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By Irving Fatt, Herman Dykstra

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By C. Y. Wen, H. O. HOPMAN

l. INTRODUCTION. IN casting a thermal balance of the heat generated and absorbed in a blast-furnace treating lead-, copper- and similar non-ferrous ores, assumptions have always to be made for the values of the heat of formation of slag. ? Considering that the larger part of the charge introduced into the furnace comes out in the form of slag, the significance becomes apparent of a lack of heat-values for the singulo-silicate, which is the type of slags commonly made. The aim of the present investigation is to supply these heat-values as far as possible with the apparatus and the time available. The heats of formation of the ferrous and manganous bi-silicates have been determined by Le Chatelier; 1 those of some silicates other than iron and manganese by Tschernobaeff:2 finally Richards 3 gives a figure for a copper blast-furnace slag of known composition. The existing data and those resulting from the present investigation are assembled in Table VI. II. MATERIALS USED. The materials used in the experiments were silica, ferrous oxide, and calcium carbonate. Silica.-The silica sold in the market as chemically pure usually contains small amounts of magnesia, lime, and alumina, and is therefore not suited for the work. The pure material was obtained from clear quartz crystals from Arkansas, broken in a diamond mortar and ground in an agate mortar to pass 1 Comptes rendus, vol. cxx., p. 623 (1895); vol. cxxii., p. SO (1896). 2 Revue de Métallurgie, vol. ii., p. 729 (1905); Electrochemical and Metallurgical Industry, vol. iv., No. 2, p. 72 (Feb., 1906). 3 Electrochemical and Metallurgical Industry, vol. v., No. 7, p. 266 furls?, 1907;) ; Metallurgical Calculations, vol. iii.,.pp. 474, 475 (1908).

Jul 1, 1910

COUNCIL OF ECONOMICS, AIME Formerly Mineral Economics Division Established as a Division December 15, 1948 Established as a Council February 26, 1957 Sheldon P Wimpfen, Chairman John D Ridge, Vice-Chairman (Mining) A J Philips, Vice-Chairman (Metals) Warren B Davis, Vice-Chairman (Petroleum) COUNCIL OF EDUCATION, AIME Formerly Mineral Industry Education Division Established as a Division January 15, 1932 Established as a Council February 26, 1957 James D Forrester, Chairman Charles V Kirkpatrick, Vice Chairman (and Chairman-elect) Lysle E Shaffer, Past Chairman Truman H Kuhn, Secretary-Treasurer Colorado School of Mines Golden, Colorado John S Bell, Contact AIME Director

Jan 1, 1960

By W. WANJUKOW, H. O. Hofman

(New York Meeting, February, 1313.) I. INTRODUCTION. IN the metallurgical treatment of most metallic sulphides it is usually necessary to carry on a roasting-operation. In some cases the raw ore will have to be roasted.; in others the intermediary product, matte, produced in smelting the ore; again, both ore and matte may have to be subjected to oxidation at elevated temperatures. Most metallic sulphides, when given an oxidizing-roast, pass through the state of sulphate before they are converted into oxides. All metallic sulphates are completely decomposed by heat, with the exception of those of lead and bismuth, but the temperatures at which decompositions take place vary with the metals. Some metallic sulphates are converted directly into oxides, others first form basic salts. Alkali-earth sulphates show a behavior similar to that of metallic sulphates, while alkali sulphates do not part with their sulphur trioxide even at elevated roasting-temperatures. The older data on the decomposition of metallic sulphates by beat are only approximations. Thus Kerl 1 gives the order in which metallic sulphates are decomposed with increasing temperatures as (Ag2, Fe, Cu, Zn, Ni, CO, Mn, Pb) SO4. More recent statements give definite temperatures and modify the formerly accepted order of decomposition. But the temperatures given by various observers do not agree. The reasons for this are to be found mainly in the method and manner of carrying out experiments. Four methods have been used: 1. Heating in an evacuated tube; 2, heating in a tube closed at one end, without air-cur-

