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By Gregoire Gutzeit

THE development reported in this paper was begun by the author a number of years ago, while he was a lecturer on complex chemistry and metallurgy at the University of Geneva, Switzerland, and in charge of that institution's research laboratory. Completion of the development and reduction to practice did not occur until last year at the Westport mill, laboratories and testing plant of the Dorr Company, where this method is now in general use for identifying and localizing the mineral constituents of both metallic and nonmetallic ores. It has proved to be a practical tool of the metallurgical staff at the Westport mill, devising unusual milling flowsheets for complex and refractory ore bodies. In a number of instances the findings have been successfully used as fundamental factors in the design and specification of complete metallurgical plants. Seven examples of the use of this method in solving practical milling problems are included in this paper. GENERAL OUTLINE The microscopic study of an ore, at first only of scientific interest, has proved extremely useful both in practical geology and in ore dressing. The binocular magnifying lenses for rough observation of the products of an ore-dressing plant have been in use for a long time; but only within the last few years has a systematic microscopical examination of ore samples become a normal tool of any research laboratory dealing with ore-dressing problems. Such an investigation avoids considerable loss of time as well as empirical trials and useless experimentation. It will generally indicate the correct grinding and often will suggest the proper method of treatment. The petrographic determination of transparent minerals in thin sections, or even in grains, has been perfected, and very accurate methods have been devised to meet any requirement, such as Feodorof's rotating stage on the petrographic microscope. Almost all transparent minerals can be positively identified by their optical properties; i.e., isotropism, anisotropism, color, pleochroism, refractory index, cleavage, crystal form, birefringence, and others. The identification of opaque minerals is a much more difficult problem and can be done only by using polished specimens. Unfortunately, most of the valuable metallic ores, and even some of the nonmetallic ones, are not transparent; therefore it has been necessary to develop a special technique for the determination of these minerals. Some optical properties-for instance, isotropism, anisotropism, color, cleavage, reflecting power-are often adequate in roughly classifying the mineral. Only "reflecting power" is a measurable value, provided special photometric equipment (ocular photometer or Orcel's photoelectric cell) is available. The other optical properties mentioned are more or less relative,

Jan 1, 1942

By Charles E. Glass

A steadily growing body of evidence indicates that earthquake ground motions can cause failure of rock slopes that are otherwise stable under static loading conditions. As a result, the economic optimum working slope angle is reduced when earthquake shaking is considered in surface mine design, especially in regions of high seismicity. When designing surface mine slopes to withstand seismic motion it is as important to consider the probability of experiencing various levels of ground shaking as it is to consider the characteristics of the ground motion. For most slope designs, simple probabilistic techniques such as extreme value or maximum likelihood techniques are appropriate. These techniques, however, should be applied in such a way that a probability value is assigned to characteristic ground motion parameters at the mine rather than to nearby earthquake magnitudes. Several techniques have been developed to analyze rock slopes subjected to dynamic loads. Most of these techniques do not adequately account for the ground motion parameters of concern. The best technique appears to be one that utilizes actual earthquake time histories. A simple technique that calculates block displacement for any input accelerogram, using a linear acceleration approximation between time steps, has been developed that accurately accounts for rock block response. Results using this technique indicate that the following factors are important for assessing rock slope stability in earthquake regions:

Jan 1, 1983

By Eckley B. Coxe

(WITH FIGURES ON PLATES II, III, AND IV.) I DESIRE to call the attention of the Institute to two deep vertical shafts, which are now being sunk in Schuylkill County, Pennsyl¬vania, about 1 1/2 miles north of Pottsville. These shafts are of interest to the mining engineer, not only on account of the novelty of the method of sinking adopted, which promises to produce a revolution in that branch of mining engineering, but also as examples of the manner in which such work should be undertaken. GEOLOGICAL SKETCH OF THE TERRITORY TO BE WORKED BY THE SHAFTS AND REASON FOR SINKING THEM. The Mammoth or E Vein of the anthracite coal-measures in that part of the Schuylkill region near and north of the town of Pottsville lies at a great depth below the surface, and has, in consequence, never been worked in that locality.

