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By John Wulff

IN a previous paper Burwell and Wulff1 have shown by electron diffraction studies that allotropic transformations can be induced in 18-8 stainless steel by polishing to a depth of about 5 X 10-5 cm. The development of a successful etching technique, which removes accountable amounts of metal from the surface without pitting and without changing the root-mean-square profile as measured with an Abbot profilometer, led to the application of the whole technique and material to an investigation of various mechanical methods of surface preparation, such as grinding, lapping, superfinishing and cold-rolling. Ideally suited to such a study is 18-8 of low carbon and nitrogen content. The material can be heat-treated to produce a coarse-grained single-phase structure. On cold deformation there occurs not only a reduction in grain size but, at regions of maximum stress, a change of face-centered material to body-centered material, provided the metal is worked below about 200°C. When worked between 200° and 415°C., diffraction studies evidence a reduction in grain size without the appearance of any new body-centered ferrite. Ferrite, which can be referred also to strains induced by carbide precipitation, is evident when the material is worked at temperatures between 415° and 800°C. Stainless steel is advantageous because the usual surface-finishing operations do not readily oxidize it to any appreciable depth. In order to produce detectable oxide films on the surface of austenitic 18-8 in a time equivalent to that required to produce, for example, a fine ground finish on ½ sq. in., the sample must be held in a furnace or oxygen stream above 600°C. By using longer heating times, it is possible to achieve measurable oxide films on samples whose surface temperatures exceed only about 250°C. EXPERIMENTAL PROCEDURE The apparatus, material, and technique described in the previous paper1 were employed in this investigation. Samples of 18-8, 1 by 1 cm. by 4 mm., were carefully annealed in the austenitic range to produce a coarse-grained structure. They were then quenched and pickled to remove scale. On a lapping machine of the Graton2 type, both sides of each sample were polished to a flatness of 1/6 a wave length of sodium D light. Thereafter they were electrolytically etched to remove at least 1 X 10-3 cm. of the surface, a depth that is well below that of any deformations induced by surface preparation. Samples of this material, carefully mounted in steel holders, were then sent to various industrial organizations known for special finishing techniques. In the instrument shops at the Massachusetts Institute of Technology check samples were finished by the same methods, as far as they were available. Abbot profilometer3 readings were made on all the samples, which were then carefully degreased in double distilled benzine and alcohol, dried in a hot-filtered air blast, and kept in a desiccator. Suc-

Jan 1, 1941

By N. L. Svensson

The model developed by Tuylor for the calculation of Polycrystalline yield strength has been applied to the case of an aggregate hawing a preferred orientation. In general this procedure requires the specification of texture by means of weighting factors applied to specific orientations. The problem to which the model has been applied is that of the yield-strength aniso-tropy of cold-rolled aluminum whose rolling texture was described as a combination of (110)[112] and (311) [112] In this case yield-strength anisotropy is defined by the rutio of yield strength measured at an angle 8 to the rolling direction to that measured along the rolling direction. The method of calculation of yield-strength ratio as a function of ? is described and the results show good agreement with experimental values. The orthotropic yield criterion suggested by Hill has been applied to the results and the strain ratio R also calculated as a function of ?. This has been compared with calculations using the method suggested by Elias, Heyer, and Smith which does not exhibit suck good agreement with observation. one deficietlcy of the method presented is that the strain ratios used by are those applying to iso-Irobic materials. The method should therefore be reg-clrded only as a first abbroximation to the prediction of anisotropy. THE problem of calculating the stress-strain characteristics of polycrystalline aggregates from the properties of single crystals has attracted attention for a number of years. The most important contributions to this study have been those due to: Sachs,' Cox and sopwith,2 Taylor,3 Kochendorfer,4 Batdorf and Budiansky,5 Calnan and Clews,6 Bishop and Hill,7,8 Kocks,9 Budiansky, Hashin, and sanders, 10 Kroner,11 Cyzak, Bow, and payne, 12 Budiansky and Wu,13 and Lin.14 While the earlier work has been largely superseded, recent developments tend to support Taylor's solution" within the restriction imposed by his assumptions. The essential features of Taylor's approach were: 1) the material is rigid-plastic; 2) each grain experiences the same strain components as the aggregate as a whole (the problem was that of uniaxial deformation with principal strain components in the ratio 3) all regions of each grain deform uniformly; 4) work hardening occurs equally on all slip systems. While Bishop and Hill7 have generally validated this approach, there has been some criticism offered. Kocks? as pointed out that since multiple slip must occur the single-crystal data must be determined from orientations arranged such that polyslip takes place. Boas and Hargreaves,15 and others, have shown experimentally that the strain distribution within grains is not uniform, the strains in the vicinity of grain boundaries being less than those in the center of the grains. Both of these criticisms can be largely offset by the suitable choice of single-crystal critical shear stress. However, for the problem analyzed below, the critical shear stress is not directly used and, consequently, these criticisms lose their importance. The more recent contributions have attempted to obtain a more complete analysis by considering an elas-toplastic material and considering interactions between grains of differing orientations. Lin14 has considered the early stages of yielding for a polycrystalline aggregate having specific regions of defined slip plane orientations. On the other hand, Budiansky and Wu13 have allowed for these interactions for randomly disposed grain orientations and have calculated the polycrystalline stress-strain curves for crystals exhibiting either elastic-ideally plastic or kinematic hardening characteristics. This work has shown that yielding commences when the macroscopic stress is 2.2 times the critical shear stress for slip in a single crystal (7,). The yield stress-strain curve then rises becoming asymptotic to a value of 3.072 7,. This is close to the value obtained by Bishop and Hill (3.06) in their confirmation of Taylor's method. This, of course, is to be expected since, at large strain values, the elastic strains are negligible and the rigid-plastic model is satisfactory. The results of Budiansky and Wu indicate that the result obtained by Taylor is 7.7 pct high at a plastic strain which is two times the elastic strain at the initiation of yield. By defining the anisotropy in terms of relative values, the ratio of yield strength at orientation ?, to that measured in the rolling direction, the effect of the discrepancy in Taylor's solution is considered to be of lesser consequence. Therefore, it is anticipated that an analysis based on Taylor's solution, which can be quite straightforward, should provide a reasonable estimation of the anisotropy of materials having a preferred orientation texture. OUTLINE OF TAYLOR'S METHOD In fee metals there are four possible slip planes (the octahedral planes) and in each there are three possible slip directions (the edges of the octahedron), that is a total of twelve possible slip systems. von Mises16 has shown that at least five independent slip systems must become operative in each grain of the polycrystalline aggregate in order to preserve continuity of strain. With this geometrical requirement as basis and the assumptions previously listed, Taylor determined the operative slip systems for a number of orientations of the tensile stress axis specified in the unit stereographic triangle. For the ith slip system, the critical shear stress

