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By Zárate G. E.

Practical and statistical considerations concerned with the sampling, sample preparation and chemical analysis of precious metal ores are reviewed. The principal requirements related with the characteristics of sample cutter, sample preparation, equipment and methods are discussed. The main errors introduced in the different stages of the sampling systems are defined. The application of statistical techniques to evaluate these errors to determine the ore grade variation and to design the number of increments needed to get an accurate assay are presented. Finally, results obtained with the application of this method to gold and silver ores are analyzed and some recommendations are given.

Jan 1, 1984

By R. H. Jacoby, M. J. Rzasa

Experimental equilibrium vaporization ratios (K values) were obtained for nitrogen, methane, carbon dioxide, ethane and hydrogen sulfide in two natural gas-absorber oil mixtures and in two natural gas-Elk Basin crude oil mixtures. For each mixture of constant over-all composition, data were obtained at 100°, 150° and 200°F and at various pressures in the range 200 to 5,000 psia. Some effects of composition on the K values were obtained to serve as a guide in choosing K's for engineering calculations on other mixtures. The pressure cell used to obtain the data is a new type and is described here for the first time. INTRODUCTION The phase equilibria of complex hydrocarbon mixtures such as natural gases, crude oils and their mixtures have been studied previously for the purpose of finding equilibrium vaporization ratios for the hydrocarbon constitutents. In a few cases, such non-hydrocarbon.: as nitrogen, carbon dioxide, and hydrogen sulfide were included in the mixture. studied because they occur. in the fluids obtained from petroleum reservoirs. The increasing occurrerce. of these non-liydrocarbon.; antl their growing economic importance. make it necessary to account for them more accurately in engineering calculation.: than is now possible using the meager published data. The available data for non-hydrocarbons may he classified into two groups: namely, binary mixtures of a hydrocarbon and a non-hydrocarbon. and mixtures containing three or more components, only one of which is a non-hydrocarbon. Amon: the former. phase analyses are available for two nitrogen-HC mixtures, tve carbon dioxide-HC mixtures and three hydrogen sulfide-HC mixtures. Data for more complex mixtures are available as follows: Nitrogen-Methane-Pentane'; Nitrogen-Methane-Hexane,'; Nitrogen-Methane-Heptane'; Carbon dioxide-Natural Gas-Natural Gasorline": Carbon dioxide-Natural Gas-Crude Oil". These data have been used generally lor engineering calculations, often with little regard for their precise applicability because data for the non-hydrocarbons in the complex mixtures being dealt with were not available. The use of K values from binary data for calculation:; involving complex mixtures is open to criticism because such K's are not a function of composition and very often show large differences from the K's for the same components in a complex mixture. Thus the effects of composition must be evaluated when obtaining K's for components in complex mixtures. Poettmann and Katz " varied the carbon dioxide content of their mixture.; from about five to ten mol per cent and found substantially no effect on the K values due to this change. This was not surprising since one might expect that changing a minor com-ponent by * three mol per cent would have little effect. It is more important to find the composition change which have the largest effect on the K values. For example. varying the methane or heptanes — plus compositions over a wide rangr may have a large effect on the K'. of all components in the mixture. Interesting data to this effect were obtained by Eilerts and Smith." It was toward these problems that the experimental data presented here were directed. EQUIPMENT The pressure cell used to obtain the data i:. somewhat dif-ferent from those which have been described in the past. Photographs of the equipment are shown in Figs. 1 and 2. Fig. 1 Shows. the front panel: from a .rated position at the right the

Jan 1, 1952

By AIME AIME

TWO papers, "Calcium, Strontium, and Barium Metals," by Charles Hardy and Paul M. Tyler, and "The Mining of Gems and Ornamental Stones by American Indians," by Sydney H. Ball, were presented before the Rare Minerals and Metals group at its session Tuesday afternoon in the Auditorium. Donald M. Liddell, chairman, presided. Mr. Tyler summarized the first paper, outlining the uses, history, occurrence, manufacture, production and trade, markets and prices of the three metals. In discussion, in response to the chairman's query on "what are they doing in Russia with calcium, strontium, and barium," Guy C. Riddell replied that nothing is being done on a production basis. The great rare metals plant in Moscow is active, however, on other elements. "They are making radium chloride, uranium oxide, vanadium, cadmium, tungsten, molybdenum, selenium, antimony compounds; and mercury, nickel and arsenic are under production at interior plants. The rare metals plant is busily conducting research on beryllium, rhenium, lithium, bismuth, strontium and zirconium. These are the main rare metal activities. Much hard-alloy work. for cutting and facing, is under way:

Jan 1, 1933

By W. R. McMillan, E. A. Gulbransen, K. F. Andrew

Annealed and electrolytically polished pure iron was oxidized between 650° and 850°C at oxygen pressures of 0.1 to 2 microns Hg. Electron optical studies showed that oxidation occurs discontinuously over the surface and orients crystallographically with the substructure of the metal grains. IN previous papers', " the authors described the formation of oxide films on high purity iron at norrnal pressures and at temperatures below 300°C. Electron optical studies showed that the oxide film consisted of many individual oxide crystallites having nearly random orientation on each metal grain. The size of the oxide crystallites depended upon the temperature and upon the extent of oxidation. In these studies the crystallite size varied from 250 to 1800Å. Recently, Bardolle and Benard3 studied the crystal habit of the oxide crystallites formed on Armco iron between 650" and 850°C in what might be defined as a "poor vacuum" atmosphere in which the pressure could be varied between 10-1 to 10-3 mm of Hg. Their results showed that, at 850°C and a vacuum of l0-2 to 10-3 mm of Hg, a few well oriented nuclei of oxide were formed on the metal grains. At pressures between l0-1 to 10-2 mm of Hg, many oriented nuclei of oxide were formed. At 750°C the metal surface was bright although an oxide was present. Unfortunately, the extent of oxidation, the oxygen pressure, and the influence of carbon in the metal were not determined, and it was, therefore, impossible to give a theoretical interpretation to the very beautiful light micrographs. Bardolle and Benard used the light microscope to determine the crystal habit of the oxide and X-ray diffraction to determine the orientation relationships. It was believed that the use of controlled amounts of oxidation at high temperature is an important method for the study of the initial stages of oxidation of metals at high temperatures. This paper presents the first results of an electron optical study of this problem for iron. Since the electron microscope and electron-diffraction methods using stripped oxide films and surface replicas yielded finer details of the crystal habit and structure of oxide film, these methods were used in this study. Two types of iron having different carbon contents were used: Puron and Armco* iron. A com- parison of the results for these materials made possible a study of the influence of the surface oxide-carbon reaction on the initial stages of oxidation. Before discussing the experimental results, the thermodynamic equilibria of 1—the oxidation reaction, 2—the surface oxide-carbon reaction, and 3—the solubility of oxygen in iron, will be considered. In addition, it is important to consider the kinetic-theory predictions on the rate of collision of oxygen with the iron surface. Thermodynamic and Kinetic-Theory Calculations Only one type of reaction is usually considered in the oxidation of iron at normal pressures at high temperatures: Fe(a) + 1/2O2(g) = FeO(s) 3Fe(a) + 2O2(g) = Fe3O4(s) 2Fe(a) +3/2O2(g) = a-Fe2O3(s). [11 However, two other reactions may occur: FeO(s) + C (solid solution in Fe) + Fe(a) + CO(g) [2] and Fe(a) + O2(g) e Fe(a) (solid solution of 0,). [ 3 ] In addition, iron will react with the higher oxide at certain temperatures to form FeO. For a complete interpretation of the oxidation of iron at low pres-

