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The annual report of the Secretary of the Southern California Local Section for the year ending May, 1919, says that the Section was called upon to give all the assistance possible for the different Liberty Loan drives, for the Red Cross drives and not only in the canvass of our membership, but the canvass of all of the mining companies represented in this city. The committee on the Red Cross drive on which we were represented raised a larger proportion of the total amount than any other in the city. The subscriptions for Liberty Bonds from the members of our' Section that were credited to the Committee of the Joint Technical Societies exceeded in amount the subscription from the members of all the other technical societies combined. Members of our Section slid splendid and efficient work throughout the first half of the year at the Red Cross headquarters in this city, and under the leadership of A. B. W. Hodges and F. B. Close, systematized the work of handling the enormous quantity of material that passed through that organization. Mr. E. A. Montgomery directed the canvass of the mining companies of this city in the bond drives, and the Executive Committee did its part in solicitation among the mining engineers. The Section, together with the local sections of the American Chemical Society, American Institute of Architect, American Institute of Electrical Engineers, American Society of Civil Engineers, American Society of Mechanical Engineers, and the local Engineers and Architects Association, forms what is called the Joint Committee of the Technical Societies. of Los Angeles. The honor of having the first president of this combined organization of engineers was given to us with, the election of Mr. Seeley W. Mudd. Upon Mr. Mudd's entering the service, Mr. George A. Daman of the Electrical Engineers was elected to the position and served splendidly during the latter part of the year. It devolves upon this Section to be represented upon this Joint Committee by three members, and it is our duty to supply a speaker once in six weeks to address the engineers in attendance at the weekly luncheon. During the year not a few of the most prominent men of the engineering professions have spoken upon subjects of the greatest interest to us all. Had it not been for the organized team work in the engineering profession available through this Joint Committee, there would have undoubtedly been passed in the recent session of the legislature of this state a bill for licensing and registering all professional engineers in this state, which, in the opinion of your Executive Committee and a large proportion of the membership of this Section, would have fallen far short of either protecting the engineer or protecting the public from impostors. That the public is awakening to the importance of what our National Society represents in the profession of mining engineering can be well inferred from the increasing number of inquiries your Secretary receives regarding the reputation of mining engineers. The necessary qualifications which a membership in the Institute requires and the membership of an engineer in this National Organization is more and more a criterion as to the ability of an engineer who represents himself as such, to the general public.

Jan 9, 1919

By D. G. Westlake

NUMEROUS hydride habit planes in zirconium, Zircaloy-2, and Zircaloy-4 have been observed by various researchers and have been compiled by Louthan and Angerman.1 While only partial agreement exists on the identification of these habit planes, there is a growing consensus that a tensile stress applied on a polycrystalline rod during slow cooling will cause the hydride platelets to lie perpendicular to the tensile axis. walters2 agrees with Louthan and Angerman who reason that "The particular plane on which precipitation will occur is the plane that will result in the maximum relief of stress by precipitation of the low-density hydride." The experiment described below was initiated to test this hypothesis on a single crystal of zirconium. A single-crystalline tensile specimen of zone-refined zirconium, designated number 13 in a previous study,3 had a square cross section with one pair of parallel faces only 4 deg from the basal plane of the hcp structure. The tensile axis was about 86 deg from the (0001) pole, 14 deg from the (1010) pole, and 16 deg from the (1150) pole. The specimen was charged to 50 ppm H by allowing reaction with the correct amount of hydrogen at 1073°K, homogenizing at this temperature for 2 hr, and cooling in the furnace. Two- surface analysis revealed that hydride platelets had precipitated parallel to the three {1010} prism planes. The specimen was heated to 673°K, in air, for 16 hr to bring the hydrogen back into solid solution, and furnace-cooled to 573°K.* It was then stressed in ten- sion at 1.2 kg per sq mm. (This produced a resolved shear stress of 0.6 kg per sq mm for glide on the prism plane with the highest Schmid factor. A higher stress would have produced significant strain at this temperature because the critical resolved shear stress for prism-plane glide in this crystal was only 1.0 kg per sq mm at ambient temperature.) The poles of the three prism planes were at angles of 14, 46, and 74 deg to the tensile axis so that an applied stress would exert normal stresses on the three planes in the approximate ratios 10:5:1, respectively. As soon as the stress was applied, the sample was furnace-cooled to room temperature. It was ground on wet Sic paper and chemically polished in 50 parts HNO3, 50 parts water, and 7 parts HF before examination. The result of the experiment was negative; i.e., the three (1010) planes were of equal importance as hydride habit planes.* It must be admitted that the ex- periment is not entirely comparable to those performed by walters,2 Louthan,5 and Louthan and Marshall6 on polycrystalline materials. They have found that some critical stress (below the macroscopic yield stress) is required for stress-orienting the hydrides. The applied stress in the present experiment was, by necessity, smaller by an order of magnitude than the critical stresses they report for the various materials. If the critical stress was related to the microstructure, one might postulate that it should be decreased by increasing the degree of perfection of the metal lattice and by increasing the grain size. But the experiment above suggests that, for the extreme case of a zone-refined single crystal of zirconium, the critical stress lies above that which one can apply without introducing gross plastic strain as another variable.

Jan 1, 1967

By Meguru Nagamori

DURING the smelting of the sulfide ores of copper, nickel, and certain other metals, a matte phase is formed. For a better understanding of the physico-chemical properties of mattes, binary systems such as Cu-S, Ni-S, Fe-S, and so forth, should be studied, especially in the vicinity of liquid compounds such as Cu2S, Ni3S2, FeS, and so forth. These compounds are relatively stable in the solid state although they can exhibit appreciable deviations from stoichiometry. With small deviations from stoichiometry there are large changes in the activity of both sulfur and metal this is a characteristic of both solid and liquid sul-fides near the stoichiometric compositions. In the vicinityof molten Cu2S,1 for instance, the activity of sulfur increases about 100 times for a 0.012 increase in the mole fraction of sulfur and, correspondingly, the activity of copper decreases greatly. In this sens the minor deviations from stoichiometry should be carefully taken into account in studies of such metal-sulfur melts. Metal-sulfur melts may be considered to have properties intermediate between metallic solutions and molten salts, i.e., neither entirely metallic nor entirely ionic. The radius of the ion sZ- is 1.84 as compared with 1.04? for a single bond covalent s.2 It is therefore inferred that when the sulfur is more ionic its partial molar volume is larger, although metal-metal, metal-sulfur, and sulfur-sulfur interactions may bring about further complexities. Thus, it is to be expected that the molar volumes, which are derived from density-composition relations, will help in resolving the structure of the melts. In this study the maximum bubble pressure method with bubbling gases of H2, H2S, and Ar, .was employed to measure the density. EXPERIMENTAL Materials. Silver of 99.95 pct purity was melted in an alumina crucible and hydrogen gas was then bubbled through the liquid for the deoxidation. In preparation of Cu2S, electrolytic copper powder (>99.9 pct Cu) was mixed with precipitated sulfur and heated to 1200°C in an alumina crucible under a hydrogen atmosphere. Mixtures having the approximate compositions FeS and Ni3S2 were prepared by heating reagent grade electrolytic iron or reduced nickel powder with precipitated sulfur under a hydrogen atmosphere. The H2S gas was of 98.5 pct purity, the impurities being mostly CO2 and CS2 which hardly contaminate the melts. Apparatus. The crucible system is shown schematically in Fig. 1. To minimize the variation of melt composition during a density measurement, the apparatus was designed in such a way that either Ar, H2, H2S, or mixtures of these gases could be used as the bubbling gas. When the melt had a high partial pressure of sulfur, H2S gas was used. When the partial pressure of sulfur was so low that oxygen might dissolve in the melt, the use of H2 was preferred. In intermediate cases, argon or mixtures of H2-H2S were used. Density of Dibutylphtalate. Dibutylphtalate was used as the manometer fluid. Relative to distilled water, the density of the dibutylphtalate, pdib g per cc, was measured and found to be: pdib (25°C) = 1.046 i 0.002. With the use of the temperature coefficient reported by Kemppinen and Gokcen,3 the following value was

