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JOHN W. BELL (communication to the Secretary*).-I have to thank Mr. Merrill not only for his very kind remarks, but for the weight of his implied opinion that the work accomplished probably has an important practical aspect. I think there is a distinct although unuttered impression among engineers, that it will be time enough for them to begin to take an interest in the law of crushing when it emerges from the cloud of violent and even vituperative controversy that has hovered over it during the last 6 or 7 years. I have a very confident feeling that as the result of the work done by Mr. Gates, by me and by Messrs. Mitchell, Baily and Cockfield, who so loyally helped me to obtain the necessary data, at least the practical law of crushing has emerged; that it is ready and available for use by our fellow engineers, and that it will help them to unravel a number of the many practical problems they are con¬stantly confronted with. In regard to Mr. Gates' discussion, I would indeed like to believe that McGill could claim, as a minor achievement, the credit which Mr. Gates so generously bestows of having established the "law" of crushing. I think that more work would be required to establish this claim in the, strict sense of the word, as there is a fairly large gap between the coarse and fine crushing results. I am not worried about that gap, because the reason for it is quite clear to me; at the same time I-think it will be well to bridge it by a series of tests, and I am bound to admit that the testing machine is the most promising machine right at hand to work with, although whether the minute amounts of power required to crush small quantities of rock can be so accurately integrated as to insure high accuracy in the final result is still a question in my mind. If we had an Amsler-Laffon machine I would certainly try it. Mr. Gates' remarks about choke crushing are extremely interesting. He compels me to wonder, too. It is a new and probably a very important factor to be considered in this connection. I am in perfect accord with Mr. Gates about the desirability of the determination of crushing constants, because when this is accomplished the efficiencies (not relative mechanical, but real efficiencies) of different types of rock-crushing plants in any part of the world will then be comparable. For this reason it would, seem desirable that the American Institute Committee should not only consider ways and means for accom-

Jan 6, 1917

By S. A. Hovanessian

Analytical solutions are obtained for calculating the pressure distribution in rectangular fields due to injection and/or producing wells located anywhere within the field. The field is assumed to be homogeneous with either constant pressure or no-flow boundaries. These solutions are extended to include the calculation of average reservoir pressure and permeability from pressure build-up curves. Numerical examples are given to illustrate the application of equations to practical problems. INTRODUCTION Pressure distribution analyses are of considerable importance in the field of reservoir mechanics. A number of papers dealing with this subject have appeared in the petroleum literature. perrinel in 1956 presented a summary of the methods available for pressure build-up calculations and discussed the applicability of each in some detail. More recently (1958), Hazebroek, et a1,2 discussed a theoretical method for obtaining pressure distribution in a radial field. Also in 1958, Nisle3 gave a theoretical solution of the pressure distribution in a field extending to infinity with a partially penetrating line source at the origin. Mathews, et a1,4 applied the method of images to existing solutions for pressure distribution in radial fields and obtained expressions for calculating pressures in bounded reservoirs. However, a literature survey revealed that a general analytical solution for the pressure distribution in a rectangular field, with injection and/or production wells located anywhere within the field, was not available. Such a solution could be used to approximate the pressure distribution in a field the shape of which is nearly rectangular. Furthermore, it could be applied to pressure calculations pertaining to a single well taken from a system of wells which were drilled in a rectangular pattern. In this case the boundaries of the well drainage area are considered to be the perpendicular bisectors of the lines joining the well and its nearest neighbors. The basic problem considered in this paper consists of a rectangular field with either constant-pressure 01 no-flow boundaries and with either an injection or production well located anywhere within the field. The physical properties of the rock and fluids present are considered to be constant. Analytical expressions are obtained for the pressure distribution within the field during the production or injection periods. These expressions, which are infinite series, can be used to evaluate pressure at any point within the field as a function of time and position. For fields containing more than one well (production and/or injection), the solutions for each well acting independently are superposed. That is, at any point in the field, the pressures due to each injection 01. production well acting alone can be algebraically added to give the pressure resulting from all wells acting simultaneously. Evaluation of the series solutions given in this paper is readily accomplished by means of an electronic digital computer; and, in most cases, sufficient accuracy is obtained by setting the upper limits of summation at 20. These solutions are extended to include the calculation of average reservoir pressure and permeability from build-up data. A number of numerical examples are given to illustrate application of the solutions to actual field problems. ANALYTICAL SOLUTIONS The partial differential equation representing the pressure distribution in a homogeneous rectangular field (see Fig. I.), having a single source or sink of strength (2, can be written*

By E. W. Stewart, G. P. Conard, J. F. Libsch

The effects of several additives upon the reduction characteristics of hydrogen-reduced ferrous formate are described. The various additives inhibit sintering of the reduced iron particles by apparently different mechanisms. The magnetic properties of the low density compacts produced from the resulting ultra-fine iron powders were improved markedly. THE permanent magnetic characteristics of ultra-fine iron powder prepared by various means have been a subject of considerable interest and experimentation in the past few years. When such particles are small enough to show single domain behavior, they possess' 1—permanent saturation magnetization, and 2—high coercive force. In the absence of domain boundaries, the only magnetization changes in a particle occur through spin rotation which is opposed by relatively large anisotropy forces. With decreasing particle size, the coercive force tends to increase to a maximum and then decrease because of the instability in magnetization associated with thermal fluctuations. Kittel' has calculated the critical diameter at which a spherical particle of iron can no longer sustain domain boundaries or walls to be approximately 1.5x10-' cm. Stoner and Wohlfarthr in England and Neel4,6 in France have shown from purely theoretical calculations that the high coercive force expected from single domain particles is dependent upon crystal anisotropy, shape anisotropy, or strain anisotropy contributions. Further work by Weil, Bertaut,' and many others has contributed much to the understanding of fine particle theory. Neel and Meikeljohn" have demonstrated that a decrease in particle size below a critical value of approximately 160A leads to a quite rapid decrease in coercive force because of the prevention of stable magnetization by thermal agitation. Lih1, working with powders prepared by the reduction of formate and oxalate salts of iron, has shown the marked influence of powder purity upon magnetic properties. Maximum coercive force was obtained in powders of approximately 65 pct metallic iron content while the maximum energy product, (BxH) occurred in powders of 85 pct metallic iron content. Careful consideration of the preceding theoretical considerations and experimental results has led to the manufacture of permanent magnets from ultra-fine ferromagnetic powders by powder metallurgy techniques. Such work has been done by Dean and Davis," the Ugine Co. of France, and Kopelman." The aforementioned work of Kopelman and the Ugine Co. was concerned somewhat with the effect of various additives upon the properties of hydrogen-reduced ferrous formate. Virtually no work, however, has been published on the effects of additives on the reduction rates of metal formates, although unpublished work by Ananthanarayanan16 howed promise of improved energy product in ultra-fine iron compacts prepared by the hydrogen reduction of a coprecipitated mixture of magnesium and ferrous formate. After consideration of the preceding information, it was hoped that a better balance between the metallic iron content and particle size of the reduced iron powder could be accomplished by a prevention of the attendant sintering of the partially reduced iron powder during the reduction reaction. It appeared possible that magnesium oxide might interpose a mechanical barrier between adjacent iron particles and prevent their sintering together, while metallic cadmium and metallic tin would interpose a liquid barrier which might accomplish the same purpose. The degree to which these materials were effective in accomplishing the foregoing objective and the experimental details associated with the work are reported in the following sections of this paper. Experimental Procedure Preparation of Formate and Oxide Mixtures: To obtain ferrous formate of reproducible reduction characteristics, a slight modification' was made in the technique of Fraioli and Rhoda." A supersaturated solution of ferrous formate was mixed with an equal volume of 95 pct ethyl alcohol and the formate crystals precipitated by stirring and screened to —325 mesh. These crystals were in the shape of elongated hexagons, approximately 4x10 micron in dimension. Various preparations of such ferrous formate, designated as lot 111, were reduced for 2 hr, yielding ultra-fine iron particles of exceedingly reproducible size, metallic iron content, and magnetic properties. The magnesium and cadmium formates were prepared by the reaction of dilute formic acid with their respective carbonates, while the tin formate was prepared by the reaction of dilute formic acid with stannous hydroxide. To evaluate the effect of metallic formate additives in intimate mixture with the ferrous formate, varying amounts of magnesium, cadmium, and tin formates were coprecipitated with the latter. The designations of these materials and their chemical compositions are given in Table I. Due to the differing solubilities of the various formates in aqueous media,