Sep 1, 1912

By J. C. Fisher

Nucleation theory is applied to martensite nucleation in substitutional iron alloys. Composition fluctuations are neglected, and a steady rate of nucleation is predicted for any composition and temperature. The maximum rate of nucleation (as a function of temperature) is shown to be measurable only for on extremely narrow composition range, being too great or too small outside this range. A number of experimental observations, including completely isothermal transformation in some alloys and composition-dependence of M. temperature in others, are compared with the calculated behavior. IN a previous report,¹ nucleation theory was applied to the formation of isothermal martensite in an Fe-Ni-Mn alloy. The experimental observations of Cech and Hollomon² were accounted for quantitatively. It now is of interest to examine the predictions of nucleation theory with respect to martensite transformation in substitutional iron alloys of other compositions. Since Fe-Ni alloys have received considerable attention, both as to their transformation kinetics and their free energies, they will be treated in detail, although the results apply with equal validity to other substitutional alloys. In substitutional alloys, where composition fluctuations can be neglected in volumes of critical nuclear size, the rate of nucleation of martensite in subcooled austenite is¹ n - Nv exp (—W*/kT) [I] where the free energy of formation of the critical size nucleus is W* = 8192 p (?² s³) [2] In the expressions for n and W*, the symbols have the following meanings: N is the number of atoms per unit volume; v, the atomic vibration frequency; 8, a function of the elastic constants of austenite and the shear angle of martensite; , the austenite/mar-tensite inter facial free energy; and ?fc is the free energy change per unit volume accompanying the transformation. Jones and Pumphrey² have determined the austenite to martensite free energy change as a function of nickel content and temperature for Fe-Ni alloys. Their expression is ?F = 2500 C + 1.25 (1 —C)?FFc cal per mol [3] where C is the atom fraction of nickel, and ?Ffe is the free energy change per unit volume for pure iron as tabulated by Zener4 (or, equivalently, Fisher"). From Eqs. 1 to 3, it is possible to calculate isothermal nucleation rates as a function of temperature and composition for Fe-Ni alloys. The only unknown parameter is (?² s³). The best value of this parameter for Fe-Ni alloys, determined from M. temperatures in a manner to be described shortly, is (?² s³)= 9.92 (10)21 cgs units [4] Taking this value of (?² s³), C-curves for isothermal nucleation were calculated for Fe-Ni alloys of several compositions, and are plotted in Fig. 1. It is evident from Fig. 1 that completely isothermal nucleation of martensite in Fe-Ni alloys can be observed experimentally for only a very narrow range of compositions. Cech and Hollomon find that a nucleation rate of about 10' nuclei per cc per sec is as fast as they can follow dilatometrically, and a rate of about 10-1 nucleus per cc per sec is about the slowest that can be measured conveniently. If the nucleation rate is to lie between the limits 10-1 10 the nickel content of an Fe-Ni alloy must fall in the atomic fraction range 0.299 5 C 5 0.302. Nickel contents lower than 0.299 correspond to nucleation rates too great to follow, and those higher than 0.302 to nucleation rates too slow to measure in a reasonable time.* In view of the narrow corn- position range in which successful isothermal measurements can be made, it is not surprising that only one substitutional alloy has been described' that comes close to being in the proper range.

