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By George Collins

AT the meeting of the Western Division of the American Mining Congress, held in Denver last September, papers were read by F. H. Brownell, a vice-president of the American Smelting and Refining Co. and chairman of its finance committee, and by H. Foster Bain, former director of the United States Bureau of Mines and now secretary of the A. I. M. E.. which dealt thoroughly with certain phases of my sub-ject. These addresses can hardly have failed to awaken serious reflection in all who listened to them; but their implications have apparently not penetrated the con-sciousness of bankers, economists and statesmen, whose business it is, or should be, to prepare for the economic and social changes which must inevitably follow, if the conclusions which I shall outline hereinafter are true. In discussing this subject I wish to disclaim any intention or desire to forecast the course of the metal markets or the immediate prospects of the mining in-dustry. The facts' adduced must inevitably influence the value of metals, the activity and profitableness of mining, and perhaps also the social status of those en-gaged in it. But my forecasts do not refer to this year, next, year, or the year after. The nearest ap-proach to a date on which I will venture is that the relative scarcity of gold may begin to make itself felt in something like ten years from now, but its effect will not culminate for several years thereafter. Scarcity of new gold is likely to be offset, to some extent, by increasing use of currencies based on credit; but unless it is found possible to dispense with the gold standard altogether, this can hardly prevent a great ultimate fall in commodity prices. This fall, moreover, is likely to be more severe in manufactured goods than in what are, popularly termed raw ma-terials; and most of all in those manufactured goods which are susceptible to the greatest degree to cheapen-ing by mass production, and which are least counter-affected by increasing metal prices; by which I mean those in which the cost of metal contained forms a relatively small, element in the total cost of production.

Jan 6, 1927

Established as a Division November 17, 1948 B W Gonser, Chairman J C Kinnear, Jr, Past Chairman H H Kellogg, Chairman-Elect R C Cole, Vice-Chairman, '58 A E Lee, Jr, Vice-Chairman, '59 W R Opie, Vice-Chairman, '60 R W Shearman, Secretary AIME, 29 West 39th Street New York 18, N Y

Jan 1, 1957

By R. M. Brick

EDUCATIONAL benefits for veterans of World War II have largely removed one of the two former barriers to a college education for everyone, namely financial means and intellectual capacity. This latter limita¬tion has not kept privately endowed institutions from increasing 50 to 100 percent in size of student body, even after applying moderately rigid entrance standards. Growth of some land-grant universities, which cannot well exercise such restrictive judgements, has been even greater. After a weary board of admissions, subject to student, alumni, faculty, and even political pressures, has admitted double the former number of freshmen, the university's worries really begin: to find laboratory, classroom, and instructional facilities. If this were a one- or two-year problem, the answer would be simple: double up, hold night classes, particularly of laboratories, rent space, and have instructors work 24 class or contact hours a week instead of twelve (it takes usually two to three hours of outside work by the instructor for one hour in class). However, most engineering school faculty men are worn out now from four to five years of "accelerated" (frequently downward!) programs and they couldn't continue teaching in a way satisfactory to their own consciences on

