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By Hugh O?Neill

IN PREVIOUS papers,1 the author has reported the results of experiments on the straining in tension of a single crystal test piece, about 0.6 in. long, of vacuum-melted electrolytic iron containing 1.8 per cent. of silicon. The crystal was originally in the "as cast" condition, and was stressed slowly along a tetragonal axis so that slipping along conjugate gliding planes finally transformed the original cylindrical portion into a pair of fracture wedges. One of these fracture wedges was sectioned along the stress axis in a plane at right angles to the edge of the wedge. A metallographic study of this plane of -section led to the conclusion that slip had taken place in the (111) direction along (112) planes making a V shape with the stress axis. The present paper describes the results of scratch-hardness tests conducted on the same section, in order to determine the distribution of strain hardness therein, followed by annealing, and considers the resulting variations in hardness. These observations supplement those made by Krivobok2 on similar material reduced 25 per cent. by hammering (i. e., by impact) in the cold. In order to investigate ageing effects, two small crystals of the same alloy were also tested.

Jan 1, 1928

THIS chapter and the one following deal with the heat quantities involved in open-hearth steelmaking, including the thermal efficiency of the furnace as a generator of high-temperature heat, the heat storage in the steel and slag produced and in the furnace walls, and the heats of the various chemical reactions involved in combustion, in the formation of slag, and the refining of steel. The fundamental laws to be considered are the simplification of the first two ' laws of thermodynamics as applied to problems involving sensible and potential (or latent) heat only 1. Heat input equals heat outflow plus storage. 2. Heat may be transferred only from a hotter body to a colder one. The first of these laws relates to the various heat quantities or the "heat balance" of the process. No one has as yet made an open-hearth heat balance that came out almost exactly balanced, and we assume that the cause lies in the difficulties of accurate temperature and flow-rate measurements at the high temperatures involved and the inherent complexities of flow distribution, air leakage, etc., present in any real, open-hearth furnace system. Some idea of the magnitude of the heat quantities involved can be obtained- by a brief, crude outline of the heat balance of a 90-ton heat of steel. We will assume a 60 to 70 per cent hot-metal charge in a fairly fast working and only moderately efficient furnace, burning fuel oil, with a fuel consumption of around 4 million B.t.u. per net ton. of ingots produced. The time from start of charge to tap is 9 hr. During this period, the oil burned represents 360 million B.t.u., and the sensible heat in the preheated air at the port ends is 117 million B.t.u. so that the total heat input at the ports is 477 million B.t.u. Heat stored in the steel and slag at the end of the heat, plus the various amounts absorbed by certain bath reactions, amounts to a total of 195 million B.t.u., but 120 million of this is supplied by the heat in the hot metal and by various heat--evolving reactions in the bath, so that only 75 million B.t.u. need be supplied to the bath by the flame.

Jan 1, 1944

By J. Spotts McDowell

INTRODUCTION The magnitude of the thermal expansion of silica brick, and its inability to withstand rapid temperature changes, present problems of considerable importance in the manufacture of siliceous refractories. In the study represented by the experimental data herein described, these problems are considered from the point of view afforded by the results of recent investigators: Fenner and his associates of the "Geophysical Laboratory, Washington, D. C., who have established the stability relations of the silica minerals, and Endell and co-workers in Berlin, who have studied the changes brought about in the constitution of siliceous refractory materials upon the application of heat. In the process of manufacture, the quartzite from which the brick is made changes in part into cristobalite and tridymite. The attempt is herein made to determine by microscopic methods the degree of transformation in various specimens of test bricks manufactured at slightly varying temperatures of burning, with varying coarseness of grain, and to determine the effect of repeated burning. The effect of variations