Jan 1, 1954

The Role of the Drilling Contractor BY FERRIS E. SAINSBURY Ron Haxby, Occidental Minerals What is the best method for drilling a 12-in. diam hole to a depth of 1200 ft and maintaining the deflection within 25ft from vertical? Ferris Sainsbury: In order to drill a 12-111. hole down to 1200 ft, In most places you would have to employ a rotary tricone bit With a down-the-hole hammer, I expect by that depth significant Inflows of water would be experienced Even with foams, we would not be able to get the water out of a hole of that diameter So the down-the-hole tricone method of drilling would be best. To keep it straight, we would probably employ the largest square drill stem compatible with the diameter of the hole. Ron Haxby: Is it common in drilling contracts to put in a vertical hole clause? Ferris Sainsbury: You can put in the vertical hole clause Ron Haxby: Does it cost more? Ferris Sainsbury: Normally, if the hole deviates, the driller can correct it with deflection wedges and will charge it back to you at cost, plus 10% or somewhere along that range Any drill hole has a tendency to go perpendicular to the dip, and there are times when stabilization systems are not successful in preventing the hole from turning into the dip of the formation. The only solution, in this situation, is to go in with an oriented wedge and kick the hole back out.

Jan 1, 1979

By George C. Stone

Since the Troy meeting I have received several additional results of analysis of the same sample of spiegel, which I give below: P. I know only by correspondence. His methods are : for results Nos. 47, 48 (13.03, 13.26) dissolve In hydrochloric acid, evaporate, oxidize with nitric arid, filter from silica, separate iron as basic acetate, precipitate manganese as sulphide, dissolve in hydrochloric acid; and precipitate as carbonate. No. 49 (13.72) was obtained by Eggertz's method. Nos. 50, 51 (13.10, 13.10) were dissolved and oxitfized as before, the iron precipitated by oxide of zinc, filtered and washed four times with cold water; and the manganese titered hot with permanganate. P. regards these two results as low. Nos. 52, 53 (13.75, 13.69) were dissolved and treated like the last two, the precipitated iron was again dissolved, separated, and titered as before; the results are the sum of the manganese joined in both

Jan 1, 1884

By JAMES BRADLEY

THE Spanish mine is in Nevada County, California, 21 miles northeast of Nevada City by road, and 3 miles north of the town of Washington. The mill and surface buildings are on Poorman's Creek at an ele¬vation of 3,000 ft. About 35 men are employed at the property, which is producing 50 tons of ore per day. Electric power, purchased from the Pacific Gas and Electric Co., is brought in from Alleghany, seven miles away. In the early days the mine was operated by F. W. and P. R. Bradley. Between 1883 and 1899 the production was approximately $900,0)0 in gold. The ore treated during; that time yielded an average of 60 cents per ton and was mined and milled at a profit. The surface, oxidized, ore deposit was 30 to 100 ft. wide and was mined by the glory-hole method. The milling-plant at first consisted of a Blake crusher an-1 a small Huntington mill; later three large Huntington mills were added to the plant. In 1893 a new mill was built at a lower adit- It consisted of 10 stamps and four Huntington mills. The gold was secured by amalgamation, the recovery being about 50 per rent.

