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By J. E. Flinn, S. A. Duran

The steady-state creep behavior of poly crystalline cad mi inn was studied over a temperature range of (1.56 to 0.94 Tm. Two distinct mechanisms were found to occur over this temperature range. They were described by: where and represerqt the minimum strain rates corresponding to the low- and high-temperature regions, respectirely. The two regions of constant acti11ation energy were connected by a transition region where the strain rate was controlled by both mechanisms acting in parallel. At temperatures below a transition temperature of about 0.7 Tm the agreement between the activation energy value for creep and that for self-diffiision suggests a rate-controlling mechanism of dislocation climb. For cadwzium, steady-state creep at temperatures above 0. 7 Tm appears to be controlled by another mechanism, perhaps involving the behavior of dislocation jogs. FRENKEL et al.1 studied the high-temperature creep of polycrystalline cadmium and reported an activation energy of 21 kcal per mole for the 0.5 Tm < T < 0.8 Tm range. Based on observations of creep rate at only two temperatures, a value of 22.1 kcal per mole was determined by Medbury. These two investigations were for the purpose of showing agreement between the activation energy for creep and that for self-diffusion, reported3 as 18.2 and 19.1 kcal per mole, respectively, for diffusion parallel and perpendicular to the hexagonal axis. Gilman4 investigated prismatic glide in single crystals of cadmium over a higher-temperature range of 0.72 to 0.93 Tm, and found an activation energy of 29 kcal per mole. He also reported5 an activation energy higher than that of self-diffusion for prismatic glide in zinc single crystals deformed at temperatures near the melting point. This value was in good agreement with those found for an equivalent temperature range by Flinn and Munson6 and by Tegart and sherby7 for polycrystalline zinc. These two independent studies also disclosed at lower temperatures another value of activation energy near that for self-diffusion. It would be expected from the creep results on zinc and single-crystal cadmium that creep studies on polycrystalline cadmium, extended to temperatures near the melting point, might yield an activation-energy value higher than the 22 kcal per mole value found in earlier studies. The purpose of this paper is to report the steady-creep behavior of polycrystalline cadmium over a temperature range of approximately 0.5 to 0.9 Tm EXPERIMENTAL METHOD The cadmium used in this study was obtained in the form of as-cast rods, 0.5 in. diam, through the courtesy of the Bunker Hill Mining Co. The material was of 99.995 pct purity, as determined by spectro-chemical analysis. The creep specimens, which were 0.250 in. diam by 0.400 in. long and annealed at 300°C for 45 min to produce a stable average grain diameter 0.25 mm, were tested in compression using an apparatus similar to that described by Sherby.8 The specimen temperature was controlled to within ±0.5°C with the help of appropriate constant-temperature baths. The applied stress was maintained within 1.0 pct of the desired value by the additions of lead shot at fixed strain increments. No barreling was observed over the strains encountered during testing. Isothermal creep tests9 were used in the study with only a few differential temperature tests10 run for comparison purposes. Steady-state creep data were obtained over a temperature range of 60 to 287°C (0.56 to 0.94 Tm) at five stress levels ranging from 28.1 to 140.6 kg per sq cm. RESULTS The minimum or steady-state creep rate may be described by an equation of the following form:" where i is the minimum strain rate, S is the structure factor, F is a stress function, Qc is the energy of activation, T is the absolute temperature, and R is the gas constant. The minimum strain rates obtained in this study for cadmium were recorded on a semilogarithm plot as a function of the reciprocal absolute temperatures for the various stress levels, as shown in Fig. 1. This figure shows a characteristic transitional behavior" with a parallel interaction of two mechanisms. It is obvious that the activation energies corresponding to the individual processes are insensitive to stress because the curves are parallel. The discrete activation-energies values for the low- and high-temperature regions for the various stress levels are reported in Table I, and were determined by the least-mean-square method. For the low-temperature region, an activation energy of 20.7 ± 0.6 kcal per mole was obtained, and for the

Jan 1, 1967

By William H. Callahan

"For his exceptionally successful career as a geological mentor, for his ore-finding skills, and particularly the discovery of the Central Tennessee Zinc District and for his lecture, &apos;Prospecting in the USA-Promise and Problems.&apos; " Recipient of the 1982 D.C. Jackling Award

