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By C. C. Harris

The characteristics of some common size distribution equations are critically discussed. A generalized form of several well-known size distribution equations is obtained from a differential equation describing statistical distributions. The equation contains three parameters and can describe the major features of size distributions in the fine and the coarse size regions. A graphical method for its implementation is provided. The application of this and other equations to sets of data are compared both for the quality of fit and from a comminution kinetics viewpoint. If a narrow size range of a brittle material is broken sufficiently to obliterate the feed sizes, but not so severely that excessive secondary breakage occurs, a plot of cumulative fraction by weight undersize (Y) vs. sieve size (X) on a log log grid (sometimes called the Gates-Gaudin-Schuhmann plot)1-3 gives a straight line of slope ~ 1 over much of its range. On closer inspection, deviations in the extreme coarse range covering perhaps 10 to 30% of the total sample may be apparent (frequently, a change in slope from ~ 1 to a value different from unity) together with over-all slight irregular departures from a smooth line. One model of breakage postulates that the same fracture pattern persists throughout all size ranges.4 The fracture pattern is characterized by the slope of the line on a log log grid. Accordingly, a distribution of sizes broken in the manner specified earlier is expected to produce a size distribution having the same slope as that of a broken narrow size range. Additionally, the slight irregularities mentioned above should even out in the summation process, giving a smooth straight line of slope ~1 on a log log plot. This idealized state of affairs does not, however, describe the distribution of a multi-event process such as that for a tumbling mill product. On the average, these curves (plotted again log log) tend to have a slope in the fine region different from and usually less than unity,5 while the coarse size region curves with increasing slope for cases of mild reduction, and with decreasing slope when moderate or severe size reduction has occurred. In addition, there are usually slight irregular deviations from a smooth curve. Most curves display two distinct regions — fine and coarse — and a few curves show one or more intermediate regions. Feed size studies6,7 show an effect which theory is required to explain. For the same material, mill loading and other operating conditions, and the same time of grinding, plotting the dimensionless ratios Y vs. X/(feed size) does not reduce the size distribution data to the same curve. Y vs. X does not correlate the coarse region, but it can provide a crude correlation of the fine region which improves as size diminishes and as grinding time increases. The size distribution in the coarse region is somewhat more dependent on the feed size than is the distribution in the fine region wherein the degree of dependence diminishes as time proceeds; the distribution of sizes in the fine region are determined largely by the nature of the material and the comminution conditions. A comprehensive model of comminution must recognize that several different patterns or modes of breakage can occur in a mill; 5,8,9 that there can be some selection in that some size ranges are broken more than others; and that, while some particles may be the product of a single fracture event, or may even remain unbroken, others result from multiple rebreak-age. Thus, breakage in a tumbling mill is more complex than the Schuhmann4 model admits in that several different types of comminution micro-events* occur rather than just one type, and these events, though different in size scale, are of the same overall pattern as that which is visualized by the model. The concept of an average comminution micro-event has, therefore, a mathematical rather than a physical connotation, at least for tumbling milling. Equations with which to describe particle size distributions have been sought for over half a century.10-13 No equation presently in general use was first derived from an analysis of the statistical mechanics of breakage; whatever theoretical basis the existing

Jan 1, 1969

By Charles A. Ashburner

' I. Natural-Gas Explorations. The rapid development of the natural-gas* industry in Western Pennsylvania, and the great economy which results from its use, both for manufacturing and domestic purposes, has led to an inquiry as to the occurrence of this gaseous mineral in all thickly populated and large manufacturing centers of the United States. Natural-gas springs are to be found in almost every State in the Union, and in many States gas has been obtained in wells sunk either for water, oil, or gas, or in search of solid mineral deposits. The occurrence of natural gas is, however, not dependent upon mere chance, as is popularly supposed, but upon the existence of special geological phenomena; this fact is now recognized by professional men and by many practical men concerned either in the exploration for or in the use of this gas. The desire among our leading manufacturers, to emulate Pittsburgh, has led to the sinking of many wells in many localities, in search of natural gas. Some of these wells are now being located and drilled under the direction of professional experts, but many more have been, and are still being located by "quack " explorers, who often depend upon spiritualistic communications, or the diviningrod, or by intelligent persons, who are ignorant, however, of the geological and physical conditions under which gas has already been found. My attention has recently been directed to a number of these exploring operations where holes have been drilled, and, after failing

