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By James A. Finch, Yue Hua Tan, Wei Zhang

"The paper is part of our study of the frother structure-property relationship using bubble rise velocity. Single bubble rise velocity profiles were determined in a 350 cm column for surfactants from the polypropylene glycol (PPG) family. Using velocity at 300 cm, the concentration to reach minimum velocity (CMV) is determined. The CMV is shown to decrease as alkyl chain length (n, number of carbons) increases and as the number of propylene oxide groups (m) increases. Linear correlations log CMV vs. n and m were observed. Taking literature data for critical coalescence concentration (CCC), linear log CMV vs. log CCC correlations were also noted. Mechanisms are briefly discussed, and prediction of CCC made for a commercial polypropylene glycol.INTRODUCTIONAs one of the great enabling technologies of the 20th century, froth flotation is a highly versatile method for physically separating minerals by exploiting differences in wettability (hydrophobicity). Over the last century, flotation reagents have undergone significant developments (Khoshdast and Sam, 2011). One important group of reagents is frothers which are used to reduce bubble size, slow bubble rise velocity and help stabilize froth (Klimpel and Isherwood, 1991).Frothers, originally derived from natural sources (e.g., pine oil and cresylic acid), are largely replaced today by synthetic products which provide more consistent properties. Polyglycols, based on PEO (polyethylene oxide), PPO (polypropylene oxide), or PBO (polybutylene oxide) groups, were first described by Leja and Nixon (1957) and have attracted wide use since then (Farrokhpay 2011). The chemical structure of polyglycols can be represented by a general formula: R(X)mOH, where R = H, or CnH2n+1 and X stands for EO (-C2H4O-), PO (-C3H6O-), or BO (-C4H8O-). The polypropylene glycol ethers (CnH2n+1(PO)mOH) are the most common of these reagents (Pugh, 2007) and the focus of this study.In general, the chemical structure of frother molecules comprises two parts, a non-polar hydrophobic hydrocarbon (alkyl: CnH2n+1) chain and a polar hydrophilic head. By introducing the ether -Olinkage, which acts as another polar site, the propoxy group (-OC3H6-) in the structure makes the frother readily soluble in water (Somasundaran and Wang, 2006), facilitating the industrial use of these frothers. Available as by-products, Dow Chemicals introduced as series of polyglycols, e.g., Dowfroth (DF) 200, 250, 263, and 1012, the most familiar being DF250 (CH3(PO)4OH), a polypropylene glycol methyl ether. While no longer available from Dow, these and other polyglycols are still widely used."

Jan 1, 2016

By R. W. Guard, W. R. Hibbard

As part of a program to determine the deformation characteristics of pure metals, the tensile creep properties of high purity aluminum (99.994 pct Al) have been determined using a constant stress loading. The effects of prior annealing temperature, stress, and temperature were studied. These data have been examined on the basis of present-day theories. None of the methods was found to give an accurate representation of the data over all conditions studied. The structures of several specimens after creep were examined by optical and X-ray metallography. Marked changes in the grain size were found and it was substantiated that the magnitude of these changes was greatly influenced by the applied stress (or creep strain). The changes in fiber texture which occur on creep deformation are shown to be consistent with those observed on deformation at lower temperatures. UNDERSTANDING the properties of new mate-*-J rials under different experimental conditions must be based on considerable knowledge of the mechanisms involved in plastic flow and how to control them. Tension and creep tests have been carried out on a number of pure metals in order to document their deformation characteristics. It is hoped that a comparison of these data with theory will indicate those areas where work on mechanisms and their relation to metallurgical variables may be most fruitful. Since aluminum has often been used for studying the qualitative aspects of creep behavior, it was chosen for detailed study. The effects of annealing temperature, stress, and test temperature on the constant stress creep behavior were studied. Although most of the tests were made above one half the absolute melting temperature, a few tests were made at lower temperatures to give qualitative comparisons. Some specimens were examined metallo-graphically and by X-ray diffraction techniques after creep. Since only a limited number of specimens could be made from the available material, no effort was made to study detailed changes in sub-grain structure or other metallographic features. Servi and Grant3 nd Dushman et al.' have previously published studies of high temperature creep of high purity aluminum. In both cases, a great deal of emphasis was placed on the minimum creep rate.