Jan 10, 1916

By G. Van Esbroeck, M. Van Weyenbergh

The copper mines of the Katanga region in the Belgian Congo lie along the same mineralized belt as those of Northern Rhodesia. There are two distinct types of deposits in that belt, the dolomitic and the quartzitic. In the dolomitic type the metallic minerals are found in a dolomitic limestone country rock. Through oxidation and enrichment, large deposits of high-grade oxidized copper ores were formed, some of which are being worked by the Union Minière du Haut Katanga. Such deposits are all in Katanga. The quartzitic deposits are found in Katanga and Northern Rhodesia. Here the primary mineralization occurred in sandstones and quartzites, in horizons stratigraphically lower than the dolomites. These rocks are not favorable to secondary enrichment and the oxidized zone is poorer than the sulphide zone, which alone contains the ore. There are also in Katanga a few ore-bearing veins. One of them is being worked in the Prince Leopold mine at Kipushi. Prince Leopold Mine The Kipushi ore body fills a fault vein and invades the wall rocks more or less extensively by metasomatic replacement. The vein strikes north-northeast and south-southwest and dips to the west. The variable dip averages 60' to a depth of 300 ft., and more uniformly 80' below 400 ft. In the upper section the average width is 200 ft. and below the width is about 150 ft. The length of the ore body is 2300 feet. The eastern side of the vein—the footwall—is dolomitic and contains irregular masses of ore sometimes extending 100 ft. or more from the main

Jan 1, 1940

By M. Van Weyenbergh, G. Van Esbroeck

The copper mines of the Katanga region in the Belgian Congo lie along the same mineralized belt as those of Northern Rhodesia. There are two distinct types of deposits in that belt, the dolomitic and the quartzitic. In the dolomitic type the metallic minerals are found in a dolomitic limestone country rock. Through oxidation and enrichment, large deposits of high-grade oxidized copper ores were formed, some of which are being worked by the Union Minière du Haut Katanga. Such deposits are all in Katanga. The quartzitic deposits are found in Katanga and Northern Rhodesia. Here the primary mineralization occurred in sandstones and quartzites, in horizons stratigraphically lower than the dolomites. These rocks are not favorable to secondary enrichment and the oxidized zone is poorer than the sulphide zone, which alone contains the ore. There are also in Katanga a few ore-bearing veins. One of them is being worked in the Prince Leopold mine at Kipushi. Prince Leopold Mine The Kipushi ore body fills a fault vein and invades the wall rocks more or less extensively by metasomatic replacement. The vein strikes north-northeast and south-southwest and dips to the west. The variable dip averages 60' to a depth of 300 ft., and more uniformly 80' below 400 ft. In the upper section the average width is 200 ft. and below the width is about 150 ft. The length of the ore body is 2300 feet. The eastern side of the vein—the footwall—is dolomitic and contains irregular masses of ore sometimes extending 100 ft. or more from the main

Jan 1, 1940

By F. E. Jaumot, R. L. Smith

Self-diffusion in zinc has been used as an instrument for comparison of the absorption and sectioning techniques as a means of studying diffusion. Single crystal as well as poly-crystal samples were used asanda the temperature range of diffusion extended from 200° to 415°C. For temperatures above 200°C, the data indicate that the results obtained from the absorption technique agree with those obtained from the sectioning technique. The effect on the values of the diffusion coefficient of electroplating vs evaporation as a means of applying the tracer was investigated and no significant difference observed. It was found that an excess or deficiency of tracer did not materially affect the results obtained from the sectioning technique, but invariably caused errors with the absorption technique. NEARLY all self-diffusion experiments and many alloy diffusion experiments have employed radioisotopes as the instrument for following the diffusion. Of the various techniques in which radioisotopes are applicable, the two most widely used are the sectioning and absorption techniques. In the former, the diffusion coefficient is obtained from a curve of log concentration vs the square of the mean penetration depth. In the latter, the diffusion coefficient is calculated from a knowledge of the decrease in activity at the surface after diffusion. In spite of the importance of knowing the reliability of the diffusion data and the widespread use of these two techniques, they had not been directly compared experimentally on the same samples. Thus, such a comparison was worthwhile. The specific system chosen for this comparison was the self-diffusion of zinc, since the metal was readily obtainable in high purity, single crystals were easily grown, and the anisotropic features of the diffusion added an additional factor of interest to the comparison. Self-diffusion in both single and polycrystals was investigated, since the possibility existed that grain boundaries and grain boundary diffusion might produce different effects for the different techniques. Also, the effects of electroplating vs evaporation as a means of applying the radioactive tracer, and the effects of applying an excess or deficiency of tracer material were studied. The general experimental procedures and the mathematical analyses of both techniques have been described previously in some detail, and only those points essential to an understanding of the present work will be discussed here. The mathematical analysis of the sectioning data requires only a knowledge of the solution of Fick's equation. where C,, is the initial concentration, C is the concentration at depth x, D is the diffusion coefficient, and p is the absorption coefficient of the solvent metal for the radiation from the solute. Having obtained F from the experiment, the value of z can be read from a plot of F vs In z, and D can then be calculated if is known. The necessity of knowing the absorption coefficient causes most of the criticism of the absorption technique. It is very difficult to measure accurately under the conditions existing in the diffusion experiment, but it is absolutely necessary, as will be indicated briefly later. Portions of this problem have been discussed in detail elsewhere." The difficulties involved in the measurement of the absorption coefficient arise from three principle factors: the physical characteristics of the absorber, the geometry, and complex radiation spectra. The first two are heavily dependent upon the third. If