Jan 1, 1956

I HAVE previously shown you in the Fifth Book the process of making guns and gun carriages, together with other preparations and methods of moving them. If I now failed to show you more about them, it would be as if I had pointed out only the useless shadow of a thing, for I did not show the kinds and arrangement of their supplies or how the effects for which they are made are achieved. For these reasons I now wish to tell you, in addition to what I have already said, how saltpeter is made and the methods of refining it well; what it is and how without it guns and many effects of violent and artificial fires would have been discovered in vain. After this, I also wish to tell you the methods of compounding the powders for large and small guns, and finally how these are loaded and discharged. I also wish to tell you how mines are made, and fire tubes, [149v] fire pots, squibs, fireballs, rockets, shells, grapeshot, and other similar devices for shooting fire in order to bum ships, supplies, bridges, and ramparts, or, in offense, for firing on batteries. I also wish to teach you to make certain bronze balls for shooting, which carry fire and break in many pieces when they hit. For surely, besides being terrifying to the sight, they would be harmful to armies lined up in battle when they are fighting. Likewise, I wish, to enlighten you as to how artificial fires are made that last long and are difficult to extinguish. Since these are fine and useful things in wars, every captain and soldier should give them consideration and know how to use them when necessary. You will be pleased to have this information if for no other reason than that you can teach it to those who take delight in celebrating holidays with festivities and with fires.

Jan 1, 1942

By S. F. Ravitz

IN his excellent book on the Principles of Flotation, Wark' makes the following significant statement concerning the theory of flotation: Two questions of first-rate importance must be considered . . . First, it must be decided whether the sulfide minerals require a collector in order that they may float, or whether as has been claimed, they possess an inherent floatability and need no collector. Second, it must be decided whether the xanthate type of collector can react with or be adsorbed by the unchanged sulfide minerals themselves, or whether, as many claim, reaction with the collector is dependent upon initial oxidation of the mineral surface. In the theory of flotation there are no two questions of greater importance than these. Ravitz and Porter' presented evidence that galena can be floated without a collector, and even without any reagent, provided oxidation products are thoroughly removed from its surface. They found also that thoroughly cleaned galena floated faster when xanthate was used than when a frother alone or no reagent was used, and that, without a collector, the recovery decreased gradually upon exposure of the mineral to air. Their work, however, has met with considerable criticism. I(127).3-6 This paper is presented to answer the objections that have been raised, and to present additional data that confirm their results. EXPERIMENTAL PROCEDURE The apparatus used to provide oxygen-free conditions for flotation has been described in detail by Ravitz and Porter. An atmosphere of purified nitrogen was maintained within the apparatus; all water and solutions used were freed of dissolved air, and could be transferred where desired by the use of nitrogen pressure; nitrogen was used as the gaseous medium for flotation. The flotation cell was essentially a glass cylinder 15 cm. long and 4.6 cm. in diameter. Near the bottom was sealed a fritted glass filter, which broke up the gas into small bubbles, and 6 cm. above this filter was a side arm through which the froth overflowed. The pulp was agitated by a glass impeller, which entered the cell through a mercury seal. For each test 17 grams of galena and 75 ml. of water were placed in the cell, after which the speed of the impeller and the rate of gas flow were adjusted. Water was added gradually during the test to keep the froth level at the proper height. The mineral was prepared and cleaned in the following manner. Exceptionally pure galena was crushed by hand on a clean bucking board, screened to - 150+ 200 mesh, and deslimed on a zoo-mesh sieve with a fine spray of water. It was then boiled on a hot plate for a number of hours with several changes of the desired cleaning solution, after which both the solution and the mineral were placed in the "mineral flask" of the apparatus. The cleaning solution was drained off, and the mineral was boiled with oxygen-free water

Jan 1, 1940

By William A. Johnson

The fundamental role of diffusion in many reactions occurring in solid metals has long been recognized, and there have been careful measurements of rates of diffusion in numerous alloy systems; but our understanding of the atomic mechanism by which diffusion occurs is scarcely in an advanced state.l-3 It is doubtful that this mechanism can ever be directly ascertained; rather, all imaginable mechanisms must be examined and the one that is in best accord with such data as can be obtained from suitably chosen experiments should be selected. Because of its relative simplicity, diffusion in a system containing only one kind of atomic species—commody called self-diffusion—is of considerable theoretical interest. It may be expected that diffusion theory will not be advanced appreciably until a wide variety of diffusion experiments—of which diffusion in a chemical concentration gradient and self-diffusion are two important types—are carefully performed and inter-compared. Aside from the purely theoretical interest in self-diffusion measurements, such studies will be of considerable engineering importance. The rate of any process in a pure metal requiring the movement of atoms, of which recrystallization and creep are two familiar examples, will be understood more readily with the aid of self-diffusion data.† Self-diffusion implies the diffusion of something into its exact counterpart; the detection of such a process is patently impossible, and it is necessary to substitute for it the diffusion of one isotope (in this case radioactive) into another isotope (in this case stable) of the same chemical element. There is, however, no reason to suppose that a radioactive atom will not diffuse at the same rate as its stable isotope, for all of the isotopes of the same element have exactly the same chemical properties; neither the difference in nuclear energy nor the difference in mass would be expected to exercise an important influence in this phenomenon. In this sense, self-diffusion may be thought of as the diffusion of radioactive atoms down a radioactivity concentration gradient, just as usual diffusion is the diffusion of one kind of atom down its chemical concentration gradient. The first measurements of self-difiusion were made by von Hevesy4-6 using the radioactive lead isotope thorium B in ordinary lead. The recent development of means for producing artificial radioactive elements has made possible similar measurements on gold,7, 8 copper,2, 9 and zinc.10, 11 Many of the data that have been obtained are rather poor, and no adequate reason has been given for their poorness; it appears, however, that the unsatisfactory results are characteristic of the particular experimental procedure employed, and not of self-diffusion measurements in themselves. The experimental technique that has yielded the poorer results is the deposition of a thin layer of radioactive atoms on the surface of a specimen and the determination of the rate of inward diffusion

