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By E. Martinez, M. L. Hollander

Sulfurization of copper oxides was investigated using differential thermal analysis (DTA) and thermal gravimetric analysis (TGA). When mixtures of cuprous oxide and sulfur were heated, the surface of the cuprous oxide was converted to cupric sulfide at the melting point of sulfur (119°C); additional sulfuriza-tion took place when the sulfur vaporized above 200°C. Cupric oxide also reacted with sulfur to form cupric sulfide but the starting temperature was approximtely 225°C. When the cupric oxide and sulfur were physically separated, sulfurization still occurred indicating a reaction with the vapor phase of sulfur. Sulfurization was obtained in runs with cuprite, chrysocolla and basic copper carbonate. Further decomposition of cupric to cuprous sulfide was noted at somewhat higher temperatures. The DTA-TGA data made it possible to set up postulated reactions in each system. These techniques were found to be well suited for studies of this type. Because of the difficulty encountered in flotation of many metallic oxide minerals, efforts have been made to find suitable reagent combinations to sulfi-dize these minerals in the flotation circuit. Recently Bautista and Sollenberger,1 using a different approach, showed that the surfaces of many oxide minerals can be converted to sulfides by heating them with sulfur to temperatures between 150° and 225°C. This technique was effective even with chrysocolla, a mineral which is very difficult to sulfidize. The primary objective of the present study was to obtain information on the reactions between the oxide minerals and suIfur. A better understanding of the mechanisms involved might prove useful in pointing the way to improvements in the process. A secondary objective was to demonstrate the value of thermo-analysis in investigations of this type. Bollin and Kerr2 have reported the use of a modification of differential thermal analysis to study the thermal reactions which occur on heating elemental constituents in a closed system to synthesize copper sulfides and iron sulfides. Differential thermal analysis (DTA) was used to detect enthalpic changes as mixtures of minerals and sulfur were heated. The DTA indicated the temperatures at which reactions started and whether they were exothermic or endothermic. Weight change data were obtained by thermal gravimetric analysis (TGA). These data could often be used to support postulated reactions and to eliminate consideration of other possible reactions. EQUlPMENT Differential thermal analysis (DTA) involves measuring the temperature difference between the sample being tested and a thermally inert reference, generally aluminum oxide, as both are heated at a uniform rate. Series connected thermocouples in the sample and reference are used to detect the temperature differences that occur as the sample undergoes enthalpic changes.3 Crystalline transitions, fusions, vaporizations, dehydrations, decompositions and many solid state reactions can be detected. A DTA unit manufactured by the Robert L. Stone Co., Austin, Tex., was used in this investigation with a temperature rate increase of 10°C per min. The samples and reference were placed in Inconel cups with wells in the bottom into which the differential thermocouples fit, and run in a nitrogen atmosphere. Thermal gravimetric analysis (TGA) measures the changes in weight that a sample undergoes as it is heated. A Chevenard thermobalance converted electronically for graphic recording was used with a heating rate of 5°C per minute. An X-Y recorder plotted temperature on the X axis and weight changes on the Y axis. A flow of 250 ml per min of nitrogen was streamed through the furnace. Samples were placed in a porcelain crucible open at the top, unless otherwise noted. EXPERIMENTAL RESULTS Sulfur: Two sulfur samples from different sources were tested. The DTA of a high purity sulfur and a reagent grade sublimed sulfur are shown in Fig. 1. Nearly all the tests were run with the sublimed sulfur due to the difficulty in grinding and high electrostatic charge encountered with the high purity sample. Sulfur undergoes three endothermal reactions below 200°C. The first is a solid-solid crystalline transi-

