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By C. Dean Starr

The physical basis of the equation correlating electrical conductizlity and temperature coefficient of resistance of solid solution alloys has been inzlestzgated and the nature of the constants evaluated. It is shaun that the same form of correlation is valid irrespective of the magnitude of the temperature coefficient. However, the effect of therma1 expansion and change in resistivity with temberature nust be considered when the magnitude of the temperature coefficient of resistance is near zero. In a comprehensive literature survey conducted at the Armour Research Foundation in 1950, it was found that a linear relationship exists between the electrical conductivity, K, and the temperature coefficient of resistance, a, for solid solution alloys. This was expressed by the equation where B, a constant, depends on the solvent metal but not the solute. A continuing investigation by Hansen, Johnston, and Parks showed this equation was generally appropriate for Cu, Ag, Au, Pd, Pt, and Co base binary solid solution alloys as well as for many ternary alloys of copper over a range of conductivities and temperature coefficient of resistances from 0.02 to 0.60 reciprocal pohm cm and-0.00015to0.004Q per 0 per "C respectively. Eq. [I] was not always valid for alloys that exhibited a change in state (magnetic to nonmagnetic) or for alloys that had a temperature coefficient of resistance near or below zero. For example, in nickel alloys, a simple linear curve as predicted by Eq. [l] was not obtained when the conductivity was plotted against the temperature coefficient of resistance. Hansen suggested that deviations observed were caused by transitions from a ferromagnetic to a nonmagnetic state. Subsequent and more extensive data by ronin on Ni-Mn alloys confirmed Hansen's postulate. While both states independently showed a linear relationship between K and a, the value of B was different for the two states. In some copper and gold base alloys, as well as the platinum and palladium alloys investigated by Hansen, the conductivity did not extrapolate to zero at zero a as demanded by Eq. [I]. This deviation can be readily corrected by simply adding a constant to Eq. [I.] whence Eq. [2] shows the K decreases as a decreases but that K has a positive value when a = 0 which is observed for commercial solid solution alloys as well as the experimental alloys tested by Hansen. While other methods of correlation of electrical properties have been made such as the one by Starr and Wang3 who found a linear relationship between resistivity and temperature coefficient of resistance for Ni-Cr-Al-Cu alloys, the data, in general, can also be correlated by a form of Eq. [2]. Thus, Hansen's empirical equation has considerable merit. The objective of this paper is to determine the physical basis for this equation and to examine the region near zero a in more detail. ELECTRICAL CONDUCTIVITY VS TEMPERATURE COEFFICIENT OF FU3SISTANCE The resistance of a metal or alloy is defined as

Jan 1, 1963

By Henry M. Howe

If a bar of wrought iron or steel is suddenly cooled from a bright red-heat, the contraction which then occurs is considerably greater than the expansion previously caused by heating the bar, so that its final length is considerably less than its initial length. Mr. Thomas Wrightson has investigated this phenomenon,* and has shown that not only does this permanent contraction occur on sudden cooling, but, if the heating and cooling be repeated, say fifty times, a further permanent contraction occurs at each successive cooling. In Mr. Wrightson's opinion, this contraction cannot be explained on mechanical grounds, and he ascribes it to some molecular change caused by sudden cooling; but I think that we need not invoke mysterious molecular changes to explain this phenomenon, which appears to me to be due to very simple and purely mechanical action. Let us consider the cooling as divided into two periods, in the first of which the exterior or skin of the bar becomes almost completely cooled, and hence tends to contract almost to its initial dimensions, while the still hot arid plastic interior contracts but little; in the second period the already cool skin remains nearly constant in temperature, and hence tends to contract but little, while the interior cools from a comparatively high temperature to the ordinary temperature, and hence undergoes great contraction. The excess of the contraction of the skin over that of the interior during the first period tends to make the bar bulge in the middle of its length. This, as well as the decrease of density which occurs, Mr. Wrightson correctly explains. The interior of the bar just sufficed to fill the skin when both were in their initial condition, before being heated at all. At the end of the first period, the volume of the still hot interior is more than the now contracted skin can hold while maintaining its initial shape; and the effect is much the same as when we powerfully blom into a soft India-rubher Lag of the shape of the skin of the bar—it bulges, and tends to approach the spherical shape, in which the ratio of surface to

