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By W. R. Davis

This paper presents a sunimary of the results of a study of the Dornick Hills-Springer sand reservoir of the Velma Pool. Stephens County, Oklahoma. The data are of interest because this type of reservoir is unusual in the mid-continent area. The reservoir is characterized by very steep dips and a relatively thick producing section. Its up-dip productive limit is defined by truncation of the productive sands, and the down-dip limit is defined by deterioration of sand quality rather than by the presence of an oil-water contact. The crude oil is of 29" API gravity, is relatively viscous and was saturated with dissolved gas at the original reservoir pressure. Consideratiqn of the physical characteristics of the reservoir indicates that natural water encroachment will be negligible, and that the producing mechanism will be a dissolved gas drive augmented by gravity drainage. Performance to date tends to confirm this. INTRODUCTION It is the purpose of this paper to present some of the features of the Dor-nick Hills - Springer sand reservoir which are unusual in mid-continent operations. The study was undertaken in an attempt to define the producing mechanism or mechanisms that will control reservoir performance, as an aid in determining well completion and production practices. GEOLOGY The reservoir under consideration is a series of sand bodies of Pennsylva-nian age found in the Lower Dornick Hills and/or Springer formations. For the purpose of this paper, the sand series is referred to as the Dornick Hills-Springer sand. This sand series lies on the northeast flank of the Velma anticline, and dips very sharply to the northeast in TWP 1S-5W, the average dip being about 45º. However, as shown in Fig. 1. the trend of the pool swings eastward in TWP 1S-4W with a coincident de- crease in dip angle. In this portion of the pool the average dip is about 25". Faults in Sections 30-1S-4W and 32-1S-4W are shown in Fig. 1. These faults show only minor displacements for the horizon contoured in Fig. 1, but they do show a pronounced displacement of the immediately overlying beds. Similar faults are thought to exist in TWP 1S-5W; however, since the detailed geological studies necessary to properly define these faults were not available to the author, no attempt to show them in Fig. 1 has been made. The up-dip productive limit throughout the pool is determined by the truncation of the Lower Dornick Hills-Springer sand. The down-dip productive limit does not appear to be defined by edge water, but by a gradual reduction in permeability of the sands. No dry hole has produced a significant volume of water from this sand section. There was a small gas cap in TWP 1S-5W. Most of the wells in TWP 1S-SW encountered an oil sand 70 ft to 150 ft thick, a shale 20 ft to 80 ft thick, and another oil sand 50 ft to 130 ft thick. A few scattered wells in this area encountered other and bodies below these

Jan 1, 1951

By F. W. Glaser, W. Ivanick

A pressure-sintering method was used to produce binder-free and very dense TiC specimens. Some physical properties of these TIC bodies were determined and found to compare favorably with those of certain cemented Tic grades. It was also observed that the hot transverse rupture strength of TiC bodies remained substantially the same regardless of the amount or type of binder material used. STUDIES of the structure and physical properties of refractory materials have been intensified recently because of the urgent need for nonstrategic materials that retain their strength at high temperatures. Research aimed at determining and improving the physical properties of cemented carbides and borides has been accelerated with a view toward possible use of such materials in connection with turbine blades, rocket nozzles, and other high temperature applications. On the hypothesis that the strength requirements in connection with some of the above applications could be met only by proper choice of cementing agents for such refractory materials, the literature describing the physical properties of borides or carbides was reviewed. However, with a few exceptions,'-" references were found only to compositions containing at least one or more auxiliary binder metals. Cobalt and nickel are among the most frequently employed cementing agents. The melting point of Tic (approximately 3250°C) and therefore the sintering temperature, at which notable densification of a cold pressed Tic powder compact could be expected in the absence of a liquid binder phase, is relatively high. The present study makes use of a high temperature, pressure-sintering procedure, recently described by one of the authors in connection with the sintering of binder-free ZrB,," to produce dense bodies of sintered Tic—free of any cementing agent. During the course of this sintering study, some physical properties of dense Tic bodies produced by this method will be discussed. Materials, Preparation of Samples, Testing Methods The procedure for the forming of Tic powder consisted of mixing graphite and TiH, powders in stoi-chiometric proportions, and heating this mixture in a H, atmosphere and carbon crucible by high frequency, to temperatures ranging between 1900° and 2100°C (3452" and 3812°F). The powdered carbide was then comminuted and screened to the desired particle size. Table I shows the chemical analysis of the two grades that were employed for the production of samples during this work. Bodies of Tic, approximately 2.5xlx0.5 cm were produced in graphite molds that were heated by direct conduction. Sintering was carried out at temperatures for time intervals ranging from approximately 0 to 30 sec under a constant pressure of about 1.3 tons per sq in. An alternate method for the production of samples consisted in cold pressing the individual Tic grades at pressures ranging from 4 to 10 tons per sq in. and sintering in a hydrogen atmosphere in graphite crucibles heated by high frequency induction. Sintering temperatures ranged from 2600° to 2900°C (4715° to 5255°F). Electrical testing was done by measuring potentiometrically the voltage drop over a length of 1.5 cm for a current of 10 amp at room temperature. Cross-sectional areas as well as densi-