Jan 1, 1964

By M. E. Volin, D. W. Fuerstenau, A. L. Mular

This paper presents the results of an investigation of the effect of feed size on the integral rate at which feed material is dry ground in a laboratory rod mill. The data are interpreted in terms of the Gaudin-Meloy distribution equation. The equation, Mo — Mt/t = Aoxo r-1, is found to hold for feed sizes smaller than some critical size or for grinding times larger than some critical time. It is shown that a feed grindability is related to this critical size, which appears to be the transition between predominately impact and predominately attrition grinding. Detailed research on feed size effects in comminution has been rather limited. Gaudin1 ground single-sieve fractions of quartz for extended time periods (four hours) in a laboratory ball mill. His work, which was designed to study the nature of size distributions, showed that there is a critical feed size above which comminution occurs primarily by attrition. For his system, the critical size was about 2-mm when using 22-mm balls. In a more recent investigation2 single-sieve fractions of quartz were ground in a laboratory rod mill for constant time periods (15 min) to determine how feed size affects the grindability of the material. This work showed that grindability is essentially independent of feed size in the rod mill after this moderately long grinding period. To further clarify this observation, a study in which feed size and grinding times are varied over a fairly wide range, and particularly, a study of the dependence of the integral rate of grinding on feed size during the initial stages of rod milling is necessary. For an analysis of such data, it is desirable to use a parameter which is very sensitive to change during the initial grinding period when reduction ratios are

Jan 1, 1964

By John C. Hartley

Three systems that monitor ventilating fans are described. These electronic monitoring systems automatically perform most of the operations required to conform with the provisions of the Federal Mine Safety Code in the event of fan failure or slowdown.

Jan 1, 1964

By Bernadette C. Michalski

THE RAPID GROWTH of the small Albanian mineral industry in the 1950's began to taper off by 1961 and slackened sharply in 1963. The abandonment of Soviet and East European technical assistance programs in mid-1961 greatly affected Albania's mineral development, since four-fifths of all technical aid personnel were engaged in mineral activities. Chinese assistance apparently has not been able to fill the void. Overall mineral production increases during 1961-63 averaged 1 percent per year in value, as compared with 3 percent in 1959 and 5 percent in 1960. Although by world standards Albanian mineral output, except for chromite, is insignificant, it is vital to the country's domestic economy. The mineral industry generated about 14 percent of the gross industrial product in 1962 and employed a notable share of the industrial labor force. In recent years, mineral products have provided about three-fifths of the country's exports by value. Chromite and iron-nickel ores together constituted from one-fourth to one-third of the total export value. In 1963, total trade turnover increased 12 percent over 1962.

Jan 1, 1964

By Lauren W. Choate

Wollastonite, a calcium metasilicate, derives its name from the man who discovered the mineral, Doctor William H. Wollaston, an English scientist. OCCURENCE Occurences of the mineral have been noted in Finland, Switzerland, Russia, Japan, Mexico and in the United States in Texas, California, Arizona, and New York. The only commercial deposit now being exploited is at Willsboro, New York. It is mined and processed by the Cabot Corporation whose home offices are in Boston, Massachusetts.

Jan 1, 1964

1. Scientific prospecting has had a profound and some-what unexpected effect on the world's supply of raw materials over the past twenty years. Where shortages were recently anticipated, abundance now prevails. It seems probable that, for the foreseeable future, adequate metallic resources will be found at costs well within the world's economic means. 2. The amount of research devoted to scientific prospecting has been extremely small in relation to the possible importance of the problem and to what could be done. It has been dominated by the thought of a dozen brilliant men, and true research expenditures have not amounted to more than a few million dollars. 3. An undue proportion of the expenditures have been for so-called geological research -mostly of a petrologial character. The results have essentially been of historic interest only. However, there has been some in-crease in genetic understanding, and this is of great importance for future resources. 4. Basic advances in mineral exploration have been made in detection techniques, generally called geophysics and geochemistry.

Jan 1, 1964

By Douglas F. Crickmer

Pocahontas Land Corporation, a wholly-owned subsidiary of Norfolk and western Railway Company, owns a 100,000-acre block of coal lands in Martin, Johnson, Pike, Floyd and Lawrence Counties, Kentucky. These holdings were largely acquired in three major purchases between the years 1942 and 1959. The area is undeveloped and constitutes a part of the coal reserve for future mining. This block, which is principally in Martin County, lies in a triangle formed by the Levisa and Tug Forks of Big Sandy River on the sides with Dewey Dam at its base and the Town of Louisa at the apex. The topography'is typical of eastern Kentucky and consists of steep hills rising from 500 to 800 feet above creek level. There is little level ground in the area. As a matter of fact, some roads are on the creek bottoms with what little bottom land is available in the hollows being utilized for small-scale farming. The steep hills are marked by three separate massive sandstone formations which form cliffs ranging from 40 to 100 feet in height.

