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By Richard T. Newcomb

Federal and utility industry research has largely ignored coal beneficiation techniques in the implementation of SOx control. This paper accepts the hypothesis that beneficiation cum scrubbing is the cheapest way for the vast majority of seams in the eastern coal provinces to comply with standards. Comparisons are based on point estimates of average beneficiation costs from a model of coal preparation (COBET) designed to simulate four levels of cleaning. The paper describes how economic theory can be applied to derive econometric supply functions from actual data on the geology of minable seams, washability and technical constraints. West Virginia is taken as an example of a producing region. Spatial supply functions are derived empirically from the engineering model simulations.

Jan 1, 1977

HE purpose of this chapter is to present a general outline of the basic open-hearth process for the benefit of students, practicing open-hearth operators, and metallurgists who wish to review the subject. The discussion is limited to a description of the sequence and purpose of the operations, illustrated by data and examples. Subsequent chapters deal with more detailed and fundamental studies of the subject. The function of the basic open-hearth furnace is to convert various types of ferrous material into finished steel of given composition and quality. In comparison with other steelmaking methods, the basic open-hearth process is one of the most versa- tile, both from the standpoint of the raw materials that can be used and the types of steel that can be produced. The process can be considered as a sequence involving melting, refining, and deoxidation. With some types of liquid-metal charges, the melting stage is not present, but refining and deoxidation in varying degrees are fundamental features of the process. GENERAL DISCUSSION OF BASIC OPEN-HEARTH PROCESS The first consideration in open-hearth practice is the type of charge on which the operation is based. This consists of three components-fluxing, oxidizing, and metallic materials. Fluxes. In the basic process the fluxing material is primarily lime, added in the form of either limestone (CaC03) or burnt lime (CaO). This is supplemented by magnesia (MgO) and lime from the furnace bottom and banks. The function of these fluxes is to form a slag with the silica (SiO2) , manganese oxide (MnO), iron oxides (FeO and Fe2O3), and phosphorus oxide (P2O5) that are produced by the oxidation of varying amounts of the silicon, manganese, iron, and phosphorus in the charge during melting and refining. The slag, composed of the basic fluxes and the neutral and acid oxides, floats on top of the steel bath when the charge is melted. The composition of this slag depends on the amount of each slag-forming element present in the charge and on the extent of oxidation of these elements during the course

Jan 1, 1951

By R. A. Bloom, John Birtalan

CONSIDERABLE interest has been shown in recent years toward determining the crystal structure, mode of formation, and chemical composition of the x phase, designated as such by Andrews,' who was the first to establish its presence in Fe-Cr- Ni-Mo alloys . Later work2 by the same author has shown that the occurrence of x depends on the presence of some molybdenum in the alloy. The phase, which appears to be identical or very similar to a manganese, has a body-centered-cubic structure and is closely related to s phase. Koh observed a similarity in composition between x and s and speculated as to whether x might be an ordered structure of u which is known to have a tetragonal crystal

Jan 1, 1957

International Trade in Nonmetallic Minerals. BY J W FURNESS AND E W PEHRSON (Man &. Met, Sept, 432 2500 words) International trade in nonmetalic minerals (exclusive of fuels) is dominated largely by fertilizer raw materials such as phosphate rock, potash, nitrates, sulphur and pyrites and the miscellaneous group of minerals including asbestos, mica, graphite, fluorspar and china clay Cost of trans¬portation deters any substantial movement of the building materials which usually occur widely in nature and are thus available near consuming centers at relatively low cost This paper, which presents a summary for 1932 of the world production, consumption and principal trade relations of asbestos, china clay, fluorspar, graphite, gypsum, mica, phosphate rock and potash illustrated by world charts, is based on an original study of 15 nonmetallic minerals conducted by the U S Bureau of Mines Practical and Legal Aspects of Mme Financing See METAL MINING Economic Significance of High-grade Concentrates See MILLING AND CONCENTRATION

