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By Winston W. Spencer

ALTHOUGH by far the largest A consumer of platinum metals in the world, the United States until recently has been in- significant as a producer. Writing in the "Minerals Yearbook" for 1939, H. W. Davis states that 1938 probably marked the beginning of an- other period of transition in the world production of the platinum metals. In that year, he says, their production in the United States jumped to 49,380 oz., or fourth in the rank of world output. In the ten-year period 1925 to 1934 United States output ,averaged only 8300 oz. Practically all of this sudden in- crease in production is attributable to the introduction of mechanized equipment at the placer deposits in the Goodnews Bay district of Alaska. This district adjoins the Bering Sea and Kuskokwim Bay (accented on the first syllable), and is approximately 120 miles south of the mouth of the Kuskokwim River. The nearest village and post office is Platinum, which lies about eleven miles north- east of the Goodnews Bay Mining Company's camp. A good gravel road connects the mine camp and the village.

Jan 1, 1940

By Laurence Delisle, Aaron Finger

THE alloys formed by the addition of nickel to iron by convelltional metallurgical procedures show physical properties that differ widely from those of the individual metals. The effect of alloying on the mechanical properties is most pronounced in alloys containing between 15 and 25 per cent nickel. The tensile strength of an alloy containing, for example, 20 per cent nickel and 80 per cent iron (with 0.06 per cent carbon), in an annealed condition, is above 150,000 lb. per sq. in.? owing to a martensitic type of transformation, as compared with about 50,000 lb. per sq. in. for pure iron in the same condition. The object of this work was to determine whether the same beneficial alloying effect could be obtained in alloys of iron and nickel prepared by powder metallurgy technique. PROCEDURE Bars and pellets for tension and compression tests, respectively, were made. Two groups of specimens were prepared: (I) by cold-pressing the powders and sintering; (2) by cold-pressing the powders, sintering, repressing and resintering. Raw Materials Nickel powder supplied by Metals Disintegrating co., marked MD-151, was used. A typical analysis of this powder was as follows: sulphur, 0.040 per cent; copper, 0.18; iron, 0.23; manganese, 0.002; magnesium, 0.001 5 ; lead, 0.035; tin, 0.025 ; silicon, 0.08; chromium, 0.008. Electrolytic iron powder supplied by Plastic Metals Inc. was used. A representative chemical analysis for impurities other than gases, supplied by the vendor, gave the following results: carbon, 0.005 per cent; manganese, 0.002; silicon, 0.003; phosphorus, 0.001; sulphur, 0.004; nickel, 0.008. The fractions from these powders passing a 3 2 5-mesh sieve were reduced in hydrogen at 600°C. for one hour, to clean the surfaces of the particles. The reduced powders, slightly caked, were ground in a mortar and screened again through a 325- mesh sieve. Mixing The proper proportions of the powders were mixed overnight on rolls, in glass jars fitted with iron-wire baffles to break aggregates of particles that might form. Pressing All specimens were compacted on hydraulic presses. The pellets were compacted in a cylindrical die, ½ in. diameter. The ratio of thickness to the diameter of the pellets was maintained as nearly as possible at 0.9, as specifed for standard short compression pieces. The tensile bars were made by compacting 30 grams of powder. Their shape is shown in Fig. I. The compacting pressures for the pellets and the tensile bars were:

Jan 1, 1946

By Hagh H. Bein

MOST mining engineers and geologists realize the value of photographs in their professional work. Members of each group use photographs to illustrate their reports, and articles and photographs, when available, will often save many words of written text in explaining some point or in proving some pet theory. No one hesitates to take aboveground pictures but many rarely take their cameras underground. However, underground photography, too, is really simple. I do not believe that anything new is offered here and the procedures given are merely a compilation of various methods I have tried and used, with some success, over the past six or seven years. The article will deal with photographs to be taken in metal mines, but only in those where no gas hazard exists, with resultant danger of explosions and fire. Some mining company geologists consider the camera a necessary part of their equipment and carry one on their daily trips to the various parts of the mine under their observation. I know of one company whose files of geologic sketches of heading, backs. and veins are supplemented by actual photographs so that a nice geologic picture