Jan 1, 1983

DEPENDENCY on foreign sources for many mineral raw materials is a characteristic of our economy which is becoming painfully evident. Although investment in foreign mining projects has increased, it has not kept up with the growing demand for foreign minerals. The sphere of American investment capital in mining ventures abroad has been severely limited by the rise of nationalism in many underdeveloped countries. Consequently, we can look back over half a century in which mining investment, exclusive of petroleum, has increased by 50 pct whereas other American investments abroad have multiplied by better than 300 pct. Investment in foreign mining or petroleum encounters different problems than capital investment for other industries. It is rarely invested in industrialized nations. Most of it goes to countries with expanding frontiers, like Canada, or to underdeveloped nations like Liberia. It must be used for building communities, recruiting and training labor, and establishing lines of communication and transportation. These complications are an accepted part of the mining game. However, the most complex problem is in those countries which consider mineral exploitation a usurpation of the people&apos;s natural heritage. This is a characteristic of the young government existing by a tenuous balance of power in an underdeveloped nation. American mining capital understandably has shunned these nations as being poor investment risks. However, they possess minerals which are needed by industry. Our government has attempted to stimulate mineral supplies beyond those provided from abroad by private capital. ECA, now under DMPA, makes loans to foreign mining companies. Since the ECA program cannot be expected to continue indefinitely, Point IV seems to be the logical next step to encourage foreign countries to fill our shortages. However, only 1 pct of the $35 million budget provided in the first year for Point IV was alloted for mining programs. Considering the need for minerals and the difficulties of procuring them by private investment, a larger share is needed and justifiable. Those who have been engaged in foreign mining can vouch for the fact that it takes many decades to teach the complex technology and economics of mining to the natives of under-developed countries. For this reason Point IV must be considered a long range program. Mineral requirements for the present must be met by more direct measures. Encouragement of private investment in foreign mining by such incentives as tax relief on profits from foreign sources, international bank-borrowing facilities for private capital, and diplomatic assistance in encouraging foreign countries to cooperate are imperative for our future mineral security.

