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Jan 1, 1881

By George Sachs, S. M. Clark, George Espey

he tendency of a commercially drawn cartridge case to crack in the mercury test and the relation of cracking tendency to residual stress retained after drawing were studied. The fourth drawpiece (next to the final) of caliber 0.30 cartridge cases produced by Frankford Arsenal were selected as test pieces. These exhibited an exceptionally high cracking tendency, making a detailed study possible. To obtain fast cracking in the mercury test, about 0.0015 to 0.003 in. must be removed from the wall thickness of the drawpiece by pickling, and it must be subjected to the mercury test immediately after washing. Removal of the adhering mercury by annealing and subsequent squeezing of the case in a vise was used to reveal definitely the presence or absence of cracks. Various lots of apparently identically fabricated cases were shown to possess a different cracking tendency. Machining off or boring a hole in the base gradually reduced and eventually eliminated the cracking tendency. On the contrary, shortening of the wall (body) reduced the cracking tendency only if the wall became so short that the cracking zone was directly affected. By boring out the base and pickling from the outside and then splitting the resulting rings, it was possible to determine the approximate stress distribution in the base and in the adjacent part of the wall. Small compression stresses were present in the core and the major part of the base, while the surface of the base and the adjacent wall contained high circumferential tensile stresses. On the contrary, the wall when parted from the base contained only insignificant residual stress. The conception is advanced, that the stress distribution in a drawn cartridge case corresponds fundamentally to that of a tube (wall) shrunk on a disk (base). Such a stress distribution results from the tendency of the base to recover elastically by an increase in diameter from the biaxial compression during drawing while the wall exhibits little tendency to change its diameter after progressing through the die. This is confirmed by measurements which show the base diameter to be slightly larger than the wall diameter.

Jan 1, 1945

By Edward O’Toole

THe Pocahontas district occupies the extreme southern end of West Virginia, principally McDowell, Mercer and Wyoming counties, and a part of Tazewell county, in southwestern Virginia. The first record of the coal field is a report by Prof. J. P. Lesley, of Pennsylvania, about 1880, in which he mentions a coal opening at the upper end of Abbs Valley, Tazewell county, Va. C. R. Boyd, a mining engineer of Wytheville, Va., published a series of articles in 1881, mentioning coal on Indian Creek, Tazewell county, and on Horse Pen creek, which coals, he stated, extended toward the Ohio River. He also mentions the Abbs Valley coal reported by Lesley. In 1881, F. J. Kimball (who became president of the Norfolk & Western R. R. in 1883)) after examining the Scott mine in Abbs Valley, went northward across Abbs Valley Mountain to the place now known as Pocahontas, where he located what has since been called No. 3 vein of Pocahontas coal. In November, 1882, Jed Hotchkiss and others prepared a cross-section of the Flat Top Mountain coal measures, some notes on which were published by Mr. Hotchkiss, between 1880 and 1892, under the title of " The Virginias.' In May, 1881, the Norfolk & Western R. R. was organized through the purchase of the Atlantic, Mississippi & Ohio R. R., an old line running from Norfolk, Va., to Bristol, Tenn., with branches from Petersburg to City Point and from Glade Springs to Saltville. At that time, charters had been granted for three railroads tributary to the New River Valley, but their proposed routes would indicate that the promoters were concerned with minerals, timber, and a connection with the Chesapeake & Ohio R. R., rather than the development of any coal in the Pocahontas district. One of them was projected to extend up Bluestone River a short distance, but not far enough to reach the coal in the Bluestone Valley, and a little grading was done for a narrow-gage road between New River Station and a point in Giles county, Virginia, near the West Virginia line. All charters and railroads in this district were acquired by the Norfolk & Western R.R.

