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

A program of scaled flow model experiments has been undertaken to study the performance of five-spot water floods. The modeling procedures are discussed and the construction and operation of the flow models are described. The tests were specifically designed to investigate the effects of injection rate and of oil-to-water viscosity ratio on oil recovery. The areal sweep of five-spot water floods was also studied, and direct comparisons between five-spot and linear flooding behavior have been established to permir better utilizatfon of core analysis results for purposes of field waterflood evaluations. INTRODUCTION For a long time reservoir engineering procedures have been confined to the consideration of idealized, one-dimensional or linear systems.11* However, direct application of the linear waterflood mechanism to the evaluation of actual field performance is justifiable only for the purposes of rough approximation. To obtain a realistic analysis of field behavior, it is necessary to account for reservoir geometry and well distribution, and to take into consideration the configuration of the flow of fluids between injection and producing wells. In the past it has been attempted to account for the complex nature of the fluid movement in the reservoir by associating each well pattern with a certain "sweep-efficiency constant", e.g., a sweep efficiency of 72 per cent for the conventional five-spot pattern.' More recently, methods of waterflood evaluation have been improved by the introduction of variable sweep-efficiency factors, defining the areal coverage as a function of cumulative water injection and viscosity or "mobility" ' ratio.""' These variable sweep-efficiency factors, derived from miscible fluid displacement experiments, require the assumption of piston-like displacement of oil by water. This implies that only one fluid, either oil or water, is moving at any one point of the reservoir ht any moment. Such an assumption, however, is incompatible with the bulk of the experimental evidence and also theoretical considerations which indicate that usually in the area invaded by water, both oil and water are flowing in varying proportions, in accordance with the relative permeability characteristics of the porous medium. Another recent approach toward the evaluation of five-spot flooding behavior involves correlations of the areal sweep efficiency (observed in immiscible fluid experiments) with a "mobility ratio," based on the consideration of the "average" relative permeability to the displacing fluid. Combination of these correlations with a modification of the Buckley-Leverett frontal-drive equation leads to a computational procedure for predicting the recovery performance of areal water floods. While of considerable interest, this approach has no complete theoretical justification and, therefore, does not entirely clarify the features of five-spot water floods. Rigorous, theoretical treatment of waterflood behavior in two- or three-dimensional systems as encountered in the reservoir, including proper consideration of relative permeability and capillary-pressure functions, is as yet beyond the scope of analytical or computational methods. The, behavior of such water floods can, however, be studied by means of scaled flow model ekperiments, which is the approach followed in these investigations. The flow model experiments described in this paper simulate a uniform, horizontal formation of constant thickness with fully penetrating wells. The system under consideration is entirely liquid saturated and not influenced by compressibility effects, which is representative of the situation achieved after gas fill-up under practical conditions. Gravity segregation effects are assumed to be negligible, which implies a relatively thin reservoir formation and/or low vertical permeability. THEORETICAL CONSIDERATIONS For a flow system of uniform thickness with no appreciable effects of gravity segregation, the analysis of water-oil displacement can be confined to a two-dimensional treatment based on the consideration of a "slice" of unit thickness. Referring to previously established derivations," the displacement of oil by water in such a system can be described by the following, dimen-sionless equations:

