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[ PRESIDENTS DAVID THOMAS 1871 'R. W. RAYMOND 1872-1874 'A L. HOLLEY 1875 'ABRAM S. HEWITT 1876 'T. STERRY HUNT 1877 'ECKLEY B. COXE 1878-1879 'WILLIAM P. SHINNY 1880 'WILLIAM METCALF 1881 'RICHARD P. ROTHWELL 1882 'ROBERT W. HUNT 1883 'JAMES C. BAYLES 1884-1885 ROBERT H. RICHARDS 1886 'THOMAS EGLESTON 1887 'WILLIAM B. POTTER 1888 'RICHARD PEARCE 1889 'ABRAM S. HEWITT 1890 'JOHN BIRKINBINE 1891-1892 'H. M. Hows 1893 'JOHN FRITZ 1894 'J. D. WEEKS 1895 'E. G. SPILSBURY 1896 'THOMAS M. DROWN 1897 'CHARLES KIRCHHOFF 1898 'JAMES DOUGLAS 1899-1900 'E. E. OLCOTT 1901-1902 'ALBERT R. LEDOUX 1903 'JAMES GAYLEY 1904-1905 'ROBERT W. HUNT 1906 'JOHN HAYS HAMMOND 1907-1908 'D. W. BRUNTON 1909-1910 'CHARLES KIRCHHOFF 1911]

Jan 1, 1940

By Philip Lindstrom

T he Radon mine is in the north end of the Big Indian mining district in San Juan County, Utah. Hecla Mining Co. operated the mine from early 1955 to early 1964 through an operating agreement with Federal Resources, Inc. Development consisted of a 3-compartment, 690-ft shaft, 4 main levels driven on the ore horizon and a haulage level below the ore. Evaluation of physical and economic factors showed that this flat-dipping ore occurrence could be mined by a low-cost coal mining method. The value of the deposit was high and unusual pre¬miums were possible by clean mining. Complete extraction without loss of ore pillars, minimum ore dilution and high production per man were obtained by longwall mining.

Jan 12, 1964

By James W. Neill

Bituminous coal has for many years been used for the smelting of iron-ores in the blast-furnace. In some districts in Scotland it is used alone, in others it is used mixed with coke. The similar use of certain bituminous coals in the United States has been repeatedly mentioned in the Transactions. (See, for instance, as to the Hocking Valley coal, the papers of Dr. T. Sterry Hunt, Trans., ii., 275, and vii., 313; and as to Indiana "block-coal," the paper of Mr. J. S. Alexander, Trans., i., 225.) Phillips (Elements of Metallurgy, p. 250) says: " Raw coal for blast-furnace use must be of a non-cokiog kind, and, when of suitable quality, is perhaps the most advantageous fuel." In the first

Jan 1, 1892

By A. Patton

E. T. McCLEARY, Youngstown, Ohio (written discussion).-Perhaps there is no question before the steel manufacturers of America today that causes them more worry than that of maximum production, together with good quality, and Messrs. Patton and Speller have clearly shown in their excellent paper how this may be accomplished. Any operation that tends to uniformity is certainly conducive to good practice, and as the use of roll scale in the converter eliminates to a large extent the variations in temperature due to varying silicon content in the pig iron, it should certainly give a more uniform product. At the plant of The Youngstown Sheet & Tube Co. the use of roll scale was started in the year 1908. A great many tests have been con-

Jan 4, 1917

By Frank C. Greene

Drilling in Missouri in 1943 continued at a lower rate than in 1942, only 28 wells being completed. Following the completion of the Cities Service Oil Company's No. I Jim Cook near Tarkio, in the northwest corner, NW. 'fi sec. 32, T. 65 N., R. 39, W., Atchison County, four dry holes were drilled by other parties, all a mile or more from the Cook well. Later the Cities Service Oil Co, completed No. 2 Cook for 60 bbl. Table I gives a summary of activities by counties. The total footage drilled was 23,83134 ft., of which 12,802 1/2 ft. was by cable tools and 11,029 by rotary. Four of the dry holes were drilled into Mississippian or older beds.

Jan 1, 1944

By Frank C. Greene

Drilling in Missouri in 1943 continued at a lower rate than in 1942, only 28 wells being completed. Following the completion of the Cities Service Oil Company's No. I Jim Cook near Tarkio, in the northwest corner, NW. 'fi sec. 32, T. 65 N., R. 39, W., Atchison County, four dry holes were drilled by other parties, all a mile or more from the Cook well. Later the Cities Service Oil Co, completed No. 2 Cook for 60 bbl. Table I gives a summary of activities by counties. The total footage drilled was 23,83134 ft., of which 12,802 1/2 ft. was by cable tools and 11,029 by rotary. Four of the dry holes were drilled into Mississippian or older beds.

