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By Ö. Valla, A. Muan, K. Grjotheim

The solid miscibility gap between CaO and "FeO" in the system CaO-"FeO" in contact with metallic iron gradually closes as MnO is added as a third component. On the liquidus surface of the system CaO-"FeO"-MnO, this situation gives rise to a boundary curve which originates in the bounding system CaO-''FeO", proceeds a short distance into the composition triangle of the ternary system, and then vanishes. A new approach has been used to follow the course of this boundary curve. It is shown that the curve vanishes at a much lower temperature and at much lower MnO contents than has been inferred previously. The oxides CaO, "FeO", and MnO together with SiO2 are the major components of the slag phase formed in the basic oxygen process. Hence, the system CaO-"Fe0"-MnO is of considerable technological interest. In addition, the system is theoretically interesting. The three oxides above all have sodium chloride structure. The size differences among the cations are such that in the bounding "binary"* systems CaO-MnO and "FeO"-MnO complete solid-solution series are formed,1,2 whereas in the system CaO-"FeO" there is only limited mutual solubility in the solid state,3 see Fig. 1. Hence, a solid miscibility gap exists in a part of the "ternary"* system Ca0-"Fe0"-Mn0, and a liquidus boundary curve originates at the peritectic point, point a in the insert in Fig. 1, in the system CaO-"FeO", extends a certain distance into the ternary system, and then vanishes. Very little quantitative information on the system Ca0-"Fe0"-Mn0 is available in previous literature. Fischer and Feischer4 sketched isothermal sections at 1600° and 1700°C, and estimated that the vanishing boundary curve extends to approximately 1650°C and a composition of 42 wt pct MnO. The work to be described in the following was aimed at locating experimentally the "vanishing" liquidus boundary curve, determining its end point, and deriving representative isothermal sections below and above the temperature of the end point of this curve. EXPERIMENTAL METHODS The phase relations were determined by the well-known quenching method. (For a description of this method as applied to oxide systems, see the original paper of Shepherd, Rankin, and wright.5) Prereacted oxide mixtures of desired compositions were contained in iron crucibles and heated in a vertical tube furnace in an atmosphere of purified nitrogen. After equilibrium was judged to have been attained, the samples were quenched to room temperature, the phases present were identified by microscopic and X-ray examination, and total iron oxide contents were determined by chemical analysis. "Fisher Certified" reagents (MnCO3, CaCO3, Fe2O3, and Fe) served as starting materials. The calcium carbonate and ferric oxide were heated in air at 400° and 800°C, respectively, for 24 hr prior to use. Manganese oxide was prepared by decomposing the carbonate in a graphite crucible in hydrogen atmosphere at 1000°C. The product was ground under acetone to -100 mesh. The iron powder was used directly without any preparation. Dicalcium ferrite was used as a starting material for some mixtures. It was made by mixing some of the above prepared CaCO3 and Fe2O3 in proportions corresponding to the formula 2CaO. Fe2O3. This mixture was then fired in air for

