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By T. B. Counselman

C. G. McLachlan—In the foregoing paper the author has presented a very neat method for calculating the solution recovery for a countercurrent flowsheet. He has, however, based his calculations, as he states, on the assumption that "the concentration of dissolved value must be exactly the same in the overflow and underflow of any thickener." This assumption, which is usually made regardless of the type of calculation used, is "not strictly correct because diffusion of the dissolved gold in the solution associated with the solids as it progresses through the countercurrent system is far from being instantaneous, with the result that on a ton for ton basis, the assay of the solution in the thickener underflow is higher than in the corresponding thickener overflow. An agitator introduced into the flowsheet between thickeners will reduce, but not entirely eliminate, this difference. In practice we have found that the best way to take care of this condition— in addition to the use of one or more intermediate agitators—is to circulate 20 pct or 25 pct more solution than called for by the cheoretical calculation. This presents no difficulty provided that adequate thickener capacity is provided in the original design of the countercurrent circuit.

Jan 1, 1951

By James Douglas

PROBABLY no well-informed engineer would ques¬tion the accuracy of the statement that the piece of equipment that comes nearest to being in universal use in modern hydrometallurgical and ore-dressing plants is the Dorr continuous thickener. The function of the device is to separate a thin mixture of liquid and solid particles into a thick pulp and a clear liquor. Another machine in wide use is the Dorr classifier, the purpose of which is to separate the coarse and fine particles in a pulp containing solids of various sizes. It is in recognition of the invention of these two devices and the vast amount of technical work in the successful application of them in the beneficiation of ores that the James Douglas Medal for 1930 has been awarded to John Van Nostrand Dorr. To gage the importance of the development of the thickener, particularly, it is only necessary to imagine the loss of time, capacity, and metallurgical efficiency that would result if all the Dorr tanks in the world were put out of operation for a day and replaced by the old methods of intermittent settling and decantation. Truly, the record is one of "distinguished achievement in non-ferrous metallurgy" that deservedly ranks the medalist with those who have preceded

Jan 1, 1930

By Luiz C. Correa da Silva, Robert F. Mehl

A. D. Le Claire and R. S. Barnes (Atomic Energy Research Establishment, Harwell, Didcot, Berks., England)-—This much awaited paper admirably confirms that the Kirkendall effect is a true diffusion phenomenon and likely to be found in all diffusing systems. The most likely explanation put forward so far to account for the shift of interface is that the two components of the system, diffusing in opposite directions, do so with unequal rates so that there is a net loss of material from that half of the diffusion zone rich in the more rapidly diffusing component. This loss is accompanied, and at least partly compensated for, by a closing up or decrease in volume of this latter half of the diffusion zone and an expansion of the other half so as to tend to keep constant the overall volume per atom. This is manifest as a movement of the original interface. If this is a true picture of what is taking place then there are at least two important matters requiring further study."1—The quantitative relating of the observed shift with the independently measured separate diffusion coefficients of the two diffusing species."2—A detailed study of the mechanism and characteristics of the closing up process."We would like first to make a few remarks pertinent to these topics. In connection with the first of these, it is a pity that more and detailed measurements were not made on the Au-Ag system, the only one for which the separate diffusion coefficients of the two species have been measured.'" One of us (A. D. Le C.) has calculated from Johnson's results the shift to have been expected in samples D.2 and D.3. Darken4 showed that the velocity v with which the markers move is related to the separate diffusion coefficients Dau, Dag, by the eauation:"dN"v = (Dag — Dau "dx"dN"where .is the concentration gradient at the mark-ax"ers. Under certain conditions,4, 20 it can also be shown that:"Xm"v = "2t"where x, is the total marker shift after time, t:"dN". . xm = 2t (Dag — Dau) [9]"dX"Johnson measured Dag and DAu in a chemically homogeneous alloy and so his reported figures represent the true or ideal diffusion coefficients"; the same quantities in eq 9 represent the actual diffusion coefficients as would be measured in the presence of a chemical concentration gradient, so we need to multiply Johnson's reported values of Dag and Dau by the"1 before insert-dlogN "ing them in eq 9. 7 is the activity coefficient of Ag at the concentration prevailing near the markers which we shall assume to be - 50 pct. The values of the thermodynamic factor for N = 0.5 and the temperatures at which D.2 and D.3 were annealed were obtained from thermodynamic data quoted by Darken.' aN/ax was computed from the coefficient of inter-diffusion of Au and Ag given by Johnson on the assumption that in the samples D.2 and D.3, the concentration distance curve could be represented by the standard equation:""No is the original difference in concentration between the two halves of the couple, and + is the error or probability function."aN/ax at x = 0 is then given by:"adN/dx "2/nDt"and we assume that this represents the concentration gradient at the markers, although it is probable that the figure is slightly high."When all the appropriate quantities are inserted in eq 9, we find that the expected shifts are: for D.2, 0.0134 cm and for D.3, 0.0119 cm."The agreement between these results and those

Jan 1, 1952

By S. R. Mitchell, M. C. Fuerstenau, A. M. Gaudin

The two principal attributes of a thickener pulp are its settling rate and the ultimate pulp density of the thickened mud. Testing for evaluation of thickening attributes of a pulp has usually been done batch-wise by placing the pulp in a one-liter glass graduated cylinder and noting the position of the boundary between clear liquor and mud as a function of time. Refinements in testing have included repulping a thickened mud to various dilutions and evaluating the settling rate on these various repulped muds. This is considered to make possible an estimate of the settling rate as a function of pulp density and therefore to pinpoint the slowest settling pulp which ought to be critical from the standpoint of thickener plant design. Finally, tests are sometimes made with model-size continuous thickeners of arbitrary size. In batch tests it is generally accepted that the behavior of a pulp is described by a curve such as the one shown in Fig. 1, in which the position of the boundary between clear liquor and mud (the mudline) is plotted against time. It has also been assumed that the initial settling rate (the slope of the line segment AB) is descriptive of the pulp and independent of the size and shape of the container. Where the settling rate is slower and clearly a function of time (portion CD of the settling curve), it has been assumed that the data are not of much use because of the intrusion of compacting phenomena. The next important datum is the height. PE, which is a measure of the so-called ultimate pulp density. This quantity is assumed to be characteristic of the pulp and independent of the container. When actual data are recorded, results are rarely exactly according to this theory and numerous deviations may be noted. For example, some pulps seem to require an appreciable delay before beginning to settle, as in line AF. This is spoken of as representing the need for an induction time for flocculation. It has seemed desirable to explore thickener data with a more sensitive charting tool than is afforded by the coordinates of Fig. 1. Instead of relating the position of the mudline to time, it has seemed desirable to relate the rate of descent of the mudline to time. This, in effect, amounts to charting the slope of the line in Fig. 1, or the derivative of its ordinates, against the same abscissas. Fig. 2 shows the new chart for the curve ABCDE of Fig. 1. When this new tool was applied to data obtained, for example, with sized clay pulps, astonishing differences appeared. Apparently the traditional tool conceals differences instead of revealing them, whereas the new method emphasizes them. It seems, also, that both charting methods have their uses. In this article attention is focused on the effects of pulp density and container height as they affect the settling behavior of flocculated suspensions of a sized kaolin. The thesis by M. C. Fuerstenau' gives more details than this summary, as well as some information about the effect of other variables. Sized fractions of kaolin were used, supplied through the courtesy of S. C. Lyons of the Georgia Kaolin Co. Large batches were made by agitation in a flotation machine and in a glass jar equipped with a mixer. The settling vessels were 2, 4, and 6-in. diam glass cylinders of various heights. Pulp Dilution: The effects of pulp dilution on sedimentation behavior are shown in Figs. 3, 4, and 5. Fig. 3 shows data on pulps ranging from 2.44 to 16.7 pct solids initial pulp density, flocculated with Separan and charted in the traditional manner. At least two of the lines appear nearly straight in their early sections, but neither of the others does. Each of the curves in this figure includes a region labeled