Jan 1, 1967

By R. D. Pehlke, J. V. Gluck, R. L. Louvet

A study has been made of the effect of small additions of bismuth on the activity of zinc in dilute solution in molten tin. Free-energy interactions have previously been determined between zinc and various third elements where the solvents were molten bismuth or molten lead.'-4 In both of these solvents, the activity of zinc exhibits a strong positive deviation from ideal behavior (at 550°C y° for zinc in lead is 11.4 and for zinc in bismuth is 3.0). The present work, using tin as the solvent, is an extension to a case where the positive deviation is considerably diminished (y°Zn at 550°C is 1.63). Several previous investigators have studied the Zn-Sn binary system; however, little data is available in the range below 0.1 mole fraction zinc.5= Previous high-temperature galvanic cell studies in the Sn-Zn-Bi ternary system included the determination by Gluck and Pehlke of interactions in the bismuth-rich corner1 and separate investigations of the central region by Oleari and Fioriani6 and by Ptak and Moser.7 Yokokowa et al.8 conducted Knudsen effusion studies in the central region; however, their experiments at 625°K were conducted somewhat below the present experimental temperature range. Their results indicated an increase in zinc activity with the addition of bismuth. The present series of experiments was conducted in galvanic cells represented as follows: Zn Zn++ in LiCI-KC1 eutectic Zn + Bi in Sn (pure reference (fused salt electrolyte) (molten alloy) standard) The experimental apparatus. a multi-electrode system employing alumina crucibles and contained in a Vycor tube under a helium atmosphere, has been described previously, as have been the experimental procedures, precautions, and the methods of data reduction.1-4,- The experimental measurements were made over the range from 450° to 650°C. Between thirty and forty measurements were made in each run. The linearity of the electromotive force vs temperature relations was verified by linear regression techniques. The correlation coefficients exceeded 0.99. The experimental results summarized in Table I include the interpolated electromotive force at 550°C and the temperature dependence of electromotive force. Only results from stable and consistent cells containing more than 0.025 mole fraction zinc are reported. Attempts to run cells at 0.01 or 0.02 mole fraction zinc were not satisfactory. This is attributed to the closeness of the free energies of formation of the chlorides of tin and zinc. Calculations employing Wagner and Werner's criteria for displacement reactions10 indicated that reduction of the zinc content to 0.01 mole fraction places the cell near the borderline concentration for a 1 pct error in measured potential. The compositions shown in Table I are the actual weighed-in amounts. Previous experience has indicated that compositional changes during the running of a stable cell are negligible.' Over the range of compositions studied for the binary alloys, the activity coefficient of zinc was essentially constant indicating that Henry's law is followed to 0.05 mole fraction zinc. The temperature, OK, de-

Jan 1, 1969

By M. Muskat, H. H. Evinger

A METHOD has been developed whereby one may calculate the productivity factors of producing formations from a knowledge of the reservoir conditions. Account is taken not only of the heterogeneous character of the gas-oil flow system but also of the detailed variations with pressure of the shrinkage and viscosity of the oil, the solubility of the gas in the oil, and even the variability of the gas viscosity and the deviation of the gas from ideal behavior. Curves are shown giving the results of numerical calculations on the production rate as a function of the pressure differential for a high-pressure and a low-pressure system, three values of gas-oil ratio being treated in each case. Curves are also given showing the variation with distance from the well of the pressure, oil saturation, and permeability. The effect of connate water is briefly discussed in relation to the apparently large discrepancies between the calculated and observed productivity-factor values. INTRODUCTION The significance of the productivity factor as a measure of the capacity of an oil-bearing formation to produce is well recognized; for it is the composite and integrated resultant of the physical properties of both the porous medium and the fluid stream passing through it with respect to the ease with which the particular petroleum fluids present in the formation can flow through it and into producing wells. The most direct method of determining the productivity factor of a well consists, as is well known, in the simultaneous measurement of reservoir-pressure differentials and rates of production and the expression of the data in terms of rate of flow per unit pressure drop.1 Actual measurements carried out in this manner on producing wells have given factors that generally lie in the range of 0 to 100 bbl. per day per pound pressure drop. This wide range arises not only from variations in permeability but also from the varying sand thickness of producing formations. One of the aims of developing a theory of the mechanics of oil production obviously is that of predicting what the productivity factor should be from a knowledge of the individual characteristics of the producing formation and the fluids produced. For homogeneous fluid systems passing through a porous medium into a producing well, it has been known for some time that the steady-state rate of liquid flow Q is given by the formula:* [ ] where k is the sand permeability, h its thickness, µ the liquid viscosity, [Ap] the pressure drop between the well and the distant parts of the reservoir, in particular that at a radius [ro ]and [r ] is the well radius. This gives the productivity factor: [ ] which will have a numerical value for a liquid of I centipoise viscosity of 0.9316 or

Jan 1, 1941

By J. C. Fisher, J. H. Hollomon, David Turnbull

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl's formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith's6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.' The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl's paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949

By David Turnbull, J. H. Hollomon, J. C. Fisher

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl's formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith's6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.' The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl's paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949

