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By W. C. Meyer, R. R. Klimpel

A physical model of flotation, derived from viewing froth as a kinetic species since it constitutes the carrier of ore particles, not only agrees with and is simulated by engineering mathematical models, but is statistically verified by actual laboratory flotation data. The model couples the mechanical removal of froth using paddles with the more rapid interactions taking place in the bath. It clearly shows that the kinetics of mass removal is dictated by flotation cell dimensions, paddle speed, and, more importantly, froth characteristics. Some conclusions and model predictions are presented.

Jan 1, 1984

While there is reasonable agreement on the basic chemistry of the slag fuming process, there has been an on-going debate for nearly 50 years as to the nature of the rate controlling factors in its industrial application. There have been advocates in the technical literature for thermodynamic limitations on the one hand or kinetic limitations on the other. The different viewpoints result in very different predictions as to the technical and commercial potential of the process. A resolution of the debate becomes of importance as pyrometallurgical processes are advocated as a means of extracting environmentally deleterious elements from metallurgical wastes. The present paper reviews the arguments in favour of both equilibrium and kinetic control and puts forward the view that much of the evidence for limitation of the process by kinetic factors under all conditions is unconvincing. It is maintained that the process can approach thermodynamic equilibrium under industrial conditions and that this determines the ultimate limitation on its technical performance. It is acknowledged, however, that kinetic considerations may cause the batch process to fall well short of performance predicted on thermodynamic grounds. The strong process limitation arising from the influence of chemical thermodynamics on the likely outcome of a hypothetical continuous fuming process is contrasted with optimistic forecasts resulting from the extrapolation of process models based only on kinetic considerations.

Jan 1, 2000

By R. Zaragoza M., M. C. Fuerstenau, C. O. Nebo, J. R. Kelso

The rate of adsorption of gold cyanide on activated charcoal was examined as a function of charcoal concentration and size, temperature, initial gold concentration, pH, and initial concentration of gold on the charcoal. Rate was found to be proportional to temperature, concentration of charcoal and initial gold concentration on charcoal, and to the inverse of charcoal particle size squared. An activation energy of 2.0 kcal/mol was determined

Jan 1, 1988

By Alexander Field

THE rate of elimination of carbon largely controls the time required to make a heat of steel by the basic open-hearth process and to an important degree determines the cost of refining. Practical experience has led to the generally accepted belief that the use of slags relatively high in iron oxide, such as are required to bring about rapid refining, leads to a certain sacrifice of quality in the product. As a consequence, a compromise must be made between the exceedingly slow rate of carbon drop which would correspond to the ideal case and the rapid rate which would best satisfy the condition of minimum cost. An increase in rate of refining necessarily implies an increase in the concentration of iron oxide dissolved in the metal. However, even for the infinitely slow rate that corresponds to slag-metal equilibrium, the metal would contain a certain definite concentration of dissolved iron oxide. It is a matter of great practical importance, therefore, to determine the quantitative relation between the minimum or equilibrium concentration of iron oxide in the metal and the higher concentrations which must actually obtain in practice. The present paper is devoted to the development of certain equations, derived from the established laws of physical chemistry, which will enable this relation between rate of refining and the degree of oxidation of the metal bath to be computed from operating data. No attempt is made to exhaust the possibilities of this general method of treatment. In considering rate of refining, attention is mainly confined to rate of carbon elimination. However, the equations are of a more general nature and their application may readily be extended. The results of the preliminary calculations given herein indicate that increased rate of refining may have a decided effect in increasing the concentration of iron oxide dissolved in the metal. The uncertainty. which attaches to the calculated value for this relationship arises in part from probable errors in experimental data on which the calculations are based, and in part from the lack of complete or favorably disposed information on basic open-hearth practice.

