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By A. G. Jordan, W. Jeitschko, Paul A. Beck

The occurrence qf the V phase structure /Zr,Co,Ge, type) in ternary syste7ns (titanium, zivconium, niobium, lanta1urn) -(nickel, cobalt, iron)-(silicon, germanium) was incestigated. Nine V silicides and four V gertrlanides were found and their lattice constants are reporled. The lattice constants of twenty-one preri-ously identified E phases (TiNiSi type) are given. The average atomic volumes of these phases are discussed in relation to similar binary phases. ThE occurrence of a phase Ti4Ni4Si7 was first reported by Westbrook. DiCerbo, and peat' who gave it the name "V phase". They also reported the existence of an E phase TiNiSi. Subsequently a systematic study was undertaken in this laboratory to explore the occurrence of E' and V phases3 in related ternary systems. In the meantime the crystal structure of the E phase TiNiSi 4 and of the V phase Zr4CO4Ge 75,6 was determined. In the present paper the details of the V phase investigation and the lattice constants of the E and V phases are presented. V PHASES Alloy specimens of approximately 10 to 15 g were prepared by arc melting under argon (99.996 pct Ar) atmosphere. The starting materials were all of purity higher than 99.9 pct, with the exception of cobalt. which contained 0.14 pct Fe as the only major impurity. The weight losses were in all cases less than 2 pct, in most cases less than 1 pct. The samples were encapsulated in fused silica tubes with sufficient argon to yield about 1 atm pressure at the annealing temperature. After the homogenization anneal. Table I. the specimens were water-quenched. A representative portion of each specimen was then examined metallographically (etchant: 20 pct HNO,. 10 pct HF. 25 pct glycerine, 45 pct H20). Only minor amounts of second- and third-phase particles were observed in the specimens listed in Table I, with the exception of alloys Zr4Fe4Si7 and Ta,Fe,Si,. which contained an estimated 10 pct by volume of foreign phases. X-ray powder photographs were taken with a Seeman-Bohlin type focusing camera and Fe-KO radiation. Of the thirty possible combinations of elements in the ternary systems (titanium, zirconium. vanadium. niobium. tantalum)-(iron. cobalt, nickel)-(silicon. germanium) thirteen V phases could be identified. In the remaining seventeen ternary systems and also in the systems Cr-Ni-Si and (M0.W)-(Ni.Co)-Si no V phase was found at the composition 4:4:7 after annealing at temperatures between 900" and 1200'C. For the determination of the lattice constants of the V phases Debye-Scherrer photographs were taken using the asymmetric film arrangement and CrKcr radiation (ka1, = 2.28962A). Using the positional parameters, as determined6 for Zr,Co,Ge,. Table 11. intensity calculations were carried out for each of the V phases with the aid of a computer program.: Thus unequivocal indexing of the diffraction patterns was greatly facilitated. The lattice constants. Table I. were then computed by a least-squares fit of the high-angle lines with f (0) = cos2 Q as extrapolation function. Only few. if any. very weak impurity lines were observed, with the exception of the three iron alloys Zr,Fe,Si7. Zr4Fe,Ge7. and Ta,Fe,Si7. The agreement

Jan 1, 1970

By J. S. Osoba, J. G. Richardson, F. M. Perkins

Laboratory experiments have shown profound diffcrences in the behavior of so-called "fresh cores" from the East Texes field and of the same cores after ex~ractio~l with organic solvents. The residual oil satura/ion remaining after waterflooding fresh cores was appreciably lower than the corresponding saturations after flooding extracted cores. This behavior was also reflected in the water-oil relative permeability-saturatiorl relations, which were more favorable for high oil recovery from the fresh cores. These differences were evident not only in the amount of residual oil left after wafer flooding, but also in the saturation water remaining in the core after displacernent by oil. Residual water saturation after displacernetzt of water by oil was higher in the fresh cores than in the extracved core,. Capillary pressure-saturation relations were also different for the fresh crnd extracted cores. Imbibition experiments indicated that both fresh and extracted Bast Texas cores imbibed water spontarteOLISIY, but- the rate of imbibition of water was higher for samp1es after. extraction than it was for fresh core. material. INTRODUCTION Several years ago a series of waterflooding tests was made in the laboratory on a number of Woodbine core samples from the East Texas field. These samples had been stored in containers open to the air and were extracted with organic solvents before they were subjected to the laboratory tests. After water flooding, the residual saturation of kerosene, which was the oil used in the tests, was found to average about 30 per cent. This saturation was higher than expected. In investigating the circumstances which might have been responsible for such a high residual oil saturation, attention was given to possible changes in wetting properties of the rock brought about by the procedure employed in extracting the cores. Preliminary results indicated that the explanation for the high residual oil saturation lay in the wetting behavior of the cores, though what effect extraction had on this behavior was not clear. In consequence, the work described in this report was undertaken in an attempt to investigate the mechanism responsible, and to ascertain the actual residual oil saturation to be expected in the reservoir after water flooding. It was soon found that there were profound differcnces in the behavior of so-called "fresh cores" from the East Texas field and of the same cores after extraction with organic solvents. These differences were evident not only in the amount of residual oil left after water flooding, but also in the saturation of watet remaining in the core after displacement by oil. The complete explanation of this behavior is not yet apparent. The description of work and results described in following sections, therefore, must be considered as an interim report presenting facts which must await additional information before they can be fully interpreted.