Jan 1, 1957

By Shiro Ban-ya, John F. Elliott, John Chipman

The activity of carbon in Fe-C austenite at 1150°C has been determined for concentrations up to about 2.1 pct C using the equilibrium: C + COz = 2CO; equations have been derived expessing the activity as a function of carbon content on the basis of twelve mathematical models. Several of these represent the data satisfactorily. ACCURATE information on the thermodynamic properties of austenite in the binary system Fe-C is needed as a basis for studies of transformation and precipitation in steels of all sorts, alloy as well as plain carbon. The many attempts to approach this problem through statistical thermodynamics require sound and dependable experimental data in order to evaluate the several models which have been suggested. In this paper we are concerned with the experimental determination of the activity-composition relation in austenite at the temperature of its widest range of stability, approximately the eutectic temperature (1153°C). Accurate investigation of the activity of carbon in austenite may be said to have begun with the work of Dunwald and wagner.' A more detailed study was carried out by R. P. smith2 on the two equilibria: More recent work on these two equilibria has been reviewed by Chipman,3 who pointed out the experimental hazards associated with studies of Eq. [I]. Studies of this reaction involve rather small values of the ratio these are susceptible to errors due to traces of moisture in the apparatus according to the reaction: Ellis, Davidson, and Bodsworth4 evaluated K, for their experimental temperatures and used desiccants to control water vapor pressure. While they were able in this way to obtain consistent values for K1 it cannot be said that all of the uncertainties of the method have been overcome. Results by both methods reported by Schurmann, Schmidt, and wagener5 appear to be consistent except at very low carbon content. Reaction [2] was employed in the experimental work reported here. It is to be recognized, however, that it is not applicable to projected studies of certain alloy steel compositions involving stable oxide-formers.

Jan 1, 1970

Part 1. Coal Part 2. Industrial Minerals

Jan 3, 1977

EDITORIAL comments on the anthracite report of the Federal Fact-finding Coal Commission, which became public on July 5, together with an analysis of its more important conclusions, will be found on another page of this issue. In this place, only a few extracts from the report, bearing more directly on technical matters, can be quoted, for lack of space. COST OF MINING Mining cost, as it stands on the books of each mining company, represents the average cost of the total output, all sizes, of anthracite. Egg coal has at least five times the market value of barley, but these' sizes are mined together and their costs can not be separated. Mine costs directly reflect the conditions under which these deposits of coal are recovered. Even within the few counties in which anthracite is found there is a conspicuous range of natural conditions. The distinc-tion between the Northern, Middle, and Southern field, or, as they are also termed, the Wyoming, Lehigh, and Schuykill regions, is primarily geologic and topo-graphic, but the effects of the natural conditions largely control costs. The contrast is great between Some of the level-lying beds of moderate but fairly constant thickness under the broad Wyoming Valley, where mining and underground haulage present relatively simple problems to the engineer, and the steeply pitching or overturned and faulted beds of variable thickness in the Schuykill field, where crushed coal' and treacherous roof multiply the difficulties of mining; and increase the unavoidable waste. Even more direct is the connection between geologic processes and the, differences in the character of the coal as mined, the varying proportions of large and small sizes demanding differences in preparation and resulting in different average prices realized for the product of the mines.