Jan 1, 1928

By Alexander Field

IN THE light of the experimental data on equilibrium for the reaction C + FeO = Fe + CO in molten steel recently obtained by Kinzel and I Egan,1 it is necessary to revise current theories regarding the nature of equilibrium between carbon and FeO in the basic open-hearth furnace. According to the measurements of these investigators the equilibrium constant m for the above reaction for a pressure of dissolved CO equal to 1 atm. is equal to 0.0005 at 1550° C., when concentrations of carbon and. FeO are expressed in percentages by weight. Their work also shows that, with the pressure of CO fixed at 1 atm., not only is the product of carbon and FeO constant, but carbon and FeO are each independently constant-a circumstance which might have been predicted from theoretical considerations. At 1550° C., carbon is constant at about 0.025 per cent. and FeO at about 0.020 per cent., with the pressure of dissolved -CO equal to 1 atm., the product of these two constants being equal to the originally mentioned constant of 0.0005. Available data on the dissolved FeO content of samples taken from the metal bath at practical slag-metal equilibrium prove that this FeO content is determined solely by temperature and the effective FeO content of the slag. The distribution constant r at 1550° C., as determined by Herty, Gaines, Larsen, Simkins, Geruso and Watkins2 is equal to 0.0086. A slag would have to contain 0.020/0.0086 = 2.3 per cent. effective FeO or less in order to prevent the metal from containing more dissolved FeO than that required for equilibrium with CO at 1 atm. pressure. Such low percentages of FeO are never found in basic open-hearth slags at the completion of a heat when rate of carbon drop has become practi-

Jan 1, 1930

By J. B. Goddard

Abstract. Leaching of, uranium in situ from sandstone deposits with ammonium carbonate solution containing: dissolved oxygen occurs rapidly compared with the leaching of the bulk of the sulfur present as FeS2. However because of their high reducing, capacity and their relative abundance, the FeS2 minerals consume; the bulk of the oxidants A pressure leach apparatus was-construtted which permitted the measurement of oxygen consumtion by FeS2. Oxygen consumption by FeS2 is best described by a first-order reaction. The experimental rate constants for various cores are roughly proportional to their FeS2 contents.

Jan 1, 1980

By John B. Goddard, David R. Brosnahan

Leaching of uranium in situ from sandstone deposits with ammonium carbonate solution containing dissolved oxygen occurs rapidly compared with the leaching of the bulk of the sulfur present as FeS2. However, because of their high reducing capacity and their relative abundance, the FeS2 minerals consume the bulk of the oxidant. A pressure leach apparatus was constructed that permitted measuring oxygen consumption by FeS2, best described by a first-order reaction. The experimental rate constants for various cores are roughly proportional to their FeS2 contents.

Jan 1, 1983

By Cyril Wells

THE diffusion of carbon in gamma iron plays an essential role in many metallurgical processes. In carburizing, in graphitizing, in homogenizing, in the formation of pearlite from austenite, and in other processes, migra-tion of carbon in gamma iron occurs.1,2 A full understanding of the rate at which these processes occur obviously requires a knowledge of the rate of diffusion of carbon. In carburizing, for example, the depth of carbon pentration is determined by the carbon concentration in solid solution at the surface, and by the rate of diffusion inward of the carbon. Until reliable data on the rates of diffusion of carbon are available it is unlikely that a full quantitative description of this process will be obtained. In the formation of pearlite from austenite, the segregation of carbon and alpha iron from the austenite obviously requires the diffusion of carbon; the rate at which pearlite nodules grow is evidently controlled at least in part by the rate of diffusion of carbon; it is unlikely that we shall understand the factors that determine the rate of growth unless data on rates of diffusion of carbon, and the variation of these with com-position, grain size, and temperature are available. Accordingly it was decided: (1) to determine, more accurately than hitherto, the diffusion coefficients of carbon in austenite over a wide temperature and a wide concentration range, (2) to study the influence of grain size and impurities on this diffusion coefficient, and (3) to study the effect of manganese and nickel on the rate of diffusion of carbon in the austenite of manganese and nickel steels, respectively; the influence of carbon on the rate of diffusion of manganese and of nickel will be made the subject of later papers. The rate of diffusion of carbon in gamma iron has been studied by Runge3 by Tammann and Schönert4, by Bramley and co-authors,5-14 and

