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By G. Sachs, G. Espey

Simple methods can be used for the determination of the residual stresses in thin walled tubing if the stresses consist of high tensile stresses at the one surface and high compressive stresses at the other surface. Such a stress distribution is approximated in sunk tubing and in deep-drawn shells. It is possible to cut sections from such articles in such a manner that a major part of the residual stress is relieved by a bending of the Part that is separated from the adjacent metal. The circumferential stress is evaluated from the change in diameter D, occurring on splitting a length of tubing (Fig. Ib) or from deflection resulting from the cutting out of a circumferential tongue (Fig. Ia) .6 The bending moment M released by such a flexure is. M - EI (I-I) = EI R1-R0 I - u2(R0-R1) I -V2 R0XR1 where E = modulus of elasticity, v = Poisson's ratio, I = moment of inertia of the section, R0 =. mean radius before splitting, R1 = mean radius after splitting. The release of this bending moment corresponds to the release of stresses, which, in a thin section, vary linearly from one surface to the other, and have the following value in a particular fiber a certain distance (x) from the surface: S = c d I - V2 x c x d 2 2 RI - R0____E (d ) R1 - R0 X R0 X R1 ~ i - u2 (2 x) Ro X R1 where C is the section modulus and d is the thickness of the section, the ratio M:C being d: 2 for a rectallgular section.* The maximum stress values at the surfaces are. Smax = +E X d X R1-R0 I — u2- 2 R0 X R1 For most purposes the simpler equations: EXd AD1 = ± I - u2 x dm2 and will be satisfactory, where D,, is the aver. age of the mean diameters of the tubing

Jan 1, 1942

Feb. 18 to. 21, 1918 Committee on Arrangements J. E. JOHNSON, JR., Chairman BRADLEY STOUGHTON, Vice-Chairman A. R. LEDOUX RALPH W. DEACON F. T. RUBIDGE L. W. FRANCIS E. M. SHIPP MRS. S J. JENNINGS J. V. N. DORR A. L. WALKER G. D. VAN ARSDALE R. M. RAYMOND Finance Committee ALBERT R. LEDOUX, Chairman WALTER H. ALDRIDGE J. H. JANEWAY GEORGE D. BARRON CHARLES F. RAND WALTER DOUGLAS BENJAMIN B. THAYER

Jan 4, 1918

By Robert A. Laurence

Ore deposits in the Southern Appalachians are ( 1) sedimentary or syngenetic, ( 2) epigenetic, and ( 3) residual. In general, deposits characteristic of high temperature and pressure are found in the Blue Ridge and Piedmont provinces and those of low and intermediate temperature and pressure, including the sedimentary ores, are found in the Valley and Ridge and Appalachian Plateaus provinces. Residual deposits are present throughout the area. Recognition of several periods of intrusion and metamorphism in the Appalachians has changed former concepts which held that most mineralization was of late Paleozoic age in a zonal pattern including all four provinces. Many deposits probably are of early or midPaleozoic age. Similarly, recent studies in geomorphology indicate that the formation of residual deposits is a continuous process and not related to specific cycles of peneplanation.

Jan 1, 1968

By AIME AIME

THE American Institute of Mining and Metallurgical Engineers will hold its annual meeting in New York City, Feb. 9-12. The technical sessions, excepting the Sunday afternoon and evening sessions of the Mineral Industry Education Division (see the M.I.E.D. program) will be held in the Engineering Societies Building. The "All-Institute" luncheon on Monday will be at the Commodore Hotel; the Annual Banquet and President's Reception, the Smoker, and the Informal Dance will be at the Waldorf Astoria Hotel. The dinners of the Petroleum Division and the Institute of Metals Division will be at the Roosevelt Hotel.

