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By David M. Parkes, Junie Lindsay

A review of the movement of coal in water is undertaken from a practical rather than a theoretical view point. Installations are described in which coal is transported on gradients down to 2.5' and others which move coal at a water-coal ratio of 1:l by weight. The water cycle of the hydraulic mining system is discussed. In many applications this can be a closed circuit. The coal dewatering system is illustrated, making particular reference to the problems of storage of coal-water mixtures between the mine and the plant. Water treatment is done in thickeners down to 100 ppm which is normally sufficient for re-circulating through high pressure pumps and monitors.

Jan 1, 1978

By E. R. Parker, D. L. Martin

During the heat-treatment of silver specimens for tensile tests it was observed that the bars blistered and became brittle when heated in a hydrogen atmosphere. To check this unexpected result, a wide variety of commercial silvers were heated in hydrogen at 850°C. Only a few of the materials developed blisters, the most severe of which is the tube pictured in Fig. I. The microstructure of a cross section of the tube is shown in Fig. 2. The embrit-tlernent is extremely severe at the edge; the blisters result from the severe deformation of the surface material by large under- lying gas pockets. The effects resulting from hydrogen embrittlement of silver have been observed by numerous investigators over a long time l,2,3 although it was only recently that a clear explanation was offered.4 However, the damage resulting from hydrogen embrittlement has not been generally recognized; and it is of advantage to know more about this phe- 1 References are at the end of the paper.

Jan 1, 1943

By D. L. Martin, E. R. Parker

During the heat-treatment of silver specimens for tensile tests it was observed that the bars blistered and became brittle when heated in a hydrogen atmosphere. To check this unexpected result, a wide variety of commercial silvers were heated in hydrogen at 850°C. Only a few of the materials developed blisters, the most severe of which is the tube pictured in Fig. I. The microstructure of a cross section of the tube is shown in Fig. 2. The embrit-tlernent is extremely severe at the edge; the blisters result from the severe deformation of the surface material by large under- lying gas pockets. The effects resulting from hydrogen embrittlement of silver have been observed by numerous investigators over a long time l,2,3 although it was only recently that a clear explanation was offered.4 However, the damage resulting from hydrogen embrittlement has not been generally recognized; and it is of advantage to know more about this phe- 1 References are at the end of the paper.

Jan 1, 1943

By S. C. Termes, P. E. Richardson, R. L. Wilfong

This paper discusses recent Federal Bureau of Mines research on the selective flocculation of various minerals with insoluble cross-linked starch xanthate (ISX). ISX is insoluble, has a shelf life of more than a year when kept cold, and has a higher molecular weight due to cross-linking than the soluble, non-cross-linked starch xanthate used in previous flocculation studies on nonsulfide minerals. ISX readily flocculates a number of sulfide mineral fines, but no silicious gangue. Floc formation, floc size, and settling rate are dependent on pH. The pH dependence, however, differs for each mineral. Bornite has been selectively flocculated from bornite-quartz mixtures, and the bornite-containing flocs were separated from the unflocculated quartz using decantation and washing procedures.

