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By H. G. HYMER

B ECAUSE of its remote geographical position and inaccessibility, little is generally known of the mining and prospecting in Northern Rhodesia. In this rather new and promising region, the development of mines presents many difficulties. Although many mineral discoveries have been made, progress in .prospecting the huge mining concessions has been handicapped by the lack of roads, communication, transportation, native population and incomplete knowledge of geology.

Jan 1, 1929

By Scott, Turner

MY whole life has been spent in the mining business, PO I naturally tend to address my remarks particularly to the newly-graduated mining and metallurgical engineers among you. To a certain extent, all forms of engineering principles are involved in the training of the mining engineer, and most sorts of engineering are certainly utilized by him, so every one of this graduatins class is concerned with the field I propose to discuss.

Jan 1, 1932

By S. E. Szasz, E. J. Moore, B. F. Whitney

An accurate value of formation water resistivity R, is essential in calculating formation porosity and fluid saturation from electrical well logs. In the cases where R, has not been measured directly, it must be obtained from other data, e.g., the SP curve. This paper deals with another approach: how to calculate R, from the chemical analysis of the formation water. INTRODUCTION It is known that the resistivity of aqueous solutions of pure salts depends on their concentration and on the temperature; the concentrations are given in MPL (mg of solute per liter of solution), or sometimes in ppm (mg of solute per kg of solution): MPL = ppm X specific gravity. Values for different pure salts are available in the literature, but not for solutions of mixtures which are of practical interest. The major component of the dissolved material in almost all formation waters being sodium chloride, it is customary to express the resistivity of formation waters in terms of equivalent sodium chloride concentration, i.e., the concentration of a solution of pure NaCl which has the same resistivity at a given temperature as that of the formation water under consideration. Thus, the problem of calculating R, from the chemical anaylsis can also be stated as how to convert the other constituents of the solute into equivalent NaCl concentration. Salts dissolved in water are at least partly dissociated into ions, and do not conserve their identity. If known amounts of several salts are dissolved in water, the solution does not necessarily contain the same salts in the original proportion, but perhaps some other combination of the ions, along with free ions in solution. This is why the chemical analysis of formation waters is often given in terms of ions, as if all dissolved salts were completely dissociated. Our problem then boils down to how to convert the concentrations of the various ions to equivalent concentrations of Na' and C1-. Dunlap and Hawthorne' have proposed to convert the concentration of all other ions to equivalent Na' and C1-concentrations by means of constant multipliers; e.g., 0.95 for Ca"; 2.0 for Mg"; 0.27 for HCO 3-; 0.5 for SO, -, etc. Their factors were based on measurements made at 68F on 26 formation water samples from the Texas Gulf Coast, ranging in concentration from 1,500 to 75,000 ppm. The Dunlap method is widely used in electric log interpretation, and is often extrapolated beyond its original concentration range. A comparison of R, values calculated by this method and values actually measured on formation water samples has shown large discrepancies, especially at higher concentrations. Therefore, two new methods were developed at Sinclair Oil Corp.'s Tulsa Research Center to calculate equivalent sodium chloride concentration from the chemical analysis of formation water samples. FUNDAMENTAL CONSIDERATIONS The resistivity of a solution, or its reciprocal the conductivity, at a given temperature is determined by the charge, concentration and mobility of the ions actually present. Monovalent ions such as Na' or C1- always carry the same charge. Compounds of polyvalent ions, however. may show incomplete dissociation, e.g., NaSO; + Na' instead of SO,-- + 2Na'. This happens especially in more concentrated solutions. Only very dilute solutions are completely dissociated, as assumed in the chemical analysis report. At higher concentration, the degree of dissociation depends not only on the nature and concentration of the particular salt under consideration but also on the nature and concentrations of the other solutes. Mobility of the ions depends on the viscosity of the solution. It also depends on the degree of hydration of the ions, which in turn is a function of the nature and the charge of the ions and also of the amount of free water available per ion, i.e., the total ionic concentration. The net effect is that the conductivity increases slower than proportional to the concentration, even if a solution contains only one salt such as NaC1, and is different for different salts (Fig. 1). Conductivity can even decline with a further increase in concentration, e.g., if additional salt is little dissociated but ties up some of the free water and/or causes an increase in viscosity. In solutions containing more than one salt, the contribution of one salt to the total conductivity depends not only on the fractional concentration of this same salt, but also on the concentration of all other solutes. A perfect method would give the conductivity or resistivity of a solution as a function of the concentrations of all solutes present. This is so complicated as to be impractical, and a simpler method must be found which is of acceptable accuracy. The Dunlap method, on the other hand. is too simple because it askmes that at any concentration the contrih-

