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By M. Cohen, R. T. Howard

It has long been realized among metallurgists that a fast, reliable method for the quantitative determination of the percentage of microconstituents in an alloy would be of great benefit in studies of equilibrium and transformation in the solid state. For example, Polushkinl has shown that the compositions of two coexisting phases in a binary system at a given temperature may be calculated very simply with the aid of two alloys lying in the two-phase field if the relative amounts of the two phases in each alloy can be determined. Recently, Grange and Stewart2 have traced the course of the austenite-martensite reaction in a series of commercial steels by making visual estimates of the percentage of martensite formed as a function of cooling temperature. The correlation of mechanical properties with structure, a subject of wide-spread current interest, is likewise dependent upon quantitative microanaly-sis. Yet, there are very few investigations described in the metallurgical literature, wherein methods of quantitative microscopy are employed. Usually, the relative amounts of the microconstituents are estimated in a qualitative or semiquantita-tive way. The authors were faced with this problem some time ago in studying the kinetics of austenite decomposition. Several aspects of this research could not be treated satisfactorily by other quantitative tools, such as specific volume,' magnetic,6 dila-tometric, electrical resistance7 or x-ray measurements.a It became necessary to find an impersonal quantitative method that could be applied to microstructures. Fortunately, it was noted that geologists and petrographers had coped with quantitative microscopy to a considerable degree in their attempts to evaluate the mineral contents of rocks. A number of excellent articles were found on this subject, and since they appear to be unknown generally to many metallurgists, the first part of the present paper is concerned with a review of the literature in some detail. With this survey as a background, the authors have adapted the so-called methods of point-counting and lineal analysis to metallography, as described in the second part of the paper. Austenite-martensite structures were selected for illustration not only because they are important in many ways, but because such fine intermixtures are notoriously difficult to estimate visually. Literature Survey Perhaps the earliest work on quantitative microscopic analysis goes back to Delesse9 (1848) who proved mathemati-

Jan 1, 1948

By M. Cohen, R. T. Howard

It has long been realized among metallurgists that a fast, reliable method for the quantitative determination of the percentage of microconstituents in an alloy would be of great benefit in studies of equilibrium and transformation in the solid state. For example, Polushkinl has shown that the compositions of two coexisting phases in a binary system at a given temperature may be calculated very simply with the aid of two alloys lying in the two-phase field if the relative amounts of the two phases in each alloy can be determined. Recently, Grange and Stewart2 have traced the course of the austenite-martensite reaction in a series of commercial steels by making visual estimates of the percentage of martensite formed as a function of cooling temperature. The correlation of mechanical properties with structure, a subject of wide-spread current interest, is likewise dependent upon quantitative microanaly-sis. Yet, there are very few investigations described in the metallurgical literature, wherein methods of quantitative microscopy are employed. Usually, the relative amounts of the microconstituents are estimated in a qualitative or semiquantita-tive way. The authors were faced with this problem some time ago in studying the kinetics of austenite decomposition. Several aspects of this research could not be treated satisfactorily by other quantitative tools, such as specific volume,' magnetic,6 dila-tometric, electrical resistance7 or x-ray measurements.a It became necessary to find an impersonal quantitative method that could be applied to microstructures. Fortunately, it was noted that geologists and petrographers had coped with quantitative microscopy to a considerable degree in their attempts to evaluate the mineral contents of rocks. A number of excellent articles were found on this subject, and since they appear to be unknown generally to many metallurgists, the first part of the present paper is concerned with a review of the literature in some detail. With this survey as a background, the authors have adapted the so-called methods of point-counting and lineal analysis to metallography, as described in the second part of the paper. Austenite-martensite structures were selected for illustration not only because they are important in many ways, but because such fine intermixtures are notoriously difficult to estimate visually. Literature Survey Perhaps the earliest work on quantitative microscopic analysis goes back to Delesse9 (1848) who proved mathemati-

Jan 1, 1948

By Robert T. Howard, Morris Cohen

IT has long been realized among metallurgists that a fast, reliable method for the quantitative determination of the percentage of microconstituents in an alloy would be of great benefit in studies of equilibrium and transformation in the solid state. For example, Polushkin1 has shown that the compositions of two coexisting phases in a a binary system at a given temperature may be calculated very simply with the aid of two alloys lying in the two-phase field if the relative amounts of the two phases in each alloy can be determined. Recently, Grange and Stewart2 have traced the course of the austenite-martensite reaction in a series of commercial steels by making visual estimates of the percentage of martensite formed as a function of cooling temperature. The correlation of mechanical properties with structure, a subject of wide-spread current interest, is likewise dependent upon quantitative microanalysis.3 Yet, there are very few investigations described in the metallurgical literature, wherein methods of quantitative microscopy are employed. Usually, the relative amounts of the microconstituents are estimated in a qualitative or semiquantitative way. The authors were faced with this problem some time ago in studying the kinetics of austenite decomposition. Several aspects of, this research could not be treated satisfactorily by other quantitative tools, such as specific volume,4 magnetic,5 dilatometric,6 electrical resistance7 or x-ray measurements.8 It became necessary to find an impersonal quantitative method that could be applied to microstructures. Fortunately, it was noted that geologists and petrographers had coped with quantitative microscopy to a considerable degree in their attempts to evaluate the mineral contents of rocks. A number of excellent articles were found on this subject, and since they appear to be unknown generally to many metallurgists, the first part of the present paper is concerned with a review of the literature in some detail. With this survey as a background, the authors have adapted the so-called methods of point-counting and lineal analysis to metallography, as described in the second part of the paper. Austenite-martensite structures were selected for illustration not only because they are important in many ways, but because such fine intermixtures are notoriously difficult to estimate visually. LITERATURE SURVEY Perhaps the earliest work on quantitative microscopic analysis goes back to Delesse9 (1848) who proved mathemati-

