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By W. Kennedy

THROUGHOUT northeastern Texas we have an extensive series of iron-ore deposits, occupying portions of nineteen counties and having approximately an actual ore-covered area of 1000 square miles. The existence of these ores has long been known. Kennedy* says: "Iron-ore is distributed in profusion throughout Texas, being found almost everywhere except in the level region of the coast." Before this, C. Newell† had mentioned the existence of these ores thus: " Iron is found in abundance in the eastern, northern and middle portions of Texas;" and in 1849 Edward Smith‡ said: " We met with immense hills of iron which were said to be, and appeared to be, of excellent quality, in Cass and Titus counties.. . .. It is well known that Texas abounds with iron of first-rate quality." In 1859, Dr. Shumard? reports that detailed surveys had been made in several counties, and says: " Our labors have demonstrated the important fact that we have a vast iron-region in the eastern part of the state, embracing considerable areas in Cass, Harrison, Rusk, Panola, Smith, San Augustine and Shelby counties. The ore-deposits belong to the Tertiary era and consist chiefly of hematites and limonites, of which there are several varieties. We have also found in this district extensive beds of carbonate of iron." Dr. Shumard gives no very exaggerated description of Cass county§ as it then existed when he says : " Cass county alone is capable of supplying a number of furnaces with an abundance of excellent iron-ore for many years." Of Rusk county he says: "Our de-

Jan 1, 1895

By Enrique Hauser

FiRE-damp is a mixture of methane with other inert gases or combustible gases. The inert gases in question are carbonic acid, water vapor, nitrogen, etc. The combustible gases are hydrogen, ethane, etc. The study of the properties of fire-damp, therefore, becomes a study of the properties of methane and the influence on its properties of the different gases we have mentioned. Characteristic Properties of Methane 1. Respirability.—Methane being a paraffin is characterized by its weak chemical affinities. Prom the physiological point of view one could substitute it for nitrogen of the air at least momentarily, without experiencing any difficulty in breathing the mixture consisting of 21 per cent. 02 + 79 per cent. CHI. I have tried this on myself, making the gas exhaled from the lungs burn subsequently in a Bunsen burner.' From the chemical point of view, this weak affinity permits the gas to be burned in certain circumstances with hydrogen and oxide of carbon in an oxygenated mixture, with the result that the last two gases achieve only a fractional combustion. This practice has been utilized with success in the methods of analysis which I have perfected and which I describe later in this paper. 2. Retardation of Flashing Point.—A characteristic property of methane is its retardation of flashing point, noted by Davy in 1816 and studied by Mallard and Le Chatelier in 1883.2 Taffanel and Le Floch have recently confirmed these results.8 Let us recall the nature of this retardation: When a mixture of combustible gases with air or with oxygen is

Jan 1, 1916

By Paul D. Foote

Most of the treatises on metallurgy intimate that simultaneously with the development by the atomic physicist of a really satisfactory theory of the atom will be inaugurated a new epoch in the science of metals. Metallurgically and metaphorically, we shall dwell in the Utopia of Sir Thomas More. It is my privilege this afternoon to demonstrate that this state has not arrived. An atom is a miniature planetary system consisting of a positively charged nuclear sun about which revolve electrons each carrying the negative charge e. The charge on the nucleus is + Ze where Z is the atomic number and the number of planetary electrons in a neutral atom is equal to Z. These electrons are arranged in several groups having different binding energies. Ordinary x-ray phenomena relate to processes occurring deep within the atom, usually with electrons in the so-called K or L shells. Such electrons in the heavier atoms are so closely bound to the nucleus that the forces exerted by neighboring atoms in a solid are relatively inappreciable. For most practical x-ray investigation, the atom may be considered as in the gaseous phase completely isolated from its neighbors. The K radiation from an element in the gaseous state, in the solid or liquid phase, or even in combination with other elements in all its possible valences, is almost identical.‡ Visual and ultraviolet spectroscopy is concerned with disturbances of the most loosely bound outer or valence electrons of the atom, always in the vapor state. The remarkable progress of the last year in both theo-

