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By Harrison R. Cooper

This section will outline procedural, statistical, and model applications developed for specific problem solving and for specific applications in beneficiation processes. Iron Ore Processing Introduction of taconite as a basic raw material in the iron ore industry took place with application of high order technical resources for process development and engineering. This investment of resources encouraged computer utilization to maximize efficient use of capital. From this recognition, process control computers have been installed for operations use in the major taconite plants of the iron range. One of these installations, the Minntac Division of U. S. Steel at Mountain Iron, Minnesota, is described in the paper by Chase in these proceedings. Other computer techniques used in taconite processing are outlined by Tuttle, Ahlquist and Carlson, representing Erie Mining. In this volume Tuttle, et al. describe statistical methods for development of information in taconite beneficiation. Statistical methods used in iron ore processing are described by Volin in treating flotation data as outlined in prior proceedings of the symposia and in other publications. 1,2,3 Industrial Minerals The use of linear programming for feed blending at the Carlsbad operation of International Minerals and Chemicals was outlined by Nunnekoven in 1963.4 Subsequent application of this procedure at the Kingston phosphate operation in Florida was described by Loper. Continued development led to installation of an on-line computer in the Kingston plant which reached operational status in 1967.6,7,8 Application of an on-line computer to industrial mineral production accomplished at Kingston is regarded as a milestone in computer use development. Following this achievement, the Cominco potash beneficiation plant near Saskastoon in Canada was automated by installation of an on- line computer programmed to carry out direct digital control functions to effectively operate the plant by process computer. The procedures used in the Cominco operation are described by Madge in this volume. Development of a mathematical model

Jan 1, 1969

By R. S. Rickard, M. C. Fuerstenau

Anodic polarization curves for iron dissolution and cathodic polarization curves for copper deposition and ferric and hydrogen ion reduction were studied. These results were used to predict the relative rates of the reactions: The rates of the first two reactions were found to be first order with respect to the reacting ion, and the rale-controlling step was diffusion of the ions to the callzode surface. The rate of hydrogen ion reduction in an oxygen-free solution is dependent on the reciprocal of the square root of the hydrogen ion activity. In solutions containing oxygen, the rate of hydrogen reduction becomes dependent on the square root of the partial pressure of oxygen. At equal concentrations copper precipitation occurs about twice as fast as ferric ion reduction. In an air-saturated solution containing 0.01 M cupric ion at pH 2, the rate of hydrogen ion reduction zs about 10 times slower than that of copper precipitation. At pH values below 3, the rate of hydrogen reduction in oxygen-free solutions is very slozu. COPPER cementation has been utilized industrially for many years as a means of recovering copper from aqueous solutions. There are many different types of cementation plants, but all simply provide a means of contacting iron with relatively dilute copper solutions. In the past little or no attention has been paid to rates or mechanisms of the reactions involved. As a result, this and other studies'-3 have been undertaken recently to establish the important parameters in this system. The reactions involved in copper cementation by iron are: Since transfer of charge is involved in every case, these reactions should be considered from an electrochemical point of view. In any electrochemical system involving electrolytic conduction, passage of electrons necessitates ion transfer to the respective electrodes according to Faraday's law. The current in the system will be proportional to the rate of ion transfer, and, therefore, when the current in the galvanic cell is known, the rates of the reactions involved can be determined. Galvanostatic electrode measurements5" are applicable for these electrochemical studies, in that with this technique polarization curves (current density vs electrode potential) are established by impressing a constant current through an electrode and measuring the electrode potential. Once the current density, electrode potential, and reacting area are known for each reaction in this cementation system, the rates of the iron-consuming reactions can be determined. EXPERIMENTAL MATERIALS Several metal electrodes were used in this investigation; they are shown in Table I. Solutions were made with reagent-grade salts and conductivity water. Air, nitrogen, and oxygen were employed. All of these gases were saturated with water and degreased prior to use. EXPERIMENTAL PROCEDURE The experimental work was divided into two general areas. The first area involved galvanostatic measurements, which were used to determine the rates of reactions as a function of various parameters. The second area comprised actual cementation experiments to check the rates predicted from the electrode measurements. Galvanostatic Electrode Experiments. Polarization curves were obtained using a standard galvanostatic technique5'= with the apparatus shown in Fig. 1. The various electrode polarization experiments were run the same way except for changes in solution composition, polarity, and type of measured electrode. The general procedure involved the following steps: 1) a solution was made 0.5 M in sulfate ion and to the desired cation concentrations; this solution was placed in a constant-temperature bath and saturated with the desired gas; 2) the electrodes were cleaned and placed in the electrode holder; 3) the previously cleaned apparatus was assembled and immersed in a constant-temperature water bath (temperature controlled to ± 0.05"C); 4) the electrode was then positioned; the solutions were introduced, and the polarization meas-