Jan 1, 1952

By K. A. Jackson, J. D. Hunt

A general theory for the growth of lamellar and rod eutectics is presented. These modes of growth depend on the interplay between the diffusion required for phase separation and the formation of interphase boundaries. The present analysis of these factors provides a justification for earlier approximate theovies. The conditions for stability of rod and Lanlellar structures are consitleved in terms of the mechanisms by which the structure can change. The mechanisms considered include both small adjustments to the lnnzellar spacing due to the motion of lamellar faults, and catastrophic changes due to instabilities. It is concluded that stable growth occurs at or near the minimum interface undevcooling for a gizierz growth rate. The conseqrlences of the existence of a diffusion boundary layer at the interface are discussed. The experimental results for the variation of growth rate, undercooling, and Lanzellar spacing are cornpared with the theory. We believe that the theory presented in this paper provides an adequate basis for understanding the complex phenomena of lanzellar and rod eutectic growth. The growth of lamellar eutectics has been the subject of several theoretical and many experimental studies. The foundations for the theoretical work were laid by zenerl and Brandt2 in their analyses of the growth of pearlite. Zener estimated the effect cf diffusion, and took into account the surface energy of the lamellar structure. He found that the lamellar structure could grow in a range of growth rates at a given undercooling provided the lamellar spacing was appropriate for the growth rate. Since pearlite grows with only one growth rate and one lamellar spacing at a given undercooling, there is clearly an ambiguity in the theory. Zener removed this ambiguity by postulating that the growth rate was the maximum possible at the given undercooling. He predicted then that the product of the growth velocity v and the square of the lamellar spacing A should be constant, i.e., A2v = const. Brandt2 started out by assuming that the interface between the lamellae and austenite was sinusoidal. Because of this, the ambiguity encountered by Zener did not arise. Brandt was able to obtain an approximate solution to the diffusion equation, but, since he did not take into account the surface energy, his considerations are incomplete. Tiller3 applied some of these ideas to the growth of eutectics, and proposed a minimum undercooling condition to replace the maximum velocity condition used by Zener. These conditions are formally identical. Hillert4 extended the work of Zener. He found a solution to the diffusion equation assuming the interface to be plane. Taking surface energy into account, and applying Zener&apos;s maximum condition, he was able to calculate an approximate shape of the interface. Jackson et al.5 used an iterative method employing an electric analog to the diffusion problem to refine the calculation of interface shape. It was found that the interface shape calculated from a plane-interface solution to the diffusion equation was negligibly different from the exact solution. The method provided an analog only for eutectics for which the volumes of the two phases are equal, growing from a melt of exactly eu-tectic composition. There has also been considerable experimental work on eutectics, Several experimenters8-10 found that A2v is constant as predicted by Zener.1 Hunt and chilton10 demonstrated that ?T/v1/2 is also a constant for the Pb-Sn system as predicted. Lemkey et al.11have recently found A2v to be constant for a rod eutectic. In the present paper, we present the steady-state solution for the diffusion equation for a lamellar eutectic growing with a plane interface, for the general case, that is, with no restriction on the relative volumes of the two phases, and with the melt on or off eutectic composition. A similar solution is also found for a rod-type eutectic. Expressions are obtained for the average composition at the interface and the average curvature of the interface. These equations for the average composition and curvature are similar in form to those derived by Zener1 and Tiller,3 and provide a justification for some of the approximations made by these authors. The mechanisms by which the spacing in a lamellar structure can change are considered. The important mechanism for small changes in lamellar spacing involves a lamellar fault. Examination of the stability of lamellar faults leads to the conclusion that the growth occurs at or near the extremum.* The insta- bilities which can develop in a rodlike structure are also discussed, resulting in the conclusion that this structure also grows at or near the extremum. Comparison of the conditions for rod and lamellar growth permits a prediction of the surface-energy anisotropy required to produce rods or lamellae for various volume-fraction ratios. The diffusion equation predicts the existence of a diffusion boundary layer at the eutectic interface unless the eutectic has 0.5 volume fraction of each phase and is growing into a liquid of eutectic composition. This boundary layer is such as to make the composition in the liquid at the interface approximately equal to the eutectic composition. This boundary layer permits changes in composition during the zone refining of eutectics. Photographs of the eutectic interface of a growing transparent organic eutectic system have been made. Both the components of this eutectic are transparent organic compounds that freeze as metals do.12 The in-

Jan 1, 1967

By E. Teghtsoonian, K. G. Davis

Cobalt crystals of commercial purity have been tested in tension. Their resolved shear stress-shear strain curves are very similar in form to those for zinc, magnesium, and cadmium. There is an initial linear region for shear strains up to around 150 pct, the ratio of work hardening slope to shear modulus at room temperature being about 2 X x This is followed by an upturn, which is, PLASTIC deformation in metal single crystals with close-packed structures has been found strongly dependent on stacking-fault energy. The high stacking-fault energy hexagonal metals magnesium, zinc, and cadmium have been quite extensively tested, but up to now no data have been available for a comparable hexagonal metal with low stacking-fau1t energy&apos; An however, smaller in magnitude for cobalt than for the other metals. Values for the critical resolved shear stress rise from 97 kg per sq cm at room temperature to approximately 170 kg per sq cm at -196 °C. The Cottrell-Stokes ratio is not constant either for variations in the strain rate or for temperature changes, its value decreasing with strain. investigation into the plastic deformation of cobalt, which has a very low stacking-fault energy, has therefore been undertaken. EXPERIMENTAL PROCEDURES Cobalt crystals in the form of rods 0.3 cm in diam were grown in an electron-beam floating-zone refiner at a rate of zone travel of 25 cm per hr. Details of the growing procedure are given in Ref. 1. The zoned cobalt rods had the following analysis:

Jan 1, 1963

By Olof Löfgren

PART 1 INTRODUCTION All modern pelletizing plants are equipped with either the drum or the disc circuits. Choice of one or the other circuit is not simple and it is desirable to establish a firm basis for such a task. For a meaningful and a fair comparison it is necessary to have the two systems working in parallel in the same plant with the same concentrate under the same supervision. Furthermore, the comparison has to be based on a defined green ball quality and size distribution. BALLING CIRCUITS The LKAB straight grate plant at Malmberget, Sweden, was started up in Septenber 1973. It was designed for a 2.5 Mton annual capacity and was equipped with five balling drum circuits. During the first year of operation it was found that the induration plant had the potential for a higher capacity which required increased balling capacity. For this purpose it was decided to install a balling disc circuit complete with a roll screen. The reasons for selecting a disc were space limitations and LKAB&apos;s desire to gather experience on balling disc circuits. The disc circuit was started up in 1975 and was run in parallel with the balling drums in the same plant and with the same raw material and under the same operating personnel. The necessary conditions for a comparison were thereby fulfilled. The data for the size distribution and quality of the green balls were obtained on random sampling during one year of operation, so that all the variations which appear in a commercial plant are covered.

Jan 1, 1977

By J. W. Evans

ONE possible method for the separation of hafnium from zirconium is by the vapor phase oxidation of the purified mixed chlorides. An important factor for success depends on the difference in free energies of the following reactions: ZrCl(g) + O2 = ZrO2(s) + 2C12 [1] HfCl4(g) + O2 = HfO2(s) + 2C12. [2] Prakash and Sundaram1 have calculated these values from certain data and carried out experimental work with partial success. However, their free energy values for reaction 2 diverge rather widely from other data which are presented here. The possibility of successful separation is briefly considered in the light of these alternative values. Table I shows the free energy values (?F°) for reactions 1 and 2 derived from the recent compilation of data on oxides and chlorides by Glassner.2 The corresponding values of Prakash and Sundaram for the same temperatures are also shown. The alternative values to those of Prakash and Sundaram for reaction 2 are substantially confirmed by the data of Kubaschewski and Evans" and Cough-lin&apos; on heats of formation, entropies, and heats of vaporization. In spite of the considerable uncertainty in the hafnium data it is reasonable to suppose that the oxide-chloride free energy difference for two such chemically similar elements would not be very far apart. These figures indicate clearly that the oxidation of hafnium chloride is appreciable at all temperatures. Nevertheless, there is a significant difference between the values for reactions 1 and 2

Jan 1, 1959

By S. Wallden, R. Lindstrom

The electrolytic copper refining process is an excellent method for producing high-purity metal for electric conductors and other demanding applications. However, the process involves very high capital expenditure, especially the amounts of metals bound in the process. Efforts have therefore been made for many years to increase the production rate by increasing the current density, without impairing the quality of the copper. One of the approaches has been to diminish the polarization by mechanical means, while another was to "polish" the cathode surface by periodic brief reversals of the current. Reversed current electrolysis was first developed for electro- plating purposes and in 1952 Boliden AB and the Dept. of Electrochemistry at the Royal Inst. of Tech., Stockholm tested the method for copper refining with good results. However, no suitable electrical equipment for current reversal was then available. The thyristor-controlled silicon rectifier became available during the &apos;60s and provided the scope for industrial application of the process and the first large-scale development was made by the Bulgarian copper refinery in Pirdop. Many copper refineries are now studying or adapting the reverse current process. Further lab and pilot investigations have been carried out at Boliden AB during the past 4 years and these were mainly aimed at studying the optimization of factors influencing the quality of copper. A production unit containing two tank sections with a total of 56 cells and equipped with a rectifier for cur- rent reversal has been installed and will be started during 1973.