Jan 1, 1953

By M. C. Flemings, P. J. Ahearn

Dendvite morphology of unidirectionally solidified Sn-12 pct Bi alloy was determined with the aid of X-ray and macroetch techniques. Columnar growth direction (growth direction of primary arms) in this alloy is [110]; secondary arms grow in the [lii], [111), and [112] directions. Interstices between [112] dendrite arms fill in during early stages of solidification so that well-defined (110) planes are seen in the final structure (parallel to the heat-flozo direction). Similarly, interslices betweex the [111] secondary arrlls fill in to form (112) planes, and interstices between [1111 ] arms fill in to form (112) planes. DENDRITE morphology in alloys is conveniently studied in unidirectionally solidified castings. In this type of solidification, heat is extracted from a single chill surface of the casting while other surfaces are insulated. Solidification progresses from the chill and results in cast grains that are columnar with the long axis of the grain perpendicular to the chill. Dendrite morphology is conveniently studied by examination of etched surfaces parallel and perpendicular to the chill, as previously described.'" Experimental studies on the growth direction for tin are in general agreement. The major growth direction is [110]:-' although this is altered somewhat by supercooling. In one study, tin dendrites pulled from a supercooled melt had a growth orientation 12 deg away from the [110] direction toward the [002] direction.' This orientation could be changed back to the [110] or close to the [110] direction by changing the tempera- ture gradient in the melt. In a study using autoradio-graphic techniques, (111) directions were shown to be directions of preferred growth in addition to the [110) direction.7 PROCEDURE The samples employed in this study were cut from 12 pct Bi-88 pct Sn castings, 1.5 in. in diam and 3.5 in. tall. The casting procedure consisted of heating the charge to 390°C and then pouring the molten alloy directly into a gypsum sleeve mounted on a massive copper chill. Specimens were cut from the ingot, mounted, polished, and etched with Taffs reagent [FeC13 .6H2O, 2 g; HC1, 5 cu cm;H20, 30 cu cm; CzHaOH (95 pct), 60 cu cm].' The dendritic pattern was clearly visible after etching. Photomicrographs at about 8 and 35 times were taken on surfaces parallel and perpendicular to the chill. Laue back-reflection patterns were obtained from three different columnar grains in a singIe polished face 2 in. from the chill. The cut face was polished and positioned in the beam of a Laue camera, so that diffraction occurred from a single dendritic grain. The resulting diffraction pattern was interpreted to determine crystal log raphic orientation in relation to the heat-flow direction and in relation to microstruc-ture of the given grain. RESULTS Fig. 1 shows a horizontal and vertical section of the columnar structure, at low magnification. Light regions are rich in tin, and darker regions tin-poor; the primary phase is tin-rich a phase. The two sections shown were taken orthogonally from the same metallographic specimen. It is readily seen from Fig. 1 that the dendrites have

Jan 1, 1968

By W. C. Ellis, E. S. Greiner

METALLIC titanium has been prepared in small quantities since the beginning of the century. Hunter1 reported in 1910 that he obtained a malleable product of 99.9 pct purity by the reduction of the tetrachloride by sodium in a closed container. Later Van Arkel2 and Fast3 prepared small quantities of malleable titanium by thermal decomposition of titanium iodide. Another method for producing malleable titanium from tetrachloride was reported by Kroll4 who used magnesium as the reducing agent. More recently Dean, Long, Wartman, and Anderson5 working at the U.S. Bureau of Mines have reported the preparation of the metal on a pilot plant scale by the reduction of titanium tetrachloride by magnesium in an atmosphere of helium. Their product, which is malleable, was used in the present investigation. Early in 1948 after the work of this paper: was completed Campbell, Jaffee, Blocher, Gurland, and Gonser6 described the strength and working characteristics of pure titanium which was prepared by the iodide method on a scale producing 300 to 600 g per run, in the form of 0.3- to 0.4-in. diam rods. Their product is characterized by low hardness and large capacity for cold work which they attribute to a high degree of purity with respect to oxygen, nitrogen, and carbon. Titanium has a melting point of about 1725°C5 it may be classed as a light metal since the specific gravity is 4.5 g per cc-1. The crystal structure is close-packed hexagonal from room temperature t0 885°C. Above this temperature the structure is reported7 as body-centered cubic. The change in crystal structure has been associated with discontinuities in specific heat8 electric resistance9 and thermoelectric force10 at temperatures near 890°C. It is reported11 that annealed titanium has a tensile strength 0f 78,700 psi which can be increased by cold-work to 123,000 psi. In the present investigation, the lattice constants at room temperature, the thermal expansivity between 30 and 800°C, as well as the electrical resistivity and thermoelectric force against platinum between - 200 and 1000°C have been determined. MATERIALS For the measurements, two series of specimens were prepared from titanium furnished by the U. S. Bureau of Mines. The first was lade from an annealed sintered compact, 0.38 in. thick. Sections of the compact were cold-swaged with intermediate anneals in vacuum to the sizes used. Sizes over 0.25-in. diam were annealed at 1000°C and smaller sizes at 800°C. Specimens originating from the sintered compact are designated in this paper as A. The second series of specimens was lade from a rod of titanium, 0.19 in. in dial, which was cold-swaged with the necessary intermediate anneals to the required sizes. This series of specimens is designated B. The impurities in the specimens of titanium, determined by chemical analysis, are given in Table I. Oxygen and nitrogen which were not determined by analysis, are probably present although in small quantities in view of the ductility of the material.

Jan 1, 1948

By M. Herman, G. J. London

A series of dilute Fe-Co alloy specimens were prepared from zone-melted iron. The iron used was given ten floating-zone passes in purified hydrogen. Alloying was accomplished by plating a gradient of metallic cobalt onto a 1/4-in.-diam bar of material from a pure plating bath. The deposit was radioac-tively tagged by a small addition of co80 to the plating bath. Alloy homogenization was accomplished by passing an additional floating-zone pass through the plated section of the bar. The final concentration gradient achieved was from residual to about 1000 ppm (0.1 pct) added Co. After homogenization, the bar was swaged to 0.057 in. wire and cut to tensile specimen blanks 1-1/16 in. long. Each specimen was counted in a well-type scintillation counter. The concentration of cobalt was computed by combining the normalized specimen counting rate with the known weight (measured to the nearest 0.01 mg) of cobalt added during plating. Fig. 1 shows the cobalt gradient obtained, exclusive of residual cobalt which was estimated by neutron-activation analysis to be approximately 50 ppm. Results of recrystallization for 1 hr at 750°, 700°, 650°, and 600°C with specimens containing 40, 170, 470, and 870 ppm added Co are shown in Figs. 2, 3, 4, and 5. Recrystallization was accomplished in a dynamic vacuum of less than 1 x 10 torr. The specimens were mounted and polished parallel to the swaging direction. The recrystallization re- sults show a radical coarsening of structure with increasing cobalt concentration. The coarsest structure obtained was at the 470-ppm level (at all recrystallization temperatures) with a slight grain refinement at the 870-ppm level shown. A more normal solid-solution effect is seen in Fig. 5 (60OoC, 1 hr) where the only specimen completely recrystallized is the one containing 47 ppm Co. Since the possibility existed that some atmosphere-contamination phenomenon might be responsible for the observed results the recrystallization series was repeated using sealed quartz capsules. These were filled with purified argon which was gettered during heat treatment on metallic titanium included in the capsules. The results obtained were essentially the same as shown. Another identical alloy was made using a 5-mm-diam bar of Westinghouse Puron. Specimen preparation and recrystallization treatment were also as described. The results obtained (see Table I) were somewhat erratic. Some coarsening in structure does appear at the highest cobalt concentrations. There is no apparent relationship between the coarse, columnar, directionally solidified structure of the as-melted bars and any of the recrystallized grain structures observed, all of which are much finer than the former structure. A recrystallization process can be most simply described as one of homogeneous nucleation of recrystallized grains in a cold-worked matrix followed by more or less uniform growth of the strain free grain into the cold-worked material.' An impurity element may influence one or both of these processes. Aust and utter' have shown that impurities strongly influence grain boundary mobility in lead. Moreover, definite recrystallization textures are produced by small concentrations of tin,3 while additions of silver or gold4 produce large boundary in-

