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By C. J. Rosa, W. C. Hagel

An attempt is made to determine the diffusion coefficients of oxygen ions in hypostoichiometric zirconium oxide. A phenomenological theory is developed for three-phase, unidirectional volume diffusion of a gaseous species from a planar source. Knowledge about oxygen diffusion in a and ß zirconium and experimentally measured rates of movements of interfaces permit the evaluation of oxygen ion diffusivi-ties in ZrO2-x. The results conform to the relationship: sq cm per sec, for the temperature range of 875" to 1050° C. DIFFUSION coefficients of oxygen ions in stoichio-metric oxides have been studied by many investigators. The obtained results not only supplement the knowledge about the lattice-defect structures of oxides and conduction mechanisms but also provide information of technological importance. Rate processes such as oxide sintering, high-temperature creep deformation, and oxidation of metals and their alloys are directly dependent on diffusion phenomena. Unfortunately, diffusion coefficients obtained from studies on stoichio-metric oxides cannot be treated without restraints when applied to oxidation kinetics, if precise evaluations of oxidation rates are desired. Oxides formed on metals are usually nonstoichiometric and exhibit nonuniform distribution of either cation or anion vacancies across their thicknesses. Debuigne and Lehr1 extended Danckwerts'2 mathematical analyses and furnished a semitheoretical treatment for evaluating oxygen diffusion coefficients in zirconium oxide in terms of weight gain measurements during oxidation of zirconium in the temperature range 400° to 850°C. Their calculations are based on theoretical partitioning3 of the total amount of oxygen between a zirconium and its oxide phase. An inherent discrepancy appears to continue throughout their calculations. The amount of oxygen confined to the oxide phase should be corrected by multiplying the calculated oxide thickness by the inverse of Pilling-Bedworth ratio, if expansion of zirconium dioxide is taken into account. The purpose of the present investigation is to provide a new semitheoretical treatment for evaluating diffusion coefficients of moving species in hypostoichiometric oxide. The analyses are relevant to unidirectional volume diffusion. Although the presented method is quite general, its applicability will be discussed in terms of kinetic measurements from oxidation of zirconium at temperatures above the a/ß transition, for reasons stated in the later part of this paper. EXPERIMENTAL Pure, 99.93 wt pct, zirconium samples of approximately 2 by 1 by 0.35 cm were exposed to oxygen for various times at four temperature levels: 875°, 950°, 1000°, and 1050°C. High-purity, better than 99.9 vol pct oxygen was passed through a cold trap and columns containing anhydrous CaSO4 to remove residual water vapor. Before exposing to oxygen at a pressure of 500 Torr, specimens were subjected to wet abrasion on 200- through 600-grit Sic papers and polished with 1—p diamond dust. Prior to oxidizing, all zirconium samples were vacuum-annealed at 10-6 mm Hg for about 15 min at the test temperature. The temperature variation across the uniform heat zone was ±2°C from the preset value. Final polishing, for phase thicknesses measurements, was performed by using 8- and 1-p diamond dust and followed by vibrator polishing with 0.05-µ ? Al2O3 solution. Measurements of phase thicknesses were made by projection on a metallographic viewing screen. Conventional powder X-ray analyses for the oxide were employed. RESULTS Fig. 1 is an example of the cross section of oxidized zirconium. Designations of phases given below this figure are the same as those used in the three-phase diffusion system represented by Fig. 5 in the following section. Zirconium oxidized for longer exposure times showed two types of oxides: white oxide at the surface and an underlaying layer of gray oxide. X-ray powder patterns of these oxides at room tern-

Jan 1, 1969

By D. A. Rice, M. C. Fuerstenau

Flotation data indicate that sulfonate and amine adsorb physically on manganese oxide; oleate also adsorbs physically if the zero point of charge is sufficiently high. Chemisorption of oleate occurs on pyrolusite between pH 8 and 9, and possible mechan- isms of collector adsorption involving metal ion hydrolysis are discussed. The flotation characteristics of most metal oxides1-15 have been examined with standard collectors such as fatty acids and sulfonates. From these studies it would appear as though electrical phenomena are important when shorte r-chained collectors are involved. For example, Iwasaki, Cooke, and Choi9 have shown that dodecyl amine and dodecyl sulfate float iron oxide above and below the zero point of charge, respectively. In another system, D.W. Fuerstenau and Modi10 have shown that dodecyl sulfate, dodecyl