Jan 1, 1925

By Charles Austin

IN an earlier series of studies on 18-8 stainless steel at 600°, 700°, and 800°C.1 one pretreatment was used throughout; viz., 15 min. in hydrogen at 950°C., followed by an air quench. Several manufacturers of this alloy since have expressed doubt as to the suitability of the temperature employed, recommending instead the more customary Strauss treatment as promising superior results. In this subsequent investigation on the effects of the temperature of pretreatment several interesting points have arisen, which are described in this paper. Previous work on our equipment had shown a marked difference between alloys of "similar chemical composition" that had been manu-factured by different companies. Accordingly, one mill-bar length was selected from which to prepare all specimens. It could then be assumed that any marked differences in creep characteristics would be due to effects resulting from variations in the pretreatment of the alloy. The material was furnished by the Allegheny-Ludlum Steel Co. in the form of 5/16-in, dia. rod, finished by air cooling from a mill anneal at 1950°F. (1066°C.). It was analyzed only for the elements shown: carbon, 0,07 per cent; chromium, 18.73; nickel, 9.46; manganese, 0.40. Three pretreating temperatures were chosen, the specimens being held for 15 min. in hydrogen at either: (1) 1150°C., to conform to the recom-mended Strauss treatment; (2) 950°C., to compare with the results of previous tests; or (3) 750°C., to initiate precipitation of carbides in the material before testing. As the test cross sections were only 1/8 -in. dia., air cooling followed the annealing treatment. These treatments per-mitted two direct comparisons: (1) between the 1150° and 950°C. treat-ments to indicate the effect of grain size when all carbides were probably in solution at the start of the test; and (2) between the 950° and 750°C. treatments to indicate the effect of carbide "nucleation" for similar grain sizes.

Jan 1, 1940

"Mining as an industry of Utah had its inception in the activities of United States soldiers who came to the Salt Lake valley under the command of Gen. P. E. Connor, founder of Fort Douglas, in October, 1862. Many of these soldiers were from California and naturally employed their spare time in the search for minerals. Although their military status did not permit them to make locations in their own names, they assiduously prospected the region in accordance with their own knowledge and with information conveyed to them by Indians and others. Their efforts were encouraged by their commander, who thereby fairly earned the title of father of the industry here, and by their other officers, and many discoveries that subsequently proved of great value were made by the soldiers.No systematic prospecting or mining had been done in the Territory previously, although early Mormon settlers in the southern portion had mined a little ore from time to time in order to provide supplies of lead for bullets. The Mormon leaders at that time did not encourage mining. They held that agriculture was more important and profitable for their followers.Coal was discovered and produced in 1850. Iron was discovered in 1850 and the first iron plant was in operation in 1852 in Iron County. The first non-ferrous metal production was in 1854, in Beaver County, when Isaac Grundy treated ore from the Rollins mine in what is said to have been the first lead furnace west of the Rocky Mountains. The first mineral location was the West Jordan claim in Bingham canyon, located September 17, 1863, now owned by the United States Smelting, Refining & Mining Co., and still productive. The first district organized in the state was the West Mountain (Bingham), December I 7, 1863. Other important districts of early organization are: Little Cottonwood, December 20, 1869; Big Cottonwood, July 11, 1870; American Fork, July 21, 1870; Uintah (Park City), July 8, 1871; Tintic, December 13, 1896; Ophir, August 6, 1870. The first silver-lead smelting was by J. W. Gibson at Stockton in 1866. Lieut. James Finnerty had previously erected two small trial furnaces there, but made no quantity production."

Jan 1, 1925

1944 WALTER HULL ALDRIDGE New York, N Y 1946 PETER M ANDERSON Johannesburg, South Africa 1946 CHARLES CAMSELL Ottawa, Ont, Canada 1946 CHARLES AUGUSTUS CARLOW Fife, Scotland 1946 CECIL H DESCH London, England 1946 WILLIAM FRASER London, England 1917 HERBERT HOOVER New York, N Y 1941 DANIEL COWAN JACKLING San Francisco, Calif 1939 HENRY KRUMB New York, N Y 1942 ESSINGTON LEWIS - Melbourne, Vic , Australia 1921 C MCDERMID London, England 1944 WALTER C MENDENHALL Washington, D C 1942 PAUL DYER MERICA New York, N Y 1913 EZEQUIEL ORDONEZ Mexico City, Mexico 1938 A M PORTEVIN Paris, France 1937 GEORGE S RICE Washington, D C 1934 T A RICKARD Victoria, B C, Canada 1946 JOHN R SUMAN Houston, Texas 1946 WONG WEN-HAO Chungking, China

