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By Fred C. Bond

SIX years have passed since the last grindability table was published.1 In that time the list has been increased with many new tests, and the development of the new Third Theory of Comminution2 has made possible the reduction of all results to a consistent work index value. In this tabulation all grindability and crushability test results are given in terms of the work index, with formulas for reversion to the older units if desired. The average values for 57 different classes of materials are listed in Table I. The total number of work index values listed is 1211, and the overall average work index is 14.42.

Jan 3, 1953

Michigan State Department of Conservation, Lansing, Mich The Department of Conservation has two divisions issuing publications which should be listed in this directory. Geological Survey Division. R. A Smith, State Geologist Land Economic Survey Division L R Schoenmann, Head. A price list of publications of either division will be sent upon request to that division Geological Survey Division.-Citizens of Michigan may obtain publications of this Division on payment of forwarding charges Prices to others for available publications are given below: Vol 5 (1881-1884): Pt 1, Geological report of the Upper Peninsula of Michigan, by L L Hubbard, pt 2, Geology of Lower Michigan with reference to deep borings, by A C Lane, $125. Annual Report for 1908. Pt b, Geological section of Michigan, by A C. Lane and A E Seaman, 50 cents. Publication No 5, The Late Glacial and Post Glacial Uplift of the Michigan Basin, and earthquakes in Michigan, by W. H

Jan 1, 1933

By Robert Longyear

IN, diamond-drill work, a true sample consists of all the material cut by the bit-both core and cuttings. As the recovery of this sample is the object of diamond drilling, the utmost care should be taken to secure it. Speed of drilling and low costs are of little value if an inaccurate sample is obtained. The engineer in charge must study his material and lay out the plan of sampling, and then see that the drill runner follows his instructions; for the runner may be more interested in obtaining a large footage than in developing accurate methods of sampling. FIG. 1.-CORE BOX. When the core has been removed from the core barrel, it should be placed in a core box in the exact order in which it is taken from the ground. This box, Fig. 1, is usually a shallow tray 4 or 5 ft. (1.2 or 1.5 m.) long, with partitions running lengthwise between which the core

Jan 12, 1921

By Persifor Frazer

Among the geological problems with wliicli the present PenufiyI vanirr Geological Survey has had to deal is the relative age of wries of atrata passing around and through the city of' Philadelphia, Bucks, Chester, and Delaware counties. Rogers includes all these roclrs in 11is hypc~zoic series, and every student, so far as the writer knows, with one exception, has assigned to them a position beneath the Pobdam sandstone, or Primal" of that eminent and gifted geologist. So far as regards the srllall portions of this belt, to which it is the intention of the present paper to draw attention, even the oiie geolo-

Jan 1, 1881

By B. Amadei

INTRODUCTION Laboratory studies on the deformability and strength of intact rocks generally involve the uniaxial compression test, the standard triaxial compression test and direct or indirect tension tests. If [al ,a2 ,a3] are principal stresses [(al>a2>a3)] with compression taken as positive and tension taken as negative, the applied stress field for each one of these tests can be represented as shown in Fig. 1. However, for most in-situ conditions, such as those that exist at any point around an underground excavation, the stress field is truly three-dimensional or multiaxial [(al+ a2+a3)] and none of the tests shown in Fig. 1 can be used to predict the mechanical behavior of the rock. There are special cases for which one of the three principal stresses vanishes. Biaxial loading of rocks in-situ takes place, for instance, when rocks deform and fail in plane stress conditions. This can occur in a free unloaded surface of a rock structure such as in the wall of an underground excavation or a rock slope. Parallel to the free surface, the stress field components can be both compressive [(al>a2>0)], both tensile [(O>a2>a3)], or mixed, one component being compressive and the other one tensile [(U~>O>U~)]. The purpose of this paper is to present the results of 25 true biaxial tests that have been conducted on cubical specimens of Indiana Limestone using the multiaxial cell available at the University of Colorado at Boulder. The tests include uniaxial compression and tension, biaxial compression and combined biaxil compression- tension. Flexible fluid cushions and brush bearing platens were used for compressive and tensile loading respectively in order to minimize loading end effects on the test specimens. The paper begins with a review of previous investigations on the multiaxial behavior of rock. Then, test results are presented in terms of