Jan 1, 1947

By Fred Jones

The Cripple Creek district is in Teller County, Colo., about 18 miles in an air line west of Colorado Springs and at an elevation of 10,000 It. A line drawn through Colorado Springs and Pikes Peak will, if continued, about pass through the district. The character of the country generally is rolling, with few trees and little snow fall. The annual precipitation is about 20 in. All the water used by the mines is supplied by the Altman Water Co., which pumps from the west slope of Pikes Peak. Gold was discovered in 1891, since which time the district has produced $411,000,000. The peak of production was reached in 1900 and amounted to $25,000,000. At present the production amounts to about $400,000 per month. Geology In general, the geology of the district is simple; ash veins and dikes traverse a volcanic plug of breccia. The ore occurs as enriched spots along these dikes and veins. The dikes represent the most recent extrusions and consist of basalt and phonolite. (For a complete geological description reference is made to Professional Paper 54, 1906, of the U. S. Geological Survey.) The ore consists of small parallel seams of high grade. In only a few cases is the gold disseminated through the rock; much of the gold in the broken ore is found in the fines. The wall rock is hard blocky granite or breccia. About 25 per cent. of the rock mined is shipped as ore to the Golden Cycle mill at Colorado Springs. The height of an ore deposit is usually several times its length. Few flat oreshoots have been found. The veins are all steep and have a dip of 70 to 80°. Development The claims are all 300 by 1500 ft. and are held by location or patent. All mining is done through shafts, one of which has reached a depth of 2600 ft. The main working shafts are 41/29 by 1335 It. and are made up of three compartments, each 4 by 41/2 ft. in the clear. They are timbered with 10-in. Oregon posts and plates and 8-in. spreaders. Two compart-

Jan 1, 1925

By L. D. Wooddy, Robert Moscrip

The simultaneous solution of the volumerric balance and the unsteady-state equation has been used for several years to make performance calculations for combination drive reservoirs. This method makes possible the calculation of volumetric changes of fluids in the gas cap, oil zone, and aquifer which occur as a result of withdrawals and reservoir pressure changes. It does not provide a means for the determination of reservoir fluid distribution changes corresponding to these vollrmetric changes. A knowledge of the fluid saturation distribution in the reservoir at various stages of depletion is important for the determination of the efficiency of gas and water as oil-displacement media and, therefore, for the reliable predicrion of ultimate oil recovery. To provide this knowledge, the displacement equations are solved simultaneously with the volumetric balance and unsteady-state equations. The described calculation procedure has been used satisfactorily to analyze the past performance and to predict the future behavior of combination drive reservoirs under both primary and pressure-maintenance operations. INTRODUCTION The three basic mechanisms by which oil is displaced from a reservoir are: (1) dissolved gas drive—the displacement of oil by the expansion of liberated solution gas, (2) water drive—the displacement of oil by water which enters the oil zone from the aquifer, and (3) gas cap drive—the displacement of oil by gas which ex- pands into the oil zone from the gas cap. The action of gravitational forces may be effective in increasing the efficiency of the basic drive mechanisms. Gravitational forces favor the segregation both of gas and oil and of oil and water, thus tending to shorten the transition zone between oil and displacing fluids. Most reservoirs produce under the influence of a combination of these drives and are designated "combination drive reservoirs". Fig. 1 is a cross section of a typical combination drive reservoir. A calculation procedure for analyzing the performance of combination drive reservoirs has been developed by combining the displacement equations' with the volumetric balance equation' and the unsteady-state equations. The pressure-production performance and the positions of the gas-oil and oil-water contacts are calculated for several stages of reservoir depletion by solving these equations simultaneously, thus affording a basis for: 1. Determining instantaneous and ultimate oil, gas, and water production under various operating conditions. 2. 'Establishing a maximum efficient rate of production, 3. Determining the advantages of pressure maintenance and unitization, and 4. Designing surface installations necessary for primarv and pressure-maintenance operations. DEFINITIONS The calculation procedure for combination drive res-