Jan 1, 1955

By WALTER CARROLL

Between cross currents of economic factors and international expediencies the iron and steel industry in 1948 made an outstanding contribution to the general economic picture. Were it not for an unfortunate episode during the month of April involving a temporary shortage of coal, 1948 would have been an all-time record year in output. Exceeded in no previous peacetime year, the production of iron and steel in 1948 totaled some 88,500,000 tons. That it was a worthwhile effort of no small magnitude is evidenced by the fact that in three and one half years following the war, this nation has produced as much steel as in the five years preceding the war. This figure of 88,500,000 tons is 68 per cent greater than that for 1939.

Jan 1, 1949

By B. K. Larkin, H. R. Bailey

A model Of heat flow in an underground combustion process is studied. This model includes convection effects and thus is more general than previous studies which considered conduction as the only mechanistn for heat transfer. Both linear (tube run) and radial (field application) geometries are considered. The effects of ignition heaters, vertical losses and finite source width are considered for the linear case. The results are in the form of equations and are presented in graphical form for a number of cases. Convection effects increase frontal temperatures about 25 per cent over those computed for conductive transfer for typical field operating conditions. This increase in temperature is a result of heat being transported toward the front by the injection gas. Even greater temperature increases are realized as the per cent oxygen in the injection gas decreases. It is well known that compression costs are of considerable importance in estimating the economic feasibility of underground combustion. By assuming an ignition temperature for the combustion fuel, predictions of limiting conditions on fuel density and injection rate necessary to sustain the combustion zone are made. For typical field conditions, at least 0.75 lb/cu ft of fuel are needed with air as the injection gas. If the injection gas is 10 per cent oxygen and 90 per cent nitrogen, this figure is 0.69 lb/cu ft. INTRODUCTION The possibility of increasing oil recovery by underground combustion has been considered for many years. Recent field tests indicate that the underground combustion process is technically feasible. The economic feasibility depends to a large extent on the amount of air which must be injected to sustain combustion. Prediction of the success of employing underground combustion in a particular reservoir must be based on existing field tests, laboratory tube runs"' and solutions of mathematical or analog models. Vogel and Krueger5 devised an electrical analog of the heat transfer problem in an underground combus-ion process. They considered the problem of heat conduction from a cylindrical source with increasing radius assuming no vertical losses. Bailey and Larkin and Ramey solved the corresponding problem including vertical losses by considering a mathematical model of the conduction process. Ref. 9, 10 and 11 also present information related to the subject study. The present paper generalizes these results to include both conduction and convection mechanisms for heat flow. A model of the conduction-convection process is described. The partial differential equations governing this model are written and solved for a number of cases of interest. The formulas are evaluated and the results are presented graphically. A CONDUCTION-CONVECTION MODEL Description of the Model A number of models are employed in this paper, each of which approximate a particular physical situation depending on the geometry, i.e., linear or radial flow, the type of vertical heat losses, the nature of the source, etc. The geometry for both the linear and radial case is shown in Fig. 1. A particular linear model is described in this section, and variations from this model are described in later sections of the paper. Consider a homogeneous, semi-infinite porous prism with lateral sides insulated as shown in Fig. 1. The left end, x = 0, is heated for a time t, with a plane heater supplying a constant heat flux and during this time; gas (nitrogen) is passed through the pores of the prism at a constant mass flux. At time t, the heater is turned off and air is injected in place of the nitrogen. This causes combustion to take place, and a uniform source of width 1 is formed which moves at a constant velocity v, to the right. The frontal velocity v, is related to the gas velocity v,, through stoichiometric considerations

By D. A. Koss, R. O. Gordon

Changes in the ultrasonic attenuation in steel specimens have been observed during tensile tests. Samples of AISI 1020, 1045, and 1095 steel quenched and tempered to a spheroidized condition have been used. Both attenuation and microstrain measurements fail to reveal preyield dislocation motion in the as-tempered specimens. Upon reapplication of the load to samples in the strain-aged condition there is a large preyield attenuation increase but no observable micvostrain up to 90 pct of the flow stress. These and other observed changes can be related to changes in the free disloca-tion density and the average dislocation segment length. The results show that the increase inflow stress in the strain-aged condition is caused by increased fric-tional stresses rather than by dislocation pinning. Strain aging is found to proceed through three distinct stages. The second of these follows the t2,3 law and is characterized by an activation energy of 20 kcal per mole. RECENT years have seen substantial progress in the understanding of the sharp yield-point phenomenon in metals; the influence of solute atom pinning of dislocations, of dislocation multiplication, and of the stress dependence of dislocation velocity on the stress-strain curve has been investigated. Evaluation of the relative importance of these factors in the various metals and alloys is not complete, however, because observation of the stress-strain curve alone is not sufficient to determine the yield mechanism. In the experimental study of the sharp yield point it would be desirable to be able to directly observe the dislocations in a bulk specimen. Ideally, the observations should be made during deformation because of the rapidity of recovery processes in lightly strained metals. While direct observation of dislocations under these conditions is not possible, certain physical properties sensitive to the dislocation structure can be observed while a test specimen is undergoing deformation. Of these properties, one of the most useful is the ultrasonic attenuation. The total observed attenuation, a, is due to a number of causes: acoustic diffraction, scattering by inhomogeneities in the structure, heat flow, magnetostriction, and dislocation damping. Satisfactory measurements of the absolute a are difficult to make because all of these factors cannot be evaluated in any given specimen, but changes in a due to changes in the dislocation contribution alone can be reliably observed by appropriate technique. Because dislocation damping is sensitive to small concentrations of long, free dislocation segments, observation of acoustic attenuation due to dislocations is particularly useful in the study of the early stages of plastic deformation. In the experiments to be described, acoustic-attenuation measurements have been made on steel samples as these were pulled through their yield in tension. While many details of dislocation-damping phenomena in the bee metals remain obscure, the main characteristics of this type of internal friction are established. At low strain amplitudes and at frequencies well below that of dislocation resonance (the conditions of these experiments) the dislocation contribution to a is given by1 where A is the density of freely oscillating dislocation segments, L is the average segment length, B is the damping constant for a moving dislocation, w is the frequency, O is an orientation factor, C is the dislocation line tension, and t is a numerical factor relating average segment length to the distribution of lengths. Because of its fourth-power dependence on L, a is highly sensitive to changes in dislocation free segment length such as might arise from unpinning, recovery, jog formation, or dislocation intersection. The above equation is not valid near the resonant frequency of dislocations, but the segment length in steel is believed to be much too short to cause over-damped resonance near 10 Mc; this will be discussed later. In the present experiments plastic-strain measurements with a sensitivity of 2 x 10-5 were also made during the early stages of loading in order to detect preyield strain. The general plan of the experiments is to observe