By A. Taylor

NICKEL-RICH alloys hardened with small additions of titanium and aluminum and centered around that region of face-centered-cubic primary solid solution, 7, where the atomic ratio of nickel chromium is about 3 to 1, form an important series of high temperature materials because of their resistance to oxidation, high temperature strength, and excellent creep characteristics at elevated temperatures.' With suitable heat treatment it is possible to precipitate a phase based on the ordered face-centered-cubic y' phase, Ni,,Al, from the randomly ordered nickel-rich y face-centered-cubic primary solid solution. By adjusting the ratio of aluminum to titanium the precipitation of needles of the hexagonal intermetallic compound n-NiaTi may be effected. In the present investigation, the main interest was focused on the interrelationships among the y, y, and 7 phases. By using alloying elements of high purity and a suitable melting technique the presence of carbides and nitrides could be completely obviated, although it is realized that their presence is probably essential in alloys of commercial importance. As a preliminary to the study of the Ni-Cr-Ti-A1 system, it was necessary to establish the constitutional diagrams of the three contiguous systems, Ni-Cr-Al, Ni-Ti-Al, and Ni-Cr-Ti, which together form the nickel-rich corner of the Ni-Cr-Ti-A1 quaternary tetrahedron. Accounts of this work on the ternary systems have already been published by the author. A preliminary disclosure of the author's investigations on the ternary and quaternary systems has been made by Hignett2 and has since stimulated work in the same field by Nordheim and Grant." Before the detailed account of the quaternary system, a brief description will be given of the three contiguous ternary diagrams on which it is ultimately founded. Ni-Cr-Ti System The 750° and 1000°C temperature isothermals of the Ni-Cr-Ti system as determined by Taylor and Floyd' are shown in Figs. 1 and 2. The single phase fields of greatest interest are occupied by the extensive face-centered-cubic y primary solid solution of chromium and titanium in nickel, and the close-packed-hexagonal Daltonide, n-Ni3Ti, from which tie-lines radiate across the very wide y+n two-phase field. The chromium-rich primary solid solution is represented by a. As may be seen from the diagrams, the extent of the y phase field increases quite appreciably as the temperature is raised from 750" to 1000°C. Isoparametric lines for the y phase are shown in Fig. 1. They are interesting in that they are almost parallel to the y/r+n boundary. Thus the determination of the tie-line directions is entirely dependent on the exact stoichiometry of composition of the 7 phase. Ni-Ti-Al System The 750°C isothermal section of the nickel-rich portion of the system Ni-Ti-A1 as determined by Taylor and Floyd is shown in Fig. 3.' The regions of greatest interest are the extensive y primary solid solution of titanium and aluminum in nickel, the y' Berthollide phase field based on the ordered face-centered-cubic structure of Ni3Al, and the hexagonal Daltonide phase, n-Ni3Ti. As may be seen from Figs. 3 and 4 the area occupied by the y phase is substantially the same at 750°C as at 1000°C, but the area of the 7 phase is considerably greater at the higher temperature. The tie-lines radiate from n-Ni3Ti across the y+v and y' + v two-phase fields and are evenly distributed