Jan 1, 1944

1944 WALTER HULL ALDRIDGE New York, N Y 1946 PETER M ANDERSON Johannesburg, South Africa 1946 CHARLES CAMSELL Ottawa, Ont, Canada 1946 CHARLES AUGUSTUS CARLOW Fife, Scotland 1946 CECIL H DESCH London, England 1946 WILLIAM FRASER London, England 1917 HERBERT HOOVER New York, N Y 1941 DANIEL COWAN JACKLING San Francisco, Calif 1939 HENRY KRUMB New York, N Y 1942 ESSINGTON LEWIS - Melbourne, Vic , Australia 1921 C MCDERMID London, England 1944 WALTER C MENDENHALL Washington, D C 1942 PAUL DYER MERICA New York, N Y 1913 EZEQUIEL ORDONEZ Mexico City, Mexico 1938 A M PORTEVIN Paris, France 1937 GEORGE S RICE Washington, D C 1934 T A RICKARD Victoria, B C, Canada 1946 JOHN R SUMAN Houston, Texas 1946 WONG WEN-HAO Chungking, China

Jan 1, 1952

1944. Walter Hull Aldridge New York, N. Y. 1946. Peter M Anderson Johannesburg, South Africa 1946. Charles Camsell Ottawa, Ont. Canada 1946. Charles Augustus Carlow Fife, Scotland 1949. Erie Victor Daveler New York, N. Y 1946. Cecil H. Desch London, England 1946. William Fraser London, England 1917. Herbert Hoover New York, N. Y. 1941. Daniel Cowan Jackling San Francisco, Calif. 1939. Henry Krumb New York, N. Y. 1942. Essington Lewis Melbourne, Vic., Australia 1921. C. McDermid London, England 1944. Walter C. Mendenhall Washington, D. C. 1942. Paul Dyer Merica New York, N. Y. 1938. A. M. Portevin Paris, France 1934. T. A. Rickard Victoria, B.C., Canada 1946. John R. Suman Houston, Texas 1946. Wen-Hao Wong Chungking, China

Jan 1, 1952

In opening the meeting I wish to express my greatest pleasure at being able to greet this joint session of the Mining and Electrical Engineers. As engineering develops, we find that the border lines between the different branches of engineering become more and more indistinct; the several fields overlap so much that they are three or four layers deep in places. It is only an accident that we couldn't have had the Mechanical Engineers also as a formal part of this gathering, because they are quite as much interested in this subject as the Electrical or Mining Engineers. A little history may enlighten some of those who have not been close to this work. A year ago last summer, there was brought to the attention

Jan 4, 1919

1944 WALTER HULL ALDRIDGE New York, N Y 1946 PETER M ANDERSON Johannesburg, South Africa 1946 CHARLES CAMSELL Ottawa, Ont, Canada 1946 CHARLES AUGUSTUS CARLOW Fife, Scotland 1949 ERLE V DAVELER New York, N. Y 1951 EVERETTE LEE DEGOLYER Dallas, Texas 1946 CECIL H DESCH London, England 1946 WILLIAM FRASER London, England 1917 HERBERT HOOVER New York, N. Y 1941 DANIEL COWAN JACKLING San Francisco, Calif. 1950 ZAY JEFFRIES Pittsfield, Mass 1939 HENRY KRUMB New York, N Y 1942 ESSINGTON LEWIS Melbourne, Vic, Australia 1944 WALTER C. MENDENHALL Washington, D. C 1942 PAUL DYER MERICA New York, N Y 1938 A M PORTEVIN Paris, France 1934 T A RICKARD Victoria, B C, Canada 1946 JOHN R SUMAN Houston, Texas 1946 WONG WEN-HAO Chungking, China

Jan 1, 1952

By John V. Beall

There were no easily identifiable tourists. Everybody carried attaché cases and sported the buttoned-down look in dress. They were all there at the Hotel Indonesia to make a deal. But deals don't come quickly over there and those that staved and persevered became bored. They clung to the air conditioning of the Hotel and sought hobbies to while away the weeks-and even months. It is not an easy life but it can pay off fog sonic company. The government officials are neither stupid nor lazy. They are new at their jobs. Many are ex-army men and they know they must learn before they can enter into a contract with confidence. So they take time, and time is on their side.