Jan 8, 1923

OFFICERS AND DIRECTORS For the year ending February, 1935 PRESIDENT AND DIRECTOR HOWARD N. EAVENSON PITTSBURGH, PA. PAST PRESIDENTS AND DIRECTORS SCOTT TURNER WASHINGTON, D. C. FREDERICK M. BECKET NEW YORK, N. Y. VICE-PRESIDENT, TREASURER AND DIRECTOR KARL EILERS NEW YORK, N. Y. VICE-PRESIDENTS AND DIRECTORS EUGENE MCAULIFFE OMAHA, NEB. PAUL D. MERICA NEW YORK, N. Y. HENRY KRUMB SALT LAKE CITY, UTAH EDGAR RICKARD NEW YORK, N. Y. LOUIS S. CATES NEW YORK, N. Y.

Jan 1, 1934

By A. A. Bauer

The ?-to-? transformation has been studied in zirconium alloys containing 22 to 70 wt pct U. In this range of compositions the ? phase can be retained by quenching. Transformation to ? occurs by a nucleation-and-growth process. The diffusion of atoms to preferred lattice sites to yield a partially ordered structure apparently controls the rate of reaction. Alpha uranium and a zirconium precipitate from the supersaturated E phase initially formed in alloys outside the equilibrium E phase composition limits. ZIRCONIUM-Uranium alloys have long been of interest for reactor-fuel applications because of the low thermal-neutron cross section of zirconium. Considerable information is available on the various properties and behavior of these alloys1 although there had been a number of areas where information was incomplete. As part of a program to provide more detailed knowledge in these areas, the presently reported investigation was undertaken. The constitutional diagram of the zirconium-uranium system is shown in Fig. 1.' The system is distinguished by a region of complete solid solubility between the body-centered cubic ß-zirconium and ? uranium phases and the existence of an intermediate phase in the vicinity of 50 wt pct U. This intermediate phase, designated as E, is reported3 to have a primitive hexagonal structure with a = 5.03 and c = 3.08A. The structure is partially ordered with zirconium atoms at the 0, 0, 0 position and zirconium and uranium atoms located randomly at the 1/3, 2/3, 1/2, and 2/3, 1/3, 1/2 positions. While the E phase may be nominally designated as of UZr2 stoichio-metry, the random distribution of uranium and zirconium atoms permit a considerable range in composition. Of interest in the research performed were alloys in the range from 20 wt pct (10 at. pct) to 70 wt pct (47 at. pct) U. In this range of compositions the body-centered-cubic ? phase can be retained either completely or partially on quenching. The nature and kinetics of transformation of the ? phase were the subject of study. Proceeding concurrently with the presently reported work was an investigation by Kearns4 which has since been reported. Kearns studied alloys containing 50 to 60 wt pct U prepared from sponge zirconium. While the work reported here is for alloys prepared from crystal-bar zirconium and the techniques of study are to some extent dissimilar to those employed by Kearns, general agreement so far as results and interpretation can be reported. Experimental Techniques—Alloys were prepared and the transformation of the ? phase studied during interrupted-quench and quench-and-temper isothermal heat treatments by means of hardness measurements and X-ray diffraction and metallographic techniques. The isothermal transformation of the ? phase on quenching and tempering was investigated further employing dynamic-modulus measurements. Electrical resistivity and limited Hall coefficient measurements were also obtained as part of the study. Alloy Preparation and Heat Treatment— Alloys containing 15, 20, 22, 30, 40, 45, 50, 55, 60, and 70 wt pct U were prepared from as-reduced uranium and crystal-bar zirconium. The alloys were double arc melted by consumable-electrode are-melting techniques. The final ingots were forged and rolled at temperatures between 790" and 840oC to 1/4-in. rod and 1/8-in. sheet. Chemical analyses of the fabricated alloys were