Jan 1, 1969

By H. I. Aaronson, C. Laird

The kinetics of thickening and of lengthening of ?' plates in an Al-3.93 pct Cu alloy in the temperature range 203" to 300" C were determined by means of transmission electron microscopy. The rate of thickening was found to be less than that allowed by volume diffusion control at all temperatures, by amounts which increased with decreasing temperature, in agreement with the predictions of a general theory of precipitate morphology.1 Thickening was treated on the basis of the ledge mechanism. Ledges were deduced to spread across the broad faces of ?' plates at volume dzjrfusion-controlled rates, as anticipated from the disordered structure of their edges. Lengthening of 8' plates, on the other hand, took Place more rapidly than allowed by volume dzjrfusion. This occurred despite clear morPhological evidence of a bmrier to growth at the edges of these plates. It was concluded that the misfit dislocation structure comprising the barrier requires that lengthening take place by a jog mechanism. The tnisfit dislocations, however, also serve as diffusion short circuits, and allow high overall lengthening rates to be achieved. In Part I' it was shown that, within the range of aging temperatures and times studied, the broad faces of 8' plates formed in Al-4 pct Cu are fully coherent with the a, matrix. Virtually .all of the dislocations present in these faces were found to have developed as a result of plastic deformation in the a phase. Such dislocations are thus "intruders", rather than the more usual misfit-compensating variety. The edges of 8' plates were confirmed, by extension of the earlier studies of Mat-suura and Koda,3 to be made up of edge-type misfit dislocations, in sessile orientation with respect to lengthening of the plates. These interfacial structures should cause 8' plates to thicken and to lengthen at rates less than those allowed under the condition of volume diffusion control, such as would be expected if the interphase boundaries had disordered structures.' The narrow width of 8' plates, the reproducible crystallography of their broad faces, and the appearance of these plates in cross section as octagons rather than as circular discs2 provide qualitative support for these deductions. The present study of the rate of thickening and the rate of lengthening of 8' plates was undertaken in order to examine them on a quantitative basis. I) THICKENING KINETICS OF THE BROAD FACES OF?' PLATES A) Literature Review. The measurements now available on the thickening kinetics of single-phase precipitate plates consist of one plot of the thickening of a proeutectoid ferrite plate in an Fe-C alloy,' showing (as predicted) thickening rates less than those allowed by volume diffusion control. B) Experimental Procedure. Details of the preparation of the 4-3.93 pct Cu alloy used in this study have been previously reported.4 As in Part 1,' transmission electron microscopy was the observational tool employed. A general description of the apparatus and procedures of the electron microscopy studies is given in Section I of Part I. In thin foils, 0' plates tend to form at and parallel to the foil surface.' A direct investigation of the thickening process by means of hot-stage transmission electron microscopy was therefore not feasible. It was thus necessary to use the conventional method of aging individual bulk specimens for a wide range of different times at the various temperatures studied. In each specimen, the thicknesses of a number of plates were measured. Since thin foils prepared from "bulk-aged" material contain a large proportion of grains with orientations near (001) , it was relatively easy to find, near the edges of the foils, the characteristic multifold patterns of intersecting extinction contours which indicate regions where the foil is exactly at an (001) orientation. The thicknesses of large numbers of plates were measured along the (200) branches of the "stars" so that the 8' plates were precisely parallel to the optical axis of the microscope. Wherever possible, intersecting extinction contours were adjusted with the parameter s > 0 to improve the visibility of the plates in bright-field illumination. These precautions, in combination with taking the measurements at the thinnest parts of the foils, minimized the errors in the measurement of the thickness of the plates resulting from inexact parallelism to the electron beam. Since the plates were very thin, it was not easy to measure their thickness on the photographs. The techniques of enlargement and of microdensitometry were employed to minimize errors from this part of the measurement. A further source of possible error, that the plates can appear thicker because of contrast associated with mismatch normal to the plane of the plate, was also considered. The images of the plates were usually thinner than those of dislocations, however, and no anomalous changes in apparent plate thickness were observed when regions of foil containing plates were tilted through various diffracting conditions. Any error from this cause must therefore be small. Other sources contributing errors were: a) the microdensitometer traces per se and the subjective estimates of their peak limits, and b) slight fluctuations in magnification associated with small changes in the current of the objective lens of the electron microscope. The overall error probably amounted to no more than 5 to 10 pct. In order to obtain readily interpretable data on thickening kinetics, it is essential that the diffusion fields of adjacent ?' plates not be allowed to overlap. Calculations'-' showed that this condition is definitely not ful-

Jan 1, 1969

By F. A. Veer, W. G. Burgers, B. H. Kolster

Starting-- from Cu-Si diffusion couples a study of diffusion in the intermetallic compound Cu3Si of the Cu-Si system has been made. Mmker experiments showed copper to be the diffusing element. From the rate of growth of the Cu3Si phase diffusion coefficients were derived. The activation energy for diffusion is 18.6 kcal per mole. The couples show some interesting microscopic features, for which a tentative explanation is given. THE synthesis of dimethyldichlorosilane, (CH3)2SiC12, an important compound in the manufacture of methyl-silicones, takes place at the surface of a thin Cu3Si layer deposited on a mass of silicon particles."' By passing CH3C1 vapor at about 350°C, silicon atoms are consumed from Cu3Si in forming the volatile silane molecules, thus leaving copper atoms at the surface. It is well-known that copper acts as a poison for the above-mentioned reaction by catalyzing the dissociation of methylchloride.' However, no poisonous effect is observed, at least not before most of the silicon from the particles is converted into silane.3 This would be understandable, if either the copper atoms diffuse through the Cu3Si deposit to the underlying silicon or silicon atoms diffuse in the reverse direction to the copper, both processes resulting in the formation of new Cu3Si and so ensuring the proceeding of the reaction. In this paper experiments are described, demonstrating copper to be the diffusing element. Also a very low activation energy for the diffusion is observed. EXPERIMENTAL The silicon used contained 1 ppm Mg and 1 ppm Cu; the copper was spectroscopically pure (Fe: 2 ppm; Ag, Mg, Si: 1 ppm). The copper and silicon samples were prepared in the form of blocks of approximately 10 by 10 by 5 mm with two parallel sides by spark-machining. The blocks were ground on emery paper (grit 600), etched (copper with nitric acid, silicon with a 4:l nitric acid:hydrofluoric acid mixture), and cleaned with alcohol. As the brittleness of the silicon did not allow a welding procedure to prepare the diffusion couples, the copper and silicon blocks were pressed together in a steel clamp. The pressure exerted by the clamp brought about contact between the parts of the couple and so ensured proceeding of the diffusion. The couples were heated in a vacuum furnace (about 10"5 Torr). The temperature was stabilized within 1 pct. After a heat treatment a section parallel to the direction of diffusion was examined in the microscope and in the X-ray scanning microanalyzer. To determine whether copper or silicon is the diffusing element marker experiments were carried out using tungsten wires with a 20-p diam. EXPERIMENTAL RESULTS Figs. 1, 2, 3, and 4 give micrographs of diffusion zones of Cu/Si couples. Analysis by the electron mi-croprobe of the Cu/Si samples after a definite heat treatment revealed the existence of only one intermetallic phase as can be seen from the line scan shown in Fig. 5. From the X-ray diffraction pattern it could be deduced that this phase was CU 3 Si.4 Even when diffusion zones of considerable width (up to 600 p) were obtained, no other phases occurring in the Cu-Si system could be detected, neither by the electron microprobe nor by X-ray diffraction analysis. The optical anisotropy of the Cu3Si phase made it possible to observe the columnar shape of the crystal-

Jan 1, 1969

By E. P. Pfleider, W. G. Pariseau

This paper reports the theoretical and experimental results of an analysis of ore pass drawdown as a problem in soil plasticity. The method of analysis developed appears to be a promising technique of investigating the mechanics of fragmented materials. A reconstructed plasticity theory brings experiment and theory into reasonable agreement, and hence may provide the foundation needed for rational ore pass design. The gravity-induced movement of broken rock through ore passes is an economical method of transporting fragmented materials through large vertical distances in underground mines, provided the ore pass is well designed. Unfortunately, the design procedures now followed do not very often result in ore passes that function properly. On the one hand, the huge accumulation of empirical data pertaining to the movement of materials in gravel bunkers, storage bins, deep grain silos and other structures that have features in common with ore passes remains uncorrelated. On the other hand, there is a dearth of experimental data substantiating theoretical models of material behavior. Consequently, reliable generalizations encompassing the broad spectrum of problems involved have not been forthcoming. AS an initial step towards improving the situation, a detailed case study of two-dimensional ore pass drawdown was made. The mechanics of the process were analyzed theoretically as a problem in soil plasticity and tested experimentally through observations of a laboratory ore pass model. THEORY Taylor1 defines a soil as a "mass commonly considered to consist of a network or skeleton of solid particles, enclosing voids of varying size." Broken rock in an ore pass is such a material. In plasticity theory this material is replaced by an idealized substance that deforms elastically up to some state of stress at which slip or yield occurs,2 For com-pressive states of stress, the Mohr-Coulomb criterion is a satisfactory yield condition. After the yield point is reached, the ideal soil deforms in accordance with the concept of plastic potential.4 Under plane strain conditions the governing equations separate into a system of stress equations and a system of velocity equations.' Only stress variables appear in the stress system. The velocity system, however, contains a stress variable. The two systems are, therefore, coupled. Both systems are hyperbolic, and each has two real, distinct families of characteristic curves that coincide according to the classical theory of ideal soil plasticity. The