Jan 1, 1964

By T. J. Whalen, S. M. Kaufman

Surface-tension measurements for liquid Fe-C-Co and Fe-C-Ni alloys were performed by the sesszle-drop technique at 1350o and 1425°C. Cobalt was shown to he more effective than nickel in lowering the surface tension of Fe-C alloys A minimum value for surface tension of 1640 dynes per cm was found in the Fe-C-Co system at a concentration of 1.5 pet C and 12pet Co. Analysis of these measurements in terms of adsorption and desorption behavior indicated that cobalt and nickel lower surface tension in Fe-C alloys by replacing carbon at the liquid-vapor interface. Comparison of results to date for Fe-C liquid alloys has shown that most substitutional-type elements having about the same atomic diameter as iron also have relatively the same influence on surface tension when present in dilute amounts. It has been shown previously that surface-adsorption behavior in liquid Fe-C ternary alloys is related to the manner in which the ternary addition affects the activity of carbon in the bulk solution.' Certain ternary additions, such as chromium, tending to decrease carbon activity cause adsorption of carbon and chromium to the liquid-vapor interface. Additions, such as silicon, increase the carbon activity, resulting in a desorption of carbon and an adsorption of silicon. Both cases were shown to cause a decrease in surface tension due to adsorption. It is the object of this paper, as part of the writers' continuing interest in the effect of alloying additions on the surface tension of Fe-C alloys, to present and discuss surface-tension data on solutions in the ternary systems Fe-C-Co and Fe-C-Ni. Available activity measurements for these systems in the solid state indicate a strong increase in carbon activity when either nickel or cobalt is added to Fe-C alloys.2, 3 EXPERIMENTAL PROCEDURE The alloy compositions used are shown in Table I. These alloys were prepared by vacuum melting in stabilized zirconia crucibles and then vacuum casting into cold-steel molds. The nominal analyses for the alloys used in this investigation are given in Table I. Surface tensions and densities were measured by the sessile-drop method4,5 in conjunction with the tables of Bashforth and bdams.' Specimens were prepared by slicing 1/4-in. cubes from the center of the vacuum-cast ingots and grinding the edges of these cubes until their shapes approximated spheres with flat bottoms. Proper handling techniques, including an acetone rinse immediately before use, assured minimum contamination from sources extraneous to the actual melting. For each experimental run a sample was placed on a BeO plaque and positioned and leveled inside a vacuum induction heating apparatus. The sample and plaque arrangement sat inside a molybdenum tube which acted as the susceptor. Diagrams of this apparatus may be found in the literature.= After heating to temperatures just above the liquidus at pressures of the order of 10-4 to 10- 5 mm Hg, photographs of the drop profile were made using its natural thermal radiation as a light source. Some measurements were made with partial pressures (-1 cm Hg) of a mixture of H2 and He gases. The H2-He atmospheres proved to be necessary at higher nickel contents to retard excessive vaporization losses. Chemical analysis for carbon and the ternary addition was performed for each alloy sample after completion of the experimental run.

Jan 1, 1964

A semi-automatic device has been constructed that can be used to check the solution strength of cyanide solutions. It consists of a wheel on which a gold-foil-bearing glass slide is mounted. The wheel moves the gold foil through the solution under test and intercepts a light beam. As the gold foil is attacked by the cyanide solution its light absorption diminishes. The successive in-crease in transmitted light intensity is recorded and gives a measure of the gold dissolution rate. Curves have been obtained to show the effect of cyanide concentration and oxygen content on dissolution rates. Details are presented of the construction of the unit, and some practical operating procedures are outlined. 0 NE of the important, although often neglected, factors in the extraction of gold by cyanidation is the actual dissolving strength of the cyanide solution. This depends in a

Jan 1, 1964

By DeVerle Harris

The enthusiasm with which individuals have participated in mineral exploration in the development of this country testifies to the fact that there was once a very real probability of making a worthwhile discovery. Over the years, the discovery and subsequent exploitation of the accessible ore deposits have made the finding of new deposits progressively more difficult. Present day mineral exploration has evolved from the lone prospector with the grubstaker behind him to a very costly and complex business, involving large sums of money and a staff of experts in the fields of exploration technology. Exploration today must be carried out on a large scale to be profitable. With the involvement of large amounts of capital, there has been a good deal of interest in methods of optimization of the allocation of the resources of a firm 'engaged in mineral exploration. As a step toward this, mathematical models have been formulated which are designed to quantify those variables of mineral exploration in such a manner that they can be integrated with all phases of the firms operations so as to optimize its profit objective or more simply, to make exploration more efficient and effective.