Jan 1, 1941

By William A. Johnson

The fundamental role of diffusion in many reactions occurring in solid metals has long been recognized, and there have been careful measurements of rates of diffusion in numerous alloy systems; but our understanding of the atomic mechanism by which diffusion occurs is scarcely in an advanced state.l-3 It is doubtful that this mechanism can ever be directly ascertained; rather, all imaginable mechanisms must be examined and the one that is in best accord with such data as can be obtained from suitably chosen experiments should be selected. Because of its relative simplicity, diffusion in a system containing only one kind of atomic species—commody called self-diffusion—is of considerable theoretical interest. It may be expected that diffusion theory will not be advanced appreciably until a wide variety of diffusion experiments—of which diffusion in a chemical concentration gradient and self-diffusion are two important types—are carefully performed and inter-compared. Aside from the purely theoretical interest in self-diffusion measurements, such studies will be of considerable engineering importance. The rate of any process in a pure metal requiring the movement of atoms, of which recrystallization and creep are two familiar examples, will be understood more readily with the aid of self-diffusion data.† Self-diffusion implies the diffusion of something into its exact counterpart; the detection of such a process is patently impossible, and it is necessary to substitute for it the diffusion of one isotope (in this case radioactive) into another isotope (in this case stable) of the same chemical element. There is, however, no reason to suppose that a radioactive atom will not diffuse at the same rate as its stable isotope, for all of the isotopes of the same element have exactly the same chemical properties; neither the difference in nuclear energy nor the difference in mass would be expected to exercise an important influence in this phenomenon. In this sense, self-diffusion may be thought of as the diffusion of radioactive atoms down a radioactivity concentration gradient, just as usual diffusion is the diffusion of one kind of atom down its chemical concentration gradient. The first measurements of self-difiusion were made by von Hevesy4-6 using the radioactive lead isotope thorium B in ordinary lead. The recent development of means for producing artificial radioactive elements has made possible similar measurements on gold,7, 8 copper,2, 9 and zinc.10, 11 Many of the data that have been obtained are rather poor, and no adequate reason has been given for their poorness; it appears, however, that the unsatisfactory results are characteristic of the particular experimental procedure employed, and not of self-diffusion measurements in themselves. The experimental technique that has yielded the poorer results is the deposition of a thin layer of radioactive atoms on the surface of a specimen and the determination of the rate of inward diffusion

Jan 1, 1941

By David W. James

DURING a recent investigation of the transition from a planar to a nonplanar solid/liquid interface for the systems H20-NH4F and 0-AIR,' an apparatus was developed which enabled the morphology of the ice-water interface to be examined during the transition. The slightly curved interface was viewed at a glancing angle with a Bausch and Lomb X30 stereomicro-scope. The interface was obliquely illuminated by a polarized light source. It was thus possible to differentiate between small projections or depressions at the interface, both by a shadowing effect and by the way in which they distorted the colored interference fringes across a particular crystal surface. Many attempts were made to photograph the various stages of interface breakdown. Unfortunately, the limited depth of focus of the microscope rendered the system unsuitable for photographic recording. Visual examination, however, was facilitated by continuous adjustment of the microscope focus control. The following observations of the interface transition were recorded for dilute solutions of ammonium fluoride in water. They are compared with iller's postulated morphologies shown in Fig. 1. i) The initial departure from planarity was characterized by the appearance of a large number of small depressions or "pores" in the interface. ii) The pores were arranged in wavy rows all lying roughly in the same direction within a particular grain. iii) The pores did not appear to form near to grain boundaries. iv) The pores appeared in certain grains before others. v) The transition from the pore structure to the elongated cell structure, Fig. l(d), was difficult to follow. It occurred quite rapidly and no truly irregular cell structure, Fig. l(c), was noticed. vi) The elongated cells gradually became more uniform in size and shape, with straight cell boundaries. They remained elongated, however, and no regular hexagonal cells were observed, cf. Fig. l(e). Several conclusions may be drawn from these observations. Firstly, the appearance of a poxed or, more accurately, a pore structure can be used as a criterion for the onset of constitutional supercooling. Care should, of course, be taken to distinguish between the true pore structure and artifacts caused by splashed-back liquid, particles of oxide, or inefficient decantation of liquid retained between cell boundaries, as described by Spittle et al? Secondly, and contrary to the suggestions of Tiller el l., it seems that interfacial perturbations are characterized not by curved projections but by small depressions or pores. A recent independent investigation by Biloni, Bolling, and cole5 reported in this issue indicates that the depressions might be explained in terms of dislocations intersecting the solid/liquid interface. It is possible that the dislocation concentration is reduced in the vicinity of grain boundaries. This would then explain the grain boundary depleted areas noted in (iii) above. This work was partially supported by the Air Force Office of Scientific Research, Contract No. AF 49-(638)-1029.