Jan 1, 1926

By W. A. Roper

Since 1950, several papers have been published which have described various methods for studying mobility ratio effects. The methods which have been described for studying mobility ratio effects include X-ray shadowgraph techniques, stepwise potentiometric model procedures, stepwise numerical procedures, gelatin model studies and fluid mapper model studies. The purpose of this paper is to describe a procedure for using a resistance network for studying mobility effects. DESCRIPTION OF APPARATUS The basic unit of the experimental model consisted of a network of 840 resistors fastened to a sheet of black Lucite which was mounted on a wooden frame, Fig. 1. The dimensions of the Lucite sheet were 36 X 36 in. The resistors were fastened to the Lucite sheet at mesh points by means of snaps. The mesh points were arranged in a square pattern, 30 X 30 in., spaced at intervals of l1/2 in. The snap fasteners permitted several resistors to be "stacked" in parallel. By adding additional resistors to the basic unit, the specific resistance on each side of the flood front could be varied. The square network of resistors represented one of four symmetrical elements of a five-spot well pattern. The current input was analogous to an injection well and the current output was analogous to a production well." The power supply was essentially a full wave transformer-rectifier system for converting alternating-current into direct-current. The DC voltage could be varied from 41.43 to 290 v in steps of 41.43 v by selecting the proper outlet jacks. The major components of the power supply were: a Triro power transformer, R 11-A; a dual 5Y3 vacuum tube; two gas filled OD-3 tubes; and a Triplett voltmeter, model 227-1, range 0 to 500 DC v. The voltages at the mesh points were determined with a Keithley electrometer, model 210, No. 185, manufactured by Keithley Instruments, Cleveland, Ohio. A Heathkit vacuum tube volt-

By George S. Rice

The subject of violent bumps in coal mines has been again brought to attention by a recent succession of such occurrences in the coal mines of the Cumberland field of eastern Kentucky and southern Virginia, which have caused fatalities and injuries to underground employees, a report on which is being issued by the United States Bureau of Mines1. The A.I.M.E. has had two valuable papers on bumps in the No. 2 Mine, Springhill, Nova Scotia, each followed by general discussion on bumps and their causes2. This paper gives a brief review of suggested causes and remedial measures given in English, Canadian and United States reports on blimps in coal mines, and then presents suggestions arising from the writer's recent investigation of the bumps in the Cumberland mines, made at the request of the mine operators, to determine the causes and remedies. These bumps, which occur under the simplest natural conditions, provide better opportunity for analysis of causes and effects than afforded under more complex conditions. The simple conditions in this field consist of relatively thin and level coal beds and uniform roof strata free from folding and faulting. Definition of Bumps Bumps in coal mines, as defined in this paper, are sudden violent bursts of coal that usually occur without warning in the extraction of pillars and may or may not be accompanied incidentally by falls of draw slate, upheaval of bottom and smashing of timbers. They are not known to occur where the advancing longwall method of mining, accompanied by

Jan 1, 1936

By George S. Rice

The subject of violent bumps in coal mines has been again brought to attention by a recent succession of such occurrences in the coal mines of the Cumberland field of eastern Kentucky and southern Virginia, which have caused fatalities and injuries to underground employees, a report on which is being issued by the United States Bureau of Mines1. The A.I.M.E. has had two valuable papers on bumps in the No. 2 Mine, Springhill, Nova Scotia, each followed by general discussion on bumps and their causes2. This paper gives a brief review of suggested causes and remedial measures given in English, Canadian and United States reports on blimps in coal mines, and then presents suggestions arising from the writer's recent investigation of the bumps in the Cumberland mines, made at the request of the mine operators, to determine the causes and remedies. These bumps, which occur under the simplest natural conditions, provide better opportunity for analysis of causes and effects than afforded under more complex conditions. The simple conditions in this field consist of relatively thin and level coal beds and uniform roof strata free from folding and faulting. Definition of Bumps Bumps in coal mines, as defined in this paper, are sudden violent bursts of coal that usually occur without warning in the extraction of pillars and may or may not be accompanied incidentally by falls of draw slate, upheaval of bottom and smashing of timbers. They are not known to occur where the advancing longwall method of mining, accompanied by

