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By J. Weertman

An explanation is advanced for the recent results of Barrett and Sherby on the high-temperature creep of fee metals. Their measurements indicate that metals with a low stacking fault energy creep at a much slower rate than metals with a high stacking fault energy. The explanation is based on the assumption that the rate of core diffusion is much smaller in partial dislocations than in perfect dislocations. An experiment is suggested to test this assumption. The explanation also requires that the jog density is small on widely split dislocations. SHERBY and Barrett1,2 recently established an important result in the field of high-temperature steady-state creep. They have shown that fee metals whose dislocations split into partial dislocations separated by a wide stacking-fault ribbon creep at a much slower rate than fee metals whose dislocations are not split appreciably. The creep rates in the two cases may differ by a factor as high as 6000. (For the purpose of comparison, the test temperature of each metal was chosen so that its rate of self-diffusion was equal to a standard value. Similarly the stress levels were such that the ratio of the stress to an appropriate elastic modulus was the same for each metal. In all cases the stresses were sufficiently low that the steady-state creep rate was proportional to the stress raised to a power.) It is the purpose of the present paper to attempt an explanation of this interesting and significant result of Sherby and Barrett. The activation energies of high-temperature creep of the metals tested by Sherby and Barrett (aluminum, nickel, copper, and silver) were equal to their self-diffusion activation energies. Hence it appears reasonable to assume that this type of creep is controlled by a dislocation-climb process, which in turn is controlled by the diffusion of vacancies to or from dislocation lines. (It will be assumed that the diffusion of interstitial atoms is unimportant in the climb process. The analysis could be repeated for the case in which interstitial atoms are important.) In prior papers374 I have treated dislocation climb by using the assumptions that core diffusion is extremely fast down a dislocation and that a dislocation always maintains an appropriate vacancy concentration in its immediate vicinity. In this

Jan 1, 1965

By George R. Cowan

A number of studies hare been reported of the effects produced in metals subjected to deformation by shock waves with maximum pressures ranging from tens to hundreds of kilobars. On the basis of the equations for the flow of mass, momentum, and energy through a stationary shock front, the macroscopic stress-strain curve for the resulting shock deformation can be calculated within narrow limits from the experimentally determined Hugoniol curve. In relatively weak shocks which are preceded by an elastic wave, the stress rises above the clastic limit only as plastic deformation proceeds cold thus the shock has a long toe. In strong shocks that override the elastic wave a high stress is applied without prior plastic deformation. A more important effect of increasing the shock pressure is the generation of shear stresses, called supercrilical shear stresses, that exceed the strength of the perfect lattice. A change in the mechanism of deformation is expected to result from the onset of supercritical shear. The shock disordering of ordered Cu3Au in strong shocks appears to be an example of such a change. It is suggested that the formation of fine twins in copper and nickel and the formation of structures which enable visible twins to be formed in the rarefaction ware, observed in copper and presumably in disordered Cu3 Au, are related to the occurrence of supercritical shear in shock dcformation. In recent years several studies1,2 have been made of the changes in structural and mechanical properties of metals produced by the passage through the metals of strong shock-compression waves ranging from about 50 to 800 kbar pressure. Recent work involving dynamic measurements of the shock compression "Hugoniot" curves 3-8 of many metals has developed techniques and provided data required to obtain the shock pressure and the (transient! plastic deformation produced in the shock-conlpression experirnents.9 Shock deformation has been found to be much more effective than slow deformation in changing the mechanical properties of metals, when the two are compared on the basis of equal plasti strain, Holtzman and Cowan9 made quantitative estimates of the shearing stress occurring in a shock front in a metal by assuming that the shearing stress is similar to that occurring in a shock front in a viscous, heat-conducting fluid, with the addition of a yield stress. Taylor's solution9 for a weak shock was used to estimate pairs of values of shearing stress and thickness of the shock front obtained by assumed choices of the ratio of effective kinetic viscosity to thermal diffusivity. It was noted from these values that. unless the shock front is extremely thin. heat conduction has slight effect, and the shearing stress is nearly independent of the mechanism of deformation. This mechanism does, however, determine the thickness of the shock front and the rate of strain. Furthermore, since the maximum possible shearing stress occurring in shocks of moderate strength does not greatly exceed the shear stress occurring in conventional slow deformation, the mechanism of deformation is not expected to be qualitatively different. The greater effectiveness of shock deformation in changing the mechanical properties of metals can be attributed partly to the fact that dislocations, when driven by near-conventional stresses, cannot keep up with the shock front, thus necessitating a higher dislocation density than required for an equivalent slow strain. The fast uni-axial strain occurring in the thin shock front would also be expected to cause a larger number of dislocation intersections to occur. In the upper range of shock pressures that have been studied the estimated values of the shearing stress exceeded the estimated shear strength of a perfect crystal. Under these circumstances it is reasonable to expect that the mechanism of deformation might be considerably different from that involved in slow deformation. Except for the observation by smith1 of twins in shocked copper, the effects of shock waves on metals did not show any obvious or large changes in properties that would indicate the onset of a change in the mechanism of deformation. The recent investigation of the effect of shock waves on ordered and disordered specimens of Cu3Au by Beardmore, Holtzman, and ever" showed a spectacular decrease in the amount of long-range order retained by initially ordered Cu3Au when the shock pressure was raised from 290 to 370 kbar. Since Dr. Holtzman and I suspected that this behavior probably was due to the onset of a shearing stress in the shock front in Cu3Au which exceeded the limiting shear strength of the perfect crystal. it was considered appropriate to examine directly the shock-front equations for a solid. and to obtain a sound estimate of the shearing stress occurring in the front using equation of state data obtained from shock studies. In this paper an estimate is made of the