Jan 1, 1967

By Richard H. Olson, Lawrence A. Roe

Talc, when it can be isolated as a pure mineral, has a composition of 63.36% Si02, 31.89% MgO, and 4.75% H20. However, as an industrial commodity, talc rarely approaches theoretical purity. Nevertheless, the impure talc products of commerce find a multitude of uses and few substitutes in many industrial applications. Minerals commonly associated with and sold together in talcose mixtures are tremolite, chlorite, dolomite, mica, and magnesite. Steatite was originally a mineralogical name applied to pure talc. In today's commerce steatite generally refers to the massive variety of talc suitable for electrical insulator manufacture. Block steatite ore can be machined into various shapes. Impure varieties of massive or block talc are still commonly referred to as soapstone. Soft massive talc, suitable for crayon manufacture, has been referred to as French chalk. It has been common practice to discuss talc, soapstone, and pyrophyllite under the same general heading. In the case of soapstone and talc, this is a natural thing since many different types of platy, soft minerals exhibiting a high degree of lubricity (commonly referred to as "slip") have been grouped together and called soapstone or talc. Further, there is a mineralogical relationship of pyrophyllite to montmorillonite and talc to hectorite. Thus, talc and pyrophyllite are sometimes referred to as clay minerals. When finely divided talc or pyrophyllite are combined with water in proportions to make a slurry, the end product does have the appearance of a clay-water mixture. Soapstone for utensils and ornaments was mined by prehistoric Indians on Santa Catalina Island, CA. In the mid-1800s, soapstone from deposits along the western foothills of the Sierra Nevada mountains was used by white settlers for building and ornamental stone and in the linings and foundations of furnaces (Anon. 1956). Previous to 1916, the annual recorded production in California did not exceed 2000 tons. In the period 1912 to 1918, output rose sharply when the Talc City, Western, and Silver Lake mines were put into operation. From 1916 to 1935, the state's annual output of talc was in the range of 9,000 to 20,000 tons. In the mid-1930s, the use of talc in wall tile grew rapidly. In California, the production of talc grew to 63,000 stpy in 1943. The post-war building boom helped California production to grow to 120,000 tons in 1951. In 1968, production was 165,000 tons, 1969 was 145,000 tons, 1970 was 185,000 tons, and 1972 was 155,000 tons. Talc mining in New York state dates to about 1878 when a Colonel Palmer and associates opened the first commercial talc mine on the Nelson Freeman farm near Talcville, New York. In 1893, this operation was sold to the International Pulp Co. which changed its name to the International Talc Co. in 1944. The company was acquired by R.T. Vanderbilt Co., Inc. in 1974. A new talc operation, the Gouverneur Talc Co. owned by the R.T. Vanderbilt Co., began operations near Balmat, NY, in 1948. The initial capacity of the processing plant was 200 stpd (Gillingham, 1950). Subsequent expansions have increased capacity to over 600 stpd. The Vermont talc industry began just after the start of the 20th century. Talc was discovered in the area of the present Johnson, VT, talc mine in 1902. The American Minerals Co. initiated plant operations at Johnson in 1904. The Magnesia Talc Co. opened a plant at Waterbury, VT, in 1913 (Burmeister, 1963; Trauffer, 1964) and acquired American Minerals Co. in 1923. The Waterbury mine has a long history as a producer of talc crayons. The Eastern Magnesia Talc Co. was formed in 1924 by a merger of the Eastern Talc, Co.

Jan 1, 1983

By O. D. Gonzalez, R. A. Oriani

The migration of hydrogen and of deuterium dissolved in a iron and in nickel induced by an applied electrical potential has been measured over a range of temperature. In all cases the intevstitial solute migrates to the cathode. The deduced charges of transport are positive, independent of or slightly dependent on temperature, and markedly larger for the beavier mass. These results are interpreted as showing predominating momenlum transfer between electron holes and the acticated complex of the elementary diffusion act. THE migration of components of a metallic system under the action of an applied electrical potential is called electromigration or electratransport. This phenomenon has been known since 1861 and is becoming of increasing interest to metal scientists because of the opportunity it offers to explore the connections between mass transport and electron transport. Until recently, reliable data have been very scarce because of the difficulties inherent in the measurements. In addition, theoretical understanding has been either nonexistent or rudimentary and at present this situation is only moderately improved. Whereas the prevalent notion had been (and is still widely held) that electromigration directly reflects the state of ionization of a component in its equilibrium state in the metal, it is now becoming clear that the major, if not the sole, factor is the momentum transfer between the charge carriers, themselves in motion because of the applied field, and the metallic components in their activated state. It becomes important therefore to obtain reliable data over a range of temperature on electrornigration in systems where only one component moves, that is, either in pure metals (vacancy motion) or in interstitial solid solutions. Our choice of systems was dictated by our measurements' of the Soret effect in solid solutions of hydrogen and deuterium in iron and nickel. Indeed, the main reason for making measurements on electromigration at all is that we suspected a mechanistic connection between thermal diffusion and electromigration. In our former paper' we proposed that what is common to both phenomena is the momentum transfer between the charge carriers in the metal and the atom as it jumps from one equilibrium position to another. In Soret diffusion, however, there is in addition the dissipation of the energy of the jumping atom via pho-nons. We have since found that similar ideas for this interconnection have been developed by Fiks.2 In the present paper we will discuss in more detail our understanding of the mechanism of electromigration itself, but we turn first to a presentation of the experiments and results. EXPERIMENTS AND RESULTS Let us consider a metallic system in which only one component, m , can diffuse at the temperature in question, and to which are applied simultaneously an electrical potential gradient, grad cp, and a chemical potential gradient, grad p,. One may write3 for the material flux Jm and the electronic charge flux Je by applying the condition, grad = 0, to Eq. [I] and evaluating grad(um/T) for the isothermal case and for activity coefficient independent of composition over the relevant composition range. ere, c is the concentration and D the diffusivity of the mobile component. The experimental technique that we have used to measure Z* for the isotopes of hydrogen individually dissolved in each of two transition metals has been developed from a method used by Wagner and Heller.4 (A somewhat similar method was also used by Herold.5) A wire or thin rod of the metal under study connects two volumes of gaseous hydrogen at identical pressures; hence grad um = 0. A direct current is made to pass through the specimen, serving to maintain the specimen at the desired temperature and also to produce the electromigration of the hydrogen dissolved in the metal in equilibrium with the gaseous hydrogen. Under these conditions, the flux of hydrogen from one volume to the other is given, from Eq. [I] for grad( um/T) =0by