Jan 1, 1937

By John G. Tate, George W. Nicolson, James L. Bruce

FOR more than 25 years modern mining has been carried on in the Island of Cyprus, Mediterranean Sea, by the Cyprus Mines Corp. of Los Angeles, Calif. The general features of these operations have been described.1 From 1935 to June 30, 1940, top slicing in the Mavrovouni mine produced in excess of 2,000,000 long tons. The rate for the last part of this period was approximately 50,000 tons per month. DESCRIPTION OF ORE BODIES The shape of the ore body now being top sliced in the Mavrovouni mine is an inclined irregular pyritic pipe or chimney of large dimensions, extending from unknown depths below the bottom level at elevation 250 ft below sea level, to the highest level at elevation 400 ft above sea level. The present surface above the ore body lies between 550 and 650 ft elevation. Undoubtedly the ore body extended to surface and was mined by the ancients by opencast and underground methods. The old pits were gradually filled up by erosion until now they show as slight depressions in the topography. The largest area of the ore body is at elevation 170 ft below sea level, where the horizontal section is almost elliptical, with a width of 600 ft and a length of 1000 ft. Below this elevation the shape of the ore body continues to be elliptical but with reduced dimensions. Above this elevation it rises flatly towards the south with a substantial depression in the upperside of the chimney and irregular ridges or wings rising on each side. It gradually grows smaller as it rises. The ore body is a pyritic replacement of andesitic extrusives which occur as flows and pillow lavas. With the exception of the upper portions of one or two small offshoots rising from the main ore body, all ore is completely surrounded by andesite. Most of the andesite lying above the ore body is covered by marl and clay sedimentaries of Miocene and later age. The Miocene is presumed to be older than the ore mineralization. That portion of the andesites which lies between the sedimentaries and the ore body has been broken by slumpage, and weathered, and iron-stained by the descending meteoric waters. It is a mass of crushed material that caves and follows downward readily as the top-slice stopes retreat. The main ore body is a heavy cupreous pyrites mass assaying on the average about 4.0 pct Cu; 48.0, S; and 42.0, Fe. In places the copper drops below 1.0 pct. On the borders of this heavy sulphide ore body lie disseminated cupreous pyrites ore deposits of large dimensions. Some portions of these appear to be closely related to the heavy sulphide ore, as the ratio of copper to pyrite is about the same. The greater part of the disseminated ore, most of which lies immediately to the east of the main ore body, contains less than 0.10 pct Cu and about 25.0 to 30.0 pct S. This probably can

Jan 1, 1947

By B. Post, F. W. Glaser

Three borides of zirconium have been reported: ZrB,l ZrB2,2,3 and ZrB12, 4 The phase relationships, ranges of stability, and some physical properties of these compounds are described. THE zirconium borides differ considerably from one another, particularly with respect to their relative stabilities at high temperatures in the presence of carbon.4,5 ZrB2 is extremelv stable at all temperatures (to the melting point) in contact with carbon. Both ZrB and ZrB12 tend to decompose at elevated temperatures when carbon is present in excess of about 0.5 pct. ZrB forms ZrB2 and ZrC, and ZrB12 decomposes to form ZrB2 and a boron-carbide phase. In the ZrB12 preparation, boron present in excess of that needed to form ZrB2 reacts with carbon, if present, to form carbides, in preference to forming the higher boride. Similar instability of borides, other than diborides of the transition metals of the 4th and 5th groups of the periodic table, has been reported.5,6 special precautions had, therefore, to be taken to minimize carbon contamination in the preparation of ZrB and ZrB12. Reactions below 1400°C were carried out by heating powdered mixtures of zirconium hydride and boron in quartz tubes in a hydrogen atmosphere. For temperatures above 1400°C, reactions were carried out in graphite molds. Carbon contamination from the molds was minimized by employing extremely rapid heating rates to reduce carbon diffusion into the body of the specimen, and by subsequent "shaving" of sample surfaces that had been in contact with the graphite dies. A heating rate of about 2000°C per min was obtained by heating the dies (by direct conduction), using a current of 40,000 amp. Although this type of heating cycle apparently allowed little time for "homogenization," close approximations to equilibrium conditions were usually obtained as a result of the very strongly exothermic reactions between zirconium hydride and boron at elevated temperatures. Reproducibility of results in repeated runs under varying conditions was taken as a reasonable indication that equilibrium conditions had been effectively achieved. Quenching was accomplished by rapidly immersing the entire die, containing the reaction products, in water. Specimens could also be cooled at controlled rates by adjustment of the rate of flow of water through the water-cooled copper electrodes in contact with the graphite dies.

