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By W. O. Philbrook, R. S. Kaplan

Rates of oxidation were studied for levitation-melted samples of Fe-C, Fe-Si, Fe-C-Si, Fe-C-P, Fe-C-Mn, and Fe-C-S alloys oxidized by mixtures of either 5 or 10 pct O2, in helium at several temperatures in the range 1850o to 2050°C. The concentrations of the oxidized elements decreased linearly with time. Mass transport in the gas phase was found to be the rate-controlling step. Ilowever, a mulliple -film model was necessary to account for the flux of iron and manganese vapor counter to the oxygen flow. THE advent of the basic oxygen and spray-refining processes of steelmaking has generated considerable interest in the kinetics of reactions between oxygen-bearing gases and liquid iron alloys. The object of this research was the determination of the role of mass transport in the gas and metal phases and of surface chemical reactions in the overall oxidation process. Of the reactions for elimination of elements dissolved in liquid iron, the oxidation of carbon has been investigated most extensively. Studies by Fuji and Ura,1 Fuji,' and Gunji et a1.,3 done with pilot-scale basic oxygen furnaces, indicated that mass transport of gaseous oxygen was rate controlling when the metal carbon content was greater than 0.15 to 0.30 pct. When the carbon content was less than this critical amount, diffusion of carbon dissolved in the iron was thought to be rate limiting. L. A. Baker et a1.4,5 levitated samples of iron-carbon alloys and oxidized them in CO-CO2, CO-C02-He, and O2-He atmospheres at 1660°C. These investigators found that the metal carbon concentration decreased linearly with time and their samples exploded when the carbon content fell below about 0.8 pct. They concluded that the rate-limiting step was the transfer of oxidant to the gas-metal interface. A model based on this rate-limiting step predicted decarburization rates within a factor of two of those experimentally observed. The explosion of the samples was attributed to a shift in rate-controlling step from gas-phase mass transport to transport of carbon dissolved in the metal. L. A. Baker and R. G. ward6 and R. Baker7 used freely falling droplets to investigate oxidation kinetics. In both papers, the authors speculated that flame fronts may have been partially responsible for the lack of better agreement between experiment and theory. Swisher and Turkdogan8 oxidized liquid iron having an initial carbon content of 0.97 pct with CO-CO2 and CO-C02-Ar mixtures at 1580°C. They concluded that a surface reaction was the rate controlling step. Iron-silicon alloys have been oxidized by R. Baker7 and Filipov and Martynov.9 R. Baker 7 also studied iron-carbon-silicon alloys falling as liquid droplets through oxygen. He found that the rate of both carbon and silicon oxidation varied inversely with the drop radius. When the initial silicon concentration was greater than 6 pct, the samples cooled during their fall. Manganese oxidation has been studied by R. Baker,7 and by Filipov and Martynov.9 ward10 investigated the loss of manganese from liquid iron under vacuum. He found that mass transport of manganese vapor was rate limiting in argon atmospheres of 0.02 torr to 700 torr pressure. Iron-sulfur alloys were desulfurized with H2-He and H2-Ar mixtures by Peters et al.11 A model based on the transport of H2S from the gas-metal interface into the bulk gas gave fair agreement between the predictions of the model and the experimental results. EXPERIMENTAL TECHNIQUE Essentially, the technique consisted of using helium-oxygen gas mixtures to oxidize levitated samples of liquid binary and ternary iron-base alloys. The fused silica reaction tube is shown in Fig. 1. The coil design is similar to that of L. A. Baker et al.4'5 A Tef-lon-sheathed, ferritic stainless steel lifter (B) and an alumina pedestal (C) were used to support the sample in the coil prior to levitation and for the recovery of the sample. Samples were inserted into

