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By R. B. Adair, J. S. Browning

The Bureau of Mines conducted laboratory research to determine the applicability of heavy liquid separation to the evaluation of certain mica ores and plant products. After careful standardization of the particular mica ores and associated gangue, accurate analysis of muscovite content could be obtained from results of heavy liquid separation. Where applicable, the method should be particularly suited to the analysis of ores and control of plant operations wherein savings in time would be of considerable advantage. Specifically, there are many instances where a quick plant control method should enable the production of a more uniform grade of mica concentrate. The laboratory use of various heavy liquids for separating minerals of different specific gravities has been recognized for many years.1-8 Sink-float procedures have proven their utility as a rapid and moderately accurate means for determining the mineral content of ores, test products, and plant products in certain nonmetallic concentrating operations. A standard method of analysis for mica in ore samples has not been published or generally accepted by the mica industry. Recently, the U.S. Bureau of Mines investigated methods for analyzing mica by heavy liquid separation. This report has been prepared to make the methods available to others who may need simple, relatively rapid methods of determining the mica content of ores and plant products. The heavy liquid method of mica determination has recently been adopted by one of the major mica producers for evaluating exploration and mill control samples. DESCRIPTION OF THE ORES AND HEAVY LlQLllD The weathered mica pegmatite ores used in the investigation were obtained from commercial mica op erations in Alabama, Georgia, and North Carolina. The major mineral constituents of the ores were muscovite, quartz, kaolin, and minerals of the feldspar group. The ores also contained minor quantities of biotite, limonite, and tourmaline. A comparison of the specific gravities of the major constituents of the ores (muscovite 2.76 +, quartz 2.65, kaolin 2.61, and feldspar 2.57), indicates that an effective separation of muscovite from the other minerals can be made in heavy liquids at a specific

Jan 1, 1968

By Alden Greninger

ALTHOUGH the crystallography of lattice transformations has been studied extensively during the past few years, these studies have been limited, with few exceptions1,2, to specimens in which the transformed lattice appears as a, segregate phase. A realization of the technical importance of the segregation mechanism, especially in the formation of martensitic structures and in age-hardening phenomena, has undoubtedly stimulated research in this direction. In the crystallographic studies of segregation, the general problem has been to relate the orientation of the parent crystal to that of the segregate crystals. The technique has been complicated by the fact that it has been necessary to deal with the presence of as many as 24 ideal segregate orientations within one parent lattice; furthermore, the segregate lattices are invariably scattered (seldom less than ±2°, often as much as 15° or 20°) about these ideal positions. It is probable that a more complete picture of phase transformations may result from a study in which complete lattice relationships between individual grains are evaluated, thereby providing an additional param-eter which, when it is necessary to work with multiple segregate-orienta-tions, cannot be evaluated. The present paper presents the results of such a study, ? wherein a peritectic reaction is made use of to produce the transformed lattices.

Jan 1, 1937

By W. J. Keep

Those who have observed the influence of various elements upon cast-iron will be interested in the methods used by us to form the several series of test-bars, which form the basis of the conclusions presented in this paper. We found that we could not, by adding ordinary white stickphosphorus to molten iron, produce bars which would exhibit to the eye the peculiar influence of phosphorus. By melting wrought-iron drillings with red phosphorus, Mr. H. S. Fleming produced in his laboratory 10 pounds of phosphide of iron, containing 10.22 per cent. of phosphorus. With this we made two series of test-bars, the first with our white-base iron, and the second with our FLM gray-base iron. Before the time of making these bars we had been unable to procure regularly made pig-iron which contained enough phosphorus to permit of the production of