Jan 1, 1886

By J. J. Gilman

WHEN a zinc crystal is immersed in liquid N, and then plastically bent, it is observed that it bends a certain amount and then fractures. This fracture occurs at a fairly reproducible radius of curvature, and the radius varies systematically with the crystal orientation. Because this phenomenon provides an unusually well-defined set of fracture conditions, it is possible to examine various possible fracture criteria and select the best one. Zinc crystals of various orientations were bent about axes lying in their glide planes (0001) and perpendicular to their glide directions [1210]. The crystals were 0.150 in. diam and had chemically polished surfaces. They were immersed in liquid N, while they were being loaded on an Instron testing machine. A three-point bending jig was used to load them. Table I lists the beam radius at which fracture occurred for each orientation. Each value is the average of at least six measurements. The normal stresses on the cleavage planes, at the time of fracture, were calculated as follows: First, from the fracture radius, R,, the orientation angle, x,, of the (0001) plane at the outer fiber was calculated. If x, = angle between the (0001) and the rod axis prior to bending, d = rod diameter, and X, = angle between the (0001) plane and a tangent to the bent crystal, then1 sinX, _ 2R, sin xn 2R, + d Since the glide shear strain is given by' y ' cot X, — Xo the glide strain at fracture, x,, can be calculated. Next, it is necessary to know the tangential stress in the outer fiber at fracture. This depends on the plastic flow curve, so a series of tensile tests were performed at —196°C on another set of zinc crystals. A curve of the average resolved shear stress versus glide strain was prepared. From this curve, shear stresses, r,, corresponding to the glide strains in the bend tests were taken. These values are listed in Table I. Then the normal stresses in the outer fibres, u,, were calculated from the relation U, = r, tan X, This analysis assumes that the fiber stresses in a bent beam are the same as the stresses in simple

Jan 1, 1959

By John R. Anderson, Michael B. Bever

CARBON may affect the alloys of copper in several ways. Provided an alloying element does not oxidize preferentially, even minute quantities of carbon dissolved in liquid alloys of high copper content will form insoluble carbon oxide gases under oxidizing conditions. Gas porosity in castings of high-copper alloys can originate in this way. In certain alloys of low copper content carbon may have considerable solubility and may be an effective deoxidizer. In these alloys carbon will tend to suppress porosity. Carbon that is dissolved in the molten alloy is likely to be retained in the solidified metal. The effects of carbon on the physical properties of the metal are determined by the form in which it is present. Depending on the alloying elements and also on the cooling rate, carbon may precipitate as graphite, may form a carbide or may remain in solid solution on cooling. As solid copper does not dissolve a measurable amount of carbon, a carbon-bearing solid solution can occur only if the copper is alloyed with a large excess of an element that forms such a solution. The effect of graphite or of carbides on the properties of an alloy will depend on the size and distribution of the precipitated particles. As Hensel pointed out in discussion,1 the formation of an alloy carbide may interfere with the age-hardening properties of a copper alloy. One would also expect that the presence of carbides or of graphite will under certain conditions promote corrosion or high-temperature failure in nonferrous alloys. Since carbon has an effect on the soundness of castings and affects the structure and behavior of solid copper alloys, its solubility in the liquid alloys is of practical importance. The isothermal change of carbon solubility with alloy composition is of interest from a theoretical standpoint. The binary alloys of copper with manganese and with nickel are used industrially and serve as a base for more complex alloys. The solubility of carbon in each of these metals is known, but its solubility in their alloys has not been determined. EARLIER DATA The solubility of carbon in molten pure copper is about 0.0001 pct at 1100 °C and 0.0004 pct at 1475°C.1 Various authors2-6 have published data on the solubility of carbon in molten manganese. There is agreement on a value of about 6.7 pct in the temperature range 1217° to 1245°C. This solubility value corresponds to the formula Mn3C. It increases very little with increasing temperature. Corson7 states that carbon is soluble in copper-manganese alloys and that the

