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By F. N. Rhines

DESPITE the large amount of study which has been devoted to the subject our present knowledge of the copper-oxygen system remains incomplete and unsatisfactory in many respects. This applies particu-larly to those regions in which solid metallic copper exists. The primary object of the present paper is the contribution of new information relative to the solid solubility of oxygen (or cuprous oxide) in copper at atmospheric pressure, together with certain observations in the low-pressure regions of the system. It seems appropriate also to present a brief summary of the outstanding previous work on the constitution of mixtures of copper with its lowest oxide in order to show the relation between the new facts and the system as a whole. The earliest recorded investigations of the copper-oxygen system are those of M. S. Lucas (1) § and of M. Chevillot(2) in 1819 and 1820. Lucas believed that liquid copper is capable of dissolving its oxide, but neither he nor Chevillot was able to furnish convincing proof of this property. It was not until 1866 that T. Graham° definitely established the existence of such a solubility. Nine years later W. Hampe(4) measured its extent and roughly outlined the copper-rich portion of the system. The first really precise examination of the constitutional relationship between copper and cuprous oxide, however, was that of E. Heyn(5) who in 1900 published a temperature-concentration diagram covering the range from 0 to 10 per cent of cuprous oxide at atmospheric pressure. Within these limits of composition cuprous oxide was found to dissolve in liquid copper, forming at 3.4 to 3.5 per cent a eutectic which melted at 1065° C. R. E. Slade and F. D. Farrow(6) extended these studies to mixtures of higher

Jan 1, 1934

By Alfred W. Gauger, George A. Burrell

The senior author of this paper, while in Colorado on other official business, made a trip to the Cripple Creek gold-mining district to get more data than are at present available regarding the composition of the gas that issues from the rock into the mines of the district. This was done at the suggestion of George S. Rice, Chief Mining Engineer of the Bureau of Mines. There are -many questions of interest and importance in connection with the ventilation of the mines in the Cripple Creek district, such as the menace to life and mining of a suffocating gas entering the mines from the rock, the danger due to powder smoke (from blasting operations), and danger of continued inhalation of rock dust by the miners. This report confines itself to the first problem, the gas from the rock, and principally to one phase of this question, the composition of the gas and its effects on men and lights. A more thorough study of this and other ventilation problems is planned. That the rock gas is a real menace is shown by the fact that miners (variously estimated from 25 to 50 by different persons interviewed) have been killed by it in the 25 years that mining has been vigorously carried on at Cripple Creek. Many men have had narrow escapes from death, some of them having been incapacitated for days. In addition, much loss of time results because at certain periods of the year or on certain days it is impossible to enter some workings. At a few mines, fans force air into the workings, thus supplementing the natural ventilation and much improving conditions, but the improvement is not entirely adequate at all times. Origin of the Gas Lindgren and Ransome1 think that the gas found in the rocks of the Cripple Creek mining district represents the last exhalations of the ex-

Jan 1, 1917

By C. O. Swanson

In the iron ranges of northern Michigan, magnetic data have been used as an aid in geologic field work since the time of the earliest surveys. The presence of complex structures containing magnetic formations, and the general scarcity of exposures, guided the early work into this line of attack, and later field studies tended to place more and more emphasis upon this geophysical relationship, until, at present, the collection of magnetic data is a matter of routine in any areal survey. At first, horizontal deflections of the compass needle were the only data collected. In subsequent surveys, greater dependence was placed on dip-needle readings, which record variations in the intensity and inclination of the earth's magnetic field. Recently the trend has been toward adjusting the instrument so as to reduce the influence of changes in inclination, and using a more sensitive modification, called the Superdip,' in weakly magnetic areas. To a minor extent, the magnetometer has also been employed. The object of this paper is to present the writer's experience with magnetic data in this region. The conclusions are based on work covering a period of 10 years, and spread over nearly all of the iron ranges and a large part of the intervening areas. The viewpoints expressed are purely geological ones. In other words, any opinion as to the usefulness of a certain relationship is based upon the writer's experience with it as a guide in interpreting the structures of this region, and not upon its soundness theoretically, nor its usefulness under other conditions. A very brief summary of the conclusions is as follows. The most important step is that of collecting the magnetic data. This requires a suitable adjustment of the dip needle, and sufficient readings to accurately portray the variations in the magnetic field, which are apt to be irregular. Once the readings are taken and plotted in some clear fashion, the interpretation of them is usually merely a matter of observing their relation-

