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By H. D. Williams, R. A. Scriven

The distribution of elevation angle of finite plane facets distributed symmetrically about a given axis is derived in terms of the angular distribution of lines which these facets produce in a plane section parallel to the axis. It is assumed that the facets are not markedly elongated in preferential directions. The theory is intended for application to the angular distribution in polycrystalline metals of slip planes and of particular grain boundaries on which certain phenomena such as cavitation can occuv. Illustrative examples are given in closed form and simple numerical techniques are de-ueloped for practical application. The results are applied to the distribution of cavitated boundaries in a copper specimen after fatigue at 400°C and it is found that voids form on the boundaries that exper~enced maximum shear stress. When investigating the distribution of elevation angle between a given axis and planes symmetrically distributed about this axis the angular distribution observed in a plane section parallel to the axis is not necessarily the same as the required distribution. Consequently a technique for processing the results obtained by sectioning methods is required. An example where such a technique would find application is in the problem of intercrystalline void formation during uniaxial tensile creep. Two theories have been proposed to explain this cavitation in terms of the normal and the shear components of stress, respectively. Hull and Rimmer (1959) postulate that the growth of intercrystalline voids is controlled by the rate of supply of vacancies from the grain boundary, the local vacancy concentration being proportional to the normal stress on the boundary. Gifkins (1956) considers that slip arising within a grain causes a ledge to be formed at the grain boundary which is subsequently opened up into a cavity by grain boundary sliding. It might be possible to differentiate between these mechanisms by determining the angular distribution of grain boundaries containing cavities since the former theory predicts a predominance of cavitated facets normal to the stress direction whereas the latter should favor an angle of 45 deg to this direction. In a similar manner an indication may be obtained of the type of mechanism responsible for intercrystalline cavitation during high-temperature fatigue. Davies and Wilshire (1962) have analyzed the slip-plane distribution in a nickel specimen but the problem was not treated in any detail nor was any account taken of the finite extent of the planes being sectioned. Hilliard (1962) has given a very general account of how anisotropy in the microstruciure can be related to measurements taken in one or more plane sections by expressing both the measured and the true angular distributions as expansions in spherical harmonics.* The present analysis is con-

Jan 1, 1965

By C. G. Dunn

It is well known that plastic deformation alters many of the properties of a metal and subsequent heat-treatment partially or completely restores these properties.l In the deformed or strained state, the metal is unstable and tends to change toward a condition called a "strain-free state." The transformation occurs through recovery, recrystallization, and grain growth—processes that may take place singly or in combination. The distortion of the lattice of an individual grain of a metal in a state of strain may be rather complex in nature, because plastic deformation produces: (I) dislocations within mosaic blocks; (2) elastic variations of the lattice spacings; and (3) gross alterations throughout the lattice, especially along slip planes, along composition planes between a grain and its mechanical twins, and along boundaries of deformation bands. These gross alterations are of the nature of bent planes or rotated regions of the crystal lattice and are revealed by a spread in the orientation of the grain. Although we cannot describe these strains and their formation accurately because of insuffcient knowledge, we can, nevertheless, use the information as well as possible to obtain a better understanding of recovery processes. In recovery, the lattice of a grain is not made anew as it is in recrystallization, but is improved or mended in such a way that the basic structure remains unaltered: Until recatly observations were .that recovery produced no marked changes in the shapes of spots in Laue diffraction patterns, whereas recrystallization did, but now it is known for silicon ferrite2 that Laue spots may become quite sharp entirely through recovery. Consequently, the shape of Laue spots alone would not be a suitable test to distinguish between recovery and recrystallization. There is considerable evidence that the micro-structure usually does not change visibly during recovery. Absence of a visible change in the microstructure, therefore, provides a sufficient test of recovery in many cases. However, including this observation in a definition of recovery as a necessary condition (this is usually done) is unfortunate, because recovery may, as will become evident later, produce new grain boundaries that are visible not only in the microstructure but also in the macrostructure. For the present, therefore, let us say that a necessary condition for a process to be one of recovery is that the principal orientation or orientations of a deformed grain be essentially unchanged throughout the transformation toward the strain-free state. Several transformations may occur that fulfill this condition, and the nature of the distortion in a grain indicates what these must be if the lattice is to be mended in part or fully. Consequently, it will be convenient as well as

Jan 1, 1947

By James W. Malcolmson

This paper treats of the history and development of the Sierra Mojada mines in the north of Mexico, the character and extent of the ore-deposits, and the methods of mining the ore. The growth of the smelting industry in Mexico in recent years is, to a large degree, due directly to the output of the lead-bearing ores from the Sierra Mojada mines, and at the present time (1901) new smelters are being built, looking to this district for their supply of lead-ores. These mines are located in the southern part of the State of Coahuila, in the Republic of Mexico, in latitude 27 24' N. and longitude 103O 43' W. of Greenwich. The last account of the Sierra Mojada published in our transactions was contributed by Mr. Richard E. Chism, in October, 1886.* Since that time some 3,000,000 tons of ore have been extracted from the mines, and much additional information has been developed regarding the mineral deposits. Since 1886, the Mexican Northern railroad, 78 miles in length, has been built from Escalon, connecting the camp with the Mexican Central railway, a trunk-line from El Paso, Texas, to Mexico City. The distances by rail from Sierra Mojada to the principal smelting-centers are as follows : To Torreon, Coahuila, Mex., 179 miles; to Monterey, Nuevo Leon, Mex., 422 miles; to El Paso, Tex., U. S., 494 miles; to Aguas Calientes, A. C., Mex., 522 miles; to San Luis Potosi, 8. L. P., Mex., 644 miles; to Pueblo, Colorado, U. S., 1158 miles; to Argentine, Kans., U. S.,