Jan 1, 1970

By P. Dayal, L. S. Darken

THE migration of carbon in austenite under the influence of an electric current has been observed qualitatively several times.14 Lebedev and Guterman5 recently have reported quantitative measurements; their method consisted of welding a low-carbon to a high-carbon wire, passing current, and later estimating the carbon distribution metal-lographically. We believe the method reported in this paper is superior in principle since electrolytic migration and ordinary diffusion are not necessarily coupled as in the weld method; also for the first time the extent of migration is determined by combustion analysis for carbon. A uniform tubular specimen (S.A.E. 1045 or 1095) was mounted as illustrated in the figures. the whole assembly being in an atmosphere of purified nitrogen. Direct current (129 to 226 amp at 0.65 to 1.0 v) served as source both of heat and of potential gradient for carbon migration. The duration of experiment was 7.5 to 12 hr, during which time the temperature was controlled (±10°C) manually. The experimental conditions are indicated in the first five columns of table I. With this experimental arrangement, the temperature initially has a maximum value at the central plane. Also, in this vicinity (by virtue of the symmetry), the carbon entering any volume element is equal in quantity to that leaving; the loss or accumulation of carbon occurs near the electrodes since the carbon moves uniformly near the center and is "frozen" at the cold ends. Hence, providing the time of experiment is not sufficiently long to seriously influence the conditions at the central plane, carbon crosses this plane only under the influence of the electrical potential gradient and not under the influence of temperature or concentration gradient. The amount of carbon which has crossed this plane was determined by combustion analysis of the two halves of the specimen. The results of these analyses are shown in the sixth and seventh columns of table I. It will be noted that substantial amounts of carbon migrated from the anode portion to the cathode portion (except at 920°C, which temperature was too low to exhibit the effect in the allotted time). In spite of precau-tions taken, considerable decarburization occurred as may be seen by comparing cols. 8 and 5. In three cases (indicated by asterisks in table I) the specimen was ground on one side, polished, and examined metallographically before analysis. One specimen was normalized and re-examined. Micrographs of selected areas in specimens 4 and 6 are shown in figs. 1 and 2, respectively. Evidence of carbon migration from the anode toward the cathode is quite apparent. Fig. 2 shows abundant graphite as well as cementite in a region near the cathode. The temperature of this zone is estimated at about 800°C. In fig. 1, particularly in the micrograph on the extreme right (the right side of which is of unaltered carbon content), there is evidence of slight depletion of carbon in the immediate vicinity of the cathode as contrasted to the general increase in carbon of the cathode half of the specimen. Although this may be attributed in part to decarbur-ization, it is believed that it is occasioned also by thermal diffusion—migration (of carbon) from a cool to a hot zone4—a phenomenon superimposed upon the electrical migration. Evidence of carbon migration was visible particu-larly during the course of the high-temperature,

Jan 1, 1951

By M. W. Clegg

The application of the Laplace transformation to problems in the flow of compressible fluids in porous media has provided a large number of exact solutions. For plane radial flow, however, these solutions are either complex integrals or infinite series and are of little value to the field engineer. In the case of production at constant well pressure, the available approximate solutions me valid for large times only. In this paper it is shown that an approximate inversion formula for the Laplace transform, developed for the solution of viscoelastic problems, is applicable to radial flow problems and provides simple analytical solutions to constant terminal pressure problems. The method may be used to obtain approximate solutions to many problems, including media with radial permeability discontinuities, multi-layer formations and pressure buildup in wells after shut-in. The results are compared with the few available computer solutions as well as the large time solutions, and it is shown that this approximate method greatly extends the time interval over which a simple analytical solution is acceptable. INTRODUCTION The study of transient problems in the flow of fluids through porous media has benefited greatly from the application of transform methods. The use of the Laplace transformation for solving parabolic equations has been widely discussed in the field of heat conduction and diffusion as well as in the petroleum literature. Removal of the time variable with the Laplace transformation generally reduces the problem to a boundary value problem which may be solved by standard techniques. A much more formidable problem then faces the engineer, however, for frequently the transform does not possess a simple inverse. The result is that the general inversion integral must be used and this leads to either an infinite integral or an infinite series, both of which are difficult to handle from a computational standpoint. Asymptotic approximations for the inverse have been known for some time and these yield approximate inverse functions that are valid for very large or very small times — but frequently the times of interest lie somewhere between these two extremes. Therefore, some acceptable approximation valid over a larger interval of time is desirable. During the past few years a number of methods for achieving this have been developed and some of these are discussed briefly in this paper. The relative merits of the various methods are not evaluated here, but some general conclusions reached by other authors are given. One of these methods has been applied to problems associated with the radial flow of compressible liquids to producing wells. In the case of production at constant well pressure, the method leads to simple analytical solutions for a number of standard problems; e.g., homogeneous formation, permeability discontinuities, pressure buildup. These solutions greatly extend the range of validity of the asymptotic ones (valid for large times only) and should be of value in studying the behavior of wells producing under constant pressure conditions. METHOD FOR THE APPROXIMATE INVERSION OF LAPLACE TRANSFORMS Much of the work that has been done on the approximate inversion of Laplace transforms has originated in viscoelastic problems. Apart from the asymptotic approximations,1 one of the first approximate methods was due to Alfrey.2 If (s) is the Laplace transform of f(t) defined by