Jan 1, 1961

By Gerald F. G. Sherman

The ore deposits of the Warren district, in which the mines of the Copper Queen Consolidated Mining Co. are situated, have been described in a number of technical publications, and will not be discussed here in detail. Certain of their characteristics, however, control methods of underground transportation and hoisting of ore. In the Copper Queen mine, the majority of the ore has occurred in a zone encircling the west boundary of the porphyry intrusion of Sacramento Hill. It has a width varying from 800 to 1,200 ft., and a thickness of about 400 ft. It reaches the surface in the older part of the mine to the northwest, but dips to the southeast, where it is reached at 1,400 ft. below the Czar collar, in its farthest extension at present developed on Copper Queen ground. There is one major extension from the northwest end of the zone toward the west along the Czar fault, and others of minor importance. Individual orebodies are scattercd through the zone in an eccentric manner, only matched by their own irregularities of form and size. Their most gencral characteristics are the softness of the ore and their grcat horizontal rather than vertical extent. It has been estimated that the average vertical thickness of ore in the Czar and Lowell divisions is between 30 and 35 ft. It is calculated by assuming it to be uniformly distributed over its horizontally projected area. In this zone, and for some distance above it, the ground has been subjected to intense alteration and intense but irregular oxidation. It has resulted in an enormous quantity of earthy or clayey material, which may be either ore or waste, which when wet is both heavy and tenacious. Below alteration, the ground is fairly hard, and the limestones contain primary ores differing from those heretofore considered typical of the camp, and which have not yet been thoroughly exploited. The mine production has been drawn from many orebodies spread over a great area.l A diagram map (Fig. I), of haulage drifts and loading stations, illustrates the situation in 1914.

Jan 1, 1916

By Edward B. Durham

The refinery at the San Francisco Mint takes the bullion purchased by the receiving department, and carrying Illore than 200 parts of precious metals in 1,000, or, in mint parlance, over 200 fine, and separates and refines the various metals contained therein, using electrolytic processes exclusively. Bullion containing silver is treated in cells charged with a nitric electrolyte. These cells produce fine silver and leave a residue rich in gold. The residue from the silver-cells, together with crude gold-bullion, is treated in cells having a chloride electrolyte. These produce fine gold and leave a residue containing silver chloride. The latter is reduced to the metallic state with zinc and is then treated in the silver-cells. The various waste solutions and the wash-waters, after being freed from the bulk of their precious metals, still contain copper and other metals. These are removed by scrap-iron, and are then treated in the copper-cells, having a sulphate electrolyte. These cells produce pure copper, and collect a residue containing lead, some gold and silver, and all the metals of the platinum gronp that were in the bullion. This residue is relatively small, and is melted into bars and stored until suEcient accumulates to warrant treating it for platinum, etc. The refinery occupies three large and three small rooms. The large ones are, a melting-room, 30 by 34 ft.; a cell-room, 39 by 46 ft.; and a wash-room, 30 by 33 ft. The small rooms are used as foreman's osce, laboratory, and , re- spectively. The methods here described are those in use in December, 1909, when notes for the present paper were taken.

Jan 1, 1912

By J. R. McWilliams

Several of the current concepts of brittle fracture involve consideration of the existence of defects or flaws. Griffith 1 observed that the tensile strength of brittle materials was several orders of magnitude less than might be expected from the calculated strength of the molecular bonds. He was able to show that the stress concentration at the tip of an elliptical crack is sufficient to raise the local stress level many fold. He therefore proposed that real materials do contain such stress risers in the form of minute cracks and that this accounts for the rather large difference between theoretical and actual strengths of brittle materials. The degree of stress magnification depends to a great extent upon the orientation of the crack with respect to the general stress system, and to the general geometry of the crack.

Jan 1, 1967

By R. J. Woody

DESIGN of the most economic continuous counter-current decantation (CCD) circuit is based on selection of the number of stages and the wash volume that will give the minimum summation of the following items: 1) Capital and operating costs of the CCD circuit. 2) Capital and operating costs of the precipitation circuit. 3) Value of the dissolved product lost.

Jan 7, 1958

By C. H. Jr. Herty

ALMOST every metallurgist who has given the Howe Memorial Lecture has had a personal contact with the distinguished gentleman to whose honor this hour is devoted. Unfortunately for me, such personal contacts were not possible. However, in the preparation of a thesis on the open-hearth process, one of my earliest tasks was to make a survey of the literature, and it was from Professor Howe's Metallurgy of Iron and Steel that I drew a number of references to previous work which formed the foundation for my reading. In his volume there is such a complete exposition of the then current thought on the subject of slags and on their role in the elimination of phosphorus from steel that I feel no hesitation in discussing in this Howe Lecture the subject of "Slag Control." In the present era of close specification, the drive for uniformity of product, and the close inspection of the product and of the cost sheet, the utmost efforts must be made to control the steelmaking variables to the best advantage of the steel producer. One of the major variables is the slag in the furnace and its effect upon the composition and quality of the metal. What advantages are to be gained from slag control? In the broad sense the advantages must be tremendous, because the very foundations of good steel melting are based on "shaping up" the slag to a point where, with proper temperature, the heat is ready for the final additions. Every melter works toward these ends through his experience with innumerable heats of steel. The elimination of undesirable constituents such as phosphorus and sulphur is entirely a matter of slag composition and physical nature, a point well known for over half a century. The role played by the slag in assisting in proper heat transfer from roof and flame to the steel has been equally well known. In more recent years there has come the problem of oxygen control in the more accurate gaug-ing of additions for making high-grade rimmed steel for the new strip mills, and in the deoxidizing additions for grain-size control and cleanli-ness of forging steels, both carbon and alloy. In this problem the oxidiz-ing characteristics of the slag are of prime importance.