Jan 1, 1902

By G. T. Pruitt, T. L. Irby, P. B. Crawford, H. Ferrell

In water flooding peripheral, center-to-edge, line-drive or water-encroachment patterns the question has arisen, "when should a producing well be converted to a water-injection well?". It is realized that, if the producing well is shut in when water breakthrough occurs, some oil could be left in an unswept area. Yet, operation to high water-oil ratios may require processing much additional water. If a well is shut in, "where should the allowable be transferred?". A review of the literature indicates that very few data are available to the engineer to assist him in answering these questions. It is the purpose of this paper to present information which may be of value in selecting the flooding technique and the injection and producing wells and in scheduling injection and production rates. Certain phases of these problems can be studied in the laboratory. The Potentiometric model is well suited for studying many waterflooding problems. This model assumes that steady-state flow exists, that the mobility ratio is equal to one and that gravitational effects are neglected.'-' The three-phase sand model also has been recognized as an effective means for studying certain reservoir problems. Both models were used in making the study reported here. This paper discusses seven cases utilizing various waterflooding techniques. Data for the first five cases were obtained on the potentiometric model. Data for Cases VI and VII were obtained by constructing and flooding an unconsolidated sand pack (a three-fluid-phase system) and by determining the swept area and cumulative oil recovery for various types of operations. APPARATUS AND PROCEDURE The potentiometric model reservoir was 30 in. long X 10 in. wide by about 1/2 in. deep. Four wells were equally spaced in a line array along the lateral center line. (See Fig. 1.) Well No. 1 initially was an injection well for each of the patterns reported. The cases studied with the potentiometric model and sand model are described herein. The laboratory sand model reservoir was a 30- 10-in. rectangular Lucite vessel packed with sand to a depth of about 0.65 in. Four wells were equally spaced in a line array along the lateral center line. The reservoir material was an unconsolidated sand into which the reservoir fluids were mixed to yield fluid saturations of 55 per cent oil, 25 per cent water and 20 per cent gas. The water was added to the sand and the material mixed, after which the oil was added. Kerosene and water, the fluids used, gave a viscosity ratio of 1.64:1. In packing the reservoir, care was taken to assure constant fluid saturations and constant porosities. A new mixture was prepared for each run. During water flooding, a colored water was injected by a constant rate pump. The injection rate was 1.1 B/D/ft of sand thickness. For this series of tests, each of the producing wells was open to the atmosphere and, as in the potentiometric model study, Well No. 1 initially was an injection well for each of the patterns. KESULTS OF POTENTIOMETKIC MODEL STUDlES Two cases (Cases I and 11) involving equal pressure injections were studied, with the following results. Case Water injection was initiated at Well No. 1; the producing wells (Nos. 2, 3 and 4) were operated at constant and equal bottom-hole pressures. When water broke through at Well No. 2 and achieved the selected water-oil ratio, Well 2 was converted to a water injection well, resulting in two injection and two producing wells. The injection pressures at Wells 1 and 2 were maintained equal and constant; pressures at the producing wells were held equal, but they were lower than those at the injecting wells. A similar process was repeated when water broke through at Well No. 3. The flood was terminated when

By J. M. Flaitz, A. S. Parks

OF the various methods of sampling gas-condensate wells, a method that secures a continuous representative sample of the well stream is desirable. Such a method, consisting of a sampling tube introduced into the well tubing, has proved satisfactory. The method is sufficiently accurate for operating and engineering problems A portable testing apparatus can be used with the sampling tube to obtain data useful in studying the economic and technical aspects of the development and operation of gas-condensate properties. Introduction The recent discovery and development of gas reserves that contain hydrocarbons that condense with reduction of temperature or Pressure, or both, to form a product known as condensate, has brought many new problems to the oil and gas industries. With further discovery of deep, high-pressure fields it is presumable that many more gas fields of this type will be added to the steadily increasing number. Such gas reserves are found either associated with oil as a gas cap or in separate formations. There seems to be no positive correlation between the physical or geological nature of the reservoir, and the chemical composition or phase characteristics of its contents. Knowledge of the chemical make-up and phase behavior of gas-condensate reserves is needed to cope with many problems. A knowledge of the chemical composition and phase characteristics of the reservoir material is necessary to properly design a gasoline or recycling plant, to estimate natural gas and condensate reserves, to enable the operator to study the economic and technical aspects of various methods of operation and development, and to carry Out the plan of operating subsurface and surface lease equipment. This information is often useful in questions of mineral ownership, proration, legal position, and taxation. It is the purpose of this paper to discuss methods used by the writers to determine the chemica1 composition and phase characteristics of the fluids produced from a condensate well. The scope of the paper includes a discussion and description of the method of sampling, the results of tests on the accuracy of the sampling method, a description of a portable testing apparatus used to examine the phase characteristics, typical results of tests on wells from several condensate fields, and some of the applications of these data to production problems. References to previous work on this subject are cited at the end of the paper. The Problem At reservoir conditions of temperature and pressure, the fluids produced from a condensate well exist in a homogeneous vaporous condition. The consequent reduction of temperature and pressure that occurs as this gas enters and flows up the well tube results in condensation of some of the hydrocarbon material to form a liquid. The relative amount of liquid condensed at any point in the flowing system