Jan 1, 1968

By R. E. Cook

This paper presents results of a study to determine to what extent errors in estimated free gas saturation affect the results of static pressure calculations from build-up curves in two-phase systems. Use is made of the method of pressure build-up curve analysis developed by Miller, Dyes and Hutchinson1 , with modifications for two-phase flow advanced by Perrine2. Cornhined fluid compressibility of gas-oil mixtures is included, with special attention given to the discontinuity that occurs in fluid compressibility at the saturation pressure and its effect on static pressure calculations from build-up curves. The sensitivity of static pressure calculations to errors in gas saturation is considered over wide ranges of formation and fluid properties and reservoir pressure conditions. It is concluded from this study that for analyses of two-phase pressure build-up curves (I) the use of under-saturated crude compressibility data, even when producing GOR's are at or near solution values, will result in very significant negative errors in calculated static pressrrre, and (2) except for large values of buildup curve .slope and/or very low crude gravities, rather large errors in calculated gas saturation can he tolerated without .significant effect on calculated static pressures. The conc1usions arc qualified as referring only to the effects of gas saturation and excludc possible errors in the nuumerous other factors that enter into the ancllysis of pressure build-up curves. INTRODUCTION As part of the analysis of basic data for several major Eocene reservoirs in the Bolivar Coastal field (Western Venezuela), it was necessary to analyze a large number of pressure build-up curves for oil permeability and static reservoir pressure. From performance data it became apparent that gravity segregation is very active in these reservoirs. As a result of this performance it was recognized that the free gas saturation within the oil leg of the reservoirs would be small but would be subject to certain errors in calculation due to the inaccuracy of relative permeability data in the low gas saturation region. Since all of the various methods of build-up curve analysis were originally derived for sin- gle-phase, constant compressibility systems, and since the presence of a small but rather indeterminate gas saturation would greatly affect the reservoir fluid compressibility, a study was undertaken to investigate the effect of gas saturation on the results of two-phase pressure build-up analyses. TWO-PHASE BUILD-UP CURVE ANALYSIS The method of analysis used in this investigation is basically that originally developed by Miller, Dyes and Hutchinson1, with modifications for two-phase flow advanced by Perrine2. Miller, et al, showed that the original equation for single-phase permeability away from the well bore, held for two-phase flow except that the calculated permeability is the effective permeability to oil away from the wellbore. This finding was acknowledged by Per-rine, who also presented the equation for effective gas permeability* as Since Eqs. 1 and 2 contain no terms influenced by fluid compressibility, no distinct problem should develop in calculating permeability from two-phase build-up curves. In regard to the calculation of static reservoir pressure from build-up curves in single-phase systems, the modified Miller, et al, method as presented by Perrine is briefly as follows. 1. From build-up curve data, PVT data for the reservoir fluid and the well spacing and sand thickness, calculate the climensionless shut-in time corresponding to the highest value of actual shut-in time (t, hrs) on the straight-line portion of a semi-log build-up curve. Dimenrsionless shut-in time is related to actual shut-in time by the relation, t- 0.000264 kt 2. From a graph of dimension less shut-in time vs dimensionless pressure difference (Fig. 1 1 ) find the value of dimensionless pressure difference corresponding to the value of 7 calculated under (1) above. Dimen-

By Edward W. Parker

IF one is to place any credence at all in the reports published in the daily press, the subject of conservation has been a very lively topic of conversation during the past 60 days, and it does not appear that the temperature of the summer months has been in any way moderated by the discussion. It is a subject in which we are all vitally interested and to which, so far as our mineral resources are concerned, both the Institute and the Geological Survey have liberally contributed. The report of the National Conservation Commission, appointed by President Roosevelt, contains a series of papers on the conservation of mineral resources, all of which were prepared by members of the Geological Survey and were compiled largely from information previously collected by that Federal bureau in the performance of its regular duties. It is not the purpose of this paper to reiterate in extenso any of the material already published. The contributions of the Survey officials to the Commission's report have been published in a separate document as Bulletin No. 394. This docunient is for free distribution and may be obtained upon application to the Director of the Survey. In the preparation of this paper I desire merely to make a few suggestions regarding the possible necessity of some restraint upon or control of one branch of the mining industry with which I have been somewhat closely associated for the past 20 years-that of coal. Most of the members of the Institute are cognizant of the suits brought by the government against the anthracite-operators in Pennsylvania, or the combination of interests commonly known as the ? hard-coal trust." No defense of any illegal combination in restraint of trade is intended, but there are some facts which should not be lost sight of, and unfortu-\

Nov 1, 1909

By G. R. St. Pierre, M. J. Pool, R. Speiser

The activities of chromium in solid Cr-Ti solulions contaitning from 10 to 90 at, pct Cr were measured over the temperatutre range 1250" to 1380°C. The Knzudsen effusion technique with direct weighing of the Knudsen cell was used. This was possible because the vapor pressure 0f chromium is about 600 times greater than the capor pressure of titanium so that the amount 0f titanium effusing could be neg-Lected. the activities of titanium were determined by g-raphical integration of the Gibbs-Duhertz equatiotz. The solutio~ls sllcdied exhibited positive deviations from Raoult's law, but they approached ideality as the temperature was raised from 125 to 138t C. The integral free energy of mixing was calclated from the activity values. AF has a maximum value of - 1.66 kcal a1 1390°C and a composition oj 55 at. pcl Cv. The free energy of formation of 'TiCr, is —0.76' lzcal a1 1250°C. The heats and entropies of mixing usere determined using the second law and thus tile mlues could be in error by a considerable amount. The Cv-Ti system is not a regular solution. ThE increasing emphasis on application of various models to alloy formation and solution behavior has led to an intensified interest in the thermochemistry of alloys. In a majority of the cases where different models have been applied the alloy system used was a simple one. However, the amount of data available on more complicated systems is small and in order to fully understand the behavior of metallic solutions more experimental work has to be carried out on these systems. The Cr-Ti system is reasonably complex and even though this system was being investigated as early as 1937 by Kroll,' no previous work has been done on the thermodynamic properties of either the liquid or solid state. This research was undertaken to determine the thermodynamic properties of solid Cr-Ti alloys. EXPERIMENTAL PROCEDURE The experiments on the Cr-Ti system were carried out in a water-cooled metal vacuum system. This system is composed of a brass vaporization chamber wound with copper tubing for cooling purposes, a brass liquid-nitrogen trap, an oil diffusion pump, and a Duo-Seal forepump. The pressure in the system is measured with an ionization gage. The interior of the vaporization chamber is shown schematically in Fig. 1. The Knudsen cell is supported by the molybdenum tripod, and a magnetically operated shutter is provided to protect the Pyrex sighting glass against deposition of metallic vapors in the intervals between temperature measurements. Heating is accomplished by means of a 20-kw 450-kc Westinghouse oscillator. The susceptor in this case is 10-mil tantalum seamless tubing which also forms the outside of the sample container. The remainder of the sample container consists Of an im~ervims re-crystallized alumina crucible and a 10-mil-thick tantalum lid. Two holes are drilled in the lid. The diameters of these holes were measured with the calibrated stage of a "Tukon" microhardness tester. The thicknesses were measured with a micrometer. A Leeds and Northrup disappear ing-filament optical pyrometer was used to measure the temperature. This is sighted through the smaller of the two holes in the lid and corrections for the emissivity of the sample were not necessary since the ratio bf cell length to hole diameter was large enough to insure a hohlraum. The pyrometer was calibrated at the ~~t~~~l Bureau of Standards, and the correction for the Pyrex sighting window was determined in the laboratory. The titanium used in this investigation was obtained from Mallory-Sharon and the chromium from The Union Carbide Metals Co. The reported purities were