Jan 1, 1965

By T. S. Spice, H. L. Lovell, R. W. Utley

With the increased demand for lightweight aggregate, such materials have been manufactured from slags, clays, slates and, to a minor extent, the refuse of coal preparation processes. The latter source is attractive due to current interest in eliminating air pollution and improving the unsightly appearance of refuse piles as well as potential economic advantages, if a satisfactory product can be manufactured. A study has been made relating the composition of coal refuse, expressed as washability data, and the properties of a resulting aggregate. Three different refuse samples (bituminous and anthracite) were separated at gravities ranging from 1.4 to 2.96. Their chemical composition was determined. Aggregates were prepared in the laboratory from these fractions before and after ashing, at temperatures between 1250' and 1350°C. The specific gravity, expansion and compressive strength of the products were measured. The response of the refuse to bloat is related to the chemical composition of the ash to yield a glass of desirable viscosity and to the presence of a material which will form a gas in the appropriate temperature range. Carbonaceous material within the particle is a negative factor since after the glassy phase forms, oxygen cannot enter the mass thus inhibiting bloating. Precombustion of the refuse is also detrimental since it removes substances of gas-forming capability. The fraction sinking at 2.60 yielded an aggregate which had the lowest specific gravity, greatest expansion and greatest compressive strength. The purpose of this study was to seek and evaluate possible relationships between the composition of coal refuse, as expressed by washability data and factors affecting the production of a lightweight aggregate from refuse by bloating. The study was related to an intense program in the Department of Mineral Preparation at the Pennsyl- vania State University to study the possible elimination of air pollution from coal refuse fires by producing a low-carbon secondary refuse. Another phase of this program is considering possible uses of such a secondary refuse. Thus one study was to determine if a lightweight aggregate could be produced from this new refuse material and what effect the nature of refuse beneficiation would have upon the characteristics of a commercial aggregate product. It was hoped that these studies would assist in the design of a process and in establishing the optimum specific gravities at which refuse separation could be made in respect to the production of a low grade fuel from the float product and a raw material for lightweight aggregate from the sink product. The combination of producing a saleable low grade fuel and a lightweight aggregate, while at the same time minimizing disposal costs and air pollution contributions would be attractive to the coal mining industry. MECHANISM OF BLOATING Austin, Nunes and Sullivan,1 Ehlers,3 Everhart, 4 Riley7 and others, have stated that bloating is an expansion process in which two essential conditions exist simultaneously. These are: the development of a glassy phase over a relatively wide temperature range (the viscosity of this glassy phase plays a major role in the retention of the evolved gases) and the evolution of gases (SO2, SO3, CO2 and O2) from mineral decomposition in sufficient quantities at appropriate temperatures to form a cellular structure in the mass. Unless these two "type" reactions take place at the same time or in overlapping ranges of time and temperature, cellulation will not occur. In this event, the gas will escape or the melt will be too fluid to retain it; or if retained, the cells may be too large or the walls too thin for good strength in the product. The stages that occur when clays and shales are heated in an oxidizing atmosphere may be summarized as follows: 1) Drying and removal of free water to 200°C. 2) Absorbed water dehydration period (200 to 480°C). 3) Chemically-combined water dehydration period (480 to 700°C).

Jan 1, 1965

By Wayne L. Worrell

Thermodynamic data for the stable carbides and oxides of chromium, molybdenum, and tungsten have been critically eualuuted and are used to determine the stable condensed phases at 1 atm total pressure in each metal-carbon-oxygen system. Pourbaix-Ellingham diagrams have been constructed and are used to estimate the minimum temperatures neces.see)*y to oblain these metals by corbolhermic redlrction under reduced pressures. USING recently reported data for the carbides and oxides of chromium, molybdenum, and tungsten, the stable phases in the Group VI metal-carbon-oxygen systems at specific temperatures and pressures can be determined. The thermodynamically stable regions in each metal-carbon-oxygen system can be completely pictured using a Pourbaix-Ellingham diagram in which the two coordinates are oxygen potential (-RT In Po2) and temperature. Worrell and chipman' have described and constructed such diagrams for the metal-carbon-oxygen systems of vanadium, columbium, and tantalum. Downing2 has used similar diagrams to provide a description of the reactions in submerged arc furnaces. One of the examples which he cited was the Cr-C-O system; however, an improved diagram is presented in this paper using recently obtained data for the carbides of chromium. Although some of the oxides and carbides of the Group VI metals exist over slight ranges of composition,3 all solid phases are represented as stoi-chiometric compounds in the subsequent diagrams. Any error introduced into the calculated equilibria by neglecting the compositional variation of these phases is less than the uncertainty in the thermodynamic data. In a Pourbaix-Ellingham diagram for a three-component system, the phase rule requires that at equilibrium four condensed phases specify a point, three condensed phases determine a line, and two condensed phases define an area. To obtain a well-defined area at high oxygen potentials and teniperatures, the initial carbon to oxygen mole ratio is specified to be more than sufficient to reduce the oxide but not enough to convert all the metal to carbide. Thus, the lowest regions in the subse- quent Pourbaix-Ellingham diagrams represent areas in which the metal and its carbide are the stable condensed phases. Cr-C-O SYSTEM A) Thermodynamic Data. To simplify the subsequent calculations, all thermodynamic data are presented in the form of linear Gibbs-energy-of-formation* equations which were derived for the temperature range 505° to 2000°K and are reasonably accurate over the entire temperature ranges of the diagrams. The thermodynamic data for the compounds occurring in the Cr-C-O system are summarized in Table I. Several volatile chromium oxides have been reported,4 but their influence is negligible in the Cr-C-O system. Thermodynamic data for CO and CO2 were taken from the compilation of Coughlin.5 The only solid chromium oxide sufficiently stable to exist below 1800°K in the Cr-C-O system is Cr2Os.11 The Gibbs-energy-of-formation equation for Cr2O3 was obtained by revising the data tabulated in Coughlin,5 using the heat of formation of ah' and the high-temperature thermal data for chromium.7 In 1953 Richardson8 re-evaluated the original work of Kelley and coworkers,9 who measured the thermodynamic properties of the chromium carbides. However, the high-temperature equilibrium results of Boericke9 yield values for ?G°f of Cr2O3 which are 2 kcal more positive than the accepted data. His results for the chromium carbides are based on the same questionable equilibria. Gleiser10 recently determined the Gibbs energy of formation of Cr3C2 and the equation in Table I was calculated from her data and the thermal data of Kelley and coworkers.9 Thermodynamic data for the Cr7C3 and Cr23C6 carbides were obtained by combining the Cr3C2 data

Jan 1, 1965

By I. A. Lesk

The various materials utilized in the construction of integrated circuits, and the resultant materials interfaces, are discussed with emphasis on a materials system that is compatible with all types of integrated circuits and minimizes the number of different interfaces. Problems with interfaces may originate in the silicon, on its surface, and between other materials within the integrated-circuit package independent of the silicon. ThE difference between integrated-circuit theory and practice may generally be spelled out in terms of the difficulties in fabricating a desired structure. There are, of course, problems in forming the requisite materials, of the necessary composition and geometry, where needed. A distinct class of problem, however, is associated with interfaces— generally between different materials, but occasionally between regions of the same material. We require that each interfacial system perform its proper electrical, mechanical, and thermal function, and do so in an unchanging manner with time under the most severe operating conditions. In a practical sense, we deal in nonideal systems, such that it is generally not possible to form an interface exactly the way it was intended, even if we allow for a knowledge of the practical limitations of the fabrication system. Another way of looking at this situation is to realize that, when we form a group of interfaces under apparently the same experimental conditions, there are often differences of important consequence between them. Very high-magnification pictures, such as are obtained by an electron microscope, reveal fine structure that often differs over the area of a given sample, as well as from sample to sample. Low-magnification pictures look better, but don't eliminate the problem. The trend towards integrated circuits, and away from circuits fabricated utilizing separate components, is very strong in many areas of electronics. A typical silicon monolithic integrated circuit, still in place in the wafer on which it was fabricated, is shown in Fig. 1. The increased reliability which is being experienced through the use of integrated circuits can, to a large extent, be credited to the reduced complexity of the interface system that is present in the electronic system. A glance at Fig. 1, however, with all of its epitaxial and diffused p-n junctions, and interconnect system, shows that interfaces have been far from eliminated. Fig. 2, depicting a schematic cross-sectional view of a (partial) typical integrated circuit, illustrates in detail the numerous interfaces that occur in this type of structure. Besides the individual circuit elements, there are interfaces for isolation, and, Fig. 3, even a crossover requires a series of interfaces. What has been accomplished, however, irrespective of whether or not the total number of interfaces in the circuit is increased or decreased, is that the variety of interfaces is very much reduced. This is because there are fewer materials involved. Since the expense incurred in an R & D program to improve reliability is pretty much directly proportional to the variety of interfaces involved, it is economically advisable to work with integrated circuits for highest reliability. That is not to say that circuits built using standard components could not be made as reliable as integrated circuits, but that the expense involved because of the more complex over-all interface system would be much greater. Although electronic performance utilizing integrated circuits with all silicon elements (i.e., transistors, diodes, resistors, capacitors) is adequate for many applications, there are numerous instances where thin-film passive elements must