Jan 1, 1931

By AIME AIME

LOCAL COMMITTEES. GENERAL RECEPTION COMMITTEE.-Mr. and Mrs. H. S. Chamberlain, Mr. and Mrs. J. T. Lupton, Mr. and Mrs. T. H Lasley, Mr. and Mrs. R. S. Faxon, Mr. and Mrs. H. Clay Evans, Mr. and Mrs. C. E. James, Mr. and Mrs. B. F. Thomas, Air. and Mrs. H. S. Probasco, Mr. and Mrs. W. M. Lasley, Mr. and Mrs. L. W. Llewellyn, Mr. and Airs. T. G. Montague, Mr. and Mrs. E. B. Thomasson, Mr. and Mrs. C. F. Milburn, Mr. and Mrs. C. A. Raht, Mr. and Mrs. C. C. Notting¬ham, Mr. and Airs. Z. C. Patten, Mr. and Mrs. Willard Warner, Mr. and Mrs. S. R. Read, Mr. and Mrs. Carl White, Mr. and Mrs. M. M. Allison, Air. and Mrs. C. E. Buck, Mr. and Airs. H. F. Temple, Air. and Mrs. M. M. Hedges, Mr. and Airs. X. Wheeler, Mr. and Airs. John A. Patten, Air. and Airs. N. T. Montague, Mr. and Mrs. R. H. Williams, Mr. and Mrs. T. R. Preston, Mr. and Airs. Morrow Chamberlain, Mr. and Airs. T. C. Thompson, Mr. and Airs. T. L. Montague, Mr. and Mrs. O. L. Hurlbut, Air. and Mrs. C. A. Lyerly, Mr. and Mrs. Garnett Andrews, Air. and Mrs. M. B. Ochs, Mr. and Airs. Webster James, Mr. and Mrs. D. P. Montague, Mr. and Mrs. Z. C. Patten, Jr., Mr. and Mrs. W. A. Sadd, Mr. and Mrs. J. B. Pound, Air. and Mrs. George D. Lancaster, Air. and Airs. J. F. Johnston, Mr. and Mrs. R. W. Barr, Air. acrd Mrs. W. B. Davis, Mr. and Airs. Douglas Baxter, Air. and Mrs. W. R. Crabtree, Mr. and Mrs. Lewis M. Coleman, Mr. and Mrs. Newell Sanders, Mr. and Mrs. E. Y. Chapin, Mr. and Mrs. W: B. Riddell,. Mr. and Mrs. J. B. Frazier, Mr. and Mrs. John A. Moon, Mr. and Mrs. C. D. Mitchell, Dr. and Airs. J. H. Race, Mr. and Airs. A. W. Chambliss, Mr. and Mrs. J. P. Smartt, Mr. and Mrs. J. F. Tarwater, Mr. and Mrs. L. D. Drewry, Capt. and Mrs. A. B. Putnam, Mrs. Minnie C. Ewing, Mr. G. F. Meehan, Mr. Sam S. Gerstle, Mr. P. A. Brawner, Mr. C. M. Preston, Air. George M. Guild, Mr. L. M. Mansfield, Dr. J. W. Johnson, Dr. J. AI. Hogshead. EXECUTIVE COMMITTEE.-H. S. Chamberlain, Chairman; H. S. Probasco, C. M. Preston, H. Clay Evans, J. T. Lupton, M. B. Ochs, C. C. Nottingham, Al. Al. Alli¬son, R. S. Faxon, C. E. James, C. A. Raht. EXCURSION TO CHICKAMAUGA PARK.-T. C. Thompson, Chairman; B. F. Thomas, G. F. Meehan, Morrow Chamberlain, W. J. Bass, J. K. McGoodwin. EXCURSION TO HALES BAR LOCK AND DAM.-R. H. Williams, Chairman; John A. Patten, Newell Sanders, George M. Guild, Capt. A. B. Putnam. EXCURSION TO ROCK-WOOD.-F. H. Clymer, Chairman; T. L. Brown, T. A. Wright, J. P. Tarwater, T. L. Peterman. INSTITUTE HEADQUARTERS.-The Hotel Patten. THE first session, held Thursday evening, Oct. 1, in the Banquet Hall of the Hotel Patten, was called to order by Capt. H. S. Chamberlain, Chairman of the Local Committee, who, in behalf of the city of Chattanooga, extended a hearty welcome to the members and guests of the Institute.

Nov 1, 1908

By Max Hebgen

Within the State of Montana the streams rise in the high mountains at. an elevation of from 5,000 to 8,000 ft. These streams leave the State line both east and west at elevations from 3,500 to 2,400 ft. It is, therefore, apparent. that all these streams have an average fall of 3,000 ft. within the confines of the. State, and many opportunities are presented on all streams. for the development of power, by taking advantage of the natural fall. It is probable that 1,000,000 h. p. can :be developed in the State of Montana. I. NATURAL FEATURES OF STATE AFFECTING POWER DEVELOPMENT. The main. range of the Rocky mountains, forming the Continental Divide, cuts the State of Montana into two parts. The eastern part is drained by the Missouri river and its tributaries, the Madison; Jefferson, Gallatin and Yellowstone, rivers. The western part is drained by tributaries to the Columbia river, the Clarks fork and the Kootenai river. The Clarks fork in turn is formed by the junction of Missoula and Flathead rivers, the latter, draining Flathead lake. The western part of the State. is mountainous and the eastern part is comparatively level. As a natural result the rivers in the western part are capable of generating large amounts of power, while in the eastern part of the State natural power sites are much fewer and farther apart. It also follows that in the mountainous districts large amounts of power are required for the mining industry, while in the eastern part of the State, which is principally devoted to agriculture, power is required in smaller quantities. ?