Jan 1, 1969

By Sylvan Z. Beer

The factors that determine the yield and crystal size in the two-temperature synthesis of A lp were examined. Low yields and small crystals were associated with low temperatures and pressure. Attempts to grow large crystals in the critical and supercritical region of phosphorus were unsuccessful. Crystal size increases markedly at elevated temperatures. Crystals grown at temperatures as high as 1450° C fluo-resced, under uv excitation, at energies close to the estimated band gap of about 2.4 ev, while crystals grown at lower temperatures tended to fluoresce in the red region of the spectrum. Those grown in the supercritical region showed no ALP fluorescence. Heating the high-temperature-grown ALP under vacuum greatly increased its fluorescence efficiency and moved the emission peak to higher energies. I HE III-V compounds, with few exceptions, have been prepared by the two-temperature method. In its classic form this technique is applicable to closed systems where at least one of the components, in this case the column V element, is a liquid or a solid with a high vapor pressure. One advantage of this method over flow systems is in its simplicity. In addition, because it is a closed system, it can, under the circumstances to be described later, be run at higher pressures of the volatile species than in flow systems. In instances where the III-V compound is soluble in the parent III metal to about 1 mol pct or higher, solution growth can be made to take place by slow cooling. This, for instance, is one way in which single-crystal GaP1 and Inp2 have been grown. Initial attempts to synthesize and grow A1P by this technique were not too successful; the yield was low and the crystals obtained were exceedingly small. The conditions required for improving the yield and growth by this technique were, therefore, sought. Two obvious conditions which could be controlling were examined. These were the temperature of the aluminum and the pressure of the phosphorus. The range of temperatures studied extended from about the melting point of aluminum, 660° to about 1450°C. The latter is dictated by the vapor pressure of aluminum which reaches about 1 Torr at that temperature and the limitations of the materials of construction as described in the next section. The pressure range of interest covers from below 1 atm to above the critical pressure of phosphorus, 82.2 atm. EXPERIMENTAL The Temperature of Aluminum as a Variable. A series of experiments were run in the conventional two-temperature manner. All refractories and quartz were dried by heating at 800° to 900° for a minimum of 24 hr, and usually much longer, before use. The aluminum

Jan 1, 1969

By A. Mitchell, M. Etienne

VARIOUS'-3 reports on the electroslag remelting process refer to the "thin skin of slag" existing around the slag pool and the solidifying ingot, but none considers the various mechanisms by which this layer forms and thus influences the surface quality of the ingot. A vertical section4,5 of the Cao-CaF2-Al2O3 diagram is shown in Fig. 1 between CaF2 and 6Al2.CaO3 From this, it is seen that a typical "70:30" CaF2:A1a3 slag will solidify to produce 6Al2O3.CaO primary phase in a eutectic matrix. The commercial slags contain sufficient CaO to produce* this composition by both the