Jan 1, 1969

By A. Coskun, J. F. Elliott

The activity of aluminum in liquid Al-Fe alloys .has been measured by an improved version of the transportation method in which the metallic vapor has been collected by its solution in a metallic condenser. The results can be represented by the equation: log yAl = -3.0(1 - xAl2) (0.6 < XAl < 1.0) This equation applies at 1315°C. MORRIS and zellarsl adapted the transportation method for measuring the vapor pressure of a com- ponent of an alloy at high temperature. We have modified their technique further2 for use with metals that are strong oxide formers. In the present case the method has been applied to the Al- Fe system to obtain the activity of aluminum in the liquid region at 1315°C. Dried ultrahigh-purity hydrogen (Matheson) is the carrier gas. The operations, Fig. 1, of deoxidizing the gas, equilibrating the gas with the sample at 1315";, and then collecting the aluminum vapor are all accomplished within a single, continuous alumina tube to avoid contamination of the system by leaks. De-oxidation to a very low level of PO2 (<10-25 atm) is Obtained by passing the hydrogen through a tightly packed bed of aluminum powder. The temperature of this bed increases to approximately 550°C in the direction of the gas flow. The boat containing three pellets of the alloy is supported on the end of a

Jan 1, 1969

By Juan Sodi, John F. Elliott

The standard free energy of ReS2 has been measured in the range of 1050° to 1250°K using H2/H2S mixtures and a slight variation of the method described by Hager and Elliott.1 The result is: The experimental method and apparatus were modified slightly for this study. Measurements on Cu2S were made to verify the application of the method to the work on ReS2. THE EXPERIMENTS AND RESULTS Briefly, the experimental method consisted of exposing a chip of copper or rhenium at a known temperature for 8 hr to a slowly flowing gas stream at the same temperature in which Ph2S and PH2 were known. The chip was withdrawn quickly from the hot furnace, and subsequently it was inspected for the presence of a sulfided surface. In the experiments described here, there was no ambiguity in any case as to the presence or the absence of the sulfide. At a given temperature, gas compositions for sulfidization were explored systematically until two compositions were found whose values of ?G°, Eqs. [I] and [2], were within approximately 100 cal of each other, one of which was sulfi-dizing and the other was not. These are termed the "straddle" compositions and it is assumed that the equilibrium composition lies between them. The chief modification to the apparatus, which is shown schematically in Fig. 1 of Ref. 1, was to support the metal specimen on a small alumina boat which could be moved along the reaction tube, 6 mm ID, by platinum wires. An appropriate seal at each end of the reaction tube permitted the sample to be moved from the cold end of the tube into the hot zone in 2 to 3 sec, and the sample could be withdrawn equally rapidly. Thus, it was possible essentially to quench the specimen from the reaction temperature with the reaction gas or helium flowing and without danger of breaking the reaction tube. The usual practice at the end of the experiment was to switch the gas system to the helium tank, flood the reaction chamber with helium, and pull the sample out of the hot zone. The purpose of the modification was to permit study of the sulfidization of copper without the complication of the back-reaction between the gas and the specimen as the latter cooled during slow withdrawal of it from the hot zone; this was a problem in the earlier work.&apos; A further improvement located the tip of the temperature-indieating thermocouple and the specimen precisely at the hottest part of the furnace. A carefully calibrated thermocouple, with its tip at the position of the specimen and with other conditions duplicating those of an actual experiment, showed that in the temperature range of 900° to 1122°C the temperature of the specimen differed from that of the tip of the indicating thermocouple by less than 0.5°C. The two positions were 0.5 cm apart. The reaction gas was prepared from ultrahigh-purity hydrogen (<l ppm O2, <0.5 ppm H2O) and CP grade hydrogen sulfide (99.5 pct H2S). High-purity helium (99.995 pct He) was used. All of these gases were purchased from the Matheson Co. All flow meters were recalibrated by the soap-bubble method with hydrogen, H2S, helium, and several gas compositions used during the study. These calibrations gave a linear relationship with a slope of 1.0 for the plot of log flow rate vs log pressure drop across the flow meter, in accordance with the Hagen-Poiseuille equation. The analysis of the gas was determined in the same manner as was reported previously. Good checks were obtained between the composition of the gas established by the flow-meter settings and by chemical analysis of the gas taken after the mixing bulb and ahead of the furnace. The pressures of H2S, H2, S2, and HS in the equilibrium gas at temperature were calculated from the following data :3 The pressures of the species S and S8 were negligible for the conditions of the experiments.3 There was no sign of vaporization of ReS2 either by weight loss or deposits in the reaction tube. Thus it is not possible to account for the apparent volatility of the compound reported by Juza and Biltz.2 The inlet gas composition and the calculated equilibrium ratio of PH2 S/PH2 for the "straddle" points of each experiment are shown in Table I. The specimens of metal for the experiment were small clippings of annealed copper (99.9+ pct) sheet 0.005 in. thick that was obtained from Baker and Adamson and of "high-purity" rhenium (99.9+ pct) sheet 0.005 in. thick that was purchased from Chase Brass and Copper Co. A specimen was removed from the apparatus; inspected for the presence of the sulfide, and then stored in a sealed vial. A fresh clipping was used in each measurement. The condition of the surface of each specimen after the experiment is noted in Table I.