Jan 1, 1970

(There are 67 Student Chapters in the United States, 2 in Canada ) University of Alabama-University, Alabama, Mining & Metallurgical Society, James W Stewart University of Alaska-College, Alaska, Mining Society of the University of Alaska, Guinn Metzger University of Arizona-Tucson, Arizona, Miners' Society, A E Gorum Birmingham-Southern College-Birmingham, Alabama, Pick & Hammer Club, Daniel D Arden University of British Columbia-Vancouver, British Columbia, G M Dawson Club, A Gunning University of California-Berkeley, California, Mineral Technology Association, Bernard York Carnegie Institute of Technology-Pittsburgh, Pennsylvania, The Metals Club, Gerhard Derge Case Institute of Technology-Cleveland, Ohio, Pick and Shovel Club, Gerald M Cover City College of New York-New York, New York, CCNY Student Chapter AIME, Daniel T O'Connell

Jan 1, 1954

By R. A. Wolfe, H. W. Paxton

Self-diffilsion coefficients for cr51 and Fe55 in 12 pct Cr-Fe and 17 pct Cr-Fe for Fe55 in chromium, and for Cr51 in vanadium have been measured. The results are compared with other values for the Fe-Cr system, and with the various theories of diffusion in hcc metals. Some empirical correlations are discussed between Do and Q in hcc systems, or, expressed differently, the constancy of ?G*/T solidus for seveval bcc metals and alloys is noted. It appears very probable that a vacancy mechanism is operative in bcc metals, hut this cannot he stated with certainty. THE great bulk of work on diffusion in metals, both experimental and theoretical, was for many years concentrated on those with close-packed and, in particular, fcc lattices.1,2 There appears to be little doubt that the mechanism of diffusion in these solids is vacancy migration, leading to mass transfer and in substitutional solid solutions to a Kirken-dall effect.3,4 For bcc metals, the picture is much less clear. The Kirkendall effect certainly occurs in several alloys.5-10 However, attempts to understand the factors contributing to the pre-exponential in the usual expression for the diffusion coefficient D =D, exp {-Q/RT) by extension of ideas useful in close-packed lattices have not always been successful. Zener,11 Leclaire,12 and Pound, Paxton, and Bitlerl3 have suggested that various forms of ring diffusion may be important in some bcc metals. For close-packed metals, Do is usually about 1 sq cm per sec and Q - 35Tm kcal per mole (Tm = melting temperature in OK). The theory of Pound et al. suggests for ring diffusion that Do may be about 10-4 and Q, although difficult to calculate with any precision, would be significantly less than 35 T,. The experimental results on self and solute diffusion in ? uranium14,15 and ß zirconium,10 and for solutes in 0 titanium,17 and possibly for self-diffu- sion in chromium below about 0.75 T,," gave some credence to this theory. However, not all bcc materials display low values of DO and Q, and the exceptions were not predicted by any theory. Furthermore, it has recently become apparent that, in bcc materials, log D is not always linear with T-l if a sufficiently wide range of temperature is studied.16,18 This variation may be such that Q may increase18,19 or decrease20 with increasing temperature. The present work was undertaken in an attempt to provide further diffusion data on bcc metals, and to try to understand the factors which contribute to differences in behavior between the various elements. For part of this work, the Fe-Cr system was chosen since it is of considerable technological importance, and data on 12 pct Cr and 17 pct Cr alloys appeared well worthwhile to supplement that existing for the remainder of the stern.18,22 The diffusion of Fe55 in chromium was studied as an example of a more or less "normal" tracer element in a possibly abnormal host lattice. Finally, no data were available for vanadium, the neighbor of chromium in the periodic table, because of lack of a suitable isotope so cr55 was used as a tracer in a few preliminary experiments. For convenience, we shall refer to elements whose Do and Q are low compared to those predicted by Zener's theory as "anomalous". PROCEDURE This investigation determined self-diffusion rates by means of radioactive tracers and the integral-activity method first utilized by Gruzin.23 In this method a thin layer of radioisotope of the diffusing element is plated or coated onto a planar surface of the diffusion sample, which is then given an isothermal-diffusion annealing treatment. The determination of an activity-penetration curve involves measuring the residual activity of the specimen after each successive layer or section has been removed parallel to the original planar surface. The method used here is essentially the same as that used by Gondolf18 and Kunitake.21 Two radioactive tracers, cr51 and Fe55, were used in this investigation. Diffusion coefficients were determined for the diffusion of one or both of these tracers in four different materials, viz., Fe-12 wt pct Cr alloy, Fe-17 wt pct Cr alloy, chromium, and vanadium. The diffusion samples had nominal dimensions of 1.5 cm diameter and 0.5 cm thickness. The grain size was several millimeters for the Fe-Cr alloys and at least 1 mm for the chromium and vanadium samples. Accurately planar surfaces