Jan 1, 1957

By H. W. Hitzrot

THE new 4800-ton fine-grinding plant at the Hollinger Consolidated Gold Mines property at Timmins, in the Porcupine district of northern Ontario, went into operation in November 1937, and represents the culmination of an experimental program. The plant is a moderately low rectangular building of hollow tile on a steel frame, large enough to house four 7 by 15-ft. ball mills, with a 12 by 27-ft. classifier beside each mill. At one end is space for the addition of another mill and classifier or a mill and classifier for the regrinding of table concentrates. This regrinding is now done in the old grinding department of the main mill building. Also within the new building are the four 6-in. sand pumps for lifting the product from the low-dis- charge ball mills up to the classifier feed launders and the containers and appurtenances of a complete dust-collecting system. Together with the usual overhead crane, these constitute the major units of equipment within the new plant. The location is at the lower end of the main mill buildings toward the old tailings pond, now so neatly leveled off and sodded to rival the very best of our own W.P.A. projects. Close by the new grinding plant is a large dome-shaped structure-the new fine-ore bin designed arid built by Mr. Longmore and the Hollinger milling and engineering staffs. There are four separate automatically loaded inclined belt conveyors leading up from the bottom of the bin to the grinding plant. Each belt is equipped with a recording weightometer, in the grinding building. The whole structure and the machinery within it give the impression of permanence and a carefully integrated design with close attention to details, giving the operators every advantage for consistently good work. The many ideas and opinions behind this achievement were all ably organized and executed by the Hollinger milling and engineering staffs, anti not a few were directly initiated by them. Excellent cooperation was afforded by the Hollinger staff to the engineers helping to conduct the grinding and classification test program. It was the author's privilege

Jan 1, 1939

By L. C. Morganroth

Magnesites are of two general classes - massive and crystalline.

Jan 1, 1915

By M. Mujahid, A. Maqsood, M. H. Asghar, K Iqbal

"Thin film multilayer anti-reflection coatings (Si02/Si/Si02) having thicknesses 286/571/143nm were deposited by RF magnetron sputtering deposition technique on 0.5mm thick Si(100)-substrates. Post-deposition annealing is also carried out in the temperature range 150-650°C for 4hr at the rate of 10°C /min. Si Optical window was designed at 4.21lm wavelengths and correlated with modeling software. The films are transparent in the 3-51lffi band of the electromagnetic spectrum, firmly adhered to the substrate. The prepared multilayer thin films are characterized optically and structurally using a spectrophotometer, an atomic force microscope, x-ray diffraction and a scanning electron microscope. Optical and structural characterizations show that the %transmittance is between 60% and 75%, no appreciable change in crystal structure and roughness of coatings vary between 9 and 25 nm when annealed in the temperature range of 150-650oC. Local elemental characterization on the surface of the thin film was carried out using energy dispersive spectroscopy. The quantitative result of energy dispersive spectroscopy has also shown that the ratio of Si to 0 on the film is 0.67: 1.IntroductionSi02 thin films have unique properties in the interfaces with Si and most studied materials in the field of microelectronics and optical devices [1]. Multilayer thin films are using nowadays in the design and fabrication of the shrinking systems with a variety of fields such as optoelectronic devices. The physical properties and parameters can be controlled at scales of microns down to nanometers by using RF magnetron sputtering system [2].Silicon and Silicon dioxide are used as coating materials [3]. These thin films are laid on top of each other in SiO2/Si/Si02 order by RF magnetron sputtering on top of a substrate as given in Table 1."

