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Jan 1, 1969

By OTTO HERRES

TITANIUM is estimated to be the ninth most plentiful element, ranking after iron, aluminum, and magnesium, and ahead of copper, lead, and zinc. Vast quantities of titanium are widespread throughout the world in ore deposits and beach sands. Before the war, processing plants were operated in England, France, Italy, Czechoslovakia, Norway, Russia, Australia, United States, and Japan. In spite of its widespread occurrence, however, the U. S. Department of Justice has held the titanium industry to be a world monopoly and action was taken in the Federal court during the summer of 1945 to enjoin international patent and marketing agreements and to restore free competition. Possibly the rather surprising lack of public familiarity with this industry of international importance arises from its astonishingly rapid development and growth in the strong hands of some of the greatest chemical companies in the world, including the important foreign companies, Imperial Chemical Industries (British), Montecatini (Italian), I. G. Farben (German), and Titan Kogko Kabushiki Kaisha (Japanese). The rapid growth of the titanium industry in the United States is indicated by a tenfold increase of ore imports in the 1930 to 1940 decade before the war began to affect shipments from overseas. The fact that the industry formerly derived practically all ore for chemical processing in American plants from foreign sources probably also accounts for lack of general public knowledge of titanium. In 1939, to meet the requirements of increasing demand for the white pigment. titanium dioxide, more than 250,000 tons of titanium concentrates moved to this country, principally from the Travancore coast of India where the ilmenite concentrate from the beach sand runs as high as 60 per cent in titanium dioxide. Global warfare put a stop to shipping and thus gave rise to the development of titanium mining on a substantial scale in the United States during 1941.

Jan 1, 1946

By D. B. RUSHNORE, K. A. Pauly

Bulletin. No. 41, May, 1910. ABBREVIATIONS. Al. Ind., Alliance Industrielle. am. Elec'n.. . American. Electrician. Bull. As. Ing. El Bulletin de la Association des Ingenieurs Elec- triciens Sortis de l'Institut Electrotecnique Montefiore, Liege. Bull. Soc. bilge d' Elec Bulletin de la Société belge d'Electriciens. Col. Guard . Colliery Guardian. D. R. P Deutsches Reich Patent. Dilly. Poly Dingler's Polytechniches Journal. E. & DI. Jour Engineering and Mining Journal. E. T. Zeit Electrotechnische Zeitschrift. Eclair. Elec. L'Eclairage Electrique. 1;1. Anzeig Elektrotechnischer Anzeiger

Sep 1, 1910

By L. C. Graton

[CONTENTS PAGE INTRODUCTION AND ACKNOWLEDGMENTS. By George M. Fowler2 Question 1-Is Structural Deformation of Some Character Always Necessary for the Migration of Mineralizing Solutions, Especially in Limestone or Other Dense Rock? DISCUSSION by: A. M. Bateman 10 S. F. Kelly 15 C. H. Behre, Jr 8, 13 G. B. Langford 13 T. M. Broderick11 H. E. McKinstry6 R. H. Clarke 13 D. H. McLaughlin8 J. D. Forrester for M. H. Gidel . . . 4 W. H. Newhouse13 G. M. Fowler 2, 6, 11 R. H. Sales 6 L. C. Graton 11 Edward Sampson 12 R. D. Hoffman 10 J. S. Stevenson 7 I. B. Joralemon11 L. B. Wright 2 Question 2-What Are Some of the Chemical and Physical Characteristics in Certain Beds within a Limestone Formation that Determine Their Favorable or Unfavorable Aspects as Reservoirs for Ore and Other Introduced Minerals? DISCUSSION by: G. W. Bain 17G. M. Fowler 21 C. H. Behre, Jr21L. C. Graton18 J. S. Brown 16G. F. Loughlin18 E. L. Bruce 19R. H. Sales 19 R. H. Clarke 20A. K. Snelgrove 20 Question 3-Are There Any Criteria by Which One Can Determine When Mining Operations Have Reached the Roots of an Ore Deposit? DISCUSSION by: J. M. Boutwell29G. B. Langford 29 T. M. Broderick28G. F. Loughlin25 E. Y. Dougherty27R. H. Sales 24 G. M. Fowler 22F. A. Thomson 26 I. B. Joralemon 22Edward Wisser 30 General S. F. Kelly35 References36