Jan 1, 1887

By Charles D. Borror, George K. Foster

The Jeffrey mine of the Canadian Johns-Manville Co., Limited, is in the town of Asbestos, situated approximately 100 miles northeast of Montreal and about the same distance southwest of Quebec, in Richmond County, Quebec. Mining operations were started in 1881 on outcrops on a hill, as a side-hill cut, followed by a second and third cut. This development was the forerunner of the present large open-pit operations, the mine now ranking as the largest open-pit asbestos mine in the world. Operations were first carried on by hand, then by horsepower and later by stem cableways. By 1924 the derrick spans, 2000 ft. or more long, became unwieldy. To overcome this, and also to eliminate hand labor as much as possible, steam shovels and railroad haulage were introduced. The steam shovels were replaced in 1928 by larger electric shovels of the full-revolving type. The Ore Body The ore body is a serpentinized peri-dotite rock mass. The chrysotile fibers form a network of veins throughout, varying from microscopic width to two or more inches measured across the veins (Fig. I). These veins may be continuous for a few or many feet; they may increase or decrease in width within a few feet. The veins in which the fibers occur per- pendicular to the veins are known as cross fiber. Those in which the fibers lay parallel to the veins are known as slip fiber. The cross fibers are of better quality, and more in demand. The majority of the fiber

Jan 1, 1948

By George K. Foster, Charles D. Borror

The Jeffrey mine of the Canadian Johns-Manville Co., Limited, is in the town of Asbestos, situated approximately 100 miles northeast of Montreal and about the same distance southwest of Quebec, in Richmond County, Quebec. Mining operations were started in 1881 on outcrops on a hill, as a side-hill cut, followed by a second and third cut. This development was the forerunner of the present large open-pit operations, the mine now ranking as the largest open-pit asbestos mine in the world. Operations were first carried on by hand, then by horsepower and later by stem cableways. By 1924 the derrick spans, 2000 ft. or more long, became unwieldy. To overcome this, and also to eliminate hand labor as much as possible, steam shovels and railroad haulage were introduced. The steam shovels were replaced in 1928 by larger electric shovels of the full-revolving type. The Ore Body The ore body is a serpentinized peri-dotite rock mass. The chrysotile fibers form a network of veins throughout, varying from microscopic width to two or more inches measured across the veins (Fig. I). These veins may be continuous for a few or many feet; they may increase or decrease in width within a few feet. The veins in which the fibers occur per- pendicular to the veins are known as cross fiber. Those in which the fibers lay parallel to the veins are known as slip fiber. The cross fibers are of better quality, and more in demand. The majority of the fiber

Jan 1, 1948

By Desio S. Oddone, Mark C. Malamphy, Irnack C. Do Amaral

Most igneous rocks, and particularly those of the basic type, contain relatively high percentages of magnetite and other iron oxides, which give them moderately high magnetic susceptibilities and make them responsible for an important percentage of the magnetic anomalies observed during the course of geophysical surveys by the magnetic method. The irregular form and high susceptibility of the igneous rocks make them readily polarizable and the position and strength of the magnetic poles formed are not always explicable by theoretical calculations of anomalies due to certain assumed forms in the normal magnetic field of the area under study. During the last four years our field work has permitted us to make detailed observations of anomalies due to igneous rocks in all the states of south Brazil. The form and position of the igneous rock at some places were fairly accurately known, which made it possible to calculate theoretical anomalies and compare them with the observed data. Some of the data we obtained have been published and additional cases are now awaiting publication. In this paper, we will present a few specific cases where the geology is moderately well known and which we believe to be of considerable value as representing typical magnetic anomalies in the south magnetic hemisphere, where the inclination of the magnetic field is very low. Although the vertical intensity is negative in the Southern Hemisphere, we have adopted the convention of plotting increase in intensity (negative) as a positive anomaly; i.e., above the x axis. This convention facilitates comparison with anomalies in the north.