Jan 1, 1984

By H. H. Rachford, D. W. Peaceman

A system of partial differential equations describing miscible displacement of fluids in porous media is derived The system takes into account the influence of gravity, the spatial distribution of permeability, diffusion, and fluid viscosities and densities. A numerical procedure for approximating solutions to the differential systems has been tested for a horizontal two-dimensional geometry. In end-to-end displacements of oil with less-viscous solvents, the numerical solutions exhibited fingering qualitatively similar to that observed in laboratory models. Small random spatial variations in permeability about the mean value are sufficient to initiate fingering. Quantitative comparisons of computed results with laboratory data show good agreement. INTRODUCTION Miscible flooding of oil by solvent is receiving increasing consideration for field use.1-4 Unfortunately, such floods potentially present severe problems in loss of recovery through the by-passing of oil by expensive solvent. Consequently, their economic evaluation requires sound techniques for predicting recovery. The purposes of this work are to present a finite-difference method for calculating the multidimensional displacement of oil by solvent and to investigate the validity of the method by comparing results of calculations with data from displacements in laboratory models.5 The formulation of the method to simulate the model experiments treats a case of limited scope in the description of solvent flooding in the reservoir. The model experiments were carried out with fluids that were assumed to form an incompressible, ideal, two-component system with constant diffusivity. Establishing the validity of the method even in its present form provides a major step toward the goal of quantitatively evaluating individual solvent flooding projects. First, it demonstrates the fea- sibility of calculating the course of displacements which are dominated by an inherent macroscopic instability, i.e., viscous fingering. In addition, the method provides almost the only practical means of examining the effect of the size and extent of reservoir inhomogeneities on the development and propagation of the fingers, taking into account the important influences of diffusion and gravitational segregation. It might be inferred that such studies cannot yield results of practical value because in displacements dominated by macroscopic instability the pattern of finger development and the resulting performance should depend critically on small variations in the geometric distribution of reservoir inhomogeneities. The present method offers the capability inherent in computational techniques of predicting performance reproducibly with any arbitrary distribution of reservoir properties and, as such, provides a means of evaluating the sensitivity of behavior to uncertainties in reservoir definition and, thus, assessing the reliability of prediction of performance. THE PHYSICAL PROBLEM DATA USED FOR QUANTITATIVE TESTS OF CALCULATIONS In this work, a calculation for treating the miscible-displacement process is tested by comparing calculated results with experimental data. The experiments chosen for comparison have been described in detail,5 and the quantitative features are summarized in a later section. Briefly, oil was flooded by solvent of equal density from a thin rectangular channel in Lucite packed with uniform Ottawa sand. Under these conditions, two-dimensional geometry is considered adequate to represent the process. Inasmuch as the present work is concerned with testing of the method by comparison with specific two-dimensional data, the system of equations presented in the succeeding section will be oriented to defining the physical system specifically. THE DIFFERENTIAL EQUATIONS Suppose x, y to be a Cartesian co-ordinate system and define h(x, y) to be the height of a point above a horizontal reference plane. It will be assumed

By Arthur A. Brant

Let us start back as far as possible, to the beginnings of this universe, some 5 billion or more years ago. This is a time interval that can be crudely underestimated by the moon-earth tidal friction effects that have increased the length of the day by about 1/1000 second per century-from a 5 to 7 hour day to its present 24-and have moved the moon away at 5 inches per year to its present 240,000 miles. The oldest stony meteorites from interplanetary space give an age dating of some 4.6 billion years, approximating the time of formation of our earth. Further, certain stars pulsate, the period of pulsation being related to their absolute brightness. Measuring apparent brightness and comparing, gives the distance away. Thus Hubble and Shapley of Harvard, from 1925 on, were able to show that the universe reached as far as our telescopes could scan. The Doppler shift of the hydrogen red lines could only mean that the nebulae, or galaxies, were moving away at velocities increasing with their distances, by 180 km/ sec velocity increase for every million light year's distance. In short, the universe is expanding like an exploded bomb.

Jan 4, 1964

By P. M. Blair, D. W. Peaceman

The shape and position of the gas-oil transition zone during downdip displacement of oil by gas has been calculated using flow equations which include the effects of gravity, relative permeability, capillary pressure and compressibility of the fluids. The calculations treat the problem in two space dimensions, and results are compared with data from a laboratory model tilted at 30° and 60° from the horizontal on displacements near and above the maximum rate at which gravity segregation prevents channeling of the gas along the top of the stratum. The good agreement between calculated and experimental results demonstrates the validity of the tecbnique as well as that of the flow equations. INTRODUCTION Knowledge of the fluid distribution and movement in an oil reservoir is important in producing operations and estimation of reserves. The history of the oil industry has included steady progress in improving the accuracy of calculations which provide the required knowledge. The earliest method of calculating reservoir performance consisted of material-balance equations based on the assumption that all properties were uniform throughout a reservoir.l For many reservoirs such a simple formulation is still the most useful. However, when large pressure and saturation gradients exist in a reservoir, the assumption of uniform values throughout may lead to significant error. To reduce these errors, Buckley and Leverett2 introduced a displacement eqation which considers pressure and saturation gradients. Methods available at that time permitted solutions to the Buckley-Leverett equation in one space dimension; these solutions have been very useful in solving many problems related to the production of oil. However, the one-dimensional methods are not adequate for systems in which saturations vary in directions other than the direction of flow. An example of such a system is the case of gas displacing oil down a dipping stratum in which the gas-oil contact becomes significantly tilted. Of course, the Buckley-Leverett displacement method cannot predict the tilt of the gas-oil contact. Recent improvements3,4 of the one-dimensional Buckley-Leverett method achieve some success in predicting the tilt of the gas-oil contact at sufficiently low flow rates. However, at rates high enough that the viscous pressye gradient nearly equals or exceeds the gravity gradient, even these improved one-dimen,sional methods incorrectly predict the shape and velocity of the contact. Further progress in estimating such fluid movements in a reservoir appears to require consideration of the problem in more than one space dimension. The recent two-dimensional method of Douglas, Peaceman and Rachford5 appears adaptable to calculate changes with time of the saturation distribution in a vertical cross-section of a reservoir. The movement of saturation contours should represent the moving fluid contacts and include the effects of crossflow due to gravity, as well as variations in the rock and fluid properties. The nonlinear nature of the equations used in the method has prevented proof of the validity of the solutions. Douglas, Peaceman and Rachford made some comparisons with experiment but did not include cases in which gravity was important nor cases involving displacement by the nonwetting phase.For these reasons, a test of the two-dimensional method for a case in which these factors are included would be very desirable. The test selected was a comparison of calculated results with those from a carefully controlled laboratory experiment on a model with measured physical properties. The model selected was one in which gas displaced oil down a tilted, rectangular sand pack. The model can be thought of as representing a vertical cross-section taken parallel to the dip of a reservoir. The displacement thus simulates gas displacing oil downdip that might result from gas-cap expansion or gas injection. This report outlines the calculation method used