Jan 1, 1954

By Cyril Wells, Robert F. Mehl

The practical importance of a knowledge of the rates of diffusion of carbon and of alloying elements in steel has often been pointed out.l,13 This importance lies chiefly, though by no means only, in the study of carbufizing and in the study of reactions involved in the eutectoid inversion in steel. The present paper is one of a series in which the rates of diffusion of carbon and of alloying elements in ?-Fe and their mutual effects are measured with precision. The present paper reports the results of measurements of diffusion coefficients D of manganese in ?-Fe over wide ranges of temperature, and concentration, and of the effect of carbon and impurities and of grain size upon these diffusion coefficients.‡ Data on the rate of diffusion of manganese in ?-Fe have been reported by Fry2 and by Paschke and Hauttmann.3 Claussen4 calculated the diffusion coefficient D from Fry's data as 3 X 10-10 sq, cm. per set. at 960º, which will be shown to be incorrect by many orders of magnitude. Paschke and Hauttmann gave a rough value of 9.6 x 10-8 Sq. cm. per set. at 14000. Neither of these workers considered the variation of D with concentration and with temperature, and neither studied the effect of carbon. Method and Materials Method.—The method employed is identical with that used earlier.5 Owing to the volatility of manganese and the consequent loss of manganese from the outer surfaces of the welded diffusion bars, these surfaces were discarded. The diffusion anneals were performed in argon, except One (test 18) in which hydrogen was employed for purposes noted below. The temperatures reported are accurate to about 3" and constant within 1°C; the diffusion times are reported to the nearest half hour. The specimens were furnace-coo1ed after the diffusion ation, at about 2° per min. Layers, usually 0.004 in. thick, parallel to the welded interface, were machined from the specimens after the diffusion anneal and analyzed for manganese to 0.I Per cent Mn; the distances of these layers from the interface was measured to ±0.0002 in. The concentration-penetration curves obtained were analyzed by both the Grube and the Matano solutions.8 The D values calculated by these two methods do not differ appreci000. The Grube solution was used except in tests in which the effect of concentration upon D was greater than so per cent; in such cases the Matano method, which explicitly provides for the variation of D with concentration,' is the more reliable. In general, the number of layers machined from the zones of variable composition were large enough to permit the use of the average layer composition as that of the center of the layer. In 3 of the 3' tests, however, this is not justified, and the D values

Jan 1, 1941

By Cyril Wells, Robert F. Mehl

The practical importance of a knowledge of the rates of diffusion of carbon and of alloying elements in steel has often been pointed out.l,13 This importance lies chiefly, though by no means only, in the study of carbufizing and in the study of reactions involved in the eutectoid inversion in steel. The present paper is one of a series in which the rates of diffusion of carbon and of alloying elements in ?-Fe and their mutual effects are measured with precision. The present paper reports the results of measurements of diffusion coefficients D of manganese in ?-Fe over wide ranges of temperature, and concentration, and of the effect of carbon and impurities and of grain size upon these diffusion coefficients.‡ Data on the rate of diffusion of manganese in ?-Fe have been reported by Fry2 and by Paschke and Hauttmann.3 Claussen4 calculated the diffusion coefficient D from Fry's data as 3 X 10-10 sq, cm. per set. at 960º, which will be shown to be incorrect by many orders of magnitude. Paschke and Hauttmann gave a rough value of 9.6 x 10-8 Sq. cm. per set. at 14000. Neither of these workers considered the variation of D with concentration and with temperature, and neither studied the effect of carbon. Method and Materials Method.—The method employed is identical with that used earlier.5 Owing to the volatility of manganese and the consequent loss of manganese from the outer surfaces of the welded diffusion bars, these surfaces were discarded. The diffusion anneals were performed in argon, except One (test 18) in which hydrogen was employed for purposes noted below. The temperatures reported are accurate to about 3" and constant within 1°C; the diffusion times are reported to the nearest half hour. The specimens were furnace-coo1ed after the diffusion ation, at about 2° per min. Layers, usually 0.004 in. thick, parallel to the welded interface, were machined from the specimens after the diffusion anneal and analyzed for manganese to 0.I Per cent Mn; the distances of these layers from the interface was measured to ±0.0002 in. The concentration-penetration curves obtained were analyzed by both the Grube and the Matano solutions.8 The D values calculated by these two methods do not differ appreci000. The Grube solution was used except in tests in which the effect of concentration upon D was greater than so per cent; in such cases the Matano method, which explicitly provides for the variation of D with concentration,' is the more reliable. In general, the number of layers machined from the zones of variable composition were large enough to permit the use of the average layer composition as that of the center of the layer. In 3 of the 3' tests, however, this is not justified, and the D values

