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By J. A. Dos Santos

High angle conveyor (HA C) systems in open-¬pit mining offer many advantages over the traditional, truck only, haulage systems. These include superior energy efficiency, less dependency on petroleum products, less sensitivity to inflation, less excavation for the amount of ore recovered, and less ramp construction and maintenance costs. Various high angle conveying systems and the corresponding characteristics of the high angle conveyor are illustrated. Discussion includes the range of HAC systems from the low capacity (up to 1.8 kt/h or 2000 stph), low lift (10.7 to 36.6 m or 35 to 120 ft), continuously mobile to the moderate capacity (1.8 to 3.6 kt/h or 2000 to 4000 stph), moderate lift (36.6 to 76.2 m or 120 to 250 ft), intermittently mobile to the high capacity (greater than 3.6 kt/h or 4000 stph), high lift (greater than 76.2 m or 250 ft), semimobile. Combinations of the above as required for the various open-pit mining operations are also discussed.

Jan 1, 1985

By Will Coghill

FLOTATION has been so closely allied with the sulfide minerals and their early and associated oily reagents that the term "oil flotation" has erroneously been applied to the entire flotation process. Today, the term "chemical flotation" might be used to advantage. Flotation literature has dealt primarily with the removal of sulfides from non-sulfide gangues, and the separation of one sulfide from another. Now, the application of the process to the separation of nonsulfide minerals is coming to the fore; and from the standpoint of the number of commercial minerals involved, the flotation of nonsulfides offers the larger field. Here, soap or soap-forming substances, such as the fatty acids and their derivatives, are used; hence there may well be a subdivision of the chemical flotation process called "soap flotation." Early experimenters learned that it was easy to form a froth or foam that would carry a part or all of the ore charge over the lip of the flotation machine; but this could not be regarded as flotation because of the lack of selectivity. Doubtless soap was one of the first reagents tried, and doubtless it was rejected on account of its gangue-carrying properties. Now this same gangue-carrying ability makes soap an acceptable reagent, for we are dealing with that, which among sulfides, is considered "gan-gue." As in the flotation of sulfides, so in the flotation of nonsulfides, the selective flocculation of the mineral and the dispersion of the gangue are the first objectives. In fact, these two phenomena epitomize flotation. They depend upon the unlike surface properties of the respective miner-als; and as long as the components of an ore have unlike surface proper-ties, a separation is possible, at least in theory. Often in nonsulfide flotation it makes little difference which mineral floats and which is depressed; generally only a separation is sought.

Jan 1, 1932

By H. S. Rankin, F. A. W. Davis, R. A. Laurence, L. L. McMurray, E. C. Houston

This paper is coodensed from several reports by members of the staff of the Minerals Testing Laboratory of the Tennessee Valley Authority, on a series of experimental tests in the beneficiation of barite of the Valley area. These experiments were conducted upon a large number of samples taken from several mines in three different districts. The area contains numerous producing deposits, nearly all of which are hampered by the high iron and silica content of the ores. Because of the small difference in specific gravity between the iron oxide and the barite, a gravity separation is generally poor. The removal of the iron thus offers a special problem. Some of the operators have turned to magnetic separation to meet the shipping requirements for less than one per cent iron. The present experiments were conducted to determine the application of decrepitation or flotation in simplifying the concentration of the barite by removing the iron oxide and silica in one operation. Practically all the barite marketed in the area has been as "off-color" crude. The bleaching studies were made to determine the bleach-ability of the ores to alleviate this inferior grading, placing them on the market as bleached barite. Geology Barite has been produced at many places in the Tennessee Valley area, and prospects and minor deposits are known at many other places, but practically all the production of barite in the Valley has been from the Sweetwater district of East Tennessee. Other leading areas of former production are the Tazewell-Russell counties areas of southwest Virginia, the Del Rio-Stackhouse district of East Tennessee and western North Carolina, and the Fall Branch district of upper East Tennessee. The areas described in this paper are those from which samples used in the concentration tests were obtained.

