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By J. G. Eisele

Solvent-extraction characteristics of dodecyl phosphoric acid (DDPA) were investigated to determine its potential as a fractional or selective extract-ant for individual elements in a rare-earth-yttrium mixture. The DDPA is an effective extractant for splitting rare-earth mixtures into light and heavy subgroups. Yttrium normally extracts with the heavy rare-earth elements but may be shifted toward an extraction sequence with the light rare-earth elements by increasing the pH. Elements in the light and heavy ends of the rare-earth series can be separated from middle-group rare-earth elements by using diethylenetriaminepentaacetic acid (DTPA) as an aqueous phase counter-extractant. Hydrogen-ion dependency of the distribution coefficients differs from that reported for similar systems at tracer-level concentration.

Jan 1, 1965

By Ralph H. Whaite

The Bureau of Mines program for microfilming maps of abandoned mines in the Pennsylvania anthracite region is described. A catalog of the maps that have been microfilmed in the Eastern Middle anthracite field--the first area to be covered in the program--is presented. Additional catalogs will be published as significant mining areas are completed.

Jan 1, 1965

By F. M. Smith, R. H. Moore, J. R. Morrey

Electrodiffusion in y cerium reported by Henrie has been confirmed and a Preliminary estimate made of the relative rates of electrodiffusion of iron, cobalt, and nickel. These diffuse to the anode at rates decreasing in that order. In addition, copper and manganese exhibit slow, but detectable, diffusion to the anode and molybdenum exhibits detectable diffusion to the cathode. The electrodiffusion of carbon, .zirconium, antimony, magnesium , and silicon in y cerium could not be detected. Iron and cobalt diffuse in y cerium at rates proportional to the current density and with no apparent dependence on temperature. Decreasing polarization of iron and cobalt with increasing temperature, which cancels the expected rate increase, would account for this behavior. The electrodiffusion rate of iron in y uranium and in E plutonium has been measured. Diffusion of iron is anode-directed. Tin was found to diffuse to the cathode, in y uranium, at an appreciable rate. In all of these solvent metals, negative ions diffuse to the anode and positive ions to the cathode. The potential field effect appears to account satisfactorily for these results. FROM early experimental work summarized by Jost1 and Seith,2 the driving force for electrodiffusion was attributed to the potential field acting on ions in a metal. More recently, Heuman,3 Wever,4 and Huntington5 have shown that momentum interchange between conduction electrons and mobile entities in the metal contributes to electrodiffusion. Electron momentum interchange is anodically directed and the direction of diffusion resulting from the field force is dependent upon the charge on the diffusing entity. These two effects may either reinforce or oppose each other. Glinchuk6 has pointed out that momentum transfer in defect conductors should be cathode-directed and this appears to be the case as demonstrated by wever's4 work on iron. Barnett's7 work, on the other hand, indicates that, even in defect conductors, electrons show a negative E/m ratio when accelerated with respect to the lattice and should lead to anode-directed momentum transfer. In discussing this problem, Wever and seith8 suggest that defect electrons interact preferentially with activated ions so as to allow a net movement toward the cathode while still maintaining an electron momentum transfer in the anode direction. Williams and Huffine9 and Henriel0 have demonstrated that electrodiffusion may be useful for purification of yttrium and cerium. In yttrium, Williams and Huffine note that movement of several metallic impurities toward the anode is in keeping with observations in most other metallic systems and indicates that yttrium remains a normal electronic conductor at least to 1230°C. Close inspection of their data shows, however, that oxygen, nitrogen, and the transition elements diffused toward the anode, while nontransition elements diffused toward the cathode. This suggests that potential field effects may have been appreciable. The present work was concerned with the applicability of electrodiffusion as a technique for purification of plutonium, but, because of the obvious hazard inherent in work with this metal, experiments to develop the technique were carried out using cerium and uranium. The results of electrodiffusion measurements on these metals and on plutonium are reported here. EXPERIMENTAL The metal specimens prepared for this work were 6 in. long, 1/4 to 1/2 in. wide, and 1/16 to 3/32 in. thick. The uranium specimens were machined from a bar which analyzed 310 ppm Fe and the electrodiffusion of iron was followed by spectrographic and by chemical analysis. Cerium and plutonium specimens were cut from sheet rolled from ingots obtained from molten salt-metal equilibrations during which radioactive tracers were introduced. The electrodiffusion of the tracers was subsequently determined by counting methods. The specimens were electrolyzed between nickel electrodes containing resistance heaters used to equalize the specimen and electrode temperatures, thereby reducing thermal gradients. The temperature of the electrodes adjacent to the ends of the specimen was measured with chromel-alumel thermocouples which were connected to the heater controls. The surface temperature of the specimen at a point midway between the electrodes was measured with a sapphire rod pyrometer, the output of which controlled the dc power supply. This assembly was enclosed within an evacuable chamber containing a quartz viewing window. The temperature of the specimen over its entire length could be scanned with a portable pyrometer through

