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By H. I. Aaronson, S. Toney

When the component grains of .ferritic hicrystals of an Fe-1.55 pct Si alloy are disoriented through an angle "6 " about a conzmon [ll0] axis, the tendency for preferential growth of austenite crystals along the grain boundary during transformation at elevated temperatures is small when 11 deg, but increases rapidly at larger angles. This type of orientation-dependence indicates that grain boundary diffdsion promotes preferential growth along large-angle boundaries. Morphological differences between austenite crystals formed at small-angle [1101 and [loo] boundaries suggest that precipitate morphology can be dependent on the dislocation structure of the boundary. ThE morphology of precipitate crystals nucleated at a grain boundary can be significantly affected by the structure of the boundary.' The limited amount of experimental evidence available in the literature indicates that the morphological effects of boundaries made up of arrays of dislocations, such as subbound-aries and small-angle grain boundaries, are different from those of boundaries having essentially disordered structures, i.e., large-angle grain boundaries. On the basis of indirect evidence, it has been concluded that large-angle grain boundaries give rise to the formation of grain boundary allotriomorphs (crystals which nucleate at grain boundaries, and grow preferentially and more or less smoothly along them)2 in the proeutectoid ferrite and the proeutec-toid cementite reactions in plain-carbon steels, and apparently also in many non-ferrous alloys.' At small-angle grain boundaries in a plain carbon steel, on the other hand, ferrite crystals were found to take the form of primary side plates. Similarly, Guinie, loys. Primary sideplates formed at a subboundary with a constant orientation tend to be parallel to only one, or occasionally two matrix habit planes, and a marked change in the orientation of the boundary is accompanied by a change in the habit plane. Previous studies on the morphological effects of grain boundary structure were performed on poly-crystalline aggregates. Information on the disorien-tation of the pairs of grains forming the boundaries at which the various morphologies appeared in these specimens was largely either qualitative or semi-quantitative. Precipitate morphologies accordingly could not be accurately and systematically correlated with grain boundary structure, and thus theories which have been proposed for the various morphological effects could not be satisfactorily tested. This investigation was undertaken in an attempt to remedy these deficiencies by studying the morphological effects of grain boundary structure with a method in which the boundaries are formed by matrix grains whose disorientations are known and controlled with reasonable accuracy. EXPERIMENTAL PROCEDURE The crystallographic requirements of this study were fulfilled by means of oriented bicrystals of silicon-iron. Disorientation of the component ferrite crystals was carried out about common, major crystallographic axes through angles ranging from 1/2 to 44 deg. The silicon content was low enough SO that the bicrystals could be partially transformed to austenite by heating to elevated temperatures. The silicon-iron used had the following initial composition: 1.55 pct Si, 0.04 pct C, 0.0031 pct N, 0.17 pct Mn, 0.020 pct S, and 0.002 pct P. The alloy was obtained in the form of 0.036-in. sheet. The procedures employed to prepare seed crystals in strips of this sheet, to reorient the seeds, and to grow them into bicrystals are essentially those described by Dunn and Nonken and aynes." The characteristics of the bicrystals are given in Table I. The "bicrystal type" indicates the crystallographic plane parallel to the broad faces of the strip in both grains and the crystallographic direction which was parallel to the long edges of the strip in both grains prior to disorientation. The angular disorientation of the grains, 8, which was performed about the direction normal to the plane of the broad faces of the strip, was measured between the [ 00l] directions. Orientation of the grain boundary, , was taken as the angle between the plane of the grain boundary and a plane containing the axis of disorienta-

