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By R. S. Busk, R. F. Marande

The magnesium-aluminum-zinc 'system contains most of the magnesium-base alloys used commercially, although in practice the ternary alloys are usually modified by the addition of a small amount of manganese. Table I contains the magnesium-base commercial sand-casting alloys most widely used throughout the world, together with their typical tensile properties. These alloys may be regarded as a single family of varying aluminum and zinc content, disregarding manganese. A concise means of presenting data for them is by means of iso-property lines plotted on triangular coordinate paper. Constitutional, casting, and mechanical properties are presented in this manner. The data are given with the obiect of providing reference material, and to aid in the choice of a commercial alloy to serve a particular purpose. Detailed, critical analysis of the commercial alloys has been covered in a previous paper.' All alloys reported were made in rj-lb. melts, superheated to r700°F. for 15 min., cooled to r400°F. and poured in sand molds. The test bars produced had a 1/2-in. reduced section and were about 6 in. long. Except for the data represented in Figs. I and 3 the alloys used were of commercial purity and contained 0.1 to 0.2 per cent Mn in addition to the aluminum and zinc. Constitutional Data Under the heading of Constitutional Data are included all known data on con-

Jan 1, 1946

By R. F. Marande, R. S. Busk

The magnesium-aluminum-zinc 'system contains most of the magnesium-base alloys used commercially, although in practice the ternary alloys are usually modified by the addition of a small amount of manganese. Table I contains the magnesium-base commercial sand-casting alloys most widely used throughout the world, together with their typical tensile properties. These alloys may be regarded as a single family of varying aluminum and zinc content, disregarding manganese. A concise means of presenting data for them is by means of iso-property lines plotted on triangular coordinate paper. Constitutional, casting, and mechanical properties are presented in this manner. The data are given with the obiect of providing reference material, and to aid in the choice of a commercial alloy to serve a particular purpose. Detailed, critical analysis of the commercial alloys has been covered in a previous paper.' All alloys reported were made in rj-lb. melts, superheated to r700°F. for 15 min., cooled to r400°F. and poured in sand molds. The test bars produced had a 1/2-in. reduced section and were about 6 in. long. Except for the data represented in Figs. I and 3 the alloys used were of commercial purity and contained 0.1 to 0.2 per cent Mn in addition to the aluminum and zinc. Constitutional Data Under the heading of Constitutional Data are included all known data on con-

Jan 1, 1946

By Oscar Harder

IT is now just a quarter of a century since Fred W. Taylor§(23) pub-lished his classical paper On the Art of Cutting Metals, describing -his researches in which he, in cooperation with Maunsel White, had developed what is essentially the modern method of heat-treating high-speed steels. Regarding this research, Dr. Sauveur, (22) in his address on Steel Wizards, Past and Present, at the annual banquet of the American Society for Steel Treating in Philadelphia in 1920 said, "The discovery of high-speed steel, or if you prefer, of the treatment imparting high-speed properties to certain steels by Taylor and Maunsel White I am inclined to consider as our one epoch-making contribution to the metallurgy of steel." It was at about that same time (1900) that Taylor exhibited high-speed steels, heat-treated by the improved process, at the World's Exposition in Paris and attracted much attention by showing that the steels would operate at such feeds and speeds that the tips of the tools were visibly red hot. This observation must have started metallurgists to wondering regarding the relative hardness of the various steels at red-heat temperatures. Considerable work has indeed been done in an effort to measure the hardness of high-speed steels and. related materials in the red-heat range, using various methods. . The results, however, have been only partly satisfactory, owing to experimental difficulties. The present investigation had as its immediate inception an address by J. V. Emmons, of the Cleveland Twist Drill Co., to the Columbus Chapter of the American Society for Steel Treating in 1931, in which he deplored the fact that comparatively little was known with regard to the hardness of high-speed steels at elevated temperatures, in spite