Jan 1, 1936

By Paul Foote

MOST of the treatises on metallurgy intimate that simultaneously with the development by the atomic physicist of a really satisfactory theory of the atom will be inaugurated a new epoch in the science of metals. Metallurgically and metaphorically, we shall dwell in the Utopia of Sir Thomas More. It is my privilege this afternoon to demonstrate that this state has not arrived. An atom is a miniature planetary system consisting of a positively charged nuclear sun about which revolve electrons each carrying the negative charge e. The charge on the nucleus is + Ze where Z is the atomic number and the number of planetary electrons in a neutral atom is equal to Z. These electrons are arranged in several groups having different binding energies. Ordinary x-ray phenomena relate to processes occurring deep within the atom, usually with electrons in the so-called K or L shells. Such electrons in the heavier atoms are so closely bound to the nucleus that the forces exerted by neighboring atoms in a solid are relatively inappreciable. For most practical x-ray investigation, the atom may, be considered as in the gaseous phase completely isolated from its neighbors. The K radiation from an element in the gaseous state, in the solid or liquid phase, or even in combination with other elements in all its possible valences, is almost identical. ? Visual and ultraviolet spectroscopy is concerned with disturbances of the most loosely, bound outer or valence electrons of the atom, always in the vapor state. The remarkable progress of the last year in both theo-

Jan 2, 1926

By Albert Sauveur

Iron, like other metals, solidifies through the formation of dendritic crystals; iron alloys forming solid solutions, like other solid solutions, solidify likewise through the formation of dendritic crystals. The alloying elements or impurities as well as the inclusions segregate generally in the interstices, or "fillings," between the axes and branches of the dendrites; that is, in the portions last to solidify. This results in dendritic segregation or heterogeneity, which is generally persistent and makes possible the revelation of the dendritic crystallization of the metal through the selective action of a suitable etching reagent.' For this purpose, a cuprie solution, such as Le Chatelier's, is generally used, copper being deposited on the pure, or relatively pure, ferrite present in the axes while the fillings remain free, or relatively free, from copper deposition. The dendritic structure, formed on solidification in a steel containing 0.50 per cent. carbon, 0.37 per cent. manganese, 0.12 per cent. silicon, 0.07 per cent. sulfur, and 0.035 per cent. phosphorus is shown, after treatment with Le Chatelier reagent, in Fig. 1 under a magnification of 8 diameters. Commercial steel always contains inclusions of manganese sulfide, which are located in the fillings of the dendrites. Comstock has shown that boiling sodium picrate imparts a dark coloration to these inclusions. We find that this reagent likewise reveals dendritic segregations in commercial steel, as shown in Fig. 2, under a magnification of 8 diameters. which represents the same spot as that shown in Fig. 1. The fillings have been darkened while the axes remain white, the action being, therefore, the reverse of that of cupric reagents. On closer examination, under higher magnification (Fig. 3) it is found that the picrate blackens the small particles of manganese sulfide, that these are frequently surrounded by a rim of white, or relatively white, ferrite, and that both the ferrite

Jan 1, 1924

By Frank T. Sisco, Selma F. Hermann

gancse constituent in the alpha grains. Nickel produces a structure of alpha plus cutectoid almost identical with that of the normal aluminum bronze (Fig. 38), except for the rod-shaped nickel constituent in the alpha grains. Silicon produccs a light structure with small regular needles, possibly a modified form of beta. Fig. 45 shows the alpha plus beta structure of the normal 10 per cent. aluminum alloy as quenched. Manganese produces large grains of beta with alpha as a tiny constituent scattered throughout the spceimen. Silicon, on the other hand, produces all alpha, with free silicon present. One per cent. iron produces alpha plus beta, with a tiny constituent present in the alpha grains. Five per cent. iron introduces twins in the alpha and a nodular iron constituent in both the alpha and the beta. Figs. 50-58 include the structures of the alloys with 8 per cent, aluminum, tempered at 400" C. and at 650" C. Fig. 50 is the normal structure as drawn at 400" C!. It consists of large grains of twinned alpha plus a very small amount of beta. One per cent. silicon increases the amount of beta enormously, but when tempered at 650' C, the beta degenerates to a hard blue network constituent. One per cent. cobalt results in a structure of exceedingly fine-grained, twinned alpha, heavily mottled. Nickel produces large soft grains of alpha with a dot constituent in some of the grains, when tempered at 650" C. Manganese, when tempered at 400" C. produces alpha grains and shows the decom-