Jan 1, 1960

By J. Szekely, G. P. Martins

A formulation is given and a general analytical solution is presented for the problem of spherical phase growth in multicomponent systems. The results are valid for describing the rate of bubble growth in the absence of translational motion and, therefore, should be relevant to heterogeneous nucleation processes. Typical worked examples are given, which include bubble growth due to the simultaneous diffusion of hydrogen and nitrogen in molten steel, and the growth of CO bubbles in steel, due to the reaction: C + 0 = CO. The calculations predict that the presence of additional components would enhance the growth rate and also increase the absolute rate at which the individual components are transferred into the bubble. These findings should be relevant to degassing processes. THE problem of spherical bubble growth in the absence of translational motion is appropriate to the description of the heterogeneous nucleation and subsequent growth of gas bubbles while attached to a solid surface. Such problems are of considerable practical relevance to various vacuum degassing and steelmaking processes where bubble nucleation and subsequent growth play an important part in the overall reaction mechanism. A definitive formulation of spherical phase growth has been given in the now classical paper by Scriven1 and the analogous problem for solid phase growth has been discussed by Horvay,2 furthermore a thorough review of the relevant literature has also become available.3 All this previous work was concerned with one component or binary systems. The purpose of this paper is to show that the technique developed by Scriven may be generalized to alow the consideration of multicomponent systems. The results of this generalization would be particularly relevant, as gas bubble nucleation in the metallurgical systems previously mentioned frequently involves the simultaneous diffusion of several components. In the following a general formulation is given and typical worked examples are presented. FORMULATION Consider the growth of a spherical gas bubble due to diffusion in a quiescent liquid of infinite extent, as sketched in Fig. 1. The formulation of such problems requires the statement of the following conservation equations relating to the liquid phase: Equation of continuity Equation of motion Conservation of the diffusing species—Diffusion Equation. The following assumptions are made: a) The fluid is incompressible, quiescent, and of infinite extent b) The bubble is stationary, i.e., it undergoes no translational motion c) Spherical symmetry is observed throughout d) The mass diffusivity is constant e) Chemical equilibrium exists at the surface of the bubble, and any reactions occurring there are fast compared to the diffusion process f) Inertia and surface tension effects are neglected. Equations derived on the basis of these assumptions by previous investigators were found to provide a reasonable representation of bubble growth while attached to a surface in organic and aqueous systems4,5 For gas bubble growth in molten metal systems assumptions a) to d) chould hold reasonably well. The exclusion of chemical kinetics as a possible rate limiting step may not be universally valid, but should hold for many systems operating at high temperatures. The effect of hydrodynamic inertia may be neglected for moderate growth rates; finally, the assumption neglecting the effect of interfacial tension on the bubble growth was made for the sake of mathematical convenience; its inclusion would have required the use of quite cumbersome numerical techniques. While surface tension effects could be appreciable on the initial values of the overall growth rate, especially at low absolute pressures and in case of small bubbles, they are not thought to modify the relative effects present in multicomponent systems, the study of which is the objective of this paper. Within the framework of the above assumptions

Jan 1, 1970

By W. A. White

UNDERCLAY squeeze is the plastic flowing of underclay below coal pillars into mined-out entries and rooms. Squeezes may be caused either by wet mine conditions where the moisture is taken up by the clay—making it more plastic—or by the presence of certain clay minerals, such as mont-morillonite, which are plastic when there is enough natural moisture. Under either condition, sufficient stress will cause the underclay to flow. Squeezes may fill an entry or room within several hours, or it may be several months before movement stops. Squeeze areas commonly cover hundreds or thousands of square yards. The Coal Div. of the Illinois State Geological Survey has collected samples of underclays from various mines and from cores drilled by coal companies in the state. From these samples natural moisture content, particle size and particle size distribution, and clay mineralogy are determined. Data from samples collected from the underclay below Herrin (No. 6) coal in the Lumaghi Coal Co. mine near Collinsville, Ill., are used in this report to clarify points in the discussion. Data from samples taken from other mines lead to the same conclusions. A generalized geological section for the area is given in Table I. The underclay below coal No. 6 ranges from a few inches to 3 or 4 ft thick. The upper 6 to 18 in. are noncalcareous; the lower part becomes more calcareous with depth. Limestone nodules become larger with depth, almost grading into the limestone below. In areas where the clay is nearly absent the limestone may thicken to take its place; thus they may complement each other in thickness. There are two types of squeeze areas in a mine. In one type up to 3 or 4 ft of underclay lie in what appears to be a depression in the limestone underneath. This is suggested by a rim surrounding the squeeze area where the underclay is thin and the limestone lies within a few inches of the coal. In the second type the underclay of the squeeze area is surrounded by underclay of similar thicknesses which does not squeeze. Test Methods: Natural moisture content, particle size and particle size distribution, and clay mineralogy were determined by the following methods: Natural moisture is the moisture content a clay contains in its natural environment, expressed in percentage of the weight of ovendried clay (110°C or 230°F). To obtain the natural moisture content, given in Table 11, the clay samples were sealed in containers as soon as the samples were taken in the mines. Particle size and particle size distribution were determined by the pipette method,' and the data were plotted as cumulative curves, Fig. 1, on semi-logarithmic paper. Particle size was plotted on the logarithmic scale and percentage on the arithmetic scale. The quartiles (diameters that correspond to frequencies of 25 and 75 pct) and medians (diameters that correspond to the frequency of 50 pct) of the samples were determined from these curves. The clay minerals were identified from the data obtained by differential thermal' and X-ray powder" techniques. The differential thermal analyses were made on the whole samples, whereas the X-ray analyses were made on fractions of less than 2p. Data and Discussion Moisture Content: After the sealed jars had stood for 24 hr, those that contained squeeze samples had perspired, so that droplets of water had accumulated on the insides of the jars. Table II shows the moisture in the clay after it had perspired for 24 hr. (This perspiring was not noted in samples from nonsqueeze areas.) After perspiration one of the squeeze samples still had a higher moisture content than the samples that did not squeeze. Clay Mineralogy: The thermal analysis, Figs. 2 and 3, indicates that the clay minerals are chiefly micaceous in type; the low-temperature endothermal

