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By F. J. Plecity, W. C. Leslie, F. W. Aul

During isothermal recrystallization, the rate of grain growth in dilute Fe-hlo alloys decreased rapidly with increasing Mo content, up to -0.04 at pct, and less rapidly therea-fter. Rate of growth also decreased sharply with time at constant temperature. The observed rates of boundary migration did not cor,espond to predictions of the Lucke-Detert theory. It is proposed that the growth of recrystallized grains is inhibited by clustering of solute atoms at inzperfections in the unrecrystallized matrix. It is now firmly etablished" that the rate of re-crystallization of cold-worked metals, i.e., the rate of growth of recrystallized grains into the deformed matrix, is greatly inhibited by the presence of alloying elements in solid solution. The effect is greatest with the first very small quantity of alloying elements, and additional increments cause much less pronounced retardation of growth. The early papers on this subject were reviewed in Ref. 6. The mechanism of retardation of growth is not clear; only one theory, due to Lucke and Detert? has been advanced. This assumes an elastic interaction between grain boundaries and solute atoms which tends to increase the concentration of the latter in the grain boundaries. Except at very low solute concentrations or at high temperatures, the mobility of the boundary is assumed to be controlled by the rate of diffusion of the accompanying solute atoms. Abrahamson and Blakeney2 have noted a correlation between "recrystallization temperature of binary alloys of iron and the number of d-shell electrons in the solute atoms. There is need for considerably more experimental data on the effect of solute elements on the rate of migration of grain boundaries into the deformed matrix, to provide the basis for an understanding of the annealing process in metallic solid solutions. Only a start has been made in this direction. To avoid unnecessary complications, alloys in which precipitation does not occur should be used, but to produce the maximum effects it is desirable to select alloys with a large difference between the sizes of the atoms of the solvent and solute. For these reasons, alloys of iron and molybdenum sen for this study. MATERIALS AND PROCEDURES A 30-lb. ingot of iron and four similar ingots of Fe-Mo alloys were vacuum melted in magnesia crucibles and poured into cast-iron molds. The molybdenum contents were planned according to the results of Abrahamson and Blakeney2 sothattwoalloyswould fall in the region of rapid change of recrystallization kinetics with change in composition (0.006 to 0.015 and 0.030 to 0.045 at. pct Mo) and two alloys would fall in the region of gradual change (0.18 to 0.24 and

Jan 1, 1962

By Charles C. Fatino, Joel S. Hirschhorn

Loose compacts of strained and annealed stainless-steel powders were sintered at various temperatures and times to determine the effect of residual strains on the sintering behavior. The atomized powders were prepared by annealing, ball milling, and rean-nealing. The residual strains and domain size were determined by a Fourier analysis of X-ray diffvaction dala. The specimens were prepared by siwzultaneously sintering cylinders of both strained and unstrained powder. The evaluation of the sintered compacts included density measurements, metallographic examinations, and analyses of X- ray diffraction data. The results of these studies reveal a definite increase in sintered density and sintering rate for the strained powders. THE pressure compacting of metal powders causes deformation of the particles, mechanical interlocking, and increased contact area. After the deformation, severe residual strains remain in these particles. The subsequent contributions of these strains to the sintering process have been considered to be negligible, since the recovery and recrystallization temperatures usually occur prior to the temperature required for the sintering process. Sintering is con-sidered to be the process by which the powders are transformed into solid compacts at temperatures below their melting points. The sintering operation for stainless steel usually takes place in the range of 2050" to 2400°F (0.84 to 0.95 T,, where T, is the absolute melting point or liquidus temperature) while the temperature required for recovery is approximately 1800°F (0.75 T,). However, it has been shown for several metal powders that densification becomes significant in the range of 0.35 to 0.45 T,.' It is the purpose of this study to determine what effect residual strains have upon the sintering behavior of stainless-steel compacts. Loose compacts were selected for study in order to isolate the strain contributions and eliminate the variables inherent in sintering of pressure-formed compacts. Additional variables were minimized by using only one mesh size, one composition, one particle shape, and also by simultaneously sintering both types of powder. Very little work has been carried out previous to the present study to delineate the effect of strains on sintering behavior. Lenel et 01.2 observed that residual stresses in copper compacts caused shrinkage at comparatively low temperatures. Delisle3 loose-sintered ball-milled electrolytic iron and observed that bonding among particles began at a lower temperature as compared to the behavior of annealed powder. Increased densification of ball-milled oxide powders has also been noted.4'5 EXPERIMENTAL PROCEDURES Powder Preparation. The powder used for this study was a commercial-type 316L stainless steel made by the atomization process. A typical chemical analysis is: C- 0.025 pct Mo- 2.2 pct Cr-18.6 pct Ni-12.5 pct Fe—Balance The atomizing process is essentially the rapid freezing of liquid droplets. This nonequilibrium cooling causes coring to occur and two distinct phases are present within the solid particle, the austenitic phase and the ferritic phase. Due to the presence of this ferritic phase, the particles tended to fracture as well as become cold-worked during the subsequent ball-milling operation. (It was also found that this type of cooling produced a broadened and shifted

Jan 1, 1968

By A. N. Crownover, H. T. Kennedy, E. P. Miesch, C. H. Bowman

The paper presents correlations of (l) molar volume of gaseous hydrocarbon mixtures with pressure, temperature, composition and properties of the C,-plus fraction; (2) shrinkage of oils during flash and differential liberation of gas, including the calculation of formation volume factor under various conditions; and (3) bubble-point pressure with temperature, composition and characteristics of C, plus. The data on which the correlations are based comprise 1,615 measurements on 900 hydrocarbon systems, including numerous systems containing nitrogen, hydrogen sul-fide and carbon dioxide. In each correlation, the number of data points covered and the accuracy is substantially greater than in previously available work. Thus, the equation yielding molar volumes of gases has an average deviation of 2.04 per cent, applied to mixtures having temperatures up to 313F and pressures up to 9,800 psis, compared to 2.37 per cent for the Benedict-Webb-Rubin equation applied to the same data, and 4.53 per cent for the method based on the law of corresponding states. he equations resented are all explicit in the dependent variable, and require no iteration on the digital cow puter. INTRODUCTION The ease and accuracy of determining the composition of hydrocarbon mixtures, compared to the difficulty of measuring their properties under reservoir conditions, makes it desirable to utilize composition as the key to physical behavior to the greatest possible extent. As a result, there are available correlations between composition, or easily measured characteristics dependent on composition, and practically every important engineering property of reservoir fluids. The task confronting us is one of finding more exact relationships between important variables rather than extending correlations to new properties. This paper describes new correlations of molar volumes of gases, formation volume factors, and bubble-point pressures with composition, temperature and where possible, pressure. Each correlation is obtained by employing a sufficiently large amount of data so the calculated properties are probably as least as accurate as the measurement on which they are based. MOLAR VOLUME OF GASES Although many equations of state have been proposed for pure gases, only a few methods are applicable to hydrocarbons at conditions comparable to those in petroleum reservoirs. Still fewer arc useful in describing the behavior of mixtures, with which the petroleum engineer is largely concerned. The correlation presented here involves procedures similar to those of Alani and Kennedy The van der Waals equation is modified to make a and b functions of temperature instead of being constants for each material.This is a cubic equation, which may have either one or three real roots. The lowest root corresponds to liquid volume, while the highest applies to gas. When the procedure was applied to 703 pressure-temperature points of 164 gases of known composition and volume, the average deviation was 12.08 per cent, and the standard deviation 8.15. The above calculations were made using the constants derived for liquids by Alani and Kennedy and the mixture equation developed by them. A closer approximation to measured molar volumes is obtained by employing different sets of constants for different areas on the pressure-temperature chart, and by changing the relationship between a,,, and b,,, for mixtures and the a, and b, for individual hydrocarbons. The various sets are shown in Table 1, and the areas for which they are recommended are plotted in Figs. 1 through 7. In these figures, the area designated by zero is in the critical region for pure materials, and the values obtained for them may be unreliable. For normal mixtures, however, the area may be added to any of the bounding areas without substantial error. The new relationships employed are