Jan 8, 1913

By K. H. Heino

Two 200 T/da Lurgi Turbulent Layer fluid-bed roasters have been in operation at Canadian Electrolytic Zinc Limited since 1966. Zinc concentrate containing 52-54% Zn, 9-11% Fe,31-33% S is treated to produce calcine containing 60-62% Zn,10-12% Fe, .l-.3% S as sulphide and .8-1.2% S as sulphate. Each roaster train comprises a waste heat boiler, two cyclones in parallel and a two-field electrostatic precipitator. Distribution of calcine collected is 10-15 percent from bed overflow, 55-65 percent from boilers, 20-25 percent from cyclones and 2-6 percent from precipitators. A Monsanto designed contact plant produces acid at a rated capacity of 365 T/da (100% H2304 basis) from roaster gases diluted to 7.0-7.5% S02. The process steps are gas cleaning and cooling by weak acid scrubbing, acid mist removal in electrostatic precipitators, gas drying in 93.5-96.5% H2304, conversion of sulphur dioxide to sulphur trioxide in a four-pass converter containing vanadium pentoxide catalyst, and absorption of the sulphur trioxide in 98.1-98.3% H2S04. Product acid is 93.2% H2S04. Conversion efficiency is 97-98 percent and overall sulphur recovery from concentrate is 87-90 percent. The adjacent fertilizer plant has a capacity of 135 T/da of P205. The products are 54 percent phosphoric acid, run-of-pile triple superphosphate, and diammonium phosphate. The plant is of Ugine-Kuhlman design and consists of an air-cooled multiple tank reactor, a tilting pan filter, and a forced circultation vacuum evaporator. Triple superphosphate is made on a continuous belt and partially cured in a rotary dryer. Diammonium phosphate is produced by ammoniating phosphoric acid in a single stage reactor. The slurry of ammonium phosphate is granulated in a blunger and dried.

Jan 1, 1970

By AIME AIME

EITHER the 2300 people who came to the Annual Meeting were in a better frame of mind or they were resigned to their fate, or it was a better meeting than usual. Whatever the reason, at the 1nstitute?s 148th meeting the attendance was better than ever before, things went more smoothly than in some previous years, and complaints appear to have been almost entirely absent. Patience was sometimes reauired but. almost without exception, it was forthcorning the well-known recession seems to have given many members enough leisure time to come to the meeting without depriving them of the tangible wherewithal to come.