Jan 1, 1965

By A. L. Mular

The flotability of crushed zinc oxide pellets which were doped to produce more n-type or less n-type (more p-type) properties was studied with a Halli-mond tube. Flotation data are presented to show that the pH at which 50% recovery occurs and the collector concentration for 50% recovery depends upon the concentration of doping agent added substitu-tionally for zinc in zinc oxide. The time of sintering of pellets has a slight effect on flotation behavior. A speculative model is proposed to explain the observed behavior in light of the fact that zinc oxide is a semiconductor and has a space charge region at the surface. Experimental verification is necessary before the proposed model can be established as correct. In recent years, the attachment of flotation reagents to minerals has been shown to depend upon the behavior of an electrical double layer which exists in the liquid near the mineral-liquid interface.' Thus, a mineral placed in water will undergo a surface re-arrangement, most likely be preferential dissociation of lattice atoms or by surface adsorp-tion-desorption reactions, to form a dissociation electrical double layer with the solution. Among the many factors which influence adsorption processes, the past history of the mineral itself is one of the most important. Because of trace impurities, minerals from different localities may exhibit marked differences in flotation behavior. This is not unexpected, since investigators who have studied the detailed structure of the double layer's3 have known for some time that the impurity content of many minerals may exert strong influence on double layer variables. For this reason, their studies were usually made with minerals of high purity. The precise relationship between impurities in a mineral and double layer parameters such as capacity and electrostatic potential has been obscure. However, impurities in a semiconductor type mineral which is in contact with a solution have been recently shown to produce changes in the properties of a space charge layer which extends into the bulk of the semiconductor to a distance of one micron or more.4 The double layer is influenced by the space charge layer, whose origin is best discussed in terms of the band theory of solids. A qualitative description of the behavior of impurities in the bulk of a semiconductor, from a chemical point of view, is useful at this point. Briefly, impurities or defects (lattice vacancies, interstitials, etc.) in semiconductors such as PbS, ZnS, FeS2, Cu2S, NiS, NiO, Fe2O3, ZnO, CdS, MnO2 and many others, behave somewhat like acids or bases in water. For example, water dissociates into hydrogen and hydroxyl ions according to

Jan 1, 1965

By Carlos G. Valenzuela

The value generally accepted for stacking-fault energy, of copper has been approximately 40 ergs per sq cm based on Fullman's2 value for the coherent twin-boundary energy and the assumption that is twice the twin boundary energy However, Thornton and coworkers8 determined that the lower limit of for copper is approximately 60 ergs per sq cm, based on measurements of dislocation-node radii. They suggested that the assumption of = 2t is invalid. It is the purpose of this note to present results which indicate that the values of obtained by measurement of twin-grain boundary intersections and the values obtained by measurement of dislocation-node radii are actually compatible. The most reliable values for of the a brasses, based on electron-microscope observation of dislocation nodes, are probably those values reported by Smallman and Green6 who applied the Siems correction (1961) to data obtained by Howie and Swann.3 These values shown in Fig. 1 give an extrapolated value of approximately 70 ergs per sq cm for pure copper. In the present work, Fullman's method for determining the stacking-fault energy of copper was extended to the a brasses. High-purity copper (99.999 pet) and high-purity zinc (99.999 pet) were mixed in proportioned amounts and melted in sealed and evacuated quartz tubes. The alloys were homogenized for a week at 750°C and chemically analyzed by means of X-ray fluorescence. These alloys, along with a specimen of pure copper, were rolled to 98 pet reduction and a thickness of 0.009 in., resealed, and annealed for 40 hr at 715°C. Values for the ratio of twin-boundary energy to the grain-boundary energy, it gb, were obtained from measurements of dihedral angles formed at the intersections of twin boundaries and grain boundaries by using Fullman's2 mechanical analogy of surface tensions acting at the intersection of an annealing twin and a grain boundary. The angles between the twin traces and the grain boundaries were measured for a large number of twin-grain boundary intersections at a magnification of X500 using a rotating mechanical stage on a Reichert metallograph. The rotary stage has a calibrated angle scale with vernier so that measurements can be made to 0.1 deg. The mean twin-grain boundary energy and standard deviation were calculated for copper and each of the brasses by the use of an IBM 7072 computer. It was found that the mean value of gb stabilized after approximately 100 twin-angle measurements. This was determined by plotting the mean against the number of angles measured. Since the measured angles deviate from true dihedral angles, a correction factor for grain orientation, discussed below, was applied. The stacking-fault energy was then calculated from these values and the values of grain-boundary energy derived by Taylor.7 The data obtained are tabulated in Table I. Values for stacking-fault energy are plotted in Fig. 1. The value of gb for the specimen of 1.03 pet Zn is close to the value obtained by Fullman2 for OFHC (99.98 pet) copper, 0.045. It is believed that the purity of the copper affects gb significantly. The 99.999 pet purity Cu used in this investigation yielded a value of yt/ygb, 0.76, which is much higher than that obtained by Fullman. Additional evidence suggesting that the purity of