Jan 1, 1940

Jan 1, 1881

By F. E. Buch

The smelter is designed for a production capacity of 10,000 short tons of blister copper per month, when operating on the present concentrate grade. The :smelter lay-out is shown in Fig I. The major units of equipment comprise two reverberatory furnaces, three 13 by 30 ft Peirce-Smith converters, two straight line casting machines, one being served by a 13 by 30 ft holding furnace and the other by a ladle tilting quadrant, two converter aisle cranes and two converter blowers. The plant is compact and the general arrangement of standard gauge railway tracks and conveyor belts provides for a smooth flow of incoming materials and metallurgical products. Concentrate is received by conveyor belts and fluxes in standard railway trucks. The local track system is covered by an electric trolley locomotive. The Smelter treats a wet (10 pet moisture) flotation concentrate containing approximately 53 pct total copper and 0.9 pet oxide copper. The predominating minerals are chalco-cite, chalcopyrite and bornite accompanied by small quantities of malachite and cuprite. The gangue is highly siliceous and requires limerock as a flux. Metallurgy would be straightforward were it not for the necessity for eliminating bismuth which occurs as an impurity in the ore along with the copper. Directly or indirectly most of the Smelter problems can be traced to the necessity for bismuth removal. Copper recovery, based on new copper treated, averages 97.5 pct. General Description Flotation concentrate, containing 10 Pet moisture, is conveyed from the filter plant to the smelter storage bins by conveyor belts, the material being weighed in transit by a revolving drum type of weigh-hopper manufactured by Samuel Denison and Son, Ltd. The weigher consists of a steel drum with dished ends carried on a horizontal shaft and rotated by an 8 hp squirrel-cage motor through a worm and Spur reduction gear. A feed mouth in the drum permits of filling and discharging. The whole unit is supported on a framework resting on weighing levers, which in turn connect to transfer levers, thence to an indicator of the steelyard type situated 16 ft from the centre line of the drum. The indicator is of the "Denison" patent equilibrium controlled ticket stamping type, insuring mistake-proof records by a combination of electrical and mechanical movements which Prevent the operator from printing until the cover enclosing the steelyard is closed and until the poise-weights have been Set correctly to the weight of the hopper and contents. The machine is capable of weighing 30 short tons at a time but the usual load is 28 tons. After obtaining the gross weight the drum is rotated and discharged into a receiving bin situated below it. The empty drum is weighed and the net weight re-

Jan 1, 1949

By Warren B. Davis

Introduction If a subject this broad were to be covered in even moderate detail, it would require a set of books about the size of an encyclopedia. Since an acceptable length for this paper is a small fraction of one book, it will have to consist of a few samples of the subjects that I think are the most pertinent to World Fossil Fuel Economics. I plan to discuss the trends in world energy demand, particularly in the U. S. and Europe; the consumption patterns and cost patterns of oil, gas and coal; the prospects of synthetics; and some of the effects of government regulation of fuel economics. World Energy Demands Fig. 1 shows Free World energy consumption by principal areas for the period from 1950 to 1970 and a forecast for the period from 1970 to 1985. These figures include only the measurable forms of energy. An example of energy consumption that is not measured is the wood a peasant might cut in the forest and bum in a fireplace to heat his home. This omission probably is a very small part of the total. This forecast is not identical with that of Wayne E. Glenn (see Page 22), but the differences in total energy consumption are not significant. The U. S. consumption, which was 55 percent of the world total in 1950, had declined to 45 percent by 1970, and is expected to decline further to 38 percent by 1985. Western Europe has consumed 28 percent of the total from 1950 to 1970 and is expected to lose share slightly between 1970 and 1985. The most spectacular gainer is Japan, which increased consumption from 2.5 percent in 1950 to 7.5 percent in 1970, and is expected to reach nearly 17 percent by 1985. The over-all Free World total has grown from 62 quadrillion Btu (equivalent to 29 million B/D of crude oil) in 1950 to 151 quadrillion by 1970, an average growth rate of 4.5 percent/year. This total is expected to grow at a rate of 5 percent/year between now and 1985, reaching 315 quadrillion Btu (equivalent to nearly 150 million B/D). Fig. 2 shows which fuels supplied this energy between 1950 and 1970, and gives an estimate of how it will be supplied between 1970 and 1985.