Jan 1, 1947

By T. M. Geffen, J. L. Sanderlin, F. F. Craig, D. W. Moore

Scaled reservoir models have been used to study the effect of gravity on oil recovery performance in frontal-drive operations; namely, water, gas, or solvent flooding. The difference in density between the reservoir oil and the injected fluid causes their segregation, resulting in a non-uniform advance of the fluid front. In the laboratory flow tests, which simulated both five-spot and linear injection operations in flat reservoirs, the viscous, capillary, and gravity forces present in these operations were scaled. Dyed fluids were used so that the gross movement of the injected fluid could be observed. The studies covered a range of injection rates, formation thicknesses, and rock and fluid properties normally encountered in field operations. The results of the model tests indicate that the volume of the reservoir contacted by the injected fluid at its breakthrough into the producing well is less than that expected based on information which neglects gravity effects. This difference can often be as much as 80 per cent by gas or water injection in uniform sand bodies. Preliminary flow tests on a non-uniform sand body indicate that the uniformity of the flood fronts may in some situations be influenced to a much greater degree by permeability variations within the rock body than by gravity effects. The magnitude of fluid segregation due to gravity is controlled by the average injection rate, rather than day to day or week to week variations. INTRODUCTION One of the important factors controlling the oil recovery from a frontal-drive operation, such as water, gas, or solvent injection, is the volumetric sweep efficiency. This factor is a measure of the gross portion of the reservoir that is contacted by the displacing fluid. The volumetric sweep efficiency is influenced by gravity effects, well arrangements, and variations in rock permeability within the reservoir. The gravity effects are due to the displacing fluid being of different density than the reservoir oil. This causes the displacing fluid to move preferentially toward either the top or bottom of the formation. Non-uniform advance of the flood front can be caused by the relative positions of the injection and production wells. Variations in rock permeability also result in an uneven advance of the displacing fluid. Gas zones, representing paths of low resistance, may result in non-uniform movement of the injected fluid. The more uneven the advance of the displacing fluid, the lower is the volumetric sweep efficiency and thus the lower the oil recovery efficiency. The effects of well arrangement and permeability variations, upon the gross movement of the injected fluid have been the subjects of extensive investiga-ti0ns.1,2,3,4,5,6 Gravity effects have been recognized as being present in frontal-drive operations'.' but there has been little quantitative measure of their magnitude. Very likely the reason gravity effects have not been studied is that this problem does not lend itself to simple experimental or mathematical analysis. The development of reservoir modeling techniques has made possible a quantitative determination of the effect of gravity on fluid segregation and thus upon the oil recovery performance of frontal-drive operations. This paper presents a progress report on a laboratory investigation of gravity effects in fully liquid-saturated, horizontal, uniform as well as non-uniform systems. These results were obtained from scaled experiments on both linear and five-spot systems within the range of conditions normally encountered in secondary recovery operations. This study is concerned with the gross movement of the injected fluid to the time it first reaches the production wellbore. Therefore, it should be emphasized that the results of this paper can not be used to determine the effect of gravity segregation on oil recovery efficiency at abandonment conditions. MODEL SCALING The science of scaling models is relatively new as applied as petroleum production problems, Many of the scaling techniques have been adaptions of those used in basic studies of heat and fluid flow. There are

Jan 1, 1958

THE Institute conducts jointly with the American Society of Civil Engineers, American Society of Mechanical Engineers and American Institute of Electrical Engineers, certain activities as listed below, and is joint owner with them of certain properties situated at 29 West 39th Street in New York City.

Jan 1, 1946

By William L. Batt

FROM the time the Japs overran the Far East, the United Nations faced a serious military problem in the critical shortage of many raw materials desperately needed to prose¬cute the war on two fronts. For many months this critical shortage threatened substantially to limit the gigantic effort to get shooting equipment into the hands of the fighting men on the far-flung battle lines. Now this crisis has been met. Solvency in raw materials has been achieved. Simply stated, this job of producing solvency has been done by "cutting cloth to fit the garment." This does not mean that we have all the raw materials we need. Unfortunately, a few raw materials are still short, thereby limiting the total production of certain war goods, or making these goods less effective. Where the supply of raw materials is known to be limited, however, substitutions have been made or production schedules have been geared to the amounts available, and an over-all balance has been achieved between various parts of the war-production program.

Jan 1, 1943

ARTHUR PHILLIPS, Chairman C. S. SMITH, Past-Chairman L. W. KEMPF. Vice-Chairman. E. E. SCHUMACHER, Vice-Chairman H. A. MALONEY, Treasurer FRANK T. SISCO, Secretary °9 West 39th Street, New York 1S, N. Y. Executive Committee 1945 1946 S. BARRETT H. L. BURGHOFF T. A. WRIGHT GERALD EDMUNDS L. L. W MAN A. A. SMITH, JR.

Jan 1, 1944

President MRS THORNS E LLOYD 14 Green Hill Road Morristown, N J First Vice-President MRS A B PARSONS 52 Edgewood Road Scarsdale, N Y Second Vice-President MRS H A PROSSER 1001 Park Avenue New York, N Y Third Vice-President MRS HARRY J WOLF 3 Glenwood Avenue Littleneck, N Y Fourth Vice-President MRS MARK LAWRENCE REQUA 140 North Plymouth Blvd Los Angeles, Calif Fifth Vice-President MRS NEWELL G ALFORD 314 South Homewood Avenue Pittsburgh, Pa

