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By W. B. Coleman

Considerable discussion on the effect of iron and steel scrap in blastfurnace burdens was presented in the January, 1927, issue of Mining and Metallurgy. Therein the question is asked as to what causes the difference in physical properties of pig irons where the chemical analyses are practically the same. This point no doubt has been noticed by a number of furnace operators, but several years ago very little thought was given to it. The foundries purchased pig iron, had it analyzed and found it to be within their specification. The castings made from this iron at times would be satisfactory and at other times hardness and shrinkage would occur. Since the iron was chemically correct the foundries generally were at a loss as to what to do. They changed their method of melting in the cupola and in some cases this corrected the trouble. In some instances the foundry would continue eliminating a brand of iron until the castings produced were satisfactory. Through this process of elimination they would finally arrive at the conclusion that a certain brand of iron was causing the trouble. During the course of this elimination minor changes might have been made in the melting and in the end satisfactory castings were secured without discovering any definite reason for the trouble. Frequently the foundries blamed the manufacturer of the pig iron although the seat of the trouble was in their own method of melting. I have in mind one foundry in particular that was using three brands of pig iron for producing their castings and their losses were rather high. Three entirely new brands of iron were substituted in the charge and still the losses continued. Even after using six brands of pig iron the management felt that the pig iron was the cause. The difficulties encountered in the melting of iron in the cupola, over the past several years, reflect in a great many cases on the operation of the cupola. At different times certain brands of iron were unsuitable for producing a certain class of castings, but at the same time one could see no reason why the iron should be considered abnormal. Irons from furnaces where production and low cost are the main factors that are being used in foundries produce in most cases harder cast-

Jan 1, 1927

By J. H. Henderson, H. J. Ledbetter, N. B. Gove, J. D. Griffith

INTRODUCTION The results of a series of laboratory flood tests using liquid Iso-butane to displace refined oils from test cores are pre- ented and interpreted on an empirical bask. The study Revealed the similarity of the miscible liquid displacement to that of the immiscible-fluid displacement mechanism. The efficiency of the iso-butane flood decreased markedly as the oil Viscosity increased. but the effect of injection rate on the effectiveness of the primary production stage was negligible over the range investigated. The presence of free-gas saturation prior. to iso-butane breakthrough increased the volume of iso- Butane required to recover a given percentage of the oil present. Injection of liquid i.e.-butane prior to water follicle sculpted in a marked improvement in oil recovery by the water flood. INTRODUCTION The production of petroleum is often enhanced by the injec-1i1)n of extraneous fluids into the reservoir. It has been suggeited that the injection or cycling of a wet gas or a liquefied petroleum gas would he instrumental in increasing the effic.ienr!; of oil recover! to a greater degree than the commonly injected fluids. dry pas and water. Although instances of injection of light liquid hydrocarbons are not unknown, a systrmatic recording of the result is unavailable and superfi- cially, the practice gives the impression of being economicaIIy unsound. For specific types of displacement, analytic: solutions have been advanced which aid in understanding the physical mechanisms involved. However, there is no generalized theoretical concept which permits adequate prediction of displacement efficiency from a knowledge of readily measured reservoir rock and fluid properties. The Buckley-Leverett approach to oil displacement by an immiscible phase is an admirable analysiy of that type of mechanism. Dykstra and Parsons have introduced a useful concept in their evaluation of the role of the mobility ratio and its merit in rationalizing displacement phenomena. Everett, Gooch and Calhoun3 in their report on the effect of viscosity ratio and miscibility have pointed out the lack of a comprehensive theoretical approach and the desirability of investigating the mechanism of miscible-miscible displacement. In lieu of a well-developed theory concerning miscible-111isci1)le displacement and in view of the scarcity of engineering information on actual LPG injection trials, the limited program of laboratory experimentation described below was undertaken. OBJECTIVES The original broad objectives of the program, to study the oil recovery process using LPG as the displacing phase, defined the direction and scope of the laboratory tests. The specific objective. of the experimentation were to evaluate