By S. W. Churchill

A digital computer was used to obtain an exact numerical solution for the transient behavior of the insulation and earth adjacent to an isothermal, submerged flat surface for a single set of parametric values. Comparison of the computed results with analytical solutions for limiting conditions revealed that a complete and general solution for all parametric values could be constructed from these limiting solutions. Complete and general solutions for insulated spheres and cylinders can also be constructed from limiting solutions. The procedure is illustrated in part for an insulated spherical tank. The heat flow was found to fall rapidly to a pseudo-steady state; after some time, it then decreased slowly to zero for a flat plate and cylinder, and to a low steady-state rate for a sphere. The accumulative heat flow during the initial falling-rate period may be a significant fraction of the heat flow during the entire first year. INTRODUCTION Underground storage of liquefied natural gas and liquefied petroleum gas has received considerable recent attention. The rate of heat flow from the earth to the storage cavity and the resulting temperature field in the earth are important factors in the technical and economic evaluation of such storage facilities. The objective of this paper is to indicate how complete solutions can be developed for the transient flux and temperature field for various geometrical configurations. The representative properties and dimensions, and the resulting parameters utilized in the illustrative results, are indicated in Table 1. The results presented herein are for dry earth. The effect of the latent heat of solidification of water in the soiI will be described in a subsequent paper. The temperature field in the insulation and earth is determined by energy balances, boundary conditions and initial conditions. The physical problem can be described mathematically with virtually no idealizations insofar as physical properties are known. It appears possible to solve the equations by numerical integration on a high-speed digital computer for any geometrical configuration and conditions. For complex situations, however, the computations are expensive and the results are highly specific. Analytical solutions have been developed for a few simple but important geometrical configurations and conditions, including one-dimensional heat transfer from (or to) earth at an initially uniform temperature to (or from) flat plates, spheres and circular cylinders. The solution for an insulated flat plate has also been derived but is in the form of a slowly converging series involving taklated functions. It was planned to use a computing machine to evaluate this series for a number of representative conditions. However, upon examination of the results of preliminary computations it was discovered that a complete, general and accurate solution could be developed by interpolation between several much simpler solutions for limiting conditions. This technique then was used to develop a a complete solution for an insulated sphere. The equations presented herein are derived in Carslaw and Jaegerl and other books on applied mathematics, or they are simple extensions of these previous results. Hence, all derivations are omitted. Emphasis is instead placed on the results and their

By Foster Fraas

INTRODUCTION THAT variations in the humidity of the air and in the moisture content of a mixture of broken solids being separated electrostatically cause trouble is not new.1 Much of the reputation for unreliability commonly ascribed to the electrostatic separation processes is probably due to this one factor alone. Some operators dry thoroughly before separating; and while this is good in many instances, there are others in which it is not the remedy for trouble. Some mixtures behave best in very dry air and with the mixtures fed to the separator while hot to reduce the adsorbed water content. On the other hand, an overdried mixture on coming to equilibrium with more humid air, has been known to take up moisture selectively on one family of particles, as of coal in the presence of slate and clay, and give sharper electrostatic separation. From these observations it is concluded that there is a permissible moisture content for a particle and also for the atmosphere surrounding it, if in equilibrium, at which the particle will have a conductivity or contact potential2-4 that is ideal for electrostatic separation. This permissible moisture content varies between a wide range of limits for the different materials that are separated and with the kind of electrostatic separating process used. Water can be present as a result of adsorption and condensation from the atmosphere, as an accumulation before or during mining, or as a residue from a previous process step. The water may exist as a liquid film or as an adsorbed layer of vapor. If the water exceeds permissible limits it must be removed. Its state determines the method. Drying by evaporation is necessary for adsorbed water, for part of the liquid-film water (that is, up to several percent of the dry weight), and for free water in the internal structure. Large water contents may be removed by drainage or filtration. At just what point mechanical removal should cease and drying by evaporation begin depends upon the method of mechanical removal and its cost. Particles can also be separated according to their differences in dielectric constant when suspended in a liquid of intermediate dielectric constant. Recovery of this liquid presents a similar problem. PERMISSIBLE MOISTURE The adsorbed moisture on the outer surface of minerals can be quickly removed or replaced. Accordingly, in speaking of adsorbed moisture contents, either that of the solid or that of the surrounding air may be considered, the two values being connected by a distribution coefficient which varies with the temperature. However, such a condition does not necessarily exist in processes where an initially dry material is suddenly introduced into an atmosphere having a partial pressure of water vapor or where a moist material is suddenly introduced into a dry atmosphere. Here the resultant differences in the

Jan 1, 1947

By R. E. Delavault, H. V. Warren

In normal soils there are usually 10 to 50 parts of copper in every million parts of .soil. Only 0.2 to .5 pct of this copper can be found by any simple cold chemical attack. Now, with rubeanic mid reagent paper, a prospector or field geologist can detect as little us 4 ppm of readily available copper ill soil. This degree, of sensiticity is enough to determine the presence. of copper anamalous an as and, ecentually, to discouer copper mineralization. Circumstances determine whether it is better to make analyses in the field or in a permanent laboratory. The rubeanic acid test described in this article has been designed primarily for field use: it is simple and virtually foolproof, and it requires a minimum of field kit." It is sensitive, easily de- • Ed. Note: Persons Interested in purchasing kits suitable for rubeanic acid prospecting can obtain information by writing Eldrico Geophysical Sales Ltd., 633 Hornby Street. Vancouver 1, B.C. The University of British Columbia does not produce these kits for sale and has no financial interest in their production tecting 4 ppm of readily extractable copper in a soil. This is by no means a quantitative test, but it is accurate enough to provide a valuable indicator of copper anomalous areas for both prospectors and field geologists. The easiest method for detecting metal deposits that do not produce visible float or stains is to make a simple chemical test for the metal in overlying soil, or in the silt of a stream that may have picked up metal farther upstream. In Brief: Testing for copper may be done easily by shaking a soil sample with strong acetic solution in a small test tube and pouring the mud into a small filter, the tip of which rests upon a strip of reagent paper impregnated with rubeanic acid (di-thio-oxamide). When copper is present—and only when it is—a blue spot develops. The more copper, the darker the spot. If the copper content is merely the small amount present everywhere, there is a pale blue or hardly visible spot; if it is abnormally high, the spot will be dark. There are, of course, intermediate cases where the experienced geochemist cannot tell offhand whether a medium-strength spot represents rich agricultural soil, weak copper mineralization, or distant rich copper mineralization. Reagents and material are inexpensive; the test may be readily done on the spot with a simple kit easy to pack and handle. Anyone interested in general problems of soil sampling as applied to prospecting may refer to an article recently presented to the AIME. In exploration work it is the contrast between the metal content of anomalous and background areas that is important; absolute values become of greater interest when an anomalous area is being investigated in detail. With specific reference to copper, it has been the authors' experience that the amounts of metal extracted from anomalous and normal soils with buffer solutions of decreasing pH show better contrast if an acid reagent is used. This contrast tends to increase with increasing acidity until 3 to 4 pH is reached. Using a short cold attack on unheated soil, it has been found that further increases in acidity do not produce better results, and only increase the hazards involved in carrying strong acids. An acidity of about pH 4 is satisfactory for direct determination of copper by dithizone. But dithizone itself introduces some problems: it must be made up fresh at frequent intervals, and with some soils, notably those with much ferric iron, oxidation mag take place before all the copper has reacted with the dithizone. Rubeanic acid keeps its strength unimpaired for long periods, is unaffected by oxidation, and is practically specific for copper at pH 4. Consequently it seems an ideal reagent to use in prospecting for copper. History and Background: Rubeanic acid (systematic name: dithio-oxamide (SC-NH2) has long been known as a spot test reagent for some heavy metals with which it gives a number of compounds. Only copper and some metals of the platinum family are believed capable of providing any ru-beanate compounds under conditions of moderate