Jan 1, 1957

By Samuel Hoyt

SOME of the more important properties of finished materials are strength, ductility, toughness, resistance to alternating and repeated stresses, etc: Of these, the property that appears to have received the least consideration, at least in this country, is toughness, which is clue, possibly, to our regarding toughness as a qualitative property or, at any rate, as one that, parallels ductility. This arises out of our greater experience with the simple carbon steels in the rolled or forged (non-heat-treated) condition which, qualitatively, are tough if ductile and are not tough if brittle. In this way we have erroneously become, accustomed to judging the toughness of a material from its behavior in the tensile or similar test. The point of view presented in the present paper is that toughness, like hardness or tensile strength, should be regarded as an independent property and of sufficient importance to require, in so far as that may be possible, quantitative determinations. If such be true, it becomes at once necessary to devise experimental means for measuring, or valuating toughness, and the notched-bar impact test (the Charpy test) is advanced as the most logical test that has so far been developed for this purpose. It is further advanced, with particular emphasis, that we have two kinds of toughness to deal with and, accordingly, they will be dealt with independently. CLASSIFICATION OF MATERIALS ACCORDING TO TOUGHNESS Toughness has been defined somewhat as follows: Tough materials are those that offer considerable resistance to permanent deformation but which, once such resistance has been overcome, may' be deformed plastically, but only by the expenditure of considerable energy. In other words; tough materials may be deformed plastically but they absorb a considerable amount of work in the process. This kind of toughness may be called "static" toughness when the rate of loading is reasonably slow or "dynamic" toughness when the rate of loading is

Jan 2, 1919

By George Comstock

IT seems a common opinion among metallographists that all light-gray inclusions seen with the microscope in polished sections of steel are manganese sulphide. Examples of this belief are continually appearing, as for instance in the paper by Dr. Henry Fay on manganese sulphide as a source of danger in steel rails,1 and in Lieutenant-Commander Cook's paper on Metallography of Steel for U S. Naval Ordnance.2 Slate FIG. 1-TRANSVERSE VIEW OF THE EDGE OF A SMALL HOT-ROLLED STEEL ROD. ETCHED WITH PICRIC ACID. X 200. colored inclusions are considered to be silicates, and dove-gray inclusions, manganese sulphide. To show the danger in the latter unqualified assumption, it should be sufficient to examine the edge of any piece of steel that is covered with a fairly thick scale, and that has been polished in such a way as to prevent the scale from breaking away entirely below the polished surface. This can be done by protecting the scaled edge of

Jan 12, 1916

By Robert Glass Cleland

THIS IS a history of a company whose roots run deep into the nation's past and whose field of operations has never been narrowly confined. The men who founded Phelps Dodge were men of initiative and imagination. They were men of strong convictions and upright character. They held fast to the simple virtues and traditions of the days when America was young. This heritage they passed on to their successors. From the very beginning, under such leadership, Phelps Dodge became a company of large affairs. It bought and sold, exported and imported, built factories and organized railroads, converted great forests into lumber, and operated coal and iron mines. Much of the iron, copper, and tin plate used in the United States for a generation was under its control. Its business abroad was extensive enough to warrant the organization of a separate partnership in England. Then, almost half a century after its foundation, the company began to substitute new activities for old and eventually transferred its major operations to the West, primarily to Arizona. The family partnership became a corporation. Exporting and importing gave place to mining and metallurgy. Phelps Dodge became one of the largest

Jan 1, 1952

By Akinobu Kasami, Keiji Maeda, Makoto Naito, Masaharu Toyama

Gap electroluminescent diodes have been prepared by the vapor phase diffusion of zinc into n-Gap crystals which were grown from a gallium solution (10 wt pct Gap) doped with tellurium and Ga203. A marked improvement in the efficiency of the red electrolumines -cence has been achieved by heat treatment after diffusion. External quantum efficiencies of diodes annealed under optimum conditions are 0.2 to 0.6 pct at room temperature, or about 200 times higher than the efficiencies of diodes quenched after diffusion. The optimum dopant concentrations in the gallium melt from which the crystals were grown are 3to6 x at. pct Te and 4 to 8 x 10-2 mol pct Ga203. The efficient diodes are characterized by linearly graded junctions with an i-layer 0.1 to 0.2u thick. Annealing increases the emission intensity by a factor of 20 to 50 and decreases the current density to 1/3 to 1/8 that of quenched diodes at a given bias. The decrease in current is attributed to an annihilation of deep recombination centers in the depletion layer. The increase in emission intensity is interpreted in terms of an increase in lifetime of minority carriers and an increase in the relative intensity of red-to-infrared emission. The dependence of these quantities on the tellurium and oxygen doping levels is also discussed. A number of studies have been made of the red light emission from for ward-biased Gap diodes.' At room temperature this emission band is centered at 7OOO? with a spectral width of nearly 1000?. Low-tempera-ture photoluminescence indicates that this emission is due to either the radiative annihilation of an exciton bound to a pair of zinc and oxygen atoms substituting on nearest neighbor lattice sites2,3 or the radiative recombination of an electron bound to this Zn-O pair with a hole bound to an isolated zinc shallow acceptor.3 An emission band is also observed with a spectral peak at 9800?. This infrared emission has been shown to be due to the recombination of an electron trapped at an isolated oxygen deep donor with a hole trapped at an isolated zinc acceptor.4 The red emission from Gap diodes is fairly efficient at room temperature because the nearest neighbor Zn-0 pair forms a deep electron trap at 0.3 to 0.4 ev below the edge of the conduction band.2'4 In diodes grown by liquid epitaxy an external quantum efficiency of 2.1 x 10-2 (photon/electron) has been attained by heat treatment at relatively low temperatures.5 This heat treatment was found to increase the efficiency by a factor of 3 to 6. However, no detailed studies have-been reported on the effects of heat treatment. We can only cite Onton and Lorenz's work6 on the change ; in the relative intensity of red-to-infrared emission. Heat treatment has also been tried on junctions built in during growth, but contrary to expectations the efficiency decreased. In-diffusion is a simple and controllable method of fabricating p-n junctions. For Gap, zinc is generally used to form a p-type layer on n-type crystals. The emission efficiencies of in-diffused diodes are, however, extremely low in comparison with liquid epitaxial diodes.' Although efficiencies as high as 2 x 1O-3 have been reported, values from 10-6 to 10-4 are generally obtained by typical diffusion techniques. Out-diffused diodes are known to be a little more efficient than in-diffused diodes. Nevertheless, the quantum efficiency is at most 7 x 10- 3 and ordinarily of the order of 10-4.8 NO results have been reported on heat treatment of either in-diffused or out-diffused diodes. This paper reports a marked improvement in the efficiency of the red emission observed for in-dif-fused diodes as a result of heat treatment after diffusion. The method described reproducibly yields diodes with external quantum efficiencies of 2 to 6 x 10-3. The observed dependence of efficiency on annealing time and on doping level will be discussed in terms of the lifetime of minority carriers and the formation of Zn-O complex pairs. EXPERIMENTAL A) Diode Fabrication. The n-Gap crystals used in this study were grown from a saturated gallium solution by a slow cooling method.8 The Gap content in the gallium melt was fixed to 10 wt pct corresponding to a growth temperature of about 1100 Tellurium was chosen as the n-type dopant and added to the melt in concentrations ranging from 0.001 to 0.06 at. pct. Oxygen was added in the form of Ga2O3, whose concentration was varied from 0.004 to 0.2 mol pct. The resulting crystals were platelets with well-developed (111) surfaces. Typical electrical properties were Hall mobilities of 130 to 30 sq cm per v-sec and carrier concentrations of 1016 to 10" cm-3 at room temperature. Diodes prepared from crystals with relatively low doping levels, in which u = 130 to 100 sq cm per v-sec and n = 0.6 to 6 x 1017 Cm-3, were examined in detail. The p-n junctions were produced in these n-Gap crystals by the diffusion of zinc from the vapor phase by the following procedure. The platelets were carefully lapped on both sides to a thickness of 150 to 200 u while maintaining the (111) orientation. After being etched in hot aqua regia, the crystals together with the zinc were sealed in an evacuated 12 mm ID quartz ampoule 20 cm long. The crystals and the zinc were then separated from each other at opposite ends