Jan 1, 1965

The Industrial Minerals Milling Section of the Mineral Processing Division has been engaged for the past three years in a study of the separation of minerals, by means of electronic sorting equipment, on the basis of their colour. Considerable knowledge of the subject has been built up. Because the object of this study is application as a means of beneficiation, a number of examples of the separations achieved are presented. Introduction T 0 the mineral collector, the colour of a mineral may be pleasing, even fascinating; to the mineralogist, student or professional, it may also be practical. It serves, to some extent, as a distinguishing feature in many minerals, and helps to fix with reasonable accuracy the identity of a few. It may now become a useful tool of the mineral dresser. The idea of using a difference in colour as a means of separation of one mineral from another is not new. Hand sorting dates back to ancient time. However, the means by which this can be done mechanically was developed only during the past decade. As far as the Mineral Processing Division is concerned, interest dates from March, 1960, when the following item was observed in the

Jan 1, 1965

By R. L. Solmer

During 1959-61, the Bureau of Mines investigated the strain and deformation induced in rock and concrete linings around mine openings by retreat panel caving at the Climax Molybdenum mine. Two concrete-lined slusher drifts on the Phillipson level of the mine were instrumented with both electrical strain gages and extensometers. Changes in strain and deformation were recorded over an 18-month period during the undercutting and caving of the mining panel. General agreement was found between the strain and deformation measurements and the hypothesis that the vertical component of the stress field on the openings is almost completely removed by undercutting. This phenomenon is a possible explanation for the structural failures that occur in the slusher drifts during the undercutting cycle.

Jan 1, 1965

By Gilbert M. Farrior

The electrical resistivity the coefficient of electrical resistivity the Hall coefficient, and the absolute thermoelectric power were determined in this Bureau of Mines investigation for nine compositions of the TiB2-CrB2 sub-system. The numerical values of the electrical resistivity and the thermo-electric power were greater for the intermediate compositions than for the end members. The absolute values of the Hall coefficients and the coefficients of electrical resistivity were less for the intermediate compositions than for the end members. The electrical resistivities and Hall coefficients were about the order of magnitude of most metals--from 34 to 202 microhm-cm and from about 0 to -23.3 X 10-4 cuP/coulomb. The thermoelectric power was somewhat greater than that of most metals--up to 15.6 microvolts per 0 C.