Jan 1, 1952

By Luther Lennox

DURING the last few years, one of the great problems in the milling of all ores has been that of crushing. This subject involves not merely the cost of the operation, but also the selection of the proper degree and character of crushing to yield the best metallurgical results on the given ore. Considering the diversity of machinery, one is led to wonder at the variety of crushing methods employed, even when realizing that metallurgy demands varying products. In an attempt to investigate the relative crushing resistances of a number of ores now being milled in this country and Alaska, the management of the Portland mills requested samples of average mill-run of ore from various companies. The request met with a ready response, indicating the desire of all operators to gain information on the subject. The difficulties involved in this investigation were numerous, lack of time for outside problems during this strenuous period being a serious one. Also, we were unable, in the time, to obtain a correct 150-mesh . screen; in the screen analyses tabulated and plotted herewith, the 150 mesh screen was used merely to protect the 200-mesh screen, not to ascertain points on the curves.

Jan 8, 1918

By Thomas N. Walthier

If current trends continue, the shrunken world of exploration will keep on shrinking and the number of new mines will be insufficient to meet production requirements. Mineral shortages-not natural, but government induced-will then occur.

Jan 5, 1976

By T. H. Oxnam

The predominating value of the ores now being treated by the Palmarejo and Mexican Gold Fields, Ltd., is silver, although some gold also is carried. The present method of treatment consists of wet-crushing and concentrating, followed by the cyanidation of the un-roasted sands and slimes. The sands are treated by leaching, and the so-called " accumulated slimes " by a system of agitation and decantation. It is only within very recent years that the cyanidation of unroasted silver-ores has been commercially successful. In fact, at the time operations were begun at the cyanide-plant at Chinipas, February, 1902, I knew of no other leaching-plant treating similar ores successfully. The cyanide treatment of the Palmarejo ores differs but little from the ordinary practice in cyaniding gold-ores; and perhaps but little, if any, new information concerning the metallurgy of silver is to be gleaned from it. Palmarejo Mines. The Palmarejo mines are located in the southwestern part of the State of Chihuahua, Mexico, on the foothills of the Sierra Madre mountains, at an elevation of 3,200 feet. The mills, 12 miles distant, are situated on the Chinipas river, near the town of Chinipas, which is about 150 miles northeast of Agiabampo, on the Gulf of California. Supplies are shipped via this port as this route is the best and most direct to the property. The ore-bodies in the Palmarejo mines have been deposited along a series of rock-fractures, caused by an intrusion of eruptive rock. The most important of these fractures or fissures, both in width and value, are the Prieta and Blanca veins, which