Jan 1, 1957

By M. E. Wadsworth, C. H. Pitt

Nickel corrosion in sulfuric acid solutions at elevated temperatures and oxygen wer-pressures was imestigated. Weight loss was 1inear with time and varied directly with oxygen concentration. Independent variation of the possible active species in solution indicated that the undissociated sulfuric acid molecule plays an important part in the corrosion mechanism. The rate determining step was considered to be the adsorption of oxygen on a site containing adsorbed H2SO4. THE tendency for a metal to go into solution depends on a number of factors some of which are: 1) the position of the metal in the electrochemical series; 2) the type and concentration of corroding species in solution; 3) the concentration of oxygen in solution; 4) the type of film formed at the liquid-metal interface; and 5) the physical state of the metal. The corrosion of a metal in an aqueous solution may be considered to be a heterogeneous reaction that occurs at the liquid-metal interface. The reaction is generally considered to occur as a result of electrochemical potential differences within the system. Little work has been published in the literature concerning the corrosion of pure nickel. A great deal has been publistled dealing with the experimental and theoretical aspects of the over-all corrosion process. Evans,1 Uhlig,' and recently Todt 3 and Tomashoff,4 have published books which review the results of experiments which have been conducted on corrosion, and have developed some of the basic ideas of the more widely accepted theories of corrosion. Friend5 states that. nickel does not readily discharge hydrogen from any of the common nonoxidiz-ing acids and that a supply of some oxidizing agent is necessary for appreciable rates of corrosion. He further notes that at temperatures between atmospheric and close to boiling, corrosion rates tend to vary with concentration, temperature, and aeration in acid concentrations up to 25 pct. Whitman and Russel6 studied the effect of dissolved oxygen on a number of metals in acid solutions and found that oxygen accelerates the rate of corrosion of nickel in sulfuric acid. Flowers and Kelley7 in studying the action of dissolved CO, on electroplated nickel postulated that nickel dissolves as NiHCO3 in the presence of CO, and air. It was found that oxygen was necessary for corrosion to take place and that the rate increased with increasing amounts of oxygen in solution. Flowers and Kelley attributed the oxygen effect to cathodic depolarization. MacGillavry, Rosenbaum, and wensson' determined metal solution potentials of nickel in various electrolytes. They found that nickel has no tendency to corrode in alkaline solutions in the presence or absence of air. In acid solutions in the presence of air, metal solution potential increases in the order of 1/2 v were observed. This increase was attributed to probable chemisorption of oxygen on the nickel surface and the corrosion mechanism suggested was the interaction of H+ ions with the nickel oxide formed at the surface. Delahay9 observed the reduction of oxygen on various metals. A polarograph was used to measure the course of the reaction. With some metals hydrogen peroxide was produced as an intermediate compound. However, nickel was not considered to be a hdrogen peroxide producer. Van Rysselberghe 10,11 and associates attributed the accelerating effect of carbon dioxide on the corrosion process to the presence of percarbonic acid produced in solution reacting with the hydrogen peroxide. The percarbonic acid can be reduced at less negative potentials than hydrogen peroxide and as a result accelerates the reaction. EXPERIMENTAL Since a complete description of the apparatus used can be obtained elsewhere,12'13 no attempt will be made here to describe the equipment other than to note that it consisted essentially of an autoclave unit from which samples could be withdrawn periodically without disturbing the interior state of the autoclave. A titanium autoclave liner was used to protect the autoclave from the solution.

Jan 1, 1961

By Ken-ichi Hirano, B. L. Averbach, Morris Cohen, N. Ujiiye

The influence of plastic deformation in compression on the self-diffisivity of a iron has been measured in the temperature range of 742º to 885°C. The diffusivity is enhanced in proportion to the strain rate, but this dependence decreases with increasing temperature. The magnitude of the strain is relatively unimportant in this connection. Strain rates from 0 to -2 x 10-3 sec-1 were investigated, with a corresponding increase in diffusivity up to 3 x 103 times. The results are analyzed in terms of vacancy diffusion and the excess vacancies introduced during dejornzntion. It is concluded that grain boundaries are the main vacancy sinks in polycrystalline iron and that the vacancy lifetime is therefore dependent on the grain size. A typical vacancy lifetime at 800°C with a nzean grain-boundary intercept of 0.3 cm is of the order of 1 sec. LATTICE imperfections are considered to be the dominant mechanism of diffusion in close-packed crystals. Vacant lattice sites are usually the most important defect, but the enhancement of diffusion along grain boundaries and other short-circuiting paths has been well documented. Inasmuch as plastic straining produces a variety of defects, it would be expected that the application of stresses sufficient to cause plastic flow during a diffusion run might result in an increase in the self-diffusivity. Enhanced self-diffusion in a iron under compressive creep has been observed by Buffington and Cohen' and subsequent coworkers.2 Lee and Maddin3,4 have also found an enhancement in the self-diffusivity of silver single crystals undergoing torsional deformation. On the other hand, Darby, Tomizuka, and Balluffi5 have not observed any significant diffusion increase in single crystals of silver deformed either in tension or in compression, although the results in this case may have been affected by the occurrence of recrystallization. With poly crystalline silver, however, Forestieri and Girifalco6 have found en- hanced diffusion during compressive creep. A small decrease in the self-diffusivity of zinc single crystals under compressive loading has been reported,7 but the applied stresses in these experiments were too low to cause appreciable plastic deformation. For the cases in which enhanced diffusion has been found, a number of common effects have been noted. Usually, the ratio of the diffusivity during straining, Ds, to the diffusivity in the unstrained condition, D,, varies linearly with the strain rate, and does not seem to be a function of the plastic strain, at least up to ? = 0.2. Values of Ds/Du of the order of 100 have been reported'-4 but the enhancement decreases with increasing diffusion temperature. The activation energy for diffusion decreases markedly with increasing strain rate and approaches a level of roughly one-half the unstrained value. Most of the current explanations of these observations assume that excess vacancies are generated by the deformation, but rather large concentrations of excess vacancies and/or long lifetimes are required by these theories.',',',' Since the original work on iron, there has been an important improvement in the compressive-loading technique.2 The early data were also analyzed without taking into account the motion of the coordinate system in the specimens undergoing plastic deformation. This problem has now been solved by a number of investigators (see Refs. 11, 12, and the appendix of the present paper). Consequently, the strain-diffusion runs on iron for the Ds measurements were repeated and extended over wider ranges of temperature and strain rate. In addition, the original diffusivity data9 on the unstrained iron have been corrected for the divergence of the beam in the counting system and new data points have been added, resulting in somewhat different values for the self-diffusi-vities in a iron.10 The new values for Du are used in this paper. A comparison of Ds and Du confirms the large enhancement in the self-diffusivity of iron during compressive creep, as previously reported.',2

