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By Homer Turner

COALS, other than anthracite, have been so thoroughly studied under the microscope during recent years, that we now know what kinds of plants and what parts of plants form the bulk of lower rank coals from peat to bituminous coal. The microscope has also shown the state of preservation of such vegetation as well as the nature and distribution of products of plant decay. These and further details have been ascertained mainly through the employment of two methods of attack, section cutting and maceration. Anthracite has failed to respond to these methods, so well adapted to the study of lower rank coals and, therefore, has been neglected by investigators to such an extent that there is much doubt as to its microscopical characteristics. The object of this paper is to lift anthracite from its realm of obscurity by demonstrating the wealth of microscopical detail that is revealed when reflected light is used on a properly polished and etched surface and, further, to show the relationship between anthracite and bituminous coal.

Jan 2, 1925

By LESTER W. STRAUSS

OUR early knowledge of history and geography attracted most of us to the mineral resources of South America. The romantic tales of the Spanish activities, which were curiously alluring, and Prescott's exceptional bi-Conquest histories-Mexico and Peru-no doubt fired our minds with the .then metallic wealth of the Spanish colonies. Later developments, intensified within the past eighty years, have, however, changed its fame which now rests on such metallics as copper and tin, and among the non-metallics on nitrate of soda and petroleum. South America proper, excluding Panama, is made up of thirteen countries, a coincident parity with our original thirteen States. Its area is given as 7,231,300 square miles, or slightly less than North America (8,037,000 square miles), is made up as follows:

Jan 1, 1930

By William Glenn

In their account of chromium, Roscoe and Schorlemmer (Treatise on Chemistry, London, 1879) state that "In 1762 Lehmann, in a letter to Buffon, de nova minerœ plumbi specie crystalline rubra, described a new mineral from Siberia, now termed crocoisite." In 1786 Lehmann analyzed it (Nicholson's Jour., Dee., 1798) and found that it contained chiefly lead, and that the " mineralizers " were arsenic and sulphur. It was next examined in 1189 by Macquart and Vauquelin, who stated that it contained an intimate mixture of iron, alumina, and lead peroxide. The account of their work was published over the name of Macquart. Vauquelin (Louis-Nicolas) was a Norman peasant, who had studied in the village school, and at the age of fourteen was a laboratory-boy in a pharmacy at Rouen. Later, he found his way to Paris, and in 1789 was assistant to Fourcroy, a pharmacist and a teacher of note. It was here that he met Macquart, with whom he did the work on Siberian red lead, and at this time his friend Cheradame taught him his Latin.

Jan 1, 1896

By M. M., Fine

In a laboratory study of grinding and classification' of silica sand, a satisfactory means of producing the medium-fine specification sand desired by producers of flint-glass containers was developed. The best procedure consisted of ball-mill grinding and double classification, which gave a properly sized sand containing less iron than the feed.

Jan 1, 1950

By J. L. Bray

LEAD has often been suggested as a protective coating for iron and steel. Such a protective coating should possess: (1) good adhesion, (2) durability, (3) ease of application, (4) freedom from pinholes, (5) good appearance and (6) low cost, but, unfortunately, lead coatings so far produced do not have all of these characteristics. Because of the necessity of carrying out the coating process cheaply, and because lead solutions have poor plating characteristics, most of the efforts have been directed toward the hot-dipping process rather than electroplating. The hot-clipping processes using lead have not been successful chiefly because of the lack of adherence between iron and lead. In any coating process involving iron a bond can be obtained only by the formation of an intermetallic compound, the formation of a solid solution, or mechanical means. Lead forms with iron two immiscible liquid solu-tions, and in the solid state no intermetallic compounds or solutions. It is necessary, therefore, to employ some other element or elements as a binding agent. Tin may be used as in terneplate, or copper in the form of a thin film of electrolytically deposited metal to which the lead will adhere. Because of its physical and chemical properties, lead as a coating medium would undoubtedly be limited in its use to sheet and wire and then only when the article is not subject to abrasion or wear. A very large tonnage of these products are being used under such conditions and a successful lead-coating process should be a valuable contribution to the science. Two other difficulties stand in the way of successful lead coating-that of poor appearance of the weathered surface and the tendency of the lead to form pinholes during solidification. Since lead is commonly accepted as cathodic to iron, these exposed areas are ones of accelerated corrosion.