Jan 1, 1984

Gardner I?. Williams, authority on diamond mining, died at San Francisco, Cal., on Aug. 22, after an illness of nearly a year. Mr. Williams, who was in his eighty-first year, was born in Saginaw, Mich. He was graduated from the University of California in 1865, and afterward took a course at the Freiberg Mining Academy in Saxony. He was awarded the degree of LII. D. by the University of California in 1910, and Doctor of Engineering by the University of Michigan in 1917. Beginning in 1870, Mr. Williams spent two years as assistant assayer at the United States Mint in San Francisco. He successfully developed

Jan 1, 1923

Gardner I?. Williams, authority on diamond mining, died at San Francisco, Cal., on Aug. 22, after an illness of nearly a year. Mr. Williams, who was in his eighty-first year, was born in Saginaw, Mich. He was graduated from the University of California in 1865, and afterward took a course at the Freiberg Mining Academy in Saxony. He was awarded the degree of LII. D. by the University of California in 1910, and Doctor of Engineering by the University of Michigan in 1917. Beginning in 1870, Mr. Williams spent two years as assistant assayer at the United States Mint in San Francisco. He successfully developed

Jan 1, 1923

US 4,152,143-Continuous precipitation of cement copper from an aqueous ore leach solution mixed with pieces of iron as the precipitant Copper depositing on the pieces of iron is loosened and removed therefrom by means of constant but regulated oscillating movement of the pieces of iron in a horizontal elongated chamber, and the loosened copper is separated and collected from the mixture E Kausel and R Nissen, assigned to Klockner-Humboldt-Deutz A G May 1, 1979 8 pp (75-100) Filed 1-12-78 (868,981) (Drawings below) [ ] US 4,156,711-Removal of metal impurities from an acidic zinc or cadmium solution prior to electrolysis. Impurities such as manganese, cobalt, nickel, and thallium are selectively precipitated by contacting the solution with persulfuric acid or an ammonium or alkali metal salt thereof while maintaining a pH value of from 1 5 to 4 5 This patent is a continuation-in-

Jan 1, 1980

By P. E. Landolt

MILITARY necessities and economic scarcities, occasioned by the first and second World Wars, led to the search for substitute materials and new products to meet the demands of advancing technology accelerated by research development. Among others, lithium came to attention. Its chemistry had been studied for a long period, but its general use was quite restricted due to limited known sources of raw material. In World War I, Germany used lithium metallurgically for two principal purposes: 1-hardened lead alloy, B-Metal, for railway bearings as a substitute for lead-tin-antimony alloys; and 2-light strong aluminum alloys, Scleron, in which zinc was largely substituted for copper.

