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Discussions of the papers of DORSET A. LYON and SAMUEL S. ARENTZ, RICHARD D. DIVINE, H. A. WENTWORTH, and S. E. BRETHERTON, presented at the Salt Lake meeting August, 1914, and printed in Bulletins Nos. 91 and 92, July and August, 1914. GEORGE W. RITER, Salt Lake City, Utah.-We have every reason to believe that oil flotation Will soon come into general use as a final guard against slimes losses in concentrating mills, not only in the case of zinc ores, but also in the case of other semi-precious ores. It also promises much as a primary process for the concentration of minerals that are not adapted to gravity methods. Moreover, modifications of the process involving selective or preferential flotation are gradually becoming understood, and will make it possible to eliminate pyrite and other minerals occurring as undesirable impurities in zinc concentrates. And what perhaps is of equal importance, further modifications promise an effective method of separating zinc blende from ores that are chiefly valuable for copper, lead, anti precious metals, thereby making an asset out of zinc which has heretofore been a liability. The tendency of certain pulverized minerals to float on water, especially after having been in contact with grease, has been known to mill-men for a long time, and was formerly something to be deplored and to be striven against. All at once, this tendency has become a saving grace; and now, like tardy converts to a new faith, we are zealous advocates of something we once despised. I was once employed at a mine in the Tintic mining district of Utah¬the old Eureka Hill property-where ores that were too low in value to Warrant being sent to copper or lead smelters were treated in a combination mill. The ores contained gold, silver, lead, copper, zinc, manganese, arsenic, etc., in varying quantities and in varying mineral forms, mingled in a quartz and calcite gangue. The material was stamped fine and then concentrated on Frue vanners so as to make a smelting concentrate, after which the tailings were thickened and treated in amalgamating pans for the recovery of non-concentratable precious metals. In the amalgamating pans, under the influence of heat and agitation, a dark greasy froth or scum sometimes formed on the surface of the ore mixture. This froth or scum was composed mainly of mineral sulphides, and its occurrence might have meant only casual losses in the previous concentration, except that the phenomenon was accompanied by faulty amalgamation of the precious metals and by excessive losses in the mill tailings. Grease and oil, present by accident, were the cause of the trouble.

Jan 11, 1914

By M. J. Salkind

In discussing the possible contribution of plastic deformation to neck growth during sintering, Wilson and Shewmon State that Lenel, Ansell, Salkind, and Early34, 35 concluded that dislocation flow is the rate-controlling process in sintering under zero external load. The experiments cited34, 35 were done with applied external loads, and the conclusions were that the same kinetics could be controlling sintering due to the force of gravity with no additional applied load. The effect of gravity on sintering behavior was previously cited.34, 31 In addition, Wilson and Shewmon argue that the conclusions of Refs. 34 and 35 are doubtful because the strain rate is proportional to stress for plastic flow. This assumption is true only for certain kinds of plastic flow such as Nabarro-Herring Microcree38 As Early, Lenel, and Ansell point out3' plastic flow, based upon dislocation movement, can exhibit strain rates which exhibit a power law relationship to the applied stress.39, 40 Wilson and Shewmon also doubt the results of Refs. 34 and 35 because the stresses in the necks are too small for x/a > 0.1. This is true, and the experiments described in Refs. 34 and 35 were done for small values of %/a. The conclusion was that plastic flow by dislocation movement was important during the early stages of sintering when x/a is small.