Jan 1, 1947

By W. T. Roberts, N. G. Turner

A study of the fatigue properties of several grades of commercially pure titanium has established that the strain-aging process is of minor importance in the development of a fatigue limit and a relatively high fatigue strength ratio. Metallographic observations and damping measurements at room temperature indicate that striations are able to spread from grain to grain only at stress levels above the fatigue limit. This suggests that the fatigue limit represents the stress above which large-scale dislocation unlocking takes place. Fatigue tests on annealed material at - 60" and - 196" c showed that under conditions when a thermally activated diffusion process would be suppressed the fatigue limit is not eliminated. Prestraining at room temperature did not have a detrimental effect on fatigue strength at room temperature but a decrease was recorded at — 60°C. This is further evidence that initial dislocation locking is a important strengthening mechanism. TITANIUM and titanium alloys have S-N curves with a definite fatigue limit, and a high ratio of fatigue limit to UTS can be attained. Other materials which show similar fatigue characteristics are mild steel and some Al-Mg alloys. The fatigue limit of these materials has been associated with their strain-aging capacity. It is well-known that commercial-purity titanium contains interstitial impurities which can give rise to a sharp yield point, and a small strain-aging effect following static strain has been demonstrated.7 This type of aging reaction is differentiated from the dynamic aging process when aging occurs during plastic deformation, and which is generally observed at elevated temperatures. In a titanium at room temperature, dislocation locking is associated with the interaction of interstitial oxygen, nitrogen, and carbon atoms with dislocations. Ehr-lich has shown that the distortion produced by introduction of these atoms into the hcp lattice has no shear stress component and hence there is no interaction between the stress field and the screw component of a dislocation. Thus the dislocations as a whole are only weakly locked. It is clear that strain-aging effects in hcp a titanium will be much less pronounced than those observed in bcc iron and steel. In recent years, the attribution of the fatigue limit solely to strain aging has been questioned. It has been pointed out that a definite fatigue limit is observed at temperatures as low as -196°C in some titanium alloys,' and strain aging is not expected to be effective at this temperature. The role of initial locking of dislocations in determining fatigue behavior has been examined in low-carbon steel by Oates and Wilson. They showed that under conditions in which the aging potential is low the factors which control the buildup of local stresses and hence affect dislocation unlocking, e.g., grain size, are important. There are indications that other metals can have a definite fatigue limit with no established strain-aging capacity, an example being magnesium12 which has the same crystal structure as a titanium. The spread of plasticity from grain to grain in hexagonal metals may be more difficult than in cubic metals because of the limited number of slip systems in the former, and this may account in part for their fatigue behavior. The present work was undertaken to elucidate the relative importance of crystal structure, strain aging, and initial dislocation locking in determining the properties of commercially pure titanium when subjected to cyclic stressing. 1) EXPERIMENTAL METHODS Three grades of commercial-purity titanium were used and a material of lower interstitial content was prepared by melting high-purity Japanese sponge titanium (referred to as H.P. Ti). The compositions and typical mechanical properties of the materials are shown in Table I. Fatigue tests were made in push-pull (zero mean stress) using an Amsler Vibraphore machine at a frequency of about 160 cps. Two types of fatigue specimen were used—one with a waisted gage length for determination of S-N curves and the other with a parallel gage length for metallographic studies and damping measurements. After careful machining and mechanical polishing, all specimens were electropolished prior to fatigue testing. The electrolyte consisted of 10 parts methyl alcohol, 6 parts 2-butoxyethanol, and 1 part perchloric acid (SG 1.54) and it was maintained at a temperature of -10" to -20°C during polishing. Tests at room temperature were normally carried out with the specimen immersed in a silicone oil bath which could be heated for elevated-temperature tests.

Jan 1, 1969

By J. Serra, M. Turpin, R. Alberny

A new method is proposed to obtain automatically an unbiased estimate of the interdendritic spacing A. It is shown that the structure can be built by a random distribution of a rectangular basic unit. The usual definition of the interdendritic spacing yields a value 1 which, coupled with A, gives the shape of the basic rectangular unit. A study of the relationship between dendrite arm spacing and solidification rate was conducted as a part of a research program on dendritic solidification. For any comparison between theory and experiments to be meaningful, it is necessary to measure reproducible and clearly defined spacings. Fig. 1 shows clearly that even in a fairly simple structure such measurements are difficult. if we compare photos (a) and (b), we can hardly assess which one shows the larger spacing. Moreover, the quantity to be measured can be defined in several ways. On a small scale, dendrites seem to be distributed in a very regular and ordered way. However, on a larger scale, this regularity no longer exists. The usual way to measure spacings is to pick up some rows of dendrite stalks; such measurements are obviously biased since less orderly regions are not taken into account. A more objective method is to section the picture with randomly oriented straight lines and average the measured interdendritic spacings. The purpose of this paper is to show that such measurements, which can be conducted automatically, yield objective and reproducible results which are directly related to characteristic features of the dendritic structure. I) THEORETICAL ANALYSIS 1-1) Mathematical Morphology and Function of Co-variance. Matheronl and Serra2 enlarced- the definition and geometrical meaning of the notion of covariance to encompass problems in mathematical morphology. A brief review of part of their theory can be stated as follows. Let A' be an isolated particle, and let us consider a group of two scanning points h is the vector joinlng these points, h its modulus, and a its direction. Let us also define a boolean function, k(x), whose value is 1 if x lies inside the particle and 0 if it 1s outside. The total number of events in which both points are inside A' IS the covariance Ii',(h): is the measure of the intersection of A' with the particle ALh obtained by translating A' of -h Obviously K,(O) is the volume of the particle A', or its area if A' is a two-dimensional body. The average value of K,(h), when the direction of a vector h of constant modulus is rotated, is: An important property of the covariance is illustrated on Fig. 2: if the shape of a particle shows some regularity along a direction a, K,(h) generally presents a maximum. We now consider a group A, made of many particles A' distributed in space; then k(x) is taken as the realization of a stationary random f~nction.~ The volume fraction (or fraction of area if the problem is two-dimensional) occupied by A equals the average value q of k(x): meaning "average value of"). We also replace