Jan 1, 1963

By Gordon H. Geiger, John M. Svoboda

One mechanism of metal penetration into mold aggregates by cast steels is vapor state mass transport. In order to further understand and quantify this mechanism, the steady-state diffusion of metallic vapors was studied at 1250" to 1600°C in controlled oxygen pressure atmospheres by measuring the weight loss from a metal bath whose vapors were allowed to diffuse through a porous aggregate compact held at constant temperature. Mass transport rates substantially greater than those predicted from the assumption that the vaporizing species was the elemental metal vapor were observed. Vaporization rates were found to increase with an increase in the oxygen partial pressure in the gas atmosphere with maximum vaporization occurring at oxygen partial pressures just below those in equilibrium with a liquid oxide layer at the given temperature. When the liquid oxide layer was present, no vaporization was observed. Metal carbonyls were ruled out as the vapor species involved because of their thermodynamic properties. The species with the enhanced volatility were deduced to be gaseous metal-oxygen molecules, probably the polynuclear oxides (FeO)2 and (Mn0)2. Diffusion followed the ordinary diffusion mode, and Knudsen diffusion is not important in normal foundry molds. The interdiffusivities of the metallic vapors and the mold atmosphere, through the porous aggregates, were measured. The effective interdif-fusivity of the vapor species and mold atmosphere through the aggregate may be expressed as follows: Deff,12 - — where E is the void fraction of the aggregate and 7 is the "tortuosity factor". Aggregate material had no effect on diffusion rates, and the only relevant parameter was the void fraction. Values for 7 ranged from 3 to 6 for normal foundry aggregates with 4 being considered a good representative value. An area of interest in high-temperature metallurgical processes which has received little attention in the past is the diffusion of metal vapor species in porous aggregates. Research into the metal penetration phenomenon' in foundry molds has shown that a major penetration mechanism is the vapor transport of metallic species into the porous foundry sand molds, followed by condensation of metallic films on the sand grains. Considerable study of the vaporization of metallic species has been reported in the literature, and the vapor transport properties of many metallic species have been determined.2'3 Many instances have been observed where the vaporization behavior could only be explained by the existence of a metallic species with a vapor pressure greater than the elemental metallic species. These species were identified or, in some cases, presumed to be carbonyls,4,5 hydroxides,6-9 or vaporous oxides.10-16 The diffusion of gases through porous aggregates has received considerable attention in the literature pertaining to catalysis, although primarily at low temperature, and more recently in the literature concerned with ore reduction.17-22 The following experiments were devised and carried out in order to determine the nature of the metallic species involved in the metal penetration phenomenon, and the effective diffusivities involved. EXPERIMENTAL APPROACH Steady-state diffusion was selected for experimental convenience. The experimental systems used, shown in Figs. 1 and 2, consisted of a porous aggregate specimen contained in an impermeable alumina tube held above, and just separate from a metal bath. The entire system was held at constant temperature and pressure in a furnace with a controlled oxygen partial pressure atmosphere. After a brief period of nonsteady state behavior, a steady flux of metal vapor through the porous aggregate will develop due to the concentration gradient of metallic vapor in the gas phase. The flux of metallic vapor from pressure may be neglected because there is no pressure gradient. There is no flux from convection because there is no net flow of gas within the metal-aggregate system, and thermal diffusion is negligible compared to the flux from ordinary diffusion. If the material being studied is allowed to vaporize until steady-state behavior is attained, the experimental results may be analyzed using Fick's First Law.

Jan 1, 1970

By F. F. Skiba, J. E. Warren

An idealized miscible displacement process in a three-dimensional, heterogeneous porous medium has been studied via experimental computation based on a "Monte Carlo"' model. The macroscopic dispersion which results solely from variations in the permeability of the porous system is related to the scale of the heterogeneity as well as the distribution function for the permeabilities. The interpretation of laboratory data is often subjective and may bt? misleading since ambiguities are not always recognized. Furthermore, an experiment performed on a conventional oil-field core does not yield a valid measure of Macroscopic dispersion for reservoir engineering purposes since the scale of heterogeneity that is significant in the laboratory is not significant in the reservoir. The analysis of field-performance data is discussed and it is shown that a unique characterization of the reservoir can not be obtained from this information alone. A possible method based on a minimum of data, for estimating the spatial distribution of permeabilities in a reservoir is postulated INTRODUCTION Many studies concerned with diffusion and dispersion in porous media have been undertaken because of the potential importance of miscible displacement processes for increasing the recovery of oil. The results from a large number of these studies have been published; in a recent paper Perkins and Johnstonl presented a comprehensive survey of the pertinent literature and excellent appraisal of the "state of the art". In this investigation, dispersion resulting from macroscopic variations in the properties of the porous medium is of primary interest. Dispersion, in this sense, is caused by fluctuations in the velocities of the individual fluid elements as they move through the porous system. This phenomenon is the result of inhomogeneities in the permeability and/or porosity, but it can be amplified by differences in the characteristics of the fluids involved. The objectives of this study are the following: (1) to determine the qualitative manner in which macroscopic rock properties affect the observed dispersion coefficient; (2) to evaluate the possible influence of macroscopic dispersion on laboratory experiments; and (3) to appraise the significance of macroscopic dispersion with regard to reservoir performance. Investigations of this type are essential since many miscible displacement processes, while seemingly understood from a mechanistic point of view, do not behave in a predictable manner under field conditions. Although a plausible explanation is that the process is dominated by the environment, little serious effort has been devoted either to describing the reservoir itself or to determining the probable effect of the reservoir properties on the process. This study is intended to be exploratory in nature; however, it is hoped that it will provide additional insight into the physical problem and that it will suggest areas suitable for further investigation. EXPERIMENTAL COMPUTATION MODEL To limit the observed dispersion to that which results solely from variations in the properties of the porous medium, an idealized process in which one incompressible fluid displaces another identical fluid is simulated. This simulation is achieved by means of a modified Monte Carlo method — by tracking a number of mathematical particles (tracer) through the system according to the steady-state, single-phase velocity distribution. Then the system is characterized by the distribution of the residence times of the particles. Since any number of particles can be injected simultaneously (a true delta-function distribution) and only pressure conditions are imposed on the boundaries, the model is completely determinate. Furthermore molecular diffusion, microscopic dispersion, adsorption and/or reaction are automatically precluded from the model. The heterogeneous medium is represented by a rectangular, three-dimensional array of uniform, homogeneous porous blocks which are randomly arranged; it is assumed that any two opposing faces of the system are held at fixed potentials

Jan 1, 1965

By J. N. Chew, C. A. Connally

A correlation is presented for predicting the viscosity of gas-saturated crude oils under reservoir conditions. It is based on the dead oil viscosity and the solution GOR. The correlation was developed from a study which showed that at a fixed solution GOR, the relation between the gas-saturated oil viscosities and the correrponding dead oil viscosities is a straight line on logarithmic coordinates. Data from 457 crude oil samples from the major producing areas of the U. S., Canada and South America were used. The best straight lines through the data were fitted by the method of least squares with a digital computer. The correlation is presented in the form of an equation and also in a convenient gra-phical form. INTRODUCTION The viscosity of gas-saturated crude oils under reservoir conditions is an important physical property used in reservoir engineering calculations. Many difficulties are inherent in the sampling of gas-saturated oils and in the laboratory measurement of their viscosities. Therefore, it is frequently neither possible nor convenient to obtain measured values, so the viscosity must be estimated from other, more readily available data. This paper presents a correlation for predicting the viscosity of gas-saturated crude oils. The correlation is based on the amount of gas in solution and the viscosity of the dead oil at the temperature of interest. A previous correlation of these variables was presented by Beal. In comparison, the correlation presented here extends to a higher GOR and to a lower dead oil viscosity. Over the range of variables covered by both, this correlation is based on approximately 11 times as many oil samples. DEVELOPMENT OF CORRELATION A study was made of the variables or parameters which could be used to relate the viscosity of a gas-saturated oil to its dead oil viscosity. Preference was given to those variables which are easily and commonly measured in the field or in the laboratory. It was found that either the differential liquid formation volume factor or the solution GOR of the gas-saturated oil could be used as a correlating parameter. The solution GOR was se- lected for the correlation because of its simplicity and availability. In an attempt to refine the correlation by introducing a second parameter, the following additional variables were tested: differential liquid formation volume factor at the reservoir bubble point, the formation volume factor at the saturation pressure for the GOR of interest, reservoir temperature, viscosity of C+ fraction at 100°F and atmospheric pressure, weighted average gravity of gas in solution, oil gravity, reservoir bubble point pressure, saturation pressure at the selected GOR and reservoir temperature, and gas mol fraction. None of these improved the correlation to any significant extent. It was found that at any fixed solution GOR, the relation between the gas-saturated oil viscosities and the corresponding dead oil viscosities is a straight line on logarithmic coordinates, for the range of variables investigated. This straight-line relationship was used for the correlation. Viscosity data on a total of 457 crude oil samples were used. The data were obtained with rolling ball-type viscometers. The samples came from all of the important producing areas of the U. S., as well as from Canada and South America. Their geographical distribution is shown in Table 1. The ranges of properties represented by these samples are as follows: For each crude oil sample the viscosity of the liquid phase from each step of a differential liberation was plotted against its solution GOR on semi-logarithmic paper. A smooth curve was drawn through the points and values of viscosity in centipoises were read from