Jan 1, 1953

By F. J. Plecity, J. T. Michalak, W. C. Leslie

W. M. Williams (McGill University)-The authors are to be congratulated on completing this detailed investigation of recrystallization behavior. The present writer has recently completed some research at the University of Toronto on the recrystallization and grain growth behavior of a number of "pure" irons, and he would like to take issue with the authors' contention that recrystallization cannot be followed by means of hardness measurements. Two series of specimens of Ferrovac E, a com- mercially available iron, were annealed to complete recrystallization at 525" and 620" C, measurements being made both of Rockwell hardness and of volume percent recrystallized as a function of annealing time. Good correlation was found between these two quantities and, following the earlier practice of Cook and Richards for copper, hardness measurements were used in an extensive investigation of recrystallization. No anomalous behavior was observed as a result of this practice. Specimens which showed complete softening always showed, (metallographically and by X-rays), completely re-crystallized structures. These observations do not, of course, detract in the least from the results of the work under discus-

Jan 1, 1962

By Frederick G. Coqueron, Joseph E. Pogue

The purpose of this study is to present the results of a detailed survey of the financial and operating aspects of 30 oil companies comprising a major sample of the American petroleum industry. This review supplements a previous paper entitled "Capital Flow and Capital Formation in the Petroleum Industry, 1934-1941,"a and deals not only with a longer period but also gives new and more revealing analyses of the capital movements and characteristics. The data are gathered from published financial statements of the companies, especially the annual reports to stockholders and Form 10-K to the Securities and Exchange Commission, supplemented by confidential information. The 30 oil companies covered by this study are listed on the leading stock exchanges and for the purpose of analysis are grouped as follows: 9 companiesb engaged principally in crude production, 4 companiesc with production averaging in excess of refinery requirements, and 17 companiesd with refinery throughput in excess of crude production. These samples are sufficiently broad and representative to constitute norms against which individual company performances may be profitably compared. The 30 companies in 1942 produced 54 per cent of the Nation's total output of crude oil and refined 79 per cent of the country's crude run to stills. The financial data apply predominantly to the domestic oil business, although 15 of the companies have investments and operate facilities in foreign countries. The net value of these foreign holdings amounted to 724 million dollars, or 12 per cent, of the combined net assets of the 30 oil companies at December 31, 1942.

Jan 1, 1944

By John B. Hastings

THE occurrence of such a large amount of gold in the Hartsel granite, even though the surmised existence of similar areas is not new, brings freshly to mind the pegmatite type of magmatic differentiation lately brought again to attention by occurrences at Silver Peak, Nev., described by Spurr; and in Alaska, described by both Spurr and Brooks. In both localities graunitic rocks or dikes are thought to pass into metalliferous quartz-veins. An interesting association in this connection is the occurrence of diamonds in residual pegmatitic clay of San Juao de Chapado, Brazil, described by Derby :1 (P. 142) "Bodies of pegmatite are quite common in the older rocks of Brazil, both in the. diamond regions and elsewhere, occurring not only in the gneiss and granite, but in the schistose series as well. Those that have been examined are dike-like in their mode of occurrence and granitic in composition." (P. 143) "The question of the eruptive or secretionary origin of pegmatites has long been a subject of discussion among geologists. . . . The recent studies . . . seem to have clearly established that most if not all of them are essentially eruptive masses, though possibly modified in some way by aqueous agencies. Even before becoming acquainted with the literature of the subject this view had seemed to me to be the only acceptable one as regards the typical pegmatites of Brazil." What is pegmatite ? J. F. Kemp says ". . . veins or dikes-it is an open question which is the more correct term-are met formed of very coarsely crystalline aggregates of the same minerals that constitute granite. These are called pegmatite and in them is the home of graphic granite, the curious intergrowth of quartz and feldspar, such that a cross fracture of the blades of quartz suggests cuneiform characters. . . . In regard to the larger veins or dikes it seems improbable that true igneous fusion could have afforded such coarsely crystalline aggregates, and so we are forced to assume such abundance of steam and other vapors, i.e, mineralizers, as to almost, if not quite, imply solution."

Jan 5, 1908

By John Fritz

MEMBERS of the American engineering societies who were in London and Paris during the last days of. June and early July were present at many interesting gatherings. The official delegates of the Founder societies were the specially honored guests of the foreign engineering societies, but other American engineers took part in the meetings. The members of the delegation were: Arthur S. Dwight, Charles F. Rand, William Kelly, representing A. I. M. E.; Ambrose Swasey (general chairman of deputation), Ira N. Hollis, Jesse M. Smith, representing A. S. M. E.; F. B. Jewett, A. E. Kennelly, G. O. Squier, representing A. I. E. E.; Charles T. Main, Robert A. Cummings, John R. Freeman, D. C. Henny, representing A. S. C. E.