Jan 1, 1942

By Robert Sisselman

If we are lucky," says Hollis M. Dole, Assistant Secretary of the Interior, "coal, uranium and hydropower will provide us with maybe a third of the energy we require in 1985. The other two- thirds will have to be made available in liquid and gaseous form." Luck, however, may have run out, for if the facts and figures relating to supply and demand of natural gas over the next 20 years prove accurate, the United States may fall short in its attempts to bring the energy crisis under control. By the year 1990 the world will need to consume a minimum 150 quadrillion Btu of energy with gas requirements running as high as 42-43 trillion cu ft. By 1990, the U.S. alone will require 45-46 trillion cu ft. To meet anticipated demand, this country will have to overcome a deficiency of about 20 trillion cu ft since, by all pragmatic estimates, it will produce only 15-20 trillion cu ft of gas. The importation of natural gas into the U.S. will help but will not solve the problem. Adequate gas supplies will have to be supplied domestically. The Arctic, with its predicted huge reserves of gas, combined with imports of liquid natural gas (LNG) may provide as much as 15% of the 45-46 trillion figure, however, such reserves will not come into play as quickly as originally thought. The Alaskan gas fields, for instance, will provide a substantial supplement to domestic gas needs, but only after 1976.

Jan 10, 1972

By J. Price Wetherill

The coal-seams that are worked vary from 3 1/2 to 100 feet in thickness, and occur at all angles of inclination, but are never flat for any great extent. They contain coal, slate, and an unsolidified coal, called dirt by the miners, in various proportions, a uniform seam of coal alone being rare. The upper walls are composed of conglomerate, sandstone, or slate; the first two hard and solid in texture, and withstanding the action of the atmosphere and moisture sufficiently well to offer but little trouble to the mining operations; while the latter crumbles rapidly, owing, in part, to the decomposition of iron pyrites which it contains in large quantities, and in part to its own friable character, and requires constant care to avoid accidents to the men working below it, and to prevent its mixing with the coal mined. The floors are composed of slate. As in all mining operations, the general system pursued is to reach with a permanent outlet such a point in the seam as will

By W. S. Morris, R. R. Bradenthaler, G. Wade

Petroleum engineers generally are of the opinion that the flow conditions and, therefore, the formulas that apply to the flow of oil and gas in long pipe lines differ in many ways from flow conditions in oil wells. One of the reasons why the formulas in common use for pipe-line flow do not correctly apply to oil wells is that the flow lines are vertical and not horizontal. Another factor to be considered is that the fluid is a mixture of oil and gas and that the physical characteristics of these two components are affected differently by changing conditions of pressure and temperature during upward flour. Realizing the need for accurate data on flow in vertical pipes under conditions caused both by natural flow and the gas-lift, the U. S: Bureau of Mines has installed equipment at the Petroleum Experiment Station, Bartlesville, Okla., for the purpose of studying this problem. In additon a study will be made of the comparative effects of different natural-flow and gas-lift methods of producing oil on ultimate production from reservoir sands. Experimental Equipment The experimental equipment consists of a regular oil-field steel derrick, a large pressure tank installed in a concrete pit beneath the derrick floor, compressors and pumps, gas separators and absorbers, metering and control devices, and the necessary pipe connections. The crown-block level represents the derrick floor at an oil well, and the "producing sand" is the pressure tank below the derrick floor. The difference in elevation between the crown-block level and the tank is 90 ft. Figs. 1, 2 and 3 show the construction and exterior arrangement of the equipment. The success of the experiment will of course depend largely upon the accuracy of the oil and gas measurements and the temperature and pressure determinations. Because extreme accuracy is necessary, all oil and gas measurements will be checked at least twice, and in some