Jan 1, 1962

By Louis E. Reber

Jan 1, 1922

By Ernst F. Eurich

(Cleveland Meeting, October, 1912.) ALEXANDER PARKES patented in England in 1851-52-53 a process for desilvering lead by means of zinc, making use of the greater affinity of silver for zinc than for lead, discovered by Karsten in 1842. The efforts in England to develop it commercially were not particularly successful, nor was the attempted introduction into the United States. This last was not surprising, as it was about the beginning of our Civil War, and at that period there was very little lead-bullion produced in the united States and there was no field for the process here. There was at that time on Staten Island an establishment that pattisonized lead, probably from Rossie, N. Y., and Chester, Pa., and possibly some Spanish lead, but the production of lead-bullion in the Far West had not yet begun. In 1864, Edward Balbach, of Newark, N. J., patented in this country a process for desilvering lead by means of zinc, and in 1867 Edward Balbach, Jr., patented a " movable black-lead retort with a neck, placed in a furnace," for the purpose of distilling the alloy of zinc, lead, and the precious metals. A brief comparison of the Parkes and the Balbach processes is interesting. The Parkes process as practiced in England consisted in stirring into silver-bearing lead, melted in a kettle, from 1 to 2 per cent. of zinc, cooling, skimming the alloy of lead, zinc, and silver that rose to the surface, liquating it in an iron retort, distilling the residual rich alloy in fire-clay retorts, thus regaining the zinc, and refining the desilvered lead at a low heat in a shallow cast-iron pan that formed the hearth of a reverberatory furnace. If the lead was too impure, it was first softened * Presented also at the Joint Meeting of the Institute and Section IIIa, Metal¬lurgy and Mining, of the Eighth International Congress of Applied Chemistry, New York, September, 1919, and here published by mutual agreement.

Dec 1, 1912

By Francois E. Heuze

INTRODUCTION Rock slope stability typically is governed by the geological discontinuities. This stability can be improved by drainage, unloading, adjustment in slope orientation, adjustment in slope angle, and also by reinforcement such as bolts or tendons. This paper addresses the modeling of bolt reinforcement in rock slopes. Most geological discontinuities such as joints have rough surfaces; they dilate during shear displacement. Their shear strength is characterized by two envelopes (Fig. 1); the peak envelope is distinct from the residual envelope when the joints can dilate. If the dilation is restrained transversely, such as with bolts, the normal stress will increase and the joint strength also will increase. It has been demonstrated that this increase may be considerable (Obert et al., 1976). The new normal stress at peak strength is a com- posite function of the properties of the rock mass and of the steel (Heuze, 1979). Hence, the dilation and its resultant effects on joint shear strength must be included in the analysis and design of the reinforcement. We present a model which can be used to perform such an analysis. Early studies of rock reinforcement in mining and civil applications (Lang, 1957 - Panek, 1962 - Osen and Parsons, 1966 - Lang, 19721, did not consider the specific effects of bolts on joint shear strength. In 1973, Heuze and Goodman reported direct shear tests on rough sandstone joints with bolts perpendicular to the joint plane (Fig. 2). The peak shear strength of such joints was greatly in excess of the shear strength of the unbolted joints. The excess

Jan 1, 1983

Ahrenholz, Herman William, Jr., Student, Lehigh Univ Bethlehem, Pa. '35 Allen, Carl A., Student, Colorado School of Mines Golden, Colo. '35 Allen, Paul W., Student, Mass. Inst. of Tech Cambridge, Mass. '35 Allen, R. M., Jr., Student, Virginia Polytechnic Inst., "G" Co Blacasburg, Va. '35 Amberger, K. H., Student, Michigan College of Min. & Tech Houghton, Mich. '35 Andersen, Burton Lee, Student, School of Mines, Univ. of Washington Seattle, Wash. '35 Anderson, Joseph S., Student, Univ. of Texas El Paso, Tex. '35 Anderson, R. C., Student, Univ. of Washington Seattle, Wash. '35 Ansel, Gerhard 627 Clyde St., Pittsburgh, Pa. '34 Anutta, Frederick P., Student, Michigan College of Min. & Tech Houghton, Mich. '35 Apsouri, Constantin N., Graduate Student, Univ. of Arizona Tucson, Ariz. '35 Arakelian, Haig Mark, Student, Mass. Inst. of Tech Cambridge, Mass. '34 Archer, George K 1420 Court Pl., Denver, Colo. '34 Argall, George O., Jr., K. E. House Golden, Colo. '35 Argiielles, Alfredo, Student, Univ. of Texas El Paso, Tex. '35 Atwater, Ralph, Student, South Dakota School of Mines Rapid City, S. D. '35 Austin, Robert B., Miner, Page Mine, Federal Min. & Smelt. CoSpokane, Wash. '34