Jan 1, 1942

By R. Bakish, M. A. Badiali, N. W. Kirshenbaum

One pound of ultra pul-e molybdenum has been produced containing both metallic and nonmetallic impuvities close to or less than the limits of detection. various purification methods were investigated; althouglz the use of move than one purification step was consideved, it was found that a single, caefully-controlled sublimation of MoCl5 yielded a highly puvified product without prior treatment or recourse to repeated sublimation. Hydrogen reduction of MoC1, to metal was attempted at atmospheric pressure; however, reduced pressure was necessary to obtain substantial yields. The tubular deposits of metal were consolidated into bulk fovm by electron beam melting undev high vacuum yielding a very low gas content. Boblems involved in monitoring the puvity of these materials and analytical results obtained are also presented. THE pronounced effect of even trace amounts of impurities upon fundamental properties of materials is well known to metallurgists and solid-state physicists. Consequently, groups interested in basic studies of metals have in recent years immensely stimulated the preparation and production of numerous ultra-pure metals. Increased demand by scientists for these high purity materials has necessitated development of facilities to prepare them in significant quantities; the procedures reported here were devised to produce significant quantities of ultra-pure molybdenum. Previous work performed in the field of vapor phase purification and hydrogen reduction of several other refractory metal chlorides had demonstrated valuable techniques applicable to molybdenum.' Various purification and reduction steps were individually investigated. Those procedures which showed the most favorable results with respect both to attainment of high purity and to ease of operation were then incorporated in the process utilized to produce the metal.' STARTING MATERIALS It is well known that because of differences in volatility, chlorides may be separated by fractional distillation. It was presumed that distillation of molybdenum pentachloride offered a simple and straightforward method of purification due to its relatively low boiling point. Alternatively, sublimation of the solid chloride also appeared feasible since MoC15 has both a reasonably narrow temperature range in which it exists as a liquid (a property typical of refractory metal chlorides) and a low enthalpy of sublimation. Pertinent thermochemical data of MoC15 are given in Table I. It should be noted that this compound must be handled with care as it is extremely hygroscopic. Anhydrous MoC15 was obtained from the A Metal Climax Co. METHODS OF PURIFYING MOLYBDENUM PENTACHLORIDE Distillation. It was expected that distillation methods, while affording an efficient purification, would prove simple to control and would have a higher production rate than sublimation processes. Also considered was the possibility of effecting a high degree of purification by using both these volatilization methods in conjunction—possibly a distillation followed by sublimation of the solidified condensate. Distillation of MoC15 was investigated using a single stage distillation column packed with chemically resistant glass beads. Heating coils were wound around the column and collection tube (condenser). As-received MoCl5 was charged into a flask connected with the column using a side loading arm under an argon flow. After the column and condenser were brought to about 270" and 210°C, respectively, the apparatus was lowered until the flask was fully immersed in a constant temperature fused salt bath maintained at about 285 °C. Distillation was continued for about 10 or 15 min until 50 to 70 g of distillate had been collected. Analyses of these distillations indicated that several elements, e.g., Cu, Fe, Ni, Cr, and Mg, were lowered in quantity although not all were removed to the same extent. The occurrence of Na, B, Si, and A1 in the distillates appeared to be due to contamination, possibly from corrosion of the pyrex glass. An improved distillation system of larger capacity and longer distilling column was built. Improvements were effected in lowering the amounts of such impurities as B, Mn, Ni, Na, Mg, Cr, Cu, and Fe. These studies were pursued concomitantly with efforts to purify by sublimation; it was subsequently found that although improvements in purity were obtained by distillation, sublimation processes were simpler to control and effected a high degree of purity.

Jan 1, 1963

By T. S. Lundy, R. E. Pawel, F. R. Winslow, C. J. McHargue

The volume-diffusion coefficients of Nb-95 and Ta-182 in niobium have been measured over the temperature range 878° to 2400°C. High-temperature specimens (T 21500°C) were sectioned by conventional lathe and grinding techniques while low-temperature specimens were sectioned by an anodizing and stripping technique previously described. Over a range of more than ten orders of magnitude in diffusivity, the self-diffusion data is well-represented by the equation: D = (1.1+ 0.2) exp [- (96,000 * 900)/RT ] cm2/sec Upward deviations from this line are explained by short-circuit diffusion in combination with the loss of resolution of the sectioning techniques. Oxygen contamination within the range 100 to 450 ppm was found to have little or no effect on the self-diffusivitj 01 niobium. In a limited number of measurements, the diffusivity of Ta-182 in niobium was found to be about half that of Nb-95 in niobium. These data may be described by D = (I.0+0.90.5)exp [- (99,300 * 2400) /RT ] PREVIOUSLY reported studies of self-diffusion in niobium were by Resnick and Castleman1 and Peart, Graham, and Tomlin.2 The data of Resnick and Castleman over a temperature range 1585" to 2120°C show considerable scatter but. can be represented by D = (12.4 *0.8) exp [-(105,000+3OOO)/RT] cm2/sec The limited data of Peart, Graham, and Tomlin follow the equation D = 1.3 exp (-95,00O/RT) cm2/sec In view of recent diffusion data for ß zirconium3 and 0 titanium4 in which Arrhenius-type plots do not yield straight lines and of the potential high- temperature uses of niobium and its alloys, we thought it important to investigate the diffusion behavior of this bcc refractory metal over a large temperature range. This has recently been done for molybdenum,5 chromium,6 vanadium,"" and tantalum.9 Niobium was a particularly suitable material for this study largely because of the development of an anodizing and stripping sectioning technique which enables diffusivities as small as l0-19' sq cm per sec to be determined accurately.10 In addition to self-diffusion data, data were obtained for the diffusion of Ta-182 in niobium and for the effect of varying oxygen content on self-diffusion. I) EXPERIMENTAL PROCEDURE Materials. The niobium was obtained from three sources: 1) melting stock from Shieldalloy Corp., 2) electron-beam melted single crystals, 1/2 in. diameter, from Semi-Elements, Inc., and 3) oxygen-doped, electron-beam melted single crystals from Materials Research Corp. The melting stock was electron-beam melted and specimens 5/8 in. diameter by 1/2 in. long were machined from the center of the bar. The analysis supplied by the vendor and an interstitial analysis of one of the specimens are given in Table I. The single crystals (type 2 above) were cut with a jeweler's saw to specimens about 3/8 in. long. The interstitial analysis of this material is given in Table 11. This material was used

Jan 1, 1965

By Charles W. Henderson

THE influence of mineral production on the development of the western United States has been profound. From 1848 to 1860, there was only gold production, the effect of silver began in 1860, and from then on both had a powerful influence. Lead production started in 1863, copper in 1863, and zinc in 1885, but was small until 1898. Gold alone was therefore the stimulus of the early settlement and exploration of the Western States.. But mineral deposits caused neither acquisition of territory nor determination of boundary lines. Arizona, California, Nevada, New Mexico, and parts of Utah, Wyoming, and Colorado were formally acquired from Mexico fourteen days after the actual date of the discovery (January 19, 1848)1.2 of gold at Sutters Mill, near the present town of Coloma, California (a discovery which, with the immediate new discoveries, aroused the world several months later) ; but the acquisition was by treaty (under negotiation for some time but signed February 2, 1848)3 in settlement of a war involving the boundaries of the grassy plains of Texas, an area at that time not known to contain any metals, and to date found to have but few metal deposits.4 The international boundary at 49º latitude for the far northwest states was determined by causes other than mineral deposits.