Jan 1, 1970

By D. T. Camp, J. A. Clum

WITH experience, the indexing of back-reflection Laue patterns for cubic crystals is usually a straightforward matter. However, for noncubic systems where in general tables of interplanar angles are not available or when inexperienced personnel are involved, properly indexing a crystal is normally a tedious, time-consuming affair. The authors have written a digital-computer program which calculates and prints out a table of interplanar angles for an arbitrary crystal structure and then systematically searches through this table attempting to obtain a consistent fit to back-reflection Laue data supplied by the user. Of course it is possible simply to calculate a desired set of interplanar angles should this be the only requirement. The program was originally written in ALGOL for use on a Control Data G-21 computer and a preliminary version is described elsewhere.' A version in FORTRAN TV which has been run on an IBM 7040 and one in FORTRAN II run on an IBM 1620 are also available. While it is not the purpose of this communication to describe the program in detail, an indication of how the program operates may help one to decide whether the program would be useful under particular circumstances. The hypothetical example chosen involves the indexing of the zinc crystal which has a hexagonal structure and a c/a ratio of 1.856. Input data for this example consists of only nine cards: The first card controls the list of families of planes to be considered. If the Miller indices of a prospective family are (h k 1), the first digit places a limit, in this case 3, on the absolute values of any individual index. The second digit limits the sum (h +k + l + 1), in this case to 5. Therefore the families (013) and (112) are considered but the family (122) is not. All systems, including the hexagonal, are treated using three-digit Miller indices. The second card contains the crystallographic parameters required to define the system. The first digit is 0 if the system is rectangular, that is all angles are 90 deg. If the system is nonrectangular, as in this example, the digit 1 so indicates. The next three values are the lengths of the sides of the reference cell, a, b, c. The final three entries on the card are the angles, a, 8, y between the sides. The digit 0 on the third card indicates that more data follows, the digit 6 shows that a set of six planes is to be indexed, and the value 2.0 indicates that agreement between a tabulated angle and an input angle is considered adequate if their absolute difference is less than 2 deg. The fourth card lists the measured input angles. a12 = 38 deg, a13 = 24 deg, and so forth. More input angles are listed on cards five to eight with the latter giving the input angle 058 = 40 deg. The final card in this series indicates by the digit 1 that no more data is to be processed. The program operates in the following manner: 1) The input data from cards 1 and 2 is read, thereby indicating the crystal system to be examined and the crystallographic parameters of the particular crystal to be indexed. 2) A table of interplanar angles is generated. 3) The input angles contained on cards 4 to 8 are read. 4) The measured input data is systematically compared with the generated table of standard angles. All combinations of poles whose interplanar angles compare with the requisite, specified accuracy are printed out. If no adequate fit is found an indication of this is printed. A typical line from the generated table of interplanar angles is: (001) - (111) 74.92 64.99 It can be shown that in the Miller-Bravais system the first value corresponds to the angles between (0001)-(1121) and the second to that between (0001)-(1011). This particular set of data gave the following result for the planes 1 to 6: (011) (110) (121) (111) (112) (010) The ALGOL version also has the option of simply providing the Greninger-chart coordinates ? and 6