Jan 1, 1969

By C. G. Bieber, J. R. Mihalisin, R. T. Grant

A growing demand for longer service life of gas turbines has placed increasingly rigorous requiret~rents upon superalloys employed for that application. Long-titne testing at high temperature has revealed that phase transformations occur in all superalloys. A common one of particular interest is o formation. Presented here are studies made to identify a and to characterize its formation and effect on properties in three cast nickel-base superalloys—IN 100 alloy, alloy 713C, and alloy 713LC. Methods are discussed by which o can be eliminated or inhibited in IN 100 alloy and alloy 713C. Evidence was obtained to indicate that some types of o may be more detrimental than others. Limitations in the electron vacancy approach to o prevention are pointed out, and it is shown how alternative approaches, such as reducing a complex superalloy matrix to the form of a pseudo-ternary system permitting equilibrium diagram treatment, lead to additional insights into the formation of in these alloys. AROUND 1960. Beiber1 developed IN 100 alloy, which still remains one of the strongest commercially available nickel-base superalloys. The principle used in the design of this alloy was to produce large quantities of y' phase in a y matrix through the use of copious amounts of aluminum and titanium. In 1963, ROSS' showed that when certain heats of this alloy were held for a long time at 1650°F they formed an acicular phase, subsequently identified as a.3 a is a hard and brittle phase first discovered in the Fe-Cr system by Bain and Griffiths.4 They termed it the "B" constituent. Subsequently this same phase was found in other systems, primarily those of the transition elements, and acquired the name "a" by which it is now known. The crystal structure of the a phase was first determined in the Fe-Cr system in 1950.5 It was shown to be tetragonal with a c/a ratio of about 0.52. as is the case with a found in other systems. This characteristic crystal structure is now the means by which a is identified. In superalloys, such as IN 100 alloy. large amounts of o impair the high-temperature creep strength and drastically reduce room-temperature tensile ductility. Discovery of o phase in some heats of IN 100 alloy quickly led to investigations of other superalloys for similar transformations. It was found that many of the stronger, more highly alloyed. super-alloys were indeed susceptible to o formation. This investigation has been concentrated on three commercial alloys: IN 100 alloy, alloy 713C, and alloy 713LC. J.R.MIHALISIN,MemberAIME, and C.G.BIEBER are with The International Nickel Co., Inc., Paul D. Merica Research Laboratory, Sterling Forest, Suffern, N. Y. R. T. GRANT, Member AIME, is with The International Nickel Co., Inc., Pittsburgh, Pa. Manuscript submitted May 22. 1968. IMD A detailed study has been made of the phase transformations and their relation to a formation along with a consideration of electron vacancy approaches for predicting a-forming propensity in these alloys. EXPERIMENTAL PROCEDURE Phase transformations were studied by light and electron microscopy, electron diffraction, microprobe investigations, and X-ray diffraction. Specimens for light micrographic examination were prepared by conventional grinding and polishing followed by etching with glyceregia (2:l HC1/HNO3 + 3 glycerine by volume). Photomicrographs of stress-rupture specimens were taken adjacent to the fracture unless otherwise noted in the text. Negative replicas for electron microscopy were taken from surfaces electropolished with a solution of 15 pct H2SO4 in methanol. For carbon extraction replication, a solution of 10 pct HC1 in methanol was used. A Siemens Elmiskop I was used for all electron microscopy. Selected-area diffraction studies were made at 80 kv using evaporated aluminum for standardizing the patterns. A nondispersive electron microprobe attachment was used to analyze the extracted precipitates chemically. The fluorescent X-rays were recorded using a flow counter containing P10 gas (90 pct Ar-10 pct methane) with a beryllium window and a single-channel pulse-height analyzer. The pulses from the analyzer were passed to a scaler-ratemeter and differential curves of counting rate vs pulse amplitude were obtained. The base line of the analyzer was driven with a synchronous motor at 0.5 v per min and a channel width of 0.5 v. The time for 105 counts was printed out for each 0.5-v increment. The microscope was operated at 80 kv with beam currents of 1 to 20 pa. This equipment detects elements from atomic number 13 to 40. X-ray diffraction studies were usually made on residues electrolytically extracted in 10 pct HC1 in H2O, although in one case a pattern was obtained from an etched surface of a metallographic specimen. A Siemens Crystalloflex IV was used with iron-filtered CoKa radiation. X-ray patterns were recorded using a goniometer speed of : deg per min. The scintillation counter and pulse-height analyzer operated at a channel height of 10 v and a channel width of 12 v. The equipment was calibrated with a powdered gold standard. The residues usually contained a number of phases. several of which could not be found in the ASTM card file. In addition, as is shown for the case of a phase in IN 100 alloy, other phases had a somewhat different lattice parameter from that reported in the ASTM card file, making it difficult to separate and identify constituents by comparison with ASTM d spacings. For these reasons, phases were identified on the basis of the lattice parameter obtained by indexing the ob-

Jan 1, 1969

By J. D. Miller Discussion by N. P. Finkelstein, M. C. Fuerstenau

The point designating 10 -4 nole/per liter sulfonate addition in Fig. 1 has been presented incorrectly. This figure, with the corrected scale, is shown at right. N. P. Finkelstein (National Institute for Metallurgy, Johannesburg, South Africa) - The qualitative conclusion the authors of this paper have reached in evaluating the influence of hydrocarbon chain length on collector effectiveness agrees with conclusions in several published reports. However, in two other