Jan 1, 1965

By Harry M. Conger

Kaiser Steel Corporation's Eagle Mountain Mine is located in the Colorado Desert, 60 miles east of Indio, California. Concentrates from the mine are shipped by rail 164 miles to the company's steel mill at Fontana, and also to Longbeach, California for export. Temperatures are typical of the lower desert ranging from a high of 120 degrees in the summer to a low of 25 degrees in the winter. The average annual rainfall of about two inches comes mainly as cloud bursts during the summer months. From its inception, the Eagle Mountain Mine has had the problem of breaking its mine rock. Practices followed from 1949 until 1962 were very costly, did not produce uniformly good fragmentation, and were incapable of sustaining high production. During this period, every conventional type of explosive then in use was tried and found to be unsatisfactory for one reason or another. The first slurry test work at Eagle Mountain was started in 195E and finally by 1962, after having tried all the slurry mixtures then available including some "home made" formulas, a metallized slurry was perfected at the mine which overcame all of the disadvantages of former blasting methods.

Jan 1, 1965

By J. M. Kuchta

Experimental data are presented on the autoignition temperature (AIT) characteristics of the hydrocarbon jet fuel, JP-6, in various oxygen-nitrogen atmospheres under conditions of constant volume and constant pressure. AIT's of this fuel in air varied little with fuel injection pressure but increased greatly with decreasing fuel content at low fuel-air-ratios. They also increased with decreasing oxygen content of the fuel vapor-oxidant atmosphere. Consistent with thermal ignition theory, the ignition temperatures increased with decreasing initial pressure, ignition delay, and vessel radius; expressions are given which define the observed variation of AIT with these variables for JP-6 fuel vapor-air mixtures. The significance of autoignition temperature data obtained using various ignition criteria is discussed to show the usefulness of such data in evaluating fire and explosion hazards. In addition, data are presented on the extent of oxidation that occurs prior to autoignition of this fuel in air at various temperatures.

Jan 1, 1965

By M. R. Geer

Samples of coal from six beds in the Roslyn-Cle Elum field of Washington were subjected to float-and-sink tests to determine their amenability to the production of high-ash boiler fuel for on-site power generation. Grindability tests and analyses of ash were made. All of the coals would require some degree of cleaning to insure a product of 25 percent ash. With two of the coals the entire size range would have to be washed. With the other four, it would suffice to clean only the coarse coal and bypass the raw fines.

Jan 1, 1965

By A. G. Weber, H. J. Welge

A published calculation method for predicting incompressible, multidimensional fluid displacement has been adapted to the problems of water and gas coning in oil wells. Since depth and radial distance from the wellbore are the two key dimensions affecting the shape of a gas or water cone, coning calculations are well suited to the use of two-dimensional methods. The alternating direction implicit procedure (ADIP) was used for relaxation calculations of two-phase potentials in a two-dimensional grid. From the potentials and the capillary pressure relationship, saturation and pressure distributions were calculated which trace cone growth with time. Predictions have been made for well producing histories both before and after core breakthrough. To check validity of the method, two-dimensional calculations have matched the coning behavior and produced water-oil ratio history of a laboratory sand-packed model. They have also matched the coning behavior of several producing wells, for which the calculations were compared with produced water or gas cuts and logs showing water or gas cone movements. INTRODUCTION The application of two-phase, two-dimensional calculations using ADIP to various reservoir flow problems has been described in the literature.1-3 When adapted for computer solution, this method has proved to be a powerful tool for simulating well and reservoir behavior. This paper discusses the method as applied to well coning calculations. Single-well and coning calculations comprise an especially difficult class of two-dimensional problems which require special techniques for computer calculation and determination of reservoir characteristics. Refs. 4 through 8 describe previous approaches to the coning problem. Several examples of water and gas coning calculations, including studies on both laboratory models and producing wells, are presented here. The two-dimensional method accounts realistically for the most critical parameters affecting coning behavior, including production rate, formation stratification, horizontal and vertical permeabilities, depth of well penetration, gravity and capillary forces. The method considers the different densities and viscosities of the two phases and the relative permeability and capillary pressure characteristics of the rock and fluids. In addition to tracing cone growth in the vicinity of the wellbore, the method calculates the overall movement of the fluid interface throughout the well's drainage volume. Incompressible fluid flow is assumed to occur between the producing interval and the well's limit of drainage. Calculations can be made for the producing history both before and after cone breakthrough. A typical two-dimensional grid or array of blocks used to solve a coning problem contains about 400 blocks. The well's cylindrical drainage volume can be represented by about 20 radial subdivisions and the formation thickness by 20 vertical subdivisions. The grid spacing is normally smaller near the withdrawal interval to define the cone shape accurately. For this work we used an IBM 7074 digital computer having a core memory of 10,000 ten-digit words. A typical study, covering 5 to 10 years of well producing history, required from three to six hours of computing time. MATHEMATICAL SIMULATION OF CONING BEHAVIOR BASIC METHOD In coning calculations, the reservoir volume drained by the producing well is represented by a two-dimensional system of blocks as shown in Fig. 1 for water coning studies. The horizontal dimensions of the blocks increase with radial distance from the well axis in geometric progression, i.e., the block size is small near the wellbore and large near the well's drainage radius (re). Vertically, the blocks are bounded by horizontal planes located at different depths through the