Jan 1, 1952

Robert T. Hill, Washington, D. C.: Having studied very minutely the geology of the district referred to by Prof. Branner, I beg to state that his quotation of my classification of the Cretaceous deposits of Arkansas is not the one which I originally gave,* nor is it the one which has since been published and is now generally accepted.? I did not assign ally of the Cretaceous formations of Arkansas to the " middle Cretaceous,"

Jan 1, 1898

J. H. HEGINBOTHAM, a, metallurgist of the General Engineering Co., talked on "Current Milling Practice at Kirkland Lake," at the December meeting of the Utah Section. The ore is enough alike through the whole district so that some generalizations and comparisons may be made. The question as to whether or not the flotation process should be used in the flowsheet for extracting gold by cyanide solutions is still being vigorously debated, and it will seemingly need some years for a definite answer to be given. Most of the gold is either free, though much of it is finely dispersed in quartz, or occurs with pyrite. At times there may be 2 per cent of telluride compounds in the ore, but the amount of gold telluride present is small and has not been definitely established. It has been shown by Dr. Haultain and others that though gold tellurides may be so finely disseminated that it is necessary to grind the ore exceedingly fine, the compounds themselves are not difficultly soluble. (An increase in temperature helps to dissolve tellurides, and also to settle pulps.) It is likely that if the ore were ground through 400 mesh, practically all of the gold would be soluble. As it is, with 96 to 98 per cent of the ore ground to minus 200 mesh, and some 70 per cent minus 325, the cost of

Jan 1, 1934

By A. E. Brugger

SOME 2,000 years ago Pliny is supposed to have said, "Out of Africa always something new." It may perhaps even now be news to a great many that the Belgian Congo has in recent years been producing approximately a quarter of a ton of diamonds annually. For that is what the 1 1/4 million carats, the recovery from 40-odd operating mines, and about 20 or 25 per cent of the world's normal consumption, amounts to. In 1915, first exploitation operations produced less than 50,000 carats from two mines. The rapid expansion of operations following the Euro¬pean war meant a most rapid development of a virgin land. The interior is now reached by air in one day from the mouth of the Congo River, where steamers unload mail and passengers from Antwerp. This trip formerly consumed 4 to 6 weeks by a narrow-gage, wood-burning, railroad around the rapids of the lower Congo and Livingston Falls; by river boat to the heads of navigation, Djoko Punda on the Kasai or Luebo on the Lulua; and thence by caravan of native porters over narrow-trails to head¬quarters on the Tshikapa. Hundreds of miles of automobile roads have been constructed over veldt and through forest, bridging streams and ferrying rivers. The railway from Capetown to the Katanga copper district to the East, once two months away by trail is now reached in 2 or 3 days over fair automobile highway. Native "boys" who a few short years ago wore little more than a smile and a string of beads and to whom a wheelbarrow was a complicated piece of machinery, are today driving Fords, tending boilers and engines and operating electrical equipment, or are capable mine workmen, machinists and artisans, and dressed in all manner of cast-off white man's clothing. Even as late as 1920, due to difficulties of securing and transporting machinery during and just after the war, the crudest hand operations were the rule for the excavation, sizing, and concentration of the diamondiferous gravel. All washing and concentration is now mechanized, using steam or electric power, and where operations are sufficiently large to permit competition with native labor costs, excavation and transportation are also accomplished by machinery.

Jan 1, 1932

By P. R. Bradley

NO thought had been given to deep level mining at the Alaska Juneau mine prior to 1930, but in that year a prospect winze was started and continued for 1000 ft. vertically below the main haulage or adit level. The point at which this winze was started was selected entirely by the prevailing physical conditions, such as proximity to established workings, convenience, and the presence overhead of a substantial pillar of dimensions sufficient to lo¬cate the sheave wheel and loading pocket. It was, therefore, with some surprise that the unusually high-grade ore found just below the collar of the winze persisted, with certain vari¬ations, to a full depth of 1000 ft. vertically. Likewise this unusually high-grade ore was found to persist on the various crosscuts driven on levels at 200-ft. vertical intervals. To be brief, this deep level work found richer ore than any yet found in the mine over like areas, and inasmuch as the area was sufficient to plan for extensive deep level mining, plans for such work were given extended consideration.