Jan 1, 1940

CORPORAL SHEPPARD B. GORDY Sheppard B. Gordy, a brief biography of whom was printed inn the January Bulletin, entered the employ of the Braden Copper Co. immediately on his graduation from the Sheffield Scientific School in 1912. He remained with this company four years, working up through the various grades to assistant foreman and foreman to one of the individual mines. The last year he was in its employ, he acted as general mine foreman. He was for a short time with the Chile Exploration Co. and then went with the Andes Exploration Co. (Anaconda) and remained with CORPORAL SHEPPARD B. GORDY. the latter, doing mine exploration and development work, until he sailed for home in June, 1918, to give a more personal and active service to his country in her need. He declined a tender of induction into an officers' training camp, at the urgent request of Professor McClelland supplemented by Mr. Potter, because they demonstrated to his satisfaction that he could give more valuable service to his country in helping out with the aircraft production. Being within the draft age, in order to carry out this plan, it was necessary for him to be called by his Local Board and sent to camp. This call came Aug. 26. Two weeks before that time lie had gone to Dayton, Ohio; to begin the study of aircraft production, and was sent by the Dayton Board to Camp Sherman, Chillicothe, Ohio, where he died of pneumonia on Oct. 9.

Jan 3, 1919

By W. L. Remick

THE hydrotator coal-cleaning process was developed as an economic necessity to meet the ever-increasing demand for an inexpensive method of cleaning coal down to the sizes ordinarily referred to as "dust." As the most urgent demand seemed to be in the anthracite field, all experimental work has been conducted in that territory during the past 2 years, with the exception of a few months during the strike of 1925-26, when some experiments were performed in the Alabama bituminous fields. The first commercial plant was constructed at the Middle Creek Colliery of the Philadelphia & Reading Coal & Iron Co., Pottsville, Pa. This plant is now operating. APPLICATION The field of application of the process is: 1. Cleaning anthracite fines, ordinarily described as "slush" or "silt." Slush contains all sizes from %2 in. down to and including "dust." (Anthracite passing a 32-in. mesh is also referred to as No. 2 Barley and No. 4 Buckwheat.) 2. Cleaning sizes too fine for recovery by other methods. 3. Removal of coal from sand circulated in the Chance sand-flotation process. 4. Cleaning of bituminous sizes. from 3/8 in. down to "dust. 5. As equipment for the performance of the froth flotation process. 6. Other separating, extraction and _washing. processes which may be considered outside the realm of coal cleaning. PRINCIPLE OF OPERATION Fig. 1 shows the method of classification practised under the Hydrotator patent:1 In coal cleaning the machines are operated as "hindered settling" classifiers, the flow of solids and liquids being so controlled that the units may be combined in series.

Jan 1, 1927

By W. L. Remick

The hydrotator coal-cleaning process was developed as an economic necessity to meet the ever-increasing demand for an inexpensive method of cleaning coal down to the sizes ordinarily referred to as "dust." As the most urgent demand seemed to be in the anthracite field, all experimental work has been conducted in that territory during the past two years, with the exception of a few months during the strike of 1925-26, when some experiments were performed in the Alabama bituminous fields. The first commercial plant was constructed at the Middle Creek Colliery of the Philadelphia & Reading Coal & Iron Co.,. Pottsville, Pa. This plant is now operating. Application The field of application of the process is: 1. Cleaning anthracite fines, ordinarily described as "slush" or "silt." Slush contains all sizes from 3/32 in. down to and including I(dust." (Anthracite passing a 3/32-in. mesh is also referred to as No. 2 Barley and No. 4 Buckwheat.) 2. Cleaning sizes too fine for recovery by other methods. 3. Removal of coal from sand circulated in the Chance sand-flotation process. 4. Cleaning of bituminous sizes from % in. down to "dust." 5. As equipment for the performance of the froth flotation process. 6. Other separating, extraction and washing processes which may be considered outside the realm of coal cleaning. Principle of Operation Fig. 1 shows the method of classification practiced under the Hydrotator patent.' In coal cleaning the machines are operated as "hindered settling" classifiers, the flow of solids and liquids being so controlled that the units may be combined in series.