Jan 1, 1934

K. Baumgarten has returned from active service in France. He reports that he saw C. W. Campbell, formerly with the 2d Engineers on the Chateau Thierry front, and believes that the latter returned to the United States on August 1. He also saw J. J. Croston; G. J. Sielaff, recently transferred to the Gas Service; Thomas M. Smither, survivor of the Tuscania after a 10-mile swim to Ireland. While in Paris he en-deavored to see Prof. Sauveur, but was unsuccessful. F. K. Borrow was given a commission as Lieutenant in the Royal Garrison Artillery in 1914, but had to relinquish it, on account of ill health, in August, 1915. His health has much improved and he hopes to resume active work toward the end of this year. Davis, A. W:, see British Columbia Engineers, below. Alfred Fox, Jr., enlisted in the Public Schools Brigade, Royal Fusiliers, in September, 1914; was gazetted Lieutenant in the Royal Field Artillery in December, 1914, promoted to Captain in November, 1915, and Adjutant to 78th Brigade, Royal Field Artillery, in January, 1916. He was appointed Staff Captain of the 12th Divisional Artillery in November, 1917. He has served continuously in France since July 1, 1915. He was awarded the Military Cross in January, 1917, and four times mentioned in despatches. E. Fraser-Campbell writes that he joined the London University 0. T. C. in January, 1918, for five weeks; enlisted with the Argyll and Sutherland Highlanders in February, 1918, and attended a training course for officer cadets at Chatham for six weeks. He was commissioned 2d Lieutenant, Royal Engineers, in April, 1918. After two months on home training at Chatham, he landed in France on June 23, 1918, posted to 180th Tunnelling Co., R. E., and is now with his unit up on the line.

Jan 10, 1918

By George W. Healy, Ko Yamaguchi

In typical calorimetry the energy given off by a material under study is transferred to a water bath, whose temperature is sensed by a thermometer; for correct measurement the water bath must attain a uniform temperature to which the thermometer must respond. This introduces two sources of error, non-uniformity of the heat sink and a time lag until its temperature is registered. These errors may become important where a rapid process such as solidification of metals and alloys is being studied by means of Oelsen'sl quantitative thermal analysis. To overcome this difficulty, a calorimeter sink was conceived in which the water bath is replaced by a copper coil, which serves simultaneously as heat

Jan 1, 1967

By Joseph N. Morrison

A comprehensive solution is offered to the problem of dust emissions at belt conveyor transfer points. Details of enclosure design are discussed and a straightforward procedure for calculating required dust control exhaust volume is presented. Many design variables are taken into account which heretofore have been commonly ignored or inadequately considered. These include belt widths, belt speeds. enclosure openings, material flow rate, material bulk densities, material lump sizes, height of material fall, material temperature, and ambient air temperature. All of these questions are handled by means of a "fill-in-the-blanks" type of calculation form, permitting quick, reliable solutions by relative "non-experts."

Jan 1, 1972

Jan 1, 1890

By Arthur F. Johnson

Plant sites for the light metal industry must be located where ample low cost power is available. In the first half of the century hydroelectric development was the only source of this power-now the best sites have been exploited and those remaining do not promise enough water to permit year-round capacity power plant operation. In searching for economic plant sites engineers have concentrated on locations with vast water power potential. Olin Mathieson Chemical Corp. has been studying the economics of developing water power to make aluminum. However natural gas, lignite, and even atomic energy have also been considered as possible power sources for aluminum production. Economic studies have given consideration not merely to investment and production costs, but to total costs of delivering fabricated products to the market center of the U. S. When delivered costs are considered and when full account is taken of the newest techniques of mining bituminous coal and utilizing it to make electric power, one arrives at the inescapable conclusion that coal has emerged as the economic answer to American aluminum production.

Jan 4, 1955

By David J. Dunn

GENERAL NOTES Liner Design for Comminution Liners in crushers and mills are the mechanical link between machine and ore. The way liners transfer energy to media and ore determines to large degree the production rate, liner wear rate, maintenance cost, energy use, and availability of the comminution process. Plant capacity and mineral recovery economics, and return on investment, are thus strongly dependent upon these simple, low cost metal shapes of which so much is demanded. The complexity of dynamic relationships between liner configuration, material properties, ore characteristics, and operating parameters defy simplistic generalization. Rules-of-thumb and axioms of years past fall into disuse almost daily as new analytical methods, assisted by computers and sophisticated control systems, are applied to crushing and grinding processes. Recent literature is well supplied with references citing production benefits that improved liner designs produce. This chapter is intended to review especially promising liner designs and material developments and presents cameo case studies showing the benefits derived from their application to comminution circuits (Tables 1,2,4,5,7). Complete discussions of liner design and wear materials are beyond the scope of this chapter. Norman's comprehensive studies in references (1) and (2) and Mclvor's analyses of mill speed/configuration effects (3) are especially useful reading for designers and operators of crushing and grinding circuits. Changing trends in ore, product value, and costs of wear materials, interest, labor, and energy, make ongoing evolution of liner design equally important for existing mines and for projects still on the drafter's board. Original designs supplied as new equipment must, of necessity, be best estimates. These can usually be improved as operating experience replaces engineering forecasts. Advent of new materials or design concepts such as the Angular Spiral Liners (Korpi (4) ) or Norman's Bimetallic design (2) offer improvement potential that must be evaluated if a given circuit is to be kept competitive versus others making similar products.

