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By S. G. Bankoff

Ince1 proposed that electrostatic attraction between oppositely charged particles was responsible for slime-coating. Del Giudice2 postulated the metathetic formation of a cementing compound. Wark3 suggested that prevention of slime-coating was related to peptization of the slime. In the experiments of Table I the technique employed was essentially that of del Giudice, with the difference that the particle was examined under a film of water rather than dry.4 In general, the polished particle was agitated for 2 min. in a pulp consisting of 12.5 grams of the slime (—200 mesh) and 50 C.C. of distilled water, washed in three baths of distilled water, and examined at 220 diameters with the Leitz Ultropak. Observations of Brownian movement were made at 850 diameters with dark-field illumination. Several of these experiments do not jibe with the metathesis theory. According to published solubilities,5,6 the lead salts of the anions in experiments c through g are more insoluble than lead carbonate, there- fore should prevent the formation of lead carbonate on the galena surface. In experiment i the calcium oxalate, which precumably was on the calcite surfaces, should have permitted the formation of a lead carbonate cement by virtue of its greater solubility. Experiments j through m show that the addition of lime accelerates the deposition of quartz onto a galena surface. The writer is unable to postulate a satisfactory cementing compound, according to the metathesis theory, to explain this effect. These experiments led to the conclusion that the metathetic formation of a cement-

Jan 1, 1943

By Daniel R. Hull

IN 1026 Genders' reviewed the existing theories of this subject and stated his views in support of the gas-pressure theory. Again, in 1937, the subject was thoroughly reviewed by N. B. Vaughan,3 and by Phillips and Brick,2 so that no resume is called for here. The purpose of this paper is to describe certain observations made in the course of mill work, and to point out that they mostly tend to confirm the gas theory of Genders. VAPOR SEGREGATION There is, however, one type of inverse segregation that can be accounted for by considering the volatility of one of the constituents of an alloy. The most familiar case is ordinary brass, which is subject to a zinc enrichment of a few tenths of a per cent at the surface of a chill casting. This has been noted in 70-30 brass by Genders, and a typical example of it is given in Table I, which represents a [ ] cylindrical billet 7 in. in diameter by 5; in. long. After lathe-turning 1/32 in. from the surface, the remaining distance to the center was sampled at six equally spaced intervals. The lead, which is essentially the same throughout, will be mentioned later. Consider a brass-mill mold, either round or rectangular in cross section, standing several feet high. It may require a minute or two for pouring. Before it is full, the metal in the lower end has partly solidified and contracted somewhat away from the mold. The initial shell of solidification follows not far behind the top of the column, even if the central portion is liquid for a long way down. There is, then, a space between metal and mold that is filled with zinc vapor. The vapor has no exit, because the liquid at the top of the rising column is not only in contact with the mold but keeps up a fresh supply of zinc vapor, which has, perhaps, already begun to condense in the lower portion. The cycle is short. Within a minute or two after the mold is full the bar has cooled enough to condense all the zinc. Some of it may condense on the mold; it might be expected that most of it would condense there, but the mold at that time is well coated with a velvety carbon residue from the oil dressing, overlain by fluffy zinc oxide that commenced covering the inside of the mold as soon as pouring began. The clean skin of the freshly cast brass offers a preferred surface for condensation. Reabsorption is quick and inevitable. A simple experiment indicates that a surprisingly large quantity of zinc vapor is trapped in the space between mold and

Jan 1, 1941

By W. E. D. Stokes

WHEN history is written, the year of the blitzkrieg will go down as giving aviation its greatest impetus. No perceptible drop in military business, even with cessation of hostilities abroad, seems likely. The combined air force of the U. S. Army and Navy on July 1 was approximately 5000 planes, as against 50,000 planes currently discussed as necessary. Observers at the fronts are giving designers and metallurgists back home some realistic ideas to shoot at. As conventional runways reveal the location of airports to enemy raiders, operating bases are now masked. Difficult, often muddy and rough landing strips, requiring strong landing gears and exacting take-off and maintenance characteristics, are the specifications of war. This is "old stuff" to numerous mining operators in mountainous jungle areas where gradients up to 8 per cent are in more or less common use in such mountain landing fields. Although airplane building is not readily adaptable to assembly-line methods, a trend towards mass productions is now in evidence. Incidentally, a U.S. Army "Curtiss P-40" requires about 10,000 man hours of work to complete and is tied together with 75,000 rivets. During the past year a number of aircraft factories adopted the "shot-