Jan 1, 1921

By S. R. Gilbert, B. W. Burdett, L. B. Hales

A brief review of grinding control systems is given with a review of the most popularly reported control loops. The trend toward more sophisticated control systems in terms of control strategies and control equipment is discussed, and the reasons for the popularity of distributed control equipment are outlined. The evolution of the interface between the operator and the process and its importance in plant control is described. Finally, the authors' view is given as to the future of grinding control.

Jan 1, 1984

By Joseph C. Mead, James R. Cudworth

THE Birmingham district of Alabama has utilized the slag from its blast furnaces consistently since the earliest development of the slag industry. Today there are producers of slag cement who started business in 1900, and who have, under a progressive policy, expanded the number of their products to meet present demands. There are producers of slag aggregates and other crushed slag products who have been successful for periods of over thirty years. There are at the present two companies, Cheney Lime and Cement Co. and the Southern Cement Co., manufacturing puzzolan cement; two companies, Birmingham Slag Co. and Woodstock Slag Co., making slag aggregates and by-products; one company, Tennessee Coal, Iron and Railway Co., a subsidiary of the U. S. Steel Corporation, producing ground open-hearth basic slag for soil conditioning. Two companies, the Sloss Sheffield Steel and Iron Co. and the Woodstock Slag Co., make slag concrete in ready-mix plants and one company, the Superock Company, manufactures fine and coarse slag aggregates under a new granulation process. No Portland cement is made with slag as an ingredient, because dolomite is used so extensively as a blast-furnace flux that the magnesium content of the slag is excessive. Sources Of Slag In the Birmingham district there are 22 blast furnaces, of which the majority are in blast. The present production is 165,000 tons of pig iron monthly; the production in 1935 was 1,297,960 gross tons1. There are also two blast furnaces at Gadsden and one ferroalloy electric furnace at Anniston. From these two sources is obtained slag to approximately 1.1 tons per ton of pig iron.

Jan 1, 1937

By Roger M. Nendick

The recovery of precious metals from heap leach solutions can be accomplished by two processes: 1. The Carbon Adsorption Process 2. The Merrill-Crowe Zinc Precipitation Process A brief review of the relative process economics is made. Each process presents certain design considerations that must be addressed during the evaluation and engineering design for the project. Discussion is presented on the design criteria for each process.

Jan 1, 1984

By T. Sterry Hunt

THERE are about sixty bodies which chemists call elements ; the simplest forms of matter which they have been able to extract from the rocky crust of our earth, its waters, and its atmosphere. These substances are distributed in very unequal quantities, and in very different manners. As regards the frequency of these elements in nature, neglecting for the present those which constitute air and water, and confining ourselves to the solid matters of the earth's crust, there are a few which are exceedingly abundant, making up nine-tenths, if not ninety-five hundredths, of the rocks so far as known to us. The elements of which silica, alumina, lime, magnesia, potash, and soda are oxides, are very common, and occur almost everywhere. There are others which are much rarer, being found in comparatively small quantities. Many of these rarer elements are, however, of great importance in the economy of nature. Such are the common metals and other substances used in the arts, which occur in nature in quantities relatively very minute, but which have been collected by various agencies, and thus made available for the wants of man. It is chiefly of the well-known metals, iron, copper, silver, and gold, that I propose to speak to-night; but there are two other elements not classed among the metals, which I shall notice for the reason that their history is extremely important, and will, moreover, enable us to comprehend more clearly some points in that of the metals themselves. I speak of phosphorus and iodine. You all know the essential part which the former of these, com- * An address before the Polytechnic Association of the American Institute, during the meeting of the American Institute of Mining Engineers in New York. Printed in this volume by request of many members.