Jan 1, 1982

By O. C. Wheeler

The principal interest in the oil situation in Colombia during the year centered around the enactment of the new petroleum law and the applications for concessions subsequently made by various interests. The year was a comparatively uneventful one from the standpoint of actual operations of drilling and development. There was a falling off both in exploratory work and in the development of producing properties; and as a result of curtailment of production, the output of oil from the country dropped to the lowest level since the completion of the looping of the Andian pipe line to the coast in 1927. Legislation Law No. 371 of 1931, with its Regulatory Decree No. 1270, was enacted during the year and marked Colombia's attempt to encourage more extensive exploration and development of the prospective oil resources of the country. Some of the outstanding provisions of the law are as follows: Tracts may be acquired by a concessionnaire directly and by transfer ranging from 5,000 to 100,000 hectares, except in certain reserved territories east of the summit of the eastern cordilleras where the maximum is increased to 200,000 ha. A security deposit of $1 per hectare, minimum $25,000, is required on government grants, and is returned to the concessionnaire only upon the fulfillment of stipulated terms of the law. Rentals, increasing progressively from 10c per hectare per year the first two years to 50c per hectare the sixth year, are required up to the start of the production period (beginning of development). The concession terminates 30 years after the beginning of the production period and can be extended for 10 years more at the option of the contractor. Wells must be produced at no less than 25 per cent of their maximum capacity. Royalties on oil from national lands vary from 2 to 11 per cent of the gross product, depending on the distance of the concession from the port of loading. Petroleum from private property is subject to a governmental tax varying from 1 to

Jan 1, 1932

By R. W. Diamond

THREE mills are now operated by the Consolidated Mining & Smelting Co. of Canada, Ltd:: (1) The Sullivan concentrator, Chapman, B. C. (near Kimberley, B. C.), (2) the St. Eugene concentrator, Moyie, B. C., and (3) the Tadanac (customs) concen-trator, Trail, B. C. Differential flotation is the only concentration method employed in all three plants. Tables are used for pilot work only. Flotation equip-ment and control are similar in the three mills, and the flow sheets at the St. Eugene and Tadanac mills, while much simpler, are modeled after that of the Sul-livan concentrator. Successful differential flotation of Sullivan ore com-menced in the spring of 1920, in the pilot concentrator at Trail. During 1920, 193,804 tons were treated by this process. This operation continued without interrup-tion and with steady growth. For the first 7 months of . 1923, which concluded the pilot plant operation, ap-proximately 1100 tons were treated daily. I believe the Sunnyside plant of the United States Smelting &. Refining Co. was the only successful and large scale operation practising differential flotation prior to 1920. in North America. The Sullivan ore, because of its high iron content, was quite a different problem from that at Sunnyside. The entire tonnage of Sullivan ore had to be separated into three sulfide concentrate products-lead concentrate, zinc concentrate and iron concentrate. The choice and arrangement of equipment, and the original flow sheet for the Sullivan concentrator were controlled by the results of the exhaustive pilot mill test. These covered a continuous period of 3 1/2 years and involved the treatment of 1,076,368 tons of Sullivan ore. Satisfactory recoveries are made from feed; 11.0 per cent lead and 7.5 per cent zinc in the form of lead concentrate containing 69 per cent lead, 4.5 per cent zinc, and zinc concentrate containing 3.0 per cent lead and 49 per cent zinc. (The pure zinc mineral in Sulli-van ore is marmatite, 'containing approximately 54.5 per cent zinc and 10 per cent iron. It is apparent, there-fore, that 49 percent concentrate is high grade for this particular ore.)