Jan 1, 1942

By D. S. Sanders

IN the four mills of the Cerro de Pasco Copper Corp. in Peru, some 3000 tons of complex sulphide ores are treated daily, with four kinds of concentrates produced: copper, lead, zinc, and pyrite, each containing values in silver, gold, bismuth, and some other metals. Copper occurs in the various ores as chalcopyrite, enargite, tetrahedrite, tenantite, bournonite, and chalcocite; lead as galena; and zinc as sphalerite and marmatite. Small amounts of silver and tungsten minerals are also present. The gangue consist mainly of shale, quartzite, calcite, rhodochrosite, pyrite, and pyrrhotite. In general the values are freed with a relatively coarse grind, about 70 prr cent minus 200 mesh being the finest to which the pulps are ground. In Morococha and Casapalca however. sphalerite particles much finer than this contain inclusions of chalcopyrit r. At Cerro de Pasco the silver and gold are present in all sizes of the ground pyrite.

Jan 1, 1945

Vice-Chairmen GEORGE D. BARRON, PHILIP N. MOORE, EDWARD H. BENJAMIN, ROBERT H. RICHARDS, FRED H. BOSTWICK, MILNOR ROBERTS. ELI T. CONNER, CARL SCHOLZ. C. R. CORNING, WILLIAM WRAITH, WALTER DOUGLAS, THOMAS T. READ, Secretary, Woolworth Bldg.. New York, N. Y.

Jan 1, 1917

By RUSSELL C. FLEMING

GILSONITE is a brilliant black, tarry-like bitumen, classed technically with glance pitch and graharnite as an asphaltite. As found it is brittle, breaking much like ice, and has a conchoidal fracture. Purest forms are used in the manufacture of paints, varnishes, electrical irisulatiorl, and inks for rotogravure; molded articles such as switch handles, telephone mouthpieces, and but- tons are made from the intermediate grades, and the poorer grades are used for the saturation of felt. According to the U. S. Bureau of Mines figures, production grew from about 4000 tons mined in 1904 to 55,000 tons in 1929. This asphaltic substance is found only in the Uintah basin in northeastern Utah, in veins over a wide area. Veins in the vicinity of Fort nuchesne were first discovered about 18G2, on what was then the Uintah Indian reservation, and the vein matter was originally called Uintaite because of that fact, In the early days, S. H. Gilson. of Salt Lake City, was so persistent and zealous in his efforts to develop the deposits and find a market that the name gilsonite was given to the material. Later, the wider and more renowned wins near Wayson and Dragon, in extreme eastern Utah, became the main supply.

Jan 1, 1932

By AIME AIME

MOST recently elected to the limited group of Honorary Members in the A.I.M.E. is the distinguished Australian metallurgist, Guillaume Daniel Delprat. His citation reads: "in recognition of his distinguished achievement as metallurgist, engineer, and administrator in the production of ferrous and nonferrous metals," Mr. Delprat's ability and experience in both the ferrous and nonferrous fields at once distinguishes him from most of his professional brothers. Mr. Delprat's nativity was neither Australian nor English, for he was born in Delft, Holland, in 1856, and educated in Amsterdam. At the age of 22 he went to Spain, as metallurgist for the Tharsis Sulphur and Copper Co., Ltd. Afterwards he spent some time with the Bede Metal and Chemical Co., which had mines in both Spain and Norway, and of which company he became general manager. Other positions of responsibility held by Mr. Delprat before he went to Australia included the managing directorship of the Cordova Exploration Co., with properties in Spain and Canada; of the Rincon Silver-Lead Mining Co., in Spain; and of the Deloro Gold Mines, in Canada.