Jan 1, 1964

By K. Huessener

INTRODUCTION THIS paper attempts a survey of the principles involved in the com¬bustion of blast-furnace gas in boilers and stoves. I do not expect to be able to give much information which is actually new, since the laws and methods of calculation pertaining to this problem are contained in a number of handbooks; but, so far as I am aware, they have nowhere been treated exclusively with reference to this one problem of gas economy. The road which I follow is less that of strictly scientific research than that of the practical engineer, faced by operation problems which require a. quick solution by easily accessible means without a prolonged search in scientific handbooks. For this purpose I give a number of tables and diagrams, as well as the results of many years' practical working experience as combustion engineer, which I trust will prove useful to my readers. HISTORICAL Considering the tremendous efforts made during the last 15 years to increase the efficiency of all kinds of power plants, it is highly surprising that until a comparatively very recent period, progress in the economical combustion of blast-furnace gas has been so slow. The explanation generally put forth, that fuel has been so cheap that it was hardly worth while to bother about this economy, will not hold good, for the greatest trouble was taken to improve the combustion of coal and to reduce the consumption of steam. The most plausible explanation appears to be the general impression, held as an accepted fact, that gas, especially hot, uncleaned, blast-furnace gas, was not a good boiler fuel. Many managers of high repute had tried unsuccessfully to improve the conditions of its use, and the dictum went forth that efficiencies of over 60 per cent., particularly with high loads, were impossible. This was the situation not only in the United States, with very cheap fuel, but also in Europe, where fuel prices are twice and three times as high.

Jan 2, 1916

By Thomas Fraser, David R. Mitchell

THE primary purpose of the loading plant is to transfer the finished product from the preparation machines to the railroad car, truck, or barge in which it is to go to market. Secondary purposes of the loading plant are: to prevent excessive degradation of sizes during loading, to reduce segregation as much as possible, and to prevent excessive quantities of very good or off-grade coal from entering any one car. Nonuniformity of consignments is one of the chief sources of com- plaints by consumers and coal merchants. A properly designed loading plant will do much to reduce complaints and ensure uniformity, not only from shipment to shipment but also in each individual consignment along the length of the car and in cross section. DEGRADATION IN STORAGE, LOADING AND SHIPMENT The object in loading is not only to handle the coal without breakage and segregation, but also to produce a well-trimmed load that will ride to its destination without spillage or breakage en route. The small sizes present in a car of prepared coal as received by the purchaser consist of: missed small sizes not screened out in the preparation plant, breakage during loading, and breakage caused by handling en route. For domestic sizes of anthracite shipped from the Pennsylvania anthracite field to Atlantic coast cities, the dealers' loss because of break- age in loading and shipment amounts to from 2 to 5 per cent and for anthracite shipped to Middle West cities, the loss is 8 to 9 per cent. This difference is in part because dealers in the Middle West rescreen their coal more thoroughly than is usual in the East. One dealer handling Illinois No. 6 coal shipped from southern Illinois mines to Chicago reports an average size loss of 10 per cent when lump coal is unloaded with a fork. This runs as low as 5 per cent for carefully loaded coal and as high as 15 per cent for carelessly loaded coal.