Jan 8, 1927

By N. H. MacMillan, O. C. Dias

Recent work by Westwood et al. (reviewed in Refs. 1-6) has established that many rocks, minerals, ceramics, and glasses exhibit phenomenologically similar chemomechanical (Rebinder) effects when deformed in different liquid environments, apparently as the result of chemisorption-induced variations in their near-surface flow and flow-dependent fracture behavior. In particular, it appears that there exists an empirical, but apparently general, correlation between the near-surface flow stress of an inorganic nonmetal and its surface charge- namely, that such a solid is hardest at its zero point of charge (i.e., when its zeta potential [ ] = 0) and softens as [ ] increases, regardless of the sign of zeta. Moreover, because near-surface flow and fracture phenomena are two of the important determinants of the rates of machining and comminution processes, both Westwood et al. and others7 have been able to use this so-called "[ ]-correlation" to develop cutting fluids and grinding aids that in many instances have given rise to several fold increases in performance. In addition, Westwood et al. have demonstrated that both aqueous and organic environments can give rise to similar improvements in cutting rate for a given combination of tool and workpiece, provided that both impart the same surface charge to the work- piece (i.e., transfer the same number of electrons to or from its surface). This last finding implies that in any application it should always be possible to find some cutting fluid that is at once effective, cheap, nontoxic, and nonpolluting. Thus, reports of apparently similar environmental influences on the mechanical behavior of diamond,8 certain organic crystals and polymers,9-14 and coa1-15-21 suggest that it is pertinent to ask: (a) whether the [ ]-correlation (or any analogous relationship) extends to coal; and (b), if so, whether this relationship can be used to guide the development of superior aids for grinding coal. Accordingly, correlations have been sought between (1) the zeta potentials, (2) the hardnesses, and (3 and 4) the drilling and grinding characteristics of coals of different rank in different aqueous and organic environments. This paper reports the results of that search.

Jan 1, 1980

By L. O. Howard

The practice of using acid-lined converters at the plant of the Old Dominion, Copper Mining & Smelting Co. was discontinued early in January, 1913, and replaced by basic-lined converters. The new equipment consists of one electrically operated 12-ft. upright converter stand and two basic-lined shells for same. These shells are provided with twenty-four 1 1/4-in. tuyeres. The mouths are 5 ft. in diameter. Owing to the fact that there is no bedding system or other large storage capacity between the mine and the smelter, the furnaces must handle as fast as produced ore and concentrates, which may vary considerably from day to day, both in tonnage and copper content. Consequently the converter is often crowded to its utmost capacity by the frequent fluctuations in the daily matte supply. From the foregoing, it will be seen that in no way can the 'converter be favored by running light charges or by transferring to it from other stands in operation. Neither can it regularly be allowed to cool between blows, and only occasionally can it be run at as low a temperature as might be wished. No copper precipitate or other foreign material high in copper is available to help out the tonnage. Repairs and alterations or the removal of defective tuyeres must wait until such time as a slight falling off in.the matte supply allows the converting operations to ease up. These variable conditions all combine to interfere with the systematic operating of the converter. The first 12-ft. shell was blown in on Jan. 6, 1913, and ran until June 27, 1913, when it was removed to patch the brick. A record of operations covering this period follows: Shell No. 1. First Campaign, Jan. 6,to June 27, 1913 Commenced blowing............................Jan. 6, 1913. Taken off stand for patching.....................June 27, 1913. Total blowing time..........................2,689 hr. 40 min. Total number of, blows made.............................. 664 Average time of blow............................ 4 hr. 3 min. Tons matte charged.................................. 18,157 Average copper content of matte................ 43.9 per cent. Average time blowing one ton. copper................ 22.5 min. Total copper made............................... 7,250 tons

Jan 1, 1915

By John M. Warde, Raymond M. Richardson

What to do with atomic wastes is one of the major problems of the atomic age. Unlike other waste materials, these cannot be burned, evaporated, or filtered, and the transfer of radioactive material from one physical or chemical state to another is not a complete answer, because only time diminishes radioactivity. Rate of decay of radioactive materials varies from a few seconds to several thousand years and cannot be altered by known economic methods. At present the Atomic Energy Commission and its contractors are coping with the situation adequately. Intensification of private development of atomic power could, however, pose problems in the nation's nuclear energy program.

Jan 5, 1955

By B. K. Parekh, W. M. Goldberger

A novel process is proposed for continuous removal of ash and unreacted solids which become suspended in the oils obtained during coal liquefaction. The proposed method uses water in direct contact with the oil under conditions which cause the suspended residue solids to transfer from the oil to the water phase. Separation of the phases yields a product oil essentially free of suspended solids. The water is cooled, clarified or filtered by conventional low-cost systems, and recirculated. The paper describes experimental work leading to development of the novel concept and includes the result of batch experiments that establish the feasibility of the process.