Jan 1, 1970

By A. N. Crownover, H. T. Kennedy, E. P. Miesch, C. H. Bowman

The paper presents correlations of (l) molar volume of gaseous hydrocarbon mixtures with pressure, temperature, composition and properties of the C,-plus fraction; (2) shrinkage of oils during flash and differential liberation of gas, including the calculation of formation volume factor under various conditions; and (3) bubble-point pressure with temperature, composition and characteristics of C, plus. The data on which the correlations are based comprise 1,615 measurements on 900 hydrocarbon systems, including numerous systems containing nitrogen, hydrogen sul-fide and carbon dioxide. In each correlation, the number of data points covered and the accuracy is substantially greater than in previously available work. Thus, the equation yielding molar volumes of gases has an average deviation of 2.04 per cent, applied to mixtures having temperatures up to 313F and pressures up to 9,800 psis, compared to 2.37 per cent for the Benedict-Webb-Rubin equation applied to the same data, and 4.53 per cent for the method based on the law of corresponding states. he equations resented are all explicit in the dependent variable, and require no iteration on the digital cow puter. INTRODUCTION The ease and accuracy of determining the composition of hydrocarbon mixtures, compared to the difficulty of measuring their properties under reservoir conditions, makes it desirable to utilize composition as the key to physical behavior to the greatest possible extent. As a result, there are available correlations between composition, or easily measured characteristics dependent on composition, and practically every important engineering property of reservoir fluids. The task confronting us is one of finding more exact relationships between important variables rather than extending correlations to new properties. This paper describes new correlations of molar volumes of gases, formation volume factors, and bubble-point pressures with composition, temperature and where possible, pressure. Each correlation is obtained by employing a sufficiently large amount of data so the calculated properties are probably as least as accurate as the measurement on which they are based. MOLAR VOLUME OF GASES Although many equations of state have been proposed for pure gases, only a few methods are applicable to hydrocarbons at conditions comparable to those in petroleum reservoirs. Still fewer arc useful in describing the behavior of mixtures, with which the petroleum engineer is largely concerned. The correlation presented here involves procedures similar to those of Alani and Kennedy The van der Waals equation is modified to make a and b functions of temperature instead of being constants for each material.This is a cubic equation, which may have either one or three real roots. The lowest root corresponds to liquid volume, while the highest applies to gas. When the procedure was applied to 703 pressure-temperature points of 164 gases of known composition and volume, the average deviation was 12.08 per cent, and the standard deviation 8.15. The above calculations were made using the constants derived for liquids by Alani and Kennedy and the mixture equation developed by them. A closer approximation to measured molar volumes is obtained by employing different sets of constants for different areas on the pressure-temperature chart, and by changing the relationship between a,,, and b,,, for mixtures and the a, and b, for individual hydrocarbons. The various sets are shown in Table 1, and the areas for which they are recommended are plotted in Figs. 1 through 7. In these figures, the area designated by zero is in the critical region for pure materials, and the values obtained for them may be unreliable. For normal mixtures, however, the area may be added to any of the bounding areas without substantial error. The new relationships employed are

Jan 1, 1966

By W. C. Hagel, H. J. Beattle

DURING an earlier examination of high-temperature alloy, A-286, the presence of an unknown intermetallic compound was verified by X-ray diffraction. Owing to its prominent appearance at grain boundaries, the arbitrary name of G phase was assigned.' Low-silicon, vacuum-melted heats were found to contain no G phase, and this investigation was initiated to determine the influence of silicon on G-phase formation; additional work was undertaken to extend existing data on other intermetallic compounds and the aging reactions in this group of alloys. Taylor and Floyd2-4 observed that the Ni3Al phase (y') and the Ni8Ti phase (7)) are the only equilibrium intermetailic compounds in nickel ternary alloys containing up to 25 pct Cr and 10 pct Ti or Al. They found that y' can dissolve considerable nickel, chromium, and titanium, although the stoichio-metric composition of 7 remains fixed. Nordheim and Grant5 confirmed that age hardening of 80 pct Ni-20 pct Cr alloys of the Nimonic-80 type is due to precipitation of y', where aluminum is partially replaced by titanium. They suggest that optimum hardness and ductility result from increasing the titanium to aluminum ratio toward the end of the y' solubility range and from increasing total titanium and aluminum content to the maximum limit permitted by processing. Such information is necessary for those seeking to improve the service-temperature range and long-time structural stability of high-temperature components. Experimental Methods Compositions of materiais studied. are listed in Table I. Alloys D, E, and F possess representative A-286 analyses; silicon increases from less than 0.02 to 1.75 pct in alloys A to H; in alloys I to K, titanium decreases from 2.24 to 0.39 pct, and aluminum increases from 0.1 6 to 240 pct. Alloys A and D were solution heat treated for 4 hr at 1700°F, oil quenched and aged for 0.5, 2, 6, 12, 30, 70, 200, and 1000 hr at 1200°, 1300°, 1400°, and 1500°F. Therefore, a total of 33 specimens was required for each