Jan 1, 1936

By E. T. Turkdogan, W. L. Worrell

The rate of reaction of hydrogen sulfide with ferrous sulfide was studied by measuring the initial rates of sulfidation of iron strips in hydrogen sulfide-hydrogen-argon mixtures at 670°, 800°, and 900" C. The time-dependent surface sulfur activity is derived from the instantaneous rate of sulfidation with the assumption that diffusion in the sulfide layer is in a pseudo-steady state with the gas-sulfide chemical reaction. The rate of sulfur transfer from hydrogen sulfide to the surface of iron sulfide is proportional to the partial pressure of hydrogen sulfide and inversely proportional to the activity of sulfur at the surface of the sulfide layer. The derived rate equation is based on the assumption that most of the surface sites on the chemisorbed layer of iron sulfide are occupied by sulfur atoms and that the slow rate-controlling reaction is the dissociation of hydrogen sulfide on the chemisorbed layer. The experimental results are in reasonable accord with this reaction model. 1 HE slow approach to parabolic growth rate in the sulfidation of iron in hydrogen sulfide-hydrogen mixtures is a manifestation of slow approach to surface equilibrium between the gas and the surface of the sulfide layer. For example, at 800°C and Fig. 7 in Part I, the parabolic growth rate begins after approximately 1 day of sulfidation time. With decreasing temperature and decreasing partial pressure of hydrogen sulfide, the time necessary to reach gas-sulfide surface equilibrium is much longer. These observations are similar to those reported previously by Turkdogan et al.' on the oxidation of iron to wustite in hydrogen-water vapor mixtures. The slow approach to gas-sulfide equilibrium is well-demonstrated by the results in Fig. 1 where the square of the weight gain per unit area, ( g S per sq cmI2, is plotted against time for gas mixtures having PH g//>H = 1.0 with 0, 25, 50, and 67 pct Ar at 800°C. The value of 1.5 X lo-' (g S per sq cm)' corresponds to almost complete sulfidation of the iron strip (- 0.05 cm thick) to iron sulfide. The points fall on S-shaped curves. If the inflection parts of the curves are considered to be linear, thus indicating parabolic growth rate and the establishment of gas-sulfide equilibrium, their slopes would have to be the same for a fixed ratio in the gas mixture. Such is not the case, and the slopes for the "linear" parts of the S-shaped curves are lower than the value when gas-sulfide surface equilibrium is established. The subject matter of this paper is the kinetics of the surface reaction of hydrogen sulfide with iron sulfide during the early stages of sulfidation of an iron strip. EXPERIMENTAL RESULTS The apparatus and materials used were the same as those discussed in Part I. In the present experiments of relatively short duration, a purified iron strip, 5 by 2 by 0.05 cm, which was suspended in the uniform hot zone of a vertical zircon tube, reacted with a flowing gas mixture of hydrogen sulfide-hydrogen-argon. The sample was suspended from a gold chain attached to a calibrated silica spring. The amount of sulfur picked up by the iron, which formed a layer of iron sulfide, was determined by measuring the displacement of a reference point on the silica spring, using a cathetom-eter. In all cases, the degreased sample was first annealed in a stream of oxygen-free dry hydrogen for several hours to remove any impurities such as oxygen, nitrogen, or carbon which might have been present on the surface of the sample.' The rate measurements were carried out at 670°, 800°, and 900° C in hydrogen sulfide-hydrogen-argon mixtures with pH2 s/Ph2 ratios from 4 to 0.1. In a few experiments of short duration no sulfur deposition was observed in gas mixtures with (comments concerning sulfur deposition at high pH s/ph ratios were made in Part I.) Typical examples of the results obtained are shown in Fig. 2 for two temperatures and two gas compositions. With the present experimental technique, reproducible rate data could be obtained only after a uniform

Jan 1, 1969

By Bernard MacDonald

Introduction. OF the treatment of the slime-pulp of gold- and silver-ores by cyanidation, agitation is an essential part. When prepared for treatment, this pulp, consisting of ore reduced to such fineness that approximately 80 per cent. of it will pass through a 200-mesh screen, is mixed with a certain proportion of water, carrying in solution the quantity of cyanide (KCN) and other chemicals required. The water-constituent of the pulp thus prepared usually ranges from 1 to 2 parts by weight to 1 of the dry ore. Thus constituted', the pulp is charged into treatment-tanks, the shape and capacity of which vary, according to the quantity of pulp to be treated daily and the method of agitation to be employed. Tanks have no other function in a cyanide-plant than that of being economical and convenient containers or receptacles for holding the pulp, solution, or water used in the operations. It is by agitation that the solids in the pulp charged into the tanks are kept in suspension in, and mixed with, the solution in the proper proportions required for the treatment. If the proper mixture of solution to solids be determined to be 2 to 1 by weight (which is, approximately, 5 to 1 by volume), this proportion should be maintained in every part of the charge ; -that is, each solid particle of the pulp, whether it be of 180- or 400-mesh size, should, be surrounded by five times its own volume of solution throughout the whole period of treatment. The reason is, that the amount of chemicals ascertained to be necessary for dissolving the gold and silver contained in the solids, is held in uniform solution in the water-constituent of the pulp, and, therefore, the determined proportions of solution and solids must be maintained at all times during treat-