Jan 1, 1936

By Clarence Woods

ONCE a millionaire's plaything, the Santo Domingo mine, in Peru, is now, because of its metallurgical problem, an engineer's nightmare. It is deep in the montaña jungles of the Amazon basin, 140 mi. northeast of Tirapata, which is a rail- way station between Puno and Cuzco, and about 250 mi. east of Mollendo on the Pacific. The discovery was 111ade by Marian(-) Quispe, an Indian, who, while searching for quinine bark, was attracted by a slab of gold quartz 1x1 the rock wall of a narrow canyon. He broke off a piece, weighing 47 Spanish ounces and, that time, worth approximately $900. This he took to Francisco Velasco and Manuel Estrada, merchants of Coaza, who persuaded Quispe to lead them to the place, five days' journey on foot through a tangled wilderness. Velasco ' and Estrada denounced the claim

Jan 1, 1938

By Walter V. Knopp, Laurence Delisle

INTRODUCTION THE aim of this work was the preparation of nickel-steels from elemental metal powders by powder metallurgy techniques. It was known that plain carbon steels could be made from a mixture of iron powder and graphite and that the effect of carbon on iron in powder form was of the same nature as that produced in fusion metallurgy. The problem in making nickel steels from elemental powders consisted therefore in finding out whether sufficient diffusion of the nickel and other incidental metals normally present in such steels could be induced in the solid state to modify the properties of plain carbon steels made from powders and produce the beneficial effect of alloying. The composition selected originally was that of an S.A.E. 2330 steel. Metal powders, in the proportion corresponding to that composition, were mixed with graphite, pressed, and heated at different temperatures for different periods of time, to produce bonding of the metal particles and mutual diffusion of the various elements without melting. Temperatures up to 1325°C and sintering periods as long as 6 hr were first investigated because it was expected that such conditions would produce maximum diffusion with an accompanying improvement in the properties of the alloy. It was found that, although diffusion proceeded to a large extent under the conditions investigated, it would not be complete unless sintering were carried out at a high temperature for much longer than 6 hr. Relatively high temperatures and long sintering times are objectionable from a practical point of view, particularly when a low cost material is to be produced, because they necessitate the use of special, costly equipment. Work could be done to improve the diffusion of iron and nickel by changing conditions other than the sintering temperature and time, i.e., finer primary or alloy powders could be used. However, a marked change in the properties of the steel had been observed even with only partial diffusion. It was thought, therefore, that instead of trying to improve the diffusion, advantage might be taken of its incompleteness to produce a special structure consisting, in the unquenched condition, of a hard constituent, rich in nickel, dispersed in a tough pearlitic matrix. Steels with such a structure, not readily obtainable by fusion, should have desirable mechanical properties. Besides, it should be possible to prepare them from elemental powders under economical conditions. This latter alternative was therefore adopted for the second phase of this work. This report is divided into four parts: 1. General Procedure. 2. Effect of Sintering Temperature. 3. Effect of Varying the Nickel Content. 4. Effect of Alloying Elements. GENERAL PROCEDURE The general technique of cold pressing as used in powder metallurgy was applied.

Jan 1, 1948

By Fred C., Bond

DETERMINATIONS of circulating load in a classifier operating in closed circuit with a grinding mill are usually made from screen analyses of the mill feed and classifier products. The percentage remaining on someone selected screen size must be used in the calculation, and, because of the wide variation in average particle size between the mill feed and classifier overflow, an accurate and representative result at the selected mesh is often difficult to obtain. To overcome this difficulty and reduce the time required in making the determination, I have devised a method which uses the liquid-solid relationship in the circuit rather than screen analyses. The quantities required for the calculation include only the usual dilution and feed tonnage measurements, which should be made regularly in the course of ordinary mill operation and, in addition, the amount of new water added to the classifier, or to the head of the mill with the new feed. If measurements are obtained on both of these quantities it is possible to check the calculated circulating load, and to calculate the percentage of moisture in the new feed to the mill; or, if the latter is known, to check the feed tonnage.