Jan 1, 1965

By M. A. Dayananda, R. E. Grace

Vapor-solid diffusion couples were employed in a study of ternary diffusion in the single-phase copper-rich corner of the Cu-Zn-Mn system Interdiffusion coefficients were measured at three different compositions corresponding to the intersections of diffusion paths determined at 850°C. Intrinsic diffusion coefficients were determined at two compositions by the Philibert-Guy method. New relations between the various intrinsic diffusion coefficients are also presented. MOST of the investigations of ternary diffusion have been made with "sandwich" couples formed by welding together two homogeneous solid solutions with or without markers placed at the interface. With such couples Kirkaldy and his coworkers1,2 have determined interdiffusion coefficients which describe ternary diffusion in the substitutional alloy systems, Cu-Mn-A1 and Zn-Cu-Al. Guy and Leroy3 have reported intrinsic diffusion coefficients for Co-Ni-Cr alloys as a function of composition using the analysis of Philibert and Guy.4 The use of semi-infinite diffusion couples, for example, vapor-solid couples, where the diffusing species are supplied from a vapor source in contact with a diffusion disk, has so far been confined to studies of binary diffusion. Balluffi et a1.5,6 have successfully determined the interdiffusion as well as the intrinsic diffusion coefficients in several binary metallic systems employing vapor-solid couples with markers initially placed at the vapor-solid interface. They have also discussed the general advantages and limitations of such couples. Vapor-solid diffusion couples can successfully be employed in ternary diffusion studies. The importance of such couples in ternary diffusion lies in the fact that inert markers lie close to the vapor-solid interface, and the composition of the marker plane is virtually known before experimentation begins. Another minor advantage is that the method of Philibert and Guy4 may be used with three alloys instead of four. Lastly, the diffusion paths need not be S-shaped, as pointed out by Meijering7 for "sandwich" couples. The Cu-Zn-Mn system is convenient for ternary diffusion studies because of the large single-phase field in the copper-rich corner. The vapor pressure of zinc above such alloys is known, and X-ray measurements indicate that the molar volume is nearly constant over a wide range of compositions.8,9 It is the purpose of this paper a) to extend the analysis of Balluffi and seigle5 to permit an evaluation of interdiffusion coefficients in ternary vapor-solid couples, b) to use the method of Philibert and Guy to determine intrinsic diffusion coefficients with such couples, and c) to present experimental data on both interdiffusion and intrinsic diffusion coefficients for the Cu-Zn-Mn system at 850°C. INTERDIFFUSION IN TERNARY VAPOR-SOLID COUPLES The analysis of Balluffi and seigle5 is extended in this section to a vapor-solid couple where two solutes diffuse from a vapor source into a ternary solid solution. To take into account the expansion of the diffusion disk caused by the absorption of mass from the vapor phase, the total fluxes are expressed on the basis of a coordinate system that moves with the velocity of the vapor-solid interface; thus. where D3ij are the intrinsic diffusion coefficients,4 v(x, t) is the local Kirkendall velocity of mass flow, and F(t) is the negative velocity of the vapor-solid interface (x = 0). Both these velocities are based on a fixed coordinate system far removed from the diffusion zone. Using the continuity relations and Darken's method1' for a ternary system in which components 1 and 2 diffuse from the vapor phase into a solid of negligible vapor pressure, one obtains

Jan 1, 1965

By S. E. Bronisz, R. E. Tate

s-plutonium samples possessing a strong growth texture have been produced by allowing them to transform under pressure from p to a. A fiber texture with [010] parallel to the pressure axis results. The textured samples are expected to be useful in determining the effects of crystallographic orientation on the physical properties of a plutonium, and initial results of measurements of resistivity and mechanical properties are described. THE crystal structure of a plutonium1 is mono-clinic, P21/m, and many of the metal's properties should reflect the crystallographic anisotropy. Unfortunately, it has not yet been possible to grow useful sizes of single crystals of a plutonium. Therefore, few of plutonium's orientation-sensitive properties have been determined as a function of crystallographic orientation. One way to gain information about at least some of the orientation-dependent properties is to study a highly textured sample. Such samples have been produced by cold rolling a plutonium,2 but they are necessarily very small in one dimension. We have now successfully used two other techniques to produce highly textured samples, not limited to small thicknesses. METHODS OF PRODUCING PREFERRED ORIENTATION The texture is produced by causing the plutonium to transform from ß to a while under pressure. It was observed by Gardner3 that applying a compres-sive load during the transformation resulted in the formation of columnar grains of a plutonium, and Cramer4 observed a similar structure in some diffusion couples rolled in the P phase. Neither of these workers, however, investigated the subject beyond these observations. The more flexible of the two methods developed is that of compressive loading. The technique is to enclose a sample of plutonium in a die assembly before applying the load. It is possible, of course, to dispense with the die and simply press the sample between two platens. In this case, however, the unrestrained sample deforms during the pressing, making it difficult to maintain the load and to control the final sample thickness. This compressive loading technique has been used on specimens ranging from 1/4 to 3 in. diameter, with height-to-diameter ratios ranging from 5 : l to 1:6. The procedure begins with loading the sample, a right cylinder of a plutonium, into the pressing die. Plastic deformation of the sample while it is being pressed is minimized by machining the sample so that its diameter is nearly the same as that of the die barrel. Then the loaded die assembly is placed in a vacuum pressing can that fits on a hydraulic press. After a vacuum is achieved the die assembly is heated to 180°C and equilibrated. The load is then applied and the specimen and die are allowed to cool to about 40° to 50°C before the pressure is removed. The resulting sample is composed of rod-shaped a -plutonium grains, the rod axes being parallel to the cylinder axis and the pressing direction. Photomicrographs of the oriented structure are shown in Fig. 1. Although most of the specimen is composed of grains whose rod axes are parallel to the cylinder axis, a thin, peripheral layer consists of rod-shaped grains whose rod axes are perpendicular to the cylinder axis. Presumably, the highly plastic nature of p plutonium leads to approximately hydrostatic conditions during the initial stages of the P — a transformation under pressure. At this time, the grains in the peripheral layer would have grown parallel to the local force direction. During the latter stages of the transformation, the accompanying volume contraction would have eliminated the radial forces, leaving only the axial force and resulting in the growth of the observed structure. The growth texture did not form without the application of pressure. Attempts were made to produce the texture by repeating the standard temperature cycle without