Jan 1, 1937

By Arnold K. Reese

It is not the purpose of the writer to set forth in these notes anything new or surprising in blast-furnace practice, but simply to lay before the Institute the somewhat unusual results obtained during a period of six consecutive months, ending April 30, 1896, at the Dover furnace of the Penn Iron and Coal Co., and to give, with these results, the conditions under which they were obtained, and all figures pertaining to that period. This plant was entirely rebuilt, on thoroughly modern and improved plans, in the spring of 1895, by Frank C. Roberts & Co., of Philadelphia.

Jan 1, 1898

By A. D. Fernie

Growing interest in pit crushing and conveying is evident from the recent many articles, technical papers, and new equipment development. Application of a pit crushing and conveying system is complex. Many factors, such as mine design, production scheduling, as well as initial and ongoing capital and operating costs must be thoroughly and realistically examined. This paper will address the fundamentals to be considered and review several approaches to developing a total system for a new and existing mine situation. The planning function will be outlined and operating and design criteria defined to interface the mining operation and the pit crushing conveying system.

Jan 1, 1986

By M. Muskat

A theory has been developed describing the behavior of wells and reservoirs producing by the action of bottom water drives. It is assumed that the pressures are maintained above the bubble point, and that the permeability to viscosity ratio of the water in the flooded zone is the same as for the oil in the oil-saturated pay. Accordingly, the treatment is based on the homogeneous fluid potential theory. The effect of the difference in density between the oil and water is neglected. .4fter deriving the proper potential distrihutions, the nature of the rise of the water-oil interface below the producing wells is calculated. The primary clean-oil-production phase is expressed in terms of the displacement efficiency, defined as the fraction of the pay flooded out by the rising water table at tlle time of first water entry. The variation of this displacement efficiency is calculated as a function of the well spacing, pay thickness, the ratio of the horizontal to vertical permeability, and the well penetration. The important parameter, other than the well penetration, is found to be the ratio of the well separation to the thickness of the oil pay multiplied by the square root of the ratio of vertical to horizontal permeability. It was found that the displacement efficiency continually decreases as this parameter increases, and for values of the latter >3.5, the efficiency varies inversely as the square of the parameter. It also increases with decreasing well penetration. Perhaps the most striking result of this phase of the analysis is the conclusion that in order to explain the delay in entry of water in wells producing by bottom water drives for periods longer than a few days normal production, with drawdowns large compared with the differential density head between the oil and water, it is necessary to assume that the vertical permeability is a very low fraction of the horizontal permeability. An analysis is also given of the production history after the water has broken through, on the assumption that the production mechanism and details of the flow distribution continue to be the same as during the phase of clean-oil production. As is to be expected, it is found that the water cut will increase at an accelerated rate as production proceeds. However, the initial differences between systems of different well penetrations or well spacings with respect to the total clean-oil production gradually decrease in terms of the variation of the water-oil ratio with cumulative production. In particular, by the time the water-oil ratio has reached values of the order of 5 or greater the cumulative recoveries will generally differ much less among various producing systems than their corresponding clean-oil recoveries. Introduction On the basis of elementary geological principles, one may classify effective water-drive fields in two groups. In the first, the entry of water into the oil-producing formation may be characterized as an edge-water encroachment. This term is used to suggest that the motion of the water proceeds largely in a direction parallel to the planes of stratification. This type of water intrusion occurs usually in thin producing zones and in strata lying along structural flanks of appreciable dip. In the second group—"bottom water-drive" fields—the water-oil interface lies in a plane of zero or slight inclination to the