Jan 1, 1965

By Robert C. Johnson

Single crystal whiskers of ZrO2 and TiO2 were grown by solution and crystallization of these oxides in molten baths. Mixtures of Na2B407 and LiC1 were the most suitable growth media for zirconia. Sodium borate alone and Na2CO3 plus SiO2 were best suited for titania. The solubilities of zirconia and titania in molten sodium borate were determined, Whether zirconia whiskers were dendritic or nondendritic depended on the temperature used. The best single crystal whiskers were grown below 1,100° C. Titania whiskers always grew as single crystals. The tensile strengths of zirconia and titania whiskers were about 15,000 psi and 50,000 psi, respectively. Modulus of rupture was about 49,000 psi for zirconia whiskers and 75,000 psi for titania whiskers. Chemical analyses showed the zirconia and titania whiskers to be pure. The zirconia and titania whiskers were shown by X-ray analysis to be, respectively, baddeleyite and rutile.

Jan 1, 1965

By A. K. Mukherjee, J. E. Dorn, J. D. Mole

Investigations were carried out on the effect of polyslip on the strain hardening of aluminum single crystals. The orientations investigated were those lor which the tensile axis was in the [001], [111], [112], and [012] directions plus another for which the Schmid angles for {111}(110) slip were 1 deg. The experimental data were analyzed on a model based on the intersection of dislocations with particular emphasis on the effect of polyslip on the activation volume for inter-section. It is shown that the rate of strain hardening inreases for those orientations wherein attractive dislocation intersections occur and that those orientations which produce the greater number of such intersections exhibit the greater strain hardening. Good correlation of the data is obtained with the concept that attractive junctions, as proposed by Saada, Play an important role in accounting for the rate of strain hardening. EXISTING concepts on the nature and cause of strain hardening in fcc metals have been deduced principally from experiments on the deformation of single crystals under single slip. The effect of crystal orientation on the shapes of the stress-strain curves for single slip have been summarized by seegerl and more recently by Clarebrough and Hargreaves.2 Tensile specimens whose axes fall near the center of the [001]-[011] line of the standard triangle of the stereographic projection exhibit the longest range of easy glide (Stage I) and the lowest rates of linear hardening (Stage 11) whereas specimens whose axes lie near fie [001]-[111] line of the standard triangle have limited or no easy-glide range and exhibit somewhat higher linear strain-hardening rates. Specimens whose axes lie near the [001] or the [ill] poles do not exhibit easy glide and have the highest rates of linear hardening. Kocks3 has shown that the highest rates of linear hardening Occur under Polyslip when the tensile axis coincides with the [111] or the [ 001] pole. Since the rate of strain hardening is sensitive to specimen orientation and the incidence of polyslip, these relationships might help to discriminate between various dislocation models for strain hardening in fcc metals. Previous attempts to analyze the effect of orientation on strain hardening,1"3 however, did not provide a unique answer to this problem. Consequently the present investigation was undertaken wherein additional data, particularly that for the effect of polyslip on the activation volume for intersection, was also determined in order to provide more complete information on the details of strain hardening. Whereas analyses of these data reveal that several recommended models for strain hardening are at variance with the facts, good correlation of the data is obtained with the concept that attractive junctions4 play an important role in accounting for the rate of strain hardening. I) EXPERIMENTAL APPROACH seegerl demonstrated that slip in fcc crystals at low temperatures is dependent on thermally activated intersection of glide dislocations with forest dislocations. This has been confirmed by tests on single crystals of aluminum by Mitra, Osborne and Dorn5 and on polycrystalline aluminum by Mitra and Darn.' Thus in accord with Seeger's theory, the shear strain rate, ?, below a critical temperature, T, is where .V is the number of points of contact per unit volume between forest dislocations and glide dislocations, A is the area swept out per successful intersection, b is the Burgers vector, v is the frequency of vibration of the segment of the glide dislocation undertaking intersection, U is the activation energy for intersection, k is Boltzmann's constant, and T is the absolute temperature. For aluminum, which has an extremely high staeking-fault energy, the constriction energy is negligibly small and therefore the activation energy decreases practically linearly with the stress according to as will be recomfirmed later, where Uo is jog energy at the absolute zero, G and Go are the shear moduli at the test temperature T and O°K, respectively, L is the spacing of the forest dislocations, t is the applied shear stress for slip, and tGo is the stress field that must be surmounted athermally.