By A. Long, A. Silverman, J. L. Kulp

Garth Crosby has written an excellent geologic description of the deposits surrounding the Gem stocks in the Coeur d'Alene district. The ore deposits in the area of the Gem stocks may hold the key to the age and mineralization history of the entire Coeur d'Alene district. A recent isotopic study10 of the Coeur d'Alene district in this laboratory illustrates that a classical geologic interpretation of these deposits, with its implications for the whole district, may lead to erroneous conclusions. For this reason it seems pertinent to submit a summary of these results and an interpretation of the mineralizing history of the Coeur d'Alene districts. Pitchblende from the Sunshine mine has been dated as 1100-1200 million years (m.y.) by Kerr and Kulp,11 and Eckelmann and Kulp.12 This pitchblende is known to predate the major sulphide introduction in the Sunshine mine, but it clearly follows the metamorphism and folding of the Belt Series. Recently, Goldich (personal communication) dated sericite from the Belt rocks as 1200 m.y. by the potassium-argon method. This date establishes a minimum Belt age if the sericite is of metamorphic origin and a maximum age if detrital. The Belt Series, therefore, is not latest Precambrian. Lead isotope ratios of galenas have been measured and model ages calculated by Bate, et all3 for the Sunshine mine, Farquhar and Cummingl4 or the Bunker Hill and Sullivan mine, and Cannonl6,18 for a few other deposits in the district. Galenas from similar deposits in Southern British Columbia have been measured by Bate, et al,23 Farquhar and Gumming,11 and Wanless and Leech." The new work in this laboratory includes leads from ten widely scattered mines north and south of the Osburn fault, and through a vertical distance of over 5000 ft (Star mine). Included in this group are the Hercules, Sunset, and Mountain Goat mines, which are adjacent to the Gem stocks. In addition, galenas from stringers which cut the Gem stocks in the Success and Sunrise mines and the Hercules hanging wall dike in the lower western portion of the Hercules mine, were included in the study. All of the above leads, except one, give model ages of 1300-1400 m.y. for the time of segregation from the parent material. The concordance of the common lead and U-Pb ages, the great horizontal and vertical uniformity of the lead ratios, the sulphur ratios of two Sunshine mine galenas and three galenas from the Edith, Page, and Hercules mines indicating average crustal sulphur, and the U23/Pb204 ratio inferred for the original lead environment, indicate that the entire mineralization of the Coeur d'Alene-British Columbia base metal belt was derived from a deep source and emplaced in the Precambrian. One sample of galena from sulphide stringers cutting the North Gem stock at the Sunrise Prospect mine gave a modern (i.e., Tertiary) lead ratio. This mine is located at the northern tip of the stock. The presence of modern lead suggests mobilization of some rock lead during the intrusion of the Gem stocks and their outliers. Larsen et al.l8 have dated the Gem stocks as Tertiary by the lead alpha method. If Coeur d'Alene mineralization was genetically related to Tertiary magma formation and intrusion

Jan 1, 1961

By J. A. Snyder, W. L. Finlay

G. Edmunds—Solid solubility is considered to be of either the interstitial or the substitutional type. Is it possible, in a binary alloy as the simplest case, that some of the solute atoms are present in the normal lattice sites (substitutionally or filling lattice vacancies) while simultaneously others are in interstitial positionss One might even ask whether a distribution of the two types may be the normal situation. H. M. Meyer—Metastable states of interstitial atoms occupying vacant lattice sites possibly occur as well as of substitutional atoms squeezed in between regular matrix positions. However (as we know since Hume-Rothery), the solute atoms choose between the two kinds of solutions; consequently, every solute will be unequivocally either substitutional or interstitial in the equilibrium state of the solid solution. M. Balicki—In view of the fact that the authors apparently correlate the analysis of the alloys at the ingot stage with the properties exhibited at the testing stage, I would like to ask whether this is a fully justifiable procedure. In other words, how good are their determinations of solute concentration for correlating them with the mechanical properties. The answer to this question may explain some of the divergencies. Assuming good enough homogenization of the samples and exact determination of mechanical properties the position of the plotted experimental points will depend solely upon the accuracy of composition determination. If this is not accurate, say due to loss or pickup of elements during processing from the ingot to the testing stage, or due to a systematic error in the method employed for obtaining solute concentration data, the points will deviate from their true position and may align themselves along a different curve than the one expected. H. V. Kinsey—We have been studying the creep-rupture properties of titanium-base alloys at 1000°F. In the course of this work, anomalies in behavior of the alloys that would suggest that the material under test was becoming stronger as the test progressed have been observed. If this was so, the most likely explanation that we could think of was that the test bars were absorbing oxygen and nitrogen from the air during the test and were thereby becoming strengthened. In an attempt to determine the strengthening effect of absorbed oxygen and nitrogen the following experiment was conducted. A length of cold-rolled titanium was supplied by the E. I. du Pont Co. Two test bars, having a 1/4 in. diam gauge length, were prepared from this material. One bar was tested in the as-received condition. The second bar was heated in air at 1550°F for 100 hr and subsequently air cooled prior to testing. A testing temperature of 1000°F was employed. The results of these tests are tabulated in table 11. In the author's opinion, is it reasonable to assume that the bar that was exposed to air at 1550°F for 100 hr was stronger because it absorbed oxygen and nitrogen from the air during this heat treatment? W. L. Finlay (authors' reply)—Direct experimental evidence for or against Mr. Edmunds' interesting suggestion will probably never be available. It seems possible, however, that mixed interstitial-substitutional solid solution might well occur with interstitial elements. The less likely possibility of interstitial solution of a normally substitutional element like copper in aluminum was recently discussed at length by the

Jan 1, 1951

By P. K. Koh

Isothermal salt bath annealing of 0.014-in. thick 3 pct Si-Fe sheet was conducted at temperatures ranging from 927" to 1260°C in order to investigate the grain-growth behavior. Within the temperature range studied normal grain growth did not take place; instead nucleated grain growth prevailed. The nucleation frequency was found to increase with the annealing temperature, with corresponding decrease in grain diameter of ultimate secondaries after long-time annealing. Large secondaries grown by low-temperature isothermal annealing are essentially of (110)[001] orientation, and the (110)[001] texture is strong. The relatively small secondaries grown by high-temperature isothermal annealing also have orientations near (110)[001] as an average but widely scattered; thus the amount of (110)[001] texture is found to decxease with isothermal annealing temperature. Grain growth and texture development at various annealing temperatures can be described by families of sigmoidal curves with the time axis. ThE cube-on-edge (110)[001] texture and predominating large secondaries in fully annealed 3 pct Si-Fe are customarily produced by a 1100°C annealing of a primary recrystallized sheet. On annealing the primary recrystallized sheet above the temperature at which secondary recrystalliza-tion starts May and turnbull' have demonstrated that secondary grains decrease in size as the temperature is increased. The phenomenon was attributed to a decrease in the (G/N) ratio where G is the growth rate of secondary grains and N is their nucleation frequency. In addition, the growth of grains in orientations rather far from (110) [0011 occurred. The present investigation is devoted to detailed rate studies of the same phenomenon. Mi-crostructure, magnetic anisotropy, and texture data were obtained on strips of 3 pct Si-Fe isothermally annealed for various lengths of time in a BaC12 salt bath at temperatures ranging from 927' to 1260°C. The texture results are reported elsewhere.2 EXPERIMENTAL PROCEDURE Commercial 0.014-in. cold-rolled silicon-iron strip (3.16 pct Si), prepared by two stages of cold rolling with an intermediate short anneal, was given a decarburizing 3-min anneal at 800°C. Metallo- graphic studies indicated complete recrystallization. In order to provide a protective atmosphere and to obtain a rapid rise to an elevated temperature, a BaC12 and NaCl fused salt bath was used to heat samples isothermally at temperatures from 927" to 1260°C for various lengths of time. Torque magnetometer measurements were made on 1-in.-diam disc specimens before and after annealing, since magnetic torque curves supply information on textures and texture changes. Surface layers of the strip samples were polished and etched to reveal the grain structure. The diameters of grains were measured from micrographs at X100. The average value of diameters of matrix grains was established. Individual grains in the micrograph were cut out separately along grain boundaries. These grains were classified either as matrix grains or growth grains. The percent weight of growth grains in the cut-out patterns was reported as percent growth. Manv of the individual grains in the annealed samples were large enough to be X-rayed with a 5-mil beam for Lauegrams. Complete (110) pole figures were obtained for the primary recrystallized structure and short-time annealed structure with CoKa radiation at 30 kv in the back-reflection range, such as (220) for (110) poles, as described recently by Newkirk and ~ruce.~ Both the X-ray optics and the technique for pole figure differed slightly from those adapted previously.4