Jan 1, 1968

By Glenn B. Southward

The V system of mining used at the Norton mine of West Virginia Coal & Coke Co. was designed as a modified long wall with face conveyors, for use under roof conditions that would not permit regular long-wall methods. This mine is in the Lower Kittanning seam, which averages about 6 ft. in height. There is from 20 to 30 ft. of slate and shale immediately over the coal and above this is a bed of sandstone 40 ft. or more thick; the total cover will vary from 50 to 250 ft. In the room-and-pillar workings, the top in the rooms and headings is generally good but it is

Jan 1, 1924

By G. F. Ziesing, E. F. Loros, T. J. Smolik

The Golden Sunlight mine began full-scale operations in February 1983 with a conventional open-pit mine supplying 4536 t/d (5000 stpd) of milling ore. After crushing and grinding, the ore is leached with cyanide solution in large agitation tanks. Soluble gold values are removed from the sand portion of the leached ore with five stages of countercurrent washing cyclones. After thickening of the cyclone-wash overflow slurry, the gold is recovered in activated carbon with a six-stage carbon-in-pulp circuit and a five-stage upflow carbon column circuit. Pressure stripping, carbon reactivation, electrowinning, and refining complete the gold recovery process.

Jan 1, 1985

By F. Galasso, A. Paton

ThE recent emphasis on producing boron fibers by reacting boron trichloride and hydrogen on a hot tungsten wire has brought about a renewed interest in the tungsten boride phase diagram. The reaction of the boron with the tungsten core results in the formation of 6 WB, W2B5, and another tungsten boride phase, which was suspected of being the WB4 phase reported by Chrbtien and Helgorsky.1 While the powder-diffraction data for the boride in the fiber and those reported

Jan 1, 1967

PAST AND PRESENT CHAIRMEN OF DIVISIONS Institute of Metals Iron and Steel Mineral Industry Industrial Minerals Year Division Petroleum Division Division Coal Division Education Division Division 1918 W. M. CORSET 1919 " 1920 W. H. BASSETT 1921 " 1922 W. B. PRICE RALPH ARNOLD 1923 E. DEGOLYER 1924 G. B. ELLIOTT 1925 F. JULIUS FOHS 1926 P. D. MERICA 1927 11 JOHN. M. LOVEJOY 1928 S. SKOWRONSKI A. W. AMBROSE RALPH H. SWEETSER ' 1929 " J. B. UMPLEHY G. B. WATERHOUSE 1930 ZAY JEFFRIES C. V. MILLIKAN W. J. MACKENZIE HOWARD N. EAVENSON 1931 SAM TOUR C. E. BEECHER F. M. BECKET 1932 C. H. MATHEWSON EARL OLIVER F. N. SPELLER THOMAS G. FEAR C. H. FULTON 1933 T. S. FULLER W. E. WRATHER JOHN JOHNSTON ELI T. CONNOR " 1934 J. L. CHRISTIE H. D. WILDE, JR. L. F. REINARTZ " T. T. READ 1935 W. M. PEIRCE HARRY H. POWER A. B. KINZEL JOHN T. RYAN SAMUEL H. DOLBEAR 1936 E. H. DIX, JR. HALLAN N. MARSH C. E. WILLIAMS EUGENE MCAULIFFE WILLIAM B. PLANK OLIVER BOWLES 1937 A. J. PHILLIPS M. ALBERTSON FRANCIS B. FOLEY J. B. MORROW " CHESTER A. FULTON 1938 R. F. MEHL G. B. CORLESS J. T. MACKENZIE PAUL WEIR FRANCIS A.THOMSON J. R. THOENEN 1939 R. H. LEACH W. H. GETS J. HUNTER NEAD C. A. GIBBONS " M. M. LEIGHTON 1940 E. M. Wise T. V. MOORE F. T. SISCO C. E. LA WALL W. R. CHEDSEY W. M. WEIGEL 1941 D. K. CRAMPTON E. A. STEPHENSON C. H. HERTY, JR. JULIAN E. TOBEY " PAUL M. TYLER 1942 CARL E. SWARTZ HARRY P. STOLZ E. C. SMITH NEWELL G. ALFORD A. F. GREAVES-WALKER B. L. MILLER

