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By H. Mori

Construction of cast-in-place piles with enlarged bases has become popular in the cities in Japan facing to the sea coast, where the subground soil is soft alluvium deposited to depths often exceeding 30 m. The groundwater table is a few meters below the ground surface. Skin friction of piles may become negative due to ground subsidence or reduced due to liquefaction of loose sand during an earthquake. To support highrise buildings, depths of bearing strata to which piles are embedded often exceed 50 m. Due to such geotechnical conditions, methods and equipment to build cast-in-place concrete piles mainly built by the reverse circulation method have been developed since the 1970s. In the first half of this paper, the authors review the cur-rent practise of building cast-in-place piles with enlarged bases. Then they introduce the TFP system developed in recent years, and discuss about the procedures to control and monitor enlarging of bases.

Jan 1, 1989

By Newell G. Alford

Forecasts of future timber consumption in soft-coal mining are handicapped by the lack of adequate experience records for estimating properly the timber requirements of the industry. Data were obtained from plants where records are kept or from operators who collected the information and to these were added composite figures for the continental United States in 1905 and 19191 and for central and western Pennsylvania and for Illinois in 1922.2 The result, representing slightly over 928,000,000 net tons, is shown in Table 1. Some of the companies furnishing data were unable to segregate the timber into classes of use but for those who did, Table 2 shows the board feet of posts and cross ban used per ton of coal mined and the percentage of the total timber consumed that was used in roof support. The wide variation in amounts of timber per ton of coal mined is the result of

Jan 1, 1924

By John Ward Smith

Methods for estimating the amounts of nahcolite, dawsonite, and the sum of these two sodium carbonate minerals from oil-yield assay data are developed and evaluated for Green River Formation oil shales from the saline section of Colorado's Piceance Creek Basin. Derived statistically, these estimation methods depend on the fact that these minerals yield water and gas measured during oil-yield assay. The estimation procedures yield values for nahcolite and nahcolite-plus-dawsonite of sufficient accuracy for stratigraphic plotting and correlation, whereas estimates for dawsonite are more generalized. However, resource estimates and reserve computations for both nahcolite and dawsonite accurate within 10 percent of the real value are readily available by summing the mineral amounts calculated by the procedures presented. These estimation procedures are applicable to oil-yield assay data on core samples from more than 30 coreholes which have penetrated the saline section of the Green River Formation in Colorado.

Jan 1, 1972

By J. D. Meakin, H. G. F. Wilsdorf

An etching technique.has been used to investigate the dislocation structure of deformed @-brass single crystals. Isolated single ended pileups have been observed, and it is shown that, in certain cases, the configurations of such pileups agree with theoretical predictions. Many discrete pileups within heavily deformed regions have also been detected and the influence of surrounding dislocations on these groups are reported and discussed. Divergences between the experimental and theoretical spacings in the isolated pileups and the origin of the stress maintaining the pileups are discussed. THE spatial configuration of a linear array of identical dislocations has been evaluated theoretically by Eshelby, Frank, and Nabarro.' Of particular interest is the equilibrium spacing of a series of dislocations under a uniform shear sti-ess when the leading dislocation is held fixed in the lattice; such an array is termed a single ended pileup. Eshelby, Frank, and Nabarro' found that an explicit analytical solution to the problem of n dislocations in a pileup is not possible, but they were able to derive approximate formulae applicable under various limiting conditions. An alternative method of determining the equilibrium configuration was proposed by Leibfried and Leibfried and Haasen in which the discrete dislocations are replaced by a continuous dislocation density. This technique was used by Head and Louat to solve in first approximation, a number of problems of particular interest, eg., single and double ended pileups. Head has also solved numerically a number of specific configurations involving up to six dislocations. Recently Kuhlmann-Wilsdorf has obtained numerical solutions for single-ended pileups containing between three and seventy dislocations, thus making possible a comparison between appropriate experimental results and accurate theoretical values. The considerable use of the pileup concept in theories of plastic flow has stimulated a number of attempts to observe such arrays experimentally. There is of course considerable intrinsic value in revealing an isolated pileup because a direct check on the elastic theory of dislocations then becomes possible. The only technique generally applicable for studying pileups in bulk metal specimens is selective etching of the point of emergence of individual dislocations. Confining our attention to etching studies which have revealed pileups, the earliest reported work