By K. Takahashi, I. Iwasaki

The methyl stretching vibrations for a series of normal xanthates, isoxanthates and normal amines were determined with the aid of an infrared spectro-photometer, and the results were compared with published information on the corresponding alcohols. The frequency shifts of methyl stretching vibrations may be attributed to the inductive effect of polar groups. The hydrogens in the shorter chain alkyl groups are somewhat polar and can be expected to interact with water molecules by hydrogen bonding. Contact angle, surface tension lowering, solubility, and critical micelle concentration appear to be related to the induced polarity of the alkyl groups. Traube's rule states that in homologous series of compounds solubility decreases and surface activity increases regularly with the size of the hydrocarbon group. Analyzing the work of transfer of a solute from solution to surface, Langmuir' interpreted this rule to mean that each CH2 group added to a molecule produced its effect independently of the others. It is also well known2 that the maximum equilibrium contact angle with sulfhydryl collectors is independent of the polar groups and of the sulfide minerals, and that it increases to a certain limit with the number of carbon atoms in the alkyl group. This observation is thought to demonstrate the orientation of the collector molecules at the sulfide surfaces. The dependence on the hydrocarbon chain length is usually explained as due to the screening of the force field of polar mineral surfaces.3-5 Here again, Langmuir's principle of independent surface action appears to be implied. Heteropolar compounds consist of nonpolar and polar groups, the former being the hydrocarbon group and the latter containing such electronegative atoms as O, N, S, P, or halogens. According to Palit6 the hydrogens in the alkyl groups are more electroposi- tive than in the paraffins owing to the negative inductive effect of the polar groups and a possibility that a hydrogen bond with water molecules ensues. Goto and Takenaka7 provided direct evidence of the inductive effect by measuring the shift of the C-H stretching vibrations of alcohols, acids, and alkyl bromides with an infrared spectrophotometer. Their approach appeared to be directly applicable to the studies of surface activity both at air-water and water-mineral interfaces encountered in flotation systems. The present article attempts to relate the C-H stretching vibrations of alkyl xanthates, alcohols, and amines with such flotation chemistry parameters as contact angle, surface tension lowering, solubility, and critical micelle concentration. MATERIALS AND METHODS Normal xanthates from methyl to octyl inclusive and the isopropyl, isobutyl, and isoamyl xanthates used in this investigation were prepared in the usual manner.8 Normal amine hydrochlorides with carbon chain lengths of 1, 2, 4, and 6 were from Distillation Products Industries, of 8 from Archer-Daniels-Midland Co., and of 10, 12, 14 and 16 from Armour and Co. Normal propylamines, pentylamines and heptylamines from Distillation Products Industries were used both as received and as hydrochloride formed by converting the amines according to the procedure described by Li9 Perkin-Elmer Model 521 and 621 infrared spectro-photometers were used to investigate the spectra in the frequency region of 3050 to 2800 cm-' with frequency scale expansion. The accuracy of the frequency readings was within + 1 cm-1. The KBr micropellet technique was used to prepare the xan-thate samples for measurements, and the halocarbon mull technique was used for amines and amine hydrochlorides. EXPERIMENTAL RESULTS Fig. 1 shows the CH3 asymmetric stretching vibrations as a function of the number of carbons in the alkyl group for normal xanthates, isoxanthates and amines. Also included in the figure are data for normal alcohols and isoalcohols taken from the article

Jan 1, 1970

By R. E. Goodman, M. A. Mahtab

The, state of stress around a vertical wellbore in rock following nonlinear stress-strain laws is examined by means of finite element analysis. The wellbore, is considered an axisymmetrier body with axisymmetric loading. The initial vertcal and borizontal stresses are "locked" in the rock elements around the wellbore and a new state of stress is generated by the displacements which occur around the borehole. A point-uise variation of the elastic moduli is made on the basis of the new stress state and the triaxial data. The initial stresses tire now reintroduced along with tile changed moduli and original boundary constraints. This procedure is repeatrd until convergent stresses are reached. The effect of nonlinearity on streases is examined for a 6,000-ft wellbore in a scbistose gnezss and Berea sandstone using results of laborratory triaxial compression tests. The results sbou that the effect is restrited to one well radius from the bottom periphery of the bole. Beyond a distance of one-quarter radius, the elfect of nonlinearity on stresscs IS almost always less than percent for the cases conszdered, The consideration of a static pressure inside the well does not magnify the effect of monlinearity on borehole stresscs. INTRODUCTION The terms " wellbore" and "borehole" here designate cylindrical openings in the ground with vertical axis and a circular cross-section. A knowledge of the stress redistribution that occurs on excavating a wellbore is important in understanding (1) the behavior of the lined or unlined hole, (2) hydraulic fracture response, and (3) the effect of stress redistribution on drillability; also it is important in predicting initial stresses in the virgin ground, and in analyzing the response of measuring instruments placed in the borehole. Our knowledge of the state of stress around a wellbore has been restricted to homogeneous, isotropic, elastic material and derives chiefly from the analysis by Miles and Toppingl and the photoelastic work of Galle and Wilhoit2 and Word and Wilhoit.3 In this investigation the state of stress is examined for a nonlinear elastic material by means of finite element analysis. Many rocks possess stress-strain curves that depart notably from straight lines in their initial or final portions. While the literature contains abundant stress-strain data from triaxial tests (axisymmetric loading) on cylindrical rock specimens, there is little information on rock deformability under nonaxisymmetric loading conditions such as occur at each point around the bottom of a wellbore. Although there is some knowledge of the effect of intermediate principal stress on rock strength, there is virtually nothing known about its effect on rock deformability; therefore, we have assumed here that the effect of intermediate principal stress can be ignored. A schistose gneiss4 and Berea sandstone5 were selected as representative rocks for this analysis. The traditional graphs of deviator stress (ol -o3) vs axial strain were reworked to give the tangent modulus as a function of the deviator stress for varying values of the minor principal stress. The result is a nesting family of skewed, bell-shaped curves for tile gneiss (Fig. 1A) and the sandstone (Fig. 2A). A similar replotting of the lateral strain data defines the variation of Poisson's ratio (v) with the deviator stress and confining pressure. These curves, shown in Fig. 1B for the gneiss and in Fig. 2B for the sandstone, are not so well ordered as the tangent modulus curves. However, all of these display an increase of v with deviator stress application, but the rate of increase diminishes with confinement. The ET and v curves for the two rock types are tabulated in Tables 1A and 1A for use in a digital computer so that material properties corresponding to a given state of stress can be assigned by interpolation. STATEMENT OF THE PROBLEM Given a state of stress in the ground prior to drilling a hole (initial stresses), we assume that