Jan 1, 1970

By P. Bolsaitis, L. Skolnick

A model of metallic solutions is postulated which explains the energy of formation of alloys on the basis of changes in electron density around solute and solvent atoms and changes in pairwise interactions between atoms. The model is based on the Wigner-Seitz cell model of metals, with the electronegativities of the metals as the parameter for the electron-attracting power of the constituent atoms. In contrast to models based on the description of cohesive energy in terms of pairwise interactions only, which require an empirical, adjustable correction parameter to the Berthe-lot relations in order to predict negative energies of formation, the electron cell model accounts for both negative and positive energies on the basis of parameters of the pure components. Calculated heats of mixing based on published parameters of the pure metals are found to compare favorably to experimental values, despite the absence of any adjustable parameters in the model. THE formulation of an "exact" quantum mechanical model for the energy of cohesion of metals reduces ultimately to the many-body problem and for a complete solution would require the knowledge of wave functions and energy levels of all the particles in the system. The case of alloys is further complicated by the fact that the potential fields around the constituent atoms are different and the matching of boundary conditions in terms of the resulting wave functions is still an unresolved mathematical problem. It appears that in spite of the numerous investigations that have led to an elucidation of many properties of the metallic state, the formulation of the Hume-Rothery rules in 1931 marks the lone accomplishment toward simple, qualitative prediction of the energy of formation of alloys. More recently Friedel'' and Arafa have utilized the modern concepts of the electronic structure in metals in combination with the Hume-Rothery rules to arrive at quantitative estimates of the energy of formation of alloys with low solute contents. The relative success of the Hume-Rothery rules and Friedel's and Arafa's studies encouraged broaching the subject of formulation of a model based on realistic physical parameters and of conceptual and mathematical simplicity that could be applied to alloys regardless of concentration. On the basis of the free-electron theory, the cohesive energy of pure metals can be expressed as a function of "valence" (number of free electrons per atom), lattice parameter (or density), and the ioniza-tion energy. In addition to the electronic contributions to cohesion, one has to consider the pairwise exchange interaction energy between neighboring ion cores and the contribution from van der Waals forces. The energy changes upon alloying are viewed as resulting primarily from a redistribution of electron densities around the ions (a simplification of the more basic concept of a change of the wave functions of the electrons in the presence of a perturbing potential field). In addition there is a change in the pairwise interactions between neighboring ions which is usually the only factor taken into account in commonly used adaptations of the quasichemical theory. The electronegativities of the metals forming the alloy are used as the measure of the electron-attracting power of the ions in the alloy and the difference in electronegativities as the driving force for changes in electron energy on alloying. The interplay of pairwise interactions and electronic forces results in positive or negative energies of formation of alloys. Results obtained for systems to which the free electron model is best applicable are in good agreement with experimental values. 1) COHESIVE ENERGY OF METALS IN TERMS OF THE ELECTRON CELL MODEL The simplest physical model of a metal is that of a lattice of positive charges immersed in a sea of uniform, negative charge distribution represented by the