Jan 1, 1966

By Herbert Kilburn Scott

The information in this paper was collected by the author during a five years' residence in the State of Minas Geraes. Outside the State itself, very little is known of the gold-field. Such accounts as have been published are antiquated and contained in publications mostly out of print. The increased attention now attracted to the natural resources of Brazil, and the probability that American capital will be, in the near future, largely invested there, will make an up-to-date account specially useful at this time. I. Historical and General. Soon after the Jesuits founded what is to-day the city of S?o Paulo, gold was discovered in the streams of the neighborhood; and this incited the natives, known as paulistas, to look for it farther afield. After many expeditions into the interior, gold was found in quantity in placer-deposits in the vicinity of Ouro Preto, in 1699, by a prospecting party headed by Antonio Dias. The name of Ouro Preto (black gold) was given because of the superficial dark coating of the gold, and the inhabitants of the district were known as mineiros (miners). Later on, the placers of Cuiaba, in the State of Matto Grosso, were discovered in 1718, and those of the State of Goyaz in 1724. All this territory was at the time a private colony, but on account of its increasing importance it was taken over by the Crown, and in 1739 a royal governor was appointed, with his nominal capital in S?o Paulo, though for a number of years the real capital was Ouro Preto. In 1711 Ouro Preto was raised to the rank of a city, with the name of Villa Rica de Ouro Preto (" rich city of black gold"); and in 1720, by reason of administrative difficulties, Minas Geraes was constituted a separate colony from S?o Paulo, with Villa Rica as its capital. The site of this city

Jan 1, 1903

By R. W. Fountain, J. Chipman

THE solubility of nitrogen in iron and steel has been of considerable interest due to the role of nitrogen in strain-aging and in quench-aging. It is generally considered that quench-aging is the result of precipitation of carbide and nitride particles from supersaturated solid solution, while strain-aging results from the segregation of carbon and nitrogen atoms to dislocations.1-9 The rate of strain-aging is controlled primarily by the amount of carbon and nitrogen in solution and the temperature. In experiments on strain-aging of pure iron with only carbon or nitrogen as impurities, Fast" has shown that even after 40 hr at 50°C carbon did not give any strain-aging while

Jan 1, 1959

By Shiro Ban-ya, John Chipman

Equilibrium in the reaction was investigated at temperatures of 1500°, 1550°, and 1600°C for sulfur concentrations up to 7.2 wt pct. Multisample crucibles contained the liquid alloys in a resistance-heated furnace using a technique especially designed for the study of more complex alloys to be reported separately. Modern free-energy data are used to correct the H2S:H2 ratio for dissociation of H2S and calculalion of the partial pressure of S2. Published data on the equilibrium are similarly corrected. Thermodynanzic treatment of the data employs the composition variable zs = nS/(nFe — nS) and the activity coefficient Gs = as/zs The data at 1500" and 1550°C are fitted by the equation log s = —2.30zs. Within the limits of experimental error the same coefficient is applicable to the data at higher temperatures. Equations are given for the free-energy change in Reaction [I] as well as for the solution of S, gas in the metal. The heat of solution of 1/2 s2 is -32.28 i2.5 kcal. Uncertainty in the free energy is very much smaller. For dilute solutions of interest in steelmaking, the activity coefficient of sulfur is unchanged from that listed in Basic Open Hearth Steel-making. DETERMINATIONS of the thermodynamic properties of sulfur in liquid iron by Morris and williams1 and by Sherman, Elvander, and chipman' provided a basis for control of sulfur in steelmaking processes. From the standpoint of understanding the chemistry of metal plus nonmetal in liquid solution they left several questions unanswered. The activity of sulfur in dilute solution at about 1600°C was well-established but temperature coefficients were uncertain, due at least in part to the use of the optical pyrometer and uncertainty regarding the effect of sulfur on emissivity. It appeared that deviation from Henry's law increased with increasing temperature, a most unusual behavior requiring either confirmation or disproof. These studies were based on experimental determination of equilibrium in the reaction: At high temperatures H2S is partially dissociated so that the gas mixture contains HS, S2, and S in addition to HS. At the time of the earlier studies the free energies of these constituents were unknown and it was therefore impossible to make adequate correction for dissociation. Observations on the effects of alloying elements by Morris and coworkers1, 3 and by Sherman and Chip-man4 enable us to assess the effects of alloying elements on the activity and to make corrections for incidental impurities in the binary liquid. These studies as well as a number of more recent investigations will be reviewed in detail after out own experimental results have been presented. It was our purpose in planning this study to avoid uncertainties regarding the emissivity of alloys and the errors of thermal diffusion which plagued some of the early attempts,5 by using a resistance furnace and thermocouple in preference to induction heating and optical pyrometer. Modern data on free energies of the gaseous species are to be applied to our data and to those of other investigators to obtain corrected values of K1 and of the activity coefficient and ultimately to relate the sulfur content of the bath to the equilibrium partial pressure of S,. Extension of the study to include ternary and complex solutions will be described in a later section. EXPERIMENTAL METHOD a) Preparation and Calibration of H2-H2s Gas Mixture. The source of hydrogen sulfide was a preparer mixture of 43 pct H2S, balance hydrogen, contained in a large aluminum cylinder. This was passed through anhydrone and through a microflowmeter. Hydrogen was passed through platinized asbestos, ascar-ite, and anhydrone, and through a capillary flowmeter. Argon was passed through copper wool at 500°C, then through ascarite, anhydrone, and a flowmeter. The flow rate of hydrogen was kept constant at 200 ml per min, to which an arbitrary amount of the hydrogen-hydrogen sulfide mixture was constantly added and then the prepared gas mixture was introduced into the reaction tube through a gas mixer. In certain experiments 200 ml per min of argon was added to the hydrogen-hydrogen sulfide gas mixture to increase the total flow rate of gas. The ratio of hydrogen-hydrogen sulfide in the inlet gas was checked for each run by chemical analysis. A sample of the gas taken from a bypass was bubbled through zinc and cadmium acetate solution (4 pct zinc acetate, 1 pct cadmium acetate, and 1 pct acetic acid) to remove hydrogen sulfide from the gas mixture, and the flow rate of the remaining hydrogen was measured by a soap bubble method to determine the volume of hydrogen. The amount of hydrogen sulfide absorbed in solution was determined by titration with iodine against sodium thiosulfate, with starch used as the indicator. The ratio of hydrogen sulfide to hydrogen in the inlet gas could be kept within ±2 pct in the range from 10-2 to 5 x 10"4 which corresponds to from 0.2 to 7.0 wt pct sulfur in liquid iron. b) Furnace Arrangement. Fig. 1 shows the furnace arrangement and the shape of the alumina crucible used in this experiment. A vertical-tube silicon carbide electric resistance furnace contained the reaction tube which consisted of two parts, the gas-tight