Jan 1, 1967

By R. T. Hukki

This paper presents a series of equations for mechanical ball wear, relating parameters of ball size, mill speed, and mill diameter. The fundamental equation, Eq. 12, presented here is introduced to correlate these basic parameters and thus define and clarify the concept of ball wear. This equation is offered as a general rule, which may be modified to apply to individual problems of grinding. BALL wear as observed in grinding installations is the combined result of mechanical wear and corrosion. Corrosion should be a linear function of the ball surface available. Ball corrosion, however, has been studied so little that its effect, although of great importance, cannot be included in the analyses given here. In a separate paper' it is shown that 1 n = 0.7663 np----=— rpm [1] vD P = c, np D kw [2] T=c²(np)n De tph [3] In these equations n — actual mill speed, rpm np = calculated percentage critical speed D = ID of mill in feet P = power required to operate a mill, kw T = capacity of a mill, tph C¹ and c² - appropriate constants in = exponent of numerical value of 1 5 m 1.5 Exponent m is the slope of a straight line on logarithmic paper relating mill speed (on the abscissa) and mill capacity (on the ordinate). It is generally accepted, although not sharply defined, that ball wear in mills running at low (cascading) speeds is a function of the ball surface available. Accordingly, the wear of a single ball may be considered to be a homogeneous, linear function of its surface and of the distance traveled. Thus dw = f¹(d2) . f2(ds) [4] where dw is the wear of a single ball in time dt, d the diameter of the average ball in ball charge, and ds the distance traveled by the ball in time dt. Indicating that ds - a D n dt, the wear of the average ball in time dt becomes dw = f¹(d2) . f2(Dn dt) 1 --- f¹ (d1) f² (D c3 np-----— dt) \/D = c,d² n, D dt The rate of wear of the average ball is given by dw/dt. dw/dt = c, d² np D lb per hr [5] The weight of the ball charge per unit of mill length is a function of D The number of balls of size d in the ball charge is = f³(D2)/f4(d³). The rate of wear of the total ball charge equals the number of balls times rate of wear of the average ball. Thus rate of total ball wear = — . (dw/dt) w. c, . (l/d) . n,, D lb per hr [6] which is the equation of ball wear in low speed mills. In a mill running at a low speed, grinding is the result of rubbing action within the ball mass and between the ball mass and mill liners. When the speed of the mill is gradually increased toward the critical, the impacting effect of freely falling balls becomes increasingly prominent in comparison with the rubbing action. Reduction of ore takes place partly by rubbing, partly by impact. The share of the freely falling balls in the reduction of ore reaches its practical maximum at a speed somewhat less than the critical; at that speed grinding by rubbing has decreased to a low value. It may be reasonable to think that size reduction by freely falling balls should reach its theoretical maximum at the critical speed, if the fall of the balls were not hindered by the shell of the mill beyond the top point; grinding by rubbing would cease at the critical speed. As a first approximation, wear of freely falling balls may be considered to be a homogeneous, linear function of the force at which they strike pieces of rock and other balls at the toe of the ball charge. The force equals mass times acceleration. The mass of a ball is a function of d3 and its acceleration is a function of the peripheral speed of the mill. The wear of a single ball of size d representing the average ball in a ball charge will therefore be w¹ = f3(F) = f (d3) f7 (v). [7] Indicating that v = D n, and n = c³ np 1/vD, Eq. 7 becomes W1 = cn d3 np Do.5 lb per hr. [8] Total wear of the ball charge equals number of balls times the wear of the average ball. Number of

Jan 1, 1955

By M. P. Tixier, M. Gondouin, G. L. Simard

In the quantitative interpretation of the SP logs, the electrochemical component is generally taken equal to — K log Rm /Rw where K has the theoretical value corresponding to solutions of pure sodium chloride. This method may be misleading when relatively large quantities of salts other than NaCl are present in form-rrtion waters—as is generally the case for low salinities —or in gyp-base muds. In such cases recourse is made in the field to changing the K value or to adding a correction term to the equation on the basis of local experience. An investigation has been made in the laboratory of the influence of HCO3, SO4=, Ca++, and Mg++ on the amplitude of the SP deflection, which included in par-ricular determinations of the activity coefficients of Ca++ and Mg++. The theory, the experimental techniques and a tentative method for applying the results are described. So far, applications to actual field cases where chemical analyses of waters were available have provided an excellent confirmation of the proposed method. The case of the SP in very salty brines is also considered and it is shown that the use of activity data for sodium gives satisfactory results. HISTORICAL In early times of electrical logging, the SP curve was used exclusively as a tool for the location of permeable beds and the definition of their boundaries. Later, with the introduction of methods of quantitative analysis, attention was called to the possibility of deriving from the SP log some information on the formation water resistivity, which constitutes one essential element for the computation of water saturation from log data. The first laboratory experiments' in 1932 had shown that, as a result of electrochemical phenomena arising at the contact of the niud and the formation, the amplitude of the deflection of the SP curve was, at least partly, a function of the salt concentration of interstitial water and accordingly of its resistivity. It was indicated that the amplitude of the electrochemical component of the SP should be equal to K log R1/R2, R1 and R2 being the resistivities of the mud and of the formation water respectively. However, the exact value of the K coefficient was not determined at that time because the surface clay used for a laboratory model was far from an ideal shale membrane. Consequently, the way was not yet open towards quantitative interpretation. In the early forties, Tixier reported2, on the basis of field log observations, the following equation for the case of NaCl solutions, SP = -71 log f1c1/f2c2, c1 and c2 being the concentrations and f1, f2 the mean activity coefficients. The local variations observed in the empirical values of K, chiefly in the Rocky Mountains, led him to advance the opinion that, besides the relative amounts, the nature of the salts present in the solutions had a bearing on the magnitude of the SP. At about the same time Mounce and Rust- ad published laboratory results which emphasized the part played by the shale in the generation of the SP. On the basis of laboratory tests and theoretical considerations, Wyllie in 1948' published the following equation of the electrochemical SP for the case of NaCl solutions, SP= - 71 log (a1)m/(a2)m

Jan 1, 1958

By M. R. Tek, M. L. Katz

The flow of fluids in stratified porous systems, in which adjacent layers of the system are in communication over part or all of their common interface, in many instances involves crossflow between layers. A theoretical study has been made of the unsteady-state flow of slightly compressible fluids during depletion of bounded stratified porous systems. Consideration has been restricted to single-phase flow, with negligible capillary and gravity effects. Analytical expressions have been derived for pressure distribution and for (luxes at the producing face in two-layer systems with complete fluid communication between layers. These expressions occur in the form of double Fourier and Fourier-Bessel series. The method of extending the solution to any number of layers is demonstrated by deriving the equation for pressure distribution in a three-layer system. On the basis of the exact results for two-layer systems, certain generalizations regarding the behavior of stratified systems in general are presented. The performance of stratified systems, in terms of cumulative flux as a function of time, is shown to lie at all times between bounds established from single-layer theory. The upper bound is given by treating the system as a single layer with arithmetic average physical properties. The corresponding lower bound is the summation of the fluxes from each layer as treated individually. Variation in performance of stratified systems between the upper and lower bounds is determined by the extent to which crossflow occurs in the system. The principal parameters affecting the amount of crossflow are the vertical permeability of the system, the ratio of system thickness to "radius of drainage" and, for radial systems, the ratio of system thickness to interior radius. At very early times, the system performance is near the lower bound. As time and the radius of drainage increase, the per- formance tends toward the upper bound. INTRODUCTION One of the principal problems confronting the reservoir engineer today is the incorporation of the effect of reservoir heterogeneity into predictions of reservoir performance. The first part of this problem is the characterization of the actual reservoir heterogeneity in a mathematically useful manner.1, 2 It is then necessary to calculate the effect of this heterogeneity on the system performance. It is frequently possible to estimate this effect by comparison with the known behavior of an idealized system. One such idealized system is the stratified or "layer-cake" model. Many studies have been made of the behavior of stratified systems, from both a theoretical and experimental standpoint. The great majority of the theoretical studies have been concerned with systems of separated layers, with no fluid crossflow. Among the more noteworthy of such theoretical papers is that recently published by Lefkovits, et al,3 in which a comprehensive analysis was presented for the behavior of bounded stratified systems which are unconnected except at the wellbore. Three recent references have dealt with stratified systems including the effect of crossflow. Jacquard4 has presented mathematical derivations pertaining to depletion of two layer systems producing at constant rate. A doctoral dissertation by Katz5 contains analytical solutions and tables of results for pressure distribution and fluid flux during constant-terminal-pressure depletion of two-layer and three-layer systems with crossflow, together with tables of eigenvalues necessary in the computations. The dissertation also presents results from experimental studies of stratified systems using a heat-transfer analog model. This paper is largely based on the material in this dissertation. A third paper has been presented by Russell and Prats6 since completion of the work resented herein, containing mathematical derivations for and discussion of the behavior