Jan 1, 1956

By Arthur F. Taggart

The major portion of the work described in this paper was performed by R. W. Young, † a graduate student in the department of Mining and Metallurgy, Sheffield Scientific School, Yale University, working under a cooperative agreement between the Hardinge Conical Mill Co., the Sheffield Scientific School, and himself. Since this cooperative scheme is at present in effect in the case of a considerable number of other students in the department and since it is the hope of the school that the privilege thus extended may be utilized even more freely in the future by mining and manufacturing companies, it may not be amiss at this point to give a summary of the general plan. Briefly it is as follows: A graduate student, whose undergraduate work in this or other universities shows promise of ability to handle research work, is chosen by conference between the company and instructor involved. The aim of the company in the agreement then entered into is to obtain the solution of one or more of the technical problems with which it may be confronted, or, at the end of 1 or 2 years, to obtain as an employee a man especially trained in its work. As a means to accomplish one or both of these ends, the company furnishes the machine, apparatus, or material to be tested and pays the student during his graduate work a small salary, usually just sufficient to cover his living expenses, tuition and fees. The aim of the student is special training along a line in which he is particularly interested, the attainment of his advanced degree, and the chance to show to his future employer ability to handle such problems as may be presented to him. In return for the financial aid which he receives he agrees to devote at least half of his working time to the special problem submitted by his company. The other half is devoted to study of the collateral subjects required by the department for the granting of the degree which the student seeks. The student further agrees to enter the employ of the company in question at a wage not greater than that paid in like positions to recent graduates not specially trained and to remain with his employer at such wage for at east 1 year. If the student is to obtain a degree, the special work forming the basis of his investigation must be such as will involve real research and not mere routine manipulation. The subject is chosen by conference between the three parties to the agreement. The work is carried on under the direct supervision of the instructor involved. The school furnishes the general laboratory and library equipment essential to the pursuit of any extended investigation. In

Jan 1, 1918

By Edward Wisser

The environment of an ore body is taken to mean not only its physical surroundings but every factor, passive or active, that conditioned the ore shoot, saving only the original composition of the solutions that formed the shoot. Collection of data related to the shape and characteristics of veins should be followed by correlation of the data and the formulation of generalizations regarding ore formation. The nature of the criteria used in arriving at these generalizations is discussed. Certain of the criteria, when used with an understanding of their underlying causes, become "ore-guides." In the course of his study the geologist must not confine himself to the immediate surroundings of the veins, but should attempt to work out the geologic history of events culminating in the crucial epoch for any mining district, the period of mineralization. The work may involve study of features far removed from the veins and related to them only indirectly. It commonly means thorough study of the geology of the entire region surrounding the ore deposits. The following question has been suggested for discussion: "Are there any criteria by which one can determine when mining operations have reached the roots of an ore deposit?" The question deals less with the roots of a particular ore body than with the lower limit of the vertical range within which ore bodies may be expected. It concerns a critical line upon the longitudinal vertical projection of a vein.† Below this line it is useless to look for ore shoots; above the line exploration below the bottoms of individual ore shoots may be justified. Can we learn to determine the position of such a line? In some multivein districts the line for any given vein may be approximated by simple interpolation or extrapolation. Where this is possiblc the bottoms of the lowest ore shoots in the various veins are points on an imaginary, gently rolling surface. The trace of this surface upon the vein is our critical line for that vein. The imaginary surface rolls so gently that it may be projected from two or more known veins to an unexplored vein near by. Here is a criterion for the bottoming of ore that has nothing to do with changes in the appearance of the vein in question; it rests solely on the depth at which the ore bottomed in adjacent veins. The method is not applicable in districts only slightly explored in depth, nor where the lower limit of the ore-bearing horizons

Jan 1, 1941

By G. Gutzeit

METAL-ORGANIC INNER COMPLEXES AN inner complex is a cyclic chemical structure containing an inorganic cation that is bound simultaneously to several atoms in a single organic molecule; on the one hand by means of ordinary valence bonds (electron exchange), on the other hand through the action of the electric field thus created, which satisfies the so-called secondary valences. The relative positions of the salt-forming and complex-forming groups are such that most frequently a four, five, or six-membered ring results through this double attachment of the cation.1-6 The formation of inner-complex ring systems depends not only upon the nature and suitable position of the salt-forming and complex-forming groups for ring closure, but, to a great extent, also on the nature of the metallic cation entering the reaction. This selective character of chelate-forming organic compounds is one of their most interesting and most valuable properties. As a matter of fact, the largest number of their practical applications is based upon their specificity. 4,1-13 Once a chelate compound is formed, its character is definitely "organic" in nature. In other words, its properties are conditioned to a much larger degree by the carbon chains or rings than by the metallic atom. Many inner complexes are soluble in nonpolar solvents such as benzene, paraffin oil or carbon tetrachloride, while the chelate-forming reagent before closure of the metal-organic ring is water soluble. (Example: copper complex of salicyl-aldoxime.) It is obvious that such particular properties as those indicated above can be utilized whenever specificity and practically complete binding of inorganic ions into an undissociable complex are required. One of the well-known applications of chelate-forming compounds has been the development of specific reagents in analytical chemistry,, creation of the spot-test method,4,14-16 and the application of the same principles to the contact print method for determining minerals.17 CHELATE-FORMING COMPOUNDS AS COLLECTORS In the field of flotation, where selectivity is often a quality of paramount importance for the collector, various workers have lately attempted to apply their knowledge of specific organic analytical reagents to this purpose. A. C. Vivian18 has concentrated cassiterite by using ammonium nitrosophenylhydroxylamine (Cupferron) C6H5NO(=NONH4). Holman19 has tested dimethylglyoxime for the flotation of nickel oxide minerals, while deWitt has shown in a series of systematic experiments that alpha-dioximes were generally selective collectors for nickel ores. Taurin NH2(CH2)2SO3H has been proposed for the concentration of oxidized lead ores.19 Diphenylthiocarbazone