Jan 1, 1969

By K. Torssell, U. Lindborg

The kinetics of precipitation deoxidation is considered from a theoretical point of view. The size distribution and the total content of deoxidation products are estimated statistically as a function of time, taking into account Stokes and gradient collisions between the particles and separation at the top surface of the bath. The assumption is made that two particles coalesce into one larger particle as a result of a collision. General expressions are derived and calculations are carried out numerically for the case of silica particles in liquid iron. The analysis predicts a three-stage behavior for the removal of oxygen, an incubation stage, a stage of rapid separation, and a slow final stage where the content approaches the equilibrium value. The agreement with experimentally determined size distributions and deoxidation times is considered to be good. A quantitative estimation of such growth mechanisms as diffusion from the melt and redistribution of oxygen from small particles to large ones shows that these latter mechanisms cannot explain the experimentally observed gvowth of inclusions. This also indicates that collisions provide the important growth mechanism. OXIDE inclusions precipitate when a deoxidizer like silicon or aluminum is added to a steel bath. The inclusions grow and the large particles tend to separate from the bath. For each type of oxide the growth determines the sizes of the final inclusions as well as the total inclusion content of the steel. The mechanism of growth is controversial, however. It has been suggested that an inclusion grows principally by diffusion of atoms through the melt to the inclusion particle or principally by collisions and coalescence with other inclusions. Diffusion growth is always present to some extent but recent experiments and calculations by Torssell,' Kniippel et 'a1.,2 Sano et al. and Miya-shita4 indicate that collisions may be more important than previously realized. A detailed analysis has so far been lacking. The present paper is a quantitative, statistical analysis of the growth and separation of inclusions and is based on a collision theory. Nuclea-tion is not considered. The numerical estimates are based on the experimental conditions of Torssell's' investigation and comparisons are made with his observations. Torssell' studied the growth and separation of silica particles in liquid iron. Samples were taken from a 0.6 kg iron bath at various times after the addition of silicon. By a particle-counting technique developed by Bergh and Lindber~the size distribution of the inclu- sions was determined. The number of particles at the first sampling, 10 sec after silicon addition, was of the order of 3 x lo7 to 10' per cu cm, the largest particles having a radius of 2 to 4 pm. The volume fraction was 0.001 to 0.004; i.e., the dispersion was very dilute. During subsequent holding the largest particles increased their radius by a factor of 10 after about a minute, and the whole size distribution was displaced toward larger values. These results were obtained with allowance for precipitation of the equilibrium concentration of oxygen during solidification. The bath contained less than 0.01 pct of C. Figs. 1 and 2 show the typical appearance of the inclusions. Most particles are very closely spherical and appear to have been liquid or semiliquid in the melt. The observed number of inclusions, about 5x 10' per cu cm, is of the same order of magnitude as found by ~er~h.' This is a large value. It follows that the diffusion distances are very short and that the precipitation

Jan 1, 1969

By R. C. Gifkins

The ideas expressed in this paper interest me very greatly, partly for their own sake and partly because they are very close to some speculation I have recently made concerning grain boundary diffusion. This is in a paper describing an extension to Mott's "island" theory of the grain boundary, to be published shortly.37 The facets or islands of good fit are identified in terms of specific crystallography, as in the model put forward by Brandon et al., and the bad fit between them is suggested to be interlinked "channels" of relaxed vacancies, associated with grain boundary ledges.