Jan 1, 1973

By D. G. Westlake

Resistance was measured as a function of temperature, 77° to 350°K,for niobium with hydrogen concentrations up to 3.76 at. pct. Cooling curves exhibited a discontinuity in slope that was attributed to the initiation of hydride formation. A thermal hysteresis was explained in terms of diffusion and the effects of mechanical constraint on nucleation and growth. The heat of solution of hydrogen in saturated Nb-H solid solution was 2. 737 * 0.045 kcal per g-atom, including an unknown stress contribution. The critical ternperatures for hydride formation during cooling and for embrittlement are correlated but not coincident. This, too, has been explained in terms of mechanical constraint and stress-itlduced tratzsfomtation. Nb-H alloys undergo a ductile-brittle transition with decreasing temperature.&apos;-3 Similar behavior has been noted for v-H.1,5 For the latter system, there is evi-dence6 suggesting coincidence of the temperature of minimum ductility and the critical temperature T, for initiation of metal hydride precipitation during cooling. A decrease in ductility due to the presence of brittle hydride particles is readily explainable. The fact that ductility begins to decrease at some temperature higher than T,4,5 has led us6 to suggest that precipitation may be strain-induced locally during tensile testing. Wood and Daniels&apos; have reported that a plot of temperatures for 10 pct reduction in ductility vs hydrogen concentration in niobium is not coincident with, but parallels, the solvus.7,8 They believe this indicates a correlation of precipitation and embrittlement. Unfortunately, the two reported solvuses 7,8 to which Wood and Daniels refer are not in agreement with each other. Furthermore, neither solvus was determined experimentally: each was a plot of calculated solubilities. Thus. neither is highly dependable for determining whether embrittlement coincides with initiation of hydride precipitation. Longson 9 studied phase relations in the Nb-H system between 77° and 473°K by dilatometry. Comparison with metallographic observations convinced him that discontinuities in the slopes of his dilatometric plots were coincident with the initiation of hydride precipitation. Plotting the logarithm of the hydrogen concentration vs the reciprocal of the temperature at which precipitation was initiated during cooling, he obtained a straight line shown in Fig. 1. Walter and chandler,&apos;&apos; using X-ray techniques to detect the for mation of a second phase? have obtained three experimental points in the temperature range 295° to 338°K which fall within Longson&apos;s experimental error for this plot. A similar plotg of temperatures at which dissolution was completed during heating was a parallel line shifted toward higher temperatures. A straight-line plot was obtained, also, for the temperatures of the ductile-brittle transitions,9 but it was shifted toward still higher temperatures. Longson calculated an activation energy of 2.980 * 0.300 kcal per mole for the hydrogen embrittlement mechanism, compared with 3.180 * 0.400 kcal per mole for hydride formation. Despite this agreement, he concluded, "It seems unlikely that embrittlement results from hydride formation..." because hydrogen embrittlement was observed at temperatures above the solvus. It is our contention that embrittlement is correlated with precipitation of the hydride.6 Because only Longson has investigated Nb-H phase relations at sub-ambient temperatures, we deemed it advisable to re-determine the temperature dependence of the solubility using the resistometric technique already proven successful for the V-H system.6 Coincidence of our solvus with temperatures for embrittlement would

Jan 1, 1970

W. M. CURSE, Mansfield, Ohio.-Outside of the commercial valu-ation of the material, for what purpose does this alloy-90 per cent. of copper, 6 ½ per cent. tin, 2 per cent. zinc, and 1 ½ per cent. Lead-seem to be eminently fitted? C. P. KARR.-So far as our tests go, it would be eminently fitted for steam valves and pistons, and for the work for which 88-10-2 bronze is generally used, although for very large castings it would not be superior to 88-8-4 bronze. P. E. MCKINNEY, * Washington, D. C.-Some time hack, clue to a desire to avoid some of the objectionable features of 88-10-2 bronze, particu-larly on heavy castings, also to save tin where possible, we took up the question of a substitute for 88-10-2 bronze, where red bronze was ordinarily specified. After trying most of the mixtures, we found that when using as low a tin content as is given in this proposed composi-

Jan 12, 1919

By G. K. Burgess

J. W. RICHARDS, South Bethlehem, Pa.-I think my affections are still rather with the radiation pyrometer than the optical pyrometer, for practical use, and I wish that Prof. Burgess would use the two together, under the same conditions, using the optical as his standard, if he prefers. Then, assuming the optical emissivity which he feels is correct for the optical pyrometer, he could calculate the thermal emissivity for use with .the radiation pyrometer. If we could thus get reliable values for the thermal emissivity, we could then use the radiation pyrometer, and would avoid the use of the standard lamp, which has to be frequently calibrated for use in the optical pyrometer. It is very advisable to distinguish carefully between the terms optical emissivity and thermal emissivity. There -is considerable confusion caused by the bare statement that molten iron has an emissivity of so much, meaning by that its optical emissivity, for a light wave of a certain length; whereas what we want in the radiation pyrometer is its total ther-