Jan 1, 1946

By Edward Wisser

The environment of an ore body is taken to mean not only its physical surroundings but every factor, passive or active, that conditioned the ore shoot, saving only the original composition of the solutions that formed the shoot. Collection of data related to the shape and characteristics of veins should be followed by correlation of the data and the formulation of generalizations regarding ore formation. The nature of the criteria used in arriving at these generalizations is discussed. Certain of the criteria, when used with an understanding of their underlying causes, become "ore-guides." In the course of his study the geologist must not confine himself to the immediate surroundings of the veins, but should attempt to work out the geologic history of events culminating in the crucial epoch for any mining district, the period of mineralization. The work may involve study of features far removed from the veins and related to them only indirectly. It commonly means thorough study of the geology of the entire region surrounding the ore deposits. The following question has been suggested for discussion: "Are there any criteria by which one can determine when mining operations have reached the roots of an ore deposit?" The question deals less with the roots of a particular ore body than with the lower limit of the vertical range within which ore bodies may be expected. It concerns a critical line upon the longitudinal vertical projection of a vein.† Below this line it is useless to look for ore shoots; above the line exploration below the bottoms of individual ore shoots may be justified. Can we learn to determine the position of such a line? In some multivein districts the line for any given vein may be approximated by simple interpolation or extrapolation. Where this is possiblc the bottoms of the lowest ore shoots in the various veins are points on an imaginary, gently rolling surface. The trace of this surface upon the vein is our critical line for that vein. The imaginary surface rolls so gently that it may be projected from two or more known veins to an unexplored vein near by. Here is a criterion for the bottoming of ore that has nothing to do with changes in the appearance of the vein in question; it rests solely on the depth at which the ore bottomed in adjacent veins. The method is not applicable in districts only slightly explored in depth, nor where the lower limit of the ore-bearing horizons

Jan 1, 1941

By R. F. Evans, J. M. Avert

Much has been written of the glamour of magnesium from sea water, the Aladdin-like creation of a huge magnesium plant in the Nevada desert using cheap hydroelectric power from Boulder Dam; the marvels of the Hansgirg process for the electrothermal reduction of magnesium oxide by carbon, and the ferrosilicon process for producing magnesium from dolomite. This is the story of the production of magnesium by the electrolytic process, using steam-electric power supplied by a public utility, in a plant at Painesville, Ohio, 30 miles east of Cleveland on the shore of Lake Erie. The story is not without interest, since it involves several unique developments that provide the answer to a question frequently asked: How is it possible to produce magnesium metal economically at such a location as Painesville, Ohio? Basically, the answer lies in making use of facilities already in existence for the production of soda ash, which makes it possible to manufacture magnesium chloride, the principal raw material, cheaply enough to offset the high cost of electric power. To this is coupled the successful conversion of by-product chlorine into a product required for the war program. The source of magnesium for this opera- tion is the enormous surface deposit of high-grade dolomite in the region south of Toledo, within reasonable freight haul of Painesville. This same geological stratum underlies the Painesville plant, but unfortunately at a depth of about 3000 ft.— apparently too great a depth to permit underground mining to compete with the delivered cost of rock from surface quarries in other areas. The cost of dolomite obviously is an important factor, since the rock contains only some 12 per cent magnesium (20 per cent MgO) so that one dollar on the cost of stone means more than $8 in terms of its magnesium content, and more than that in terms of recoverable magnesium metal. Production of Magnesia from Dolomite In the summer of 1941, the Diamond Alkali Co. was well along with construction of a plant intended for the commercial production of refractory and other grades of magnesia from dolomite. The process to be used was designed to make maximum economic advantage of existing plant and operations by tying the production of magnesia in with the manufacture of soda ash in such a way as to make use of the lime [CaO)., value of calcined dolomite. The process finally adopted after a lengthy research and development program has much in common with the old Clerc-Nihoul process, but includes certain innovations found to be necessary or advantageous. Essentially, the process is based upon the following series of reactions:

Jan 1, 1949

By Elmars Ence, Harold Margolin

The partial isothermal section of the Ti-Cu-Zr system at 750°C has been studied. The crystal structure of Ti2Cu has been detevnlined as tetragonal and when expressed as face-centered tetragonal, a = 4.164, c = 3.611 A, and c/a = 0.867. TITANIUM systems in which ß-titanium decomposes eutectoidally into a and a compound rather readily are known as active eutectoid systems. Recently in active eutectoid alloys based on the Ti-Cu system, and containing additionally A1 and Zr, it has been found that zirconium may produce both moderate weakening and marked strengthening at elevated temperatures.' In order to obtain some insight into the behavior of zirconium, an attempt was made to determine whether compounds of the type Tix Zr and TixZryCu exist. Only results of the Ti-Zr-Cu studies are reported here since data on Ti-Zr alloys will be presented in a separate publication. EXPERIMENTAL PROCEDURE Alloys were nonconsumably arc melted in argon atmosphere as 15-g buttons, prepared from materials of the following purities: Bureau of Mines electrolytic Ti — Bhn 63 OFHC copper Reactor Grade Zirconium Bhn .C 150 Prior to alloy preparation the electrolytic titanium was premelted to avoid excessive spattering of the charges during melting. The weight losses during melting did not exceed 1 pct of the total weight of the charge. The alloys prepared are listed in Table I together with analyzed compositions. in cases where they were determined. Specimens for heat treatment were wrapped in molybdenum sheet, annealed in argon-filled quartz capsules, and quenched by breaking the capsules under iced brine. About 1 to 2 sec are required to remove the capsule from the furnace, drop it into the iced brine and break it. Because of the insulation effect of the quartz, this delay in quenching should not produce a large drop in temperature. In many instances, no difference or little difference has been detected between the same specimen quartz capsule quenched or directly quenched in vacuum by an impinging stream of water.' Ti-Cu-Zr alloys were homogenized for 48 hr at 825°C prior to annealing at 750°C. Annealing for 5 days at 750°C produced the same results as 11 days at temperature and it was therefore assumed that 5 days was sufficient to establish equilibrium. Titanium-copper alloys were homogenized for 40 hr at 900°C prior to heat treatment for 6 days at 750°C. Specimens for metallographic examination were electropolished and etched with the following solution:

Jan 1, 1962

By H. L. Barr

THE following report covers the history of the development of the mine, present equipment, methods and costs of mining and milling. In addition, a description of the ore deposit is given with emphasis on the origin of the fractures, mode and types of ore occurrence, and mechanics of granite emplacement. An endeavor has been made to present a complete and accurate statement of the San Mauricio mine, the highest grade gold mine in the Philippine Islands. Credit is gratefully acknowledged to the mine staff for descriptions and details regarding their particular field of work. All analyses were made by Mr. T. A. DeVore, head chemist, San Mauricio Mining Co. Messrs. Edward Wisser, J. E. Fyfe, A. F. Skerl and W. B. Meek, geol-ogists, have contributed geologic information and ideas, for which thanks are extended. The Executive Committee of Marsman and Co., Inc., Managers of the Company, has kindly given permission for publication. Mr. J. B. Stapler, Division Manager, Marsman and Co., has had the courtesy to read the manuscript and to give critical and helpful suggestions.

Jan 1, 1940

By R. N. Thurston, E. A. Nesbitt, G. Y. Chin

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deformation gradient matrix, F - [axi/aXj1, where X and x refer to the initial and final positions of a particle. This matrix is readily evaluated in terms of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip system. In the case of deformation from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Goler and Sachs.4 Taylor and Elam5 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(dN as N — m while a — 0 in such a way that the Product Na = 0, a ftnite conslant designatzng the accunzulated amount of shear. It turns out that this limit is simply , where F, is the matrix whose elements are the coefficients of a in the F(a) matix. Application is made of the present treatment to a fcc crystal of Perlrzalloy compressed on the (110) plane and contrained to elongate zn the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By R. L. Dalton, L. A. Rapoport, C. W. Carpenter

Procedures have been developed to study the performance characteristics of unconfined pilot water floods using scaled laboratory models. The effects of operating conditions on pilot performance for variozrs well patterns have been investigated. The limitations of the laboratory model studies are outlined. Relationships between the oil recoveries of pilots and large-scale floods have been established. The applications of model studies to the prediction of large-scale waterflood performance and pilot flood design are discussed. INTRODUCTION Pilot water floods are undertaken to evaluate operational procedures and to gain advance information about the performance of an extensive water flood. In general, however, the performance of a pilot flood is not directly indicative of what can be expected from a large-scale pattern water flood. This difference stems from the fact that the over-all flow configurations are not the same for the two systems. A water flood normally consists of an array of identical well patterns. In such an array, the perimeters of the well patterns are axes of symmetry and act as impermeable boundaries. Thus, an extensive, pattern water flood can be visualized as a repetition of "confined" floods. In contrast, a pilot water flood involving only one or a few well patterns is "unconfined". Here the well patterns are not balanced by other flood units; hence, the perimeter of the pilot area does not act as an effective boundary. Accordingly, only a portion of the fluids injected (and also of those originally contained within the pilot area) is captured by the producers of the pilot. The rest escapes into the surrounding reservoir. This usually causes the amounts of oil and water produced in the pilot to be different from those recovered by a producer in an extensive water flood. Moreover, the recovery observed in the pilot can be expected to be greatly influenced by operating conditions, i.e., by the bottom-hole pressures at the injection and producing wells. The above considerations show that full utilization of pilot test results and reliable prediction of large- scale water floods require a knowledge of the relationship between the recovery performance of confined and unconfined well patterns. To date, only limited basic information is available on the behavior of pilot water floods. Craig, et al,' have investigated the effects of initial gas saturation, oil-to-water mobility ratio, and well damage on the oil recovered from a single, "normal" five-spot pilot pattern (Fig. 1). Rosenbaum and Matthews2 studied the effect of initial gas saturation and mobility ratio on the ratio of production rate to injection rate for various groupings of five-spot patterns. Paulse113 investigated the effect of mobility ratio and distance from the pilot to the edge of the reservoir on the areal sweep in a single "inverted" five-spot (Fig. 1). However, none of these studies considered the effect of operating conditions on pilot flood behavior. Moreover, hardly any of the work to date dealt explicitly with the oil-recovery performance of the pilot floods. The purpose of this paper is to introduce the concept of interrelation between pilot flood behavior and operating conditions, to illustrate this interrelation by means of experimental data and to compare the recovery performances of dif-