Jan 1, 1959

By R. B. Rosene, G. L. Foster, A. R. Hendrickson

he properties of some of the common fracturing oils, such as sand-falling rate, fluid loss and viscasity, are a function of the three major constituents of the oil. These are: asphaltic material, parafin waxes and a base oil. The base oil can be either high or low viscosity. Asphaltic material increases viscosity by thickening the oil, decreasing the rate of fall of sand through the oil. at temperatures up to 200" F. When large arnorrnts of parafin wax are present, much of the wax i.s not dissolved, but is present in the form of rnicroscopic crystals. 7'his, of course is limited to temperatures below the melting points of waxe.s. As a result, parafin waxes clo not function primarily as thickener.7, but rother as bullting materials. The functiori of wax, without asphaltic material, in a low viscosity base oil is uniquely unlike that of wax with asphalt coexistent in the oil. The resulting difierence in wax crystal size governs the sand-falling rate to a large extent. An ideal type of fracturing oil is one containing neither asphalt nor waxes. In such cases, the viscosity and resulting low sand-falling rate are apparently due to soluble resin- ous hydrocarbons, which are compatible with formation oils. INTRODUCTION Since the introduction of hydraulic fracturing as a method of stimulating production from oil and gas wells, a variety of fluids have been employed to open the fractures and carry the propping agent. Such fluids include gels, emulsions, and oils. In the latter category, the use of refined oils has increased tremendously, and it is probably safe to assume that such oils represent more than one-half of the total fluid used in fracturing. The general acceptance of refined oils for fracturing can be accounted for on the basis of their relatively low cost and general applicability. To minimize transportation costs, such refined oils are generally obtained within the local areas of operation. As a result there are several kinds of oil used in different areas, with a wide variation in the basic composition. These types may vary from a fair grade of lubricating stock to a highly viscous cut-back asphalt. or road oil. Originally, little attention was paid to the composition of the oils used for fracturing, and any oil which would carry sand was considered satisfactory. Recently, however, service companies and well operators have become more concerned with the type of oils used for fracturing. With this in mind, the present work was undertaken to evaluate and compare many widely used fracturing oils to determine which constituents were most desirable for fracturing purposes. Some of the important properties of fracturing fluids are sand-falling rate, viscosity, and fluid loss. Other properties, that are actually of no less importance, include flash point, pour point, emulsifying tendencies with formation brines, and compatability with the formation oils. This discussion has been limited, however, to the first mentioned properties in order to give some idea of the general composition of the refined oils, how they function, and why. PROPERTIES OF FRACTURING OILS The properties of fracturing oils are a function of the three major constituents of the oil. These may be designated as: (1) asphaltic material, (2) paraffin waxes and (3) a base oil, which may be of either high or low viscosity. The asphaltic material clas-

Jan 1, 1956

By Rex B. McLellan

Studies of the eyuilibrzum between ferrite and austenite with gas mixtures (CO + CO2 and H2 + CHe) have been used as a means of deducing the energy and vibrational entropy of carbon atoms in dilute interstitial Fe-C solutions. A simple model for dilute interstitial solutions is given which enables a solubility equation for the equilibrium between the gas mixtures and the solid to be deduced. This solubility equation is used to estimate the partial In this work measurements of the equilibrium between dilute solid solutions of carbon in iron and gaseous mixtures of CO2 + CO and CH4 + Hp have been analyzed using theoretical solubility equations deduced from a knowledge of the thermodynamic parameters of the gas mixtures and an appropriate model for the solid solution. The solubility equations are deduced by equating the chemical potential of carbon atoms in the gas thermodynamic functions of dilute Fe-C solutions from the measured equilibrium between the solid and the gas mixtures. It is shown that the vibra-tional entropy of a carbon atom in a and y iron is smaller than the corresponding entropy 01. a nitrogen atom in solid solution inferrite or austenite and that there is little difference between the vibrational entropies of both nitrogen and carbon atoms in ferrite and austenite. and solid phases. The chemical potential of carbon in the gas is found from a simple statistical mechanical analysis of the gas mixtures utilizing spec-troscopic data while that for carbon in the interstitial solution is found from a model in which the carbon atoms act as bound oscillators distributed in a random fashion in the solution. The solid solution is dilute enough to enable solute-solute interactions to be ignored. Thus the configurational entropy of the solution is ideal but the mixing entropy contains additional excess terms due mainly to the vibrational changes occurring on solution formation. The partial excess entropies (and the partial energies) do