Jan 1, 1961

By Harold Bloom, H. E. Hawkes

Streams and rivers are the principal channels into which the weathering products of rocks and their contained ores are funneled. The inorganic load of a stream system is a crude sample of all the earth materials in the drainage basin of the stream, and the heavy mineral assemblage of sediments is one of the oldest and most successful guides to certain kinds of bedrock ore in unexplored terrain. Early application of this method was made possible by the ease of separation and identification of heavy minerals in the field with the simplest equipment. Water analysis for traces of base metals became a practical possibility about eight years ago with the development of rapid chemical tests that could be carried out at the field site. Since that time the water method has been widely used in mineral reconnaissance, and a substantial number of discoveries have been reported. Here again, the techniques developed for this work were relatively simple and could be performed easily at the field site.

Nov 1, 1956

By G. J. Harmsen

is shown that in any isotropic porous medium there is a fixed ratio, : , between the numerical valrles of the total pore perimeter per unit of cross-section and the specific surface area per unit of bulk volume. The consequences of this fact on the use of the concept "hydraulic radius" in the case of porous media are examined. The validity for consolidated sands of Kozeny's rela- tionship and of the formula derived by Carman for capillary rise are discussed. INTRODUCTION In the course of time several quantities and relations have been put forward in order to describe the texture of a porous medium and the flow of fluid through it. Among these relations the so-called Kozeny formula and a formula for capillary rise, for both of which Carman',' has given a derivation, will be specially considered here. These relations are of a semi-empirical nature and the derivations must be considered to have a heuristic significance only. For unconsolidated mate-

Jan 1, 1956

By Joseph P. Hodgson

JOSEPH P. HODGSON.-As to ".Safety First," I did not deal with that, but I will say that in 1913, the number of .men killed was nine, and that year the "safety first" program was commenced; the next year, 1914, the number was reduced to five. In 1915, I am pleased to say that the number was reduced to two in the Copper Queen's entire property, and we have none so far this year. THE CHAIRMAN (G. F. G. HERMAN, Bisbee, Ariz.).-I can say, further, that we have from eight to nineteen men per month incapacitated for more than 14 days. Those are classified in this State as serious accidents. The number of men injured has apparently increased, -but that is clue to our improved method of recording and classifying accidents, no matter how slight. C. W. GOODALE, Butte, Mont.-The importance of cooperation among the members of the staff of an industrial organization is well brought out by Mr..Hodgson's paper.

Jan 12, 1916

By Murray G

This paper outlines the processes involved in acid generation from sulphides and the key factors in identifying and predicting time dependent changes in the nature of acid mine drainage (AMD). The initial characteristics of mine water; whether drainage from exposed mining faces, runoff and seepage from waste dumps or seepage from process tailings; do not necessarily reflect the long term potential for AMD. The ultimate quality of mine drainage is a function of the interaction of many chemical, physical, biological and engineering (operational) factors. Techniques are available that can predict the qualitative nature of acid generation and mine drainage quality but accurate quantitative predictions are essentially impossible at the present time. As more and more mining operations exploit sulphide ore, the AMD and acid waste issue will become a. far greater concern. The significance of time dependent factors in the production of acid mine drainage-.is not just restricted to particuL.ar mine sites but needs to be recognised by the mining industry as a whole.