Jan 1, 1940

By Irnack C. Do Amaral, Mark C. Malamphy, Desio S. Oddone

Most igneous rocks, and particularly those of the basic type, contain relatively high percentages of magnetite and other iron oxides, which give them moderately high magnetic susceptibilities and make them responsible for an important percentage of the magnetic anomalies observed during the course of geophysical surveys by the magnetic method. The irregular form and high susceptibility of the igneous rocks make them readily polarizable and the position and strength of the magnetic poles formed are not always explicable by theoretical calculations of anomalies due to certain assumed forms in the normal magnetic field of the area under study. During the last four years our field work has permitted us to make detailed observations of anomalies due to igneous rocks in all the states of south Brazil. The form and position of the igneous rock at some places were fairly accurately known, which made it possible to calculate theoretical anomalies and compare them with the observed data. Some of the data we obtained have been published and additional cases are now awaiting publication. In this paper, we will present a few specific cases where the geology is moderately well known and which we believe to be of considerable value as representing typical magnetic anomalies in the south magnetic hemisphere, where the inclination of the magnetic field is very low. Although the vertical intensity is negative in the Southern Hemisphere, we have adopted the convention of plotting increase in intensity (negative) as a positive anomaly; i.e., above the x axis. This convention facilitates comparison with anomalies in the north.

Jan 1, 1940

By Albert Sir Kitson

THE manganese ore deposits of the Gold Coast, British West Africa, occur in very ancient rocks, of both sedimentary and metamorphic types. In. certain respects they strongly resemble those of India and Brazil, as contrasted with those of Tertiary age in Georgia. Viewed from the present condition of the maganiferous rocks, the oldest deposits are in the sediments. Later than these are the progressively metamorphosed representatives of these sediments; youngest are the products of decay and degradation with the concentration of manganese oxide of both areas. The oldest occurrences are in argillaceous and siliceous phyllites and slates, which show only a moderate amount of metamorphism. They belong to a series which also includes mudstones, sandstones, grits, conglomerates and subordinate limestones, with tuffs and lava-flows largely of basic types. To this series I have given the name Birrim. Its age is unknown, for no definite fossils have been discovered in it. As the characteristics of these non-fossiliferous strata at many places are the same as those of strata in many parts of the world that are suitable for the preservation of fossils and that contain them, it is assumed that the Gold Coast deposits are pre-Cambrian. These rocks of the Birrim series have normally a northeast-southwest strike and are folded, but not to any very great degree except in certain belts., From the Eastern Province of the Gold Coast they may be traversed across their strike for more than 600 miles to the extreme northwestern corner of the Northern Territories. Thence. they probably extend much further into French Territory.

Jan 5, 1927

By David Mitchell

MANY of the difficult operating problems of the preparation of coal for market, of sampling coal shipments and in the utilization of coal are caused by segregation in the coal mass. Segregation may be of two kinds: i.e., "size segregation," in which parti- cles of the same size in a mass of coal containing a range of sizes collect to-gether and "density segregation," in which particles of the same density or specific gravity in a mass of particles of varying density gather together. MECHANICS OF SEGREGATION Size segregation cannot take place with closely sized coal. As the size range increases, the tendency for size segregation increases. Similarly, cleaned coal with particles of approxi- mately the same specific gravity have very little tendency for density segrega- tion. The wider the density range of particles and the more particles of different density, the greater the chances are for density segregation. FIG. 1.-SEGREGATION IN A SIDE-FILLED The following discussion deals primarily BIN with coal of a wide size range as screenings and of wide density differ-ences as uncleaned or run-of-mine screenings. If a mass of coal containing particles of a wide size range is subject to the stream action of a moving current of water, the small particles are transported farther than the coarser. Particles of different density in a stream of moving water are subject to the laws of classification, the heavier settling out first. The familiar sluice box of the gold miner and the action of rivers and other streams in classifying material according to

Jan 1, 1937

By Samuel B. Christy

" The man is always greater than his work." The training of the men who are to develop the mineral resources of the world is the most important problem connected with mining engineering. It becomes ever more important to civilization as the mineral wealth of the earth approaches exhaustion. I have therefore decided to consider a few of the more important problems arising in the training of the mining engineer, and especially those arising in America. , The Peculiar Nature of Mineral Wealth. Mining and Agriculture are the two fundamental arts. Without the latter our existence would be precarious; without the former, our civilization impossible. Agriculture furnishes that regular supply of food and raiment which leads to the growth of large communities in which cultivated leisure first becomes possible; while mining furnishes the metallic thread from which is woven that complex fabric we call civilization. But in these two arts the conditions for success are widely different. Most of the crops that the farmer reaps may be harvested year after year, and the proper fertilizers being added, he may continue the annual harvest indefinitely, while, as a result of cultivation, his farm becomes yearly more valuable. But the crop the miner reaps can be harvested but once in the history of the race. Our mineral wealth has taken unknown ages to mature in the bosom of the earth. The ripened fruit can be plucked but once. There are no fertilizers for worked-out mines. It never pays to work over a mine that has been