Jan 1, 1958

By Enid C. Plante

To extend our knowledge of the flotation behavior of sulphide minerals, the response of the following minerals to ethyl xanthate as collector was studied by captive bubble and cylinder flotation tests: antimonite (Sb2S3), arsenopyrite (FeAsS), covellite (CuS), rnarcasite (FeS2), orpiment (As&.), pyrrhotite (FeS) and tetrahedrite (4CU2S, Sb2S3). Lollingite (FeAs2) was also exarnined to determine if its behavior could be correlated with that of pyrite or rnarcasite (FeS2. Experimental Method Mineral for Flolation and Contact Tests Mineral was prepared in the manner a1ready described1 and its behavior both freshly ground and "oxidized" was studied. Tests in which the mineral was allowed to oxidize for various periods showed that a uniform response to xanthate was reached in two days or less. Oxidation Products The soluble oxidation products from most of the above minerals were measured and their effect on the flotation of the mineral studied. The mineral samples were wet ground to minus-52 mesh and deslimed, and 20 g of this material placed in 200 ml of distilled water of a measured pH value, and CO2-free air bubbled through each suspension at a constant rate (about I bubble/sec) for 5 days. It has been shown1 that the size of the mineral is unimportant in the rate of formation , oxidation products and that probably the supply of oxygen to the mineral is the rate-determining step. At the end of 5 days the pH value of the 'supernatant liquid was measured again, the mineral filtered off and the soluble products determined. Methods for estimation of sulphur acids, ferrous and ferric iron and copper have already been described.l No satisfactory method was found for antimony. Arsenic was estimated as the arsenate.2 Flotation of "Unoxidized" Minerals with Ethyl Xanthate as Collector Fig I to 3, 4. 6, show the effect of alkali and cyanide as depressants for the minerals with 25 mg potassium ethyl xanthate per liter as collector at 35°C. Wark and Cox8 have shown that with ethyl xanthate as collector, galena, pyrite and chalcopyrite show a greater tolerance to cyanide and hydroxyl ions at room temperature than at 35°C Covellite (Fig I), marcasite (Fig 2) and pyrrhotite (Fig 3) behave similarly. The independence of the curves for pyrrhotite at 35°C with respect to cyanide