Jan 1, 1933

By Philip B. Bucky

[ ] FOREWORD THIS symposium brings together points of view, experiences and ideas on rock bursts from a goodly portion of the globe. Some conceptions, particularly those regarding the necessity of depth, have been fairly well shattered, as we find that they are present in the water tunnels of New York, on the surface at marble quarries in Vermont, and in the coal mines of the United States, as well as in the deep mines of the South African and Kolar gold fields, and in the nickel, copper and gold mines of Canada. Their occurrence under such a variety of conditions is, therefore, a challenge,

Jan 1, 1942

By C. M. Wayman, R. Bullough

The selection rules fir twinning in fcc, bcc, and hcp lattices as established in Part I are used to predict the positions, relative to the matrix (untwinned) reciprocal lattice, of reflections due to double diffraction from the twins. These doubly diffracted reciprocal lattice points, which often coincide with ordinary matrix reciprocal lattice points, are deduced from kinematical considerations. 1. INTRODUCTION. A Bragg diffracted beam under certain conditions may be rediffracted to produce a third beam i .e., the incident beam, the first diffracted beam, and the rediffracted beam). In such a case an initial incident beam is diffracted by a set of planes; the diffracted beam may then be rediffracted by a second set of crystallographically different planes. The initially diffracted beam acts as an incident beam for the second set of planes, thus resulting in a twice-diffracted beam. This twice-diffracted beam may be regarded as a singly diffracted beam from a set of lattice planes whose structure factor is zero. In order to find the reciprocal lattice point corresponding to the doubly diffracted beam, it is customary1,2 to combine vectorially the component reciprocal lattice vectors which head to the extra reflections. For example, hcp metals may exhibit the forbidden (0001) reflections.* As Fig. 1 shows, the (0001) reciprocal lattice point results from: (1010) + (1011) = (0001) Similarly, combination of the beams (1011) and (1010) gives rise to: (1011)- (1010) = (0001) As Pashley and stowell2 have pointed out, even if in fact the double diffraction points lie on the Ewald sphere, they may not actually represent observed doubly diffracted beams because the initially diffracted primary beam, i.e., the source, must also correspond to a reciprocal lattice point which lies on the sphere of reflection; however, the reciprocal lattice point corresponding to the planes causing the rediffraction need not lie on the sphere. A little consideration of the Ewald construction in Fig. 2 makes this argument clear. In Fig. 2 the incident beam is represented by the wave vector ko. This beam is initially diffracted by the lattice planes (hkl) which are represented by the reciprocal lattice vector r(hk1) The reciprocal lattice point (hkl) of course lies on the Ewald sphere in order that the Bragg condition be satisfied. The initially diffracted beam is represented by the wave vector kl. If now kl is rediffracted by a second set of planes (h'k'l') resulting in k2 the lattice point (h"k"l") must lie on the Ewald sphere if the double diffracted beam k2 is to be observed. It is clear that (h"k"l") is the vector sum of (hkl) and (h'k'l'), and that (h'k'l') need not in fact lie on the Ewald sphere. In the usual1,2 analysis the origin (000) of the reciprocal lattice is shifted to the point (hkl). However the translation (000)— (hkl) automatically shifts the point (h'k'l') to the Ewald sphere, i.e., (h'k'l')— (h"k"1"). It is to be seen that (hkl), the source reflection, must lie on the Ewald sphere; if it does not the translation (000) — (hkl) places the "new" origin off the sphere, not satisfying the Ewald construction and hence the Bragg condition. The point (h"k"1") of course must lie on the sphere if it corresponds to an observed doubly diffracted beam. It is to be noted that crystals having the hcp structure, as just discussed, are intrinsically capable (i.e., without lattice defects such as twins) of double diffraction, as contrasted to fcc and bcc crystals which are extrinsically capable (requiring lattice defects or reoriented lattice regions). The "allowed" bcc reciprocal lattice points (which comprise an fcc lattice) are (110), (2001, (211), (220), (310), (2221, (321), (4001, and so forth. The combination

Jan 1, 1967

By J. Marshall Rounsevell

It is probably not too far from the truth to say that the sulfur content of the steel bath at the first turndown of the basic oxygen furnace is influenced by every factor which varies in the operation of a BOF shop. However, the determination from normal shop operating data of the effect of a given factor on turndown sulfur content requires a means for collecting a large quantity of such data and a significant variation of the factor in question in that data. In this paper, operating data from 4000 heats collected on the computer at Inland's No. 4 BOF Shop is utilized to analyze the effect of four operating parameters -- hot metal sulfur content, hot metal manganese content, percent burnt dolomitic lime (dolomite) in the flux charge, and the presence or absence of transfer ladle slag skimming -- on first turndown sulfur content.

Jan 1, 1972

By Donald B. Evans, Robert D. Pehlke

The solubility of nitrogen in liquid Fe-A1 alloys has been measured up to the solubility limit for formation of aluminum nitride using the Sieverts method. The activity coefficient of nitrogen decreases slightly with increasing aluminum content in the range of 0 to 4 wt pct Al. Based on a nitride composition, AlN, the standard free energy of formation of aluminum nitride from fhe elements dissolved in liquid iron has been determined to be: ?F" = -59,250 + 25.55 T in the range from 1600º to 1750ºC. The solubility of nitrogen in liquid iron alloys and the interaction of nitrogen with dissolved alloying elements in liquid iron have been the subject of a number of research investigations.' Most of this work, however, has been reported for concentrations well below those necessary for the formation of the alloy nitride phase. Data in the concentration region near the solubility limit of the alloy nitride, particularly for systems exhibiting stable nitrides, are important in evaluating the denitrifying power of various alloying elements. They are also useful in determining the stability of a given nitride if it is to be used as a refractory to contain liquid iron alloys. In view of the importance of aluminum as a deoxidizing agent in commercial steelmaking and the fact that its nitride, AIN, is a highly stable compound and has merited some consideration as an industrial refractory, the following investigation was undertaken. The use of the Sieverts technique provided a measurement of the equilibrium nitrogen solubility in liquid Fe-A1 alloys as a function of nitrogen gas pressure up to 3.85 wt pct A1 in the temperature range of 1600º to 1750°C. The values obtained by the Sieverts method were checked by means of a quenching method in which liquid iron was equilibrated with an A1N crucible under a known partial pressure of nitrogen gas, and the solubility of A1N in liquid iron determined by chemical analysis. EXPERIMENTAL PROCEDURE The theoretical considerations involved in determining the solubility product of a solid alloy nitride phase in liquid iron by measuring the point of departure of the nitrogen gas solubility from Sieverts law have been discussed by Rao and par lee.' The principal problem is to determine the variation of nitrogen solubility in an alloy as a function of the pressure of nitrogen gas over it with sufficient precision to establish the break point in the curve at the solubility limit of the alloy nitride phase. A fairly large number of data points are required to do this. A second problem is the determination of the composition of the precipitated solid nitride phase. This is necessary in order to define completely the thermodynamic relationships. The Sieverts apparatus used to make the nitrogen solubility measurements in this investigation is of essentially the same design as that described by Pehlke and E1liott.l The charge materials were Ferrovac-E high purity iron supplied by Crucible Steel Co. and 99.99+ pct pure aluminum. Recrystal-lized alumina crucibles were used, and were not attacked by the liquid alloys. The hot volume of the system which was measured for each melt ranged from 46 to 50 standard cu cm and was found to decrease linearly with decreasing pressure and with increasing temperature. The temperature coefficient of the hot volume at 1 atm pressure of argon gas was essentially constant for all experiments at a value of -6 X 10-3 cu cm per "C. The melt temperature was measured with a Leeds and Northrup disappearing filament type optical pyrometer sighted vertically downward on the center of the melt surface. The temperature scale was calibrated against the observed melting point of pure iron taken as 1536°C. The emissivity of all melts was assumed to be that of pure iron, taken as 0.43. The charge weights ranged from 110 to 140 g and the range of aluminum contents covered was from 0 to 3.85 wt pct. Aluminum additions were made as 12 to 15 wt pct A1-Fe master alloys previously prepared in the system under purified argon. The compositions of the master alloys were checked by chemical analysis and found to be in agreement with the charge analyses. Vertical cross sections of the master-alloy ingots were used as charge material for the equilibrations in order to minimize the effect of any segregation which might have occurred during solidification of the master alloys. Determinations of the solubility product of

