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By Oberlin Smith

The experiments described in this paper are very incomplete and only preliminary to those I hope to make in the future. Having had a good deal of experience in cutting, forming and drawing sheet-metals, and feeling a great interest in the commercially new and wonderful metal, aluminum, I applied to my friend, Mr. A. E. Hunt, for some specimens in sheet-form, that I might, from time to time, test its working-properties in presses with which we happened to be experimenting at the works of the Ferracute Machine Company. The chances for such trials being accidental only, and the time having been limited to the last few weeks, no crucial experiments have been tried, and no exact data have been obtained for a rigid comparison with other metals. The results of what little we have done, however, are shown in the articles exhibited in connection with the reading of this paper, which comprise various cups, plates, boxes, bells and cartridge-cup and shells. For the latter I am indebted to my friend, Mr. Hobbs, of the Union Metallic Cartridge Co., who, at my request, ran several pieces of sheet-aluminum through the dies with which he was making brass cartridges. The specimens are rougher than they would be had the metal not been a little too thin for the particular dies which he happened to be running.

Jan 1, 1890

By M. G. Corson

INFORMATION regarding the use of manganese alloys has hitherto been incomplete and available only from widely scattered sources. This paper attempts a systematic description of properties and uses of alloys other than manganese bronze, manganin and duralumin, which are probably the only non-ferrous alloys associated with manganese in the minds of most metallurgists.1 PROPERTIES OF MANGANESE Manganese can react either acid or basic; it is hard to obtain in the pure state; it has two different crystalline lattice structures, both of the cubic system, one stable above 850° C. and the other below 650° C., both coexisting in the intermediate range. Although the commercial product is hard and brittle, the pure metal seems to be ductile. In fact Zhemchuzhny, in Russia, was able to obtain ductile manganese and draw it to fine wires by the simple expedient of adding about 3 per cent. copper to the alumino-thermic product. Copper most probably brings the silicides, aluminides, nitrides and carbides present in the commercial product into a much less harmful form of distribution. One industrial use that can be foreseen for wrought manganese articles is as anodes for electrolytic processes in sulfate and nitrate solutions, particularly with high voltages. A practically insoluble skin of manganese peroxide is likely to form in such cases and an insoluble and strong anode material will be available. MANGANESE AS A SCAVENGER Because of its activity manganese might become the most efficient scavenger and refiner of copper, were it not for the fact that 0.01 per cent.

Jan 1, 1928

By P. Greenfield, P. A. Beck

RECENT work by J. Darby, Jr. in this laboratory has shown that the reported vanadium-rich limit of the s phase in the Co-V system at 1200°C is in error. The appearance of a second phase in s actually is restricted to alloys containing over 68 atomic pct V. The error in the original value is due apparently to a reaction that takes place along the numerous cracks in the s specimens between the alloy and the impurities present in the He + 8 pct H atmosphere in the annealing furnace. Such a reaction and the consequent appearance of a second phase can be suppressed if the alloys are sealed under vacuum in Vycor tubing. The new value of 68 atomic pct V for the vana-dium-rich limit of the s phase in the Co-V system effects slightly the s compositions calculated from average values of N, and N,. for various s phases. The standard deviation between experimental mean compositions and those calculated from the assumption that s is characterized by a constant number of 3d + 4s electrons per atom (N,), is slightly reduced from 9.1 to 8.8 pct. The maximum divergence for the V-Mn s phase is reduced from 15.5 to 14 atomic pct. The standard deviation calculated from constant electron vacancy numbers given by N.. = 4.66 (Mo + Cr + V) + 3.2 (Mn) + 2.2(Fe) + 1.71(Co) + 1.6(Ni) is now greatly reduced, as the maximum divergence for this correlation previously occurred in the V-Co system. This maximum divergence is reduced from 7.6 to 2.3 pct, and the standard deviation for all s- phases is reduced from 4.1 to only 2.9 pct. The correlation for electron vacancy numbers given by N. 5.66 (V when with Ni or Co) + 4.88 (V when with Mn or Fe) + 4.66 (Cr + Mn) + 3.3 (Mn) + 2.66 (Fe) + 1.71 (Co) + 0.61 (Ni) is made slightly worse, and the standard deviation increases from 2.8 to 3.9 pct. These changes, however, do not affect the conclusions of the paper.' The deviation between calculated and experimental s compositions is much less for either one of the electron vacancy correlations than for the correlation with the number of 3d + 4s electrons.