Jan 1, 1949

Jan 1, 1925

Jan 1, 1881

Jan 1, 1931

Jan 1, 1889

Jan 1, 1938

By John Riegle

To date. utility company underground storage of gas has generally been restricted to depleted dry gas fields. The Playa del Rey project is probably the first to successfully store gas in a partially depleted oil reservoir with the recovery of large volumes of pas at high rates as the main objective. Oil recovery has been a secondary consideration. Problems encountered unusual to those of storage in a dry gas zone were: (1) the removal and retardation of formation of emulsion. (2) the upstructure movement of fluid during withdrawal periods which formed fluid blocks, and (3) reservoir shrinkage resulting from encroachment of edgewater. The solution of these problems as outlined in the paper has resulted in increasing the withdrawal rate from the original design capacity of 4,000 Mcf per hour to the current 10.000 Mcf per hour. Additional increase is anticipated as the operations continue. Migration. reservoir performance. operational procedure and a historical record are included to make this a resume of the project from its war-time inception in 1942 to the first of 1952. INTRODUCTION The Playa del Rey underground gas storage project is probably the first project in which gas has been stored in a partially depleted oil reservoir, with the recovery of large volumes of gas at high rates as the main objective and the recovery of oil a secondary consideration. Problems unusual to those of storage in dry gas zones have made this a pioneer endeavor. The total storage capacity of approximately 1,500,000 Mcf of this reservoir is small in comparison with other underground gas storage projects. However. by study and experiment the deliverability into transmission lines. operating at pressures in excess of 150 lbs., has been nearly tripled in the past three years. to the current 10.000 Mcf per hour late, without the use of compression. It is anticipated this rate will gradually increase as additional fluid is removed from the formation. LOCATION AND HISTORY Playa del Key is located on Santa Monica Bay about two miles south of the beach commuity of Venice and 15 miles southwest of the renter of the City city Los Angeles. Fig. 1. The discovery well was completed at 6,194 ft in 1929. An upper zone at 3,905 ft was found on June 18. 1930. Townlot development was very rapid and by the end of 1930 there were 141 producing wells in the field. The Union Oil Co. completed a lower zone well south of the Townlot Field in May, 1931, which was believed to be an extension, until additional drilling of about 50 wells during 1934 and 1935 indicated this area to be a separate accumulation as shown on Fig. 2. The lower oil horizon, which is now the storage zone, had no original gas cap and is believed to be a continental detrital deposit of conglomerate that accumulated in valleys and depressions of a weathered schist high. which later subsided and was overlain by an impervious nodular shale. This type of formation has rapid variation of porosity. permeability and thickness due to lack of sorting action common to marine deposition. and the uneven surface of the original schist high. Production was limited on the upstructure sides by the pinching out of the conglomerate, and downstructure by edgewater. Unrestricted production, together with high permeabilities, led to large wastage of gas from this new area as facilities were not available for transport of gas to market. The decline was very rapid and by 1942 the portion of the new area south of Ballona Creek was nearly depleted. ACQUISITION OF PROPERTY The rapid increase in industrialization of Southern California during World war 11 forced upon the local gas com-

Jan 1, 1953

[SATURDAY, FEBRUARY 16 10 am to 5 pm Council of Section' Delegates SUNDAY, FEBRUARY .17 1 pm Student Relations Committee 2 pm Board of Directors 2:30 pm MIED-Mineral Economics Instruction 5:30 pm MIED-Cocktails and Buffet Supper 7:30 pm MIED-Mineral Education 8 pm IMD-Program Committee]

Jan 1, 1952

By Stephen Krickovic

AS it is commonly understood in the bituminous coal mining industry, pillaring means removal, as completely as is practical, of all pillars formed in the development of headings and rooms on first mining. The degree to which this can be accomplished, termed percent of recovery, is of course dependent generally upon the physical conditions of the bottom and the overburden, the system of min-

Jan 1, 1956

By Reinhardt Thiessen

In the general study of coal, all evidence points in the one direction —that coals had their origin in a manner analogous to that of peat. The best method of studying coal, whether it concerns its chemistry, composition, or physical condition, is to study peat. The essentials in a study of peat are a knowledge of the chemistry of plants, knowledge of decay and of the transformation process of plant-substances into peat. A number of facts must be emphasized, namely, (1) peat is formed under wet conditions only; (2) plants grow in the place where peat is formed; (3) all the plant substances go into the bog; and (4) all the plant substances are subjected to a series of phases of decay which are (a) in the air completely above the water level but in relatively moist conditions; (b) above the water level, but covered by debris; and (c) completely submerged by both water and debris. Plant Chemistry Plant chemistry as a whole is remarkably well understood. The number of compounds composing plants is large, and it is not possible here to give even a comprehensive outline, but a classification into definite groups is possible; this is as follows: Carbohydrates; glucosides; pigments; tannins; acids, alcohols and ketones, etc., and their salts; essential oils; resins; vegetable bases; proteins; enzymes. Plant substances may also be grouped according to the role they play in the life of the plant, such as: Framework materials, living materials, food materials, protecting materials, waste materials. While this classification groups them well for. certain purposes, it does not group them exactly chemically; but in a consideration of the composition of coal, this is an excellent classification for our purpose here.