Jan 1, 1933

By Charles Will Wright

FRANCE will be given a large portion of the Marshall Plan funds for relief, reconstruction, and industrial development in France and in her colonial possessions. At present that country is not in position to export any large tonnages of the mineral products needed in the United States. However, if, through Marshall Plan aid and private capital investment, production of these products can be largely increased, agreement should be made by which the United States is to get a substantial portion of such increased output in part payment for the material and technical aid they receive. France issued a decree, published in the "Official Gazette" on Feb. 3, 1948, which permits conversion into dollars of dividends derived from dollar investment in Government-approved projects and will agree to a scale of capital amortization to be determined in each individual case. This decree is to encourage private capital to cooperate with local capital in industrial undertakings. The French Colonial Ministry has prepared an extensive program for aid to the mining industries in overseas possessions to be undertaken by

Jan 1, 1948

By James E. York

THE honor so fairly earned and so incompletely and tardily paid to Henry Cort, the inventor of the puddling-furnace and the, rolling-mill, has been fully set forth by Mr. Charles H. Morgan,1 and needs no further emphasis here. In view of the importance of the rolling-mill in the treatment of iron and steel, the paucity of information concerning it is surprising. With the exception of a hook, written about 35 years ago, by Peter Bitter von Tunner, an Honorary Member of this Institute, and of desultory articles on simple sections, which have appeared in technical journals, I know of no pub¬lication attempting to treat this subject, although volumes have been written on the scientific theory and technical manipulations involved in other branches of the iron- and steel-industry. This strange anomaly may be due to the fact that roll-turning cannot be called a scientific business. It does not ordinarily come within the range of an educated engineer; yet it cannot be performed by an ordinary mechanic. It demands some of the qualifications of an engineer, in designing, and those of a mechanic, in execution. The men who have followed this trade have controlled the training of their successors. In many cases the technical knowledge required bas been handed down from father to son, and there has been a motive of private interest to prevent its public dissemination. Moreover, the statement of the various principles involved in the process would require, besides manual experience, a degree of scientific knowledge which roll-turners do not usually possess; and, finally, any book on the subject, in order to possess real, practical value, would have to be so fully illustrated as to make it very costly to publish. Regarding my own experience, I may say that I served a six-

May 1, 1906

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

INTRODUCTION Data available on prophyry copper occurrences in the Andean, Caribbean, Appalachian, and Cordilleran orogens may be categorized in a manner to suggest a hypothetical evolution for deposits that occur in the western hemisphere. A classification of de- posits is also suggested. A classification dependent on internal structure of a porphyry copper deposit would lead to two broad categories, breccia pipe and stockwork models. A classification of this type is examined herein but it is not universally accepted in the literature. Modeling based on igneous petrography as well as metasomatism attendant with the sulfide mineralization is more widely accepted by economic geologists whose evaluation of porphyry systems is influenced by the presence or absence of a phyllic zone. Lowell and Guilbert model deposits ordinarily include a phyllic zone, whereas those of the diorite model do not. Position of the phyllic zone in the alteration sequence is a significant ore guide. Should the phyllic zone be absent, dependence on alteration zoning to identify metallization is weakened. Presence or absence of the phyllic zone therefore is a significant parameter in the economic evaluation of a porphyry copper deposit (Hollister. et al., 1975). The Lowell and Guilbert (1970) model commonly includes a phyllic zone in quartz- bearing rocks. Parameters of both calc-alkalic and the quartz monzonite models mentioned elsewhere in this volume are sufficiently close to the Lowell and Guilbert (1970) model that it should be expanded to encompass them. The diorite model remains separate and distinct because deposits of this type are characterized by an absence of quartz in the pluton, commonly highly gold: copper ratios, low molybdenum content, and regular absence of sericite in the alteration zones. Therefore, for the benefit of those

Jan 1, 1978

By W. Rostoker, A. Siede

THE venerable problem of hydrogen embrittlement of ferritic iron lacks as yet a complete explanation. Possibly part of the difficulty has been the exclusive preoccupation with the total ductility prior to fracture. In the past few years it has been noted at least twice1,2 that hydrogen charged into iron has the ability to depress the upper yield point and, at room temperature, to eliminate completely the discontinuous yield phenomenon. Cracknell and Petchl rationalize that the depression of the yield stress is an example of the behavior of inhomogeneous stresses. Their explanation requires that microcracks exist in the annealed metal, and that hydrogen collect in these cavities under high hydrostatic pressure. The hydrostatic pressure of hydrogen generates localized tensile stresses in the iron which, with external loading, reach the critical stress for yield prematurely. The local plastic zones will spread across the specimen before the Lüders bands can be generated, and the yield-point elongation phenomenon is eliminated. This viewpoint will be discussed in succeeding paragraphs. Rogers,2 on the other hand, represents the depression of the initial flow stress as a result of the interaction of hydrogen with dislocations. He submits two alternative modes of interaction. In the