Jan 1, 1890

By Lawrence W. Aldrich

At the San Francisco meeting of the Institute last year, I presented, through the courtesy of Dr. James Douglas, some results of experiments on the roasting and leaching of concentrator tailings. After it became apparent that flotation rather than leaching was clearly the better method of handling the particular problem under consideration, before dismantling the experimental equipment, some data were secured on roasting and leaching the concentrate itself in competition with smelting. Some of the results obtained are given in the following paper and they are of particular interest at this time in view of the large quantities of flotation concentrates with their somewhat difficult smelting characteristics now being produced. A complete wet processt consists of roasting and leaching the calcines in dilute sulphuric acid produced from the roaster gases, roasting the residue with salt and leaching with dilute tower liquors (the well-known Longmaid-Henderson process) and recovering the copper, silver and gold by cementation or electrolysis or a combination of both. It is evident, however, that the residue from the first leaching, carrying about 20 per cent. of the copper and all of the silver and gold, can be smelted if preferable. In considering the application of the scheme to individual cases, it must be remembered that freight plays a large part in any reduction process wherein smelting is not conducted at the mouth of the mine, and that it is not practicable today to build small smelting plants for individual operations, The experiments may be grouped under four main heads: Roasting, leaching, chloridizing residue, and recovery of copper from solutions. The products of two concentrators were used: The Nacozari concentrates were the product of a large modern mill not using flotation, the copper mineral being largely chalcopyrite; and the Tyrone concentrates, the product of an experimental mill including flotation, the copper mineral being chiefly chalcocite. Typical analyses are given in Table 1. Fig. 1 shows screen analyses of calcines obtained by dead roasting the

Jan 1, 1917

By Selma Hermann

For the past century, the so-called aluminum bronzes have been assuming a role of ever-increasing importance in the metallurgical field. The last quarter of that century has marked many efforts to find alloying elements that would alleviate some of the undesirable qualities of the aluminum bronzes-for example, the heterogeneity of the alpha solid solution and the extreme hardness of the beta. Much of this work, however, has been rather haphazard-compositions and heat treatment are usually so much at variance as to make comparison impossible. It is the object of this research to study the effect of certain percentages of common alloying elements on aluminum bronzes of analogous compositions and heat treatments. It is hoped that the material gathered here will at least serve as a basis for further systematic study.

Jan 1, 1930

By W. M. Courtis

SINCE many accounts of Silver Islet Mine, in Lake Superior, have already been published, it is supposed that the members of the Institute are familiar with the location and character of the mine. To many, however, a more detailed account of the ore and manner of treatment will, perhaps, not be without interest. The extraordinary richness of Silver Islet ores, and the difficulty of obtaining correct assays, induced the company to erect smelting works of its own. Accordingly, ground was broken at Wyandotte, Mich., early in the spring of 1871, and the work was pressed on with indomitable energy by Captain E. B. Ward of Detroit, as president, and Mr. Thomas MacFarlane, the discoverer of Silver Islet, as superintendent of the works, so that by July 1st the works were so far completed that smelting could be commenced. The intention was to work Western ores with those from Lake Superior, since the latter contain but a small amount of lead. Hence the capacity of the works is much larger than is needed for the present yield of the mine. The planned process for treatment was smelt-

Jan 1, 1874

By Hendon R. Johnston

In the Tennessee Valley Authority's program of investigation and treatment of foundations for major structures, many chert, or flint, bodies have been encountered during the diamond-drilling operations. These chert bodies occur most frequently in the Knox dolomite and

Jan 1, 1948

The library of the above-named Societies is open from 9 A. M. to 10 P. M. except on holidays. It contains about 70,000 volumes and 90,000 pamphlets, including sets of technical periodicals and publications of scientific and technical societies. Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library, through its Library Service Bureau, can render valuable service through, correspondence; letters requesting information will receive especial attention. The Library is prepared to furnish references and photographic copies of articles on mining and metallurgical subjects; to determine the existence of mining, maps, and to furnish general information on the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be of interest. The time spent in searching for such collateral matter will be saved, and the information will be sent more promptly and in more usable shape.