Jan 1, 1964

By K. A. Johnson, F. H. Ellinger, C. C. Land

The Pu-In phase diagram has been determined by thevmal, filtvation, micrographic, and X-ray diffraction methods. This alloy system is characterized by 1) limited solubility of indium (-2 at. pet) in 6 and e plutonium, 2) one eutectic, and 3) fizte intermediate phases. Of the latter, PuIn and PuIn3 melt con-gruently, and Pu31n, Pu31n5, and the high-temperatuve 7 solid solution are formed peritectically. The n phase decomposes eutectoidally into Pu3In and PuIn at 865°C. Although the 6 phase can readily be retained to room temperature, it is not thermo-dynamically stable below 300°C. The Pu-In system has been investigated at Los Alamos as part of a study of the alloys of plutonium with the group 111-B elements. Constitutional studies of the Pu-A1 and Pu-Ga systems have been reported earlier.'9' To date, published information on the constitution of Pu-In alloys covers only the identification of the intermediate phases Pu3In and PuIn3.3,4 EXPERIMENTAL The alloys were prepared from five different lots of plutonium and three different lots of indium. The principal impurities in the plutonium differed from lot to lot within the following limits (in ppm): iron, 30 to 80; nickel, 30 to 60; aluminum, 15 to 30; silicon, 20 to 145: thorium, 50 to 300; carbon, 75 to 335; and oxygen, 20 to 135. Spectroanalysis of the indium showed that two of the lots were 99.9 wt pct pure, and the third was 99.98 wt pct pure. The alloys, in the form of about 5-g buttons, were prepared by arc melting in conventional equipment. The components for each alloy were weighed to the nearest 0.1 mg. In most instances the weight losses during melting were negligible; therefore confirmatory chemical analyses were usually not made. A few results are given in Table I. Density measurements of the arc-cast buttons were made by the liquid displacement of bromoben-zene. Heat treating was done in muffle furnaces controlled to +2°C. The alloy buttons were wrapped in tantalum foil before being enclosed in evacuated clear silica capsules. As a precaution against breakage, each capsule was in turn placed in a silica tube closed with a refractory wool plug prior to being charged into the furnace. For a moderately fast quench of the alloys, the outer protection tubes containing the capsules were plunged into cold water. Differential thermal analyses (DTA) in racuo were performed at heating and cooling rates of about 1.5°C per min. Tantalum crucibles having inverted thermocouple wells were used for most of the analyses. It was found micrographically, however, that the liquid alloys containing more than about 35 at. pct In reacted with the tantalum, resulting in contamination of the surface of the alloy. A search for a more satisfactory crucible material was not successful: tungsten and yttria behaved comparably to tantalum; thoria, vitrified magnesia, and vitrified alumina severely contaminated the alloys. So as to minimize the contamination by the crucible mater-

Jan 1, 1965

By I. Nilsson, G. Sundkvist, A. Danielsson

A spectrochemical method of slag analysis is descibed which utilizes fusion of the sample with a flux, then cooling and crushing to put all samples into a common form. The powder, is then fed onto adhesive tape and passed through a spark by means of a special device to provide very reproducible discharge conditions. Combined with a direct-reading optical emission instrument, this system provides speed and accuracy of antilysis heretofore unobtainable for. slag samples by any other method. THERE are many suggested methods for spectro-chemical analysis of slags. The most important are fusion-pellet methods and solution methods. In our company the fusion-pellet method has been used earlier, and is described by Lounamaa. W. H. Tingle and C. K. Matocha have made refinements of the pellet method.' A Committee of the British Iron and Steel Research Association has investigated different methods of spectrochemical analysis of slags. Its purpose was to formulate a method which would give the complete analysis in 30 min with an accuracy of ±3 pct. The committee recommends a solution technique, which was thought to correspond best to their requirements. The method to be described is a fusion-tape method. The sample is isoformed by fusion and grinding. The powder is analyzed with the tape technique. The tape machine and some of its applications are described earlier.4'5 The powder to be analyzed is continuously fed onto a moving adhesive tape, which passes through the spark gap. The sparks break through the tape and vaporize and excite the material to be analyzed. The most outstanding feature of the tape machine is its very high reproducibility. The concept of isoformation has been introduced earlier.= It means a pretreatment of the samples to make them uniform from the spectralanalytical point of view, i.e., cancelling systematic differences between the samples. The purpose of the isoformation is to reduce the influence of particle size, as well as chemical and mineral composition. Before describing the isoformation by fusion plus grinding, which is the purpose of this paper, a few words will be said about two other types of isoformations, i.e., grinding with buffer and ion exchange plus grinding as they have been considered during the application of the tape technique for slag analysis. Grinding with buffer might be a sufficient isoformation in some special cases, where the mineral composition is defined. The time of grinding must, however, be rather long, at least 5 to 10 min, even when using such an efficient mill as the Swing Mill from Messrs. Siebtechnik, Mühlheim, Germany. This type of isoformation is not recommended due to its limitations and due to the fact that the gain in time compared with the fusion technique is almost negligible. The principle of ion exchange plus grinding and some of its applications have been described.5 The following elements of interest in slag analysis can be determined in this way: Na, K, Cu, Mg, Ca, Ba, Zn, Pb, Al, Cr, Mn, Fe, Co, Ni. The very important element Si, however, cannot be analyzed with this method. Although the ion exchange isoformation for slag analysis cannot be looked upon as a routine method, it can be used for