Jan 1, 1941

By S. E. Bronisz, J. O. Brittain

Experiments have been carried out to study the effect of an applied stress on strain aging in steel. It was found that the stress-induced strain aging reaction proceeds rapidly in the temperature range of 0° to 60°C. The variation of stress-induced strain aging with plastic strain, aging time, and temperatures is reported. The activation energy for the stress-induced strain aging was found to be 10,000 cal per mol for the steel used in this investigation. VARIOUS observations1-5 have been made of the influence of an applied stress upon the yielding of iron and steel. However, there have been only cursory studies of the effect of an applied tensile stress upon strain aging in iron and steel1,2 The following represents the results of a preliminary study of strain aging as influenced by the application of an external tensile load during the aging process. For the most part, previous experimental work on strain aging can be classified into two parts. First, the experimental technique involved a direct determination of mechanical properties of a suitable specimen that has been plastically deformed to a constant strain and aged generally at a temperature of the order of 200°C, with the aging times varying from about 1/10 to 2 hr.6-8 The second classification of strain aging experiments involves an indirect determination of strain aging by means of physical property such as electrical resistivity or internal friction as a function of the aging time at a constant temperature and strain.9-12 The latter results have

Jan 1, 1961

By A. T. Beckwith

This paper concerns measurements of low-velocity air currents and investigations on mine ventilation by means of chemical smoke. The chemical smoke used is produced without flame and at ordinary mine temperatures, and therefore presents no ignition hazard in gaseous mines. Mining men who have worked in open-light mines are familiar with the use of tobacco smoke in determining the direction of air travel and approximately measuring low-velocity air currents. The use of chemical smoke is merely a refinement on the use of tobacco smoke and the flameless low-temperature source of chemical smoke has the additional advantage that it can be used in gaseous mines. Ventilation smoke apparatus, Fig I, is a simple device for producing dense white smoke. The apparatus as shown consists of a rubber aspirator bulb which is used to force air through a glass "smoke tube" containing a chemical substance that produces a dense white smoke on contact with air. The apparatus was developed by engineers of the U. S. Bureau of Mines.' It is inexpensive, weighs less than 3 oz, is easily carried in a pocket, and requires no skill to operate. Smoke apparatus is invaluable in practical mine ventilation work for: (I) measuring low-velocity air currents, (2) detecting air leakage, (3) observing airflow characteristics. This paper is written to show the merits of the apparatus, and is based upon findings through its extensive use, during the past six years, in mines operated by the Lehigh Navigation Coal Co. Inc. The Apparatus Certain chemicals, such as stannic chloride (SnCl4) and pyrosulphuric acid (H2S2O7) produce "white smoke" when exposed to air. Stannic chloride gives off vapors which on contact with moist air cause the formation of solid hydrates, of which SnCl4.5H20 is the most important. Pyrosulphuric acid decomposes when exposed to air with the evolution of sulphur trioxide (SO3) fumes, which become white upon contacting moisture in the air. A chemical, such as one of the above, is the active substance in a smoke tube. The glass tubes are hermetically sealed during manufacture, and are made ready for use by merely breaking off the tips at the conveniently located file cuts. When the smoke tube is connected to the aspirator, depressing the aspirator bulb forces air into contact with the chemical, and smoke discharges from the open end of the tube. A white solid (a hydrate if stannic chloride is used, or sulphur trioxide if pyrosulphuric acid is used) may occasionally form a cake in the outlet opening of a smoke tube. A small wire such as an ordinary paper clip can be conveniently employed to dislodge the cake should it seal the tube. When the assembled apparatus is not