By J. R. Thoenen, M. C. Malamphy, G. K. Dale

The beginning of the war and the events leading up to it precipitated a near crisis in the aluminum industry. Demands for the metal reached proportions far beyond the prewar production capacities and, in addition, the submarine menace seriously curtailed the importation of bauxite from South America, hitherto a chief source of high-grade ore. The situation required an intensive search for domestic ore to augment the reserves and in October 1941 Congress directed the Department of the Interior to investigate the extent, mode of occurrence, and quality of bauxite in the United States. In December of that year the Bureau of Mines and the Geological Survey began the search for bauxite in Arkansas, where more than go per cent of the domestic ore had been produced and where the greatest amount of bauxite was known to occur. The program involves the geophysical and geological investigation of the Arkansas bauxite region and the core drilling of areas considered favorable for the occurrence of bauxite deposits. Cores taken from the bauxite-kaolin zone are sampled and analyzed in the Bureau of Mines laboratory in Little Rock. The information from each of the deposits discovered is then assembled, the bauxite is graded with respect to its possible utility, tonnage estimates are made, and the whole is presented in the form of a war minerals report. Thirty-eight new bauxite deposits had been discovered and investigated at the end of the calendar year 1944, and the presence of several others had been indicated by the drilling. More than 5000 holes had been drilled throughout the bauxite region, and more than 60,000 chemical analyses had been made of samples taken from the bauxite-kaolin zone. A study of the chemical analyses led to certain general conclusions not only with regard to the chemical composition of Arkansas bauxite, but also with regard to its component minerals. Charts and diagrams based on these conclusions have been developed for practical use by the Bureau of Mines: (I) to serve as a check against laboratory analyses, (2) to present tonnage estimates of ore bodies based on mineral composition, (3) to illustrate the relationship of tonnages of bauxite to the alumina, silica, and iron content, and (4) to serve as a control for mining operations by providing a means for quick estimates of the value of the ore from a partial analysis of its chemical constituents. The use of charts and diagrams similar to those discussed in this paper-- is not new. The use of the trilinear diagram for studying the ultimate analyses of coals as of proposed by Ralston in Bureau of Mines Technical Paper 93 (1915) showed that the various ranks of coal fell in different areas on the diagram and that volatile matter, calorific value and other properties could also be plotted by the use of contours. A considerable subsequent literature, largely on classification of coals, has accurnulated since then, showing the utility