Jan 1, 1947

By M. Muskat

A theory has been developed describing the behavior of wells and reservoirs producing by the action of bottom water drives. It is assumed that the pressures are maintained above the bubble point, and that the permeability to viscosity ratio of the water in the flooded zone is the same as for the oil in the oil-saturated pay. Accordingly, the treatment is based on the homogeneous fluid potential theory. The effect of the difference in density between the oil and water is neglected. .4fter deriving the proper potential distrihutions, the nature of the rise of the water-oil interface below the producing wells is calculated. The primary clean-oil-production phase is expressed in terms of the displacement efficiency, defined as the fraction of the pay flooded out by the rising water table at tlle time of first water entry. The variation of this displacement efficiency is calculated as a function of the well spacing, pay thickness, the ratio of the horizontal to vertical permeability, and the well penetration. The important parameter, other than the well penetration, is found to be the ratio of the well separation to the thickness of the oil pay multiplied by the square root of the ratio of vertical to horizontal permeability. It was found that the displacement efficiency continually decreases as this parameter increases, and for values of the latter >3.5, the efficiency varies inversely as the square of the parameter. It also increases with decreasing well penetration. Perhaps the most striking result of this phase of the analysis is the conclusion that in order to explain the delay in entry of water in wells producing by bottom water drives for periods longer than a few days normal production, with drawdowns large compared with the differential density head between the oil and water, it is necessary to assume that the vertical permeability is a very low fraction of the horizontal permeability. An analysis is also given of the production history after the water has broken through, on the assumption that the production mechanism and details of the flow distribution continue to be the same as during the phase of clean-oil production. As is to be expected, it is found that the water cut will increase at an accelerated rate as production proceeds. However, the initial differences between systems of different well penetrations or well spacings with respect to the total clean-oil production gradually decrease in terms of the variation of the water-oil ratio with cumulative production. In particular, by the time the water-oil ratio has reached values of the order of 5 or greater the cumulative recoveries will generally differ much less among various producing systems than their corresponding clean-oil recoveries. Introduction On the basis of elementary geological principles, one may classify effective water-drive fields in two groups. In the first, the entry of water into the oil-producing formation may be characterized as an edge-water encroachment. This term is used to suggest that the motion of the water proceeds largely in a direction parallel to the planes of stratification. This type of water intrusion occurs usually in thin producing zones and in strata lying along structural flanks of appreciable dip. In the second group—"bottom water-drive" fields—the water-oil interface lies in a plane of zero or slight inclination to the

Jan 1, 1947

By F. R. Brotzen, L. D. Whitmire

Single crystals of high-purity molybdenum were de-formed at temperatures from 195°to 473°K, and the effect of deformation on the electrical resistivily was deler-mined. To separale the resislivity components of point and line defecls some cryslals were annealed at 473°K. The vale of resislivily increase wilh strain was nearly linear and was strongly dependent upon the deformation temperature. Point dejects are annealed out without any effect on the flow stress. At low temperatures the flow stress is a linear function of the square root of the resistivity increase attributable to dislocations. ELECTRICAL-resistivity measurements have been used successfully to gain information on structural changes in metallic materials. During plastic deformation the electrical resistivity rises because of electron scattering from newly created lattice defects. Such measurements lend themselves, therefore, to corroborating results from direct observation of lattice defects and, to a certain extent, to correlating defect densities and distribution with mechanical properties. Published information on research with single crystals of the bcc metals of Group VI, particularly molybdenum, is still limited. Yet, molybdenum single crystals of relatively high purity can be readily prepared by electron-beam-melting techniques. Furthermore, some valuable information on the defect structure of deformed crystals by direct observation is available. Lawley and Gaigher,1 for example, have examined dislocation configurations in deformed molybdenum crystals by means of transmission electron microscopy. Their results revealed that the dislocation density and distribution were strongly dependent upon the deformation temperature. These findings differed from those by Keh and weissmann,2 who found that the average dislocation density in polycrystalline iron deformed between 138° and 298°K depended only on the degree of strain and not on the deformation temperature. Martin3 and peiffer4 showed that point defects introduced in polycrystalline molybdenum by cold work can be eliminated by annealing at a relatively low tempera-ture. In view of their work it became apparent that resistivity measurements of suitably annealed crystals could disclose changes in their dislocation structure and contribute to the understanding of the work hardening of molybdenum crystals. EXPERIMENTAL PROCEDURE Crystals were grown by electron-beam zone melting5,6 of 0.062-in.-diam molybdenum rods (99.99 pct) supplied by General Electric Lamp and Wire Division, Dover, Ohio. The crystals, about 4 in. long, were prepared by using five zone-refining passes at a speed of about 6 mm per min in a vacuum of about 5 X l0-6 Torr. The resistivity ratio of the crystal, p(4.Z°K)/p(273°K), was generally near 10-3. These crystals were used as tensile specimens of uniform diameter in the "as-grown" condition. They were oriented for maximum shear on the (011)[111] slip system (Schmid factor >0.49). The specimens were held in spherically seated Templin-type grips so as to minimize bending. Samples were deformed on an Instron machine at a strain rate of about 5 X 10-5 sec-1 in an isopentane bath with dry ice at 195°K, in ice water at 273°K, and in a vegetable-oil thermostat at 373° and 473°K. The temperature in the latter was maintained constant within +2°K. Resistance measurements were carried out with a Kelvin double bridge. The resistance of the potential leads was kept low by using large-diameter wires outside the low-temperature bath. Many of the resistance data were checked by measurements made with an ac bridge. Current and potential leads were spot-welded to the specimens. The distance between the potential leads, about 3 in., was also considered to be the gage length for the strain measurements. Diameter and gage length of the samples were measured optically with an error of less than 2 pct. These measurements were used also to insure that the deformation had been uniform over the gage length of the specimen. Resistivity changes were then determined from the resistance measurements at 4.2°K assuming constancy of volume. In the course of a test, the crystal diameter, gage length, and resistance at 4.2°K were determined first in the initial state and subsequently for various amounts of elongation.