Jan 1, 1962

By Charles Trotter

AN instrument has recently been developed for determining the inclination and azimuthal direction of boreholes. This instrument is known as the Tro-Pari Instrument and is the invention of C. Trotter and G. Pajari of Sudbury, Ontario. DESCRIPTION The instrument is characterized by a unit mounted in gimbals and provided with a clockwork mechanism to clamp a compass to indicate azimuthal direction and simultaneously to clamp the unit in its plumb position to indicate inclination (Fig I). By means of a timing ring suitably calibrated in 5-min divisions, the unit may be set to lock after a lapse of time sufficient to allow the placing of the instrument at the desired point in the drill hole where readings are to be taken. The maximum time lapse obtainable with the instrument designed for use in EX or AX size holes is 1 hr 30 min which is considered to be ample time to lower to the greatest depths that may be drilled with this size of equipment. Larger sizes could be developed for larger diameter holes such as BX and NX sizes or the larger oil-well sizes and a correspondingly greater time lapse could be provided for. Up to the present time only the EX-AX size has been built. OPERATION Assuming a borehole is to be surveyed at 1000-ft depth and assuming it will take 30 min to lower the instrument to this depth, the timing ring is rotated through seven divisions which represent a time lapse of 35 min (5-min leeway) and is then returned to its zero position. This operation imparts energy to a spring which drives the clockwork mechanism. Simultaneously the compass needle is freed to swing to its magnetic north-south position and the encased mechanism is freed to hang plumb within a semicircular portion of the frame which is graduated in degrees after the fashion of a protractor. This semicircular protractor portion has a V-shaped notch at each degree division of its inner periphery. The instrument, now in its free position, is inserted in a bronze container made to suit the size of hole to be surveyed (Fig 2). Soft rubber washers are provided within the container to prevent undue shock. The container is connected to the drill rods with three 5-ft lengths of brass or aluminum alloy rods separating it from the steel rods in order to prevent distortion of the magnetic field. The assembly is then lowered to the desired point where readings are to be taken and is allowed to remain at rest until a period of time has elapsed slightly in excess of the time for which the timing ring was set. In the example cited above, when the 35 min has elapsed the compass needle is locked in its north-south position and the protractor locking pin is extruded and locks in the V notch opposite its plumb position. The device may now be removed from the borehole and it will remain in this locked position in spite of jarring or shak-

Jan 1, 1947

By Strathmore R. B. Cooke, Marcus Digre

That calcium will activate quartz for flotation with anionic collectors such as soaps has been known for a number of years,12'3 and the method has been applied to the concentration of various iron ores4 5 6 as well as to other materials. Clemmer gives the permissible pH range for the activation of quartz by calcium as between 9.5 and 12.5 with an optimum value of 11.0, and Hertzog7 has determined the calcium abstraction of iron ores and of Ottawa sand, but otherwise little quantitative data are available. The purpose of the present investigation was to determine those conditions under which dilute solutions of calcium chloride will activate quartz for anionic flotation and to determine the amount of calcium ion adsorbed by quartz. Those variables, the influence of which was primary, such as calcium, sodium, and hydrogen ion concentrations, were studied. Other factors which influenced the results are discussed in the description of the experiments. Three different experimental methods were used to determine the activation of the quartz. The first method was to treat a sample of ground, deslimed quartz with solutions of calcium chloride and sodium hydroxide, and to determine the calcium adsorbed by chemical analysis of the solution. Advantages are that a direct value for the amount of calcium adsorbed is obtained, and introduction of a collector which may affect the adsorption is avoided. The difficulty is to determine the extremely small differences in the calcium concentrations before and after the abstraction. The second method was to determine the activation of the quartz by observing the contact angle obtained on pressing an air bubble against the polished surface of a piece of quartz immersed in a solution of calcium chloride, sodium hydroxide, and sodium oleate. This is the well-known "contact angle" method. The third method was to determine those conditions under which an air bubble will pick up quartz particles immersed in a solution of the desired reagents. Disadvantages common to the sec- ond and third methods are that introduction of a collector is necessary to obtain bubble contact with the mineral; very small quantities of contaminant can give erroneous results; and no information is obtainable concerning the amount of calcium adsorbed. Advantages are that tedious analyses, which at best give approximate results, are avoided, and the conditions, especially for the third method, closely simulate those of actual flotation. Although the most consistent results were obtained with the third method, this paper describes the techniques used and the results obtained from each of the three methods. Distilled water and analytical grade reagents were used throughout except where otherwise stated. Between tests all glass articles were cleaned with a chromic-sulphuric acid mixture and sodium hydroxide. Abstraction Method The raw material for the tests was Ottawa sand sized between 14 and 28 mesh. Batches of 500 g of this sand were dry ground for 1 hr in an Abbe porcelain mill with 2700 g of quartz pebbles. The batches were split down to samples weighing approximately 30 g, and the weight of each sample was adjusted to exactly this value.

Jan 1, 1950

By M. R. Geer, H. F. Yancey

Coal washing assumed an important role in the mining industry of the Pacific Northwest long before washing practice became firmly established in the Appalachian field. A Scaife washer was operated in the state of Washington in 1887; and by 1927, the fist year for which complete statistics were compiled, nearly a third of the state's coal production was washed, in comparison with only about 5 pct for the country as a whole. Mechanical preparation was adopted in Alaska in 1922 in a plant constructed by the United States Navy at Chickaloon to provide bunker coal for naval forces operating in northern waters. Many of the coal beds mined in Washington and Alaska contained more impurities than those mined elsewhere, and this circumstance contributed to the early interest in mechanical cleaning. A much more important factor, however, was the inclination of the coal beds. With steeply pitching beds, hand sorting by the miner at the face is impossible; consequently, all material must be loaded and dealt with on the surface, just as is now proving the case with mechanical mining of flat beds. Thus "full-seam" mining afforded the same stimulus to the early development of coal washing in the Northwest that it is providing under mechanization in the rest of the country today. Objeet and Scope ' This report is intended to provide a general summary of the status of coal-washing practice in Washington, Oregon, and Alaska—an area in which some of the coals mined are more difficult to wash than those mined elsewhere in the country. Detailed flowsheets of plants, statistical data on production, and cost figures have been omitted, largely for the sake of brevity but also because such information is principally of only local interest. On the other hand, considerable washability data have been included because they are Washington At present Washington leads all other states in the percentage of its total production that is cleaned mechanically, 82.1 pct in comparison with the national average of 25.6 pct in 1945.' The washing problems encountered in this state are highly variable because the mountain-building forces that created the Cascade Range caused such intense folding and faulting of the beds in some fields that the rank of the coal was increased to anthracitic, while in other fields more distant from the mountains the beds were relatively undisturbed, and the rank of the coal ranges down through subbituminous to lignitic. The complicated and burdensome schedule of sizes prepared in most coal fields has never been required by the Washington market. With but few exceptions, lump is prepared on a round-hole screen of about 3 in. size, egg is about 3 to 1 5/8 or 1½ in., and nut is 1 5/8 or 1½ in. to either 1 or ¾ in. Some mines screen no finer than ¾ in. and market a slack coal of that top size, but generally the coal is screened at about ¼ in. to give a stoker coal of ¾ or 1 to ¼ in., and a ¼ in. to 0 "buckwheat." During recent years the market for lump coal has largely disappeared, and lump is crushed to supplement the pro-