Jan 1, 1969

By José Geraldo Vieira

Companhia Vale do Rio Doce (CVRD), founded in 1942, is located near the town of Itabira, Brazil. Its iron ore deposits include over 500 million metric tons (mt) of high-grade hematite and about 2 billion mt of itabirite (banded rock formed by thin alternate layers of hematite and silica). These deposits are part of the Iron Ore Quadrangle, of which the overall reserves have been estimated at more than 30 billion mt. The magnitude of the project meant difficult early years for the company, including large investments, extensive railroad rehabilitation, and construction of ore port and ore handling facilities. Companhia Vale do Rio Doce was organized as a stock company, and 91% of its shares are presently owned by the Brazilian government. Financing has been accomplished in part through loans from international monetary agencies foreign banks, and foreign industry, as well as Brazilian banks. The company markets mainly abroad. In 1967, it exported 10.6 long tons (It) of ore, principally to West Germany, Japan, Netherlands, Italy, France, United Kingdom, and the United States. The Rio Doce geographic region where CVRD operates is strategically located among the large population centers of Rio de Janeiro, Belo Horizonte, Salvador, and Vitoria (Fig. 1). It covers an area of approximately 81,000 sq km in the states of Minas Gerais and Espirito Santo, and its population in 1968 was about 3.5 million. This region presents excellent prospects for development, with factors favorable for forestry, agriculture, grazing, and exploration for minerals other than iron ore, Electric power (hydroelectric plants) is available, as well as two main systems of transportation: the Rio-Bahia highway and the Vitoria-Minas Railroad. Pioneer activities at Itabira started about 1720 as small gold mining centers. The town is about 80 km northwest of Belo Horizonte and

Jan 1, 1969

By G. C. Rauch, T. H. Courtney, J. Wulff

The superconducting behavior of Nb-Ti alloys containing 40 and higher wt pct of Nb and variable oxygen content was studied as a function of thermomechanical processing. Critical current density (Jc) us applied transverse magnetic field (H) data were obtained for 0.010 in. diam wires at 4.2° Kin steady fields up to 120 kOe. The precipitate responsible for increase in Jc in each of the alloys studied was related to niobium and oxygen content. In alloys containing 40 to 60 wt pct Nb with less than about 1600 ppm of oxygen, w precipitation in the range 350° to 450°C appears to be responsible for the maximum value of Jc observed. In alloys of higher oxygen content (-2500 ppm), the oxygen-enriched a phase which precipitates in the temperature range 450° to 550°C is a more effective fluxoid pinner. Maximum Jc in low oxygen (350 ppm) 80 wt pct Nb alloys was achieved by 600°C aging heat treatments. Measurements of resistive critical field also reflect the changes in composition accompanying precipitation in these alloys. It is well known that the superconducting critical current density, Jc, of solid solution superconducting alloys can be increased by precipitation heat treatments.1-4 The precipitate, to serve as an effective superconzlucting fluxoid pinner and increase Jc, must be of proper size and spacing.&apos; Its electronic properties must also be different from those of the matrix.6 As in age-hardenable systems, optimum temperature and time of aging are dictated by the composition and history of the particular solid-solution alloy under consideration. The alloy diagram of Ti-Nb7-9 shown in Fig. 1 is typical of ß-stabilized Ti alloys. Precipitation to achieve high Jc in Ti-Nb and Ti-Ta alloys is usually carried out in what is believed to be a two-phase a + ß region.1,2,4,10 Previous work on Ti-Nb4,11 and on other ß-stabilized systems such as Ti-V, Ti-Mo,12-14 has shown, however, that the first precipitate to appear is not necessarily (Y. Under specific conditions the meta-stable w phase is precipitated instead. A further complication arises in such alloys from the strong influence of contained oxygen on the phase stability and on the kinetics of precipitation.15,16 The superconducting critical current density of Nb-Ti alloy containing less than 36 wt pct Nb has been studied by Vetrano and Boom1 and Kramer and Rhodes.4 The most effective aging temperature was found to be about 425°C; fluxoid pinning was attributed to the precipita- tion of a by Vetrano and Boom and of w by Kramer and Rhodes. Although the latter workers used recrystal-lized material and the former cold-worked, studies carried out in our laboratory lead us to believe that the type of precipitate responsible for increased Jc is unaffected by prior cold-work.17 That other types of precipitates may also be effective, especially in higher oxygen-containing alloys, has been demonstrated by Reuter, et al.2 in this laboratory with the aid of electron microscopy. Reuter et al. found that at an aging temperature of 600°C, fee-TiO is precipitated, resulting in high values of Jc. Even higher values of Jc were observed after heat treatment at 500°C, but the precipitate could not be indexed as fee-TiO. Whether the precipitate was oxygen-rich w or a could not be clearly distinguished. The work nevertheless indicates that appreciable amounts of oxygen alter the nature of the phases precipitated at different temperatures, at least in alloys containing more than 36 wt pct Nb. Since such compositions are more readily worked into suitable wire than lesser niobium content alloys, it was decided to study the response to aging of the alloy compositions reported in the present paper with the hope of clarifying the effect of composition on the precipitation processes responsible for high values of Jc. I. EXPERIMENTAL Nb-Ti alloys containing 40, 50, 60, and 80 wt pct Nb were prepared by are-melting 35 g ingots of iodide crystal bar titanium and electron-beam melted niobium.

Jan 1, 1969

By George L. Montgomery

In a recent article Heckler, Elias, and woods1 have described an automatic computer technique for plotting of pole figures. To anyone who has constructed pole figures manually from raw X-ray data, the development of computer plotting techniques has been a very welcome development. The purpose of the present note is to describe an alternative computer plotting method which, if somewhat less precise than the method described by Heckler et al., has the advantages of being faster and of not requiring the availability of a plotter. The plot is made directly by the printer of the terminal system and, by its nature, has a good deal of visual impact. Each character of output symbolizes a level of intensity. For example the numerals 1 to 9 might represent intensities referred to some reference obtained from a randomly oriented sample. Should more levels be required (this is seldom necessary) alphabetic or other characters may be used in addition. When these are arranged in the proper fashion, the result is a pole figure such as is shown in Fig. 1. It is the purpose of the computer program to transform the data and carry out the arrangement in a suitable manner. The computation is carried out on a line by line basis in order to reduce the amount of storage required and thus keep the program "small". It is, thereby, well within the limitations of the time-sharing systems which are becoming increasingly available. The inaccuracies introduced are slight and the plot can easily be made as precise as the technique used to collect the data. Comparison of pole figures produced by this method with those constructed manually shows a high degree of equivalence. To the present, the technique has been applied to reflected X-ray data only. X-ray data are collected in a manner identical to that described by Heckler et al. That is, as the goniometer rotates the specimen, a series of counts, accumulated over a preset time, is recorded. The method by which the proper symbol, representing an intensity level, is assigned to each print position is up to the ingenuity of the programmer. Perhaps the simplest method is to section the stereograph in the fashion of a polar net, and to assign all print positions lying within each segment a symbol representing the level of intensity recorded at the data point nearest to the center of the segment, see Fig. 2. The number and arrangement of the segments are selected to conform more or less with the number of accumulated counts and the geometry of the goniometer path used to collect them. Since the angular distance between accumulated counts is usually not infinitely controllable, it is impossible to locate one reading within each segment and, at the same time, maintain symmetry in the sectioning of the stereograph. This latter requirement is essential to keep the computer program simple and flexible. As an expedient it was found that the number of data points could be increased to conform with the number of segments, with very little loss of