Jan 1, 1941

By E. O. Kirkendall

THE investigation reported herein was undertaken to obtain data to supplement those presented in an earlier paper,' particularly for longer times at a higher temperature. This information may further develop our knowledge of the mechanism of diffusion in substitutional solid solutions. Diffusion of solute atoms interstitially dissolved is not difficult to visualize; it can take place without much disturbance of the solvent atoms. The mechanism of diffusion of solute atoms substitutionally dissolved is not so easily understood. Many theories have been advanced. Rosenhain,2.3 Frenkel,4 Smekal,5 Langmuir,3,6 Steigman, Shockley and Nix,7 and Johnson8 all proposed theories to explain diffusion. Langmuir's proposed mechanism consisted of a simple cyclic interchange of atoms involving an interchange in lattice positions of four or more atoms. This mechanism, accepted by the author at the time of his previous publication,' and apparently quite generally accepted, required a net exchange in positions of both solute and solvent atoms in equal numbers. In other words, the rate of diffusion of the solvent and solute atoms would be the same. That this cyclic interchange in lattice positions of solute and solvent atoms in equal numbers is the only true mechanism of diffusion is denied by the evidence presented in this paper. EXPERIMENTAL PROCEDURE This modification of similar procedure1 will be outlined briefly. The method consisted of the following steps: I. A pure Muntz metal (60.6 per cent Cu, 0.1 per cent total impurities) that was almost all beta brass at 780°C. was chosen. 2. The brass was turned between centers in a lathe to a diameter of 0.5965 inches. 3. After the brass was cleaned, it was electroplated with pure copper to a diameter of about one inch. 4. The sample was heated slowly to 400°C. under reduced pressure and held at that temperature for 4 hr. to remove occluded gases. It was then cooled to room temperature. 5. The sample was heated to 780°C. ±3°C. and held at that temperature for different lengths of time; then quenched. Samples were cut off each time after quenching. Metallographic samples 34 in. thick were removed at I hr., 6 hr., 24 hr., 96 hr. and 701 hr. After 96 and 701 hr. samples of about I in. were removed for X-ray analysis. 6. The metallographic samples were polished on the cross section and photo-micrographs were taken. 7. The I-in. samples were polished and etched on both ends. With the aid of a microscope each was carefully mounted in a four-jaw chuck in a lathe, so that they could be accurately bored for an arbor. 8. Turnings were taken for each X-ray sample. After each set of turnings, the sample was heated in an oil bath for about 3a hr. at 300°C. It was then etched in 25

Jan 1, 1942

By J. R. Cain

ROLE OF GASES IN FERROUS -METALLURGICAL PROCESSES IN every process for making steel there are one or more stages where the metal is exposed to gas of one kind or another. Thus, in the open-hearth furnace, the carbon dioxide and water vapor in the products of combustion are oxidizing toward the ferrous and manganous oxides in the slag, tending to convert these to higher oxides; the higher oxides then oxidize the steel, so that indirectly the products of combustion are oxidizing toward the steel. In the Bessemer process, there is direct contact of air and steel; also, the water vapor in the air blown into the converter is continually decomposed by the molten steel, yielding hydrogen and ferrous oxide, both of which are in part taken up by the metal. In the electric-furnace processes, there is always more or less air in contact with the slag covering the metal, and this air and the gaseous reaction products from it are dissolved in the slag to some extent and thus transmitted in part to the steel. In the crucible processes, there is always entrapped air in the charges and the crucibles are more or less permeable to the gaseous products of combustion from the furnace. In all the processes of manufacture, the molten metal is exposed to air while tapping into ladles and ingot molds and has an opportunity to saturate itself with air or with gaseous or solid products generated by chemical reactions between air and steel. Sieverts1 has shown that molten metals require but a few seconds to saturate themselves with a surrounding gas. No one familiar with the operations at a steel plant needs to be reminded of the important role that gases play at all stages. The familiar "boil" of open-hearth furnaces, due to evolution of carbon monoxide when iron ore is added to the molten steel; the spectacular operation of the Bessemer converter brought about entirely by a gaseous reagent; the almost magic effect of small quantities of silicon manganese or