Jan 1, 1931

By Frank E. Woolley, Robert D. Pehlke

Jan 1, 1965

By G. H. Alani, H. T. Kennedy

One of the major difficulties in predicting the performance of oil reservoirs from their early pressure history lies in the uncertainty of estimating the volume of the liquid hydrocarbons contained in them. As a first step in filling this need, an equation was developed to determine the Inolal liquid volume of pure hydrocarbons over a wide range of temperature and pressure. The second step consisted of adapting the equation to apply to mixtures, with the heary hydrocarbons expressed as c The equatious are similar in form to van der Waals equation. hut the constants a and b tire considered as furnctions of temperature. In addition to the gas constant R, there are four constants characteristic of each hydro- When comptired with experimental values jound in the literal the. the average absolute deviation in the calculated molal volumes is found to be a Maximum of 0.33 per -cem for any of the pure liquid hydrocarbons studied. This maximum deviation was that found when comparing the calculated and observed values over a temperature range of 86° to 482°F and a pressure range from the bubbl-point ro 10,000 psis. The equations expressing the correlation for. mixrurrc were developed from 647 experimental measure-rilents of volume on 47 bouom-hole samples covering ; temperature range of 72" to 250°F and a pressure znge from bubble-point ro 5,000 psig. The average absotute deviation was found to he 1.6 per cent with the maximum for any measurement of 4.9 per cent. INTRODUCTION Accuratc information of the pressure-volume-temper-iiture behavior of hydrocarbon liquids is of considerable importance in the field of both applied and theoretical science and, especially, in the solution of petroleum reservoir engineering problems. These PVT relationships can be expressed graphically, in tabular form or as equations of state. Equations of state for gases have been developed based on the ratio of pressure, temperature and volume to the pressure, temperature and volume at the critical points of the hydrocarbons. These equations have been successful in yielding values fairly accurate for reservoir engineering purposes. For liquids, however, relations of this type are more complex and have not yielded useful results. The composition of reservoir liquids is normally expressed in terms of the moles of hydrocarbons C,? C,. C,. elc, per mole of mixture. The composition must include the fraction of a mixture such as C,,, which cannot be separated with reasonable time and effort into specific hydrocarbons. Although there are several equations of state having variable degrees of accuracy applicable to pure liquid hydrocarbons, none includes a means for estimating the volume of mixtures as a function of temperature. pressure and composition expressed in this manner.

By C. P. Proctor, J. T. Crawford, John Griffen

TROUGH washers were among the earliest methods used for concentrating ores; they are referred to by Agricola about the middle of the sixteenth century as already being used while the hand- operated jigging sieve had only recently come into use. For cleaning coal the trough washer apparently was first used in France and Belgium about 184.1. The early trough washers were intermittent and the refuse at least was shoveled out by hand. The invention of a continuous jig washer, by a Frenchman, Berard, in 1848, acted as a stimulus to coal washings in jigs and retarded progress in trough washing in the nineteenth century. Chapman and Mott 1 describe a number of trough washers developed in England and on the Continent from 1850 to 1900, such as the Bell and Ramsay, Ramsay, Bell and Green, Wunderlich, Scaife, McLellan, Lodge, Elliott, Blackett, and Murton. The later of these removed the refuse mechanically, either intermittently or continuously, but in ways that interfered with stratification. THE RHEOLAVEUR A Belgian engineer, Antoine France, is responsible for the development of means to remove refuse materials continuously from a trough washer, while preserving stratification and preventing the loss of coal with the refuse. The methods and equipment devised, which have become known throughout the world as rheolaveur, were initiated at the St. Nicholas mine near Liége, Belgium, about 1912. This installation consisted of two units to wash 20 to 8-mill. (3/16 to 5/16-in.) and 8-mm. to 0 (5/16-in. to 0), each having only two superimposed inclined troughs. The first few "Rheo" boxes on the top trough removed refuse directly and the remaining Rheo boxes discharged impure refuse to the lower trough for rewashing. On the lower trough the first few boxes removed refuse and the following boxes removed a middling product used for boiler fuel or other purposes. The overflow of both troughs was joined to form the washed coal product.