Jan 1, 1960

By N. S. Bornstein, M. A. DeCrescente

ThE nickel and cobalt base superalloys employed in gas turbine engines under some conditions' oxidize at an accelerated rate when exposed at elevated temperatures to atmospheres containing minor quantities of sea salt. It is generally agreed by investigators in the field that the major steps comprising this phenomena of accelerated oxidation, also called hot corrosion or more commonly, sulfidation, are a) a slag composed primarily of Na2S04 is formed on turbine components, b) the protective oxide scale is rendered ineffectual, c) the slag reacts with. the substrate to form metal sulfides, and d) the substrate is rapidly oxidized. Sodium sulfate, a minor constituent of sea salt, is formed within the gas turbine engine from the reactions between NaC1, the major constituent of sea salt, and the oxides of sulfur.' Depending upon concentration, engine compression ratio, and temperature, the Na2S04 will be present in the gaseous or condensed state. It has been determined that in order for sulfi-dation to occur the Na2S04 must be present in the condensed state.' Although a number of sulfidation mechanisms have been postulated, there is no consistent explanation of oxide scale breakdown and subsequent catastrophic oxidation. Some investigators believe that after oxide scale breakdown, the Na2SO4 reacts with the substrate to form lower-valent sulfur compounds. The accelerated rate of oxidation is due to oxidation of a nickel-sulfide phase." Other investigators believe that sulfur from the fused salt reacts with chromium in the alloy to form chromium-rich sulfides; thereby depleting the alloy of an element which imparts oxidation resistance.3,4 This publication will demonstrate that the accelerated rate of oxidation associated with sul-fidation is due to interactions between Na20, a con-stituent of NazSO.,, ancl the substrate. The aim of this study was to separate and determine the effect of compounds of sulfur and sodium on the oxidation kinetics of various nickel-base superalloys, in order to elucidate the sulfidation mechanism. The work reported herein is sponsored in part by the Naval Ship and Development Center-Investigation of EXPERIMENTAL PROCEDURE The nickel base alloys B-1900, U-700, and Waspaloy were chosen for this study. The nominal compositions are presented in Table I. The specimens, approximately 1 in. by 1 in. by 0.060 in. received in the "as cast" condition were polished with 600 grit emery, washed, and rinsed with acetone immediately prior to oxidation experiments. Sulfida-tion attack was duplicated in the laboratory by apply-ing a saturated aqueous solution of Na2S04 onto the al loy substrate and subsequently exposing the specimens in oxygen at elevated temperature. The method of Na2S04 application is described elsewhere in detail.6 In another set of experiments the affected substrate microstructure associated with sulfidation was reproduced free of the normal oxide scale, by reacting and diffusing elemental sulfur into the alloy. The experimental procedure is also described elsewhere in detail. All oxidation studies were performed using an Ainsworth thermobalance type RV-AU-1, which is readable to 0.01 mg and is reproducible to ±0.03 mg. The specimens, introduced into a heated furnace, were exposed in the temperature range 800" to 1000°C

Jan 1, 1970

By Gerald C. Mathis

FERGUS County, Mont., shown in Fig. 1, is known for its once famous gold mines near the old towns of Gilt Edge, Maiden, and Kendall. But at Heath, a small farming community near the foothills of the Snowy Mountains, thousands of tons of gypsum have been mined since 1916. The value of the gold taken from the mines of Fergus County runs into millions of dollars; the value of the products made from the gypsum of the Heath mine is also in the millions. The gypsum mine will continue to produce for many years, while the gold mines are closed today. The Heath gypsum mine was developed by the Northwest Gypsum Co. in 1916. The products of the small mill built by this company were plaster, agricultural gypsum, and raw gypsum for cement manufacturing. The United States Gypsum Co. prospected the adjacent property in 1916 and 1917 by means of two adits and some exploration drill holes. During World War I, the company abandoned operations at Heath, but again became active in this area in 1928 hen it purchased all the property of the Northwest Gypsum Co. A long range program of expansion was begun with the building of a block plant and the purchase of additional land and mineral rights. A modern wall board plant was built in 1936. When the old wooden mill purchased from the Northwest Gypsum Co. burned in 1937, an all-metal calcining plant located at Blue Rapids, Kansas, was dismantled, moved to Heath, and erected on the site of the mill. In August 1951 a new mine was opened 3000 ft north of the mill. Rock is conveyed from the mine to the mill by an 18-in. belt conveyor. The Heath gypsum deposit lies at the base of the Ellis formation of Jurassic Age. The Ellis at Heath lies unconformably on the black fissle shale of the Heath formation of the Big Snowy Group, which is Mississippian in age. The strike of the gypsum bed is N45°E and the dip approximately 3" NW; the regional strike and dip of the area. The gypsum lies in a series of six layers separated from each other by thin seams of shale. The lower layer is composed of' gypsum and shale intermingled and is not of commercial grade. The upper five layers are high in purity, but only the middle four layers are mined on the advance, as the top layer is left for roof support. This top layer is mined on retreating operations at the same time the pillars are robbed. Total thickness of the gypsum layers varies from 12 to 14 ft. Fig. 2 shows the average thickness and arrangement of the layers. Mining Methods The mine was originally developed by driving an adit into the gypsum horizon. The Northwest Gypsum Co. mined in the top four layers, the top layer being split, leaving about 12 in. for roof support. A modified room and pillar method was used: entries were 15 ft wide and rooms varied between 20 and 30 ft and were turned on 90" from the entries. Crosscuts between the rooms left pillars from 10 to 20 ft square. The rock was loaded by hand into 1-ton mine cars and pulled to a central gathering point by mules; from the gathering point, mules or horses were used to pull the string of cars to the mill tipple. This method was continued by the United States Gypsum Co. from 1928 to 1937.