Jan 8, 1919

By Luiz C. Correa da Silva, Robert F. Mehl

A. D. Le Claire and R. S. Barnes (Atomic Energy Research Establishment, Harwell, Didcot, Berks., England)-—This much awaited paper admirably confirms that the Kirkendall effect is a true diffusion phenomenon and likely to be found in all diffusing systems. The most likely explanation put forward so far to account for the shift of interface is that the two components of the system, diffusing in opposite directions, do so with unequal rates so that there is a net loss of material from that half of the diffusion zone rich in the more rapidly diffusing component. This loss is accompanied, and at least partly compensated for, by a closing up or decrease in volume of this latter half of the diffusion zone and an expansion of the other half so as to tend to keep constant the overall volume per atom. This is manifest as a movement of the original interface. If this is a true picture of what is taking place then there are at least two important matters requiring further study."1—The quantitative relating of the observed shift with the independently measured separate diffusion coefficients of the two diffusing species."2—A detailed study of the mechanism and characteristics of the closing up process."We would like first to make a few remarks pertinent to these topics. In connection with the first of these, it is a pity that more and detailed measurements were not made on the Au-Ag system, the only one for which the separate diffusion coefficients of the two species have been measured.'" One of us (A. D. Le C.) has calculated from Johnson's results the shift to have been expected in samples D.2 and D.3. Darken4 showed that the velocity v with which the markers move is related to the separate diffusion coefficients Dau, Dag, by the eauation:"dN"v = (Dag — Dau "dx"dN"where .is the concentration gradient at the mark-ax"ers. Under certain conditions,4, 20 it can also be shown that:"Xm"v = "2t"where x, is the total marker shift after time, t:"dN". . xm = 2t (Dag — Dau) [9]"dX"Johnson measured Dag and DAu in a chemically homogeneous alloy and so his reported figures represent the true or ideal diffusion coefficients"; the same quantities in eq 9 represent the actual diffusion coefficients as would be measured in the presence of a chemical concentration gradient, so we need to multiply Johnson's reported values of Dag and Dau by the"1 before insert-dlogN "ing them in eq 9. 7 is the activity coefficient of Ag at the concentration prevailing near the markers which we shall assume to be - 50 pct. The values of the thermodynamic factor for N = 0.5 and the temperatures at which D.2 and D.3 were annealed were obtained from thermodynamic data quoted by Darken.' aN/ax was computed from the coefficient of inter-diffusion of Au and Ag given by Johnson on the assumption that in the samples D.2 and D.3, the concentration distance curve could be represented by the standard equation:""No is the original difference in concentration between the two halves of the couple, and + is the error or probability function."aN/ax at x = 0 is then given by:"adN/dx "2/nDt"and we assume that this represents the concentration gradient at the markers, although it is probable that the figure is slightly high."When all the appropriate quantities are inserted in eq 9, we find that the expected shifts are: for D.2, 0.0134 cm and for D.3, 0.0119 cm."The agreement between these results and those