Jan 1, 1964

By R A. Stevenson

The purpose of this paper is to outline a recent development in ground fault protection. The paper deals with the A problems of both grounded and ungrounded systems, with regard to hazards to personnel and equipment, and shows that the increased sensitivity and speed of operation of this new detector results in increased safety to personnel and reduced stresses on equipment, and permits the detection of leakage currents before they become serious faults. The detector can be applied to all distribution systems, either A.C. or D.C., up to 15 kv., and the detector itself can be tested at regular intervals without interrupting line circuits. T HERE is always controversy among engineers as to whether distribution systems should be grounded or ungrounded. There are many experi-enced engineers on both sides of this controversy, and each have valid reasons for their choice

Jan 1, 1964

By William C. Ellis

Underground water is part of a continuing hydrologic cycle, which involves all elements of water occurrence. All groundwater of economic importance is in process of movement through a porous rock stratum from a place of intake or recharge to a place of disposal. Groundwater moves and is contained in fractures in the rock and/or in intergranular spaces of porous formations. Where there have been no water developments by man, groundwater is in a state of approximate equilibrium and the forces of replenishment and discharge are in balance. Thus, groundwater, unlike other mineral resources, is constantly being replenished in most areas at a rate which is measurable and which is important in the planning of its utilization. As illustrated by Figure 1, replenishment of groundwater supplies results from the direct penetration of rainfall through the soil to the water table, by seepage from surface streams or ponds, and/or by subsurface movement from an adjacent groundwater body. Under natural discharge conditions, water is commonly consumed by transpiration of trees and other types of vegetation, by flows from springs, by evaporation from shallow depths below the surface, and seepage into streams that traverse the area.

Jan 1, 1964

The methods employed for the addition of uranium to steels and cast iron in the Physical Metallurgy Division are outlined. It has been found that the segregation of? uranium is a major problem in aluminum and/or silicon killed steels and that the cooling rate is important in al-lowing the segregate to settle to one area, which can subsequently be discarded. The unsegregated areas were found to be extremely low in total oxygen, acid insoluble aluminum (AizOg) and, in some cases, slightly lower in nitrogen. Uranium recoveries, based on analyses of the unsegregated areas, were quite constant, at about 45 per cent, regardless of the type of uranium master alloy used for the addition. No segregation of carbon, manganese, silicon, sulphur, phosphorous, chromium or copper was observed in these steels. In commercial heats, the recoveries ranged from 7 to? 29 per cent for ladle additions to oxygen converted steel. When the steel was fully deoxidized prior to the uranium addition, recoveries ranged from 49 to 66 per cent, regardless of the steelmaking process.