Jan 1, 1965

By John S. Berber

Tar produced as a byproduct from low-temperature carbonization of coal contains only small amounts of valuable lower boiling tar acids but relatively high percentages of high-boiling tar acids. These high-boiling tar acids are characterized by a high degree of alkylation and can be converted into the lower boiling homologs by catalytic treatment to remove the alkyl groups or decrease their chain lengths.

Jan 1, 1965

By J. B. Moritz

From the beginning, man has concerned himself with the task of controlling the elements and forces about him so as to provide a better and easier life. In the accomplishment of this task, he is required to utilize in the best way possible the resources which are available to him. In many cases, the available resources must bee refined before they are in a useable form. Many products in the mining industry fall into this category, as some form of refinement is generally needed to produce a saleable product. Over the years man developed more efficient ways of extracting the resources from earth through the use of electrical and mechanical devices. A reduction in manual labor, which is a by-product of increased efficiency through machines, has also been enjoyed. The combination of man's senses and new devices has also enabled man to reach a high level of control in the refinement process. Control of a process through machinery and man's senses has been termed an "art." Until recently man's senses (sight, feel) were the only method available for making measurements simply because suitable measurement devices (instruments) were not available. Even today some items cannot be measured and man's senses must be used. However, the development in our instrument laboratories tends to indicate that time will eliminate this. In recent years, control of many processes has been reduced to a science and part or all of the art eliminated. This does not imply that process art should be degraded; however, when a process is reduced to a science, uniformity of the product from day to day is attained. Decreased processing time and more efficient use of additives and raw materials are other benefits that result from control of a process when it is reduced to a science.