By A. Vifian, I. lwasaki

Several samples of copper-nickel ore from the Duluth Gabbro were studied to relate their mineral-ogical characteristics with their amenability to concentration by flotation. The most common rocks in the samples were norites, gabbros, and troctolites. The texture of the rocks varied from coarse pegma-titic to very fine. The copper contents ranged from 0.2-0.7% and the nickel contents from 0.07-0.15%. The ore minerals were chalcopyrite, cubanite, pyrrhotite, and pentlandite. Most of the ore minerals occurred in interstices between laths of plagioclase, but some were included in the gangue grains. The samples responded readily to xanthate flotation. After a 65 to 100-mesh grind about 95% of the copper and 85% of the nickel were recovered in a bulk sulfide concentrate. Such recoveries remained constant even with grinds as fine as 270 mesh due to the extremely fine inclusions of sulfides in the silicate gangue. A finer grind than 270 mesh was necessary to free the copper-iron sulfides from the nickel-iron sulfides. A combination of time and British gum* was quite effective in producing concentrates analyzing 25-30% copper. The nickel concentrate averaged 1.5% nickel. Most of the nickel lost in the tailing was present as un-liberated sulfides and not as nickel in the olivine structure. The nickel content of the olivine was only about 0.05 or 0.08%. Western world nickel usage in 1967 is expected to be the second highest on record, amounting to 825 million lb. Despite a rise in mine production, however, demand is expected to exceed supply in 1968. ' Hence, exploration, development, and production expansion projects are being accelerated on a world scale. In Minnesota the copper-nickel bearing Duluth Gabbro is receiving much attention. During the past year 11 companies have been granted leases in the region, and the 1967 Minnesota legislature enacted a tax law designed to encourage the development of a copper-nickel industry. Although it is only during the past few years that mining companies have shown an active interest in the Minnesota copper-nickel deposit, copper-nickel minerals have been known to exist in northeastern Minnesota since 1899.3 At the 28th Mining Symposium, Dr. P. K. Sims, from the Geological Survey of Minnesota, gave a review of copper-nickel exploration in northeastern Minnesota,4 in which he emphasized that the potential of the Duluth Gabbro complex is large. Tests on samples from the Kawishiwi River area were reported by the United States Bureau of Mines in 1955.' In 1964, the Mines Experiment Station described tests on samples from the Gunflint Trail: and in 1966 the Minnesota Geological Survey published a geological map of the Gabbro Lake Quadrangle. The Mines Experiment Station published a study of the concentration of a Minnesota copper-nickel ore in 1967.7 The present paper is divided into three parts. The first describes the mineralogy of some rock samples from the Kawishiwi River area of northeastern Minnesota; the second summarizes the results of numerous flotation tests that were made on the samples, and the third explains the loss of nickel in the flotation tailing. MINERALOGY OF KAWlSHlWl ROCKS Recently five samples of mineralized gabbro from the Kawishiwi River area, a few miles east of Ely, were received at the Mines Experiment Station. One of the samples was a 175-lb composite, which was designated Ore 1556. The other four samples were 7-lb grab samples that had been obtained from four different exploration pits. They were designated Ore 1626, Lots 1 through 4. Basic Mineralogy: Many authors have reported that the rocks of the so-called gabbro of the Duluth Intrusion vary widely in composition.8-9 The samples on which our studies were based also contained a wide range of rocks. A gabbro, olivine-gabbro, anorthosite-gabbro, norite, and a troctolite were represented. The essential minerals in the samples were plagio-clase, pyroxene, and olivine, in variable proportions.

Jan 1, 1969

By Harry M. Mikami

Chromite is the only ore mineral of metallic chromium and chromium compounds and chemicals. Because of this fact, chromite and chrome ore are used synonymously in trade literature. In commercial market quotations, chrome ore is the term commonly used. Chromite per se, because of properties imparted by its chromium content, is used in refractories and in special purpose molding sands for metal casting. There are many other minerals containing some, generally minor, amounts of chromium, but none are commercial sources of the element (Thayer, 1956). Chromium and chromite have many diverse uses that, directly and indirectly, critically affect vast segments of our modern industrial system. Most important are probably the metallurgical applications wherein chromium is a component of heat-, abrasion-, corrosion-and oxidation-resistant and high-strength alloys of many types. Stainless steels are the largest volume category of chrome-bearing alloys. Chromium chemicals are used in leather tanning, in pigments, dyes and mordants, printing, chemical process industries, photography, pharmaceuticals, metal plating, pure chromium metal production, and for many other purposes. Chromite is a necessary constituent in basic refractories indispensable for the production of steel, copper, cement, and glass. Under present conditions, the US and North America, with the possible exception of Cuba, have no commercial ore reserves. There are chromite deposits, as will be described, but they would be used only under highly abnormal conditions if all outside sources were cut off for an extended period. All chromite used in the US is imported from the eastern hemisphere in which are contained the principal world reserves. The main suppliers in 1980 were the Republic of South Africa (43%), the USSR (21% ), the Philippines (12%), Albania (11 %), Turkey (8%), and others (5%). The strategic nature of chromite is obvious. End Uses-Grades and Specifications As noted before, the three principal uses for chromite are metallurgical, refractories, and chemical with a fourth minor use as foundry molding sand. For metallurgical applications chrome ore is first reduced in electric carbon arc furnaces to various types of ferrochromium alloys. There are high, medium, and low carbon ferrochromiums with carbon ranging from 0.01 up to 10%. Chromium itself ranges from 50 to 73 %. Ferrosilicon chromium and ferrochromium-silicon grades have chromium from 33 to 67% and silicon from 3 to about 48%. Since iron is reduced with chromium, the Cr:Fe ratio of the ore will determine the ultimate grade of the ferrochromium whereas carbon and silicon can be controlled during processing. MgO, A12O3, CaO, and excess SiO2, are removed in slag. A small amount of pure chromium metal is prepared by alumino-thermic and electrolytic processes from essentially iron-free chrome components that have been made via the chemical route. The higher grades of ferrochromium with chromium in the 66 to 73% range can only be made from ores with not only high chromium content, but low iron, i.e., high Cr:Fe ratio. These ores, conventionally termed metallurgical grade, have Cr2O3 contents of 45 to 56% with Cr: Fe ratios of 2.5 to 4.3. A standard composition is generally 48% Cr2O3 and 3:1 Cr:Fe ratio. Very high grade ores are often blended with lower grades even with the high iron chemical grade. For some ferrochromiums, additions of high alumina refractory grade are used as slag conditioners to facilitate smelting while still contributing chromium values. A lower grade ferrochromium, the high carbon charge chrome, has become the predominant grade in use today for making chromium-bearing steel alloys. This