Jan 1, 1929

By L. S. Castleman, L. L. Seigle

THE formation and growth of intermetallic phase layers is of considerable practical importance to metallurgists interested in diffusion bonding and cementation processes and has been the subject of extensive qualitative investigation. In contrast, it is somewhat surprising that so little quantitative data have been amassed. The need for additional fundamental work was pointed out by Mehl in 1936,' and persists to a large extent to the present day. The early studies have been reviewed by Rhines,2 and his conclusions have been summarized by Lustman and Mehl3 substantially as follows: 1) All phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two metals; however, in some cases, certain of the phases may be too thin to be observed and identified easily. 2) The isothermal growth of intermetallic phases generally obeys a simple parabolic equation of the form X2 = Kt, where x is the thickness of the alloy layer, K the temperature dependent reaction rate constant, and t the time. 3) The rate of thickening varies with temperature according to the Arrhenius equation k = Ae -Q/RT , where k is the parabolic rate constant, A, a temperature independent constant, Q the heat of activation for the process, R the gas constant, and T the absolute temperature. Subsequently, Lustman and Mehl made a quantitative study of the laws of growth in intermediate layers in a number of binary systems, in which one of the components was either zinc or cadmium, and the other component was one of the following: nickel, copper, silver, cobalt, gold, iron, or Monel metal; the interdiffusion times used were for the most part less than 24 hr. It was found that the simple parabolic law was not obeyed in general, but that a generalized parabolic law of the form xn = kt was valid, where n was a temperature dependent constant; also,

Jan 1, 1959

By C. C. Singleterry, D. L. Katz

The critical phenomena have been studied during the past century but our knowledge of the critical temperatures and pressures of complex hydrocarbon mixtures still is very limited. The critical temperatures and pressures of pure substances have been examined in large numbers120 and in great detail.11.17 No experimental determinations of the critical phenomena have been reported on such complex hydrocarbon systems as a reservoir fluid. The critical temperature is defined by Taylor18 as follows: "there is some temperature for each gas above which the gas cannot be liquefied. This temperature is called the critical temperature." The critical pressure of a pure substance is the vapor pressure at the critical temperature. It should be noted that these definitions refer to a given substance in the pure state and do not mean that the pure substance cannot be liquefied in the presence of a second constituent. The normal procedure for obtaining the critical temperature of a substance is to heat it in a glass tube 1,20 under pressure until the meniscus between the liquid and vapor phase disappears, although other methods, especially for mixtures, have been used.13,14 However, when considering oil and gas reservoirs, it is more enlightening to consider a critical phenomenon that occurs when a mixture of oil and gas are compressed at a reservoir temperature until the meniscus disappears because the two phases become equal in composition. This conception, along with erroneous applications of the definition of the critical phenomena of a pure substance to that pure substance when it is part of a complex mixture, has caused confusion even among persons familiar with the classical theories. The purpose of this paper is to discuss the critical phenomena of pure substances and mixtures and to report experimental data on a mixture of

Jan 1, 1939

The classification here used is one of convenience only; it is not intended to include all known types of ore deposits. The characteristic features of the several well-marked types of primary mineralizations are described without reference to the ultimate source of their metals. The minerals of many deposits of obscure origin were probably introduced through fissures that are now healed, or are due to the migration of metals from such deposits. [ ] It is not within the scope of this book to enter into a general discussion of the genesis of ore deposits but, in view of the progress being made in our comprehension of the conditions under which ore deposits were formed, mention should be made of recent work. J. E. Spurr's two volumes, "The Ore Magmas," are recommended as crystallizing the views of those who are inclined to ascribe the origin of most ore deposits to a differential precipitation from magmatic rock masses and to the migration and precipitation of the viscous, liquid or gaseous exhalations from those masses. He has especially emphasized the role