Jan 1, 1955

By C. P. Sandberg

C. P. Sandberg, London, Eng. 1 think we should all be grateful to the Pennsylvania Railroad Company, and to their chemist, Dr. Dudley, for spending so much time and money in order to solve an important question; nor are me less indebted to the public spirit which leads them to impart tlie experience thus gained. In Europe nothing similar has hitherto been done, either by a company or by any private individual. In England the great railway companies employ their engineers in other ways, and do not keep a chemist or specialist to study rails; bat even if they did they would probably not publish the results. The chief professional engineers are so occupied with their private practice of railroad construction generally, that they cannot be expected to devote their time and energies to so special a question. The German Railway Union has, in my opinion, missed the real object of its elaborate researches by falling into the error of specifying costly, impracticable tests for rails—tests at the same time which do not infallibly expose the impurities that may be in the rails under examination. There has, therefore, been nothing done on this side of the Atlantic in the way of exhaustive study to determine the best composition for steel rails. America should consequently have full credit for the enlightened example which she has set. I wish, however, to make a few remarks on Dr. Dudley's second paper,—& paper which follows very much upan the same lines of argument as the first red three years ago, upon which I have previously touched in my pabr on the same subject read at the meeting in August last. If Dr. Dudley had discovered a new metal he could hardly, I think, have taken wore pains to prove that he was correct in his first formula for the best chemical colnposition of steel rails. But I hare seen so much done in the way of proof by experiment that I am inclined to think that almost anything can be proved by experiments and by satnples. If Dr. Dudley would only give up his formula, which would not suit any country—not even America—

Jan 1, 1881

By J. E. McDonald, J. G. Eberhart

A model is discussed from which the work of adhcslon .tor liquid transition metals on aluminum oxide surfaces can he calculated, A close-packed (00011 oxygen surface on A12O3 is assumed with two different types of surface sites: one type involving metal-oxygen bonds and the other man der Waals into actions. The work of adhesion is thus expressed as the sum of these two bonsding free energies. Calculated works of adhesion for nickel, titanium, chromium, and zirconium on sapphire agree well with the experimentally determined quantities. The model is extentled to the calculation of the work of adhesion and shear stress required to remove a thin metal film from a sapphire substrate and is in good agreement with experimental values. The obsewed dependence of the work of adhesion on the free energy of oxide formation of the metal is shown to also provide an interpretation of the tittle dependence of thin-film adhesion. THIS paper presents a model for the type of bonding which occurs across a metal-A12O3 interface. The model is used to explain the results of two types of experiments in which such an interface exists: 1) the adhesion of thin metal films on Al2O3 substrates and 2) the wetting of A12O3 by liquid metal drops. The adhesion of thin films to various substrates has been the subject of a variety of investigations.'-' Benjamin and weaver3 and Bowie,6 using the scratch test developed by Heavens,10 studied the adhesion of metallic films to glass substrates. Their observations for noble-metal film adhesion agree well with an adhesion model involving a van der Waals type of bonding between the film and the substrate. For films of metals whose free energy of oxide formation. ?F°f, has a negative value. Benjamin and weaver3 and Bowie6 found a time-dependent adhesion with an initial value that can be interpreted in terms of van der Waals interactions but a larger terminal value which was related to ?F°f, Karnow-sky and Estill7 deposited films on sapphire at elevated temperatures and noticed no time dependence of film adhesion but a similar correlation with ?F°f. Because of the kinetic problems associated with thin-film adhesion it is desirable to examine adhesion in an equilibrium system. The wetting behavior of liquid-metal drops on Al2O3 provides such a system. Systems of this metal-ceramic type have been studied extensively.11 Humenik and Kingeryl2 have measured the wetting of A12O3 (and other substrates) by several metals and have pointed out that the wetting ability of these metals increases with increasing values of -?F°f. It is thus seen that thin-film adhesion and metal wetting on A12O3 are both related to the tendency of the metal to react with the surface oxide ions of the Al2O3 substrate and, because of this, both phenomena should be explainable by an appropriate model for the metal-Al2O3 interfacial bonding. In the sections that follow, wetting and adhesion data on A2O3 are reviewed and a model is presented by which these phenomena can be interpreted. ANALYSIS OF WETTING EXPERIMENTS In an equilibrium system involving a liquid-metal drop on a solid Al2O3 substrate, the work of adhesion, WAD, is defined by the Dupre, equation as WAD = ?s + ?L -?sL [1] where ?s and ?L are the surface free energies of the solid substrate and the liquid drop, respectively, and ?sL is the interfacial free energy. The work of adhesion is the work required to separate a unit area of the solid-liquid interface into two surfaces. The work of adhesion is usually determined from a sessile-drop experiment in which yL and the contact angle, ?, are measured. The Young-Dupr6 equation is then used to calculate WAD Wad = ?L (1+ cos ?) [2] The literature of this subject has been examined and Table I shows work of adhesion data for various liquid metals as measured on A12O3 substrates. The standard free energy of oxide formation of the metal at the temperature of the wetting experiment, ?F°f . is also tabulated in kcal per g-atom of oxygen. The data is grouped according to the gaseous atmos-