Jan 1, 1968

By F. P. Bullen

Empirical relationships between fracture stress, orientation angle, and diameter of crystal have been determined at 77°K. Orientation ranges of markedly different behavior were found—a law of constant normal stress&apos; of value a (diameter)-1/2 for the fracture of ductile crystals, and a condition of shear stress (or strain) for more brittle crystals. The observations are not consistent with current theories. An interpretation is advanced which is also applicable to observations on the effect of prestrain at room temperature on the subsequent fracture stress at 77°K and to the effect of cyclic stressing on the cleavage strength.&apos;&apos; The law of constunt normal stress&apos; and the brittle ductile transition are also explained. The interpretation is more consistent with the initiation of cracks by intersecting dislocations than with theories based on stress -concentration by dislocation arrays. ZINC single crystals are particularly suited to the study of cleavage because fracture occurs on the basal plane over a wide range of crystal orientations. Analysis of the conditions of stress and strain at fracture in crystals of different orientations should indicate which parameters control the cleavage process. Unfortunately, controversy has arisen over the correct empirical relationship between tensile fracture stress and orientation. Schmid&apos;s observations1,2 favored a &apos;law of constant normal stress&apos;, as observed in other materials.2 For zinc, however, the observed values are far below the theoretical strength and cannot represent the true limit of cohesion between neighboring atomic planes. Hence, the interpretation of such a &apos;law&apos; is not straightforward. Deruyttere and Greenough3,4 found a complex variation between tensile fracture stress and orientation; this variation did not agree with a &apos;law of constant normal stress&apos;. Two theories have been advanced to account for their observations: a) the propagation of cracks from low-angle boundaries,5 and b) the release of energy from piled-up dislocations during crack-propagation.4 The present work resolves the apparent discrepancy between the observations and shows that neither of the above theories are applicable to the tensile fracture of zinc single crystals. A phenomenological explanation, along the lines suggested by Gilman,&apos; is advanced and successfully applied to previously unexplained effects. EXPERIMENTAL DETAILS &apos;Crown Special&apos; redistilled zinc was used, except for one comparison series op tests using &apos;Tadanac&apos; electrolytic zinc. Crystals of 1 mm diam, subsequently called &apos;1 mm crystals&apos;, were grown from the melt in vacuo in precision-bore Pyrex tubes internally coated with graphite. Several specimens 1 in. long were cut from each crystal and chemically polished. Jigs were used to minimize handling strains, and crystals were mounted in the Polanyi machine the day prior to testing to allow recovery from any such strains. One-mm crystals were chemically polished for long periods to obtain 0.1 mm (approx) crystals. One-mm crystals were cemented into miniature gimbals by &apos;Araldite&apos; casting resin. The Appendix gives the reasons for using gimbals and the results obtained by other methods. More complete details of all techniques are given elsewhere.7 The symbols and terminology used are as follows: X = orientation angle (angle between tensile axis and line of greatest slope in the basal plane). T = tensile stress (on true cross-section) S,N = shear and normal stress (components of T with respect to the basal plane) ? = shear strain D = crystal diameter. The subscript &apos;f&apos; will be used to denote values at fracture. PART I-ANNEALED CRYSTALS EXPERIMENTAL OBSERVATIONS One-mm crystals were used to establish the variation of fracture stress at 77°K with orientation at fracture (Xf), Fig. 1. For 18 deg = Xf = 55 deg, a &apos;law of constant normal stress&apos; was observed. For Xf > 55 deg, the fracture condition approximated to a constant shear stress. At Xf< 18 deg, twinning occurred before fracture so that the results were not typical of homogeneous single crystals,4,8— such specimens will not be considered herein. The dependences of fracture stress upon Xf were of similar type for 6 mm,* 1 mm, and 0.1 mm crystals,

Jan 1, 1963

By M. A. Dayananda, R. E. Grace

Vapor-solid diffusion couples were employed in a study of ternary diffusion in the single-phase copper-rich corner of the Cu-Zn-Mn system Interdiffusion coefficients were measured at three different compositions corresponding to the intersections of diffusion paths determined at 850°C. Intrinsic diffusion coefficients were determined at two compositions by the Philibert-Guy method. New relations between the various intrinsic diffusion coefficients are also presented. MOST of the investigations of ternary diffusion have been made with "sandwich" couples formed by welding together two homogeneous solid solutions with or without markers placed at the interface. With such couples Kirkaldy and his coworkers1,2 have determined interdiffusion coefficients which describe ternary diffusion in the substitutional alloy systems, Cu-Mn-A1 and Zn-Cu-Al. Guy and Leroy3 have reported intrinsic diffusion coefficients for Co-Ni-Cr alloys as a function of composition using the analysis of Philibert and Guy.4 The use of semi-infinite diffusion couples, for example, vapor-solid couples, where the diffusing species are supplied from a vapor source in contact with a diffusion disk, has so far been confined to studies of binary diffusion. Balluffi et a1.5,6 have successfully determined the interdiffusion as well as the intrinsic diffusion coefficients in several binary metallic systems employing vapor-solid couples with markers initially placed at the vapor-solid interface. They have also discussed the general advantages and limitations of such couples. Vapor-solid diffusion couples can successfully be employed in ternary diffusion studies. The importance of such couples in ternary diffusion lies in the fact that inert markers lie close to the vapor-solid interface, and the composition of the marker plane is virtually known before experimentation begins. Another minor advantage is that the method of Philibert and Guy4 may be used with three alloys instead of four. Lastly, the diffusion paths need not be S-shaped, as pointed out by Meijering7 for "sandwich" couples. The Cu-Zn-Mn system is convenient for ternary diffusion studies because of the large single-phase field in the copper-rich corner. The vapor pressure of zinc above such alloys is known, and X-ray measurements indicate that the molar volume is nearly constant over a wide range of compositions.8,9 It is the purpose of this paper a) to extend the analysis of Balluffi and seigle5 to permit an evaluation of interdiffusion coefficients in ternary vapor-solid couples, b) to use the method of Philibert and Guy to determine intrinsic diffusion coefficients with such couples, and c) to present experimental data on both interdiffusion and intrinsic diffusion coefficients for the Cu-Zn-Mn system at 850°C. INTERDIFFUSION IN TERNARY VAPOR-SOLID COUPLES The analysis of Balluffi and seigle5 is extended in this section to a vapor-solid couple where two solutes diffuse from a vapor source into a ternary solid solution. To take into account the expansion of the diffusion disk caused by the absorption of mass from the vapor phase, the total fluxes are expressed on the basis of a coordinate system that moves with the velocity of the vapor-solid interface; thus. where D3ij are the intrinsic diffusion coefficients,4 v(x, t) is the local Kirkendall velocity of mass flow, and F(t) is the negative velocity of the vapor-solid interface (x = 0). Both these velocities are based on a fixed coordinate system far removed from the diffusion zone. Using the continuity relations and Darken&apos;s method1&apos; for a ternary system in which components 1 and 2 diffuse from the vapor phase into a solid of negligible vapor pressure, one obtains