Jan 1, 1949

Jan 1, 1900

Jan 1, 1893

By H. Hubert

The first attempts at direct utilization of blast-furnace gas in engines were made in 1895. For a considerable time the gas had been burnt in Cowper stoves for heating the blast for the furnace, and under the boilers which supplied steam to the blowing-engines, and others serving the furnaces. It was natural, therefore, that the idea of directly employing it in gas-engines should have occurred simultaneously to several engineers, notably to Lurmann and to Lencauchez, who had pointed out the blast-furnace as a powerful gas-producer. Nevertheless, nowhere had any attempt been made to apply it to this purpose up to the end of 1894, when Thwaite proposed it to Mr. James Riley, of the Glasgom Iron & Steel Company. About the same time investigations were being made in Belgium and in Germany, independently of Thwaite's experiments, which were not generally known on the Continent. The industrial world, which up to that time had hardly favored the idea, had thus been gradually prepared to receive it. The gas-engine, long restricted to small sizes and dependent upon the use of an expensive fuel obtainable only in large centers, now began to make headway. At the Paris Exhibition of 1889 two engines of 100 h.p. were shown and excited much interest among engineers. One had four cylinders, and was made at the celebrated works of the Deutz Company, and the other was a single-cylinder engine, exhibited by two French designers, Messrs. Delamare-Deboutteville and Malandin. In the meanwhile the design of gas-producers had made important progress, completely freeing the new engine from its

Jan 1, 1907

By Robert E. Green, Kenneth Reifsnider

Several experiments have been performed in order to illustrate the application of a recently developed X-ray image intensifier system to metallurgical investigations. In the present work the system has been used to study the instantaneous alterations in Laue transmission X-ray diffraction patterns during tensile deformation of aluminum single crystals. Expem'mental results are presented which demonstrate the capability of the system for crystal orientation, for following orientation changes due to lattice rotation during tensile deformation, and for showing changes in the homogeneity of the lattice planes along the specimen length as a function of strain rate. RECENTLY, a new X-ray system has been developed which incorporates a cascaded image intensifier and permits direct viewing and recording of X-ray diffraction patterns produced on a fluorescent screen.1"3 In the present work the results of several experiments are presented which demonstrate the usefulness of this system for metallurgical applications. EXPERIMENTAL PROCEDURE A schematic diagram of the experimental arrangement is shown in Fig. 1. In this system a Machlett AEG-50-S tungsten target X-ray tube, normally operated at 50 kv and 40 ma, serves as the X-ray source. The X-ray tube is placed in direct contact with a 10-in.-long collimator, which transforms the X-ray beam from one with a circular cross section to one with a rectangular cross section 3 in. high and 1/6in. wide. By blocking off all but a small portion of the rectangular slit, it is possible to work with the more conventional "pinhole" collimated X-ray beam commonly used for obtaining Laue diffraction patterns. In the present work the test specimens were 99.99+ pct aluminum single crystal wires & in. in diam and 3 in. long. For the deformation tests the wire crystals were mounted in a special set of grips in a table model Instron machine so that diffraction patterns could be recorded during specimen deformation. For the orientation tests the wire crystals were mounted in a rotating goniometer so that diffraction patterns could be recorded during specimen rotation. At a distance of 3 cm from the specimen axis, a 6 in. diam DuPont CB-2 fluorescent screen is positioned to transform the X-ray image to a visible one. A Super Farron f/0.87 72 mm coupling lens, corrected for 4 to 1 demagnification, transmits the visible image to the image tube. The image intensifier used is a three-stage magnetically focused RCA type C70021A with an S-20 input photocathode and a P-20 output phosphor. The tube has unity magnification and useful input and output screen diameters of 1.5 in. The image on the output phosphor is of sufficient intensity to be viewed directly, to be recorded cine-matographically, or to be displayed by vidicon pick-up on a television monitor. The recording device most commonly used is a 16 mm Bolex motion picture camera fitted with a Canon f/0.95, 50 mm lens. The overall gain of the system is 16,000 for direct viewing and 2240 for recording on 16 mm movie film. The resolution of the system is limited to 1 line pair per mm which is approximately that of the fluorescent screen. This system has been used for cine recording of transmission Laue X-ray diffraction patterns with exposure times as short as 1/220 sec and for vidicon television pick-up and display at a scan time of 1/30 sec. Quantitative information may be obtained from each frame of the movie film, by either stopping the vertical slit down to a point source in order to obtain a conventional Laue photograph or else by retaining the linear beam and introducing fiducial marks as described in a previous paper.4 In either case, each frame may be enlarged to appropriate size for analysis by either using a photographic enlarger and making prints of the desired frames, or, more conveniently, by using a microfilm reader. EXPERIMENTAL RESULTS The first series of photographs which are presented in Fig. 2 serves to demonstrate the usefulness of the system for crystallographic orientation determination. This series of prints, made from enlargements of a 16 mm movie film, shows the dynamic Laue transmission patterns produced by an aluminum single crystal wire which was rotating about the wire axis when the patterns were recorded. The movie films were taken at 16 frames per sec and the crystal was rotated at a rate of 15 rpm.