Jan 1, 1940

By Cyril Wells, Robert F. Mehl

THE practical importance of a knowledge of the rates of diffusion of carbon and of alloying elements in steel has often been pointed out 1,13 This importance ties chiefly, though by no means only, in the study of carburizing and in the study of reactions involved in the eutectoid inversion in steel The present paper is one of a series in which the rates of diffusion of carbon and of alloying elements in y-Fe and their mutual effects are measured with precision The present paper reports the results of meas¬urements of diffusion coefficients D of manganese in -y-Fe over wide ranges of temperature, and concentration, and of the effect of carbon and impurities and of grain size upon these diffusion coefficients [$] Data on the rate of diffusion of manganese in y-Fe have been reported by Fry2 and by Paschke and Hauttmann 3 Claussen4 calculated the diffusion coefficient D from Fry's data as 3 X 10-10 sq cm per sec at 960°, which will be shown to be incorrect by many orders of magnitude Paschke and Hauttmann gave a rough value of 9 6 X 10-8 sq cm per sec at 1400° Neither of these workers considered the variation of D with concentration and with temperature, and neither studied the effect of carbon METHOD AND MATERIALS Method -The method employed is identical with that used earlier 5 Owing to the volatility of manganese and the consequent loss of manganese from the outer surfaces of the welded diffusion bars, these surfaces were discarded The diffusion anneals were performed in argon, except one (test 18) in which hydrogen was employed for purposes noted below The temperatures reported are accurate to about 3° and constant within I°C , the diffusion times are reported to the nearest half hour The specimens were furnace-cooled after the diffusion anneal at about 2° per min Layers, usually 0 004 in thick, parallel to the welded interface, were machined from the specimens after the diffusion anneal and analyzed for manganese to 0 01 per cent Mn, the distances of these layers from the interface was measured to ±0 0002 in The concentration-penetration curves obtained were analyzed by both the Grube and the Matano solutions e The D values calculated by these two methods do not differ appreciably 5 The Grube solution was used except in tests in which the effect of concentration upon D was greater than 50 per cent, in such cases the Matano method, which explicitly provides for the variation of D with concentration,1 is the more reliable In general, the number of layers machined from the zones of variable composition were large enough to permit the use of the average layer composition as that of the center of the layer In 3 of the 30 tests, however, this is not justified, and the D values

Jan 1, 1941

By Cyril Wells, Robert F. Mehl

THE two earlier papers in this series1,2 presented data on the rate of diffusion of carbon and of manganese in gamma iron. Apart from their scientific interest, these [] data are needed chiefly in order to treat data on carburization, on the rate of formation of pearlite, and on the rate of austenizing in a quantitative way. 1,2,9,10 In the present investigation rates of diffusion of nickel in -?-Fe over wide temperature and concentration ranges have been determined, and the effects of carbon, of impurities, and of grain size on these rates have been studied. Claussen,3 using the data of Fry,4 has calculated the diffusion coefficient of nickel [ ] in -?-Fe as 9.2 X 10-11 sq. cm. per sec. at 1200T., but had no data from which to calculate the variation of D with concentration, temperature, and percentage of carbon. METHOD AND MATERIALS Method.-Nickel was diffused along the axis of a cylindrical specimen across a concentration gradient, concentration-penetration curves were determined and D values calculated from Grube or Matano solutions.5 Details of the method are given

Jan 1, 1941

By R. F. Mehl, B. Lustman

THE formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.1 It is necessary here only to enumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type-i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained-the isothermal growth of the phase follows a simple parabolic equation: [1 = ki [I]] where X is the thickness of the alloy layer, k the reaction rate constant, and [t] the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such a plot has been considered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.3 In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varies with temperature according to the Arrhenius equation: [k = Ae-QIRT [2]] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. All phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase.4 The reaction layers tend to have a

Jan 1, 1942

By R. F. Mehl, B. Lustman

THE formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.1 It is necessary here only to enumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type-i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained the isothermal growth of the phase follows a simple parabolic equation: X2 = kt [I] where X is the thickness of the alloy layer, k the reaction rate constant, and t the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such. a plot has been con¬sidered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.3 In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varies with temperature according to the Arrhenius equation k = Ae-Q/RT [2] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. All phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative, thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase .4 The reaction layers tend to have a

Jan 1, 1942

By Sadegh Safarzadeh, Anne-Marie Suriano, Stanley Howard

The electrodeposition of metal ions from aqueous electrolyte solutions has been a well-known process for the last half century. With numerous industrial applications such as electroplating, electrowinning and electrorefining, the kinetics of electrochemical reactions involved in the process has been extensively researched. Arrhenius-type rate equations, the Butler-Volmer equation, and the empirical Tafel equation are among the most important models to explain the rate of electrochemical reactions. The study of the kinetics of metal deposition is critical to understanding the underlying mechanisms through which a certain morphology of metal deposit is formed on the cathode. The purpose of this paper is to elucidate the influence of experimental parameters such as pH and additives on the rate and the reaction mechanism determining the rate limiting step of the electrodeposition reactions.