Jan 1, 1969

By J. W. Downey, M. V. Nevitt

The phase boundaries for the 950" isothermal sections in the ternary systems Zr-Co-0 and `Zr-Ni-0 have been determined for the composition range from 50 to 100 at. pct Zr. The two systems show very similar phase relations, having no extensive solid solution phase fields. Each contains a ternary phase. These phases are apparently isostructural, but their structure has not been determined. Some aspects of the phase relations are discussed in terms of the alloying behavior of transition metals. THE work described in this paper is the outgrowth of a recent study of the occurrence of phases having the Ti2Ni-type structure (structure-type E9,) in certain ternary systems involving Ti, Zr, or Hf with another transition metal and O.", In the Zr-CO-0 and Zr-Ni-0 systems no Ti2Ni-type phases were found to occur. However, there are several interesting aspects of the phase relations in the two systems which have significance from the point of view of the alloying behavior of transition metals. The results of this investigation may also have some importance in studies of the oxidation of Zr-Co and Zr-Ni alloys. In both the Zr-Co-0 and Zr-Ni-0 systems only the 950" isothermal sections were investigated and, as a further restriction, the study was limited to the composition range from 50 to 100 at. pct Zr. A tentative Zr-Co binary diagram has been published by Larsen, Williams, and Pehin. In the composition range pertinent to the present work they report a eutectic at 980°C and 75.9 at. pct Zr, the products of which are the terminal solid solution based on /3 Zr and the compound Zr2Co, and a eutectic at 1080" and 64.8 at. pct Zr whose products are Zr,Co and ZrCo. The solid solution based on /3 Zr is shown to decompose eutectoidally at 826°C into a Zr and Zr2Co. The limits of solubility of Co in a and /3 Zr have not been established. The structure of Zr2Co is not identified in the publication just cited. Dwight has reported that ZrCo has the CsC1-type strcture. The Zr-rich portion of the Zr-Ni diagram has been determined by Hayes, Roberson, and Paasche." The phase relations are very similar to those of the ZrCo system. A eutectic reaction whose products are /3 Zr containing 2.9 at. pct Ni and Zr,Ni occurs at 961°c, and a eutectic between Zr,Ni and ZrNi is found at 985". The solid solution based on /3 Zr decomposes eutectoidally at 808°C. The solubility of Ni in a Zr is not known accurately but is believed to be very small. Smith, Kirkpatrick, Bailey, and Williams7 have found that Zr2Ni has a tetragonal structure of the A1,Cu-type and that ZrNi is orthorhombic. Domagala and McPherson8 have published a constitution diagram for the system Zr-ZrO,. At 950" their diagram indicates that the solid solution of 0 in 0 Zr is stable from 0 to 0.5 at. pct while the phase field of 0 in a Zr extends from 6 to 29 at. pct. These solubility limits were adopted in the present study and no binary Zr-0 alloys were made. No previous data on the phase diagrams of the ternary systems are known to exist. EXPERIMENTAL PROCEDURE The experimental details involved in the preparation of alloys in this laboratory by arc melting have been described in several previous papers"3 and they will not be repeated here. Information concerning the purity of the metals used is given in Table I. Oxygen was added in the form of reagent grade ZrO,. All of the cast specimens in both alloy systems were annealed in air-atmosphere tube furnaces at 950 3' for 72 hr and water quenched. The specimens were protected from oxidation by wrapping them in Mo foil and sealing them in quartz tubes that had been evacuated at room temperature to a pressure of 1 x 10B mm of Hg. The phase boundaries were determined by metallography, and identification of the phases was accomplished primarily by X-ray diffraction methods which employed a powder camera having a diameter of 114.6 mm. The diffraction techniques which are in use in this laboratory have been previously described.' An etchant that proved satisfactory for most of the alloys consisted of 5 pct by vol of AgNO

Jan 1, 1962

By Maurice K. Seguin

It is a difficult task to find enriched soft iron ore deposits in the central part of the Labrador Trough, New Quebec, Canada, when the areas investigated are covered by glacial drift. A qualitative interpretation of either a combined gravity-magnetic-seismic-resistivity survey or gravity-magnetic-seismic or gravity-magnetic-resistivity survey permits (with a low probability level) the detection of iron formations and ore zones as well as their delineation from most of the country rocks. This is possible because most of the altered iron formation underwent a slight increase in density through enrichment and because the accompanying geochemical alteration changed their magnetic properties. In order to increase the chances of success in finding ore bodies when using geophysical methods, different types of correlation were done for many deposits. These are: I) A quantitative correlation of the residual gravity anomaly intensities with the specific gravity, the iron content, the silica content, the porosity factor, and the dimensions of the underlying ore bodies. 2) A quantitative correlation of the ground magnetic intensity relative to a reference lithologic unit with the percentage of Fe.,O, recovery and with the volume ferromagnetic susceptibility. A few discoveries already have been made with this method. The details of the location, the description of the geology, and the history of previous geophysical surveys and their qualitative interpretation have already been given.', ' A very brief paragraph describing the regional and local geology is necessary in order to facilitate the understanding of this paper. The sedimentary iron formations of the Labrador Trough consist of a 700-mile geosynclinal segment composed of tightly folded and faulted Proterozoic sediments, volcanics, and intrusives that are rich in mineral deposits. The complex sequence rests unconformably on the basement of Archean granitic gneisses. The direct-shipping iron deposits are scattered along a northwest-trending strip, 5 to 10 miles wide and some 60 miles long in the facies rich in iron oxides and preferentially in localities where the original sedimentary environment favorized the deposition of a large concentration of magnetite associated with chert by physicochemical processes, e.g., oxidation-reduction potential, pH, temperature, pressure. Once leached of its silica and/or iron carbonate content and enriched with secondary a-hematite (occasionally goethite), this original magnetite associated with some primary hematite makes the blue direct-shipping ore which constitutes the important ore reserves in this mining district.

Jan 1, 1971

By James H. Courtright, Kenyon Richard

SILVER Bell is situated 35 airline miles northwest of Tucson, Ariz., in a small, rugged range rising above the extensive alluvial plains of this desert region. Its geographical relation to other porphyry copper deposits of the Southwest is shown on the inset map in the lower left corner of Fig. 1. The climate is semi-arid. Altitudes range within 2000 and 4000 ft. Opening of the Boot mine, later known as the Mammoth, in 1865 was the first event of note in the district's history. Oxidized copper ores containing minor silver-lead values were mined from replacement deposits in garnetized limestone and treated in local smelters. Copper production had approached 45 million pounds by 1909 when the disseminated copper possibilities in igneous rocks were recognized. Extensive churn drill exploration carried out during the next three years resulted in partial delineation of two copper sulphide deposits, the Oxide and El Tiro. Although the then submarginal tenor discouraged exploitation of these disseminated deposits, selective mining of orebodies in the sedimentary rocks continued intermittently until 1930, providing a production total of about 100 million pounds of copper. The American Smelting & Refining Co. began exploratory and check drilling in 1948 and subsequently made plans for mining and milling the Oxide and El Tiro orebodies at the rate of 7500 tons per day. Production began in 1954 at a rate of about 18,000 tons of copper annually. Formations ranging in age from Pre-Cambrian to Recent are exposed in the Silver Bell vicinity. The more erosion-resistant of these, Paleozoic limestone and Tertiary volcanics, predominate in the scattered peaks and ridges comprising the Silver Bell mountains. The porphyry copper deposits are located along the southwest flank of these mountains in hydrothermally altered igneous rocks. These are principally intrusives which cut Cretaceous and older sediments and are considered to be components of the Laramide Revolution. For three-fourths of its length the zone of alteration strikes west-northwest, Fig. 1. There now is no single structure that accounts for this alignment. However, indirect evidence suggests that a fault representing a line of profound structural weakness existed in this position prior to the advent of Laramide intrusive activity. This line will be referred to as the major structure. It was obliterated by the Laramide intrusive bodies but exerted a degree of control on their emplacement, as evidenced by their shapes and positions. The influence of fault structures on the shapes of intrusives in other porphyry copper districts has been noted by Butler and Wilson' and by others. As shown on the inset map on Fig. 2, a fault of parallel trend and considerable displacement lies to the north. This fault is now marked by a line of small Laramide intrusive bodies. To the south is a third fault of large displacement. Evidence of its age in relation to the Laramide intrusions and mineralization is not recognized, but its conformance in strike with the other two major faults is significant. These three breaks establish a pronounced trend of regional faulting. They are high-angle, and the southerly one may be reverse, Stratigraphic separations on these faults are of the order of several thousand feet. The local Paleozoic section is about 4000 ft thick. It is composed predominantly of limestone with a basal quartzite member. The Cretaceous section appears to exceed 5000 ft. Conglomerates, red shales, and arkosic sandstones (the youngest) characterize the three principal members. Intrusion of alaskite marked the beginning of Laramide igneous activity. It was emplaced as an elongate stock with one side closely conforming to the major structure line throughout a distance of nearly 4 miles. The alaskite was at one time regarded as a thrust block of pre-Cambrian rock'; however, its intrusive relationship and consequent post-Paleozoic age has been established by inclusions of limestone found in outcrops north of El Tiro. The next event was the intrusion of a large stock of dacite porphyry into Paleozoic sediments and alaskite. The stock was some 3 miles wide and at least 6 miles long in a northwesterly direction. It was sharply confined along its southwest side by the major structure line. A number of large pendants of moderately folded Paleozoic sediments occur within and along its southwest edge. Thus the inferred, original major fault between Paleozoic and Cretaceous sediments became a contact between alaskite and Paleozoic sediments and then a contact between dacite porphyry and alaskite. Andesite porphyry may have been intruded later than the dacite porphyry, but relationships are not clear; it may be simply a facies of the latter. The intrusive activity was at this stage interrupted by an interval of erosion. The erosion surface probably was rugged, as there were local accumulations of coarse, angular conglomerate. Subsequently a series of volcanic flows and pyroclastics several thousand feet thick was deposited. A similar unconformity has been recognized elsewhere in the Southwest, particularly in the Patagonia Mountains near the Flux mine some 75 miles southeasterly. Here, as at Silver Bell, volcanics were deposited on an erosion surface cut in Cretaceous and older sediments which had been intruded by alaskite. Though no evidence is offered that closely defines the age of this unconformity, and proper analysis of the problem is beyond the scope of this paper, it is