Jan 1, 1927

By Milton H. Fies

THE writer wishes to acknowledge at the outset his great sense of obligation to those who contributed so broadly and expertly to the preparation of this paper: Dr. Albert DeSmaele, Chairman of the Board of Directors of Socogaz, Belgium; Dr. Julien Venter, Director of the National Institute of Coal Mining and Coal Utilization Industry, Belgium; Dr. Roger Loison, Chief Engineer, French National Coal Research Board, France; and Dr. Erich Sarapuu of the Sinclair Coal Co., Kansas City, Missouri. Liberal use has been made in this paper of a recent publication on Russian, Italian, Belgian, and French experiments prepared jointly by the Centre d'Etudes et Recherches des Charbonnages de France (Cerchar) and the Institut National de l'Industrie Charbonnière of Belgium (Inichar).1 The writer is particularly indebted to Dr. E. T. Wilkins, of the Fuel Re¬search Station, London, and to Mr. James L. Elder, of the Alabama Under¬ground Gasification Experiment at Gorgas, Alabama, for their unfailing patience and effective support. Not only did these experienced and capable men edit and revise this discussion, but much of its content is a direct con¬tribution quoted in full from their memoranda. Without the assistance of all these colleagues, this presentation would not have been possible. It has been a privilege to serve and work with them and to acknowledge repeatedly their loyal cooperation. The recovery of the energy inherent in coal beds throughout the world has been done through the years by methods that today may be justly regarded as primitive. While the techniques of coal mining through the application of machines and the enhancement of information and skills have advanced to an extraordinary extent, particularly during the past 20 years, the underlying means is essentially the same as when man first began to mine coal. Despite this progress in the manner of coal mining, it continues today as a hazardous, toilsome, grimy task. Coal mining per se has advanced at a greater and more rapid stride in the past 25 years than the mining of any: other mineral, but the basic method is fundamentally the same as it was the first day a miner took a pick into his hands many centuries ago. This situation presents a challenge to mining engineers everywhere, from

Jan 1, 1953

By W. H. Hough, P. B. Leavenworth

Development in the Upper Texas Gulf Coast during 1943 resulted in the discovery of 11 new fields as compared with 12 discovered in the same area during I942. Of the 11 new fields, eight are classed as oil and/or condensate and three as gas fields. In addition to the new discoveries, several more or less important new horizons and extensions were encountered in some of the older fields, as noted in the text under the heading "New Pays and Extensions.'' Drilling During the year, 418 wells were drilled, as compared with 356 drilled during 1942. Of these, 323 were field wells, of which 188 produced oil, 21 were gas wells and 114 were dry holes. The remaining 95 viere wildcats, 12 of which produced oil, 4 produced gas and 79 dry holes. Distribution of themwildcats with respect to the various trends may be summarized as follows: over the 91,340,492 bbl. produced in the same area during 1942. The production statistics in the text and the accompanying tables include condensate or distillate as oil production, because many Gulf Coast fields produce oils with a wide variation of specific gravities, all of which are commingled in pipe lines. Table 3 shows by counties all of the drilling and production" data applicable to this particular area. Outstanding Fields of 1943 The Upper Texas Gulf Coast covered in this report has 178 more or less active oil and gas fields, including the 1943 discoveries. Of these Table 4 lists those that were most important from the standpoint of production. Each of these fields pro duced in excess of one million barrels of oil during 1943. Some of the interesting facts to be noted from this list of some 26 oil fields are: (I) four of the fields— namely, Conroe, Hastings, Friendswood and Thompson—each produced more than 10 million barrels during 1943, whcrcas Conroe and Hastings were the only fields that produced 10 million barrels during 1942; (2) some of the older fields (discovered prior to 1920), such as Barbers Hill, West Columbia, and Hull, are still producing in excess of one million barrels annually; (3) some of the fields more than doubled their 1942 production—e.g., Anahuac and Friendswood. The large increase in production in practically all instances is the result of increased allowables from wells drilled prior to 1943 and