Jan 1, 1964

By W. L. Mamme, G. Y. Chin

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain was analyzed by Taylor and by Bishop and Hill in terms of a minimum (internal) and a maximum (external) work criterion, respectively. These two criteria have now been generalized to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (noncrystallographic) pencil glide. The generalized treatment also takes into account the possibility of a Bauschinger effect and of unequal hardening among the shear systems, which were considered in the Bishop and Hill work. Optimization techniques of linear and nonlinear programming are shown to be applicable for the numerical calculation of the minimum or maximum work. In the case of crystallographic shear, the constraint functions are linear and hence the optimal work is obtained as the saddle value of the lagrangian function Wi(y) e minimum and W,(u) + (a) for the maximum, where Wi is the (internal) work, We is the (external) work, Y is the crystallographic shear strain, u is the applied stress, and and are constraints. It is shown that the Lagrangians are functionally the same and the saddle value of one problem is identical to the saddle value of the other, proving that the two analyses are completely equivalent. In the case of pencil glide, although the constraint functions are nonlinear and neither convex nor concave, the equivalence of the optimal values to the saddle value of the Lagrangian (which is again identical for both problems) is still valid. WHEN a crystal deforms plastically by crystallographic shear, five independent shears are generally required to accommodate five independent strain components specifying the deformation. Assuming slip as the only shear mechanism, Taylor1 in 1938 analyzed the deformation in terms of a minimum work criterion. He hypothesized that of all combinations of five slip systems which are capable of accommodating the deformation, the active combination is that one for which the internal work C is a minimum, where 1 TI is the critical resolved shear stress for slip on the 1-th slip system and is the corresponding simple shear. By further assuming equal 72 for all equivalent slip systems and no Bauschinger effect, Taylor re- duced the minimum work problem to one of minimum and applied the analysis to the case of axisym- Metric flow by {111}(110) slip in fcc crystals. However, he did not consider the question of whether the resolved shear stress has in fact attained the critical value for slip on the newly found active systems without exceeding it on the inactive systems. In 1951 Bishop and ill' put forth the maximum work analysis in which slip is again assumed as the only deformation mechanism. In this analysis, the work o1 done in a given strain ij by a stress ujj not violating the yield condition is maximized. In addition, the analysis takes into account the possibility that the critical resolved shear stress for slip may not be equal among the slip systems and that the slip behavior may exhibit the Bauschinger effect. As with Taylor, a single set of slip systems—{111)(110) — was analyzed numerically. It thus appears that the Bishop and Hill treatment is on a more sound physical basis than the Taylor treatment. However, Bishop and Hill showed that where there is equal hardening among all slip systems and when there is no Bauschinger effect, Eq. [11 ] of Ref. 2, as assumed by Taylor, the results of their maximum work analysis are the same as those of Taylor's minimum work analysis. Hence at least under those conditions there is an implication that the Taylor analysis does lead to a critical resolved shear stress for slip on the predicted active systems without violating the yield condition on the inactive systems. Recently, the Taylor analysis was applied for numerical solutions of the axisymmetric flow problem, for slip on {110}(111), {112}(111). {123)(111) systems as well as a mixture of all three sets of svstems."1 Computational techniques based on the optimization theories of linear and nonlinear programming4 were employed in these solutions. The same techniques were employed in the solutions of an axisymmetric flow problem of deformation by slip on (111) (110) systems and twinning on (111)(112) systems5 which had been considered theoretically from a modified Taylor approach. The utilization of these techniques has led to the realization that the solutions of Taylor's minimum work problem imply the solutions of Bishop and Hill's maximum work problem. The two problems turn out to be dual problems in the well known sense of mathematical programming. It is thus the purpose of this paper to first generalize the minimum and maximum work analyses to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (non-crystallographic) pencil glide, as well as the possibility of a Bauschinger effect and of unequal hardening

Jan 1, 1970

By C. D. Woodward

THE Anaconda Copper Mining Co. purchases 25,000 kw. of electric power for its mining operations at Butte Mont. This power is delivered, over duplicate feeders, in the form of 60-cycle, 2400-volt, three-phase current, to five compressor plants, where most of the energy is used for driving air compressors. At the compressor plants are located the switching apparatus for controlling the 2400-volt power and distributing it to the various mines. At these points, also, there are a number of motor-generator sets for converting the alternating current to 275-volt. direct current for the haulage systems. Pole lines convey the power from the compressor plants to outdoor transformer substations at most of the mines. When it is not economical to distribute the power at the lower voltages in the mines, transformers and motor-generator sets are placed at strategic points .underground. All power is purchased on a maximum-demand basis, therefore there is installed at one of the compressor plants an eight-element totalizing graphic wattmeter. This instrument records simultaneously the value of all power taken at the numerous points of delivery, which not only eliminates the diversity factor but permits load dispatching between compressor and pumping plants, and thus materially reduces the maximum demand from the power system. As most of the mine hoisting is done, by 90-lb. compressed-air winding engines, the air-compressor equipment for the winding engines and mining operations is quite extensive. The standard air compressor has a rating of 7500 cu. ft. per min. of free air, and most of the compressors are directly connected to synchronous motors. The synchronous motors are designed for 80 per cent. leading power factor, thus facilitating power-factor correction of total mine load. Consequently by cooperation with the power company, the voltage of the power received at the compressor plants is constant.