Jan 1, 1965

By P. M. Robinson, M. B. Bever

THE heats of formation at 273°K of the compounds InBi, In2Bi, and TIBi2 have been determined by metal solution calorimetry with bismuth as solvent. The published information on the thermody-namic properties of these compounds is limited. The structure of the compound InBi (mp, 383°K) is tetragonal of the PbO (B10) type.1 The compounds In2Bi (mp, 362°K) and TIBi2 (mp of highest-melting composition, 486°K) are now believed to have structures of the NizIn (B8) type273 and not the A1B2 (C32) structures reported earlier.4, 5 The compounds In2Bi and TIBi2 have limited homogeneity ranges at room temperature, while the compound InBi has no detectable homogeneity range.' Samples of the compounds were prepared from 99.99 pet Bi (Mallinckrodt Chemical Works), 99.999 pet in (American Smelting and Refining Co.), and 99.99 pet Tl (Amend Drug and Chemical Co.) by melting the components in sealed, evacuated Vycor tubes. The compounds InBi and in2Bi were of the stoichiometric compositions. The compound TIBi2 contained 40 pet T1; this composition was chosen because at room temperature the alloy of stoichiometric composition does not lie within the homogeneity range.' The melts were held approximately 50°C above the liquidus for 8 hr and then quenched into iced brine. The samples were homogenized for 48 hr at temperatures 20°C below the temperature of complete solidification. Metallographic examination of sections taken from the center and the ends of the ingots did not reveal second phases or segregation . The heats of formation were determined as the difference in the heat effects on solution of a compound and of a mechanical mixture of its components added from the reference temperature of 273°K to liquid bismuth at 623°K. The details of the calori-metric procedure and method of calculation have been described elsewhere? The calorimeter was calibrated by adding bismuth at 273°K to the bismuth bath at 623°K. The calculated values of the heats of formation of the compounds, listed in Table I, are based on a value of 4.96 keal per g-atom for the difference between the heat contents of bismuth at 273" and 623oK7 No published values are available for the heats of formation of the compounds InBi and In2Bi. Hultgren et a1.7 have calculated a value of -0.50 i 0.10 keal per g-atom for the heat of formation at 423°K of the compound TIBi2 containing 40 at. pet T1 from heat-content measurements in the range from 398" to 700°K and the heats of formation of the liquid alloy. The difference between this value and the value of -0.66 * 0.01 keal per g-atom at 273°K is too large to be attributed to a difference between the heat capacities of the compound and the components over the temperature range 273o to 423oK7 However, the direct determination of the heat of formation by a calorimetric method should give a more accurate value. The heats of formation at 273°K of the compounds InBi and In2Bi lie on a straight line when plotted as a function of composition, Fig. 1. The compound In2Bi, therefore, appears to be barely stable with respect to its neighboring phases. In order for the free energy vs composition curve to be concave towards the composition axis, the entropy change on formation of In2Bi must be more positive than that on formation of InBi. As the compounds are ordered,2, 3, 8 there is no configurational entropy change on formation. The difference between the entropy changes on formation of the two compounds, therefore, is probably associated with the vibrational entropies. In view of the low heats of formation, the changes in vibrational entropy, due to changes in bond strength on formation of the two compounds, are likely to be small. Owing to the volume contractions on formation of the two compounds,5 the vibrational entropies probably decrease slightly but the decrease of the vibrational entropy of InBi is expected to be larger than that of In2Bi.

Jan 1, 1965

By Arnold B. Hubbard

Automatic control instruments were utilized by the Bureau of Mines for routine assays of large numbers of oil shale samples and other bituminous materials. The standard Fischer assay method was automated by automatically controlling the heating cycles of a battery of 12 electric heaters with electronic controllers and programmers. The condensers were cooled with a modified automatically controlled refrigeration bath. The complete assembly consisted of 12 retort units, necessary control instruments, and the refrigeration bath. This equipment was capable of producing more consistent results than those previously obtained with the gas-heated retorts and of increasing the output of assays substantially with no increase in operating personnel.