Jan 1, 1969

By V. N. Antaki

ELEMENTAL phosphorus (referred to as P,) is a true mineral product that has developed, in the relatively brief span of a century, from a laboratory curiosity to a heavy chemical. Annual production now exceeds 300,000 short tons. Continued rise in production has been predicted, consistent with new applications for P, derivatives and the expected population increase. In itself elemental P, is valuable chiefly as an 'intermediate chemical. The principal end uses at present are in inorganic phosphates, both simple and complex, of sodium and potassium, used in water treatment and detergent compounds, leavening agents, food supplements, and dentifrices. Organic P, compounds are important as plasticizers, oil additives, flotation agents, and more recently as gasoline additives (TCP being the outstanding example). The increasing use of high-analysis water-soluble and liquid solution fertilizers, as well as the direct application of phosphoric acid to the soil, will probably be the most significant factors in P, production growth rate. Coke oven plants now using sulfuric acid to fix byproduct ammonia values will gradually switch to phosphoric acid in order to market a fertilizer with completely available values. Recently sponsored experiments show that phosphoric acid can be directly admixed with cattle and poultry feed to produce rapid growth. Both P, compounds and modifiers for oil well drilling mud show increasingly promising significance.

Jan 3, 1957

By N. A. Gokcen, John Chipman

SILICON is the most commonly used deoxidizer and an important alloying element in steelmak-ing; hence a detailed study of this element in liquid iron containing oxygen is of considerable interest. The equilibrium between silicon and oxygen in liquid iron has been studied by a number of investigators but generally with inconclusive or incomplete results. The variation of the activity coefficients of silicon and oxygen with composition is entirely unknown. Published investigations deal with the reaction of dissolved oxygen with silicon in liquid iron and the results are expressed in terms of a deoxidation product. For consistency and convenience in comparison of the published information, the deoxidation product as referred to the following reaction is expressed in terms of the percentage by weight of silicon and oxygen in the melt in equilibrium with solid silica: SiO (s) = Si + 2 O; K'l = [% Si] [% 012 [I] Theoretical attempts to calculate the deoxidation constant for silicon in liquid iron from the free energies of various reactions yielded results which were invariably lower than the experimental values. Thus, the deoxidation "constants" calculated by McCance,1,2 Feild,3 Schenck, and Chipman were of the order of 10, which is below the experimental values by a factor of more than 10. Experiments of Herty and coworkers" in the laboratory and steel plant resulted in an average deoxidation constant of 0.82x10 ' at about 1600°C. The technique employed in their investigation was crude and the reported temperature was quite uncertain. The concentration of silicon was obtained by subtracting silicon in the inclusions from the total. Since at least some of the inclusions resulting from chilling must represent a fraction of the silicon in solution at high temperatures, such a subtraction is not justifiable. Results of Schenck4 for K'1 from acid open-hearth plant data yielded a value of 2.8x10-5, which was later revised as 1.24x10 at 1600°C. Similarly Schenck and Bruggemann7 obtained 1.76x10-5 at 1600OC. The discrepancies and errors involved in the acid open-hearth plant data as compared with the results of more reliable laboratory techniques were attributed by these authors to the lack of equilibrium and the impurities in liquid metal and slag, and are sufficiently discussed elsewhere." Korber and Oelsen" investigated the relation between dissolved oxygen and silicon in liquid iron covered with silica-saturated slags containing varying concentrations of MnO and FeO. The deoxidation products obtained by their method scatter considerably, and their chosen average values of 1.34x10, 3.6x10-5, and 10.6x10-5 1550°, 1600°, and 1650°C, respectively, represent the best experimental results which were available until quite recently. Darken's10 plant data from a steel bath agree approximately with their data at 1575° to 1625°C. Zapffe and Sims" investigated the reaction of H2O and H2 with liquid iron containing less than 1 pct Si and obtained deoxidation products varying by a factor of more than 20. Inadequate gas-metal contact and lack of stirring in the metal bath should require a longer period of time than the 1 to 5.5 hr which they allowed for the attainment of equilibrium. Furthermore, their oxygen analyses were incomplete and irregular and confined to a few unsatisfactory preliminary samples. Their results did indeed indicate that the activity coefficient of oxygen is decreased by the presence of silicon, although they made no such simple statement. They chose to attempt to account for their anomalous data by the unlikely hypothesis that SiO is dissolved in the melt. Hilty and Crafts" investigated the reaction of liquid iron with acid slags under an atmosphere of argon, making careful determinations of silicon and oxygen contents at several temperatures. Despite erroneous interpretation of the data at very low silicon concentrations, their data represent the most dependable information on this equilibrium that has been published. In the range 0.1 to 1.0 pct Si, their data yield the following values for the deoxidation product: 1.6x10-5, 3.0x10- ', and 5.3x10 at 1550°, 1600°, and 1650°C, respectively. The purpose of the work described herein was to study the equilibrium represented by eq 1 as well as the following reactions, all in the presence of solid silica: SiO2 (s) + 2H2 (g) = Si + 2H2O (g);