Jan 1, 1968

Jan 1, 1969

By Charles Janin

(San Francisco Meeting, October, 1911.) THE first successful bucket-elevator dredge to operate in California was put in commission at Oroville in March, 1898. There had been numerous previous attempts at dredging, but none of the earlier boats proved a success. The gold-miners in California early conceived the idea of a machine to dig gravel from the beds and bars of auriferous streams that were inaccessible by the methods then employed, and it was only a few months after the discovery of gold in California that such a machine was. shipped around Cape Horn from New York to San Francisco. This was, however, but the forerunner of many failures in gold-dredging, and was soon at the bottom of the Sacramento river. During succeeding years many other unsuccessful attempts were made, and it was not until 1897 that a dredge of the single-lift bucket-elevator type was floated on the Yuba river. This dredge was built by the Risdon Iron Works for R. H. Postlethwaite, and would probably have been a success if it had been operated on some of the rich Oroville ground instead of in a turbulent stream, where the dredge was wrecked during a flood, and was not repaired. Fig. 1 is a sketch-map of California, showing gold-dredging areas. It is not my intention to narrate in detail the history of the early failures in gold-dredging, and the various steps in the development of the modern boat, but merely to touch upon this in a general way, and to call attention to the wide difference in capacity and operating-cost between the first successful dredge, with an actual capacity of 600 cu. yd. per day-though its rated capacity was in excess of this-and the present modern dredge with 15-cu. ft. buckets, and an average capacity of 250,000 cu. .yd. per month. Even this enormous capacity has several times been exceeded on monthly runs. The first successful dredges

Mar 1, 1912

By John C. Osmond

One of the least known geologic regions in the U.S. is the area now called the Basin and Range Province. It is paradoxical that so little geologic information has been compiled for a province that has yielded billions of dollars worth of metals and is currently producing a small amount of oil. Regional stratigraphic studies of parts of this large territory have been published only recently, and regional structural interpretations of even parts of the province are rare in the literature. This, of course, does great injustice to the earliest workers: Gilbert, Russell, Le Conte, Spur, Louderback, and others, who recognized the area as distinctively different from the rest of North America. Their simplified picture of the structure of the ranges and the province as a whole is the groundwork for present understanding and has never been superseded. Since their early works, however, geologic data from the province has consisted largely of detailed reports of widely scattered mining districts. Each district has been described as though it were an island in an unknown sea.

