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By Sidney A. Swensrud

About a year ago, I attempted in a general way to trace the origin and development of some of the marketing problems of the petroleum industry, and to describe certain trends which it then seemed possible to foresee. To summarize briefly, it was pointed out that the consumption of gasoline, after increasing for more than a decade at an almost unbelievable rate, was slowing down, but that the two factors which determine the supply of gasoline —-namely, the production of crude oil and the percentage of gasoline derived therefrom—were tending steadily to mount. It was suggested that, while the increase in gasoline outlets began with and probably was justified at the start by the rapidly increasing demand, long after all reasonable requirements as to number of outlets had been met the number continued to increase—if anything, at a still more rapid rate—because by that time the overproduction of crude had begun to exert an impelling urge upon the owners of that crude to seek assured outlets for it in the form of gasoline. As more and more companies became integrated all the way from crude oil to marketing, there took place an ever-increasing competition among them, not only for the existing outlets but for new ones. The wide margin between wholesale cost and retail price, which is characteristic of the early stages of most new industries, persisted in the oil industry longer than in most industries, for various reasons. The existence of that wide margin provided in large measure the means of attracting new outlets, for as the gallonage per outlet declined with the increasing number of outlets, competing companies simply offered the dealers a larger part of the total margin. The very nature of competition suggests that such a process would continue until practically all of the available margin was thus given away, and such was clearly the tendency. It was a system that in turn produced increasing marketing expense per gallon on account of the diluted gallonage per outlet; this increased expense might seem to have provided a justification for continuing wide margins. Economics, like its parent, nature, however, progresses by mutations and so began to throw out new types of marketers, in the form of tank-car service stations, cut-price jobbers, and the like—heretics or

Jan 1, 1932

By E. Northcott, I. M. LeBaron

Before describing the electrostatic processing of feldspar, it might be well to review some of the basic definitions and terminology of feldspars. The feldspar minerals constitute a group of alumino-silicates of potassium, sodium, and calcium. Barium feldspar sometimes occurs naturally but is very rare. Hardness varies between 6 and 6.5 and specific gravity between 2.5 and 2.8. Color is generally white or pale shades of red, yellow, or green. The approximate chemical composition of the principal feldspars is given in Table I. The albite (sodium aluminum silicate) and an orthite (calcium aluminum silicate) feldspars are the end members of a series called plagioclase. These two molecules form a complete solid solution series ranging from pure soda feldspar at one end to the pure lime feldspar at the other end. Intermediate solid solutions are known as oligoclase, andesine, labradorite, and bytoconite. The general structure throughout this series is the same. Sodium and calcium may replace each other and silicon and aluminum may replace each other in the structure.

Jan 10, 1958

By Henry U. Ross

The behaviour during reduction of iron-ore pellets and sinters was investigated. Several methods for the preparation of agglomerates and their reduction were tried. Commercial agglomerates from world-wide sources as well as experimental samples were tested. The effect of coke additions to pellet and sinter plant feeds was given special consideration. An analysis of the test results has helped to explain many of the phenomena associated with the reduction of iron-ore agglomerates such as swelling, loss in strength and wear resistance, changes in porosity, changes in mineralogy and the formation of metallic iron and slag. A double-layer pellet with all of the coke concentrated in the core proved particularly interesting. Although large quantities of coke showed that partially reduced agglomerates containing metallic iron could be produced in the laboratory, the problem of producing reduced pellets and sinters by the existing agglomerating processes still remains.