Jan 1, 1957

By J. W. Rutter, K. T. Aust

The migration of individual, large-angle grain boundaries has been studied as a function of tempereature and solute concentration in specimens of zone i.e filled lead containig very small additions of silver and of gold. Tile results are compared with various the-ories of grain boundary migration and with observations made prev.iorlsly of grain boundary migration in similar specimens of zone-refined lead containing tin additions. A previous investigation by the authors dealt with [he temperature dependence of grain boundary migration in bicrystals of zone-refined lead containing small additions of tin.' It was shown that tin additions as low as a few parts per million cause a large decrease in the grain boundary migration rate at any given temperature, as well as a marked increase in the temperature dependence of the migration rate. It was found that existing theories of grain boundary migration. based on the motion of dislocations. or upon the concept of atom transfer in groups across the boundary (group process theory). or upon the control of grain boundary motion by volume diffusion of impurity atonls along with the boundary. are incapable of accounting for the observations. The single process theory of grain boundary migration. which is an absolute reaction rate calculation based on the transfer ui atoms singly across the moving boundary, was found to predict the migration rate reasonably well for a number of boundaries whose motion was shown to be very little influenced by impurities, but not for boundaries whose illation was influenced markedly by impurities. It was concluded that the elementary process of grain boundary migration involves the activation of single atoms during transfer across the boundary. and that inadequate knowledge is available to permit the influence of impurities to be properly taken into account. The present study was initiated to check the validity of the above conclusions with other alloy systems, namely high-purity lead with small additions of silver and of gold. Both silver and gold diffuse faster. and with a lower activation energy of volume diffusion. than does tin in lead;' consequently, a study of the effects of silver and gold on grain boundary migration in high-purity lead offered a means of testing theories of boundary migration based on bulk diffusion of the solute (eg. ref. 3). In addition. it was hoped that the present work, in comparison with the results for tin in lead, would provide information concerning which factors are important in determin- ing the interaction between solute atoms and a grain boundary. EXPERIMENTAL PROCEDURE The preparation of bicrystals of zone-refined lead, with various silver or gold additions, was identical to that previously described for the lead-tin alloys.''4 Each bicrystal consisted of a striated crystal which was grown from the melt. and an adjacent striation-free crystal which was introduced by artificial nucleation and growth.''4 The striation or lineage substructure in the melt-grown crystal provided the driving force for grain boundary migration. During the preparation of striated single crystals by growth from the melt, it was found that silver or gold concentrations as low as 2 or 3 ppm by atoms were sufficient to cause formation of the hexagonal cell structure. which is due to the presence of impurity, during freezing. This structure is revealed on the solid-liquid interface by decanting the liquid during freezing. The hexagonal cell structure was observed previously4 in zone-refined lead crystals with tin contents above approximately 200 ppm by atoms. These concentrations of silver, gold, or tin are in agreement with the predicted amounts required for cell formation in lead,5'6 under the present conditions of freezing.4 The absence of cell structure at decanted interfaces, therefore, served as a useful indication that the silver or gold contents were less than 2 or 3 ppm by atoms in the specimens as grown. It was found that grain boundary migration occurred only very slowly when the solute content approached that necessary for cell formation. As a result, the present experiments were conducted with silver or gold additions less than 1 ppm by atoms. This impurity level is well within the solid solubility limits for silver and gold in lead.7 The annealing treatments, measurements of grain boundary velocities, and orientation determinations were carried out as described previously.' However. each bicrystal was also chemically polished in a solution consisting of 8 parts glacial acetic acid and 2

Jan 1, 1961

By John C. Sawyer

The mechanism of catastrophic oxidation of chromium and 446 stainless steel is examined. Data are presented to show that accelerated oxidation of these two materials, as caused by lead oxide, can occur in the absence of a liquid layer contrary to presently accepted theory. An alternate theory is proposed in which the rate of accelerated oxidation is a function of the rate at which lead oxide destroys the protective oxide formed on the base metal. An example of the application of the theory is given for the catastrophic oxidation of chromium in the presence of lead oxide. WHEN stainless iron-, nickel-, or cobalt-base alloys are heated in air to moderate temperatures in the presence of certain metallic oxides, oxidation will proceed at an accelerated rate. This phenomenon, often called "catastrophic oxidation", is most pronounced for the stainless steels. With these alloys the condition is so severe that large masses of oxide will form on the surface of the alloy in 1 hr or less at temperatures of 1200o to 1700oF. While a number of oxides are known to cause this effect, PbO, V2O5, and Moo3 are the most familiar, having been the subject of one or more investigations which have appeared in the literature.1-7 In presenting the results of these investigations, many of the authors have offered possible explanations to account for the more rapid rate of oxidation observed; however, the liquid layer theory as proposed by Rathenau and Meijering 2 has been the most commonly accepted mechanism. The liquid layer theory proposes that a low-melting oxide layer is formed on the surface of the alloy as the result of the interaction of the alloy oxide and the contaminating oxide. When the temperature of oxidation is above the melting point of the oxide on the surface, a liquid layer will form and oxidation will proceed at an accelerated rate. At temperatures below the melting point of the surface oxide, oxidation will proceed more slowly in the normal manner. It is argued that the rates of diffusion of oxygen and metal ions through the liquid layer are extremely rapid thereby accounting for the high rate of oxidation. Various experimental data have been presented to show that the temperature at which accelerated oxidation first becomes apparent coincides with the melting point of the eutectic oxide which would be present on the surface. Some exceptions have been observed, e.g., silver will oxidize in the presence of Moo3 at temperatures below the lowest melting eutectic; on the other hand, stainless steel will not be catastrophically oxidized at 1500oF in a molten bath of PbO and SiO2. In reviewing the various theories which have been used to explain catastrophic oxidation, Kubaschewski and Hopkins 8 favor the liquid layer theory, but note that, ".. .as experimental observations are not altogether in agreement with this theory (liquid layer theory), one should consider it a necessary but not a sufficient condition." In contemplating the liquid layer theory, it appears that sufficient evidence has not been presented to establish the theory beyond question. As a means of further clarification, a program of research was undertaken to determine in greater detail the mechanism of accelerated oxidation as caused by lead oxide. The first part of the program deals with a comparison of the oxidation of both AISI 446 stainless steel and chromium metal in the presence of lead oxide, vs the oxidation of these two materials in air alone. These comparisons are made at a number of different temperatures, most of which are below the melting point of the surface oxides. The second part of the program is concerned with a presentation of an alternate theory of accelerated oxidation exemplified by the system Cr-PbO-Air. PROCEDURE AND RESULTS Several experimental methods are commonly used to follow the progress of oxidation. One of these, the weight-gain method, was chosen for this work. This procedure requires that a specimen of the alloy be weighed, oxidized for a given period of time at an elevated temperature, and reweighed—the difference between the two weights being noted. The weight gain of the specimen represents the amount of oxygen acquired from the atmosphere to transform a portion of the specimen to oxide. In those cases where there is a tendency for the specimen or oxide to volatilize at the testing temperature, additional data must be collected so that a correction factor can be determined. This factor must be applied to the weight change in order to ascertain the actual amount of oxidation which has taken place. The specimens used for this work were 1 1/2 in.