Jan 1, 1965

By R. Wiesenthal

A method is developed for improving the low recovery efficiency which results when viscous oils are flooded by water. Viscous oil has been diluted with a lighter liquid miscible in it in any ratio which produces a mixture possessing a reduced viscosity and which is then displaced by water. Light gasoline was used in these tests to reduce the viscosity of the oil in place. Oils possessing viscosities in the range of 1.28 to 324 cp at the test temperature of 30C were displaced from a cylindrical unconsolidated sand core, with a length of 2 m (6.6 ft) and a diameter of 10 cm (3.9 in.) at a flood of 6.27 cc/sq cm/hr. In two test series up to I PV of light gasoline was injected into the core before water flooding. In the first series the recovery of a low-viscosity oil (1.28 cp) increased as the volume of light gasoline was increased. However, only the oil which could not be recovered by water flooding alone could be replaced by the light gasoline. In the other series, the recovery of a more viscous oil (13.5 cp) was not increased even if large quantities of light gasoline were injected. An oil bank built up ahead of the water front so that the flood water met with equivalent saturation conditions, as would be the case in flooding solely with water. However, the recovery of more viscous oils could be increased substantially when the core was first flooded with water, followed by a slug of light gasoline, and then flooded with water again. Furthermore, an oil bank ,built up ahead of the second water front. The formation of this oil bank is particularly favorable for the displacement process; the greater part of the light gasoline injected was pushed out of the core ahead of the oil and recovered. Using a light oil of low viscosity, it was possible to replace only the residual oil that could not be recovered by water flooding by the light gasoline. As the basic study had shown that highly viscous oils could be recovered by flooding first with water, then with light gasoline, followed by a second injection of water, the study was extended by tests made with reservoir fluids and cores taken from the low-gravity oil reservoir of the Wietze field, Germany. A great increase in recovery over flooding with water alone was obtained in these tests. The results may show a way to recover high-viscosity oils by a comparatively simple flooding procedure. INTRODUCTION In fields where oil recovery has not benefited from natural water drive, increased recovery may be obtained by the injection of water into the reservoir, especially in the case of fields which produce high-gravity, low-viscosity oil. There is a rather close relation between the viscosity of the reservoir fluid and the recovery that can be obtained by water flooding. As the viscosity increases the oil recovery decreases proportionately, so that an oil viscosity about 30 times that of water is generally considered to be the upper limit for an economically successful water flood.' This limitation has been recognized theoretically by Buckley and Leverett,' and has been verified by numerous laboratory flooding tests, such as by Croes and Schwarz,V n the viscosity ratio range of oil to water from 1 to 500. The reason for the inferior recovery of viscous oils by water flooding can best be understood by considering the mechanism of flood tests. In such tests water is introduced into one end of a sand-packed tube which is saturated with oil of the viscosity to be tested, and oil is produced from, the other end. Oil, with a viscosity lower than that of water, is pushed ahead of the advancing water with considerable uniformity, and irregularities in the displacement process tend to be eliminated as the oil saturation decreases and the water saturation increases. However, oil recovery is not complete, for the water forms interfaces with the oil and traps residual oil droplets in certain of the pore spaces. These residual oil droplets are distributed rather uniformly through the sand, and they are not susceptible to recovery regardless of the amount of water passed through the test cylinder. In the case of an oil possessing a viscosity greater than that of water, the injected water tends to move irregularly through the sand in the test cylinder. At the place in the sand where initial water movement takes place, resistance to the movement of water is lowered and the water finger so formed will grow perceptibly; it will extend to the outlet end of the test cylinder so that a breakthrough of water takes place long before much of the oil-saturated volume of the sand has come in contact with water. Once the breakthrough of water takes place, the water-oil ratio is gradually approaching the economic limit, even though much of the oil in the test cylinder remains unaffected by water. Disconnected drops of oil are trapped in the portion of the sand that has been invaded by water, just as when an oil of low viscosity is flooded. The poor recovery of the more viscous oils, therefore, is due to the irregularity of water movement through the test cylinder, and the rate of water movement through restricted sections of the oil-saturated sand increases with the more viscous oils. There are three ways whereby the recovery of viscous oils by water flooding can be improved:' (1) adding materials which will increase the vis-

Jan 1, 1965

By R. J. Walter, W. T. Chandler

The Ch-H phase diagram was determined for by-drogen concentrations up to ChHo.9 at temperatures below 400°P'. The phase diagram includes a mis-cibility gap and a eutectoid transformation. A peri-tectoid transformation is postulated at the hydrogen-rich end of the diagram, Phase diagrams were determined for two levels oj purity, of the columbium. A single solid solution exists in the Cb-H system above 400°F. There has been considcrable disagreement among investigators concerning the system at temperatures below 400°F. Albrecht, Goode, and ~allett' proposed a miscibility gap containing two bcc phases with the two lattice parameters converging at about 140°C (285-F), and Brauer and ~erman' found a two-phase room-temperature region between 10 and 41 at. pct H. At sufficiently high hydrogen concentrations in the one-phase region, the hydrogen-rich phase was found to be face-centered orthorhombic. Wainwright, Cook, and Hopkills3 recently reported that the face centered orthorhombic hydride phase is derived from a unit cell which is slightly tetragonal with a small departure from 90 deg of the angle (y) opposite the r axis. The orthorhombic hydride phase was observed for hydrogen concentrations between 0.2 and 0.8 H/Cb atom ratio. Paxton and coworkers4 found that needlelike hydride plates formed in a hydrogen-charged columbium single crystal and suggested that this transformation possessed the characteristics of a diffusionless phase transformation. On the basis of room-temperature, X-ray diffraction data, komjathy' suggested that an order-disorder or martensitic transformation occurs. In the present study, the Cb-H system was investigated to resolve the discrepancies found in the literature for this system. PROCEDURE The columbium specimens were prepared from two heats of wrought 1/2-in.-diameter electron-beam melted columbium rod and from two columbium powders of -80 mesh size of different impurity contents. The columbium bar stock was pur chased from Urah Chmg Corp.; the 99 and 99.5 pct purity colulnbium powders were obtained from Fansteel Metallurgical Corp. and Kern Chemical Co.. respectively. The chemical analyses of the columbium bar and powders are listed in Table I. Hydrogen charging was performed by exposing the columbium specimens to hydrogen at 1 atm pressure at various temperatures. After exposure the specimens were quenched to prevent the hydrogen pickup which would take place if cooled in hydrogen, or the hydrogen loss that would occur if cooled in an inert gas. Adequate hydrogen purity was achieved by passing high-purity tank hydrogen (maximum 5 ppm total impurities) through an Engelhard catalytic Deoxo unit, magnesium per chlorate desiccant, and finally through activated charcoal at the temperature of boiling nitrogen. Activated charcoal at -321°F has been reported6 to remove impurities from hydrogen to a nondetectable level. A schematic representation of the heat-treating apparatus is shown in Fig. 1. A metal-sheathed thermocouple embedded in the colun~bium specimen was used to control the temperature during heat treatment and to pull the specimen boat into