Jan 1, 1953

By T. A. Read, H. K. Birnbaum

Deformation of AuCd alloys having the 8 (orthorhombic) and (3" (tetragonal) structures occurs by the stress induced motion of twin boutdaries. A restoring force acts on displaced twin boutdaries as a result of internal energy increases in the volume through which the boundaries are displaced. The phenomonology of the twin boundary motion is described and a mechanism for twin boundary motion and the restoring force is proposed. A time-dependent stabilization behavior of the twin boundaries, which is observed after the twins are formed by the diffusionless phase transformations, is described. THE AuCd 8 phase (ordered bcc structure) exhibits a transformation to a phase having an orthorhombic structure, 8' (space group D'), for compositions in the vicinity of 47.5 at. pct Cd and to a phase having a tetragonal structure, 8" (point group 4/m, m,m), for compositions in the vicinity 50.0 at. pct Cd. Both transformations are diffusionless, occur on cooling at 60" and 30OC, respectively, and are crystallo-graphically reversible.' They are accompanied by an inhomogeneous deformation which was observed to be twinning in the low-temperature phase. 3'4 The transformations may occur by a "single interface" or by "multiple interfaces."5'6 In the "single interface" transformation, the twinned product phase consisted of two twin orientations as shown in Fig. 1. In the multiple interface transformation the product phase contained "domains" each of which contained two twin orientations, Fig. 2. Deformation of specimens containing transformation twins was achieved by motion of the twin boundaries. Releasing the applied stress resulted in the displaced twin boundaries returning towards their initial positions. This "pseudo-elastic" behavior of the boundaries varied with time after the formation of the twin boundaries by the transformation.

Jan 1, 1961

By Sir Albert E. Kitson

The manganese ore deposits of the Gold Coast, British West Africa, occur in very ancient rocks, of both sedimentary and metamorphic types. In certain respects they have a strong resemblance to those of India and Brazil, as contrasted with those of Tertiary age in Georgia, but in this paper no careful comparison with them can be made. Viewed from the present condition of the manganiferous rocks, the oldest deposits are in the sediments. Later than these are the progressively metamorphosed representatives of these sediments. Youngest are the products of decay and degradation with the concentration of manganese oxide in the rocks of both groups. The oldest occurrences are in argillaceous and siliceous phyllites and slates, which show only a moderate degree of metamorphism. They belong to a series which also includes mudstones, sandstones, grits, conglomerates and subordinate limestones, with tuffs and lava-flows, largely of basic types. This has been named the Birrim System. Its age is unknown, for no definite fossils have been discovered in it. Since these non-fossiliferous strata at many plaees are of a character which in many parts of the world are suitable for the preservation of fossils, and which contain them, it is assumed that the Gold Coast deposits are pre-Cambrian. These rocks of the Birrim System have normally a northeast-southwest strike, and are folded, but not to any very great degree except in certain belts. From the Eastern Province of the Gold Coast they may be traversed diagonally across their strike for upwards of 600 miles, to the extreme northwestern corner of the Northern Territories. Thence they probably extend much farther into French territory.

Jan 1, 1927

By W. J. Leas, L. A. Rapoport

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas' which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy's law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy's law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

By L. A. Rapoport, W. J. Leas

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas' which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy's law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy's law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