Jan 1, 1906

26. G. H. S. Price, S. V. Williams, and G. J.O. Garrard: Heavy alloy, its production. properties and uses. Metal Industry (1941) 599 354s 372. 394. 27. R. Kieffer and W. Hotop: p. 320 of ref 12. 28. F. R. Hensel. E. I. Larsen, and E. F. Swazy: Physical properties of metal compositions with a refractory metal base. Chap. 42, 483, Powder Metallurgy, ed. by J. Wulff (1942) Cleveland. 29. R. Kieffer and W. Hotop: p. 290 of ref. 12. 30. H. Freundlich: Kapillarchemie. 211 (1923) Leipzig. 31. W. Ostwald: Zisch. f. Phys. Chemie. (1900) 34, 503. 32. G. A. Hulett: Zisch. f. Phys. Chemie. (1901) 37. 385; and (1904) 47, 357. 33. J C. Chaston: Discussion to Price, Smithells and Williams, p. 257 of ref. 4. 34. W. Dawihl: Untersuchungen ueber die Vorgaenge bei der Abnuetzung von Hartmetallwerkzeugen. Ztsch. f. techn. Phys. (1940) 21 336. 35. W. Dawihl and J. Hinnueber: Ueber den Aufbau der Hartmetallegierungen. Kol-loidzlsch. (1943) 104, 233. 36. F. Skaupy: Dispersoidchemische und verwandte Gesichtspunkte bei Sinter-hartmetallen. Kolloidzlsch. (1942) 98, 92; and (1943) 102, 269. 37. F. C. Kellcy: Cemented tantalum car- bide tools. Trans. ASST (1932) 19, 233. 38. E. W. Engle: Cemented carbides. Chap. 39, 436, Powder Metallurgy, ed. by J. Wulff (1942) Cleveland. 39. W. Dawihl: Zlsch. f. Melallkunde. (1940) 32, 320. 40. P. M. McKenna: Tool Materials (Ce- mented Carbides). Chap. 40. 454. Powder Metallurgy, ed. by J. Wulff (1942) Cleveland. 41. G. A. Meerson. G. L. Sverev, B. Y. Osinovskaja: Zhurnal Prikladnoi Khimii. (1930) 139 66. 42. A. G. Metcalfe: The mutual solid solubility of Tunesten Carbide and Titanium carbide- Metal Trealmenl (1946) 13, 127. 43. P. Schwarzkopf: Powder Metallurgy. 196-201 and 354-356 (1947) New York. 44. H. Burden: The manipulation and sintering of hard-metals. Special Rep. No. 38, p. 78. Iron and Steel Inst.. 1947. London. 45. W. D. Jones: Principles of powder metal- lurgy. 150. (1937) London. 46. J. E. Drapeau: Sintering of powdered copper-tin mixtures. Chap. 32. 332, Powder Metallurgy, ed. by J. Wulff (1942) Cleveland. 47. H. E. Hall: Sintering of copper and tin powder. Metals and Alloys (1939) 10, 297. 48. F. Sauerwald: Present status of powder metallurgy. -.Melallwirlschafl. (1941) 20, 649. 671. 49. H. L. Wain: Powder metallurgy; influence of some processing variables on the properties of sintered bronze. Report ACA-25. Australian Council for Aeronautics (1946) Melbourne. 50. S. L. Hoyt: Constitution of copper-tin alloys. Metals Handhook, 1364. (1939) Cleveland. 51. T. Ishikawa: Studies on the interdiffusion of copper, tin and graphite powders. Nippon Kinzoku Gakkai-Si (1937) I, 226. 52. A. Carter and A. G. Metcalfe. The struc- ture of porous bronze bearings. Special Rep. No. 38, p. 99. Iron and Stecl Inst. (1947) London. 53. R. P. Koehring: Sintering atmospheres for production purposes. Chap. 25, 278. Powder Metallurgy, ed. by J. Wulff (1942) Cleveland. 54. C. G. Goetzel: Some properties of sintcred and hotpressed copper tin compacts. Trans. AIME (1945) 161, 569. 55. J. W. Lennox: The production of some non ferrous engineering components by powder metallurgy. Special Rep. No. 38. p. 174. Iron and Steel Inst., 1947, London. . P. Duwez and H. E. Martens: The power metallurgy of porous metals and alloys having a controlled porosity. TP 2343, Metals Tech. April 1948. This volume. p. 848. 57. E. A. Owen and L. Pickup: X-ray study of the interdiffusion of copper and zinc. Proc. Royal Soc., London, Series A. (1935) 149, 283. 58. C. G. Goetzel: Sintered and hotpressed compacts of copper-zinc powder. Chap. 34. 352, Powder Metallurgy, ed. by J. Wulff (1942) Cleveland. 98, R. Chadwick. E. R. Broadfield, and S. F. Pugh: Observations on the pressing. sintering, and properties of iron-copper powder mixtures. Special Rep. No. 38, p. 151, Iron and Steel Inst. (1947) London. 60. A. Squire: The properties of iron-copper compacts. Watertown Arsenal Lab. Rep. WAL No. 67101. 61. F. C. Kelley: Properties of sintered iron- comer uowder. Iron Age (Aug. 15. 193) 158 57. 62. G. H. Howe: Sinterinn of Alnico. Iron Age (Jan. 11. 1940) 14.5, 27. 63. R. Kieffer and W. Hotop: p. 359 of ref. 12. 64. W. Hotop: Permanent magnets from sintered iron-nickel-aluminum. Stahl und Eisen (1941) 61, 1105. 65. P. R. Kalischer: Some experiments in the production of aluminum-nickel-iron alloys by powder metallurgy. Trans. AIME (1941) 145, 369. 66. S. J. Garvin: Production of sintered per- manent magnets. Special Rep. NO. 38. p. 67. Iron and Steel Inst. 1947, London. 67. F. C. Kelley: Discussion to P. R. Kalischer. p. 375 of ref. 65. 68. R. Kieffer and W. Hotop: p. 357 of ret, 12. 69. C. H. Howe: Sintered alnico. Chapter 48, 530, Powder Metallurgy, ed. by J. Wulff (1942) Cleveland. Powder Metallurgy Seminar (C. G. Goetzel presiding) C. G. Goetzel—The seminar has been opened by a man who has been active in the field for over fourteen years and has made, since then, some major contributions to the advancement of the art. After having been associated with the Moraine Products Division of General Motors Corporation for over ten