Jan 1, 1945

I HAVE now traversed for you in the small and fragile bark of my writing all the shores of the deep and spacious sea embracing the uses of material fires, drawn on by my own desire to enrich you with more learning and with the procedures of these things, as much as to satisfy your demands. Having through the grace of God arrived at the appointed end of my voyage and neither knowing nor perceiving a way of going farther, I had decided to furl the [167] sails and cast die heavy anchors into the water in order to enjoy in tranquillity respite from my sailing, when I was warned by my pilot that before I could disembark I should turn my glance backward and reexamine my work in detail to see if there were any part that had by chance remained undescribed in the obscurity of silence. When I did this there immediately appeared in my mind's eye the many sublimates and smoky tinctures that had been made by the burning and most powerful fire of love. I need not say that I knew of it in far-off countries or from the knowledge of others, but I knew it in my own breast and as my very own and can therefore surely esteem it as hotter than all the other fires that the world calls by that name. Although today its sparks and living flames are spent because of my cold and hoary season, nevertheless it is true that the memory of acts of love of long ago still remains with some smoke and warmth. Therefore, since in this work of mine I wish to describe for you the effects and powers of fires, I should logically have spoken of this before any of the others, because of its actual nearness and the great acquaintance I had with it. But since I have had the glance of my intentions directed at distant things, I have behaved as one does who does not see where he places his feet because he is looking at the sky, or as one who thinks about the affairs of others and forgets his own. But now I do not wish to pass over this thing and I wish to correct my error, particularly in order to provide a happier ending to my written work than by remaining among the horrible uproar of guns, powder, and saltpeter, which would be a harsher ending than speaking of love. Never-

Jan 1, 1942

By D. Weinstein, F. C. Holtz

AS a possible method of improving the elevated temperature strength properties of zirconium, an investigation was initiated on the feasibility of producing a dispersion-strengthened material. Because of the high reactivity of zirconium, its high solubility for oxygen, and the stability of the Zr-0 solid solution, the major problem in such a development is choice of a suitable dispersant. Thus, in the present investigation we were concerned primarily with the stability of various dispersants in the zirconium matrix. The experimental procedure consisted of blending powders of zirconium and a dispersant, followed by cold compaction and extrusion. The best available source of -325 mesh zirconium powder contained between 1500 and 3500 ppm Oz; to this material, powders of zirconium carbide (5 p max), vanadium carbide (5 p max), alumina (0.03 p average), lan-thana (0.8 to 2 p), ceria (0.8 to 2 p), yttria (0.8 to 2 p), calcia (44 p rnax), or thoria (0.6 to 0.8 p) were added in amounts of 7 vol pct and compacted at 65 tsi. A cylindrical compact having a density between 70 and 80 pct of theoretical and dimensions of 1 in. diam by 1-114 in. high was thus produced. After canning in copper, these billets could be extruded (5: 1) on a 54-ton capacity, slow-traverse hydraulic press with the billet temperature at 1550°F and the extrusion die at 900°F. However, lack of densifica-tion of some of the extruded billets necessitated ratios of at least 23 :1. Ultimately, all billets were successfully extruded at 1500°F to 0.190 in. diam (32 :I), fully dense rods using a 200-ton capacity press and a ram speed of 90 ipm. The microstructures of as-extruded Zr-7 vol pct LazOS and Zr-7 vol pct Y2Os are shown in Fig. l(a) and (c), respectively. These structures are similar to all the as-extruded materials and consist of an elongated, single-phase zirconium matrix dispersed with oxide or carbide particles. Very little porosity is observed, and the interface between matrix and particles appears satisfactory. The size and distribution of particles, however, are not ideally of the type desired for dispersion strengthening. Since the primary study was of particle stability with respect to zirconium, no attempt was made to overcome agglomeration during powder blending and fabrication. Some areas exhibit fine, well-distributed particles; undoubtedly, a small proportion is submicroscopic and has the