Jan 12, 1951

By Y. C. Liu, W. R. Hibbard

Based on pole figure data and microstructural observations, the re-crystallization orientation found in a copper strip previously cold-rolled 99.5 pct from a single crystal with an initial (110) [112] orientation may be described as: a 30° rotation, clockwise and counterclockwise, about octahedral poles of the cold-rolled texture such that all four poles function at a low annealing temperature (400°C) and only three of them function at high temperatures (500' to 1050°C). The relative intensity of deformation stresses on various slip planes can be correlated with the choice of poles affecting the rotations found in the recrystallized orientations. ROTATIONAL reorientation about the poles of densely packed crystallographic planes is an important characteristic of secondary recrystallization" in face-centered cubic metals. Some evidence has also been interpreted to show that such a rotational relationship also exists in the primary recrys-tallization process." In an investigation of the crystallographic relationships in the recrystallization process, several aspects of the experimental procedure should be considered. With cold-rolled poly-crystalline metal as the initial material, pole figure analysis leaves many ambiguities as to whether or not simple indices can be assigned to adequately represent its orientation. The rolling texture does not consist of a single texture. Minor deformation textures are usually present. In all cases, twin textures are present. The presence of both minor and twin deformation textures influences the recrystallization texture. In order to study the recrystallization mechanism, a more precise knowledge of the history of the material before recrystallization is necessary. Tensile deformation of a single crystal usually produces residual stresses which are concentrated at slip bands. Since the exact nature and orientation of these potential nuclei sites cannot be experimentally evaluated, the tensile deformation of a single crystal was not considered adequate. From the work done by Barrett and Steadman6 n copper, it appeared that cold rolling of a single-crystal specimen with an initial (110) [112] orientation would yield a specimen which fulfills the conditions required for the present investigation, namely a highly preferred single rolling texture with relatively homogeneous stress distribution. By investigating the recrystallization texture of this material, additional details of reorientation during recrystallization might be obtained. The purpose of this paper is to describe such an investigation. Experimental Procedure Copper used in the present investigation was cathode sheet with a purity of 99.94 to 99.97 pct. A copper single-crystal specimen, 1.15x0.8720x0.5322 in. (thickness) was cut from a cylindrical crystal which was grown in a Bridgman furnace.' The cutting was accomplished on a horizontal milling machine operated at a very slow speed to obtain a (110) plane in the rolling plane and a [112] direction in the rolling direction. The disturbed surface was removed by electrolytic polishing in dilute orthophos-phoric acid (H3PO4) with a specific gravity of 1.14, and a current density of about 1 to 2 amp per sq cm. A 3-min polishing was needed to eliminate the disturbed surface causing Debye-Scherrer rings and a 45-min polish produced a surface which yielded sharp rounded Laue spots. It was estimated that about 1/16 in. of metal was removed from the original cut surface. The final orientation of this specimen before rolling was about 2" from the (110) plane in the rolling plane with a [112] direction aligned in the rolling direction. It is possible that a small amount of strain was still present in the cube despite the fact that the Laue spots seemed very sharp. It is doubtful, however, that this would be an important factor after a subsequent rolling reduction of 99.5 pct. This copper specimen was rolled on a laboratory rolling mill with two highly polished rolls 37/8 in. in diam in the following manner: 0.010 in. per pass to 50 pct reduction, 0.005 in. to 70 pct, 0.002 in. to 85 pct and, finally, 0.001 in. per pass to a 99.5 pct reduction. Specimens, about 1 in. sq with the rolling edges intact, were cut from the rolled strip by the electrolytic method previously described, after the strip