By J. P. Hirth, C. S. Hartley

A simple graphical technique is presented for rapidly determining the ratio of resolved shear stress on slip systems in single crystals to the applied stress (Schmid factor) for various simple states of stress. Master plots are presented which, when used in conjunction with an appropriate stereo-graphic projection, allow one to determine the Schmid factor for all slip systems in a crystal of given orientation. It is shown that one such plot suffices for simple tension or compression, flex-ural bending, and biaxial compression, while a combination of two different plots must be used for torsion and simple shear. STUDIES of the deformation behavior of single crystals are most valuable when the applied stresses are resolved onto the various slip systems of the crystal. A careful study of the available slip systems and proper selection of the state of stress used and the specimen orientation can then yield quantitative information about the probability of specific dislocation reactions, the strength of barriers to plastic flow, and the mechanisms of yielding and flow in general. It is the purpose of this work to analyze some common states of stress used in deformation studies and to present a simplified way of determining for these cases the ratio of the resolved shear stress on the slip systems to the applied stress (Schmid factor). I) CALCULATIONS We first define two orthogonal coordinate systems: one based on the specimen geometry (a right circular cylinder of radius, R, is considered here) and one based on the particular slip system of interest. The unit vectors and angles specifying the two coordinate systems and the relationship between them are listed in Table I. The relationships among the various angles and unit vectors are shown on a stereographic projection in Fig. 1. The transformation matrix between the (XI X2 X3) and (x'1 x'2 x'3) system is x1 x2 x3 X'1 a11 al2 a13 x'2 a21 a22 a23 x'9 a31 a32 a33 where in this case the direction cosines aij are given by a11 a12 a13 aij = a21 a22 a23 a31 a32 a33 sin 0 cos F cos 0 sin F cos 9 = -cos 0 cos F sin 0 sin F sin 6 [1] 0 -sin F cos (p In terms of Eq. [I.], the stresses sij, referred to the slip system, are determined from oij, referred to the specimen axes, by1,2

Jan 1, 1965

By J. D. McClung

INTRODUCTION The ever increasing demand for coal sues that meet exacting specifications has made necessary the installation of thousands of dollars worth of crushing equipment by the coal industry. At one time the operator at- tempted to recover as much lump as possible but today he is confronted with the necessity of crushing to facilitate the mechanical cleaning process and to meet the demand for a variety of uniform sizes. As a matter of fact, about 65 percent of the coal mined in the United States today goes through preparation plants where it is crushed and cleaned. One becomes more aware of the importance of the art of comminution when it is realized that practically all of the operations in mining are involved in comminution in one way or another. Whether the coal is mined conventionally or by continuous miners it is separated from the solid by a breaking, ripping or milling action which essentially amounts to a comminution operation. Even degradation resulting from material handling from the mine working face to the preparation plant might in a broad sense be so classified, Then of course crushing is usually necessary in the plant before the coal is ready to be marketed. THEORY Despite the various comminution operations there is a lack of satisfac- tory information concerning the fundamentals of crushing and their relation to the variable factors associated with the operation. There are certain laws and theories on mechanical reduction, such as those of Rittinger, Kick and Bond that are helpful and useful. The difficulty in developing exact mathematical relationships for specific crusher applications is due to the many variable physical characteristics found in coal. Hardness, as measured by the Hardgrove grindability index, is one parameter that has been used for years to determine the resistance of coal to comminution. While the coal properties as measured by grindability are complex, recent work has shown that a high correlation exists between the grindability of some coals and their petrographic analysis. Early research on the hardness of petrographic entities from an Illinois coal2 demonstrated that durain was the hardest constituent followed by clarain, vitrain and very soft fusain. Other research demonstrated that, for different size fractions of the same coal, a wide variation in hardness commonly exists. For example, the fines in about half of 39 coals studied were softer than their corresponding coarse sues while most of the remaining coals were uniformly hard in all sizes. A few coals contained fines which were harder than their coarser constituents. These variations in hardness give insight into the heterogeneous nature of coal.