Jan 1, 1965

By James W. Neill

The occurrence of minerals of nickel and cobalt at Mine La Motte is probably known to every mineralogist. I will not attempt to describe these minerals, but, before entering on my subject, will briefly mention the ores, etc., which call for metallurgical treatment and enter into the composition of our mattes. Our staple lead-ore, the dressed galena, is the chief source of nickel and cobalt. It carries but a small percentage of these metals, viz.: 0.2 to 0.3 percent. usually, though when much copper pyrites is contained in the gangue, the amount of nickel and cobalt may be as great as 1.0 to 1.5 per cent. Next in importance is the ((middle product" of the dressingworks, consisting of the sulphides of iron (and copper) with gangue and galena. This usually carries 20 to 23 per cent. of lead, 0.5 to 1.0 per cent. of copper and 2.5 to 3.5 per cent. of nickel and cobalt. A larger percentage of copper always carries with it an increase of nickel and cobalt. In some few cases 12 to 15 per cent. of copper gives 6.5 to 8.0 per cent of these metals. Resides these products of the dressing-works, there is a small quantity of true nickel-cobalt-ore

Jan 1, 1885

By GUY B. HUNNER

THOSE magnetite ore bodies comprising the Clifton Mines are situated in the south central part of St. Lawrence County, New York, on the western slope of the Adirondack Mountains. The topography is made up of gently rolling hills densely wooded with second-growth maple, birch, and hemlock. Drainage is north and west to the St. Lawrence River.

Jan 1, 1943

By Ernest Gayford

When the United States Government started buying gold at varying prices per ounce, set by the President and the Treasury Department, the gold miner found himself facing new conditions, as gold became a commodity with a fluctuating market price. While it was self-evident that the miner was to receive more for his gold than the old established price of $20.67 per ounce, there was an element of uncertainty, which made it difficult, and perhaps dangerous, to decide to invest his time and money to produce gold, especially if the profit would represent only the difference between $20.67 an ounce and the new price as set from day to day by the Government. When, however, on Jan. 30, 1934, the United States went off the gold standard, the price of newly mined gold being rather definitely set at $35 per ounce, with some assurance that the price would be maintained at or near this figure for a long time to come, the gold miner was justified in revaluing his property on the basis of the new price, and the prospector was offered inducement to spend his time and energies hunting for new mines, or going back to old locations previously abandoned as of doubtful value. It is interesting to see what this new price means to the producer of newly mined gold, and how much of the increase is passed on to the producer. It will be found that, as with the base metals, the nearer he can get to producing a finished product himself the greater his reward will be; the net returns for bullion being necessarily higher than for the same amount of gold shipped in concentrates to the smelter. Bullion can be shipped to the United States mints or Government assay offices under the following terms and conditions. An affidavit must accompany the shipment, stating, among other things: 1. The source of the gold; whether ore, tailings or placer. 2. The tons of ore, tailings or cubic yards of gravel from which the shipment was recovered.