Jan 1, 1934

By D. B. Kibler

Pill Florida hard-rock field extends from Suwanee and Columbia Counties in northwest Florida to south of Croom, Florida, in Hernando County this area is approximately 100 miles long and varies from 2 to 30 miles 1n width Florida hard-rock phosphate was discovered at Hale Springs, about one mile northwest of the town of Dunnellon Marion County, in the year 1888, by Albertus Voight who lived within a few hundred yards of the spring Soon after this discovery there was a great influx of land speculators and wildcat operators into the vicinity of Dunnellon A few years later phosphate was found in Alachua, Levy, Citrus and Hernando Counties, and a great number of small crude plants were built from Newberry, Alachua County, all the way to Croom, Hernando County Phosphate was found in many places as "outcrops " Looking for outcrops was the first method used by the early prospectors in searching for deposits Several years passed before any systematic method of prospecting was used EARLY MINING The early method of mining hard-rock phosphate was with picks and shovels, wheelbarrows, mules and wagons The pick-and-shovel method was used altogether until about 1900, when some of the larger operators began to use railroad-type steam shovels of from 1/2 to 1-yd capacity Picks and shovels, with negro labor loading the phosphate ore (called "matrix") into wooden side-dump skip-cars, was continued until about 1907 From the discovery of hard-rock phosphate until approximately 1905, overburden was removed with mules and scrapers At some places, the overburden was loaded into side-du nip skip-cars by negro laborers and the cars were then pulled up an incline with a steam hoisting engine The maximum depth of overburden that could be economically removed by hand labor mules and scrapers was approximately 15 feet About 1905 one of the companies erected a producer-gas powerhouse near Dunnellon and generated its own electricity and about the same time the larger companies began using hydraulic methods for the removal of overburden From the year 1888 through the year 1939, approximately 75 companies were operating at one time or another in the hard-rock territory, on approximately 500 locations The hard-rock deposits are more irregular and have higher mining costs than the pebble-rock deposits, therefore they have not been competitive in the domestic market, but because of the higher grade of the hard rock it is in demand for the export trade Discovery of phosphate outside of the United States has made it increasingly difficult in recent years for the hard-rock companies to survive, so today only three companies are operating These

Jan 1, 1941

By H. H. Stout

THE high copper price during the war stimulated the capacity to produce far beyond a possible normal consumption. The curves in Fig. 1 show this. The line YZ indicates, what the world production and consumption of primary copper nor-mally would have been, had not the 3 war upset the rhythm of industry. Granting that the maximum world production of 3,150,000,000 lb. in 1917 was obtained by crowding both the equipment and the grade of ore mined, yet in many instances addi-tional capital was invested, upon which the producer will be driven to earn at least a reasonable interest. During the period of deflation, or C liquidation, which we have entered, the consumption of copper will nat-urally be below the normal. Fig. 1 shows the actual consumption ex-pressed-in per cent. of normal : 1919, 96 per cent.; 1920, 94 per cent.; 1921, 70 per cent. The copper industry, consequently, faces: (1) Potential over-production capacity; I (2) Diminished consumption. To deny the existence of these factors would be illogical. To minimize the menace of this potential producing capacity might lead to regret. All past attempts at artificial control have not proved very successful. Obviously the remedy is to increase, if possible, the consumption of copper to a point where these factors cease to be dangerous. In ultimate analysis, this means: Produce an article so cheap and so good that no one can afford to use substitutes. The problem can be solved by: (1) Re-ducing price; (2) Improving product offered.