Jan 1, 1967

By Y. Dardel

Since the first determination of Dumas1 in 1880, many authors have tried to measure the solubility of hydrogen in solid aluminum, or at least the amount of dissolved gas in it. However, the interpretation of the results which have been obtained is still difficult. Sieverts? then Baukloh and Oesterlen,a during their gassing experiments could not determine any solubility of hydrogen in solid aluminum. On the other hand, Portevin, Chaudron and Moreq4 leaving the determination of the hydrogen solubility beyond the scope of their experiments, measured only the amount of gas that they could extract by high voltage positive ion bombardment and found up to 151 cm3 of gas per I00 g of metal. Winterhager,6 by repeated vacuum extraction during severe cold rolling, extracted up to 161 cm3 per 100 g. In both series of experiments, the extracted gas contained chiefly hydrogen with a small amount of nitrogen, carbon monoxide, carbon dioxide and methan. Later, Schmidt and von Schweinitze as well as Chaudron and Moreau7 showed the importance of the adsorbed layer of hydrogen, the extracted quantities being proportional to the surface and not to the weight of the sample, when its cleaning was not perfect. In earlier experiments, Steinhausers extracted from more massive samples nothing but a little amount (< 0. 5 cm3 per I00 g) of hydrogen, carbon monoxide and methane. Thus, according to these experiments the quantity of dissolved gas is probably very small and the effect of the surface could falsify the results of the extraction. However, owing to the care taken by Chaudron and his coworkers, it was clear that all the hydrogen extracted could not come from the superficial layer, or that the links which bound hydrogen to the surface were so strong that the usual method of cleaning could not destroy them. After the main parts of the experiments reported here had already been carried out, Eborall and Ransley9 published the results which they obtained with an analysor having an accuracy of 0.03 cm3 per I00 g, while that of the usual apparatus was only about 0.2 cm3 per I00 g. During all their experiments the adsorbed layer would have been a difficulty, for the value of the adsorbed hydrogen was approximately equal to that of the dissolved amount. Table i—Amount of Adsorbed and Dissolved Hydrogen (After Eborall and Ransley) Extraction Hz Adsorbed „ h2 dissolved Temperature Calculated Extraction OCcma 500 0.057 0.050 600 0.062 o.096 Since always keeping the same adsorbed layer is very difficult, an error in the correction for the adsorption can be made when using the apparatus of. Eborall and Ransley, as well as the earlier apparatus.

Jan 1, 1949

By G. Sachs, G. Espey

IT is well known that high residual stresses are created in tubing by the sinking process, in which no internal tool or mandrel is used.1-4 In this process, the wall thickness is usually slightly increased.4,5 In tube drawing with a plug, the residual stresses are gradually reduced with increasing reduction of wall, and, by the conventional approximation methods of stress measurement, no stress is detected in tubing in which the wall reduction is over 50 per cent of the total reduction in cross-sectional area.1-6, It has also been observed that higher stresses are set up by the use of wide-angle dies than by the use of acute dies.2 The actual stress distribution in drawn .tubing has been investigated by a few workers,7-9 but has not been related to the conditions of the drawing process: Some attempts have been made to correlate accelerated cracking tests for stresses in brass products with the magnitude of the circumferential stresses and the condition of the metal.1-10 MATERIALS AND PREPARATION The material used in this experiment was commercial cartridge-brass (70 per cent Cu, 30 per cent Zn) tubing in the straightened and annealed condition.‡ This tubing was of various outside diameters and had a wall thickness of 0.032 in. It was sunk to 1/2-in. outside diameter by means of an experimental 10,000-lb. hydraulic draw-bench, with a maximum drawing speed of 8 ft. per minute. All dies were of 1/2 -in. diameter. Various die materials and contours were used in order to study the effect of die design on residual stresses in the tubing; the specifications for the dies are given in Fig. I. Castor oil was used throughout as lubricant. Chattering occurred in sinking some of the tubing, particularly when dies having the more acute angles were used, but the tubes showing chatter marks did not differ markedly from those with a smooth surface regarding the magnitude of residual stress. The source of the chattering has not yet been revealed. The wall of the tubing becomes thicker during sinking, as previously observed 4,5 The increases in wall thickness were 3, 7 and 9.5 per cent on the average for 6, 20 and 33 per cent reductions in diameter, no effect of the contour being noticeable. The reductions mentioned throughout this investigation do not consider this fact, but are reductions of the outside diameter. For the evaluation of the residual stress two fundamentally different methods were used. The approximation method1,11 of splitting a certain length of tubing was employed to obtain a bird&apos;s-eye view of the effect of various drawing conditions on the circumferential stress measured by the diameter change occurring on splitting. For the determination of the complete stress