Jan 1, 1969

By T. W. Watson, D. R. Flynn

Measurements have been made of the thermal conductivity and electrical resistivity of two specimens of 0.005-cm (2-mil) Be-Cufoil over the temperature range -140° to +200°C. The thermal cmductivity of Be-Cu Alloy 125 was found to be significantly higher than that of Alloy 25, which had a higher impurity content. The thermal conductivity and electrical resistivity values obtained were in concordance with the Smith and Palmer relation for copper alloys which states that ? = 0.0239 (T/p) + 0.075 where A is thermal conductivity (W cm-&apos; deg-&apos;), p is electrical resistivity (microhm-cm), and T is absolute temperature (OK) , indicating that the Smith and Palmer relation can be used to predict the thermal conductivity of this type of Be-Cu alloy over the temperature range -140" to + 200°C to within an accuracy suitable for most engineering applications. THE National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, Md., requested the National Bureau of Standards to measure the thermal conductivity of 0.005-cm Be-Cu foil which was to be used to fabricate antennae for use in Radio Astronomy Explorer space craft. It was felt that measurements had to be made on the actual antenna material, rather than on a thick bar of similar material, since the cold-working and age-hardening properties of the alloy would make it very difficult, if not impossible, to place a thick bar in the same metallurgical state as the 0.005-cm material. As discussed in Section 111 of this paper, the thermal conductivity of many copper alloys can be computed rather accurately from electrical resistivity data using an empirical relation developed by Smith and palmer&apos; and further confirmed by owell.&apos; However, there has been very little work done on correlating thermal and electrical conductivities on Be-Cu alloys. We were reluctant to assume the validity of the Smith-Palmer relation on Be-Cu alloys because of the very large mass difference between beryllium and copper. As will be seen, however, our experimental results indicate that the Smith-Palmer relation is valid for the two alloys on which we made measurements. I) DESCRIPTION OF SAMPLES Samples of Be-Cu Alloy 25 and Be-Cu Alloy 125 were furnished to NBS in the form of rolled strip material, 0.005 cm thick by 5.08 cm wide. The Be-Cu Alloy 25 was purchased by NBS in the form of a continuous length of flat strip. The Be-Cu Alloy 125 was furnished to NBS by Goddard Space Flight Center in the form of two lengths of strip that had been formed into "tubing" of about 1.2 cm diam, with one side of the strip overlapping (but not connected to) the other side by about 90 deg. This "tubing" had been opened up to be flat and then rolled onto spools of about 3 cm diam. When unrolled, the strip would spring back into tubular form. Samples of both of the Be-Cu alloys were chemically analyzed by the NBS Analytical Chemistry Division. The beryllium content was determined quantitatively by the phosphate-gravimetric method to be 1.83 wt pct for Alloy 25 and 1.80 wt pct for Alloy 125. The two alloys were also examined by a general qualitative spectrochemical method for metallic elements. The Alloy 25 specimen contained between 0.1 and 1.0 wt pct Al, Co, Fe, and Si and between 0.01 and 0.1 pct Ni. The Alloy 125 specimen contained between 0.1 and 1.0 pct Co and between 0.01 and 0.1 pct Al, Fe, and Si. Other metallic elements present were in amounts less than 0.01 pct. The NBS Engineering Metallurgy Section measured the tensile strength, elongation, and Knoop hardness of both the Be-Cu Alloy 25 and the Be-Cu Alloy 125. These are given in Table I. The NBS Engineering Metallurgy Section also prepared photomicrographs of the two alloys; these are shown in Figs. 1 and 2.

Jan 1, 1969

By Y. Mishima, R. Shiromizu

THE equilibrium y phase in Cu-Be alloys forms by discontinuous precipitation, the new phase nucleating at the grain boundaries and growing into grains on both sides of the boundary. When the alloy is aged above 500°C, however, growth may take place into only one of the grains.1&apos;2 In A1-Ag alloys it is known that the precipitate has the same orientation as the grain in which no growth takes place.3, 4 This was confirmed in the present investigation on a Cu-Be alloy. A Cu-1.79 wt pct Be alloy was solution-treated at 810°C for 2+ hr, quenched into water at O°C, and aged at 600°C for 1 hr in a salt bath. The specimen was thinned by chemical polishing and electropolishing at room temperature in a solution of H3PO4 saturated with CrOs. The foil produced was examined in a JEM 150 electron microscope operating at 150 kv. Fig. 1 shows precipitates growing on only one side of the grain boundary. The black platelike precipitates were identified as the y phase. Electron dif-