Jan 11, 1922

By Stephen Taber

Introduction.............................. 62 Asbestiform Minerals.......................... 63 Chemical and Mineralogical Relations............... 63 Physical Properties........................ 64 Types of Asbestos............................ 65 Origin of the Fibrous Structure...................... 66 Views of Previous Investigators.................... 66 Discussion of the Evidence.................... 67 Conclusions........................... 69 Origin of Cross-fiber Veins....................... 71 Chrysotile Veins......................... 72 Structural Features of Cross-fiber Veins............... 78 Veins of Crocidolite and Other Fibrous Amphiboles........... 83 Origin of Slip-fiber........................... 84 Origin of Mass-fiber........................... 86 Discussion............................... 87 IntRoduCtion The term asbestos, as commonly used, includes half a dozen minerals all having a well-developed fibrous structure, but differing in chemical composition and in some of their physical properties. In its strict application the name is limited to the fibrous varieties of the monoclinic amphiboles. Commercially, however, the most important of the asbestiform minerals is chrysotile, a fibrous variety of serpentine. About 95 per cent. of the asbestos used in manufacturing is chrysotile, and it commands a much higher price than any of the other fibrous minerals now on the market. Although the production of asbestos has increased rapidly in recent years, comparatively little has been published concerning its origin. The present paper is preliminary in its nature, and therefore does not pretend to exhaust the subject. The ideas herein developed are the result of field investigation, laboratory experiments in the growth of fibrous

Jan 1, 1918

By D. N. Collins, J. R. Stevens

New expressions in the technical assessment of mineral concentration processes have been defined as Concentration Efficiency: Concentration Index: where h is the percentage of head grade; c, percentage of concentrate grade; maximum percentage of concentrate grade obtainable at 100 pct recovery; and R, percentage of recovery. In developing these expressions, the basic requirements for the technical assessment of concentration operations have been defined and the various expressions suggested by others for asses-sing the results of such operations reviewed and criticized. The derived expression for E, depends on a simple combination of recovery (R) and a new term selectivity (s), where S is (c-h)/(c,,, -h), by definition. Limitations of the new expressions are discussed and examples given of applications to concentration operations. It is also shown that the formulae for E, and I, can be applied to scatter diagrams, multi-component systems, size-assay analyses, and classification data. Many methods of quantifying concentrating operations have been proposed. These include direct presentation of weights and assays together with the derived data for other items such as ratio of concentration, recovery, rejection losses, and enrichment ratio. These terms are now accepted mineral dressing nomenclature, and in the assessment of the results of concentration processes, concentrate grade and recovery are together the most widely accepted measures of concentration efficiency. For practical purposes when the concentrate grade is equal to or greater than a predetermined acceptable value, test or operation results may be assessed by the recovery figures alone. Similarly when recovery is within specification, the operation can be assessed by concentrate grade. The ultimate assessment and selection of a concentration operation is—admittedly with a few ex-ceptions—a matter of economics. There is however an intermediate stage in laboratory and pilot plant testing when evaluations must be made without the assistance of an economic yardstick. Numerous techniques are employed to facilitate such evaluations among which may be mentioned graphical plots of grade vs recovery, cumulative weight vs cumulative recovery, scatter diagrams, etc. The desirability of combining metallurgical results and product weights and assays into a single value has been recognized and discussed by many workers1-" with the resultant suggestion and use of such terms as Metallurgical Efficiency ,' Summation Index,' Selectivity Index,'- and Absolute Efficiency B None of these expressions completely satisfies all the requirements of a selectivity or efficiency formula and it is proposed in this report to define the terms, relating to the technical efficiency of a concentrating operation, concentration index and concentration efficiency. Examples are given of their application and a comparison is made of their use in relation to other formulae. All product grades in this paper will be referred to in terms of mineral percentages and a list of symbols is given in Table I. CONSIDERATION OF EXISTING FORMULAE A number of the existing efficiency and index terms used in quantifying concentrating operations are considered below. Metallurgical Efficiency:

Jan 1, 1961

By J. W. Freeman, J. P. Rowe, R. F. Decker

HEAT-to-heat variations in properties of an alloy of constant nominal chemical composition have been a perplexing problem to the metallurgist. These heat-to-heat differences have been especially baffling in high-temperature metallurgy. In order to establish fundamental reasons for these heat-to-heat variations, the National Advisory Committee for Aeronautics has sponsored and financially assisted an extended research program on heat-resistant alloys at the University of Michigan. As part of the program to find the contribution of processing variables, Frey, Freeman, and white' studied effects of heat treating on nickel-base alloys and Ewing and reeman' investigated effects of hot-working practice on N155 alloy. To extend the program to the study of effects of melting practice on high-temperature properties, a 55 Ni-20 Cr-15 Co-4 Mo-3 Ti-3 pct A1 composition was selected for experimentation. The objective of this program was to establish the melting-practice variables which influenced the hot-working characteristics and creep-rupture properties and, at the same time, establish the metallurgical mechanisms for the effects. During the course of the investigation of practices using vacuum melting, it became increasingly evident through chemical analyses supplied by industrial concerns that a major variable was melt reaction with the crucible. This paper is devoted to the results of this phase of the melting-practice study. EXPERIMENTAL PROCEDURES Experimental 10-lb heats were induction melted in the University of Michigan vacuum-melting unit with the melting practices outlined in Table I. Aim analysis for the basic alloy, in wt pct, for all heats was as follows: Cr Co Mo Ti Al 20.0 15.0 4.0 3.1 3.1 Mn Si C Ni 0.12 0.12 0.08-0.15 Bal. Small amounts of boron and zirconium were added to certain heats as listed in Table I. These additions

Jan 1, 1959

By Arthur C. Forsyth, R. L. Dowdell

A search through the available literature shows that the cobalt-nickel-silicon system has not been systematically studied. This seems rather odd because all three elements are fairly abundant and have better than average corrosion resistance; however, they have high melting points, which makes experimental work difficult. Cobalt and nickel form a continuous series of solid solutions and each metal dissolves about 7.5 per cent silicon. Many ternary alloys have been studied and the results have been published in a great many different ways, but to present such data in a short but clear and understandable manner is still a problem. The following pages describe the results of the study of 76 alloys from which the partial ternary diagram (Fig. 1) of the cobalt-nickel-silicon system has been drawn. The alloys were chosen according to the plan in Fig. la by taking definite ratios of cobalt and nickel, such as 70 Ni, 30 Co or 40 Ni, 60 Co, and adding silicon in various percentages. Each section was studied in detail by means of thermal analysis and microscopic examination, but only two of these detailed sections were thought necessary in the point perspective drawing to give a comprehensive picture of the liquidus, solidus and solid transformations that take place over the temperature ranges studied. Complete thermal analyses and microscopic data are given in Table 1. Experimental Procedure The alloys were prepared from metals of commercial purity, as follows: electrolytic nickel 99.60 + 0.35 Co; chemically purified silicon 99.79 per cent plus impurities of Fe 0.027, A1 0.008, Ca 0.014, C 0.004, N² 0.10; and cobalt 98.82 per cent plus impurities of Ni 0.42, Fe 0.12, CaO 0.27, S 0.012, Mn 0.10 and SiO² 0.15. It should be noted that the largest impurity in cobalt is nickel, one of the alloying elements. The alloys were melted in a small Ajax induction furnace, the nickel and cobalt being melted first because of their better ferromagnetic

Jan 1, 1940

By Arthur C. Forsyth, R. L. Dowdell

A search through the available literature shows that the cobalt-nickel-silicon system has not been systematically studied. This seems rather odd because all three elements are fairly abundant and have better than average corrosion resistance; however, they have high melting points, which makes experimental work difficult. Cobalt and nickel form a continuous series of solid solutions and each metal dissolves about 7.5 per cent silicon. Many ternary alloys have been studied and the results have been published in a great many different ways, but to present such data in a short but clear and understandable manner is still a problem. The following pages describe the results of the study of 76 alloys from which the partial ternary diagram (Fig. 1) of the cobalt-nickel-silicon system has been drawn. The alloys were chosen according to the plan in Fig. la by taking definite ratios of cobalt and nickel, such as 70 Ni, 30 Co or 40 Ni, 60 Co, and adding silicon in various percentages. Each section was studied in detail by means of thermal analysis and microscopic examination, but only two of these detailed sections were thought necessary in the point perspective drawing to give a comprehensive picture of the liquidus, solidus and solid transformations that take place over the temperature ranges studied. Complete thermal analyses and microscopic data are given in Table 1. Experimental Procedure The alloys were prepared from metals of commercial purity, as follows: electrolytic nickel 99.60 + 0.35 Co; chemically purified silicon 99.79 per cent plus impurities of Fe 0.027, A1 0.008, Ca 0.014, C 0.004, N² 0.10; and cobalt 98.82 per cent plus impurities of Ni 0.42, Fe 0.12, CaO 0.27, S 0.012, Mn 0.10 and SiO² 0.15. It should be noted that the largest impurity in cobalt is nickel, one of the alloying elements. The alloys were melted in a small Ajax induction furnace, the nickel and cobalt being melted first because of their better ferromagnetic