Apr 1, 1912

By Louis E. Reber

Jan 1, 1922

By Clarence Zener

The internal friction of nonferrous metals vibrating at low stress amplitudes has so far always been successfully interpreted in terms of inhomogeneities of one sort or another. Examples are the fluctuation of stress across a specimen vibrating transversely,1,2,3 the stress inhomogeneities due to the elastic anisotropy and partial random orientation of the individual crystallites, localized weak regions introduced by cold-working,6'7 grain boundaries and possibly twinning planes.8'9 Perfect single crystals are, by definition, homogeneous. Actual single crystals usually, perhaps always, contains some imperfections. The present investigation was undertaken to determine whether the internal friction of single crystals may likewise be attributed to inhomogeneities. This study was made possible through the gift of a large single crystal of 70-30 alpha brass by H. L. Burghoff, of the Chase Brass and Copper Co. The specimen, 3.i in. in diameter and 10 in. long, was similar to samples previously described by Mr. Burghoff. Experimental Method The experimental method used has previously been described in institute papers.5'6'9 The measure of internal friction adopted here, I/Q, is X the logarithmic decre- ment, a measure used by some writers, and is also X the specific damping capacity, a measure used by other writers. In all measurements the stress level was kept so low that the measurements were independent of stress level. In all measurements in which the temperature was varied, observations were made as the specimen slowly cooled from its highest temperature. The specimen was vibrated transversely. Observations were made at the fundamental frequency and at the first overtone, of about 620 and 1710 cycles per second, respectively. No attempt was made to avoid acoustical losses. Experimental Results The specimen was annealed for several hours at 450°C. The temperature dependence of the internal friction was then determined from room temperature to 400°C. As shown in Fig. I, the internal friction increased by only a factor of 2 from room temperature to 300°C., then by a factor of 100 during the next Ioo° interval. These measurements are consistent with the view that the observed internal friction is the superposition of two distinct parts. One, dominant at room temperature, is nearly independent of temperature. This part may be accounted for by acoustical losses and by transverse thermal currents. It was not further investigated. The second part, when plotted in the manner of Fig. I, lies upon a straight line. Therefore it has a heat of activation H; i.e., it varies with temperature as Internal friction e-H/RT [I]

Jan 1, 1943

By Clarence Zener

The internal friction of nonferrous metals vibrating at low stress amplitudes has so far always been successfully interpreted in terms of inhomogeneities of one sort or another. Examples are the fluctuation of stress across a specimen vibrating transversely,1,2,3 the stress inhomogeneities due to the elastic anisotropy and partial random orientation of the individual crystallites, localized weak regions introduced by cold-working,6'7 grain boundaries and possibly twinning planes.8'9 Perfect single crystals are, by definition, homogeneous. Actual single crystals usually, perhaps always, contains some imperfections. The present investigation was undertaken to determine whether the internal friction of single crystals may likewise be attributed to inhomogeneities. This study was made possible through the gift of a large single crystal of 70-30 alpha brass by H. L. Burghoff, of the Chase Brass and Copper Co. The specimen, 3.i in. in diameter and 10 in. long, was similar to samples previously described by Mr. Burghoff. Experimental Method The experimental method used has previously been described in institute papers.5'6'9 The measure of internal friction adopted here, I/Q, is X the logarithmic decre- ment, a measure used by some writers, and is also X the specific damping capacity, a measure used by other writers. In all measurements the stress level was kept so low that the measurements were independent of stress level. In all measurements in which the temperature was varied, observations were made as the specimen slowly cooled from its highest temperature. The specimen was vibrated transversely. Observations were made at the fundamental frequency and at the first overtone, of about 620 and 1710 cycles per second, respectively. No attempt was made to avoid acoustical losses. Experimental Results The specimen was annealed for several hours at 450°C. The temperature dependence of the internal friction was then determined from room temperature to 400°C. As shown in Fig. I, the internal friction increased by only a factor of 2 from room temperature to 300°C., then by a factor of 100 during the next Ioo° interval. These measurements are consistent with the view that the observed internal friction is the superposition of two distinct parts. One, dominant at room temperature, is nearly independent of temperature. This part may be accounted for by acoustical losses and by transverse thermal currents. It was not further investigated. The second part, when plotted in the manner of Fig. I, lies upon a straight line. Therefore it has a heat of activation H; i.e., it varies with temperature as Internal friction e-H/RT [I]