Jan 1, 1959

By William G. Pariseau

The flexure of geologic strata, a phenomenon of interest to geologists and mining engineers alike, is examined as a sheet bending problem in Coulomb plasticity. Fonnulae for the distribution of stress, strain, and displacement increments; volume change; change in the length of the central surface; and power of dissipation, as well as for the neutral surface shift are given. Strains of any magnitude are considered. The analysis shows that deeply buried strata may bend and develop "tensile" cracks under generally compressive states of stress. It is also shown that bed separation and high capacity props are desirable in mechanized longwall mining, a result in keeping with operating experience. Although speculative at this time, the analysis provides a rational working hypothesis as regards the problem of strata flexure and control. | he purpose of this paper is to present an analysis of the flexure of geologic strata as a problem in the bending of a sheet of material failing in accordance with a Mohr-Coulomb criterion. The flexure of strata has an obvious academic interest to the geologist concerned with the mechanics of folding. It is of interest to the economic geologist as it relates to the structural control of certain types of ore deposits. It has an intimate association with mine subsidence phenomena, and is of concern to the mining engineer. Strata flexure is also the dominant feature of roof behavior about longwall workings. An improved understanding of strata flexure through a rational mechanical analysis thus appears desirable not only from the academic view but from the economic one as well. In the field, the most commonly observed feature of folding, subsidence, and longwall roof behavior is the permanent and therefore inelastic nature of the strata movement. Fig. 1 illustrates the physical disposition of strata in the vicinity of a longwall face. Inasmuch as most rocks (with the possible exception of certain evaporites) do not exhibit significant viscoelastic behavior, at least not over time spans of engineering interest, a plastic analysis is indicated. The analysis is meant to apply to strata whose deformation is dominantly that of bending such as might be expected in the remote roof about a longwall face.

Jan 1, 1970

By L. L. Oriard

INTRODUCTION In order to make effective plans for the control of blasting effects, it is necessary to understand a few basic principles relating to the behavior of explosives. For the purposes of discussing this behavior, it is convenient to divide blasting effects into two zones. The first zone is the non-elastic zone in close proximity to the explosive charge where rupturing of the rock occurs. For this zone, our discussion will be oriented towards the factors which affect the rock breakage, and the means of controlling the limits of this breakage. The second zone is that zone more remote from the charge location where elastic vibrations are transmitted through the surrounding medium. In this zone, we are interested in the factors affecting vibration intensity, and the means of controlling the intensity so that no damage is done to structures, utilities, or excavated slopes. It has been easier to gather data in the elastic zone, because the stress levels are lower and time durations are longer. The instrumentation for obtaining data in this zone can be less rugged and less sophisticated. Consequently, more information of ad empirical nature has been gathered. In the non-elastic zone, there has been more dependence on theory, fewer measurements, and more questioning of the validity of the measurements. In spite of these questions, there has been an encouraging advancement in knowledge in recent years, both theoretical and empirical, of the effects that take place close to the source of an explosion. When discussing the problems encountered in rock excavation, we can simplify the terminology by referring to the physical phenomena encountered in the non-elastic zone as a problem in "over-break". The phenomena in the elastic zone could be called "vibration effects". Although there is some interdependence between the two, it is possible to control the rock breakage to neat surfaces and still have very high vibration levels. Similarly, it is possible to control the vibrations to moderate levels and still have a great deal of overbreak. THE ROCK BREAKAGE ZONE First, let us discuss the effects in that zone close to the blast source that we might call the non-elastic zone. This is the zone of cratering, breakage, rupturing, and fracturing. These effects will vary with the site conditions, and a meaningful, specific analysis could