Jan 1, 1940

By Colin J. Dixon

The full realization of the potential of computers in geological in- formation system demands new approaches to the machine representation of information. At the same time, the feasibility of such a system, particularly in commercial field, demands greater freedom in input preparation and a degree of standardization in the arrangement of subject matter system. The paper describes some of the basic notions of project "GEOSEMANTICA 70". The aim of the project is to devise means of storing real geological informations in a machine rather than the representation of the information in human language form. This is seen as the only long-term solution to the problems of the complex vocabulary of geology and the complex syntax of geological description. Effectively, a machine language is being defined, consisting of a set of symbols and a date structure for representation of geological and related information. Beyond this, is the definition of a set of rules allowing the use of constrained text as an input/output medium. The investigation is oriented primarily to the representation and handling of information about mineral deposits and the associated geographic, economic and engineering information.

Jan 1, 1969

By S. Norton

GEORGE C. FOOTS, Port Henry, N. Y. (written discussion).-The paper by Mr. Norton and Mr. LeFevre will bear the most careful consideration by all interested in the iron business, particularly in the East. There is much information contained therein which should be emphasized. The idea of handling iron-bearing rock in quantities comparable to the porphyry coppers does seem at first blush to be beyond the pale of commercial possibility. Yet, today in the Adirondack region 25 per cent.

Jan 4, 1917

By W. A. Backofen, B. C. Wonsiewicz

The Plasticity transition in magnesium was studied by plane-strain compression of single crystals and polycrystalline material at temperatures from about 20" to 307°C. Reduction of single crystals along the c axis was accommodated by twinning on {1011) and retwinning on (10 12}, followed by basal shear in the doubly twinned volume. Deformation in that mode can result in sufficient independent shears for arbitrary shape change. Fracture in c axis compression, below about 100°C, has been related to excessive shear caused by unloading from the stress for {1011} twinning (-50 ksi at 20°C) to that for slip within the twin (-3 ksi); ductility follows from heating because the stress difference is lowered and the twin volume, in which elastic strain energy is dissipated on unloading, is increased. The stress for (1011) twinning is strongly temperature-dependent but not given by a critical resolved shear stress law. The latter is attributed to the influence of stress concentration from prior intersecting shear on nonbasal planes, the former to the temperature dependence of the preliminary slip. THE basic symmetry of hcp crystals has the effect of limiting the number of independent slip systems and making twinning an important deformation mechanism. The general result in wrought polycrystalline aggregates is a more or less sharply developed texture (or preferred orientation) which underlies a strong anisotropy in mechanical behavior. Knowing how the one influences the other is essential background for the use of such materials. Magnesium was of interest in this work because of the unexplained plasticity transition that it undergoes somewhere in the neighborhood of 200°c.''~ At lower temperatures plastic deformation before fracture in polycrystalline material is limited, while at higher temperatures extensive deformation is possible. The transition temperature commonly determines the lower limit of the range in which magnesium is worked. The limited ductility can be traced to a lack of independent crystallographic shears. A minimum of five are required for arbitrary shape change.' Around room temperature, however, slip on all known systems provides only four.' In each case, the slip direction is in the (0001) basal plane so that slip does not allow strain along the c axis. With increasing temperature, more slip occurs on the ( 1011) pyramidal plane and the ( 1010) prism plane but without change in direction.'?' Thus, that development alone cannot explain the transition temperature.