Jan 1, 1983

By H. H. Rachford

This work presents a first-order analysis of the instability underlying viscous fingering in adverse viscosity-ratio water floods. It extends previous analyses of frontal instabilities, which were carried out with equations for parallel plate models, by including effects of the saturation transition zone observed behind the front in water floods in water wet systems. This zone tends to insulate incipient fingers from the high-mobility watet;. thus conditions for the onset of fingering differ from those in the parallel plate theory. Finite-difference solutions of the two-dimensional equations of displacement in porous media exhibited the predicted stability characteristics in six hypothetical field- and laboratory-scale floods in rectangular reservoirs. In contrast to results with parallel plate systems, this paper concludes that for waterwet reservoirs, laboratory models scaled by the usual criteria are also correctly scaled for frontal instability. Further, fingering in the systems studied can occur in any saturation range behind the front, and may occur at an intermediate saturation even though stability obtains both at the saturation corresponding to the Buckley-Leverett front and near residual oil saturation. Other points of contrast are that the likelihood of occurrence of fingering may not increase as flow rate or viscosity difference increases, but my be sensitive to changes in he relative permealdlity and capillary pressure functions. INTRODUCTION The recovery of oil by water flooding frequently involves displacing the oil by water of a lower viscosity. Displacement of a fluid by a less viscous one may lead to gross channeling or fingering like that observed in solvent floods, in which it severely lowers recovery efficiency.1 In addition to adverse effects on recovery, it has been suggested that the unstable move- ment causing fingering may interfere with interpretation of scaled model studies of proposed water floods, since the instability in the model might not be faithfully scaled to that in the reservoir prototype. In view of the serious implications of this possible breakdown of widely used scaled model techniques4-6 it is the purpose of this paper to examine the question further. Instabilities in the solutions of systems of differential equations imply a loss of smooth dependence on initial and boundary conditions. Thus, the possibility exists that in using models whose scaling is based on the differential system there may arise size- and rate-dependent factors which are not properly scaled. This possibility was examined in detail by Chouke et al., who analyzed the instability of frontal advance in a related problem, water-oil displacement in parallel plate models,2 in which a moving interface separates two regions of constant, unequal mobilities. First-order perturbation theory predicts the existence of a critical wave length for the growth of perturbations: and a wave length of maximum instability of A, = The interpretation is that wave lengths in a perturbation which are longer than A, will grow. Thus, if the width of a two-dimensional channel is greater than A,, fingers will grow, and the spacing of the fingers which grow at the maximum rate will be approximately It is important that the higher the velocity and/or the difference in flow resistance, the lower is A,, and thus the greater the number of fingers that can grow in a given model. In applying these conclusions to porous media, a pseudo-interfacial tension, , was assumed for the invasion front. Since this would not necessarily be equal to the liquid-liquid interfacial tension, an unknown constant was substituted for the foregoing expression for A, This was determined

Jan 1, 1965

By H. H. Rachford, D. W. Peaceman

A system of partial differential equations describing miscible displacement of fluids in porous media is derived The system takes into account the influence of gravity, the spatial distribution of permeability, diffusion, and fluid viscosities and densities. A numerical procedure for approximating solutions to the differential systems has been tested for a horizontal two-dimensional geometry. In end-to-end displacements of oil with less-viscous solvents, the numerical solutions exhibited fingering qualitatively similar to that observed in laboratory models. Small random spatial variations in permeability about the mean value are sufficient to initiate fingering. Quantitative comparisons of computed results with laboratory data show good agreement. INTRODUCTION Miscible flooding of oil by solvent is receiving increasing consideration for field use.1-4 Unfortunately, such floods potentially present severe problems in loss of recovery through the by-passing of oil by expensive solvent. Consequently, their economic evaluation requires sound techniques for predicting recovery. The purposes of this work are to present a finite-difference method for calculating the multidimensional displacement of oil by solvent and to investigate the validity of the method by comparing results of calculations with data from displacements in laboratory models.5 The formulation of the method to simulate the model experiments treats a case of limited scope in the description of solvent flooding in the reservoir. The model experiments were carried out with fluids that were assumed to form an incompressible, ideal, two-component system with constant diffusivity. Establishing the validity of the method even in its present form provides a major step toward the goal of quantitatively evaluating individual solvent flooding projects. First, it demonstrates the fea- sibility of calculating the course of displacements which are dominated by an inherent macroscopic instability, i.e., viscous fingering. In addition, the method provides almost the only practical means of examining the effect of the size and extent of reservoir inhomogeneities on the development and propagation of the fingers, taking into account the important influences of diffusion and gravitational segregation. It might be inferred that such studies cannot yield results of practical value because in displacements dominated by macroscopic instability the pattern of finger development and the resulting performance should depend critically on small variations in the geometric distribution of reservoir inhomogeneities. The present method offers the capability inherent in computational techniques of predicting performance reproducibly with any arbitrary distribution of reservoir properties and, as such, provides a means of evaluating the sensitivity of behavior to uncertainties in reservoir definition and, thus, assessing the reliability of prediction of performance. THE PHYSICAL PROBLEM DATA USED FOR QUANTITATIVE TESTS OF CALCULATIONS In this work, a calculation for treating the miscible-displacement process is tested by comparing calculated results with experimental data. The experiments chosen for comparison have been described in detail,5 and the quantitative features are summarized in a later section. Briefly, oil was flooded by solvent of equal density from a thin rectangular channel in Lucite packed with uniform Ottawa sand. Under these conditions, two-dimensional geometry is considered adequate to represent the process. Inasmuch as the present work is concerned with testing of the method by comparison with specific two-dimensional data, the system of equations presented in the succeeding section will be oriented to defining the physical system specifically. THE DIFFERENTIAL EQUATIONS Suppose x, y to be a Cartesian co-ordinate system and define h(x, y) to be the height of a point above a horizontal reference plane. It will be assumed