Jan 1, 1942

By G. B. Gould

THE softening temperature of coal ash, as determined in the labora-tory, has been used for years as an indication of the tendency of coal to form clinker and slag. It has not, however, provided an index of unfail-ing and complete reliability for forecasting the relative performance of different coals, even in the same plant and under the same conditions of operation. A large amount of investigation has been done in attempts to account for this, but practically all of this has been in the direction of studying the chemical constitution of coal ash. Much has been learned, but without much progress toward a better practical application of knowledge to the selection of coal. There has always seemed to be an important factor that eluded discovery. It has long been recognized that the ash-softening temperature as determined in the laboratory had one weakness, in that it represented the temperature at which a thorough mixture of the whole ash of the coal would melt, the mixing having taken place before the heat was applied. This does not, of course, simulate what takes place in practice. With certain exceptions, which will be noted later, almost all of the investiga-tions that have been made, especially the chemical studies of coal ash, have likewise dealt with a mixture of the whole ash in the coal. The present investigation differs from these fundamentally in its approach to the problem. It started from the observation that some clinkering and slagging obviously takes place in a boiler furnace at tem-peratures below the laboratory-determined ash-softening temperature of the coal. Knowing that coal as it is shipped to market is a hetero-geneous mixture of diverse mineral substances, each of which may act independently of the others in the initial stages of clinker and slag formation, it seemed logical to investigate separately the softening tem-perature of the ash in physically separable portions of the coal, and to determine the relative quantities of ash contributed by each portion.

Jan 1, 1940

Jan 1, 1949

By P. Somasundaran Discussion by Knut L. Sandvik

Knut L. Sandvik (Mining Engineer, Mineral Dressing Laboratory, Technical University of Norway, Trond-heim, Norway) — The discovery that adsorption at solid-liquid interfaces is influenced by adsorption at other interfaces may prove very fruitful in the further development of flotation theory. Having reached the same conclusions as P. Somasundaran in some experiments with amine hydrochlorides, I would like to offer more direct evidence of the interfacial adsorption mechanism based on surface tension measurements and adsorption studies.' This evidence was derived from flotation tests carried out in a Hallimond tube at neutral pH and 60°C. The amount of amine solution and quartz surface were chosen to insure measurable concentration changes during flotation due to adsorption. Adsorption data for

Jan 1, 1969

By N. Brown, M. Herman

ORDERING'S effect on the creep strength and other plastic properties of metals is unknown at the present time. Sachs and Weerts' attempted to compare the mechanical properties of the ordered and disordered state by comparing a quenched specimen with one annealed for a long time at a low temperature. This experiment is unsatisfactory because it introduces a possible effect from quenching. Barrett' used a hot impact test, but his method was not sufficiently sensitive to indicate any discontinuity in plastic behavior in the neighborhood of the critical temperature. On the theoretical side, Fisher9 as suggested that short range order would strengthen an alloy, but he gives no conclusions as to the effect of long range order. Cottrell" has discussed the interaction between long range order and dislocations, but does not indicate whether slip in a completely ordered alloy without domain boundaries is appreciably more difficult than slip in the disordered state. Because order exists in so many alloy systems, it is most important to prove experimentally whether long range order weakens or strengthens a metal. This investigation used -brass because: 1) it orders

Jan 1, 1957

By S. R. Krogh

In this investigation, a method to measure the basic characteristics of comminution has been developed. These characteristics are expressed by the three major comminution functions - crushing probability function, energy function, and breakage function. By testing three different minerals, quartz, calcite, and jasper, these three functions are determined. It is shown that the crushing qualities of a material can be valued by three constants which define the two first comminution functions. These two functions give the relation between particle size, probability of crushing, and the energy input.