Jan 1, 1965

By C. H. Schack

Extractive metallurgy techniques currently employed to recover silver from primary ores and secondary scrap were reviewed and evaluated to identify and delineate metallurgical problems whose resolution would increase the supply of silver from domestic materials. The survey revealed that practically all primary silver is recovered by froth flotation concentration of various types of ores, followed by smelting and refining of the separate lead, copper, and zinc concentrates. Silver losses during the complex processing are, with rare exception, inconsequential. Furthermore, any silver production gain from base metal ores, which contribute about two-thirds of the total primary silver, is directly dependent no improvement in the market for the base metals. Statistical data on new and old silver scrap are wholly inadequate to make reliable conclusions about scrap processing problems and the possibility of increasing the recovery of silver from the many forms of secondary silver-bearing materials. The available information indicates (1) that efficient silver reclamation practices are employed by the larger users of silver, and (2) that recovery of additional secondary silver involves solution of problems of collection rather than of processing. Several possibilities exist for limited increases in silver production from primary ores by improvement in metallurgical practices. Specifically, research is needed to (1) solve the problem of recovering silver from the copper ores of the Copper Range district, Michigan; and (2) devise economically feasible methods for recovery of silver from presently marginal or submarginal ores char because of grade, location, and frequently complex nature cannot presently be exploited by conventional techniques.

Jan 1, 1965

By G. L. Gates

The Bureau of Mines studied the scales formed in producing wells in the Wilmington field, California. The scales were primarily barium sulfate and resulted from the mixing of injected sea water and formation waters; there was excess sulfate in the injection water and the formation waters contained appreciable barium. After breakthrough, the produced brines were supersaturated with barium sulfate. Laboratory tests indicated that barium sulfate precipitated quickly When the supersaturated brines were agitated with crystals of barium sulfate and fairly rapidly when more sulfate solution was added. Precipitation occurred slowly on standing or under nonturbulent conditions. Both the apparent and equilibrium solubilities of barium sulfate in these brines were determined and compared with equilibrium solubilities in distilled water and sodium chloride solutions.

Jan 1, 1965

By R. E. Ogilvie, E. T. Peters

The X-ray Kossel-line method has been used preaioz~sly for measuring lattice parameters to accuracies of 1 part in 100,000.5 A second application of this method is described for determining the crystallographic orientation of a randomly positioned single-crysta1 spherical volume that can he as small as 50 µ in diameter, within accuracy limits of ±1/2 deg. The theory, experimental procedure, and interpretation of Kossel-line patterns and an experimenta1 verification of the predicted orientation relationship of the cph k and fee a Cu-Si phases are presented. This orientation relationship can be described as (111)a, (00.1)k; [110]a [11.0]k. In addition, the lattice parameter of the a phase was found to he a. = 3.62154 ± 0.00014Å. The Kossel-line method when used in conjunction with electron microanalysis is shown to he capable of providing a complete chemical and structural analysis of a given crystal. THE most easily accomplished methods for determining the orientation of a single crystal are variations of the Laue X-ray diffraction method. Although certain materials can be oriented to within ± 1 deg accuracy by observation of exterior macroscopic features, such as etch pits, cleavage faces, or growth features, the Laue method is generally preferred for routine laboratory application. Both back-reflection and transmission patterns are coordinated by appropriate reference charts and are plotted in terms of reflection plane poles (normals) on a stereographic projection. Orientation is deduced by relating the pole distribution (which is fixed by the crystallographic symmetry of the specimen) to two specified external reference directions. The Laue method has several limitations. 1) Orientation can rarely be determined to better than ±l deg accuracy. Principal errors involve inaccuracy in specimen-to-film distance, measurement confidence of individual Laue spots, and stereographic plotting. 2) Because of the indeterminacy of the X-ray wave length diffracted to a given spot, it is not possible to determine supplementary crystallographic data, such as interplanar spacings and lattice parameters. 3) The method is generally limited to specimens of cubic symmetry or to specimens of high symmetry and known structure. 4) The relatively large cross-sectional area of the incident X-ray beam generally precludes the measurement of relative grain orientation in a polycrystalline material.* _____ Several of these limitations can be overcome by application of the Kossel-line method, which has been previously employed for precision lattice-parameter determinations.'-= For this method, a point source of divergent monochromatic X-rays is generated within the crystal by means of an incident electron beam. The divergent X-rays which fulfill the Bragg law are diffracted by the specimen and are recorded on a film placed either in transmission or back reflection. Analysis of the film yields a direct measurement of orientation and lattice-spacing values to an accuracy of ±1/2 pct. As analyses can be obtained from spherical specimen volumes as small as 50 µ in diameter, the method provides a means for structural analysis of second-phase or impurity precipitates within a given matrix. The primary limitation of the Kossel-line method is the requirement for an electron microanalyzer or similar apparatus capable of producing a finely focused electron beam. This paper is designed to present the theory, experimental procedure, and geometrical interpretation of Kossel patterns. The experimentally determined orientation relationship between the k and a phases occurring in the Cu-Si system and a precision measurement of the a lattice parameter are presented as a practical application of the method. THEORY OF KOSSEL LINES Divergent X-ray beam photography utilizes an effective point source of characteristic X-rays which, when diffracted from a single crystal, form numerous diffraction and absorption cones that are recorded on film.7 The cones generated from a source lying within the crystal are called Kossel lines.' Although the X-ray scattering from a divergent point source contained within a crystal is described in terms of Laue dynamical theory,9 the directions of the diffracted spectra can be ade-