Jan 1, 1969

By B. Trentini

In the spectacular development of pure oxygen steel-making, the process using the vertical lance converter LD, is at the present time the most widely employed. Proper control of slag composition during the steel-making process appears to be essential in achieving satisfactory blowing from both the metallic yield and metallurgical points of view. The paper illustrates the primary importance of the presence of a large quantity of metal droplets in the slag during the process. In the case of both phosphorus and hematite pig iron, it can be deduced from the phase diagrams and confirmed by experimentation that nonhomogeneous slags are one of the causes of slag overflowing during the blow. The problem is however a complex one and further physicochemical studies appear necessary. Finally, the new continuous steelmakingprocess developed by IRSID is described. PEOPLE who knew Henri Marion Howe have said that he took great pleasure in speculating on the future of metallurgical processes. It is therefore not inappropriate to devote, in his memory, some description and discussion to processes unknown to the world of his time, in particular oxygen steelmaking and continuous steelmaking. The first industrial application to steelmaking of tonnage oxygen produced by air liquefaction was made in Germany just before the war and consisted in enriching the air blown through the bottom of a basic Begsemer converter in order to melt a higher proportion of scrap and to produce steels with lower nitrogen content than is achieved with conventional practice. While this process was being developed after the war, mostly in Western Europe, steelmakers were becoming increasingly familiar with the technique of blowing pure oxygen from the top, first by means of consumable steel pipes, with or without refractory shielding, and later by water-cooled lances, designed for the purpose and affording longer life. The field was then open for the wide use of pure oxygen in steelmaking, either in existing processes such as open-hearth or electric furnace, or in new processes. These new processes can be broadly classified according to the category of furnace employed. In the case of the vertical converter taken as the first category, bottom-blowing of pure oxygen causes extremely rapid wear of the refractory tuyeres, and although various expedients have been tried to overcome this drawback (such as mixing oxygen with CO2 or H2O or using high pressure oxygen), they have had to be abandoned. The solution for vertical converters has been found in top-blowing with a vertical water-cooled lance; this is known as the LD process or basic oxygen converter process.

Jan 1, 1969

By J. A. Herbst, G. A. Grandy, T. S. Mika, D. W. Fuerstenau, G. D. Gumtz

As a basis for interpretation of grinding behavior, the discretized batch grinding model is briefly presented and described, with solutions of the resultant equations for linear systems. Techniques for obtaining relevant experimental data are discussed for first order grinding systems, with methods for estimating other systems1 parameters from these data. Computer methods are described for conducting a sensitivity analysis which can be used to obtain an improved estimate of the system parameters. Examples of the use of the computer in conjunction with the grinding model for the simulation of batch grinding, locked-cycle grinding, and closed-circuit grinding are presented.

Jan 1, 1969

By S. E. Piper, E. M. Buchalter, R. P. King, E. T. Woodburn

The problems involved in an optimum decision making model for flotation circuit are, first of all, to characterize the feed material in terms of parameters which can quantitatively describe the network flotation action in terms of a feasible set of control actions. Once the characterization has been postulated, it is then necessary to devise tests relating to parameter sensitivity, in order that credibility of the model predictions can be assessed. Once a credible model is available, the optimum control set is determined by a hill climbing technique. Details will be reported as to the credibility of model predictions using the stochastic flotation model on a network and further, computational problems associated with hill climbing for a complex objective function are reviewed. Discussion is presented on use of the Rosenbrock technique with constraints and use of a modified objective function with constrained derivatives when employing Fletcher and Powell technique.

Jan 1, 1969

By S. D. Dahlgren

The plasticity of unalloyed P plutonium was studied by evaluating the strain-rate-hardening exponent, m, in the equation Values of m up to 0.33 and tensile elongations up to 680 pct were obtained for ß plutonium formed directly from the a phase. Casl bars that were cycled and tested had lower flow stresses and higher values for than uncycled bars , hut their total plastic elongations were not as great as expected because of premature failure at voids formed during cycling. Flow stresses were higher and m was lower (m = 0.15) for 9 plutonzutn formed from the y phase. ThE strain-rate-hardening exponent for plastic flow of p plutonium was determined as a function of strain rate, test temperature, and heat-treating history, and it was related to the rather large plastic elongation found previously for some plutonium tensile samples. Gardner and ~ann' obtained tensile elongations of up to 620 pct for P plutonium samples which had been completely transformed from the low-temperature a phase to the P phase before testing. Such a large percentage elongation is unusual for unalloyed metals or single-phase alloys.' The a phase is stable below approximately 112°C and (3 is stable between approximately 112" and 190"c.~ Both phases have mono-clinic structures. A temperature of 160°C is 0.58 of the effective absolute melting point, 475°C) of the p phase. The effective melting point is obtained by considering the enthalpy and entropy changes associated with the higher-temperature phase transformations and it is not the same as the experimental melting point of the highest-temperature allotrope of unalloyed plutonium. Nelson, Bowman, and Bierlein observed a striking difference between the ductility, as well as other mechanical properties, of p plutonium formed from the next higher-temperature phase (y) and the ductility of /3 plutonium formed from the a phase. The total elongation of /3 plutonium formed from the y phase was less than 5 pct. Earlier, the creep rate of 13 plutonium formed from the a phase was shown to be 200 to 500 times faster than the rate for 0 formed from y for the same test temperature and stress.