Jan 1, 1963

By A. O. Dady

PRODUCERS of both bituminous and anthracite coal have for many years been worrying about the gradually decreasing consumption of their product in the United States. Twenty years ago production had climbed to a peak of 569,000,000 tons of bituminous and around 90,000,000 tons of anthracite. In 1939 it was about 393,000,000 tons of bituminous and 51,000,000 tons of anthracite. This does not mean that the country is using less polver than it did twenty years ago, or that we are living in colder buildings. As a matter of fact, about three times as much electric power is now being consumed as in 1920. In general two factors are responsible for the drop in coal consumption: (1) greater efficiency in the use of coal, and (2) increased competition from hydro power, internal-combustion engines, and substitution of oil and gas for coal in conventional furnaces. As to the first factor, it took 3 Ib. of coal to generate a kilowatt-hour of electricity in central stations in 1920 and it takes 1.4 Ib. now; it took about 175 Ib. of coal in railroad locomotives to haul 1000 long tons a mile in 1920 where it talces about 120 lb. now: and marked economies have also been made in the use of coal in steel plants: in by-product coke ovens, and in other large uses. As to the second factor, three times as much electricity is produced from water power now as was produced in 1920; three times as much oil is being consumed in various ways; and likewise, the consumption of natural gas has tripled- whereas coal consumption in the same period has dropped by 40 per cent

Jan 1, 1941

By T. S. Lundy, R. E. Pawel

Effects of short-circuiting paths on observed diffusion behavior in real crystalline systems are considered. It is concluded that experimentally measured diffusion coefficients may vary widely from values associated with true lattice diffusion to those appropriate for short-circuiting paths alone depending upon the conditions of the experiment and the sensitivity and completeness of the data. IN 1961 Harrison1 classified experimentally observed diffusion behavior in systems involving both lattice and dislocation-enhanced atomic transport into three categories. His types A and C were limiting cases where the measured diffusion coefficients using the usual serial sectioning techniques were representative of lattice diffusion (with only slight effects of dislocations) and dislocation-network diffusion (with only slight effects from lattice diffusion), respectively. In both cases A and C for a sectioning experiment in which the diffusion couple has the semi-infinite geometry and unidirectional diffusion takes place from a plane source located at the origin of the coordinate system, he pointed out that Gaussian penetration behavior should be observed. For case A the lattice coefficient should be slightly enhanced by dislocation contributions, and the model of Hart2 can be used to predict the amount of this enhancement. For case C the observed coefficient should be that for the dislocation network and have little or nothing to do with lattice diffusion. Hart's model in its general form is still applicable, but the apparent diffusion coefficient for this case is virtually independent of dislocation density. Harrison's case B is that for which non-negligible contributions exist for transport by both mechanisms and "the concentration distribution does not approximate to any simple form." With the possible exception of very low temperatures where diffusion distances approach atomic dimensions, any real diffusion specimen will in general show non-Gaussian behavior provided the data are complete enough to uncover it. Thus, a "complete" set of data for any real system cannot be expected to be totally amenable to treatment by a simple mathematical model which does not take into account the relative distribution of transport by the various modes or submodes. For a particular sensitivity of specimen analysis and at a given temperature of annealing if the concentration profile could be observed as a function of time, "the behavior will initially be type C, and will develop into type B. and ultimately type A".1 Thus, it appears that the type of diffusion behavior which is experimentally observed in a given system depends very much upon the particular experimental conditions and the particular tools available to obtain the data. Interpreted in this fashion, Harrison's classification refers not to the diffusion behavior as a whole but to the relative sensitivity of the method of examination and completeness of the data. In the present paper we will: 1) assume that the measured penetration behavior follows the same general classification as that proposed by Harrison; 2) give, for diffusion in tungsten, examples of the range of diffusion coefficients that it is possible to obtain in a single experiment; and 3) speculate that some arguments which consider the possibility of short-circuiting effects being responsible for "anomalous" diffusion in several bcc metals may have been discarded prematurely.3 Both monocrystalline and polycrystalline tungsten were used in this work. The former was obtained as triple-pass, electron-beam zone-refined 6.0-mm-diam rod from Materials Research Corp.. Orange-burg. N.Y. The latter was swaged, high-purity bar stock which was annealed for 2 hr at 2200°C and 10-9 torr to yield an average grain diameter of about 25 /i. The tracer Nb95 was received in oxalate solution from the Isotopes Division, Oak Ridge National Laboratory. Experimental procedures of specimen preparation, isothermal diffusion annealing, serial sectioning by anodizing-and-stripping, and y counting of the individual sections to determine the tracer penetration profile after a given diffusion anneal have been described elsewhere.4 However, it should be noted that the anodizing-stripping sectioning technique has the particular advantage for this research of permitting sectioning to be accomplished over a wide range of