Jan 1, 1906

By E. Lancaster-Jones

THE gravity magnitudes obtained by means of observations with the Eötvös balance in the field are necessarily resultant or total effects due to all abnormalities of mass distribution, including even the effects due to the ellipticity and rotational motion of the whole earth. Since the object of the survey is to isolate the effects which arise solely from some particular subterranean feature, and to deduce therefrom the configuration and extent of this feature, the first step is to eliminate from the observed effects all those due to "disturbing" (i, e., unwanted) features, whether above or below the surface of the ground. The disturbing features have different characteristics, according to their situation relative to the center of the balance and to the horizontal plane through the foot of the balance, or station point; this diversity was recognized by Eötvös, who divided the total effects into so-called Normal, Terrain, Topographical, Cartographical and Subterranean effects. This classification has been adhered to by most subsequent investigators, but the writer prefers to employ the term "three-dimensional," which really indicates the essential character of the class of effect known as "Subterranean," at any, rate from the standpoint of the computer of effects. Before disturbing effects can be eliminated, the features must be measured up or surveyed, whether by topographical, mining, or boring methods, and then the effects of each feature calculated and subtracted from the total observed effects. After this the problem of interpreting the residual effects will itself necessitate the computation of the assumed feature, or even a series of trial features.

Jan 1, 1928

By L. D. Mullins, E. B. Elfrink, W. L. Wahl

In the past few years several articles and papers presenting results of solution gas-drive depletion calculations have appeared in the lit-erature. Such calculations are of interest to the oil industry, for investment decisions must often be made before much is known about a reservoir. At other times, an estimate of the possible benefits to be realized from alternate production methods is desirable, and theoretical depletion calculations can serve as a floor or reference level from which to work. In any case, an estimate of ultimate oil recovery based upon engineering data is commonly required. An engineer confronted with the problem of obtaining, for a specific reservoir system, an estimate of ultimate oil recovery by solution gas-drive depletion usually will be forced to perform the calculations himself. This is despite the quantity of data in the literature. Rarely will either experience or the literature provide results from a reservoir system similar in all important respects to the one under consideration, and calculated results are not so plentiful that satisfactory interpolation procedures can be devised. Performing the calculations, however, is a tedious, time-consuming task unless an electronic computer is available, and, in practice, time and manpower are not always available for this purpose. A quick, simple, consistent method was needed for reducing the uncer- tainty in estimated oil recovery from solution gas-drive reservoirs when only minimum information about the reservoir system is available. PROCEDURE Method of Calculation The usual requisite assumptions were made so that the material balance equation could be used to calculate data for the charts. The following assumptions were made: (1) the reservoir is homogeneous and isotropic; (2) oil recovery is due entirely to solution gas drive and neither a gas cap nor a water drive nor gravity drainage is present; (3) the initial reservoir pressure is the bubble-point pressure of the reservoir fluid; (4) initial total liquid saturation is 100 per cent of pore space; (5) interstitial water saturation remains at the initial value as the reservoir pressure declines from the bubble-point pressure to atmospheric pressure; (6) equilibrium gas saturation is 5 per cent of pore space; and (7) oil and gas saturations are uniformly distributed throughout the reservoir at all times. There are no saturation gradients due to a wellbore, nor is the geometry of the reservoir system considered. The material balance equation was written in the form of a differential equation' which was integrated to determine the change in oil saturation for an assigned pressure drop. Formal integration was not possible, so recourse was made to the Runge-Kutta method' of numerical integration. All computations were performed on IBM equipment. Numerical integration yielded the change in oil saturation within the reservoir as the pressure. declined from the bubble-point pressure to atmospheric pressure. The initial oil saturation minus the change in oil saturation yielded the oil saturation at atmospheric pressure. The oil originally in place was obtained by dividing the initial oil saturation by the initial formation volume factor (differential liberation) while the oil in place at atmospheric pressure was obtained by dividing the final oil saturation by the formation volume factor at atmospheric pressure. U1timate oil recovery, expressed as a percentage of the initial oil in place, was obtained by dividing the difference between the oil initially in place and the oil in place at atmospheric pressure by the oil initially in place and multiplying by 100. PVT Data Charts were based upon 135 solutions to the material balance equation. PVT properties of the reservoir fluids were variables in this equation and had to be known as functions of pressure. The required PVT data might have been obtained from either actual reservoir fluid systems or correlated data. However, correlated PVT data were developed and employed in the calculations for the following reasons: (1) it is doubtful that 135 sets of PVT data could have been obtained for the values of variables investigated in this study, and (2) results of recovery calculations from randomly obtained PVT data could not be correlated as well as rssults from selected PVT data. The PVT data used to develop the