Jan 2, 1919

By A. L. Field

Bureau of Mines Technical Paper 189 consists of a record of the scientific data obtained in the iron blast-furnace slag investigation which is reported in Technical Paper 187, "Slag Viscosity Tables for Blast-Furnace Work." It includes a description of the method of preparing the synthetic melts, construction of an improved electric furnace, and refinements in laboratory methods of measurement. Only the general features of the work and the conclusions drawn from the experimental data can be given attention here. Silicates in the Liquid State In the manufacture of refractories, Portland cement, glass, and porcelain, and in pyrometallurgical operations, importance attaches to the behavior of silicate compounds at temperatures beyond the range of common experience. This field of research has not been investigated as carefully as its scientific and industrial importance would seem to warrant. Probably the most important of the unsolved problems in the, chemistry of silicates is the question of their stability in the liquid state. That little progress toward the solution of this problem has been made is not strange if there be borne in mind the difficulties attending experiments made at temperatures at which silicates become fluid, and the comparatively short time since it became possible to measure these temperatures. On the other hand, considerable progress has been made in the study of the compounds in the solid state because of the directness and simplicity of methods of optical examination.

Jan 12, 1917

By Warren E. Wilson

PRESENT-DAY design of launders is essentially an art depending to a marked degree upon the experience of the designer, whose problem is that of determining the dimensions of a conduit that will transport the pulp within the physical limitations of the plant and in the most economical manner. This paper has been prepared in an effort to place launder design upon a more scientific basis. A method is developed from elementary principles and presented in a form that may be used directly by the designer in determining launder dimensions.. The equations that are developed are believed to represent an advance over older ones, in that they give due consideration to all the pertinent variables, either including them in the analysis or showing that they may be neglected within the limits of applicability of the equations. Experimental data from several sources are used in evaluating the coefficients that are not determined in the mathematical analysis. On the basis of the material presented, it is concluded that launders may be designed with a much greater degree of accuracy than previously believed possible, when due consideration is given to all the factors involved in the problem. However, a great deal of work still remains to be done in the laboratory before a complete answer to all the questions in launder design can be made available. HISTORY OF LAUNDER DESIGN Among the references1-11 are cited accounts of many experiments that have been conducted in an effort to advance the knowledge of the flow of liquid-solid mixtures in flumes and pipes. With three notable exceptions, this work was carried on in such a manner that the results have limited value in solving the general problem, since not all the pertinent variables were measured and controlled. The exceptions are found in the works of Blue,6 Gilbert,7 and Blatch,11 who exercised great care in controlling and measuring all the significant quantities involved in the experimentation. It is notable that much of the work done by men directly connected with the mineral industries1-4 lacks somewhat in completeness, owing apparently to preconceived notions concerning the factors that determine the flow. For example, many measurements on flow in pipes and flumes carrying liquid-solid mixtures determined only the slope and percentage of solids, with no mention of size of particles, depth of flow, roughness of channel or specific gravity of solids. Material in current handbooks8,9 and textbooks is based largely on the experimental work cited above. Although most discussions of the topic-include statements that the results to be obtained by using the data presented are limited by the fact that all variables have not been considered, it is

Jan 1, 1943

By Kenneth K. Humphreys, Joseph W. Leonard, Robert L. Llewellyn, William C. McCulloch