Jan 1, 1969

By M. C. Flemings, R. Mehrabian, G. E. Nereo

Analytic expressions were developed and applied in two preuious papers to predict effects of solidification variables on macrosegvegation. In this paper, experiments are reported to test the analyses quantitatively and qualitatively. Good quantitative agreement is obtained between predicted and measured compositions for the following types of segregation (all experiments were on laboratory-size ingots of Al-4.5 pct Cu alloy): (a) inuerse segregation, (b) composition distribution in ingots solidified with unidirectional heat and fluid flow, (c) simulated centerline segregation, and (d) segregation resulting fro, change in solidification cross section. In addition, qualitative agreement of prediction of theory with experiment is obtained for (a) segregation resulting from sudden change in heat extraction during solidification, (b) centerline segregation in a bidirectionally solidified ingot, and (c) under-riser positive segregation. IN two previous papers,&apos;&apos;2 it was shown that a variety of apparently different types of macrosegregation result from the same basic mechanism. This mechanism is the flow of solute -rich liquid to feed solidification and thermal contractions. Analytic expressions were derived and examples given of their application to predict macrosegregation. Calculations were for Al-4.5 pct Cu alloy. In this paper, we describe a series of experiments designed to test results of the foregoing calculations. All experiments were on laboratory-size ingots (weighing 10 lb or less), of A1-4.5 pct Cu alloy, nominal composition. APPARATUS AND PROCEDURE A typical mold and chilling arrangement used for unidirectional solidification is shown in Fig. 1. Before casting, this assembly was placed in an electrically heated air furnace, and heated to 680" to 700°C. When the plaster reached the desired temperature (usually 1 to 2 hr after the furnace temperature), the mold was filled through a funnel extending from the outside of the furnace into the cavity. The assembly, with liquid, was held for several minutes to allow convection to subside. The coolant, either air or water (depending on the desired solidification rate), was turned on and the ingot solidified. With the four sides and top insulated, heat removal for solidification was through the bottom surface, resulting in a fully columnar structure. Design of the casting cavity was varied, as discussed below, to produce desired macrosegregation effects. However, for castings solidified with unidirectional heat flow, the top was always open to the furnace atmosphere and temperature. The bottom sur- face rested on a chill through which the heat was extracted, and all other surfaces were insulated with plaster. In one case to be discussed, the mold design was changed to obtain bidirectional solidification. In this case, two vertical chills were used (on two faces of the mold) and the bottom was insulated. In a last case discussed, that dealing with under-riser segregation, experiments were conducted in bottom-chilled sand molds at ambient temperature. Except for this one case, all experiments were conducted in the electrically heated air furnace as described above. In many ingots, thermocouples were used to obtain continuous records of solidification. In all cases, these were chromel-alumel couples with output continuously monitored on a twelve-channel recorder. Where thermocouples were employed, these were embedded in the refractory mold walls during mold-making so their heads extended to the vertical centerline. Six to nine couples were employed, placed at intervals from the chill. METAL-MEL TING PROCEDURE Aim analysis was A1-4.5 pct Cu; alloy was prepared from high-purity aluminum (99.9 pct Al) and A1-Cu master alloy (50 pctOFHC Copper, 50 pct high-purity Al). The A1-4.5 pct Cu alloy was cast in 5- to 7-lb ingots for subsequent remelting for the macrosegregation experiments. Melting for ingot casting was as follows. After preheating the melting crucible for an hour or more, the charge was melted and superheated to a temperature of 690" to 720°C. After stirring, the melt was degassed with chlorine for 10 min. After stirring again for 1 min, a gas sample, under reduced pressure, was taken. When the sample was gas-free, the crucible

Jan 1, 1969

By P. M. Kelly, E. P. Butler

The stability of a 70/30 Mn-Cu alloy aged to peak damping has been investigated using electron microscopy, X-ray diffraction, and torsional pendulum measurements. Storage at room temperature or at 100" C causes a reduction in damping capacity. This is shown to be due to the formation of subdomains which "lock" the main domain structure and so hinder their movement. After storage the damping capacity can be restored by a retransformation treatment, which generates structures identical to those found in newly aged specimens. Plastic deformation by rolling also causes a decrease in damping capacity. In this case the damping capacity can only be restored by retransformation if the amount of deformation is less than about 5 pct. THE general metallography and structure of these high damping capacity alloys has been discussed in Part I of this work.1 Part II deals with some of the variables that affect the damping capacity. In particular, the stability of the damping capacity of a 70/30 alloy aged for 2 hr at 425° C and quenched has been investigated. The temperature sensitivity of the damping capacity of a 70/30 alloy aged for 2 hr at 450° C has been reported by Birchon.2 The damping capacity begins to decrease with increasing temperature, and is very low above the M, temperature of 125°C. The cubic — tetragonal transformation is completely reversible and there is no apparent thermal hysteresis associated with the change in damping capacity. Another important effect was first reported by Dean and his coworkers.3 They noticed a decrease in the damping capacity with time for specimens of a quenched tetragonal alloy. More recently workers at the Admiralty Materials Laboratory 4 have studied the stability of an aged 70/30 alloy. They found that the damping capacity decreased to half its original value after about 1000 hr at room temperature. EXPERIMENTAL The techniques used for electron microscopy and X-ray diffraction have been described in Part I. The damping capacity was measured by means of a torsional pendulum, using rectangular specimens, 3 by 0.3 mm with a 6 cm gage length. The specific damping capacity, S.D.C., was calculated as a percent amplitude decay in free vibrations over 10 cycles, starting at an amplitude which corresponded to a 700 psi surface shear stress. Because of the stress dependence of the damping,&apos; the values obtained were about a third those reported for a 5000 psi surface shear stress.&apos; RESULTS a) Effect of Aging Temperature. The effect of aging temperature on the damping capacity is shown in Fig. 1. The damping capacity reaches a peak of 12 pct after aging at 400° to 425°C) then begins to decrease as the volume fraction of a Mn increases. At higher aging temperatures the structure becomes cubic again with a low damping capacity. b) Stability of the Aged Structure. The damping capacity of the aged alloy decreases with time at room temperature. This process could be accelerated by storing at 100°C, when about 100 hr were required for the damping to fall to half its original value. The results of room temperature and 100°C storage, for times up to 1000 hr, are shown in Fig. 2. The damping capacity starts to decrease after about 24 hr at 18° C and 1 to 2 hr at 100°C. It was found, however, that the damping could be almost completely restored by retransformation. The specimens were held at a temperature above the M, for a short time, 250° C for 5 min, and then quenched. The values of damping capacity for specimens that were aged, stored, and then retransformed are shown by the full points in Fig. 2. X-ray measurements of the c/a ratio and hardness readings on the specimens did