By E. O. Kirkendall

THE investigation reported herein was undertaken to obtain data to supplement those presented in an earlier paper,' particularly for longer times at a higher temperature. This information may further develop our knowledge of the mechanism of diffusion in substitutional solid solutions. Diffusion of solute atoms interstitially dissolved is not difficult to visualize; it can take place without much disturbance of the solvent atoms. The mechanism of diffusion of solute atoms substitutionally dissolved is not so easily understood. Many theories have been advanced. Rosenhain,2.3 Frenkel,4 Smekal,5 Langmuir,3,6 Steigman, Shockley and Nix,7 and Johnson8 all proposed theories to explain diffusion. Langmuir's proposed mechanism consisted of a simple cyclic interchange of atoms involving an interchange in lattice positions of four or more atoms. This mechanism, accepted by the author at the time of his previous publication,' and apparently quite generally accepted, required a net exchange in positions of both solute and solvent atoms in equal numbers. In other words, the rate of diffusion of the solvent and solute atoms would be the same. That this cyclic interchange in lattice positions of solute and solvent atoms in equal numbers is the only true mechanism of diffusion is denied by the evidence presented in this paper. EXPERIMENTAL PROCEDURE This modification of similar procedure1 will be outlined briefly. The method consisted of the following steps: I. A pure Muntz metal (60.6 per cent Cu, 0.1 per cent total impurities) that was almost all beta brass at 780°C. was chosen. 2. The brass was turned between centers in a lathe to a diameter of 0.5965 inches. 3. After the brass was cleaned, it was electroplated with pure copper to a diameter of about one inch. 4. The sample was heated slowly to 400°C. under reduced pressure and held at that temperature for 4 hr. to remove occluded gases. It was then cooled to room temperature. 5. The sample was heated to 780°C. ±3°C. and held at that temperature for different lengths of time; then quenched. Samples were cut off each time after quenching. Metallographic samples 34 in. thick were removed at I hr., 6 hr., 24 hr., 96 hr. and 701 hr. After 96 and 701 hr. samples of about I in. were removed for X-ray analysis. 6. The metallographic samples were polished on the cross section and photo-micrographs were taken. 7. The I-in. samples were polished and etched on both ends. With the aid of a microscope each was carefully mounted in a four-jaw chuck in a lathe, so that they could be accurately bored for an arbor. 8. Turnings were taken for each X-ray sample. After each set of turnings, the sample was heated in an oil bath for about 3a hr. at 300°C. It was then etched in 25

Jan 1, 1942

The following correspondence relating to a paper bearing the above title, presented by J. F. Wolff, at the New York meeting in February, 1917, and published in the Transactions, Volume LVI, page 142, has passed between the author of the paper, and Mr. Anson G. Betts, and is interesting, although it was received much too late for incorporation in its proper place in Volume LVI. ANSON CT. BETTS, Asheville, N. C.-1. I should like to ask Mr. Wolff if he finds-from analysis of the iron formation and of the iron ore, and from the relative amounts of each in each unit area of the formation, unleached and after leaching, that the iron remains entirely insoluble and the total quantity still remains present; or whether he finds that some of the iron is removed, or possibly even added by deposition from the water passing through the formation. 2. The water that passed into the iron formation had to go somewhere; was it absorbed by underlying formations through hydration, or, after passing through the ore formation, did it come to the surface in springs at a lower elevation, or how did it escape from the ground? 3. I should like to ask Mr. Wolff whether he finds that the iron formation in the sedimentary series does not, come next to the quartzites and generally between the quartzites and slates. J. F. WOLFF, Duluth, Minn.-1. In common with others, you appear to have some hesitancy in accepting the fact of the removal, by solution, of the enormous quantity of silica which has been leached out of portions of the Biwabik iron formation, thus forming orebodies of merchantable iron ore. I believe that even Dr. Waldemar Lindgren once hesitated to accept this fact. However, the evidence is so simple and absolutely conclusive that the fact is established beyond all question. At the contact of orebodies with their rock walls, the bands of iron ore in the orebody can be seen in contact with the corresponding bands of original iron oxide in the rock wall, and the chert layers in the rock wall can be seen to give place to fine granular material (fine silica and iron oxide) and pore space. This is especially noticeable where slumping at the rock walls his not been so great as to displace the layers in the orebody from their contact with their corresponding layers in the rock wall.

Jan 9, 1918

By Edmund Kirby

This meeting marks the point at which the long-standing dissatisfaction with the mineral-land laves, the innumerable protests against them, and the many isolated efforts to obtain relief, have developed into a general movement for the: revision. That part of the mining industry which is affected by these laws has three general organizations to speak for it: the American Institute of Mining Engineers, Mining and Metallurgical Society of America, and the American "A Mining Congress: all of which are represented in this meeting. In the series of able and thoughtful presented here, prominent men have discussed the evils of the present laws aid some of the reforms which should be made in them. We all appreciate fully the ultimate value of these studies; but we are also painfully aware of the fact that discussion of this kind has been going on for a quarter of a century without any other effect than a steady increase in the mass of printed records stored on library shelves. In order to get any practical result we must induce an indifferent government at Washington to act, and to do this we must unite in pushing some practical plan whereby it may act in a simple and effective way and with the least possible amount of criticism or opposition. The actual question before us is not whether the mining laws are bad; for their evils and absurdities are not only beyond discussion but also beyond the resources of a temperate and dignified vocabulary. It is not what particular changes ought to be made; for it is premature to make specific recommendations until there is some one to listen to them. Moreover, we all know that there are wisdom and experience enough available, and awaiting that time, for the creation of a code which would be a model to the mining world. The practical question now is, how to obtain the revision; and since the American Mining Congress has of late restricted its attention to this phase of the problem I wish as one of its representatives here to present its views upon the matter.