Jan 1, 1965

By A. F. Crawley

The densities of some liquid Pb-Sb alloys up to 11 wt pct Sb and Pb-Sb-& alloys up to 10 pct Sb/10 pct Sh have been determined by a pycnometric technique over a temperature range of about 130°C above their melting points. The data given are accurate within 0.05 pct. Density is shown to vary linearly with temperature , and equations relating these quantities have been formulated. Molar volumes calculated from the density data indicate that volumetric deviations from ideal mixing are undetectable within the limits of experimental error. A continuing research program into some fundamental physical properties of liquid metals is being pursued at the Mines Branch, Department of Energy, Mines and Resources, Ottawa, Canada. This work has received support from the Canadian Zinc and Lead Research Committee in cooperation with the International Lead and Zinc Research Organization. This paper, which reports some density data for Pb-Sb and Pb-Sb-Sn alloys, follows previous work from this laboratory on lead, tin, and Pb-Sn alloys.' Of previous data from others, Greenaway2 and Sato and Munakata3 have reported results on Pb-Sb alloys. No previous work has been published on the ternary Pb-Sb-Sn alloys, reported here. EXPERIMENTAL METHOD Densities were measured by a pycnometric technique which has been described in detail and appraised for accuracy in earlier Mines Branch reports.475 Fig. 1 shows the densitometer with the pycnometer in position for a run. The pycnometer is also shown in some detail. The pycnometer of dense, high-purity graphite, about 14 cu cm in volume, was carefully machined to a uniform, smooth finish. The height was measured by a depth micrometer and the diameter by fitting precision gage blocks between steel balls.' In each case several readings were taken, and the final results were considered accurate within 0.01 pct. The resulting volumetric uncertainty together with small inaccuracies in the coefficients of linear expansion of graphite lead to a maximum systematic uncertainty in the method of ±0.03 pct. As shown in Fig. 1, the pycnometer lid is a threaded cap. Thus, the charge, a cylinder of the alloy, can easily be inserted and the solidified metal can readily be removed after a run. The dimensions of the cylindrical charge are chosen to ensure that, once molten, the metal will not only fill the pycnometer completely but will discharge an excess into the excess-metal float chamber. AS the temperature is increased above the melting point, the volume of metal in the excess chamber increases until the system has equilibrated at the desired temperature. At this point, the excess chamber is moved to one side by twisting the shaft F, leaving a fixed volume of liquid metal in the pycnometer. This volume of fluid is readily calculated using measured coefficients of linear expansion of the graphite which expands anisotropically. The associated weight of fluid is determined as the weight of the solidified metal removed after the furnace has cooled down. Alloys were prepared from 99.997 pct Pb, 99.999 pct Sn, and 99.999 pct Sb, being melted by an electric furnace in a graphite crucible and poured into graphite molds. Several density specimens of the same nominal size were machined from each ingot, and, by comparing specimen weights, relative differences in specimen composition resulting from segregation in the ingots could be detected. In this way, segregation was found to have occurred in Pb-Sb alloys at compositions beyond the eutectic (11.2 pct Sb) and this

Jan 1, 1969

The following is an incomplete list of members and guests who called at Institute headquarters during the period May 10, 1919, to June 10, 1919. Victor C. Alderson, Golden, Colo. E. Fleming L'Engle, Joplin, Mo. H. Foster Bain, Washington, D. C. W. D. Mainwaring, Philadelphia, Pa. J. J. Beeson, Master Engr. Sr. Gr. W. G. Matteson, Fort Worth, Tex. Gunnar Bergstrom, Stockholm, Sweden. C. E. MacDonald, Toronto, Can. Corry T. Brown, Socorro, N. Met. Francis Nicholson, Charlotte, Va. Geo. W. Brymer, Scranton, Pa. Richard A. Parker, Denver, Colo. W. Burns, Santa Fe, N. Mex. S. B. Patteson, Jr., Allentown, Pa. H. C. Carlisle, The Pas, Manitoba, Can. G. W. Ponton, Ottawa, Canada. J. Carson Adkerson, Va. W. H. Reber, Ensign, Dallas, Tex. C. A. Cheney, Madison, Wis. T. C. Roberts, New York City. J. M. Clark, Toronto, Canada W. A. Rukeyser, Ensign, N. F. Corps. John J. Doyle, St. Louis, Mo. W. H. Staver, New York City. H. S. Emlaw, Grand Haven, Mich. D. B. Sterrett, Washington, D. C. E. Francis, Birmingham, Ala. T. V. Smirnoff, Russia. Rudolf Gahl, Denver, Colo. E. C. Templeton, New York City. Emit Gthmann, Baltimore, Md. H. A. Toblemann, Ajo, Ariz. A. B. Hardie, Philadelphia, Pa. Priestley Toulmin, Birmingham, Ala. Clarence M. Haight, Franklin, N. J. M. R. Walker, Baltimore, Md. N. V. Hansell, New York City. H. A. Wheeler, St. Louis, Mo. C. A. Heberlein, Nacosari, Mexico. D. B. Whitaker, Santiago, Cuba. Pierre Hines, Milwaukee, Wis. A. W. G. Wilson, Ottawa, Can. J. S. Hollings, Brymoba, Wales. Oba Wiser, Hanover, N. Mex C. Vey Holman, Maine. Harry J. Wolf, Denver, Colo. H. H. Howry, Denver, Colo. F. H. Wood, Mt. Vernon, N. Y. W. Spencer Hutchinson, Boston, Mass. J. P. Wood, New York, N. Y. W. B. Kunhardt, Reading, Pa. Lawrence Addicks sailed on May 17 for London; lie expects to be absent from this country for several months. Roy H. Allen has accepted a position in the research engineering department of the National Aniline & Chemical Co., Buffalo, N. Y. H. Foster Bain has gone to Shanghai, China, where he expects to remain for some time. Percy J. Bandy has accepted a position with the Cia. Minera del Mirasol S. A., at Cusihuiriachic, Chihuahua, Mexico. J. H. Batcheller is now with the North Midas Copper Co., St. Helena, Alaska.