Jan 1, 1970

By Frank G. Miller, Ralph A. Seban

Problems relating to thermal methods of oil recovery have been given increasing attention during the past year. The nature of the physical and chemical processes underlying thermal recovery are not yet well understood. The need for pertinent basic information is recognized generally. One of the processes involved is the transfer of heat by conduction in oil reservoir rocks containing moving reservoir fluids. This technical note deals with heat conduction in a laboratory sand column filled with a moving hydrocarbon and therefore should be contributory to the presently inadequate fund of knowledge on thc over-all subject. In an analysis of the flow of vaporiziny propane through a horizontal column of sand, one of the present author9 demonstrated correspondence between thc measured values of pressure along the length of the column and those predicted by a theory which postulated that the enthalpy of the propane was invariable along the length of the column. This postulate way implied as a deduction from the principle of conservation of energy but the details of the deduction were not given. The specific purpose of this technical note is the presentation of these details both as an adjunct to the earlier analysis and to supply some additional details on the processes involved in this type of flow. Results disclose that rates of heat transfer by conduction, in the direction of fluid motion, generally would be small for systems of the type studied. FUNDARIENrAI. ENERGY EiQUAI-[ON The principle of conservation of energy may be applied to a section of the porous material on the basis that heat transfer, like fluid flow, is possible in the x direction only. Transfer of heat in the y and z di'rections is prevented by suitable insulation or by taking the medium as infinite in directions perpendicular to the x axis. For steady state heat conduction and conditions of steady fluid flow the principle of conservation of energy specifies that any reduction in the enthalpy rate increases the flow of heat in the same proportion. Stated mathematically, dH KA 87 —- = - — - — U) * dx W dx........ Lvhere is the flow of heat in the positive x W dx direction. TEMPERATURE DISTRIBUTION IN DIRECTION OF FLOW The column of sand used in the previoi~sly described research is divisible into three different flow regimes. each of which may be analyzed independently. In the entrance region the liquid approaches the saturation state. A transition region is postulated following the transverse section at which the saturation state of the liquid is attained. In this transition region gas and liquid phases are both envisioned as present, with no vaporization occurring and with fluid movement restricted to the liquid. The upstream end of the exit region is at the transverse section of the column where the fraction of the pore space occupied by gas first becomes great enough for gas flow and where vaporization of the liquid begins. Fig. 1 indicates schematicaHy the thermodynamic processes undergone hv the fluid in the three flow regimes.

Jan 1, 1956

By Frank T. Sisco

DURING the past year the iron and steel industry of the world as a whole operated on a satisfactory basis. No discoveries nor new processes of outstanding importance were announced either here or abroad, although rumors of such were persistent. In general, the efforts of operating and research men in the iron and steel industry seemed to be confined to improving quality and reducing cost, not a new aim, for the same efforts have been noted in nearly all of the annual reviews of the industry for at least fifty years. Most published papers on blast furnace or steel-making practice were of minor importance, at least when judged by the criterion of radical change in process or product. If the number of reports in the technical journals, or articles in the trade press, is used as a basis for comparison, continuous-mill sheet is still the most important single product of the industry; papers were published detailing the results of the investigation of various phases of the

Jan 1, 1938

By F. C. Langenberg

DURING the course of some magnetic investigations which the authors have under way, six bars of 0.43-carbon steel were tested, a permeameter designed after the Hopkinson yoke type being used. The results obtained were of some interest and although far from complete serve at least to show the necessity for a careful investigation of the previous history of the samples under study as well as the chemical composition. A steel of given chemical composition may assume a great variety of structures, depending on its treatment. Professor Sauveur has devised a very clear and effective means of illustrating this point: The accompanying microphotographs show some of the possible structures assumed by a 0.30 carbon steel (Fig. 1). It is now a well-established fact that a structural change is accompanied by changes in the tensile strength, elastic limit, hardness, etc., and it seems reasonable to assume also, a change in the magnetic properties. Six bars of a 0.43-carbon steel were used, all the bars being taken from the same rod and treated as follows: Bar 1. Heated to 1,100° and cooled in the furnace. Bar 2. Heated to 1,000° and cooled in the furnace. Bar 3. Heated to 900° and cooled in the furnace. Bar 4. Heated to 1,000° and cooled in air. Bar 5. Heated to 900° and cooled in air. Bar 6. Untreated. The bars were then turned to 13 mm. diameter and tested by the Hopkinson yoke method. After testing, three specimens were taken from each bar, one from each end and one from the middle. The homogeneity of the. bars was tested in this manner and in no instance could any difference in structure be detected between the three specimens.1