Jan 1, 1938

Jan 1, 1970

By David J. Mack

A SURVEY and critical appraisal of published information about Young's modulus was originally made by the writer because of a complete lack of information about this very important quantity in works on mechanics, physical metallurgy, physics, and other sciences. It was felt that a comprehensive summary of such information about Young's modulus might be of general interest and may suggest new problems or lines of attack on other problems that involve E. Hence this paper has been prepared even though it is only a review, with no new ideas or experimental data. The references are only those used in assembling the paper. No attempt was made to compile a complete bibliography on the subject of Young's modulus. CALCULATION OF YOUNG'S MODULUS FROM THEORETICAL OR EMPIRICAL CONSIDERATIONS Many attempts have been made to compute E from theoretical considerations. The earliest calculations were probably those of Tomlenson (1883) and Southerland (1891), but Fessenden 41,42 made extensive calculations a few years later and arrived at the relationship: [2E = 78. 101 (_L V] where V is the atomic volume. In 1923, Peczalski,43 working from the same stand-point but with more information available on atomic structure, arrived at an identical relationship, which he expressed as: [E=B(m) 2] where B is a constant of value about 8 • 10 7, p is density and m is atomic weight; the atomic volume, of course, being m/p. Portevin44 immediately pointed out that while the equations of Fessenden and Peczalski were true of the common metals, they gave low values for the refractory metals with high moduli (Fig. I). He showed (Fig. 2) that much better concordance was obtained by means of an empirical equation of the form: [E _ KT'Vb] where K is a constant; T the absolute melting point; V, atomic volume, and a and b constants of value approximately I and 2 respectively. This constant K in the Portevin equation is not necessarily the same for all elements, as shown by Thompson.45 Other equations for E based upon theoretical considerations have been derived by Honda and Yamada49 and Lasareff. 50 The most recent calculations of elastic moduli based upon quantum mechanics are probably those of Fuchs.46-48 He extended the method of Wigner and Seitz for calculating the lattice energy and compressibility of monovalent metals and computed the elastic constants of lithium,

Jan 1, 1945

By H. J. Engell, W. Frank, A. Seeger

SWISHER and ~urkdogan' have determined the solubility of oxygen in a iron. They found it to lie between 7 and 10.5 at.-ppm at 881°C. Using earlier work on the permeability of oxygen in bcc iron,' they arrived at the following expression for the diffusion coefficient of oxygen in bcc iron (k = Boltzmann's constant, T = absolute temperature): where The present authors3 have estimated the activation energy QD for the diffusion of oxygen in bcc iron in two different ways from various experimental data.2'4"6 In the first method QD + QS (QS = heat of solution for oxygen in bcc iron in thermodynamic equilibrium with solid FeO) was determined either from data on the reduction of FeO with hydrogen4 or from measurements of the internal oxidation of silicon in a iron.5 Using an estimate of QS from investigations of the oxygen solubility in 6 iron2 (in thermodynamic equilibrium with molten FeO) Q = 0.97 ev or Q~ = 1.06 ev were obtained. From the magnitude of these values it was concluded that oxygen migrates interstitially in bcc iron and that consequently the activation energy QD for diffusion of oxygen has to be identified with the migration energy E~ of the oxygen atoms. Therefore, for a second estimate of QD from the diffusion coefficient of oxygen in 6 iron at 1450" ~,~ we used the theoretical expression:3 (a = length of elementary cube edge, m = mass of interstitially diffusing atom, sM = migration entropy), applicable to diffusion via the octahedral interstices in bcc lattices. Taking sM = 3.8 k (migration entropy of carbon in a iron), one gets Q = 0.90 ev. Hence, in Ref. 3 Q = (0.98 *0.1) ev was proposed as a plausible value for the diffusion energy of oxygen in bcc iron. sM + 9 (9 = solution entropy for oxygen in bcc iron) can be determined from permeability measurements.4 Using the above-mentioned estimate for QS , the following expression for the solubility c (atomic concentration) of oxygen (in thermodynamic equilibrium with solid FeO) in bcc iron was derived: From [4] the solubility of oxygen at 881°C in a iron is calculated to lie between 0.6 and 12 at.-ppm. We see that the solubility determined by Swisher and