Jan 1, 1988

By André Bérubé

"IntroductionSince the disappearance of Les Forges du Saint-Maurice at the end of the last century, many historians have taken an interest in the lengthy past of this enterprise. They considered the political, socio-economic, administrative and anecdotal aspects of the industry, but barely dealt with the elements of technology. The purpose of this article is to try to fill this gapru.Les Forges du Saint-Maurice was an integrated industrial concern, specializing in the production of semi-finished wrought iron and finished cast iron, that operated almost without interruption between 1734 and 1883. Les Forges first came into being in 1729, when Montreal merchant Francois Poulin de Francheville submitted to the king of France a request for the right to exploit the bog iron ore deposits on his seigneury of Saint-Maurice. This request, agreed to in 1730, was one of a long series of attempts, previously unsuccessful, to establish a local iron industry in the colony. Several such proposals were held up by a lack of capital from promoters or a too rigid application of the mercantilist policy by the metropolis. In 1730, however, the French minister Maurepas favoured a more liberal policy which would encourage private enterprise. The benefits of an iron industry to the naval construction industry was a factor that caught the attention of administrators. The choice of the site for Les Forges was based on the following factors:• the abundance of surface deposits of bog iron ore in the Saint-Maurice region;• the presence of a vast supply of hardwood and conifers needed in large quantities by this industry;• the proximity of sandstone and limestone deposits, indispensable materials for the construction and operation of the blast furnace;• the presence of a water stream, with sufficient flow to provide the hydraulic power needed for the operation of the machinery."

Jan 1, 1983

By Luiz C. Correa da Silva, Robert F. Mehl

An experimental study of the movement of markers in the systems Cu/a-brass, Cu/Sna-solid solution, Cu/Ala-solid solution, Cu/Ni, Cu/Au, Ag/Au, employing many types of markers and a variety of temperatures. Marker movement is confirmed and undoubtedly associated with the manner in which atoms move during diffusion. EVERAL years ago Smigelskas and Kirkendall' •S reported measurements on the interdiffusion of copper and a-brass and on the movement of inert markers placed at the original join. These markers were observed to move toward the a-brass side of the join, and from this it was inferred that zinc diffuses in a-brass more rapidly than copper. Similar results were reported a little earlier for the diffusion of solvents into high polymer solids.' This has attracted much attention, particularly from those interested in the mechanism and the theory of diffusion: Seitz3 has employed it in supporting the vacancy theory of diffusion; from the data Darken4 has calculated separate diffusion coefficients for copper and zinc, developing a "phenomenological" theory of diffusion; and Bardeen5 has employed it in constructing a general theory, including therein the work of Seitz and Darken, as has Le Claire. These matters have recently been reconsidered in a sympo~ium.7 Some reason has existed for questioning the work of Smigelskas and Kirkendall.' Their technique consisted in electroplating copper on a-brass, upon the surface of which Mo-wires had been secured, and then diffusing, measuring the extent of diffusion along the normal to the join, and measuring the marker displacement in the same direction by a comparator determination of the distance between Mo-wires on opposite sides of the electroplated brass sample. It has been suspected that the copper plate might have been porous, and that the original interface might have been an imperfect join, both contributing to the transfer of the volatile zinc by vapor transfer;' it has also been questioned whether the marker movement might not in a measure be a property of the marker itself; etc. These legitimate questions require experimental answers; the present paper offers such answers. Moreover, Smigelskas and Kirkendall studied the effect only in the Cu-Zn system and at one temperature; the attention which the work of Smigelskas and Kirkendall has commanded recommends similar