Jan 1, 1980

By H. R. Hose

The total crude fluorspar reserves in Western Europe, including the USSR and the Soviet sphere, Thetotalare estimated to exceed 17 million metric tons. The total fluorspar production in 1951 in Western Europe, excluding the USSR and Soviet sphere, amounted to 371,109 metric tons. The chief fluorspar-producing countries in Europe, excluding Russia and the Soviet sphere, are France, Western Germany, Italy, Spain, and the United Kingdom. TOTAL crude fluorspar reserves in western Europe, containing more than 35 pct CaF2, are estimated at 12 million metric tons, while reserves in the USSR and Soviet sphere may exceed 5 million metric tons. The bulk of these reserves are concentrated in the USSR, Spain, United Kingdom, Western Germany, and Italy. Since published estimates of the tonnages of individual mines and explored deposits are not available for most countries in Europe, the estimates given in Table I for individual countries are necessarily approximate, as they have been compiled from various sources and modified and combined according to the author's judgment. The majority of fluorspar deposits in Europe belong to the late Paleozoic metallogenetic epochs and have been found within or along the borders of the Hercynian massifs. Deposits in the Central and Esterel massifs of France, those of Western and Eastern Germany, Sardinia, the Catalonian coastal range and the Sierra de los Santos in Spain, and those of Devonshire and Cornwall belong to the Hercynian metallogenetic epochs. The deposits in southern Norway and Sweden belong to the middle Paleozoic or later, those of northern England to the late Paleozoic or later, those of northern Spain and Greece to the late Mesozoic, and those of northern and probably central Italy and Switzerland to the early Tertiary. Fluorspar occurs typically in veins, lenses, and stringers, but also in bedded replacement deposits and pockets, and may be colorless to white, yellow, green, pink, brown, blue, or purple to almost black. Except for the colorless variety, the only kind which can be used for the optical industry, the color of the fluorspar does not affect its ultimate use. Crystalline cubic or octahedral fluorite of CaF2 composition, with 48.9 pct fluorine and 51.1 pct calcium, has a specific gravity of 3.18. The ore in place, however, usually averages 3.0 metric tons per cubic meter owing to the quantity of other minerals asso- ciated with the fluorspar in the veins and the physical state of the fluorspar, which may vary from sugary to massive crystalline or microscopic inter-growths with barite or quartz. Barite of 4.5 sp gr, quartz of 2.66 sp gr, and chert and calcite are commonly associated with fluorspar. Other minerals usually present in lesser amounts are celestite, wad, silver, lead, zinc, copper, iron, and uranium minerals. In some cavity fillings the rhythmic deposition of the fluorspar, barite, and quartz into successive crusts may make it possible to handpick the crude ore on belts or to separate the fluorspar from other minerals while the actual mining is carried on. Where metallurgical grade lump spar is required for foundries, separation of quartz and barite may be made also by jigs and heavy media, and in some mines the lead and zinc sulphides may be separated and recovered by vibrating tables. However, except in the case of unusually high grade deposits, acid grade fluorspar is obtained by flotation. By this process fluorspar deposits grading down to 35 pct CaF2 in the crude ore can be worked at a profit when fluorspar, lead, zinc, and silver prices are high, as the sulphides of these ores can be separated from the fluorspar by flotation and concentrated.