Jan 1, 1965

By I. R. Kramer

The stress associated with the high-dislocation layer at the surface of deformed aluminum crystals was measured by progressively polishing the specimen and determining the change in the initial flow stress when the specimen was reloaded. This surface stress increased linearly with strain in the Stage II and Stage III region. The depth to which the high-dislocation layer extends was found to be 0.0025 in. The influence of the surface layer on Stage I is discussed and it is shown that Stage I ends when, on the secondary slip system, the difference between the applied stress and the opposing stress due to the surface layer is equal to the critical resolved shear stress. In previous papers&apos;-3 it was shown that the surface exerts a pronounced effect on the plastic-flow characteristics of metals. For fcc metals it was possible to increase the extent and decrease the slope of Stages I and II and decrease the work-hardening coefficient of Stage II by removing the surface of the specimen continuously during the deformation process.2,3 More recently,L it was shown that the activation energy for plastic deformation and the activated volume were also influenced by the surface. These changes were related to the existence of a high concentration of dislocations in the region near the surface of the deformed specimen and it was concluded&apos; that the effective stress, T, acting on a dislocation was T = Ta-Ti-Ts [1] where 7, is the applied shear stress, Tj is the internal stress, and TS is the stress associated with the surface region containing the high concentration of dislocations. From Eq. [I] it is seen that the effective stress, 7, acting on a dislocation is a function of 7,. Therefore 7, becomes important in any description of the work-hardened state. In this paper the value of 7, as a function of strain and its variation with depth are reported for aluminum single crystals. In particular, it will be shown that the end of Stage I occurs when the net stress, 7, on the secondary slip system is equal to the critical resolved shear stress. To measure Ts, single crystals of aluminum were deformed in tension to various strains, whereupon the load was removed and a known amount of metal was removed by electrolytic polishing. The differ- ence between the final flow stress before the specimen was unloaded and the initial flow stress upon reloading is designated as ?Tp and is the decrease in the stress due to the removal of the surface layer in whole or in part. The value for Tp is taken equal to -Ts. EXPERIMENT PROCEDURE The details of the tensile apparatus, method of electrolytic polishing, and crystal preparation were the same as those used previously,1"3 The single crystals were 1/8 by 1/8 in. in cross section with a 3-in. gage length. The initial purity of the aluminum was 99.997 pet. The specimens were held in vacuo at temperatures 50°C below their melting points for 16 hr and furnace-cooled. Just prior to the application of the tensile stress the specimens were electrolytically polished to remove 0.004 in. from the thickness. This latter operation was conducted after the specimen was placed in the tensile apparatus. The tensile tests were conducted at a strain rate, i, of 10"5 sec-&apos; and a temperature of 3°C. The aluminum crystals used for the determination of 7, are designated A1-3-12 and A1-116. The orientation of the various crystals used throughout the investigation is shown in Fig. 1. The ?Tp values for specimens A1-3-12 as a function of Ax were determined mainly at four strain levels, i.e., ? = 0.0217, 0.0381, 0.0593, and 0.075, where Ax is one half of the total reduction of the thickness after polishing and ? is the re-

Jan 1, 1965

By T. D. Mueller, H. Dykstra

This paper describes a method for obtaining compositions of gas and oil phases in equilibrium with each other at a given reservoir temperature and pressure as lean or enriched gas is injected into a reservoir oil not in equilibrium with the gas. The method is based on calculation of equilibrium constants, K, from the equation log Kp = A + B F, where p is pressure and F is component characterization factor. A and B are constants that vary with a composition parameter. The paper explains how A and B could be determined with a minimum amount of data. The method consists of calculating equilibrium constants as a function of liquid composition and using the K&apos;s to calculate changes in compositiort of injection gas as it successively contacts original resetvoir oil at the gas-oil front and the change in composition of reservoir oil as it is successively contacted by the injection gas in the vicinity of an injection well. An iterative process is required. Two examples of the method are given which show how oil and gas compositions and properties are calculated with the aid of a computer. INTRODUCTION The calculation of recovery from lean-gas or enriched-gas injection into a saturated or under-saturated reservoir oil requires a knowledge of how phase properties change in a reservoir between injection well and producing well. To determine the phase compositions or properties experimentally would be difficult and time consuming, especially if one wanted to look at the effect of various injection gas compositions. For some fields an engineer would want to make preliminary calculations on the economics of gas injection before he makes the decision to spend a corrsiderable sum of money for laboratory work to obtain the necessary fluid properties. A method for calculatine compositions and properties based on a minimum of laboratory data is described. The minimum amount of data required is injection gas and reservoir oil composition and injection gas solubility as a function of pressure for an undersaturated oil, or the compositions of mixtures of reservoir fluid with two or more enriched gases, which mixtures have a bubble-point pressure that is the same as the expected average displacement pressure. On the other hand, if the economics appear to be attractive, more laboratory data can be obtained in the form of equilibrium constants for three or more mixtures of the reservoir fluid and injection gases. The method is based on the calculation of K&apos;s from the equation, log Kp = A + B F, where K is equilibrium constant, p is pressure and F is component characterization factor. This method of plotting K data by means of the above equation is described by Hoffman, Crump and Hocott.1 A and B are constants that vary with a composition parameter. It is shown how experimental data are used to determine how A and B vary with composition. BASIS OF METHOD EQUILIBRIUM CONSTANTS Equilibrium constant (K) data are required for this method. The K of each component is obtained from an equation that gives the product of K and pressure as a function of component characterization factor. The characterization factor F = b(l/Tb — l/T), where b is a constant characteristic of a given component, Tb is the boiling point in OR at atmospheric pressure of the given component, and T is the temperature of the system in OR. This method of plotting K data is described by Hoffman, Crump and Hocott.l The straight-line equation of the log Kp - F plot is log hp = log Kop +BFi, where Kop is at F =0, i designates the component, and B is the slope of the line. The factor F can be