Jan 7, 1919

By Russell G. Haworth

Three companies, United States Potash Company, Potash Company of America, and International Minerals and Chemical Corporation, are now operating potash mines and reGneries in the Carlsbad, New Mexico, area. The three mines are located approximately twenty miles east of Car1sbad. The deposits have been found ideal for mechanized mining methods. This summary has been compiled from information made available by the three operating companies. Prospecting Since outcrops of potash are nonexistent, prospecting is accomplished by drilling and coring of the salt section to establish the grade, thickness, and outline of the potash beds contained in the salt deposits. Information regarding the nature of the formations in the cover of 400 to 600 ft thick over the salt and potash beds is also obtained from drill cuttings in the same operation. By proper interpretation of assembled data the best location for shafts may be determined. The overburden varies in character but consists in general of interbedded shales, sand, gravels, limestones, and anhydrite beds. Water, in unpleasant quantities, especially in the sands and limestones, often completes the geologic section. Some of the shaftas in the area have been sunk without undue difficulties, others have been delayed by flows of water. Most of the shafts are concreted from the surface to the salt section. Each of the three mines in the Carlsbad area has one shaft for hoisting ore and one for hoisting men and supplies. Mining Methods Information acquired from initial drilling and prospecting affected the choice of mining methods. Since the tabular, slightly rolling deposits were similar to coal seams, the room-and-pillar system used in coal mining was adopted by all the companies. Pillars have not been removed in any of the mines on a large scale. One company has conducted experimental robbing of pillars in one restricted area. Where it is known that overlying strata contain water in large amounts, it is not considered practical to risk flooding of the mines by removing pillars without fill. Some thought is now being directed toward development of economical methods of filling for pillar recovery. The problem is not identical at the three mines and local conditions will govern the methods employed for eventual pillar recovery. The important point is that, with large reserves, it has not been necessary to resort to mining of pillars for adequate production. The ore deposits are laterally extensive but are irregular in shape and lie at a depth of 700 to 1100 ft below the surface. The major operations of all mines are on the same bed strati-graphically, except for the langbeinite level at International Minerals and Chemical Corporation. The deposits are apparently not connected and in many parts of the deposits being mined, "salt horses" or barren zones occur. From 400 to 700 ft of salt with minor beds of polyhalite and anhydrite lie immediately above the ore horizon. The ore differs from the salt only in the potassium chloride content and color due to small amounts of iron associated with the sylvite, giving the ore a somewhat mottled red and white cast. Thickness of the ore varies from 5 to 14 ft. Rooms and break-throughs in the mines vary from 24 to 40 ft in width, the overlying salt forming an excellent roof and providing safe mining conditions. Almost no timber is used in any of the mines for roof support. Drilling is normally the first step in mining the face of a room. Electric motor driven auger drills are used in the area. Jack hammers were used to some extent when the mines were first opened but the ore is easily drilled if bits are sharp and the coal type

Jan 1, 1950

By E. T. Turkdogan, P. Grieveson

Molten silver is equilibrated with silicon nitride at 1400°C in nitrogen + hydrogen gas mixtures, and from the solubility data the activity coefficient of silicon is found to be 1.76 at silicon concentrations below 1 pct. Using this value, and that available from the silicon cmbide solubility measurements, together with those derived from the phase equilibrium diagvam, the activities of silver and silicon are estimated for the entire composition range. The main feature of the activity data is that there is a pronounced positive deviation from ideality. The activity of silver in molten silver containing up to 5 pct Si was determined by Schadel, Derge, and Birchenall1 by measuring the vapor pressure of pure silver and of the alloy over a temperature range of 850º to 1050°C. They deduced from their results that there is a positive deviation from Raoult's law and that the activity coefficient of silver increases with decreasing temperature. However, as pointed out by Kubaschewski and Catterall,2 their activity coefficients are much too high, giving silver activities greater than unity. At a later date McCabe and Birchenal13 showed that the previous vapor pressure data on silver4 were high by a factor of about 1.3; presumably a similar error must have occurred with the vapor pressure measurements on the Ag-Si alloys. The activities of silicon and silver calculated by tager' from the phase diagram and by Gibbs-Duhem integration, respectively, show a positive deviation from Raoult's law for silicon activity and positive and negative deviations for the silver activity. According to these computations, at infinite dilution of silicon ygi = 1.12 at 1420°C. d'Entremont and chipman6 measured the solubility of silicon carbide in molten silver at unit carbon activity; the equilibrium silicon content is found to be Nsi = 0.017 ± 0.002 atom fraction for 1420°C. Using the data of Grieveson and Alcock7 for the free energy of formation of silicon carbide from pure silicon and graphite, the activity of silicon for unit activity of carbon and of silicon carbide is asi = 0.0308 at 1420°c; therefore for the above solubility data on silver, YSi = 1.81, which is somewhat higher than that given by Hager. Use is often made of silver alloys in the measurements of activities of solutes in metals where silver has a very low solubility; in fact, Ag-Si and Ag-A1 alloys have been used in the past for such purposes. In an attempt to gain more thermodynamic data on molten Ag-Si alloys, measurements have been made in the present study on the solubility of silicon nitride in molten silver; the results on these solubilities are given in this paper together with a detailed discussion of activities of silver and silicon. SOLUBILITY OF SILICON NITRIDE The standard free energy of formation of silicon nitride is known with a reasonably high degree of accuracy. According to the measurements made by Hincke and Brantle8 and by Pehlke and Elliott,' the following are the free energy data for the standard states of solid Si3N4, liquid silicon, and Nz at 1 atm pressure:

Jan 1, 1963

By Carle R. Hayward

WHEN lead production began to recede from the peak productions of 1929 many plants took advantage of the curtailed operations to make necessary improvements and repairs about the plant. There followed a period of adjustment to synchronize production and demand, which merged in the present period of marking time. The lead smelting and refining industry has produced little that is new during the past year except in what might be called makeshifts, which have been introduced to make operation at fractional capacity profitable. This is more particularly true in refineries than in smelters. The Parkes process had become standardized during the period of normal production, with softening, desilverizing, and dezink-