Jan 1, 1873

By James Kemp

(New York meeting, February, 1913.) IN the study of ore deposits water plays a very prominent part. The small group of igneous ores involve it least, but in all the rest it is an invariable feature. The ground-water, therefore, is perhaps as appropriate a subject for discussion before a session of the American Institute of Mining Engineers as any topic which might be selected. The theme is if anything the more appropriate, because two very important contributions to it have already appeared in the Transactions. The great essay in 1893 of Franz Posepny,1 systematized and classified the subject, and was doubtless not without its influence in leading to the presentation in 1900, by C. R. Van Hise, of an important contribution entitled Some Principles Controlling the Deposition of Ores.2 We all recall the discussions of 10 or 12 years ago, and the interest in these themes which then prevailed in the Institute. They are collectively accessible in the separate edition wisely assembled by Dr. Raymond, and now to be supplemented by the Emmons Volume. Views have been progressing in the past decade or more, and new evidence has been brought to light. A general summary and concise statement may, therefore, not be without interest.

Jan 4, 1913

By Charles R. Keyes

I. Introductory,.......... 185 II. Hypotheses oF the Origin of OzaRk Ores..... 186 1. General Considerations........ 186 2. Schmidt-Leonhard and Gage View...... 187 3. Jenney Opinion.......... 187 4. Posepny Idea,.......... 188 5. Winslow-Robertson Hypothesis....... 188 6. Branner Proposition......... 189 7. Keyes Statement.......... 189 8. Van Hise-Bain Theory........ 190 III. Requirements of an Adequate WoRking-Hypothesis,... 190 IV. GeneRal Geotectonics of the OzaRk Region.... 192 1. Salient Aspects.......... 192 2. Geologic Formations......... 192 3. Character of Faulting...192 4. Extent of Flexing......... 193 5. Unconformity Inequalities....195 6. Warping of Strata...195 V. Classes of Ore-Deposits... 196 VI. Vadose ORe-ConcentRation,........ 197 VII. GeogRaphic DistRibution of the Ore-Bodies,... 199 VIII. Relation of ORe-Deposit to Geologic Structure... 201 1. General Occurrence of Ore-Bodies in Basins.... 201 2. Deposits of the Central Missouri District..... 203 3. Deposits of the Southwestern Missouri District.... 203 4. Deposits of the Northern Arkansas District... 305 5. Deposits of the Southeastern Missouri District.... 206 6. Synclinal Ore-Deposits of Other Districts.....207 7. Significance of Ore-Troughs in Prospecting... 209 8. Origin of the so-called Synclines,...210 9. Significance of the Cross-Bars of Joplin..... 213 10. Relation of Ore-Run to Ancient Relief-Features,... 215 IX. Direction of GRound-Water Circulation..... 216 X. VeRtical Range of Workable Ore-Bodies,... 218 XI. Oscillation of Ground-WateR Level...... 219 XII. Relations of Ore-Bodies to Lithoclasic Features,.. 220 XIII. PRimaRy Source of Ore-Materials,...... 220 XIV. Zone of Ore-Enrichment,......... 222

Jan 1, 1910

By Charles J. Moore

It seems a duty incumbent on the older members of the Institute to set forth in permanent form some of the results of their experience for the benefit of the younger members; this is the principal object of the present paper, which is the result of a recent examination requiring somewhat unusual geologic investigation. History. The London vein mas first discovered by float and occasional outcrops in the year 1873, four years before the great lead carbonate discoveries of Leadville, but the mine was not definitely located and opened until two years later, when the present locations, Mother, Paris, London, and Hard to Beat, were surveyed for patent. Since 1875 the London mine has been worked almost continuously until 1911, when the force was reduced to a few men only. In its early life the ore was assumed to be free-milling gold-quartz, although lead was a constituent of the vein throughout, and much useless expenditure was made in the erection and operation of a free-gold stamp-mill, with plates and tables for saving concentrates. The vein then opened was in the porphyry-limestone contact, a siliceous lead-ore, clearly most amenable to reduction by lead-smelter. The losses due to this process led in time to the close of the mill. For 20 years past, the mine has been worked under lease and the ore shipped to the lead-smelters in Denver or Salida. In January, 1912,I examined the mine to ascertain whether it was advisable to run a cross-cut tunnel some 4,200 ft. in length to intersect the main vein at a depth of 650 ft. below the present lowest workings. Finding a greatly-faulted zone, a close determination of the geological conditions became necessary to the solution of the problem.