Jan 1, 1968

By Alden Greninger

THE time-honored description of the growth of metal crystals to form polycrystalline aggregates is one in which two important steps are con-sidered: (1) nucleation, and (2) dendritic growth, each dendrite starting from its individual nucleus and resulting (upon slow cooling, assuming no solid phase changes) in a macrograin. This picture of the process of crystallization is incomplete, and it is with the hope of enlarging upon it that the following summary and correlation of experimental results are given. MOSAIC STRUCTURE For an exact definition of the mosaic structure of metal crystals-if, indeed, one can be found that will hold for all metals-one must await the results of much experimental work in this field. The writer's investiga-tions have been confined almost entirely to copper and a few of its alloys. The following terms are proposed, and will be used in this report: Macromosaic Structure l.-Large-scale mosaic structure; more specif-ically, mosaic structure of a scale large enough to produce splitting of Laue spots on back-reflection Laue X-ray patterns2. The deviation from exact parallelism of neighboring macromosaics varies from a few

Jan 1, 1935

By Walter Harvey Weed

The Republic of Mexico is traversed by many mountain ranges, and presents a great diversity of climates, soils and geographical features, yet its grander geographic provinces are few and peculiarly well defined. The Gulf plain, the Cen tral plateau, the Sierra Madre, and the lowland or Tierra Cali ente of the western coast are the main features of the geogra phy of the Republic, and in the northern half these provinces are particularly well defined. The Sierra Madre separates the Republic into eastern and western parts, and from the City of Mexico north to the Texas line presents an almost impassable barrier to east and west travel. On the north, the first wagon road pass from east to west is at El Paso del Norte, the site of the Texan city of El Paso. Southward for many hundreds of miles the Sierra Madre, traversed by well-worn trails, over which all travel from the west coast to the interior must pass, is a stupendous barrier to social and commercial intercourse. The Sierra Madre is commonly described as a range or con geries of mountain ranges. In fact, it is, in Chihuahua at least, a great plateau, fringed by mountains on the east, trenched by deep canons in its center, and bordered by a wild and rugged complex of mountains carved out of the plateau on the west. Professional duties took me across this region from Parral westward to the Gulf of California via Guadalupe y Calvo. As it includes some of the great ore-deposits of Mexico, and its geological features have never, so far as I am aware, been described, I have prepared a diagrammatic section made from my observations on a horseback trip across the Sierra, and added such notes as seem to be of general interest.

Jan 1, 1902

By T. Lane Carter

It is a curious fact that while in our Transactions there are papers dealing with mining-districts in all parts of the world, in Europe, Asia, Africa, and Australia, there is not one which describes the mining possibilities of Nicaragua, our near neighbor. To be most interested in distant objects, like the moon, and to neglect what lies at our feet, appears to be a trait of human nature. The neglect of Nicaragua is not confined to the American Institute of Mining Engineers. In no other transactions am I able to find papers dealing with mining in Nicaragua, some parts of which are as much in need of discovery and research as the North Pole. I hope this paper will be the precursor of many others to be printed in our Transaclions, dealing not only with the miniilg possibilities of Nicaragua, but with the whole of Central America, where there are vast areas a,waiting skill and capital for their development. Much of this capital and skill should come from the United States in the future, although it is probable that European capitalists, when they appreciate fully the possibilities, will investigate more and more the mining-resources of Nicaragua and ot'her Central American republics. Fig. 1 is a sketch-map of Nicaragua showing the principal mining-districts. 11. History. Mining in Nicaragua did not begin yesterday. It was commenced by civilized man when the Spanish conquerors pene-' trated into the interior and forced the natives to procure the precious metal for them. It is strange that the Spaniards did not find more gold, and work on a scale as extensive as in Colombia and other parts of South America. Probably in Nicaragua the Indians covered up most of the rich prospects

