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By Lyman Johnson

Single crystals qf copper in "single slip" orientatiorzs have been deformed in compression. During defortnation all of the independent deformation parameters have been measured. These parameters consist of thefive strain components and three components descrihing the lattice rotation. By a finite strain analysis these pararmeters , forrming a deformation gradient martrix, are related to the amounts of slip on each of the twelve slip systems. The results show that the amount of secondary slip is about equal to the amount of primary slip. This is an order of magnitude larger than has been believed previoutsly. ACCORDING to early theory and experiments, when a single crystal of a fcc metal is deformed in tension or compression it should deform by slip on only one slip system until the stress axis reaches a symmetrical orientation.' However. the observation of a large increase in the secondary dislocation density during ..single slip" makes it clear that some slip does occur on secondary systems. Knowledge of the amount and distribution of this secondary slip is essential to a complete understanding of the mechanisms of single-crystal deformation. Ahlers and Haasen 2 and Mitchell and Thornton1 have tried to detect the amount of secondary slip in single crystals of silver and copper, respectively. Each simultaneously measured the angle A, between the tensile axis and the primary slip direction and the length 1 of a gage section of the specimen after incremental amounts of deformation in tension. The measured A, was then compared with the theoretical single slip angle hp. given by sin Ap = j sin . hO where ?o was the initial angle between the tensile axis and the primary slip direction and lo was the initial gage length. In both sets of experiments a small but systematic difference between ?e and ?p was found. This difference must be due to the occurrence of secondary slip. However, as Mitchell and Thornton1 pointed out. nothing quantitative can be said about the amount and distribution of this secondary slip from the measurements that they made. The reason that no quantitative conclusions could be made is because no unique solution for the distribution of slip on the twelve fcc slip systems can be determined from only two measured deformation parameters such as A and 1. There are, in fact, eight independent macroscopic deformation parameters that can be measured when a single crystal undergoes a homogeneous deformation. Physically these can be thought of as the five finite strain components and the three angles describing the crystal lattice rotation. All eight of these parameters were measured by Taylor4,5 for aluminum deformed in tension and compression. At that time the concern was to show that slip occurs on {111 (110) systems in fcc metals, and the mathematics were not available to determine what slip distributions were compatible with the measurements. In this paper the mathematics6,7 are developed that allow the slip distribution to be determined from these measurable macroscopic deformation parameters. The analysis is applied to the measurements of the strain and lattice rotation of copper single crystals deformed in compression. The results show that the amount of secondary slip is an order of magnitude larger than had previously been thought. CRYSTALLOGRAPHIC DESCRIPTION OF A HOMOGENEOUS DEFORMATION The deformation of a solid body can be represented by a transformation matrix F that transforms the un-deformed state into the deformed state. Consider a vector X connecting two material points in the unde-formed material and the vector x connecting the same two material points after deformation, where both vectors are referred to the same set of Cartesian axes. The final vector x is related to the initial vector X by the equation: X = FS. [2] Eq. [2] can be considered as the equation defining F, which is called the deformation gradient matrix. Its components are: If the deformation is homogeneous, the transformation is linear and the components of F are constants. Using subscript notation, if P is the unit vector in the initial direction of a material line, the components of the unit vector p in the direction of the same material line after deformation are given by:

Jan 1, 1970

By John E. Hockett

The need for basic information about the relationship between resistance to dejormatim (flow stress), temperature, strain, and strain rate, for the solution of metal-fovming problems, is pointed out. Some early attempts to satisfy the need are mentioned. A brief description of a machine called a Cam Plastome-ter is given, including the processing of results of testing in the machine. Next, a program of testing aluminum in compression over a wide range of constant true-strain rates (0.1 to > 200 sec-1) and a modevately broad range of temperatures (223° to 673°K) is described. The results of this program are presented in the form of true-stress us true-strain cuvves. The data in these curves are presented in the form of relationships between true stress and true-strain rate in sermilogarithmic and log-log form, as functions of temperatures—for several true strains. Finally, true stress, for a given true strain, is displayed as a function of log true-strain rate and absolute temperature, i.e., a surface. SINCE the publication of Hill's book1 on plasticity theory, increasingly rapid advances have been made in analytical solutions to forming problems. Methods in common use are the slab method, the uniform deformation energy method, the limit analysis method, the slipline field method, and the semiexperimental method called "visioplasticity". These approaches, and examples of their use, are covered in detail by Johnson and Melloor2 and by Thornsen, Yang, and Kobayashi.3 unfortunately, practically all of the above work has had to rely upon a number of basic assumptions, e.g., homogeneous deformation and Coulomb (sliding) friction; and virtually no dependence of the mechanical behavior of the deforming metal, upon temperature, strain, and strain rate, has been included. It is with this dependency that this paper is concerned. Loizou and sims4 looked at the above relationship for lead using both a constant compression-speed Cam Plastometer and a constant true-strain-rate Cam Plastometer designed by Orowan.5 Alder and Phillips8 investigated the relationships for aluminum, copper, and steel in the same constant true-strain-rate Plastometer. cook7 tested twelve steels at temperatures ranging from 1170° to 1473°K in the same Plastometer over a range of true-strain rates of 1.5 to 100 sec-'. The writer tested commercially pure aluminum at room temperature and depleted uranium at temperatures from 573" to 873°K at strain rates from 10-3 to 1.0 sec-1 in a Cam Plastometer designed and built at Los Alamos Scientific Laboratory.8 During the past few years the Cam Plastometer at Los Alamos has been used for a number of relatively minor experiments on brass, mild steel, duralumin, Armco iron, and depleted uranium. In this time the machine has been continually modified and improved. It was decided to utilize fully the wide range of strain rates now available with the machine by testing a material about which some information was already in the literature. Prior work on commercially pure aluminum6 appeared to deserve confirmation and expansion. So it was decided to explore the resistance to compression of this material over the currently available range of constant true-strain rates and a convenient range of temperatures. This paper is a report of that exploration. I) EQUIPMENT AND PROCEDURE The principal item of equipment is, of course, the Cam Plastometer, the working part of which is shown in Fig. 1. In this figure, an aluminum specimen may be seen between two tungsten carbide platens, in position for a room-temperature test. Above the upper carbide platen is a load cell. Output from the load cell is amplified and applied to a galvanometer in a recording oscillograph. Auxiliary equipment includes the oscillograph, the control console, a counter, and a time-mark generator. The counter is first used in adjusting the time base. Then it registers the count, of sixty pips per revolution generated by the rotating cam, in each second. These pips and the time base are also applied to galvanometers in the oscillograph. Thus, load, time, and cam position are recorded simultaneously. Heating of a specimen prior to compression is done

Jan 1, 1968

By J. D. Verhoeven

The effectiue distriblltion coefficient has been Measured in a series of vertical, normal freezing experirtzents with large current densities passing through the solid-liquid interface. The results indicate that the effect of the current on solute redistribution is due to electvotransport in the liquid. The high currents produced extensive mixing in the liquid which was considerably reduced by solidifying in small lubing. Analysis of the convection indicates that it probably vesulls from a horizontal temperature gradient produced by the Joule heating- of the electvic crirver~t. Due to the strong dependence of this convection upon the specimen radius, it is conclnded that only for specit~ens with radii of less than somewhere between 1 and 2 mm wilt electric field freezing be getlerally effec-tire at enhancing the purification of zone-melting experittierats in loe-melting alloys. Experiments on 0.8-mm lubes illustrate some interesting potential applications of this techniqne as a means of solute control on smcrll specimens. In a number of papers published within the last few years'-4 it has been found that passage of large dc currents through the solid-liquid interface of a freezing alloy produces a change in the solute redistribution accompanying the solidification. It had been predicted theoretically by Hucke et al.s and by Pfann and Wagner that such an effect would occur as the result of electrotransport within the liquid boundary layer at the solid-liquid interface. These authors independently derived the following relation between the effective distribution coefficient and the variables of the process: Where k0 is the equilibrium distribution coefficient, V is the mobility of the solute relative to the solvent, E is the electric field intensity, D is the solute diffusion coefficient, R is the rate of interface motion, and 6 is the boundary layer thickness. Both groups of authors show that this equation predicts the possibility of extending the purification ability of zone-melting experiments by the addition of an electric current. However, there are other effects in addition to electro-transport which could be produced by the high dc current and might, perhaps, invalidate the applicability of Eq. [I]. For example, high electric current might affect the interface reaction or perhaps the equilibrium distribution which was assumed to exist at the interface. It was the purpose of this work to determine the applicability of Eq. [I] by systematically investigating a simple system for which all of the necessary parameters were known. It was of particular interest for speculating on the potential usefulness of this technique to determine the maximum practical field intensities obtainable, and the effect of these high fields upon convective mixing in the liquid. The initial work in this study was published in a previous paper3 which will be referred to as I. In that work, a current density of 2000 amps per sq cm was used with specimen diameters of 5 mm. The results gave a qualitative confirmation of Eq. [I.], and also showed that a large amount of convective mixing was produced in the liquid by the current. The present study is an extension of that work to smaller specimen diameters and higher current densities. Two points were overlooked in I and will be emphasized here: a) the value of ko has not been well-established in the Sn-Bi system and b) the observed convection could be due to thermal convection produced from the Joule heating. EVALUATION OF k0 To evaluate Eq. [ I.] it is necessary to know the value of the equilibrium distribution coefficient, k,. Tn I the value of k, was taken as 0.3 from a published phase diagram.7 According to ansen' the best data on the phase boundaries of the Sn-Bi system are those of Davidson.5 The data of Davidson give a k, value ranging from 0.21 to 0.25 for the compositions studied in this work, or an average value of around 0.23. In a recent publication, Rigaud and Tougas'10 determined ko by means of a solidification technique. For an alloy of approximately the same composition as that used in this work they obtained a ko value of 0.39. Hence, there is considerable uncertainty in the value of ko and, consequently, a series of experiments were made to determine k, more accurately.