Jan 1, 1965

By H. E. Biber

DURING the production of tin plate a thin layer of FeSn2, is formed at the interface between the steel sheet and the protective tin coating. Because excessive amounts of this alloy layer are undesirable, the kinetics of its formation is a subject of interest in the tin-plate industry. A recent study of this subject at our laboratory uncovered a relationship which should be of general interest to anyone studying kinetics of reactions in metallic systems. It had been previously concluded that, at any given temperature in the range 175" to 330°C, the Fe-Sn alloy layer would have a parabolic growth rate.1,2 However, our studies showed that this rule apparently holds only when the tin plate is heated very slowly to the "reaction" temperature; when the tin plate is rapidly heated, considerably different growth rates occur. An example of this effect of heating rate on growth behavior is contained in the accompanying results of alloy-layer growth measurements at 240°C in oil baths stirred at 10,500, 1800, and 0 rpm. The heating curves for these three conditions are given in Fig. 1, and the growth data are presented in Fig. 2. With the rapid heating rate, provided by the stirring at 10,500 rpm, the alloy layer had three distinct stages of growth. In the initial stage, which persisted well beyond the time required to heat the tin plate to bath temperature, the alloy layer formed very rapidly. The growth followed a rate law of the form w = ktn where n > 1. This initial stage was followed by a growth-retardation stage of about 50-sec duration in which little additional alloy was formed. In the third stage the growth again followed a rate law of the form w = ktn, but here « =0.3. With the intermediate heating rate provided by stirring at 1800 rpm, the three-stage nature was less pronounced and the slope of the third stage increased (i.e., n > 0.3). With the slow heating rate provided by the unstirred oil bath, the alloy layer grew in two stages. The initial rapid-growth stage persisted only until the specimen was heated to bath temperature, no growth retardation was observed, and the slope of the main portion of the plotted data was greater than in the stirred baths, having a value of almost 0.5. Similar results were obtained for other bath temperatures in the range 200" to 300°C. This effect of heating rate on growth behavior may be due to changes in the rate of nucleation of FeSn, crystallites. The iron and tin are in contact from the onset of heating. Thus the initial formation of FeSn, occurs not at the "reaction" temperature but rather while the tin plate is being heated to that temperature. Because nucleation is in general temperature-dependent, different heating rates could cause different over-all nucleation rates, which in turn could cause different growth behaviors. A more detailed discussion of the growth of Fe-Sn alloy layer and the effect of heating rate will be published shortly.

Jan 1, 1965

By C. Feng, I. R. Kramer

A study was conducted to determine the influence of the surface on the yield point of fcc metals and high-purity iron. For the high-purity fcc metals, the yield Point produced by restraining a specimen may be eliminated by removing a sufficient amount of the layer. A yield point similar to that in fcc metals was found when iron specimens were pre-strained after a prior deformation. This yield point is not due to an aging effect but is associated with the surface layer. The yield points in age-hardenable aluminum alloy and those connected with "work softening" are not affected by a surface-removal treatment and are, therefore, caused by bulk-type dislocation reactions. The yield point which appears in previously strained fcc metals has been the subject of numerous studies. Several theories have been advanced to explain this "unloading-reloading" yield point. Cottrell and stokes,' from their study on the effect of temperature on plastic properties of high-purity aluminum, considered that it was the result of an avalanche "breakdown" of Lomer-Cottrell sessile dislocations. Haasen and Kelly2 extended this concept of dislocation-dislocation interaction to account for the yield point when unloading and reloading was carried out at the same temperature. On the other hand, strain aging was found to be responsible for the yield point in A1-Mg alloy by Westwood and Broom,3 and in aluminum alloys containing various amounts of alloying elements by Smallman, Williamson, and Ardley.4 In these cases, the yield point is considered to be associated with the locking of dislocations by impurity atoms. Birn-baum and filer5,6 and Takamura and muira7 reported that, when a high-purity copper specimen was prestrained, then held at a lower stress, and finally reloaded at the prestrain temperature, a larger yield point was observed. Such an increase was attributed to the locking of dislocations by point defects. In addition, Bolling8 suggested that both mechanisms, i.e., dislocation-dislocation interaction and strain aging, are responsible for the yield phenomenon, at least in a brass. Thus, there appears to be experimental evidence for both the strain aging and dislocation-dislocation interaction theories to explain the yield point in the fcc metals and alloys. In a previous article,9 one of the authors observed that, if sufficient amounts of metal were electrolti-cally removed after deformation of a high-purity aluminum single crystal, the yield point did not appear upon reloading. Continued pursuit in this area revealed that the effect of the surface on the yield-point phenomenon is not limited to one metal but affects a variety of metals of different lattice structures. Nor is the effect limited to the yield points produced by simple unloading-reloading at constant temperature; the surface exerts an important role on the yield point even when the temperature is changed at some stage during the test. It is the intent of the present article to give additional information regarding the effect of the surface on the yield-point phenomenon and to show the association between the yield point in both fcc and bcc metals and the existence of a heavy concentration of dislocation in the region near the surface of a deformed specimen.10 EXPERIMENTAL Materials. The single crystals used in this study had a nominal cross section of 0.125 by 0.125 in. and a 3-in. gage length and were prepared by a modified Bridgman technique. The initial purity for the metals was 99.997, 99.999, and 99.999 pct for aluminum, copper, and gold, respectively. Bar stock of these same materials was used in the preparation of the polycrystalline specimens of aluminum and copper. The iron specimens were machined from rods of "ferrovac", reported to have a purity of 99.98 pct. In addition, a precipitation-hardening aluminum alloy, containing 1.5 pct Cu, 2.5 pct Mg, and 5.5 pct Zn, was used. The polycrystalline specimens of iron, copper, and the aluminum alloy had a diameter of 0.17 in. and a gage length of 2 in. while the high-purity aluminum specimen had a nominal rec-

Jan 1, 1965

By H. H. Rachford

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

Jan 1, 1965

Jan 1, 1965

By D. C. Shelton

This paper discusses the metallurgical testing procedures and their applications at the laboratories and mills of Pima Mining Co. The author shows, using discussions and case histories, that routine sampling and evaluation of daily and monthly data can be as valuable as thorough laboratory investigations and mill test work. A great deal of valuable information can be made available this way. This paper discusses laboratory and mill metal-lurgical testing procedures and their applications at Pima Mining Co., located about 25 miles southwest of Tuscon, Ariz. The Company, incorporated in 1951 (the year the orebody was found) in California to operate the Pima mine, is jointly owned by Cyprus Mines Corp., Utah Contruction and Mining Co., and Union Oil Co. Milling started in December 1956. The main Pima orebody is a contact metamorphic vein of copper-bearing hornfels with an average dip of 45° to the south with an east-west strike. The hanging and footwalls are quartzitic pyroclastics (arkosite) containing some sulfides. Barren igneous intrusions are also present. Conglomerates and alluvial wash cover the deposit to a depth averaging about 200 ft. The principal copper mineral is chal-copyrite. Native copper, chalcocite, and minor amounts of chrysocolla and other copper minerals are also present, together with sphalerite and some molybdenite. Generally, it has been noted that the ratio of chalcocite to chalcopyrite is higher in the lower grade ores, while as the grade increases, there are only minor amounts of chalcocite. Open pit mining is employed at Pima, using both trucks and an inclined skiphoist system. A detailed description of Pima Mining Co. operations was presented by Spaulding et all. More recently another orebody to the north and east of the present pit has been discovered and will be placed in operation within a few years. This ore is of a porphyritic rather than a lode nature since values are disseminated in both igneous and metamor- phosed sedimentary rocks. The new orebody is expected to be harder and cleaner than the present deposit. The views expressed in this article are those of the author and do not necessarily reflect those of Pima Mining Co. nor of the profession in general. PlMA MILL The following outline of milling practice is presented to furnish a background for later chapters of this report wherein specific problems will be detailed and analyzed. Run of mine ore is crushed in three stages, using conventional equipment to 85% minus 1/2-in. for feed to two 10 x l6-ft rod mills operating in open circuit. Each rod mill discharge is split between two 10% x 13-ft ball mills in closed circuit with three 20-in. cyclones. In addition, a 7 x 12-ft ball mill with one 20-in. cyclone receives part of the discharge from one of the rod mills. This equipment was manufactured by Allis Chalmers and Equipment Engineers. The cyclone overflows are combined, sampled and, after joining the regrind cyclone overflow, are distributed into 12 10-cell Fagergren 66-in. flotation machines. The primary rougher concentrate produced