INTRODUCTION The particular field of application of machines utilizing air currents as the primary separating medium is in the cleaning of the fine sizes of bituminous coal. Approximately 25,400,000 tons of bituminous coal were cleaned by air machines during 1965. They have not found any application for cleaning anthracite. Since the development and introduction of the first successful commercial pneumatic oscillating machine for cleaning bituminous coal in 19 16, by the Sutton, Steele and Steele Co, Dallas, Texas, and the American Coal Cleaning Corporation, formerly of Welch, W. Va., seven other successful pneumatic coal-cleaning machines have been developed and introduced to the American coal-mining industry: 1. Peale Davis: "Pneumo-Gravity" machine. 2. Arms "Concentrator," oscillating table. 3. Hey1 and Patterson oscillating table. 4. "Stump Air-Flow," pulsating air jig. 5. "Super Airflow," pulsating air jig. 6. Ridge air jig. 7. Phillip air jig. While not all coals can be beneficiated by air washing, the air washing of coals that are easy to clean can be readily proved advantageous. Of all the preparation methods, pneumatic cleaning is the most acceptable from the standpoint of delivered Btu cost. This is based on the premise that a percent of moisture is just as detrimental as a percent of ash. The principle of dry concentration has never been determined with scientific accuracy. To the present time the study has been more of an art than a science. It is possible to forecast the results of wet concentration from a study of the washability characteristics of the raw coal but only after applying rule-of-thumb methods of interpretation to the specific gravity and size distribution can it be ascertained that the raw coal is amenable to dry concentration. Air as a separating medium dates back to biblical times as exemplified in the winnowing of chaff from the grain. However, the same application of air to coal serves merely to blow the dust away and size the remaining particles. Pulsating air was the solution to the problem and largely eliminated the necessity for close screen sizing which was required on early separators. Because of the low density of air, a medium of sufficient density has to be built with the material itself. Hence there must be some device to impart to the bed the necessary mobility for proper classification. Also, the

Jan 1, 1968

By R. H. Tien

This paper presents an analytical solution of the problem of freezing of a semi-infinite slab with constant surface temperature; in this analysis accoz~nt is taken of the heat evolution during the solid-state transformations in the frozen skin. The regions where transformations occur are treated as plane isothermal heat sources; i.e., the rates of transformations are assumed to be infinite. In the model considered, three plane heat sources are assumed to be present in the frozen solid. The solution yields the temperature distribution in the solid, the rates of movement of the heat sources , and the rate of movement of the solidification front. It is shown that, although the sum of the heats of transformations in the solid is about 20 or 43 pct of the heat of fusion of iron or manganese, respectively, the effect of the heat evolution in solid-state transformations on the rate of solidification is insignzficant. IN several recent mathematical studies of solidification of liquid metals'-3 no account was taken of the heat evolution accompanying the solid-state transformations. In the case of, for example, steel, there are several phase transformations 6 -y, y -a, and the magnetic transformation. Whether or not a significant error is introduced into the mathematical simulation of solidification processes by the omission of the heat effects associated with these phase transformations is not known. The purpose of the present study is to investigate the effect of these phase transformations on the temperature distribution and the rate of solidification based solely on the heat transfer point of view. That is, for the sake of simplicity, freezing of a pure metal with solid-state transformations will be considered. The mathematical model which represents the present problem includes four moving heat sources representing freezing and phase transformations, 6— y — a — ferromagnetic. The thermal properties such as conductivity and specific heat, and so forth, are different from one phase to the other. But they are considered to be uniform over any particular phase. The usual Fourier heat flow law is employed. The concept of conservation of energy is applied at every heat source in order to estimate their rate of movement. The temperature distribution in the solid and the positions where transformations occur are expressed analytically in terms of error function solutions and four coefficients which are determined from four nonlinear algebraic equations. These coefficients can be calculated either by trial and error or by any numerical method. MATHEMATICAL ANALYSIS Fig. 1 is a schematic diagram showing the zones of different phases 1, 2, 3, and 4 in the solidified portion of a semi-infinite pure liquid metal. The heat is subtracted from the system at x = 0 which is maintained