Jan 1, 1950

By John M. Crowl, L. E. Sawyer

5.3-1. General Public Resistance to Strip Mining. Surface (strip) mining is the oldest recorded method of extracting coal and other minerals from the earth. This method of mining completely alters the topography of the earth's surface, leaving an area of more or less parallel ridges or of peaked mounds of the materials which overlay the mineral seam. It destroys all original vegetation and provides materials for new type soil. During the early years the acreage mined by this method was small, land was plentiful, and with a growing young nation no thought was given to the restoration of the disturbed areas to some form of productive use. Early in the present century the development of steam shovels and drag-lines made it possible to remove thicker overburden to recover the products. With the deeper digging, the size of the disturbed areas increased. With this increase in the size of equipment and the improvement of blasting techniques, mining was expanded into more prominent locations and to areas of more valuable land. The more progressive operators became aware of the need to reclaim those areas for some productive use. Electric shovels with capacities of up to 200 cu yd and draglines with capacities of 145 cu yd, capable of uncovering products over 100 ft below the surface, are now in use. Combined with the increase in the size of equipment, the expansion of contour mining or rim stripping in the mountainous areas has focused public attention on the need for a sound reclamation program for all disturbed areas. APPEARANCE. After mining, the areas consist of varying percentages of rock, shale, slate, and soil material devoid of all plant and animal life. Unless a definite reclamation plan is carried out, many of the mined areas will remain bare for a period of years. The topography of the area is completely altered. What may have been level to rolling land in cultivation, in grass, or in timber is thrown up into a series of ridges or mounds.

Jan 1, 1968

By James W. Shaffer

Aluminum is the most abundant metallic element of the earth's crust and is a constituent of nearly every type of rock (Clark, 1924, p. 13). The sources of aluminum and aluminous material most commonly used by modern industry are the bauxitic raw materials consisting of bauxite, bauxitic clay, and aluminous laterites. These are mixtures of hydrated aluminum oxide minerals and mineral impurities. End Uses Bauxite is used as an aluminum ore and in the manufacture of refractory products, aluminous chemicals, and abrasives. Other raw materials are used for aluminum ores, but their use is minor compared to bauxite. Refractory products made from bauxite are synthetic mullite, high-alumina fire bricks, castables, monoliths, cements, and ramming mixes used by the iron, steel, and cement industries. Chemicals made from bauxite are aluminum sulfate and sodium aluminate for water treatment and aluminum chloride used in refining crude petroleum. Among the abrasive products made from bauxite are coated abrasives, sharpening stones, and grinding wheels. Special grades of bauxite are used in the decolorization and clarification of raw sugar and lubricating oils. Bauxite has been used for road surfacing but mainly because other material was not more readily available. Perhaps the oldest use of bauxite and aluminous laterite is for a building stone. Ancient temples and more recent structures in India have been made from these and some varieties are suitable for decorative stone. Geology Mineralogy and Properties – Bauxite is a mineral raw material composed principally of one or more hydrated aluminum oxide minerals and impurities of silica, iron oxide, titania and elements in minor or trace amounts. The hydrated aluminum oxide minerals are gibbsite, boehmite and diaspore. Corundum is not included as a bauxite mineral although it does occur in some bauxite deposits. Boehmite and diaspore are both alumina mono-hydrates and have essentially the same composition, but diaspore has a greater hardness and a higher specific gravity because of a more tightly bonded and compacted atomic structure. Gibbsite is an alumina trihydrate mineral. Properties of bauxite minerals are shown in [Table 1].