Jan 1, 1950

By T. K. Prentice

ABSTRACTED AND REVIEWED BY E. W. DAVIS,* MEMBER A.I.M.E. THE January-February number of the Journal of the Chemical Metallurgical and Mining Society of South Africa is made up entirely of a discussion of Ball Wear in Cylindrical Mills. Following the principal paper by T. K. Prentice are several remarkably pertinent and carefully prepared discussions. Few persons in this country would be likely to see this publication, and since the information presented is new and of current interest, it seems desirable to abstract and review this publication for the benefit of the members of the A.I.M.E. The purpose of the investigation is stated in the first two paragraphs of Prentice's paper, as follows: Early in 1941, The Chamber of Mines Steel Products, Limited, initiated a series of tests under semi-working scale conditions to determine, if possible, those physical and chemical properties of a ball which make it resistant to wear when used in a cylindrical mill as a grinding medium, with the primary object of incorporating those beneficial qualities in the balls being produced at their works. This paper describes the tests carried out and discusses the results obtained. From these results it was possible to formulate a new theory relating to ball wear in cylindrical mills. This theory is presented in the second portion of this paper. PRACTICAL BALL-MILL TESTS IN A CYLINDRICAL MILL Part I of the paper begins with a discussion of the methods used for the manufacture of grinding balls in South Africa. The following paragraph is of particular interest. The cast steel ingots, 4 ¼ - in. square by 3 ft. 6 in. long, are re-heated in a gas-fired sloping stationary-hearth furnace and then rolled in a six-pass continuous mill into 2 5/8 in. round billets. Some of these billets are then removed and cut into suitable lengths for forging into 4 in., 3 ½ in., 3 in. or 2 ½ in. balls by means of three Drop and two Beché hammers, but the greater number, whilst still at about 1,000 ºC., pass directly into a set of scroll rolls which produce, in an ingenious manner, finished 3 in. balls direct from the 2 5/8 in. billets. Except in special cases, all balls are allowed to cool in the atmosphere and are not water quenched. Details of the Tests In order to enable the reader to evaluate properly the results and conclusions in the rest of the paper and in the discussions following the paper, most of the information presented by the author under this heading is quoted: ….. The testing unit was a nominal 30 in. diameter and 18 in. long centre discharge Denver Ball Mill. The ore pulp to the ball mill comprised a small portion of the normal feed to one of the fourteen City Deep 5 ft. 6 in. X 22 ft. tube mills, and the grinding media consisted of the balls under test plus other balls to give the desired load. The running time of the test-mill was divided into approximately equal periods of five days 13 ½ hours each. The usual procedure was to examine and make up the load

Jan 1, 1944

By D. F. Kaufman, E. D. Levine, L. R. Aronin

ThE primary slip plane in hcp metal crystals can usually be inferred from the c/a ratio. Basal slip is the primary system at room temperature for zinc, cadmium, magnesium, cobalt, and rhenium, all of which have a c/a ratio greater than 1.60. Zirconium and titanium, on the other hand, each with a c/a ratio of 1.59, deform primarily by (1010) [ll20] prismatic slip. The increasing tendency toward prismatic slip in these materials is generally thought to be associated with the increase in atomic density on (10i0) as c/a is reduced. Beryllium, with a c/a ratio of 1.57, would, according to the above scheme, be expected to exhibit prismatic slip. However, in beryllium of commercial purity, the primary deformation mode at room temperature is basal slip.' The ratio of critical shear stress for prismatic to that for basal slip at room temperature is approximately 5:l. The critical shear stress for prismatic slip decreases quite rapidly with increasing temperature, however, and at 500°C the ratio is approximately unity. The apparently anomalous behavior of beryllium has led to speculation that prismatic slip in this material may be restricted by an anisotropic effect of impurities,' and that, if beryllium could be purified to a sufficient extent, prismatic slip might predominate at room temperature. In such a case, the conditions under which basal cleavage can occur would be suppressed, and enhanced low-temperature ductility might result. With the advent of the floating-zone method for purification of beryllium,3 it has become possible to determine experimentally the effects of purification on basal and prismatic slip. Tensile tests were performed at room temperature on single crystals oriented favorably either for basal or prismatic slip. The crystals had been purified to various extents by zone-refining, employing procedures that have been described elsewhere.4 Relative purities of the crystals were estimated by measuring the ratio of electrical resistance at 4.2"K to that at 298°K. Typical values ranged from 0.40 for commercial-purity material to 7.7 X 10"4 for crystals prepared from vacuum-distilled beryllium and subjected to six zone-refining passes. The purity dependence of the critical shear stresses for basal and prismatic slip is shown in Fig. 1. In the purity range studied, the critical shear stress for basal slip is decreased from 1.4 to 0.14 kg per sq mm. The critical shear stress for prismatic slip is decreased from 6.7 to 5.3 kg per sq mm. The decreases in critical shear stress for each deformation mode, therefore, are approximately equivalent. No purification anisotropy is observed. Because of the absolute magnitudes of the critical stresses, the ratio of the critical shear stress for prismatic slip to that for basal slip actually increases from 5:l to 38:l at the highest purity level studied. It is evident, therefore, that basal slip is the primary deformation mode in high-purity beryllium. This fact must be accounted for in any rationalization of the deformation behavior of hcp metals. This work was performed at Nuclear Metals, Inc., under the sponsorship of the U.S. Atomic Energy Commission.