Jan 1, 1972

By Donald L. Katz

Charts for predicting the pressure to which natural gases may be expanded without hydrate formation have been prepared for gases of even gravity. Pressure-temperature curves for hydrate formation were established for gases having gravities from 0.6 to 1.0. These curves and the thermal behavior of the gases during free and adiabatic expansion were used to prepare the charts for estimating the permissible expansion of natural gases without hydrate formation. The problem was solved by L. F, Albright, W. T. Boyd, J. J. McKetta, G. Martin, P. Poettman. and A. P. Snyder.-, who are first-year graduate students in the department of Chemical and Metallurgical Engineering at the University of Michigan. This paper is essentially a summary of their results. Prediction of Conditions for Hydrate Formation in Natural Gases Each natural gas under a given pressure will form solid hydrates at a corresponding temperature provided sufficient water is present.1-5 The temperature of natural gases below about 5000 lb. per sq. in. decreases when the gases are expanded freely.6,7 This decrease in temperature may cause the expanding gas to enter the region of temperature and pressure at which hydrates will form' The final pressure to which a natural gas may 'be expanded without hydrate formation depends upon the initial temperature and pressure and the gas composition. This paper presents charts that give the final pressures to which gases of gravity 0.6 to 1.0 at given initial temperatures and pressures may be expanded without formation of hydrate. Hydrate-forming Temperatures and Pressures as a Function OF Gas -Gravity Experimental data of pressure versus temperature at which solid hydrate will form, provided sufficient water is present, are available for a series of gases.2,3 A method of predicting the pressure-temperature curve for a given gas composition has been reported.' The solution to this problem requires that these curves relating pressure to temperature be established for gases of given gravities.

Jan 1, 1945

By Arthur F. L. Bell

Prior to 1908 the oil production in the State of California had been almost entirely a heavy fuel oil, with a high flash point, but changed within a short period to a large percentage of refining oil with a low flash, by reason of the heavy production of light oil coming in from the Santa Maria field, the Midway field, and the increased production of the Fullerton field. This is clearly shown in the following tabulation of California's pro- The bringing in of these high percentages of light oil with their dangerous low flash and the increasing demand for the refined products necessitated the devising of some cheap and efficient means of quickly separating the lighter elements either in the field or at the main distributing points; also it became necessary to remove the excessive percentage of water which many of the light oils carried in emulsion. Union Oil Co. Port Harford Plant Probably the first important attempt to top light oil in California by other means than the ordinary stills was tried about 1908 by the Union Oil Co., at its plant at Port Harford, San Luis Obispo County, with Santa Maria oils. The process was the invention of Hubert G. Burroughs who afterward obtained a patent for the process, No. 998,837, dated July 25, 1911. The apparatus used consisted of a series of 12-in. pipes mounted in units of three pipes, one above the other, the crude oil being admitted to the upper pipe and filling it about two-thirds of its

Jan 1, 1916

By M. A. Scheil

Austenitic stainless alloys are susceptible to stress-corrosion cracking which may occur under certain corrosion environments irrespective of their susceptibility to intergranular corrosion. Test samples are described for investigating stress-corrosion susceptibility of alloys for industrial equipment. A laboratory test using a solution of magnesium chloride boiling at 309 F. was found to produce transgranular cracks in several alloys investigated and in types 347 and 316 stainless steel tubing a residual stress of the order of 10,000 psi. was observed to initiate cracking. The susceptibility to stress-corrosion cracking as judged by the boiling magnesium chloride test indicates that alloys may be selected which will withstand a high stress in service Stressed specimens of stainless alloys included in a corrosion testing program will aid in determining the acceptibility of these fabricated alloys, when stressed, to the service conditions.

Jan 1, 1945

By C. R. Kuzell

INTRODUCTION KNOWLEDGE of the thermal capacity of gases is of great importance in making metallurgical calculations. The metallurgist is, frequently called upon to investigate and determine furnace efficiencies in which the heat carried into or out of the furnace by gases is a large item in the heat balance. Not only do such problems present themselves in the determination of furnace efficiency, but also in the study of the application of heat is accessory apparatus, such as stoves, regenerators, waste-heat boilers, driers,.etc. The thermal effect of the use of excess air in the combustion of fuel, the theoretical temperatures of combustion, the quantity of heat in hot blast at various temperatures, the effect of hot blast on furnace temperatures, are a few more examples of frequently occurring calorific problems involving gases. So many are the applications of the data on the heat capacity of gases that the subject merits careful study. The heat in a gas maybe due to its heat of combustion, if it is a combustible gas, and to its temperature. The latter is called its sensible heat and is the heat absorbed or evolved by a gas as its temperature is raised or lowered. The heat of combustion of gases is well established and is commonly known. The values can be found in almost any mcdern treatise on metallurgy. The sensible heat of gases has not been so well established because it is in most cases a function of the temperature, and the values of specific heats of gases over a wide range of temperatures have only recently been determined. It is the purpose of this paper to deal with the sensible heat of gases.