Jan 1, 1968

By A. D. Rovig, D. W. McGlashan, Donald M. Podobnik

Crystal-chemical and stntctural properties of sulfide minerals are considered. The information gained is to be used to interpret (I ) freshly broken mineral surfaces, (2) modifications of the mineral surfaces, and (3) reactions at the mineral surfaces. From these basic disciplines, concepts with regard to the changes that surfaces undergo, reactions that might take place, the geometry of the interface, the state of different atoms and ions in the interface, and other physical and chemical properties of an interface must be developed, weighed and applied. The authors first deal with these conceptual considerations from which hypotheses are set forth to describe the environ men tal-interfacial relationships for several sulfide minerals. Qualitative and quantitative explanation of par-ticulate solid separations are unknown entities because of the lack of adequate models and mathematical relationships to explain the activity occurring between the solid and liquid phases. It is a transitional region in which it is difficult to ascertain the mechanisms of adsorption of ions, molecules, etc., on mineral surfaces, as well as other secondary reactions which occur in interfacial regions. Thus, in this paper the authors deal with conceptual considerations from which hypotheses are set forth to describe the environmental-interfacial relationships for sulfide minerals. GENERAL CONSIDERATIONS Interfacial Reactions:Interfacial reactions are the cruxes of flotation schemes as well as other processes such as thickening, filtration and hydrometallurgy. However, as noted by Klassen and Mokrousov: 1 "The problems concerning the surfaces of natural minerals, the laws governing simultaneous adsorption from aqueous solution on these surfaces of a whole series of reagents, the laws of the surface reactions and the properties of water layers separating the minerals, are all known to a first approximation only." An investigator has the privilege of postulating methods of solid-liquid interfacial reactions. REACTIONS WITH WATER - Water consists of hydronium (H3 O 4) and hydroxyl (OH-) ions in the ionized state. That this is so forms the basis for the postulated reaction of the hydrated hydrogen ion with net-negative mineral surfaces as depicted in Fig. 1. In this case water is bonded to mineral surfaces through hydrogen-bridge-type bonds - possibly hydrogen bonds. Although bonding of the van der Waal type may be responsible for this reaction, it is most likely that stronger bonds are involved. Once firmly bonded to the surface, the water layer is known to be quite tenacious. It is further speculated that a shear plane exists at some distance (see Fig. 1) away from the mineral surface. Exact location of this plane is not known, but in all probability it will be positioned across a weak bond of the hydrogen-bond type where the surface-attached water is coordinated to the original hydrated hydrogen ion. REACTION WITH METAL IONS - Klassen and Mokrousov ' state: "The presence of an ion in water leads to an immediate formation around that ion of a highly condensed atmosphere of water dipoles and thus to hydration of the ion." The fact is known that multivalent cations are strongly hydrated, usually by six or eight molecules of water, and that anions are not so strongly hydrated. Conceding the fact that thermodynamics, concentration, pH, and physical considerations are of utmost importance in truly explaining a mechanism of metal ions reaction with a hydrated mineral surface, it does seem logical that the mechanism illustrated in Fig. 2 is feasible. In this reaction, the metal ion (M) is coordinated in one dimension - to the mineral-surface hydration layer. Note also that explanation of this reaction requires that the shear plane move to a less stable bond configuration; that is, the shear plane has moved to a position between the metal ion and the other coordinated water molecules which are more free to dissociate. Reactions as depicted in Fig. 2 should cause the formation of an apparent mineral surface which is net-positive. Immediately, it must be noted that measurements of apparent-mineral surfaces serve - within limits - to indicate a degree of ion-surface reaction capability. The major limiting factor he re is one related

Jan 1, 1970

By Craig R. Barreft, Oleg D. Sherby

The steady-state creep characteristics of pure polycrystalline copper were studied in the temperature range 400" to 950°C and in the stress range 400 to 7000 psi. Tests were conducted in dry deoxidized hydrogen and all specimens exhibited high ductility before fracture. Two activation energies for creep were established as a function of temperature. Above about T/T, = 0.65, the activation energy for creep was 48,000 cal per mole whereas between 0.5 and 0.65 T, it was 28,000 cal per mole. The observed temperature dependence of the activation energy for creep follows the same trend as exhibited by the self-diffusion coefficient of copper in copper single crystals and silver in silver single crystals. It is therefore believed that the rate-cmtrolling mechanism in creep of copper in the stress and temperature range studied is diffusion-dependent and is probably associated with a dislocation-climb process. The low activation-energy region is attributed to enhanced volume difFusion from the presence of dislocations which act as short-circuit paths for diffusion. THERE is extensive experimental evidence1,2 that the activation energy for creep, Q,, for pure poly-crystalline metals tested at temperatures above one half the absolute melting temperature (0.5 Tm) is a constant and equal to the activation energy for volume self-diffusion, Qsd This equality is generally interpreted as meaning that creep in this temperature range is controlled by a dislocation-climb process. The existence of high-temperature creep activation energies not equal to the respective self-diffusion values has been suggested both theoretically3"5 and experimentally.6-8 Two examples of apparent nonequality between Q, and Qsd have been reported for the cases of silver7 and copper,' where activation energies for creep much lower than those for self-diffusion persist to rela- tively high temperatures (up to 0.6 T,). These observations suggest that dislocation climb may not be the only important process in the high-temperature deformation of these metals. That dislocation climb does indeed occur relatively slowly in these two metals due to their low stacking-fault energy has been suggested by many investigators.9-10 Although the creep behavior of copper has been studied extensively at low temperatures, the high-temperature activation energy for creep is not well-defined. The data of Feltham and Meakin8 indicated that Q, is temperature-dependent above one half the melting temperature, equaling a value of -30,000 cal per mole at temperatures up to 550°C and increasing to a value of -49,000 cal per mole at 700°C. No data has been reported above 700°C. The value of 49,000 cal per mole is very near the value of Qsd for copper reported by Kuper et al." as 47,100 cal per mole. In view of the lack of high-temperature creep data and the apparent temperature dependence of Q, for copper the present investigation was undertaken to determine the value of Q, over the temperature range of 400" to 950°C. It was hoped that such a study would clearly document the temperature dependence of Q, and yield significant information as to the nature of the rate-controlling creep mechanisms. MATERIALS AND PROCEDURES The material used in this investigation was high-purity OFHC copper. After rolling and recrystal-lization treatments spectrographic and chemical analyses showed only 0.0008 pct Ag, 0.0002 pctCa, 0.0002 pct H2, and 0.002 pct O2 as trace impurities indicating a purity of greater then 99.995 pct. Specimens were machined from cold-rolled sheet and the gage sections polished with 2/0 emery paper prior to annealing treatments. Annealing was done in both vacuum and dry deoxidized hydrogen atmospheres. No variation in creep strength was found as a result of the different annealing atmospheres. The final annealing temperature was either 700°, 800°, or 1000°C depending on the temperature range to be studied. These treatments resulted in average grain diameters of 0.03, 0.4, and 1.0 mm, respectively. The precise mechanical-thermal history of these