Jan 1, 1914

By Richard P. Rothwell

A REFERENCE to the geological map of Alabama shows the coal- measures of that State to form three distinct fields. The Coosu, or most easterly, contains about one hundred square miles ; the Cahaba, or middle field, which is also the most southern true coal in the United States, contains about 230 square miles ; and the Warrior field, which contains in the State of Alabama some 5000 square miles, is the southern extremity of the great carboniferous deposit, which extends through Pennsylvania, West Virginia, Kentucky, Tennessee, and Georgia. But very little has yet been done towards developing those coal- fields, partly owing to the absence of all commercial manufacturing enterprise in the South under slavery, and partly owing to the want of capital and the disturbed condition of the South since the war. During the past three or four years I have devoted a large part of my time to the examination of the coal and iron ores of this range,

Jan 1, 1874

By Paul Tyler

THE ferroalloying elements are connecting links between the steel industry and the nonferrous metal industries. Although ferroalloys are distinctly nonferrous themselves, they serve the steel industry either in the manufacturing process or in modifying the product-in some cases so that it may compete in the markets with nonferrous metals. Of the 92 elements generally accepted by chemists as constituting the primary building blocks of matter, all but the very rarest have been investigated with a view to employing them in steel manufacture. The surprising thing is that so few have been found commercially acceptable. Despite the relatively small number of elements involved, the employ-ment of alloys in steelmaking is one of the most complicated and probably one of the least well understood of modern industrial enterprises. A great deal has been written regarding the action of individual elements and a profuse and somewhat acrimonious literature covers pretty much the whole field of ferroalloy ore supplies. In the middle ground between the miner and the steelmaker developments are less carefully watched by most observers, and except for an occasional description of the technique of some conversion process or the tariff hearings in Congress, very little is said about them. The purpose of the present paper is to describe in relatively nontechnical terms this highly complex industry and to study its relations to our national progress.

Jan 1, 1933

By Irwin Roman

NUMEROUS results and formulas have been published for analyzing seismic records, but most of them apply only to large-scale phenomena such as are encountered in studying earthquakes. In a few cases,1 formulas have been published for some of the simpler structures. In the present paper, an attempt will be made to analyze several types of struc-tures without using methods more advanced than those of a first course in calculus. In, tracing a disturbance through a medium, it is almost always possible to base the analysis on Fermat's Principle of Extreme Time, which states that waves of displacement travel between points in such a manner as to make the time of travel an extremum with respect to all neighboring paths. In the simpler cases, comprising most of those used in optics or geophysical prospecting, this time is a minimum and the principle is often referred to as the Principle of Least Time. Within a homogeneous medium, having a uniform speed of transmission of the disturbance in all directions and throughout the medium, the paths are straight and are refracted at the interfaces in accordance with the Snell law of refraction, which states that the ratio of the sine of the angle, made by the ray with the normal to the interface, to the speed of trans-mission is the same on both sides of the interface. Thus, in any medium composed of homogeneous sections, this same ratio has a constant value at all points. In particular, if all interfaces are horizontal, it is apparent that the angles of incidence are the angles made by the ray with the vertical direction. Furthermore, the incident ray, the refracted ray and the normal to the interface are all in the same plane at each refraction;