Jan 1, 1964

By L. D. Clark, S. S. Saluja

A physical law, governing the rupture of rock by confined explosive charge correspondent to current expressions for determining weight of charge to rupture rock burden, W, was developed in the form Q = cVw3 by two early investigators performing unique experiments with ice. The coefficient C, is found by trial blast. Recent physical tests conducted with rock, synthetic materials and ice to establish the validity of the theory on which it and other related formulae are based indicated: (a) that failure under hydrodynamic impact pressure is by tension rather than shear as was assumed; (b) that the fundamental law of mechanics, enabling the determination of Q = cvw3, modified to the form P = R x Sa x Wb is valid when low velocity explosives are used; (c) that rock breakage under the action of low velocity explosives is entirely due to explosion gas pressure, as was believed; (d) that under the action of high velocity explosive it is due to the joint effects of scabbing and gas pressure; and that further possible modification could make the above equation also applicable to these joint mechanisms. shape could be easily frozen and because large loads would not be required. They found: (a) that the not unfamiliar shearing equation for metals was applicable to ice where P = load in lb; S = periphery of pressure surface, in.; W = burden, in.; K = modulus of rupture by shear in lb per in.2; and (b) that "the form of cavity produced by the application of gradual pressure is similar to that obtained by blasting in rock under similar conditions of free face and pressure surface!" This similarity in crater shapes leads to the conclusion that rock would rupture by shear, as did ice, and its behavior under the force of a blast could be governed by such a relationship as P = S x W x K. Three important interrelated empirical expressions were derived and rock, charging and spacing coefficients C,, C, and e were established and substantiated by trial blasts. In checking the accuracy of the main assumptions, duplication of the ice tests, substituting rock, suggested that K is not constant and that P = K x W x S, though valid for ice, does not necessarily hold for homogeneous limestone.' Conclusions from this later work raised questions making continued investigation desirable because such conclusions do not destroy the practical value of the empirical equations or theory. Further study for the establishment of the relationship between load, burden and periphery of the pressure surface and possible application of these to the mechanism of rock blasting was undertaken by the authors of this paper. MECHANICAL TESTING - EXPERIMENTAL PROCEDURE Certain inconsistencies in the results of the aforementioned tests repeated on three types of limestone suggested these inconsistencies be attributed to rock inhomogeneity. It was also suspected that the loading speed, which could not be held uniform, may have contributed. The earlier work with both rock and ice

Jan 1, 1964

By A. R. Conroy

Microscopic observation of physical and chemical changes which take place in various materials under conditions of elevated temperature and controlled atmosphere can often yield valuable insight into the fundamental physical-chemical reactions which control processes in which these materials play an active role. The technique of high-temperature microscopy thus becomes an important tool for basic and applied research in pyrometallurgical and allied fields. Investigators have long been aware of this and through the years have applied the technique to a wide variety of problems. However, up to this time, application has been on a rather limited scale due to the high initial cost of equipment and the relatively low rate of production of data resulting from the complexity of the apparatus and attendant problems in manipulation.

Jan 1, 1964

By Forrest T. Moyer

The National Safety Competition was inaugurated in 1925 by the Bureau of Mines, U.S. Department of the Interior, in cooperation with the Explosives Engineer. In the first nationwide contest, 210 mines and quarries were enrolled. In 1962, the thirty-eighth anniversary of the competition, 910 mines and quarries were enrolled. These participating plants were worked a total of 133,292,989 man-hours. Of the enrolled plants, 415 achieved injury-free operations for the year, the largest number of perfect safety records in the history of the contest.

Jan 1, 1964

By E. J. Dulis, A. Kasak, R. C. Westgren

The potential of uirought tungsten- and tantaluw-rich alloys of the W-Ta-Mo-Cb system was investigated for high-strength structural applications above 2500° F. Appreciable strengthening of tung-sten and tantalum—essentially attributable to solid-solzction effects—was obtained with binary, ternary, and quaternary alloys. Tensile strengths as high as 67,000 psi were achieved at 3000 OF. ThE quest for wrought structural materials which possess good strength properties at temperatures above 2000°F has led to a considerable research effort during the past decade. In addition to exploring the potential of various high-melting-point refractory metals (such as molybdenum, columbium, tantalum, and tungsten) for very high-temperature structural applications, alloy-development programs have been undertaken to achieve greater strengths than could be achieved with unalloyed refractory metals. The methods of strengthening refractory metal alloys have included both solid-solution and dispersion strengthening. General relationships among the relevant properties (melting point, recrystallization temperature, and high-temperature strength) of refractory metals indicate that the highest strengths at temperatures of 2500°F or higher would be obtained with tungsten-or tantalum-base alloys. Therefore, the present investigation was undertaken to determine the high-temperature strength potential of solid-solution strengthened alloys based on the binary system W-Ta; to effect further strengthening, minor additions of molybdenum and columbium (at the 6 and 12 pct levels) were made. The portion of the W-Ta-Mo-Cb quaternary alloy system of interest is shown schematically in Fig. 1. The component metals—W, Ta, Mo, and Cb—have a bcc structure at all temperatures, and their binary systems are mutually completely soluble.' Complete solid solubility in the W-Ta-Mo and W-Ta-Cb alloy systems has been demonstrated,' and, therefore, it was expected that the quarternary alloys of the system would also exhibit complete solid solubility at all temperatures. In the virtual absence of contamination by interstitial elements, all the alloys would be truly solid-solution strengthened. Twenty specific compositions of this investigation included binary, ternary, and quaternary alloys of the W-Ta-Mo-Cb system as well as unalloyed tungsten and tantalum. The compositions are shown in Table I. EXPERIMENTAL PROCEDURE Consumable-electrode vacuum-arc melting with ac power was used to produce small laboratory-sized, cylindrically shaped ingots (1-1/4 in. in diameter and 2 to 3-1/2 in. long) of the twenty compositions. A furnace was specially constructed to melt as many as four electrode rods simultaneously into molds lined with tungsten or tantalum sheet. High-purity rods of tungsten, tantalum, molybdenum, and columbium were used for consumable electrodes; the diameter of each rod was determined by the desired weight percentage of the component metal in a given alloy. The details of the construction and operation of the melting furnace will be discussed in another p~blication.