Jan 1, 2015

The kinetics of desorption of nitrogen from molten iron were investigated using the electromagnetic levitation technique. The respective influences of gas flow rate and surface active element (S) were examined. A second order behaviour with respect to the nitrogen concentration in the melt prevailed at all experimental conditions. Sulphur had a marked inhibiting effect on the desorption rate. The experimental results on the rates of nitrogen desorption have been interpreted with the aid of a reaction mechanism consisting of a sequence of elementary steps.

Jan 1, 1991

By Frederick C. Hull, Robert F. Mehl, Robert A. Colton

IT is known that pearlite forms from austenite by a process of nucleation and growth, and that the rate of formation of pearlite may be described by a rate of nucleation and a rate of growth 12 The manner in which these two quantities operate to produce the observed isothermal reaction curve has been analyzed in a paper published in 1939 3 Two types of process were described (I) that in which nucleation occurs at the grain boundaries of the parent phase, with the nodules growing toward the centers of the grains, initially as hemispheres and then after impingement as roughly radial-columnar structures, and (2) that in which nucleation occurs generally, with the nodules growing to full spheres until impingement with other growing nodules restricts growth Both cases are met in the formation of pearlite from austenite (Fig 1),2,3 the former, occurring near the knee of the S-curve has been named "grain-boundary transformation," and the latter, occurring at temperatures near AeI, has been named "group-nodule transformation " In developing our knowledge of the factors that determine the rate of formation of pearlite from austenite, it is important''' to obtain data on the rate of nucleation and the rate of growth of pearlite Such data, when obtained near the knee of the S-curve, will furnish information of use in understanding the actors that affect hardenability, when obtained at higher temperatures, such data will be useful in understanding the behavior of steels that during heat-treatment react to pearlite 2 It is the purpose of this paper to present data on the rate of nucleation and the rate of growth of pearlite in dependence upon composition, grain size, temperature,, and the degree of homogeneity of the parent austenite The studies are restricted chiefly to plain carbon commercial steels PREVIOUS DATA ON RAID OF NUCLEATION AND RATE OF GROWTH Data on the rate of nucleation and the rate of growth of pearlite have been published by Scheil and Lange-Weise,5 by Mirkin and Blanter,6,7 by Mehl,1 and by Dorn, De Garmo and Flanigan22 It is difficult to interpret the data, for in most cases too little information is given on austenitizing temperatures and times, the state of homogeneity of the austenite (presence or absence of carbide, etc ), austenite grain size, and mode of formation of pearlite at the temperatures given

Jan 1, 1942

By Frederick C. Hull, Robert F. Mehl, Robert A. Colton

IT is known that pearlite forms from austenite by a process of nucleation and growth, and that the rate of formation of pearlite may be described by a rate of nucleation and a rate of growth.1,2 The manner in which these two quantities operate to produce the observed isothermal reaction curve has been analyzed in a paper published in 1939.3 Two types of process were described: (1) that in which nucleation occurs at the grain boundaries of the parent phase, with the nodules growing toward the centers of the grains, initially as hemi¬spheres and then after impingement as roughly radial-columnar structures; and (2) that in which nucleation occurs generally, with the nodules growing to full spheres until impingement with other growing nodules restricts growth. Both cases are met in the formation of pearlite from austenite (Fig. 1);2.4 the former, occurring near the knee of the S-curve has been named "grain-boundary transformation," and the latter, occurring at temperatures near Ae1, has been named "group-nodule transformation." In developing our knowledge of the factors that determine the rate of formation of pearlite from austenite, it is important 1,2 to obtain data on the rate of nucleation and the rate of growth of pearlite. Such data, when obtained near the knee of the S-curve, will furnish information of use in understanding the factors that affect hardenability; when obtained at higher temperatures, such data will be useful in understanding the behavior of steels that during heat-treatment react to pearlite.2 It is the purpose of this paper to present data on the rate of nucleation and the rate of growth of pearlite in dependence upon composition, grain size, temperature, and the degree of homogeneity of the parent austenite. The studies are restricted chiefly to plain carbon commercial steels.* PREVIOUS DATA ON RATE OF NUCLEATION AND RATE OF GROWTH Data on the rate of nucleation and the rate of growth of pearlite have been published by Scheil and Lange-Weise,5 by Mirkin and Blanter,6,7 by Mehl,1 and by Dorn, De Garmo and Flanigan.2 It is difficult to interpret the data, for in most cases too little information is given on austenitizing temperatures and times, the state of homogeneity of the austenite (presence or absence of carbide, etc.), austenite grain size, and mode of formation of pearlite at the temperatures given.