Jan 1, 1969

By D. A. Elgillani, M. C. Fuerstenau

In this paper, oxidation potentials measured in the presence of various concentrations of cyanide, ferro-cyanide, and ferricyanide and ethyl xanthate at various values of pH are related to flotation response. Eh-pH diagrams are presented to show that the formation of surface ferric ferrocyanide is probably responsible for depression when cyanide is added. The influence of cyanide on the depression of pyrite with xanthates as collector has been the subject of a number of investigations,'-6 and several theories on the mechanism of depression have evolved from these studies. Wark and Cox7 and Gaudin8 have suggested that the depressing effect is due to a competition of cyanide ion with xanthate ion for the surface. Cook and his colleagues9-11 have explained this phenomenon in terms of competition between hydrocyanic acid and xanthic acid. Sutherland 12 has shown that although both of these theories accurately describe the relation between pH value and cyanide addition at constant collector addition, they fail to describe the relation between pH value and the amount of collector required to cause flotation. Taggart 13 suggested that depression in these systems is due to the formation of a reaction product between ferric ion at the pyrite surface and ferrocyanide ion derived from solution. Majumdar4,6 has attempted to prove this hypothesis by measuring the contact angles of pyrite in the presence of 25 mg per liter ethyl xanthate and different concentrations of potassium ferrocyanide and ferricyanide. In all cases the contact angles were quite high up to pH 10. These results indicate that pyrite should not be depressed by either potassium ferrocyanide or ferricyanide. In view of these facts, Majumdar has assumed that the compound Fe(CN)2 forms at the surface. Gründer and Bornl4 have stated that depression may be due to the formation of the compound K2Fe(II)Fe(CN)6 at the pyrite-solution interface. This compound is thought to be an interaction product between the K2Fe(CN)6-2 ion from solution and the Fe++ ion at the pyrite surface and, accordingly, K4Fe(CN)6 should depress pyrite at least as effectively as KCN. This was proven experimentally, but there was no simple relation between the depression of pyrite and the concentration of either KCN or K4Fe(CN)6 in solution. In view of the many mechanisms that have been proposed for pyrite depression by cyanide, it is apparent that a clear understanding of the phenomena occurring in these systems is lacking. One reason for this may be the fact that the species responsible for pyrite flotation in the presence of xanthate is not the xan-thate ion but rather dixanthogen.15 Since the oxidation of xanthate to dixanthogen is dependent on the oxidation potential of the solution, it would seem that knowledge of these potentials would be a requisite to understanding the pyrite-xanthate-cyanide system. It is the object of this paper to measure both the oxidation potential and pH of the pyrite systems in the presence of various concentrations of cyanide, ferrocyanide, and ferricyanide and xanthate and to relate these values to flotation response. EXPERIMENTAL MATERIALS AND 'TECHNIQUES In the experiments discussed here, pure potassium ethyl xanthate was used as collector, and reagent grade potassium cyanide, potassium ferrocyanide, and potassium ferricyanide were used as depressants. Reagent grade HC1 and KOH were added for pH adjustment. Conductivity water, made by passing distilled water through an ion exchange column, was used in all experimental work. Two natural samples of pyrite were used in the investigation. Sample preparation for flotation included dry grinding with a mortar and pestle and sizing the product to 100 x 200 mesh. Prior to flotation, a 0.75-gm sample of pyrite was added to a solution containing a known amount of depressant at the desired pH value, and the system was conditioned for 4 min. Following this, a known amount of collector was added and the system was conditioned for another 4 min. The pH — termed flotation pH - was measured; the pulp was transferred to a Hallimond cell, and flo-