Jan 1, 1969

By R. E. Goodman, M. A. Mahtab

The, state of stress around a vertical wellbore in rock following nonlinear stress-strain laws is examined by means of finite element analysis. The wellbore, is considered an axisymmetrier body with axisymmetric loading. The initial vertcal and borizontal stresses are "locked" in the rock elements around the wellbore and a new state of stress is generated by the displacements which occur around the borehole. A point-uise variation of the elastic moduli is made on the basis of the new stress state and the triaxial data. The initial stresses tire now reintroduced along with tile changed moduli and original boundary constraints. This procedure is repeatrd until convergent stresses are reached. The effect of nonlinearity on streases is examined for a 6,000-ft wellbore in a scbistose gnezss and Berea sandstone using results of laborratory triaxial compression tests. The results sbou that the effect is restrited to one well radius from the bottom periphery of the bole. Beyond a distance of one-quarter radius, the elfect of nonlinearity on stresscs IS almost always less than percent for the cases conszdered, The consideration of a static pressure inside the well does not magnify the effect of monlinearity on borehole stresscs. INTRODUCTION The terms " wellbore" and "borehole" here designate cylindrical openings in the ground with vertical axis and a circular cross-section. A knowledge of the stress redistribution that occurs on excavating a wellbore is important in understanding (1) the behavior of the lined or unlined hole, (2) hydraulic fracture response, and (3) the effect of stress redistribution on drillability; also it is important in predicting initial stresses in the virgin ground, and in analyzing the response of measuring instruments placed in the borehole. Our knowledge of the state of stress around a wellbore has been restricted to homogeneous, isotropic, elastic material and derives chiefly from the analysis by Miles and Toppingl and the photoelastic work of Galle and Wilhoit2 and Word and Wilhoit.3 In this investigation the state of stress is examined for a nonlinear elastic material by means of finite element analysis. Many rocks possess stress-strain curves that depart notably from straight lines in their initial or final portions. While the literature contains abundant stress-strain data from triaxial tests (axisymmetric loading) on cylindrical rock specimens, there is little information on rock deformability under nonaxisymmetric loading conditions such as occur at each point around the bottom of a wellbore. Although there is some knowledge of the effect of intermediate principal stress on rock strength, there is virtually nothing known about its effect on rock deformability; therefore, we have assumed here that the effect of intermediate principal stress can be ignored. A schistose gneiss4 and Berea sandstone5 were selected as representative rocks for this analysis. The traditional graphs of deviator stress (ol -o3) vs axial strain were reworked to give the tangent modulus as a function of the deviator stress for varying values of the minor principal stress. The result is a nesting family of skewed, bell-shaped curves for tile gneiss (Fig. 1A) and the sandstone (Fig. 2A). A similar replotting of the lateral strain data defines the variation of Poisson&apos;s ratio (v) with the deviator stress and confining pressure. These curves, shown in Fig. 1B for the gneiss and in Fig. 2B for the sandstone, are not so well ordered as the tangent modulus curves. However, all of these display an increase of v with deviator stress application, but the rate of increase diminishes with confinement. The ET and v curves for the two rock types are tabulated in Tables 1A and 1A for use in a digital computer so that material properties corresponding to a given state of stress can be assigned by interpolation. STATEMENT OF THE PROBLEM Given a state of stress in the ground prior to drilling a hole (initial stresses), we assume that

Jan 1, 1969

By H. J. Ramey, I. S. Bousaid

Experimental results on the oxidation reaction kinetics in the forward combustion oil recovery process are presented. A total of 48 runs were made wherein a stationary thin layer of coked, unconsoli-dated sand was burned isothermally in a combustion cell. Individual runs were made at various temperature levels to permit determination of the effect of temperature upon the reaction. An expression was obtained for the burning rate of carbon as a function of carbon concentration, combustion temperature and oxygen partial pressure. The carbon burning rate for two types of crude oil indicated a first order reaction with respect to both carbon concentration and oxygen partial pressure. The effect of combustion temperature on the reaction rate constant matched the Arrhenius equation. The activation energy was similar for the two crude oils examined. The activation energy decreased for a porous media containing clay. The rate of oxidation of crude oil at reservoir temperature was found to be significant. Other significant findings included information on hydrogen-carbon content of fuel residues, fuel reactivity and the products of combustion. INTRODUCTION The production of crude oil by underground combustion has been studied in the laboratory by many investigators.1-5 Results of laboratory and field experiments have been reported in the literature describing the forward combustion process. But as yet, no qualitative or quantitative study of the kinetics of fuel combustion involved in this process has been reported. The fuel concentration and the rate at which fuel is burned at the front are important factors governing the air requirement in a forward combustion operation. Although the fuel is essentially unrecoverable crude, the air required to burn the fuel is an important economic factor in this process. Because fuel is burned, the heat transport associated with forward combustion is a key and unique feature of this new oil recovery method. Many investiga-tors5-9 have presented information on the heat transmission and fluid mechanics involved in forward combustion. Berry and Parrish10 demonstrated the utility of considering reaction kinetics in reverse burning. From differential thermal analysis, Tadema11 presented a qualitative discussion of the nature of reactions between oil and oxygen in combustion oil recovery. Although little quantitative work has been done on the reaction kinetics involved in forward combustion oil recovery, an extensive literature does exist on combustion of carbons and oils, and carbonaceous residues from cracking catalyst pellets. Dart, et al., 12 studied the combustion rate for oxidation of carbonaceous residues on clay catalyst pellets, and found the reaction to be second-order with respect to carbon concentration, and first-order with respect to oxygen partial pressure for carbon concentrations less than 2 weight percent of the catalyst weight. The reaction appeared to be first-order with respect to carbon concentration for concentrations greater than 2 percent. Metcalfe13 noted that other workers had found that aging of the fuel during the combustion process was responsible for changing coke properties, and it accounted for the apparent second-order carbon concentration effect found by Dart, et al. It appears that burning of residues from cracking pellets is first-order with respect to both carbon concentration and oxygen partial pressure. Dart, et al., also observed that hydrogen in the hydrocarbon residue appeared to react faster than the carbon. Lewis, et al.,14 studied oxidation of charcoal, coke and graphite in a fluidized bed. Gas velocities were high enough to partially lift and circulate the carbon particles. Their results indicated first-order reaction dependency with respect to both carbon concentration and oxygen partial pressure. One

Jan 1, 1969

By Reino Kurppa

The Pyhäsalmi mine of the Outokumpu Co. is located in central Finland (Fig. 1). The deposit was discovered in the autumn of 1958. Construction of the mine was started a year later, and production began on Mar. 1, 1962 (Fig. 2). At present, 750,000 metric tons (mt) of ore and a nearly equal amount of country rock are mined annually. Slightly over one-half million tons of various concentrates are produced per year, of which 85% is pyrite concentrate, 10% zinc concentrate, and 5% copper concentrate. The pyrite concentrate is treated in the company&apos;s pyrite smelter,1 yielding elementary sulfur, sulfur dioxide, and iron-oxide cinders, as well as electric power. Thus all the sulfides, totaling 75% of the ore, are of economic value. This is a fact which had a bearing on the development of the stoping method. GEOLOGY The ore is of breccia type containing fragments of country rock of varying sizes. It is coarse-grained pyrite ore containing sphalerite and chalcopyrite as a matrix between the pyrite grains. Only small amounts of pyrrhotite have been observed in certain marginal parts of the orebody. The ore averages 0.85% Cu, 3.0% Zn, 38% S, and 33% Fe. The orebody extends from the surface down to at least 500 m, which is the lowest level from which present information has been obtained. Horizontally, the orebody is 650 m long. It is 75 m wide at its central part, narrowing towards the ends (Fig. 3). At a depth of 115 m, the orebody suddenly narrows down to a thickness of 25 to 30 m. In the northern part of the orebody, the dip is 50° to 70°, but elsewhere it is almost vertical (Fig. 3).