Jan 4, 1917

Zinc is just now a very important metal. Its use in cartridges and shrapnel brass are in the public eye. But its uses after the war are no less important. Brass as an engineering material for electrical machin-ery, journal bearings, and plumbing fixtures takes fully 50 per cent. of the production, and its use in these lines would have been increased in the last few years but for the price. Its use for barbed wire is probably more in war time than in peace. In the composition of paints, it is becoming more and more necessary. One of the forms of pigment, litho- pone, is the base of nearly all interior wall paints; of all the sanitary enamels for bath-rooms and bath-tubs, and is now in great demand. Zinc oxide is also increasing in use for paint, and for manufacture of linoleum. When we realize that this district-Missouri, Oklahoma, Kansas and Arkansas-produces now over one-third of the zinc ore of the world, it is at once seen that a meeting where the geology, mining, concentration

Jan 6, 1917

By Charles D. Russell, L. H. Jenks, W. J. Leas

A detailed description is given of an experimental method for determining relative permeability of porous media to gas. Results are presented for natural and synthetic cores. The experimental data for two and three phase systems are compared. The reproduci-bility of the equilibrium gas saturation ii demonstrated and the effects due to a variation in rate of gas flow are discussed. An attempt is made to correlate total permeability and rock textural factors with relative permeability to gas. Capillary pressure curves obtained simultaneously with the relative permeability curves are shown to be equivalent to those obtained in conventional displacement cells. INTRODUCTION The advances in petroleum reservoir technology during the past decade have made increasingly apparent the desirability of a simple, rapid, reliable metliod for obtaining relative permeability data on small cores. Such data are needed in order to study fluid mechanics in porous media and for the more refined reservoir behavior prediction calculations now under development. The early experimental work in this field was done by Wyckoff and Botset1 who measured relative permeabilities for gas-liquid mixtures flowing through

Jan 1, 1950

By Donald M. Hausen

Microscopic evaluation of trace quantities of metalliferous phases in flotation products requires counting large numbers of particles. Particle counts of many thousands may be required for precision, but cannot be obtained practically by conventional microscopic techniques. A less tedious microscopic method for evaluating trace sulfides in mill tailings was developed for the O&apos;okiep Mining Co. in South Africa. Hundreds of thousands of particles were evaluated by this method called "gross-counting." Gross-counting consists of counting microscopic fields rather than point-counting individual particles. Total counts are calculated by multiplying the average number of particles per field by the total number of fields examined over the entire mount. Total gross-counts range from about 20,000 particles for +200 to 100,000 or more for -400 mesh size material in lucite mounts. Sulfides and metallic particles in each field are identified and tallied along with field counts. Totals for each type of metallic particle are divided by the total gross-count to give volume percent which is corrected to weight percent by specific gravity factors.

Jan 1, 1973

By J. V. Calara, J. D. Miller

The sign of the surface potential for complex non-reactive ionic solids cannot be predicted solely from consideration of the hydration energy of gaseous ions which constitute the ionic lattice. Accurate analysis of these systems must involve the hydration energy of surface ions, which requires knowledge of the crystal structure, the identification of cleavage planes, and the calculation of binding energies of surface ions. Surface binding energies for ionic solids can be determined if the Surface Madelung Constant is known. A computational technique was developed for the calculation of Madelung Constants for infinite lattices which gives excellent agreement with the values calculated by other more complicated methods reported in the literature. Extension of this technique permits the calculation of Surface Madelung Constants and binding energies of surface ions, [Aus], for semi-infinite solids. The hydration free energy of gaseous ions, [AFh], together with the calculated binding energy of surface ions, [Aus], allows calculation of the hydration energy of surface ions,[AGh], as for the case of the ionic solid, MX: [ ]

Jan 1, 1976

By J. B. Clark, F. N. Rhines

brittlement or notch sensitivity progressively increases. Further, in contrast to results obtained with the impact test, the notch strength for the large specimens does not reveal a 500°F embrittlement range. The notch sensitivity as determined with the 0.3-in. specimen of 4340 steel given the stepped austenitizing treatment has been discussed elsewhere. This quantity as measured for the 1.1-in.- diam notch tensile test and given in Fig. 3, is taken to signify that reduced notch sensitivity is encountered in the 600" to 800°F tempering range for specimens given the stepped austenitizing treatment. The stepped austenitizing treatment may, there- fore, be of use in promoting deeper hardenability for a 4340 steel while at the same time giving reduced notch sensitivity in the high-strength range in which this steel is now being used. Acknowledgments The work reported was supported by the U. S. Navy Bureau of Aeronautics. The authors are indebted to the Bureau of Aeronautics for granting permission to publish results of this research and to N. E. Promisel, H. Hessing, and J. Maltz for their interest.