Jan 1, 1968

By H. H. Alexander

PRIOR to 1915, numerous attempts were made to treat tin concentrates in the United States, but for various reasons they were unsuccessful. Tin ore is said to have been found in nearly every state, but none of the deposits have proved to be of commercial importance. The only domestic production is in Alaska, but only a few hundred tons annually have been produced; hence any considerable production of tin in the United States must be from foreign ores. The most promising occurrence of tin was found in the Black Hills, S. Dak.; in the early development stage, it was called the Cornwall of America. Associated with the tin is tungsten. The story is told that an exceedingly fine specimen of the Black Hills ore was sent to England to encourage stock promotion; the desired effect was produced until a skeptic chipped off a small piece, which the analysis showed to be wolframite. FIRST ATTEMPTS AT SMELTING One of the first promising attempts at tin smelting in the United States was made by R. T. White at Bayonne, N. J., in 1903. Mr. White, after spending some time in England studying the methods of tin smelting, organized a company called the International Tin Co., and erected a plant to treat tin concentrates from the Straits of Malacca. About the time the plant was completed, the English Government placed an export duty of 40, per cent. ad valorem on tin .concentrates exported to other than British smelters, which duty made it impossible to operate this plant so the enterprise was abandoned. As this export duty is still effective, the only source of tin-ore supply for 'the United States is the Bolivian concentrates.

Jan 3, 1924

By George D. Graffin.

The first use of graphite is lost in the mists of time. It was used by primitive man to make drawings on the walls of caves and by the Egyptians to decorate pottery. As early as 1400 A.D. graphite crucibles were being made in the Haffnerzell district of Bavaria. Through the Middle Ages graphite was confused with other minerals, especially galena and molybdenite. Two common names that are still used for the mineral are "Plumbago," meaning leadlike, and "Black Lead." The latter name implied that graphite is either composed of lead or at least contains a large percentage of it. Gessner is credited with having recognized it as a separate mineral in 1565, but its composition was not determined until 1779, when Scheele demonstrated that graphite oxidized to carbon dioxide, thus proving its carbon constitution. In 1789, Werner named it "graphite" from the Greek word "graphein," meaning to write. The United States has long relied on foreign countries for its graphite supplies. This reliance has been due more to the lack of suitable domestic graphites than to any particular preference for buying minerals overseas. Ceylon (now Sri Lanka) graphites were imported as early as 1820, and Madagascar graphites have been imported since the properties on that island were opened up about a hundred years later. Mexico has long supplied the United States with most of its requirements for amorphous graphite. Physical Properties and Classification Graphite is found in laminated, flaky aggregates disseminated in schistose rocks. It also occurs in veins and exhibits a foliated or fibrous structure. Graphite is a black lustrous mineral that crystallizes in the hexagonal system, with rhombohedral symmetry. The crystals have tabular form and are six-sided; the faces are commonly striated. The flakes have perfect basal cleavage and are opaque. When well crystallized, the flakes have a black metallic luster while the amorphous material is black and earthy, with a microcrystalline compactness. The flakes feel greasy. Graphite is an excellent conductor of heat and electricity. It melts at approximately 3550°C at a triple point under 1250 psi. It sublimes between 3300-3500°C at 14.7 psi. At 3726°C a second triple point occurs at approximately 100,000 atmospheres. Thermal oxidation in the presence of oxygen begins at 300°C and the rate increases with temperature. The three forms of carbon (charcoal, graphite, and diamond) are distinguished by chemical and physical tests. The specific gravity of charcoal is 1.3 to 1.9, of graphite 2.266 g/ cm3 (crystal density), and of diamond 3.5. Graphite has a hardness of 1 to 2 (Mohs' scale). Natural graphite can be divided into three classes: disseminated flake, crystalline vein (fibrous or columnar), and amorphous. Flake graphite is a lamellar form found in metamorphic rocks, such as marble, gneiss, and schist. Each flake is separate, having crystallized as such in the rock. Crystalline vein graphite is found in the form of well defined veins or as pocket accumulations along the intrusive contacts of pegmatites with limestones. The graphite of such deposits is of two types, foliated and columnar. The important Sri Lanka (Ceylon) deposits are vein type. Amorphous graphite is commonly found as minute microcrystalline particles more or less uniformly distributed in feebly metamorphic rocks, such as slates and shales, or in beds consisting practically entirely of graphite. The latter usually are metamorphosed coal seams and carry as much as 80-85% graphitic carbon, while the former, being altered carbonaceous sediments, commonly range from 25 to 60%