Jan 1, 1943

By Gerhard Bockstiegel

Kuczynski's formula has been derived for the case of nonspherical particles. TWO formulae of Kuczynski's type have been derived, one describing the increase in tensile strength, the other describing the progress of shrinkage of a powder compact. It has been strength,shown that the exponents of all three formulae each contain two magnitudes of different physical characters, viz, the geometrical factor a and the kinetic factor ß. The interrelationships between the three exponents are stated. SOME years ago Kuczynski1 experimentally showed that the radius, x, of the area of contact between very small spherical metal particles and a metallic block is related to the time of sintering, t, by the following equation x = constant tk [11 where k has the value 1/5 or 1/7. Assuming that the metal particles were perfect spheres and the metallic block was perfectly flat, he derived the foregoing equation from theoretical considerations of the process of material transport in metals, and he showed that exponent k is different for different mechanisms of transport, e.g., k = 1/2 for viscous flow (according to Frenkel2), k = 1/3 for evaporation and condensation, k = 1/5 for volume diffusion, and k = 1/7 for surface diffusion. From this Kuczynski concluded that the mechanism of transport was either volume diffusion or surface diffusion, depending on whether the value of k, as found in his experiments, was 1/5 or 1/7. Subsequently. Cabrera8 corrected Kuczynski's calculations with regard to surface diffusion, showing that the theoretical value of exponent k is 1/5 for both volume and surface diffusion. He supposed that the different experimental values of k were due to slight differences in the shape of the metal particles. An exponential relationship similar to the aforementioned was found by Okamura, Masuda, and Kikuta,4 Masuda and Kikuta, and Takasaki8 when studying the rate of shrinkage on powder compacts during sintering. The authors measured the shrinkage by means of the fraction w = Vp — V./Vp — V,,,, where V,, is the volume of the green compact, V, is the volume of the sintered compact, and V,,, is the volume of the compact in its densest state. This fraction, w, they found, is related to the time of sintering, t, by the equation w == constant tm. [21 Further, Bockstiegel, Masing, and Zapf7 observed that the tensile strength, s, of sintering iron powder compacts can also be related to the time of sintering, t, by an equation of the foregoing type, i.e., s = constant tn. [3] For exponent n the values 0.28 (S=2/7) and 0.35 ( 2/5) were obtained, and the authors pointed out that there might exist a simple interrelation between exponent n as found in their experiments and exponent k in Kuczynski's equation. The authors supposed that 2k = n, since the strength of adhesion between a metal sphere and a block (as in Kuczyn-ski's experiments) must approximately be proportional to their contact area, p. x2. Theoretical Considerations This paper is an attempt to correlate the fundamental experiments of Kuczynski's type with the results obtained with powder compacts as represented by Egs. 2 and 3. In particular, the paper is to show how the rate of sintering is influenced by the geometry of the sintering particles and by the type of material transport. As the geometry of particles conglomerating in a powder compact is very complex, some simplifying assumption has to be made, of course, in order to adapt the problem to mathematical treatment. In the following paragraph a suitable simplification is introduced, and Kuczynski's formula is derived for the case of nonsphcrical particles. Relation Between Area of Contact and Sintering Time—As the face of contact between two particles in a sintering powder compact is not necessarily a circle (as in the case of spheres sintering to a block), Kuczynski's formula is modified as follows: Let the perimeter of the face of contact be described by means of polar coordinates R, 4, as shown in Fig. la, so the area of contact, f, is determined by f= 1/2 . S112p[R(Æ) ]2 dÆ [4] Then, let the two particles be intersected by a plane perpendicular to area f. The intersection is shown in Fig. lb. According to the nomenclature in this figure, the distance, h, between the surfaces of the two particles is a function of T and Æ: h = h(r,Æ). For the particular case of spherical particles, as in Kuczynski's theory, this function becomes: h = constant r2. It shall be assumed here that in the close neighborhood of their