Jan 1, 1933

By J. R. Bridge, D. A. Vaughan

The phase diagram of the Zr-H system over the range 0 to 65 atomic pet was determined by high temperature X-ray diffraction methods. Results show a eutectoid between a zirconium and the hydride phase. The eutectoid temperature was established at 560±10°C with a eutectoid composition of 42*3 atomic pet H. The hydride phase of the lowest hydrogen content is stable only above the eutectoid temperature, but is formed and retained in a metastable state during reaction of zirconium with hydrogen at temperatures below 560°C. One hydride phase is indicated that exists over the composition range 55 to 65 atomic pet H. RECENT increase in the industrial importance of zirconium has stimulated several investigations of the reaction of zirconium with hydrogen. Review of the literature on interpretation of absorption isotherms' ' shows that attempts were made to relate the observations to the room temperature hydride phases reported by Hagg.3 However, more recently Schwartz and Mallett' reported the existence of a new hydride phase, isomorphous with the lower hydride in the Hf-H system described by Sidhu.4 This phase was found adjacent to the metal in a diffusion gradient sample. In addition to the new phase, Schwartz and Mallett reported on only two of the five hydrides found by Hagg. Gulbransen" confirmed the existence of only three hydrides of

Jan 1, 1957

By B. Kopelman, C. C. Gregg

THE reduction of tungstic oxide to tungsten metal powder by hydrogen is a process by which one might expect the resultant metal powder to he porous. In- deed, sponge iron, prepared by rcduction of the oxide in a reducing gas, is generally accepted as quite porous. with pores large enough to be seen readily under the optical microscope at relatively low magnifications. However, any pores that may exist in tungsten metal powder are not resolved by the optical microscope, and apparently, not even by the electron microscope. Fig r shows commercial tungsten powder magni- fied at I0,000 X by the electron microscope,' both etched and unetched. In an earlier paper by one of the authors,* the existence of ports in tungsten powder was required to explain adequately the particle size changes occurring during the reduction of tungstic oxide. The inability to detect these pores under the electron microscope at 10,000 X implies that these {pores} are of a size of 100 A units or less. (This in itself is by no means proof that pores above 100 A would not exist, since polishing effects on the specimen might smear up holes of such small magnitude). If, then, these pores are less than IOO A. and of the order of molecular size, then the density of the metal powder should be

Jan 1, 1949

By Henry Hibbard

This paper aims to put into useful form the information, at hand regarding temperatures of molten steels, covering all carbon contents up to 1.5 per cent., in the hope that if the assumed ideal temperatures tabulated are incorrect the right ones may . be brought to light. THE finishing and casting temperature of steel is a subject concerning which there is so much to learn that some temerity is required to write about it. This paper is, therefore, suggestive rather than dogmatic, though the views expressed seem now to the writer to be correct; nevertheless, they may be modified by future developments or discoveries but until then may be of some utility, particularly to beginners in the making of steel. Consideration is limited to the temperatures of simple steels, also called carbon steels,, which are those in which carbon is the only element introduced for the purpose of conferring desired physical properties. Alloy steels will receive attention later. Three things largely determine what a batch of steel really will be; viz., composition, casting temperature, and rate of teeming. Each has its advocates as being the most important; but they are so interrelated that each must conform to or be right for the, other two. When one is claimed to be the most essential to have right, that, probably, was the one that it was found had to be of a certain description, within narrow limits, to suit the already adopted variations of the other two; that is, it was the last of the three to be brought into line.