Jan 1, 1943

RACAL COMMITTEE OF ARRANGEMENTS Henry McCormick, Chairman; David Watts, Secretary; H. H. Campbell, A S. McCreath, S H. Chauvenet, C. E. Stafford, George S. Comstock, Jones Wister, E. C. Felton, F. W. Wood, Harvey Fisher. CITIZENS' RECEPTION COMMITTEE Governor H. M. Hoyt, Hon John C. Herman, Hon Simon Cameron, Hon. J. D. Cameron, W T. Hildrup, Charles L. Bailey, W. W. Jennings, Lane S. Hart, H. U. Carter, Gilliard Dock, T. T Wierman, Jr, James Boyd, D. L. Jauss, Dr. T J. Dunott, S. C. Gilbert. William J Rose, James Lynah, Dr. H. B Buehler, William N Lamberton, John Wister, G. M. McCauley, David Fleming, John Q. Donney, M. E. Olmsted, H. S Gross, Henry Gilbert. John B. McPherson, Lyman D. Gilbert, F. W. Forman, L. S. Bent, A. J. Dull, F. R. Leib, Dr. G. W. Belly, James McCormick. The opening session of the meeting was held in the hall. of the Young Men's Christian Association, on Tuesday evening, October 25th. Mr. Jones Wister, of the Local Committee of Arrangements, introduced the Hon. John C. Herman, mayor, who, in a brief address, extended to the members present a welcome to the city, of Harrisburg ; Lieutenant Governor Stone made an address of welcome on behalf of Governor Hoyt and the Commonwealth of Pennsylvania. President Metcalf responded, on behalf of the Institute, to the cordial addresses of the mayor and lieutenant-governor. The following persons proposed for members and associates of the Institute, and recommended by the Council, were unanimously elected :* MEMBERS. William F. Aldrich, - Montevallo, Shelby Co., Ala. George H Blake, - Steelton, Dauphin Co., Pa. L. Bertram Cady, - Salisbury, N. C. John B. Church, - Pottsville, Pa. Walter S. Church, - Pottsville, Pa, Frank L Clark, - Pittsburgh, Pa. * In the following list are included those elected at a subsequent session of this meeting.

Jan 1, 1882

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who registered at Institute headquarters during February: Paul S. King, Wilmington, Del. William Kelly, Vulcan, Mich. A. Del Mar, South Pasadena, Cal. F. H. Armstrong, Vulcan. Mich. T. D. Babbitt, Nampa, Idaho. Reginald E. More, Toronto, Canada. H. L. Williams, Newtonville, Mass. Tom M. Owen, Broken Hill, Australia. F. W. Bacorn, Pittsburg, Pa. Percy E. Barbour, Candor, N. C. Huntington. Adams, Mexico, D. F. Karl Nibecker, Youngstown, Ohio. Clifton B. Johnson, New. York, N. Y. G. A. Reinhardt, Youngstown, Ohio. W. Spencer Hutchinson, Boston, Mass. Herbert B. Cox, Boston, Mass. F. Louis Grammer, Leesburg, Va. E. C. Pechin, Buchanan, Va. H. C. H. Carpenter, London, England.