Jan 1, 1977

By F. Lynwood Garrison

The future of the Witwatersrand depends upon the possibility of mining and milling profitably the large tonnage of relatively low-grade gold ores known to exist in that area. The problem must be solved if the existence of the gold-mining industry in South Africa is to be saved and continue. To show that this disaster may be avoided, or at least postponed for another decade or longer, the following official statement is of interest: "There is a fairly large area of possible orebody on the East Rand of whose value and depth from the surface we have some though not very accurate knowledge. There is a far larger area south of the Central Rand which probably carries much payable ore, but at depths that at present appear too great to mine. Finally, there is a narrow strip of country over 100 miles in length stretching south from the Rand to Klerksdorp and beyond, which may contain large ore-bodies. The Witwatersrand rocks outcrop over portions of this ground and in places conglomerates occur in it that carry small bodies of payable ore. There is reason to believe that conglomerates of the Witwatersrand system exist over all this strip, though they are for the most part covered by later sediments. It seems probable also that there are large blocks of payable reef in this belt, at any rate in the area that lies close to the present western limit of the developed mines. The structure in this neighborhood is however very complicated and to prove the orebodies will be both difficult and costly." Ores in the Witwatersrand It should be explained in this connection that the conglomerates mentioned here were originally old gravel beds now consolidated into bedded sedimentary rocks, very hard because strongly cemented with secondary silica. The gold exists in this cement and is rarely found in the pebbles composing the rock or bed called locally reef. It is important to realize that these gold deposits are beds; not veins as generally understood by mining engineers and geologists. In addition to these low-grade ore reserves we have also to consider the ore left behind in the old stopes of the upper levels near the surface,

Jan 1, 1931

By John P. Hager, Igor A. Wilkomirsky

The thermodynamic properties of the Pb-Ag system have been determined between 775° and 950°C by the cell: Electrotransport measurements on silica-saturated PbO-SiO2 melts established that the conduction was entirely ionic and that lead is present only in the divalent state. The activities of lead and silver exhibit Positive deviations from ideal behavior. In dilute solutions the activities of lead and silver follow Henry's law. The values obtained for yhb and yig at 1200°K are 1.49 and 1.69, respectively. Determination of a portion of the liquidus curve agrees well with the established phase diagram. provides an accurate means for the thermodynamic study of liquid alloy systems. However, Wagner and wernerl have shown that cells of type I are limited to alloy systems for which the reaction at the alloy-electrolyte interface will be extremely small. The traditional electrolyte for cells of type I has been a low melting point mixture of group IA chlorides, to which a small amount of the compound ACIZa has been added. However, the choice of a chloride electrolyte may not always be practical, in that the Gibbs free energies of formation of the compounds ACIZ, and BCIZb may not be sufficiently different to minimize Reaction [I]. On the other hand, the Gibbs free energies of formation of the oxides of metals A and B may be sufficiently different to minimize Reaction [I]. In this case, the use of molten oxide electrolyte would be clearly advantageous. In the present study, the thermodynamic properties of the Pb-Ag system have been investigated using the cell: Previous galvanic cell studies on the Pb-Ag system2'= are not reliable due to the displacement reaction between the alloys and the chloride electrolyte. Wagner and ~erner,' using Laitinen and Liu's' value at 450°C for the standard electrode potential of Reaction 111, have estimated the percent error in the activity of lead bPb) when using a chloride electrolyte. At 1000°C the error for xpb = 0.10 is 12 pct. Taking the Gibbs free energies of formation for PbClz and Ag cI,' and the equations of Wagner and Werner,' the error in apb at 1000°C and Xpb =0.10 was calculated to be 140 pct. However, using the Gibbs free energies of formation for Pb O' and an estimated value for Ag 20, the error in apb when using a molten oxide electrolyte at 1000°C was estimated to be less than 1 pct for The virtual reaction of cell I1 for the passage of n Faradays of positive electricity from left to right in the cell is: where 5 is the Faraday equivalent (23,063 cal per v equivalent), E is the electromotive force of the cell in volts, and n is the number of Faradays of electricity required for the transfer of 1 g-atom of lead through the cell. The value of n should be equal to 2 since lead is generally divalent in oxide melts. However, the presence of either tetravalent lead ions or electronic conductivity through the molten oxide electrolyte will result in a value of n greater than 2. Bockris, Kitchener, and Davies' have determined the amount of ionic conductance in a liquid PbO-SiO2 mixture (xPbO= 0.50) at 920°C by measurement of the volumes of CO and C& evolved at a carbon anode during electrolysis. From their data a value of 2.13 * 0.16 was calculated for n. Although their measurements indicate the possible presence of multivalent lead ions and/or electronic conductivity, their measurements were not at silica saturation and no definite conclusions can be drawn. However, as a result of the electrotransport measurements described in the next section the ;due of n can be taken as equal to 2.