Jan 1, 1964

Agnico-Eagle Mines Ltd. comprises a Gold Division at Joutel, Quebec, and a Silver Division at Cobalt, Ontario. In 1979 the Silver Division milled 41,700 mt (46,000 st) of ore at a recovered grade of 139 g per mt (4.06 oz per st) for a production of 5,816 kg (187,000 oz) of silver. The 100 -year -old mining, camp of Cobalt has long been noted for its high-grade silver ores, and now seems to be on the threshold of being revived with several companies operating in the area. In 1979, the Gold Division milled at the rate of 27,200 mt per month (30,000 st) and processed 333,000 mt (367,000 st) at a grade of 6.58 g per mt (0.192 oz per st) with a mill recovery of 91.670 to produce 2,013 kg (64,700 oz) of gold. The average total cost per ton milled was $22.10 per mt ($20.05 per st) which was $3.66 per g ($1 13.90 per 0s). These figures make Agnico-Eagle one of the lowest cost producers in North America. Gold occurrence in the Joutel ore is fine-grained and contained within sulfide facies composed mainly of pyrite with minor pyrrhotite. Two underground mining methods are employed with long hole stoping accounting for about 75% of the ore mined and shrinkage stoping the remainder. Ore from underground is hoisted into a 545 mt (600 st) coarse ore bin from where it is conveyed to a 45 mt (50 st) surge bin ahead of the 10-51 Hydrocone crusher. Crushed ore is then screened to make a 13 mm (112 in.) product with the oversize being recrushed in a 7-60 Hydrocone. Mill feed is conveyed to two 900 mt (1,000 st) fine ore bins. The Hydrocones were installed as part of a new crushing plant in March of 1980 and have contributed substantially to an increase in mill capacity. Space has been left to install a third crusher in the future. The fine ore bins discharge to a 2.75 m by 3.66 m (9 ft by 12 ft) rod mill, followed by a 3. 7 m by 5.5 m (12 ft by 18 ft) ball mill in closed circuit with a Krebs 380 mm (15 in.) cyclone to produce a 7070 minus 37 micron (400 mesh) .flotation feed. This pulp is first treated in a 34 cu m (1, 200 cu ft) Maxwell flotation cell and then in an additional twelve 2.8 cu m (100 cu ft) cells. Combined flotation concentrates are reground to 9070 minus 37 microns (400 mesh) in a 1.8 m by 4.9 m (6 ft by 16 ft) ball mill in closed circuit with a single Krebs 254 mrn (10 in.) cyclone. Flotation tailings are sent to the tailings dam. Reground concentrates are then aerated with lime to a single Pachuca and thickened in a 16.75 m (55 ft) diameter thickener with the addition of diesel fuel to render any activated graphite inert to adsorption of

Jan 1, 1981

By R. A. Swalin, B. W. Roberts

ONSIDERABLE controversy has centered about the existence of an order-disorder transformation in alloys in the composition vicinity of 75 atomic pct Ni and 25 atomic pct Cr. All the evidence to date for such a transformation is of a rather indirect nature, since direct X-ray confirmation is difficult to obtain as a result of the small difference in X-ray scattering factors between nickel and chromium. As a result, superlattice lines would be very faint if present. Several investigators1-5 have observed anomalies in the electrical resistivity vs temperature curves of alloys in the vicinity of 25 atomic pct Cr. The observed change is characterized by a rather broad resistivity peak at about 540°C. A discontinuous drop in resistivity is normally associated with ordering. However, Taylor and Hin-ton4 have rationalized that the discrepancy could conceivably be caused by changes in the Brillouin zones upon ordering. The same investigators measured the specific heat as a function of temperature and have also observed anomalies in the vicinity of 540°C. Nordheim and Grant5 have proposed, because of the absence of superlattice lines and the absence of a discontinuity in the resistivity vs temperature curve, that long-range order is improbable and that the results could be better explained by short-range ordering. To date, however, the question has not been resolved satisfactorily. Neutron diffraction techniques provide a method for partially resolving the question since nickel and chromium have considerably different atomic scattering factors in the case of neutrons and, therefore, superlattice peaks, if ordering occurs, should be readily discernable. The results of a neutron diffraction investigation* coupled with a dilatometric in- vestigation are reported here. An alloy containing 28.0 atomic pct Cr was prepared from carbonyl nickel and electrolytic chromium in the form of a 1-in. diam x 10-in. ingot. Melting was done in an alumina crucible and casting in a graphite mold. The ingot was homogenized at 1250°C for seven days, after which a 5-in. long piece was cut into shavings in order to obtain a suitable neutron diffraction sample. Hardness samples and samples suitable for dilatometric analysis (% in. diam x 2 in.) were prepared from the remainlng piece. The neutron diffraction sample, along with a hardness sample, was annealed at 501°C for seven days, at which time the temperature was lowered to 479°C and held at this temperature for twenty-four more days. The hardness was observed to increase from 133 to 147 Vhn during the course of the annealing treatment, in qualitative agreement with Nordheim and Grant." Neutron diffraction traces taken at room temperature and at 42 °K are shown in Fig. 1. The insert shows the trace taken at room temperature with short counting times and thus only fair statistical accuracy. No evidence for superstructure reflections of Cu3Au-type ordering is observed. The statistical accuracy of the 4.2°K trace was improved by using longer counting periods. Several weak intensities are observed at small angles, including an aluminum reflection from the cryostat assembly and a very

Jan 1, 1958

By Charles Trotter

An instrument has recently been developed for determining the inclination and azimuthal direction of boreholes. This instrument is known as the Tro-Pari Instrument and is the invention of C. Trotter and G. Pajari of Sudbury, Ontario. Description The instrument is characterized by a unit mounted in gimbals and provided with a clockwork mechanism to clamp a compass to indicate azimuthal direction and simultaneously to clamp the unit in its plumb position to indicate inclination (Fig I). By means of a timing ring suitably calibrated in 5-min divisions, the unit may be set to lock after a lapse of time sufficient to allow the placing of the instrument at the desired point in the drill hole where readings are to be taken. The maximum time Lapse obtainable with the instrument designed for use in EX or AX size holes is I hr 30 min which is considered to be ample time to lower to the greatest depths that may be drilled with this size of equipment. Larger sizes could be developed for larger diameter holes such as BX and NX sizes or the larger oil-well sizes and a correspondingly greater time lapse could be provided for. Up to the present time only the EX-AX size has been built. Operation Assuming a borehole is to be surveyed at 1000-ft depth and assuming it will take 30 min to lower the instrument to this depth, the timing ring is rotated through seven divisions which represent a time lapse of 35 min (5-min leeway) and is then returned to its zero position. This operation imparts energy to a spring which drives the clockwork mechanism. Simultaneously the compass needle is freed to swing to its magnetic north-south position and the encased mechanism is freed to hang plumb within a semicircular portion of the frame which is graduated in degrees after the fashion of a protractor. This semicircular protractor portion has a V-shaped notch at each degree division of its inner periphery. The instrument, now in its free position, is inserted in a bronze container made to suit the size of hole to be surveyed (Fig 2). Soft rubber washers are provided within the container to prevent undue shock. The container is connected to the drill rods with three 5-ft lengths of brass or aluminum alloy rods separating it from the steel rods in order to prevent distortion of the magnetic field. The assembly is then lowered to the desired point where readings are to be taken and is allowed to remain at rest until a period of time has elapsed slightly in excess of the time for which the timing ring was set. In the example cited above, when the 35 min has elapsed the compass needle is locked in its north-south position and the protractor locking pin is extruded and locks in the V notch opposite its plumb position. The device may now be removed from the borehole and it will remain in this locked position in spite of jarring or shak-