Jan 2, 1915

By J. E. Johnson

At the Cleveland meeting of the Institute in October, 1912, I had the honor to present a paper outlining the conditions surrounding the charcoal iron industry…

Jan 1, 1915

By Francisco Cadena

THE construction of Norris Dam, built by the Tennessee Valley Authority on the Clinch River, a tributary of the Tennessee River, involved the production of coarse and fine aggregate for approximately 1,000,000 cu. yd. of concrete. A hammer-mill plant for the manufacture of sand from quarried rock was indicated as the most economical method of providing this material. The abrasive character of the feed as compared to the average hammer-mill feed made it necessary to control operations rather closely, and this resulted in the accumulation of many data bearing on production and maintenance. This paper will deal only with three specific sets of data, accompanied by such general information as may be necessary to explain the conditions under which they were obtained and followed by discussions on the relation of silica content to hammer wear, comparative costs of slugger and stirrup hammers, and comparative costs of tool-steel and manganese-steel grate bars. Coarse Aggregate Aggregate for the concrete poured at Norris Dam came from a dolomite quarry within 2000 ft. of the west abutment of the dam. Geologically this rock is known as a Knox dolomite. A typical chemical analysis is given in Table 1. TABLE 1 .-Typica.1 Chemica1 Analysis [PER CENT H20,1100F ............................................ 0.0'2 Ignitionloss ............................................. 43.56 MgO .................................................. 19.19 CaO .................................................... 29.07 FezO .................................................... 0.39 A1203 .................................................... 1.94 FezO .................................................... 0.39 A1203 .................................................... 1.94 ..................................................... 5.75 SO2.. .................................................. Tr.] Rock was carried by 12-yd. dump trucks to a 42-in. gyratory crusher set at 6 1/2 in. The product of the primary crusher was taken by a belt conveyor to a double-deck vibrating screen followed by a 5 1/2-ft. cone

Jan 1, 1937

By Joseph A. Holmes

The public is already familiar with the general fact that the scope and the financial resources of the approaching St. Louis World's Fair are much larger than those of any of the preceding great expositions; and both the visitor and the exhibitor, when he comes to St. Louis in 1904, will find it to be a real World's Pair, with exhibits and visitors from every known country. Passing over the subject, as to the general Exposition, with this brief statement, I ask Sour attention to the consideration of a few important facts connected with the proposed mining exhibits at this Exposition. First of all, I may say that. reading- and writing-rooms and library facilities will be furnished in the Mines Building for miners and mining engineers, and it is expected that when they visit the Exposition they will make these rooms their headquarters, and give the Chief of the Department and his assistants an opportunity to extend to them such courtesies as may be possible. One of the exhibits in the Mines Department will consist of models and maps arranged to show the nature and extent of the mining operations in the United States at the time of the purchase of the Louisiana Territory in 1803, the event which

Jan 1, 1903

TO metallurgists generally, Arthur S. Dwight is no stranger even to those who do not know him personally. He is one of those contributors to technical progress whose names will go down to posterity because of their being attached to a successful machine or process, such as Dorr, Hardinge, or Marcy, or Wedge, MacDougall, or Herreshoff. The roasting and sintering method and equipment developed by Colonel Dwight and his associate, the late Richard L. Lloyd, may be found in lead smelters throughout the world, and also in many metallurgical works dealing with other ores, including those of iron. It is ordinarily used to desulphurize and agglomerate fine ores for subsequent smelting. Colonel Dwight's citation as James Douglas Medalist reads: "For his contributions to the art of smelting nonferrous ores; and particularly for his pioneer work in developing equipment and technique for sintering such ores and metallurgical products." The medal was awarded at the last Annual Meeting of the A.I.M.E. but unfortunately the medalist was unable to leave Florida at the time to receive it in person.