By Alden B. Greninger

That metallographic structures analogous to the martensite of steel may be found in certain copper-aluminum and copper-tin alloys has been known for many years; similar structures recently were found in certain copper-zinc a1loys.l In all three of these alloy systems the martensite structures result from transformation of the metastable fi phase when the speed of cooling from the B range is sufficiently high to suppress decomposition into equilibrium phases. In the normal decomposition of solid solutions into equilibrium phases, diffusion is needed to bring about the necessary changes in concentration, and the rate of reaction falls almost to zero at temperatures slightly above room temperature. The rates of reaction for martensite processes, however, are not dependent upon temperature; the transformation does not require rendjustments of concentration. For example, the martensite transformation in 60:40 (B) copper-zinc does not begin until the temperature has dropped to about minus 30" C., and then continues down to minus 130" C. and probably even at lower temperatures.' Furthermore, martensite processes apparently proceed only while the tempcrature is falling, within the proper range, and cease completely while the temperature is held constant ;$ and they cannot be suppressed by extremely rapid cooling although the rate of cooling for some alloys may be increased to over 10,000 times the critical cooling velocity. Isaitschew, Kaminsky and Kurdjumow2 account for these observed behaviors of rnartensite processes by postulating that the mechanism 6I... consists in a regular rearrangement of the lattice in such a way

Jan 1, 1939

By T. PH. D. Egleston

THE Boston and Colorado Smelting Works are situated in the town of Black Hawk, Gilpin County, Colorado, on the Clear Creek Narrow Gauge Railway, 55 miles from Denver, in the Rocky Mountains, at an altitude of 7800 feet. It was one of the first works erected for the metallurgical treatment of gold ores, and the only one established in Colorado on a large scale which has been uniformly successful. Both gold and silver ores are treated, and gold, silver, and copper produced. The lead is not separated from the ores nor paid for, if it exists, and is entirely lost in the residues. The works were planned and built by Professor Hill, formerly Professor of Chemistry in Brown University, Providence, R. I., and is still managed by him, assisted by Mr. Richard Pearce, formerly professor in the School of Mines at Truro, England. They are very advantageously situated with regard to the ore-producing regions, having Boulder County on the north, which produces, besides ordinary gold ores, a series of tellurium minerals, such as altaite, sylvanite, and hessite, which are very rich in gold and silver. They are associated with copper and iron pyrites, blende, galena, and the carbonate and oxides of iron. Gilpin County itself produces for the most part the pyrites of iron and copper rich in gold, with a small quantity of galena and blende, which is rich in silver. In * By consent of the council of the Institute, this paper was first published in London Engineering, from which the engravings are here reproduced.

Jan 1, 1876

By Alden B. Greninger

That metallographic structures analogous to the martensite of steel may be found in certain copper-aluminum and copper-tin alloys has been known for many years; similar structures recently were found in certain copper-zinc a1loys.l In all three of these alloy systems the martensite structures result from transformation of the metastable fi phase when the speed of cooling from the B range is sufficiently high to suppress decomposition into equilibrium phases. In the normal decomposition of solid solutions into equilibrium phases, diffusion is needed to bring about the necessary changes in concentration, and the rate of reaction falls almost to zero at temperatures slightly above room temperature. The rates of reaction for martensite processes, however, are not dependent upon temperature; the transformation does not require rendjustments of concentration. For example, the martensite transformation in 60:40 (B) copper-zinc does not begin until the temperature has dropped to about minus 30" C., and then continues down to minus 130" C. and probably even at lower temperatures.' Furthermore, martensite processes apparently proceed only while the tempcrature is falling, within the proper range, and cease completely while the temperature is held constant ;$ and they cannot be suppressed by extremely rapid cooling although the rate of cooling for some alloys may be increased to over 10,000 times the critical cooling velocity. Isaitschew, Kaminsky and Kurdjumow2 account for these observed behaviors of rnartensite processes by postulating that the mechanism 6I... consists in a regular rearrangement of the lattice in such a way