Jan 2, 1922

By F. L. Bosqui

The history of the development of gold metallurgy in South Africa is divisible into two periods: That preceding the introduction of the cyanide process on a commercial scale in 1890; and the 24 years intervening between that important event and the present time. The period between the discovery of the banket reefs of the Witwaters-rand and the year 1890 was one of phenomenally rapid progress in mining development, but of no special interest to the metallurgist, There were no strikingly original or distinctly local advances in the treatment of gold ores. Californian practice in stamp milling and amalgamation prevailed, in mills ranging in equipment between 5 and 50 stamps, operating within a wide range of efficiency, and under the trying conditions usually encountered in a new and isolated field. The somewhat incomplete records of gold output of that period show that in December, 1887, there were 20 producing companies in the Witwatersrand district, of which 10 had mills, the largest being of 20 stamps. The only official record of returns for May, 1887, was that of the Wemmer mine, whose modest achievement with a 5-stamp mill was 100 tons crushed, producing 887 oz. 3 dwt. of gold. This is interesting in view of the present-day output of this field, which in 1913 reached 8,430,998 oz. The rapid increase of production during this first period (May, 1887, to January 1891) is shown by the following summary for the year 1890:1 Total tone crushed.................................. 702,828 Number of stamps in operation....................... 1,046 Average number of tons crushed per stamp per day..... 2.36 Yield of gold, ounces................................ 494,817 Yield per ton, pennyweights.......................... 13.36 The stamp duty ranged between 11/2 and 4 tons per day, according to weight of stamp, fineness of screen, and operating skill available. The prevailing weight of stamp was about 900 lb., and the screen, 900 meshes to the square inch.

Jan 1, 1916

By H. D. Hodges, J. K. Godbey

In order to better understand the fracturing process, bottom-hole pressures were measured during a number of typical fracturing operations. A recently developed system was used that allows simultaneous surface recording of both the bottom-hole and wellhead pressures on the same chart. The results from six fracruring treatments are summarized on the basis of the pressure data obtained. Al-though no complete analysis is attempted, the value of accurate pressure measurements is emphasized. Important characteristics of the bottom-hole pressure record do not appear at the wellhead because of the damping effect of the fluid-filled column. In four of the six treatments described, the formations apparently fractured during the initial surge of pressure with only crude oil in the well. The properties of the fluids used during the treatments are given and the fluid friction losses are obtained directly from the pressure records. This technique is also shown to be adequate for determining when various fluids, used during the process, enter the formation. INTRODUCTION Hydraulic fracturing for the purpose of increasing well productivity is now accepted in many areas as a regular completion and workover practice. Numerous articles have appeared in the literature discussing the various techniques and theories of hydraulic fracturing'. In general, three basic types of formation fractures are recognized today. These are the horizontal fracture, the vertical fracture, and fractures along natural planes of weakness in the formation'. Any one or all three of these fracture types may be present in a fracturing operation. However, with only the wellhead pressure record as a guide, it is difficult at best to determine if the formation actually fractured, and is almost impossible to determine the type of fracture induced. These difficulties arise in part because the wellhead pressure record, especially when fracturing through tubing, does not accurately reflect the pressure variations occurring at the formation. Several factors contribute to this effect and preclude the possibility of using the wellhead pressure as a basis for accurately calculating the bottom-hole pressure. These factors are: 1. The compressibilities of the fluids which damp the pressure variations. 2. The changes in the densities of the fluids or apparent densities of the sand-laden fluids. 3. The flowing friction of the various fluids and mixtures, which is dependent on the flow rates and the condition of the tubing, casing, or wellbore. 4. The non-Newtonian characteristics of a sand-oil mixture and its dependence upon the fluid properties, the concentration of sand, and the mesh size used. 5. The unknown and variable temperatures throughout the fluid column. Because of these reasons it was determined that in order to obtain a more accurate knowledge of the nature of fracturing, the bottom-hole pressure must be measured along with the pressure at the surface during a fracturing treatment. Even with accurate pressure data, a reliable estimate of the nature of fracturing is still dependent upon knowledge of the tectonic conditions. However, the hydraulic pressure on the formation is basic to any approach to a complete analysis. In order to accomplish this objective a system was developed to record the wellhead and bottom-hole pressures simultaneously at the surface. By recording both pressures on a dual pen strip-chart recorder, it was possible to greatly expand the time scale so that rapid pressure variations would be faithfully recorded. By such simultaneous recording, time discrepancies inherent in separate records are eliminated, thus overcoming one of the most difficult problems associated with bottom-hole recording systems. This paper illustrates the results obtained by using this system during six typical fracturing operations. All of these tests were taken in wells that were treated through tubing. By a direct comparison of the wellhead and bottom-hole pressures, the importance of obtaining complete pressure information during a fracturing treatment is emphasized. THE INSTRUMENTATION AND PROCEDURES The bottom-hole pressure measuring instrument consisted of a pressure-sensing element, a telemetering section, and a lead-filled weight or sinker bar. The pressure-sensing element used was an isoelastic Amerada pressure-gauge element. By using an isoelastic element, no temperature compensation was necessary in the tests described, since the temperature was believed to be well below the maximum temperature limit of 270°F. The rotary output shaft of this helical Bourdon tube element was coupled to a precision miniature potentiometer. The rotation of the pressure-gauge shaft thus changed the resistance presented by the potentiometer