Jan 1, 1964

By Sidney Fischler

Large striation-free single crystals of bismuth have been grown from the melt by rapid freezing. Zone-refined bismuth, together with doping impurities if desired, is placed in a shallow flat-bottomed graphite boat and melted in air with a propane hand torch. The torch is then withdrawn in a manner which causes the melt to freeze direction-ally. Crystallization, which resuires only a few minutes, usually results in the formation of a single crystal even when a seed crystal is not used. Crys -tals of any desired orientation may be grown by using oriented seeds. Undoped crystals grown by this method have residual resistivity ratios greater than 200. THE growth of large single crystals of bismuth by either the Czochralski or horizontal zoning technique is not entirely satisfactory. Specifically, difficulties are encountered in producing single crystals of the required dimensions in all desired orientations, and striations caused by low-angle polysynthetic twins are frequently present in the crystals. In addition, both methods are time-consuming and require special apparatus of some complexity. A simpler method has now been developed for growing large striation-free bismuth single crystals of desired orientation in a short time. Fig. 1 shows a typical setup consisting of a rectangular graphite boat which contains zone-refined bismuth, a 1/8-in.-thick flat quartz plate which covers the entire inner bottom of the boat, and three additional quartz plates about 1/4 in. thick which are used to separate the bismuth from the graphite everywhere except at a small area at the left of the boat. The graphite boat is 1 in. high, and its sides and bottom are about 1/8 in. thick. The quartz plates should be smooth and clean. The graphite boat is heated from the right with a propane torch, as shown in Fig. 1, until the bismuth is completely melted. The melt has the shape of a triangle with a narrow neck at the apex farthest from the torch. The melt is frozen direc-tionally by gradually moving the torch toward the right, away from the boat. The bismuth in contact with the graphite, at the left end of the neck, freezes first. The freezing interface then moves down the neck into the main bulk of material, where it develops a convex shape ideal for the continuation of single-crystal growth. The interface continues to move through the melt until the entire bulk is solid. The entire procedure may be completed, in air, in a matter of minutes. The technique described almost always yields a single crystal whose basal plane is nearly perpendi,cular to the bottom of the graphite boat. In earlier experiments, in which the bottom of the melt was in direct contact with the graphite boat, single crystals were grown with basal planes parallel, perpendicular, or at some intermediate angle to the bottom of the boat. At times the orientation of the bulk of the material differed from the orientation of the material in the narrow neck. In these cases, a nucleation site initiated the growth of a differently oriented crystal, and the thermal conditions favored the new orientation over the initial one. The thermal conditions depend on a number of factors, including the heating technique, the placement, shape, and thickness of the quartz plates, the thickness of the walls and bottom of the graphite boat, and the quantity of bulk bismuth employed. All of these factors, plus the initial orientation and the presence and effectiveness of nucleation sites, will determine the orientation of the final large single-crystal slab. When a crystal of specific orientation is desired, an oriented section of a rapid-freeze crystal is shaped by spark cutting and grinding for use as a seed. To grow a doped crystal, the desired impurity is placed in the graphite boat together with the bismuth chunks and seed. Crystals doped with mercury, cadmium, lead, and selenium have been grown. The rate of freezing is so great that the distribution coefficient of any impurity approximates unity. On a gross scale, therefore, impurities should be more homogeneously distributed in rapid-freeze crystals than in Czochralski or zoned crystals. Because of the possibility of constitutional supercooling, however, it is quite possible that impurities are not homogeneously distributed on a microscopic scale in the rapid-freeze crystals. Generally the single crystal slabs which have been prepared are initially 5 to 7 mm thick. Thicker crystals may be obtained by using one of these slabs as a seed. The slab is placed in a graphite boat resting on a large aluminum block, either air- or