Jan 1, 1949

By Louis Moyd

In the preparation of illustrations to accompany reports of investigations concerning particle shapes of various natural and manufactured materials proposed for use as he aggretates in concrete structures, it was found that stereoscopic views of such materials presented the information much more effectively than the usual two-dimensional photographs. With the whole-hearted cooperation of the Photographic Section, a technique was developed in the petro-graphic laboratory of the Concrete Research Division, U.S. Corps of Engineers, at Clinton, Miss., for simple and rapid preparation of paired stereoscopic photographs and micrographs. The method requires only equipment which is usually part of the general stock of any laboratory, and it is adaptable for all purposes in which three-dimensional views would be found superior to ordinary photographs. Stereoscopic Photographs Where the subject or subjects to be photographed are small but not of microscopic size, an ordinary camera having a ground-glass focusing screen is set up vertically over the field. The material to be photographed is placed on a card, the surface of which is suitable as a background. The card is mounted so that it can be tilted about 5' above and below the horizontal plane, on an axis that coincides with the north-south diameter of the viewing screen. A simple way of achieving this is to mount the card on an object having a convex lower surface. In our laboratory, a watch-glass has been used, with plasticene as the mounting medium. The convex surface should be mounted on a support having a round opening on top and a flat bottom. A roll of tape, a petri dish, a beaker, or any other piece of equipment having the proper shape to give stability to the setup will be satisfactory. The arrangement of the required equipment is shown in Fig 1. For the best results, the subject to be photographed should be mounted in the plane of the axis of rotation. To achieve this effect, the depth of the mass of plasticene between the background and the watch-glass is varied so that when the watch-glass is tilted back and forth on the axis, the subject to be photographed does not appear to move back and forth across the viewing screen. A permanent piece of equipment, embodying an adjustable vertical screw, with lock-nuts, could be made for this purpose. The subject may be illuminated in any manner desired. It was found that the presence of shadows intensifies the effect of depth. In taking the photographs, the concave surface is mounted so that one side of the background card is about 5' below the horizontal, while the axis remains in the horizontal plane. The subject is focused carefully on the ground glass and a picture is taken. The card is then tilted so that the opposite side is about 5' below the horizontal, while the axis still remains in the horizontal plane. The subject is again put in focus and another picture is taken. After both pictures are developed and printed, they are placed side by side in the same orientation and examined with a stereoscopic viewer. If depressions appear where there ought

Jan 1, 1950

By H. Siebel, N. A. D. Parlee

MIZIKAR, Grace, and parlee' studied rates of absorption of oxygen in stagnant liquid silver in a new type of open-ended gas-liquid metal diffusion cell, where the capillary diameters used were 1.5, 2, and 3 mm. They reported that the rates appeared to be controlled by the rate of diffusion of oxygen atoms in liquid silver and they used their data to arrive at the following equation as a reasonably good representation of the diffusivity (D) of oxygen in liquid silver: D = (14.7)10-4 exp (-7100 ± 3200)/RT cm2/sec Since this type of diffusion cell offers a promising method of measuring diffusivities of gas atoms in liquid metals, the senior author of this note and his students are carrying on a critical examination of the method, and are attempting to improve and extend the technique. The research reported briefly here was designed to examine more carefully the earlier conclusion1 that the absorption rate is diffusion-controlled, and to find out whether the diameter of the cell could be greatly increased and thus extend the method to systems where gas solubilities and diffusion rates are much smaller than in the case of oxygen in silver. For the purpose of these experiments, the open-ended capillary cell used by Mizikar, Grace, and Parlee was replaced by a small cylindrical crucible (1 to 1.7 cm in diam) containing pure silver (to a depth of 1.3 to 3 cm) resting in the bottom of a closed-ended vertical quartz tube, with an evacuated quartz filler tube just above the crucible to reduce dead volume. The method of measuring the rate of absorption was otherwise very similar to that of Mizikar, Grace, and Parlee and all the same precautions were taken. A much smaller and shorter tube furnace was used for heating, but simi- lar precautions about temperature gradients were observed. This technique was nothing more than the application of a Sieverts apparatus to the measurement of rates of absorption in small crucibles of stagnant liquid silver. In each run the volume of gas absorbed (V) was plotted against the square root of time (vt) and apparent diffusivities were calculated from the slope of the line, as described by Mizikar, Grace, and parlee.' Care was taken to use only the data obtained during the early part of the total absorption period while the cell functioned as one of infinite depth. The results at 1000°C are summarized in Table I and Fig. 1. The following conclusions may be drawn: 1) Diffusion cells up to 1.7 cm in diam yield, within experimental error, the same values for the diffusivity of oxygen (D) as the capillary cells of 1.5, 2, and 3 mm in diam employed by Mizikar, Grace, and Parlee. Cell diameters as large as 1.7 cm are probably not desirable for the most precise work. Intermediate sizes, perhaps 0.5 cm, will be most practical. 2) All absorptions measured were consistent with a model where the rate is controlled by the diffusion of gas atoms in the metal. The fact that runs at absorption pressures ranging from 0.1 to 1 atm (at any one temperature) give

Jan 1, 1965

By R. A. Stauffer

The chief ore of lithium is spodumene, a lithium-aluminum silicate containing up to 3 pct lithium. The preparation of lithium salts from spodumene is costly because of the low concentration of the metal and the difficulty of separating it from the other alkali metals present. Dr. Kroll's and Dr. Schlecten's recent paper1 has reviewed various methods proposed for preparation of lithium. It will be seen from this paper that the methods proposed to date have required one or another of the lithium salts as a raw material. The high cost of these salts has been the chief item of expense in the lithium metal produced. This situation has made it interesting to investigate the possibility of producing the metal directly from spodumene. When spodumene is calcined at 1000ºC in the presence of lime, lithium oxide is replaced in the ore as is evidenced by the fact that it may be leached from the reaction mixture with water.2 Free energy calculations suggested that lithium oxide might be reduced with aluminum or silicon and the lithium produced distilled from the reaction mixture by heating-to about 1000ºC in a vacuum. These facts taken together suggested that it might be possible to prepare lithium metal directly from spodumene by heating a mixture of the ore, lime, and a suitable reducing agent in vacuum and distilling off the lithium metal as formed. The Replacement of Li2O in Spodumene A series of experiments were undertaken to determine the ratio of lime to spodumene necessary to free substantially all the lithium oxide Present in the Ore. The spodumene used in these experiments was supplied by Foote Mineral Co. in the form of powder of about 200 mesh' Analysis of the spodumene was as follows: PCT SiO2......................... 62.7 Al2O3........................ 29.9 Li2o......................... 4.9 Na2O........................ 0.89 CaO......................... 0.75 MgO........................ 0.49 K2O......................... 0.44 Lime (cp —200 mesh) was added in various ratios to spodumene and thoroughly mixed in a ball mill. Two hundred gram samples of spodumene-lime mixtures were charged loosely in fireclay crucibles and held at 1000ºC in a gas-fired furnace for 5 hrs. The product in each case was ground to pass 140 mesh and then placed in a thimble in a soxhlet extractor. Extraction with water was carried on for 6 hrs. After this period the extract was reduced in volume by evaporation in order to precipitate dissolved lime and was then filtered and titrated with 1/4 normal hydrochloric acid. After correcting for residual calcium oxide in solution, the alkali present was calculated as lithium oxide. The results of these experiments are shown in Table I and Fig I. At lime-spodumene ratios less than 1.5, the products were invariably fused. At the ratio of 1.5 and above, the product was loosely sintered with little evidence of fusion. When the ratio of lime to spodumene was three, replacement of alkali oxides in the