Jan 1, 1969

By W. F. Hosford, E. W. Kelley

Deformation studies have been conducted at room temperature on single crystals of magnesium and magnesium alloys with thorium and with lithium. Single crystals oriented to suppress shear on the easily activated basal slip systems were deformed by plane-strain compression. Compression along the C axis was accommodated by {1011} banding. Compression perpendicular to the unconstrained c axis activated {1012} twinning, and, after virtually complete twinning, deformation continued by {1011) banding in the twinned material. Compression perpendicular to the constrained c axis was accommodated by the simultaneous operation of (1012) twinning against the constraint and (1011 ) banding. Although this orientation was favorable for {1010)(1210) prism and {1011}(1~10) pyramidal slip, these modes were not observed in pure magnesium or in Mg-0.5 pct Th. However, {10i0)(1~10) prism slip was observed in crystals of Mg-4 pct Li during compression perpendicular to the constrained c axis. Fracture in all materials occurred parallel to (1124) or {l~il) depending on the orientation and composition of the specimen. THE mechanical behavior of the hcp metals is strongly anisotropic. Although several slip systems have been reported the slip is cpmmonly in the directions of closest packing, the (1210),' and this does not produce strains parallel to the c axis. Hence the inherent anisotropy. The deformation mode most easily activated in magnesium at room temperature is (0001)(1210)- basal slip. Also {1010}(1~10) prism slip and {1011)(1210) pyramidal slip have been reported, primarily at elevated temperatures.2"4 However, at room temperature the shear stresses to activate the prism and pyramidal modes are roughly a hundredfold greater than that required for basal slip.'j4 Thus prism and pyramidal slip may be expected only under special conditions of loading. Strains normal to the basal plane can be produced by twinning, however. Many twinning modes have been reported for magnesium,' with (1012) twinning the most common and relatively easy to activate. Magnesium can deform by (1012) twinning when stressed along the c axis jn tension, but not in compression. In contrast, (1011) twinning is activated by compression along the c axis and not by tension. In addition to primary twinning, secondary twinning or slip can occur within the reoriented material of primary twins.' In general at least five independent shear systems must be active to bring about an arbitrary shape change such as that in the individual grains of a deforming polycrystalline material.' Because basal slip can_ provide only two independent shear systems and (1012) twinning can only accommodate an extension of the c axis, other deformation modes must be active in magnesium for an arbitrary shape change to occur. The purpose of this investigation has therefore been to study the various deformation modes in magnesium at room temperature, with special emphasis on those modes that are less easily activated. The effect of the alloying elements, thorium and lithium, has also been investigated. In polycrystalline aggregates, unambiguous identification of deformation modes is extremely difficult and the direct evaluation of the resolved shear stresses to activate them is not feasible. On the other hand, uni-axial tension and compression experiments on single crystals may not activate some of the- deformation modes because basal slip and/or {1012) twinning cannot be suppressed in most orientations. However, it should be possible to activate all possible deformation modes using oriented single crystals and plane-strain compression. Identification of active deformation systems and evaluation of the resolved shear stresses required to activate them should be facilitated. Wonsiewicz and Backofen have recently completed an investigation of the plasticity of pure magnesium crystals at various temperatures utilizing plane-strain compression and selected crystal orientations. This technique has also been used in the present work. The seven orientations selected for study are indicated in Table I. Plane-strain compression along the c axis (orientations A and B) should activate some deformation mode _other than basal, prism, or pyramidal slip, or (1012) twinning. In orientations C and D, prism or pyramidal slip would be expected to take place. When the compressive load is applied perpendicular to an unconstrained c axis (orientations E and F) the three slip modes should be suppressed but not (10i2) twinning. In orientation G, basal slip should occur.