Jan 1, 1966

By H. C. Brassfield, R. E. Fryxell, E. C. Duderstadt, E. A. Aitken, P. K. Conn

Permeation rates of hydrogen through are-cast tungsten were measured at temperatures from 1300" to 2600°C with hydrogen pressure differentials of 1 and 0.1 atm across isothermal membranes. Rates were nearly Proportional to square root of pressure, were inversely ProPortional to membrane thickness, and were temperature-dependent according to the equation: p = permeation coefficient in cu cm (stp)-mm per sq cm-min-atmlr2, R = gas constant in cal per mole-OK, T = absolute temperature in OK. Permeation rates of oxygen through tungsten were deternlined in the range 1965" to 2300°C and at calculated oxygen (02) pressures of 3.3 x 10-4 to 2.2 x at?n using sealed capsules containing Kmown quantities of tungsten oxide. Permeation coefficients obtained in this manner had a temperature dependency in the range of 40 to 45 kcal per mole of permeating species. Permeation coefficients for oxygen were higher than those for hydrogen in the temperature range studied. This is probably the result of oxygen solubility being much greater than hydrogen solubility at these temperatures at a gzven pressure. The purpose of this investigation was to determine experimentally the permeabilities of hydrogen and oxygen through polycrystalline tungsten at temperatures ranging from 1300° to 2600°C. Permeation rates of hydrogen through tungsten have been measured at temperatures up to 925°C,but no previous measurements have been reported for the temperature range covered in this investigation. Some diffusion measurements3&apos;&apos; and solubility measurements3 have been made for hydrogen at temperatures below 2200°C. No previous permeability studies of oxygen through tungsten are known to the authors; however, efforts have been made to determine diffusion rates5-&apos; and solubilities PERMEATION THEQRY Permeation has been defined by ortton" as the overall steady-state flow process from the gas phase on one side of a membrane or wall to the gas phase on the other side and includes the steps of adsorption, solution, diffusion, exsolution, and desorption; in a given temperature range, any of these processes may be rate-controlling. For diatomic gases, which dissociate prior to diffusion, the quantity of gas which permeates through a membrane or wall at a given temperature is directly proportional to the surface area of the membrane, the length of time of permeation, and the difference between the square roots of the pressures on each side of the membrane, and it is inversely proportional to the thickness of the membrane when diffusion-controlled, thus: q = total amount of gas permeating a membrane, p = temperature-de pendent permeation coefficient, A = area of membrane exposed, / = time, p i = gas pressure of high-pressure side, p2 = gas pressure of low-pressure side, d = thickness of membrane. When the surface reactions are not rate-controlling steps and the solution of the gas in the metal follows Henry&apos;s law, the permeation coefficient, P, is equal to the product of diffusivity and solubility. The permeation coefficient is also temperature-dependent according to the equation: Po = permeation constant, Q = activation energy, R = gas constant, T = absolute temperature. MATERIALS The tungsten materials used in this investigation were greater than 99.9 pct pure. The interstitial impurities ranged from < 1 to 50 pprn C, 7 to 35 ppm O, less than 15 pprn N, and undetectable quantities of hydrogen. Previous high-temperature studies of are-cast tungsten have shown that thermal treatment similar to that which the hydrogen permeation cells experienced reduces the carbon content from starting levels of 50 to 60 ppm to about 30 ppm. Metallic impurities were in the low (1 to 50) ppm range. The argon gas used in this investigation contained about 8 ppm N. None of the following gases were

Jan 1, 1968

By B. R. Berger

The Getchell area in the northern Osgood Range, Humboldt County, Nevada, was first prospected in the late 1800s for silver, copper, and gold; the first recorded mention of mining activity concerned a silver discovery. The September 17, 1874 edition of the Winnemucca Silver State notes that the Crystal Mining District was newly organized in the Fremont Range (as the Osgood Range was then called) to include discoveries of silver, lead, and antimony made on the Louisa claim. The name Crystal was derived from the plentiful quartz crystals found in-cavities near the prospects. This same area, occurring on the northwestern margin of the Osgood granodiorite stock, was later mined as the Richmond tungsten property, and crystals may still be found there in cavities in a massive garnet tactite. By 1878, how-ever, the name Crystal had been abandoned in favor of Potosi. The next flurry of activity in the Osgood Range was reported in 1899 when a copper strike on Granite Creek in the southern portion of the range received attention. The copper occukences were in a granite contact zone on the southeastern edge of the Osgood stock and, in 1916, the first tungsten in the district was discovered in the same deposit. During the last part of the nineteenth century, cattle and sheep were brought into the Kelly Creek Valley east of the Osgood Mountains by various ranchers. Alphonso and Adrian Bernard were among these ranchers, and in the first decade of the twentieth century, one of them recognized the altered rock where the Getchell Center it is now located. A 3-m (10-ft) deep prospect pit was dug on the outcrop, but the highest assay ran about $11/t ($10 per st). No further work was done on the gold-bearing rock. In 1934, Emmet Chase of Battle Mountain and Ed Knight of Golconda prospected in the area of the Bernard prospect pit and located several lode claims. At this time, Noble H. Getchell, a state senator, was looking for new mining opportunities to develop. He held interests in the Gold Circle Consolidated at Midas, which was becoming a losing venture. Chase and Knight brought their discovery to his attention, and he grubstaked them to prospect further in the area. In need of financial backing, Getchell solicited the help of George Wingfield, Sr., who held a minor interest in the Gold Circle. Wingfield was a successful banker and mine operator during the heyday of Tonopah and Goldfield, and he had become good friends with Henry C. Frick and Bernard Baruch. Wingfield let Baruch in on several very successful mining ventures in Goldfield, and Baruch returned the favor by underwriting the financing of the Getchell mine. Eleanor Roosevelt and Jack Dempsey were early stockholders in the Getchell operation. George Wingfield brought his brother-in-law, Roy A. Hardy, a consulting engineer who had constructed the American Flat mill near Virginia City, to look at the property. Upon inspecting the Chase-Knight claims, Hardy declared the whole area to be mineralized. A crosscut was driven to check the extent of the ore, and the results were better than anticipated. The locators were reportedly given $50,000 for the claims. The Getchell Mine, Inc., was organized on November 5, 1936. A small railroad that ran from Battle Mountain to Austin was purchased, and the ties and rails were moved to Getchell to be used in underground exploration. Enough reserves were found in the Center and South pit areas to construct a 40 t/d (44 stpd) mill. The financial and engineering help for the mill was provided by the Newmont Mining Co. for a 17 1/2% interest in the corporation. Newmont set about trying to solve the metallurgical problems with the sulfide ore, and also directed the early development work. Newmont wanted to grind the sulfide ore underground and oxidize it in the atmosphere by spreading salt on it. Detrital Flat in Arizona was purchased to provide salt for