Jan 1, 1969

The granulites and related "dry" igneous rocks tend to be passed over during exploration for metals. Preliminary data show that high trace concentrations of eu, Ni, and other metals of economic interest are commonin orthopyroxene and some of the other granulite minerals. During retrograde metamorphism of granulites, pyroxenes are converted to amphiboles or phyllosilicates, and significant quantities of metals are released andbecome available for incorporation into new mineral phases, or may be transported elsewhere. S-rich scapolite is the normal scapolite of granulites. Its retrogression to secondary plagioclase provides much S which scavengesCu and Ni, from pyroxenes undergoing retrogression, thus producing ore-fluids. A full analysis of a scapolite with 5·10 per cent SOg is given.Beryl is unstable in granulites but the rare Be mineral taaffeite (Al4Mg(Be, FeII)Os) with 5·50 per cent BeO occurs in central Australia as a pale green tabular mineral easily confused for chloritoid in hand-specimen.Metamorphic differentiation and mobilization of primary ore concentrations are major factors controlling their post-granulite attitude and grade.Zones of retrograde metamorphism are commonly found cutting or engirdling granulite terranes. As the "volatiles" for the new hydrous minerals of many of these zones are of deep-seated origin and may be juvenile, sulphide mineralization in them may also be of mantle origin. However, it is likely that much of the metal content could be scavenged from the granulites as they are down-graded by juvenile volatiles. Major Bouguer gravity anomalies delineate some granulite terranes (e.g. Fraser Block, Western Australia), and are related to deep-seated geosutures and mantle disturbances.Many granulite terranes are linear belts and appear to be welded to older cratonic blocks.

Jan 1, 1969

By Knut L. Sandvik, Aage Solbakken

it is an established fact that the collecting properties of xanthates and anionic collectors are dependent on the hydrocarbon chain length. This is ascribed to the greater adsorption densities caused by increasing the xanthate chain length. As batch flotation tests showed similar trends for amines, an investigation of the adsorbing properties of amines was undertaken. Because earlier investigations showed adsorption densities for dodecylamine salts on quartz varying as much as 20 times under apparently similar conditions,1-4 it was decided to make a survey of the changes in adsorption density due to the drying conditions of the quartz. EXPERIMENTAL PROCEDURE The quartz, handpicked in the pegmatite quarries of Iveland, Setesdal, had the following composition: SiO2 99.81, A12O3 0.01, Fe2O3 0.05 and loss by ig-

Jan 1, 1969

The Tuesday morning session opened at 9:00 a.m. and was presided over by Mr. Homer Hyatt, Safety Director, North American Coal Corporation, Western Division, Castle Gate, Utah. Mr. Hyatt introduced Mr. Richard F. Walker, Vice President, Engineer & Planning, Electric Department, Public Service Company of Colorado, Denver, Colorado. Mr. Walker is a native of the State of Nebraska, a graduate of the University of Colorado with a BSEE degree in 1949. He has been associated with the Public Service Company of Colorado for almost twenty years and in the above capacity for the last one and one-half years. Mr. Walker?s subject was "Our New Plants and Coal. (See index for printed text of Mr. Walker's paper.) Mr. John F. O'Leary, Director, U.S. Bureau of Mines, Washington, D. C. spoke on the ?High Cost of Economy.? Mr. O'Leary graduated from George Washington University in 1950 with a degree in Economics. In 1950, he joined the Bureau of Mines. In 1963 he was appointed Deputy Assistant Secretary, Mineral Resources, U.S. Department of the Interior. In 1967, he was appointed Chief, Bureau of Natural Gas, Federal Power Commission. In 1968, appointed Director, U.S. Bureau of Mines, Washington, D.C.

Jan 1, 1969

By O’Brian. Daniel T.

Ore reserve determinations supporting property appraisals and economic analyses leading to investment decisions typically require many repetitive calculations. Computers have become well-accepted tools for accomplishing these computations, and are partly responsible for the development of new evaluation methods during the last decade. Excellent descriptions of manual ore reserve may be compared with current computer reserve methods1,2 in North America2 and South Africa3. A comparison indicates that computers are used in two cases: a) when a cost savings can be achieved by the simple conversion of a manual method to a computer processed equivalent, and b) when the quantity of data and ore reserve estimation purpose justifies adoption of a complex ore reserve computational method not feasible on a manual basis. Ore reserve computations essentially consist of using sample data and a mathematical method to arrive at an estimated geometry, tonnage, and grade for a mineral deposit. The mineral deposit is then subdivided, if necessary, into ore and waste components. This separation is based on economic factors which may be explicitly introduced in the computation or incorporated in a numerical cutoff grade4. Computer methods for accomplishing these tasks are presented in three papers. "The Use of Contour Surfaces as Predictive Models for Ore Values" discusses the requirements for a satisfactory value prediction model and the importance of considering auto -covariance. A weighted moving average method is described and compared to other mathematical surface development methods. In the second paper, "The Applications and Limitations of Computer Techniques in the Evaluation of Hypothermal Tin Lodes," particular problems encountered in estimating geometrically erratic economic deposits with a low valuable mineral content are documented. Economics and probabilistic concepts are introduced, allowing a comparison of risk and speculative value for a deposit. Economic considerations are integrated with ore estimation techniques in the third paper, "Method of Calculation of the Iron Ore Reserves in the Lorraine Deposit." The prediction model