Jan 3, 1960

By Robert T. Howard, Morris Cohen

THE purpose of this paper is to direct attention to the lower part of the austenite transformation diagram, or TTT curves, where considerable uncertainty still exists as to the blending of the bainite and martensite reactions. The dissimilarities between these two low temperature trans- formations have been summarized recently by Troiano and Greninger.1 Of particular importance to the present work is the fact that martensite formation, unlike bainite formation, is not suppressed by the fastest quenching rates attainable. However, most of the investigations in this direction have been concerned primarily with the start of the martensite transformation [(M,)] during cooling, rather than with the quantitative aspects of the subsequent reaction on either further cooling or isothermal holding. Several years ago, Cohen2 suggested a form of transformation diagram which reconciled, at least schematically, the isothermal characteristics of the bainite transformation with the insuppressible nature of the martensite transfoi mation. In essence, the diagram consisted of a family of horizontal lines (representing the progress of the austenite-martensite reaction during quenching) which were interrupted in point of time by the bainite family of C-curves extending down from higher temperatures. This picture received later support by metallographic3 and dilatmetric4,5 studies, but the techniques employed were not sufficiently critical to substantiate some of the details. Elmendorf6 and Grange and Steward7 have shown that the Greninger-Troiano metallographic techniques may be used not only for [M,] determinations, but for studying the course of further austenite decomposition. In fact, the latter investigators have observed the amount of martensite formed as a function of temperature below [M,] in fourteen commercial steels. In the present paper, the Greninger- Troiano technique has been combined with the lineal method of Howard and Cohen9 to provide a unique, quantitative treatment of the austenite-martensite reaction. Furthermore, isothermal transformations have been similarly measured on holding at temperatures above and below M,, thus permitting a fairly detailed presentation of the lower part of the conventional austenite transformation diagram. EXPERIMENTAL DETAILS Materials The steels, listed in Table I, were selected for study because they exhibit a satisfactory range of M, temperatures and have not received as much attention as the lower carbon grades. They were prepared as 30 lb induction furnace heats in the laboratories of the Vanadium-Alloys

Jan 1, 1947

By Lawrence K. Jetter, Robert F. Mehl

SOME advances have been made recently in the theory of the kinetics of precipitation from metallic solid solution despite the complexities of the problem, but there is surprisingly little quantitative information available on rates of precipitation with which to test present theory or upon which to build new theory.? Attempts to measure rates of precipitation have been beset with difficulties which originate both in the anomalies that attend the changes in the properties selected for measurement, as, for example, in electrical conductivity or mechanical properties, and also in the complexities in the structural changes in some systems, as in the aluminum-copper system. If the functional relationship between the quantity of precipitate and the value of the selected property is uncertain, measurements of that property are obviously of uncertain utility in determining absolute rates of precipitation. If the precipitating system passes through one or more transition stages, the interpretation of measured rates lacks definiteness; in such cases, it is necessary to measure the rate of reaction in each separate stage, if the rate measurements are to have any significance from the kinetic point of view.* These difficulties cannot be wholly avoided, for at least in some measure they are characteristic of the process of precipitation from solid solution, but they can be minimized both by the selection of a simple system and by the use of a method of measurement relatively free from anomalous behavior. The present paper reports dilatometric measurements on the rate of precipitation of silicon from the aluminum-rich solid solution in the aluminum-silicon system-a study that approaches the desiderata of simplicity. The aluminum-silicon system offers advantages from these points of view: there are no known anomalies in the property changes accompanying precipitation ;2,3,4 there are no known transition stages; the precipitate is an element, not a compound, and both matrix and precipitate are cubic, and while the structures are not identical (the solid solution is face-centered cubic and the precipitate is diamond cubic), the system at least approaches the ideal case of a crystal precipitating from a matrix of the same crystal type-the ideal case which Becker5 assumed in treating the precipitation process theoretically. The dilatometric method, while not free from disturbing effects, as the subsequent dis-

Jan 1, 1942

By Theodore B. Comstock

The existing topographical features of the United States present many points of interest to the student of dynamical geology, but there is, perhaps, no subject which offers a more promising field for investigation than the relations between the geological structure and the mineralogical characteristics of the principal mining districts. There are seven prominent culminating points in the relief of North America, each one of which can be used as a type of the physical features of all the others. Again, if we divide these seven elevated districts into two sets, we shall discover a still more striking parallelism between the individual members of each group. But the most remarkable revelation is the fact that each one of these points is more or less closely the centre of an area of economically important mineral resources. It is interesting to note in this connection that six of these mineral tracts lie mainly within the borders of the United States, three of them being almost wholly in our territory. For