Jan 1, 2012

By R. E. Ogilvie, J. I. Goldstein

The a and y solubility limits in the Fe-Ni phase diagram have been redetermined at temperatures above 500°C. Both a diffusion-couple and a quench and anneal technique were used. The solubility limits were measured with an electron-probe micro-analyzer. The nickel concentration at the phase boundary is increased below 700°C and the a solid-solubility range is much larger than had been previously measured. The solubility limits are also extrapolated to 300°C. It is suggested that the solubility of nickel in a FeNi reaches a maximum in the temperature interval 400o to 500°C. THE equilibrium diagram has been of great use in the field of meteoritics, where the phase relations between kamacite (a) and taenite (?) in metallic meteorites can be described by means of the Fe-Ni diagram. The study of metallic meteorites by electron-probe microanalysis has cast some doubt on the accuracy of the presently available Fe-Ni diagrams.1, 2 Recent thermodynamic studies of the Fe-Ni system also suggest that the diagram may be in error.3 For these reasons the high-temperature (800o to 500°C) part of the diagram was redetermined. INTRODUCTION The currently accepted Fe-Ni diagram is that of Owen and Liu.4 Above 910°C, there is a region of complete solid solubility, ? (fee). Below 910°C, the a (bee) phase is stable in pure iron. The effect of increasing amounts of nickel is to stabilize the y phase. The phases that form when Fe-Ni alloys are heated or cooled bear little relation to the equilibrium diagram. If an alloy is cooled from the y state and held at a temperature within the a + y field, no evidence has been found for the occurrence of the y - a transformation.5 If the alloy is cooled to low enough temperatures the y phase breaks down into a supersaturated bee phase called a2. In fact, in alloys over 27 pet Ni the y phase is retained at room temperature.6 The a, phase has the same composition as the original y. The temperature at which a2 forms, the M, temperature, has been determined experimentally.' A state of equilibrium can be approached by cooling below M, to form a2 and then reheating the alloy into the two-phase region of the diagram. The y phase will then begin to precipitate out of the a2 phase and grow. The growth of the phase, however, is quite slow. Using the interdiffusion coefficients -Da of Goldstein et al.,8 it is estimated that it takes about 1 year to grow a 10-µ-wide region of ? at 700°C in a 5 pet Ni alloy. Owen and Liu4 used the technique just described to form the equilibrium phases. The phases present were determined by means of X-ray analysis. The accuracy of their diagram depends on the number of alloys available near the phase boundary at a given temperature. In this study two different techniques were used to determine the a/a + ? and ?/a + ? solubility limits. The inherent accuracy of both techniques was greatly improved over that used by previous investigators because the phase-boundary compositions were measured with an electron-probe microanalyzer. PROCEDURE The two methods used to determine the Fe-Ni diagram are the diffusion couple (D.C.) and the quench-and-anneal (Q.+A.) techniques. In the first method, diffusion couples whose diffusion path goes through a two-phase region of the phase diagram were used. A description of the technique used for making the diffusion couples has been described in a previous paper.' After the diffusion treatment a discontinuity in the resultant concentration vs distance profile was measured. The nickel concentrations in the a and ? phases at the interface of the discontinuity are the solubility limits of the a and ? phases in the phase diagram at the diffusion temperature. If the interface com-

Jan 1, 1965

By Franklin D. Cooper

Three model dwelling units were redesigned to achieve specific levels of noise reduction above that provided by conventional construction. Using 1968 prices, the added costs of materials and installation were found to range from $500 to $5,000 depending upon the size of the dwelling unit and the degree of insulation. The potential aggregate expenditures for sound insulation materials are projected to reach $617 million in 1975, including about $408 mil- lion for the mineral-based materials, in 1968 constant dollars. The report includes a brief review of the mechanics and effects of sound.

Jan 1, 1970

By Thomas M. Nasiatka

Tests with a high-pressure water jet were conducted in the steeply pitching Roslyn No. 5 bituminous coalbed in the Roslyn No. 9 mine, Roslyn, Wash., to determine the feasibility of extracting coal from pillars and from a solid coal face in development without drilling and blasting. During pillar mining, using a hand-held monitor, the best results were obtained with a 0.150-inch- diameter nozzle, a water pressure of 3,500 psi, and a flow rate of 38.5 gpm.3 The rate of mining and productivity were 0.74 ton per minute and 16.6 tons per man-shift, respectively. During development mining, using a monitor mounted on a roof jack, the best results were obtained with a 0.148-inch-diameter nozzle, a water pressure of 4,500 psi, and a flow rate of 40.0 gpm. In one section of the mine where the coal was relatively hard, the rate .of mining and productivity were 0.10 ton per minute and 5.7 tons per man-shift, respectively in another section of the mine where the coal was relatively soft, the rate of mining and productivity were 0.51 ton per minute and 8.3 tons per man-shift, respectively. The tests showed that hydraulic mining methods were more productive than conventional mining methods in pillar mining. In development the productivity of hydraulic mining depended primarily upon the coal hardness. Compared with conventional methods, hydraulic mining methods were less productive where the coal was relatively hard and equally as productive where the coal was relatively soft.