Jan 1, 1969

By M. H. Yoo

Possible interactions of the perfect dislocations of six slip systems or the c dislocation with the (10i2f (ioii), {ioIi}(ioiZ), {1122}(1123), and {1121}(ii26) type twins in hcp metals have been analyzed from the crystallographic and the energetic points of view. Twenty-six distinct types of possible interactions were identified, and those selected based on crystallographic constraints were examined for their energetic feasibilities by use of the anisotropic energy factors. No long-range elastic interaction exists for a dislocation when its Burgers vector is parallel to the twin interface. Under a suitable applied stress, a screw dislocation can cross slip at the twin interface. For basal mixed dislocations in cadmium and zinc, the interaction with {1012} twins is found to be attractive, indicating that incorporation of these dislocations into the twins is energetically feasible and that twin growth will result. On the other hand, the interaction between both basal and Prism mixed dislocations and the {1012} and (1121) twins is found to be repulsive in Mg, Co, Re, Zr, Ti, Hf, and Be. This indicates that under an applied stress a local stress concentration will develop due to a dislocation pileup at the interface, which may result in a site for either the nucleation of other twins or the formation of a crack, depending on the cleavage strength. WHEN a metal undergoes plastic deformation, a certain configuration of slip dislocations will result in a state of dislocation pileup against an obstacle. The stress concentration thus developed may enhance the process of twin nucleation and also twin growth. Furthermore, once formed and dispersed in the crystal, twins can act as effective barriers against slip dislocations. The degree of such mutual influence or interrelation between slip and twinning is generally known to be pronounced in the case of hcp, metals. It is also known that deformation by twinning occurs more commonly in hexagonal metals than in cubic metals. In fact, under suitable stress states, all hexagonal metals exhibit {1012) <1011> type twinning.&apos; In addition to this common type, deformation by (1151) <1126> type twinning occurs in zirconium, titanium, and rhenium, which show remarkable ductility.&apos; The importance of twinning during general deformation to the ductility of hcp polycrystals has been briefly discussed in recent review works.2&apos;3 The purpose of this paper is to analyze the interaction between slip dislocations and twins in the hcp structure and to discuss the nucleation and growth processes of twinning and the role of twinning in the <"°" noil) o, 1/3[112O] (OOO2) 1/3[1123] Fig. l—-Slip systems in hcp structure. ductility of hexagonal metals. The problem will be discussed from the geometric and the energetic points of view in a manner similar to that of the previous work on zinc.4 Since hcp crystals deform by several slip and twin systems, numerous interactions result as possibilities. The Burgers vectors of six slip systems and the c dislocation shown in Fig. 1 and the four twin systems listed in Table I are considered here. A complete tabulation of the possible interactions is followed by discussion of those that are more likely to occur on the basis of crystallographic constraints and energetic considerations. 1) CRYSTALLOGRAPHY OF TWINNING The crystallographic elements, K1, K2, n1, and n2, for the four compound twin systems are now well established.= A unit cell with the base vectors n1, and n2 is shown in Fig. 2 for each twin system. The unit cell before twinning is shown in solid line, and the corresponding unit cell after twinning is shown in dashed line. Also shown in Fig. 2 are the following crystallographic parameters: S is the plane of shear, d the interspacing of the twin habit planes K1,Ø Iis the acute angle between n1, and n 2, e is a numerical factor, and q is the number of K, lattice planes intersected by 17&apos;. These parameters can be expressed in terms of the axial ratio, y = c/a, as listed in Table 11. The macroscopic shear strain of twinning, s, and the magnitude of a "unit twin dis-l~cation,"4 bt, are also expressed in terms of y and given in Table 11. In Table 11, K1 and q1 are given in both Miller-Bravais and Miller indices. In double lattice structures, shuffling of atoms in addition to a homogeneous shear of the lattice is generally required if the original crystal structure is to be restored after twinning. The extent of current understanding on this problem of atom shuffling is per- Table I. Four Twin Systems in Hcp Structure

Jan 1, 1970

By Sydney H., Ball

ONE of the important mineral discoveries of the eighteenth century was , that of the Minas Geraes, Brazil; diamond fields. The production of this and of .other diamond discoveries in neighboring states made Brazil the premier producer of diamonds, succeeding India; its 140 years of supremacy finally passed to- South Africa- 60 years ago. Three times have diamonds contributed heavily to Portugal&apos;s somewhat checkered financial history; first in the sixteenth and seventeenth- centuries when the diamond trade of India was controlled by its citizens residing in ,Goa, later in the late eighteenth and the first 75 years of the nineteenth century when the Brazilian fields were the world&apos;s source of diamonds, and now, when the Angola diamond mines are the principal source of revenue of its colony, Portuguese West Africa. Certain phases in the history of the administration of the Brazilian field are sufficiently curious to warrant description.