Jan 1, 1969

By S. H. Brockunier

During the examination of a gold-property in Georgia, last summer, I had occasion to study the effect of different chemicals upon the ore; the object being to find a more economical method of extraction than chlorination, as practiced there, had proved to be. Some of my notes and results may be of interest to others. The country-rock consists of mica-schist, hornblende-schist and black slate. The vein-matter is quartzite and schist, containing some stringers of quartz, the whole forming a body from 20 to 50 ft. wide. All of the rocks in the vicinity have become disintegrated to a depth of from 50 to 75 ft., forming the so-called saprolite. I found the workings to represent two distinct classes : I. Open-cut surface-ore: very soft,oxidized and disintegrated; containing much alumina, silica and iron. Average value, $4 per ton. 11. Ore from lower levels : quartzites and schist; very hard ; containing much silica and manganese, some alumina, and from 2 to 10 per cent. of pyrites. Average value, $8 per ton. Class I. was soon dismissed. The only way to make it pay would have been by the use of steam-shovels and a large crushing-plant. The tendency to slime would be the principal difficulty.

Jan 1, 1902

Charles T. Malcolmson, Chicago, Ill.:—Mr. Blauvelt's admirable paper is a valuable contribution to the literature on briquetting of coal in this country. It should have a special significance for those interested in the commercial development of the coal-briquette industry. I believe that the data included in Mr. Blauvelt's paper will be particularly useful because they represent costs taken from a briquette-plant in actual operation. There are several points touched on in Mr. Blauvelt's paper which may bear comment in the way of emphasis rather than of criticism. In the first place, he has stated a fact which becomes axiomatic to any one who has had any experience in the design, building, or operation of coal-briquette plants, and that is, that the press is only one factor in the successful opera-

Jan 1, 1911

Jan 1, 1901

By O. G. Lellep

IN every country economic circumstances prescribe the method used to produce a commodity at lowest cost. In Pennsylvania a man's wages for working 4 hr buys a ton of coal wholesale; in Germany a laborer must work 40 hr, or ten times as long. In western Europe, therefore, conservation of fuel is of primary importance, and recent practices of burning lime and cement differ from those employed in the United States. This paper presents data collected during a trip through western Europe in 1953. Considered uneconomical, shaft kilns for burning cement disappeared in the United States two generations ago. But because required capital investment is low and operation greatly improved, shaft kilns are still used to some extent in Europe, where fuel costs are high, and are even included in designs for plants under construction. During the last 50 years shaft kilns have been maintained at the same physical size, while their output has been increased at least four times.

Jan 7, 1954

By Nelson Severinghaus

Consolidated Quarries Corp. must conduct operations for an average sales price of $1.25 per ton, about the same price at which stone was sold 25 years ago when the dollar was worth twice what it is now. To maintain success in a competitive business, the company must solve the usual production problems, which will be discussed here in the order they occur in the flowsheet. Most crushed stone quarries must first remove soil and decomposed rock. Although seasons of lower sales sometimes release regular quarry excavating and haulage equipment for this purpose, overburden is often too extensive for this method to be used. In such cases, special equipment must be assigned or the job may be contracted. As many earthmoving contractors have heavy duty specialized equipment well suited to overburden removal, they should be seriously considered before the job is undertaken. Pockets of clay beneath peaks of hard stone sometimes defy mechanized removal. Pick and shovel laborers at this point might be supplanted by more ingenious use of pumps and water or some other mechanical means. Where overburden is extremely heavy or difficult to remove, underground mining must be considered.