Jan 1, 1954

By W. A. Backofen, D. Lee

Titanium of commercial purity (RC-70) and two all-a (hcp) alloys (4Al-1/4O2 and 5Al-2.5Sn) were tested in sheet form under conditions of combined-stress loading. Plane-strain compression and plane -strain tension together with uniaxial compression and tension provided information for constructing the tension-tension and compression-compression quadvants of the plane-stress yield locus. Coordinate values were obtained from yield-strength measurements; the slope at each point was based on a plastic-strain ratio. The materials represented a wide range of plastic anisotropy, which was reflected in correspondingly varied departures of the yield locus from that for iso-tropy. The tension-tension and compression-compression quadrants were not identical. If the uniaxial yield strength is insensitive to direction and the sign of the applied stress, the Mises or perhaps the Tresca criterion is adequate for predicting the onset of yielding under combined-stress loading. The prediction is not so straightforward in plastically anisotropic material. Depending upon details of texture, combined-stress yielding resistance may be substantially different from that indicated by the usual criteria.' However. a continuum theory of yielding under such conditions is available for reasonably direct application.2,3 Whether or not it can be used successfully must, of course, depend upon how closely the conditions of the theory are satisfied in the material in question. In its present form the theory contains no provision for Bauschinger-type effects, nor does it allow for the consequences that might grow out of deformation by more than one mechanism, e.g., by slip and twinning.4 With those limitations, more importance must be attached to experimental information about the yield surface for anisotropic materials. Studies of the yield surface have generally been confined to states of plane stress (tension-tension and tension-compression) established in thin-wall tubes by externally applied forces and internal pressure. That approach would be entirely suitable for anisotropic materials if they were available in tube form or in sufficient bulk to be machined into test specimens. 6-9 It would not serve for the textured and anisotropic sheets of much current engineering interest, unless sheet could be formed into high-pressure tubing without structural change. Since there would seem to be little chance of the latter, practical alternatives are needed. One such alternative is the subject of this paper. It involves the use of a few selected but relatively simple uniaxial loading tests on sheet specimens. The underlying idea is presented here with some details relating to application and a few results bearing on how well it has worked. THE BASIS OF TESTING Conventional Measurements. Yielding for a general case of anisotropy is described by the plane-stress locus in Fig. 1. Reference directions in the sheet specimen are related to the stress coordinates as shown with the insert: x is the rolling direction, y the transverse direction, and z the through-thickness direction. The four reference-direction yield strengths (t, tension; c, compression), Xt, Xc, Yt, and Yc, are all different. Nine paths that can be followed in uniaxial loading experiments are identified. Paths 1, 2, 3, and 4 represent conventional tension and compression testing to establish Xt, Yt,.Xc, and Yc. Useful information also comes from the ratio of the transverse plastic-strain components associated with yielding and flow in conventional tension or compression. A condition to be satisfied in locus construction is that the plastic-strain vector be everywhere normal to the locus.10 The projection of the vector which would

Jan 1, 1967

By H. I. Aaronson, C. Laird

Cold rolling by 50 pct a A1-4 pct Cu alloy containing many 0' plates has been found to accelerate markedly the transformation of 8' to 0 upon further aging. Although the basic mechanism of this transformation remains unchanged by plastic deformation, the nuclea-tion kinetics of 8 become appreciably more rapid and also less dependent upon temperature. Particularly at lower aging temperatures, rounded idiomorphs replace several faceted rnorphologfes. The rates of growth of 9 idiomorphs in deformed specimens aged at 300°C are appreciably more rapid than simple volume diffusion control allows. This observation is shown to be explained by an excess vacancy, rather than by a dislocation Piping mechanism of growth. ThE rather complex phenomenology of the 8' —8 transformation in Al-Cu alloys has been recently elucidated in considerable detail by means of transmission electron microscopy.'-4 This technique was also employed in the present investigation in order to examine the effects of plastic deformation upon the transformation of 8' to 8. The mechanism of the transformation in undeformed Al-Cu alloys has been established as the following sequence of events.1"4 The first step is the nucleation of 9 at (Y:8' boundaries. Nucleation of a 0 crystal takes place, however, at only a very small proportion of the 8' plates present. Each 0 crystal simultaneously consumes the host 8' plate and the a! in the immediate vicinity, with growth into a being the rate-controlling process. The remaining 8' plates are then dissolved as they fall under the concentration shadow of the growing 8 crystals. The evidence on the effects of plastic deformation upon these processes is intriguing, but much less detailed. The careful X-ray studies of Graf and Guinier have shown that the aging times required to form detectable amounts of 8' and 8 are reduced by prior cold working. Thomas and Nutting confirmed these results by replication electron microscopy. Nile-shwar,* on the other hand, reported that creep deformation decreases the rate of formation of 0. While this difference may have been caused by the use of concurrent rather than successive deformation and ag- ing, the X-ray technique which he used was able to monitor only the 0 phase. It is thus possible that the times needed to form 8' were increased moreg than the kinetics of 8' — 8 transformation were accelerated. At 90 pct deformation by cold rolling, Graf and Guinier found that the usual 0' —0 8 sequence is reversed: 0 forms first. von Heimendahl 10 confirmed this result with transmission electron microscopy. Pollard and Nutting, 11 and more recently Driver and Barrand, 9 having used the same technique, report that 9 also forms first during creep deformation. In the present study, the maximum amount of deformation was limited to 50 pct reduction by cold rolling in order to insure that 8 formed principally by the decomposition of . I) EXPERIMENTAL PROCEDURES This investigation was conducted on an Al- 3.93 pct Cu alloy, prepared as previously described. 4 Morphological and crystallographic effects of plastic deformation were studied in specimens annealed 6 hr at 548°C, quenched, and then aged for either 3 or 8 hr at 250°C to form large numbers of 0' plates. After cold rolling to a 50 pct reduction in thickness, the