Jan 1, 1925

R. H. Sweetser, Sault Ste. Marie, Ont. (communication to the Secretary*):—The recent work of furnace No. 1 of The Algoma Steel .Co., at Sault Ste. Marie, Ontario, using for fuel, first all charcoal, then a mixture of charcoal and coke, and finally all coke, upsets the estimates given by Mr. Hall in the last two paragraphs of his interesting paper. Furnace No. 1 was built for a charcoal-furnace, and it was run on charcoal fuel from March 6 until July 9, 1905; then, for a week, a mixture of charcoal and coke was used, and, since then, coke alone has been the only fuel. It is to be regretted that at no time, during the run on charcoal, was there enough charcoal on hand and " in sight" to warrant blowing the furnace as hard as it should have been blown. During April and May the supply of charcoal limited the amount of blast to about 8,000 cu. ft. of air per min.; in June, to about 8,900 cubic feet. For a few days in July about 10,000 cu. ft. were blown, and then the maximum daily output, 173 tons (2,240 lb.), was reached. At all times the quality of the charcoal was poor, having been made from wood cut from three to four years before. Doubtless this furnace could have produced 200 tons of iron per day, even with this quality of charcoal, provided the supply had been sufficient; and with

Jan 1, 1906

By Smith Bracewell

First evidence of bauxite in Jamaica resulted from an analysis of a soil sample collected at Bull Savannah in 1938 during a systematic local investigation of the island's soil types. Results of subsequent work indicated the possibility of the occurrence of deposits of commercial grade and dimensions, and in 1942, with a view to emergency development of the deposits as a war measure, the Jamaican Government declared all bauxite in the colony to be Crown property.

Jan 10, 1958

By Nelson B. Russell, Donald C. Bond

The effects of various antifreeze agents on the formation of hydrogen sulphide hydrate have been studied. On a molar basis the relative lowering of Tm (the maximum temperature at which solid hydrogen sulphide hydrate can exist in equilibrium with the given solution) for the various agents is: sodium chloride 1.00, calcium chloride 1.71, methyl alcohol 0.57, ethyl alcohol 0.68, ethylene glycol 0.73, diethylene glycol 0.73, sucrose 0.87, dextrose 0.71. On a weight basis the relative lowering of TM is: sodium chloride 1.00, calcium chloride 0.91, methyl alcohol 1.08, ethyl alcohol 0.89, ethylene glycol 0.69, diethylene glycol 0.41, dextrose 0.23, and sucrose 0.15. Introduction The solid hydrate of hydrogen sulphide, H2S.6H20,1 is in equilibrium with water and liquid hydrogen sulphide at 85°F at a partial pressure of hydrogen sulphide approximately equal to the vapor pressure Of hydrogen sulphide at that temperature. At temperatures below 85°F, in the presence Of excess hydrogen sulphide (greater than the amount required to react with the water present) the hydrate is in equilibrium with liquid hydrogen sulphide at approximately the vapor pressure Of hydrogen sulphide. In the presence of excess water, the solid hydrate is in equilibrium with liquid water, containing dissolved hydrogen sulphide, at a pressure lower than the vapor pressure of liquid hydrogen sulphide at the same temperat~re.2 The lower the temperature, the greater the difference between the decomposition pressure of the hydrate and the vapor pressure of liquid hydrogen sulphide at that temperature. Conditions conducive to the formation of solid hydrogen sulphide hydrate may exist in wells producing a gas containing a high percentage of hydrogen sulphide under high pressure, or in the lead lines from such wells. This paper gives the results of tests made with various antifreeze agents which might be useful in decomposing the hydrate or in preventing the formation of the hydrate of hydrogen sulphide Apparatus Fig , shows a diagram of the apparatus used. The sample under observation was contained in a glass tube 34 cm long, having a 6 mm id and a wall thickness of 2.5 mm. The lower end of this tube was closed- with a plug of butyl rubber. The upper end of the tube was connected to a diaphragm gauge, with a stainless steel diaphragm, a manometer, a vacuum pump, and a cylinder of hydrogen sulphide, The tube was held nearly horizontal, with the liquid resting along the lower side of the tube. It was found that when the tube was held in a vertical position, it broke with ex. plosive violence as soon as it became filled with solid hydrate. Presumably this was caused by the expansion which occurred on solidification of the hydrate. The difficulty disappeared when the tube was held in an inclined position during the tests.