Jan 1, 1941

By B. Yarar, J. Kaoma

[Introduction The critical surface tension of wetting of hydrophobic materials has been investigated extensively by Zisman et al. (1973) and relates the spreading of a liquid on a solid to the surface tension of this liquid. Thus, the Zisman ap¬proach shows that a plot of Cos 0 versus ?LV where, 0 is the contact angle and ?LV is the surface tension of that liquid in contact with its own vapor at equilibrium, produces a straight line which can be extrapolated to Cos 0 = 1. The intercept corresponds to a given ?LV, termed the critical surface tension of wetting. In instances, however, Cos 0 - ?LV plots show deviations from linearity. Alternative approaches have also included the plotting of adhesion tension (YLV COs 0) versus ?LV that can be interpreted in terms of critical surface tension data (Lucassen-Reynders, 1963). It has, on the other hand, been customary to correlate contact angle (0) with flotation data, although it is recognized that surface inhomogeneities and related contact angle hysteresis limit the interpretations pertaining to solid surface structures purely based on contact angle measurements. It is nonetheless true that 0 = 0, when the liquid is water, corresponds to a hydrophilic solid. Determination of ?c by contact angle measurements in conformity with the Zisman approach can encounter experimental difficulties, especially when solids are in a powder form. Following the reasoning that 0 = 0 corresponds to the hydrophilic state of a solid, froth flotation experiments can be expected to produce critical surface tension of wetting values for powders. The technique that consists of plotting recovery (% R) versus YLV data and extrapolating the linear part of the curve to % R = 0, has been described elsewhere (Yarar and Kaoma, 1984). This paper describes some of the results obtained by the extrapolation technique mentioned above, using various sulfide minerals. Experimental Materials Molybdenite (MoS2), sphalerite (ZnS), chalcopyrite (CuFeS2), chalcocite (Cu2S), and galena (PbS) were handsorted from massive samples and ground by mortar and pestle, and the -147 Fan fraction used in experiments; sulfur (S) was a C.P. Fisher Scientific Co. product. Method One gram powder samples were conditioned for three minutes in methanol-water solutions of predetermined surface tension values and the percents recovered by flotation using a Partridge-Smith Cell (Partridge and Smith, 1972), were plotted against each ?LV value. Results and Discussion The percent recovery versus ?LV for two naturally hydrophobic solids, i.e., natural molybdenite, MoS2 and sulfur are given in Fig. 1 where it is seen that ?c for sulfur is obtained as 31.5 mNm-1 whereas for MoS2, it is 26 mNm-1. Figure 1 also shows that the new flotation technique described, for estimating ?c is in good agreement with the Zisman method. Curves obtained by the same method for the minerals Cu2S, PbS, and ZnS are given in Fig. 2, where it is seen that for Cu2S, ZnS, and PbS, the extrapolation to % R = 0 produces ?c values of 36, 39, and 49 mNm-1, respectively. CuFeS2, on the other hand, gives a curve that does not permit such an extrapolation to obtain a ?c value with certainty. Nonetheless, treatment of the powder with 8.95 X 10-5 molar Na2S solution followed by washing with distilled water prior to flotation effects the curves as shown in the insert of Fig. 2. The type of curves given in Fig. 1 appear to be typical of hydrophobic solids as can also be observed in Fig. 3. The composition of solid and minute quantities of inclusions seem to play an important role as regards the surface properties of solids as reflected by the slope of the linear part of the % R - ?LV plot and thus the value of ?c obtained by this technique. For example, MoS2 of three different stoichiometric compositions produced the data given below. [MoS2MoS2.14Mo1.002S2 ?c mNm-126.029.031.0 dR/d?8.95.23.0]]

Jan 1, 1985

By J. Chipman, J. A. Cordier

Equilibrium in the reaction H2 (g) + 2 = H2S (g) was studied at 1600°C for sulphur dissolved in Fe-Ni alloys of 0 to 100 pct Ni. Within experimental accuracy, the equilibrium ratio pH2s/pH2 [pct S] is independent of the Fe-Ni ratio. Its variation with sulphur content is the same in nickel and the alloys as in iron. Recent data on dissociation of S2 into atomic sulphur are used to apply a small correction to earlier equilibrium data. Equations are presented which define the thermodynamic properties of sulphur in liquid Fe-Ni alloys. ACTIVITY of sulphur in liquid iron was determined by Sherman, Elvander, and Chipman.&apos; The effects of a number of alloying elements on the activity of sulphur also have been determined, that of silicon by Morris and Williams,2 that of carbon by Morris and Buehl,8 and the effects of manganese, phosphorus, and aluminum by Sherman and Chip-man.&apos; The data of Rosenqvist and Cox5 have been used to establish the effect of copper. A summary of all of these data is included in the paper by Sherman and Chipman. In each case, the experimental method depended upon the study of equilibruim in the reaction of sulphur in the liquid metal with hydrogen gas to form H,S. Despite wide differences in the design of apparatus used by the several investigators, all of the results are in excellent agreement. Experimental Study Since the experimental method has already been described,&apos; it will be sufficient to mention its general