Jan 1, 1985

By P. R. Sahm, T. V. Pruss, D. A. Gandolfo

Cb 3 Sn powders were hot-pressed to estahlish densi-fication conditions and assess the possible use of such compacts in multiphase structures with ceramic or magnetic inclusions. Superconducting transition temperatures, Tc, were measured as a function of powder particle size, pressing temperature, and second-phase admixtures. The highest transition temperatures were found in coarse powder (5 to 500 u) compacts and were only weakly depended on pressing temperatures up to 1200°C. Fine powders (below 5 p), however, both single-phase CbsSn and Cb3 Sn-composites, showed a stronger dependence on hot-pressing temperatures. While Al2 O3 phase admixtures did not affect T, much more, a Pronounced T, degradation was observed upon the addition of ferrimagnetic Fe2 Mno. 5 Zno.5 O4 powders. Likewise, critical current densities, Jc, at 4.2° K were lowered appreciably in the ferrite doped samples, whereas the neutral A1203 inclusiow gave slightly improved Jc values. MULTIPHASE structures in electronically active materials have recently gained in interest as pointed out by Galasso in a review article.&apos; In superconductors the most widely reported group are eutectic alloys which have been mostly investigated with respect to the proximity effect.2"4 In addition, "artificial eu-tectics", for example in the form of mercury-vycor glass sponge5 or fine niobium wires imbedded in a copper matrix,= have been prepared to attain higher critical fields and critical current densities. The idea was to enhance flux pinning phenomena by second-phase inclusions or ho1es. 7 Flux pinning should also be possible by the introduction of insulator inclusions into a superconducting matrix. Ceramic-metal combinations are most easily produced by hot pressing (= pressure sintering), as it permits an almost unlimited selection of material combinations. Cb 3 Sn has been prepared by vapor phase growths or in the form of thin films. Large compacts must be sintered,1° however, and normally present difficulties. At temperatures below 1350°C insufficient densities are obtained and at higher temperatures the loss of tin due to dissociation upsets the stoichiometry. Hot pressing is a natural approach to circumvent the problems, since one can obtain satisfactory densities despite low sintering temperatures. This work was mostly concerned with establishing conditions to hot press Cb3 Sn and Cb3 Sn multiphase structures (= composites), because no data are presently available, and to evaluate these with respect to their transition temperatures. However, a few measurements on critical current densities were also carried out, in particular to assess the value of ferrimagnetic inclusions. I) EXPERIMENTAL PROCEDURE The experimental procedure involved the preparation of feed material and powders, hot pressing, and evaluation of the resulting ingots. As no attempts were made to synthesize Cb3Sn from the elements during hot pressing, feed material had to be produced. For this purpose, a stoichiometric Cb-Sn powder mixture was compacted into a 3-cm-diam ingot (80,000 psi) and then inserted into a quartz tube and evacuated. Rf heating was employed. Above the tin melting point (230°C) liquid tin was forced out of the ingot, but was pulled back by capillary action after approximately 0.5 hr of continuous pumping at 700°C. Thus, it appears that evacuation at this temperature caused desorption of impurity gas creating wetting surfaces which, later on, favored alloying at relatively low temperatures. After a presintering period of 17 hr at 800°C, the quartz tube was tipped off and sealed into another such larger-diameter tube which, in turn, was connected to a pump system. This configuration permitted a temperature treatment at 1400°C, carried out for 65 hr, without collapsing of the glass walls or unfavorable chemical interaction of Cb3Sn with the quartz. The resulting material was

Jan 1, 1969

By J. Szekely, Robert J. Fisher

A formulation is Presented and solutions are given for the problem of transient heat conduction in a sphere that undergoes a spatially uniform radiative heat exchange with its environment. The solutions were obtained by the numerical integration of the appropriate Partial differential equation and are Presented in a graphical form by Plotting a dimensionless average temperature against the Fourier number with the radiation number as a paranreter, for various initial sphere and environment temperatures. In addition to these numerical results asymptotic analytical solutions are also given. PROBLEMS involving the transient heating or cooling of droplets and particles frequently arise and are of importance in metallurgical operations. Spray refining, vacuum degassing, high-temperature gas-solid reaction systems, and pebble heaters are but few of the numerous examples that may be quoted. The practical interest in these problems from a design or operational point of view is to evaluate the change in the particle temperature with the time given its physical properties, initial temperature, and that of the environment. At the high temperatures encountered the principal mode of heat transfer between the particles and their environment is by thermal radiation; in case of vacuum degassing due to the very low thermal conductivity of the gas space the convec-tive components are negligible and radiation is the only heat transfer mechanism. Although much work has been done on transient heat conduction problems, the special class mentioned here, in which thermal radiation is specified at the bounding surface, received little attention to date. One contributory factor to this situation may be the nonlinearity of the radiation term in temperature, which in general precludes the use of analytical techniques and requires numerical or analog solution of the appropriate differential equations. In fact the only solutions of general nature that are available at present pertain to semi-infinite media and slabs.&apos;-3 The work on which the paper reports forms part of a program aimed at the theoretical and experimental study of transient radiative heat exchange between particles and their environment. The purpose of the present paper is to develop a formulation and solutions to the problem of transient heat conduction in a sphere that undergoes a spatially uniform radiative heat exchange with its surroundings. The solutions, obtained by the numerical integration of the appropriate differential equations, will be presented graphically, by plotting dimensionless parame- ters covering the range of variables relevant to metallurgical interests, thus affording a ready reference for design calculations. In addition to these results, approximate analytical solutions are also given which represent asymptotes, corresponding to extreme values of the variables mentioned. FORMULATION Consider a spherical particle of radius, a, initially at uniform temperature, Ti (T measured on the absolute scale), having a thermal conductivity, k, density, , specific heat, C, and thermal diffusivity, a. At time = 0 let this particle be exposed to an environment which is at a temperature T, and subsequently let there be a purely radiative heat exchange between the particle and the environment resulting in a spatially uniform heat flux at the surface. If in addition to the above we make the assumptions that the sphere is a gray body radiator, homogeneous, isotropic, and opaque, and that the physical properties are independent of temperature, conservation of heat in the sphere may be written as follows: The boundary condition contained in Eq. [3] states that the initial temperature of the sphere is considered uniform, equalling Ti, whereas Eq. [4] is readily obtained from symmetry considerations. Eq. [5] expresses the continuity of the heat flux at the surface of the sphere, or in other words the condition that the rate of heat exchange between the sur-

Jan 1, 1969