Jan 1, 1873

By C. Altstetter, Y. Huang, E. de Lamotte

Nitrogen was introduced into pure niobium (colutn-bium) and dilute Nb- Zr alloy wires by equilibration with pure nitrogen gas at high temperatures. Room-temperature hardness was correlated with the alloy composition, heat treatment, and microstructure. Hardness was found to be most sensitive to the amount of nitrogen in solution; however, a significant hardening up to 500 Dph look place upon aging of quenched alloys. A coarse dispersion of nitride did not significantly increase the hardness of the material though the nitride was found to have a hardness of 1400 Khn. BY now the marked effect of nitrogen on the properties of bcc refractorv metals is we ll-documented. There are few studies, however, in which the state of the solute has been carefully controlled. Indeed, the composition-temperature-pressure relationships in nitrogen-refractory metal systems have been determined precisely for only niobium and tantalum.'-4 Most investigations on niobium have dealt with alloys High-nitrogen alloys cleaved on (100) planes and had negligible ductility. Precipitation was found to occur in either a discontinuous or a continuous fashion, depending on the composition and cooling rates. Upon cooling, the precipitation first proceeded discontinu-ously by the nucleation of nilride needles at subbound-aries and subsequent growth of a two-phase microcon-stituent. At lower temperatures continuous precipitation occurred in the subgrain interior ahead of the discontinuous precipitation interface. containing nitrogen, carbon, and oxygen in significant but uncontrolled and, in several instances, undetermined amounts. Thus, there has been some uncertainty regarding the presence and the distribution of precipitates. This paper presents results which relate the hardness and microstructure to the heat treatment and nitrogen content of niobium and Nb-Zr alloys. Niobium rod* produced by the Wah Chang Corp.

Jan 1, 1968

By Arthur Coffinberry

EVE have studied the gold-aluminum system by X-ray diffraction and by the microscope over the entire range of composition for temperatures between 300° and 500° C. Results obtained are shown in Fig. 1, com-bined with the work of Heycock and Neville1 at higher temperatures. The diagram differs in important details from that given by Hansen2 in his critical compilation of the literature of binary alloy systems. This work was, undertaken both because of the intrinsic value of a knowledge of the phase diagram of this system and because of the need of theoretical metallurgy for precise and accurate data, particularly X-ray diffraction data. Systematic studies of equilibrium diagrams, particularly by Hume-Rothery,3 have shown regularities that yield a certain insight into the nature of alloying forces. It has been shown, for example, that solid solubility depends on the concentration of free electrons in the alloy, on the relative radii of solvent and solute atones, on the forces of attraction between atoms, and on the relative stability of intermediate phases. The well-known Hume-Rothery rule states that the crystal structures and compositions of many intermediate phases depend on the electron-to-atom ratio. This has been confirmed and extended by wave mechanical calculations.4 A knowledge of the forces between atoms in alloys, even an imperfectly developed empirical one, should be a valuable guide in the preparation of technological alloys of desirable properties. Furthermore, such informa-tion is basic in such problems as rate of diffusion, age-hardening, phase transformations, and others. The most valuable data for this purpose are furnished by X-ray diffraction studies. Unfortunately, work has been

Jan 1, 1938

By AIME AIME

AN unusually interesting meeting devoted to the discussion of the ways and means of improving coal mining practice, through the larger use of machinery underground, was held in the Auditorium of the Engineering Societies Building on March 11. The meeting was organized by the Materials Handling Division of the A. S. M. E. and held under the auspices of the Metropolitan Section of that Society and the National Coal Association. The New York Section of the A. I. M. E., which had been invited to participate, found itself unable to do so formally because of a conflicting date for its March meeting but informally did its part to aasure the success of the meeting. As a result of the discussion at and preceding the meeting, the National Coal Association, through Walter Barnum, chairman of its research committee, has asked the A. S. M. E. and A. I. M. E. to join the Association in a study of the present problems of the bituminous coal industry. Messrs. Harry L. Gandy, Calvin W. Rice and H. Foster Bain have been selected to act as a committee which shall develop plans for a joint program.

Jan 1, 1926

[Trans. No. Place Date Vol. Page 1. Wilkes-Barre, Pa.* May, '71.. 1 3 2. Bethlehem. Pa Aug., '71.. 1 10 8. Troy, N. Y Nov., '71.. 1 1S 4. Philadelphia, PaFeb., '72.. 117 5. New York, N. Y.*May: '78.. 120 5. Pittsburgh, PaOct., '72.. 125 7. Boston, MassFeb., '78.. 128 8. Philadelphia, Pa.* May, '78.. 2 3 9. Easton, POct., '78.. 27 10. New York. N. YFeb.. '74.. 2 11]

Jan 1, 1946

By C. M. Fellman

THE over-all picture of safety in mining has been encouraging during the past few years, and in mining activities as a whole the trend in accident occurrence is downward. This is the more noteworthy when the type of labor used in mines during the war period is taken into consideration. The drafting of young mining employees into the armed services and the departure of others for work in other war industries took a heavy toll of young, husky, active men. Their places were taken in large part by older men who returned to the mines, or by inexperienced men with little if any knowledge of mining. Despite the lack of labor and especially of skilled labor, and the difficulty of obtaining new equipment as well as maintaining and replacing worn or broken equipment, and numerous other difficulties the mining industry not only reached and maintained maximum production but made the increase with little if any sacrifice of safety. In fact, in many instances better safety records were. established than in normal