Jan 1, 1956

By J. J. Fischer

COMPOSITES containing cold-drawn, high-strength steel wires have shown promise for normal and slightly elevated temperature applications, particularly where strength-to-weight ratios or corrosion resistance are important.&apos;-3 Although tensile strengths up to 500,000 psi may be obtained by cold drawing these wires, processing the composite at elevated temperatures will result in a rapid decrease of the wires&apos; strength. In wrought maraging steels, high-strength levels can be obtained by aging at 900&apos; . Because these alloys do not rely on heavy cold working to achieve their strength, and because they do not overage readily, they are of potential interest for use in composites. In view of this, the tensile strengths of composites containing The total heat effect thus represents the heat of formation, AHf of the compound at 273&apos; . Since the heat of solution of tin in the tin solvent bath is zero, AHz = 3( - H273)Sn and Hf is given by: For LaSn3, AH3 had a measured value of 11,285 i 380 cal per g-atom while for La2Sn, the corresponding value was 33,658 870 cal per g-atom. Using the measured data for the compounds and pure lanthanum, a value of -15,150 200 cal per g-atom was calculated for the heat of formation of LaSn, at 273°K, while Hf for La2Sn3 was found to be -28,090 400 cal per g-i&om. The authors would like to acknowledge the financial support of the Army Research Office, Durham, North Carolina. under contract No. DA-31-124-ARO-D-384.

Jan 1, 1969

By W. H. C. SIMMONDS

The mining, metallurgical, and petroleum industries can be viewed as financial or as social institutions or both. The differences between these two conceptions of their businesses will influence their environmental &apos;and social actions. During the next 10-20 years western industry will be subject to a drop in the growth of a more highly educated labour force and to the emergence of holistic economics, new national goals, and a new ecological perspective. The profitability of the mining industry may therefore be influenced by the human side of its business to a greater degree. The increasing human, social, and environmental responsibilities can be discharged by improving the miner&apos;s equipment; by learning to look at situations through the eyes of all those involved; by developing common &apos;languages&apos; which governments and the public can understand; and by mediating where feasible on the international scene.

Jan 1, 1978

By Donald Barton

THE theory of gravitation is based on Newton&apos;s law that any two bodies exert a mutual attraction which is proportional to the product of their masses and inversely proportional to the square of the distance between them; i. e., A = K MM/R2 (1) where K is a constant, M and m are the respective masses of the two bodies, and R the distance between them. In the earth&apos;s gravitational system, the earth is one of the bodies; the other may be any body within or without the earth. In theoretical discussions and calculations in regard to gravity, that other body usually is taken as a unit of mass: in the C. G. S. system, a body of one gram in mass. GRAVITY AND LEVEL SURFACES Gravity is defined in geophysics as the force of attraction exerted by the earth, towards itself, on a body of unit mass. The intensity of gravity is usually expressed in dynes of force or in centimeters of acceleration. In geophysical work in America, most commonly it is expressed in dynes (per gram) with the "per gram" understood and not directly expressed. In geophysical work in Europe, most commonly it is expressed in centimeters per second per second (cm./sec 2) and less commonly merely as centimeter-gram-second units (C. G. S.). At sea level, the intensity of gravity amounts very nearly to 980 dynes. The vertical is the direction along which the attraction of gravity is exerted at any point. In most cases, it is very nearly, but not quite, perpendicular to the earth&apos;s surface. The path that would be taken by a body falling freely through space toward the earth is vertical at each point and may be spoken of also as "the vertical," or as the line of the vertical, or as a line of force of gravity. At the earth&apos;s surface it commonly is very nearly, but not quite, a straight line.