Jan 1, 1969

By R. P. Alger, M. P. Tixier, D. R. Tanguy

In the combination induction-electrical log used at present in the field, the induction logging tool is appropriate for the investigation of moderately invaded formations. A new induction sonde with a radius and investigation about twice as large has been developed recently for the case of deep invasion. It has very nearly the same vertical resolution as the present sonde so that thin beds are defined as accurately as before. The characteristics of the new tool are described, the corresponding interpretation charts are given and field examples are discussed. The design of the sonic logging tool has been modified to improve the calibration and the reliability. The fact that porosity can be accurately recorded by means of the sonic log has prompted new interpretation procedures for saturation estimation, wherein the data concerning the various permeable beds in a given well are correlated. One approach consists of plotting transit time vs true resistivity, with an appropriate scale. With this approach, saturations can be estimated conveniently even in cases where formation water resistivity is not well known. In another approach, a comparison is made of the values of the formation waters computed from the re- sistivity and sonic logs. Using the concept of continuity, this procedure makes possible a quick determination of zones of saturation in shaly sands and/or in case of appreciable variations of formation salinities with depth. It has been found that the comparison of porosity from the sonic log with the apparent porosity computed from a short-investigation resistivity log may reveal, in many cases, the presence of residual oil and thus detect potentially productive formations; this procedure is valuable when the true formation resistivity and the resistivity of the formation water are in doubt. INTRODUCTION During the past year, the efficiency of log interpretation has been vastly improved. The improvements have largely resulted from the introduction of a deep-investigation induction device and from the application of new interpretation techniques that utilize sonic vs resistivity readings. Since the new interpretation techniques depend, in part, upon good values of true formation resistivity, the new induction log will be discussed under Part I. The sonic interpretation techniques will be studied under Part 11. Early in 1959, the 6FF40 induction equipment was introduced in the field. This device was designed for a better approach to true formation resistivities in deeply invaded zones. The greatly improved radial investigation of the 6FF40 equipment has been achieved without sacrificing vertical resolution. The first combination induction-electrical log, the 5FF40, was introduced as a standard tool in 1956 for the logging of wells drilled with fresh muds. The tool has received wide industry acceptance in the United States. 'The 5FF40 induction log has a radial investigation sufficient to overcome average depths of mud filtrate invasion. At 5d invasion, for example, the 5FF40 induction log will read about 1.4 R. in a water sand where R., = 10R,. At 10d invasion, such induction log would read 2.45 R. in the same water sand. In either case, the effects of invasion would not be sufficiently great to cause a water sand to be mistaken for a shale-free oil- or gas-producing zone. Some formations, however, invade deeply — in excess of 10d. Such water zones could be mistaken for oil-or gas-saturated sands unless the porosity balance' can clearly make the distinction. It is for these deeply invaded formations that the 6FF40 was developed. CHARACTERISTICS OF THE 6FF40 Radial Investigation Characteristics To describe the comparative responses of the 5FF40

By H. R. Hanley

The characteristics of alloyed anodes and their influence on the products of electrolysis and power consumption have been noted previosly ously in the literature.' This paper presents data in continuation of the subject given in an earlier paper by the authors.2 As noted in the authors1 previous paper, the objectives of this work are the reduction in the cell voltage and the purity of the cathode product resulting from the use of alloyed lead anodes. The fundamental facts developed in the previous paper were: (I) that the presence of a small amount of calcium lowers the anode potential approximately 50 per cent. below that of pure lead; and (2) that thallium when present to the extent of 4 per cent. rendered the anode practically stable, thereby lowering the contamination of the cathode by lead to a very insignificant amount. The specific features determined in this recent work are as follows: 1. The lowest limit of calcium in the lead which will still give maximum lowering of the anode potential. 2. The characteristics of the thallium-calcium-lead anode. 3. The characteristics of the silver-calcium-lead anode. 4. The characteristics of the thallium-silver-calciurn-lead anode. It was determined that 0.1 per cent. calcium in the anode was sufficient to lower the anode potential approximately 50 per cent. Table 1 shows the characteristics of alloyed anodes tested. The anode composed of 0.1 per cent. calcium, 4 per cent. thallium, and 95.9 per cent. * Professor of Metsllurgy, Missouri School of Mines. t Professor of Metallurgy and Ore Dressing, Hea.d of Department, Missouri School of Mines. Assistant Professor of Metallurgy, Missouri School of Mines. 1 Among others, see C. G. Fink and Li Chi Pan: Insoluble .Anodes for the Electrol-ysis of Brine [Trans. Amer. Electrochem. Soc., (1926) 49, 83-1341 and other papers by these authors. U. CJ. Taintori, 8. G. Taylor arid H. P. Ehrlinger: Lead Alloys for Anodes in Electrolytic Production of Zinc of High Purity. Truns. A. I. M. E. (1929) 192-200. 2 H. R. Hanley, C. Y. Clayton, D. F. Walsh: Investigation of Anodes for Production of Electrolytic Zinc. Trans. A. I. M. E. (1930) 275

Jan 1, 1931

By L. G. Austin

If S (x) is the specific rate of breakage of size x and B (x, y) (see Table 1 for Nomenclature) is the cumulative breakage distribution function, the Herbst Fuerstenau2 assumption is that Inserting this assumption into first-order grinding equations it has been shown" that there are then simple analytical solutions to the grinding equations, as shown in Table 2. In this context "plug flow" is defined as all material passing through the mill in the same length of time, the residence time t. The term "n fully-mixed" means that the mill has a residence time distribution" which can be treated as if the mill were n equal fully mixed sections in series. In addition it has been shown that the assumption of Eq. 1 also leads to simple analytical solutions for closed-circuit, steady-state grinding with an ideal classifier at the mill exit returning oversize to the mill feed. The solutions are also given in Table 2, with µ as the ideal classifier cut size, C the circulation ratio, and Q (x) the size distribution of the circuit product. The specific surface area of these size distributions is where the density-shape factor k. is assumed to be constant with size. In practice, most methods of size analysis or area [ ] measurement have a finite lower limit, so that the integration is really performed from xm, to xm, For a realistic degree of grinding the value of So is dominated by the fine sizes because of the 1/x factor. Consider batch grinding of a feed of size y to y + dy. The batch grinding solution given in Table 2 is then [ ] The fresh surface area produced is the area of the fines plus the area of the original material remaining minus the area of the original material, [ ] Little error is introduced by neglecting the last term on the right-hand side since at t = 0 it is zero, and when t is significant the first term dominates because of the fine sizes produced. In addition, the form of P (x, t) for [ ] realistic values of S (x) 2t ax° is such that the major fraction of fresh surface produced is contained within the bottom 10% of weight of broken material, that is, for sizes for which P(x, t) < 0.1 (providing y is not near x.,). Thus for surface area purposes Eq. 3 can be approximated by [ ] becomes providing again that the feed sizes are coarse relative to xmi. Then the fresh area production is and W is the mass in the mill. The rate of surface production is WK, and the specific surface is Kt. From Table 2, the specific energy is mt/W so surface production per unit energy is [ ] Surface produced per unit energy input = KW/m (8) where m is the energy input of the mill. Clearly, identical reasoning applies to open-cycle, plug-flow grinding, with t replacing t, and Eq. 8 is obtained again. Considering open-cycle, fully mixed grinding, similar reasoning gives P(x) - t S(x) for surface area purposes, and