Jan 1, 1967

By M. E. Wadsworth, L. H. Raby, A. S. Peck

Infrared spec troscopy was used to study the adsorption of oleate collector on three varieties of hematite. Each of the minerals was found to react with either oleic acid or a solution of sodium oleate to form a mineral cation-collector anion chemisorbed layer at the solid-liquid interface. The chemisorption reaction displaced surface hydroxyls and was found to be pH dependent. The infrared band characteristic of the antisymmetrical C = 0 structural group of chemisorbed oleate appears between 1520 and 1540 cm-'. Evidence is presented which shows that molecular filming of the mineral surfaces with un-dissociated oleic acid precedes chemisorption. Infrared absorbance is correlated with the flotation behavior of the mineral. Adsorption processes are usually classified into two types which are distinguished and character- ized by the nature of the bond formed between the adsorbate and adsorbent. The process in which molecules chemically bond to solid surfaces is termed activated adsorption or chemisorption. If only weak van der Waals forces bind the molecules to the surface then the process is termed physical adsorption. Chemisorption is of primary interest in flotation systems since selectivity may be obtained if a single mineral is rendered air-avid by a specific collector mineral adsorption reaction. In previous studies infrared spectroscopy was used to define the mechanisms involved in the adsorption of oleic acid and sodium oleate on fluorite, barite, and calcite. Infrared techniques were particularly useful since adsorbed monolayers were identified in situ. Further, the infrared method permitted identification of reaction products in the solid, liquid, and vapor phases of the systems. The chemisorption reactions displaced F- from fluorite, SO4 from barite, and CO3 from calcite. This investigation was pursued in an effort to characterize and interpret the adsorption processes for synthetic hematite, compact red hematite, and specular hematite (crystalline hematite). Adsorption tests were performed using either oleic acid or

Jan 1, 1967

By William Blauvelt

THE type of gas producer in which the ashes are fluxed and run off as slag was among the very earliest made. Ebelmen built the first one in 1840 at Audincourt, France, only a year after the installation of the first gas producer of which we have record. Charcoal was used as the fuel, with blast-furnace slag and clay is flux. My interest in this type of producer began when as a boy I saw the fluxing producer at Chester, N. J., which was invented by W. J.. Taylor, and described by him in 1881.1 This producer was invented independently by Mr. Taylor to meet the difficulties he experienced in making producer gas for roasting sulphurous iron ores. It will be of interest to review briefly his description of his producer. It was built like a small blast furnace, having a hearth 24 in. in diameter and 24 in. high. The bosh angle was 25° from the vertical; the diameter at the bosh 4 ft. and at the top 3 ft.; the total height 12 ft. The producer contained one water-cooled tuyere 12 in. above the bottom, with a 1.5-in. nozzle.. Depth of the coal above the tuyere; 6 ft. Mr. Taylor mixed the coal with from 30 to 40 per cent. of basic blast-furnace slag to flux the ash. Occasionally some limestone was also used, but never limestone alone, as the use of the furnace cinder gave a larger volume of slag and made it easier to maintain a proper fluidity. . The producer was blown with a small Weimer blowing engine, delivering 300 ft. of air per minute, at from 1 to 1.5 lb. pressure. The slag was tapped every 2 hr. and was black and glassy in appearance. Broken or egg size anthracite was used. The fine sizes of anthracite could not he made to work. Mr. Taylor expressed the belief that bituminous coal could be used if not too fine, but no experiments were made with this coal. Runs were made of four weeks' duration, with no stops or changes. Mr. Taylor reported the following advantages:

Jan 12, 1913

By D. J. McAdam, R. W. Mebs

The technical cohesive strength of a metal means, not the interatomic forces, but the technically estimated resistance to fracture. An example of such resistance to fracture is the so-called "true" breaking stress of a tension-test specimen, the breaking load divided by the sectional area at fracture. According to the prevalent view,8 the technical cohesive strength of a metal. in any particular state as regards prior mecharlical treatment and heat-treatment, is determined by a limiting value of the algebraically greatest principal stress. In two previous papers by one of the authors, evidence was presented to indicate that the technical cohesive strength of a metal cannot be represented by a single stress value, but that it comprises an infinite number of values corresponding to the infinite number of possible combinations of the principal stresses. The technical cohesive strength thus comprises an infinite number of technical cohesion Limits, each representing a specific stress combination at fracture. In the same papers, evidence was presented that plastic extension causes a continuous increase in the technical cohesive strength. Such a variation is not in accordance with the prevalent view that plastic extension first increases, then decreases, the technical cohesive strength.' In this paper, as in the previous papers,14.15 the algebraically greatest principal stress will be designated S1, the least principal stress will be designated 33, and the intermediate principal stress will be designated S². The technical cohesion limit under polarsymmetric tension (S1 = S2 = S3) will be termed the "disruptive stress," and the cohesion limit under unidirectional tension (S2 and S3 = o) will be termed the "severing stress."l4, .l5 The yield strength of a metal, according to the generally accepted theory, may be represented by a constant value of the shearing-strain energy, and hence by a constant value of the sum of the squares of the three principal stress differences. In the second of the previous papers,15 however, evidence was presented that the limiting yield stress decreases with increase in the volume stress, the algebraic average Of the three principal stresses.* This in fluence of the volume stress becomes prominent only in the field of triaxial tension. In the two previous papers,".'5 diagrams were presented to show the variation of the technical cohesion limit, yield stress, and ultimate stress with the combination of principal stresses and with plastic extension. Those diagrams and the resultant • Any stress system ma? be resolved into a polarsymmetric stress causing pure volume strain and a combination of pure shearing stresses. which cause no change of volum