Jan 1, 1928

By Donald Barton

THE theory of gravitation is based on Newton&apos;s law that any two bodies exert a mutual attraction which is proportional to the product of their masses and inversely proportional to the square of the distance between them; i. e., A = K MM/R2 (1) where K is a constant, M and m are the respective masses of the two bodies, and R the distance between them. In the earth&apos;s gravitational system, the earth is one of the bodies; the other may be any body within or without the earth. In theoretical discussions and calculations in regard to gravity, that other body usually is taken as a unit of mass: in the C. G. S. system, a body of one gram in mass. GRAVITY AND LEVEL SURFACES Gravity is defined in geophysics as the force of attraction exerted by the earth, towards itself, on a body of unit mass. The intensity of gravity is usually expressed in dynes of force or in centimeters of acceleration. In geophysical work in America; most commonly it is expressed in dynes (per gram) with the "per gram" understood and not directly expressed. In geophysical work in Europe, most commonly it is expressed in centimeters per second per second (cm./sec.2) and less commonly merely as centimeter-gram-second units (C. G. S.). At sea level, the intensity of gravity amounts very nearly to 980 dynes. The vertical is the direction along which the attraction of gravity is exerted at any point. In most cases, it is very nearly, but not quite, perpendicular to the earth&apos;s surface. The path that would be taken by a body falling freely through space toward the earth is vertical at each point and may be spoken of also as "the vertical," or as the line of the vertical, or as a line of force of gravity. At the earth&apos;s surface it commonly is very nearly, but not quite, a straight line.

Jan 1, 1928

By C. R. Kuzell

STAFF: Editor, Gerhard Derge Carnegie lnstitute of Technology Schenley Pork Pittsburgh 13, Pa. Editorial Assistant, M. A. Redmerski Production Editor, Otto T. Johnson THE METALLURGICAL SOCIETY: C. C. Long, President; John Chipman, Past-President; J. S. Smart, Jr., Vice-President, T. D. Jones, Treasurer; R. W. Shearman, Secretary. PUBLICATIONS COMMiTTEE OF THE METALLURGICAL SOCIETY: D. J. Carney, Chairman; Robert Maddin, Past-Chairman; J. H. Hollomon, J. H. Jackson, H. H. Kellogg, T. B. King, F. C. Langen-berg, D. L. McBride, W. O. Philbrook, J. S. Smart, Jr., R. L. Smith, J. D. Sullivan, and F. L. Vogel Review and selection of manuscripts is under the supervision of the following Publications Committees: Extractive Metallurgy Division: H. H. Kellogg, Chairman; T. 8. King, Post-Chairmon; R. P. Hermsdorf, W. A. Krivsky, R. E. Lund, C. L. McCobe, Poul Queneou, A. 5. Russell, M. E. Wadsworth, and W. D. Wilkinson. Institute of Metals Division: R. L. Smith, Choirman; P. A. Beck, I. I. Bessen, J. O. Betterton, Jr., R. S. Davis, J. J. Gilmon, R. 8. Gordon, C. D. Graham, Jr., R. W. Guard, J. C. Gurlond, J. J. Heger, M. Hermon, J. N. Hobstetter, H. H. Johnson, Jr., I. R. Krarner, W. C. Leslie, R. A. Meussner, R. R. Nosh, G. E. Pellissier, T. N. Rhodin, A. U. Seybolt, L. L. Seigle, I. S. Servi, P. G. Shewmon, L. Slifkin, J. K. Stanley, C. D. Starr, and J. Washburn. Iron and Steel Division: F. C. Longenberg, Chairmon; H. L. Bishop, C. W. Sherman, J. 8. Wagstaff, and E. Whittenberger. Published bimonthly by the American lnstitute of Mining, Metallurgical, and Petroleum Engineers, Inc., 29 West 39th Street, New York 18, N. Y. Telephone: PEnnsylvania 6-9220. Subscription $20 per year for nan-AIME members in United States and North, South, and Central America; $25, foreign; $5 far AlME members. Single copies, $4.00, single copies foreign, $5.00. The AlME is not responsible for any statement mode or opinion expressed in its publications . . . Copyright 1960 by the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. . . . Registered cable address, AlME New York ...Indexed in Engineering Index, Industrial Arts Index, and Chemical Abstracts ... Second class postage paid at New York, N. Y., and Ann Arbor, Mich. Volume 218, Number 4

Jan 1, 1961

By G. G. Reed

G.G. Reed, Jr. The authors are to be commended for finding a material for pellets binding that we were unable to uncover during the investigations that led to US Patent No. 3,748,116, "Method for producing metallic iron powder from iron ore concentrate," July 24, 1973, by G.G. Reed, Jr., J.M. Karpinski, and S.V. Fox. This patent concerns a method of processing "super"-concentrates prepared from magnetite or "blue dust" into molding-grade metallic iron powder for use as a bulk commodity, in contrast to current methods which produce small batches that are custom-blended with additives and/or alloys to customer specifications. The one thing we had not found at that time was an organic binder (mineral-matter-free) that would allow induration to produce hardened pellets that would survive SL/RN Direct Reduction. Peridur appears to provide this missing link needed for large scale (200 t/a, or 220,460 stpy) single line plant capacity consistent with a low market price to ensure greatly broadened use of metallic iron powder. I hope that industry will adopt this combination so that metallic iron powder usage can fulfill its potential. ?