Jan 1, 1942

By S Bankoff

INCE1 proposed that electrostatic attraction between oppositely charged particles was responsible for slime-coating. Del Giudice2 postulated the metathetic formation of a cementing compound. Wark3 suggested that prevention of slime-coating was related to peptization of the slime. [ ] In the experiments of Table I the technique employed was essentially that of del Giudice, with the difference that the particle was examined under a film of water rather than dry.4 In general, the polished particle was agitated for 2 min. in a pulp consisting of 12.5 grams of the slime (-200 mesh) and 50 c.c. of distilled water, washed in three baths of distilled water, and examined at 220 diameters with the Leitz Ultropak. Observations of Brownian movement were made at 850 diameters with dark-field illumination. Several of these experiments do not jibe with the metathesis theory. According to published solubilities,5,6 the lead salts of the anions in experiments c through g are more insoluble than lead carbonate, there- [ ] fore should prevent the formation of lead carbonate on the galena surface. In experiment i the calcium oxalate, which presumably was on the calcite surfaces, should have permitted the formation of a lead carbonate cement by virtue of its greater solubility. Experiments j through m show that the addition of lime accelerates the deposition of quartz onto a galena surface. The writer is unable to postulate a satisfactory cementing compound, according to the metathesis theory, to explain this effect. These experiments led to the conclusion that the metathetic formation of a cement-

Jan 1, 1941

By Charles Janin

ONE of the most interesting features of the world's platinum situation has been the steady increase of Russian production, which had dropped to 11,000 oz. in 1920, but increased to 92,000 oz. in 1926, and to probably over 100,000 oz. for 1927. It is ex-pected that Russian production of platinum will, be-fore long, closely equal its pre-war production, or approximately 200,000 oz. annually. The world production before the war was around 250,000 oz.; that for 1925 has been estimated at 160,000 oz., and for 1926 probably 170,000 oz. The consump-tion of platinum has, however, decreased. The esti-mate of the International Selling Agency was a de-mand of 130,000 oz. new platinum against a normal pre-war demand of over 200,000 oz. The high price of platinum during the war gave an added impetus to the search for substitutes for the metal, and sev-eral were developed that are now used extensively in place of platinum. The demand for platinum for high-class jewelry, however, was not greatly affected by the high prices, but "white" gold did replace platinum in the cheaper jewelry. Colombia is the most important producer of plati-num, next to Russia, and the production has increased from around 10,000 oz. pre-war production to 55,000 oz. or more in 1927. In 1924 important discoveries of platinum were made in South Africa. Prior to these discoveries practically all platinum was recovered from alluvial deposits, and the South African opera-tions are first to work an ore profitably for the pri-mary recovery of platinum. A number of companies were formed to develop these deposits, but only a few made any real progress. Total production for 1926 was about 5000 oz. The United States production is unimportant; that in Canada has increased to around 9000 oz., principally as a by-product in nickel-copper ores.

Jan 5, 1928

New Jersey Zinc Co. - The Plants Canon City Palmerton Depue

Jan 12, 1953

By Wolfgang Gartner

METALLURGISTS engaged in the pulling of single crystals of germanium and silicon, and their zone purification and zone levelling for transistor and diode production, have found that the lifetimes of minority carriers in low resistivity samples tend to be shorter than in high resistivity material, although equal care is taken in the crystal preparation. In other words, it is more difficult to obtain long lifetimes in single crystals of low resistivity semiconductors. It is the purpose of this note to point out that this phenomenon follows directly from the Hall1 and Shockley-Read' theories of lifetimes in semiconductors." In general, the recombination mechanism may be very complicated,' but experiments seem to indicate that the simple formula2 for the lifetime of excess carriers given by n0 + n3 Pn + P1 T = Tpo,------------------+ Tjpu ----------------------- [ 1 ] nu + pn na+ + Pa is a good representation of the situation prevailing in transistor grade semiconductors. In this formula, no and pa are the equilibrium densities of electrons 6+ - E./ET and holes, n1 = N,e is the number of electrons E1- E2/KT in the conduction band, and p1 - N,e is the number of holes in the valence band, both for the case in which the Fermi level falls at the trap level, E1. N,. is the effective density of states in the conduction band; E1, the recombination level; E1, the lower edge of the conduction band; k, Boltzmann's constant; T, absolute temperature; N,., effective density of states in the valence band; and E,., the upper edge of the valence band. t,.,, denotes the lifetime of holes injected into highly n-type material, and The indicates the lifetime of electrons injected into highly p-type material. Eq. 1 holds for nondegenerate semiconductors in which only one recombination level is active and the charge in the recombination centers is neglected. It is further assumed that the number of injected ex-

Jan 1, 1957