Jan 1, 1952

By Robert E. Green

Formulae are given for calculating the modes of wave propagation in a single-crystdl specimen possessing a given crystallographic orientation. Such calculations lead to determination of the orientation factor appearing in the Granato-Lucke theory for the attenuation of these waves due to dislocation damping. A detailed treatment is given for the case of an aluminum crystal possessing the orientation having a maximum Schmid fac -tor of 0.5. FOR a number of years the attenuation of ultrasonic waves propagating in metals has been used to investigate various phenomena causing internal friction.Most of the experiments were performed on polycrystalline test specimens and the waves were assumed to be propagating in an isotopic medium. However Alers 6 in 1955 and more recently Hikata et at. Chiao and Gordon,8 and Swanson and Green 10 have used measurements of attenuation of ultrasonic waves to study internal-friction changes in single crystals. These authors were concerned with the energy losses experienced by the ultrasonic waves due to dislocation motion induced by plastic deformation of the crystals. Alers measured the attenuation of 7 mc per sec ultrasonic pulses propagating in zinc single crystals before, during, and after plastic deformation. Simultaneously he measured the time-dependent plastic strain at constant stress in order to study the correlation between this strain and attenuation. The crystals were oriented in such a way that the applied stress provided a direct shear on the slip plane, thus causing the deformation to proceed by slip on this plane. At the same time the high-frequency sound pulses were sent through the crystal perpendicular to the slip plane. He found that the attenuation of transverse waves, the stress vectors of which lie in the slip plane, was very sensitive to the deformation. The polarization of the particle displacements, associated with these waves, relative to the applied static shear stress, and hence the direction of slip, had no obvious effect on the results. The attenuation of longitudinal waves was affected by the deformation only when the slip plane was not perpendicular to the propagation direction. This indicated that the attenuation was caused by dislocations introduced by the deformation and moving only in the slip plane. Hikata et al. made simultaneous measurements of attenuation, velocity changes, and stress-strain relations on aluminum single crystals deformed in tension. Both longitudinal and shear waves were used, at frequencies of 10 and 13 mc per sec. They placed emphasis on the choice of propagation modes and polarization of the ultrasonic waves, such that interactions between these waves and dislocations on selected slip systems could be investigated. They also selected specimens possessing specific crys-tallographic orientations, which allowed investigation as a function of the number of equally favored slip systems under the applied stress. They found that, for symmetrical orientations, the change of attenuation decreases with the increasing number of equally favored slip systems, i.e., in the order

Jan 1, 1964

By P. A. Riveros

The literature on the arsenic disposal practices of the metallurgical industry and the long term stability of the disposed arsenic compounds were reviewed from a Canadian perspective. The review was complemented with visits to selected operating metallurgical sites to obtain information on their specific arsenic disposal practices and the behaviour of their impounded residues. The arsenic disposal procedure currently favoured by the industry involves the formation of an insoluble ferric arsenate compound which is allowed to sediment at the bottom of tailings or residue ponds. It has been shown recently that this poorly formed crystalline compound is similar to ?arsenical ferrihydrite? which is ferrihydrite containing strongly adsorbed arsenate anions. Despite concerns about its long term stability on thermodynamic grounds, arsenical ferrihydrite appears to be stable for many years in the proper environment which includes a slightly acidic pH and oxidizing conditions. A high Fe/As ratio and the presence of heavy metals appear to increase the stability of arsenical ferrihydrite. High temperature operations, such as those encountered in the autoclave treatment of refractory gold ores, are conducive to the formation of scorodite, FeAsO42H2O, and/or a series of ferric arseno-hydroxy-sulphate compounds depending on the solution composition. Scorodite has several advantages over arsenical ferrihydrite as a disposal compound including a lower iron demand, a higher density and a greater thermodynamic stability. New procedures have been developed to generate scorodite at ambient pressure. These procedures would offer significant reductions in capital cost because of the elimination of the need for autoclaves. Lime precipitation which was widely used in the past is being abandoned as a result of strong evidence showing that calcium arsenate compounds decompose slowly in contact with atmospheric CO2 to form calcium carbonate and soluble arsenic acid. In all cases, the long term stability of the disposed arsenic compounds depends on a number of factors including disposal site characteristics, particle crystallinity and size distribution, the presence of complexing agents and the effect of bacterial activity.

May 1, 2002

By Nélida Tantavilca, Pablo Espinoza, Claudia Barreto

En el sector minero uno de los principales problemas lo constituye el drenaje ácido de mina (DAM), sobre todo en operaciones mineras abandonadas y en operaciones activas que no logran controlar adecuadamente la calidad de sus vertimientos. Se investigó el grado de remoción de metales cobre, hierro, plomo y zinc disueltos en drenaje ácido de mina por aplicación de diferentes proporciones de mezclas de reactivo neutralizante (RN) cal hidratada al 67% de óxido de calcio (CaO), con material adsorbente bentonita sódica natural (BE), comparado con la aplicación de reactivo neutralizante sin mezcla, comúnmente utilizado en la neutralización de los drenajes ácidos de mina.