Jan 1, 1986

By John S. Alexander

By M. J. Pool, P. J. Spencer

Using liquid tin as the solvent metal, the heats of solution of silver and gold in dilute Ag-Au-Sn alloys have been determined at 723°K by solution calorimetry. From the values obtained, the various enthalpy interaction coefficients in the liquid solutions have been calculated. The self-interaction coefficients Au and Ag values of 2413 and -6322 cal per g-atom in binary Au-Sn and Ag-Sn alloys, respectively. For an alloy containing 0.04 mole fraction Ag, Au is equal to 2443 cal per g-atom, and in an alloy containing 0.04 mole fraction Au, Ag has a value of —8883 cal per g-atom. Ag Au has been determined as —2650 cal per g-atom. ADDITION of a second solute to a dilute binary alloy may cause striking changes in the thermodynamic characteristics of the alloy. As yet, such influences cannot be reliably predicted and it is only by accumulation and critical assessment of data that definite patterns can be established. Solute interactions in dilute solutions were first treated mathematically by Wagner,1 who derived expressions for the Gibbs energy interaction coefficients. For an alloy consisting of. two dilute solutes, i and j, in a solvent s, these coefficients are given by: where yi is the activity coefficient of component i and x represents the mole fraction of solute or solvent. Other interaction coefficients have since been established in terms of the various partial molar thermodynamic properties of an alloy; the definitions of these are summarized in a recent paper by Lupis and Elliott.2 Mathematical and experimental studies of such coefficients have received much attention recently, providing a very useful theoretical background to an understanding of the nature of solute interactions taking place in dilute solutions. One of the definitions to arise from such work has been the extension of Wagner&apos;s treatment by Lupis and Elliott4 to include an enthalpy interaction coefficient, defined as. where ?Hi is the relative partial molar enthalpy of component i. ?Hi is related to the relative partial molar enthalpy at infinite dilution, ?Hio, and to the enthalpy interaction coefficients by the expression: Values of ?Hi can often be obtained with a high degree of accuracy by calorimetry, and, if the composition of the alloy is carefully controlled by making calculated solute additions throughout a series of measurements, application of Eq. [2] will enable reliable enthalpy interaction coefficients to be determined. Partial heats of solution must be investigated as a function of solute concentrations down to xi = 0, and, since ? values are obtained from the slope of mi plotted against x, great care must be taken to obtain precise data. The data for binary systems which are presently available often require extrapolation of ?Hi values from compositions as great as xi = 0.05 or even 0.1 to obtain limiting heats of solution. Reliable enthalpy interaction coefficients are thus impossible to obtain from published data for most of the alloy systems already investigated. The aim of the present work was to determine values of Au, Ag, Ag, and Au in the limit xsn -1 for the relatively simple Ag-Au-Sn system and from these results to gain some insight into the possible influence

Jan 1, 1969

By Horace R. Graham

CHEMICAL nitrogen and the "nitrates" of commercial significance are derived mainly from three basic sources: (1) the natural deposits in the form of nitrate-bearing earth and clay, which, being largely water-soluble, can exist only in the most arid portions of the earth; (2) coal, which yields not only nitrogen but also the additional by-product hydrogen required for the synthesis of ammonia and its compounds; (3) the atmospheric air, which contains 75.5 pct by weight of pure nitrogen gas. NATURAL NITRATE DEPOSITS Occurrence Although natural nitrate deposits consisting principally of the salts of sodium and potassium have been reported in Egypt, South Africa, Mexico, Argentina, Colombia, Peru and the USA, the only known natural nitrate resources of commercial importance are the vast deposits found in the Atacama, Tarapaca and Antofagasta regions of northern Chile, lying in a narrow strip 10 to 50 miles wide and roughly 450 miles long, between latitudes [19O] and [26OS]. In addition to yielding nitrates of sodium and potassium, these deposits are the source of the major portion of the world&apos;s supply of iodine. The nitrate-bearing ores known in Chile as caliche are variable in composition and may contain from 5 to 30 pct each of nitrate, chloride and sulphate. While the deposits are present chiefly in the form of the sodium salt, potassium, magnesium and calcium also occur in percent- ages from 0.1 to 5; usually as double salts with sulphate, which are but slightly soluble in nitrate leach solutions. These double salts are bloedite(Na2S04.MgS04.4H,0), glauberite (Na2S04.CaS04), polyhalite (K2SO4.- MgS04.2CaS04.2H20). Some deposits contain up to30 pct of their ni-