Jan 1, 1932

Jan 1, 1885

By Marshall D. Himes

The Pima mine, Pima County, Ariz., a 53,500-tpd copper mine, is located 17 miles south of Tucson, Ariz. The mine is in a sequence of Paleozoic and Mesozoic sediments striking east-north-east and dipping southeasterly. These sediments are intruded by a Tertiary quartz monzonite porphyry. The Paleozoic Permian (?) dolomites, limestones, and sandstones have been altered to calc-silicate skarn, marble, and quartzite. The overlying Mesozoic Triassic (?) clastic sediments have undergone some recrystallization and hydrothermal alteration. The clastic metasediments are divided into three distinct lithologic units: lithic arenite, arkose, and interbedded and overlying black argillite. Three types of hydrothermal alteration in the clastic rocks are propylitic alteration (epidote, chlorite, and quartz, with or without sericite), quartz-sericite alteration, and potassic alteration (K-feldspar, quartz, and sericite, with or without chlorite and calcite). The porphyry has undergone potassic alteration. Dominant structures are an east-west postmineral fault in the western part of the pit, and strong low angle faulting and shearing which truncates the ore body at depth. The two joint sets, one parallel to bedding and the other at right angles to bedding are prominent in the mine. Faulting is in two dominant directions, one striking northwest, dipping northeast, and the other striking northeast, dipping northwest. Economic mineralization is prediminantly disseminated pyrite and chalcopyrite, and molybdenite-quartz veinlets. There are less important amounts of magnetite, hematite, sphalerite, galena, tennantite, and bornite. Mineralization is believed to be both structurally and chemically controlled.

Jan 1, 1974

By C. C. Singleterry, D. L. Katz

The critical phenomena have been studied during the past century but our knowledge of the critical temperatures and pressures of complex hydrocarbon mixtures still is very limited. The critical temperatures and pressures of pure substances have been examined in large numbers120 and in great detail.11.17 No experimental determinations of the critical phenomena have been reported on such complex hydrocarbon systems as a reservoir fluid. The critical temperature is defined by Taylor18 as follows: "there is some temperature for each gas above which the gas cannot be liquefied. This temperature is called the critical temperature." The critical pressure of a pure substance is the vapor pressure at the critical temperature. It should be noted that these definitions refer to a given substance in the pure state and do not mean that the pure substance cannot be liquefied in the presence of a second constituent. The normal procedure for obtaining the critical temperature of a substance is to heat it in a glass tube 1,20 under pressure until the meniscus between the liquid and vapor phase disappears, although other methods, especially for mixtures, have been used.13,14 However, when considering oil and gas reservoirs, it is more enlightening to consider a critical phenomenon that occurs when a mixture of oil and gas are compressed at a reservoir temperature until the meniscus disappears because the two phases become equal in composition. This conception, along with erroneous applications of the definition of the critical phenomena of a pure substance to that pure substance when it is part of a complex mixture, has caused confusion even among persons familiar with the classical theories. The purpose of this paper is to discuss the critical phenomena of pure substances and mixtures and to report experimental data on a mixture of

Jan 1, 1939

By Elmer R. Kaiser

COMBUSTION of coal and transfer of heat from flames and gases to boiler surfaces continue to be of great interest to engineers here and abroad. Numerous investigations have been in progress to improve furnace and boiler performance and economy. The importance of better understanding of the processes and opportunities for improvement is apparent when it is remembered that heat from at least 500 million tons of coal a year the world over is being transferred to boiler water at efficiencies ranging mostly between 50 and 90 pct. Even slight gains in efficiency, economy, and labor saving become very significant when multiplied by the enormous quantity of fuel consumed. Also the competitive position of the large coal, oil, and gas industries in satisfying the fuel consumers is greatly affected by the achievements made through technical progress with each fuel. This paper is part of a continuing activity of Bituminous Coal Research, Inc., to extend the knowledge of coal utilization for steam generation and to seek promising directions for future research and development in cooperation with others. Particularly in the latter regard, numerous interviews were held during the last three years to seek the experience and advice of boiler and combustion- equipment manufacturers, electric-utility executives, and fuel engineers. A wealth of published information was also reviewed, which together with the interviews pointed to the advisability of further work on ash and sulphur control.