Jan 1, 1970

By W. S. CAYPLESS, H. O. Hofman, E. E. HARRINGTON

I. INTRODUCTION. LIME-ROASTING is a term proposed by Ingalls 1 for the operation of forcing air under pressure through a mixture of galena and lime at the kindling-temperature with the object of oxidizing lead and sulphur and of fritting or fusing the charge. If, finely-divided galena were treated in this manner without the addition of lime, the heat set free by the oxidation of part of the lead and the sulphur would be sufficiently great to fuse undecomposed sulphide, and thus stop desulphurization. Besides the chemical action that the addition of lime, limestone or gypsum to the charge may have, the admixture has the physical effect that it keeps the particles of galena separated from one another and accessible to the oxidizing effect of the air. At present, three methods of lime-roasting are carried out on a working-scale, the Huntington-Heberlein, the Carmichael-Bradford and the Savelsberg2 processes. In the last, which interests us here, an 8-ton charge is made up of galena, limestone and perhaps some siliceous or ferruginous flux; the whole is crushed to pass a screen with 3-mm. holes and moistened with 5 per cent of water. It is fed gradually into a bowl-shaped converter, 6.56 ft. in diameter, supported by trunnions attached to a truck. On the .bottom the converter has a grate with blast-inlet beneath. In starting, the truck with the converter

Jan 1, 1907

Jan 1, 1955

By W. W. Duecker

SULPHUR is a peculiar combination of a nuisance and a useful element. Most of the nonferrous metallic ores contain large amounts of it in the form of sulphides, which the metallurgist has wasted up the chimney, since the sulphur dioxide formed is generally too dilute to make recovery economical and practical. Iron ore does not contain much of the unwanted sulphur; in pig iron and coke it is most unwelcome. Gold metallurgists can get along nicely without sulphides in their cyanide plants and yet they find matte-a sulphur compound -an excellent collector for gold and silver in base-metal smelting. Also, sulphur appears in the non-metallics as in barite, gypsum, Glauber's salt, and celestite, all to useful purpose.

Jan 1, 1938

By A. A. Brant

Mining men, quite as exploration minded as petroleum interests, are in the position where most of the exposed crustal portions of the earth have been examined, where the demand for metals is high and likely to continue so, and yet where, perhaps, the tools fail for the economic exploration of many of the possible mineral areas more deeply covered with drift, alluvium, and later formations. At the same time the incentive exists to create acceptable substitutes for many of the duties of metal. The problem of the economic exploration of possible mineral-bearing areas is hence a vital one. In oil exploration, the absence of surface or shallow occurrences and the high cost of test drilling has led to the intensive study of geophysical techniques. Hence the development of the seismic method with its high certainty factor and its adaptability to standardized procedure.

Jan 1, 1949

By C. R. Kuzell

GEOGRAPHICAILY the industry of reducing and refining of copper continued to migrate from the .United States during 1931. While this country is losing the predominant position of its copper industry, our engineers still enjoy their pre-eminent position as leaders in the design and operation of the new plants being brought into production in the four quarters of the globe. Progress in the art, as indicated by the construction of the recently completed works, has not been revolutionary. Standard methods have been followed, augmented by novel features in flow-sheets demanded by the results of progress in the art of ore-dressing, and by reason of problems incidental to the peculiarities of the new ores being treated. Design and construction progress has likewise been orderly and without radical departure from less recent practice; new features in primary and secondary equipment being logical developments to provide for special conditions to keep abreast of improve¬ments in accessory apparatus. The new plants are being rapidly brought in without hazardous novelties and for the purpose of yielding the principal ingredient, copper, in as large a volume as it will he possible to market; the old United States procedure. In the meantime the domestic plants are shut down or operating at a very low capacity, threatened with untimely demise unless the metallurgist can extract and develop other valuable products from the ores. International agreements .and tariff protection may be a temporary reviving stimulant, but for many mines the days of profit will be numbered unless the ores can be made to yield as values the ingredients now being discarded. Invisible progress in this direction has been made during the past year, and it is to he hoped that time will prove that the outstanding progress of 1931 was in the development of processes for the ultimate recovery of by-products from copper ores, perhaps even relegating the value of the copper yield to secondary importance.