Jan 1, 1949

P. W. BRIDGMAN.-Owing to a misunderstanding, I did not see Dr. McAdam&apos;s and Dr. MacGregor&apos;s remarks on my paper on Flow and Fracture (Metals Technology, December 1944, Pp. 32-38), until after their publication. Both Dr. McAdam and Dr. MacGregor speak of my analysis for the stress distribution at the neck of a tension specimen as containing several assumptions; in particular, that the strain is uniform across the section of the neck, that there is no hoop tension at the periphery, and that the plasticity conditions of von Mises hold. As far as the mathematics goes, the situation is no different in this problem of plastic flow than in a conventional problem of elasticity. That solution is unique which satisfies the boundary conditions on the stresses, the stress equations of equilibrium, and in addition the constitutive equations connecting stress and strain in the elastic case, or a corresponding set of equations, of which the von Mises relations are a special form, in the plastic case. In the particular case of the necked tension specimen I have found that there is a solution satisfying the boundary conditions, the stress equations of equilibrium, and the von Mises plasticity conditions in which the strain is uniform across the section, and there is no hoop tension at the periphery. This is therefore the solution, and the uniformity of strain and vanishing of hoop tension at the periphery are to be described as discoveries, over which the operator has no control, rather than as assumptions. The only part of the solution that can properly be described as an assumption is the von Mises plasticity condition. With regard to this it is to be noted that the condition is needed only in a much weakened form, for the analysis uses the condition only at the neck, where the strain is approximately constant. Thus, in the extreme case referred to in a footnote of my paper (p. 37, Met. Tech. Dec. 1944) the actually measured strain across the section varies from 2.4 to 2.6. Obviously it is a much weaker assumption to postulate that the von Mises condition holds in the strain range 2.4 to 2.6 than to assume it to hold for the entire range of strain from o up to 2.6, which would be necessary if the solution applied to the entire tension specimen rather than to the immediate region of the neck only. Furthermore, it is to be commented that under the special conditions of this problem the von Mises condition becomes identical with the maximum shearing-stress criterion of plastic flow; this amounts also to a weakening of the restrictions imposed by the von Mises condition. Dr. MacGregor refers to actual experiments of his own in which the strain was found not to be uniform across the neck. It is to be emphasized, however, that these were experiments on bars of rectangular section, and that the nonuniformity established was a nonuniformity around the perimeter, not a nonuniformity from the surface toward the axis. My method of solution applies only to a circular cross section. It can be said that the solution that satisfies the boundary conditions, etc., would definitely not be expected to demand a uniform strain for noncircular sections. In discussing my results, Dr. McAdam uses a definition of "flow stress" different from mine, so that the immediate applica-