Jan 1, 1965

By J. J. Taber, W. K. Meyer

Experiments on consolidated sandstones have shown that a variety of conditions are responsible for the wide range of behavior observed when oil and water are displaced simultaneously by a solvent which is miscible with both. The type of displacement is influenced most strongly by the relation between the plait point of the ternary phase diagram and the composition path followed by the system as it achieves mis-cibility. Neglecting viscosity, the displacement becomes less efficient as the distance between the composition path and plait point is increased in either direction so that a very wide spectrum of displacements is possible with different alcohol, oil and brine systems. It is possible by choosing various composition paths as miscibility is achieved to exercise some control over the actual displacement mechanism. Control over the composition path is exercised by adding oil or water in specific amounts to the alcohol prior to its injection into the porous medium. This technique apparently makes it possible to obtain piston-like displacements with systems which are usually characterized by the efficient displacement of only one of the two phases i.e., either oil or water, while the other phase lags behind. However, the simultaneous displacement of oil and water is not as efficient as other miscible displacements at a similar mobility ratio. The evidence indicates that both oil and water "leak" into the alcohol "piston" in compensating amounts. With oils of low viscosities the displacement is inefficient because the low oil saturation in the stabilized bank causes oil to be trapped by water before miscibility is attained. INTRODUCTION The simultaneous displacement of oil and water by solvents such as alcohol has been investigated in the laboratory and in the field. The laboratorv workers investigating all-liquid miscible systems have recognized the great importance that the nature of the traingular phase diagram exerts on the efficiency of the miscible displacement. Gatlin and Slobod pointed out that displacement efficiency will be improved if miscibility can be retained for long periods and that this behavior tends to be followed if the applicable phase diagrams have very low binodal curves. In their unconsolidated sand tests the alcohol was considered an ideal miscible piston displacing both oil and water phases. Later workers have pointed out that an important feature of the phase diagram as far as oil recovery is concerned is the location of the plait point. This is particularly true in the case of consolidated Sandstone.3 Since the original discussion of this effect, the importance of plait-point location has been confirmed and discussed by other author The early workers394 recognized that the position of the plait point could be altered by changing the oil or the alcohol used in an experiment. In addition, recent work has demonstrated that the plait point can be shifted by altering the nature and concentration of dissolved salts in the aqueous phase. However, the entire scope of the relationship between displacement and plait point has not been discussed previously and a technique for changing the composition path as miscibility is achieved in a particular ternary system, i.e., oil, water and solvent, has not been demonstrated. * The importance of oil viscosity on the efficiency of oil displacement by alcohol has not previously been observed, probably because the range of viscosities used in earlier experiments was too restricted. It is the object of this paper to describe the relationships between the ternary phase diagram, fluid properties and the displacement achieved. A technique for controlling the nature of the displacement is also presented. THEORY AND DEFINITIONS PISTON-LIKE THEORY The theory of alcohol flooding has been discussed in some detail.2-4 The concept was advanced that

Jan 1, 1965

By A. J. McEvily, R. C. Boettner, C. Laird

The processes leading to fatigue failure in the low-cycle range were studied to obtain an understanding of the basis of Coffin's law. Particular attention was paid to the manner of mack nucleation and to the determination of the portion of the total lifetime spent in crack propagation. It was observed that cracks are nucleated at surface notches meated during reversed plastic deformation, Principally at grain boundaries, and that crack growth occupies greater than 75 pct of the fatigue life. When inclusions are present, they are often the primary sites of crack initiation. From consideration of the incremental distances advanced by a crack in each cycle and of the lifetimes of different materials, it appears that the universality of Coffin's law arises from the similarity of crack-tip strain for a given applied strain amplitude, irrespecti7:e of material. STUDIES of low-cycle fatigue have been particularly rewarding in that a simple correlation between fatigue lifetime and plastic-strain range has been shown to exist. This empirical relationship takes the forml,2 Nner=C [1] where N is the number of cycles to failure, Er is the plastic-strain range defined as the total plastic strain per cycle (the sum of the tensile plastic strain plus the compressive plastic strain), n, the exponent, is a constant independent of the material to a first-order approximation and often has a value of about 0.5, and C is a constant which for a number of ductile and metallurgically stable materials is approximately 0.65 for fully reversed strain.3 This relationship has been shown to be valid for a wide variety of metals and alloys and is often referred to as Coffin's law. However, it is yet not clear why so many different metals and alloys exhibit the same over-all behavior in the low-cycle range. Less is known about the mechanisms of fatigue failure in the low-cycle range than in the high-cycle range, but it is expected that the processes would have much in common. For example, an important characteristic common to both high-and low-cycle ranges is that fatigue crack propagation can occupy a considerable portion of the total lifetime. This has been shown by Laird and smith4 by a count of the number of ripples present on the fracture surface of copper specimens, each ripple corresponding to one cycle of load. On the other hand, some marked differences have been noted. For example, in copper,5 nickel, and aluminum4 there is a greater tendency for grain boundary cracking to occur as the strain amplitude is increased. The purpose of the present work was to study further the processes leading to fatigue failure in the low-cycle range and to obtain an understanding of the basis for the validity of Coffin's law. Particular attention has been paid to the manner of crack initiation and to the determination of the portion of total lifetime spent in crack propagation. MATERIALS A number of metals and alloys were tested, although more attention was focused on a particular few, once general trends had become apparent. Alloys were selected so as to investigate the effects of crystal structure, number of phases, stacking-fault energy, and impurity content. The materials in this grouping were: high-purity copper OFHC copper 1100 aluminum (commercially pure) 70-30 brass (Cu-30 wt pct Zn)