Jan 1, 1968

By R. C. Davis, R. F. Berry, G. W. White, B. T. O’Connell, L. A. Stacha

The formation density logging tool provides a radioactivity measurement that yields formation densities in situ. The relationship between bulk density and porosity is well understood. With knowledge of grain and fluid densities, porosity may be computed from the indicated formation bulk densities in shale-free formations. The porosities thus determined may be used with a resistivity log for water-saturation determinations. One technique utilizes a density vs resistivity plut. A plot of density vs Sonic-log transit time is used for porosity determinations in shaly sands. This method is particularly suited to wells drilled with oil-base or salt muds. In shale-free formations, comparisons of density values nnd neutron-log readings are used to identify lithologr and, thus, to select appropriate values of grain density for porosity computations. Through the use of Formation Density, Sonic and neutron logs, the interpretation problems caused by complex matrix lithologies are simplified. Other applications of the Formation Density log are found in the identification of minerals in evaporite deposits and in yield determinations of "oil shales". INTRODUCTION Widespread field application has demonstrated that the measurement of formation density is a useful and revealing technique for well logging. Responding to the bulk density variations of the formation, the Formation Density log affords valuable data on the porosity, lithology and fluid content of the formations. Although not without its own limitations, the Formation Density tool may provide effective interpretation under conditions that hamper or preclude the use of other porosity devices. When used in conjunction with other devices, such as the Sonic or neutron, complex matrix conditions may be better understood, defined and evaluated. A previous paper' described the valuable contribution of the Formation Density tool in the logging of empty, or gas-filled, holes. The purpose of the present paper is to describe applications of the device in liquid-filled holes. THE FORMATION DENSITY TOOL The Formation Density tool was devised to measure the bulk densities of formations in situ. Actually, the device responds to electron density, but in the overwhelming majority of cases of interest, the electron density is very closely proportional to the bulk density. In other cases appropriate corrections can be made if necessary. Comparisons of log-derived densities with true densities for the more common matrix minerals are shown in Table 1. The tool consists of a gamma-ray source and detector mounted in a skid which, during the logging operation, is in contact with the borehole wall (see Ref. 1 for schematic). Gamma rays are emitted by the source and diffused through the formation. The number of diffused gamma rays reaching the detector at a fixed spacing from the source are counted. An increase in counting rate by the detector indicates a decrease in bulk density in front of the skid. Conversely, a decreased counting rate signifies an increase in bulk density. A measurement of hole diameter, between the face of the skid and that of the eccentering arm, is recorded simultaneously with the measurement of diffused gamma rays. Since the tool is a wall-contact device, the size of the borehole has little influence, provided good contact is maintained with the wall of the hole. Only in extremely large or small boreholes does the actual diameter become significant. However, for most accurate measurements the borehole size should be taken into account. Fig. 1 presents the departure curves for the conversion of counting rate to bulk density for liquid-filled holes of various sizes. It is of utmost importance that the skid maintain good contact with the wall of the hole. If, due to roughness or caving, there is mud between the skid and the formation, the tool will include in its response the relatively low-density mud, and the apparent density reading will be too low. Normally, permeable beds do not cave appreciably, so that reliable readings are usually available for zones of interest. Nevertheless, the caliper reading over the zone of interest should be examined for any wall roughness. When mud cake exists between the skid and the formation, the Formation Density log sees it as part of the formation. When thick mud cakes exist, a correction is required. For best results in wells having thick mud cakes,

By Loyd R. Kern

A procedure for determining the behavior of a reservoir under a gas or water injection program was reported by Buckley and Levertt in 1942.1 This method, which allowed the calculation of the phase saturation distribution behind the front of a displacing fluid, has been extended to apply to a more general situation. The reservoir may initially contain flowing quantities of the displacing fluid, or the fluid in the reservoir may be above saturation pressure SO that solution effects are present. Production may occur behind the front as in the case of a well which is produced after breakthrough of the displacing fluid. The calculating procedure is simplified in that the graphical integration necessary to determine breakthrough saturation is eliminated by performing a direct integration and the graphical differentiation necessary to determine saturation distribution is eliminated by representing the displacing phase fraction of the flowing stream by an empirical equation. This representation results in simple expressions for the producing gas or water/oil ratio and cumulative production. INTRODUCTION A method for the calculation of the saturation distribution behind the front (interface between the displaced and displacing phases in a gas injection or water flooding operation) was reported by Buckley and Leverett in 1942. The method leads to a curve for the saturation distribution which is double-valued; consequently, part of' the curve was interpreted to be physically meaningless. That part of the curve which has physical significance was determined by a graphical integra-tion (material balance). In this paper it is shown that the integration may be performed analytically with a resulting equation for the saturation of the displacing phase at the front. The case in which the displacing fluid is initially flowing and the case in which the reservoir is initially above the saturation pressure so that some injected gas goes into solution are included in the integration. The calculations are considerably simplified by representing the fraction of the flowing stream which is oil by an exponential function of saturation. The methods is extended to apply approximately to reservoirs in which wells located between the injection well and the front are produced. An illustrative example utilizing the methods presented is included. RESERVOIR BELOW SATURATION PRESSURE In the case of a water flooding operation or in the case of a gas injection operation in which no gas goes into solution in the displaced oil, the equation for saturation in a linear flow system as a function of time and position as given by Buckley and Leverett is where* q = total reservoir volume flow rate, rvb/day A = cross sectional area of system, sq ft / = porosity of formation x = distance from injection point, ft t = time, days Pj = saturation of the displacing phase /dx velocity of planes of constant saturation, ft/day *The nomenclature used here is not the same as that used by Buckley and Leverett A complete nomenclature is given in Appendix A.