Jan 1, 1964

By Stephen C. Brown

THE expansion of the world economy which has been in process since 1958 continued in 1963 and both production and consumption of minerals rose. Gross national product (GNP) rose sharply in the United Kingdom and Japan, continued to expand in the United States and Canada, and maintained a high though slightly declining rate of growth in the European Economic Community (EEC) despite the appearance of excess capacity in certain lines and inflationary pressures in Italy and France. The steel and motor vehicle industries both increased output in North America, Western Europe, and Japan. The less developed areas benefited substantially from an improvement in their terms of trade, and their export earnings increased some 8 percent in 1963; although estimates of GNP for the majority of them are 110t yet available, it is probable that this increase was partly reflected in a substantial rise of GNP.2 In the United States the expansion was steady and extended through all sectors of the economy producing no distortions likely to disturb its continuing growth; at yearend with unemployment still at about 5.5 percent of the labor force and operating rates of industry estimated at about 87 percent of capacity, there was a substantial margin for further expansion. Though the balance of payments was still in heavy deficit for the year, in the last half it was moving rapidly toward equalibrium as net exports rose and capital outflows declined; prices were relatively stable, inventories increased only slightly and the activity of mineral-consuming industries remained high, steel output rising by 11 percent to highest level since 1957 and the auto industry output equalling the 1955 record.3

Jan 1, 1964

By W. N. Carr, J. R. Biard, B. S. Reed

An analysis of the semiconductor injection laser is presented which is based on a phenomenological model using device and material parameters. The intent of the laser threshold analysis is not to predict from theory the actual threshold current density but rather to provide a logical means of interpreting experimental results. The device and material parameters have been selected such that they describe both the threshold conditions and quantum efficiency of the lasev. A technique is proposed whereby the current required to obtain a population inversion is predicted from device 1-V characteristics. Experimental data are presented which support the analysis. THIS investigation is concerned with the characteristics of GaAs lasers fabricated in this laboratory. However, the assumptions used in these calculations should not limit their application to GaAs alone. It is felt that the analysis is sufficiently general to be useful in describing the operation of other semiconductor-laser materials. ANALYSIS heavily doped semiconductors to be considered. The absorption and/or generation of optical radiation may be completely specified in terms of q(E) and the probability functions f,,(E) and f,(E) which define the occupancy of the valence-band and conduction-band levels, respectively. The symbols used in this analysis are listed at the end. Following the approach of all' it can be shown that the effective gain coefficient, g, in the plane of a forward-biased P -N junction is g(E)=-ai@)[1-fv(E)-fc(E)] [1I In particular Eq. [I] holds for the photon energy at which lasing occurs, Ep. Throughout the following discussion Eq. [I] is considered only for the lasing transition E = Ep. For simplicity the functional energy dependence of the various factors is omitted in subsequent equations. Unless otherwise stated the symbols used represent the values at Ep. If the analysis is limited to the P-type side of the laser junction, the function q(l -f,,) is recognized as the band-to-band absorption in the P-type material at thermal equilibrium. Under forward-bias conditions the function f, is determined by the electron quasi Fermi level in P-type material. For sufficiently large forward bias the second term in Eq. [3] will become dominant and net gain will result; i.e., g will become positive. In order to simplify the subsequent analysis several assumptions are in order at this point. a) No conductivity modulation occurs. /„ is independent of f, and therefore go is a constant. b) The P-type material is heavily doped such that the degeneracy of the valence band permits popu-

Jan 1, 1964