Jan 1, 1945

By E. Houdremont, H. Schrader, H. Bennek

The different influences exerted by the various alloying elements in iron and iron-carbon alloys give rise to a great number of complexities, which are difficult to grasp. It is important therefore to study any systematic relations that may exist between the effects exerted by the various alloying elements, in order to obtain a general classification and thus a clearer conception of the nature of alloy steels. A systematic survey of the alloys of iron, based on an investigation of the binary equilibrium diagrams, was recently published by Wever. Although his work deals little with properties of importance in works practice, its purpose being rather to point out the theoretical agreement among the types of binary equilibrium diagrams and the position of the alloying elements in the periodic system (atomic radii, etc.), the classification proposed nevertheless also suggests relationships among the properties of the alloys in question, even though the alloys may contain carbon in addition to iron and the alloying element. Wever divided the alloys of iron into one group exhibiting an open or enlarged gamma field and another exhibiting a closed or restricted gamma field, with both groups capable of further subdivision depending upon whether a continuous series of solid solutions is formed, or, owing to the separation of compounds, etc., only a limited series. Thus all alloying elements which with iron form a closed gamma field, a "gamma loop," produce alloys that beyond the composition corresponding to the greatest extent of the gamma loop are composed of ferrite alone at all temperatures. Alloys of this composition accordingly are not susceptible to ordinary heat treatment because of the lack of transformations. Steels of this class may thus be divided into steels that contain less than the critical amount of alloying element, and are subject to heat treatment, and those that contain more than the critical amount of alloying element and are not subject to heat treatment. Thus chro-

Jan 1, 1935

By H. Schrader, E. Houdremont, H. Bennek

The different influences exerted by the various alloying elements in iron and iron-carbon alloys give rise to a great number of complexities, which are difficult to grasp. It is important therefore to study any systematic relations that may exist between the effects exerted by the various alloying elements, in order to obtain a general classification and thus a clearer conception of the nature of alloy steels. A systematic survey of the alloys of iron, based on an investigation of the binary equilibrium diagrams, was recently published by Wever. Although his work deals little with properties of importance in works practice, its purpose being rather to point out the theoretical agreement among the types of binary equilibrium diagrams and the position of the alloying elements in the periodic system (atomic radii, etc.), the classification proposed nevertheless also suggests relationships among the properties of the alloys in question, even though the alloys may contain carbon in addition to iron and the alloying element. Wever divided the alloys of iron into one group exhibiting an open or enlarged gamma field and another exhibiting a closed or restricted gamma field, with both groups capable of further subdivision depending upon whether a continuous series of solid solutions is formed, or, owing to the separation of compounds, etc., only a limited series. Thus all alloying elements which with iron form a closed gamma field, a "gamma loop," produce alloys that beyond the composition corresponding to the greatest extent of the gamma loop are composed of ferrite alone at all temperatures. Alloys of this composition accordingly are not susceptible to ordinary heat treatment because of the lack of transformations. Steels of this class may thus be divided into steels that contain less than the critical amount of alloying element, and are subject to heat treatment, and those that contain more than the critical amount of alloying element and are not subject to heat treatment. Thus chro-

Jan 1, 1935

By V. K. Grotzky, F. J. Fraikor

A number of investigators have noted the importance of various precipitation reactions on the properties of commercial-purity beryllium.1-5 Carrabine, for example, has demonstrated the interaction of iron and aluminum on the mechanical properties of hot-pressed polycrystalline beryllium.6 He considered the determining factor on elevated-temperature properties to be a reversible AlFeBe, precipitation reaction which could be directly related to the Fe/Al impurity ratio of the beryllium. Any aluminum in excess of the stoichio-metric amount required to form A1FeBe4 was presumed to remain primarily in the grain boundaries. We have observed, by transmission electron microscopy, such a grain boundary effect after various heat treatments of beryllium sheet. The starting material in this investigation was bare-rolled beryllium ingot sheet (0.001 to 0.005 in. thick), in contrast to the hot-pressed powder utilized by Carra-bine. It should be noted from the ingot sheet analysis shown in Table I that the Fe/Al weight ratio was near unity which would provide some free aluminum although the total aluminum and iron content was still small. Fig. l(a) shows some aluminum or aluminum-rich precipitates in the grain boundaries of a beryllium foil which had been quenched from 1200°C into brine at -TPC. Similar grain boundary precipitates were found, particularly at grain boundary intersections, in other samples quenched from 1100° and 1000°C. The length of annealing time at these elevated temperatures did not appear to substantially alter the amount of grain boundary precipitates, thus attesting to their relative insolubility. No matrix precipitates were observed other than the normal BeO and Be2C inclusions. A microprobe analysis of the larger precipitates at