Jan 1, 1883

By Cyrus Garnsey

NECESSITY FOR PRICE FIXING DURING the latter part of 1916 and the early months of 1917, clue to war activities, there was a threatened shortage of coal which resulted in panic among consumers and a rush to obtain coal at once at any price. As a result of this insistent demand for immediate delivery, prices were bid up by the consumers to unprecedented heights; spot coal which had previously been selling at from $1.50 to 82 per ton was bid up to $5, $6, and, in exceptional cases, as high as $7.50 or more per ton. Then when the April, 1917, contract period arrived, contracts could be made only at prices ranging from $3 up to $5 and $6 per ton for the year's delivery. This condition caused such a demoralization of the business, and so much complaint, that some action to regulate prices was considered essential by the National Administration. LANE-PEABODY AGREEMENT In May, 1917, a committee under the chairmanship of F. S. Peabody, of Chicago, was appointed by the Council of National Defense, through Mr. Lane, to consider the whole question of bituminous coal. This committee, with the Secretary of the Interior, Mr. Lane, after numerous meetings and long negotiations with the operators throughout the country, announced on June 29 an agreement between the Committee and the producers, fixing a tentative maximum price for bituminous coal throughout the country at $3 per net ton f.o.b. mines, to which was added 25 c. for selling commission to wholesalers. This plan was based on the idea of fixing a maximum price, high enough to greatly-stimulate production, with the expectation that the laws of supply and demand would, with ample production, operate to maintain fair and just prices for coal throughout the country.

Jan 9, 1918

By J. D. Miller Discussion by N. P. Finkelstein, M. C. Fuerstenau

The point designating 10 -4 nole/per liter sulfonate addition in Fig. 1 has been presented incorrectly. This figure, with the corrected scale, is shown at right. N. P. Finkelstein (National Institute for Metallurgy, Johannesburg, South Africa) - The qualitative conclusion the authors of this paper have reached in evaluating the influence of hydrocarbon chain length on collector effectiveness agrees with conclusions in several published reports. However, in two other

Jan 1, 1969

By N. A. D. Parlee, I. D. Shah

The solubilities of oxygen in liquid Ag-Au, Ag-Pt, and Ag-Pd alloys have been determined in the range of 940° to 1200°C at 1 atm pressure of oxygen using an improved Sieverts technique. The additions of gold (0 to 57 pct), platinum (0 to 27 pct), and palladium (0 to 22 pct) to liquid silver continuously decrease the solubility of oxygen in liquid silver. Activity coefficients and interaction coefficients of oxygen in these alloys and have been calculated. The interaction coefficientscan be described by the following equations: Approximate second-order interaction coefficients (pM have been calculated. The contribution of the product, pMxNM, to In yo only becomes significant at high alloy concentrations. RECENTLY several investigators1"3 have redeter-mined the solubility of oxygen in liquid silver. In general the recent findings1" for Po, = 1 atm are in good agreement with the equation:4 log %O = 695.4/T + 1.086 [1] It is established1, 2 that the solubility of oxygen follows Sieverts' law reasonably well, at least up to 1 atm partial pressure of oxygen. It should be noted that a very slight deviation from Sieverts' law has been reported by Lupis and Elliott.3 Only recently has the solubility of oxygen in Ag-X binary liquid systems received much attention, and only the Ag-Cu, Ag-Au, Ag-Pt, and Ag-Pd systems have been studied. Par lee, Sacris, and zoellners reported that the solubility of oxygen in liquid silver increases progressively with the small additions of copper (0 to 0.5 pct) up to the point where the copper oxide phase appears. Lupis and ~lliott~ have reported that the solubilities of oxygen in liquid silver decrease progressively with the additions of gold, platinum, and palladium. However, their investigation was limited to 0 to 5 pct of these alloying elements, a range too limited to satisfy the requirements of the research program of this laboratory, where the solubilities of oxygen in the range of 0 to 30 pct were required for the calculation of chemical diffusion coefficients of oxygen in these alloys. The present paper deals only with the solubilities of oxygen in these alloys while another paper will deal with the diffusion of oxygen in these alloys. EXPERIMENTAL METHOD A Sieverts technique was employed which involved an improved design of the reaction tube, Fig. 1, as described briefly in a previous communication.4 Liquid melts (70 to 100 g) were held in Norton Alun-dum crucibles. The induction furnace used had a maximum output of 2.5 kw with very fine control. This induction system had excellent stability and the final equilibrium temperatures measured by calibrated Pt-Pt, 10 pct Rh thermocouples are believed to be within ±2C. These thermocouples were checked against the melting point of pure gold wire, and the results agreed with standard tables (±l°C). Each run involved a careful sequence of operations. The sample was heated to and held at about 900°C in vacuum for 3 to 4 hr with the thermocouple in a retracted position. After melting, the melts were usually exposed to a small amount of oxygen (0.5 to 2.0 cu cm) and then degassed slowly for 1 to 2 min to remove any oxidizable volatile impurities such as carbon and sulfur as CO, CO2, SO2, and SO forth. Argon gas was then allowed to enter the system. The protection tube containing the thermocouple was then