Jan 1, 1952

By William S. McAleer

Two major trends in the coal industry today focus attention on the need for heat-drying equipment of a simpler, more flexible and less expensive type than has been considered standard equipment for drying coal. These trends are: I. The tremendous growth in the use of mechanical equipment to load coal both in underground mining and strip mining, which necessitates efficient mechanical cleaning of the fine as well as the coarse coal and thus means a growing tonnage of washed fine coal? with its attendant moisture problems. 2. The growing consumer demand for the smaller sizes for use as domestic stoker coal, with increasingly rigid specifications covering size, ash, and moisture analyses. ACCEPTED PRACTICE In the past, when, for example, 4 in. too coal has been washed, there was little trouble in producing a washed product 4 to o with a satisfactory resultant moisture. The 4 to 3/8-in. could be taken from dewatering screens at a surface moisture ranging from 2.5 to 3.5 per cent, depending upon the size consist. The 3/8-in. to o coal was generally dewatered satisfactorily with centrifugal driers, to final surface moistures from 5.5 to 8 per cent, again depending upon size consist. The centrifugal type of drier has definitely proved itself to be the most economical type of machine to handle coal approximately 3/8 in. to o as recovered by dewatering screens or drainage elevators with 15 to 25 per cent surface moisture and turn out a product with moistures as stated above. Sometimes such moistures (5.5 to 8.0 per cent) in the product are satisfactory. If not, an ultimate moisture, lower than 3 per cent, is seldom required and the centrifugal drier removes 70 to 85 per cent of the total moisture to be removed. In certain districts there has been a growing tendency to circumvent the use of centrifugals or other types of driers, by dewatering over screens of the wedge wire type and wasting all the finer sizes. Sometimes all the minus 28-mesh has been wasted and often the size wasted has been as large as 1/8-in. By wasting these finer sizes, a lower moisture can be obtained in the finished product, but taking into account the cost of the tonnage so lost, plus the added cost of ultimately disposing of this wasted tonnage, often the cost will be greater than the cost of heat-drying in a modern plant, which makes possible the recovery of all the tonnage. Moreover, with the moisture standards for domestic stoker equipment even these wasteful approaches to its solution do not solve the problem and there remains only the alternative of heat-drying. HEAT-DRYING Until about four years ago, heat-drying of coal at the preparation plants was confined chiefly to drying the fine sizes (approximately 3/8 in. to 0). Occasional

Jan 1, 1941

By C. H. Ma, J. S. Makris

This paper describes a modified X-ray diffraction microscope wzethod based on the general principles of Berg-Bawett's Method, Lang's Method, and Woosters1 Technique. This new method may be used for stationary or oscillatory photomacrographs, with both reflection and transmission techniques. In the stationary technique, a small point-source of a divergent X-ray beam of white radiation is used; in the oscillatory technique, a monochromatic divergent beam is employed. The chief advantages of the method described herein are that only approximate alignment of the Bragg angle -of-interest is needed during exposure, and that a large portion of a crystal-specimen surface can he irradiated. In recent years, the study of dislocations through X-ray diffraction microscope techniques has received considerable attention as concerns the per,fection of single crystals. Very promising results have appeared in the literature.'-' These techniques are very useful when the dislocation density of a crystal is near 105 per sq cm or lower. The principle of X-ray diffraction microscopy is based on the differential effect of X-ray primary extinction between the distorted parts and the perfect parts of a crystal. When an X-ray beam impinges on a set of planes of a crystal at the correct Bragg angle, diffraction of X-rays will occur with a 90-deg phase shift of the diffracted beam. This once-diffracted beam still forms the correct Bragg angle with the planes ahead of it, if the planes are not distorted. Thus, part of the strength of the once-diffracted beam is rediffracted and the beam continues to travel in the direction of the primary X-ray beam. This twice-diffracted beam not only takes away part of the strength of the once-diffracted beam, but also causes destructive interference with the primary beam because it now is exactly 180 deg out of phase with the primary beam. As the primary beam goes farther and farther into the crystal, its intensity is continuously weakened. Asa result, the ultimate X-ray diffraction power of a set of undistorted planes is largely extinguished. This phenomenon is called primary extinction.1,2'4 If the set of planes ahead of it is distorted, the once-diffracted beam will have less chance to be rediffracted, because it could not meet the exactly correct Bragg angle for rediffraction. If a part of the beam does rediffract, this twice-diffracted beam is not exactly 180 deg out of phase with the primary beam, and thus it causes less destructive interference. As a result, the registered X-ray diffraction power of the distorted part of a crystal appears stronger than that of the perfect part. Thus, point-by-point contrast of a diffraction image is theoretically possible from a crystal containing dislocations. Two most popular X-ray diffraction microscope techniques today are Berg-Barrett's Method and Lang's Method. Both of these techniques require a

Jan 1, 1964

By R. N. Thurston, E. A. Nesbitt, G. Y. Chin

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deformation gradient matrix, F - [axi/aXj1, where X and x refer to the initial and final positions of a particle. This matrix is readily evaluated in terms of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip system. In the case of deformation from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Goler and Sachs.4 Taylor and Elam5 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(dN as N — m while a — 0 in such a way that the Product Na = 0, a ftnite conslant designatzng the accunzulated amount of shear. It turns out that this limit is simply , where F, is the matrix whose elements are the coefficients of a in the F(a) matix. Application is made of the present treatment to a fcc crystal of Perlrzalloy compressed on the (110) plane and contrained to elongate zn the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By R. T. Hukki