Jan 3, 1954

By W.C Ellis, Earle E. Schumacher

Nonferrous alloys upon which desirable properties can be conferred by heat treatment are becoming of increasing industrial importance. The alloys of copper with a constituent which has a solubility varying with temperature are materials of this character. Some of the constituents which are effective in producing a change in the mechanical properties of these alloys upon heat treatment are, according to Corson,' nickel and silicon, iron and silicon, cobalt and silicon, and chromium and silicon. In addition to these elements, Gregg2 states that the combination of beryllium and silicon is effective in producing age-hardening characteristics in copper. The effect of these elements, however, as dispersion-hardening constituents in the copper alpha solid solutions does not seem to have been studied in any considerable detail. This paper deals with the heat treatment and properties of three alpha brasses containing 3 per cent. of nickel plus silicon in the proportion necessary to form the compound nickel silicide, Ni2Si. Some information of a preliminary nature in regard to the hardening by heat treatment of phosphor bronze containing the same percentages of nickel and silicon is included. The method of hardening the alloys, which is effective in increasing the tensile strength and proportional limit, is similar to that used in the case of duralumin type aluminum alloys. It consists of a quench from a temperature at which the hardening constituent is in solid solution, followed by an aging at a lower temperature to precipitate the dissolved constituent in a dispersed condition. This results in an increased resistance of the alloy to deformation with an attendant improvement in the tensile properties.

Jan 1, 1929

By Albert E. Wood, Edgar R Shepard

The interest of the Federal Government in improvement of waterways dates from 1820, when Congress appropriated $5000 for making a survey of the Mississippi and Ohio Rivers and assigned this work to the Corps of Engineers of the Army. Since that time the Government has gradually assumed increasing jurisdiction in the matter of improvement and control of inland waterways until, by the River and Harbor Act of Jan. 21, 1927, Congress assigned to the Secretary of War and to the Chief of Engineers the duly of making surveys, in accordance with House Document No. 308, 69th Congress, to formulate plans for the most effective improvement of the navigable streams of the United States and their tributaries, for navigation, development of water power, control of floods, and the needs of irrigation. Virtually all the preliminary investigations and surveys required by this act have been completed. The reports made to Congress have been published and often are referred to as ''308 Reports." The map shown in Fig. 1 is merely a skeleton distribution of the projects covered by these reports, but it serves to indicate the magnitude of the proposed undertaking. In many instances, a single character on the map stands for a major development involving several dams and reservoirs or many miles of canals or levees. The devastating floods of 1936, and the need for worthy public works to take up the slack in employment, gave further impetus to this program and in 1936 led to the enactment of a bill authorizing a large number of these projects. The National Flood Control Act of 1936 specifically authorizes some 270 flood-control projects in 31 states, and affecting nearly every state in the Union, with an estimated construction cost of about $300,000,000. In addition, the 1936 Act directs the Secretary of War to make preliminary examinations and surveys for flood control in some 230 additional localities, and to continue surveys and studies of 18 reservoir sites. The Corps of Engineers is proceeding rapidly with foundation investiga-

Jan 1, 1940

By Horace V. Winchell

The laws here referred to are those which define the status of the prospector for mineral deposits in the soil or beneath it, establish his methods of procedure, protect him in his possession while searching for the subterranean treasures, and give him assurance of title when all required conditions have been fulfilled and valuable minerals discovered. Regulations for the operation of mines and the safety and health of mine employees are likewise subjects of Federal and State legislation, but are not within the scope of the present program. Various features of our present laws will be discussed in detail by able students of the subject, and specific remedies will be proposed for the most glaring defects. It is my purpose to present in this paper a summary review of the reasons why revision is needed and demanded by the great majority of those in daily contact with the industry. Reason Number One The first objection to the continuance of the present law is that it was not planned by its framers and the Congress which passed it to apply to many of the kinds of mineral deposits, nor to the mining conditions, which are controlled by it to-day. In 1866, under the title, "An Act granting the right of way to ditch and canal owners over the public lands, and for other purposes," was surreptitiously smuggled into existence our first mining law (14 Stats. at Large, Chap. 262, p. 251). This law provided that "whenever any person or association of persons claim a vein or lode of quartz or other rock in place, bearing gold, silver, cinnabar or copper, having previously occupied and improved the same according to the local customs or rules of miners in the district where the same is situated," etc., a patent might be granted an certain conditions. This was evidently an Act intended to validate claims already initiated, and to accord Federal recognition to mining locations made in