Jan 1, 1935

By AIME AIME

THE Engineering Education Committee of the Institute convened at the Engineering Societies Building on Feb. 18, .1929, with. E. A. Holbrook, dean of the Schools of Mines and Engineering, University of Pittsburgh, in the chair. STATISTICAL' STUDY OF STUDENTS IN MINING The first paper, a statistical study of the students enrolled in courses leading to a mining degree in 40 institutions, was presented by H. D. Keiser,, assistant editor of the Engineering and Mining Journal; who gave a brief outline of an article he was about to publish in ?that journal?. The complete article appears in the issue for March 30; 1929: To avoid repetition the results are summarized as follows: A request was sent to 42 institutions which give courses in mining' for the number of students enrolled as freshmen; sophomores; juniors, seniors and special students in mining for the years 1925-26, 1926-27, 1927-28, 1928-29. Two of these colleges replied that there were no students in mining. Students' enrolled in courses in metallurgy, geology and engineering, other than mining, were excluded from the statistics:. The statistics received were arranged in, four groups, according to the completeness of the information. One complete group of 25 institutions 'shows as follows:

Jan 1, 1929

By Charles White Merrill

Money is one of the most .pervasive elements in human life. The compensation for a workman's daily efforts is expressed as a wage and is measured in money. What an individual may consume depends largely on his income which also is expressed in terms of money. If he would start an enterprise its size would be determined in large part by the amount of money available for capitalization and its success would be measured in net income expressed in money. In short, the most widely used common denominator for comparing merchandise, real property, jobs, enterprises, gross national product, or personal success is money. Despite this use of money by almost everyone past infancy to express his appraisal of the in- numerable values he sees around himself, the complexity of the device called money makes its nature and workings a mystery to most users. Some of the difficulty in understanding money results from the fact that it has three distinct but interrelated functions: (1) a medium of exchange, (2) a unit of account, and (3) a store of value. In many statements about money the discussion moves from one function of money to another without the speaker or the listener recognizing the changes. For example, the housewife says "We took the money we had saved up to make the down payment and after twelve monthly payments the television will be ours." When this housewife spoke of "saving up the down payment" she referred to money in its function as a store of value; when she spoke of "the down payment" she was using money as a medium of exchange; and when she referred to the "monthly payments" she spoke of money as a unit of account. Another cause of confusion in understanding money is its paradoxical nature in that it represents both the power to produce and the power to consume. For example, when the rich uncle dies one nephew may regard his inheritance as an opportunity to buy a farm and leave the ranks of the wage earners to become an independent producer, whereas the other nephew may regard his portion as the means of living in complete leisure as a pure consumer.

Jan 1, 1959

I have attended these meetings, every year, since 1926 and have served on both the Pittsburgh and the National Executive Committees, so that I am fully aware - of the ruling of this organization regarding, "No Papers by Vendors". Since I am now classified as a VENDOR, I wish to express my sincere appreciation for the invitation to formally discuss these very interesting papers --all of which herald the coming of an entirely new era in the manufacture of quality steels. I also appreciate the references by Mr. Mosser and Dr. Swinkels to my first paper on the oxygen probe which was presented at the meeting of this group, here in Chicago, in 1966 and was subsequently published in the NOH Proceedings of that year. (1)

Jan 1, 1972

By Charles R. Wilson, Thomas W. Doe, Jane C. S Long, Howard K. Endo

An approach to treating flow through fractured rocks is presented which involves (1) determining statistical distributions for fracture area, density, orientation, and aperture from field data, (2) computer generation of fracture systems from the statistical distributions, and (3) analysis of the permeability and porosity of the fracture systems. The fracture density and orientation data my come from core logging or mapping. The hydraulically appropriate apertures and areas of the fractures come from transient flow analyses of single fracture well tests. These tests my also yield information on fracture deformability. Analysis of flow through computer generated fracture systems shows that an equivalent porous medium permeability can be defined for some fracture systems if a large number of fractures is taken into account.