Jan 1, 1964

By B. H. Caudle, L. G. Davies, I. H. Silberberg

This paper presents a method of predicting the recovery and performance of a five-spot steam injection project, in which a realistic approach to pattern sweepout efficiencies is made. Published methods for radial systems were modified for the five-spot pattern by approximating the stream lines with straight lines radiating from the injection well and then converging to the producing well. In each radial segment, the position of the steam front and the temperature profile ahead of the steam front were determined by heat balance equations, which included an estimation of heat losses to surrounding formations. The location of the saturations behind the cold water front was determined from a Buckley-Leverett solution to the material balance equation. Results from this program show steamflood recovery in a five-spot pattern to be considerably less than that predicted for true linear or radial flow systems. For a specific reservoir containing 900-cp oil, a steamflood in a purely radial flow system was predicted to recover more than 75 percent of the original oil in place when 2 PV of water had been injected as steam. A five-spot steamflood with otherwise identical properties was predicted to recover 10 percent of the original oil in place when 0.15 PV of water had been injected as steam and to recover almost no oil thereafter. A cold water five-spot flood in this system was predicted to recover approximately W percent of the oil in place with I PV of water injected. For a five-spot pattern in an example reservoir with 10-cp oil, steam injection similarly showed lower ultimate recovery than water injection but no improvement in recovery rule. Introduction The thermal recovery method considered in this study is steam injection in a five-spot pattern. Pattern steam injection has been given little attention in the past, possibly because of some rather obvious disadvantages. Unless steam temperature is maintained throughout the entire swept area, the process will revert to simple waterflood with all heat being lost prior to reaching the oil bank. Also, the oil viscosity reduction takes place near the steam front and not around the producing wellbore, so that low producing rates must still be endured. This is the reason for the success of the steam stimulation, or cyclic injection, in which the fluids are produced from the same well used for injection. On the other hand, steamflooding can offer some advantages. Oil displacement is by four methods: (1) mechanical displacement by the condensed water, (2) viscosity reduction of the crude oil, (3) swelling of the crude oil, and (4) distillation of the crude oil in the steam zone. Although dependent upon the crude, laboratory experiments have shown displacements up to 80 percent by steamflooding. In addition, steam is a good heat transport medium, since it is cheap and has a high heat content. Previous Investigations Previous publications have reported methods for predicting recovery in a steamflood for linear and radial systems. Since no pattern sweep efficiency is taken into consideration, the recovery even from a radial system must be greater than from more realistic geometries such as the very common five-spot patterns. Probably the broadest coverage is given by Willman who reported experimental results and offered a method of predicting recovery for a radial flow system. They concluded that both hot water and steam injection recover more oil than an ordinary waterflood, and that steam injection could yield recoveries "as much as 100 percent greater than by water flood." They also concluded that both the heat requirements for a reservoir and the residual oil remaining in the reservoir after steam injection were independent of the amount of oil originally in place, that short exploitation times were desirable, and that a high percentage of net sand in the reservoir with a high initial oil saturation was desirable. The method assumes that the flood occurs in three concentric cylindrical zones: (1) an inner steam zone, (2) a central hot water zone, and (3) an outer cold waterflood zone. Displacement in the steam zone is based on laboratory-determined residual oil saturations while the hot water and cold water zones use the conventional Buckley-Leverett equations. Although the results shown by Willman et al. are for a radial system flowing out from the well to an assumed external circular boundary, their equations did

Jan 1, 1969

By Kenneth A. Moon

An exact statistical treatment of a one-dimensional model is used as a basis for evoluating the reliability of certain simplified expressions for the activity of the solute in interstitial solutions, including one obtained from the exact expression by setting the repulsive interaction equal to infinity. The latter approximation is found to be satisfactory at low and moderate concentration if the repulsive interaction is large, even though not infinite. A similar expression (identical if the co-odination number is two) is derived from the quasichemical expression of Lacher, and is recommended as the best available expression for the excess configurational entropy of interstitial solutions with excluded sites. Some reasonable models are discussed, and the nature of the saturated solutions is determined by inspection. Some of the models reduce to the one -dimensional case. An analysis is given of the excess partial entropy of hydrogen in V-H; Nb-H; and To-H solutions. MOST treatments of the statistical thermodynamics of interstitial solid solutions have followed the classic paper1 of Lacher in making the simplifying assumption that the configurational entropy of the solution is ideal. However, it is becoming increasingly apparent that there are many interstitial solutions with very large so lute-solute repulsions, and for these the assumption of ideal entropy is not valid or useful. It is important to realize that with substitutional solutions large repulsions between the component atoms must lead to phase separation, whereas in interstitial solutions the free energy of the solution is not drastically increased by large solute-solute repulsions until intrinsic saturation is reached at the concentration where further solute would be forced to enter a site in which it would experience the repulsive effect of one or more solute atoms already present. In the limiting case of an infinitely large repulsive interaction, the excess free energy would be attributable entirely to excess entropy, the enthalpy of mixing being zero. AS will be shown below, even if the repulsions are less than infinite, a treatment based on an assumption of infinite repulsions may be very satisfactory up to moderately high concentrations of the interstitial component. Often in solutions where large repulsive interactions exist, there are also small interactions — often attractive—between solute atoms in configurations other than that corresponding to the large repulsion. In such cases the excess free energy will consist of an excess entropy term attributable to the large repulsive interactions, and an enthalpy term corresponding to the other small interactions. Nomenclature to differentiate succinctly between important cases would be a convenience. In this paper the nomenclature shown in Table I will be used. In Table I, and in the preceeding discussion, excess quantities are defined in terms of standard states which are pure solid solvent and pure (possibly hypothetical) solid saturated phase of the structure in question. In practice, it is more convenient to choose the interstitial element as a component, and its conventional standard state. This will add a composition-independent term to the excess entropy and the enthalpy. The earliest paper known to the present author which treats the thermodynamics of athermal interstitial solutions was given by schei12 in 1951, but the statistical derivations in that paper are open to criticism. Speiser and Spretnak were the first to give a correct statistical treatment,3 limited, however, to concentrations sufficiently low that the number of empty sites excluded from occupancy by more than one filled site is negligible. The purpose of the present paper is to extend the statistical treatment to more concentrated solutions, and to examine the magnitude of the errors introduced by assuming that the repulsive interactions are infinite when in fact they must be finite. THE QUASICHEMICAL APPROXIMATION Fortunately, a standard method already exists for taking into account the effect of large interactions upon the entropy of mixing. This is the quasi-chemical method, in which the probability of existence of a given pair of solute atoms in a certain proximate configuration is assumed to be proportional to exp(-w/kT), where w is the energy increase of the solution when the two atoms are moved from isolated locations in the solution to the configuration in question. A quasichemical treatment of interstitial solutions was given in 1937 in a widely neglected paper by Lacher.4 The result comes out

Jan 1, 1963

By Charles R. Stewart, William W. Owens

Reservoir performance predictions based on laboratory core test data assume that fluid flow is laminar for the laboratory test. A study has been made to determine the validity of this assumption for laboratory tests on various types of porosity found in producing limestone formation. Data are presented which show that turbulence and slippage can occur during laboratory tests on hetero-geneous-type porosity limestones, thus causing serious errors in measured single-phase permeabilities and two-phase relative permeability characteristics. In single-phase flow tests it is possible to eliminate turbulence and correct for slippage or to eliminate both factors by controlling test conditions. It is not always possible to control test conditions and thereby eliminate turbulence and slippage in two-phase .flow tests. A correction method is presented which can be used to calculate the true two-phase laminar flow relative permeability characteristic even though furbulence and slippage exist. .INTRODUCTION It is customary to make use of Darcy's law and modifications of this law, together with laboratory data on formation core samples to predict the performance of producing reservoirs. Such predictions are based on an assumption that fluid flow is in the laminar or streamline region for the laboratory test. It was the purpose of this inves- tigation to determine the extent to which turbulent flow may occur in laboratory fluid flow tests on hetero-geneous porosity limestones. Considering that turbulent flow conditions might exist in some laboratory fluid flow tests, additional emphasis was placed on the development of a method to correct for turbulence when laminar flow conditions could not be attained. FLUID FLOW CONCEPTS FOR POROUS MEDIA The Influence of Pore Geometry on Fluid Flow One of the more important factors influencing fluid flow in porous media is the geometry of the pore space which includes such characteristics of the pores as size, shape, distribution, roughness, uniformity, etc. In general, oil- and gas-producing formations can be divided into two broad types on the basis of pore geometry. One has been called sandstone-type porosity media, which is characterized by a small range in pore size, uniformity in shape of the pores, smooth pore surfaces and a regular and uniform distribution of pores. The other type has been called heterogeneous porosity media and is usually limited to the dolomites and limestones. This type is characterized by a wide variation in the size, shape, and distribution of the pores and rough, irregular pore surfaces. It is therefore apparent that conditions are much more favorable for turbulent flow* in heterogeneous-type porosity media than in sandstone-type porosity media. Interrelationship Between Turbulence and Gas Slippage In studying the problem of turbulent flow in laboratory tests on porous media, it is necessary to be aware of the interrelationship between slippage and turbulence for gas flow. As a result of slippage or the Klinken-berg effecta, apparent perrneabilities to gas are greater than the true value because there is no stationary layer of gas in contact with the walls of the flow channels. Gas slippage decreases as the mean free path of the gas molecules decreases. Since the mean free path of any gas decreases with increasing density, increases in static pressure result in lower apparent gas permeabilities. However, a reduction in gas permeability can also be due to turbulence. Therefore, in studying only turbulent flow in porous media, it is necessary to hold gas density, and slippage, constant or to reduce slippage to a negligible value by operating at high static pressures. Presentation of Laminar and Turbulent Flow Data A graphical relationship between permeability and a pseudo-Reynolds number, N,, will be used to show the two types of fluid flow, i.e., laminar and turbulent. The usual graphical method for such a description has been the use of friction factor-Reynolds number charts4. On such a logarithmic diagram, the laminar region appears as a straight line having a slope of 45 degrees. As the friction factor decreases and the Reynolds number increases, the turbulent region is reached and appears as a deviation from the 45-degree slope line. However, in petroleum engineering literature resistance of por-