Jan 1, 1915

By Charles O. Burgess

The improvement in the quality of cast iron by means of alloy additions has been a metallurgical accomplishment of recent years. Work in this field has shown that chromium is one of the most effective of such additions but, in general, the influence of chromium has been studied only in connection with other alloying additions, with irons other than foundry irons, or with relatively high percentages of chromium. The present study was initiated for the purpose of determining the influence of small additions of chromium (0.25 to 1.00 per cent) on the quality and resultant properties of cast irons of various foundry grades. The effect of small chromium additions on cast iron was investigated with particular reference to casting characteristics, hardness vs. section, strength, machinability, heat resistance and structure. Material Tested Three separate types of cast iron were investigated as to the effect of small chromium additions. The first series of these irons was prepared from remelted foundry cast iron at the Union Carbide and Carbon Research Laboratories, and the other two series consisted of cupola melts made under usual operating conditions. The first series was made by melting 30-lb. charges of foundry scrap iron containing 2.86 per cent carbon, 2.72 silicon, 0.50 manganese, 0.062 sulfur and 0.794 phosphorus in a carbon resistance furnace. The chromium was added as high-carbon ferrochrome just before pouring. The irons were cast at approximately 1250" C. (2282" F.). The analysis and physical properties of these irons are given in Table 1, test 1. The second set of cast irons was made in a cupola in accordance with normal practice, the charge containing approximately 42 per cent steel scrap and the chromium additions being made to the ladle. Analysis and tests of these heats are shown in Table 1, test 2. A small amount of copper was present in heat C of this series. Further data on the effect of chromium on strength were obtained from a third series of 13 cupola heats containing from 0.06 to 0.50 per cent chromium and made without steel additions. The heats were all

Jan 1, 1933

By Albert E. Wood, Edgar R. Shepard

The interest of the Federal Government in improvement of waterways dates from 1820, when Congress appropriated $5000 for making a survey of the Mississippi and Ohio Rivers and assigned this work to the Corps of Engineers of the Army. Since that time the Government has gradually assumed increasing jurisdiction in the matter of improvement and control of inland waterways until, by the River and Harbor Act of Jan. 21, 1927, Congress assigned to the Secretary of War and to the Chief of Engineers the duly of making surveys, in accordance with House Document No. 308, 69th Congress, to formulate plans for the most effective improvement of the navigable streams of the United States and their tributaries, for navigation, development of water power, control of floods, and the needs of irrigation. Virtually all the preliminary investigations and surveys required by this act have been completed. The reports made to Congress have been published and often are referred to as ''308 Reports." The map shown in Fig. 1 is merely a skeleton distribution of the projects covered by these reports, but it serves to indicate the magnitude of the proposed undertaking. In many instances, a single character on the map stands for a major development involving several dams and reservoirs or many miles of canals or levees. The devastating floods of 1936, and the need for worthy public works to take up the slack in employment, gave further impetus to this program and in 1936 led to the enactment of a bill authorizing a large number of these projects. The National Flood Control Act of 1936 specifically authorizes some 270 flood-control projects in 31 states, and affecting nearly every state in the Union, with an estimated construction cost of about $300,000,000. In addition, the 1936 Act directs the Secretary of War to make preliminary examinations and surveys for flood control in some 230 additional localities, and to continue surveys and studies of 18 reservoir sites. The Corps of Engineers is proceeding rapidly with foundation investiga-