Jan 1, 1983

By Carl E. Williams

A computer program has been developed which will locate the economic limits of an open-pit mine and also designate which ore and waste blocks to remove per period (years or quarters) to maximize the discounted cash flow over the life of the mine. A set of operating constraints was carefully selected so that the following functions are controlled: (1) the removal of overburden by preproduction and production stripping exposes a fixed amount of ore; (2) a constant manpower and equipment usage is insured (except for trucks); (3) the tons of mill ore, concentrate, and stockpiled ore are regulated; (4) the number and extent of shovel moves are minimized; (5) the grindability of the rock is considered as well as the variable haulage cost caused by variable haulage distances and depths; and (6) the size of the shovel working area is regulated. As many as 50 alternate schedules can be produced per computer run. They are arranged in descending order starting with the best solution.

Jan 1, 1975

Jan 1, 1937

By G. K. Burgess

THE question of the allotropy of iron, in spite of a vast amount of experimental work and perhaps an even greater amount of theorizing, is not yet settled. That there is a definite transformation in iron near 900,° the A3 point, is generally recognized, as well as the fact that the temperature of this transformation is lowered by the addition of carbon and metallic elements. On heating, the transformation Ac3 is always found at a higher temperature than the transformation on cooling, Ar3. Whether the A3 transformation is sharp like the melting point of a pure substance, or extends over a considerable range of temperatures, embracing perhaps as a lower limit the A2 change, appears to be still an open question for pure iron. The nature and identity of the A2 transformation, it would appear from recent publications, has not yet been satisfactorily settled. In the present paper a critical, historical summary is given of the experimental investigations of the location of A2 and A.3 in pure iron, together with brief mention of some of the theoretical aspects of the subject, and an account is given of a series ?of experiments carried out with several samples of very pure iron which were studied by two methods of thermal analysis in the range from 5000 C. to 1,000° C., and which it is believed furnish a contribution of considerable interest as to the location and nature of the A3 and A2 transformations. Great attention has been given to the details of experimental manipulation and to the preparation of the samples, as it was soon found that some of the discrepancies noted in the work of many experimenters may be traced largely to lack of precautions which we have found essential. For example, to anticipate somewhat, it is necessary to provide a suitable practically gas-free furnace, the heating and cooling of which may be regulated to a nicety. To render a minimum the deforming effects on the cooling and heating curves of the poor conduction of the sample, it must be of a form and mass to pass on its heat rapidly and completely to the thermocouple; and finally the sample itself must be freed from gases which, if present, further mask the definiteness of the heating and cooling curves. We, have also varied within wide limits the several factors which may influence the determination of the exact location and shape of the transformation ranges, especially the mass and preparation of sample, rate of heating and cooling, design of furnace; and finally, as nearly as it is experimentally possible, we have worked with a substance approaching pure iron, free from occluded gases and other impurities, and contained within a vacuum.

Jan 10, 1913

By Wayne A. Greenwalt

A method that determines venture participation when the decision maker's level of risk aversion varies according to venture profitability and risk investment is presented. The decision maker's fundamental aversion to risk is established by the selection of a desired working interest for a venture that anticipates only a discounted payout.