Jan 1, 1935

By F. X. Tartaron

The comparison of actual energy of comminution with theoretical surface energy presents a wide gap. On the other hand, Solid State Theory presents a viewpoint that places actual energy of breakage in understandable relationship with the theoretical strength of materials. Therefore the physical background of comminution theory favors Kick's Law. A11 discussions of comminution theory appear farfetched when comparison is made of the actual energy of crushing with the energy input called for by thermodynamic theory. Quoting Taggart:' "The work required to crush halite was of the general order of 0.10 kg cm per sq cm of new surface produced (based on air percolation) whereas the theoretical energy of this new surface, based on thermodynamic calculation by a number of investigators is 1 x 10'4 kg cm per sq cm or the work expended was 1000 times the new surface energy — an indicated crushing efficiency of 0.10 pct." It is frustrating to probe into comminution theory with the prospect that the energy one is measuring is 99.9 pct waste energy. Do the laws of comminution deal with energy consumed by mineral breakage or with waste heat energy? There seems to be something wrong. Solid State Theory may provide the answer. The following statement is particularly apt to the situation: "The fundamental fact about metals and indeed all materials, is that they are much weaker than they should be. By this, we mean that if the stress required to cause a given plane of atoms to slip past a neighboring plane is calculated from basic atomic and Solid State Theory, the resulting number is some 1000 times too large to be accounted for by errors in approximations or assumptions. We know now that this is due to dislocations, and we even have a fair understanding of the details of the process by which dislocations make a crystal weak. An intriguing possibility which suggests itself, results from the discovery of very minute metallic crystals which are apparently free of dislocations and which have a strength approaching the ideal value for a perfect crystal." Here we have an extraordinary reversal of the situation. The actual energy for breakage is only one-thousandth the theoretical instead of 1000 times as given by Taggart. But the theoretical energy presented by Solid State Theory is the binding energy between atoms (or ions) in a crystal lattice. This is the kind of energy envisaged by Kick's law. The surface energy or the other hand corresponds to Rittinger's law. Comparison of theoretical with actual, on the basis of surface or on the basis of Rittinger's law, seems to present an absurdity; yet Rittinger's law is confirmed by an impressive array of experimental evidence. Comparison of theoretical and actual on the basis of Solid State Theory or, in other words, on the basis of Kick's law seems reasonable; yet there is not a scrap of evidence to verify Kick's law. The situation appears paradoxical, but the developments in the next section of this paper show that the paradox is a hint to a strange turn of events. ENERGY-WEIGHT FRACTION FUNCTION charles3 has presented a final equation showing the relation of energy consumed in comminution to size of product n{-1) a-n + 1 E is energy, C is proportionality constant, a and n are constants and k is the coarsest size in the ground product (size modulus). In the course of study of a large amount of experimental evidence, Charles discovered that in the general case, a-n + 1 approximated zero. For some reason, a and n differed only by unity. But if a—n + 1 = 0 within experimental error, then it is obvious that Eq. 1 states that it requires an infinite amount of energy to grind any sample to any size. This is a case where nature gives an absurd answer to a man-made mathematical equation, hence something is wrong with the equation. An adjustment must be made to fit the equation with experience. TO reveal the nature of the adjustment, the differential equation preceding the second integration in Charles' group of equations is given When Charles integrated the quantity xa-n it was almost impossible for him to realize that he was dealing with a special case of integration and that

Jan 1, 1962

By John E. Young

U.S. Steel Corp.'s Winifrede mine is operated by Lynch District in the mountainous region of eastern Kentucky. This region is characterized by narrow finger ridges and precipitous slopes, which present both an opportunity and challenge in the design and selection of coal-handling facilities for the movement of coal from the section belts to the railrod cars. Lynch District selected diesel-powered locomo¬tives and 100-ton articulated cars capable of negotiating sharp curves. The drop¬bottom mine cars are equipped with longitudinally hinged doors that are auto¬matically opened and closed. Lynch District selected a large-diameter steel-lined borehole for lowering the coal approximately 1000 ft from the seam level to the valley floor railroad load-out point. Taking advantage of gravity, the presized coal is "lowered" vertically approximately 720 ft to existing entries of a previously abandoned mine. The coal is then conveyed horizontally into storage. The coal¬handling facility from the mine-car dump to the railroad load-out point is fully automatic through use of tone control. TV cameras are installed along the facility to continuously monitor the strategic points. The diesel locomotives are either directly operated or remotely radio-controlled, depending on the functions Per¬formed. U.S. Steel Corp.'s Winifrede mine is operated by Lynch District in the mountainous region of eastern Kentucky. This region is characterized by narrow mountain ridges and precipitous slopes which present both an opportunity and challenge in the design and selection of coal-handling facilities for the movement of coal from the section belts to the railroad cars. The narrow finger ridges precluded use of under¬ground haulage and, thereby, presented the opportunity to use high-capacity equipment on the outside bench. The precipitous mountain slopes, steepest at the Wini¬frede seam horizon, presented a challenge to select a solution for lowering the coal approximately 1000 ft from the seam level to the valley floor railroad load-out point. It was evident from the start of planning that these two factors predominated; namely, rail haulage and coal lowering, and solutions to these would determine the final design of the Winifrede mine coal-handling facilities. The Winifrede mine derives its name from the Wini¬frede Seam which comprises the total reserve recov¬erable from this facility. The seam is 5 ft high with a good siltstone bottom and competent shale or sandstone roof. The seam is at an elevation of 2700 ft where the mountain ridges are long and narrow. This configuration of the reserve was ideal for conveyor belt installation to transport the coal from the working face to the outside bench. The preclusion of underground rail haul¬age permitted an opportunity to review the type of locomotive power and to select high-capacity equipment without the limitations associated with underground systems. Since the basic electrical design of the mine was al¬ternating current, with rectification to direct current for shuttle cars required only in the face areas, there was no point in bearing the burden of additional cost of dc trolley installation. And, since the haulage would re¬quire only a few tunnels to negotiate sharp points and to reach the back side of the reserves, diesel power was selected for the haulage locomotives. To provide stability on the almost continuously curv¬ing track and to provide the maximum width of haul¬age equipment, both locomotives and mine cars, stan¬dard railroad gage was chosen to offer the largest choice of equipment. The decision was made to select a standard 45-ton railroad diesel locomotive but to lower the cab height to reduce tunnel excavation requirements. The mine car was the next challenge. Past experience in Lynch operations indicated that drop-bottom cars would be a successful application with the free-flowing coal. The search was for a drop-bottom car within the dimensions of the locomotive to discharge the coal in the shortest time. Numerous types were considered and visits made to various sites to observe cars in operation.