Jan 1, 1968

By Robert S. Dewey

AS a result of drilling operations during 1943, West Texas again added sufficient new oil reserves to replace the oil produced during the year, but failed to maintain its position in currently available reserves because the deeper discoveries will require years for development. Drilling failed to provide the additional oil necessary to meet the increase in current and anticipated market demand. Although 13.3 per cent of the total footage drilled was in wildcat exploration, the ratio of oil discoveries to total wildcats was less in 1943 than in 1942, but comparable to that in 1941. Of the 732 field wells completed, 270 were at Slaughter, 55 at Wasson, 45 at Mascho and 31 at North Cowden. As of Dec. 31, 1943, there were 361 drilling wells including 71 wildcat and 290 field wells; 19.7 per cent were wildcats. It is anticipated that the percentage of wildcats of the total wells will be higher during 1944 than in either 1942 or 1943. Tables 3 and 4 present a three-year comparison of drilling activity and illustrate the downward trend of development that has been in effect during that time. Because of development lag in the deeper Ordovician fields, several years elapse before 2 sufficient number of wells is completed to give a substantial producing rate. As these new oil reserves cost more to find, and will cost more to produce on a barrel basis than the oil marketed during the year, their reserve replacement value to the industry is less in money. Costs While complete costs for deeper drilling are not yet available for analysis, it is evi- dent from the data on drilling rates to comparable depths, contract prices, and general increases in costs, that the cost of drilling has risen approximately 20 per cent during the year. One representative drilling contractor estimates that the average drilling time on a 5000-ft. field well has increased nearly one third and that out-of-pocket costs have increased a dollar per foot. Three major factors contribute to this increased cost: (I) less experienced labor, (2) deterioration in mechanical equipment and expendable material, and (3) increased contract prices. In the past, when there were more drilling rigs than wells to be drilled, some contractors would cut their drilling profit to keep their personnel and rigs working. As this practice is no longer necessary, the contract prices are adjusted upward to assure a profit. On deep and difficult drilling, contracts are let on a cost plus basis. A number of mechanical difficulties have become evident. Inferior quality of steel used in drill pipe and rock bits has added appreciably to drilling time and cost. Contractors are experiencing delay in obtaining repair work and repair parts for prime movers. As the length of drilling time required an shallow-field wells has not increased in proportion to that on deeper wells, it seems that the medium-sized drilling rig is better adapted mechanically than the heavy one to the work imposed. One of the main deficiencies in the heavy rig equipment is inadequate pump capacity. Drilling Mud The increasing amount of deep drilling has emphasized the importance and relationship of good mud to efficient and suc-

Jan 1, 1944

By Robert S. Dewey

AS a result of drilling operations during 1943, West Texas again added sufficient new oil reserves to replace the oil produced during the year, but failed to maintain its position in currently available reserves because the deeper discoveries will require years for development. Drilling failed to provide the additional oil necessary to meet the increase in current and anticipated market demand. Although 13.3 per cent of the total footage drilled was in wildcat exploration, the ratio of oil discoveries to total wildcats was less in 1943 than in 1942, but comparable to that in 1941. Of the 732 field wells completed, 270 were at Slaughter, 55 at Wasson, 45 at Mascho and 31 at North Cowden. As of Dec. 31, 1943, there were 361 drilling wells including 71 wildcat and 290 field wells; 19.7 per cent were wildcats. It is anticipated that the percentage of wildcats of the total wells will be higher during 1944 than in either 1942 or 1943. Tables 3 and 4 present a three-year comparison of drilling activity and illustrate the downward trend of development that has been in effect during that time. Because of development lag in the deeper Ordovician fields, several years elapse before 2 sufficient number of wells is completed to give a substantial producing rate. As these new oil reserves cost more to find, and will cost more to produce on a barrel basis than the oil marketed during the year, their reserve replacement value to the industry is less in money. Costs While complete costs for deeper drilling are not yet available for analysis, it is evi- dent from the data on drilling rates to comparable depths, contract prices, and general increases in costs, that the cost of drilling has risen approximately 20 per cent during the year. One representative drilling contractor estimates that the average drilling time on a 5000-ft. field well has increased nearly one third and that out-of-pocket costs have increased a dollar per foot. Three major factors contribute to this increased cost: (I) less experienced labor, (2) deterioration in mechanical equipment and expendable material, and (3) increased contract prices. In the past, when there were more drilling rigs than wells to be drilled, some contractors would cut their drilling profit to keep their personnel and rigs working. As this practice is no longer necessary, the contract prices are adjusted upward to assure a profit. On deep and difficult drilling, contracts are let on a cost plus basis. A number of mechanical difficulties have become evident. Inferior quality of steel used in drill pipe and rock bits has added appreciably to drilling time and cost. Contractors are experiencing delay in obtaining repair work and repair parts for prime movers. As the length of drilling time required an shallow-field wells has not increased in proportion to that on deeper wells, it seems that the medium-sized drilling rig is better adapted mechanically than the heavy one to the work imposed. One of the main deficiencies in the heavy rig equipment is inadequate pump capacity. Drilling Mud The increasing amount of deep drilling has emphasized the importance and relationship of good mud to efficient and suc-