Jan 1, 1969

By H. E. Cook

The Ising model for the internal energy of a binary alloy has been used to obtain a general equation for the critical resolved shear stress of partially ordered crystals. The equation expresses the stress in terms of the Warren "alphas " and can be used to estimate the variation in strength with order without the assumption, present in the original formulation of this problem in terms of domain size, that order is complete within each domain and that the domains are of ungorm size and shape. In addition, it is the general equation, according to the Ising model, for strengthening by short-range order. Two applications of the equation are considered: One is an estimate of the variation in strength of CkAu with long-range order. The other is an estimate of the variation in strength of FeCo with quench temperature. Reasonable agreement is found with the variations reported in the literature. When the internal energy of an alloy crystal depends upon the distribution of solute, the strength of the crystal will also depend upon it because a portion of the applied stress for plastic deformation will be: where V is the volume of the crystal and E(E) is the energy change associated with the solute redistribution caused by the plastic strain, E. We expect T to equal zero for a crystal having a random arrangement of solute because the arrangement would remain random after plastic deformation. Likewise, we expect it to equal zero when the crystal is perfectly ordered because the motion of paired dislocations found in such crystals does not disrupt order. However, when short-range order exists or when long-range order is incomplete, plastic deformation will decrease the amount of order and additional work, proportional to the ordering energy, will be expended. Fisher' estimated T for crystals having short-range order by assuming an interaction energy between neighboring atoms and estimating the change in the number of unlike neighbors as a dislocation moved through the crystal. (His analysis was limited and several workers2"6 have since given more complete ones.) Fisher minimized the importance of a strengthening mechanism of this type for paired dislocations in a structure having long-range order. ~ottrell,' however, pointed out that T could be appreciable for ordered crystals having antiphase domains. He attributed the strengthening to the increase in surface energy of the domains as they were cut by paired dislocations. Ardley,' in his test of Cottrell's theory, found that r for Cu3Au crystals obeyed the equation: for 1 > t where 1 is the domain size, t is the domain wall thickness, and y is the surface energy of an antiphase boundary. His experiments represent the classic confirmation of the strengthening mechanism proposed by Cottrell. However, the assumptions involved in using Cottrell's theory are valid only for large domain size in CU~AU,~"~ i.e., when Eq. [2] reduces to: For small domains, ~linn~ has questioned Ardley's assumption that order was complete, and, indeed, Stoloff and ~avies" fpnd it incomplete until a size of approximately lOOA was reached. Even when the order within a domain is complete, it is not obvious how one determines the appropriate value for I in a structure where domains vary in size and are irregularly shaped. The purpose of this paper is to estimate T without restrictions upon the degree of order and domain shape. Our major assumption will be the use of a generalization of the model proposed by Bethe" (the Ising model) for the internal energy. This will in fact allow us to combine the theories for strengthening by short-range order and by antiphase domains into a single, general formalism. We will use the results to estimate the variation in strength of Cu3Au crystals with long-range order8 and the variation in flow stress of FeCo crystals with quench temperature.12'13 INTERNAL ENERGY For simplicity, we restrict our considerations to those binary solid solutions which can be described as an arrangement of atoms on a Bravais lattice. An atom site will be indexed by three numbers (PI, pz, p3) determined by the vector: from the origin fixed at atom (0, 0, 0) to the atom site where a', an, and a, are the lattice translation vectors. We write: For the energy of the crystal where pi(p) is the probability (either zero or one) of finding an atom of type i (i = 1, 2) at site (p), which is shorthand for (pl, pz, p3) and pj(p + r) is that for an atom of type j (j = 1, 2) at the site (p + r), which is shorthand for (pl + rl, The coupling parameter, resents the energy associated with the pair Pi(p), Pj(p + r). The crystal is assumed large enough so that surface effects can be neglected; therefore, trans-lational and inversion symmetry require the coupling parameters to obey the relations

Jan 1, 1969