Jan 6, 1914

By A. Taylor

IN a previous communication,l the quaternary system Ni-Cr-Ti-A1 was described in detail and it was shown how certain alloys used for high-temperature applications could be construed as consisting of Ni,Cr suitably modified by the addition of aluminum and titanium in relatively small amounts. With the correct aging treatment, the ordered face-centered-cubic Berthollide phase, y'-Ni,Al, could be precipitated from the face-centered-cubic primary y-solid solution. By increasing the proportion of titanium with respect to aluminum, it was also possible to precipitate the very brittle hexagonal-close-packed Daltonide phase, ?-Ni,Ti. From the nature of the system it seems reasonable to expect the y and y'-phases to take appreciable amounts of cobalt and iron into solid solution. In the case of the present investigation it was decided to confine the work to iron additions only. This element may be introduced in two quite distinct ways: 1) as a simple replacement for nickel; and 2) as a replacement for chromium, titanium, and aluminum. The second method of iron addition forms the basis of the present investigation, which is, in effect, a study of the pseudo-quaternary system Ni,Cr-NiPe-Ni,Ti-NLAl. For purposes of reference, Figs. 1, 2, and 3 have been included and illustrate the quaternary system Ni-Cr-Ti-A1 described in the previous paper along with sections through N&Cr-Ni,Ti-Ni,Al at 750" and 1000 "C respectively. As will be shown below, the pseudo-quaternary system with components Ni,Cr, NiPe, Ni,Ti, Nihl is remarkably similar in many ways to the face defined by Ni,Cr-Ni,Ti-Ni,Al because of iron re-

Jan 1, 1958

By A. W. Griffith, R. G. Beverly, W. A. Millsap

THE Grand Junction Pilot Plant, operated by National Lead Co. Inc., for the U. S. Atomic Energy Commission, is engaged in the amenability testing of orebodies to establish design and cost data for commercial mills and to test new processes for recovery of uranium from ores. Test work was performed to study the effects of several variables on leaching of uranium ores in carbonate solutions. Many of these variables had been investigated in the laboratory, but pilot plant tests were desirable to evaluate their importance in semi-works equipment and to predict optimum operating conditions for future commercial mills. The results of these tests should serve as a guide in selecting the most efficient and economical method of leaching uranium ores amenable to a carbonate process. This article is concerned with a process in which uranium is extracted from the ore by a hot Na2CO3- NaHCO3 solution; the uranium-bearing solution is separated from the solid residue by filtration, and uranium is then precipitated by chemical means.

Jan 9, 1957

By W. L. Austin

The advance made in recent times in this branch of metallurgy is indicated by the attention the subject is receiving from important American copper-producing companies. Reference to the files of publications devoted to the mining industry discloses that some 20 American companies are actively investigating the amenability of their ore, or other material, to leaching methods, and that plants of varying capacities up to 10,000 tons per day arc under construction or are projected. Several leaching works are in commercial operation. It has been frequently pointed out that no method of leaching is universally applicable, for the reason that each ore differs in some particular from apparently similar ore found elsewhere, and also because local conditions are rarely the same even where the ore closely approximates in character that being worked at some other point. For this reason the older companies are approaching the matter in a conservative manner, experimentally determining for themselves the salient features in each instance. In considering a leaching proposition three factors at once fix the attention: (1) disengaging the metal from mineralized forms in which it is found in nature; (2) recovering the metal in a commercial state after it has been dissolved; (3) the apparatus best adapted to carrying out the several operations. Bringing the Metal into Solution This feature.has been found to present no serious difficulties. Numerous solvents for copper are known, and it has been repeatedly demonstrated on a commercial scale that from 80 to 90 per cent. of the metal contained in an ore can be rapidly brought into solution. It is interesting to note, however, that all of the companies above referred to have selected sulphuric acid as the basis for a lixiviant. Where oxidized ore practically free from precious metals is treated simple leaching with

Jan 1, 1915