Jan 1, 1932

By D. B. RUSHJIORE

(New York -Meeting, February, 1912.) TORCHES were used by the early Romans for mine-lighting, and these were followed by open lamps or earthen jars filled with tallow or oil, and later by candles. In early coal-mining, explosive gases seldom occurred, and, if they were encountered, the danger of explosion was materially diminished by the absence of any ventilating-system and the consequent insufficient circulation of air to form with the methane an explosive mixture. As the art advanced, the danger of fire-damp became more apparent, and methods for testing the air were resorted to as early as in the fifteenth century. The method of testing consisted in lowering a clog in a, basket down the shaft. As soon as he encountered fire-damp he would commence to howl, after which he was withdrawn, and a leafy bush was fastened to the end of the rope and run rapidly up and clown the shaft. This so disturbed the accumulation of gas as to cause it to rise out of the shaft. Later this odd method of testing was improved upon through the discovery that a light inserted in a body of fire-dam p would produce a blue flame. Candles were used for this purpose, and, when fire-damp was thus discovered, brushing or some other primitive method of fanning was resorted to for driving out the gas. In some instances the gas was burned away, regardless of the danger thereby incurred. A man, wearing a well-moistened coat and a mask with glass spectacles, descended in the mine a few hours before each shift. With a long stick, to which was fastened a burning torch or candle, lie would crawl on the floor with the stick so raised that the light would sweep the roof and ignite the gas which it encountered. In this position the flame of the explosion would pass over him, after which he would retreat from the gases resulting from the combustion. The occurrence of serious accidents resulted in

Jul 1, 1912

THE annual meeting of the Lake Superior Mining Institute was held on Sept. 7 and 8, Crystal Falls and Iron Mountain, Mich., being the principal centers of activity. Members of both institutes began assembling early, and by the evening of Sept. 6, some 60 had already arrived at Crystal Falls. The greater number arrived the following morning, however, and after the usual formalities of registration were attended to, the party were loaded into automobiles and set out on a tour of inspection of the mines near Iron River; some properties were passed through, and some were briefly visited to permit the inspection of any unusually interesting piece of equipment or detail of practice. The last stop of the morning was at the Caspian, Iron River, where the entire party was entertained at luncheon at the Caspian Club House. Both the food and the company were excellent, and as the weather was superlatively good (though the natives of the district modestly declared it was only ordinary autumn weather) the lunch was served on the lawn at the rear of the club, where the green turf, abundant flowers, and music by the band, added to the charm of good fellowship. The degree to which mining men have become addicted to golf was indicated by the large number of plus fours in evidence, whose wearers appeared just before lunch and disappeared immediately afterward.

Jan 1, 1928

Jan 1, 1985

By Paul M. Tyler

DOES mining pay? Inasmuch as the whining of minerals from Nature is one of the world's principal sources of new wealth, this question is of general economic interest but it is obviously of even more vital concern to investors and those engaged in mining. In a previous article on "Wage Costs in the Mineral Industries,' published in the November issue, I attempted to show that wages paid workers on the job accounted for, roughly, 50 per cent of the mine dollar. Salaries normally range over 5 per cent - lower for large metal mines but higher in stone quarries and minor nonmetallic min. in, industries. Purchases of supplies, materials. fuel, and power generally aggregate within the range of 15 to 25 per cent of total receipts, with the average well under 20 per cent. The total of all such specified expenditures which may he loosely described as