Jan 1, 1975

By F. H. Buchella, J. F. Buchanan

The San Manuel copper deposit is located about 45 miles northeast of Tucson. The concentrator, smelter, administration building, and other plant facilities are located about seven miles southeast of the ,nine area at the new town of Sari Manuel as shown on Figure 1 (Sketch).

Jan 1, 1961

By G. T. Engel, W. G. Gruzensky

Jan 1, 1960

By J. H. Wernick

IN temperature-gradient zone-melting1 a molten zone is moved through a solid or across a solid surface by the establishment of a temperature gradient. This technique has both practical and fundamental aspects. One practical application is to make p-n junctions for semiconductive devices, particularly for devices in which the junctions are desired within the semiconductor. From a fundamental point of view, the technique is being investigated as a method for determining diffusivities in liquid alloys, and preliminary diffusivity results have been reported by the writer." In this paper, the effects of crystal orientation, temperature, and molten zone thickness in temperature-gradient zone-melting, and the bearing of these effects on diffusivity measurements and n-p-n junction formation are discussed. Experimental Procedure An effect of crystal orientation was noted in early experiments. To facilitate its study, movements of wire zones across a surface, rather than through the body of a single crystal, were observed for various surface planes and travel directions. The experirr-entai setup is illustrated in Fig. 1. The graphite end-section for the high temperature heater has an apron about 1/16 in. above the upper surface of the crystal. This apron insures that the surface temperature of the block is equal to or greater than the temperature within the block at every point, Thus, the zone does not penetrate the block and convection in the liquid is minimized. The experi-through a block is shown in Fig. 2,

Jan 1, 1958

By Thos Stroup

RECENT contributions to the literature relating to the problems of coal mine management have discussed the pros, and cons of unionism among the miners as bearing upon the immediate problems of the industry, but have devoted singularly little thought to the underlying causes, and the fundamental reasons. for the remarkable growth of union sentiment among the miners, a growth paralleled only in the case of the railroad workers. It is all very well to revile their organization, its obvious stupidity and stubbornness, its multitude of economic and social crimes, but it is also well to realize that there have been deep-seated causes for all these things, causes that, while operating in all industries and amongst all workers, have in none of them found the optimum conditions for development such as exist in the coal mining industry. The rise of the United Mine Workers of America to a position of importance in the industry synchronizes roughly with the introduction of short-time operation; of course seasonal shutdowns and slow-time working have always been evident in our bituminous fields, but these evils have grown steadily worse since 1895 and the U. M. W. of A. has grown steadily stronger; yet short-time operation alone cannot account for this tremendous growth for, witness the signal failures that have always attended the attempts to organize the harvest workers, the fruit packers and other highly seasonal workers.

Jan 9, 1923

Ahrenholz, Herman William, Jr., Student, Lehigh Univ Bethlehem, Pa. '35 Allen, Carl A., Student, Colorado School of Mines Golden, Colo. '35 Allen, Paul W., Student, Mass. Inst. of Tech Cambridge, Mass. '35 Allen, R. M., Jr., Student, Virginia Polytechnic Inst., "G" Co Blacasburg, Va. '35 Amberger, K. H., Student, Michigan College of Min. & Tech Houghton, Mich. '35 Andersen, Burton Lee, Student, School of Mines, Univ. of Washington Seattle, Wash. '35 Anderson, Joseph S., Student, Univ. of Texas El Paso, Tex. '35 Anderson, R. C., Student, Univ. of Washington Seattle, Wash. '35 Ansel, Gerhard 627 Clyde St., Pittsburgh, Pa. '34 Anutta, Frederick P., Student, Michigan College of Min. & Tech Houghton, Mich. '35 Apsouri, Constantin N., Graduate Student, Univ. of Arizona Tucson, Ariz. '35 Arakelian, Haig Mark, Student, Mass. Inst. of Tech Cambridge, Mass. '34 Archer, George K 1420 Court Pl., Denver, Colo. '34 Argall, George O., Jr., K. E. House Golden, Colo. '35 Argiielles, Alfredo, Student, Univ. of Texas El Paso, Tex. '35 Atwater, Ralph, Student, South Dakota School of Mines Rapid City, S. D. '35 Austin, Robert B., Miner, Page Mine, Federal Min. & Smelt. CoSpokane, Wash. '34