Jan 1, 1958

By J. E. Warren, J. H. Hartsock

Because of the extensive utilization of hydraulic fracturing for the stimulation of low-productivity wells, the two related problems of fracture design and evaluation have become economically significant and, as a consequence, helve motivated this investigation. The producing characteristics of horizontally fractured wells were studied to determine the fracture configuration that should be employed as the basis for the design of the treatment and to develop a method that can be used to establish the degree to which the design objectives have been achieved. The equations which describe the steady-state flow of a single-phase fluid into, and through. a finite-capacity fracture were solved numerically for an idealized reservoir-fracture model. The numerical results were used to obtain an apparent skin effect for each combination of the parameters considered. Based on the computed results, subject to the limitcitions implied by the assumptions that were made, the following general conclusions were drawn. 1. For a radius of drainage at least four times us large as the radius of the fracture, an apparent skin effect that is independent of the radius of drainage can be calculated. 2. The productivity of the hydraulically fractured system, relative to that of the unfructured well, can be determined from the apparent skin effect and can be used to establish design objectives. 3. In the evaluation of a fracture job, it is not Possible to determine both the radius of the fracture and its flow capacity uniquely from the apparent skin effect; an independent determination of one of the quantities is necessary. lNTRODUCTION Although hydraulic fracturing has been employed as a method for stimulating the productivity of literally hundreds of thousands of wells during the past 10 years, it is only in the last few years that improvements in fracture design1-6 and fracturing technique&apos; have combined to increase the probability of obtaining a successful treatment to such an extent that the mechanics of the method may be considered to be standardized. From an economic point of view, however, two related questions must be satisfactorily answered before hydraulic fracturing can be used in the most profitable manner. The two questions are the following. I. For a particular well in a given formation, what are the optimum design specifications for the fracture treatment? 2. Have the design objectives been achieved by the fracture treatment? The significance of these questions has been recoguized, and some attempts to obtain answers have been made. Howard, et al,8 endeavored to determine the optimum treatment, based on maximizing profits, for any given formation; unfortunately, this work was based on a crude method for approximating the productivity of a well. Carter and Tracy9 utilized the same approximation to study the effect of fracturing on the behavior of a well producing by virtue of a solution-gas drive. Electrolytic models were used by van Poollen10 to investigate the variation in productivity due to fracturing; however, only a limited number of results were presented. Later, from the same model results, van Poollen, et al,11 attempted to justify an approximate expression for determining the productivity of a fractured well. It is quite apparent that there is a definite lack of the practical information necessary for specifying the optimum fracture configuration to be considered for design purposes. The only detailed attempt to develop a procedure for evaluating the result of a given fracture treatment appears to be that of van Dam and Horner.12 These authors described a technique for analyzing pressure build-down data, obtained immediately after fracturing, to determine the final fracture volume, the final fracture porosity, the fracture area, the fracture thickness and the in situ fluid loss of the fracturing fluid. While this approach should be useful whenever acceptable pressure measurements are available, it does not yield a value for the flow capacity of the fracture. Since the problems of fracture design and evaluation are inversely related, it should be sufficient to study the effect of the fracture configuration on the performance of a well. The primary objective of this investigation is to evolve a technique for computing the desired solutions. The secondary objective is to analyze these computed results in order to prescribe a method for evaluating fracture treatments. Because this study is exploratory in nature, its scope