Jan 1, 1969

By S. G. Epstein

Electromigration has been measured in dilute liquid alloys of lead in antimony and antimony in lead. In these alloys antimony migrates with the electron current; lead migrates in the opposite direction. These results, which contradict the mass criterion, were predicted by the electron drag model for electromigration in liquid alloys. The existing experimental data are shown to correlate with the difference in electrical resistivities of the alloy components. FOR many years investigators have attempted to relate observed electromigration phenomena in liquid alloys to the physical properties of the alloy components. The most successful correlation was found by Angus et&apos; al.,1 who in 1959 proposed an empirical criterion for predicting the relative direction of motion of the components of a liquid alloy in an electric field: the component with the smallest atomic mass concentrates at the cathode. While this criterion is obeyed in nearly all the alloy systems which had been investigated, the physical basis for such an effect was not understood. It was also disturbing that the mass criterion predicted the wrong sign for the Haeffner effect; observations with pure liquid metals revealed that in every instance the lighter isotope was transported to the anode.2 Klemm3 explained these isotopic separations by suggesting that the lighter isotopes were more mobile and more easily carried to the anode with the electron stream. Additionally, several deviations from the mass criterion have been found in liquid alloys, notably involving transition metals such as chromium, nickel, palladium, and zirconium, which migrate to the anode in liquid bismuth.4&apos;5 Recently, a model has been proposed6 in which electromigration in liquid alloys is attributed primarily to the interaction between the electron stream and the metal ions. In essence, this model predicts that the component with the greater electron-ion scattering cross section will be preferentially transported to the anode, displacing the other component to the cathode. The electrical resistivity of each pure component at its melting point is taken as the measure of its scattering cross section. This model was developed from the results of systematic studies with various solutes in liquid mercury,7&apos;8 bismuth,9 and sodium.10 In every alloy, the component with the greater resistivity has centrates at the anode. Coincidentally, in every instance the component with the greater resistivity has also the greater mass, apparently satisfying the mass criterion. In order to differentiate between electron-ion coupling and atomic mass as the relevant physical prop- erty influencing electromigration, measurements were made with Pb-Sb alloys. Lead has an atomic mass nearly twice that of antimony, but lead has an electrical resistivity of 91 microhm-cm while antimony has a value of 113.5 microhm-cm at their respective melting points. The mass criterion predicts that in an alloy of the two antimony will concentrate at the cathode; the electron drag model predicts that antimony will concentrate at the anode. EXPERIMENTAL To conclusively determine the relative motion of lead and antimony in each other, solute electromigration was measured in dilute liquid alloys of antimony in lead and lead in antimony. Both starting materials were 99.999+ pct pure. The measurements were made with the same capillary-reservoir technique previously used for measuring electromigration in liquid bismuth alloys.11 Several changes in the experimental apparatus were necessary, however, to accommodate liquid antimony, which has a higher melting point than bismuth. The modified apparatus is depicted in Fig. 1. In each experiment four quartz capillaries were filled with the molten alloy. A direct current was passed through two of the capillaries; the electrode in one of these capillaries was made the cathode, and the electrode in the other was made the anode. The remaining two capillaries sampled the alloy in the reser-

Jan 1, 1969

By E. T. Turkdogan, L. S. Darken

Using the quadratic formalism, thermodynamic equations are derived for the composition dependence of the heat and entropy of mixing. The applicability of these equations is confirmed by available experimental data on the activities and heats of mixing for binary metallic systems of Group ZZB elements. In a recent paper arkeen&apos; introduced a quadratic formalism describing the composition dependence of the activity coefficient in the terminal regions of binary metallic solutions. That is, in the terminal region, which may extend to as much as 60 at. pct, the logarithm of the activity coefficient, log y,, of component 2 is a linear function of (1 - N,)&apos; where N2 is the atom fraction of component 2. Similarly, for the other component, log yl is a linear function of (1 - N,)&apos;. A number of iron-base binary liquid alloys were shown to obey this quadratic formalism. arkeen&apos; extended this formalism also to any corner of a ternary system and showed that the activity coefficients of the components 1, 2 and 3 (1 is taken as the solvent) can be represented by quadratic terms involving five parameters, four of the binaries and one for the ternary system. Numerous examples given by arkeen&apos; demonstrated the general applicability of the quadratic formalism to iron-base systems over a wide composition range. In this paper further examples are given of binary liquid systems (Group IIB elements, Zn, Cd, and Hg) and of several solid solutions, again demonstrating the appropriateness of this concept. A further purpose of this paper is to extend the quadratic formalism to the enthalpy and excess entropy of binary metallic solutions and to test the equations so found using available experimental data. QUADRATIC FORMALISM FOR HEATS AND ENTROPIES OF MIXING OF BINARY METALLIC SOLUTIONS The following equations, reproduced from Darken&apos;s paper, are for the two terminal regions of binary systems. at infinite dilution and a&apos;s are temperature dependent parameters to be determined from the experimental data. Although the quadratic formalism is an assumed representation of the data, Eqs. [I] to [4] are thermo-dynamically consistent with the Gibbs-Duhem relation and satisfy Raoult&apos;s and Henry&apos;s laws as limiting cases. As pointed out previously,&apos; the following form of the Gibbs-Duhem equation facilitates the integration in general but particularly in regions I and 11, where each of the derivatives is constant. The partial molar enthalpy of solution i, (and i; the value of i, at infinite dilution) are related to the activity coefficients y, and y," by the thermodynamic relation Differentiating Eq. [l ] with respect to 1/T and substituting the above thermodynamic relation gives for region (I) It is reasonable to assume that over a temperature range of experimental interest, the enthalpy of mixing is essentially independent of temperature, implying from Eq. [7] that the derivative da,,/d(l/) is also independent of temperature. On the basis of this argument, the temperature dependence of a has the form where £ and S have the units of enthalpy and entropy respectively; they are characteristic parameters for a terminal region of a binary system, e.g. for region (I), C12, S12 and for region (II), d:,,, S2,. Using this equation gives for dff ,/ d(l/), From Eqs. [7] and [9] an expre_ssion is obtained for the composition dependence of L,. Similar calculations are made for El and the results are summarized below for the two terminal regions. For region (I), The corresponding expressions for the molar heat of solution, AHM, are readily obtained from the above equations for the two terminal regions: For region (I),

Jan 1, 1969

By Daniel T. O’Brian

Exploration targets and results in the mining industry are commonly summarized in terms of tonnage and grade. Business appraisals require, as additional information, the expected profit or loss implied by the physical summary. The early incorporation of knowledge gained through financial analysis computations can provide a means for economically resolving many common exploration and development problems. Examples of such applications from the activities of exploration planning, reconnaissance, land acquisition, and development planning are presented in this paper.

Jan 1, 1969