Jan 12, 1924

By G. Y. Chin, W. F. Hosford

It has long been recognized that, for a crystal to undergo an arbitrary shape change by crystallographic shear, at least five independent shear systems must be activated. Taylor1 analyzed the deformation of fcc crystals by {111}<110> slip and showed that the principle of minimum work could be used to determine which combination of slip systems might act to produce a given shape change. Later Bishop and Hi112 attacked the same problem by first identifying the state of stress which could physically activate five or more {111)(110) systems simultaneously and then invoking the principle of maximum virtual work to determine which combination would act for a given shape change. Taylor&apos;s general approach has been used to calculate the active slip systems and the relative strengths during axisymmetric flow of cubic crystals with other deformation modes, including {112}<111> slip3 and {111}<112> twinning.&apos; It is the purpose of this note to identify the stress states capable of activating simultaneously five or more of these systems. {111}<112> Twinning. The {111}<112> systems are defined in Table I and illustrated in Fig. 1. The sense of the shears are those for twinning in fcc crystals. The shear stress on any system may be written in terms of the stress components expressed relative to the 1,2,3 cube axes. For example, the stress For five or more of the systems ij to be activated simultaneously, it is necessary that Tij/T be equal to unity in at least five of the expressions [3], while Tij < T for the remainder. (These restrictions assume that the same shear stress T is required to activate each system and that the shear stress on any system cannot exceed that for its activation.) The discrete values of the stress components A through H which can satisfy these restrictions are listed in Table II together with the values of Tij/T for all systems. It may be noted that Tij/ T is not necessarily zero on all nonactive systems as found by Bishop and Hill for <110> {111} slip. In fact, for the case of twinning Tij/T may reach negative values as large as -2 for shear stress in the reverse direction, Table 11. This means that, if those stress states are to be valid, the shear stress to activate reverse twinning must be greater than twice that for forward twinning. Such stress states are probably valid in view of the directionality of the twinning process. There has been no documentation of reverse twinning thus far. It may be noted that the stress states fall into four classes, which may simultaneously activate eight, six, six, and five twin systems respectively. These solutions may be applied to the {112}(111)

Jan 1, 1970

By Paul Beck

IT is well known that the hardness of metallic single crystals, like that of polycrystalline metals, increases during deformation (hardening by cold-work). It is also known that, as a consequence of deformation, the metallic material acquires an evident thermodynamic instability, revealed, for example, by the fact that the increased hardness gradually decreases with time, especially at elevated temperatures (softening by annealing). The temperature at which the stabilizing process begins is different for various metals, and for any metal it depends on the amount of deformation. Such stabilization of deformed metals may proceed in two different ways: through recovery, and through recrystallization. The former process allows the unstable deformed metal body to approach stability gradually and without visible change in the grain structure; the latter process, like an allotropic transformation, yields directly the undeformed stable "phase" in the form of new undeformed crystals, which, starting out of a certain number of nuclei, grow into and&apos; consume&apos; the deformed hard material. The extent of stability attainable through recovery is limited, espe-cially if the deformation of the metal crystal or crystals involves not only the gliding along slip planes, but also the bending of the slip lamellae, or at any rate the bending of comparatively large parts of the crystal lattice. In such cases, for instance in bent single crystals or poly-crystalline metals subjected to any deformation, recovery will not as a rule be able to restore the "straight" undeformed lattice, and stability can be attained only by recrystallization; that is, by the consumption of the bent crystal lattice parts by new, undeformed crystals-a much more drastic process. It is evident that the part of the surplus free energy stored in deformed crystals, which is present in the form of the elastic energy of the bent lamellae, is in these instances not considerably involved

Jan 1, 1937

By A. F. Lucas

Belle Isle, located in the low sea marshes near Atchafalaya Bay, is the southeasternmost of the famous Five Salt Islands of Louisiana. Rising about 80 ft. (24 m.) above the level of the surrounding marsh and being some 800 acres (323 ha.) in extent, it constitutes a striking landmark on the low Gulf coast, and since the eighteenth century, when it played an important part in the operation of the buccaneers, it has been intermittently frequented by man. In 1897, the writer discovered the great mass of salt that underlies the island and shortly afterward published a brief account of the geology of Belle Isle and the neighboring salt islands.&apos; In that paper he described principally the salt, but pointed out also the occurrence of petroleum and of sulphur in the strata above the salt. Since that time the island has been extensively explored by the drill, and the developments up to 1908 have been described by Veatch2 and Harris13 and Knapp.4 The writer&apos;s early conclusions as to the probable presence of sulphur in considerable quantity have been confirmed by the later drilling, some of the wells having found quantities of gas containing hydrogen sulphide and a number of sulphur-bearing strata as well. Under the stimulus of the present keen demand for sulphur for war purposes, a syndicate of New York capitalists was recently formed to explore the sulphur resources of the island in more detail. Under the writer&apos;s direction, six wells were drilled for this syndicate during the winter of 1916-17: The present paper presents briefly the results of this work and sums up the present knowledge of the geology of this highly interesting locality.