Mar 1, 1956

By J. N. Chew, C. A. Connally

A correlation is presented for predicting the viscosity of gas-saturated crude oils under reservoir conditions. It is based on the dead oil viscosity and the solution GOR. The correlation was developed from a study which showed that at a fixed solution GOR, the relation between the gas-saturated oil viscosities and the correrponding dead oil viscosities is a straight line on logarithmic coordinates. Data from 457 crude oil samples from the major producing areas of the U. S., Canada and South America were used. The best straight lines through the data were fitted by the method of least squares with a digital computer. The correlation is presented in the form of an equation and also in a convenient gra-phical form. INTRODUCTION The viscosity of gas-saturated crude oils under reservoir conditions is an important physical property used in reservoir engineering calculations. Many difficulties are inherent in the sampling of gas-saturated oils and in the laboratory measurement of their viscosities. Therefore, it is frequently neither possible nor convenient to obtain measured values, so the viscosity must be estimated from other, more readily available data. This paper presents a correlation for predicting the viscosity of gas-saturated crude oils. The correlation is based on the amount of gas in solution and the viscosity of the dead oil at the temperature of interest. A previous correlation of these variables was presented by Beal. In comparison, the correlation presented here extends to a higher GOR and to a lower dead oil viscosity. Over the range of variables covered by both, this correlation is based on approximately 11 times as many oil samples. DEVELOPMENT OF CORRELATION A study was made of the variables or parameters which could be used to relate the viscosity of a gas-saturated oil to its dead oil viscosity. Preference was given to those variables which are easily and commonly measured in the field or in the laboratory. It was found that either the differential liquid formation volume factor or the solution GOR of the gas-saturated oil could be used as a correlating parameter. The solution GOR was se- lected for the correlation because of its simplicity and availability. In an attempt to refine the correlation by introducing a second parameter, the following additional variables were tested: differential liquid formation volume factor at the reservoir bubble point, the formation volume factor at the saturation pressure for the GOR of interest, reservoir temperature, viscosity of C+ fraction at 100°F and atmospheric pressure, weighted average gravity of gas in solution, oil gravity, reservoir bubble point pressure, saturation pressure at the selected GOR and reservoir temperature, and gas mol fraction. None of these improved the correlation to any significant extent. It was found that at any fixed solution GOR, the relation between the gas-saturated oil viscosities and the corresponding dead oil viscosities is a straight line on logarithmic coordinates, for the range of variables investigated. This straight-line relationship was used for the correlation. Viscosity data on a total of 457 crude oil samples were used. The data were obtained with rolling ball-type viscometers. The samples came from all of the important producing areas of the U. S., as well as from Canada and South America. Their geographical distribution is shown in Table 1. The ranges of properties represented by these samples are as follows: For each crude oil sample the viscosity of the liquid phase from each step of a differential liberation was plotted against its solution GOR on semi-logarithmic paper. A smooth curve was drawn through the points and values of viscosity in centipoises were read from