Jan 1, 1969

By Sylvan Z. Beer

Aluminum phosphide was synthesized and grown in solution of excess aluminum using a modified two-temperature technique. An inversion in the density difference between ALP and molten aluminum takes place at about 1100°. Dispersed nuclei can act as sources for further crystal growth in a manner resembling ripening. Advantage was taken of this phenomenon by introducing a stirring motion into the molten liquid. This was done with a split-phase 10-kH2 rotating magnetic field produced by four horizontal coils placed symmetrically about the furnace at the level of the molten metal. The method also prevents the formation of a surface film which would impede the reaction. By this technique vastly improved yields were obtained and flat crystals 5 by 5 by 0.5 mm were grown at lower temperatures and at greater rates than heretofore. THE family of III-V intermetallic compounds has received much attention since the prediction of their semiconducting properties in the early 1950s. Of the family, A1P has perhaps the highest band gap of those compounds normally possessing the zinc-blende structure. But it has been least studied because it is difficult to handle and grow. The handling difficulties have been dealt with elsewhere and it is sufficient to say here that, by various techniques, many of the difficulties can be overcome.' The difficulties encountered in crystal growth can be related to the refractory nature of A1P and in turn to its high band gap. Because of the anticipated high melting point of the material and the accompanying high phosphorus vapor pressure, the reported work on synthesis and growth was done by epitaxial synthesis-growth via chlorine2 and iodine3 transport and from solution of excess aluminum by the two-temperature technique.4'5 The transport-grown crystals take on the dimensions of the substrate but do not grow easily in thickness. In the usual two-temperature technique as applied on the synthesis of Alp, the temperature of the molten aluminum is kept at 1000° to 1250°C while the phosphorus is maintained at 1 to 20 atm. A thin film of aluminum phosphide and oxide form immediately, impeding the reaction and affecting the yield. Attempts to grow the Alp from such solutions by the methods used to grow Gap and InP from excess gallium and indium have not been successful. As discussed in the preceding paper,5 the yield can be greatly increased

Jan 1, 1969

The effect of conditioning energy input on the metallurgical results of an emulsion flotation process has been attributed by previous authors to a detergency process. This publication shows that such a process does not explain the data and that an attrition mechanism is more appropriate.

Jan 1, 1969

By K. R. Waugh, Barbara S. Brown, D. W. James

AN electronic data-processing system is described which permits rapid, accurate, low-cost processing of strain-dependent damping data utilizing equipment normally available within the service facilities of most large laboratories. On analyzing the record of a stress-dependent damping test, the operator usually measures the double amplitudes at several points on the decay curve. The logarithmic decrement is then calculated for decay between consecutive amplitudes. These values of 6 are plotted against the corresponding maximum surface shear stress, T, which is proportional to the average of the two amplitudes between which is calculated: where d is the specimen diameter. The period of the vibration is not necessarily constant during decay; thus, each cycle must be counted. A decay curve may extend to, perhaps, 1000 cycles, and at least two curves are always obtained for each specimen or set of conditions. It can, therefore, be seen that manual analysis of decay curves is both tedious and costly in terms of man-hours. Furthermore, the resolution of the record is often such that accurate measurement of amplitude is extremely dif-