Jan 1, 1934

By Sallie McCabe Johnson

LIFE IN RUSSIA for the foreign woman is hard. It is up to her whether her days are spent in tearful longing for ironic or whether she :hakes the real effort to ferret out the interesting or amusing side of such exasperating conditions as ooh a Russian can conjure. So to begin Discard all promises.. This is perhaps the most difficult thins- to learn but promises in Russia are nut what they are at home. There are many reasons for ibis, sonic good and some bad but whatever the reason. the fact remains that they are usually worthless- as each of us must slowly learn In, disappointment after disappointment. Also we must learn that we cannot expect to get or to do a certain thing just because someone else has done so. What we did yesterday perhaps cannot be dune today. What we purchased air hour ago, oxen ten minutes ago- we cannot purchase now. What our neighbor did this morning we cannot do this afternoon. Changes arc continuous. Every person's experience is different from that of another aid this in a great measure accounts for the conflicting stories brought horns. In a land of chaos we live only from hour to hour and this is one of the exceedingly exasperating conditions to face. When I wished to visit Leningrad, an overnight nip from Moscow, more than a week's lime w as required to obtain a ticket, vi en through the efficiency of lntourist: alone I might have spent a month at it. Each day

Jan 1, 1932

By AIME AIME

General Local Committee.-John Fritz, Chairman; A. B. de Saulles, Vice-Chairman.; R. M. Bird, Treasurer; Henry S. Drinker, Secretary; Robert H. Sayre, E. P. Wilbur, Charles M. Dodson, Abraham S. Schropp, E. M. McIlvain Archibald Johnston, A. B. Fichter, C. G. Convers, W. A. Wilbur, Garrett B. Linderman, Frederick Conlin, George Pettiuos, Albert Brodhead, Garrett L. Hoppes, M.B. Cutter, H. J. Seaman, C. A. Matcham, B. F. Fackenthal, Jr., A. L. J. Queneau, Geo. R. Elder, Eldridge Wilbur, William H. Chandler, Mansfield Merriman, Joseph F. Klein, William S. Franklin, William Esty, Joseph AN'. Richards, Howard Eckfeldt, John D. Irving. Transportation Committee.-H. J. Seaman, C. A. Matcham, B. F. Fackenthal, Jr., A. B. Fichter, A. L. J. Queneau, Henry S. Drinker. Hotel Committee. -Garrett B. Linderman, Charles M. Dodson, W. A. Wilbur, Garrett L. Hoppes, Albert Brodhead. Steering Committee.-William S. Franklin, William Esty, John D. Irving, R. M. Bird, the members of the Tau Beta Pi Society of Lehigh University. Committee on Meetings - William S. Drinker, Joseph W. Richards, Howard Eckfeldt. Entertainmment Committee.-W. A. Wilbur, E. M. McIlvain, Archibald Johnston, A. B. de Saulles, G. G. Convers,.A. L. J. Queneau, Garrett B. Linderman, Frederick Conlin, George Pettinos, Garrett L. Hoppes, Henry S. Drinker, William S. Franklin, Eldridge Wilbur, Robert M. Bird, Secretary. The opening session was held at 8.30 p.m., Wednesday, February 21, 1906, in Gymnasium Hall of Lehigh University, which had been tastefully decorated with flags and bunting. Dr. Henry S. Drinker, President of Lehigh University, and Secretary of the General Local Committee, called the meeting to order, and welcomed the Institute to the Bethlehems, where its first meeting, after its organization in May, 1871, at Wilkes-Barre, was held in August, 1871.*