Jan 1, 1946

By H. A. BURK

THE ores of the Tonopah, district are hard, compact and' highly siliceous. They contain from .1 to 2, per cent. of sulfide material, of which argentite is the valuable mineral; occasionally pyrargyrite is found in the richer ore. The sulfide is, chiefly pyrite with small amounts of chalcopyrite,. and sometimes sphalerite. The ore also contains a small amount of gold-about 1 per cent. by weight of the silver present. The major gangue constituent is quartz but frequently considerable rhodonite-called by the miners pink manganese-is present. For primary crushing, jaw and gyratory crushers are used. These crushers are of such capacity that, in most cases, one 8-hr. shift will supply the mill for 24 hr. The Extension Co., at the Victor ore house, passes the ore through a 13 by. 24-in. Blake type McFarland crusher set at 13 in., and at the No. 29 re house, a 14 by 24-in. Blake type Traylor crusher is used. The ore is thus crushed to stamping size in one reduction. The capacity of each crusher is about 40 tons per hr.; the power consumption is 0.6 kw. per ton.

Jan 1, 1921

By R. H. Hopkins, R. W. Kraft

X-ray and metallographic analysis reveal that the preferred cryslallograPhic relationships in direc-tionally solid~fied Pb-Sn eutectic specimens can be stated: interface growth direction, Experiments in which tin single-crystal seeds were used to nucleate the eutectic demonstrate that the normal lamellar structure observed at steady state can be forced to break down initially to a semide-generate structure when the crystallograPhic direction of the tin seed does not lie within the preferred eutectic interface plane. A normal structure eventually develops by preferred grain growth. X-ray topo-graphs and rocking curves substantiate that the perfection of eutectic samples increases as growth proceeds until steady-state conditions prevail. RECENT years have seen substantial progress made in the understanding of eutectic solidification through both intensive theoretical1'' and experimental investigations (see Ref. 7 for a review and extensive bibliography of both aspects). Several important observations concerning the nucleation and growth aspects of binary eutectic solidification have been brought to light. Briefly some of these include the nonrecipro-cal nucleation of one phase upon another,'j9 the tendency for a specific low-index direction of one or both phases of the eutectic to be aligned in the growth direction during unidirectional solidification,'0711 and the production of lamellar microstructures having a preferred interface plane between "11-13 phases. Questions quite naturally arise as to the mechanism by which preferred grain growth evolves during eutectic solidification and what relationships (if any) connect the initial nucleation of one phase upon another with the preferred growth directions and interface planes observed after a few centimeters of growth in many systems. This study was initiated in an attempt to answer these questions. An experiment was devised in which both the nucleation and growth steps in the crystallization of a binary eutectic, Pb-Sn, could be correlated with subsequently developed eutectic morphology and crystallography. This was accomplished by nucleating the eutectic upon a tin single crystal seed and then causing the eutectic to grow from the seed by directional freezing. The morphology of the structures produced in this manner was then monitored metallographically and the orientation relationships and substructural perfection determined by X-ray analysis. The information thus ob- tained was correlated to the growth history of the samples. EXPERIMENTAL DETAILS The eutectic of composition 38.1 wt pct Pb and 61.9 wt pct sn14 was prepared by accurately weighing lead and tin of 99.999+ (from ASARCO and Lytess Metals and Chemicals, respectively), melting in a clean Pyrex beaker under an argon blanket, and casting into the proper crucible for resolidification as described below. Tin seeds were grown by the method of ~halmers," saw-cut, oriented by the Laue method, and soldered to the pull rod of the Czochralski puller. All seeds were given a final electropolishing (to assure the removal of any deformed material from the cutting operation) and acetone degreasing immediately prior to the nucleation experiment in which they were to be used. Eutectic samples were unidirectionally solidified in a horizontal graphite boat1' or by pulling from the melt16 with tin (or graphite) seeds. A flowing argon atmosphere was employed in all experiments and growth rates and temperature gradients, constant for a given run, varied from 2 to 4 cm per hr and 8" to 15°C per cm over the course of all the experi-