Jan 1, 1952

By W. D. Potter, E. T. Peters

Single-crystal films of boron have been prepared by thermal reduction of purified BCl3 with subsequent deposition of boron onto oriented silicon substrates. The structural properties of films prepared under various experimental conditions have been determined by light microscopy and "grazing-" angle electron-diffraction analysis. An orientation relationship is proposed for silicon and a-rhombo-heclral boron which can be described as: (111)Si (112)B; [110]Si [110]B ElEMENTAL boron is known to have a high energy gap* and consequently has potential value as a high- *Energy gaps of 1.35 to 1.55 ev1-3 and 2.0 ev4 are reported for ß-rhombohedra1 and a-rhombohedra1 boron, respectively. temperature semiconductor.5 Exploitation of this property, however, has been hampered by the unavailability of pure, single-crystal boron. Two recent symposia6,7 have treated the subjects of purification, crystallization, crystal structure, and properties of boron and provide a foundation for further investigation in these areas. The structure, lattice constants, and observed ranges of stability for four reported polymorphs of boron8°12 are listed in Table I. The rhombohedral structures are generally accepted as true polymorphs whereas the tetragonal structures are believed to be transient. Most currently available single crystals of boron are grown by Czochralski and floating-zone methods. Unfortunately, these crystals generally contain numerous defects and are highly strained as a result of the polymorphic transformations and thermal contractions which accompany cooling. Recently, Armington, Potter, and Tanner13 have reported the formation of single-crystal films of boron on silicon single-crystal substrates through thermal reduction of BC13 by hydrogen. Boron E. T. PETERS, Junior Member AIME, is Senior Scientist, ManLabs, Inc., Cambridge, Mass., and W. D. POTTER is Research Chemist, Air Force Cambridge Research Loboratories, L. G. Hanscom Field, Bedford, Mass. formed at temperatures near 1000°C was identified as the a-rhombohedra1 form, consistent with expectation. The present paper describes a continuation of this work with specific reference to characterization of the structural features of the deposited boron films. The ultimate goal of this program is to produce large-area single-crystal films of a-rhombohedra1 boron to be used for electrical and optical studies by other workers. PREPARATION OF BORON FILMS The experimental procedure of preparing thin films is similar to that described by Theuerer14 for the epitaxial growth of silicon by thermal reduction of SiC14 and has already been described as applied to the preparation of boron thin films.13 Briefly, a mixture of BCl3 vapor and dry hydrogen is passed over a heated silicon substrate. Thermal reduction of the BC13 allows deposition of boron on the substrate. The substrates were {111}-oriented, single-crystal silicon. Square specimens 0.63 cm on an edge by 0.1 to 3.0 mm thickness were prepared by

Jan 1, 1965

By E. L. Jr. Spain

THE deposits described in this paper occur over much of Wayne County and in the southeast portion of Hardin County, Tennessee, and in the northeast and northwest portions of. Mississippi and Alabama respec-tively. The presence of tripoli in this region has been known for some time and descriptions of various occurrences in Tennessee have been made by Jewell1 and Miser2, while Hilgard3, Lowe4 and Logan5 have treated the deposits that occur in the adjacent portions of Alabama and Mississippi, but there has not been a general survey of the entire field summarizing completely the geology of the deposits with respect to their origin and stratigraphic relationships. During 1934, while engaged in surveys of mineral resources through this region for the Tennessee Valley Authority, the writer collected data with this in mind, and has assembled them in this report. He is indebted to H. S. Rankin and N. A. Rose, of the Tennessee Valley Authority Geology Division, for field assistance.

Jan 1, 1936

By S. R. Balajee, I. Iwasaki

The adsorption mechanism of corn starch and its derivatives at mineral-solution interfaces was investigated by the adsorption of cationic starch, unmodified corn starch, British Gum 9084, and anionic starch on quartz and hematite. The adsorption of these starches, which decreases in the order mentioned, is dependent on the balance between the magnitude of the electrostatic interaction and the magnitude of the hydrogen bonding. There exists a critical starch concentration for both optimum flotation and flocculation conditions of iron ores, which corresponds to a point where the starch adsorption reaches a saturation coverage. Flocculation occurs due to the adsorption of starch via electrostatic and hydrogen-bonding forces and by interparticle bridging as a result of the conformation of starch molecules at the interface. The depressant property of starches and starch derivatives in flotation' and their flocculation char: acteristics in clarification and filtration2.3 have long been recognized on a wide variety of ores. The effectiveness of a starch as a depressant for iron minerals has been the subject of much investigation in recent years both in the amine flotation of siliceous gangue and in the anionic flotation of activated silica from iron ores. It has been reported that the depressant activity of starches and dextrins in the cationic flotation of quartz from hematite increases with molecular weight, branching, and number of hydroxyl groups, 1 and that the selectivity is affected by changing the configuration of starch molecules and the composition of its polar groups.4 ,5 The manner in which starches are solubilized was shown to exert a significant influence as a depressant in the anionic silica flotation, and a series of articles covering the practical aspects of flotation and flocculation have already been reported.618 Chemical modification of the starch structure, the pulp pH, the calcium ion, and the residual starch concentration were identified as some of the more important variables affecting the flotation behavior. In the flocculation of iron ores, it was noted that most starches flocculated suspensions of hematite in water but did not flocculate similar suspensions of quartz,9 and that an excessive use of starch restabilized the suspensions due presumably to protective action. 6 An admirable application of such an observation to practice may be cited in the selective flocculation and desliming in the anionic silica flotation of iron ores, which resulted in superior metallurgy and lower reagent cost. 10 From detailed adsorption measurements, Schulz'and Cooke4 established that the adsorption of starches and their derivatives depended on the types of minerals and of starches, pH, and electrolytes present. Their adsorption data and the foregoing flotation and flocculation observations suggested that an electrical interaction between starches and charged mineral surfaces might be playing a role in their adsorption process. Adsorption of organic polymers, particularly of synthetic origin, at solid-liquid interfaces has been extensively studied in recent years,' and it is realized that their adsorption mechanism is considerably more complex than that of simple ions or molecules. A polymer molecule possesses a number of functional groups, and the adsorption at a point may restrict the adsorbability of adjacent groups. The mechanism may be further complicated by the conformation of the polymer molecules which may exist as coiled spheres, helices, or extended chains as a result of intramolecular interactions among functional groups as well as intermolecular interactions with solvent molecules. The object of the present investigation was to examine the effect of the chemical modification on the adsorption characteristics of starches and starch products on quartz and hematite at several pH values, so that by correlating this information with flocculation and flotation results, adsorption mechanism of starches on mineral-solution interface may be elucidated. EXPERIMENTAL MATERIALS Quartz: St. Peter sand was screened at 35 mesh and the undersize was scrubbed and deslimed at a Fagergren cell. The deslimed sand was cleaned with 0.1 N hot hydrochloric acid and washed repeatedly with distilled water, For anuscript, measurementsl the -200-mesh fraction of the sand was ground dry in a porcelain mill for 3 hr. The specific surface of the finely ground quartz was