By W. A. Backofen, R. L. Fleischer

AN effect of orientation on the creep behavior of aluminum at 4.2 OK has been observed. Stress relaxation was measured in a hard-type tensile device after stopping the drive. From the spring constant of the device the load-time record could be converted to strain as a function of time. The strain sensitivity was 2-10-=, and the usual creep time of 1 min normally allowed a stress drop of about 25 g per sq mm. Further details of the apparatus and sample preparation appear elsewhere.&apos; It should be noted that neither stress nor strain were constant, so that quantitative comparison with current creep theories will not be made. Shear strain (y) as a function of time (t) was consistent with logarithmic behavior: y = A In t, where A is a constant. In some cases t was made as large as lo3 sec. In the results the quantity A divided by t (the resolved shear stress, which is the driving force for creep) is plotted as a function of strain prior to creep. The quantity A/t is thought to indicate qualitatively the ease with which dislocations can move during creep. In Fig. 1 are drawn tensile stress-strain curves and A/T-strain measurements for single crystals of three orientations: l(a) and l(b) for the maximum resolved shear-stress orientation, l(c) for an orientation 2 deg from [211], and l(d) for a [111] stress axis. The following observations were made: 1) At low strains the A/t values are nearly the same for the three orientations. 2) As strains increase, A/t drops most rapidly for [Ill.] and less rapidly for [211], while for the maximum shear-stress orientation it is constant during easy glide and drops abruptly at the termination of easy glide. 3) In stage 11, A/t values are again approximately the same for the three orientations. These observations are regarded as evidence that 1) the initiation of slip produces obstacles of essentially the same effectiveness for all of these orientations, while 2) the rate at which slip obstacles are produced before stage I1 is fully developed is strongly controlled by the amount of slip on more than one system. This second statement is consis-

Jan 1, 1961

By Hugh Douglas

ANTIMONY Antimony (Sb) has been used since the early Egyptian dynasties. Prior to World War I, total demand amounted to only 6000 to 7000 tons per year (tpy). Wartime uses and rapid rise of industrialization in the Northern Hemisphere nations have pushed world antimony use to the 78,000-tpy level. An overwhelming supply of low-cost antimonial resources in the Sino-Russian bloc countries has and will continue to have a major impact on availability and price to users outside the bloc. Table 14.4.1 shows trends in world production, United States production and consumption, and prices. Demand Antimony is used principally as an alloy in lead-based metals and other alloys. Pure metallic antimony usage is small and is confined to such areas as laboratory and electronic applications. Lead-antimony alloys are used in automobile storage batteries, chemical pumps, and pipes, tank linings, roofing material, and cable sheaths. The metal increases the hardness of lead, and, for such uses as foundry printing type, reduces shrinkage for casting and lowers the melting point. Antimonial oxides are used for ceramic purposes, white paint pigments, glass forming, textile finishing, fire retardants in military clothing, matches, and solder. Wartime applications include use as hardener for bullets, an element for tracer bullets, and ingredient for producing dense white smoke for visual markers. A small but rapidly growing use for antimony is for metallic compounds in semiconductors and thermoelectric devices. In the United States demand for antimony is about evenly divided between metallic end-use markets and nonmetallic markets. In metallic end uses, antimonial lead accounts for 27% of total metallic and nonmetallic use; in nonmetallic areas major uses are flame retardants (15%) which is the fastest growing market, plastics (13 % ), and ceramics and glass (11%). While antimony has advantages in most of its applications, there are uses in which other materials can be substituted, including: mercury, titanium, lead, zinc, chromium, tin, and zirconium in paints and pigments; tin in sheathings; calcium in battery plates; and bismuth in type metal. Supply Antimony is produced from both antimony ores and as a byproduct of smelting other ores. The principal ore mineral is stibnite (Sb2S3), along with its oxidized antimonial minerals and derivatives which occur in small discontinuous replacement veins or fissure vein implacements. Stibnite occurs in quartz-gold veins and copper-lead-zinc

Jan 1, 1976

By J. P. Batcha, J. Robert Denny

Since 1964. Newmont Mining Corp. has been engaged in a systematic research and development of computer techniques for a variety of mine planning applications. The general objective of this effort has been twofold: first, to arrive at a viable near-optimum plan for mining a particular orebody and, second, to decrease the financial investment by reducing the man-hours required for mine planning. Three major phases in the evolution of Newmont&apos;s computer techniques for mine planning are discernible. In phase one, the computer&apos;s ability to duplicate manual drafting and contour mapping was developed. Obviously, all recognized geologic characteristics had to be included, and consequently the development of computer techniques for the proper incorporation of structure, stratigraphic trends, and other geological features was a significant aspect of phase one.

Jan 1, 1970