Jan 1, 1944

By W. H. Hough, P. B. Leavenworth

Development in the Upper Texas Gulf Coast during 1943 resulted in the discovery of 11 new fields as compared with 12 discovered in the same area during I942. Of the 11 new fields, eight are classed as oil and/or condensate and three as gas fields. In addition to the new discoveries, several more or less important new horizons and extensions were encountered in some of the older fields, as noted in the text under the heading "New Pays and Extensions.'' Drilling During the year, 418 wells were drilled, as compared with 356 drilled during 1942. Of these, 323 were field wells, of which 188 produced oil, 21 were gas wells and 114 were dry holes. The remaining 95 viere wildcats, 12 of which produced oil, 4 produced gas and 79 dry holes. Distribution of themwildcats with respect to the various trends may be summarized as follows: over the 91,340,492 bbl. produced in the same area during 1942. The production statistics in the text and the accompanying tables include condensate or distillate as oil production, because many Gulf Coast fields produce oils with a wide variation of specific gravities, all of which are commingled in pipe lines. Table 3 shows by counties all of the drilling and production" data applicable to this particular area. Outstanding Fields of 1943 The Upper Texas Gulf Coast covered in this report has 178 more or less active oil and gas fields, including the 1943 discoveries. Of these Table 4 lists those that were most important from the standpoint of production. Each of these fields pro duced in excess of one million barrels of oil during 1943. Some of the interesting facts to be noted from this list of some 26 oil fields are: (I) four of the fields— namely, Conroe, Hastings, Friendswood and Thompson—each produced more than 10 million barrels during 1943, whcrcas Conroe and Hastings were the only fields that produced 10 million barrels during 1942; (2) some of the older fields (discovered prior to 1920), such as Barbers Hill, West Columbia, and Hull, are still producing in excess of one million barrels annually; (3) some of the fields more than doubled their 1942 production—e.g., Anahuac and Friendswood. The large increase in production in practically all instances is the result of increased allowables from wells drilled prior to 1943 and

Jan 1, 1944

By F. H. Deily, D. S. Rowley, R. J. Howe

By Elmer R. Kaiser

G. A. Vissac (Consulting Engineer, Vancouver, B. C.) —Some of the data presented in this paper, in connection with cost studies of washed coals, should be clarified and qualified. Washing a raw coal down to a low ash content may mean higher losses in refuse, but the cost of the operation may be more than compensated by the increased value of the resultant product. However, careful engineering and accurate machinery are required to insure maximum profits. Washing at a low gravity separation demands a very accurate automatic process, chiefly when the small sizes of coal are being handled. Coal consumers today are buying mostly on a Btu basis, cognizant of the fact that low ash contents result in lower installation costs and in savings in handling and transportation charges. The attached Table X gives the actual balance sheets of the various cleaning operations corresponding to various ash contents for the two coals presented in the paper, using the old technique of a two-products separation. or the new technique, now commonly used in Europe, of a three-way separation made possible by new methods and new equipment. Savings in capital costs, handling, and transportation have been calculated on the basis of a delivered cost f.O.b. plant of $10.00 per ton of coal at 16.5 pct ash (actual 1953 average price reported by Consolidated Edison, N. Y.), and of $3.50 at the mine also for 16.5 pct ash coal. In both cases this corresponds to values of 126 and 4.26 per 1 pct of combustible and per ton, respectively, on delivered and on at the mine prices. As an example, the middle western coal at 16.5 pct ash, raw, washed down to 4 pct ash in a two-way process will give 53.75 pct of clean coal at 4 pct ash and 46.25 pct of refuse at 31 pct ash. The value of the losses will be 0.4625x(100—31)x0.042 = $1.34. Add the cost of washing, capital, and operation, which is $0.35. The total cost will then be $1.69. But with a three-ways separation we will have 53.75 pct of first-grade coal at 4 pct ash, 37.25 pct second-