Jan 1, 1954

By Gerald G. Griswold, James O. Greenslade, Cherie Tilley, Richard Reseigh

INTRODUCTION The Harrison Western Corporation, a leading Denver based mine contracting and engineering concern, is presently engaged in sinking two 1,006 m (3,300 ft) shafts for the Phillips Uranium Corporation at their Nose Rock Project, approximately 13 miles northeast of the small community of Crownpoint in McKinley County, New Mexico. The Nose Rock Project is the first attempt by the Phillips Uranium Corporation to tap the deep uranium reserves in what has become known as the Grants Mineral Belt. (See Figure 1) Project Description Phillips Uranium Corporation's plan for the large 2700 metric ton per day (2950 tons/day) mining facility calls for a series of deep access and ventilation shafts ranging from 4.27 m (14 ft) to 5.49 m (18 ft) in diameter to approximate depths of 1,006 m (3,300 ft). The initial pair of shafts consists of one production shaft and one ventilation shaft separated by a distance of 91 m (300 ft). The interbedded layers of sedimentary sandstones and shales to be penetrated by the shafts contain several major water producing aquifers, the deepest being the mineralized zone called the Westwater Canyon Member of the Morrison Formation. A series of temporary and permanent water pumping stations is planned. Generally, the temporary stations are located above major aquifers to facilitate water removal while sinking through the aquifer and the permanent stations constitute what, in the final mode, will be the mine dewatering system. In addition, Phillips Uranium Corporation has In- stalled and is maintaining a system of depressurization wells that temporarily pump the major aquifers and considerably reduce the water inflows during shaft construction. The major aquifers are also chemically grouted prior to sinking. Site work for the project was initiated in the fall of 1976. Full scale shaft sinking commenced in November of 1977 on the 4.88 m (16 ft) diameter ventilation shaft and on the 5.49 m (18 ft) production shaft by another contractor. Harrison Western Corporation began work on the project on November 4, 1979 wlth the production shaft at a depth of 633 m (2,076 ft) and the ventilation shaft at a depth of 474 m (1,554 ft). This paper will address only the portion of shaft sinking completed by Harrison Western. Geology and Hydrology The Nose Rock Project is located on the Chaco Slope in the southern extreme of the San Juan Basin in northwest New Mexico. The southern San Juan Basin is generally bound by the Defiance Uplift to the west, the Zuni Uplift to the south and the Nacimiento Uplift to the east. The Grants Mineral Belt occupies most of the southern portion of the San Juan Basin and this project is located on the northern extreme of the Grants Mineral Belt. The San Juan Basin is comprised of sedimentary rock of continental, marginal-marine and marine origin, that dip northward from the Zuni Uplift and Chaco Slope into the interior of the San Juan Basin. (See Figure 2) Major Formations The major geologic formations to be penetrated range from mudstone and shales to siltstones and sandstones. The sandstones are highly productive aquifers which, under static conditions, would flow artesian. Water temperatures in the aquifers are high and therefore are a force to be dealt with. Temperatures range from 18ºC (65OF) in the upper aquifers to 48ºC (118º'F) in the lower. The mudstones are generally bentonitlc. (See Figure 2) GALLUP SANDSTONE: The Gallup Sandstone is the first major regressive wedge in the San Juan Basin of the Cretaceous era and at this project is about 35 m (115 ft) thick. It is medium grained and prior to depressurization carried a hydrostatic water pressure of over 72.5 kg per cm2 (1,031 psi) which 1s artesian. Compressive strength ranges from 334.7 kg per cm2 (4,760 psi) to 421.8 kg per cm2 (6,000 psi). Water temperature is approximately 30°C (86°F).

Jan 1, 1982

By Jamie Deuel

The a ad on Connection" For the purpose of this paper, we will concentrate on the ubquitous radon gas as the principle, low-level radiation effect from uranium tailings piles. Standards are also proposed for gamma radiations but, by most accounts, this is much less of a low level problem than is radon. I am also aware of some just completed research at Oak Ridge National Laboratories that suggest polonium may be a major concern in tailings, but those data are preliminary at this time. What is radon gas? In the first place it is not a gas in the accepted sense in that it has no driving pressure head. It might prove a more convenient description to call it radon vapor. Radon vapor, then, is 7-1/2 times heavier than air. Radiologically, it is an alpha emitter which means it spontaneously gives off high ionizing potential but low penetrating power particles. In fact, the alpha particle has such low penetrating power that this sheet of paper will completely shield a person. The problem, though, is breathing the radon decay products, called radon daughters. If radon daughter products are ingested into the lungs, their alpha emissions may cause cancer. The principle carcinoma associated with breathing radon, or more basically, associated with radiological effects is oat cell car- cinoma of the undifferentiated mall cell type. Radon has a 3.8 day half life which means in less than four days half of its initial radioactivity has decayed away. In less than a month it essentially becomes inert or non-radioactive. The Tailings Situation The NRC, in its April 1979 Generic Environmental Impact Statement