Jan 1, 1949

By Stanley M. Moos, Richard Addison

Introduction The Pueblo Viejo gold-silver mine, located in the Dominican Republic, started production in early 1974 processing ores averaging 4 g/t gold and 20 g/t silver at a rate of 7.25 kt/d. The ore milled is a silicified siltstone with average work index of about 8 that occurs as an extensive oxide capping of a primary sulfide ore body. The sulfide ores are refractory to conventional treatment process and extensive research work is now in progress to develop a treatment process for them. The ore deposit has a long history, having been mined by the indigenous Arawak Indians for some time in the early sixteenth century prior to the arrival of the Spanish, and then by the Spaniards. In the early 1950s, Italian engineers attempted to process the sulfide ores. Mining by the Indians and Spanish was abandoned because of low grade and little coarse gold in the oxide ores and by the Italians because of the refractory nature of the sulfide ore. In 1969, Rosario Resources geologists discovered that there existed sufficient reserves of oxide ore for a viable mining operation and the plant was designed, built, and brought into production.

Jan 1, 1981

By H. D. Keiser

Minor industrial minerals included in this chapter are: the alum minerals, bromine, calcium chloride, epsomite and other natural magnesium salts, iodine, meerschaum, quartz, industrial crystals other than quartz, and nonfuel gases (air, helium, carbon dioxide). Alum Minerals The natural alums comprise a group of hydrated double sulfates, the most important of which are potash alum, KAI(S04)2.12H20, the "alum" of popular usage; ammonium alum, (NH4)AI(SO4)2, known mineralogically as tschermigite; and soda alum, NaAI(SO4)2.12H20. Kalinite, KAI(SO4)2.11H20, and mendozite, NaAl(SO4)2, 11H20, are fibrous monoclinic alums, distinct from the isometric species potash alum and soda alum.4 Alunite, KAI3(S04)2(OH)6, also known as alumstone or alum rock, has been used as a raw material in the manufacture of alum since early times. All the natural alums are highly soluble and occur as surface evaporation products in arid regions or in sheltered places. Potash alum, together with the other natural alums, commonly occurs as an efflorescence or crevice filling in argillaceous rocks and brown coals that contain disseminated pyrite or marcasite. The mineral is derived by the action of sulfuric acid, formed during the weathering of the sulfide, upon alkali-rich aluminum silicates. Ammonia alum is found chiefly in lignite or broad-coal beds and bituminous shales. Alunite is most commonly associated with acid volcanic rocks, where the rock has been largely altered and alunite formed owing to the presence of sulfuric acid solutions or vapors. Aluminum sulfate, which for most uses is the essential ingredient of alum, may be found in saline residues resulting from the evaporation of natural water and may be formed by the action of acid waters upon aluminous rocks. A deposit of natural potash alum occurs in an irregular network of veins associated with sulfur in rhyolite in Esmeralda County, Nevada, about 35 miles west of Tonopah and 10 miles north of Silver Peak. Alum was recovered at a plant operated on the property between 1920 and 1923 by crushing the ore to ¾ in., grinding to minus 80-mesh, and counter-current leaching; the resulting alum solution was then filtered and crystallized. Alunite was of much interest during World War I as a source of potash and during World War II as a source of alumina. The wellknown deposits at Tolfa, Italy, are veins in trachyte and have been the basis of alum manufacture there since the middle of the fifteenth century. Pure alunite is insoluble in water and in common acids, but if it is heated to 500°C it loses its water of hydration, and the residue consists largely of anhydrous potash alum, part of which is readily soluble in water or acids. If the heat is increased beyond 500°C, most of the sulfur combined with the alumina is released as oxides and the residue consists of potassium sulfate and alumina. Thus, either potash alum (and aluminum sulfate) or potassium sulfate and alumina may be made. In the