Jan 1, 1949

By George C. Stone

AS most of you probably know, Australia has had many strikes. The two places that had the worst reputation were the Broken Hill mines and Port Pirie, where the smelter was located. About four or five years ago, the smelter changed hands. The new proprietors - immediately endeavored to get on better terms with the men and made such progress in that respect that, the men came to them and said, "There is no use giving us any more money. You have just raised our pay one- bob a day, but the store-keeper and the boarding-house keeper have raised their prices. The boarding housekeeper raised our board three bob a week and the storekeeper took the rest of it and we are no better off." Learning that what the men needed most was firewood wood the company bought the wood on a tract of ground across Spencer's Gulf and- sent men over to cut it. The wood was brought to the works and given to a man to cut up. He thought he had an easy job and loafed, but when the committee representing the men discovered that his loafing added to the cost of 'the wood, it promptly disciplined him and made -him work as he had never worked before. The next question that arose was the distribution of the wood. The committee got bids from several cartmen whose prices varied from about two to five shillings. It gave the work to the next to the lowest bidder. The fact that if delivering the wood cost more, the user would have to pay for it, was an entirely new idea to the men.

Jan 1, 1920

By Gerald Edmunds

CASTINGS of pure metals and many alloys usually have a coarse-grained structure characterized by long columnar grains throughout the main body of the casting. Frequently, the surface exhibits finer, some-times nearly equiaxed grains, and such grains may also compose other parts of the casting. This paper deals primarily with determinations of the grain-orientation textures of the columnar and surface grains of polycrystalline zinc castings. It includes some results upon a cadmium casting and a magnesium casting. A hypothesis is devel-oped to account for the observations on columnar grains and to use as a basis for predicting orientations in other cast metals. A general description of the position of the columnar grains in castings is that their long axes are approximately parallel to the direction of the thermal gradient during crystallization. Thus, in cylindrical castings the columnar grain axes tend to be radial, and in large flat castings where most of the cooling is through one or both of the large mold surfaces they tend to be perpendicular to the mold surfaces. At the edges and corners the direction of heat flow and there-fore the position of the grains is more com-plex. Actually observation shows that even in castings made in flat molds the cooling seems to be somewhat irregular, since columnar grains tend to emanate from certain areas of the cooling surface, indicat-ing that thermal contact was better there than in neighboring areas.

Jan 1, 1940

By W. J. Taylor

The discussion on my paper entitled "Experiments with a Straight or No-bosh Furnace," read at the Philadelphia Meeting, September, 1884 (Transactions, vol. xiii., p. 489), suggests the propriety of slipplementing it with another, giving my views as to the cause of the failure, which was so decided as to create surprise among furnace men. As then stated, the Chester (8. J.) furnace, which had been 60 feet high, and 13 feet in diameter at the bosh, was altered to an 8-foot bosh, with a 7-foot hearth, 7-foot stock-line, and 4-foot bell,

Jan 1, 1886

By George Hale

(The following extracts from Mr. Hale's paper have been made by the Editor, as being of particular interest to our members.) In an address delivered on May 28, at the kind invitation of the Engineering Foundation, I briefly sketched "The War Activities of the National Research Council. "' The wide scope of my subject forced me to touch very lightly upon engineering; I therefore beg permission to return to this phase of the subject. As shown in my earlier address, the' charter membership of the National Academy of Sciences, organized in the midst of the Civil War,

Jan 10, 1918

By Frank Rieber

EVERYONE is familiar with the story of the poor Indian and his leaking tepee. He couldn't repair the leak while it was raining, naturally. And when it wasn't raining, where was the incentive? Even if this traditional Indian was apochryphal, his counterparts are certainly alive today, and operating on a world-wide scale. - A recent issue of the Wall Street Journal, for example, carried an impassioned letter from an old cocoa planter, who wants the world to know why the price of cocoa has gone skyrocketing. For years, he says, British and American interests have bought cocoa at the cheapest possible price and, incidentally, from growers willing to sell at that price. Between them, they didn't put enough money back into the business, either to fight disease in the cocoa groves or to plant new cocoa trees. Until new trees are planted and come into bearing, we will be paying exorbitant prices for our cocoa, and getting less of it.