Jan 1, 1937

By T. E. Evans, C. T. Baroch

ZrB2 was produced in batches of 4 to 6 Ib by interaction of ZrO2, B4C, B203, and carbon at around 2000°C in a simple graphite resistance furnace. Techniques of production are discussed and the final design of a suitable furnace is described in detail. Several other borides were made by the same technique and the process appears to have possibilities for commercial production. N seeking out new hard and refractory com- pounds, many researchers have turned to the investigation of the borides and excellent papers have been published on the properties of these compounds. Few papers, however, have appeared on the techniques and problems concerned with the production of these high temperature substances. This report describes progress made in developing a method for preparing zirconium diboride, ZrB2, on a pilot plant scale. The literature of the borides and other refractory hard metals recently has been reviewed, annotated, and classified so completely' that it is needless to attempt such an outline here. It is enough to say that three borides of zirconium have been reported: ZrB, ZrB2, and ZrB12.2 ZrB2 is the most stable of these and is especially stable in the presence of carbon up to and including its melting point of around 3000°C. Like most borides, it can be prepared in several ways. It can be prepared by synthesis of the elements, but these are expensive and difficult to produce in a high state of purity. Obviously, production directly from the oxides would have decided economic advantages. In electrolytic production such as that of calcium boride,:' the product is recovered as a sludge mixed with electrolyte; and separation of product from adhering electrolyte and regeneration of the electrolyte is an involved and difficult process. The work on borides was started on a small scale in 1948. Late in 1949, Naval Ordnance expressed a specific interest in ZrB2 and the project then centered on this compound. After the usual experimental work necessary in a new field, ZrB2 of good quality was produced by heating mixtures of B4C, ZrO2, B2O3, and carbon to a temperature of about 2000 °C in a resistance-type electric furnace. Over 100 lb was made for experimental use tests, and the method of production probably could be expanded into a commercial operation. A similar process has been described by Kieffer and coworkers.' The main chemical problems were the development of proper charges to insure complete reduction of the elements, determination of the proper temperature range at which these reductions took place, and adoption of techniques necessary to pre- vent inclusion of such impurities as carbon and nitrides. The mechanical problems consisted of developing a simple practical furnace that would attain the high temperatures required and permit use of a controlled atmosphere when necessary and determining of suitable refractories. Both problems were solved by designing a crucible resistance furnace. Crucible Resistance Electric Furnace Attempts were first made to produce ZrB2 in an electric arc furnace, but such a furnace would not provide the degree of carbon control required for producing clean graphite-free borides, so it was decided to try working in a crucible. Obviously, the furnace would have to be constructed of graphite, as the temperatures required are too high for other refractories or heating elements. Crucibles were made by hollowing out segments of graphite electrodes, which were fitted with a cover and clamped between two electrodes so that the current passing through the thin wall of the crucible would generate heat, using the principle of the Helberger crucible furnace."? Preliminary tests with this type of furnace were encouraging and led to the furnace design shown in Fig. 1. The essential components were a thin-walled graphite crucible resting on a graphite block, which formed the lower electrode assembly, and a top electrode assembly swung from a pipe column making contact with the top of the crucible. The space around the crucible was filled with graphite prepared from waste electrodes crushed to about ¼ in. This packing had excellent insulating properties, both electrically and thermally, and could be removed easily and quickly from around the crucible by means of an industrial vacuum cleaner. The largest resistor crucibles were machined from 8 in. electrode stock and were 26 in. long, with a side wall Yi in. thick and a 1 in. bottom. Temperatures were determined optically by sighting down a 1 in. hole drilled longitudinally through the top electrode and the crucible cover. Sealing this hole at the top was a water-cooled brass sight-glass assembly, shown in Fig. 2. An opening was provided for a light flow of helium to keep the sight opening clear of smoke, and a glass prism above the sight glass changed the line of sight to the horizontal for easier reading. More recently, the prism and optical pyrometer were replaced by a photoelectric recording pyrometer. At first the charges were placed directly in the resistor crucible but this meant that everything had to be withdrawn from the furnace every time the charge was emptied. Later, smaller crucibles were made up that could be placed inside the resistor