Jan 1, 1971

By J. E. Hilliard, J. W. Cahn

calculation has been made of the standard deviations to be expected in the measurement of volume fractions by areal analysis, lineal analysis and four point-counting Procedures. The effect of experimetztal errors is not included. Our conclusion is that a point count using a two-dimensional grid will be the most efficient method of volume fraction analvsis providing the grid spacing IS coarse enough. The predicted standard deviation for such an analysis is shown to he in good agreement with that determined experimentally. A metallurgist wishing to estimate a structural property by means of quantitative metallography is often faced with a choice between several different procedures. In such a case, he will naturally wish to know: a) Which procedure is the most efficient in the sense of requiring the least effort for a given precision? b) For a given procedure, what are the conditions for maximum efficiency? c) Under these conditions, how many measurements are required to attain a given precision? It is our aim in this paper to provide at least partial answers to these queries as they relate to the estimation of volume fractions from measurements on a random two-dimensional section of an opaque specimen. The commonly used techniques1,2 for volume-fraction analyses are based on one or more of the following principles: i) For an areal or Delesse3 analysis: That the areal fraction of a three-dimensional feature intercepted by a random plane provides an unbiased estimate of the volume fraction of that feature. ii) For a lineal or Rosiwal4 analysis: That the fractional intercept on a line passing at random through a two-or three-dimensional feature provides an unbiased estimate of, respectively, the areal or volume fraction of that feature. iii) For a point-count analysis: That the fractional number of randomly or regularly dispersed points falling within the boundaries of a two-dimensional feature on a plane, or within the boundaries of a three-dimensional feature in a volume, provides an unbiased estimate of, respectively, the areal or volume fraction of that feature. The absence of bias referred to in these principles does not, of course, imply that the results of an analysis will be free of error, but only that the expected result is equal to the true one. Application of the foregoing principles provide the following six possible experimental procedures: a) An Areal Analysis—This involves the measurement with a planimeter (or other means) of the area of a constitutent intercepted by the plane of polish b) A Two-Dimensional Random Point Count—Apos-sible experimental procedure for this analysis is to superimpose a sheet of transparent graph paper on a micrograph, and then use a table of random numbers to select coordinates for the points. c) A Two-Dimensiotuzl Systematic Point Count-Similar to b) except that the points are distributed in a prescribed manner, usually at the corners of a lattice superimposed on a micrograph or the screen of a projection microscope. d)A Lineal Analysis—A measurement of the fractional line length intercepted. It is usually performed by traversing the specimen under the cross hairs of a microscope and recording the distance travelled in each constituent. e) 4 One-Dimensional Random-Point Count— This could be performed by traversing the specimen with stops at random intervals to identify the constituent then present under the cross hairs. f) A One-Dimensionul Systematic Point Count— Similar to e) except that the traverse is stopped at prescribed (usually equal) intervals. It will be noted that the point-counting procedures b) and c) can be regarded as methods of estimating the areal fraction. Similarly, e) and f) are indirect methods of making a lineal analysis. All of the six procedures described above involve at least one stage of sampling. Thus, quite apart from any experimental errors, there will always be a statistical uncertainty associated with the final results. It is with the calculation of this uncertainty that we will be concerned. To avoid unnecessary repetition, the statistical relationships that will be used in the calculations are collected together in the appendix. For a fuller discussion reference should be made to one of the many textbooks5,6 on statistics. For symbols relating to the specimen structure we will follow as far as possible the terminology used by Smith and Guttman.7

Jan 1, 1962