This paper presents a preliminary analysis of the fundamental relationship between the net energy used and the respective product size throughout the entire range of sizes covered by crushing and grinding, and an attempt to find a sensible correlation between the existing theories. Walker, Lewis, McAdams, and Gilliland' have given the following differential equation of a general form for comminution: dE = -C§ [1] where E is the net energy required per unit weight in a certain process of comminution; x is the factor indicating the fineness of the product; n is the exponent indicating the order of the process, and C is a constant related with the material, units chosen, etc. H exponent n in the above equation is replaced by numerical figures 2, 1, and 1 1/2, the integrated form of the general equation leads to the well known fundamental theories represented by the law of von Rittinger,' law of Kick, and the third theory of comminution by Bond, respectively. The total net energies (E) from infinite feed size to a product of size x are as follows: The net energy required in a certain process of comminution is proportional to the new surface developed according to the law of von Rittinger, to the weight or size of the bodies treated according to the law of Kick, and to the length of the new cracks formed which initiate breakage according to the theory and explanation by Bond. On a logarithmic paper, where particle size is presented on the abscissa and energy consumption on the ordinate (see Fig. 21, all three relationships are represented by straight lines. The slope m of the line according to the law of von Rittinger is equal to -1.0; of Kick, 0; and of Bond, -0.5. Experimental evidence in favor of the law of Rittinger has been presented, e.g., by Gross and zimmerley5 on quartz crushed in a drop weight crusher and evaluated for surface by the method of dissolution, by Dean on magnetite crushed by a similar method and evaluated for surface by the determination of coersive force, by piret7 and co-workers on a group of minerals crushed again by a similar method as well as by compression and evaluated for surface by permeability and gas adsorption methods, and by schellinger8 on a group of minerals ground in a calorimetric ball mill and evaluated for surface by gas adsorption. Experimental evidence in favor of the law of Kick seems to be scant in the field of comminution. On the other hand, in the field of mechanical engineering Kick's law seems to be of fundamental nature in processes such as cutting, pressing, shaping, and rolling of metallic substances. Experimental evidence in favor of the third theory has been provided by Bond." To a large extent, data are based on the vast amount of grindability tests performed in the laboratories of Allis-Chalmers Manufacturing Co. In addition to the devoted proponents of one or the other of the basic theories listed above, certain investigators have indicated that one of the theories might be applied for a certain range of sizes, while another theory might be used for other sizes. In a discussion of a paper by Bond," Dobie" presented a statement at the International Mineral Dressing Congress in London (1952) indicating that 1) for large particles, the law of Kick was approximately correct; 2) for finer particles, von Rittinger's suggestion was nearer to the truth; and 3) Bond's new

Jan 1, 1961

By W. M. Peirce

FOR many years it was considered quite the proper introduction to any discussion of zinc metallurgy to remark that the methods of extracting zinc from its ores were archaic. Often there was an added implication that the industry in every phase savored of the days of alchemy. On rare occasions comments of this sort may still he heard. Fortunately, not only for the zinc industry but for the world at large, there is today no longer a basis for considering zinc metallurgy unprogressive. Progress in any industry is possible along three distinct lines. The methods of production may be improved, thereby reducing costs. In the case of basic materials, this may also have the important effect of increasing potential supply. Second, quality may be improved. Finally, the product may be made more valuable to consumers through increased knowledge of its utilization, thus holding old markets or opening new.

Jan 1, 1931

By W. F. Holbrook

THE problem of sulfur control is important in all blast-furnace operations but particularly for certain grades of steel because of the rigorous specifications. During the past decade the tendency has been to produce pig iron, and, hot metal of lower sulfur content. As most of the sulfur in the ion originates in the fuel, the use of high-sulfur coke demands modifications in practice to meet sulfur specifications. While it is generally known that high temperatures and more basic slags favor desulfurization, operators as a rule produce the most acid slag that will permit proper desulfurization. The viscosity of blast-furnace slag has been thought to be related to desulfurization and has been investigated by Feild and Royster1, also McCaffery and his associ-ates2, but apparently no systematic effort has been made to determine the relative desulfurizing powers of slags over the range of composition encountered in practice.