Jan 1, 1983

By Earl Ingerson

BORE surfaces of used guns commonly show a pattern of cracks in various degrees of development. It has been suggested that these cracks may aid erosion by providing channelways for the gases, eventually leading to the tearing out of blocks of metal. Under the general studies of gun erosion conducted at the Geophysical Laboratory it appeared desirable to consider this factor, and to determine the resistance to surface cracking offered by gun steel and by various other materials that might be used in the bores of guns. METHOD AND APPARATUS In order to make such a determination it is necessary to have (I) an arrangement in which the surface to be studied can be subjected to conditions similar to those in a gun with respect to temperature, pressure (developed by explosion gases), composition of the gases and length of time the surface is exposed to the gases; and (2) a specimen that can be examined readily after any number of shots, and then fired again, if necessary. The first of these conditions can be met by using an explosion vessel designed by H. S. Roberts of the Geophysical Laboratory. Fig I shows a cross section of the apparatus. The "gun" G from which the charge is fired is made from the receiver of a caliber 0.30 army rifle, M1903, and the charges are prepared in caliber 0.30 cartridge cases. The test specimen S is held in place by a cone-shaped plug P and by a steel ,bridge B which is bolted to the outside of the explosion vessel on either side of the section shown. The plug, in turn, is held in place by a screw collar C. Maximum pressure is controlled by a brass rupture disk R. Part of the explosion gases flow past the two flat areas on S. st the two flat areas on S. Temperature and composition of gases, and the time before the rupture disk breaks, can be controlled by amount and kind of powder used, and pressure can be controlled by using rupture disks of different thickness. While the explosion vessel used was not designed so that temperature and pressure could be measured, in other vessels of closely similar size and shape containing proportionate charges of the same kind of powder as that used for standard testing procedure, values of 2700°K and 5000 psi were obtained. Since the orifices past the flat areas on the plug are small compared to the rupture disk hole (1:16), most of the gas goes out through the rupture disk when it breaks. The amount that goes by the plug depends on (I) the pressure attained before the rupture disk breaks and (2) the time it takes for this pressure to be built UP. The second condition (examination at will after any firing) is met by using for specimens short rods that have flat areas ground on opposite sides. These flat

Jan 1, 1947

By A. Eilers

THE telluride of gold and silver, the " Tellurgold-silver" of Hausmann, and " Petzite" of other mineralogists, has been found in so few localities, that a late discovery of the mineral in a new locality may not be uninteresbing. So far this mineral has been found in Europe only in a few mines in Transylvania, and in Hungary; and in the United States in the Stanislaus Mine, in Calaveras County, California, in the Golden Rule Mine, Tuolumne County, California, and in a mine in Montana, the precise locality of which I have forgot, ten. The new locality referred to is at the Red Cloud Mine, Gold Hill District, Boulder County, Colorado.

By R. B. Gilmore

It has been the custom of the Railroad Commission of Texas to hold hearings each month with respect to existence and imminence of waste of oil and gas in Texas and its prevention, and to issue orders restricting the production of oil to the reasonable market demands and allocating production to the various fields in Texas. The practice of designating the actual days during the month on which wells are to be shut down was discontinued in the order for November 1942, and orders issued thereafter contain only the number of shut-in and producing days for the month. Orders issued by the Railroad Commission are divided into two main subdivisions, the first a general shutdown order of all oil wells in the various fields in Texas, and second, the exception of certain fields to this general order. Table I shows the producing days for all of the fields in Texas for 1944 under the first of these classifications : The fields that have producing schedules varying from the general order may be divided roughly into three subdivisions, as follows: Table 2 shows the producing days for certain fields that were prorated as a group throughout 1944. Other fields which were occasionally included with this group were also prorated under the general order and by special orders. The producing days for these irregular fields are shown in Table 4. In Table 3 are listed fields that were exempted from any shutdown days during December 1944, the majority retaining this exception throughout 1944. Certain fields included in the general order were added to this group on the first day of the month shown.