Jan 1, 1955

By George V. Smith, Daniel E. Sonon

Various mechanical properties of the Ni-Co-C alloy system were investigated to delineate the strengthening effect of carbon. Carbon concentration, cobalt concentration, vain size, temperature, and strain rate were varied so that thermal activation analysis and the Hall-Petch analysis could be used to evaluate the strengthening effect of carbon. Increasing carbon increased the strength of nickel and a Ni-60 pct Co alloy , with the effect becoming more pronounced at lower temperatures. Yield stress depended linearly on carbon concentration in nickel, but it depended on the square root of carbon concentration in the Ni-60 pct Co alloy. The Hall-Petch slope of nickel increased with carbon concentration; however, that of the Ni-60 pct Co alloy did not. The yielding behavior of these alloys was sensitive to composition, grain size, and temperature. Cobalt eliminated serrations in the flow curve of carbon-containing nickel at 300' and weakened them severely at higher temperatures. Pairs, or clusters, of carbon atoms appear to be responsible for the observed strengthening behavior. FLINN' conducted several experiments with carbon in nickel in an effort to provide information on the strengthening effect of interstitial impurities in solid solution in fcc metals and alloys. Strengthening which increased with decreasing temperature led him to conclude that carbon causes Cottrell locking in nickel. Fleischer2 analyzed Flinn's data and calculated that the strengthening effect of carbon in nickel was smaller by a factor of fifty than the strengthening effect of carbon in a! iron. Fleischer2 termed the magnitude of strengthening of carbon in nickel "gradual" and that of carbon in a! iron "rapid". He attributed "gradual" hardening to hydrostatic strains and localized changes in modulus of elasticity around solute atoms, whereas he attributed "rapid" hardening to tetragonal strains around solute atoms. Sukhovarov et a1.3-7 reported strain aging and serrated plastic flow in nickel, both of which they attributed to the presence of carbon. Serrated plastic flow has been rationalized by a process involving a series of dislocation pinning and multiplication steps.8, This process is more probable when screw dislocations are strongly pinned. Screw dislocations cannot be pinned by pure hydrostatic forces from the symmetrical strains of an interstitial impurity in an fcc lattice, except for small, second-order effects. However, they might be pinned by localized changes in modulus of elasticity around solute atoms,' by the pinning of the edge components of the partial dislocations of an extended screw dislo~ation,'~ or by clustered groups of solute atoms whose net elastic stress field is unsymmetric. The purpose of the present work was to investigate various mechanical properties of the Ni-Co-C a1loy system which are sensitive to pinning effects in order to delineate the specific pinning mechanism of carbon. Carbon concentration, grain size, temperature, and strain rate were varied so that thermal-activation analysis and the Hall-Petch analysis could be used to evaluate the pinning mechanism. Cobalt was added to lower stacking fault energy so that the number and extension of split, screw dislocations would be increased in order to test the possibility of pinning by carbon at extended screw dislocations. EXPERIMENTAL PROCEDURE Nickel and cobalt (both 99.98 pct-. pure) were melted with graphite in stabilized zirconia crucibles and cast at lo-' Torr to form Ni-C and Ni-60 pctCo-C alloys. Two ingots were heated to 1250°C and were forged to 1-in.-sq bars. These bars were machined to 4-in.-round bars, and then swaged cold to 0.144-in. -diam rods. Reductions in area of approximately 75pct were used with intermediate anneals at 900°C for 1 hr. The carbon content of batches of 0.144-in.-diam rods from each ingot was reduced to two levels by annealing 5-in. lengths in palladium-purified, dry hydrogen at 1100°C for 25 and 100 hr. The remaining material from each ingot was annealed at 10"5 Torr for 1 hr at 1100"~. These treatments gave a total of three carbon levels for both the nickel and the Ni-60 pct Co alloy. The 0.144-in.-diam rods were swaged to 70-mil wire, cut into test specimens, and then re crystallized at lom5 Torr in capsules for 1 hr at temperatures ranging from 760" to 1050" ~. The capsules were broken and the specimens were immediately quenched into water. Average grain size was measured using Hilliard's method of circular intercepts." Annealing twin boundary intercepts were counted in addition to grain boundary intercepts to establish an average grain size. Average grain sizes ranged from 5 to 140 p depending on the cobalt concentration and re-crystallization temperature. Tension tests were made in duplicate at various temperatures at a crosshead speed of 8.34 x 10"4 in. per sec with an Instron Universal Testing Machine. Specimens of 1-in. gage length with soldered ball ends were used at atmospheric and cryogenic temperatures. Pinch grips were used on specimens at elevated tem-

Jan 1, 1969

By W. A. Tiller, W. C. Johnston

The solute distribution ahead of an advancing solid-liquid interface is controlled by varying the momentum boundary layer thickness in the liquid adjacent to the interface. Single pass zone-melting experiments on Pb-Sn alloys are described in which the liquid is caused to rotate in the plane of the solid-liquid interface due to the influence of a magnetic .field rotating in this plane. The variation of the diffusion boundary layer thickness with field strength is determined. DURING the freezing of an alloy a partitioning of solute occurs at the solid-liquid interface, the magnitude depending upon the difference in the solid and liquid solubilities at the interface temperature. Because the diffusion coefficient is so small in the liquid relative to normal freezing rates, either a pileup or a depletion of solute occurs at the interface when the partition coefficient, kO, is either less than or greater than unity, respectively. This solute distribution is completely characterized by i) the solute concentration in the liquid far from the interface, C) the ratio of freezing velocityf, to diffusion coefficient, D, iii) the partition coefficient, ko, and iv) the thickness of the diffusion boundary layer, 6,, at the interface (this assumes that an electric field is not applied across the interface). For a particular system, C ko and D are fixed so that the character of the solute distribution can be changed only by a variation of either f or 6c. As is well known, the freezing velocity can be changed by varying the thermal environment of the alloy. Whereas, the thickness of the solute rich layer can be changed by varying the fluid flow conditions in the liquid. It is the purpose of this paper to describe a technique for controlling the fluid flow conditions in the liquid. During most solidification experiments the driving force for fluid flow arises from either mechanical mixing, thermal convection or electromagnetic mixing. The momentum boundary layer thickness, 6m at the solid-liquid interface, within which negligible movement of the liquid occurs, has been calculated for the special case of mechanical mixing where crystals are solidified by the Czochralski technique.l,2 The calculation of 6m for the case of thermal convection has also been made.3 In some calculations it has been assumed that the momentum boundary layer thickness, 6,, may be equated to the thickness of the diffusion boundary layer 6c, at the interface. However, as may be seen from Appendix I this is only true in very special cases and in general where a is a constant of magnitude determined by the particular liquid alloy. Neither calculations nor experimental data exist for the dependence of upon electromagnetic mixing. In this paper experiments are described in which the liquid is caused to rotate in the plane of the interface due to the torque developed on it by a magnetic field, H, rotating in this plane. The variation of is controlled by the variation of H. A magnetic field rotating in a plane perpendicular to the interface has been used for the purification of aluminum. Experimentally, we determined the variation of 5C with H by using the zone-melting technique of pfann5and a theoretical relationship of Burton et a1.2 pfann5 has shown that, after the passage of one molten zone through a long cylindrical charge of uniform concentration, CO, the solute distribution, C,, in the solid is as shown in Fig. 1. The equation describing this distribution is