Jan 1, 1974

By Frank M. Monroe, James R. Cost

The solubility of nitrogen in vanadium is determined from 275" to 575°C by measuring the height of the nitrogen internal friction peak of equilibrated V-N alloys. The proportionality constant at 275°C between the internal friction peak height (Q- 1) and the atom percent nitrogen in solution is found to be 0.095 per at. pct for nitrogen concentrations up to 0.8 at. pct. The heat of solution of the nitride in vanadium is 5500 cal per mole. The solubility of nitrogen in the Group V metals is discussed. LITTLE work has been performed on the vanadium-nitrogen terminal solid solution. Hahn1 found the solubility for nitrogen to be very small and reported the existence of a hexagonal phase of composition near that of V2N at the solubility limit. Rostoker and Yamarnoto2 reported the solubility to be at least 3.5 at. pct at the melting point and to be less than this value at 900°C. In addition, they reported from X-ray diffraction studies that nitrogen in solution produces tetragonality in the vanadium lattice. An X-ray study by Schonberg3 has confirmed the results of Hahn but indicated that the tetragonality observed by Rostoker and Yamamoto was due to the presence of oxygen in their specimens. Beatty4 has performed lattice parameter and hardness measurements on terminal solid solutions and found the upper limit of the solubility to be at least 0.66 at. pct N. No measurements have been made of the pressure-temperature-composition relationships (P-T-X) for the terminal solid solution. As a part of a research program on gas-metal equilibrium, an attempt was made to study the P-T-X relationships in the V-N system using both the internal friction and the gas equilibration methods which have been successful with the Nb(Cb)-N and Ta-N systems (see Ref. 5 for a review of this work). Extensive investigation, using the gas equilibration methods, showed this method not to be applicable with vanadium This was presumably due to the gettering action of vanadium sublimed on the walls of the Sieverts apparatus. Thus, the nitrogen pressure relationships with temperature and composition were not obtained. The internal friction methods were, however, found to be applicable, and the temperature-composition relationships are reported in this paper and compared with similar results for the Nb-N6 and Ta-N7 systems. The existence of a Snoek internal friction peak due to nitrogen in solution in vanadium has been clearly demonstrated. 8-10 Powers and Doyle found the peak to be at approximately 275°C for frequencies near 1 cps.8 In a subsequent paper10 they reported the proportionality constant at 275°C between the internal friction peak height (Q-1) and the concentration of ni- trogen in solution (in atom percent) as 0.06 per at. pct. The studies of Stanley and wert9 indicated qualitatively that the height of the Snoek peak decreased with aging at the peak temperature and thus suggested that internal friction methods were suitable for study of the solubility. EXPERIMENTAL METHOD The vanadium for this investigation was of particularly high purity. It was obtained from the Ames Laboratory of the U.S. Atomic Energy Commission, Ames, Iowa in the form of a 1/2-in. diam, three pass zone-refined ingot. The electrical resistivity ratio (p300ºk/p4ºk) was 160. The initial composition was determined as follows: Carbon 200 ppm Oxygen 150 ppm Chromium <50 pprn Iron 125 ppm Silicon <50 ppm Other metallic 100 pprn The initial vanadium ingot was fabricated to 30-mil wire by swaging and wire drawing without the need of intermediate annealing. Lengths of this wire were then further purified (particularly for oxygen) by outgassing at 10-6 torr at 1400°C for 4 hr. The outgassing treatment resulted in specimens with a bamboo grain structure and a lustrous appearance. Desired amounts of nitrogen were added to the outgassed wires in a Sieverts apparatus in which known amounts of nitrogen were equilibrated with the wire at 1300°C. Nitrogen concentrations were produced in the desired range from less than 1 to 10 at. pct N. Monitoring of the partial pressure of nitrogen in the Sieverts apparatus indicated that at 1300°C equilibrium between the nitrogen gas and the vanadium was obtained within 10 min. Relatively rapid cooling from the nitrogen addition temperature was obtained simply by turning off the specimen heating current and cooling to room temperature in the partial pressure of nitrogen. Internal friction measurements of wire specimens were made under forepump vacuum in a torsional pendulum at frequencies near 1 cps. The torsional pendulum was of low thermal inertia and was designed so that specimens could be heated both by a conventional tube furnace and by the joule heating of a separate current through the wire specimen." Use of a static atmosphere of helium gas as a quenching medium made it possible to cut the specimen current, rapidly cool the specimen to the measurement temperature, and make a measurement of the internal friction in less than 1 min. Because of the large solubility of vanadium for nitrogen, the internal friction peak heights were in some cases greater than Q-1 = 0.1. This high damping resulted in an estimated relative uncertainty in the damping measurements of approximately 10 pct. X-ray analyses made to identify the precipitated ni-

Jan 1, 1970

By P. L. Hendricks, J. W. Spretnak

The interstitial atom principally responsible for the yield point and strain aging in electron-beam-melted tantalum is identified by analysis of the kinetics of the return of the yield point after an increment of plastic deformation. Two sets of specimens contained two levels of oxygen with very low hydrogen contents and the third set had comparable oxygen and hydrogen contents. The activation energy for the return of the yield point agrees well with that for diffusion of oxygen for the first two sets of specimens. For the third set of specimens, the activation-energy value lies between those for diffusion of hydrogen and for diffusion of oxygen. The advent of the dislocation model of plastic deformation in metals has revitalized interest in the yield point and strain aging in bcc metals containing a certain minimum content of interstitial solute elements. Much theoretical and experimental work has been performed in recent years to elucidate the detailed mechanism of these phenomena. The purpose of this investigation is to attempt to identify the principal interstitial element responsible for the yield-point phenomenon in electron-beam-melted tantalum by analysis of the kinetics of the return of the yield point after an increment of plastic deformation. Some of the earlier theories of the yield-point phenomenon proposed a grain boundary film of iron carbide. Such models could not satisfactorily explain all features of strain aging and the yield-point phenomena. The most widely accepted explanation is that of Cottrell,1 later extended by Cottrell and Bilby.2 Strain aging is ascribed to "locking" of dislocations by interstitial solute "atmospheres". The yield-point phenomenon results when the dislocations are torn away from their atmospheres. The strain-aged condition is re-established after sufficient time to allow the interstitial atoms to diffuse to the dislocation lines and re-establish the locking atmospheres. Clearly, the Cottrell-Bilby model is concerned with the bulk of the grain and does not specifically involve the grain boundary. The recent modification of the Cottrell-Bilby model is a redirection of attention to the role of the grain boundary and the possibility of multiplication of a limited number of free dislocations rather than unlocking all of the dislocations. Theories have been advanced by Hahn3 and conrad4 which are modifications of the Cottrell-Bilby theory. The model proposed by Hahn indicates that, although the possibility of un- locking anchored dislocations is not excluded, it implies that unlocking is not necessarily required to explain yield drop. Locking of dislocations during the aging treatment is a necessary part of the theory; however, it assumes that dislocations once locked remain locked. It is suggested that the yield drop observed is a result of the following factors: 1) the presence of a small number of mobile dislocations initially, 2) rapid dislocation multiplication, 3) the stress dependence of dislocation velocity. In the case of bcc metals, locking is considered to be the means by which dislocations are immobilized. Cold working of the metal results in the generation of larger numbers of new dislocations and the stress dependence of the dislocation velocity accounts for yield drop observed. Conrad&apos; has proposed a model similar to the one just described which applies to strain aging of iron and steel and which logically could be extended to other bcc metals. This model also does not require large-scale unlocking of dislocations. It is proposed that, during initial loading of a specimen below the upper yield stress, a few dislocations are torn free of their Cottrell atmospheres at regions of stress concentrations. With an increasing stress, some multiplication of dislocations occurs by a double cross slip mechanism, thus giving a preyield microstrain. At some critical stress represented by the upper yield stress, sudden profuse multiplication of dislocations occurs, enabling plastic flow to proceed at a lower stress. In this model, microstrain, preyielding, and flow represent the movement of free dislocations. It should be noted that this model also requires the locking of dislocations by interstitial solute atoms for the occurrence of a yield point; however, unlocking of large numbers of dislocations is not required. If it is assumed that the yield point will return when some fraction of free dislocations produced during pre-straining are pinned, the number of solute atoms required to pin unit length of a dislocation line can be calculated when prestrain and reloading are done at the same temperature and strain rate. Since the migration of solute atoms back to the stress fields of dislocation lines is controlled by the diffusion rate of interstitial solute atoms, it is to be expected that the activation energy for strain aging would be identical to the activation energy for diffusion. It would also be expected that the strain aging observed will be controlled by the fastest diffusing species capable of producing locking over the temperature range investigated. The rate of yield-point return has been found to be adequately expressed by an empirical rate equation of the form: rate=Ae-Q/RT [1] where A = constant, Q = activation energy, R = gas constant, and T = absolute temperature. Cottrell and Bilby2 have expressed the number of atoms per unit length of dislocation line which arrive