Jan 1, 1936

By Henry Mulryan

DIATOMS are microscopic aquatic plants of the order Bacillariaceae. They are unicellular plants with skeletons made up of amorphous opaline silica. The skeletons show highly ornate, complicated geometrical designs. Diatoms live in water virtually everywhere. They are found in clean sea water, brackish water, and fresh-water lakes and ponds. When conditions are right, diatoms propagate by subdivision in huge numbers. Alkalinity, temperature, and the presence of high concentrations of silica in the water largely control diatom life. When the diatoms die the skeletons drop to the bottom of their habitat to form oozes of varying thicknesses. DIATOMITES Diatomite, or diatomaceous earth, is composed essentially of the siliceous remains of the diatoms, although other organic skeletons are also present, especially in sea-water deposits where radiolaria, sponges and silico-flagellates are common. Impurities are generally carbonaceous material, fine-grained silt, volcanic ash and dust, and occasional coarse grains of sand. Diatomites are marine, brackish, or fresh-water, depending upon types of diatoms and their method of deposition. DIATOMS More than 8000 species of diatoms have been named and classified. Some are definitely classified as to their habitat; some are so well recognized as to their living conditions that they can be stated to be diagnostic types, and when encountered in a deposit determine the origin of the deposit. Some of the commoner types of diatoms found in the fresh-water diatomites on the Pacific Coast are: [Cymbella lanceolata Agardh Fragilaria virescens Ralfs Encyonema prostratum Ralf s Diatoma vulgare Bory Surirella biseriata Brebison Eunotia major Ehrenberg Amphipleura pellucida Kutaing Stictodiscus niagarae Ehrenberg Gomphonema geminatum Lynberg Melosira granulata Ehrenberg]

Jan 1, 1939

By E. Teghtsoonian, K. G. Davis

Cobalt crystals of commercial purity have been tested in tension. Their resolved shear stress-shear strain curves are very similar in form to those for zinc, magnesium, and cadmium. There is an initial linear region for shear strains up to around 150 pct, the ratio of work hardening slope to shear modulus at room temperature being about 2 X x This is followed by an upturn, which is, PLASTIC deformation in metal single crystals with close-packed structures has been found strongly dependent on stacking-fault energy. The high stacking-fault energy hexagonal metals magnesium, zinc, and cadmium have been quite extensively tested, but up to now no data have been available for a comparable hexagonal metal with low stacking-fau1t energy' An however, smaller in magnitude for cobalt than for the other metals. Values for the critical resolved shear stress rise from 97 kg per sq cm at room temperature to approximately 170 kg per sq cm at -196 °C. The Cottrell-Stokes ratio is not constant either for variations in the strain rate or for temperature changes, its value decreasing with strain. investigation into the plastic deformation of cobalt, which has a very low stacking-fault energy, has therefore been undertaken. EXPERIMENTAL PROCEDURES Cobalt crystals in the form of rods 0.3 cm in diam were grown in an electron-beam floating-zone refiner at a rate of zone travel of 25 cm per hr. Details of the growing procedure are given in Ref. 1. The zoned cobalt rods had the following analysis:

Jan 1, 1963

Iron Ore Resources of the World (Die Eisenersvorrate der Welt)_ By G. Einicke. Verlag Stahleisen, Dusseldorf, 1950. 418 p., with 192 tables and an atlas volume containing 100 p. of reaps. 66 German Marks.-A notable work in which the latest available information on iron ore deposits has been compiled by diligent work, continent by continent, country by country. The author reveals the effect of geological formations, iron content of ore, accessability, cost of transportation, political and economic considerations. Ore beds of importance to the German iron and steel industry are given more space than others. The bibliography contains almost 250 references. A tragic comic feature is the author's complaint that as soon as a map of iron ore resources of a country has been completed, the country's boundaries are changed. Reviewed by W. Trinks, Carnegie Institute of Technology. Industrial Research Laboratories of the United States. National Research Council, Washington, D. C. Ninth Edition. 1950. 445 p. $5.-Contains information on the research laboratories of 2845 industrial and commercial organizations, including names of research executives, location of labs, types of activity, whether any consulting services are offered. There are two appendices, one of which lists data on government labo ratories which cooperate with industry, and the :)ibex naming universities and colleges offering research services to industry.

Jan 2, 1951