Jan 1, 1980

By J. W. Eckerd, P. S. Lewis, N. H. Coates

USBM designed, constructed, and operated an 18-in.-diam fluidized-bed combustor for highly caking coals to evaluate the method for possible application to power generation. In initial tests, combustion was carried on successfully, with carbon losses as low as 0.8%+ Coal ash was not satisfactory as a bed material, but mullite proved to be acceptable. Overall heat-transfer coeffients from the bed (-20 t 50 mesh mullite) to a water-cooled tube were about 75 Btuper hr-sq ft. Fluidized-bed combustion is being investigated by the U. S. Bureau of Mines (USBM) as a potentially cheaper method of firing power plant boilers. Lower combustion temperatures in fluidized beds—only 1400" to 1800°F-—should reduce fireside deposition and corrosion and nitrogen oxides production. Fluidized-bed combustion also offers possible advantages in the use of additives to control SO, emissions and amenability to processing of high-ash, high-moisture coals without special preparation. This paper describes development of a fluidized-bed combustor and the results of preliminary tests. Equipment and Procedure Fig. 1 shows the 8-ft-high combustor. A cone-shaped plate perforated by I/8-in.-diam holes supports the fuel bed and admits the fluidizing air; water passing through the 3/4-in. pipe extracts heat from the combustion bed. Fig. 2 is a flow diagram of the system. Coal is fed pneumatically to the base of the fuel bed. Combustion products are passed through two centrifugal separators to remove most of the entrained solids, then to a water

Jan 1, 1971

By Nathaniel Arbiter

THE separation of minerals by flotation can be regarded as a rate process, with the extraction of any one mineral determined by its flotation rate, and the grade of concentrate by the relative rates for all the minerals. So regarded, the significant variables for the process are those that control the rates. These variables are of two types, the first describing the ore and its physical and chemical treatment prior to flotation and the second characterizing the separation process in the cells. This paper will examine the variation in rates for a group of separations, will show that a simple rate law appears to govern, and will consider the relation of the control variables to the rates. The use of rate constants for evaluation of performance and efficiency will be discussed. Flotation involves the selective levitation of mineral and its transfer from cell to launder. The flotation rate is the rate of this transfer. It may be defined by the slope of a recovery-time curve for any cell in a bank, or at any time in batch operation. The objective in flotation rate study is an equation expressing the rate in terms of some measurable property of the pulp. This can be either the concentration of floatable mineral in weight per unit volume1,2 or a relative concentration, which will be a function of the recovery." A rate equation for an actual flotation pulp will contain at least two constants, both to be determined from the data. One of these, the initial concentration or proportion of floatable mineral, is not necessarily equal to the feed assay because of nonfloatable oversize or locked particles." The other, a rate constant, is a measure of proportionality between the rate and the pulp property on which the rate depends. The value of the rate constant will be determined by the values of all variables which control the process and will be changed by significant changes in any of them. It is, therefore, a direct measure of performance. Where recovery or grade change continuously with flotation time, the rate constant will be independent of time and will characterize the entire course of the separation. Development of Rate Equations Rate equations can be developed either by analysis of the mechanism of the process or by direct fitting of equations to recovery-time data. Sutherland's attempt by the first method' suggests that the effect of particle size variation on the rate complicates the derivation of a simple equation applicable to an ore pulp. A further problem with an ore is the concentrate grade requirement, which usually involves a variable rate of froth removal. Thus the final rate for any cell may depend on the froth character and froth height, as well as on the pulp composition. This does not imply that each cell cannot reach a steady state2 in which the rate will depend ultimately on pulp composition. The second method is the fitting of rate equations consistent with the necessary boundary conditions* to experimental recovery-time curves. On the assumption that under constant operating conditions the flotation rate is proportional to the actual or relative concentration of floatable mineral in the pulp, a generalized rate equation may be expressed as follows: Rate = Kcn [I] where K is the rate constant, c is some measure of the quantity of floatable mineral in the pulp at time t, and n is a positive number. In previous rate studies, the value of n has been taken as 1, either by direct assumption," or as a result of the hypothesis that bubble-particle collision is rate determining.' A first order equation results, which after integration in terms of cumulative recovery R, leads to Loge A/A-R = Kt [2] The quantity A is the maximum possible recovery with prolonged time under the conditions used. No conclusive proof for the validity of this equation in flotation has been advanced. The evidence cited in its support consists entirely in the demonstration that it appears to apply to a limited number of recovery-time curves."' It will be shown subsequently that this procedure is not sufficient to establish the order of a flotation rate equation. The possibility that the equation may be of higher order therefore requires examination. If, in particular, the exponent in eq 1 is assumed to be 2, then after integration there results R = A2Kt/1 + AKt [3] with K again a rate constant and A the maximum proportion of recoverable mineral. Eq 3 may be