May 1, 1906

By J. B. Dilworth

OUTCROPS of coal have bees discovered is many localities is the Philippine archipelago, and practically all of the larger islands contain deposits of this mineral. Very little prospecting has been done to determine the value of the various coal-bearing areas, but so far as known, the largest and most promising fields are found : (1) is northern Cebu; (2) is the small island of Batan, a part of the province of Albay is southeasten Luzon; (3) is the somewhat larger island of Polillo, off the east coast of Luzon, and (4) is southern Mindoro, sear the small coast tows of Bulalacao. Northern Panay, south-central Cebu, and various localities is southern Luzon, Masbate, Negros, and Mindanao also afford evidences of the existence of coal-beds, the extent and value of which have not yet bees proved. The general position of these islands and districts is shows on the map of a portion of the Philippine Islands, Fig. 1. Some of these coal-fields have been known for many years (coal was discovered is Cebu 1827 and is Batas is 1842),1 and several futile attempts were made by the Spaniards to operate mines is these districts. But owing to many circumstances, chief among which were indifferent management, the political unrest of the islands, natural difficulties of transportation, and those inherent in the mining of steeply-inclined and somewhat irregular seams, no considerable output was ever obtained from any of these mines, and the fuel required is the many departments of industrial and political life has continued to be drawn largely from Australia and Japan. These conditions exist to a great degree at present, and though much interest is the coal-deposits of the Philippines

Jan 1, 1909

By A. G. Guy

Thermodynamic activity rather than chemical composition is basic to the analysis of diffusion. This is the essential conclusion reached by Darken1-3 and by Birchenall and Mehl.4 If so, it is reasonable to expect that diffusion calculations should be carried out using activities. This paper will illustrate a method of employing activities in analyzing interstitial diffusion. For interstitial diffusion (of carbon in iron and probably generally) the diffusion of the solvent atoms, volume changes, and other such complexities not explicitly provided for in the usual diffusion equations cause a negligible error of the order of 1 pct. Therefore it is relatively easy to test the validity of an analysis based on activities in the instance of interstitial diffusion. The mathematical treatment of the more complex substitutional diffusion could be simplified once the adequacy of the activity method had been established for substitutional diffusion. Thus the present work has the purpose not only of providing a superior analysis of interstitial diffusion but also of indicating a possible approach to the more important question of an adequate treatment of substitutional diffusion. Development of the Diffusion Equation Although activities are convenient quantities to determine experimentally, they are derived from the more fundamental fugacities.9 Possible confusion in using activities can be avoided by basing equations involving their use on the relationship, dP = -D1d/ax dt [I] where, dP = the number of grams of solute crossing one cm2 in the time dt sec. D, = the diffusion constant for use with fugacities; it is assumed to be constant at a given temperature, and has units of secs. f = the fugacity of the solute in the solid solution; the units are those of pressure, dynes per cm2. x = the distance in cm. Eq 1 can be considered to be the basic form of the first Fick Law for one-dimensional diffusion. In order to convert Eq 1 into an equation involving activities, a choice of a standard or reference fugacity, f°, must be made: then. a = f [2] where a is the activity corresponding to the fugacity f. However, the value of a is also determined by the relation, a = a\c [3] where a is the activity coefficient and c is the concentration. For a given value of a (such as a = 1) it is evident that the units used for expressing concentration will affect the numerical value of a corresponding to a given amount of carbon dissolved in y-iron. Since weight per cent concentration is so widely used, this unit will be adopted as the standard in this paper. When the value off given by Eq 2 is substituted in Eq 1, the first Fick Law becomes, dP= -D,f°dl [4] Since D,f° is constant (at a given temperature), the second form of Fick's Law can be obtained in the usual manner, -dt D'f° dx [5] where c' is the concentration in g per cm3. In terms of weight per cent concentration, c, Eq 5 becomes, dc _ 100 d2a Tt = T /f w [6] where p is the density of the solid solution and will be assumed to be constant. In order to simplify Eq6, it is necessary to consider the standard state, f°. Standard states are chosen for convenience. There appears to be one especially convenient choice for the analysis of interstitial diffusion. If the activity coefficient, a, is set equal to unity at infinite dilution of the solute, 100 then — 100D1fl° is approximately equal P to the usual diffusion constant in dilute solutions. This is true since the activity, a, in Eq 6 can be replaced by the concentration, c, with little error in an infinitely dilute solution.* Here f1° is the standard fugacity necessary to achieve this standard state. It is proposed that a diffusion constant Da' be defined, Da1=100/pD1f1° [7] where A is the metal whose diffusion is * The second derivative of a is equal to the second derivative of c in dilute solution only if -da/dr- is. zero. Although theory does not require this condition, in the systems C in Fe, and Zn in Cu, dc is in fact found to be essentially zero.

Jan 1, 1950