Jan 1, 1918

By T. Leser, A. W. Jenike

The problems of caving and underground subsidence can be considered as the failure of a highly compacted rock and its subsequent flow in the form of broken rock. The problem is complex because the propagation of failure and flow have to be considered simultaneously; the yield strength of the virgin rock and the broken rock are different; and, while under certain conditions it is sufficient to consider the virgin rock as homogeneous, the density and the yield function of broken rock are both pressure and time dependent. A study of the failure and flow of solids with a pressure dependent yield function has been published recently by Jenike.&apos; In this paper the density of the broken rock is assumed to be only time dependent and the consequences are examined in the case of one-dimensional vertical subsidence into an initial cavity. The following describes an attempt to develop a tool which, in combination with other tools, may lead to mathematical solutions of real problems of caving and subsidence. STATEMENT OF THE PROBLEM An underground cavity of horizontal cross section 4 = 1 and height 6 is assumed to exist at some depth below the surface. At the time t = 0 rock above the cavity fails and completely fills out the cavity with expanded broken material. With passing time the broken rock consolidates and subsidence proceeds continuously upuard in a vertical shaft. The phenomenon is one-dimensional (see Fig. 1). The problem consists of finding the displacement and the velocity with which the frlmt of the subsidence (wave front) moves upward as a function of the time and of the rock properties. DIFFERENTIAL EQUATIONS CONTROLLING THE PHENOMENON With the assumptions that the broken rock is a continuum and that the subsidence occurs continuously, we can apply the one-dimensional differential equation of contitiuity (conservation of mass) and the equation of preservation of momentum The latter equation is replaced by an assumed relation based on experience, which takes care of the

Jan 1, 1962

By Alan Probert

IN his inaugural address in 1949, President Truman made a policy declaration which launched the foreign technical assistance program known to the world as Point Four. Congress passed Public Law 535 defining the scope of the program and holding activities to certain limitations. It also provided $34.5 million for the first fiscal year. The Technical Cooperation Administration was established within the Department of State to coordinate and direct a program to include "economic, engineering, medical, educational, agricultural, fishery, mineral and fiscal surveys, demonstration, training and similar projects." The mineral programs of Point Four have been staffed and managed by two agencies of the Department of Interior, the Geological Survey and the Bureau of Mines. The Geological Survey is concerned primarily with water-supply problems, the discovery of mineral deposits, and the determination of habit, shape, and grade of mineral deposits. The Bureau of Mines is concerned with determining the commercial potentialities of mineral deposits, mineral technology, and the production and distribution of mineral commodities. Mineral projects comprised only 1 pet of the first year&apos;s budget. In spite of the relatively insignificant expenditure compared to those for food, agriculture, and health, a commendable record has been achieved.

Jan 1, 1952

By Laurence Delisle

The aim of this paper is the description of a technique to be applied to the study of sections of metal powder particles, less than 20 microns in diam. with the electron microscope, by the replica method, using for replica a material such as formvar or parlodion. This work originated with the study of particles of tungsten powders. Such particles were too small to be examined in sufficient detail with the light microscope. On the other hand, examination with the electron microscope of the powders dispersed in the supporting film was not found satisfactory because: 1. It did not permit differentiating between single particles and aggregates. 2. It did not show the true outlines of the particles but only the projection of a whole surface. 3. No details appeared. For that reason it was attempted to make replicas of sections of the particles imbedded in a mounting material suitable for polishing and etching. The method proved satisfactory for the examination of tungsten powder and was then extended to car-bonyl nickel and carbonyl iron powders. Procedure Several mounting materials commonly used in ordinary metallography were investigated. The problem consisted in finding a mounting material