Jan 8, 1914

By F. E. Bachman

Although it has been apparent to me for a long time that too great weight was currently given to the silicon-contents of foundry-iron, and that the theory of the control by silicon of the carbon-contents of cast-iron is unsound, or that, at best, the influence of silicon is too small to be of much practical value as a guide in foundry-work, it never seemed to me desirable to enter the lists against either the " silicon-fad " or the theory, for the reason that I had neither the time nor the facilities to prove my position, nor any better theory to offer. But since Mr. Summers has taken the step, it seems but right that I should give such facts as are at hand in support of his contention. At the same time I do not think these are enough to prove the case if the contrary proposition were not itself, as it seems to me, based on insufficient evidence. Both Keep's and Turner's conclusions seem to be drawn from irons carrying less than the normal amount of carbon; Turner's " base " being, moreover, a steel rather than a pig-iron, and both the white base and the ferro-silicon of Keep being so low in carbon that compounds of them would not give a material approaching the carbon-contents of a normal casting, and having, therefore, little value as showing the effects of silicon on foundry-irons, even if his samples were treated under the same conditions as those to which pig-metal is subjected in making castings.

Jan 1, 1899

Frank Clemes Smith, Deadwood, 8. D. (communication to the Secretary): The reading of Mr. Chance's interesting paper suggests a few ideas relative to his discussion of certain Black Hills gold-ores. Mr. Chance refers to his examination, in 1897, of " the (Carboniferous) limestone plateau-country which encircles the central area of the Black Hills," and says that " it had been generally assumed that the mineralization of this formation was confined to the northern area;" further, that he "found, however, a general mineralization, extending in zones or belts throughout the region," and that the ores, being more or less specially

Jan 1, 1900

By William Campbell

The structure of iron and steel, though the object of so much study and research for the past 25 years, is by no means thoroughly understood. In the first place, we have three or more distinct iron-carbon thermal diagrams, each with its own supporters, and each representing a theory of the structure and constitution of cast-iron. In the second place, by reason of the fact that austenite, the solid solution of carbon in iron, decomposes in the solid state into ferrite, or pure iron, and cementite (Fe3C), and that quenching from above this transition-range, no matter how rapid, cannot entirely prevent the change and thus preserve the austenite by itself at ordinary temperatures, it happens that under the microscope we find, in addition to the ferrite, Fe3C, and austenite, which the thermal diagram of steel requires, a series of transition-products with distinctive structures, to which have been given the names martensite, troostite, sorbite, etc. Now these transition-products, in addition to the solid solution, austenite, have been the source of much controversy, at times very bitter. One side would insist that, say, troostite was an entity, which the other side would deny, pointing out that it must be a transition-mixture, with a particular structure. That austenite was a solid solution of carbon in iron has been denied by one school; we have been told that Fe24C dissolved both Fe3C and Fe, and thus gave rise to a whole series of quenching-pro-ducts—all this in spite of the fact that no matter how the thermal diagrams differ in regard to cast-iron, they all agree in regard to the solid solution, austenite, for Fe24C finds no place on the diagram. Thus it happens that while the authorities fight both in regard to the iron carbon diagram and the structures met with in hard-