By M. D. Arnold, P. B. Crawford, P. C. Hall

An experimental study has been made to determine the optimum flooding pressures for four different oils. The oil formation volume factors ranged from 1.08 to 2.13, and solution gas-oil ratios ranged from about 200 cu ft/bbl to 2,250 cu ft/bbl. Viscosities ranged from 0.38 to 0.95 cp at the respective bubble points of the fluids and from 0.7 to 20 cp at atmospheric pressure. Water floods were conducted at various pressure levels from run to run. The recovery as a function of flooding pressure was found to be different for each fluid, with optimum gas saturations ranging from 7 up to 35 per cent. The data indicate that substantially higher recoveries may be obtained if water floods are conducted at an optimum pressure and that this optimum pressure is a function of fluid properties. The same core was used for all tests, and the reproduction of saturations for various runs indicates that wettability in the predominantly water-wet core did not change. INTRODUCTION A paper was presented by Bass and Crawford' which described an experimental study of the effects of flooding pressure and rate on oil recovery by water flooding. This work was conducted using high-pressure models operated in a manner similar to that of an actual reservoir, with gas saturations being obtained by a solution-gas-drive mechanism. They found that the greatest oil recovery was obtained for the system studied by flooding in the presence of a 5 to 7 per cent gas saturation. Another experimental study simulating field conditions was presented by Richardson and Perkins.' They used an unconsolidated sand pack containing kerosene-natural gas fluid and interstitial water. They flooded at various pressures and flooding rates. For their system it was found that the recovery was independent of the pressure level at which the water flood was performed. Kyte, et al," found that oil recovery by water flooding was increased as the free gas saturation at waterflood initiation was increased. However, after the initial gas saturation was increased above 15 per cent, the increase in oil recovery tended to level off. All of their runs were made at the same pressure using a light oil saturated with helium. The desired gas saturation was obtained by injecting helium into the core. Dyes' made calculations which showed that an optimum gas saturation of 12 to 14 per cent may result in an increase in oil recovery of 7 to 12 per cent over that obtained by flooding at the bubble-point pressure. Others have also found that the presence of a free gas saturation may increase the waterflood oil recovery. In each case shrinkage was small and changes in fluid properties with respect to pressure were small. A careful review of the literature reveals that at the present time there is a wide difference of opinion on the factors affecting waterflood recoveries. This diversity of opinion is probably due to the fact that very little research has been done which has taken into account the many variables existing in an actual field being water flooded. Since the literature contains little information on high-pressure waterflooding studies using various types of reservoir fluids, it was believed appropriate that such a study should be made. EQUIPMENT AND PROCEDURE All tests were made using the same consolidated sandstone core. Torpedo sandstone was used to turn a cylindrical core 13.5-in. long and with a 2.92-in. average diameter. The core had a porosity of 28 per cent and a permeability to brine of 146 md. This brine was made up by adding 20,000-ppm sodium chloride and 30,000-ppm sodium nitrite to distilled water. This was used as connate water and flooding water. No fresh water was ever brought in contact with the core, as tests showed the sandstone contained argillaceous material which swelled in the presence of fresh water and plugged the stone. The core was sealed in a section of 6-in. N-80 tubing with Woods metal filling the annulus. The core was mounted horizontally; an injection well was placed in the center of one end and a production well in the center of the other. Pressure control was maintained by placing a back-pressure regulator (upstream control) on the producing well. The "live" oil was stored in a separate bottle and water was injected into this bottle to displace the oil for saturating the core using a two-cylinder standard-proportioning pump. This same pump was used for water flooding the core at a constant rate. This system was enclosed in water jackets and the temperature was automatically main-

By George Steintveit

Det Norske Zinkicompani A/S was established in 1924, on the initiative of the Compagnie Royale Asturienne des Mines. Experimental electrothermic zinc production was carried out on industrial scale for a two-year period, but the problems of electrothermic smelting were not solved. A license for the electrolytic zinc production process was then obtained from the Anaconda Copper Mining Co. A plant for electrolytic zinc production was built, near the small fjord town of Odda in Hardanger, West Norway, The production was based on zinc ore from Spain, and cheap local hydro-electric power. The plant came into operation in 1929. Annual capacity, 36,000 tons. In 1964 a long-term agreement was concluded with Boliden AB by which Det Norske Zinkkompani is secured the raw materials basis for an expansion of the annual capacity to 100,000 tons of zinc, Since World War II, the company has been pursuing extensive research and development programs. As a result, various sections have been rebuilt: nev unloading and storage facilities, a 250 ton per day Fluid Bed Roaster with contact plant, new continuous leaching system, integrating the Jarosite Residue Process, new solution purification section - upgrading the solution quality for a 600 Amp/m2 current density Tank Room operation -, installation of induction furnaces for cathode melting with casting machines and automatic stacking of slabs. Simultaneously, instrumentation, and methods of automatic control have been developed and introduced, providing conditions for optimal plant operations.

Jan 1, 1970

MONTANA LOCAL SECTION Executive Committee F. M. SMITH, Chairman J. L. BRUCE, Vice-Chairman . D. C. BARD, Secretary, Box 267, Butte, Mont. FREDERICK LAIST W. C. SIDERFIN The semi-annual meeting of the Montana Section was held at the Silver Bow Block, Butte, Mont., on Friday evening, Oct. 8, 1915. An informal, subscription dinner, at $1.50 a plate, was enjoyed inn' the early evening, by 62 members and guests. After dinner a technical session was held, and a paper entitled Preliminary Outline of Paper on Mines in the Boulder Batholith was presented by J. A. Grimes, who is joint author of the paper, with Paul Billingsley. The paper elicited a lively and interesting discussion, in which a score of members took part. After the reading of the paper the rest of the evening was spent socially. D. C. BARD, Secretary.