Jan 1, 1963

Jan 1, 1907

By Martin Chenoweth

The Metropolitan Water District of Southern California (MWD) is undertaking one of the nations largest water management projects. The Eastside Reservoir Project is being built to insure a supply of water to Southern California in the event of earthquake damage to the aqueducts supplying the region. An 800,000-acre-ft lake will result from the three dams, closing off the valley between two parallel ridges. The single largest contract of the project, the West Dam, was awarded to the joint venture of Atkinson Construction Co., Washington Construction Co. (Morrison Knudsen Co.), and HB Zachry Co. Over 50 million bank cubic yards of rock must be drilled and shot on this contract alone. AWZ relies on the TechBASE database management system for documenting drilling and blasting. The database format of TechBASE allows all production parameters to be linked to the location of the activity. This allows parameters such as drill penetration or boulder production to be analyzed for geologic trends that can either be exploited or dealt with. Shot locations are stored as 3D polygons in a polygon table. Production and cost data are stored in flat tables. Shot names are unique and link the polygon table to the flat table. This allows typical database queries to be made by date, location, cost or any production parameter. The output from these queries can be presented in table, graph and as map formats. The map output is particularly helpful in quantifying geologic conditions and blast performance. The ability to transform the data into information has been very helpful. The ability to present this information graphically has been invaluable.

Jan 1, 2000

By Michel Noël

Cet article présente une compilation partielle des mesures adoptées pour la fermeture des haldes de stériles pour des mines situées au Canada et en Alaska, et dont le climat comporte des hivers froids. L?article présente également le processus de sélection qui a été suivi pour certaines de ces mines. Les exploitations minières produisent habituellement des quantités de stériles qui peuvent être importantes. De plus, la nature du dépôt minier ainsi que la roche mère vont souvent entraîner des impacts sur l'environnement. Ces impacts doivent être gérés non seulement durant les opérations minières, mais souvent à très long terme après la cessation de l?exploitation minière. Les plans de fermeture de mine doivent par conséquent procurer des solutions à très long terme, voire même à perpétuité dans bien des cas. Le processus de sélection implique souvent l'évaluation des risques liés aux responsabilités environnementales et financières. Il doit considérer l?aspect scientifique, comporter une définition des objectifs, tout en incorporant une gestion des ressources et des plans de travail. La planification de fermeture est essentiellement un exercice de prise de décisions comportant des contraintes. Une matrice de classement basée sur la performance et le risque est souvent développée durant ce procédé pour identifier les options préférées. Les études de cas présentées dans cet article présentent quelques exemples. L?état des connaissances sur le drainage acide minier provenant des haldes de stériles a augmenté considérablement au cours des dernières décennies. Ceci n?a pas nécessairement augmenté le niveau de complexité des méthodes adoptées pour la fermeture. Une approche qui est fréquemment utilisée consiste à stabiliser les pentes des haldes de stériles en abaissant la pente des talus pour ensuite recouvrir les stériles d?une couche de sol pour soutenir la végétation. De telles couvertures empêchent les animaux d?avoir un contact direct avec les stériles, minimisent l'érosion et réduisent l'infiltration à divers degrés. L'inclusion d?un traitement des eaux dépend évidemment de la qualité de l'eau au point de déchargement.

Nov 1, 2008

By A. W. Effinger

The Bureau of Mines used regression analysis and applied statistical methods in an effort to rationalize the results of an experiment examining the effects of certain variables on carbon deposition in a reservoir for thermal recovery of petroleum. Although none of the 15 trials of the original experiment resulted in the response of weight-percent of carbon regarded by the experimenter as adequate, values calculated using canonical analysis in two trials yielded responses 33 and 54 percent higher than the minimum acceptable figure. The actual responses differed by less than 3 and 6 percent, respectively, from the predicted responses. Methods are described for defining a path of increasing response based on the minimum point and the response surfaces and for defining a set of values for the parameters in question, which result in increased response, A detailed explanation of the mathematical process used in this analysis is presented in the appendix for ease in computer programing the technique.