Jan 1, 1963

By E. F. Poncelet

Forty years ago A. A. Griffith developed a theory explaining why brittle materials displayed such low tensile strengths.' He based his views on two points. First, he found himself compelled to assume that all brittle materials are replete with flaws, cracks, and other defects that act, although quite invisible, as large stress raisers. Second, he applied the "theorem of minimum potential energy," which says that the total potential energy of a system must pass from the unbroken to the broken condition by a process involving a continuous decrease in potential energy. By this means he satisfactorily accounted for the noted low strength of such solids and also for the wide spread obtained in experimental measurement of these strengths. So successful has the theory been that it is favored by some to this day. Unfortunately this theory is of limited use beyond the explanation of these two noted phenomena and it is keenly felt that a better theoretical insight into the physics of the fracturing process is needed as the volume of experimental evidence accumulates. The author proposes in the following to build on the fundamentally sound concepts of Griffith and, with the help of increased theoretical knowledge over that available to Griffith, develop a mechanism for frac-ture which will provide far greater understanding of the experimental evidence accumulated to date than is possible from the original Griffith idea. THE GRlFFlTH THEORY Very little progress indeed can be made without accepting the first postulate of Griffith which supposes all brittle solids to be full of microcracks. It would be difficult indeed to find a better mechanism for the small strength of such brittle materials, in conjunction with the fact that the energy that must be expended for comminution is by no means small. The postulate of the existence of the microcracks permits the breakup of the various bonds a few at a time by concentrating the stress at the tip of the progressing crack, while the total energy expended is the same as if they all had been ruptured simultaneously. The only flaw in the argument is that no reasonable explanation has been proposed to account for the genesis of such cracks. Indeed their very presence is in violation of the Griffith second postulate, the potential energy theorem. This theorem is straightforward for isothermal processes, and, in spite of Griffith, there is some doubt that treating the problem isothermally is legitimate. The surface energy of bodies is a free energy, not a potential energy as stated by Griffith, and the production of new surface free energies is not necessarily an isothermal process. There is ample evidence to the contrary. Generally speaking, if heating a body increases its surface area, then, by virtue of Le Chatelier's principle, any increase of that area by other means will tend to lower its surface temperature. Lord Kelvin calculated the actual cooling that resulted in drawing out a film of liquid.2 R. A. Houston calculated the surface cooling that resulted in stretching a metal wire.3 These calculations were made by applying the Carnot cycle to the process and evaluating the thermodynamics thereof. IRREVERSIBILITY OF THE FRACTURING PROCESS While Griffith was very careful not to say so, the impression gained from studying his papers is that he considered the fracturing process as reversible, that is, a succession of quasi-equilibrium states. There is ample evidence that it is not. The indication that the new surfaces produced by the propagation of a crack are cooler than the original body points to an irreversible heat flow from the interior to the new surfaces to equalize the temperatures. If the process be reversible, any crack accidentally formed should immediately close up as, in the absence of any strain energy, the potential energy would thereby be lowered. The fact that they do not, constitutes a paradox. Such paradoxes are nothing new where certain phenomena that propagate from minuscule nuclei are assumed to be reversible. Such is, for instance, the condensation of a pure saturated vapor that is suddenly chilled by adiabatic expansion. At the beginning the tiny droplets that are formed should be only a few angstroms in size, but the vapor pressure at such droplets is so high that they should evaporate at once. A similar situation arises if a saturated pure solution becomes super-saturated upon cooling; the first tiny crystal nuclei should dissolve as fast as