Jan 1, 1969

By R. E. Reed, C. J. McHargue

Poly crystalline aluminum specimens having random and diffuse (001) initial orientations were reduced 90 pct in area at room temperature by drawing, extruding, and swaging. Although each procedure produced the duplex (001)- (111) texture, there were marked dqferences in the relative amounts of each component. This also produced variations in the tensile properties of the aluminum rods. It is generally agreed that the fiber texture found in aluminum rods consists of a strong (111) and a weak (001) component after reductions in area of 90 pct or more. An examination of data summarized in recent reviews'-3 shows much spread in the values for the relative amounts of the two components reported by different investigators. That the initial orientation has a marked influence on the final texture even after reductions in area greater than 90 pct is well-documented.4-7 Another factor which may influence the relative amounts of the two components is the method of fabricating the wires or rods. Barrett and ~assalski' state that the center of wires formed by rolling, swaging, and drawing have the same textures. The data cited in support of this conclusion came from qualitative X-ray techniques. In recent years there has been renewed interest in correlating the type of preferred orientation with such parameters as stacking fault energy and onset of mechanical twinning.'' Since these analyses have often used many sources of data, it is essential that the data be evaluated for the effect of fabrication variables. In this study we have produced aluminum rods by drawing, swaging, and extruding and have quantitatively determined their textures. All specimens had the same purity and fabrication temperature, and the amount of deformation and the starting textures were determined. We have compared our results with published studies on similar materials and fabricating parameters. We have also compared results from the same three fabricating procedures for single-crystal specimens in three instances. EXPERIMENTAL PROCEDURE The aluminum was 99.99+ pct with the only detected impurities being (by weight) 0.002 pct Cu, 0.001 pct Si, and 0.001 pct Mg. Cylinders a in. in diam by 1 in. long with a fine-grain random texture were made by the following method. Cubes 1+ in. on a side were machined from 2-in.-diam ingots. These cubes were slowly pressed about 30 pct in each of the cube directions. The material was recrystallized by annealing 1 hr at 350°C. Three deformation-anneal cycles produced the desired material. Polycrystalline specimens with a diffuse (001) texture were made by casting into a graphite tube 1 in. ID, li in. OD, by 8 in. long which had been preheated to 900°C. One end of the tube was placed on a water-

Jan 1, 1969

By H. J. Polta, R. W. Michelson

Discounted cash flow analysis is commonly used to evaluate the profit making potential of a business venture. The same method can be used to analyze the effects of varying physical and economic conditions upon the real cost of supplying a mineral commodity. If a fixed rate of return on a capital investment is specified, and the flow of cash, discounted at that rate, is just adequate to repay the investment over the life of the venture, the net present value of the venture is zero. At this condition it is possible to evaluate the unit cost of producing the mineral. It will be exactly equal to the selling price required to calculate a zero present value. Increasing a particular cost factor will not always increase the cost of supply by the same amount. For example, in iron production from magnetic taconite, an increased cost per ton associated with beneficiation would be integrated into the discounted cash flow model along with local, State, and Federal taxes, depletion and depreciation allowances, resultant increased unit recoveries, and all of the other related component cost factors. Rather than adding to the cost, the factor may have a positive, instead of a negative, effect on the discounted cash flow and cause a decreased cost of supply. This value can be determined by a computer model which iterates the necessary selling price until the net present value is essentially zero. The discounted cash flow evaluation model lends itself particularly well to an application of the Monte Carlo simulation method for calculating a probability distribution of iron unit cost resulting from the probability distributions of the component cost factors.