Jan 12, 1915

By Donald T. Hawkins, Ralph Hultgren

The lorsion effusion method has been used to measure the vapor pressure of lead over pure lead and eight Pb-Sn alloys ranging from 9.1 to 87.9 at. pct Pb in the temperature range 950° to 1125°K. The resulting ?H°y 298 = 46,630 ± 200 cal per g-atow for pure lead is in excellent agreement with previous work. Deriued ?Gph values for the alloys were smoothed and correlated with previous heat of formation data to obtain entropies for the liquid alloys. values for the tin component were calculated by Gibbs-Duhem integmtion. Surfhce depletion of these liquid alloys was found to be absent, as shown by the fact that the measured pressure remained substantially constant with time in contrast with previous measurements on iron-rich solid Fe-Mn alloys. The activities and Gibbs (free) energies of the liquid Pb-Sn system are not well known although the heats of formation have been accurately determined by K1eppa.l Vapor pressure determinations of the activity of lead by Voronin and Evseev2 disagree with those of Predel.3 Elliott and chipman4 measured activities by the electromotive -force technique in the ternary Pb-Sn-Cd system. From the resulting values of the activity of cadmium, they were able to calculate the activities of lead and tin for the binary Pb-Sn system at the compositions xsn = 0.33 and 0.67. Atarashiya, Uta, Shimoji, and Niwa5 determined the activity of tin from Hz-H2O equilibrium measurements, but their results are subject to question due to uncertainty in the final state of their samples. To resolve these differences, measurements of the activity of lead were made using a torsion-effusion apparatus. Among other advantages, this apparatus rapidly detects errors caused by surface depletion, which tends to reduce the apparent vapor pressure of the more volatile component. If the measured torques remain nearly constant with time, only bulk depletion is occurring. This contrasts with the rapid decrease in torque found in solid Fe-Mn alloys at high temperatures and low manganese contents.6 EXPERIMENTAL 99.999+ pct Pb was obtained from the American Smelting and Refining Co. and 99.999 pct Sn from Vulcan Detinning Co. Eight Pb-Sn alloys were prepared by melting together weighed amounts of the pure metals in evacuated Pyrex tubes and quenching the melts in water. Loss of weight in preparation was less than 0.02 pct in all cases. The effusion cells were made from high-purity, nonporous graphite. Graphite was chosen because of its resistance to reaction with lead and tin and because it can be accurately machined with precision orifices. Two cells were used with overall dimensions as shown in Fig. 1. The orifices of cells 1 and 2 were, respectively, 1 and 1.5 mm in diam.

Jan 1, 1968

By E. D. Gardner

In 1954, the first year the award was conferred, Fred Searles, Jr., remarked, "The earlier years are the easiest." In this, the second year, it was easy to choose the outstanding mining engineer. Our conferee this year has been destined to mine. He comes from pioneer stock, and though a son of the American Revolution he is most proud that all four of his grandparents came to the Jordan River Valley of Utah the "first summer," which all Utahns will recognize as 1847. At the time of discovery of high-grade ore in Bingham, his grandfather, Archibald Gardner, had a crew of men getting out saw timber in the area. The first claim staked in Bingham Canyon was named the Jordan, and Bishop Gardner was the colocator of the claim as well as the man to record it.