Jan 1, 1969

By J. G. Y. Chow, S. B. McRickard

The tensi1e properties of Ferrovac iron have been studied from 4° to 300°K. The stress required for macroscopic yielding was found to he constant below approximately 50°K. The effect of mechanical twinning on this low -temperature stress plateau was investigated. The onset of twinning occurs in this iron between 130° and 150°K and depending on its previous thermal history the twinning-stress curue may drop below or remain above the vield-stress curves as the temperature is lowered. Twinning has been shown to initiate slip in quenclzed iron at low temperatures. In no instances, however, did the onset of twinning alter the continuity of the yield stress -tempwature curve. Our data shows that carbon inhibits twinning and slip at low tem-peratures. This observation nay be used to explain the ductile-to-brittle transition in iron. The effect of fast neutron irradiation on yielding and embrittlement in iron and Fe-C alloys is offered as supporting evidence for this viewpoint. THE mode of yielding in iron at low temperatures was studied in an attempt to find an expression based on a single mechanism to describe the thermal dependence of the yield stress of iron. There are two types of inflections observed in the variation of the yield stress with temperature in iron and Fe-C alloys. The first is associated with ductile behavior and consists of a region extending 50" to 100°K above absolute zero in which the yield stress is independent of temperature. The second is observed in more brittle materials such as Fe-C alloys and irradiated iron and consists of an abrupt discontinuity in the yield curve as the temperature is lowered through a ductile-to-brittle transition point. The temperature dependence of the yield stress for iron with four grain diameters as found in this study is shown in Fig. 1. To varying degrees all the curves appear to flatten or approach an asymptotic value as the temperature is lowered below 50°K. Several other investigators1,2 have observed a plateau in the yield stress of iron and steel at low temperatures and in 1956 Louat3 presented a theory which contained an explanation for this behavior. In a subsequent exchange with Erickson and Low4'5 who attributed the plateau to the onset of mechanical twinning Louat8 showed that twinning first occurs in iron and steel tested in tension at temperatures as high as 140°K which is well above the observed plateau in yield stress. Furthermore he pointed out that both twinning and slip are basically dislocation processes and that with modified parameters his original theory still applied when deformation is initiated by twinning. Variables which affect the ductile-to-brittle transition in iron are test temperature, strain rate, composition and grain size.7 LOW,8 Hahn et al.,9 and Hull10 have provided evidence which links brittle fracture at a given temperature with the specimen grain size and the onset of twinning. In fact, Hull equates the brittle fracture stress to the twinning stress. On the other hand brittle fracture has been observed in the absence of twinning and priestnerl1 has given a fracture criterion which is valid whether or not fracture is preceded by extensive twinning. The data presented here clarify the role of twinning in the low-temperature deformation of iron. Strong evidence is given that the amount and distribution of interstitial impurities such as carbon are of

Jan 1, 1965

J. B. Cohen (AVCO Mfg. Co.)-The model presented by the authors is only one of several possible mechanisms for low-temperature aging. It is true that the motion of dislocations to the copper atoms, followed by diffusion along the dislocation lines, is one such mechanism. However, the details of such a process which would :result in copper-rich platelets on (100) planes in the f.c.c. matrix are not clear. Furthermore, there is at least one other mechanism that may be used to e.xplain the authors' results, so that the data do not clearly favor the Turnbull model. The zones may form by "normal" diffusion. The diffusion constants would be higher at room temperature than extrapolated data would suggest due to vacancies trapped in the specimens in the quench. The diffusivity would then be multiplied by the ratio of the number of vacancies present at the solution temperature to that present at room temperature. These vacancies could remain in the alloy specimen for long times at room temerature, due to interaction with the copper atoms. ' The activation energy for diffusion is smaller than that for bulk diffusion at elevated temperatures for it is only that for the motion of vacancies existing after the quench; after these are used up, the aging process effectively ceases. It is somewhat questionable if the laws governing transformation kinetics can be directly applied to changes in elastic moduli, especially in the case of aging where the structure and the composition of the zones may be changing during aging, If such laws are assumed, it is possible to explain the exponential factor of % with this vacancy model. It is probable that the structure of the zones and the matrix match only on (100) planes. Certainly the precipitates that form in this system after various aging treatments show orientation relationships similar to those of the zones. Strains on the edges of the zone may set up fields which do not allow the zone to grow in an edgewise manner. The exponent in the growth of a thin plate in a direction perpendicular to its face would be %. It may also be that copper atoms are attracted to dislocations. If this is the rate-controllin factor in the growth process Ifthisthen an exponent of % or % may arise. The writer would like to know if the authors have tried plotting l/a; proportional to as might be expected for "dislocation drainage." R. H. Doremus (General Electric Research Laboratory)—An important new method for following the growth of Guinier-Preston zones is presented in this paper, and I wish to congratulate the authors on their experiments. Their interpretation of the results, however, is doubtful in certain respects. To determine the exponent m in Eq. [4] the authors plotted -log at against t to various powers (their Fig. 6). The initial value of frequency used for these plots was found by extrapolating the data to zero time. In Fig. A the data from their Fig. 2 are plotted against a linear, rather than logarithmic, time scale. To obtain graphs similar to their Fig. 6 for these data one must use an initial frequency of about 52720; such a plot for m = % is shown in Fig. B. The straight line in Fig. B fits the data in an intermediate range only. The curve drawn in Fig. A was mapped from this line; comparison of

Jan 1, 1960

By R. M. Rose, D. P. Ferriss, J. Wulff

Single crystals of tantalum were grown by multipass zone melting in an electron beam apparatus. Tension tests of these crystals at 4.2 x 10&apos;* per sec-gave a resolved louler yield stress of 7300 psi at with a chisel edge; total uniform deformation increased from 1 to 2 pct at 77°K to over 20 pct at 300°K. This, and slip traces, indicated that deformation is more inhomogeneous at lower temperatures. Deformation occurred exclusively by slip in <III> directions, on planes in the <111> zones. Cross slip was frequent, particularly for those orientations where the resolved shear stress on the cross system was comparable with that on the primary plane. The existence and magnitude of the upper yield point were found to be sensitive to orientation. This effect was related to the circumvention of dislocations which were "locked" by interstitial atoms, by double cross slip, or composite slip, of screw dislocations. Prestrainirg at 300°K did not remove the upper yield point in subsequent tension at 77°K. Also, this treatment was found to cause yield points, where none existed for the unprestrained material. This behavior was also rationalized in terms of the circumvention mechanism. The mechanical properties of polycrystalline tantalum have been investigated by several workers,1"4 and may be summarized by pointing out the following features: a) Sharp rise of yield stress with decreasing temperature below room temperature. b) Response to strain aging at 300" to 400"C. c) Yielding with upper and lower yield-point phenomenon at and below room temperature. d) Low strain hardening below room temperature. e) Reluctance to twin except at very high strain rate. Furthermore, tantalum is ductile at ordinary strain rates as low as 4.2"K.&apos; This feature, in particular, makes tantalum unique among the high melting point, bee transition metals of Groups V and VI in the periodic system. Therefore, a more fundamental and detailed knowledge of the low-tempera- ture deformation of tantalum is required. Since high purity and the absence of grain boundary effects make such a study most productive and unambiguous, the method of electron beam zone melting was selected for the preparation of test specimens. This technique has the further advantage that crystals may be seeded in order to obtain any desired orientation. EXPERIMENTAL The electron beam zone-melting equipment was constructed as a modification of that described by Calverley, Davis, and Lever? All crystals were made by three passes of the molten zone at 4 mm per min to achieve an optimum purity commensurate with economy of time and material. Table I reports the chemical analyses of the starting and refined metal. It will be noted that there remain some 50 to 70 wt ppm of interstitial elements, while all substi-tutional elements have been removed by evaporation. Tungsten is picked up by evaporation of the cathode filament wire. Crystal seeding was normally successful within 3 deg, and the orientation of all crystals are given in the standard stereographic triangle in Fig. 1. Tensile bars were prepared from the crystals by centerless grinding to the shape in Fig. 2. Specimens were then electropolished to remove 10 pct of the diameter in order to remove worked material and to prepare a metallographic surface for subsequent deformation trace observations. All specimens were held in the split bushing grips as indicated in the cross section view of Fig. 2. All tests were made at a strain rate of 2 112 pct per min in an Instron testing machine.