Jan 1, 1955

By V. F. STANLEY

THERE is not the slightest doubt that the present recoveries of valuable minerals by the Broken Hill mills could be improved, and that further machinery would be installed for the purpose if it could be assured that a high price of metals would be maintained; but concentration, like all other com¬mercial propositions, is a question of profit and loss, and no sensible metallurgist would carry out his work in such a manner as to obtain high recoveries at a financial loss to his company. There is a point in all concentration at which the added money obtained from the higher recovery of minerals is balanced by the extra cost of obtaining the last part of the recovery; a wise metallurgist will be content with his work before his working-expenditure reaches this point. To a casual observer, the work being done by the various Broken Hill mills is identically the same. A closer investigation will show that this is far from being the case, for it is a remarkable fact that, although the larger mines extend over a length of approximately only 2 miles, such a difference in the physical and chemical properties of the ores exists that, from the first reduction downwards, special treatment is necessary in each case, and hardly any two mills are identical in operation. The details of this paper refer directly- to the work of one . particular mill in Broken Hill, for the reason that the ore from each mine presents special difficulties and requires its own special treatment. I have selected the mill referred to because it has been constructed and modified under my supervision.

Sep 1, 1909

By A. H. Geisler

The correlation of property changes during precipitation with structure has progressed, sometimes rapidly but other times more slowly, since the fundamental discovery of Merica, waltenberg and Scott.1 The predominent factor that hampered the progress has been limitations imposed by the various detection methods. Refiments in x ray diffraction tech-niques and in metallographic methods, which have been extended by the electron microscope, have contributed new information within the last few years. These permit an extension of the theory as proposed by Mehl and Jetter in 1940'2 Now that a sufficient number of alloys has been investigated to establish a general mechanism of the precipitation process, a correlation of the facts into a generally applicable theory of age-hardening is both warranted and desirable. The purpose of the paper is to provide an orderly correlation of the phenomenological facts of precipitation hardening. Speculation 011 mechanism of hardening will be confined to that consistent with existing theories of hardening, Age-hardening accompanies the formation of a new structure, the precipitate, as provided by a11 alloy system ill which solid solubility decreases with decreasing temperature. Upon this premise alone all such systems would be expected to include age-hardenable alloys. Alas, this is not always the case. Few attempts have been made to explain the variable degree of age-hardening among different alloys or to explain the influence of small alloying additions upon the hardening. Dispersion hardening as originally postulated3 is not adequate.* Coherency hardening—the term that will be used to distinguish the properties of a two-phase mixture in the unique and unstable transition state at which the phases are strained into precise atomic registry (continuity or coherency) in planes

Jan 1, 1949

By Waldemar Lindgeen

PART I.—General Features. PAGE Purpose and Extent of Inquiry ; Definitions (Fissure-Veins, Metamorphism, Metasomatism, Impregnation, Cementation, Weathering); Metasomatism in Connection with Mineral Deposits, Especially Fissure-Veins; Calcu lation of Analyses ; Criteria of Metasomatism; Crystallization of Sec ondary Minerals in Other Bodies; Secondary Alteration of Veins; Structure and Composition of Metasomatic Vein-Rocks and Their Rela tion to General Metamorphism,.759 PART 11.—Minerals Developed by Metasomatic Processes in Fissure-Veins. Quartz, including Chalcedonite and Opal; Rutile and Anatase; Fluorite; Calcite ; Magnesite and Dolomite ; Siderite; Muscovite and Sericite ; Biotite; Chlorite; Pyroxene and A mphibole; Garnet; Epidote ; Ortho clase ; Albite ; Tourmaline ; Topaz ; Kaolinite ; Zeolites ; Pyrite ; Mar casite ; Chalcopyrite ; Arsenopyrite; Pyrrhotite ; Galena; Zinc-blende and Other Sulphides; Tellurides; Native Copper ; Gold and Silver,. 601 Resistant Minerals,........... 619 PART III.—The Fissure-Veins Classified According to Metasomatic Processes. 1. Topaz-Cassiterite Veins (Altenberg and Zinnwald, Saxony ; Mt. Bischoff, Tasmania),..........620 2. Scapolite-Apatite Veins,.........625 3. Tourmalinic Gold-Copper Veins,.. 626 4. Biotitic Gold-Copper Veins,........ 641 5. Propylitic Gold and Silver Veins (General Features; Comstock Lode; The Veins of Nagyág, Hungary; Pachuca, Mexico ; New Zealand; Alaska ; Silver Cliff, Colorado; Silver City, Idaho),. .. .645 6. Fluoritic Gold-Tellurium Veins (Cripple Creek ; Other Occurrences),. 654 7. Sericitic and Kaolinitic Gold- and Silver-Veins (General Remarks; The Freiberg Veins ; De Lamar, Idaho; Summit District, Colorado),. . 6.58 8. Sericitic and Calcitic Gold-Silver Veins (The Gold-Quartz Veins of Cali fornia ; Idaho Types ; San Juan, Colorado ; Treadwell Mine, Alaska ; Gold Veins of Ontario, Canada; Schwarzwald Fissure-Veins),. . 664