Jan 1, 1956

Jan 1, 1927

By J. L. Lytton, T. E. Tietz

The recovery of flour stress of recrylstallized are-cast molyhdenum after 10 pet prestrain at 150°C was studied for recovery temperatures of 725o 801o and 901oC. The yield phenomenon observed after recovery was such that the yield drop diminished and disappeared as recovery proceeded. A fractional flow-stress recovery parameter fr, was developed and it was shown that, independent of recovery ternperatzwe, equal f, values of about 0.16 produced superposition of stress-strain curves except for the initial yield phenomenon. The activation energy for low degrees oj recovery was found to he 32,600 cal per mole, in close agreement with a reported valzie for difjzdsion of carbon in molybdenum. For values of fr greater than about 0.15 where recovery was thought to predominate over strain aging, the activation energy varied from 43,600 to 82,500 cal per mole and increased with increasing recovery and recovery temperature. A 10 pet pre-strain shifted the ductile-brittle transition temperature, as indicated by tensile elongation, from 10°C. to about -22"C. A 100-hr recovery anneal at 801oC was shown to shift the transition temperature to about —5oC, the major shift occurring during the first hour of recovery. ThE recovery of cold-worked metals is accompanied by changes in the arrangement of the dislocations generated during cold work. In recent years, the use of transmission electron microscopy has allowed direct observation of some of the dislocation configurations formed, such as "tangles", networks, cells, subboundaries, and loops. These observations have recently been reviewed by Keh and Weissmann.' Accordingly, some understanding has been gained concerning the nature of the dislocation rearrangements involved. The relationship between recovery and the decrease of mechanical strength, however, has only recently been explored. Previous efforts of the authors were directed toward investigating the decrease of tensile flow stress of aluminum and Al-1 pet Mg during recovery2 and the effects of concurrent elastic and plastic strain on the flow-stress recovery of aluminum.3 In addition, an investigation of the effect of four different solute additions on the tensile flow-stress recovery of aluminum has been made.4 Many important metals, however, have the bee crystal structure, e.g., iron, molybdenum, tungsten, vanadium, columbium, tantalum, and chromium. These metals might be expected to behave differently during recovery from those with other crystal structures for two reasons. First, the previous and present investigations of aluminum and its alloys have shown that tensile flow-stress recovery is strongly affected by foreign atoms in the lattice. In the bee metals, interstitial impurities are usually present and might be expected to have various effects upon both flow behavior and recovery. For example, heterogeneous yielding might occur during prestraining. The diffusion of these interstitials can also relock dislocations during recovery so that a yield point might be obtained upon restraining (strain aging). Second, some of the bee metals (e.g., iron, molybdenum, and tungsten) undergo the familiar structure-sensitive ductility transition and exhibit brittle fracture at suitably low temperatures. It is of considerable interest to determine the effects of recovery on the transition temperature of such metals. The purpose of the present investigation was to extend our knowledge of flow-stress recovery to the bee metals and to study the effects of recovery on the ductile-brittle transition temperature. Unalloyed recrystallized are-cast molybdenum was chosen as a test material, since it exhibits a well-defined ductility transition near room temperature. As in the previous studies, the degree of recovery was measured in terms of the decrease of tensile flow stress. Prestraining and restraining were carried out at 150°C to avoid the possibility of brittle fracture. EXPERIMENTAL PROCEDURE The are-cast molybdenum sheet used in this investigation was obtained from the Climax Molybdenum Co. of Michigan. It was 0.060 in. thick by 10

Jan 1, 1964

By F. D. Richardson

STAFF: Editor, Gerhard Derge Carnegie lnstitute of Technology Schenley Park Pittsburgh, Pa. 15213 Editorial Assistant, M. A. Redmerski Production Editor, Otto T. Johnson THE METALLURGICAL SOCIETY: Jack H. Scoff, President; Richard C. Cole, Past-President; Harold 0. Emerick, President-Elect; Ralph L. Hennebach, Treasurer; Robert W. Shearman, Secretary; Donald A. Parks, Assistant Secretary; Leslie S. Wilcoxson, Assistant Secretary. PUBLICATIONS COMMITTEE OF THE METALLURGICAL SOCIETY: R. E. Lund, Chairman; T. E. Dancy, H. O. Emerick, P. R. Gouwens, R. E. Grace, J. H. Jackson, H. H. Johnson, A. E. Lee, Jr., R. R. Nosh, R. D. Pehlke, and Paul Queneau. Review and selection of manuscripts is under the supervision of the following Publications Committees: Extroctive Metallurgy Division: R. E. Grace, Choirmon; G. M. Bell, D. W. Bridges, J. M. Cigon, G. W. Heoly, T. A. Henrie, R. D. (Holli-doy, C. E. O'Neill, C. S. Somis, A. W. Schlech-ten, and Charles Shull. Iron and Steel Division: R. D. Pehlke, Choirmon; T. P. Floridis, Arnulf Muon, G. R. St. Pierre, E. T. Turkdogan, L. H.Von Vlock, and J. M. Uys. lnstitute of Metals Division: H. H. Johnson, Jr., Chairman; J. B. Clark, Vice Choirmon; M. R. Achter, G. F. Bolling. J. O. Brittoin, G. P. Conard, II, R. S. Davis, L. A. Girifolco, G. T. Hohn, J. P. Hirth, L. Himmel, G.T.horn, George Krauss, J. D. Livingston, R. D. Manning, H. M. Otte, S. V. Rodcliffe, R. E. Reed-Hill, H. C. Rogers, E. ScaIa, O. Sherby, M. T. Simnad, G. R. Speich, E. A. Steigerwald, R. A. Swolin, W. A. Tiller, W. R. Upthegrove, J. B. Wagner, Jr., Derek Wolton, H. W. Weart, W. W. Webb, and D. Published seven times yearly in February, March, April, June, August, October, and December by the American lnstitute of Mining, Metallurgical, and Petroleum Engineers, Inc., 345 East 47th Street New York, N. Y. 10017. Telephone PLAZA 2 -6800. Subscription $30 per year for non-AtME members m United States and North, South, and Central America; $32, foreign; $7.50 for AlME members Single copies, $6.00, single copier foreign, $6.50. The AiME is not responsible for any statement made or opinion expressed in its publications . . . Copyright 1964 by the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. . . . Registered cable address, AiME New York Indexed in Engineering Index, Industrial Arts Index, and Chemical Abstracts. Second dost postaas poid ot New York, N. Y.,ond Ann Arbor, Mich. Volume 230, Number 6.