Jan 1, 1962

By A. Raman, P. P. Singh

The constitution of the La-Rh system was studied by powder X-ray diffraction, metallopaphic, and differential thermal analysis techniques and an equilibrium diagram is presented. Eleven intermediate phases occur in the system and the crystal structural data for nine of them were determined. La3Rh crystallizes in an orthorhombic structure of undetermined type, whose unit cell is obtained by doubling the 'a; and 'c,,' edges of an FesC type unit cell. The other intermediate phases of the system are LarRh-3( undetermined structures also occur in the system. LaRh, undergoes a polymorphic phase transformation at 1240°C. LaRh3 and La2Rh7 also exhibit polymorphisnz. The phases Laah and LazRh7 melt congruently. The latter undergoes a eutectoid transformation into LaRh, and Rh at 1205°C. Laah3 is formed by a peritectoid reaction between Laah and La,Rh,,. The other Phases result from peritectic reactions between the liquid and the adjacent rhodium-rich phases. The intermediate Phases of the La-Rh system are compared with those of the La-Co and La-Ni systems. DURING the course of a detailed investigation to study the occurrence of CrB, FeB, A1B2, and related structures in the rare earth alloys it was found that much information is lacking for the rare earth noble metal systems. Although the structures of several rare earth alloys containing the noble metals at the AB and AB2 stoichiometries have been reported, the occurrence of related structures at other stoichiometries has not been studied. We have initiated a project to study the crystal structural features of selected rare earth-rhodium alloys and to map the equilibrium diagrams of representative systems with conventional methods. The results of our investigation in the La-Rh system are presented in this paper. Two phases were known in the La-Rh system. LaRh has the CrB-type structure.' LaRhz is a MgCu2-type Laves phase.z EXPERIMENTAL PROCEDURE Alloys weighing less than 1 g were prepared from commercially pure lanthanum (99.9 pct +), supplied by Lunex Company, Pleasant Valley, Iowa, and rhodium (99.92 pct +), supplied by Engelhardt Industries, Newark, N.J., in a conventional arc melting furnace under argon atmosphere. The buttons were turned upside down and remelted three times to insure homogeneity in the samples. Since negligible loss of material was encountered during melting, a chemical analysis of the alloy buttons was not undertaken. Powder specimens for X-ray diffraction studies in the as cast state were then prepared. The buttons were wrapped in thin molybdenum foils and homogenized by heating in vacuum at suitable high temperatures for more than 1 week. They were then broken into three or four pieces for annealing experiments. The pieces were wrapped in molybdenum foils and annealed at various temperatures in evacuated quartz capsules. The annealing was carried out for 2 hr at or above 1200°C, 1 day at temperatures close to llOO°C, 2 days at 1000°C, and for 1 week at temperatures below 1000°C. After annealing the alloy pieces were again broken and powder specimens for X-ray diffraction were prepared. The powders of the lanthanum rich alloys with more than 80 at. pct La were prepared by filing. The filings were sealed in molybdenum tubings and stress-relieved at 600°C in vacuum. It was not deemed necessary to stress-relieve the powders of the other alloys, since the alloys were very brittle and were ground easily. POWDER X-RAY DIFFRACTION X-ray diffraction photographs of powders (-325 mesh size) of the alloys in the as cast and annealed states were prepared in a Guinier-de Wolff focussing camera with copper K, X radiations. These patterns were studied to identify the stoichiometries and the crystal structures of the intermediate phases. The lattice parameters of the phases were calculated after minimizing the differences between the observed sin2 6 values, calculated from the diffraction angles 8, and the sin2 8 values, calculated using approximate lattice constants obtained from a few lines. These differences were minimized manually to less than 0.0005. The latLice constants are judged to be accurate to *0.005A for values less thp about 10A and to k0.01~ for values greater than 10A. The relative intensities of the lines were calculated using a computer program written by Jeitschko and Parthk.~ No attempt was made to refine the atomic positional parameters in the phases. METALLOGRAPHY The phase equilibria in the investigated alloys in the as cast and annealed states were also studied by metallographic examination. The polished specimen surfaces were etched with 10 pct picric acid in alcohol (alloys up to 25 pct Rh), concentrated picric acid (from 25 to 37.5 pct Rh), 2 pct nital (40 to 50 pct Rh), 10 pct nital (from 50 to 66.7 pct Rh) and with concentrated 48 pct HF for the other rhodium-rich alloys. Selected microstruture~ were then photographed using a Po-laroid Land camera. THERMAL ANALYSIS Differential thermal analysis of the alloys was carried out in DTA-668 Stone differential thermal ana-

Jan 1, 1970

By S. Floreen, R. M. Pilliar, H. W. Hayden

The fracture behavior of a 50 pct Cu-50 pct Fe mi-croduplex alloy, laminated composites of copper and iron and an extruded 50-50 Cu-Fe elemental powder composite was studied. Very low ductile-brittle transition temperatures were achieved in all cases, but for different reasons. In the microduplex alloy both the initiation and also the propagation of cleavage fractures appeared retarded by the very small in-terphase distances. In the composites, crack propagation through the sumples was prevented in most cases by delamination fractures perpendicular to the advancing cracks. These delaminations occurred at different regions and by different mechanisms in the various composites. In the extruded powder composite, de-lamination appeared to take place along preexisting flaws. In the crack arrest geometry of the laminated plates, delamination took place by localized shear fractures within the copper near the Fe-Cu interfaces. In this case delamination was enhanced by thicker laminate layers, and by having the resistance to shear failure of the copper sufficiently low compared to the toughness of the iron. BRITTLE fracture in engineering materials has long been a problem, and many different ways of preventing it have been considered. One method that has been of growing interest lately is to prevent crack propagation by the introduction of mechanical discontinuities into the structure. These discontinuities may act in several ways. They may simply act as crack stoppers. They may introduce secondary fractures such as de-laminations that deflect the initial crack into new, less damaging directions. Alternatively, they may subdivide a fairly large bulk sample that would have been loaded in plane strain, for example, into a number of subunits that are individually loaded in plane stress and thus are more resistant to fracture. Other mechanisms, or combinations of mechanisms, are also feasible. A number of methods exist for introducing mechanical discontinuities into a structure. Composites by their nature have discontinuities in structure, and numerous studies have shown that fracture propagation in materials of this type can be radically changed by suitable control of the composite parameters. Of particular significance to the present work are recent investigations of layered composites made by joining high strength steel sheets by various means.'-4 These studies have shown that through proper control of the mechanical properties of the bonds joining the sheets it was possible to introduce delamination fractures that markedly improved the overall toughness of the composites and in some cases completely prevented through-the-thickness fractures. Another technique for introducing structural discontinuities is simply to use a two-phase alloy. It has been recognized for many years that a small amount of a second phase may improve toughness either by homogenizing plastic flow and thus preventing localized stress concentrations that nucleate fracture, or by interacting with an advancing crack. In most of these studies of two-phase materials, the decreases in ductile-brittle transition temperatures produced by the second phase were relatively small. More recently, work on two-phase stainless steels having a very fine grain microduplex structure has shown that the presence of on the order of 40 to 50 pct of a tougher second phase may lower the ductile-brittle transition temperature of the brittle phase by approximately 300°F. 5-7 In these alloys delaminations were seldom observed. The tougher second phase appeared to minimize the ease of both the initiation and the propagation of cleavage fractures. These results show that both the composite approach and the microduplex alloy approach are effective methods of preventing brittle fracture. Therefore, it was of interest to compare the fracture behavior of a microduplex alloy with composites made from the two-phases that were present in the alloy. To simplify this comparison the 50 pct Cu-50 pct Fe system was selected for study. At low temperatures the equilibrium tie line phases in this system are essentially pure ferrite and pure copper. A 50-50 alloy was cast and hot worked to produce a microduplex structure. Two types of composites were studied; laminated structures prepared by roll bonding iron and copper sheets of the tie line compositions, and an extruded powder composite made from high purity elemental powders. The fracture behavior of these materials was then compared. EXPERIMENTAL PROCEDURE Alloy Preparation. The 50-50 Fe-Cu alloy and the components for the roll bonded composites were prepared by vacuum induction melting 30-lb heats using electrolytic grades of iron and copper as charge materials. A carbon boil was used to deoxidize the melts. Small additions of copper and iron were made to the iron and copper heats, respectively, to approximate