Jan 1, 1939

By B. H. Caudle, M. D. Witte

In predicting the performance of a pattern injection operation, the engineer needs to know both the amount of oil to be recovered and the rate at which the recovcry will take place. This paper- describes fluid flow model studies on the effect of mobility ratio on the rate of oil recovery in a five-spot. The results show the change in fluid conductivity (total flow rate/pressure drop) as the sweep-ont pattern increases for mobility ratios between 0.1 (and 10. There data, when cornbitted with a knowledge of reservoir permeabilities and sweep-orit pattern efficiencies, cata he used to predict the cLrmulntivr oil production as a function of time for homogeneous five-spot injection systems. INTRODUCTION The flow potential in a pattern flood element is a function of the mobility ratio and how far the injected flood front has gone.1,2 For a waterflood project having a mobility ratio of one, the conductance—which is the flow rate per unit pressure drop (q/Ap)—-will remain the same throughout the life of the flood. If the mobility ratio is favorable ( < I), the conductance of the project will drop continuously throughout the operation. If, on the other hand, the mobility ratio is unfavorahlc. the conductance ratio will increase continuously. Therefore, if the reservoir engineer wishes to predict either the rate at a specified pressure or the pressure at some rate for a secondary recovery project, he must know how the conductance will vary during the flood. Other investigators have studied this problem using potentiometric models&apos; or analytical solution&apos;. The

By Donald B. Evans, Robert D. Pehlke

The solubility of nilrogen in liquid binary alloys of iron with Litanium. zivconium, columbium, vanndiurn, and tantalum was measured for alloy composiLions up to the solalbility limils of lhe alloy nitrides. All five alloying agents were found to decrease markedly the activity coefficient of nitrogen in liquid ivon. The metal/nitvogen mole ralios in the alloy nitrides formed were generally .found to be slighlly greater than 1.0, but in no case greater than 1.5. From the experimental data, the standard free energies of fortmation of titanium and zir-conium nitrides have been calculated for the Lemperaluve range 1550° to 1750 C. The solublily Products for columbium, tantalum, and vanadium nitrides are also reported. A number of research investigations have examined the effect of refractory metals on the solubility of nitrogen in liquid iron. Although data on zirconium are not available, investigators are in agreement that titanium, vanadium, columbium, and tantalum markedly increase the solubility of nitrogen in liquid iron. This fact alone makes desirable the acquisition of thermodynamic data for these elements in liquid iron. Since refractory metals are known to be stable nitride formers, they have been suggested as steel denitrifying agents, and some of their nitrides have recently been considered as containment materials for liquid iron and iron alloys. Most available thermodynamic data for these metals relate to their dilute concentrations, but effective thermodynamic treatment of these applications requires data at concentrations near the solubility limit of the alloy nitride. Although some work has been done at relatively high alloy concentrations in liquid iron (particularly for vanadium 2,3 and titanium 2,4), the results have been somewhat contradictory. Disagreement may be partly attributed to the fact that the compositions of most refractory metal nitrides have been shown to be nonstoichiometric, and to vary 2,5-8 depending on the temperature and nitrogen gas pressure with which the solid nitride phase is in equilibrium. One purpose of this study consequently has been to determine the compositions of the refractory metal nitrides precipitated from a liquid iron solution. EXPERIMENTAL PROCEDURE Rao and Parlee2 and Evans and Pehlke 9 have discussed the technique for measuring the solubility product of an alloy nitride phase in liquid iron by finding the point of departure of the nitrogen solubility from Sieverts&apos; law. The method consists of measuring the solubility of nitrogen in a melt of iron containing a known concentration of a second metal as a function of the nitrogen gas pressure over the melt. In this study the second metal was one of the refractory metals titanium, zirconium, columbium, vanadium, or tantalum. When the nitrogen pressure at which the refractory nitride forms is reached, a deviation of the measured solubility of nitrogen in the melt from Sieverts&apos; law is observed in the form of a "pressure halt." The concentration of nitrogen in the melt associated with this breakpoint in the nitrogen-absorption curve is then used to calculate the nitride solubility. The Sieverts method was used to measure nitrogen solubility as a function of nitrogen pressure and temperature. The experimental equipment for this technique has been previously described in detail. 1,9 Charge materials used were vacuum-melted high-purity iron (Ferrovac-E) and the best commercial grades of the refractory metals obtainable (in all cases at least 99.8+ pct pure). Recrystallized alumina crucibles were used to hold all melts except those containing zirconium, for which zirconia crucibles were necessary. Temperatures were measured by a disappearing-filament type optical pyrometer sighted vertically downward on the melt surface through a 1/4-in.-diameter sight hole in the crucible lid. By means of a technique previously described, 9 in which the refractory-metal nitride was precipitated at one temperature then redis-solved by raising the temperature 50°C and precipitated again at a higher temperature, it was possible to obtain data over a temperature range of up to 200°C on a single melt. It was found that this technique could not be used with melts containing zir-