Jan 1, 1964

ZAY JEFFRIES (author's reply to discussion *).-Messrs. Merica's and Humfrey's criticisms of some of my conclusions are rendered in the true scientific spirit by means of which differences of opinion are gradually smoothed out and all participants are benefited. It is true that the statement of generalizations on such a complex subject is hazardous, but I shall endeavor to point out the explanations for the discrepancies noted. Owing to the fact that I am now submitting a long paper on the same general subject to the Institute, my present remarks will be brief. Dr. Meric&s Assumptions' I agree with No. 1 and No. 2, with the modification that the A (amorphous) metal between grains of annealed metal has substantially the same properties as that at slip planes in deformed metal, but the two have different arrangements with reference to C (crystalline) metal and they may be in different conditions as regards internal stress, thickness, and nature of contact with C metal. Assumption 3.-I believe Fig. 1 is wrong. I know of no evidence to substantiate the curves. I believe cc (elongation of C phase) = 0 (approximately) at all temperatures and ?A (elongation of A phase) has finite values at elevated temperatures only; but these play no important direct role in the ordinary deformation of metals at low temperatures. I believe Ec (elastic limit of C phase) = Tc (tensile strength of C phase) because as soon as C metal begins to deform permanently it would rupture were it not for the A metal generated by its breakdown. We know that Ec = Tc in brittle crystals and a crystal cannot be permanently deformed without generation of A metal. Therefore Dr. Merica's

Jan 12, 1918

By Thomas Cox

This paper makes no claim to any new idea; it simply reviews the Treasury Department Regulations pertaining to the practical application of depreciation and depletion and other allowances governing taxation of oil and gas properties. Other methods may be existent, but as they may not conform to the legal status they must be discarded. In complying with the present laws governing the industry with regard to taxation and the allowable deductions therefrom, the following considerations are essential: Depletion, depreciation, amortization, other allowances, and items not, deductible. It is definitely understood that depletion is the loss or exhaustion sustained in the continuous operating of an oil and gas property, and that each unit of oil or gas taken out reduces the value of the property until its final exhaustion. Depletion applies only to the natural deposits of oil and gas due to their removal in the course of exploitation of any property. Depreciation is defined to cover the waste of assets due to exhaustion, wear and tear, and obsolescence of the physical property, and is separate and distinct from depletion; its allowance is that amount which should be set aside for the taxable year in such sums as for the useful life of the property will suffice to repay its original cost—or its value as of Mar. 1, 1913, if acquired by the taxpayer before that date—less the salvage value at the end of such useful life. Amortization is allowed for such facilities as were built or acquired on or after Apr. 6, 1917, for the production of articles contributing to the prosecution of the war and, in the case of vessels, those built and acquired after that date. The amount to be extinguished, in general, is the excess of the unextinguished or unrecovered cost of the property over its maximum value under stable post-war conditions. Claims for amortization must be unmistakably differentiated in the returns from all other claims of depreciation. The taxpayer is also required to furnish full information with the claims for amortization to the full satisfaction of the Commissioner. Further reference is directed to the specific rules and regulations for making these claims.