Jan 1, 1972

By Ellis H. Gates

BENEFICIATION of the manganese oxide ores at Three Kids Mine near Henderson, Nev., has evolved over a period of years. Commercial application of the process is on a secure basis, and an effective working hypothesis has been formulated to help solve the problems encountered in flotation. An outstanding difference between the Manganese Inc. operation and other flotation processes is the necessity for high recovery of slime mineral values. Part of the manganese minerals in the Three Kids ore deposit occurs as primary slime or as minerals that are easily slimed by grinding. High recovery of this slime portion is essential to an economic overall manganese recovery. The aim of much of the research at Manganese Inc. was to recover these slimed and finely ground minerals by flotation. Early Agglomeration Processes: Tunbridge' in 1880, followed by Everson2 in 1886 and Cattermole" in 1904, discovered that under certain pulp conditions precious metals and sulfide minerals could be agglomerated if enough soap or oil were mixed into the pulp slurry. These agglomerated particles, Which under ideal conditions ranged from 1/16 to 1/4 in. diam, were recovered by screening, tabling, and hydraulic classification. Even flotation by air occluded in the agglomkrate particles by vigorous stirring was suggested. Cattermole nearly succeeded in getting his process into commercial operation, but it was finally abandoned, presumably because he could nat compete with the low reagent requirements of the new agitation froth process. Since Cattermole's time Christensen in 1921, Borcherdt4 in 1926, and Chapman and Littleford- in 1934 have attempted to apply the principles of agglomeration. In the light of current research at Manganese Inc. on conditioning of pulp at high energy input levels, it is interesting to note the variety of equipment such as tumbling mills, mixing drums, and shakers described by Borcherdt in his patent to produce the agglomerated particles. Ore Characteristics: Manganese in the Three Kids ore occurs as a 'complex mixture of manganese oxides commonly Known as wad. The manganese minerals have Been identified as psilorflelane, hollandite, coronadite, and pyrolusite with minor amdunts of rhodonite and rhodochrbsite. The ppincipal gangue miherals are quaktz, opal, kaolinite, montmoril-lonite, calcite, gypsum, fcelesitite, and barite. Most of the mangandse ore minerals are either porous and sponge-like in structure or soft clay-like masses composed of fine grained mineral particles approaching the size range of colloids. Consequently the ore minerals from the Three Kids mine have relatively large surface areas and high void content per unit weight. The specific area of various manganese ore samples measured at the California Research Corp. laboratories ranged from 32 to 58 sq m per g. The great surface area and high void content explains in part the unusually high reagent consumption required in the treatment of this ore. Current Milling Practice: At Henderson6 he ore is crushed to —1 in. and ground with rod mills in a closed circuit with spiral rake classifiers and cyclones. Sulfur dioxide solution is added to the pulp as it leaves the grinding circuit, immediately followed by addition of a reagent mixture of soap, oil, and wetting agent in the form of an emulsion. The reagents are initially well mixed into the pulp during their passage through centrifugal pumps to the conditioning equipment. All reagents are added prior to conditioning. The intense conditioning or mechanical stirring of the pulp, in which large amounts of power are consumed, is the principal difference between the flowsheet used at Manganese Inc. and a standard flotation circuit. As much as 38 kw-hr of energy per dry short ton of ore in a pulp containing 18 to 23 pct solids is used for conditioning. After conditioning, the pulp passes to a flotation circuit that consists of one roughing stage, a scav-

Jan 1, 1958

By G. S. Cole, G. F. Bolling

ThE exact type of fluid flow which occurs in a solidifying ingot is important in determining subsequent grain structure. This has been shown in studies of natural Convection" and of forced stirring or other disturbances of the melt."16 We shall explicitly argue that a complement to the existing natural flow in an ingot should be more effective than other types of flow in promoting the columnar-to-equiaxed transition. The ultimate effects of fluid flow upon structure is one of the topics of solidification that we have investigated in the alloy system Pb-Sb, under conditions simulating casting. In Fig. 1, the essential features of a bidirectional growth apparatus are shown; horizontal freezing from water-cooled faces within a low-thermal-conductivity lavite boat is a reasonable simulation of an ingot section. Details such as the furnace and thermocouples are omitted in order to show the location of four permanent. magnets, each with a pole separation of 21 in. providing a central field of about 1000 Gauss. When coupled with a dc current imposed through appropriate connections made at the cooled faces, a flow of fluid is produced as shown schematically. This technique described by Pfann and ~orsi" is ideal for our purpose since the flow indicated is the same as that we observe to occur naturally in this system. Components of 99.999 pct purity were used for study and all due precautions were taken in alloy preparation to avoid contaminants. Sections of the specimens were taken to ensure results representative of the interior as well as the surface of specimens. All proportions of equiaxed and columnar regions were measured by tracing the etched grain structures onto graph paper and simply counting squares. Four alloys were examined at superheats of 40" * 5°C and 100" * 9°C. Preliminary tests had shown that no appreciable enhancement of structure was obtained with magnetic field alone, so that this condition is not reported; it should nevertheless be noted that other configurations of magnetic field will reduce convection and thus enhance columnar growth.'8 For the tests reported the magnetic field was applied to a specimen by bringing the four preassembled magnets to a position 2 mm from an outer tube immediately after the ingot was poured. The dc current of 30 amps passed through the sample throughout the entire solidification cycle, resulting in a power dissipation of 9 w per sq cm of interface. This may be compared to the evolution of latent heat of approximately 18 w per sq cm. Table I contains the results of this experiment in terms of the total area ratio, equiaxed/columnar grains, as a function of the field interactions, solute concentrations, and superheats employed. The total structure of the ingot is seen to be most influenced when both the field and current are applied simultaneously; when current acts separately, little effect may be noted in spite of the heat supplied. In addition, the change in structure from the no field-no current case to the field-current condition is more pronounced at the higher superheat, and the higher the concentration of antimony. An example of the grain refinement, as well as the increased equiaxed zone, is shown in Fig. 2. It is now important to prove that there is indeed an increase in fluid flow due to the presence of the field-current interaction; this is done by temperature measurements in the liquid metal. Let us consider a bidirectional casting in which heat is applied to and removed from the system, in such a way that rate of solidification is zero.* When a sensitive thermocouple

Jan 1, 1967