Jan 1, 1940

By C. W. MacGregor

In the testing of materials there exist various methods of recording graphically the behavior of a material subjected to tensile stress. Probably the most common method is to plot the tensile stress So, obtained by dividing the load P by the original area of cross section A0 at the start of the test, as a function of the strain e0, which is obtained by dividing the ?Lo or the change in the gauge length by the original gauge length Lo. A list of the symbols used here is given in Table 1. This method, while it has proved useful in the routine testing and comparison of various materials, does not have a very sound physical basis, as was first pointed out by P. Ludwikl, and consequently does not afford a very deep insight into the true physical behavior of the material under stress. Among the objections to this method may be mentioned: (1) that by dividing the load P at any stage of the test by the original area A. a fictitious stress is obtained, which does not actually exist; (2) that the strain e0 = ?L0 is not an exact expression for the true strain for large values of ?LO in per cent of Lo; (3) that when necking starts the strain varies considerably along the gauge length and the above expression no longer gives the true strain existing at any point on the outside of the bar; and (4) that the axial strain varies over the cross section of the necked portion and e0 does not represent an average of these strains over the cross section. Stresses taken from such a diagram would be only approximate and, if used to compare results of a test on a given material under simple tension with results obtained under combined stresses, certain errors would be thus introduced. In order to overcome some of these objections, various methods have been suggested, both as to the quantities to be measured and as to their graphical representation. In some cases the so-called "true stress," obtained by dividing the load P by the actual area of cross section A existing when the load P was applied, is plotted as a function of the strain

Jan 1, 1937

By Robert M. Asimow, Bisuddhi Riddhagni

THE use of back-reflection Laue photographs for crystal orientation is standard in many research projects. The time required for the orientation of any given crystal depends largely on luck and the skill of the investigator. In any case, where large numbers of crystals are used, this time can be quite considerable when the standard methods involving a Greninger chart and Wulff net are employed. For this reason the technique described below was developed. This new procedure applicable for cubic crystals (without preparation of new charts) largely eliminates the skill and luck factors and makes possible the determination of orientation in minutes. The procedure works in the following way: the Laue photograph is examined and arbitrarily an important hyperbola is picked out. An important hyperbola is defined as one which contains some spots through which several hyperbolas pass. Such a hyperbola inevitably corresponds to a low-index zone axis. The angles between the reflection planes causing all the spots on this hyperbola can be read directly from a Greninger chart in the usual manner. If the hyperbola contains more than five spots, these interplanar angles will positively identify the zone axis and the indices of each of the reflecting planes. However, initially since neither the zone axis nor the Miller indices of a diffraction spot are known, there are a very large number of possibilities that must be considered. Using tables of interplanar angles to check out every possibility would be quite tedious, so that this approach is not generally used. Instead, various poles are plotted on a stereographic projection. In the cubic system, however, it is possible to plot out once and for all the angles between all planes of a particular zone axis up to some upper limit of Miller indices. This has been done for all low-index zone axes in Fig. 1. Given these charts, it is quite a simple matter to identify the spots of the unknown hyperbola. All that is necessary is to plot the angles read off the Greninger chart to the same scale as Fig. l(b) on a strip of paper. Then this strip can be slid along each zone axis of Fig. l(a) until a good fit is obtained. Once this is accomplished, the Miller indices of each spot are given and thus the orientation problem is solved. To check, it is possible to pick a second hyperbola and see whether a compatible solution is obtained. This is most conveniently done by picking for the second hyperbola one that contains a spot common with the first. If the specimen axis is chosen parallel to the incident X-ray beam, then usually the [ loo] hyperbola will appear on the film as one of the more important hyperbolas and consequently will be either chosen initially or as a check. Using the [100] hyperbola, after the (001) or (011) spots have been identified, the latitude and longitude of the specimen axis can be read directly from the Greninger chart so that it is unnecessary to use a Wulff net for the entire orientation procedure. This makes the operation not only quicker but more accurate. Of course, if neither the first nor second hyperbolas correspond to [loo] then a third hyperbola can be chosen.

Jan 1, 1967