By N. Schapiro, R. J. Gray, G. D. Coe

A petrographic and chemical investigation was conducted to determine the occurrence and distribution of the organic and inorganic forms of sulfur in various size and specific gravity fractions of a high volatile, A-rank, Pittsburgh seam coal. The investigation was conducted to aid in the resolution of the problem of how metallurgical coke of lower sulfur content can be produced from high sulfur coals. The Pittsburgh raw coal contains about 2.4% S in two dominant forms: pyritic and organic. Pyritic sulfur constitutes about 57% of the total sulfur in the raw coal and occurs in macroscopic and microscopic-size particles. A plant cleaning process mechanically separates between 50 and 60% of the pyritic sulfur, mainly the macroscopic particles. The organic sulfur constitutes 41% of the total sulfur in the raw coal and 55% of the sulfur in the washed coal. Thus, organic sulfur is not reduced by physical methods of separation. Organic sulfur occurs in all the coal entities, but in general, increases as the exinoid content of the coal increases. In this study, it was found that carbonizing certain selected low gravity coal fractions containing an average of 0.45% pyritic sulfur and 1.01% organic sulfur produced cokes containing an average of 0.22% pyritic sulfur and 0.91% organic sulfur. However, the organic sulfur in the coke is probably derived in part from the heating of pyrite in the presence of carbon. Thus, the total sulfur in the coal carbonized is the most important factor affecting the sulfur content of the coke produced. Concentration of microscopic pyritic and organic sulfur in the middling-type coal indicates the necessity for rejecting as much of this material as is economically feasible. Most of the sulfur introduced into the blast furnace originates from the coke. Although the sulfur content of the hot metal can be controlled by the addition of flux, the flux used restricts the productivity of the furnace by displacing ore and requires first to be smelted; therefore, low sulfur coke is highly desirable. Since the sulfur content of coke is dependent upon the sulfur content of the coals from which the coke is produced, low sulfur coals are required to produce low sulfur coke. In the western Pennsylvania area, large quantities of good coking coal are available from the Pittsburgh seam, but this coal unfortunately contains relatively large quantities of sulfur. To provide information that might be useful in reducing the sulfur content of this coal in the cleaning process, an investigation was conducted to determine the physical and chemical forms in which this sulfur occurs and with what petrographic components it might be associated. The Pittsburgh seam coal, like most other coals, contains two dominant forms of sulfur: one occurs as the minerals pyrite and/or marcasite and is referred to as pyritic sulfur; the other is combined with the coal substance and is called organic sulfur. Pyritic sulfur is amenable to physical methods of separation, whereas organic sulfur is not. Pyritic sulfur particles must be freed from the surrounding coal if they are to be removed in the washing process. Generally, this requires crushing; the required degree of crushing being a function of the size and distribution of the pyrite. The present investigation was conducted to 1) determine the size, distribution and association of sulfur-bearing minerals in the coal and 2) to determine whether the organic sulfur has a preferential association with specific coal entities. If a preferential association exists, this knowledge may be useful in devising a method for organic sulfur reduction. In addition, a study was made to determine the extent to which pyritic and organic forms of sulfur in the coal contribute to the sulfur in the coke produced from this coal. A representative 3%-ton sample of raw coal was crushed to —3 in. and screened into square-mesh sizes: 3 to 1 in., 1 to % in., % to % in., % in. to 10 mesh, 10 to 35 mesh, and 35 to 200 mesh. Separate samples of the -200-mesh fraction and the all-size composite were also collected. Each size fraction (except the -200 mesh) was fractionated on heavy liquids of the following specific gravities: 1.280, 1.300, 1.325, 1.350, 1.375, 1.400, 1.425, 1.450,

Jan 1, 1963

By Shiro Ban-ya, John Chipman

The effects of many alloying eletnents on the acticity coefficient of sulfur in liquid iron have-been studied by the equilibriutn in the reaction Sfin Fe) + Hz = HzS at 1550°C'. Results are expressed in terms of a concentration variable for a nonmetallic or for a substitutional metallic solute. Activity coefficient of sulfur, defined as increased by B, Al, C, Si, Ge, Sn, P, As, Sb, Mo, W, Co, and PI. It is decreased by Cu,Au, Ti. Zr, V, h'b, Ta, Cr, ,23n, and Ni. Irulues oj. the interaction coejficient 0i = 6 In are labulated. The same interactions are expressed also in terms of atom fraction and of weight percent. The thermodynamic properties of sulfur in liquid iron have been fairly well established. Our recent paper1 reported new determinations of activity coefficient up an atom fraction of 0.12 and equations based on a careful review of all published data. The effects of alloying elements on the activity of sulfur have been studied by several investigators,2"11 especially by Morris and Williams for silicon,' by Morris and Buehl for carbon,~ and by Sherman and Chipman for manganese. phosphorus, and al~minum.~ However, the effects of some important alloying elements remain to be determined. The purpose of this investigation was to determine the effects of many alloying elements on the activity of sulfur in Fe-S-j ternary systems. EXPERIMENTAL METHOD This study was based on experimental determination of equilibrium in the reaction at 1550°C: The same apparatus and procedure as described in our previous paper have been retained, and the same corrections were applied for dissociation of H2S. The alumina crucibles used in the experiments consisted of four separate compartments. In a given experimental run. kach of three alumina crucibles held four different samples of about 3 g each which reached equilibrium in the same gas atmosphere and temperature. The charges were made up of electrolytic iron, pure iron sulfide, and desired alloying elements, which were pure metal or master alloys made in the laboratory. The weighed samples were held for 4 to 12 hr in the prepared atmosphere at 1550°C. They were then low- ered to be cooled as quickly as possible. The quenched metal beads were crushed to avoid the errors of segregation in the ingot. The sulfur content was determined gravimetrically and alloy content by appropriate chemical analysis. CALCULATIONS The apparent equilibrium constants of Eq. [I] are expressed as follows from the corrected gas ratios and sulfur concentrations: The term K" is the observed equilibrium constant in any given ternary solution, K' is the value for the Fe-S binary solution. and the limiting value of K' in the infinitely dilute solution is designated by K, which is the true equilibrium constant in Eq. [I]. In the thermodynamic treatment of nonmetallic elements in a metallic solution, it has been suggested1' that the lattice ratio has certain advantages over other variables to express the concentration of solute. In interstitial solid solutions the lattice ratio zj is proportional to the ratio of filled interstitial sites to those which remain unfilled. The equations derived for the activity of the solute using zj as the concentration variable are found also to be applicable to liquid solutions containing nonmetallic solutes when the nonmetal is treated as if it were interstitial. For this purpose we adopt the following definitions: The quantity vj which is negative for interstitial solutes is taken as -1 for nonmetallic and +1 for metallic solutes. For purposes of calculation however ; j may be assigned a value which results in a linear relation such as shown in Figs. 1 to 15. The activity coefficient of sulfur, Qs, and equilibrium constant. K(z). are defined as follows: According to a Taylor series expansion. the logarithm of the activity coefficient of sulfur in Fe-S-j ternary system is: However, the value of 6 In */6zi remains constant through a broad range of dilute solutions and the terms of higher order are negligibly small. As a consequence, Eq. [6] is simplified as follows:

Jan 1, 1970

By K. Mukai, M. Ishihara

This report is a brief discussion of the impurity levels both in primary aluminum and super-purily alnminim in connection with raw materials and proc-essing methods. Particularly, truce amounls of im-purities were analyzed by introducing nittss-speclro-gruphy and nenlron-aclivalian analysis techniques. Vanadium and gallium content in primary aluminum metal corresponded to theor amounls in anode coke. but the nickel content in primary aluminum was hide-pendent oj its amount in the anode cake. Sulfur in the anode colic might result in an increase of the iron content in the molten metal in the reduction cell. The content of sodium and calcium increased with increasing bath ratio. In the holding furnacc sodium content decreased rapidly, and nonmetallic inclusions merit separated front the mollen metal. Three-layer elctrolysis was effectire in eliminating many impuri-ties with the exception of copper, aluminum oxide. aluminum nitride, and some rare-earth elements. THE amount of impurities and nonmetallic inclusions in aluminum metal depends on impurities in the raw materials and various production processes. This paper presents an investigation of the behavior of impurities and nonmetallic inclusions in aluminum during the electrolysis process, the period in the holding furnace, and the process of three-layer electrolysis. Chemical analysis and emission spectrometric analysis have generally been used as methods to determine small amounts of impurities in both primary aluminum and super-purity aluminum; however. mass spectrography and neutron-activation analysis have been recently introduced into this field, and trace amounts of impurities can accurately be determined by these latter methods. EXPERIMENTAL WORK Common impurities were determined by means of absorptiometric. polarographic, flame-photometric. and emission-spectrometric methods. However, in the determination of trace amounts of impurities and non-metallic inclusions, the following methods were applied. In the analyses of trace impurities by mass-spec- trographic analysis, samples were exposed in the vacuum spark of double-focus ing Mattauch-Herzog type mass spectrograph (Japan Electron Optics Laboratory, Ltd.). Ilford Q2 photographic plates were used as ion detectors. Fe was used as the internal standard, and the atomic concentration of each element was calculated by the following expression and converted into the weight concentration: where E, and Ei are the exposures (coulomb) when isotopes of the internal standard and impurity elements (on which the estimate is based) show the same density, X is the percent (atomic) concentration of the standard, IF and Ii are the percent abundances of the isotopes of the standard the impurity elements (on which the estimate is based), and Ms and hfi are the mass of the isotopes of the standard and impurity elements (on which the estimate is based). The coefficient of variation in this method is about 40 pct in the range of 0.1 to 1 ppm. In neutron-activation analysis, irradiations were done in the nuclear reactors TRIGA-I1 (neutron flux: 4.7 x 10 11 n per sq cm per sec; Rikkyo University) or JRR-2 (neutron flux: 2 x 1013 n per sq cm per sec: Japan Atomic Energy Research Institute). After the chemical separation, a NaI (3 by 3 in.) scintillator connected to a 256-channel y-ray spectrometer (R.C.L.) was used for counting and recording various activated impurities. The coefficient of variation in this method is about 20 pct. In the analyses of nonmetallic inclusions, aluminum-oxide determination was carried out according to Fischer's method, 3 as follows. A slice of sample was cut off and the surface was cleaned. It was dissolved in bromine-methanol. The solution was filtered and the residue was washed. The residue was fused with potassium bisulfate flux. Then it was dissolved in weak acid, and oxine solution was added. The aluminum oxinate was extracted with benzene. Finally, aluminum was determined absorptio-metrically. Aluminum nitride determination was carried out as follows. A slice of sample was cut off and the surface was cleaned. It was put in the distillation apparatus and decomposed with sodium hydroxide solution. The solution was distilled. Then ammonia was absorbed and

Jan 1, 1967

By Pradeep K. Rohatgi, Clyde M. Adams

Structures obtained on freezing of several hypo-and hypereutectic Al-Cu alloys over a range of solidification rates have been examined. Dendrite spacing, L, increases linearly with solute concentration and with the square root of the inverse freezing rate. The relationship for hypoeutectic alloys is: where rate of change of fraction solid with time, is freezing rate, C is solute concentration, (pct Cu)=1. Mass transport in inter dendritic liquid during solidification is analyzed; the experimental observations suggest maximum concentration differences and constitutional supercooling in the inter dendritic liquid increase with an increase in the solute concentration. The dendrite morphology changes with freezing rate and alloy composition. The dendrites of the a phase are parallel, uniformly spaced plates with slow freezing and rods with rapid freezing. Nonor-thogonal side branching has been observed in phases with cubic and tetragonal structures. Side branches in a dendrites are orthogonal with slow freezing and at 60 deg with rapid freezing. Formation of second-phase envelopes around the Primary phase is also discussed. DENDRITIC structure is characteristic of many types of phase transformation. The most extensively studied so far has been solidification of liquid solutions. chalmersl and coworkers have interpreted the formation of dendrites in terms of the breakdown of a planar interface. Most of the work done concerns itself with the development of an instability at the interface. Little theoretical work has been done quantitatively to relate the parameters of dendritic structure to mass transport in the liquid phase. A few empirical relations based on the experimental2'3 observations exist in the literature. Several workers2 including Brown and Adams1 have studied dendrite spacing in A1-Cu system as a function of solidification variables. In most cases, dendrite spacing has been found to increase linearly with the square root of some parameter proportional to the freezing time. The effect of solute concentration is not clear; some workers report the dendrite spacing increases with solute concentration4 whereas others report vice versa.''' ~ohatgi' has observed an increase in the spacing between ice dendrites with an increase in solute concentration in water. Tiller has also suggested that dendrite spacing should increase with solute concentration. In the present work dendrite spacing and morphology have been examined as a function of solute concentration and freezing rate. The freezing rate is defined as the fraction of liquid solidified per unit time, dfs/dß?, where f, is the fraction solid and 8 the time. The fastest freezing rate studied was 4550 times the slowest freezing rate. THEORETICAL CONSIDERATIONS It is of interest to analyze the concentration distribution in the liquid phase between growing dendrites during solidification, Fig. 1. Since this distribution is a direct consequence of the rejection of solute by the growing solid, a diffusional process, the concentration gradients increase with the freezing rate. However, when solidification rate is the only variable in a series of experiments, the interdendritic liquid regions become smaller (i.e., the dendrites become more closely spaced) with an increase in freezing rate. The main purpose of the analytical treatment of interdendritic liquid diffusion will be to reveal a tendency for dendrite spacing to decrease with increasing solidification rate in just such a way that the maximum concentration differences developed in the liquid phase are remarkably independent of freezing rate. Two rather different analyses are set forth, one pertaining to the one-dimensional diffusion which obtains in the interdendritic liquid between parallel plate-shaped dendrites, and the other to the cylindrically symmetrical diffusion around rod-shaped dendrites during early stages of solidification. The results of the two analyses are quantitatively similar, correlating dendrite spacing, maximum concentration difference, and freezing rate. First consider the simpler one-dimensional case. Two parallel plate-shaped dendrites are separated by a distance, L, between centers, Fig. 1. Solidification takes place by the thickening of these plates, with solute being rejected into the liquid. It is assumed there is no diffusion in the solid. This thickening process is slow enough and the dendrite spacing small enough that the concentration differences which develop, although interesting and important, are very small (an important assumption which is verified ex-

Jan 1, 1968

By Craig R. Barrett

The influence of the stress dependence of the dislocation density on the overall stress dependence of The steady-state creep rate is discussed. Experimental measurements of dislocation densities and creep rates jor an Fe-3.1 pct Si alloy tested over a wide range of stress are presented which indicate a close correlation between the two quantities. EXPRESSING the stress dependence of high-temperature steady-state creep rates has been the subject of numerous investigations over the past decade. From these investigations have emerged a few general equations which fit most of the available data reasonably well. Garofalo 1 has proposed that for a wide range of stress and temperature the creep rate, i, can be expressed by a relationship of the form: where A, ß, and n are temperature-dependent and is the applied stress. Eq. [I] gives a stress dependence of a at low stresses and exp(nßo) at high stresses, both consistent with experimental observation where n = 5. A number of other investigatorshave proposed a similar expression where: where m and w are in general functions of temperature. Theoretical justification for Eqs. 111 and [2J comes from two different approaches, theories based on dislocation glide3-5 and theories based on the balance between work-hardening and recovery.' Dislocation glide theories predict where p is the mobile dislocation density and V is the activation volume. In order for Eq. [3] to predict a on stress dependence at low stresses with n = 5, it is necessary for p to be a strong function of stress, about proportional to u3 or u4.436 Recovery models of creep start with the general expression:' where r is the recovery rate and h is the work-hardening rate, and then employ a detailed model to determine the stress dependencies of r and h. As example, weertman2 has described a model based on pile-up hardening which results in an expression similar to Eq. [2] with m = 2 and p = 2.5. A recent, seemingly more general approach suggested by McLean is to use Friedels dislocation network growth expression to calculate the stress dependence of r. This model predicts r = p 3,2 and, as h is taken to be a relatively weak function of stress, the stress dependence of i should be about proportional to p3, 2. Once again, it is required that p be a strong function of stress to yield i This recovery model is by no means complete as the stress dependence of network growth is calculated in the absence of an applied stress meaning that r should probably be a stronger function of stress than given by p3, 2 and also some recent work by Mitra and McLean8 suggests that the stress dependence of h may be as large as Because of the importance of the stress dependence of p in determining the overall stress dependence of the strain rate it seems reasonable to examine this relationship in some detail. Measurements made on dislocation densities present during high-temperature steady-state creep generally obey the following relationship a =o0 + aGVWp [5] where uo is usually called a friction stress, a is a numerical constant about equal to unity, G is the shear modulus, and b is the Burgers vector. Depending on the magnitude of uo, data obeying Eq. [5] can give rise to a range of stress dependencies of p. For example, if we assume that the expression where 6 is some constant, adequately represents the stress dependence of p over a range of o, then from Although Eq. [6] obviously breaks down when u 5uo for uo 6 can vary over a wide range of values. In particular, if u > a, > 0 then 6 will be greater than 2. As an example the data of Ishida and McLean are plotted in Fig. 1 showing excellent agreement with dynes per sq cm) and also showing good agreement with a p cc u3 dependence when plotted on a log-log basis. As oo increases 6 tends to increase and correspondingly the stress dependence of the predicted creep rate should also increase,* as-