Jan 1, 1982

By W. D. Potter, E. T. Peters

Single-crystal films of boron have been prepared by thermal reduction of purified BCl3 with subsequent deposition of boron onto oriented silicon substrates. The structural properties of films prepared under various experimental conditions have been determined by light microscopy and "grazing-" angle electron-diffraction analysis. An orientation relationship is proposed for silicon and a-rhombo-heclral boron which can be described as: (111)Si (112)B; [110]Si [110]B ElEMENTAL boron is known to have a high energy gap* and consequently has potential value as a high- *Energy gaps of 1.35 to 1.55 ev1-3 and 2.0 ev4 are reported for ß-rhombohedra1 and a-rhombohedra1 boron, respectively. temperature semiconductor.5 Exploitation of this property, however, has been hampered by the unavailability of pure, single-crystal boron. Two recent symposia6,7 have treated the subjects of purification, crystallization, crystal structure, and properties of boron and provide a foundation for further investigation in these areas. The structure, lattice constants, and observed ranges of stability for four reported polymorphs of boron8°12 are listed in Table I. The rhombohedral structures are generally accepted as true polymorphs whereas the tetragonal structures are believed to be transient. Most currently available single crystals of boron are grown by Czochralski and floating-zone methods. Unfortunately, these crystals generally contain numerous defects and are highly strained as a result of the polymorphic transformations and thermal contractions which accompany cooling. Recently, Armington, Potter, and Tanner13 have reported the formation of single-crystal films of boron on silicon single-crystal substrates through thermal reduction of BC13 by hydrogen. Boron E. T. PETERS, Junior Member AIME, is Senior Scientist, ManLabs, Inc., Cambridge, Mass., and W. D. POTTER is Research Chemist, Air Force Cambridge Research Loboratories, L. G. Hanscom Field, Bedford, Mass. formed at temperatures near 1000°C was identified as the a-rhombohedra1 form, consistent with expectation. The present paper describes a continuation of this work with specific reference to characterization of the structural features of the deposited boron films. The ultimate goal of this program is to produce large-area single-crystal films of a-rhombohedra1 boron to be used for electrical and optical studies by other workers. PREPARATION OF BORON FILMS The experimental procedure of preparing thin films is similar to that described by Theuerer14 for the epitaxial growth of silicon by thermal reduction of SiC14 and has already been described as applied to the preparation of boron thin films.13 Briefly, a mixture of BCl3 vapor and dry hydrogen is passed over a heated silicon substrate. Thermal reduction of the BC13 allows deposition of boron on the substrate. The substrates were {111}-oriented, single-crystal silicon. Square specimens 0.63 cm on an edge by 0.1 to 3.0 mm thickness were prepared by

Jan 1, 1965

By M. H. Richman, E. S. Meieran

An analytical method is presented which enables the electron diffraction patterns from a twinned region to be indexed. The method has only been applied to (112) twins in bcc lattices, but can easily be adapted to other types of twinned lattices. Calculations of all twin spots, including those superimposed on matrix spots, is made possible by this method. SINCE the advent of transmission electron microscopy, the analysis of selected-area electron diffraction patterns has become very important in the interpretation of electron micrographs. Frequently, as in the case of some martensites, twinned areas are observed and give rise to complex diffraction patterns, which so far can be analyzed only for the simplest orientations of the thin foil specimen with respect to the electron beam. In order to simplify the analysis of twin patterns of more complex orientations, an analytical method was devised which is capable of predicting the positions of all reflections from both matrix and twin regions for all possible foil orientations. Although the method has only been applied to the case of bcc metals twinned about a (112) plane, it is equally applicable to other Bravais lattices. This method has been successfully applied to selected-area electron diffraction patterns of Fe-Ni and Fe-Ni-C martensites and drawn tungsten wire. PROCEDURE Imagine the reciprocal lattice corresponding to a bcc material, with each point hkl representing the crystallographic plane (hkl). Since the extinction conditions require that for this lattice, only reflections where h + k + 1 = even integer are allowed, the three dimensional reciprocal lattice is actually fcc. Since in real space twinned regions and matrix regions are mirrored across a (112) plane, the twinned reciprocal lattice is derived from the matrix reciprocal lattice by a rotation of 180 deg about a (112) direction. While it is possible to calculate how a point hkl will shift under a twinning transformation to a new point htktlt using only the reciprocal lattice based on the orthonormal vectors [100], [010], and [001], the calculations are greatly simplified if a new orthonormal coordinate system containing the twin axis is introduced. The twinning operation then becomes a simple rotation of 180 deg about a principal coordinate axis (in this case the twinning axis), and a retransformation back to the original reciprocal space will give the position htktIt of the twinned reflection.

Jan 1, 1963