Jan 1, 1948

By J. R. Thoenen, M. C. Malamphy, G. K. Dale

The beginning of the war and the events leading up to it precipitated a near crisis in the aluminum industry. Demands for the metal reached proportions far beyond the prewar production capacities and, in addition, the submarine menace seriously curtailed the importation of bauxite from South America, hitherto a chief source of high-grade ore. The situation required an intensive search for domestic ore to augment the reserves and in October 1941 Congress directed the Department of the Interior to investigate the extent, mode of occurrence, and quality of bauxite in the United States. In December of that year the Bureau of Mines and the Geological Survey began the search for bauxite in Arkansas, where more than go per cent of the domestic ore had been produced and where the greatest amount of bauxite was known to occur. The program involves the geophysical and geological investigation of the Arkansas bauxite region and the core drilling of areas considered favorable for the occurrence of bauxite deposits. Cores taken from the bauxite-kaolin zone are sampled and analyzed in the Bureau of Mines laboratory in Little Rock. The information from each of the deposits discovered is then assembled, the bauxite is graded with respect to its possible utility, tonnage estimates are made, and the whole is presented in the form of a war minerals report. Thirty-eight new bauxite deposits had been discovered and investigated at the end of the calendar year 1944, and the presence of several others had been indicated by the drilling. More than 5000 holes had been drilled throughout the bauxite region, and more than 60,000 chemical analyses had been made of samples taken from the bauxite-kaolin zone. A study of the chemical analyses led to certain general conclusions not only with regard to the chemical composition of Arkansas bauxite, but also with regard to its component minerals. Charts and diagrams based on these conclusions have been developed for practical use by the Bureau of Mines: (I) to serve as a check against laboratory analyses, (2) to present tonnage estimates of ore bodies based on mineral composition, (3) to illustrate the relationship of tonnages of bauxite to the alumina, silica, and iron content, and (4) to serve as a control for mining operations by providing a means for quick estimates of the value of the ore from a partial analysis of its chemical constituents. The use of charts and diagrams similar to those discussed in this paper-- is not new. The use of the trilinear diagram for studying the ultimate analyses of coals as of proposed by Ralston in Bureau of Mines Technical Paper 93 (1915) showed that the various ranks of coal fell in different areas on the diagram and that volatile matter, calorific value and other properties could also be plotted by the use of contours. A considerable subsequent literature, largely on classification of coals, has accurnulated since then, showing the utility

Jan 1, 1948

US 4,185,996 -- Removal of arsenic and sulfur Impurities from arsenic-containing cobalt sulfide ore. The ore is oxidized In air at a temperature of 700 to 800°C for 3 to 8 hr to drive off the bulk of the sulfur The oxidized ore 1s heated with a reducing gas at a temperature of 700 to 800°C for 2 to 6 hr to volatilize arsenic, and the final calcine 1s leached with an acid to eliminate substantially all of the remaining arsenic. A.R. Zambrano, assigned to Hanna Mining Co Jan. 29, 1980. 3 pp. (75-2). Filed. 2-13-78 (877,002).

Jan 1, 1982

By S. Dinda

A series of as -quenched 4340 bars were drawn through a carbide die to various reductions. The X-ray diffraction technique of Lopata and Kula was employed to detect preferred orientation in drawn martensitic steel bars with low amounts of deformation, as lord as 0.8 pct The specimen face of each bar examined was cut at a 45-deg angle to the bar axis. The reflecting planes in the 45-deg face were varied by appropriate rotation of the sample using a spectrogonionzeter. TIE X-ray bean of a diffractometer was reflected from the center of the bar and the diffracted intensity was delected with a proportional counter and recorded. Intensity peaks were developed by cold working for 110 planes oriented at 0 and 60 deg to the bar axis. The intensity peaks increased with increasing defortnalion us a preferred orientation with a 110 texture developed parallel to the drawing direction. The intensity peaks for deformed as-quenched specimens remain unchanged after tempering at temperatures as high as 1000°F. The same amount of preferred orienlalion was observed both inferritic (hot-rolled) and martensitic (as-quenched) structures after an equivalent amount of deformation. THE deformation of martensite with medium carbon content. less than 0.5 pct, has been studied by Breyer et a1.1,2 It was reported that changes in properties such as resistivity, carbide precipitation, and the introduction of a yield point phenomenon were produced after cold reduction of as-quenched AISI 4340 steel bars. Later, Breyer and Nachtman3 studied the effect of cold reduction upon X-ray line intensity. They showed that the integrated 110 line intensity increased with increasing deformation when the planes examined were perpendicular to the die drawing direction. The integrated 110 line intensity for planes oriented at 45 deg to the die drawing direction, in contrast, were found to slightly decrease. These changes were proposed to be consistent with the previously proposed model of a stress-induced ordering of carbon atoms in the vicinity of dislocations.1,2 Objections can be raised to the above interpretation of the X-ray results on two grounds: a) Rough structure factor calculations indicate that the intensity changes are too large (50 pct observed vs 2 pct calculated4,5) to be the result of changes in the location of iron atoms produced by the stress-induced ordering of the carbon atoms. b) The results might be explained in terms of preferred orientations, although X-ray evidence of the development of texture has not been reported in the literature for deformations as slight as 1 or 2 pct. The aim of the present work was to determine if preferred orientation was present in such cold-drawn martensitic steel bars. In drawn rod or wire there is generally a certain crystallographic direction which is aligned in the direction of the wire axis, and the crystallographic planes are distributed symmetrically around this "fiber axis".6-8 This type of cylindrical specimen, with the fiber axis located at the center, will show rotational symmetry. Lopata and Kula9 proposed an experimental method utilizing a specimen cut at 45 deg, see Fig. 1. The X-ray beam is diffracted from the center of this bar cross section. The specimen is rotated around an axis perpendicular to the bar axis and lying in the 45-deg cut face. This permits the angle between the normals to the reflecting planes and the bar axis to be varied from 0 to 90 deg.9 With this arrangement the errors due to absorption and irradiated volume compensate each other.' This greatly simplifies analysis of the data and is of considerable advantage for quantitative measurements. If there is preferred orientation in the specimen, more planes are oriented in a particular direction in the bar. When the bar is rotated to the favorable Bragg condition for that particular orientation, the intensity will be higher than that for some other angle. This technique was adopted for the present investigation.