Jan 1, 1911

By Edward W. Parker

At the Cleveland meeting of the Institute, October, 1912, I had occasion to call attention to the general though erroneous impression that the principal mining activities of the United States lie west of the 100th meridian of longitude. Few, I believe, realize that the States east of the Mississippi river, which comprise only 28.8 per cent. of the total area of the United States, exclusive of Alaska, contribute about two-thirds of the total mineral production, computing by values. In 1910 the percentage of the production credited to the Eastern States was 67; in 1911 it was 65. When I have, with becoming modesty, ventured to speak of these comparisons, I have usually been met with the rejoinder, " But you include coal." I surely do, for whereas coal (m petroleum, as natural gas, as limestone) is not in the strictly technical definition of the word, a " mineral," it is legally mineral, is certainly a mineral substance, and contributes by far the largest tonnage and approximately one-third of the total value of all mineral products. The production of coal-mines in 1911 weighed approximately 500,000,000 tons. In 1912 it exceeded that record by nearly, if not quite, 50,000,000 tons. According to H. D. McCaskey, of the U. S. Geological Survey, the total weight of all the metallic ores mined in the United States in 1911 was 105,000,000 tons (a little more than one-fifth that of coal). In 1910 Mr. Lindgren estimated the total weight of all metallic ores at 120,000,000 tons. The products of the quarries, clay-pits, oil-wells, phosphate-mines, and other non-metallic products, taken all together, did not in 1911 weigh in excess of 300,000,000 tons, so that the output of coal exceeds by 25 per cent. the combined tonnage of all other mineral products. The coal-mines give to

Jan 1, 1914

By J. E. Hilliard

Various methods are given for estimating the number per unit volume and average size of convex particles from measurements on a projection through a slice of the structure. The determination of the size distribution is considered specifically for spherical particles. The results are applicable to any type of transmission microscopy and also to the correction of measurements made by reflected light on semitransparent materials. WITH the advent of electron transmission microscopy, the metallurgist is confronted with the problem of relating a projected image to the three-dimensional properties of the structure. This paper deals with the estimation of the number per unit volume and size of particles dispersed in a matrix. The case of convex particles will first be treated (the results will be applicable as approximations to particles of more general shape) and then spherical particles will be considered specifically. The latter represent a special case frequently encountered in practice and one which is also amenable to a calculation of the effect of overlap on the observed particle-size distribution. Although the present treatment was prompted by the needs of the electron microscopist, the results are applicable to transmission studies with any type of radiation. In addition, they can be used in the analysis of semitransparent materials by reflected light, the depth of light penetration corresponding to the thickness of the slice or section used in the transmission studies. 1) CONVEX PARTICLES 1.1) General Expression for N,. We will suppose that a "center" (such as the center of mass) is assigned to each particle. The convention used for defining the center is immaterial providing it does not depend on the orientation or location of the particle. Consider a slice through the structure having a pair of parallel faces a distance t apart. It will be assumed that the slice is randomly located with respect to its perpendicular distance from some fixed point, but it is not necessary to assume that its orientation is random. Our problem is to deduce the relationship between the number of par- ticle images seen on an orthogonal projection through the slice with the number, Nv, of particles per unit volume in the original structure.* *Symbols are listed in the Table. The expected number of particles with centers lying within the slice is Nvt per unit area. In addition, there will be elements in the slice contributed by particles whose centers lie without. The number of such elements will be the same as the number of intersections occurring on a two-dimensional plane through the structure; namely N~K, where K is the mean distance, Fig. 1, between tangent planes to a particle averaged over all particles, i.e., Where Ni is the number of particles of class i having the same shape and size, and pi (4, 8) is the probability that an i particle will have a given orientation with respect to the slice. If the particles are randomly oriented, then K is independent of the orientation of the slice and equal to the mean cali-per diameter. The total number of particle elements in the slice is therefore Nv(t + K) per unit area, but fewer will be seen as separate images on the projection plane because of overlap. If MA is the number of elements "lost" by overlap, the number of images per unit area will be NA = Nv(t + K) -MA 121 MA is a function of the slice thickness and must vanish at t = 0. As t increases, NA at first increases, reaches a maximum, and thereafter decreases as the overlap term MA becomes predomi-