Jan 1, 1970

By William A. Johnson

The mathematical analysis of diffusion curves in solid metals is carried out ordinarily by analogy with the flow of heat in a continuous medium and no account is taken of the fact that the materials involved are composed of discrete particles that move discrete distances at irregular intervals. It is possible to treat the problem on the basis of simple assumed atomic mechanisms, in which case, because of the small scale of the elementary process compared to the gross effects observed experimentally, the two procedures lead to the same expression for the variation of concentration with distance. Thus, for engineering purposes, the usual methods are quite satisfactory. If, on the other hand, our purpose is to go beyond the mere collection of data, however desirable this may be, it is necessary to recognize and understand the factors that are of fundamental importance. One factor that has not hitherto been considered when dealing with solid metals is the difference in atomic weights of the isotopes of a single metal. While all the atoms of a given element are alike chemically, their weights may vary by a small but significant amount, and atoms of different weights may have different diffusion rates. With gases this variation in isotopic weight produces a change in the rate of diffusion by a factor inversely proportional to the square root of mass. While, except for the lightest gases, this is not a large effect, it is, for example, sufficient to permit a considerable concentration of one isotope at the expense of others. If metals exhibit a similar phenomenon, some modification of the analysis of the diffusion process will be required, since the different isotopes of a given metal will have different probabilities of moving and the heat-flow analogy will contain a fundamental error. This situation cannot be rectified by using a diffusion coefficient based on the average probability of moving, and it can be shown that even when the diffusion coefficient is independent of composition, the diffusion curve will not agree with the simple theory except in the rare cases where only one isotope exists; e.g., gold. If, however, the mass effect in the solid state were no larger than in the gaseous, the errors arising therefrom in the analysis of ordinary diffusion curves would be quite negligible. Nevertheless, our desire to obtain all possible information concerning the details of the diffusion process, and the possibility of diffusion in the solid state as a means for separating isotopes are cogent reasons for undertaking an experimental study to determine whether isotopes of different masses diffuse at different rates. Experimental Procedure If isotopes of different masses diffuse at different rates, the ratio of the concentration of one relative to another will vary with the distance from the diffusion inter-

Jan 1, 1946

By William A. Johnson

The mathematical analysis of diffusion curves in solid metals is carried out ordinarily by analogy with the flow of heat in a continuous medium and no account is taken of the fact that the materials involved are composed of discrete particles that move discrete distances at irregular intervals. It is possible to treat the problem on the basis of simple assumed atomic mechanisms, in which case, because of the small scale of the elementary process compared to the gross effects observed experimentally, the two procedures lead to the same expression for the variation of concentration with distance. Thus, for engineering purposes, the usual methods are quite satisfactory. If, on the other hand, our purpose is to go beyond the mere collection of data, however desirable this may be, it is necessary to recognize and understand the factors that are of fundamental importance. One factor that has not hitherto been considered when dealing with solid metals is the difference in atomic weights of the isotopes of a single metal. While all the atoms of a given element are alike chemically, their weights may vary by a small but significant amount, and atoms of different weights may have different diffusion rates. With gases this variation in isotopic weight produces a change in the rate of diffusion by a factor inversely proportional to the square root of mass. While, except for the lightest gases, this is not a large effect, it is, for example, sufficient to permit a considerable concentration of one isotope at the expense of others. If metals exhibit a similar phenomenon, some modification of the analysis of the diffusion process will be required, since the different isotopes of a given metal will have different probabilities of moving and the heat-flow analogy will contain a fundamental error. This situation cannot be rectified by using a diffusion coefficient based on the average probability of moving, and it can be shown that even when the diffusion coefficient is independent of composition, the diffusion curve will not agree with the simple theory except in the rare cases where only one isotope exists; e.g., gold. If, however, the mass effect in the solid state were no larger than in the gaseous, the errors arising therefrom in the analysis of ordinary diffusion curves would be quite negligible. Nevertheless, our desire to obtain all possible information concerning the details of the diffusion process, and the possibility of diffusion in the solid state as a means for separating isotopes are cogent reasons for undertaking an experimental study to determine whether isotopes of different masses diffuse at different rates. Experimental Procedure If isotopes of different masses diffuse at different rates, the ratio of the concentration of one relative to another will vary with the distance from the diffusion inter-

Jan 1, 1946