Jan 1, 1929

By T. S. Washburn

THE grades of commercial steel produced in large quantities can be divided into two general types from the standpoint of ingot structure-killed and rimmed. Killed steel covers a wide variety with carbon contents throughout the range of the steel portion of the iron-carbon diagram, and is the kind usually used in the production of alloy steels. Rimmed steel is normally associated with carbon ranges under 0.30 per cent, and is not yet used to a large extent in alloy practice, except for copper-bearing steels. The fundamental differences in the ingots made from these two types of steel can be seen most easily in Figs. 1 to 7. In the rimmed ingot shown in Figs. 5 to 7 there are two lines of blowholes approximately parallel to the sides and coming together at the top and at the bottom of the ingot. In the killed ingots shown in Figs. 1 to 4 these blowholes are not present. Also, the rimmed ingot has no well defined pipe, as com-pared to the deep pipe on the killed ingots, and there are numerous pri-mary blowholes in the lower portion of the rimmed ingot perpendicular to the surface and close to it, while on the killed ingot there are no blowholes of this type in the ingot shown in Fig. 1 and very small ones close to the surface in the lower part of the ingot shown in Figs. 2 to 4. With respect to the presence of pipe and the primary blowholes, the structure may vary considerably in both rimmed and killed ingots, therefore these cannot be considered as fundamental structural characteristics differ-entiating the two types of steel. The primary blowholes in rimmed ingots may be much less pronounced than those in the ingot shown in Figs. 5 to 7-as, for example, in "ingot iron," which is entirely free from them. An example of a cross section of an ingot-iron ingot is shown on page 16 of "Research and Methods of Analysis of Iron and Steel," published by the American Rolling Mill Co. (1920). A certain amount of pipe may also occur in rimmed ingots, though it is normally porous and not as well defined or deep as in the killed ingot of Fig. 1. In killed ingots, pri-mary blowholes may occur near the surface, as in Figs. 2 to 4, and

Jan 1, 1937

By G. W. Phelps

The field of industrial minerals is concerned with both sieve size and distribution of sub-sieve particles. A great deal of work has been reported on the techniques designed to provide information of this work. The term sub-sieve is here considered to include particular material that will pass a 325-mesh testing sieve. Plant men require rapid, precise and simple testing techniques that are, if possible, inexpensive with respect to equipment and manpower. A number of particle-size procedures have been developed, based on the Stokes equation for streamline movement of a particle of diam D, moving at velocity V through a liquid of viscosity n. 1 Particles are considered to be rigid, smooth spheres, completely dispersed at low concentration and moving at low velocity through the suspending medium with no slippage between particle and liquid. In particle size determinations the particle moves either from natural gravitational forces or those provided by centrifugal means. The diagram of Fig. 1 shows a spherical particle of density S and diam D moving downward at velocity L/T (or V) through a liquid of density So and viscosity n. The forces of gravity G (natural) or Gc (centrifugal) cause the particle to move through the liquid, thereby creating a viscous drag F or Fc. Within the streamline flow

Jan 1, 1967

By Alfred H. Bell

IN 1945, Illinois produced 75,210,000 bid. of oil, or 4.4 percent of the total for the United States, and ranked sixth in the nation in oil production for the third consecutive year. Production decreased about 3 per cent from that of 1944, when the total Illinois production was 77,413,000 bbl. This is the smallest percentage of decrease in production in the state for any year since a peak was reached in 1940. Daily average production for 1945 was approximately 206,000 bbl. Daily averages by months were as follows:

Jan 1, 1946