Jan 1, 1982

The University of Chicago Press, 5750 Ellis Ave , Chicago, Ill This Press publishes books on a wide variety of subjects of scientific interest, as well as several journals Only a few books on geology have been published, however, and the Journal of Geology. The Journal of Geology: A semiquarterly standard American publication in the geological field. $6 per year, single copies, $1, back numbers, within the past five years, $6 per volume Books on geology: The origin of the earth, by T. C Chamberlin, $2 50, Two solar families, by T. C Chamberlin, $2 50, Quantitative classification of igneous rocks, by W. Cross, J. Iddings, L V Pirsson and H. S Washington, $1.75; Studies in minor folds, by C. E. Decker, $1 50; An introduction to the study of ore deposits, by F. H Hatch, $3, A descriptive petrography of the igneous rocks, by A. Johannsen, $4 50, Essentials for the microscopical determination of rock¬forming minerals and rocks, by A. Johannsen (revised ed ) $3, Outlines of geologic history, with special reference to North America, edited by R D. Salisbury, 8150

Jan 1, 1933

By N. W. Perry

Some months ago a gentleman gave me a handful of minerals which he had collected in an arroyo, or dry stream-bed, that ran through the town of Ramos, State of San Luis Potosi, Mexico, as a sample of the class of ore that might be expected in the mines of that section. I was, however, familiar with those mines and their ores, and cast the pebbles aside as of no interest. I afterwards returned to Mexico and took charge of two groups of mines, one in the State of Zacatecas, and the other in the town of Ramos, State of San Luis Potosi. While I was thus engaged, it was a very frequent occurrence for parties to bring me specimens of rock, ores, etc., for my opinion on them; and one day a man brought me a half-dozen or more small pieces of a very black shiny mineral, desiring to know what it was. I did not recognize it, and desired him to give me the specimens for analysis, which he promised to do in a day or two. He never did give them to me, for he lost them ; but he said there were plenty more where these came from—at Ramos—and he could get them at any time for me. I thought no more of the matter until after my return to this country, when, one day, in looking over some of my old " trash," I came across the specimens at first referred to as having been cast aside so carelessly. I noticed two distinct minerals among the pebbles : one being erubescite or tetrahedrite, the predominating mineral of the mines of Ramos, and the other a hard black shining mineral, the same that I had wished to analyze in Mexico. On testing for hardness I was surprised that it scratched topaz with some degree of ease, thus placing it above 8 in the scale of hardness. Trying it with a corundum, I sometimes succeeded in scratching it, but at other times it would scratch the corundum, and at still other times neither would produce the slightest effect on the other. Crystallized topaz would be ground to a powder in attempting to scratch the black mineral, without abrading it in the slightest. It must, therefore, be placed at 9 in the scale of hardness. It is of the deepest opaque black, not unlike pitch-blende in ap-

Jan 1, 1884

By Louis Ware

BEFORE the war we often heard the term "Big Business." And there were complaints of the ills and abuses attributed to bigness in business. Although there were examples where the small businessmen spoke for their rights and sought protection from the bigger ones, it has only been in recent war years that a tendency has developed definitely to divide the business of our nation into the big and the small. In some cases, those with an eye to the political value of the vastly greater number of small businessmen of the country have fomented this division by hurrying to the protection of these more numerous voters, and intentionally or not have emphasized in their writings and verbal attacks any and all differences of these interests that could either be found or fabricated to, suit the occasion. It has become another example of breaking the people into classes and thus setting up the basis for the claims of one class against another, and the subsequent demand for legislation and Governmental aid. The terms "big" and "small" are purely relative. One businessman, employing a hundred men, told me recently he did not know which adjective would be more appropriately applied to his operation. He did not know whether he should join the small operators' group that had been organized, or should consider himself big. He said that his present plant seemed big to him when he looked back to its humble beginning many years ago with a couple of men in two rooms. Yet, when compared with many of his competitors who employ thousands, his was small. He did add, however, that he probably became big one day a few years ago when the union moved in and organized his employees.