Jan 1, 1968

By L. D. Mullins, E. B. Elfrink, W. L. Wahl

In the past few years several articles and papers presenting results of solution gas-drive depletion calculations have appeared in the lit-erature. Such calculations are of interest to the oil industry, for investment decisions must often be made before much is known about a reservoir. At other times, an estimate of the possible benefits to be realized from alternate production methods is desirable, and theoretical depletion calculations can serve as a floor or reference level from which to work. In any case, an estimate of ultimate oil recovery based upon engineering data is commonly required. An engineer confronted with the problem of obtaining, for a specific reservoir system, an estimate of ultimate oil recovery by solution gas-drive depletion usually will be forced to perform the calculations himself. This is despite the quantity of data in the literature. Rarely will either experience or the literature provide results from a reservoir system similar in all important respects to the one under consideration, and calculated results are not so plentiful that satisfactory interpolation procedures can be devised. Performing the calculations, however, is a tedious, time-consuming task unless an electronic computer is available, and, in practice, time and manpower are not always available for this purpose. A quick, simple, consistent method was needed for reducing the uncer- tainty in estimated oil recovery from solution gas-drive reservoirs when only minimum information about the reservoir system is available. PROCEDURE Method of Calculation The usual requisite assumptions were made so that the material balance equation could be used to calculate data for the charts. The following assumptions were made: (1) the reservoir is homogeneous and isotropic; (2) oil recovery is due entirely to solution gas drive and neither a gas cap nor a water drive nor gravity drainage is present; (3) the initial reservoir pressure is the bubble-point pressure of the reservoir fluid; (4) initial total liquid saturation is 100 per cent of pore space; (5) interstitial water saturation remains at the initial value as the reservoir pressure declines from the bubble-point pressure to atmospheric pressure; (6) equilibrium gas saturation is 5 per cent of pore space; and (7) oil and gas saturations are uniformly distributed throughout the reservoir at all times. There are no saturation gradients due to a wellbore, nor is the geometry of the reservoir system considered. The material balance equation was written in the form of a differential equation' which was integrated to determine the change in oil saturation for an assigned pressure drop. Formal integration was not possible, so recourse was made to the Runge-Kutta method' of numerical integration. All computations were performed on IBM equipment. Numerical integration yielded the change in oil saturation within the reservoir as the pressure. declined from the bubble-point pressure to atmospheric pressure. The initial oil saturation minus the change in oil saturation yielded the oil saturation at atmospheric pressure. The oil originally in place was obtained by dividing the initial oil saturation by the initial formation volume factor (differential liberation) while the oil in place at atmospheric pressure was obtained by dividing the final oil saturation by the formation volume factor at atmospheric pressure. U1timate oil recovery, expressed as a percentage of the initial oil in place, was obtained by dividing the difference between the oil initially in place and the oil in place at atmospheric pressure by the oil initially in place and multiplying by 100. PVT Data Charts were based upon 135 solutions to the material balance equation. PVT properties of the reservoir fluids were variables in this equation and had to be known as functions of pressure. The required PVT data might have been obtained from either actual reservoir fluid systems or correlated data. However, correlated PVT data were developed and employed in the calculations for the following reasons: (1) it is doubtful that 135 sets of PVT data could have been obtained for the values of variables investigated in this study, and (2) results of recovery calculations from randomly obtained PVT data could not be correlated as well as rssults from selected PVT data. The PVT data used to develop the

By W. A. Tiller

The conventional techniques1 for determining the liquidus and solidus surfaces of an alloy system containing more than two components are extremely tedious to use and do not provide a complete picture of the equilibrium relations between solid and liquid alloys. These techniques are unable to yield "tie-line" information concerning solid and liquid phase equilibrium, a very important parameter in the solidification description of the liquid alloy and a very necessary parameter in the preparation of "zone-levelled" alloy crystals. The tie-line in a polycomponent system is analogous to the partition coefficient, k, in a binary system, it gives the composition of the solid, Cs, in equilibrium with a liquid of composition CL. That is, CS = kCL, where CL = [CO, c1,...Cn] denotes the concentrations of the n + 1 constituents, and k = [ko, kb ,...kon] denotes the gross partition coefficient for the elements between the two phases; thus, k is the tie-line in this system. To provide complete information concerning the two-phase equilibrium in a polycomponent system it is necessary to know both the liquidus surface and the gross partition coefficient. From these two the solidus surface is obtainable. The conventional techniques are unable to provide this information in other than a binary system so we must look elsewhere. In recent years considerable insight has been gained into the correct description of the liquid-solid transformation, 2,3 and controlled solidification experiments may now be designed to both facilitate and enhance equilibrium diagram studies. In the present paper consideration is given to two methods for obtaining the liquidus surface and the tie-lines in polycomponent systems. The methods to be described below deal with the solidification of an n + 1 constituent liquid alloy of initial composition [co, Co ,...Con], where the superscripts refer to the elements present and the Oth element is considered as the solvent in which the n solutes are dissolved. The general assumptions made in the treatment are the following: (i) the solid and the liquid at their interface are in equilibrium during the growth of the solid phase, (ii) there is no diffusion in the solid phase, and (iii) the liquid phase is completely mixed and is therefore homogeneous in concentration. METHOD I In this section a general experimental method will be described which, in principle, is capable of giving an exact description of the liquidus surface and tie-lines. Consider the unidirectional solidification of the liquid alloy specimens L cm in length (freezing either horizontally or vertically). Allow the sample to be frozen very slowly from one end, as indicated in Fig. 1, with complete mixing in the liquid, and then analyze the solid bar to determine its chemical constitution as a function of position, x, along the bar. Let Fig. 2 represent a possible distribution of the ith constituent along the bar. At the point x' the concentration of the ith constituent is C1/5(x'), and the average concentration of the rest of the bar between x' and L is given by C:(X' - L) where [ A(x) c1s(x)dx c1/s(x'-L) = f A(x) dx x * and A(X) is the cross-sectional area at x. In a similar manner. all the Cf(x' - L) may be determined. Thus, the gross artition coefficient k for liquid of composition [Cs(x - L),...Cs(X' - L)] is given by -ko= CUs')/Cos(x' - L)" k0 = csn{x')/cs(x'- L) During the freezing of a charge of length L, the liquid composition may vary over a wide segment of the phase diagram and the gross partition coefficient over this segment of the phase diagram may be determined from one, bar. Fig. 3 illustrates the magnitude of Cs(g)/C,' as a function of the fraction g of the bar which has Solidified.2 We can see that the concentration in the bar will vary over a range of about 15 wt pct for C,' = 10 wt pct and k0 = 0.5. It appears that 4 or 5 specimens would be adequate to study a simple binary eutectic phase diagram.