Jan 3, 1914

By Roy P. Full, Robert M. Grantham

Regional structural adjustments in early Tertiary time resulted in the development of the Republic graben, a major down-dropped block that is from 6 to 10 miles in width and more than fifty miles in length. The graben became the center of extensive volcanic activity during Eocene and Oligocene time, resulting in a thick sequence of water-laid tuffaceous sediments, volcanic flows, and associated intrusives. A younger series of sediments, pyroclastics, and flows were deposited in structural depressions within the graben following the period of widespread volcanic activity. The Republic mining district is located along one of the major intragraben structural zones, where continuing subsidence during the period of volcanic activity resulted in an increased thickness of flows and associated flow breccias and pyroclastics. Intrusive masses in part healed early graben-forming faults, but later subsidence reopened old faults and created new fracture zones which later became the control for the gold-quartz veins. Considerable block adjustment along the subsidence area is evidenced by the structural pattern in the mines, and telescoped vein structures indicate north-south compressional stresses and east-west graben-forming tensional stresses prior to and during the emplacement of the veins. The veins, varying from a few feet to more than 50 feet in width, are filled primarily by fine-grained quartz, commonly chalcedonic or porcelain-like in appearance. Finely laminated dark-gray to black concentric banding within the veins generally distinguishes the better-grade ore zones, which contain finely disseminated sulfides and ore minerals that include principally electrum, stephanite, naumannite, and native silver.

Jan 1, 1968

By Edmund J. Korber, Donald E. Raab, Frank A. Burns

During the early 1960s, the advent of self- advancing longwall roof supports triggered serious consideration by Bethlehem management to introduce the technique of longwall mining at one of our central Pennsylvania coal mines. Although longwall mining was initially justified as a means to cope with the severe roof conditions at our Mine 32 (Watson, B., 1971), the result of the endeavor has been a consistent and reliable level of coal production, first from Mine 32 and then later from Mine 33, over a period of fifteen years. Longwall production from the Cambria Division has been the mainstay of the low volatile coal required by Bethlehem Steel for steel production. Let us review the events that led to this accomplishment, as well as where we stand today.

Jan 1, 1981

By Hans Lundberg

N OT so long ago, the discovery of an orebody took place only by accident. At the present time mineral deposits, even though concealed, may be revealed by their physical or geophysical characteristics, considered in connection with geological studies. Geophysical methods are based on sound, scientific principles and in no sense partake of the mysteries of "divining-rod " methods. Geophysical methods are divided into two main groups: Group I: Methods where fields of force surrounding mineral deposits are investigated (magnetic, gravitometric, electric) ; Group I1 : Methods where fields of force are applied (produced) and anomalies caused in these fields by mineral deposits are recorded (electric, seismic). By methods belonging to Group I, the investigation of the fields of force may be brought to an astonishing degree of accuracy by means of highly sensitive and delicate apparatus (torsion and magnetic balances) ; at least, in simple cases these methods have proved to be of great value.