Sep 30, 2022

By R. Schuhmann

Distribution of material in the fine sizes of a comminution product generally is well represented by the empirical equation' y = 100 (x/k)a [1] in which y — cumulative percent finer, x = particle size, a -= distribution modulus, and k = size modulus. Charles3 found that the energy consumption in comminution is usefully expressed by another empirical relation, E = Ak(1-D) [2] in which E = energy input per unit volume of material, A = a constant, k = size modulus based on Eq. 1, and n = a constant; (1-n) is the slope of a plot of log E vs log k. Holmes3 has presented energy equations similar to Eq. 2. The constants a and n in Eqs. 1 and 2 have been shown to depend both on the nature of the material and on the comminuting device. Moreover, Charles showed that within experimental error a and n are a — n+1 = 0 [3] Combining Eqs. 2 and 3, E = A k-a [4] In the first sections of this article it is shown that the energy equation, Eq. 4, can be derived directly from the size distribution equation for the fine sizes, Eq. 1. The derivations are made without assuming any of the specific relationships between energy and particle size which have been common in previous literature. For comminution processes in which Eqs. 1 and 4 adequately represent the experimental data, the constant A in Eq. 4 is found to be a simple and useful inverse measure of grindability. That is, A is the energy consumption per unit volume of comminution product finer than unit size as determined from the straight line portion of the log-log plot of the size distribution. These considerations all lead to a unifying hypothesis of comminution mechanism from which both Eq. 1 and Eq. 4 can be derived. Finally, it is pointed out that this hypothesis raises serious questions as to the significance of the Rittinger hypothesis, the Kick hypothesis, and other theories in which energy numbers are systematically assigned to various size fractions of comminution products in order to calculate theoretical energy consumptions. Derivation of the Energy Equation from the Size Distribution Equation: For simplicity, consider the comminution of 100 volumes of a feed material of relatively uniform particle size. The comminution process may be considered as the summation of many individual and independent comminution events. The extent of comminution is most easily expressed as the number of comminution events, z. In the first derivation, the key assumption is that the characteristics of the comminution events in a given crushing or grinding process are substantially constant and do not vary with the progress of the comminution process. Accordingly the characteristics of an average comminution event may be defined. In one such event, a quantity of energy $E is applied to a single particle of size f and volume $v. The crushing of this particle produces fine particles with a size distribution similar to that given by Eq. 1: yw=100(x/ka)a0 [51 In this equation yo, a0, and k0 are used to characterize the product of an individual comminution event rather than the product of the comminution process as a whole. In using Eq. 5, we will not be concerned with values of x close to the feed size f and will therefore assume only that the equation is applicable to the finest sizes of the material. In 100 volumes of total product, the actual volume of product finer than x from a single comminution event, or dy, is given by The total volume of material below size x, resulting from z events, is then given by y = z(dy) =z(dv) (x/ka)a0 =" Eq. 7 reduces to Eq. 1 when we let a, = a and [8a] z =100/dv (ka/k )1 or k = ka (zdv/100)-1/a [8b] Eq. 8a shows that the distribution modulus of the comminution product is the same as for the product of an individual comminution event. Eq. 8b shows how the size modulus of the comminution product k varies with the extent of comminution as measured by the number of events, z, or as measured by the fraction of the feed actually subjected to com- minution1 zdv/100. The energy input to 100 volumes of total feed, or 100E, is the sum of the energy inputs for all the comminution events: 100E =z (dE) [9]

Jan 1, 1961

By Simon J. D. Cox, Nicholas J. Archibald, Steve Nichols, Peter B. Ketelaar, Donelle C. Davies, William L. Power

In the mining industry, there is a critical need to communicate complex, three dimensional information about the geology, ore reserves and development plans for mining operations. This information has to be communicated to a diverse audience, the members of which may not be trained in all of the disciplines required to create, utilise, or interpret the information. Software developed to support World Wide Web (WWW) activities has the potential to improve and change the way exploration and mining data and in- formation is organised, presented, and processed. In this paper, we discuss the creation of interactive displays of complex three dimensional data for the mining industry.