Jan 1, 1969

By Robert D. Pehlke, Robert G. Blossey

The solubility of nitrogen in liquid iron alloys containing chromium and nickel has been measured in the temperature range 1550° to 1700°C at nitrogen pressures to 1 ah. The solubility surface has been determined for the iron corner of the liquid metallic ternary to 21 pct Cr and 11 pct Ni. The nitrogen solubility increases markedly with increasing chromium concentration. The effect of nickel and the bilinear effect of chromium and nickel are less pronounced. The solubility data are presented, and interaction coefficients are determined from them. THE solubility of nitrogen has been determined in liquid Fe-Cr-Ni binary and ternary alloys. The work in this laboratory has been directed toward a relatively limited composition range, that is to 20 pct Cr and 10 pct Ni. Humbert and Elliott1 studied the entire ternary; but their investigation was, understandably, limited in this region. The region considered here is of the greatest commercial interest. Knowledge of the solubility in these alloys is important for accurate control of the nitrogen levels in various stainless alloys. Also, the solution behavior is of theoretical interest because of its deviations from ideal dilute solution rules at moderate chromium levels. The nitrogen solubility in the iron binaries has been reviewed extensively by Pehlke and Elliott,2 particularly with respect to the dilute solution interaction parameters. More recently, there has been some interest in accurate descriptions of solute interactions in non-dilute solutions. Most of the investigators have adopted a power series fit to accommodate any non-linearity of the data. The Taylor series expansion is adopted here, using Scimar's notation3 for the interaction coefficients. An alternate method, instead of requiring higher-order expansions, is to restrict the range of the composition variables. A planar solubility surface may be fitted to the data and its range of validity determined. If the axes of this region are displaced from the usual origin—the solvent pure iron—a change in standard state is required for the solution reaction. The standard state for nitrogen in iron is commonly taken as the hypothetical 1 wt pct solution of nitrogen in pure iron. However, for an alloy of appreciable solute concentration, e.g., 13 pct Cr or 18 pct Cr-8 pct Ni, it would be convenient to use that base composition as the solvent and redefine the solution reaction in terms of that particular solvent. A brief derivation follows, defining the free energy of solution in an alloy solvent. Following the treatment by Darken and Gurry,4 for a nitrogen pressure of 1 atm: N (pure component) = N (1 wt pct in solvent) [l] AG=RT ln100/ wt pct N in solvent Taking this reaction for an alloy solvent less the same reaction for a pure iron solvent the relation between nitrogen in pure iron and an alloy is: N (1 wt pct in Fe) = N (1 wt pct in alloy) [2] AG = RT[ln(wt pct N in Fe) - ln(wt pct N in alloy)] Adding ½ N2(g) to each side and subtracting N (1 wt pct in Fe) = ½N2(g), the total free energy for solution of nitrogen in an alloy, referred to nitrogen at infinite dilution, is given by: ½N2 (g) = N (wt pct in alloy) L3] AG°3 = -RT ln(wt pct N in alloy )PN =1 atm Interaction parameters have their usual meaning when ?G°/RT is differentiated with respect to the proper composition coordinate. If desired, the dilute alloy treatment may be utilized with the new reference composition as the solvent. This has. indeed, been done by Small and pehlke5 in their analysis of nitrogen solution in liquid 18-8 alloys. The Sieverts' technique was used for this investigation on an apparatus previously described.6 The materials used in this program were: Ferrovac-E iron, 99.95 pct, Crucible Steel Co.: chromium, 99.95 pct, Union Carbide Metals Co.; nickel, 99.9 pct, International Nickel Co. Recrystallized alumina crucibles were used with no evidence of crucible-melt reaction. RESULTS The locations of the ternary compositions investigated are shown in Fig. 1. The data of Turnock7 and small8 have been alluded to in other papers.5'6 There were no departures from Sieverts' law observed for

Jan 1, 1969

By G. H. Keith

The Bureau of Mines determined the mechanism(s) involved in observed anomalous changes in mechanical properties of vanadium-base alloys. Tensile properties of electrorefined and commercial-purity vanadium-base alloys containing up to 5 atomic percent molybdenum or titanium were measured between 77° and 673° K. Snoek oxygen and nitrogen peak heights were measured to determine the changes in dissolved interstitial content caused by increasing quantities of solute. In addition, changes in lattice parameter were followed wit: precision X-ray techniques. Softening, observed in alloys containing titanium, is explained by the formation of a second-phase titanium compound with oxygen or nitrogen. However, because of partitioning of titanium between compound formation and solid solution formation, about five times the stoichiometric amount was required for complete reaction. Addition of 1 percent titanium drastically lowered the strengthening due to strain aging, at 673° K, and 2 percent titanium essentially eliminated it. All alloys were ductile at 77° K. Variations in the tensile properties of the molybdenum-containing alloys are explained by variations in the amounts of interstitial impurities present. The molybdenum did not react with these impurities and had no effect on strengthening due to strain aging. Commercial-purity vanadium alloys containing more than 2 percent molybdenum were brittle at 77° K.