Jan 1, 1969

By Richard Moldenke

The paper describes the making of pig iron from the Mayari iron ores of Cuba. The outstanding feature f this pig iron is a considerable content f nickel and chromium. As a marked improvement in the quality of castings has been noted when this iron is used in the foundry mixtures, a series f melting tests f mixtures of great variety of composition was conducted with the idea f getting comparative strengths from which the effect of nickel¬chromium could be seen. These tests, on account of their number, and degree of accuracy desired, were made by the crucible melting method. The paper gives the tables of results, a series f curves showing the inter-relation of the elements involved, and a summary of the conclusions derived. THE presence of nickel-chromium in pig iron made from Cuban ores is so well known that the word "Mayan" is unconsciously associated with it. Since 1904, when exploration of the Mayari deposits of iron ore in northeastern Cuba was undertaken, there has been increasing interest in these ores. The TRANSACTIONS contain numerous references to them. This iron ore, which is shipped to the. United States in the nodulized state, has been thoroughly tested and found very valuable; the deposit covers over 25,000 acres and there is in sight over 500,000,000 tons of ore that, by systematic mining, runs practically constant in composition. With nickel and chromium present, also titanium in sufficient quantities to attract attention, as well as extremely low phosphorus and sulfur contents, the iron founder is naturally interested in the utilization of Mayari ore for pig iron for the better grades of finished iron products. The present point of consumption of Mayari ore is at Sparrow's Point, where Mayari pig iron of any desired composition is made. The com-

Jan 9, 1922

AT A MEETING of the Shareholders of the Russo-Asiatic Cons. Ltd., in London, Oct. 23, 1922, LESLIE URQUHART, chairman of the com- pany made the following statement:* I come now to our recent negotiations with the Soviet Government and to the agreement which has resulted from them. You will remember that the conference at The Hague broke up without having achieved anything very definite. It was not, however, a failure. It elicited from M. Litvinoff an offer which will, I think, come to be regarded as a milestone in the progress of Russia from a ruinous and unpracticable Communism towards a modified form of capitalism. The offer made by M. Litvinoff at The Hague amounted in effect to this: that in return for political recognition on our part the Soviet Government would first acknowl-edge its liability for Russia's national foreign debts, and, secondly, would give the original foreign owners of property in Russia effective compensation. A very great advance that. It showed-and there have been many other signs to confirm it-how real and persistent has been the internal evolution of Russia during the past year from Marxism to the economics of the Western world. I will not now detain you with the reasons why M. Litvinoff's highly promising and significant offer came to nothing. The fact that it had been made and the further fact that The Hague Conference had separated indefinitely were the important things. The first fact seemed to indicate that the Soviet rulers, after all, proved to be people with whom one could do business. The second fact rather emphatically showed that the way to do business with them was not by unwieldy poly-glot conferences of ministers, officials and experts representing a few dozen different governments and a few dozen different sets of national interests. That method had been tried at Genoa. It was tried again at The Hague. Each time it failed, and having failed it left the road clear for a simpler and more direct approach.

Jan 12, 1922

By P. G. Shewmon, W. M. Robertson

The derivative of the surface tension with orientation, ??/??, for copper has been measured over the entire unit triangle. This derivative or torque term was determined from the variation of the dihedral angles at the intersection of twin boundaries and free surfaces. High-temperature anneals in graphite with a hydrogen atmosphere gave torque terms of 0.097 at (111), 0.066 at (100), and 0.0257 at (110). A variation from -36oto +23oC in the dew Point of the H2 had no effect on these values, nor did a change from 99.98 to 99.999 pct Pure copper. The removal of graphite from the system decreased ??/?? slightly. Considering the surface near a low-index plane to be smooth except for occasional steps, the free-energy increment per cm of step is calculated, and it is shown that the observed variation of ??/?? is consistent with a random distribution of steps and an interaction energy between steps. Integration of ??/?? gave the relative values of y at (100), (110), and (111) as comPared to ymax: (Y111/Ymax) =0.974, (Y110/Ymax) =0.996, (y100/Ymax) = 0.983. The ratio of the surface tension of coherent twin boundaries to the surface tension of the free surface was found to be (yT/ys) = 0.027 * 0.011. In a crystalline solid the surface tension y (surface free energy per unit area) depends on the orientation of the surface relative to the crystallographic axes of the crystal. Measurements of this variation of y with surface orientation have been reported for metals only within the last few years. Consider the grain boundary groove shown in Fig. 1. Here the three surfaces are all normal to the plane of the paper, and each has a different surface tension, y1, y2, and y3. If the system is at equilibrium, the total surface free energy must remain unchanged for a slight vertical displacement of the intersection (points A, B, and C are kept fixed). As shown by Herring,' the following equation is obtained:

Jan 1, 1962