By E. D. McMurry

INTRODUCTION Before discussing the use of the free piston; it may be well to explain briefly the type of gas lift valves with which the loo] is designed to function. The gas lift valve ii nothing more or less than a small back pressure regulator. It; construction consists of an outer hous ing covering a seamless metallic bellows in such a way as in form a sealed pressure vessel or pressure dome. To the bellow* in attached a stem and to this stem is attached a .rating member. When the valve is run into the hole, a pre-delermined pressure charge is placed in the pressure dome. As shown in Fig. 1. the valve is furnished in four different major assem-blies. to accomplish good results in different types of wells. The valve is mounted on a pup joint (Fig. 2a) : the eoin-plele assembly is entered into the tubing siring at the desired location. Each valve is furnished with a revere flow check valve (Fig. 2-b) to eliminate any back wash through the mechanism. Valve action is as follows: At any time the casing pressure is allowed to exceed the pressure forces within the pressure dome of the valve, the valve simply opens and passes gas from the rasing annulus into the tubing. When the casing pressure forces arc allowed to bleed to a force less than the pressure force within the dome, of the valve. the valve closes. With this type of construction. it is possible to open and close the valve or valves at will from the surface, the medium of the gas pressure in the rasing annnlus. The cycle of operation is governed by a tine cycle motor valve, commonly referred to as a gas lift interutitter or gas life surfacr controller (Fig. 3). In actual practice. after the well is unloaded only one valve is in operation . . . all other valve.: remain in the closed position. On pre-determined time cycles, it is possible to open and close this operating valve at will, and to pass the desired amount of gas through this valve wheneler needed. This method of gas lift is widelv used and has been found In be very efficient. However, it has long been known that even greater efficiency would be obtained if it were possible to place Piston between the injected gas and the fluid head. The free piston which will be discussed here was designed to accomplish this end and has been found to do so with very satisfactory results. DESIGN AND OPERATION OF THE FREE PISTON Basically. the free piston consist- of a telescoping assembly in which are incorporated the various control and operating parts (Fig. A set of sleeve valves which are opened and closed by movement of the telescoping section is contained in the. tool. A cross section of the free piston is shown in Fig. 4-11, 'rile main body cotain- a seamless monel bellows of the same type as that generally used in pressure charged gas lift valves (Fig. 4-c), and a valve core to permit placing a pressure charge in the bellows before the free piston is placed in service. The bellows is the main control unit of the free piston and performs two function: 1. It governs the opening and closing of the sleeve valves. a.: dictated by the producing activities of the well in which the piston is operating. 2. In its normal position, it holds a rubber packer in an elongated position to permit passage of fluid between the packer and the tubing walls. The lower section of the free piston contains a hydraulic shock absorber which cushions the return of the tool to its

Jan 1, 1953

By R. F. Domagala, M. Hansen, D. J. McPherson

On the basis of metallographic analysis, incipient melting data, thermal analysis work, and X-ray diffraction, phase relationships in the 0 to 50 atomic pct Cr region were carefully resolved. Phase relationships in the 50 to 100 atomic pct region were outlined. A single intermediate phase, ZrCr,, was established in the system. A eutectic and a eutectoid were found in the zirconium-rich region of the system, while a eutectic was located in the chromium-rich region. Limited solubility of chromium in both a and a zirconium was observed. THIS is another in a series of papers on zirconium-base binary phase diagrams based on a program sponsored by the Atomic Energy Commission. The Zr-Sn,' Zr-Si,' and Zr-Mo and Zr-W" systems have already been published. Previous work on the Zr-Cr system includes a partial diagram by Hayes, Roberson, and Davies' and a complete diagram by McQuillan." The phase relationships reported by these authors were determined with magnesium-reduced zirconium, whereas those reported herein are based on iodide metal. Some X-ray work on the intermediate phase in this system was also reported by Hayes et al., as well as by Wallbaum.' Comparisons with these data are made in the appropriate sections. Thermal analysis, metallographic and incipient melting techniques were employed to accurately resolve phase relationships in the 0 to 50 atomic pct Cr region, while the remainder of the diagram is outlined on a basis of cast structures and thermal analysis. A description and analyses of the metals used in the preparation of alloys for this study are included in Table I. A "low-hafnium" zirconium crystal bar (Westinghouse "Grade 3") was used. This material was produced by the decomposition of a volatile iodide onto a hot zirconium filament. The as-received crystal bar was coated with corrosion product from a standard autoclave test by which its grade designation is determined. A sand-blasting and subsequent HF-HNO, pickling treatment was employed to remove this contamination. The bars were cold-rolled to approximately 1/32-in. sheet, pickled again, sheared to 1/4-in. squares, washed with acetone, and stored for use. Ingot chromium metal from National Research Corp. and electrolytic chromium flakes from Johnson, Matthey and Co., Ltd., were available as alloy additions. The ingot chromium was received in granular form. The large granules were sized by crushing, treated for iron removal, rinsed with acetone, and stored. The flakes were broken to approximately 1/8 in. with mortar and pestle, cleaned with acetone, and stored for charging. Experimental Procedure A nonconsumable electrode arc furnace identical to that described by Hansen, Kessler, and McPher-son,' was used in this work. A 400 amp dc welding generator was the source of power. To insure homogeneity, ingots were melted in a water-cooled spun copper crucible, a total of four times without opening the furnace. No difficulties were encountered in the preparation of these binary alloys. Analyzed chromium contents were found to agree very well with the intended content. Melts of pure zirconium were interspersed in the course of preparing the alloys and their hardness was measured to keep a constant check on the melting technique. Vycor and quartz bulbs were used to contain the samples for isothermal annealing treatments. Vycor bulbs were employed for temperatures up to 110O°C, while quartz was used above this temperature. For treatments up to 950°C the bulbs were evacuated before sealing, but for higher temperatures a partial pressure of argon was admitted to the

Jan 1, 1954

By Robert B. Hall, Charles W. Bauer

Alunite, KA13(SO4)2(OH)6, was used from the 15th century until early in the present century as a source of potash alum and aluminum sulfate. Since early in this century its use for this purpose has declined to virtually nil with acid treatment of bauxite or clay replacing alunite as a source of alum. During the First World War alunite served as an emergency source of potassium sulfate fertilizer in the United States and Australia. More recently, alunite has been investigated as a nonbauxite ore of aluminum, with potassium sulfate and sulfuric acid as recoverable byproducts. The Soviet Union established a commercial-scale plant in the mid-1960s producing cell-grade alumina from alunitic ore and recovering byproduct potassium sulfate and sulfuric acid. Interest in nonbauxite ores, including alunite, is expected to continue in countries that presently are dependent on imports of bauxite or alumina to support their aluminum industries. The US has the largest aluminum producing and fabricating industry in the world but imports more than 90% of its aluminum-bearing raw materials. This chapter reviews the status of alunite as a potential source of aluminum with byproduct fertilizer, and the resources available to support this industry, whenever this becomes economically feasible. Historical Background Alunite has received little attention until recently, yet for centuries it held a higher place than many of the industrial minerals considered essential today. The deposits of alunite at Tolfa, northwest of Rome, were mined almost continuously from 1462 until about the middle of the present century (DeLaunay, 1907; Lombardi, 1977). The potash alum made from the alunite, called Roman alum, was a valued commodity in international trade, being used in the making of paper, in tanning leather, and as a mordant in textile dyeing. The industry at Tolfa is said to have been controlled by the Vatican and was a source of revenue for the Papal State until fairly recent times (Lombardi et al., 1977). Since early in the present century, the preferred method for making alum has been by acid treatment of bauxite, clay, or other aluminous material, so that alunite has fallen into near-total disuse as a source of alum chemicals. Appreciable quantities of mixed alunite-kaolin rock still are quarried in the Tolfa district for use by the Italian cement industry (Lombardi and Mattias, 1979), but the role of this material in the making of Italian cement is not clear. A large deposit of alunite-bearing rock in Chekiang province, mainland China, is said to have yielded a "great quantity" of alum over a period of several centuries (Yih, 1931). During the 19th century, alunite deposits in France, Spain, Australia, and other countries were exploited as raw material for making potash alum and aluminum sulfate. Interest in alunite was revived during the First World War, not for alum, but as an emergency source of potassium sulfate fertilizer. Large veins of nearly pure alunite had just been discovered on Alunite Ridge, 11 km southwest of Marysvale in Piute County, Utah (Butler and Gale, 1912), and these were quickly brought into production for making potash fertilizer to replace supplies cut off from the famous deposits at Stassfurt, Germany. An estimated 225 kt of Marysvale alunite was mined and processed at that time (Callaghan, 1973). Similarly, Australian alunite deposits were mined as a source of potash fertilizer during both world wars (Hall, 1978).