Jan 1, 1952

By C. B. Alcock, L. I. Cheng

By the use of radiochemical methods for the study of the gas-liquid equilibria at low temperature, and for the determination of the sulfur contents of metal beads which had been equilibrated with H2S/H2 mixtures of known sulfur potential, it has been possible to obtain the liquid solubility and the free energy of solution of sulfur in liquid tin and lead at temperatures between 500°and 680°C. THE gas-liquid equilibrium method has proved in the past to be most successful in the determination of the thermodynamic behavior of dilute solutions of sulfur in liquid metals.1,2 One of the basic requirements for success with this method is that the volatility of both the metal and its lowest sulfide should be small, otherwise sulfide will be deposited at the cool end of the furnace, where it may react with the outgoing gases to form either sulfur-rich lowest sulfide or higher sulfides. The resultant value of the apparent equilibrium constant will then be lower than the correct one. This argument applies even at sulfur potentials below that in equilibrium with a separate condensed phase of the lowest sulfide at the reaction temperature, T. The mass of sulfide which is deposited at the cold end of the furnace, and hence the extent to which further reaction occurs with the outgoing gases, depends on the time taken for equilibrium to be reached between metal and gas. Since this will depend principally on the bulk of the metal phase which is used, one should clearly attempt to uie as small metal samples as possible. These considerations are important in the study of dilute solutions of sulfur dissolved in liquid tin and lead which both have moderately high vapor pressures as metals and form volatile sulfides. The limit on the size of the metal samples which may be used is set chiefly by the difficulties of analysis for very small amounts of sulfur. The oxygen or carbon dioxide combustion method, followed by iodimetric determination of the sulfur dioxide which is formed,has been found to be successful for the determination of small amounts of sulfur in copper, iron, cobalt and nickel.4 This method was unsatisfactory for sulfur dissolved in tin and lead, mainly because the sulfur dioxide was to some extent absorbed by the copious tin or lead oxide deposits which were formed on the walls of the combustion tube. Furthermore some of the sulfur was found to segregate on the surface of the beads as flaky sulfide crystals which would easily be lost in the transfer of a bead from a boat in the gas equilibration apparatus to one in the combustion apparatus. Oxidation in aqueous media to sulfate ion followed by precipitation as barium sulfate was, therefore, adopted as the analytical procedure. The gas-metal equilibrium experiments were all carried out with radioactive sulfur and thus the analysis involved the counting of barium radiosulfate. Furthermore the use of the radioisotope meant that the approach to the gas-metal equilibrium could be followed continuously by gas counting.' The metal beads were held separately in glass crucibles during equilibration and were transferred from the furnace to the beaker for dissolution in nitric acid still in the crucibles, and thus the possibility of sulfur loss by detachment of the sulfide segregates was eliminated. The temperature range of this investigation was 500° to 680°C. EXPERIMENTAL APPARATUS AND METHOD The apparatus consisted of two furnaces placed in series in a gas recirculation system, Fig. 1. One furnace F1, which was vertical was used to heat the alumina crucible, A, holding six metal beads in separate glass crucibles. The beads weighed between 300 and 700 mg each. The crucible assembly was introduced and removed from the furnace mechanically under a stream of oxygen-free argon. The other furnace, F2, was horizontal and was used to heat a cobalt Co9S8 mixture, held in an alumina boat, and made with radiosulfur containing about 1/2 millicurie per g of sulphur. This mixture, which was finely powdered, was used as a source of known H2S/H2 mixtures6 for a given furnace temperature. The recirculation system also contained a gas re-circulation pump (P), an end window Geiger-Miiller counter (N)—placed downstream of F1 so as to monitor the H2S pressure in the gas leaving this furnace— a sample volume for chemical analysis of the gas phase (G), gas drying tubes (D), filling taps and other standard ancillary equipment. The gas sampling volume was principally used in the cali-

Jan 1, 1962