Jan 1, 1965

By P. G. Meikle, C. T. Holland

The effect of the condition of friction upon the ultimate unit compressive strength as determined between the compressed faces of precisely machined coal specimens and specially prepared testing platens has been examined. Reductions of 30 to 40% in the ultimate unit compressive strength of these model coal pillars have been verified when lubricants areused between the faces as compared to non-lubricated faces. Increase in unit compressive strength due to confinement at each of three levels of friction appears to follow generally the widely accepted "1/2 power law", i.e. S - C (L/T)1/2 where S is the unit ultimate strength, C is a constant dependent on the coal being tested and the coefficient of friction acting at the compression surfaces and L and T are the least width and thickness of the specimen, respectively. Results suggest that the surface condition of both the specimen and platens should be mentioned in detail in conjunction with compression testing, for although the term (L/T)1/2 is adequate for all practical purposes, the coefficient C is directly dependent on the condition of interfacial friction, all else remaining constant. One phase of the investigation of the confining effect of friction on the ultimate unit compressive strength of small coal specimens has recently been completed at the School of Mines of West Virginia University. The efficient control of ground is of fundamental importance to successful mining operations and the design of support pillars has always presented the mining engineer with a difficult and intriguing engineering problem. Since about the turn of the century, many investigators have performed extensive laboratory tests on small coal specimens in efforts to solve some of the perplexing problems of strata control and pillar action in coal mines. A detailed review of this work would serve no purpose here, but a brief mention of the more significant contributions is in order. Muller16 was perhaps the first to illustrate the effect of confining pressure on the strength of coal specimens in compression. His work has recently been more carefully expanded by the experiments of Murrell17 in Great Britain. Rice and Enzian l9 observed that as the size of cubical test specimens increased, the unit compressive strength decreased. These observations were later supplemented by Lawall and Holland, 13 by Greenwald4,5 et a1 at the U. S. Bureau of Mines, by Gaddy3 as well as by Steart,22 Millard15 et a1 and Evans2 et al. Gaddy3 seems to have been first to quantify this relationship with his equation: S = K/vd , where S - ultimate unit compressive strength (psi), K = a constant dependent on the coal, and D =edge dimension (in inches). Holland7 concluded that the strength of coal as affected by lateral dimensions and thickness could be expressed as where K = a coefficient dependent upon the coal, L = least width of pillar (in.) and T = thickness of pillar (in.). Data supplied by this formula have been compared to the estimated stresses in pillars that had been standing for long periods in coal mines and in the cases so far studied the results indicate that the formula predictions are sufficiently accurate for engineering purposes (Holland11 ). This equation therefore is believed to be the simplest and most accurate tool available at the present time for approximating the strength of a coal pillar (over a specified range of L/T) in situ. However, Holland7,9 has indicated that friction between the coal pillars and the top and bottom rock

Jan 1, 1965