectively, after the 180-deg rotation about the twin axis. Following the method due to Buerger,' the matrix of the transformation is obtained as follows: Using this matrix the indices of any other point in reciprocal space can be determined. This matrix is much simplified for (111) twinning commonly encountered in fcc metals, since are each equal to —1; hence

Jan 1, 1964

By E. A. Gulbransen, W. S. Wysong, K. Andrew

INTRODUCTION THE reaction of carbon in solid solution in a metal with the surface oxide film on many metals may be inferred from thermodynamic calculations for high vacua and high temperature conditions. Holm1 has recently shown that oxide films may be removed from ferrous materials by heating in a vacuum at high temperatures and that carbon is the essential element in the reaction. Considerable work has been described in the literature on the decarburization reaction. Several general references may be noted.2,3,4 However, the nature of the mechanism involved in the decarburization is not well understood. Our interest in this reaction resulted from many attempts to degas and to reduce by pure and dry hydrogen the surface oxides 0n strips of various types of chrome-nickel alloys. Some of the early experiments on the behavior of 13 pct chrome-iron in vacua of the order of 5 X 106 mm and at a temperature of 600°C have been reported.5 These experiments showed a slow reaction with the residual oxygen or water vapor in the system and no reaction with hydrogen. This is in accord with thermodynamic data which would lead to the prediction that it is extremely difficult to maintain a hydrogen atmosphere at 600°C pure enough to reduce Cr203 formed on the surface. The crystal structure of the superficial oxide film formed on 13 pct chrome iron and Nichrome V has been investigated in the thin film range by Gulbransen, Phelps and Hickman,6 and shown to be Cr203. It was surprising to us to note that when a specimen of Nichrome V containing approximately 80 pct nickel and 20 pct chromium was heated to 850°C in a high vacuum, the specimen' lost weight. The rate of weight loss was very temperature sensitive. A study of this reaction in vacua and in a hydrogen atmosphere is the subject of this communication. TYPE REACTIONS Let us consider the various reactions which may occur when a metal is heated in vacua, in a hydrogen atmosphere, or in an oxygen atmosphere. The number and kind of reactions will depend upon the chemical nature, of the metal, its alloying constituents and the location of the alloying constituents. The metals used in this study are chrome-nickel alloys of the heater type. They consist essentially of chromium, nickel and iron, small amounts of carbon, silicon and manganese and traces of zirconium, calcium, aluminum and magnesium. The trace elements are added to improve the lifetime and other characteristics of the alloy when used as a heater. Seven of the more important reactions with which we are going to be concerned here are as follows: [I. Metal • (gas) ;--* metal + gas - degassing of the metal 2. xM(s) + y ½ 02(g) tom- M.0„ (s) – oxidation]

Jan 1, 1948