Jan 1, 1969

Jan 1, 1969

Natural leaching of minerals has been recorded for some two millenia but surprisingly only in recent years has enough been known of the process for any serious design to be made. Copper has been recovered from natural mine waters since about the 17th century but again little progress was made in de- sign procedures until recently. Natural or dump leaching was started as a recovery process late in the 19th century and in the years up to the classic study of Taylor and Whelan in 1943 a series of impirical optimis- ations made it a valuable process for treating low grade or waste material. The biological nature of Sulphide leaching was proven by Colmer and Hinkle in 1947 and since then a large mass of data has accumulated on the microbiology, biochemistry, and response of ores to this form of attack. In spite of this knowledge and the vast amount of pract- ical experience available there are few recorded attempts to present methods of calculation or design procedures that can be used for setting up a leaching process. A framework is given here on which such procedures can be based and indications given of the inherent advantages and limitations of the process,

Jan 1, 1969

By L. A. Schrider, J. A. Wasson

A method of predicting waterflood performance has been developed that combines certain facets of several previously published prediction techniques. The manner of combination has required the development and use of some new and some little-known relationships and has eliminated several of the weaker assumptions inherent in the original individual prediction methods. This approach, which was designed for computer solution, has removed the necessity of referring to plotted curves and permits the analytical prediction of water flood performance for a five-spot well pattern in either homogeneous or stratified reservoirs. The Predicted values are expressed in common oilfield units rather than in abstract or dimensionless terms. The calculation procedure has been programmed in FORTRAN IV and the entire program listing is available to potential users.* Introduction Prior to initiation of secondary recovery of oil by waterflooding, the possibilities of economic success or failure must be evaluated with the greatest practical accuracy. Although many prediction techniques are available, most, if not all, have serious limitations. In recent years, the Bureau of Mines has attempted to stimulate interest in the secondary recovery of oil from Appalachian pressure-depleted reservoirs. Waterflooding, because of its widespread acceptance and success, is the principal secondary-recovery method considered. During the life of the project, several performance prediction methods have been studied and applied. Because these methods, individually, have inherent assumptions and limi-tations, portions of some of them have been selected and combined in an effort to eliminate such shortcomings wherever possible. We believe that the resulting technique is as accurate as the necessary available data will permit and that it has several distinct advantages over previously published methods. Development of the Method The fractional flow equation developed by Buckley and Leverett' from Darcy's law is the fundamental mathematical statement describing immiscible fluid-fluid displacement in porous media. A generalized form of this relationship, whose derivation is readily available in the literature, is The formation dip, a, is usually very small in those petroleum reservoirs being considered for pattern waterflooding in the Appalachian area. Therefore. in many cases. a has an almist negligible value. In addition, Ap, the difference between the density of water and the density of oil, is relatively small. For these reasons the gravitational term may often be neglected. Capillary pressure is a function of saturation, which is in turn a function of distance from the upstream boundary of the system or the injection well. In this study it is assumed that the frontal zone of the waterflooding (or zone of capillarity) has negligible length and that only those saturations in the water-swept zone at breakthrough and later are of interest. As the distance in a waterflood pattern is comparatively large and the change in water saturation with distance is usually small, the change in capillary pressure with distance is negligible. The simplified form of the fractional flow equation is appropriate, therefore, in this application. Three variables must be considered in determining that fraction of the total fluid flow that consists of water: the viscosity ratio, saturation, and relative permeability ratio.

Jan 1, 1969

By A. F. Crawley

THIS paper describes part of a series of density measurements on low melting point metals being undertaken at the Mines Branch, Department of Energy, Mines and Resources, Ottawa, Canada. This program has received support from the Canadian Zinc and Lead Research Committee and the International Lead and Zinc Research Organization. Examples of the type of work being done have already been given in earlier papers' , which deal with the densities of lead, tin, and some of their alloys. Densities were measured using a graphite pyc-nometer by a technique which has already been described." The cadmium and indium, supplied by the Consolidated Mining and Smelting Co. of Canada were of 99.999 pct purity. Density determinations on indium, as for lead and tin,1,2 were made under a vacuum of about 5 x 10-6 torr because the oxidation and vaporization characteristics of the metal do not create experimental difficulties. This contrasts markedly with cadmium which, even at the relatively low temperatures of our experiments, has a high vapor pressure and a strong oxidation potential. To suppress the harmful effects of these properties, determinations on cadmium were made with success under an atmosphere of argon, the technique having been previously established in this laboratory for measurements on zinc.3 The densities of cadmium and indium are listed in Table I and plotted in Figs. 1 and 2. From the graphs, it is readily observed that the densities of both metals vary linearly with temperature. This relationship expressed mathematically is of the form:

Jan 1, 1969

By M. J. Pool, P. J. Spencer, R. V. Miner

The partial molar heat of solution of rhodiunz in liquid lin and Rh-Sn alloys has been measured as a function of rhodium concentration at 700" , 725" , 750" , and 775°K. The values at infinite dilution are very exo thermic, ranging from -29,950 to -28,260 cal per g-atom Rh at 700" and 775"K, respectively. At the solubility limit the heat of solution becomes sharply nzore exothermic and has permitted the liquidus boundary to be accurately established at each temperature. From the measurements in the two-phase region of liquid Plus RhSn, the heat of formation of RhSn,has been determined. A large increase in the heat of formation between 725" and 750°K suggests the possibility of a phase transformation in this compound. V ERY few measurements have been made of the heats of solution of transition metals in liquid tin; yet those values that are available are of great interest because of their very large exothermic nature. For example, the heat of solution at infinite dilution of palladium in tin has been measured as about -26,000 cal per g-atom (625" to 800°~),' while the heat of solution at infinite dilution of platinum is even more exothermic at -28,591 cal per g-atom (914°K).' These values are of the same order of magnitude as the heat of formation of many intermetallic compounds and as such clearly indicate that very strong bonding must exist between the solute and tin atoms in the liquid solutions. Rhodium might be expected to display similar solution characteristics in tin in view of its close electronic resemblance to palladium and platinum. Since no thermodynamic data are available for Rh-Sn alloys, rhodium was chosen as an appropriate solute for further investigation of transition-metal systems with highly exothermic heats of solution at infinite dilution. EXPERIMENTAL The heat of solution of rhodium in dilute Rh-Sn liquid solutions was measured as a functlon of rhodium concentration at 700°, 725", 750°, and 775°K. The liquid-metal solution calorimeter used in this work has been fully described elsewhere. At the start of each series of measurements, the solvent bath consisted of about 0.5 g-atoms of 99.9+ pct pure tin. To this was made a number of small rhodium additions, about 0.0005 g-atoms each, and the heat of solution was measured for each. Rhodium of 99.9+ pct purity in powder form was used in order to promote rapid dissolution in the liquid tin. The powder specimens were contained in tin foil stated to be purified (lead-free). This foil was found to have no measurable heat of solution in pure tin so the effect of any impurities could be neglected. The energy equivalent of the calorimeter was experi- mentally determined by dropping tungsten and/or tin specimens at intervals during each series of rhodium drops. The tungsten and tin used were 99.95 and 99.999+ pct pure, respectively. The only heat effect due to a tungsten drop, or a tin drop at low rhodium concentrations in the bath, is the sensible heat of the specimen. The heat content of these materials is well-established and is presented in the compilation of Hultgren et al. 4 As the rhodium concentration in the tin bath increases a small heat effect arises from the reaction: Sn (liquid, T) — & (soln, T) where T is the temperature of the tin bath. Where necessary, this heat of solution of tin was determined by Gibbs-Duhem integration, and corrections were made to the heat effect of the tin calibration specimens and the tin foil containing the rhodium specimens. RESULTS AND DISCUSSION The calculated values of the heat of solution of rhodium in dilute Rh-Sn alloys as a function of composition are shown graphically in Fig. 1. The values have been corrected for the sensible heat of the specimens, initially at 273"K, and apply to the reaction:

Jan 1, 1969

By R. M. Douthwaite, G. Birkbeck

The effect of grain size and specimen dimensions on the occurrence and magnitude of a yield point drop in pure iron has been examined. The tests were done at room temperature. The results indicate that gain size is the critical factor determining whether a yield drop occurs. The specimen diameter:gain size ratio does not influence the magnitude of the yield drop for the range of gain size and specimen diameters investigated. HUTCHINSON,' petchY2 and worthington3 have investigated the grain size dependence of the upper yield stress (uUYP) and the yield point drop, ouyp - aLYP, in Armco iron, mild steel, and Si-Fe, respectively. These authors used center-annealed wires to avoid stress concentration from specimen shoulders and to ensure uniformity of the applied stress. Coarsegrained specimens show no yield point drop; the yield point drop then increases as d-'I2 increases (where d is the grain diameter). These results can be understood in terms of Petch's analysis2 in which the magnitude of amp depends on the strain rate in the (limited) number of grains deforming plastically at the upper yield point. If N grains per unit volume are undergoing plastic deformation, the strain rate in the deforming grains is l/Nd3 times higher at the upper yield stress than when the whole specimen deforms homogeneously. If N is constant and independent of grain size at uUyp, then all the grains are deforming when ~d~ = 1, so there is no yield point drop. At finer grain sizes, the yield point drop is given by: where AU, is the friction stress increase corresponding to a tenfold strain rate increase. Christ, Smith, and Burton studied the upper yield point in 0.050-in.-diam wire specimens prepared from zone-refined iron. Each end of the 2; -in. specimens was soldered to a & -in. diam steel ball and the load applied through the two balls. There was a yield point drop in specimens with grain diameters less than 0.1 mm; no drop was observed in specimens of grain diameter greater than 0.1 mm that were free from veining substructure, but specimens of grain diameter 0.129 mm, annealed in the y range, showed an upper yield point. and this was associated with the presence of a veining substructure in these specimens. Christ et al. suggested the upper yield point occurs when more than a specific number of grains fill the specimen cross section so a multiplicity of slip is required to initiate plastic deformation. Table I summarizes the published data on the grain size at which the yield drop disappears. On the basis of this data the ratio of specimen diameter:grain diameter = 5 to 27 appears to be the critical value for the occurrence of a yield point drop. Thus, petch2 interprets the appearance and magnitude of the yield point drop in terms of the limited number of grains deforming plastically at uuyp, whereas Christ et a1. consider that the occurrence of the yield drop depends on the ratio specimen diame-ter:grain diameter. The published data cover a wide variety of materials so some variation between the results is to be expected, but the size range covered in the data of Table I is rather limited. In an attempt to discover whether the specimen diameter:grain size ratio or the grain diameter is critical in determining