Jan 1, 1921

By A. Simkovich, C. W. McCoy

THE relationship among chromium, carbon, and temperature during the oxidation period of stainless steel melting was developed by Hilty et a1 1-3 whose studies were confined to plain chromium stainless steels. The simplified version of their relation is given by the equation:

Jan 1, 1962

Beyer Barometric Condenser The Ingersoll-Rand Co. is now offering to the trade complete steam­condensing plants for all service conditions. This equipment includes the Beyer barometric condenser, for' which the company has secured the patent rights, Imperial duplex and Ingersoll-Rogler straight-line reciprocating dry vacuum pumps and, where required, Cameron simplex and centrifugal pumps. The Beyer barometric condenser is of the counter-current type, in which air and cooling water flow in opposite directions. The steam inlet is at the bottom of the condensing v el, the water inlet above and the air-removal opening at the top. The sheets of cooling water over owing the pool at the inlet point meet the entering steam. The two are brought into intimate contact by conical baffle plates which assist the water to absorb to its full capacity the latent heat of the steam. The non-condensable air liberated in the condensing action rises through the falling water to the removal point at the top, being cooled to practically the temperature of the incoming water. It is also to be noted that ample opportunity is given for the removal of the air content of the water before

Jan 8, 1916

By J. P. Hirth, C. S. Hartley

A simple graphical technique is presented for rapidly determining the ratio of resolved shear stress on slip systems in single crystals to the applied stress (Schmid factor) for various simple states of stress. Master plots are presented which, when used in conjunction with an appropriate stereo-graphic projection, allow one to determine the Schmid factor for all slip systems in a crystal of given orientation. It is shown that one such plot suffices for simple tension or compression, flex-ural bending, and biaxial compression, while a combination of two different plots must be used for torsion and simple shear. STUDIES of the deformation behavior of single crystals are most valuable when the applied stresses are resolved onto the various slip systems of the crystal. A careful study of the available slip systems and proper selection of the state of stress used and the specimen orientation can then yield quantitative information about the probability of specific dislocation reactions, the strength of barriers to plastic flow, and the mechanisms of yielding and flow in general. It is the purpose of this work to analyze some common states of stress used in deformation studies and to present a simplified way of determining for these cases the ratio of the resolved shear stress on the slip systems to the applied stress (Schmid factor). I) CALCULATIONS We first define two orthogonal coordinate systems: one based on the specimen geometry (a right circular cylinder of radius, R, is considered here) and one based on the particular slip system of interest. The unit vectors and angles specifying the two coordinate systems and the relationship between them are listed in Table I. The relationships among the various angles and unit vectors are shown on a stereographic projection in Fig. 1. The transformation matrix between the (XI X2 X3) and (x'1 x'2 x'3) system is x1 x2 x3 X'1 a11 al2 a13 x'2 a21 a22 a23 x'9 a31 a32 a33 where in this case the direction cosines aij are given by a11 a12 a13 aij = a21 a22 a23 a31 a32 a33 sin 0 cos F cos 0 sin F cos 9 = -cos 0 cos F sin 0 sin F sin 6 [1] 0 -sin F cos (p In terms of Eq. [I.], the stresses sij, referred to the slip system, are determined from oij, referred to the specimen axes, by1,2

Jan 1, 1965