Jan 1, 1969

Jan 1, 1969

Jan 1, 1969

By J. Pinto, F. Galasso

THE current emphasis in preparing boron fibers by reduction of gaseous boron compounds on a resistively heated metal wire substrate has renewed interest in the borides of those metals which have relatively high melting points and are available as fine wires. A knowledge of the structures and properties of the borides, which are formed when boron diffuses into the metal core during boron deposition, can be of assistance in the understanding of the boron fiber formation process and the fiber properties. Many of these borides are well-known and their properties have been measured. However, when an unidentified boride is found in the core, it may be difficult to establish its composition because of the small amount of material available, the preferred orientation effects on the reflections in its X-ray pattern, and the possible overlap of X-ray reflections if several borides are present in the core. For example. the proper indexing of the X-ray pattern of WB4, which was formed in the tungsten substrate core during boron fiber formation, was accomplished only after small single crystals of this boride were grown and X-ray precession investigations were conducted.' This note presents the results of a study of the phases formed in the core when tungsten, tantalum, and molybdenum metal wires were used as substrates in the boron fiber preparation process with particular emphasis on the identification and characterization of a higher boride of molybdenum analogous to WB,. Boron was deposited on resistively heated stationary 0.0012-in.-diam tantalum, tungsten, and molybdenum wires at 1050°C for various times up to 60 sec using boron trichloride and hydrogen as the reactant gases. After 60 sec of boron deposition the fibers were approximately 0.006 in. in diam. Examination of photomicrographs of fiber cross sections showed that the boron had diffused nearly to the center of the tungsten and molybdenum cores in 15 and 30 sec, respectively, and only halfway to the center of the tantalum core in 60 sec. X-ray diffraction photographs of the fibers indicated that it was also after 15 and 30 sec deposition times that the tungsten and molybdenum metal reflections, respectively, had disappeared from the X-ray patterns of the fibers. The patterns of the boron fibers produced using tantalum wire as a substrate showed that amorphous boron, TaB2, and tantalum metal were present after a few seconds deposition time and remained even after deposition times of 60 sec. Until a deposition time of 15 sec was reached, the tungsten substrate fibers contained amorphous boron,273 6WB, W2B5, and WB4 as well as tungsten metal, while the molybdenum substrate fibers contained amorphous boron, MoBa, Mo2B5, and molybdenum metal for deposition times up to 30 sec. Just before the molybdenum metal pattern disappeared, a pattern similar to that of WB, appeared, suggesting that a phase, MOB,, isomorphous with WB,, was present in the fiber. This same pattern was obtained from the product formed by heating a mixture of molybdenum metal and excess boron powder in a boron nitride crucible at 1960°C in an argon atmosphere. As was the case with the WBn pattern, this pattern could best be indexed on the basis of a hexagonal unit cell rather than the tetragonal unit cell Chrktien and Helgorsky reported for ~0~4,~ see Table I. The unit cell parameters for MoB4 were calculated to be a, = 5.214A, co = 6.358A. Assuming the space group P63/mmc and positions5 2M01 in 2b and 2MoII in 2c found for tungsten in WB~,' a logical structure for MOB, was determined using geometrical considerations to place the boron

Jan 1, 1969

By E. F. Koch, J. L. Walter

In a study of the structure and properties of tungsten wire used for lamp filaments, it became desirable to perform transmission electron microscopy on the wire in the annealed as well as in the drawn condition. Wire used for lamp filaments is generally drawn to diameters less than 0.010 in. which is too fine for the preparation of transmission samples from single wires. Thus, it is clear that some assembly of wires must be used to form a "wire sheet" similar to that used by Glenn and Duff.' Also, because recrystallized tungsten wire is brittle at room temperature, the "wire sheetJ' must be rigidly contained during any subsequent grinding and polishing operation. With these conditions in mind, a technique was devised for thinning tungsten wire of 0.001 to 0.010 in. diam for transmission electron microscopv. Sample Preparation. The commercially doped (218) tungsten filament wire was obtained from the Lamp

Jan 1, 1969

By K. R. Carson, J. Weertman

THE fatigue-hardening curve has received much attention in recent years. This curve is obtained by plotting the peak stress required to maintain a given plastic strain per cycle vs the number of cycles. It

Jan 1, 1969

By C. C. Harris

This article presents a general equation describing the xYt surface in batch grinding. This equation contains as special cases most of the relationships which have been deduced from kinetic studies. In an earlier paper an analytical solution of the integro-differential equation of batch grinding was proposed1 as a first approximation of the xYt surface.' A more general equation will be presented here, which appears to combine in a single statement many conclusions reached by experiment. A possible underlying mechanism is that the changing product fineness leads to changes in the particle crushing strength and in the probability of encounter with the crushing media.

Jan 1, 1969