Jan 1, 1996

When a joint venture is established between a major and a minor, the co-venturers often have a number of divergent interests; the major may have put up significantly more capital into the project and will want to protect its investement; the major may have more financial resources and be more readily to commit capital to the project; the major may have more technical resources and expertise to provide to the project; the major may have other competing demands for its capital; the minor may be relying on rapid development of the project as its sole source of cash flow. Successful joint ventures arise when the co-venturers understand each others' interests and attempt to satisfy these interests. This could be achived by having a clear process and timetable for development of the project coupled with clear rules for distribution of income, the commitment of capital to the project and the provision of inter-company services. If divergent interests are either regulated clearly or eliminated, both co-venturers are more likely to seek common objectives in the joint venture with less scope for conflict. This paper, written from the perspective of a major, examines means of establishing successful joint ventures between majors and minors.

Jan 1, 1997

By S. K. Paul

"This paper briefly describes the underground crushing and conveying system at Sherritt Gordon Mines' Ruttan Mine. A series of three steel-cord belted conveyors, with a total length of 2J55 metres and a total vertical lift of 407 metres, convey the muck from the underground crushing station to the mill at the surface. The maximum size of the crushed rock is 6 in. All the conveyors are provided with numerous safety and fire suppression devices. IntroductionThe Ruttan Mine of Sherritt Gordon Mines Limited is located 20 km east of the town of Leaf Rapids, 760 km north of Winnipeg. The orebody is multilensed, with lens width varying from 6 to 45 m. Ore production started in 1973 with the opening of a 10,000-tpd open-pit mine. Initial development of the underground mine was started in 1972 with the driving of parallel conveyor and access declines at minus-2507o gradient to the I 220-m level, and then the access ramp was further extended to the 1160-m level. Exploration drifting was done on the 1280-m and 1160-m levels from the access ramp. The final development plan for the underground project was approved in January 1977, and full-scale development and constructionwere resumed.At present, Ruttan Mine is in a period of transition from open-pit to underground mining. Ore production is now coming from both operations. By mid-1980, open-pit production will cease and all production will come from the undergroundmine.The underground mining method at the Ruttan Mine is sublevel open stoping with delayed backfilling. The orebody is divided along strike into a series of 27-m-long stopes and 15-m pillars, both 60 m high."

Jan 1, 1980

The Olympic Dam copper-uranium-gold-silver deposit, located 520 km NNW of Adelaide, S.A. was discovered by Western Mining Corporation Ltd in 1975, and is now being developed as a joint venture between WMC (5107o) and the BP Group (4907o). The discovery of this deposit resulted from the application of a conceptual model for the formation of sediment-hosted copper deposits. This model postulated that the oxidation of basaltic rocks could release significant amounts of copper into solution and that, under favourable conditions, these solutions might pass upwards along faults, and the copper be precipitated in reduced- facies sediments higher in the sequence. The Stuart Shelf province was chosen for exploration because geological interpretation suggested the presence of suitable basal- tic source rocks at depth, and favourable host sedimentary rocks in the overlying sequence. The Olympic Dam site was selected for drill-testing because of the presence of coincident gravity and aeromagnetic anomalies suggesting the presence of basalts and/or mineralisation at depth. This site also had a favourable tectonic signature, indicating the presence of deep crustal structures which might have allowed fluid migration.

Jan 1, 1988

By Pierre Gouvin

This paper describes the design, installation and monitoring of a state of the art real time geotechnical/structural instrumentation monitoring system to facilitate tunnel construction under Interstate route I-5 in Seattle, Washington, USA. The project involved removal of existing highway foundation substructures on both North and Southbound lanes as well as the underground reversible high occupancy vehicle lanes. The system utilized state of the art 3-D pulsed laser scanning, wireless sensor networks, automated robotic total stations, tilt beam sensors, narrow angle tiltmeters, and in-place inclinometers. Dedicated real time data loggers, with a web based graphical interface, provided 24/7 access to critical measurements. In addition to the instrumented sections of wall and roadway subsurface which monitored physical measurements at known points, the pulsed laser scanning allowed complete site monitoring coverage where physical sensors were not located. This data allowed post processing at any location enabling the contractor and designer to respond to unforeseen structural responses to construction. Use of the instrumentation system resulted in the early detection of wall movement, and provided feedback to the designers to facilitate construction process changes in order to minimize further movement.

Jan 1, 2010

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