Jan 1, 1956

By C. L. HUSTON

MY ANCESTRAL connection with the manufacture of boiler plate runs back through four generations, and my personal acquaintance with the practice reaches back to the time, in my ,boy- .hood days, when iron plates' were made in a mill operated entirely by water power. -The mill originally was driven by an old-fashioned "'breast" water wheel 20 ft. in diameter and with a20-ft. face, geared direct to the roll train. When the mill slowed up and there was danger of its stalling, the men would jump upon the rim and help the wheel around with their weight, to prevent a "sticker." Later, as large plates were called for, a flywheel was set out of line so that it could' be speeded up by gears from the water wheel and connected back again,. by reducing- gears, to the roll train. The flywheel, with its cast-iron rim and wooden spokes, made 90 r.p.m. and the roll train 45 r.p.m. In 1870, our company installed our first steam-driven plate mill two-high rolls, 84 in. long. In these early mills the hot metal was manipulated by hand.

Jan 1, 1920

By AIME AIME

T HE Board of Directors of the A. I. M. E. held a meeting at Institute headquarters on Jan. 28, 1921. There were present 10 directors and 14 guests, the secretary and the assistant secretary. The following actions of the Executive and Finance Committees were approved: Wilkes-Barre Meeting, Sept. 12 to 17, 1921; authorization of Oregon Section; authorization of Upper Peninsula Section; appointment of Philip W. Henry and Thomas H. Leggett on special committee on Code of Ethics; and presentation of five copies of Raymond Memorial Volume to T. A. Rickard, who edited it. The By-Laws of the Ohio Section were approved. The resolutions in reference to the payment of certain contributions and assessments to the Library Board of the United Engineering Societies, adopted by the Board of Directors on June 27, 1919, were rescinded, and the resolution adopted that the income of the James Douglas Trust of $100,000 be paid over to the Library or otherwise applied by it for the purpose of maintaining the Scientific Library of this Institute in such manner as may be deemed advisable in furtherance of the purposes of such trust, and that said income shall be paid on account of and included in. the assessment levied by the United Engineering Societies on the Institute for the maintenance of the joint libraries of the Founder Societies.

Jan 1, 1921

Albin, B. R Billings, Mont. '28 Amster, Nathan L 25 Broad St., New York, N. Y. '28 Bache, Jules S 42 Broadway, New York, N. Y. '28 Barrett, C. P 5338 Harper Ave., Chicago, 111. '28 Bayless, William S Russ Bldg., San Francisco, Cal. '28 Bean, Louis, H 60 E. 42nd St., New York, N. Y. '28 Beatty, Ross J Room 604, 6 N. Clark St., Chicago, III. '28 Benwell, Oswald F Hold Mags. '28 Beymer, Albert S., V.P., Keystone National Bank Pittsburgh, Pa. '28 Blumenthal, Hugo 44 Pine St., New York, N. Y. '28 Boettcher. Charles Ideal Cement Bldg., Denver, Colo. '28 Bowlus, Thomas H., Banker, Pres., Allen County State Bank Iola, Ran. '28 Brown, Colvin B Chamber of Commerce, Washington, D. C. '28 Burt, Maxwell Struthers Southern Pines, N. C. '28

Jan 1, 1934

President-Mrs Andrew E Beer, Richardson Ave, Sea Cliff, L I, N Y First Vice-President-Mrs Lyman H Hart, 6-F Essex House, Garth Woods Apts, Scarsdale, N Y Second Vice-President-Mrs John R C Mann, 90 Edgemont Road, Scarsdale, N Y Third Vice-President-Mrs Edward P Chapman, Jr, 2632 Vista Larga Dr N E, Albuquerque, N M Fourth Vice-President-Mrs R A Cattell, 7717 14th St, N W Washington 12, D C

Jan 1, 1959

This listing of members is arranged to show company affiliation The primary breakdown is by state or country, then by company name and political subdivision At the end of each major group is a general list showing members affiliated with schools or colleges and those who did not indicate any company affiliation The listing, for countries outside United States, is broken down generally by continents and alphabetically within the continent by countries The various countries are indexed on the preced¬ing page *-The asterisk indicates members available for consulting work Anyone desiring to be listed with AIME as available for consulting work can do so by sending a written request to the office of the Secretary.

Jan 1, 1952

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