Jan 1, 1960

By C. P. Miller

In order to determine the usefulness of geochemical and biogeochemical prospecting for nickel, ten localities representing several types of nickel occurrences were selected as sites from which to collect plant and soil samples. This report covers the investigations in two of the areas. After a brief geologic description of the areas, the author presents details of the experimental tests and resulting data. Conclusions drawn from the studies led to several general guides for further prospecting. In a study of the usefulness of geochemical and biogeochemical prospecting for nickel made about three years ago, approximately ten localities, representing several different types of nickel occurrences, were sampled and about 1500 samples of plant and soil were collected. This report will cover briefly the data and results for two areas, and a summary of guides for prospecting. DESCRIPTION OF AREAS SAMPLED One locality is the Red Flats nickel prospect in Curry County, Ore., about six miles southeast of Goldbeach, and the other is the Little Rocky Creek prospect in Stillwater County, southcentral Montana, just southeast of the Benbow chromite mine. The Oregon area is a lateritic-type nickel deposit formed on a nickel-rich serpentinite peridotite complex, similar to the Josephine intrusion in southwestern Oregon. The Montana area is a nickel prospect in norite, peridotite, and related rocks of the Stillwater igneous complex. The Stillwater complex is a series of layered basic and ultrabasic rocks, with a layer of norite-gabbro at the base and a series of peridotites and gabbros above. The nickel in the Oregon deposit occurs in both the peridotite and the overlying soil. A deep lateritic soil is developed locally on the peridotite and serpentinite and constitutes the ore. The average nickel content of the lateritic soil is less than 1 pct, whereas the nickel content of the weathered peridotite is about 1 to 1.5 pct. The nickel occurs as garnierite (Mg, Fe, Ni, Mn)3 (OH)4 (SiA1)2O5 in the soil and in the olivine and pyroxene in the peridotite where it probably substitutes for Fe2+ or Mg2+ in the silicate lattices. Nickel is found in three distinct ways in the Still-water rocks: 1) it is in the olivine and pyroxene minerals in norite, harzburgite, etc.; 2) it occurs as widely disseminated grains of pentlandite-pyr-rhotite, which tend to be concentrated in the lower norite band; and 3) it occurs as discrete bodies of pentlandite-pyrrhotite and chalcopyrite which are localized in the norite zone, close to the contact with the underlying rocks. The nickel content of the norite is probably less than 1 pct, and the nickel content of the pods and lenses within the norite is about 1 pct. PROSPECTING APPROACH Although the areas are different geologically, the approach in prospecting them is fundamentally the same. The procedure is twofold: 1) a rapid reconnaissance survey to outline an area of high nickel content, and 2) a more detailed survey to outline zones of possible ore grade within the area of high nickel. The possible ore at Red Flats is concentrated in the lateritic soil, whereas at Little Rocky Creek it is in the sulfide pods. Both types are surrounded by an area of relatively high nickel content. CHEMICAL ANALYSIS Chemical analyses of nickel were made by a di-methylglyoxime colorimetric test, similar to the standard test for nickel, utilizing concentrated sul-furic acid for extraction. The lower limit of detection for nickel in soil by the method used was about 10 ppm and for nickel in plants about 5 ppm. The relative deviation was about 25 pct. SOIL PROSPECTING General Statements: A summary of the approximate average parts per million of nickel in soil, as compiled from the literature and from my study, is given in Table I. Selected references are given at the end of the paper. Few of the investigators reported the type of extraction or analysis, so the data given may not be strictly comparable to mine, which were made with a sulfuric acid extraction. Any nickel concentration greater than these average values might be considered anomalous, although each area must be studied in relation to the surrounding rocks. Method of Soil Sampling: The soil samples were taken in a zone from 1 in. to 1 ft below the humus layer, and within a 15-ft radius around a station.

Jan 1, 1961

By G. L. F. Powell, L. M. Hogan

Samples of silver and Ag-O alloy, 0.12 wl pet, have been undercooled to a maximum of 250°C by melting in a slag of commercial soda-lime glass. Grain refinement occurred in undercooled silver samples whet the degree of undercooling exceeded a critical value which varied from 153° to 175°C, depending on the melting conditions. In under cooled Ag-0 samples, the grain structure was fine and equiaxed at degrees of undercooling larger than 50oC. The grain refinement in both silver and Ag-0 alloy samples was the result of recrystallization during or immediately following freezing. When the oxygen content was increased, the degree of undercooling at which recrys-tallization occurred decreased. INVESTIGATIONS of the grain structure of strongly undercooled melts of nickel and cobalt1-4 have revealed a change in room-temperature grain size as a function of undercooling. At large degrees of undercooling the grain size was fine, but samples undercooled by smaller amounts exhibited a much coarser grain structure. The reported undercooling at which this grain size transition occurred in nickel varied between 140° and 175'C undercooling. Walker1 attributed this grain size change to an enhanced nuclea-tion rate. Cavitation at a melt-solid interface was con sidered to generate a high-pressure wave. This, in turn, produced nucleation in the liquid as a result of an elevated freezing point increasing the undercooling in the melt. A similar grain size transition was observed in undercooled silver between 133° and 153°C undercooling.5 The grain size transition in undercooled silver was found to be dependent on oxygen con tent. More recently, the authors5 showed that a simila transition occurred in an undercooled Cu-O alloy, =0.08 pet, but not in oxygen-free copper undercooled more than 200°C. The transition was attributed to recrystallization of the solidified grains after freezing; the greater the degree of undercooling, the more complete the recrystallization. In view of this effect of oxygen content on grain size transition, additional undercooling experiments were carried out with silver. This paper reports the results of these studies on silver and Ag-O alloys undercooled more than 50°C EXPERIMENTAL 1) Materials. The silver was supplied by Matthey Garrett Pty., Ltd., as fine granulate, silver mini' mum 99.9 pet, and contained the trace impurities shown in Table I. The silver originated from two different refineries resulting in the difference in impurity content shown in Table I. However, the variation in composition had no discernible effect on the undercooling behavior. Samples of the silver were melted in an open-ended, vertical, cylindrical resistance furnace, wound with Kantha] wire, the temperature of which was adjusted by means of a variable transformer, 2) Melting and Undercooling. Bulk samples of silver were undercooled by preoxidation and removal of oxidized impurities in a glass slag, as previously described,5 but special precautions were necessary to allow comparison between oxygen-free silver and a Ag-O alloy. Samples free of oxygen were prepared by first melting weights of granulate varying from 200 to 400 g in clean vitreous silica crucibles in air for approximately 15 min. A sample was frozen and a complete glass cover formed over the top surface by adding granulated glass rod. The sample was then melted and frozen several times until no oxygen bubbles appeared in the glass slag. Subsequent thermal analysis indicated that the oxygen content was negligible. The glass acted as an efficient barrier to absorption of oxygen from the air. Ag-O alloys were prepared by melting silver in silica crucibles with only a partial cover of glass, so that the top surface of the melt was in contact with air. The silver was held molten in air for several hours at 1000° to 1050°C, in the expectation that the oxygen in solution would reach equilibrium with atmospheric oxygen. At T - 1000°C the equilibrium oxygen content was calculated as 0.12 wt pet O, using Sieverts law and Eq, [l], derived by Mizikar et a!.7 from the data of Sieverts and Hagenacker8 for 1 atm of oxygen:

Jan 1, 1970

By W. M. Robertson

The rate of crack Propagation thvough a solid meta1 in the presence of a liquid metal has been calculated. The crack is assumed to propagate by solution of the solid in the liquid under the influence of an applied stress, with volume diffusion of the dissolved solute through the liquid controlling the propagation. The calculated velocities can be tens of centimeters per second or higher. THE embrittlement of normally ductile solid metals by liquid metals has been the subject of extensive study, as summarized in the book by Rostoker, McCaughey, and arkuus.' In experimental studies of liquid-metal embrittlement it is usually concluded that the observed crack-propagation rates are too high to be accounted for by diffusion processes. Diffusion is considered to be an unimportant factor and various other mechanisms are invoked to account for the experimental observations. The similarities of liquid-metal embrittlement to stress-corrosion cracking, to hydrogen embrittlement of steel, and to low-temperature embrittlement of bcc metals are frequently used as analogies for these mechanisms.1"3 The present paper assesses how rapidly a crack could propagate by a mechanism of volume diffusion through the liquid metal. We assume that the crack propagates by solution of the solid in the liquid at the crack tip under the influence of the applied stress and diffusion of the dissolved solute away from the crack tip. The model uses only macroscopic thermodynamic, kinetic, and elastic concepts. The calculations indicate that this dissolution-diffusion mechanism can give high crack velocities. In some previous treatments4'' of crack propagation in a liquid-metal environment the fundamental step has been the breaking of atomic bonds at the crack tip. The liquid greatly decreases the energy necessary to break these bonds. The present model assumes the crack is filled with liquid metal; the presence of the liquid is essential because diffusion through the liquid is assumed to control the rate of propagation. With proper modification this model could also apply to stress corrosion in a liquid environment. THEORY Consider a crack in a homogeneous elastic continuum, ignoring all the structural details of the solid. This neglects a host of metallurgical details which can be significant in the problem of liquid-metal embrittlement;' but this simple assumption is a useful approach in evaluating the role of diffusion through the liquid. The stress distribution around the crack tip establishes a gradient in the chemical potential at the tip, which causes a diffusion flux through the liquid away from the tip. The solid-liquid interfacial tension works against crack propagation, since propagation requires creation of interfacial area. From these two considerations we derive the diffusion flux, which then yields an expression for the velocity of the crack tip. The concentration of the solute in the liquid, C, is equal to the equilibrium concentration in the presence of an unstressed, flat surface, Co, plus the excess concentration due to the stress, AC(a), plus the excess concentration due to capillarity, AC(y): We calculate AC(o) and AC(y) and then obtain the diffusion flux. Consider (Fig. 1) a long flat crack of length 2L, thickness 2r, and tip radius r, where r remains constant as the crack propagates in the positive x direction. There is no stress ay in the y direction across the flat surfaces of the crack. The magnitude of the stress at the crack tip due to the applied stress, a,, is given by the relation6 ^=^[l-2^] 12] which, for long narrow cracks, becomes The stress increases the chemical potential in proportion to the strain energy.? The excess chemical potential due to the stress, Ap(a), is given by where 52 is the atomic volume of the solid and E the Young's modulus. Inserting Eq. [3] gives Now consider the crack to be filled with a liquid metal. The excess solubility due to stress, hC(a), is given by the excess chemical potential due to capillarity, Ap(y), is given by8 where y is the solid-liquid interfacial energy, and v1 and YZ are the two principal radii of curvature of any surface point. At the crack tip, r1 = -r and vz = m, so TRANSACTIONS OF THE METALLURGICAL SOCIETY OF AIME