Jan 1, 1925

By H. E. Cook

The Ising model for the internal energy of a binary alloy has been used to obtain a general equation for the critical resolved shear stress of partially ordered crystals. The equation expresses the stress in terms of the Warren "alphas " and can be used to estimate the variation in strength with order without the assumption, present in the original formulation of this problem in terms of domain size, that order is complete within each domain and that the domains are of ungorm size and shape. In addition, it is the general equation, according to the Ising model, for strengthening by short-range order. Two applications of the equation are considered: One is an estimate of the variation in strength of CkAu with long-range order. The other is an estimate of the variation in strength of FeCo with quench temperature. Reasonable agreement is found with the variations reported in the literature. When the internal energy of an alloy crystal depends upon the distribution of solute, the strength of the crystal will also depend upon it because a portion of the applied stress for plastic deformation will be: where V is the volume of the crystal and E(E) is the energy change associated with the solute redistribution caused by the plastic strain, E. We expect T to equal zero for a crystal having a random arrangement of solute because the arrangement would remain random after plastic deformation. Likewise, we expect it to equal zero when the crystal is perfectly ordered because the motion of paired dislocations found in such crystals does not disrupt order. However, when short-range order exists or when long-range order is incomplete, plastic deformation will decrease the amount of order and additional work, proportional to the ordering energy, will be expended. Fisher' estimated T for crystals having short-range order by assuming an interaction energy between neighboring atoms and estimating the change in the number of unlike neighbors as a dislocation moved through the crystal. (His analysis was limited and several workers2"6 have since given more complete ones.) Fisher minimized the importance of a strengthening mechanism of this type for paired dislocations in a structure having long-range order. ~ottrell,' however, pointed out that T could be appreciable for ordered crystals having antiphase domains. He attributed the strengthening to the increase in surface energy of the domains as they were cut by paired dislocations. Ardley,' in his test of Cottrell's theory, found that r for Cu3Au crystals obeyed the equation: for 1 > t where 1 is the domain size, t is the domain wall thickness, and y is the surface energy of an antiphase boundary. His experiments represent the classic confirmation of the strengthening mechanism proposed by Cottrell. However, the assumptions involved in using Cottrell's theory are valid only for large domain size in CU~AU,~"~ i.e., when Eq. [2] reduces to: For small domains, ~linn~ has questioned Ardley's assumption that order was complete, and, indeed, Stoloff and ~avies" fpnd it incomplete until a size of approximately lOOA was reached. Even when the order within a domain is complete, it is not obvious how one determines the appropriate value for I in a structure where domains vary in size and are irregularly shaped. The purpose of this paper is to estimate T without restrictions upon the degree of order and domain shape. Our major assumption will be the use of a generalization of the model proposed by Bethe" (the Ising model) for the internal energy. This will in fact allow us to combine the theories for strengthening by short-range order and by antiphase domains into a single, general formalism. We will use the results to estimate the variation in strength of Cu3Au crystals with long-range order8 and the variation in flow stress of FeCo crystals with quench temperature.12'13 INTERNAL ENERGY For simplicity, we restrict our considerations to those binary solid solutions which can be described as an arrangement of atoms on a Bravais lattice. An atom site will be indexed by three numbers (PI, pz, p3) determined by the vector: from the origin fixed at atom (0, 0, 0) to the atom site where a', an, and a, are the lattice translation vectors. We write: For the energy of the crystal where pi(p) is the probability (either zero or one) of finding an atom of type i (i = 1, 2) at site (p), which is shorthand for (pl, pz, p3) and pj(p + r) is that for an atom of type j (j = 1, 2) at the site (p + r), which is shorthand for (pl + rl, The coupling parameter, resents the energy associated with the pair Pi(p), Pj(p + r). The crystal is assumed large enough so that surface effects can be neglected; therefore, trans-lational and inversion symmetry require the coupling parameters to obey the relations

Jan 1, 1969

Page McGREGOR, A. G.-Features of the New Copper Smelting Plants in Arizona. Discussed by L. D. Ricketts, E. P. Mathewson 2145 HOWARD, L. O.-The Basic-Lined Converter in the Southwest. Discussed by Walter Douglas, E. P. Mathewson, Kuno Doerr 2145 SAMUEL, J. MOORE-Determination of Dust Losses at the Copper Queen Reduction Works. Discussed by Walter Douglas, E. P. Mathewson, S. J. Jennings, C. E. Arnold, A. G. McGregor, L. D. Ricketts 2148 MORSE, H. W., AND TOBELMANN, H. A.-Leaching Tests at New Cornelia. Discussed by H. W. Morse, Lawrence Addicks, G. D. Van Arsdale, S. J. Jennings, F. S. Schimerka, C. G. Grabill, F. N. Flynn, Stuart Croasdale 2151 LAIST, FREDERICK, AND ALDRICH, HAROLD W.-The 2,000-Ton Leaching Plant at Anaconda. Discussed by F. N. Flynn, E. P. Mathewson 2159 ADDICKS, LAWRENCE-Possibilities in the Wet. Treatment of Copper Concentrates. Discussed by F. N. Flynn 2160

Jan 12, 1916