Jan 1, 1970

By Richard B. Reese, George R. St. Pierre, Robert A. Rapp

The vapor pressures of pure iron and pure chromium have been measured using a Knudsen cell coupled with a mass spectrometer. The experimental results agree well with some previously reported data; heats of sublimation and vaporization have been calculated. From vapor pressure rr~easurernents, the activities of iron and chromium in their binary alloys have been determined for NcY = 0.10 to 0.65 over a 1400" to 1700~ temperature range. The activity of chromium in the liquid alloys was found to exhibit positive deviation from ideal behavior when referred to solid chromium as the standard state; however, for the activity of chromium referred to nonequilibrium undercooled liquid chromium as standard state, the activity behavior is almost ideal. ALTHOUGH the Fe-Cr system is important as the basic system of alloy steels, the thermodynamic properties of this system have not been thoroughly investigated at elevated temperatures. In view of the potential practical applications of such data as well as their contribution to alloy theory, further study of the Fe-Cr system was undertaken. In addition, further development of experimental techniques for equilibrium measurements at high temperature is required. The present research involved an application of the Knudsen effusion method in conjunction with a time-of-flight mass spectrometer. Belton and ~ruehan' have measured the activities in Fe-Ni and Fe-Co alloys by a similar method. Speiser, Johnston, and lackbburn' have determined the vapor pressure of pure solid chromium between 1283" and 1561°K by a Langmuir free evaporation technique. The vapor pressure of chromium was described by the expression: over the temperature range 1283" to 1561°K. McCabe, Hudson, and paxton3 have measured the vapor pressures of pure iron and pure chromium by the Knudsen cell technique around 1500°K. The vapor pressure and heat of sublimation at O°K, AH,", for pure chromium agreed within experimental error with the measurements of Speiser et al. at 1200°C. Kubaschewski and HeYmer~ determined the vapor pressure of pure solid chromium in the temperature range 1170" to 1400°C by the Knudsen effusion technique combined with a radioactive tracer analysis of crS1. Their results agreed with the work of previous investigators. Edwards, Johnston, and Ditmars5 have measured the vapor pressure of pure solid iron by the Langmuir technique between 1356" and 1519°K. The vapor pressure of solid iron in the temperature range studied was given by: The data of McCabe, Hudson, and paxton3 on the vapor pressure of pure iron around 1500°K by the Knudsen effusion technique were in good agreement with those obtained by Edwards et a~.~ Hultgren, Orr, Anderson, and Kelley give the selected values for the AH: of pure iron and pure chromium as 98,990 *200 and 94,340 * 500 cal per mole, respectively. These values are the average values determined in the several investigations by different methods. The Fe-Cr phase diagram7 is shown in Fig. 1. Previous determinations of activities in this system have been carried out by several investigators, but most of the work has been done on solid alloys. Using a Knudsen effusion method with cr5', Kubaschewski and Heymer4 reported that the Fe-Cr system exhibits positive deviation from the ideal behavior for compositions ranging from NCr = 0.0398 to 0.699 at 1170"

Jan 1, 1969

By Hideki Minoura

"Two novel electrochemical techniques for the preparation of highly crystallized CdS film have been presented. One is cathodization of a conductive substrate in an acidic chemical bath containing cadmium salt and thioacetamide, where electroreduction of proton at small current densities induces a growth of highly crystallized CdS thin films, whose growth is not disturbed by the reactions in the solution phase. The other technique is electoreduction of aqueous Cd2+— SCN complex. An advantage of this technique lies in no formation of solid particles in the bulk, of the bath.IntroductionIn recent years much attention has been paid to materials preparation by solution processing because of its advantages in lowering the cost as well as the stress to the environment, as compared to the conventional gas phase techniques which unavoidably require high temperature and/or vacuum. We have been trying to explore novel techniques for preparing functionalized compound semiconductors by aqueous solution process. Semiconductors which we have been mainly focusing on are CdS and ZnO, which are important semiconductors finding applications in various devices. In the present paper, some of the techniques that we have recently established for the preparation of highly crystallized CdS will be presented.Methods of the CdS film processing in solution phase (wet process), which have been reported so far can be divided into two major groups; one is chemical bath deposition (CBD) in alkaline solution containing Cd2+ and thiourea 1)4) and the other is electrodeposition (ED) in acidic solution containing Cd2+ and thiosulfate ions - 5)-8) or organic solutions containing dissolved sulfur 9)-11)."