By H. W. Winkler, Discussion, V. L. Forsyth

The development of a new gar lift valve has removed many of the obstacles limiting over-all gas lift efficiency. The valve is pressure charged in place in a well, and operating pressure can be changed without pulling. Temperature and gas gradient compensation have been eliminated. Intermitting and constant flow installations, using conventional pressure-charged valves, are compared with designs incorporating the new automatic stabilizer controlled valve. Specific well performance data are presented. The means of obtaining and controlling multiple-point injection of gas are explained and contrasted with single point injection. The effect on small diameter strings and multiple string installations is discussed. The effect of flowing temperature gradient on a design using conventional pressure-charged valves, the limitations imposed by such temperature, and the obvious benefits which result from the use of automatic stabilizer controlled valves are shown. Reduction of gas requirements is stated mathematically and demonstrated with specific examples which are identified as to oil company and well. Increased fluid recovery resulting from greater drawdown is illustrated. The economic advantages are mentioned with emphasis on reduction of capital expenditures, as well as reduction in operating expenses. INTRODUCTION Much of the engineering and research work performed with gas lift has been based upon the supposition that under producing conditions gas would be injected at a single point in a well. Many tests were performed in determining the optimum size of the opening through which gas would be passed and the exact placement of the valve equipment. The objectives in a gas lift installation are to unload the well and to efficiently produce the well after it is unloaded. Until recently, the function of upper valves was simply to unload the well. An operating valve located at a proper place in a well served as a single injection point for lifting liquid to the surface. The basic problem in using such equipment is to arrive at operating depth with sufficient operating pressure to efficiently lift the liquid. Few gas lift installations are designed with all required well data available. However, regardless of the quality and availability of data, and regardless of the accuracy of the design, there is the practical problem of preparing and placing gas lift equipment in the well in exact accordance with the plans and intentions of the engineer. In recognition of these and many other problems, attention was directed toward a means of removing the need for temperature and gas gradient compensation, a way to change the gas lift installation to meet the changing requirements of the well itself, and a manner of compensating for changes in oil-water content, fluid volumes, PI, and bottom-hole pressure resulting from flood or repres-suring activity. A device which could actually set and change the operating pressure of gas lift valves in the well would meet most of these needs. There now exists a new gas lift valve which fulfills the original objectives and in so doing actually accomplishes much more. With this device, called an Automatic Stabilizer Controlled valve, there is an exact matching of valve operating pressure and well conditions. Gas is injected at more than one point in the well, thereby making controlled multiple-point injection of gas a reality. Installation calculations are materially simplified and the need for basic temperature and gas gradient data no longer exists. Section I—The Automatic Stabilizer Controlled Valve The operation of the ASC valve is more easily understood by first studying a conventional pressure-charged valve and then inserting the stabilizer element to observe the changes which result. Fig. 1 is a schematic of a conventional precharged pressure-operated valve. The pressure in the dome pd, acts downward, against the area of the bellows A,, to hold the valve closed. The resulting force Bf plus the spring effect of the bellows Sf represents the total force acting to close the valve. Correspondingly, the tubing pressure ptbg works upward against the port area Atbg and the casing pressure pc works upward against a portion of the area of the bellows

Jan 1, 1965

By W. M. Robertson

The kinetics of grain boundary groove formation on copper surfaces immersed in liquid lead have been studied over the temperature range of 400° to 900°C. The groove widths were Proportional to the cube root of the annealing time, indicating that the diffusion of copper through the saturated liquid-lead solution is the mechanism by which grooves form. The rate constant for the process can be calculated by a theory due to Mullins. Using published data for the solubility of copper in liquid lead, for the interfacial energy of the solid copper-liquid lead interface, and for the diffusion coefficient of copper in liquid lead, the calculated rate constants almost exactly reproduce the measured values over the entire temperature range. The decay of scratches placed on copper surfaces has also been studied. The rate constant for scratch decay agrees with that for grain boundary groove growth, though scratch decay is sensitive to convection currents in the liquid. The interaction of solid and liquid metals has been studied extensively and has been found to be rather complex. Many of the studies have been complicated by a host of competing effects, including temperature gradients, concentration gradients, the formation of one or more intermetallic phases, natural or forced convection, and the presence in both the solid and liquid of considerable amounts of impurities and alloying elements. Recently theories have been developed of changes in surface profiles driven by capillary forces,' which allow the interaction of the solid and liquid to be analyzed quite directly. The present paper reports a study of the formation of grain boundary grooves on pure copper immersed in liquid lead, which allows the theory to be checked quantitatively. The Cu-Pb equilibrium diagram is quite simple: there are no intermetallic compounds, copper is just slightly soluble in liquid lead, and lead is almost completely insoluble in solid copper.2 The Cu-Pb system has been studied extensively,3-9 and all of the quantities—interfacial energy, diffusion coefficients, and equilibrium solubilities-necessary to calculate the rate of groove growth by a volume-diffusion mechanism are known. The kinetics of grain boundary grooving and scratch smoothing have been studied on the noble metals and the iron group metals in a reducing atmosphere or in vacuum.10 The main interest of these studies has been the determination of surface-diffusion coefficients at metal-gas interfaces using the theories developed by Mullins.1 The present paper uses similar methods for the study of diffusion processes at the interface between two condensed phases. There has been one previous study" of the kinetics of groove growth in a solid-liquid system, which, however, was troubled by the fact that neither interface energies nor diffusion coefficients were known in the Ni-S system studied. THEORY The theory of grain boundary groove growth has been developed by Mullins for the cases of volume diffusion," surface diffusion," and a combination of the two processes.14 He has also analyzed the kinetics of the flattening of a scratched surface by these processes.l5,l6 Several assumptions and approximations were used in the derivations of the surface profile shapes. The applicability of these assumptions and approximations to the present system will be considered in the discussion. At the intersection of a grain boundary with an initially flat interface the equilibrium between the interfacial energy and the grain boundary energy establishes an equilibrium groove angle. This induces curvatures in the interface. The chemical potential of material at a curved interface is higher than at a flat interface, so that material moves away from the region of the grain boundary. Mullins' calculations indicated that the groove profile would be similar to that shown schematically in Fig. 1. Small humps form above the level of the original flat surface. For a volume-diffusion mechanism the separation, w, of these humps at a time, t, is given by and where co is the equilibrium concentration of the solid in the liquid, y, the solid-liquid interfacial free energy, O the volume occupied by a solute atom in the liquid, D the diffusion coefficient of the solid in the liquid, and kT has its usual meaning. For a surface-diffusion mechanism the groove width is proportional to the fourth root of the time. For grooves forming by a combined surface and volume-diffusion mechanism the exponent of the