Jan 1, 1945

By William L. Fink, Dana W. Smith

In parts I1 and II2 of this series, there were presented results of investigations on the age-hardening of an aluminum-copper and an aluminum-magnesium alloy. It was shown that the simple precipitation theory of hardening3 adequately explained the aging phenomena, including certain so-called "anomalous" behaviors which had caused other investigators to reject or modify the precipitation theory. However, these papers did not discuss the double aging peaks, which have been stressed in recent articles by Dr. M. Cohen4 and Dr. M. L. V. Gayler.6 The present paper is devoted to an explanation of this "anomaly." Fig. 1 is a generalized schematic representation of aging curves at different temperatures. Curve A corresponds to the aging at the lowest temperature, and D at the highest temperature. Certain previous investigators have explained curve A and the initial peaks

Jan 1, 1938

By William L. Fink, Dana W. Smith

In parts I1 and II2 of this series, there were presented results of investigations on the age-hardening of an aluminum-copper and an aluminum-magnesium alloy. It was shown that the simple precipitation theory of hardening3 adequately explained the aging phenomena, including certain so-called "anomalous" behaviors which had caused other investigators to reject or modify the precipitation theory. However, these papers did not discuss the double aging peaks, which have been stressed in recent articles by Dr. M. Cohen4 and Dr. M. L. V. Gayler.6 The present paper is devoted to an explanation of this "anomaly." Fig. 1 is a generalized schematic representation of aging curves at different temperatures. Curve A corresponds to the aging at the lowest temperature, and D at the highest temperature. Certain previous investigators have explained curve A and the initial peaks

Jan 1, 1938

By R. M. Raymond

RECENTLY one of the Welsh coal companies, which has an excellent plant of up-to-date ma-chinery both on the surface and underground, operated under modern methods, sent one of its engi-neers to the United States to study actual operations in the mines. He visited several of the most important and best conducted collieries, went back, and reported that the greatest difference between operations in England and in the United States was. the closer con-tact between management and workmen. By manage-ment he meant management all the way through; close cooperation between office management, superintend-ents, foremen, shift-bosses, etc., and the workmen. A visit to some of the coal mines in that country by the writer made this fact rather impressive. The feel-ing on this side of the water that the methods in use in the coal mines in England are not up-to-date was found in many cases to be quite erroneous. Many mines, particularly those with very thin beds, in which profitable operations are doubtful under the best con-ditions, have necessarily had to adhere to old methods instead of making mechanical improvements. The Powell-Duffryn mines, in the center of the South Wales district, are certainly operating successfully, and have planned their business excellently. Sufficient areas of contiguous land have been leased for extended opera-tions. Mine plants are laid out in the valley, for work-ings on both sides, on a reasonable tonnage of 1500 to 3000 tons to each operation. The beds are from 30 to 48 in. thickness, and a 3-ft. seam is considered an ex-cellent thickness of coal; in fact, the miners prefer to work on the thinner beds rather than the thick ones, where they consider it more difficult to control the backs. This company is making use of its fine coal for produc-ing electric power, which is distributed to its own operations, and for use in the communities adjoining. For this purpose methods of cleaning the fine coal are being put into use. Compressed air is generated at the central power plant and is transmitted over long dis-tances to various mines in each valley. A byproduct coke plant uses more of the fine coal and gives further returns from non-commercial coal. The long-wall system applied in sections of limited size is popular in working the small seams, and me-chanical cutting is used, also handling either by shaking chutes or belt conveyors, or a combination of both. In some mines mechanical cutting is not necessary. The backs are so handled that in the softer or somewhat crushed seams hand cutting can be carried on effec-tively.

Jan 10, 1927

By Thomas Fraser, David R. Mitchell

THE primary purpose of the loading plant is to transfer the finished product from the preparation machines to the railroad car, truck, or barge in which it is to go to market. Secondary purposes of the loading plant are: to prevent excessive degradation of sizes during loading, to reduce segregation as much as possible, and to prevent excessive quantities of very good or off-grade coal from entering any one car. Nonuniformity of consignments is one of the chief sources of complaints by consumers and coal merchants. A properly designed loading plant will do much to reduce complaints and insure uniformity, not only from shipment to shipment but also in each individual consignment along the length of the car and in cross section. DEGRADATION IN STORAGE, LOADING AND SHIPMENT The object in loading is not only to handle the coal without breakage and segregation, but also to produce a well-trimmed load that will ride to its destination without spillage o~ breakage en route. The small sizes present in a car-of prepared coal as received by the purchaser consist of: missed small sizes not screened out in the preparation plant, breakage during loading, and breakage caused by handling en route. For domestic sizes of anthracite shipped from the Pennsylvania anthracite field to Atlantic coast cities, the dealers' loss because of breakage in loading and shipment amounts to from 2 to 5 per cent and for anthracite shipped to Middle West cities, the loss is 8 to 9 per cent. This difference is in part because dealers in the Middle West rescreen their coal more thoroughly than is usual in the East. One dealer handling Illinois No. 6 coal shipped from southern Illinois mines to Chicago reports an average size loss of 10 per cent when lump coal is unloaded with a fork. This runs as low as 5 per cent for carefully loaded coal and as high as 15 per cent for carelessly loaded coal. An Ohio dealer estimates the degradation in loading and shipment of West Virginia coals consigned to Ohio cities as follows: Pocahontas lump