Jan 1, 1960

By D. T. Camp, J. A. Clum

WITH experience, the indexing of back-reflection Laue patterns for cubic crystals is usually a straightforward matter. However, for noncubic systems where in general tables of interplanar angles are not available or when inexperienced personnel are involved, properly indexing a crystal is normally a tedious, time-consuming affair. The authors have written a digital-computer program which calculates and prints out a table of interplanar angles for an arbitrary crystal structure and then systematically searches through this table attempting to obtain a consistent fit to back-reflection Laue data supplied by the user. Of course it is possible simply to calculate a desired set of interplanar angles should this be the only requirement. The program was originally written in ALGOL for use on a Control Data G-21 computer and a preliminary version is described elsewhere.' A version in FORTRAN TV which has been run on an IBM 7040 and one in FORTRAN II run on an IBM 1620 are also available. While it is not the purpose of this communication to describe the program in detail, an indication of how the program operates may help one to decide whether the program would be useful under particular circumstances. The hypothetical example chosen involves the indexing of the zinc crystal which has a hexagonal structure and a c/a ratio of 1.856. Input data for this example consists of only nine cards: The first card controls the list of families of planes to be considered. If the Miller indices of a prospective family are (h k 1), the first digit places a limit, in this case 3, on the absolute values of any individual index. The second digit limits the sum (h +k + l + 1), in this case to 5. Therefore the families (013) and (112) are considered but the family (122) is not. All systems, including the hexagonal, are treated using three-digit Miller indices. The second card contains the crystallographic parameters required to define the system. The first digit is 0 if the system is rectangular, that is all angles are 90 deg. If the system is nonrectangular, as in this example, the digit 1 so indicates. The next three values are the lengths of the sides of the reference cell, a, b, c. The final three entries on the card are the angles, a, 8, y between the sides. The digit 0 on the third card indicates that more data follows, the digit 6 shows that a set of six planes is to be indexed, and the value 2.0 indicates that agreement between a tabulated angle and an input angle is considered adequate if their absolute difference is less than 2 deg. The fourth card lists the measured input angles. a12 = 38 deg, a13 = 24 deg, and so forth. More input angles are listed on cards five to eight with the latter giving the input angle 058 = 40 deg. The final card in this series indicates by the digit 1 that no more data is to be processed. The program operates in the following manner: 1) The input data from cards 1 and 2 is read, thereby indicating the crystal system to be examined and the crystallographic parameters of the particular crystal to be indexed. 2) A table of interplanar angles is generated. 3) The input angles contained on cards 4 to 8 are read. 4) The measured input data is systematically compared with the generated table of standard angles. All combinations of poles whose interplanar angles compare with the requisite, specified accuracy are printed out. If no adequate fit is found an indication of this is printed. A typical line from the generated table of interplanar angles is: (001) - (111) 74.92 64.99 It can be shown that in the Miller-Bravais system the first value corresponds to the angles between (0001)-(1121) and the second to that between (0001)-(1011). This particular set of data gave the following result for the planes 1 to 6: (011) (110) (121) (111) (112) (010) The ALGOL version also has the option of simply providing the Greninger-chart coordinates ? and 6

Jan 1, 1967