Jan 4, 1955

By J. S. Browning

The pegmatites of the Kings Mountain-Lincolnton, N. C., area constitute the largest known domestic reserve of beryl and spodumene. The reserve is estimated to contain 90 million tons of pegmatic material with 1,280,000 tons of recoverable Li2O (lithia) as spodumene.1 The pegmatites also contain 0.4 to 0.5 pct beryl disseminated throughout the orebodies. The pegmatites may contain a potential reserve of 240,000 tons beryl, equivalent to approximately 34,000 tons of BeO. Different flotation methods for separating beryl from feldspar or quartz, or both, have been developed by various investigators.2,3,4,5,6,7 On the other hand, published information is limited on concentration of spodumene-beryl ores. As the response of beryl and spodumene to flotation is essentially the same, a successful separation of the two minerals depends upon use of a selective depressant or a selective collector for one of the minerals.

Jan 7, 1961

By C. B. Smith, A. G. Guy

The power and convenience of tensor analysis are employed in deriving the equations that describe three-dimensional diffusion in an n-component system plus vacancies. A "Kirkendall coordinate system, '' defined in principle by Kirkendall markers, is used in defining the intrinsic diffusion coefficients that are of primary interest. The defining equations are then transformed to local cartesian coordinates and to fixed cartesian coordinates, the latter being convenient for experimental measurements. Finally, it is shown how the intrinsic diffusion coefficients can be calculated from the experimentally determined quantities. It is generally recognized that any treatment of the essential diffusion phenomena in metallic systems—the jumping of atoms from one lattice position to another—must be based on movement of the atoms past Kirkendall interfaces.' A logical extension of this idea is the proposal that, fundamentally, diffusion must be described mathematically in terms of "Kirkendall coordinates." The basic equations thus obtained may then be transformed into other coordinate systems, when such transformation leads to simplification of either the experimental or mathematical treatment of diffusion data. Tensor analysis is clearly the appropriate mathematical tool for this purpose, since it provides methods both for determining general equations that are valid for all coordinate systems and for conveniently transforming the equations from one coordinate system to another system related to the first in some known fashion. For the present purpose three coordinate systems are used, and it is convenient to begin with a description of the relations among these three systems. FICK LAW FOR KIRKENDALL COORDINATES The reference coordinate system, and the one that is useful for most experimental measurements, is a cartesian coordinate system, xi (i = 1, 2, 3), fixed with respect to some point in the specimen, such as an end of the alloy bar undergoing diffusion. A second set of coordinates, the Kirkendall coordinate system, is one that in principle can be described by the location of inert markers (Kirkendall interfaces). A convenient mathematical relation between Kirkendall coordinates, x'i, and the reference cartesian coordinates, ii, is obtained by specifying that the Kirkendall coordinate system coincide with the cartesian system at time, t = 0. After diffusion has occurred for some time, t = t, the Kirkendall coordinate system will differ from the reference system in the manner shown schematically for the one-dimensional case in Fig. 1. The third coordinate system is Darken's1 local cartesian-coordinate system, xi, which is identical with ii in orientation and units, but which moves with the point under consideration in the Kirkendall coordinate system. Even though most diffusion problems are essentially one-dimensional, there is an advantage in first carrying out the analysis of the three-dimensional problem to gain a clearer insight into the assumptions that are made in the usual one-dimen-

Jan 1, 1962

JOSEPH W. RICHARDS, Chairman. J. E. JOHNSON, JR., Vice-Chairman. ARTHUR S. CALLEN, Secretary, 453 Chestnut St., So. Bethlehem, Pa. SUB-COMMITTEES IRON ORE DWIGHT E. WOODBRIDGE, Chairman. ERNEST F. BURCHARD, WILLIAM KELLY, CHARLES F. RAND, FELIX A. VOGEL. BLAST FURNACES II. A. BRASSERT, Chairman. WILLIAM H. BLAUVELT, AMBROSE N. DIEHL, JAMES GAYLEY RICHARD V. McKAY. STEEL WORKS HENRY D. HIBBARD, Chairman. GUILLIAEM AERTSEN, C. F. W. RYS, .1. S. UNGER. FRANK D. CARNEY, A. A. STEVENSON, WILLIAM It. WALKER. MECHANICAL TREATMENT CHARLES A. BUCK, Chairman. ROBERT W. HUNT, GEORGE MESTA, FREDERICK W. WOOD.

Jan 6, 1915

Jan 1, 1930