Jan 1, 1934

By P. H. Wendland

Calculations are presented for the design of a silicon photodiode in which the incident light beam makes multiple passes between the detector surfaces. Total internal reflection is used for this "light-trapping" effect. By this means, the optical path length can be extended to several millimeters, while the electrode separation remains less than 102 cm, as required for nanosecond response time. Data are presented for a Schottky barrier photodiode constructed on a multiply reflecting silicon base wafer. It is shown that the long-wavelength response is considerably extended in such structures without a corresponding sacrifice in high-speed response. The development of efficient and powerful lasers at 1.06 p has stimulated interest in detectors which operate at this wavelength. In typical silicon photodiodes, for detecting 1.06 p radiation, the requirements for high speed and high sensitivity are mutually exclusive. Since the absorption coefficient is only 25 cm-', a lo-'-cm path length is required to absorb 92 pct of the incident 1.06 p radiation. If the electrode separation is greater than 10 cm, however, the carrier transit time will be greater than 1 nsec. This problem can be solved by allowing the incident light beam to make multiple passes between the electrodes. The optical path length can then be extended to several millimeters, as required for complete absorption, while the electrode separation remains less than 10' cm, as required for nanosecond response time. In a typical photodiode geometry, one ohmic contact and one rectifying contact are formed on the two opposite surfaces of a base wafer, and the wafer thickness determines the electrode separation. The objective of the multiple reflection design is to allow all 1.06 p radiation to enter the detector front surface and to form the back detector surface so that no 1.06 radiation can exit. Total internal reflection at the back detector surface is well-suited for light trapping of 1.06 p radiation because the relatively large dielectric constant of silicon leads to a critical angle of 16.5 deg for total internal reflection. LIGHT TRAPPING It is well-known that, as light passes from one medium such as air into another medium such as glass or silicon, the angle of refraction is always less than the angle of incidence. In the limiting case, where the incident rays approach an angle of 90 deg with the normal, the refracted rays approach a fixed angle +, beyond which no refraction is possible: this is called the critical angle. It follows from Snell's law that where = critical angle, n - index of refraction of air, n' - index of refraction of the medium. Applying the principle of reversibility of light rays, all internal angles of incidence greater than +, will produce total internal reflection and "light trapping". The index of refraction of silicon at 1.06 p is 3.5,' and the critical angle is thus 16.5 deg. Fig. 1 shows these relationships for silicon. This very small critical angle in silicon is significant because all incident angles between 16.5 and 90 deg will produce total internal reflection and "light trapping". This effect can be implemented with a "prismlike" geometry, so that incident light can be introduced into the sample without loss and "trapped". PHOTOSIGNALS A precise knowledge of the absorption coefficient at 1.06 in silicon is of critical importance to the design of fast and efficient silicon photodiodes for 1.06 radiation. Dash and newman2 show a value of 25 cm-l, and our measurements have corroborated this value. Assuming that the collection of photoinduced minority carriers is perfect, the quantum efficiency of a photodiode is dependent only on the absorption coefficient. It then follows from Lambert's law that where QE is the quantum efficiency in pct, a is the absorption coefficient, d is the optical path length, and the reflectivity at the surface is assumed to be completely suppressed by an optical interference layer. Fig. 2 gives the maximum quantum efficiency for 1.06p radiation of a silicon photodiode with optical path length d, using Eq. [2]. The ultimate response time of a fully depleted photodiode to an incident light pulse can be considered to be the arrival times of all photoinduced carriers at the contacts, i.e., the minority carriers at the junction interface and the majority carriers at the oppo-

Jan 1, 1968