Jan 1, 1913

By S. K. Asunmaa, W. D. English, N. A. Tiner, W. A. Cannon

This paper discusses the reaction of metal surfaces with fluorine. Fluorination reactions result in the formation of metal fluoride films which are "passive" toward further reaction of the metal with fluorine. These films are very adherent, and do not easily detach from the substrate metal by mechanical flexing or thermal shock. Exposure of passive films to a humid atmosphere produces hydrated metal fluorides which cause secondary fluorination reactions upon reexpo-sure of the metal surface to fluorine. The surface films formed range from 10 to 30A in thickness and they pow at the expense of surface oxide films. The apparent film formation is completed rapidly in 15 to 30 min on stainless steel and nickel surfaces. On copper and on Monel surfaces, the film at first grows rapidly, then increases slowly over an extended period of time. Passive films are formed at all fluorine pressures in the range from 0.1 to 1.4 atm at room temperature. ALL metals react when exposed to fluorine. These reactions generally produce surface films which consist of metal fluorides. The rate of reaction is largely determined by the extent to which these films are protective. Although there is an extensive literature concerning reactions of oxygen with metals, there are very few investigations reported concerning fluorine-metal reactions. Brown, Crabtree, and ~uncan' investigated the kinetics of the reaction of gaseous fluorine with copper metal which had been freshly reduced in hydrogen. The reaction rate was independent of pressure over the range from 6 to 60 torr. A logarithmic rate law was obeyed in the temperature range from 25" to 300" ~. There was some deviation at higher temperatures which could have been the onset of a parabolic law. The calculated film thicknesses ranged from about two molecular layers, 10A, for 5 hr exposure at room temperature to thirty-five molecular layers for 5 hr exposure at 200" . The authors concluded that no single mechanism could explain all the observations. O7Donnell and spatkowski2 studied the reaction of fluorine with copper at 450°C at pressures from lo to 133 torr. The reaction was found to be pressure -dependent and followed a logarithmic rate law. It was not entirely diffusion-controlled, and fluorine was thought to be the migrating species in the reaction. Miscellaneous metal-fluorine reactions were investigated by Haendler et ~1.~ Reaction products were identified but no rate data were determined. Air Prod- ucts and Chemicals, Inc., have conducted an investigation of reactions between fluorine and various metal powders at room temperature and 85° C. Fluoride film thickness as a function of time of exposure was reported on the assumption that the reaction takes place between fluorine and metal to form the normal metal fluoride. Surface areas of the powders were only estimated so the relative film thicknesses may not be exact. The data showed reaction rates which were generally logarithmic in character, the rate of film growth virtually ceasing after a few hours exposure time for some alloy powders. The effect of moisture on fluoride films was also investigated by measuring additional reaction with fluorine after exposure of passivated powders to atmosperic moisture. The fluorination of iron was studied by 0'~onnell~ at temperatures from 225" to 525" ~ and at pressures ranging from 20 to 200 torr. In all ranges, the reaction followed a logarithmic rate law and was dependent on the square root of the gas pressure. The author concluded that fluorine gas passes through pores in the film. As the film grows, the blocking of pores leads to a rapid decrease in reaction rate; hence a logarithmic rate law is observed. Jarry, Fischer, and Gunther' investigated the mechanism of the reaction of fluorine with nickel at about 600" to 700°C. On the basis of the metallographic examination of fluoride scales growing on the nickel and from separate radioautographic data, it was claimed that fluorine is the migrating species in the reaction. This is in sharp contrast to the growth of oxide films on nickel where it has been shown that nickel ions migrate through the scale to the gas-solid interface to react with oxygen. Few investigations have been reported of the reaction of fluorine with metal oxides. Such investigations should be of great significance for a better understanding of passivation in view of the ubiquitous oxide films on technical alloys. Haendler et al.3 studied the reaction of fluorine with oxides of copper, tin, titanium, zirconium, and vanadium. Copper (I) oxide reacted as follows in the temperature range 150" to 300"~: temperature above 300" ~ was required for the CuO to react to form additional copper fluoride. Ritter and smith7 also investigated the reaction of fluorine with copper (11) oxide. An oxide powder comprised of spherical particles with a fairly high surface area was reacted with fluorine, starting at room temperature and increasing to 100° C over a period of 3 or 4 hr. The initial reaction was slow until the fluoride film thickness reached about to or 15R at which time the reaction rate accelerated, then decreased again. Most of the kinetic data was obtained during this final phase of reaction. The authors conclude that the film grows slowly at first until the stresses developed in the distorted lattice are sufficient to rupture the initial

Jan 1, 1969

By F. W. SUTTER

IN order to have ore available on the completion of the beneficiation plant at Clifton and to provide for continuous production while underground development was carried out, it was decided to develop an open-pit through the crest of a long hill in which the ore outcropped, using 40-ft. vertical benches.

Jan 1, 1943

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