Jan 1, 1969

By L. G. Margolin

INTRODUCTION In this paper we derive an expression to predict the onset of growth of a crack in a quasibrittle material. We employ an energy criterion, which was first proposed by Griffith (1920), and is essentially equivalent to the first two laws of thermodynamics. The criterion is applied to the elastic-plastic crack of Olesiak and Wnuk (1968), which is a three-dimensional generalization of the Dugdale (1960) crack. Our expression for the onset of growth differs in several respects from a criterion based on a crack in a brittle material (i.e., using linear elastic fracture mechanics) . Furthermore, the new features are in qualitative agreement with the experimental data. Among these new features are 1) the dependence of the apparent surface energy, or critical strain energy release rate on crack size (the shape of the R-curve); 2) the effect of in-plane stresses (i.e., the stresses that do not lead to any traction on the crack faces) on crack growth; and 3) a brittle-ductile transition. The energy criterion, as a necessary condition for crack growth, rests on a firm theoretical basis. However, its role as a sufficient condition is less secure. Several alternate criteria have been proposed as necessary and sufficient conditions for the onset of crack growth. We will contrast several of these, including critical strain (Olesiak and Wnuk, 1968; Goodier and Field, 1963) and crack opening displacement ("COD", Burdekin and Stone, 1966) with the energy criterion. We will show that these alternate approaches are inconsistent with the energy criterion, in the sense of being necessary conditions, and so should be rejected as criteria for growth--at least for the elastic-plastic crack.

Jan 1, 1984

By Sven Fornander

An account is given of the way in which a new process for desulphurization of hot metal is carried out at a Swedish blastfurnace plant. In the process powdered burnt lime is used as a desulphurizing agent in a rotary furnace. Results are given. IN a paper by Kalling et al.* the fundamentals of a new process for desulphurization of hot metal using powdered burnt lime as a desulphurizing agent were outlined. The purpose of the present paper is to give a brief account of the way in which this process is being carried out in practice by Surahammars Bruks AB, Sweden, and of the results obtained. + The hot metal from the blast furnace is tapped into a ladle of 15 tons capacity and transferred to a rotary furnace, a simplified drawing of which is given in Fig. 1. The rotary furnace has a total length of about 160 in. and an outside diameter of the rings of about 130 in. The furnace is in a horizontal position, with its rings placed on four rollers, and can be rotated by a driving mechanism at various speeds of up to 34 rpm. The rotary furnace and its driving mechanism were designed and constructed at Surahammar. The hot metal is charged into the rotary furnace through the opening to the left in Fig. 1. See Fig. 2. An addition is then made to the furnace consisting of finely ground burnt lime amounting to 2 pct of the weight of the hot metal as well as 0.5 pct of coke breeze. After the additions are made, the furnace is sealed to the atmosphere by means of two lids and set in rotary motion at a rate of 34 rpm. The sulphur in the hot metal is rapidly absorbed by the lime added, the time of treatment needed is normally 30 min. The process is then stopped, the lid is removed, and the furnace is lifted up by a crane and used as a tilting ladle for pouring the metal into the pig-iron molds, Fig. 3. Process Metallurgy The hot metal charged into the rotary furnace has a composition which usually lies within the following limits: C, 3.70 to 4.10 pct; Si, 0.80 to 1.80; Mn, 0.40 to 0.80; P, 0.025 to 0.030; and S, 0.060 to 0.200. Figs. 4 and 5 give examples of the changes in hot metal composition taking place during the treatment in the rotary furnace. As will be seen from the diagrams, the sulphur content of the metal decreases very rapidly during the first 10 min of treatment from about 0.100 to about 0.020 pct S. During the following 20 min, the sulphur content goes down slowly to about 0.005 pct S. The carbon and silicon contents of the metal decrease by about 0.10 pct each during the treatment. The manganese and phosphorus contents remain unchanged. Thus, if the process is started with an iron of the composition given above, the finishing composition of the metal usually lies within the following limits: C, 3.60 to 4.00 pct; Si, 0.70 to 1.70; Mn, 0.40 to 0.80; P, 0.025 to 0.030; and S, 0.002 to 0.020. The chemical reaction taking place during the process can be written:

Jan 1, 1952

By Horace C. Knerr

It has been shown that the resistance to corrosion of duralumin sheet is greatly influenced by the quenching medium used in heat treatment, or, more specifically, by the rate of cooling during quenching. The severity of corrosive attack after exposure to salt-water spray increases in .the following order: The tensile strength, yield point and elongation are only slightly affected by the quenching medium, as shown in Table 1. Tensile test requirements: yield stress, 25,000 lb. per sq. in. minimum; ultimate stress, 55,000 lb. per sq. in. minimum; elongation in 2 in., 18 per cent. minimum.

Jan 1, 1931

Jan 1, 1892

[PRESIDENT E. DEGOLYER, District 0 NEW YORK, N. Y. PAST PRESIDENTS J. V. W. REYNDERS, District 0 . NEW YORK, N. Y. SAMUEL A. TAYLOR, District 3 PITTSBURGH, PA. FIRST VICE-PRESIDENT GEORGE OTIS SMITH, District 4 .WASHINGTON, D. C.]

Jan 1, 1928

By A. P., Svenningsen

ECONOMICAL handling of a minimum of 25,000 tons of minus 3/4-in. ore per day, grinding it to 2 per cent on 65 mesh, and effecting a high recovery of the copper at the lowest possible cost were the principal aims in the design of the new Morenci concentrating plant. Dealing with a tonnage of this magnitude, it is obvious that lost motion cannot be tolerated. When ore is carried on a conveyor an unnecessarily long distance or elevated to a greater height than necessary, or when pulp flows in a launder by a circuitous route thereby losing elevation and distance, we have lost motion which is always costly both from the standpoint of construction and operation. In addition to the 25,000 tons of ore which must be handled, 100,000 tons of water per day has to be carried through the plant in the treatment of the ore. Though water is not so difficult to handle as the ore, the combined tonnage represents a figure which could easily run into a considerable monetary loss per day if all phases of the design were not carefully followed with the idea of eliminating any unnessary handing of materials.

Jan 1, 1942

By Charles B. Henderson

DESPITE the loss, by enemy conquest, of a high percentage of our normal sources of supply for tin, the position of this important metal is easier today than that of rubber and a long list of other strategic materials, many of which are produced in this country. Actually, there is no shortage of tin for essential war purposes, owing to a strict control of its use, to increasing considerably the amount of secondary tin available, and to the foresight of the Government in authorizing the Reconstruction Finance Corp., as early as June, 1940, to acquire and produce certain critical and strategic materials of which tin was one of the most important. The construction of the Longhorn Smelter on the Gulf Coast in Texas is an important part of this program.

Jan 1, 1943

By Robert Linton

AT its meeting on May 21, the Board of Directors approved the recommendations submitted by President Lovejoy and named a nominating committee for the year that is especially well distributed as to major technical interest and as to geography. As may be seen from the list published herewith, two come from the East, two from the Midwest, and three from the far West. Mr. Linton, the chairman, has been a valued member of the Institute for 36 years. A memorandum drawn up by Paul D. Merica, representing the A.I.M.E., and W. R. Barclay, representing The Institute of Metals of Great Britain, setting forth a reciprocal plan for special memberships in each Institute for members of the other, was discussed. Both societies already have formally approved the plan in principle and Dr. Merica was clothed with full authority to agree on a few small details that have not been settled, and conclude the arrangement in behalf of the Institute.