Jan 1, 1969

By H. K. VAN POOLLEEN, W. Hurst, H. C. Bixel

In an earlier publication* I showed the development of the instantaneous point source solution for a well producing at a constant rate at the center of a system of two radial, adjoining sands of different permeabilities. I also showed how a wellbore radius could be incorporated if this were the development required. For the purpose of that paper and the point I wished to make, this solution served. It yielded a simplifying solution of sands in series identified by Eqs. VI-26 and VI-27. (These equations are reproduced in part by Bixel and van Poollen as their Eq. 3, Page 302.) I am well aware that the simplified solutions are approximations. The facts that these Ei-functions satisfy the diffusivity equation and meet the boundary conditions both at the well and at the interface between sands, and that the earliest time considerations yield zero pressure drop, are evidence that the solutions are good approximations. This was the purpose for these formulas, which I interpret that where the permeabilities are of finite order of magnitudes in the respective media, the relations give satisfactory answers. However, from the authors' point of view there are reservations, which leads me to consider their entire generalization as illustrated in their Figs. 1 through 14. What I understand from their storage capacity, relationship Fs, which is the ratio of the product of porosity and compressibility of Sand II to Sand I, that is employed here by the authors as a correlative means of identifying one figure from another, there is nothing in the exact mathematics that supports such a term as a means of correlation. This is taken out of context, unsustained that this applies. Here the mathematics are known, where the true correlation is the diffusivity term of one sand to another. This entails permeability that refers back again to the term M in their paper for the transmis-sibility of fluid from one sand to the other that should have also been a part of this storage capacity. In Figs. 8 through 14, which purported to show the simplified equation following this correlation, there are apparent discontinuities for M equal to or less than 0.1000 that differ from the trends for greater values of M. In this connection there is no reference radius given for this cumulative pressure drop in the paper that would permit me to make these calculations. However, what is clear for M equal to 0.1000 or less we are treated to almost a closed barrier at the interface; a condition entered by the writers without qualification. This across-the-board treatment of these simplified formulas, whatever the motive of the authors, enters into a range of permeabilities that even I as the contributor would have reservations that such could apply. Under comparable conditions I would be looking at a closed reservoir or some facsimile for such. The extent to which the approximation or the exact equations pertain is not evident in the generality offered by Bixel and van Poollen in their paper. Only when they or other writers show the comparison of the pressure distributions within the formations can one be able to judge the rational limits to subscribe to the simplified formulas.

Jan 1, 1969

By Thomas R. Bur

The amplitude of the first peak of an ultrasonic pulse which has traversed the diameter of a sphere is obtained for many directions in the sphere. This amplitude is relative to an input which is held constant for all measurements on a given sphere. Since the boundary conditions, distance of travel, and the controllable experimental factors are constant for all measurements, variations in this amplitude reflect variations in the attenuation or absorption with direction. The data are plotted and contoured as an equal area projection. The attenuation symmetry is the symmetry expressed by the contour pattern. Analysis of the data from several rock types indicates that the amplitude expresses a higher percentage of anisotropy than the velocity. In most cases the attenuation symmetry appears to be of the same system as the elastic symmetry expressed by the velocity. Results are shown for three rock spheres.

Jan 1, 1969