Jan 1, 1962

By R. E. Cole, A. M. Gaudin

OLEIC acid, a standard flotation reagent, has generally been preferred to other fatty acids. Because oleic acid differs from saturated fatty acids by the presence of one carbon-to-carbon double bond and because the flotation operation is one in which extremely intimate exposure of the reagent to oxygen is obtained, it appeared possible that the value of oleic acid as a flotation collector was related to the oxidizability of its double bond. To test this hypothesis, the floated mineral, fluor-ite, was leached with a solvent capable of extracting the adsorbed reagent and the extract was analyzed.&apos; Results show that oleic acid is not oxidized during flotation, although some oxidation can be obtained if the flotation operation is repeated many times and if oxygen in place of air is employed as the gas during flotation. Incidentally, it was found that lino-leic acid which has two nonconjugated double bonds is not affected appreciably more than oleic acid. Linolenic acid which has three nonconjugated double bonds is measurably altered even during one flotation step, using air. The fatty acids used, from the Hormel Foundation, were of the highest purity. The quantity of fatty acids employed in each test was sufficient to float the mineral, but less than the theoretical amount required to form a monolayer at the mineral surface. The purpose of this limitation was to eliminate droplets of oil smeared on the adsorbate-covered mineral surface. The mineral was dried in vacuum at about 60 °C. Effective leaching was obtained by use of a solution of 1 pct hydrochloric acid in absolute alcohol. The extract was separated from the solvent by distillation, with final recovery of the extract in carbon tetrachloride. The identity of the extract was tested by a combination of analytical procedures including infrared spectroscopy, saponification number, iodine number, and index of refraction. At the outset, great hopes for accurate quantification of oleic acid oxidation had been entertained in regard to the method of infra-red spectroscopy. Unfortunately, because the double bond in the oleic acid is so sym- metrically located at the center of the molecule that it provides very weak absorption bands, accurate quantitative analyses were not obtained. Nevertheless, infra-red spectrograms suggested the absence of double-bond oxidation during flotation. Iodine number, semi-micro method, provided a critical test of the extent to which fatty acids oxidized during flotation, see Table I. The index of refraction was used in a qualitative rather than quantitative fashion, and its findings corroborated those obtained by the iodine-number method. It is concluded, in the case of fluorite and C-18 fatty acids having one or two nonconjugated double bonds, that there is practically no change of the fatty acid molecule or ion during the flotation operation. It would appear, therefore, that the extraordinary utility of these reagents is related to some property of the compounds other than the oxidizability of their double bonds. Acknowledgment The research reported herewith was sponsored by the Research Division, U. S. Atomic Energy Commission, and for this help the authors express their appreciation. Reference &apos;R. E. Cole: "Double-Bond Reactivity of Oleic Acid During Flotation." Thesis submitted in partial fulfillment of the requirements for the degree of M.S. at the Massachusetts Institute of Technology.

Jan 1, 1954

By Tell Ertl

The term oil shale is defined. Foreign oil-shale developments are outlined briefly. The richest and most extensive oil-shale deposits in the United States lie in western Colorado. The Bureau of Mines is opening two adjacent areas for underground mining. in western Colorado. From the first area the oil shale is mined selectively as required by the retorting plant. The second area is being developed as a unit of a full scale oil-shale mine to ascertain the most practical methods of mining oil shale and to determine costs. In both of these mining areas, research will be carried on to develop new and improved practices for mining oil shale. Introduction Oil shale is a sedimentary rock containing a solid mineraloid of indefinite composition known as kerogen. On heating oil shale, the kerogen undergoes thermal decomposition and some of the vapor products of the decomposition can be condensed as shale oil. Oil from shale can be a major source of liquid fuels since extensive deposits of oil shale are known to exist throughout the world. The United States considers the establishment of an oil-shale industry only when doubt exists of the adequacy of the domestic supply of crude petroleum. On the other hand, oil shale is not strange to foreign oil men. The industry is an old one in other parts of the world. The French industry has been in existence since 1838, the Scottish since 1859, the Australian since 1860, the Estonian and Swedish The since World War 1, and the Manchurian industry since 1929. The most highly exploited oil-shale deposits are the Carboniferous shales of Scotland. About 20 seams ranging from 4 to I2 ft in thickness are worked. The yield during recent years in scotland has been 18 to 25 gal of shale oil per ton, from 3&"30&apos;000 tons per year&apos; The French and Swedish oil-shale deposits are of lower grade than the Scottish. The Estonian oil-shale deposits are 7 ft thick, and the oil yield averages 50 gal per ton. Over 1,000,-ooo tons are mined each year, half of which is used directly as fuel to substitute for coal and the other half is used for the production of oil. Immense deposits of oil shale that will yield 10 to 15 gal per ton exist in Germany. Because of the impending loss of the Rumanian and Polish oil fields and the bombing of synthetic liquid fuel plants, the Nazis in 1943 started a large-scale oil-shale program in Germany. By V-E Day, it is said, oil-shale production had reached the rate of 2500 tons per day and rapid expansion of the industry was imminent. Australian oil shale, known as torbanite, occurs in beds 2 to 6 ft thick. It is of a very high grade and on retorting yields 80 to 160 gal per ton. The oil-shale industry of Manchuria was the largest in the world during the past decade. The well-known Fushun coal deposit in Manchuria has an overburden of 500 million tons of oil shale about 450 ft thick that will yield 10 to 15 gal of shale oil per ton. The oil shale is

Jan 1, 1949

By T. D. Yensen, R. K. McGeary

While we have not been primarily interested in the determination of hydrogen in the alloys that we have been dealing with, we arc very glad to cooperate in this symposium on sampling and analysis for hydrogen, as we can never tell when we may find it desirable to perform such analyses. Vacuum-fusion Method Our primary interest has been oxygen and carbon, in the analysis of which we think we have become very proficient. Our oxygen-analyzing apparatus is of the vacuum-fusion type (Fig. I). This employs Dr. Derge&apos;s type of graphite cruciblc and slit sleeve, with graphite powder between, for heat insulation (Fig. 2) supported in a clear quartz bulb connected to the Pyrex glass system by means of a carefully made ground joint. The latter is kept cool by means of an air blast from a circular copper tube surrounding the joint. The crucible is heated by high-frequency induction and the 24 one-gram samples successively dropped in from the horizontal tube at the top by means of a magnet. The gases (H², CO, N2) are passed through the CuO catalyst held at 300°C. (converting CO to CO²I, H² to H²O) and the CO² and H2O frozen out in the main liquid air trap, while N2 is evacuated. At the end of the operation, shown by the termocouple vacuum gauge indicating a pressure of 10-4 mm. Hg, the analyzing system is isolated by means of the mercury cutoffs, and the CO² and H2oare determined by transferring first the CO2 and then the HzO to the small trap at the right. This is done by placing liquid air on the small trap, then removing the liquid air from the large trap for one minute, which is sufficient to evaporate the Co2 and transfer it to the small trap. The CO2 is then measured by closing the mercury cutoff at the extreme right, removing the liquid air from the small trap, warming it up to room temperature, adjusting the mercury level to one of the three marks on the glass tube (corresponding to three volumes calibrated so that I mm. Hg of CO² corresponds to 0.001, 0.002 and 0.010 mg., respectively, of oxygen) and finally reading the pressure. Liquid air is now replaced on the large trap, the mercury cutoff at the right opened, transferring the COz back to the large trap. The cutoff to the pumps is then opened, the liquid air removed for one minute, thus evacuating the CO², the pumps again cut off and the H2 O transferred to the small trap as before, except that it is now necessary to warm the large trap with a Bunsen burner in order to evaporate all the H2O. This requires about three minutes, as the inner tube must be heated to at least 100°C. In order to prevent H²O from being adsorbed on the glass walls, the glass tubing beyond the catalyst (i.e., to the right in Figs. I and 3) is kept heated to about 150°C. by means of Nichrome ribbon as shown in Fig. 3. For a I-gram sample the above amounts of oxygen (0.001, 0.002 and 0.010 mg.) 35