Jan 1, 1949

By R. C. Amero

FULLERS earth is a general name applied to claylike minerals that have high natural ad-sorptive powers. They are usually distinguished from ordinary clays by a higher content of combined moisture and a lower apparent density. The definition is based on the ancient use of the material for fulling, or cleansing woolen cloth of oil and grease; a more modern definition should mention the ability to decolorize oil and should differentiate between fullers earth, which is naturally active, and certain bentonites which only develop decolorizing power after being leached with strong mineral acids. The distinction between fullers earth and activable bentonite is not a sharp one, since all types of intermediate clays can be found that are more or less naturally active, yet more or less responsive to acid treatment. The differences seem to depend somewhat on the amount of leaching that has been effected by natural ground waters. Physical Properties The principal mineral constituent of activable bentonite is montmorillonite, a hydrous aluminum silicate to which the following formula is generally assigned: Al,Si,O,, (OH), • 12H,O Fullers earth, as well as bentonite, is usually composed of some variety of montmorillonite, but in the United States the largest tonnage of fullers earth is mined from deposits of attapulgite. Attapul- gite is a clay mineral composed of monoclinic crystals of colloidal size, having a fibrous shape similar to that of asbestos. A sectional model of the attapulgite "molecule" is shown in Fig. 1. A single unit is about 18.0 A wide and 12.9 A high. The length of the molecule is variable, but this same molecular pattern is repeated to form needlework crystals, rather than flakes, as is characteristic of the montmorillonite crystals. Attapulgite has been assigned the following formula,' although actually, the magnesia has been largely replaced by alumina: (0%) . (OH), • Mg, . Si, • Olp . 4H20. The fibrous nature of the mineral is clearly shown in the electron micrograph, Fig. 2. Although the deposits contain 5 to 30 pct quartz and carbonate minerals, impurities in the commercial products are held at a low level, principally by selective mining on the basis of oil decolorizing efficiency. The particle size distribution of this fullers earth has been estimated from settling rates, using sodium citrate as a dispersing agent.' Since Stokes' law only applies to spherical particles, the equivalent particle diameter calculated below is probably more nearly an index of diameter rather than length of the needlelike crystals: Eqnivalent Arbitrary Particle Distribution, Size Diameter Pci Classil3catian 0.05 mm 0.80 0.80 pct sand 0.05-0.02 mm 10.96 0.02-0.01 mm 9.65 42.10 pct silt 0.01-0.005 mm 11.40 0.005-0.002 mm 10.09 2-0.5 micron 10.61 0.5-0.2 micron 29.09 56.58 pct clay 0.2-0.05 micron 14.86 0.05 micron 1.96 The differential thermal analysis shown in Fig. 3 is unique and supports the theory that this is a distinct mineral species.' ~ Other general properties of the mineral as shown in Table I.

Jan 1, 1952

By D. R. de Fontaine

By computing the values of the resolved shear stress for a great many orientations of the tensile axis on all 12 (111) <110> slip systems, Taylor and Elam&apos; were able to map out a stereogram of slip systems, given here, Fig. 1, in Diehl&apos;s notation (see, for example Hauser and Jackson&apos;). The purpose of the present note is to derive such a stereogram by mathematical reasoning and to give a simple method of defining the system with highest resolved shear stress for any direction of the tensile axis, thereby eliminating tedious computation of the Schmid factor. Let the tensile axis, of direction cosines [xyz], make the angles 0 and relative to the slip plane normal [HKL] and the slip direction [hkl] respectively. Fig. 2 shows a simple cubic cell whose edges define a Cartesian coordinate system. Let A be a unit vector of origin 0 supported by the tensile axis. Its end point [xyz] then lies on a sphere of unit radius, on the positive hemisphere of which the planes z = 0, x = y, y = z limit the so called primitive triangle of a standard [loo] stereographic projection. For any point of this triangle, the following hold: 0«2 «y *sx « 1 [l] Now, for given [xpz], the most highly stressed system will be the one for which the following expression of the Schmid factor has the largest possible value: (HKL) belonging to the form (111) and [hkl] to the form <110>, the denominator on the right hand side of Eq. [2] is equal to 1.fi.a. The unknowns H, ... h, . . . can now be determined by correctly distributing +1 and -1 to H, K, L, and +1, -1,O to h,k, 1 giving the numerator of Eq. [2] its greatest positive value (the angles 0 and cpare chosen acute) subject to the condition: Hh+Kk+Ll = 0 [3] since the slip direction must lie in the slip plane. Condition [3] can be satisfied only by having one of its terms vanish and the other two equal to +1 and -1. Taking the case of the tensile axis lying in the primitive triangle, x2y, z and therefore Hh will be chosen equal to +1 with H = h = +1 in order to retain a maximum of + signs. There remain two alternatives: either 1 = 0 or k = 0. 1) take 2 = 0 Then Kk = -1 and the numerator of [2] becomes: Retaining a maximum of + signs gives L = k = +1 and becomes: 2) take k = 0 Then L1 = -1and, likewise, the numerator of [2] becomes: xz - z2 + xy + yz [5] But the difference [5] - [4] can be written: (y - z)(x+y +z) [6] positive or zero by virtue of [I]. If [6] is positive (y > z), then the largest possible value for the numerator of [2] for any xyz inside the primitive triangle is given by [5], i.e., for: That is to say, the active slip system corresponding to an orientat:~on of the tensile axis inside the primitive triangle is:

Jan 1, 1962