Jan 1, 1957

By Jei Y. Choi, P. G. Shewmon

The surfrrce-diffusion coefficients (DJ for Aulg8 on (100) and (111) surfaces of copper have been determined between 1050" and 780°C using a new avuzlysis imd experimental procedure. The results are: D, has also been determined fm cua4 at 870°C, and the values found are 4.5 times larger than those measured by the grain boundary grooving technique for the same surface orientations. This difference is felt to result from the approximate nature of the mathematical solution used in the present work. Attempts to measure D, for silver on copper and silver surfaces indicated a means of matter transport different from surface diffision was dominant in moving tracer from the source out over the surface. Cnlculations and experiment both indicate that this is the flow of silver through the vapor phase which completely masks the much smaller flow due to surface diffusion. The previous self-difhsion studies of D, for silver and copper are discussed in terms of our own analysis and found to yield values of D, factors of lo5 or more greater than those found by the grain boundary grooving tech -nique. UNTIL about 5 years ago it was widely believed that the activation energy for surface diffusion, AH, , was less than that for grain boundary diffusion, AHb,, which in turn was less than that for diffusion through the lattice, AHz.' This was concluded from various evidence that D,> Db>Dl, and one tracer study of D, for silver on silver from which AH, was inferred.2 In 1959 Mullins and Shewmon demonstrated that D, could be determined from the kinetics of the growth of grain-boundary grooves.3 Using this procedure, Gjostein measured D, on copper between 800" and 1050°C and found that the activation energy was roughly equal to AHl .4 Subsequent work on copper,5" silver,',' and goldg between the melting temperature T, and 0.87 T, confirmed that AH, as determined using the grain boundary grooving or scratch-relaxation technique was equal to or greater than AHz. During the same period, Drew and Pye again determined AH, for silver on silver using a tracer techniquelo and a mathematical solution similar to that of Nicker son and arker.' Though the values of D, Drew and Pye measured at any given temperature were about 200 times smaller than those reported by Nickerson and Parker, they again found a low activation energy of about 10 kcal, or about one fifth that found at the higher temperatures with the mass transport technique. A distinguishing characteristic of these two previous tracer studies is that they have worked at low temperatures (-1/2 T,) where they felt volume diffusion was negligible and then analyzed these data as if all tracer atoms leaving the source flowed out into and remained in a homogeneous high-diffusivity surface layer of undefined thickness. This is totally different from the model used in the mass-transport studies or the studies of grain boundary diffusion, which assume the high-diffusivity surface layer to be only a few angstroms thick. If this latter model is applied to the earlier tracer studies, it is shown that the tracer has really pe!etrated into the lattice a mean distance of 1000A. Thus the tracer distribution observed after an anneal is thought to be due to the combined effects of surface and volume diffusion. Independent of the relative validity of the two models, it seems evident to us that any comparison of the values of D, as determined in these two ways is meaningless and misleading, since the values of D, and AH, obtained in these two ways would be totally different for the same physical distributions of tracer. Once the fundamental difference in the approaches of the two techniques is established, we are faced with the question of which model better approximates physical reality. Here all the evidence seems to be on the side of the ''thin surface layer" analysis. In fact, the authors of Refs. 2 and 9 do not argue for the "thick-layer model" we have described; they simply invoke it through the equation they use to calculate D, . The primary evidence for the thin-film approach is: a) grain boundary grooves and scratches widen in proportion to tU4 and Mullins' rigorous analysis shows that this is only valid for a surface layer which is quite thin relative to the width of the groove;11 b) all accepted or seriously discussed models of solid-vapor interfaces and high-angle grain boundaries assume that the disturbed region of the interface is at most a few a0 thick. With the above in mind, it was desirable to determine D, using a radioactive tracer and a "thin-

Jan 1, 1964

By D. Turnbull, J. H. Hollomon, J. C. Fisher

Application of the concepts of nu-cleation and growth to the analysis of experimental transformation data has led to valuable descriptions of phase transformations, an outstanding example being the transformation austenite —* pearlite which has been examined with particular care by Mehl and co-workers.&apos;-5 In addition to the pearlite transformation, the proeutectoid fer-rite and proeutectoid carbide transformations are known to proceed by nucleation and growth. Martensite, on the contrary, until recently was thought to form by a mechanism involving neither nucleation nor growth; however, extension of standard nucleation theory6 suggests that martensite, bain-ite, and the other products of austenite decomposition all grow from nuclei in the parent phase. The theory that martensite forms by nucleation and growth is strongly supported by recent experimental work of Kurdjumov and Maksimova.7 The concepts of nucleatioli and growth have been fruitful also in providing a sound basis for quantitative theoretical treatments of the kinetics of phase transformations. For example, Volmer and Weber8 and Becker and Döring9 developed the theory of nucleation from fundamental considerations to a point where excellent agreement was obtained with the results of experiments on the condensation of supercooled vapors. As a result of their analysis, the kinetics of vapor-liquid transformations now can be predicted. It seems probable that application of the theories of nucleation and growth to a quantitative study of austenite decomposition similarly will clarify the nature of the individual transfor: mations involved, and will enable the calculation of austenite transformation kinetics. In the present paper, the theories of nucleation and growth are applied to the austenite ? martensite transformation in steels. The analysis begins with a discussion of nucleation in single component systems. Martensite appears to be coherent with the parent austenite, hence the nucleation theory is modified to include the effects of elastic distortion. Nucleation in the two component iron-carbon system then is discussed, for most steels are primarily alloys of these two elements. Finally, M. temperatures and martensite transformation curves are calculated for each of several alloy steels of varying carbon and chromium content, and are compared with those determined experimentally by Lyman and Troiano10 and Harris and Cohen.11 Nucleation Theory NUCLEATION IN SINGLE COMPONENT SYSTEMS6,12-14 The work required for reversible formation of a region of phase within the parent a phase is expressed conveniently as the sum of two terms: W1 = Aa, the product of the area of the interface and the interfacial free energy, and W2 = VAf, the product of the volume of the region and the free energy increase per unit volume associated with the transformation. The total work is therefore W = Aa + VAf. When a is more stable than ß, Af is positive and W increases without limit as the volume increases. The transformation a ?ß does not occur. It is nevertheless true that small regions of phase ß enjoy temporary existence here and there in the a. The equilibrium number of ß regions of given size is proportional to exp(— W/kT) per unit volume of a, assuring that larger (ß regions occur with diminishing probability. When a is less stable than ß, Af is negative and W passes through a maximum as V increases. Assuming for simplicity that regions of ß are spherical, as is true when the interfacial tension is isotropic and there are no elastic strains, W = 4r2a + (4/3)*r3Af The maximum value of W is W* = 16iro3/3Af2 [1] for regions with radius r* = -2o/Af. [2] For single component condensed systems it has been shown14 that the steady rate of nucleation of 0 per unit volume of untransformed a is nearly proportional to exp[- (W* + Q)/kT] where Q is the activation energy for the unit processes of adding or removing one atom from an embryo or nucleus. If To is the temperature at which a and ß are in equilibrium, the rate of nucleation is a maximum at a temperature 0 < T < To where (W* + Q)/kT is a minimum. P regions smaller than critical size are called embryos; they tend to grow smaller and disappear, only exceptionally growing larger. Regions equal to or larger than critical size are called nuclei. A critical size nucleus may grow indefinitely large or may shrink back to a, either process decreasing the free energy of the region.