Jan 1, 1965

By Donald R. Lessard

I. INTRODUCTION There is no question that the choice of an appropriate discount rate is a critical element in virtually all business decisions in extractive industries. The standard textbook approach relies on a single overall cost of capital for an entire firm, itself a weighted average of the firm&apos;s cost of debt and equity. But a single rate is appropriate only if the commercial risks and financing structures are similar for all projects under consideration. In extractive industries, appropriate discount rates are likely to vary greatly from project to project. Risks of projects differ markedly by mineral, by country in which the project is located, by stage in production, and by position in the project&apos;s life. Further, for a variety of institutional reasons, financing structures vary greatly in relation to these same variables and thus the discount rate appropriate to the entire investment and, in particular, to the sponsor&apos;s equity investment will vary even more markedly. Failure to select discount rates which reflect these differences can result in extremely distorted decisions. Our interest in this subject results from our ongoing research on alternative ownership and financing structures for large scale extractive ventures in less developed countries where risks to the various participants--the sponsors, the financiers, and the host government--vary dramatically with the different options. Given the magnitude of these differences, a single discount rate for all options is clearly inappropriate. However, there appear to be few guidelines for practicing managers to follow in setting appropriate rates. In this paper, we take a first step in this direction.

Jan 1, 1977

IN NOVEMBER 1933 I had the pleasure of receiving an autographed copy of a small brochure entitled "Birth of the Porphyry Coppers." The author, James Colquhoun, a distinguished British mining engineer, had been the dominant figure in the Arizona Copper Company, Limited, which, until its acquisition by the Phelps Dodge Corporation in 1921, had been the principal producer of copper in the Morenci district. In addition to the highly productive Humboldt and Longfellow mines it owned the Clay property, which, of course, has now become Arizona&apos;s No. 1 copper mine. Except for Utah Copper it is the premier Porphyry copper enterprise in the United States. Mr. Colquhoun&apos;s little volume was inspired by THE PORPHYRY COPPERS which had appeared early that year. In a most courteous and friendly way he adduces data to show that "we (Arizona Copper Company Limited) were successfully treating low-grade porphyry ores in quantity for at least four years (1901 to 19W) before the Utah Copper Company did anything at all." This last remark is based on the figures in THE PORPHYRY COPPERS showing that Utah&apos;s first production came from the Copperton pilot plant in 1905. Mr. Colquhoun traces the story of Morenci beginning in 1883 when he first arrived there. He tells how the rich self-fluxing ores (containing lime- stone, silica, and iron in proportion to permit direct smelting to produce black copper) were gradually exhausted. High-grade siliceous ore could be mixed in limited quantity with the self-fluxing ores; and oxidized ores were leached to contribute substantially to the production of the district. But