Jan 1, 1983

By J. W. Evans

ONE of the most important and frequent calculations that the extractive metallurgist is called upon to make is that of the standard free energy change of a reaction (?F°). For many reactions of metallurgical interest, the lengthy arithmetical calculations have been eliminated by the use of free energy-temperature diagrams which have been constructed by Ellingham,1 Richardson and Jeffes,2 Kellogg,3 and Osborn4 (e.g., for oxides, sulphides, halides) from critical surveys of existing data. The speed and simplicity of making calculations with these graphs make them of great practical value and, this should be stressed, in the majority of cases no greater accuracy is obtained by the individual calculations from specific heat data, entropies, and heats of reaction. With the increasing industrial application of vacuum methods to the winning of metals, notably at present magnesium and the alkaline earth metals, it is necessary to calculate low metal vapor pressures above reaction mixtures. The existing free energy diagrams usually give values where the solid and liquid metals are at unit activity. To obtain the free energy change associated with the reaction Metal (solid or liquid) = Metal (gas) it is customary to calculate this from either vapor pressure equations or from the appropriate free energy functions. This paper presents graphically the free energies of vaporization of a number of metals of economic importance which can be used in conjunction with other free energy diagrams. Certain metals have been excluded on the following grounds: titanium, tungsten, molybdenum, and platinum have very high heats of vaporization and boiling points and the uncertainty of these values arising from difficulties of high temperature measurements makes free energy values of doubtful accuracy; the data for cobalt, vanadium, and zirconium are uncertain; finally, arsenic, antimony, and bismuth could not be conveniently included. because of the presence of mixtures of polyatomic and mona-tomic vapors in the temperature range considered. Free Energy Diagram In Fig. 1, the standard free energies of vaporization per mol (?F°T) have been plotted for the temperature range 0" to 2000°C for the reaction M (solid or liquid) = M (gas) The data have been obtained from the free energy functions — (F-H298)/T for the solid, liquid, and gaseous elements and the heats of vaporization at 298°K, i.e., ?H298 (vapor). The values of these functions have been taken without change from the recent critical survey by Brewer;' the bulk of this data is from Kelley7 with adjustments in the light of more recent work. Values of the function — (F-H298) /T at T = 298°, 500°, 1000°, 1500°, and 2000°K were employed. Where possible, a further independent value was obtained by using the boiling point, i.e., where ?F°T = 0. All calculations are based on the assumption that the metal vapors are monatomic and that the boiling points refer to those temperatures at which the partial pressure of the monatomic vapor above the metal is 760 mm. For the alkali metals, e.g., sodium, potassium, and lithium, diatomic gas molecules are present as minor species; details of these are discussed by Brewer." On the basis of the above values and allowing for the change in slope at the melting point, straight line graphs were constructed and extrapolated to 2000°C. The deviation from a straight line did not exceed ±500 cal, which in all cases appears less than the probable error in the ?F°T values.

Jan 1, 1954

By J. P. G. Farr, R. Brownsword

THE role of solute segregation in the formation of cellular solidification substructures in tin and its dilute alloys is well-established, see, e.g., Ref. 1. Segregation has been shown to persist during cooling, enabling solidification structures to be studied from sections taken at some distance behind the interface. In the present work, a single crystal of commercial nickel, 99.965 pct, was examined in this way. The crystal was cut from the center of a rod given a single pass in an electron beam floating zone melter. Polished sections of a nickel specimen taken normal to the growth direction showed a very fine precipitate phase, the distribution of which varied over the section. The identification of the phase proved difficult because of the small amount present and the small particle size, about 1 p: but it was shown by probe microanalysis to contain only nickel and oxygen in detectable concentrations and was probably nickel oxide, NiO. Bulk analysis of the material before melting showed there to be only 3 to 4 ppm of oxygen present, thus demonstrating a very considerable segregation concentration effect. In some areas of the section the precipitate formed a discontinuous hexagonal network suggesting decoration of the cellular boundaries known to be present in the sample2 whereas in a restricted region the precipitate formed small clusters. Occasionally it could be seen that the clusters were at the intersections of an hexagonal network of cellular dimension. It was suggested3 that this was the result of enhanced segregation to the cell boundary intersections whereas general cell boundary segregation was insufficient to give a precipitate. Enhanced nodal segregation has since been demonstrated in a number of systems.1, 4-8 The development of a suitable electrolytic etching technique (perchloric acid 20 pct v/v; ethyl alcohol 70 pct; glycerol 10 pct; current below electropolishing plateau; 1 to 2 sec etching) suggested the association of the phase with regions of solute segregation (where ko < 1); in these regions anodic attack produced grooves or depressions. In a study of the variation of solidification substructures with degree of constitutional supercooling, Biloni et a1.&apos; appear to have used standard growth conditions and varied the solute concentration. They were able to produce in a series of individual tin crystals examples of substructure ranging from planar interface through various cellular structures to den- Fig. 1—Electroetched section taken normal to the rod axis; the center of the rod lies to the left and the periphery to the right of the micrograph. The variation of structure across the section is evident. Magnification 60 times. drites. It was possible in the present nickel crystal to observe a continuous range of substructures varying with degree of supercooling across a single section as shown in Fig. 1. Growth rate, 13 mm per min, and temperature gradient were essentially constant; the variation in structure is thought to be due to a radial gradient in solute concentration ahead of the solid interface. The liquid at the interface is likely to have been richer in solute toward the periphery of the zone, the result of curvature of this interface. The type of substructure was seen to vary with increasing constitutional supercooling as follows: a) region free of precipitate. top left, Fig. 1: 6) region of nodal precipitates which became arranged in hexagons on passing from the center of the rod: c) irregular hexagonal cells with incomplete boundary precipitation; d) regular hexagonal cells of decreasing size with complete boundary precipitation. Fig. 2 shows the transition from stage 6 and Fig. 3 shows the structure in stage d. Within stage 0, the range of conditions over which irregularly positioned nodes occur appears to be small and the nodes are soon recognizable as taking up positions at the intersections of an hexagonal network as the supercooling increases.

Jan 1, 1970