Jan 1, 1970

By D. S. Tannhauser, I. Bransky

Measurements of the electrical conductivity, the thermal electromotive force, and the deviation from stoichiometry by thermogravimetry were made on ferrous oxide (wüstite) single crystals as well as on poly-crystalline samples in the temperature range of -900" to 1330°C. In the region defined by T 2 1000°C and 1.05 5 O/Fe 5 1.10 the electrical conductivity was shown to be proportional to the sixth root of- the oxygen partial pressure and to be linearly dependent on the deviation from stoichiometry. The absolute Seebeck coefficient of single and polycrystalline wüstite was shown to be independent of temperature in the above region and a p to n transition of the Seebeck coefficient was observed at O/Fe = 1.09 in polycrystalline wüstite. Analysis of the results showed that the predominant defects in wüstite in the above region were doubly ionized cation vacancies. The analysis also ruled out the existence of complexes of the type postulated by Roth, except that below 1000°C there is some evidence of 'association of defects. Of the three oxides of iron (FeO, Fe3O4, Fe2O3) only FeO (wüstite) can exist within a wide range of the ratio O/Fe. This has been shown by several investigations of the phase diagram using for instance chemical analysis of quenched samples'-4 or thermogravimetric measurements. 5,8 Darken and Gurry's1 data for example in the temper- ature range 1100o to 1400°C show that the lowest O/Fe ratio obtainable for FeOl +. is about 1.045 and that the existence range extends to O/Fe = 1.20 at 1400oC. On the basis of detailed analysis of thermogravimetric measurements made by Vallet and Raccah6 the existence of three varieties of wüstite at elevated temperatures was suggested by these authors and by Kleman. It is well-established that wüstite has a NaCl structure with vacant cation sites.3, 8 From a neutron-diffraction study of wüstite samples quenched to room temperature Roth9 concluded that defects in wüstite are mostly complexes composed of two cation vacancies and one interstitial cation in a tetrahedral site. The atomic arrangement in the vicinity of such a defect is similar to that in magnetite, where each occupied tetrahedral site is surrounded by four vacant octahedral positions disposed at the corners of a tetrahedron, so arranged that each vacancy is shared by two tetrahedral cations. Thus there is an average of two vacancies per interstitial. Recent X-ray diffraction measurements made by Smuts10 on quenched wüstite samples confirmed the results of Roth's neutron-diffraction experiments. Roth's model of defects in FeO can be regarded as a solid solution of Fe3O4 in FeO; salmon1' used this defect model to calculate the activity of Fe3O1 in FeO at high temperature and claimed good agreement with the results obtained experimentally by Darken and Gurry.' Each missing cation in wüstite is accompanied by two trivalent cations, thus preserving charge neutrality. The "holes" which differentiate between the Fe 2+ and Fe3' states of the ions in octahedral positions can overcome the attractive field of the cation vacancies, and are then free to move through the crystal as charge carriers. A similar picture holds for COO, NiO, andMnO.l2, 13 Localization of the charge carriers in transition

Jan 1, 1968

By S. C. Sun, John A. L. Campbell

The surface properties exhibited by bituminous coal and bituminous coal lithotypes were ascertained by using streaming potential techniques. The electro kinetic prop-erties wereascertainederties of bituminous coal were found to be similar to those of anthracite. The principle electrokinetic properties of the coal and lithotypes, zero-points-of-charge (ZPC), and potential determining ions, were established. The effects of indifferent electrolytes, hydronium and hydroxyl ion sources, and polyvalent ions (cationic and anionic) were also evaluated. Location of the ZPC's with respect to pH is discussed in terms of chemical and mineralogical composition of the respective surfaces. To account for the observed electrokinetic phenomena, a generalized surface model and adsorption mechanism are proposed. Surface-dependent processes, such as froth flotation and flocculation, are important or potentially important techniques for combating some of the current major problems in coal preparation. In order to correctly apply or improve a surface-dependent process, it is of paramount importance to understand the interfacial phenomenon, especially the double layer properties, exhibited by the solid. The specific objective of this research was to determine the properties of the bituminous coal/liquid interface by an electrokinetic method, streaming potential, and to relate the findings, wherever possible, to the existing unit operations of froth flotation and floccula-tion tion. The electrokinetic properties of both the whole coal and its lithotypes were investigated. As part of the total investigation, the role played in the double layer by the reagents commonly employed in the surface dependent process was also established.' These data will be presented at a later date. Experimental Procedures The coal samples used in this research and their designations are listed in Table 1. The classical description of humic coal lithotypes as developed by Stopes" was used for the delineation of the lithotype samples. The samples were taken from the working face of a producing deep mine of the Pittsburgh seam in the area of Ellsworth, Pa. To avoid oxidation, only freshly exposed areas were sampled. The normal precautions against contamination were also exercised. Two types of samples were taken, specimens rich in a particular lithotype and a representative channel sample. The latter sample was prepared for analyses by grinding it to —35 mesh. It was screened repeatedly during the grinding to provide the largest amount of 35 x 48-mesh (standard Tyler sieves) material possible. The screened fraction was passed over a magnet and then washed several times with distilled water and finally with conductivity water. The resulting sample now termed "whole coal" was stored under conductivity water in a glass bottle. Pure lithotypes were obtained from the lithotype concentrates by hand picking, and were processed in the same manner as the representative sample. Maceral analyses, employing standard petrographic procedures," were performed on the lithotype samples to determine the purity of the samples. The results are presented in Table 2. Reflectance measurements of the vitrinites and fusinites are also reported in this table. Proximate and ultimate analyses of the samples are given in Tables 3 and 4. The electrokinetic properties of the coal samples were determined by streaming potential methods.'-' All of the chemicals used in the investigation were reagent grade (Baker analyzed). The conductivity water was prepared by doubly distilling the water in a pyrex Yoe-type still and passing the distillate through a mixed bed ion exchange column. Results In general, the electrokinetic properties of the investigated bituminous coal were found to be similar to the results of a previous study of anthracite by Camp-bell bell5 and are in accord with the suppositions of Brown." The zeta potentials of the coal and all the lithotypes were found to be negative in conductivity water. Jowett? in a study of slime coatings on coal also found bituminous coal to exhibit a negative surface. Fig. 1 shows that the negative charges, at neutral pH's, for both fusain and the gangue are very small, almost zero, while at the same pH, vitrain has the largest negative charge, almost 30 mv. Durain has a negative charge of 17.5 mv. The determination of the affect of pH on the charge of the coal surfaces revealed that hydronium and hydroxyl ions apparently behave as potential determining ions; however, they do not appear to be potential determining for the gangue. These results are illustrated in Fig. 1. As the pH of the solution was decreased, hydronium ions were adsorbed, causing the surface of the coal to reverse polarity and become