Jan 1, 1965

By William G. Pariseau, H. Douglas Dahl

Recent subsidence legislation indicates that mining engineers would be welt advised to be able to predict and control surface damage caused by mine subsidence. To date, such an ability is practically nonexistent. Model analysis is suggested as one of the alternative paths available which might yield fruitful results. Similitude requirements developed for a self-loaded body in static or quasi-static equilibrium indicate that complete similitude without centrifuging is an impracticability. However, a pilot experimental study which used a simplifying assumption to correctly model mine subsidence has produced results in qualitative agreement with field observations. The purpose of this paper is to present a discussion of the various approaches that can be taken in the study of mine subsidence phenomena. Particular attention is focused upon the rational selection and use of laboratory models. Broadly interpreted, mine subsidence is the deformation of the rock mass enclosing a mine. Depending upon a number of factors, the movement of the subsiding rock mass may disrupt gas and water lines or other buried utilities, damage surface structures such as buildings and bridges, dislocate streams, roads, and rail lines, aggravate acid mine drainage and fire problems, and generally mar the landscape. It is clearly a problem that no mine manager can safely ignore. It is also a problem that will grow with the general population increase. In the following discussion, a summary review of past and present approaches to subsidence studies is given. The possibilities of duplicating subsidence phenomena in laboratory models are examined, and an analysis of a particular type of model is presented. Some preliminary results obtained from a model of the particular type analyzed are then discussed. REVIEW OF PREVIOUS WORK Historically, subsidence investigations have been empirical studies in the field and laboratory or theoretical analyses of mathematically idealized media. Empirical and theoretical work in the United States has generally lagged behind investigations abroad. In the United States, field studies are mostly pre-World War 11. These are summarized in the Mining Engineer's Handbook. ' Field studies in Europe are more recent and more extensive. Those made in Great Britain are summarized in the Subsidence Engineers Handbook2 and represent observations made at 157 different collieries. Such studies by themselves are of limited usefulness as are all empirical studies. One can never be certain that conditions at one mine will be similar enough to those at another to warrant the drawing of like conclusions. European subsidence formulas rely heavily upon the "angle of draw" and "critical area" concepts. The angle of draw is defined as the angle between a vertical line through the face, and another line extending from the face to the surface at the point where movement is zero. The critical area is defined in relation to the least extraction necessary to produce maximum subsidence. Fig. 1 illustrates the angle of draw and critical area concepts. First and second "limits of influence" are also shown. The angle of draw and associated critical area concept are obviously not well defined, being dependent upon the accuracy of the surface survey. In Great Britain, the angle of draw has increased through the years from about 26 to 35°. In the United States, zero and negative angles of draw have been reported. In the authors' opinion, these purely geometrical concepts represent an oversimplification of subsidence phenomena and their use, in the United States at least, should be discouraged. Empirical observations of laboratory models containing layers of earth, sand, clay, and plaster were made by Fayol (cited by Peele) as early as 1885. An outgrowth of his work was the "dome theory," a verbal description of what is assumed to occur in subsiding rock masses. The dome theory has since fallen into disrepute. Theoretical analyses worthy of the name treat a subsiding rock mass as a deformable body. In these analyses, the actual rock mass is replaced by an idealized material that deforms according to a simple stress-strain relationship. The stress equations of equilibrium expressing the Newtonian laws of mechanical action and the geometry of strain furnish additional equations that must be satisfied. A loading criterion-generally understood, and in some cases stated explicitly-completes the theory.

Jan 1, 1969

By D. H. Yardley

GEOCHEMICAL investigation of trace elements in surface materials was begun near Ely, Minn., in 1953 along the basal contact of Duluth gabbro with Giants Range granite (Fig. 1). This article presents data on the distribution of copper and nickel in till and in stream sediments in the area and proposes an explanation for the types of distribution found. The Duluth gabbro, one of the world's largest basic intrusives, intrudes rocks which range in age from Keewatin to middle Keweenawan. Within the test area the gabbro is in contact with granite except for short sections where it is in contact with remnants of iron formation. Sulfide mineralization occurs within the gabbro, near and parallel to the basal contact for a distance of several miles. Schwartz and Davidson' have described the geologic setting of the mineralization. The sulfides, believed to be syngenetic, include chalcopyrite, cubanite, pentlandite, pyrrhotite, and minor amounts of bornite. They occur disseminated in the silicates and as small interstitial masses. The ratio of copper to nickel is about 3.8:1, based on 66 chemical analyses of rock samples from various outcrops (Ref. 1, p. 702, and Ref. 2). Test Procedures: With specified exceptions, all nickel and copper tests were made by the chromo-graph method,:' which measures the intensity of a colored spot formed by a reaction between the metal being determined and special reagent paper. The intensity is then compared to the intensity of spots prepared from samples of known metal content. Details of the test procedure are outlined in another article (Ref. 4, pp. 77,78). All soil samples tested in this investigation to date have been weighed on an analytical balance. However, a volumetric scoop designed to provide about 0.1 g of soil adds to the speed and ease of testing and has been found to give satisfactory results (Ref. 5, p. 531, and Ref. 19). The size of the samples used for the tests was 0.1 g. Whenever such small samples are used there is some question as to whether they are representative of the several grams in the field sample. Many repeat tests of the samples used in this investigation demonstrated that results can be reproduced within the limits of accuracy of the method without formal mixing beyond that inherent in screening the soil fractions. Furthermore, the 0.1 g is probably as representative of the field sample as the field sample is of its area of influence. Hawkes and Lakin (Ref. 6, p. 291), who considered the general problem, compared ground and quartered bulk samples of 500 g with 5-g grab samples. They concluded that "there is no significant loss in accuracy of data by substituting grab samples for bulk samples." The term soil implies somewhat different things to the geologist, engineer, and soil scientist.' For convenience the term as used in this article refers to unconsolidated material (the mantle) overlying bed rock. Sampling Procedure: Samples were taken at 100-ft intervals along north-south traverse lines across the gabbro-granite contact. The soil (till) samples were taken at an average depth of 1 ft, which was below the high-humus surface layer and into clean till. Samples taken at 1-ft intervals down to ledge showed as high a metal content at 1 ft below the air-surface as at greater depths and in two instances were slightly higher. The till at 1-ft depth did not appear to differ from material at greater depths. Total depth to bedrock has been tested at only a few points and where measured varied from 1 to 10 ft. Aerial Distribution Contours and Profiles: Plotting of copper, nickel, and cobalt content in contour form (Fig. 2) shows that anomalous amounts of these metal ions occur in till over and closely adjacent to mineralized areas of the gabbro. Contouring nickel content alone, or the copper content, outlines the same target area. Contours of the copper content provide a more distinct anomaly than nickel because of the higher copper concentration. The traverses are rather widely spread for interpolation; however, drilling has confirmed the target area essentially as shown.

Jan 1, 1959