Jan 1, 1950

By R. M. S. B. Horta, W. T. Roberts, D. V. Wilson

Evaluation of results obtained by the Harris method for inverse pole figures is discussed. Two existing analyses and a new approach are compared. In the most frequently used analysis, different reflections are accorded equal weight. A second method involves area-weighting of reflections, mainly to take account of nonuniformity of Pole distribution. In the new method, reflections are weighted according to their multiplicity factors. Intensity ratios obtained from a sample of steel sheet by the three methods are compared. INVERSE pole figures offer a convenient method of depicting the proportions of material with various orientations referred to a unique specimen axis. The technique was first applied to fiber textures, but it is now frequently used as a description of texture in sheet metal, the unique axis in this case usually being the sheet normal. The Harris method' for the determination of inverse pole figures has the great merit of simplicity. It suffers certain intrinsic limitations, but provided that these are borne in mind, the results allow useful conclusions to be drawn regarding the effects of texture components on certain mechanical properties. Much thought has been given to alternative methods of texture description, aimed at eliminating the ambiguity in the simpler methods.2"6 Refinements in the method of description are obtained at the price of increasing complexity, and it seems clear that a simple method, such as that of Harris, will continue to find application. The original derivation by Harris1 has been corrected by Morris7 and later by Mueller, Chernock, and Beck.2 Since the latter reference is more accessible, it is referred to more frequently than the work of Morris. Most users of the inverse pole figure method present their results on the basis of the treatment by Mueller et al., and it is the purpose of the present communication to comment on this treatment and to suggest a simple modification to the method of presentation which enhances the meaningfulness of the results. It will be convenient first to summarize the Mueller analysis as follows: The intensity Ihkl of a hkl reflection from a textured specimen is: Ihkl=CI0AL\Fhkl\2NhklPhkl [1] where C is a constant for a given sample I, is the intensity of the incident beam A is an absorption factor. With usual diffrac-tometer geometry and a flat specimen, A is inversely proportional to the density of the specimen. L is the Lorenz polarization factor Fhkl is the structure factor for the hkl reflection Nhkl is the multiplicity factor phkl is the fraction of crystals in the polycrystal-line aggregate with any particular (nkl) plane parallel to the surface. The corresponding equation for a specimen with randomly oriented grains is lR,hkl=CRl°ARL\fnkl\2Nnklk [2] the subscripts R indicating the factors that are different for the random sample, which will, in general, have a density different from that of the textured one. The intensity ratio is hkl , c A Phkl [3] IR,hkl CR AR PR The constants are eliminated by summing over all the measured reflections ^iRMi °R AR PR ljPkkl and from Eqs. [3] and [4] T IR,hkl The only unknown in Eq. [5] is Yj phkl and before this can be evaluated, it is necessary to adopt some form of normalizing procedure. Mueller et al. assume that when a large number, n, of reflections is used, the average value of p as defined by Eq. [6] below will be unity ? = £j**l3l [6] and the final result of their analysis follows: hkl Pkkl = i I&Jf~ [7] ±y* Ihkl ^ in,hki The normalizing procedure used by Mueller et al. involves an unrealistic assumption since it gives equal weight to each of the hkl reflections. Other normalizing procedures can now be examined with a view to selecting a more appropriate one. For an infinite number of reflections, the function p can be averaged over a continuous range of orientations covering the complete solid angle 4p by the integral relation: p =1 jp(a)dQ = l [8] This is the only exact procedure, but in practice a

Jan 1, 1970