Jan 1, 1950

By F. Claisse, R. Angers

Self-diffusion in iron has been measured during rapid a-r transformations using a variant of the Kryukou and Zhukhovitskii diffusion method. The study was performed by thermally cycling iron foils (1 to 6 cpm) through the transformation (=910°C). Some foils have been subjected to over 1000 cycles and some have spent more than 15 pct of their total diffusion time in the process of transformation. The experimental results show that the a-r transformation has no measurable effect on self-diffusion in iron. The study is completed by a quantitative analysis of mechanisms which can affect the diffusion rate during the transformation. The analysis confirms the experimental results. SINCE diffusion is an important factor in many solid-state transformations, it is of interest to study how it is affected by the stresses generated during these transformations. Clinard and Sherby1&apos;2 were the first to make a study along these lines. They measured diffusion coefficients in Fe-FeCoV couples subjected to slow thermal cycling (1.5 cph) through the a-r transformation range. They found an enhancement of diffusion by a factor of about two. The purpose of the present paper is to report measurements of the self-diffusion coefficient of iron during much more rapid thermal cyclings (1 to 6 cpm) through the a-r transformation (-910°C). These more rapid cyclings produce higher strain rates during the transformation and should emphasize any possible influence of transformation upon diffusion. EXPERIMENTAL Iron foils, 25 to 35 µ thick, were cold-rolled from 99.92 pct pure iron and annealed in pure helium for 2 hr at 870°C; the resulting grain diameter was about 150 µ. Specimens 0.5 by 8 cm were cut from the foils and I7e55 was vapor deposited on one of their surfaces. A 38 gage alumel-chrome1 thermocouple was spot welded in the middle of one of the specimen long edges, Fig. 1. Two 38 gage chrome1 wires were also spot welded along the same edge on each side of the thermocouple; they were placed 2.5 cm apart and used for electrical resistance measurements. In order to prevent twisting and crumpling, the specimens were pinched between two quartz plates 0.1 by 1 by 7 cm and the assembly was close fitted into a 1 cm ID quartz tube. Four holes were drilled through the tube to let the 38 gage wires out: these were connected to the recording equipment by means of extension wires. 20-gage nickel wires fixed at both ends of the specimens were used to thermally cycle the foils by Joule heating. The above described device was placed in a 2.7 cm ID quartz tube which in turn was placed in a tubular furnace. Either a pure helium atmosphere or circulating hydrogen was used during the experiments. Specimens were subjected to thermal cycles between a minimum temperature To and a maximum temperature Tm at rates ranging from 1 to 6 cpm. This was obtained by maintaining the furnace at a constant temperature near the minimum temperature To and periodically passing an electric current through the specimen. Cooling was achieved by heat losses to the surroundings. The forms and periods of cycles were varied from one specimen to another; however, each specimen was subjected to one type of cycle only. The temperature and electrical resistance variations of the specimens were recorded as a function of time. The temperature curves were used for diffusion calculations while the electrical resistance curves were used to monitor the transformation and to determine its starting point and its approximate duration. Diffusion was measured by the method developed by Kryukov and zhukhovitskii3 and modified by Angers and Claisse.4,5 In this method a metallic foil is coated on one side with a radioactive isotope and the activity is measured periodically on both sides during the diffusion anneal. The following equation then holds: where: I1 Activity on the surface on which the deposit is made. I, Activity on the opposite surface. t Diffusion time. B Constant. D Diffusion coefficient. d Foil thickness including the deposit. G(t) A function of time; it is a second order correction term which is given graphically in Refs. 4 and 5. The diffusion coefficient D is found by plotting ln[(Il - I2)/(I1 + I,)] -G(t) against t; the resulting slope m leads to an accurate calculation of D through Eq. [2]. The effect of the a-r transformation on diffusion is expressed by the ratio DT/DU where:

Jan 1, 1970

By J. B. Conway

Stress-vuptuve data for several of- the refractory metals are frequently found to yield a linear relationship between the Larson-Miller parameter and the logarithm of the applied stress. In such cases linear stress-rupture isotherms result with slopes bearing a definite relationship to the temperature. It also follows that the stress to produce rupture in a certain period of time will be linear in temperature. Data for several refractory metals have been reviewed and excellent linearity is shown in this type of isochronal plot. In addition, the af ore - mentioned lineavity leads to a linear relation between the log of the stress to produce rupture in a certain time and the homologous temperature. This has been illustrated for the Group VI-A metals, tungsten and molybdenum. EXTENSIVE use has been made of the Larson-Miller&apos; parameter in the interpolation and extrapolation of stress-rupture and creep data. In those cases where this particular parametric approach is applicable a convenient and fairly straightforward procedure is made available for the correlation of experimental stress-rupture data. It is quite common to employ this parameter in the form of a master rupture plot in which the parameter, T(C + log tr), is expressed as a function of log stress. In many cases this functional relationship in log stress is linear within acceptable accuracy and hence the following relation results: where P is the parameter, C is the Larson-Miller constant, T is the absolute temperature, t~ is the rupture time, a is the stress, and a and b are constants. Examples of such a relationship are contained in the work of Green, Smith, and 01son2 dealing with high-temperature rupture behavior of molybdenum and in the work of Green&apos; dealing with the high-temperature behavior of tungsten. In addition, pugh4 has shown a similar linearity for some fairly low-temperature data for molybdenum. It can be shown that when the relationship in Eq. [I] is exhibited certain generalizations can be made concerning the form of the stress-rupture isotherms. For example, rearranging yields: For a given material (constant C) at a given temperature the first term on the right-hand side of Eq. [2] is a constant and hence this equation defines a straight line when log stress is plotted as a function of log-rupture time. This is recognized as the standard form usually employed in this type of data presentation. Such linearity then suggests the linear form of the Larson-Miller parameter. Or, in other words, the linear parametric relationship in Eq. [2] results only when the stress-rupture data are linear on a log-log plot of stress vs rupture time. Another interesting observation can be made in regard to Eq. [2]. It can be noted that the slope of the stress-rupture isotherms is given by - T/b and hence a direct calculation of the constant b is available. It also follows that since the value of b is the same for all temperatures the slopes of the various isotherms on the log-log stress-rupture plot cannot be the same. Indeed, the existence of the relationship in Eq. [2] precludes a system of parallel lines on this common stress-rupture plot. As a matter of fact it further specifies that in addition to being nonparallel the slope of these isotherms must decrease (i.e., become more negative) with increasing temperature. Such a condition is indeed found to exist in the case of the stress-rupture data reported for molybdenum.&apos; As a corollary to the above, it may be stated that stress-rupture data which do not lead to a linear log-log stress-rupture plot or whose isotherms do not exhibit a decrease in slope as the temperature increases will not yield the linear relationship of Eq. [I]. Applying Eq. [2] to two different temperatures and solving for C yields: Eq. [3] affords a simple and rapid method for calculating the Larson-Miller constant from the log-log stress-rupture plot. The slope of a given linear isotherm is measured and the value of "b" calculated based on Eq. [2] as: slope = - -Tb Then at an abscissa value of 1.0 hr (making log tr in Eq. [3] equal to zero) read the stress corresponding to rupture for two different temperatures. Substitution in [3] yields: A value of the Larson-Miller constant can thus be calculated from a few simple mathematical procedures employing data read directly from the log-log plot of the stress-rupture data. Of course, it is not to be overlooked that the above reasoning has been based on the linear relationship of Eq. [I] being applicable. However, if as mentioned above the log-log plot is

Jan 1, 1967