Jan 1, 1971

By W. Mitchell, B. H. Bergstorm, C. L. Sollenberger

A unique compression testing machine was constructed to load individual 1/8 to I-in. spheres of glass, etc., at rates from 100 to 100,000 lb per min. During loading the applied load was continuously plotted us the deformation of the sphere-platen system. The load-deformation curve conforms to the theory of elasticity. The spheres were surrounded by steel retaining rings or by gelatin (to prevent secondary fracture). The product size modulus was determined from screen analyses. The data shows: 1) Energy input per unit mass is inversely proportional to the product size modulus (or directly proportional to the surface area per unit mass). 2) Increased loading rates slightly increase the energy input per unit mass required for fracture without affecting the preceding relationship. Theory and experiments show that much of the input strain energy is transformed into kinetic energy of fragments at fracture, this being a reason efficiencies based on "surface energies" are exceedingly small. This large kinetic energy component is usually dissipated as heat but may be partially reclaimed because impact of fragments against the surface of steel retaining rings causes additional comminution. There are currently several theories of crushing, all of which can be derived from the general energy equation of Gillilandl as was pointed out by Mitchellet al in 1954'and more recently by Rose and Sullivan. If the exponent of the equation dE-x-"dx is assigned values of 2,1, or 3/2, one obtains by intergration between suitable limits, the equations of Rittinger, kick,' and Bond,' respectively. Other investigators prefer to let the exponent be a variable parameter. To help resolve the controversy, the Allis-Chal-mers Research Laboratories set up a series of carefully controlled experiments in which the level of energy input required to induce the comminution of a single particle by slow compression loading was very accurately measured. The energy input requirement, in conjunction with the size analysis of the fragments produced at fracture, yielded an accurate energy-product size relationship for the conditions studied. APPARATUS The experimental apparatus was designed to apply a compressive load on opposite sides of an "ideal particle." Spherical shapes were chosen, because point contact loading is typical of the mechanics of conventional crushers. The bulk of the experimental data was obtained with glass spheres because glass is a fairly homogeneous, brittle material for which the properties follow definite statistical distributions. The spheres ranged from 1/8 to 1-in. diam. The compressive load was applied to the specimen at a uniform rate by a loading mechanism (Fig. 1) which acted through a system of levers. The uniform rates, ranging from 100 to 100,000 lb per min, were obtained by metering water into a bucket suspended at the end of the secondary level. Point contact was made with the sphere through tungsten-carbide platens. This latter material is extremely hard and has a high modulus of elasticity, thereby having a minimum of distortion when loaded. The actual load on the sphere was measured independently of the lever system by a load cell, Fig. 2, which was designed so that the voltage output of the load cell would be proportional to load. The deformation of the specimen was indirectly measured by a pair of transformers which were attached to opposite edges of the upper platen. The cores of the transformers, which were attached to the lower platen, moved relative to the transformer so that the voltage output was proportional to the deformation of the sphere-platen system. The load was plotted against the deformation on an X-Y recorder. The area under the curve, as shown on Fig. 3, was proportional to the energy input of the

Jan 1, 1961

By K. W. Smith, E. A. Thomas

Various grades of synthetic mullite have been developed in recent years to replace or supplement natural sources of mullite deriued from the mullite group of minerals consisting of sillimanite, kyanite, and andalusite. Raw materials and heat treating processes used in making synthetic mullite are described. Chemical and physical data are given for typical grades and crystalline structure is illustrated with micrographs. Use of synthetic mullite as a refractory material in the glass and metallurgical industries is discussed. Mullite (3A12O3.2siO2), the only stable compound formed in the alumina-silica system, is usually present to some degree in all aluminum silicate ceramic products. The formation of mullite is considered beneficial to give rigidity to the structure and is dependent upon the ratio of Al2O3 to SiO2 in the original composition, particle size, degree of mixing, firing temperature, cooling rate, and the presence of auxiliary glass-forming fluxes. Mullite may also be formed at the reaction interface of fire clay or alumina-type refractories in contact with glass or slag melts. The term synthetic mullite is commonly used today to identify a class of sintered and fused aggregates or grains in the alumina-silica system having a highly developed mullite structure but derived mainly from raw materials other than the sillimanite group of minerals. Within the past 15 years extensive research has been done to develop economical processes to form sintered synthetic mullite aggregate to replace calcined Indian kyanite in super-refractories. Severa1 brands of such mullite are now being produced in commerical quantity and finding extensive use in refractories. Based on the service results of such refractories in many applications throughout the metallurgical, ceramic, and glass industry these developments have been considered successful and suitable substitutes for Indian kyanite now appear assured. EARLY DEVELOPMENT The conversion of kyanite, sillimanite and anda-lusite minerals of the sillimanite group to mullite and their use in refractories and porcelain have been discussed quite extensively in the literature by peck,' Grieg,' Riddle and Foster,3 Bowen and Grieg,4 and others and will only be mentioned here for reference to compare properties with synthetic mullite. In 1928, curtis5 reported on the development of a high temperature gas-converter process for forming synthetic mullite. The raw materials were derived mainly from lumps of high alumina clay of the correct natural composition or blends of clays and alumina that was interground and briquetted to form a suitable charge to maintain a surface combustion firing within the converter. Curtis was, no doubt, the first to illustrate by micrographs in natural color the crystalline structure of mullite derived from kyanite and mullite derived by sintering clay and alumina mixtures at temperatures above cone 32 (3123°F) and by electric fusion. In 1937, sei16 was issued a patent covering the use of a mixture of alumina-silica minerals and alumina in the proportion to form a mullite-yielding material at temperatures in excess of 3100' F. During the period from 1930 to 1940, economic conditions were not favorable for the production of synthetic mullite mainly due to an adequate supply of good grades of Indian kyanite ore suitable for conversion to mullite. Uncertain conditions on availability of the Indian kyanite during the early stages of World War II fostered further study on the development of synthetic substitutes. In 1943, McVay and wilson7 reported on an extensive investigation of domestic substitute materials. Their work covered essentially the use of mixtures of electric furnace mullite, calcined topaz, and calcined domestic kyanite. Compositions were found that gave equivalent or better hot load strength than Indian kyanite in mullite-type brick compositions; however, the calcining of the topaz presented certain physical and chemical problems on the disposition of silicofluoride and hydrofluoric acid while the high cost of electric furnace mullite was a limiting factor. In this work it was pointed out that water-quenched fused mullite was found to be unstable on reheat and gave poor hot load strength due to excessive glass present whereas the slow cooled or annealed mullite contained large crystals of mullite and corundum with little glass and gave superior results.

Jan 1, 1961

By E. H. Lee, F. J. Fayers

Problems in reservoir analysis can usually he cupressed in terms of a system of nonlinear partial difjerential equations. A rnethod for .setting physically reasonable boundary conditions for these systerrls by ayplication of the theory of characteristics is discussed. A short description i.c. given of the technique for finding chnmcteristics of general first order and second orrler equations. Specific examples are quoted jrorn eqrrations occurring in theoretical reservoir studies. The princip1e. ossocicred wit11 the use of chnracteristic to set physically realistic boundary conditions me developed, and thr method is discussed in terms of boundary condition for the noncupillary, compressible, two-phase flow problen: jor the cupillary, ir~cowlpressible, two-phase flow problems for the tlrtergent flooding prohlenl; as for the compressible. noncapillary, two-phase flow pro11letn. INTRODUCTION In most problcms in reservoir analysis the physical situation is described by a system of nonlinear partial differential equations. The general solution to the set of equations usually comprises a wide range of functions ancl a particular solution is normally selectetl by applying suitable boundary conditions to the problem. In some cases it is clear from the physical situation what form the boundary conditions should take, but it is usually desirable to have an independent mathematical check of the suitability of the chosen conditions. From the mathematical standpoint, a system of partial differential equations with boundary conditions is said to be properly set if the combination determines a unique solution which is continuously dependent on the equation and the boundary conditions. Such a solution is sometimes termed "reasonable". In investigating the properties of the mathematical representation, it is useful to determine the structure of the system by the application of the theory of characteristics. This theory determines in the space of the independent variables, lines or surfaces which play a special role in thc system's behavior. The characteristics determine the possibility and nature of the propagation of discontinuities in the derivatives of the dependent variables. Along the characteristics certain differential relations hold which for some problems allow a so- lution to be obtained analytically. In the case of hyperbolic equations the characteristics can bc used as 3 basis for a numerical solution. If a complicated nonlinear system is to be solved, a study of behavior of the characteristics will indicate what boundary conditions should be chosen. By using the method of characteristics, several advances have rccently been made in solving reservoir engineering problems. Sheldon, Zondek and Cardwell' have discussed how the the method may be used grap-phically to solve the incompressible two-phase displaccmerit problem when the gravity term is included in the equations. Fayers and Perrine' have applied the method to study the equations representing detergent flooding. When compressibility and solution-gas effects are introduced into the two-phase flow problem, the equations and their characteristics become more complicated. It will be seen that in this problem the characteristics are useful for indicating a reasonable set of boundary conditions but cannot readily be used to compute a numerical solution. This problem has been solved on the IBM 701 using normal finite difference methods hy West, Garvin and Sheldon." The material to be prcscntcd in this report is divided into three sections. The first discusses the determination of the characteristics of first and second order partial differential equations; the second describes the selection of suitable boundary conditions by the application of the principle that the future cannot affect the past; the third discusses the use of characteristics for setting the boundary conditions of the two-phase solution-gas flow problem. A useful introduction to the method of characteristics has been given by Hildebrand.' A summary of the method will be given in this section of the paper. The First Order Equation The quasi-linear equation of first order is It is linear in the partial derivations of z. The properly linear equation has the form The characteristics of are curves along which the