Jan 1, 1942

By Curtis Wilson

FROM the results of his investigation of the hardenable copper-nickel-silicon and copper-cobalt-silicon alloys, M. G. Corson1 explained the dispersion-hardening effect by assuming the precipitation of the inter-metallic compounds nickel silicide and cobalt silicide, and on this basis he constructed diagrams for the pseudobinary systems copper-nickel silicide and copper-cobalt silicide. A consideration of these diagrams and of the factors that exert such an important influence upon the rate of precipitation, such as degree of supersaturation, nucleus number and rate of diffusion, leads to the expectation that the rate of precipitation of the silicides on reheating the quenched solid solutions at temperatures below the alpha-phase boundary should increase continuously as the reheating temperature is raised. The present investigation shows that while this rate does increase with the reheating temperature in a general way, it does not do so continuously. Supplements to Corson's diagrams are offered, showing the discontinuities, and slight modifications in the solubility curves are suggested.

Jan 1, 1933

By Lawrence K. Jetter, Robert F. Mehl

SOME advances have been made recently in the theory of the kinetics of precipitation from metallic solid solution despite the complexities of the problem, but there is surprisingly little quantitative information available on rates of precipitation with which to test present theory or upon which to build new theory.‡ Attempts to measure rates of precipitation have been beset with difficulties which originate both in the anomalies that attend the changes in the properties selected for measurement, as, for example, in electrical conductivity or mechanical properties, and also in the complexities in the structural changes in some systems, as in the aluminum-copper system. If the functional relationship between the quantity of precipitate and the value of the selected property is uncertain, measurements of that property are obviously of uncertain utility in determining absolute rates of precipitation. If the precipitating system passes through one or more transition stages, the interpretation of measured rates lacks definiteness; in such cases, it is necessary to measure the rate of reaction in each separate stage, if the rate measurements are to have any significance from the kinetic point of view.* These difficulties cannot be wholly avoided, for at least in some measure they are characteristic of the process of precipitation from solid solution, but they can be minimized both by the selection of a simple system and by the use of a method of measurement relatively free from anomalous behavior. The present paper reports dilatometric measurements on the rate of precipitation of silicon from the aluminum-rich solid solution in the aluminum-silicon system-a study that approaches the desiderata of simplicity. The aluminum-silicon system offers advantages from these points of view: there are no known anomalies in the property changes accompanying precipitation; 2.3,4 there are no known transition stages; the precipitate is an element, not a compound, and both matrix and precipitate are cubic, and while the structures are not identical (the solid solution is face-centered cubic and the precipitate is diamond cubic), the system at least approaches the ideal case of a crystal precipitating from a matrix of the same crystal type-the ideal case which Becker5 assumed in treating the precipitation process theoretically. The dilatometric method, while not free from disturbing effects, as the subsequent dis-

Jan 1, 1942

By Lawrence K. Jetter, Robert F. Mehl

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

Jan 1, 1942

By Daoust G, Dubois JF

The optimal sequence of decisions on rates of production and cutoff grades is obtained by a dynamic programming model. The main parameters are : 1. the size of the deposit, average grades and grade distributions, 2. the operating costs of mining and concentration, 3. the investments in mine and mill, 4. the smelter charge, 5. the price(s) of the metal, 6. the recovery and the grade of the concentrate, 7. the rate of interest, 8. the taxation formulae, 9. the upper limit to rate and the rate interval and 10. the upper and lower limits to cutoff and the cutoff interval. An amount of ore can be mined at various rates while applying various cutoff grades. It is assumed that a decision to mine at a certain rate during a period conducts to a certain state regardless of the cutoff grade. This assumption which is valid for several

Jan 1, 1977