Jan 1, 1948

By F. C. Bond, J. T. Wang

H. J. Kamack (E. I. du Pont de Nemours & Co., Inc., Wilmington, Del.)—Rittinger's law usually is stated to the following effect: "The work (or energy) consumed in particle size reduction is proportional to the new surface area produced." The law has been stated substantially in this way by Taggart20 Berry21 Dalla Valle22 Coghill and DeVaney,23 Richards and Locke," Gross,25 and many others, and, according to Gaudin,26 was originally expressed by Rittinger in the same form. Consequently there can be little doubt that this is the understanding of the law among most workers in the field of particle size reduction. Bond and Wang, however, express the law in the form "the useful work accomplished . . . ." (italics theirs). The distinction is critical, for in the form used by Bond and Wang the law becomes, as they themselves remark "merely a more or less arbitrary definition of useful work," while in its usual sense the law expresses a physical hypothesis which has been verified experimentally within certain limitations. Considering the way the law has been used, it might be stated more explicitly as follows: "In a given machine operating under a given set of constant operating conditions, the work consumed in the particle size reduction of a given material is proportional to the new surface area produced." Or, as Coghill and deVaney have said,27 "the (Rittinger) law holds only when the tests being compared are made under analogous conditions." There are occasions when the law transcends these limitations; for example, the surface area produced per unit energy consumption for a given material in a ball mill does not vary much over a fairly wide range of operating conditions. But by and large, the surface area production per unit energy consumption will vary with the operating conditions, the type of machine, and the material. The essence of Rittinger's law is that the surface area production per unit energy consumption is independent of the particle size, and this has been verified experimentally by numerous workers for numerous materials, within certain limits. An important limitation is that when one grinds to very small particle sizes, agglomerative forces may tend to interfere with size reduction so that the surface area increases less rapidly than Rittinger's law would predict. Within such limitations, Rittinger's law can be regarded as empirically established. The law has, however, certain theoretical implications, and it seems to be chiefly against these that Bond and Wang direct their criticism. Solids are believed to possess surface energy which is proportional to surface area. Thus, Rittinger's law implies a proportionality between surface energy produced and mechanical energy expended (for a particular material in a particular machine). It does not imply that all or most of the mechanical energy is transformed into surface energy; in fact it is known that most of the mechanical energy is transformed into heat. Bond and Wang assert that most of this heat arises from the damping of elastic vibrations of stressed particles. This may possibly be true for crushing (with which they are chiefly concerned), although in grinding it is probable that much of the heat arises from friction between particles. However, the fact that the surface energy is small compared to the heat energy does not invalidate Rittinger's law, which implies merely that they are proportional. The authors also criticize Rittinger's law on the grounds that "this theory cannot be justified mathematically, since work is the product of force times distance, and the distance factor is ignored," and "energy input must be the product of force times distance, and the Rittinger theory completely ignores large variations in the distance (strain dimension or deformation) throughout which a force must act to produce breakage of different materials." However, the quantities force and distance as such are irrelevant to Rittinger's law, which considers energy input as an integral quantity. The fact that different materials require different forces and strains (hence, different amounts of energy) to break them is incontrovertible but again is irrelevant to Rittinger's law, which, as mentioned before, applies -only to a single material. Even in theory, it would not be expected that the surface area produced per unit energy consumption would be the same for different materials, because the surface energy per unit area is presumably specific to each material. Bond and Wang advance another argument of a

Jan 1, 1952

Discussion of the paper of Earl S. Bardwell, presented at the Butte meeting, August, 1913, and printed in Bulletin No. 79, July, 1913, pp. .1429 to 1441. H. O. HOFMAN, Boston, Mass. (communication to the Secretary*) :-It is pleasing to the originators of the planimetric determination of oxygen in refined copper to see that the method has been taken up by a large smelting plant to be used in every-day work after it has been simplified to suit the new conditions. Several years ago Huntington and Desch 1 had improved our mode of working. They projected the developed negative on to a screen, traced the outlines of the picture with a pencil, drew a border, and measured one constituent with. the planimeter. In order to give the work greater precision, they divided the area into squares of 1 cm. side, shaded the

Jan 11, 1913

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