Jan 1, 1945

By Harry M. Mikami

Chromite is the only ore mineral of metallic chromium and chromium compounds and chemicals. Because of this fact, chromite and chrome ore are used synonymously in trade literature. In commercial market quotations, chrome ore is the term commonly used. Chromite per se, because of properties imparted by its chromium content, is used in refractories and in special purpose molding sands for metal casting. There are many other minerals containing some, generally minor, amounts of chromium, but none are commercial sources of the element (Thayer, 1956). Chromium and chromite have many diverse uses that, directly and indirectly, critically affect vast segments of our modern industrial system. Most important are probably the metallurgical applications wherein chromium is a component of heat-, abrasion-, corrosion-and oxidation-resistant and high-strength alloys of many types. Stainless steels are the largest volume category of chrome-bearing alloys. Chromium chemicals are used in leather tanning, in pigments, dyes and mordants, printing, chemical process industries, photography, pharmaceuticals, metal plating, pure chromium metal production, and for many other purposes. Chromite is a necessary constituent in basic refractories indispensable for the production of steel, copper, cement, and glass. Under present conditions, the US and North America, with the possible exception of Cuba, have no commercial ore reserves. There are chromite deposits, as will be described, but they would be used only under highly abnormal conditions if all outside sources were cut off for an extended period. All chromite used in the US is imported from the eastern hemisphere in which are contained the principal world reserves. The main suppliers in 1980 were the Republic of South Africa (43%), the USSR (21% ), the Philippines (12%), Albania (11 %), Turkey (8%), and others (5%). The strategic nature of chromite is obvious. End Uses-Grades and Specifications As noted before, the three principal uses for chromite are metallurgical, refractories, and chemical with a fourth minor use as foundry molding sand. For metallurgical applications chrome ore is first reduced in electric carbon arc furnaces to various types of ferrochromium alloys. There are high, medium, and low carbon ferrochromiums with carbon ranging from 0.01 up to 10%. Chromium itself ranges from 50 to 73 %. Ferrosilicon chromium and ferrochromium-silicon grades have chromium from 33 to 67% and silicon from 3 to about 48%. Since iron is reduced with chromium, the Cr:Fe ratio of the ore will determine the ultimate grade of the ferrochromium whereas carbon and silicon can be controlled during processing. MgO, A12O3, CaO, and excess SiO2, are removed in slag. A small amount of pure chromium metal is prepared by alumino-thermic and electrolytic processes from essentially iron-free chrome components that have been made via the chemical route. The higher grades of ferrochromium with chromium in the 66 to 73% range can only be made from ores with not only high chromium content, but low iron, i.e., high Cr:Fe ratio. These ores, conventionally termed metallurgical grade, have Cr2O3 contents of 45 to 56% with Cr: Fe ratios of 2.5 to 4.3. A standard composition is generally 48% Cr2O3 and 3:1 Cr:Fe ratio. Very high grade ores are often blended with lower grades even with the high iron chemical grade. For some ferrochromiums, additions of high alumina refractory grade are used as slag conditioners to facilitate smelting while still contributing chromium values. A lower grade ferrochromium, the high carbon charge chrome, has become the predominant grade in use today for making chromium-bearing steel alloys. This

Jan 1, 1983

By C. B. Alcock, R. A. Oriani

Some simple models of solutions are described; these include the regular solution, the subregular solution, and the quasichemical model. The assunzption underlying these models, the physical signzficance thereof, and the experimental manifestations are discussed. Examples are presented from the fields of liquid and solid metallic solutions, liquid slags, mattes, liquid and solid ionic solutions, and mixed carbides to show under what conditions and for which systems these solution models are fair descriptions. The deviations of real solutions from the models are of theoretical interest. Some such deviations, both for dilute and for concentrated solutions, arc pointed out and their Physical sigtzzficance discussed. DURING the past half century there has been a gradual accumulation of thermodynamic data for systems of interest to the metallurgist. There remain many gaps in the data, however, and the metallurgist must often face the problem of estimation of thermodynamic quantities where measured values do not exist. One might hope that the experimental progress would be matched by theoretical advances which would make such estimations possible with a high degree of confidence. However, theoretical progress has been disappointingly slow even for the simplest kinds of solutions, and since the multicomponent systems in which the metallurgist is interested are very complex, one cannot expect theory to be of much help to the metallurgist. In this situation, therefore, it seems worthwhile to examine some simple models of solutions from two points of view: firstly, to see if such crude models represent the thermodynamic facts in as many types of solutions as possible sufficiently well for the needs of the metallurgist, and secondly to see what the deviations from such models show to be important for consideration by theorists. BOND ENERGY MODELS OF SOLUTIONS The simple models that we will examine from these points of view may be termed statistical models, in that they are concerned with the thermodynamic consequences of some simple assumptions about the energy of an assembly of atoms, molecules, or ions, and do not inquire into the physical basis of the interaction. The underlying assumption of these models is that the energy of an assembly of molecules (by which we include also atoms or ions) is given by the sum over all interaction energies of molecules taken two at a time; we will discuss only those models in which the pairwise interactions are restricted to those between nearest neighbors. Thus, in a pure substance of bond energy EAA, the internal energy (with respect to some specific reference state) will be expressed as NAA EAA where NAA is the number of nearest-neighbor pairs. A solution of molecules A and B will be characterized by NAA EAA + NBB EBB + NAB EAB where the Eij represent the bond energies of the nearest-neighbor i-j pairs. If one assumes that the EAA and EBB are the same in the pure components as in the solution, and that the coordination numbers in the two pure substances and in the solution are the same, then the energy of the solution with respect to the pure components (i.e., the energy of solution) is a function of the following linear combination of the bond energies: EAB - 1/2(EAA +EBB) = w. The thermodynamically ideal solution is defined as one in which the activity of each component is equal to the mole fraction of that component at all concentrations and all temperatures. It follows that

Jan 1, 1962