Jan 1, 1957

By Raynor Linzey, Karl M. Busen

The formation of thin films of silicon oxide by anodic oxidation of silicon and the subsequent removal of these films by an etch is a process often used for the evaluation of concentration distributions Profiles) in silicon layers by the differential sheet conductance method. The accuracy of the resulting profile is very strongly influenced by the uniformity of the thickness of the reacted silicon. Normally, it would be expected that for a constant number of coulombs passed the thickness would be the same from oxidation to oxidation. Investigations show that in certain electrolytes, for a given number of coulombs passed through an n-type silicon sample, the thickness of the reacted silicon increased with increasing resistivity. Even for the same resistivity the thickness varied sometimes by a factor of 1.5. When an electrolyte was used which consisted of 10 pct water by volume in ethylene glycol with 4.0 g KNO per 1000 ml of solution, anodiza-tion at 5 ma per sq cm led to satisfying results. Short-time anodizations gave oxide layers of a higher apparent density than those experienced from thermally gown silicon oxides. THE functioning and the electrical characteristics of semiconductor devices are based upon the incorporation of "impurities" into a single-crystalline body of suitable material and on the concentration distribution (profile) of this impurity. The incorporation can be achieved by well-known processes as, for example, by diffusion, epitaxial growth, alloying, or ion implantation. Often the profile resulting from these processes is not known. A powerful tool to learn about a concentration distribution is given by the method of differential sheet conductance which employs successive four-probe measurements on a layer subjected to stepwise removal of thin sublayers. Differential sheet conductance vs position (or penetration depth) of a sublayer is plotted and a smooth curve is drawn through the data. From this curve the profile is then calculated. When the semiconductor material is silicon, the sublayers are removed suitably by anodic oxidation of the silicon and subsequent dissolving of the formed silicon oxide by an etch. The accuracy of the resulting profile is very strongly influenced by the uniformity of the sublayer thickness. Normally, it would be expected that, for a constant number of coulombs passed, the thickness would be constant from oxidation to oxidation. Investigations showed that for sublayers several hundred angstroms thick the reproducibility can be rather poor. Therefore, efforts were made to obtain a reliable technique for uniform removal. The present paper describes such a technique and certain phenomena which were encountered during the investigations. APPARATUS AND TECHNIQUE The first report on the investigation of concentration distributions, where for differential sheet conductance measurements thin silicon sublayers were removed from a diffused layer by anodic oxidation, was given by Tannenbaum. The author reports the removal of sublayers which for the most part were 400 thick. More advanced device designs now require much narrower layers. When it was tried in these laboratories to determine profiles within such layers, difficulties were encountered with respect to sublayers which by necessity had to be thinner than the ones reported by Tannenbaum. The apparatus used for the investigations is sketched in Fig. 1. Two cylindrical containers connected by a wide tube are filled with an electrolyte. The left container receives the cathode whereas the right container is closed at the bottom end by a sample support consisting of a Teflon base and a copper pedestal. The silicon sample (1 by 1 cm) is mounted to the pedestal embedded flush in the Teflon base using silver paint (Degussa) for electrical contact. Pyseal is applied to the edges of the sample to protect the copper pedestal from the electrolyte. The base is mounted to the container using a water-tight silicon rubber gasket. Fig. 2 gives a view of the sample support. The copper pedestal is connected to the positive side of a power supply operating at a constant current output (Kepco Model ABC 425M). The electrolyte which has been reported by Duffek et al. consisted of either 2 or 10 pct water by volume in ethylene glycol and 4.0 g KNO3 in 1000-ml solution. The electrolyte is best prepared

Jan 1, 1967

By E. Lancaster-Jones

THE gravity magnitudes obtained by means of observations with the Eötvös balance in the field are necessarily resultant or total effects due to all abnormalities of mass distribution, including even the effects due to the ellipticity and rotational motion of the whole earth. Since the object of the survey is to isolate the effects which arise solely from some particular subterranean, feature, and to deduce therefrom the configuration and extent of this feature, the first step is to eliminate from the observed effects all those due to "disturbing" (i. e., unwanted) features, whether above or below the surface of the ground. The disturbing features have different characteristics, according to their situation relative to the center of the balance and to the horizontal plane through the foot of the balance, or station point; this diversity was recognized by Eötvös, who divided the total effects into so-called Normal, Terrain, Topographical, Cartographical and Subterranean effects. This classification has been adhered to by most subsequent investigators, but the writer prefers to employ the term "three-dimensional," which really indicates the essential character of the class of effect known as "Subterranean," at any rate from the standpoint of the computer of effects. Before disturbing effects can be eliminated, the features must be measured up or surveyed, whether by topographical, mining, or boring methods, and then the effects of each feature calculated and subtracted from the total observed effects. After this the problem of interpreting the residual effects will itself necessitate the computation of the assumed feature, or even a series of trial features.

Jan 1, 1928