Jan 1, 1945

R. V. Norris, Wilkes-Barre, Pa. (communication to the Secretary*):—Mr. Stow's paper presents a series of arguments, numbered from 1 to 18, concerning the relative merits of four systems of colliery-ventilation, designated by the author as " plain pressure-ventilation," " plain exhaust-ventilation," " obstructed pressure-ventilation," and " obstructed exhaust-ventilation." These arguments are subsequently compared by means of tables, in which an arbitrary numerical value is assigned to each, and which consequently serve no other purpose than that of showing his opinions and predilections, as indicated by his assignment of the said numerical values. In addition to this general summary, Mr. Stow intimates his preference for a fifth method of colliery-ventilation—namely, what he calls " alternating pressure-ventilation," which consists in the running of the fan at "pressure " during working-hours, and as an " exhaust" between shifts—a system which he proposes as, perhaps, new, yet which he thinks deserves recognition " as a standard form." This proposed " standard form " is not to be found in practice ; and I think it would be impracticable in gaseous mines of large extent, for the following reasons: 1. It takes considerable time to reverse the air-current in a large mine; and the reversal would involve a period of complete stoppage of ventilation, long enough to permit serious accumulations of gas. 2. In shaft- and slope-mines, at least, it is hardly practicable to have " every man out of the mine" during the night, and certainly impracticable to avoid keeping mules and horses inside. 3. The doors necessary to divide and direct the air-current are properly hung to open against the air-pressure; and, unless

Jan 1, 1910

By Donald C. Myntti

INTRODUCTION A major segment in a successful heavy equipment maintenance and repair program is the provision of well-laid out and well-equipped shop and service facilities The facilities described here will be those required for a large, high tonnage hard rock open pit mine utilizing rotary drills, shovels, haulage trucks, support equipment, and service trucks. The term support equipment covers the equipment required to support the drill, shovel, and truck operations, these are crawler tractors, road graders, front-end loaders, water trucks, rollers, rubber-tired tractors, etc. Service trucks are the automotive type consisting of rubber-tired over-the- road equipment. The primary structures generally involved in the total maintenance effort are as follows. (1) the main shop with an attached warehouse (the structure could also house the tire and lube shops plus the equipment cleaning stalls), (2) a service station with bulk petroleum product storage tanks, (3) a heating plant, (4) a security station (lf this is a corporate requirement), (5) operating department and employee assembly buildings, and (6) an electrical substation. Under certain conditions, many of these facilities with the exception of the substation could be combined In one or several structures. This arrangement could have a great advantage especially in areas where the heating of the structures is extremely critical.

Jan 1, 1979

By D. W. Fuerstenau, L. M. Berlioz

In 1957, Charles1 first presented an analysis of a relationship between the energy expended in comminution and the extent of size reduction achieved. Subsequently, Schuhmann extended and interpreted Charles' approach to comminution. According to their analysis, the energy, E, expended in comminuting unit mass of fairly uniformly-sized material is related to the size modulus of the product, k, by where a is the distribution modulus (slope of the log-log cumulative size distribution plot) and C is a constant, which is primarily determined by properties of the solid. If there is any fundamental basis for the E vs k relationship, E must necessarily be concerned with the useful work for the size reduction process and not necessarily the work input, as discussed in detail by Harris.3 Charles and numerous other investigators tested this equation only by relating k to the grinding time, assuming expended energy to be directly proportional to time, but never directly measuring power. In our laboratories, we recently constructed a special batch ball mill with which the power could be accurately determined with torque measuring apparatus.4 With this device, a direct test of the Charles relationship could then be made for ball milling. 5 EXPERIMENTAL A stainless steel mill, 11.5 in. long and 10 in. in inside diam, lined with eight low-silhouette lifter bars, was used for these experiments. The grinding media consisted of 30 kg of single sized, 1-in. diam, stainless steel balls, which occupied about 50% of the total mill volume under static conditions. The void fraction of the static ball load was approximately 0.4, and for the dry grinding conditions used, the corresponding interstitial volume was filled when about 3300 g of the dolomite feed material was present. The 7x9 mesh dolomite used as feed was obtained as a natural, uncrushed product thus as- suring a random distribution of feed particle shapes. Charge weights of 660, 1320, 1980, 2480, 3300, 3960 and 5280 g, which correspond to 20%, 40%, 60%, 80%, l00%, 120%, and 160% of the interstitial load, respectively, were used. Grinding times of 20, 40, 60, 80, 100, 150, 200 and 300 revolutions were considered, with the mill operating at 54 rpm (approximately 60% of critical speed). The tests were made sequentially, in that the size distribution obtained after a certain grinding interval was utilized as the feed for the subsequent period of grinding. Agreement with control experiments where the mill ran continuously for the entire interval was excellent. Torque measurements were made utilizing a Baldwin-Lima-Hamilton SR-4 torque pickup in the manner that has been described previously.3 Standard wet (to obtain the -400 mesh material) and dry sieving procedures were followed using the Tyler full screen series. RESULTS The Gaudin-Schuhmann size distributions obtained in all of these experiments are characterized by distribution moduli (slopes), a, of about 0.66 and are representative of normal dry batch ball milling of a material like dolomite. As an illustration of typical