By J. L. Gillson

Historically, rock deposits and sand deposits of titanium minerals came into production about the same time, although there may be some argument as to what is meant by production. Beach deposits of heavy minerals in India (Figs. 1-4) and Brazil (Figs. 5) were worked for monazite about the turn of century, but as there was then no market for titanium minerals, these were thrown away. The rock rutile deposits at Roseland, Va., Fig. 6, were worked to supply rutile for titanium chemicals and for coloring ceramics long before there was a titanium pigment business. The pigment industry started about the middle twenties, both in Europe and the U. S., and almost simultaneously the rock deposits at Ponte Vedra Beach near Jacksonville, Fla., were worked for titanium content. Since those days, production from both types of deposits has continued to grow at a rapid rate; many deposits of both types have been found, and reserves have grown to very large figures. In total tonnage of reserves, there is no doubt that the rock deposits are far ahead of the sand deposits; nevertheless there is a very large tonnage of commercial sands available. It is the quality of titanium mineral in the sand and the relatively lower costs of operating sand deposits that have kept them abreast, at least in annual tonnage produced, with the rock deposits. The principal titanium mineral used is ilmenite, but as soon as that mineral began to be sought as a titanium ore, it was obvious that there are ilmenites and ilmenites. Textbook ilmenite should have the composition FeOTiO2 and should analyze 52.6 pct TiO2 and 36.8 pct iron as Fe. The Indian ilmenite, for almost a generation the standard ore for manufacturing pigment in the U. S., was found to analyze about 60 pct TiO, and only 24 pct. Fe, and most of the iron is in the ferric condition. The whole process of pigment manufacture in the U. S. was built up on the use of a raw material of that grade, and the American chemical engineers who operate the pigment plants shuddered at the thought of using a rock ilmenite with 45 pct or so of TiO, and nearly 40 pct Fe. Intensive search was made around the world to find other deposits of rich black sand, like the Indian beaches, but although a few were found, there was some objectionable feature about each. A deposit in Senegal, south of Dakar (Fig. 7), was worked for a while, but an organic coating on the grains made attack by acid difficult. Modern practice would have included a scrubbing operation, in a caustic soda bath, to eliminate the organic coating. Brazilian deposits were numerous, but individually small, and shipping from them difficult. Deposits on the east coast of Ceylon had many attractive features, but the ilmenite analyzed only 54 pct TiO2 and could have been used only with a penalty. Sand deposits with 2 pct ilmenite, like those now worked in Florida, would not have been considered commercial ore, even if they had been known at that time. Most rock ilmenites are associated or mixed with hematite or magnetite, which accounts for the lower titanium and higher iron values than in the sand ilmenites. The Norwegians, English, and Germans, with cheap Norwegian rock ore at hand, learned to install in their pigment plants adequate capacity on the black side, as it is calltd, and counterbalanced the extra cost of plant, and larger amount of acid used, by the lower cost of ore. When World War II arrived, two of the largest pigment manufacturers in the U. S. had to learn how to use the Adirondack ilmenite, but one of them very gladly went back to sand ores when the Florida deposits came into large-scale production after the war. The other continues to use Adirondack ilmenite and finds it commercially attractive to do so. Rutile is not a raw material for titanium pigment manufacture by the sulfate process, since it is insoluble in sulfuric acid. In addition to its small consumption in chemicals and ceramics it began to be used in quantity in welding rod coatings. With the outbreak of World War 11, and the tremendous need for welding rods in shipbuilding and other structural steel construction, rutile suddenly became in heavy demand. The sand deposits on the eastern shore of Australia (Fig. 8A) which had been worked in a small way since 1934 were brought into production, and some stream placers in Brazil were worked and rutile concentrates shipped to American

Jan 1, 1960

By R. J. Charles, G. Agar

Experiments on single particles show that the amount of material created during impact that is finer than any chosen size is proportional to the energy of the impact. As the underlying principle of comminution, it might be stated that each unit of energy input to a given comminution system tends to add to the system an identical assembly of new particles and subtract an equivalent volume of larger particles. Thus, two of the consequences of the fact that each unit of energy tends to add identical assemblies of new particles to the system are: 1) on continued application of energy the total charge in any batch comminution system tends to assume the characteristics of this assembly, and 2) the process of comminution may be described by a relationship such as E = Ak-a. Recently Schuhmannl presented a theory of comminution which puts rational perspective on the extensive controversy surrounding most of the existent theories of comminution. With hindsight the origin of controversy can be ascribed to a relatively simple circumstance. In general, a progressive shift of a size distribution curve towards finer sizes is observed as energy is added to a comminution system. It is also observed that, with continued grinding, the size distribution curves usually change and appear to approach some constant shape. Inves-tigators generally felt that an appropriate method of relating and generalizing such data would be to consider the hypothetical case where particles in the system were uniformly subjected to comminution such that each of these particles, receiving its proportion of input energy, was transformed into a number of smaller particles of uniform size. Since the changes in shape of the size distribution curves during size reduction were clearly associated with the coarse particles in the system, it was also assumed that these changes accounted for little of the input energy and one could deal solely with the equilibrium shape towards which the size distribution curves tended. Although the unrealistic nature of the foregoing points of view was realized some justification was felt for such treatments since, in most cases, the resulting mathematical formulae could, by the adjustment of at most two parameters, satisfactorily describe experimental observation. Difficulties arose, however, in that the formulae required a specific influence of the feed size on the comminution process. In actual fact, the application of a feed size term in fitting experimental data was often found to be unnecessary or contrary to the above formulae. Secondarily, much discussion arose concerning the appropriate energy number that would relate the size change of one particle to the amount of comminution energy it received. As has been previously shown3 all the above theories that treat comminution as a continuous process of size reduction may be related to a proposition of the following form: dE = -Cfn [1] where dE is the increment of energy, dx is the size change, x is the particle size, and C and n are constants. It is now clear, as pointed out by Schuhmann, that Eq. 1 is inapplicable to comminution processes, since comminution cannot be considered other than as a discontinuous mixing process in which the overall size distribution of the product results from mixing, in various proportions, finished material with unfinished, and sometimes untouched, material. A striking illustration of this mixing phenomena may be obtained by comparing the size distributions of grinds in a typical batch ball mill with size distributions calculated on the basis of mixing various proportions of feed material with a ground material which obeys a power law size distribution relationship. Figs. la and lb illustrate such a comparison and the similarity of these figures indicates that mixing plays an important role in determining the overall shape of the product size distributions. Figs. la and lb illustrate, additionally, the underlying basis of the comminution theory presented by Schuhmann.' In the preliminary grinding of relatively close sized feed particles in a batch ball mill, one may visualize that, when a successful encounter of a ball with a feed particle occurs, then the particle undergoes severe size reduction and the size range in which the resultant particles reside is far removed from the size of the feed particles. After a number of feed particles are reduced by independent but similar impacts and one examines the size dis-

Jan 1, 1961