Jan 1, 1936

By R. T. DeHoff

In any structural transfortnation which is driven by surface tension, the geometric variable of fimdamental importance is the local value of the mean surface curvatuve. Acting through the suvface free energy, this quantity determines the magtnitude of both the pressure and the chemical potential that develops in the neighborhood of an arbitrarily curved surface. A metallographic method which would permit the quaniitatiue estinzation of this propevty is of fundarnerztal irztevest to studies of such processes. In the present paper, it is shoun that the average value of the mean surface curvature in a structuve can be estimated from two simple counting measuretnents made upon a vepresentative metallograpIzic section. No simplifyirlg geonzetric assurmptions are necessary to this deviuation. It is further shoum that the result may be applied to parts of interfaces, e.g., interparticle welds in sintering, or the edge of growing platelets in a phase transformation, without loss of validity. In virtually every metallurgical process in which an interface is important, the local value of the mean surface curvature is the key structural property. This is true because the mean curvature determines the chemical potential of material adjacent to the surface, as well as the state of stress of that material. The theoretical description of such broadly different processes as sintering,1,2 grain growth,3 particle redistrib~tion4,5 and growth of Widmanstatten platelets8 all have as a central geometric variable the "local value of the mean surface curvature". The tools of quantitative metallography currently available permit the statistically precise estimation of the total or extensive geometric properties of a structure: the volume fraction of any distinguishable part:-' the total extent of any observable interface,10,11 and the total length of some three-dimensional lineal feature:' and, if some simplifying assumptions about particle shape are allowed, the total number of particles.'2"3 The size of particles in a structure, specified by a distribution or a mean value, can only be estimated if the particles are all the same shape, and if this shape is relatively simple.14-16 The relationships involved in converting measurements made upon a metallographic section to properties of the three dimensional structure of which the section is a sample are now well-established, and their utility amply demonstrated. In the present paper, another fundamental relationship is added to the tools of quantitative metallography. This relationship is fundamental in the sense that its validity depends only upon the observation of an appropriately representative sample of the structure, and not upon the geometric nature of the structure itself. It involves a new sampling procedure, devised by Rhines, called the "area tangent count". It will first be shown that the "area tangent count" is simply related to the average value of the curvature of particle outline in the two-dimensional section upon which the count is performed. The average curvature of such a section will then be shown to be proportional to the average value of the Mean surface curVature of the structure of which the section is a sample. The final result of the development is thus a relationship which permits the evaluation of the average value of the mean surface curvature from relatively simple counting measurements made upon a representative metallographic section. The result is quite independent of the geometric or even topological nature of the interface being studied. QUANTITATNE EVALUATION OF AVERAGE CURVATURE IN TWO DIMENSIONS The Area Tangent Count. Consider a two-dimen-sional structure composed of two different kinds of distinguishable areas (phases), Fig. l(a). If the system is composed of more than two "phases", it is possible to focus attention upon one phase, and consider the remaining structure as the other phase. The reference phase is separated from the rest of the structure by a set of linear boundaries, of arbitrary shapes and sizes. These boundaries may be totally smooth and continuous, or piecewise smooth and continuous. An element of such a boundary, dA, is shown in Fig. l(b). One may define the "angle subtended" by this arbitrarily curved element of arc, dO, as the angle between the normals erected at its ends, Fig. l(c). Now consider the following experiment. Let a line be swept across this two-dimensional structure, and let the number of tangents that this line forms with elements of arc in the structure be counted. This procedure constitutes the Rhines Area Tangent Count. Suppose that this experiment were repeated a large number of times, with the direction of traverse of the sweeping lines distributed uniformly over the semicircle of orientation.' Those test lines which ap- proach from orientations which lie in the range O to O + dO form a tangent with dA; those outside this range do not, see Fig. l(c). Since the lines are presumed to be uniformly distributed in direction of traverse, the fraction of test lines which form a tangent with dA is the fraction of the circumference of a semicircle which is contained in the orientation range, dO; i.e., vdO/nr or dB/n. If the number of test lines is N, the number forming tangents with dA is N(d0/n). Since each test line sweeps the entire area of the sample, the total area traversed by all N test lines is NL2. The number of tangents formed with dA, per unit area of structure sampled, is therefore

Jan 1, 1968