Jan 1, 1950

By John W. Cahn

Tile avevage value of the mean curvature of surfaces in a specimen can be precisely delermined by sitrlple measurements performed on random sections or on 1 vojectiotzs of these surfaces. For surjaces enclosing particles, the quanlity is sllown to be velated to the probable tlurrrhev ot particles intevcepted by a random platne and, under certain conditions, to the perimeter of their Projected image and to the increuse in surjace area when the particles grow. Many of the velalionsl~ips are valid for any shape or size of the particles. THE recent growth of the field of stereology or quantitative microscopy is largely the result of the discovery of a limited number of rigorously defined geometrical parameters that can be precisely measured on random sections or projections of a structure without assumption about particle shape.&apos; Such parameters have been the volume fraction and surface area and line length in a unit volume. The present paper introduces the average of the mean curvature of surfaces in a volume, and shows that it can be rigorously measured by counting methods alone. AVERAGE CURVATURE ON A PLANE Consider a curve y = v (x) on the xy plane. The curvature Kp in the plane at any point is given by Kp = (dZy/dx2)/[1 + (dy/dx)2]3/2. The average curvature along the curve may be defined as Kp = (1/L) fKpdl |1] where dl = [(dx)&apos; + {dy)2]1/2 is the length of an element of the curve and .(dl = L is the total length of the curve. The integral on the right-hand side of Eq. [l] will be called the total curvature, It is dimensionless and readily evaluated by substituting d = arctan (dy/dx) to give ah which is the change in direction of the tangents to the ends of the curve, Fig. 1. Hence, Kp = (1/L)(?h) [2] It can also be seen that Eq. [2] is applicable in the limit of sharp corners. Even though the curvature is infinite at a corner, f Kpdl remains integrable and equal to the change of angle. The signs of the quantities Kp and dl are arbitrary and, if the areas adjoining the curve are equivalent, there seems to be no compelling reason to fix the signs. For a closed curve, however, it becomes worthwhile to use the signs to distinguish among different types of areas or phases enclosed. For such a closed curve AO = t2r and As a convention, we shall take the direction of the integration along the curve in such a way that the area or phase under consideration (henceforth called a) is kept to the left side of the curve, Fig. 1. Then Kp is positive where the curve is concave and negative where the curve is convex. For a closed curve Ad - +2n if the curve encloses a, and Ad = —2n if the curve is surrounded by a. PLANAR SECTIONS OF THREE-DIMENSIONAL STRUCTURE OF ISOLATED a PARTICLES Consider next a planar section of a microstructure containing particles of a in a matrix. We place no restriction on shape of connectedness of these particles, and begin by considering the curvature of only the boundary between a particles and matrix&apos; Clumps of contiguous a particles are then treated as a single a particle. The two-dimensional section will show in a unit area na simple closed curves enclosing a particles and nh closed curves of holes, in-

Jan 1, 1968

By Edward B. Dismukes, Walter R. Dickson

Measurements of current efficiency at an iron anode during the electrolysis of FeO-CaO-SiO2 melts contained in an iron crucible indicate that compositions of high SiO5 content conduct current almost entirely by ionic mechanisms. Hozueuer, compositions of high metal oxide content give euidence for considerable nonionic conduction that can be attributed to p-type semicon-duction. Measurements of transference numbers in a Hittorf-type cell show that both calcium and iron ions are important contributors to ionic conduction. ELECTROCHEMICAL properties such as conductance, transference numbers. and oxidation or reduction at an electrode have been studied as means of delineating the structure of simple silicate melts that are related to the more complex slags encountered ir steelmaking processes.&apos; Measurement of these properties has strengthened the concept that molten silicates are constituted of metal ions and of silicate networks. Typically, the magnitude of electrical conductivity and the extent of agreement with Faraday&apos;s law have given evidence for ionic structures, and transference numbers have shown cations to be the exclusive carriers of electrical charge. However, melts containing oxides of iron, FeO in particular, have been found to exhibit nonionic conduction of curx,ent. The work by Inouye, Tomlinson, and chipman&apos; demonstrated semiconduction, presumably of the p-type, in molten wüstite. Simnad, Derge, and George3 and Dukelow and Derge,4 in studying the electrolysis of FeO-SiO2 and FeO-MnO-SiO2 melts, concluded that p-type semi-conduction occurs in these systems, although ionic conduction is generally favored by increased percentages of MnO or SIO2. Previous research on the electrochemistry of

Jan 1, 1962