Jan 1, 1967

By W. M. Yim

Experimental results are presented which indicate that transverse striations in horizontal zone-leveled Bi-Sb alloy crystals are due to irregular growth rate resulting from thermal fluctuations in the melt (Iring gowth. Thc thermal fluctutations arose from two different sources. The first type was brought about by periodic fluctuations in the furnace temperature. The second type can be attributed to turbulent therrrol conlcclion in the trzelt near the solid-liquid inteyace. Tile arrzplitlcde ond fvequency of the tetiperaticre fluctlrations vesultity from llle lhevnal con1,ecrrell. The striation spacings in Lhe crystals covvelale well with the periodicity 0.f the tempevature flueluatiors. Altliough the strialiors represenl corrlpositiozul inhoiHogeneity oh a rzicroscule, less than f.z cil. be1 S6 in Best&apos;s as deterrirzed by electron-pro be chalq&apos;sis, the slriations roerre fbund to ILUL&apos; no rrleusuanble effect on electical vesistirity rwr on weak field macgnetoresistance of. the Bi-Sb a1lu.y in the ternpevutue ),unge 4.Polo 300°K. DURING the course of an investigation on the horizontal growth of semimetals,&apos; it was found that crystals of Bi-Sb alloys contained many closely spaced parallel arrays of striations. These striations occurred perpendicular to the growth direction and parallel to the solid-liquid interface. We shall refer to them as transverse striations, or just striations&apos;&apos;, to distinguish them from lineage substructures or longitudinal striations which form parallel to the growth direction and have been known to be associated with cellular structures.&apos; Similar transverse striations have been reported previously to occur in other materials prepared by horizontal growth: metals,4 semiconductors,5 as well as their alls. - Various methods of crystal preparation have apparently little effect on the occurrence of the transverse striations. They form whether the crystals were grown by the vertical Czochralski technique, withe1&apos; or without&apos;3- rotation, or by the horizontal zoning methd.- Thus, the transverse striations are not limited to any one class of materials, nor to any particular method of preparation. It is likely, therefore, that all of the observed transverse striations may have some common cause. Previously, workers agreed that periodic changes in the growth rate bring about the striations. However, no agreement exists as to the origin of the growth-rate fluctuations. Some attributed the discontinuous growth to a purely external cause, such as fluctuations in the furnace temperature, jerky motions in the crystal pulling mechanism, or a nonsymmetrical temperature distribution in the melt (in the case of crystals grown by the Czochralski technique with rtation). Others looked for the cause in some fundamental property of the growth process itself. For instance, a certain degree of supercooling is required to initiate growth from the melt. But, with further growth, the degree of supercooling decreases because of the liberation of the heat of solidification at the solid-liquid interface. Thus, crystal growth would be brought to a halt until sufficient supercooling is resotred and the cycle begins again.3&apos;11 According to this model, periodic fluctuations in the melt temperature should exist at the solid-liquid interface. Since the periodic fluctuations in growth rate would result in changes in the segregation coefficient of solute atoms, crystals containing the transverse striations may, in some cases, show a periodic impurity fluctuation along the length, resulting in a degradation of electrical properties. The resistivity striations in doped germanium&apos;9-10 or lnsbB are well-known examples of this microsegregation. The present work was undertaken to explain the exact origin of the transverse striations, and to assess the extent of their effect on chemical homogeneity as well as on electrical properties of Bi-Sb alloy crystals. Results from our previous study of the crystal growth of Bi-Sb alloys1 indicated that the transverse striations may arise from the temperature fluctuations in the melt during growth. This paper will show that the melt temperature fluctuations are indeed responsible for the occurrence of the transverse striations. I) EXPERIMENTAL Although the transverse striations have been observed in all slow-grown Bi-Sb alloys across the entire compositional range, we selected a composition, Big3Sbs, for the present study in view of the extensive data available on the crystal growth of this alloy from a previous study.&apos; High-purity bismuth and antimony, both a 6-nine grade by the manufacturer&apos;s emission spectrographic analysis, were used throughout. Independent mass-spectrographic analysis showed, however, that the starting materials were more nearly a 5-nine grade. each containing metallic impurities of approximately 10 ppm atomic. In zone-leveled Big5Sb5 alloys, the total metallic-impurity content was slightly lower, about 7 ppm atomic, indicating that some degree of purification was achieved during the growth. None of the electrically active impurities, such as tin and lead (acceptors) and tellurium and selenium (donors), were present in significant quantity in undoped Bi95Sb5. Typical analysis of the undoped Bi95Sb5 alloy is shown in Table I. Nonmetallic impurities, such as carbon and oxygen, were detected, sometimes as much as 100 ppm, in both the starting materials and the zone-leveled alloys: but the data were only qualitative. Temperature fluctuations in the melt were monitored over 1 or more days by means of a 5-mil chromel-

Jan 1, 1967

That the chemical industries are alive to the situation that they now occupy in the sum of affairs is evident in the preparations being made by many firms for the Second National Exposition of Chemical Industries To be-held at the Grand Central Palace, New York City, during the week of September 25-30, 191 The list of exhibitors indicates that the Exposition is already twice the size of its successful predecessor. The American Chemical Society will hold its annual meeting during the whole week, the American Electrochemical Society has arranged to - hold its meetings on September 28, 29 and 30, and the Technical Association of the American Pulp and Paper Industry is also planning to meet during the week. The Bureau of Commercial Economics at Washington is again co- operating with the Exposition by arranging an elaborate program of motion pictures covering subjects dealing with the industries depending on chemistry. Many of these films will have their first showing at the Exposition. They will take the visitor through industrial plants, shops, manufactories, mines, etc., where visitors are never admitted; they will show operations that in ordinary light would never be seen; they will demonstrate more than any other kind of motion picture the great strides and improvement in the art of photography.

Jan 8, 1916