Jan 1, 1901

By Nathaniel Herz

PARTING of bullion before shipment to the mint had been considered by the Homestake Mining Co. at various times, but had never been attempted before 1933, be- cause the margin of profit appeared to be too small to warrant the complications in refining. When the gold standard was abandoned by the United States in the spring of 1933, however, parting of the bullion was decided upon. The method selected was the Miller or chlorine process, which consists of the passing of gaseous chlorine into a bath of molten bullion, converting all metals other than gold into chlorides, and remov-

Jan 1, 1935

By M. R. Geer, H. F. Yancey

Four coals were treated in the Humphreys spiral concentrator, and the products were examined by float-and-sink and screen-sizing tests to determine fundamental performance characteristics. The efficiency of the separation between coal and impurity was shown to be influenced greatly by particle size.

Jan 1, 1950

By Thomas Varley

IN THE congressional act establishing the Bureau of Mines one of the functions outlined was "to assist I the industry in the prevention of mineral waste." This had not only to do with the waste in mining but in milling and metallurgical practices, including smelting. The organization of the Bureau of 'Mines includes many divisions, each working in a particular field and charged with certain investigative work. The metallurgical division has the above duties under its immediate supervision, and the station located at Salt Lake City is directed by the chief of this division: There are ten experiment stations of the Bureau of Mines, located in various parts of the country, most of them being housed at state universities under cooperative agreements. Considerable care was exercised in locating the stations and in choosing the particular type of work to be investigated at each place. Inasmuch as the Bureau was designed to serve and cooperate with the industry it is only natural that the investigative work be of interest and importance to the territory immediately adjacent to the respective stations.

Jan 1, 1925

By G. A. Beiswenger

The application of the law of supply and demand to the sale of crude oil is generally conceded, but the motives underlying the buyer's (refiner's) demands are not always obvious to the seller (producer). In some cases this obscurity has led to the conclusion that the refiner may be unnecessarily particular when he selects one crude and rejects another. This preference, however, is very largely the reflection of the refiner's product demands and the quality of the stocks obtainable from the selected crude. The purpose of this paper is to point out critical characteristics of the major classes of refined products and to show how crudes vary in their suitability for such products. With relatively few exceptions, available processing methods and addition agents make it theoretically possible to produce any type of refined product from any crude source, although it may not be economi-cally sound to do so. The widespread application of thermal cracking for converting higher boiling stocks into gasoline is well known. More recently cracking and refining in the presence of catalysts9 have been developed, as well as various processes for polymerizing lighter hydro-carbons into gasolines having desirable characteristics.6 For several years, selective solvents have been applied commercially to refining inferior quality kerosene, Diesel fuel and lubricating oil distillates .3 Improved methods for refining lubricating oils from crude residua,4 formerly suitable only for fuel, are now in use and a number of special solvent processes are available for dewaxing lubricating oils to low pour point.5 These improved refining methods have been developed not only to meet the demand for improved product quality but also to enable the refiner to obtain quality products from crude sources that would not yield such products by the older refining methods. In many cases, the utilization of these modern refining tools necessi-tates an appreciable expenditure for equipment as well as added manufac-turing costs, and their application therefore must be justified economically. Despite the availability of such tools, the added processing costs involved and yields obtainable may render their application entirely impractical. To illustrate this point, inspections of typical cuts from various crudes

Jan 1, 1940

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