Jan 1, 1968

We would like to thank Mr. Mandolesi for his informative paper on rails from strand cast steel. The chemical and structural properties of the strand cast steel were of particular interest to us. We would like to supplement his excellent report with some of Inland's findings from our Caster with submerged nozzles and strands reduced in line from 7" x 7" to 5-5/8" square cross section. Inland has conducted extensive segregation studies on AISI 1049 steel - Fine Grain 0.50% carbon and 0.75% manganese. Based on approximately 80 heats, our normal segregation pattern results in analyses of .49% carbon in the center, and 0.50% carbon at the midway and edge position. The sulfur analysis averages .025% in the center, .027% midway, and .026% at the edge. Note the slight negative segregation between the center and midway position. This steel, being lower carbon and probably cast nearer the liquidus, resulted in less segregation than the 0.80% carbon rail steel.

Jan 1, 1972

By M. H. Mueller, P. A. Beck, W. P. Chernock

HARRIS introduced the term inverse pole figure for the diagrams previously used by Barrett' to represent the volume fraction p(a,ß) of material in various orientations with respect to the fiber axis in a specimen with fiber texture. The direction of the fiber axis with respect to the crystal lattice is specified by the two independent angle variables a and ß. In such a diagram p gives the fiber axis density distribution over the various crystallographic directions. The p(a,ß) may be given in a two-dimensional diagram by means of contour lines (p=con-stant) in a stereographic projection. The inverse pole figure incorporates in a single contour line diagram all the information given conventionally in pole charts for various (hkl) reflections and, therefore, it represents a considerable degree of condensation. Also, it gives this information directly in terms of the volume fraction of the specimen in various orientations, and it obviates the necessity of referring back and forth between the various pole charts in an attempt to interpret them in terms of orientations. Inverse pole figures undoubtedly represent the most adequate method for describing a texture in a quantitative manner and, at least in the case of fiber textures, this method is certainly a practicable one. Harris described1 a simple procedure for determining at least the rough outlines of a quantitative inverse pole figure. This method depends on the measurement of the intensity of X-ray reflections from various (hkl) planes lying parallel to the same specimen surface. In the case of a rod, reflections from a plane specimen surface perpendicular to the rod axis (fiber texture axis) are to be used. Harris has shown that the measured intensities I,,, reflected by crystal planes (hkl), aligned perpendicularly to the fiber axis of a specimen with unknown fiber texture, and the corresponding intensity Iu nkl from a random specimen are related to the p(a,ß) value for the unknown texture by the following equation IAkl/I°Aklw=c/c°.p(a, ß) [1] where C and C° re parameters depending on the crystal imperfections (extinction), surface preparation (e.g., thickness of oxide layer), the absorption coefficient in the specimen, effective line breadth, and instrumental factors. The values of the variables a and ß1 defining the crystal orientation, depend only on the indices hkl of the reflecting plane perpendicular to the fiber axis. Since p, as described by Harris1, is normalized in such a way that upon integration over the total orientation range its mean value is 1, the parameter C/C may be calculated approximately by the summation of Eq. l over all available X-ray reflections hkl, corresponding to a set of discrete orientations (rather than by integration over the complete range of orientations represented by the continuous variables a and ß). From the summation of Eq. 1 1/n SI AKL/I° Akl = C/C. SP(a,ß)/n is obtained where, as stated above 2p(a,ß) =1. n Therefore

Jan 1, 1959