Jan 1, 1962

By H. l. Burghoff, E. C. Bohlen

The work reported in this paper was carried out to supplement the existing information concerning directional properties and recrystallization textures of annealed brass sheet and strip. These characteristics are of direct interest when the forming and drawing properties of such material are being considered. Among those who have made contributions in this field are Bass and G1ocker;l Bauer, Göler and Sachs;2 Phillips and Samans;3 Pratt;4 Price;5 Cook;6 Richards;7 Brick;8 and Brick and Williamson.9 These investigators have found, in general, that in brass strip that shows directional variations in properties, tensile strength has a minimum value and elongation has a maximum value at 45' to the rolling direction. The most pronounced directional properties have been found in material given the greatest reductions in rolling followed by high annealing temperatures. Recrystallization texture of brass has been variously reported as (II3)[II2], (ooi)[ioo], and a combination of (II0)[II5] and traces of the primary rolling texture, (110)[112]. The directional studies have been very informative, but actual tests appear to have been confined to material in its final condition. Tests at intermediate stages have received little attention although previous history of some materials has been partly considered. Perhaps the most comprehensive investigation was made by Cook,' who studied the directional properties of 70-30 brass strip for which the final and penultimate, or next to the last, anneals and the final reductions were varied. He found that, for any given combination of penultimate anneal and final reduction, the tendency toward the development of directional properties was reduced as the temperature of the final anneal was decreased. In addition to drawing cups and making tensile tests of the finished material at various angles to the rolling direction, he measured the frequency and the angles of twins in grains for several specimens. Plots of his twin counts showed directionality for the materials that produced eared cups. Test Materials and Equipment For this investigation, one commercial heat of 68-32 brass was cast in the form of bars for cold-rolling, I31/2 in wide and I1/2 in. thick. The analysis was as follows: 68.83 per cent copper, 0.04 per cent lead, 0.01 per cent iron, 31.12 per cent zinc (by difference). The bars were so processed to the final thickness, 0.020 in., as to obtain on this thickness all possible combinations of the variables listed below except those involving the sequence of 84 per cent penultimate reduction and 84 per cent final reduction: I. Penultimate reductions of 37 per cent, 50 per cent and 84 per cent; 2. Penultimate anneals at 800°, 900°, 1050° and 1200°F.; 3. Final reductions of 37 per cent, 50 per cent, 69 per cent and 84 per cent;

Jan 1, 1942

By E. C. Bohlen, H. l. Burghoff

The work reported in this paper was carried out to supplement the existing information concerning directional properties and recrystallization textures of annealed brass sheet and strip. These characteristics are of direct interest when the forming and drawing properties of such material are being considered. Among those who have made contributions in this field are Bass and G1ocker;l Bauer, Göler and Sachs;2 Phillips and Samans;3 Pratt;4 Price;5 Cook;6 Richards;7 Brick;8 and Brick and Williamson.9 These investigators have found, in general, that in brass strip that shows directional variations in properties, tensile strength has a minimum value and elongation has a maximum value at 45' to the rolling direction. The most pronounced directional properties have been found in material given the greatest reductions in rolling followed by high annealing temperatures. Recrystallization texture of brass has been variously reported as (II3)[II2], (ooi)[ioo], and a combination of (II0)[II5] and traces of the primary rolling texture, (110)[112]. The directional studies have been very informative, but actual tests appear to have been confined to material in its final condition. Tests at intermediate stages have received little attention although previous history of some materials has been partly considered. Perhaps the most comprehensive investigation was made by Cook,' who studied the directional properties of 70-30 brass strip for which the final and penultimate, or next to the last, anneals and the final reductions were varied. He found that, for any given combination of penultimate anneal and final reduction, the tendency toward the development of directional properties was reduced as the temperature of the final anneal was decreased. In addition to drawing cups and making tensile tests of the finished material at various angles to the rolling direction, he measured the frequency and the angles of twins in grains for several specimens. Plots of his twin counts showed directionality for the materials that produced eared cups. Test Materials and Equipment For this investigation, one commercial heat of 68-32 brass was cast in the form of bars for cold-rolling, I31/2 in wide and I1/2 in. thick. The analysis was as follows: 68.83 per cent copper, 0.04 per cent lead, 0.01 per cent iron, 31.12 per cent zinc (by difference). The bars were so processed to the final thickness, 0.020 in., as to obtain on this thickness all possible combinations of the variables listed below except those involving the sequence of 84 per cent penultimate reduction and 84 per cent final reduction: I. Penultimate reductions of 37 per cent, 50 per cent and 84 per cent; 2. Penultimate anneals at 800°, 900°, 1050° and 1200°F.; 3. Final reductions of 37 per cent, 50 per cent, 69 per cent and 84 per cent;

Jan 1, 1942