Jan 1, 2000

By Norman E. Breslow, John A. Montgomery, Sanford W. Horstman

Reconstruction of historical exposures to silica dust is required in an ongoing cohort mortality study of workers in the diatomaceous earth (DE) industry. However, historical data were collected using three different sampling methods. This study was conducted to derive empirical quantitative relationships from linear regression equations between the three methods: standard impinger, total mass, and respirable mass. Dust from one diatomaceous earth processing plant was sampled simultaneously by all three methods. Results from 61 clusters of the three sampling devices indicate that the phcle size distribution of the dust varies with the two parent products sampled. baghouse product and main product. The relationships between particle counts and respirable mass are: Respirable mass (mg/m3) = 0.064 (mppd) impinger count for baghouse product dust, and respirable mass (mg/m3) = 0.018 (mppcf) impinger count for main product dust. The relationships between particle counts and total mass are: Total mass (mg/m3) = 0.837 (mppcf) impinger count for baghouse product, and total mass (mg/m3) = 1.21 (mppcf) for main product dust. In all four euuations, the intercept did not differ significantly from zero, and the correlation coefficients ranged from 0.90 to 0.95. Results are compared with data from four previously published studies.

Jan 1, 1991

By I. K. Gilmore

Texasgulf Inc. currently operates an open pit phosphate mine in the central coastal plain of North Carolina. The area of phosphate deposition lies within the Aurora Phosphate district which consists of an embayment which is in the center of the Neogene phosphate deposition. A variety of solid and liquid fertilizer products are produced at the Texasgulf complex. One of these products is known as North Carolina Natural Phosphate (NCNP). New potential for use of unacidulated natural phosphate, now exists in regions with acid soils due to the discovery of the findings from recent research, cost advantages, and moves to reduce chemical inputs.

Jan 1, 1995

El presente artículo señala que el proceso de exploración en superficie de la mina de Cercapuquio para determinar nuevas zonas mineralizadas, es de difícil actuación a causa de la falta de ganga en este tipo de mineralización. Para ello, se consideró oportuno proceder a una exploración de carácter geológico de la zona en estudio, antes de empezar los trabajos sistemáticos de exploración geofísica. Asimismo, los procedimientos empleados en las etapas de exploración, son las siguientes: trabajos geológicos, geofísicos y mineros.

Oct 1, 1955

By D. Spitty

Mining companies often have many disparate systems and repositories of data in their organization for planning and scheduling outbound mining supply chains. To optimize ore quality, throughput, transport logistics scheduling and delivery to contract, planning teams need to model and manage the value chain accurately and achieve a consolidated, enterprise view of operational performance. Planning teams coordinate a complex series of activities to ensure production forecast accuracy. They also negotiate and execute complex contracts often with disconnected and limited visibility of production forecasts, quality, and variability with little ability to accurately market potential product specifications over longer time horizons. This market is becoming increasingly dynamic, with increasing variability and the time for planning teams to react is decreasing. This is driving the need towards using science to generate the necessary scenarios required to support the decisions made by planners on a frequent basis. Resource-to-Market is a highly flexible, user-configurable supply chain management system for the mining and metal processing industries. This provides an integrated view of the supply chain that supports the dynamic nature of planning in a mining company, embraces variability of elements across the supply chain with the ability to optimize across all the functional areas of the operation to enable optimal decision making for often competing objectives such as throughput, quality, cost, revenue and profit.

Feb 23, 2014

By Arthur E. Belton

Ever since the industrial Revolution both major and small companies have put much emphasis on the use of incentives to compensate top management for extra effort and extra skill. For many years industries have also provided hourly rate employees with incentive plans. More recently incentive plans have been extended to include the "front line" supervisors. Many companies have what are called Christmas bonus or profit-sharing plans. The incentives for foremen in mining, which we shall discuss, differ from such bonus plans in that the incentives are paid on a definite measured performance for each individual, and thus directly reflect his effort and skill. What is the objective for paying incentives? The objective for any part of an industrial Engineering Program is to increase productivity and reduce unit cost. The unit cost must include the entire cost of the program. From what base do we start an incentive plan? One should think of art incentive program as the top rung of the Industrial Engineering ladder. Therefore, a company must take several steps before reaching this top rung. The following steps are necessary:

Jan 1, 1960

By John Chipman

The concentration of a solute in a dilute ),zetallic solution may be measured by any of several parame- ters including weight percent, atom fraction, atom ratio, and lattice ratio. The ratio of filled to unfilled interstitial sites is useful for interstitial solutes. A variable 2 proportional to this ratio is used as a measuve of concentration. For component 2 irz a bitzary solution z2 = n2/Ym - nz/b) where b is the numberber of interstitial sites per lattice atom. For a t~lul-ticortzporzent solution this becomes zz = n2/(nl + Cvjnj) in which Vj = - l/b for an interstial solute and +1 for a substitulional solute. In the infinitely dilute solution the activity of an interstitial solute 2 is proportional lo z2. At finile concentration the departure from this limiting law is expressed us an activity coefficient, his coefficient is a function of concentra1io)z expressed as tevactiolz coeffcient 8; is analogous to the jark~iliar e£ bul is found to be independent of concentvation in certain solutions for which data are available. It is found that the same equations may be used to express the activity of a nonmetallic solute, sulfur, in liquid solutions of iron containing other solutes, both metallic and nonmetallic. For a nonmetallic solute or for one which strongly increases the actiuity of sulfur, it is convenient to assign arbitvarily a value vj = — 1. When this is done the derivative is found to be constant in each of the ternary solutions studied. The activity coefficient of sulfur in a complex liquid iron solution may be expressed as where nk is a second-order cross product determined in the quaternary solution Fe-S-j-k. The equation is used to calculate tlze activity of sulfur i)z three sevetl- component solutions. IN thermodynamic calculations concerning dilute solutions it is unnecessary to invoke laws and relations which extend across the concentration range to include concentrated solutions. In most binary metallic systems, as arkeen&apos; has recently pointed out, there exist two terminal composition regions of relatively simple behavior, connected by a central region of much greater complexity. When the solute is a nonmetal there is only one such region and in many systems the concentration range is extremely limited. It is the purpose of this paper to suggest a method for the calculation of activities in such a terminal region in which one or more solutes are dissolved in a single solvent of predominantly high concentration. HENRY&apos;S LAW In the usual textbook statement of Henry&apos;s law, concentration is stated in mole fraction. This has the advantage that it makes Henry&apos;s law thermodynamically consistent with Raoult&apos;s law. Since all measures of concentration at infinite dilution are related by simple proportion it follows that mole fraction, molality, atom ratio, weight percent, or any other unit of concentration can be used with the appropriate constant. At finite concentrations, however, calculations based on the law depend upon the unit employed. Deviations from Henry&apos;s law at finite concentrations depend upon the composition variable employed. They are evaluated in terms of activity and interaction coefficients2 which have become familiar features of metallurgical thermodynamics. It is the purpose of this paper to propose a measure of concentration for metallic solutions containing interstitial or nonmetallic solutes by means of which the calculation of activities in complex solutions may be simplified. The discussion will be restricted to free-energy interaction coefficients3 typified by Wagner&apos;s c|a BINARY SOLUTIONS The several measures of concentration which are to be considered are shown in line a of Table I. The corresponding activity coefficients are in line b and the deviation coefficients, sometimes called self-interaction coefficients, are in line c. Henry&apos;s law simply states that the activity coefficient approaches a constant value at infinite dilution. By adoptihg the infinitely dilute solution as the reference state and defining the "Henrian" activity as equal to the concentration in this state, the activity coefficient is always unity at infinite dilution. This convention is far sim~ler and more useful in dilute solution than emploiment of the &apos;Raoultian" activities and it will be used in the following discussion. The several definitions and equations of Table I will be referred to by means of their coordinates in the table. Early observations of deviations from Henry&apos;s law in metallic solutions were shown graphically4 rather than analytically. For the case of sulfur in liquid iron5 the slope of a plot of logfs vs (%S) was constant in the range 0 to 4.8 pct S, indicating constancy of eh2&apos; in Ic. He was proposed by wagnerz and has been widely adopted. The a function of IIIc recently employed by ~arkenl was designed specifically for dilute solutions. Darken has shown that the value of a12 remains essentially constant for many binary solutions within a substantial range of compositions. The atom ratio is directly proportional to the molalitv.<, a conventional measure of concentration. IVb and C served as the basis for smith&apos;s6 classic studies of

Jan 1, 1968