Jan 1, 1945

By C. H. P. Lupis, Henri Gaye

There are m -I conditions for the stability of a solution of m components with respect to infinitesinzal flucturations. However, in most cases, only one of these conditions has to be considered to determine the domain of instability and the existence of this more restrictive condition greatly simplifies the calculations. It may be used advantageously for the prediction of miscibility gaps and the method is illustrated in details for the case of the Ag-Pb-Zn system. THE thermodynamic conditions for the formation of a miscibility gap may be viewed as a necessary consequence of the conditions for spinodal decomposition. A previous article1 has examined in detail the form of these conditions for multicomponent systems. There is only one condition for the stability of a binary system (with respect to infinitesimal fluctuations), but there are two conditions for a ternary system, and m — 1 conditions for an m-component system. The probability of violating a stability condition, and thus forming a miscibility gap, obviously increases with the number of components, a result which is rather intuitive since the atoms of the solution have now many more ways of redistributing themselves and introducing complexities in the form of the free energy hy-persurface. It is of interest to take advantage of this possibility of precipitating new phases and to examine which stability condition is the likeliest to be violated, that is, which stability condition is thermodynamically the most restrictive. The finding of such a condition would greatly simplify the application of the stability criteria since only one condition could then be considered, instead of m - 1. In Ref. 1, coherency strain energy terms were neglected, thus restricting the applications of the treatment to solutions where they are negligible, such as liquid alloys. In the following study the same assumption will be made. To generalize the treatment to systems where the strain energy terms are sizable, the reader is referred to Cahn&apos;s classical article on spinodal decomposition.2 Let us designate by Gij the second derivative of the Gibbs free energy with respect to the number of moles ni and n j. There are several equivalent sets of m — 1 stability conditions.&apos; The one considered here expresses that the successive diagonal determinants of order 1, 2, ... m — 1, associated with the symmetric Gij matrix (for 2 5 i, j 5 m) are positive.&apos; For a binary solution 1-2, the condition for stability is: O(u=G22^0 [1] For a ternary system 1-2-3, the condition [I.] is re- tained (the value of G22 will differ, of course, according to the concentration of 3) and another condition is introduced: £>(21 = G22G33 - Gl3 ^ 0 [2] In a composition diagram, these two conditions define two domains of instability. Starting at a point where the solution is stable (for instance at a point where the solution is very dilute) we gradually change the composition until the condition [I] or [2] is violated. As already noted in the literature, e.g., in the work of Prigogine and Defay,3 it is the boundary of the domain (2) which is first crossed. For if we assume that the boundary of the domain (1) is reached first, at this point G22 = 0 and the second condition is necessarily violated (D(2) = -& 5 0), in contradiction with our original assumption. An exhaustive study of the ternary regular solution case may be found in the work of Meijering.4 Moreover if the boundaries of the two domains have a common point, they also have a common tangent. For if the two lines were to cross each other as is illustrated in Fig. 1(a) any point M in the line QP would be such that £> = 0 and 0"&apos; > 0 which, as shown above, are incompatible results. Thus, the two lines must be tangent at their common point Q as illustrated in the example of Fig. l(b). The reasoning of Fig. l(a) implies that the point Q is not a "singular" point for either boundary line. This singularity may be of two types. First, the lines meet without crossing each other and without being tangent. Second, the tangent at Q for D"&apos; or 0"&apos; is not single-valued. Other types of singularity are unlikely because of the usual analytical forms of D"&apos; and 0"&apos;. The exception to the common tangent requirement due to the first type of singularity was pointed out by John Morral;5 it occurs when the common point, Q&apos; or (3" in Fig. l(b), is located at a boundary of the composition diagram, e.g., at the line X3 = 0. It may also be noted that at the common nonsingular point Q of D(1) and D(2), Fig. 1(b), G23 is necessarily equal to zero, whereas at a point such as Q&apos; or Q", this conclusion is no longer valid because the product G22G33 is now indefinite (of the form 0. a). The exception to the common tangent requirement due to the second type of singularity occurs when two branches of the same boundary line intersect, for example when D(1)or D(2) decomposes into a product of functions, at a point which belongs to the boundary of the other condition. It is possible to show by a simple analytical calculation that, in this case, if Q is a singular point of D(1), then it is necessarily a singular point of D(2), and that the reciprocal is true except if G33 = 0 at Q. For the present article, however, more elaboration on these singularities appears to be unwarranted. To generalize the previous results to an m -component system, we use the mathematical theorem stating that if the diagonal determinant D(r) = 0, then

Jan 1, 1970

Executive Committee Board of Directors L F Reinartz, Chairman, H DeWitt Smith, Vice-Chairman, T B Counselman, M L Haider, Philip Kraft Finance Committee Board of Directors Andrew Fletcher, Chairman, A B Kinzel, D Wilson Endowment Fund "X" G F Moulton, Chairman, Erle V Daveler, &apos;55, Philip Kraft, &apos;56, I Brigden, &apos;57 Honorary Memberships W M Peirce, Chairman, &apos;56, M L Haider, ex officio, Andrew Fletcher, ex officio, John M Lovejoy, &apos;55, D H McLaughlin, &apos;57, Henry Krumb, &apos;58, L F Reinartz, ex officio Investments Erle V Daveler, &apos;57, Chairman, W M Peirce, &apos;55, Henry Krumb, &apos;56, G F Moulton, ex officio as Treasurer, Andrew Fletcher, ex officio as Chairman Finance Committee Local Section Appropriations A B Kinzel, Chairman, M L Haider, W S. Cumings, Fred J Meek

Jan 1, 1954

By Elmer W. Pehrson

NINETEEN FORTY-SIX was an eventful year for the mineral industries. Perhaps the most significant development was the socialization of industry in Great Britain, initiated in 1945 but carried to fruition in the coal industry in 1946. On Jan. 1, 1947, management of the coal industry will be vested in a National Coal Board, responsible to the Ministry of Fuel and Power. A sum of £164,660,000 has been provided to compensate private owners for assets transferred to the Board. The British coal industry has been a problem for many years. Production has declined to a point where serious shortages of fuel for domestic needs have developed. Exports have dwindled to a small fraction of the previous trade. Costs have increased greatly, and quality has deteriorated. The industry&apos;s physical plant has not kept pace with the rapidly mounting wage scales in recent years. Some claim that the best and most accessible coal reserves of Britain are heavily depleted. The industry has been harassed by difficult labor problems, including bad morale among the workers and a shrinking labor force.

Jan 1, 1947