Jan 1, 1967

By D. S. Flett, A. W. Fletcher

Equilibrium studies on the extraction of nickel and cobalt with kerosine solutions of naphthenic acid have shown that an exchange extraction reaction occurs at pH 5.5. The nickel/cobalt separation factor is constant at 1.8 for constant total metal molarity and varying nickel/cobalt ratios. The separation factor decreases with increasing total metal molarity in the organic phase beyond 0.2 M and also decreases with increasing temperature. From the equilibrium data, it has been possible to derive a mathematical model for the separation of nickel from cobalt by exchange extraction in multistage systems. Experimental data from a continuously operated multistage mixer/settler apparatus has shown a reasonable correspondence with computer-calculated data. The effective separation of nickel and cobalt in sulfate solution remains a problem in hydrometallurgy and the hope that this would be solved by solvent extraction has not yet been fulfilled. With chloride solutions, advantage may be taken of the ability of cobalt to form anionic complexes with the chloride ion. It can then be readily separated from nickel, which does not form stable chloro complexes, by extraction with a suitable long chain amine. However, in hydro metallurgical operations, sulfate solutions are generally obtained in which no extractable anionic species are present. Thus, the possibility of using cationic extractants must be considered, and in this paper attention is directed to the use of carboxylic acids. The method of separation studied has been termed exchange extraction, which involves replacement of a metal in the organic phase with a more acidic metal in the aqueous phase. Thus, (BR2).+ (Az+)aqt=(AR,).+ (B2+)aq (I) where metal A is more acidic than metal B, R represents the acidic radical derived from the acid RH, and the subscripts e and aq refer to the organic and aqueous phases, respectively. Ashbrook and Ritcey' have used this method for the separation of cobalt from nickel using the sodium salt of di-2 ethyl hexyl phosphoric acid, which preferentially extracts cobalt. Some nickel is coextracted, and this is removed by exchange with cobalt ions in the feed solution by suitable countercurrent operation in a pulsed column. Much work has been carried out by a number of workers in Russia on the general use of exchange extraction for the separation of metal ions using car-boxylic acids. Gindin et aL a have demonstrated that this technique could be applied to the separation of nickel from cobalt using a C--C. carboxylic acid and have applied the technique to the production of high purity cobalt solutions for electrolysis. Further worka was concerned with the development of a process for the separation of nickel from cobalt in a pulsed column. This system permitted the separation of iron and copper from nickel and cobalt in one system. The procedure involved center feeding with acid backwashing at the top and alkali addition lower down the column. Thus the system operated under a pH gradient and the metals were distributed in the column in the order of their basicities. A similar application was studied by Gel'perin et al,4,5 for the removal of copper and iron impurities from a nickel anolyte by means of a C10-C,12 fatty acid fraction. Ginden et al,' and Fletcher and Wilson' have studied the effect of pH on the extraction of a number of metals with carboxylic acids. These studies showed that metals such as iron, copper, lead, zinc, nickel cobalt, and manganese are extracted at pH values close to the pH of hydroxide precipitation. Nickel is extracted at a slightly lower pH than cobalt and thus the nickel/cobalt separation factor has a value not much greater than 1. More basic work on complex identification has been reported by Fletcher and Flett: by Tanaka; and Jay-cock and Jones." These studies have suggested that at low loadings in the organic phase, the nickel and cobalt carboxylates appear to be dimeric and solvated by free carboxylic acid molecules. As the concentration of metal in the organic phase increases, the complex changes and larger polymeric species are formed. In order to permit assessment of the potential of carboxylic acids as extraction reagents for separation of

Jan 1, 1971

By R. T. O’Brien, J. M. W. Mackenzie

A microelectrophoresis technique has been used to measure the zeta potential of quartz over a range of pH and Ni (11) and Co (Ilj concentrations. Results have been discussed in terms of adsorption of Ni (11) and Co (11) cations and hydroxide precipitates. Possible relationships between the experimental results and the formation of lateritic nickel deposits have been discussed. The adsorption of metallic cations to the surface of silicate minerals is of significance in many industrial and natural processes. In an earlier publication,' the adsorption of Fe (111) to the quartz surface, a phenomenon of importance in flotation, was studied qualitatively using microelectrophoresis techniques. This paper reports the extension of this work to an investigation of the adsorption from aqueous solution of Co (11) and Ni (11) to the quartz surface. The adsorption of these metals was of interest for two reasons; firstly, the importance of such an adsorption process in the formation of nickel deposits by the lateritization of nickeliferous rocks, and secondly, the comparison of electrophoresis data for these metals, whose hydroxides precipitate in the pH range 7-8, with similar data for Fe (111) where the hydroxide first precipitates at pH 2.8. The development of laterites is essentially a near-surface geological process involving vertical and, in part, horizontal redistribution of elements derived from rock-forming minerals. This redistribution of elements leads to the formation of layers within the lateritic profile which are enriched in one or more of these elements and, depending on the nature of the original rocks, continued lateritization may give rise to iron ores, bauxites or nickeliferous laterites. The mechanisms discussed in this paper deal with the last mentioned type of deposit although the considered factors are applicable to laterites in general. Nickeliferous laterites are derived from basic and ultrabasic rocks containing ferro-magnesian silicates. These rocks may be partly or wholly converted to serpentinites. Besides their high Mg, Si and Fe contents, they also contain small amounts of Mn, Al, Cr, Ni, Co, Cu and Zn. The nickel content is usually near to 0.2-0.3%, but for economic use this must be increased during lateritization to over 1% and preferably over 2%. The zone of nickel enrichment is usually at some depth within the lateritic profile. Unpublished work by Mr. O'Brien on nickel-bearing laterites in eastern Australia indicated four visually different types of material which were separated from crushed samples under a stereo-microscope. Although chemical analyses indicated that all four types of fragments contained 2-4% nickel and smaller amounts of cobalt, X-ray diffraction and optical studies revealed only quartz, hematite and chromite as well as, in one of the types, a serpentine mineral. No distinct, nickeliferous minerals were detected. Furthermore, it was possible to extract some 60% of the nickel content of the laterites with cold 0.5N hydrochloric acid. It was therefore postulated that much of the contained nickel was present as amorphous, adsorbed material. In considering this fact, as well as the problem of the actual method of transfer and fixation of elements within the lateritic profile, it was further postulated that the transfer of these elements probably took place partly as solutions and partly as colloids and that the fixation of these was caused by adsorption and flocculation. The existence of nickel in solution in water draining from serpentinites has been confirmed by Smurov.2 Although we have no evidence for the transportation of nickel in the colloidal state, it is well accepted that colloids are important in the formation of laterites. Previous work by Mr. Mackenzie' has already indicated that iron may be adsorbed on quartz under conditions which could be expected in a lateritic profile, but no information was available for nickel or cobalt. Although adsorption possibly also takes place on minerals other than quartz, the latter is significant because silica is an important constituent of the silicate parent rocks. During lateritization, it is released to form free quartz and it is likely that it is initially extremely fine-grained. This would provide abundant opportunities for adsorption and it was de-

Jan 1, 1970