Jan 1, 1965

By W. M. Robertson

The kinetics of grain boundary groove formation on copper surfaces immersed in liquid lead have been studied over the temperature range of 400° to 900°C. The groove widths were Proportional to the cube root of the annealing time, indicating that the diffusion of copper through the saturated liquid-lead solution is the mechanism by which grooves form. The rate constant for the process can be calculated by a theory due to Mullins. Using published data for the solubility of copper in liquid lead, for the interfacial energy of the solid copper-liquid lead interface, and for the diffusion coefficient of copper in liquid lead, the calculated rate constants almost exactly reproduce the measured values over the entire temperature range. The decay of scratches placed on copper surfaces has also been studied. The rate constant for scratch decay agrees with that for grain boundary groove growth, though scratch decay is sensitive to convection currents in the liquid. The interaction of solid and liquid metals has been studied extensively and has been found to be rather complex. Many of the studies have been complicated by a host of competing effects, including temperature gradients, concentration gradients, the formation of one or more intermetallic phases, natural or forced convection, and the presence in both the solid and liquid of considerable amounts of impurities and alloying elements. Recently theories have been developed of changes in surface profiles driven by capillary forces,' which allow the interaction of the solid and liquid to be analyzed quite directly. The present paper reports a study of the formation of grain boundary grooves on pure copper immersed in liquid lead, which allows the theory to be checked quantitatively. The Cu-Pb equilibrium diagram is quite simple: there are no intermetallic compounds, copper is just slightly soluble in liquid lead, and lead is almost completely insoluble in solid copper.2 The Cu-Pb system has been studied extensively,3-9 and all of the quantities—interfacial energy, diffusion coefficients, and equilibrium solubilities-necessary to calculate the rate of groove growth by a volume-diffusion mechanism are known. The kinetics of grain boundary grooving and scratch smoothing have been studied on the noble metals and the iron group metals in a reducing atmosphere or in vacuum.10 The main interest of these studies has been the determination of surface-diffusion coefficients at metal-gas interfaces using the theories developed by Mullins.1 The present paper uses similar methods for the study of diffusion processes at the interface between two condensed phases. There has been one previous study" of the kinetics of groove growth in a solid-liquid system, which, however, was troubled by the fact that neither interface energies nor diffusion coefficients were known in the Ni-S system studied. THEORY The theory of grain boundary groove growth has been developed by Mullins for the cases of volume diffusion," surface diffusion," and a combination of the two processes.14 He has also analyzed the kinetics of the flattening of a scratched surface by these processes.l5,l6 Several assumptions and approximations were used in the derivations of the surface profile shapes. The applicability of these assumptions and approximations to the present system will be considered in the discussion. At the intersection of a grain boundary with an initially flat interface the equilibrium between the interfacial energy and the grain boundary energy establishes an equilibrium groove angle. This induces curvatures in the interface. The chemical potential of material at a curved interface is higher than at a flat interface, so that material moves away from the region of the grain boundary. Mullins' calculations indicated that the groove profile would be similar to that shown schematically in Fig. 1. Small humps form above the level of the original flat surface. For a volume-diffusion mechanism the separation, w, of these humps at a time, t, is given by and where co is the equilibrium concentration of the solid in the liquid, y, the solid-liquid interfacial free energy, O the volume occupied by a solute atom in the liquid, D the diffusion coefficient of the solid in the liquid, and kT has its usual meaning. For a surface-diffusion mechanism the groove width is proportional to the fourth root of the time. For grooves forming by a combined surface and volume-diffusion mechanism the exponent of the

Jan 1, 1965

By F. Wald, A. J. Rosenberg

The general features of the constitution of the B-Pt system were determined using standard rnetal-lograph~c, thermoanalytic, and X-ray diffraction techniques. Three compound were found. Two of these, Pt3B and Pt,B, are formed by peritectic reactions at 523° and 890°C, respectively. The third, Pt3B,, is congruently melting with a flat maximum at 940°C but decomposes eutectoidally in to Pt,B ant1 boron nt - 600° to 650°C. THE low-temperature allomorph of boron (red, simple rhombohedra1 a boron) is of scientific and technological interest as an elemental semiconductor.' However, the studies of this material have been hampered by its reported instability above 1200"~ which precludes crystal growth from the melt (mp - 2200°C). Crystallization from platinum solutions has been suggested as an alternative crystal-growth technique, but has met with only limited success.' The technique depends upon the existence of a significant difference between the eutectic temperature and the transformation temperature of boron. In order to clarify the conditions for further crystal-growth experiments, we found it desirable to redetermine the main features of the B-Pt phase diagram since previous reports on the system1'5'6'7 are in marked disagreement. EXPERIMENTAL The experimental methods used were thermal analysis, metallography, X-ray analysis, and, to a lesser extent, measurements of microhardness. Most of the alloys were prepared from spectrograph-ically standardized boron obtained from Johnson-Matthey &Co., Ltd. (212 ppm impurities, exclusive of carbon and oxygen) and platinum powder obtained from F. Bishop & Co. (200 ppm impurities, mainly of other platinum group metals). Some alloys were also prepared with very high-purity, float-zone refined boron (99.9999 pct obtained from "Wacker Chemie" and extrahigh-purity platinum (99.999 pct) obtained from Johnson-Matthey & Co., Ltd. The reported results did not depend on the choices of these starting materials. Five-gram alloy specimens containing 10, 20, 25, 27.5, 30, 33.3, 34, 35, 37, 37.5, 38, 39, 40, 41, 42, 43, 45, 50, 55, 60, 70, and 80 at. pct B were made by melting the elements together in boron nitride crucibles using rf heating of a graphite susceptor, either in vacuum or under high-purity argon. All alloys were heated to at least 1800°C for -5 to 15 min. Most of the alloys did not wet the crucibles when the latter were outgassed by preheating under vacuum. In any event, no weight loss was detected after melting, and the nominal composition was assumed for all specimens. Thermal analysis on 2.5-g samples were carried out in boron-nitride crucibles under a vacuum of 5 x X torr. The apparatus was heated in a "Kan-thal A 1" wound furnace, which limited the maximum temperature to about 1100°C. The output of the indicator thermocouple was fed to a dc recorder with a 1-mv full-scale span and an adjustable zero. The apparatus was calibrated repeatedly, using the freezing points of high-purity aluminum, silver, and gold. The results justified the use of the NBS voltage vs temperature tables for Pt/Pt 10 pct Rh thermocouples. All thermal analyses were run at least twice and both the heating and cooling effects were recorded. Most of the alloys had a very strong tendency to supercool. However, the use of mechanical vibration permitted reproducibility within *5°C for all alloys, except in the region around 40 at. pct B. Only the cooling effects are plotted in Fig. 2, since they appear to be more reliable. For metallography, the alloys were cut with a diamond cutting wheel, cast in a polymethacrylate resin, ground and polished with diamond paste, and etched with dilute aqua regia, a common etch for platinum alloys. Both copper and molybdenum radiation were employed to obtain X-ray diffraction data using Debye-Scherrer cameras and a "Norelco" diffractometer Diffractometry with high scanning speeds (1 deg per min) using nickel filtered CuK, radiation was used to identify the main regions of the diagram. However, molybdenum radiation was used for the detection of boron, since the latter showed very strong absorption and fluorescence effects with CuK, radiation. RESULTS AND DISCUSSION Three intermediate compounds, corresponding to the compositions Pt3B, Pt2B, and Pt3B2, were found in the system. Fig. 1 reproduces their X-ray diffraction spectra, together with those of pure boron and pure platinum. As can be seen from the thermal-analysis data in Fig. 2, Pt3B and Pt2B are formed by

Jan 1, 1965