Jan 1, 1944

By E. T. Knight, John D. Gill

Much has been written and said concerning the alleged wasteful and uneconomic use of natural gas and petroleum. Espccially condemned has been the use of natural gas for the production of carbon black and the use of heavy fuel oil under steam boilers.' The critics of these usages of gas and oil have sought to make effective their verbal attacks on the industry by the repetitive expression of the words "inferior" and "superior" uses2 of petroleum. Thus, to employ natural gas for residential heating was to use it in a superior way; to use it for the production of carbon black was to use it in a wasteful and uneconomic way. To use petroleum for the production of automotive fuel was to use it in a superior way; to employ it as a residential fuel and as the prime source of power in an industrial plant was to use it in an inferior and uneconomic way. No doubt the objections to such employment of gaseous and liquid natural hydrocarbons originated in the belief that natural gas and petroleum are limited, nonregenerative mineral resources, and that the functions they perform can be just as well performed by other natural resources like coal13 of which practically unlimited reserves are known. The generations that have dominated each of the last four decades have counted reserves4 of petroleum in terms of a few years supply. Meanwhile, domestic demand for motor fuel rose spectacularly from a few million barrels in 1900 to more than 500,000,000 bbl. last year.5 The more imaginative and vocal critics drew startling word pictures of the catastrophe of 25,000,000 motor vehicles made useless and of the great automotive manufacturing and allied industries brought to an untimely end, and millions of workers left hopelessly unemployed by what they called the deplorably rapid depletion of the petroleum reserve. Many of the critics have been sincere advocates of the conservation of natural resources; many others, and in recent years probably the majority, have espoused the doctrine of conservation to promote their own self-interest rather than that of the public. The latest advocate of severe restriction in the use of petroleum for the alleged purpose of conserving the petroleum resource proposes to achieve that end by a bill,6 now before

Jan 1, 1938

By C. S. Smith, L. Guttman

It is shown, from a study of geometric probabilities, that the average number of intercepts per unit length of a random line drawn through a three-dimensional structure is exactly half the true ratio of surface to volume. Since the surfaces can be internal or external, the area of grain boundary or of the interface between any two constituents in a micro-structure can be measured. Other metric relations are tabulated that may be of use in studies of the microstructure of polycrystalline, cellular, or particulate matter generally. IN many fields of scientific investigation the structure of cellular aggregates or random arrays of discrete particles imbedded in some matrix is observed on a two-dimensional section and inferences are drawn therefrom as to the real structure in three dimensions. The biologist's microtome slice, the petrologist's thin section, and the metallurgist's plane polished and etched sections are common examples, although the problem is a general one. Scientists have commonly limited their thinking to the same dimensionality as their structures, and the few attempts that have been strictly three-dimensional in character have been laborious and noteworthy. From a metallurgical standpoint it is often of considerable importance to know, in addition to the volume fraction of two or more components in an alloy, the amount of two-dimensional interface between crystals. Such grain boundaries (which may separate either two identical crystals differing only in orientation or two crystals differing in structure, and possibly also in orientation) have a determining factor upon the mechanical behavior. It is at these boundaries that melting commences, that stress-induced corrosion occurs, and that various precipitates (harmful or otherwise) first appear. The boundary is doubtless of equal importance in nonmetallic crystalline aggregates such as rocks, ceramics, and concrete, and the biologist is deeply concerned with the area of cellular membranes. Many synthetic cellular foams involve similar structural problems. The very term structure usually implies the presence of interfaces and a complete understanding of structure involves nothing but an analysis of the geometrical, metrical, and topological relations between the various interfaces (zero, one and two-dimensional) that exist in a three-dimensional structure. Even systems lacking sharp physical interfaces often have interrelated gradients of composition or velocity (as cored crystals or turbulence cells) in which a neutral surface can be treated as a two-dimensional interface. In an earlier paper by one of the authors' the question of cell shape was considered in terms of simple topological principles without regard to physical dimensions. The determination of the actual size of grains in two dimensions is carried out in a routine fashion in innumerable metallurgical laboratories (see, for example, the ASTM standard methods of grain size determination2), though this is done merely to check the uniformity of a product and has no relation to the actual three-dimensional shape or size of the grains. Some authors have discussed the three-dimensional problem but only on the basis of assumptions as to idealized grain shapes.:'-' Quantitative measurements of microstruc-tures to obtain the volumetric relations of various phases have been carried out by petrographers for many years and are of increasing popularity among metallurgists." The present paper will show how, on the basis of no assumptions other than randomness of sectioning (usually realizable in experiment), it is possible to learn a great deal about the three-dimensional structure. The relations to be derived will generally be used on random arrays of cells or other particles, although they are equally applicable to ordered arrays and even to isolated objects of complex shape provided that suitable random sections can be made. Total Area of Interfaces in a Sample Consider a typical microstructure of a single-phase polyerystalline metal, such as that shown pres- in Fig. 1. The plane cross section shown contains a network of lines which subdivides the area into two-dimensional cells. The lines, of course, represent merely the intersection of the two-dimensional plane of sectioning with the two-dimensional interfaces between adjacent three-dimensional cells. The structure also contains points at which two or more lines intersect: in three dimensions the points are, of course, lines. In the more general case there may be in three dimensions isolated particles surrounded by a single interface without contact with others, and both two and one-dimensional features which do not necessarily connect with others. On the two-dimensional section these will appear as areas delineated by a closed line (as at a and b, Fig. 2), as isolated lines

Jan 1, 1954