Jan 1, 1964

By G. K. Manning, A. R. Elsea, C. R. Simcoe

Boron increases the hardenability of hypoeutectoid steels by decreasing the nucleation rate of ferrite and bainite. It is postulated that concentrations of lattice imperfections, such as exist at the grain boundaries, furnish the necessary energy for nucleus formation. Boron, because of its atomic diameter, will concentrate at lattice imperfections where sites of suitable size are present. Boron will decrease the energy of these local areas by occupying these sites. This mechanism accounts for the large increase in hardenability observed with small amounts of boron. The loss of the boron hardenability effect and the boron precipitate formation are explained on the basis of increased concentration of boron at the grain boundaries either with increasing boron content of the material or with increasing temperature. COMMON alloying elements affect both the nucleation and growth rates of the austenite decomposition reactions.' This effect is largely a result of the slow diffusion rates of these elements. Although a small addition of boron markedly increases the hardenability of steel, the diffusion rate of boron, which is of the same order of magnitude as that of carbon, can hardly account for this effect. An addition of boron in the range of 0.001 to 0.003 pct is about as effective as an addition of 0.30 pct Mo, 0.40 pct Cr, or 1.25 pct Ni in increasing the hardenability of a 0.40 pct C steel;' however, increasing the carbon content of the steel decreases the effectiveness of the boron addition."' The difficulty in understanding why so small an addition of boron can replace much larger quantities of the more strategic alloys, together with the erratic behavior sometimes encountered in boron-treated steels, has interfered with their general acceptance by industry. In the belief that an understanding of the mechanism by which boron increases the hardenability of steel should lead to a more general acceptance of boron-treated steels, a research investigation to determine this mechanism was undertaken at Battelle Memorial Institute under sponsorship of Wright Air Development Center. Experimental Work In order to study the effect of boron on the transformation of austenite to ferrite and bainite, a group of steels was made with a basic composition similar to that of the SAE 8600 series. This base composition was chosen because it has sufficient hardenability to permit accurate measurement of the times required for transformation to start at various temperatures. The chemical analyses of the steels used in the first part of this investigation are listed in Table I. These steels were made as 200 lb heats in an induction furnace. The furnace charge was Armco ingot iron with the alloying elements added as ferroalloys. After the alloy additions were made, the heat was deoxidized with 0.125 pct Al. A 100 lb ingot was cast and an addition of 0.003 pct B, as ferroboron, was made to the metal remaining in the furnace. This metal was cast into a second 100 lb ingot. The ingots were forged to 11/4 in. diam bar stock from which end-quench hardenability specimens were obtained. Part of this material was further reduced by hot rolling to lx¼ in. bar stock from which specimens were obtained for isothermal transformation studies. Studies of Nucleation and Growth: End-quench hardenability tests were performed on these steels, using an austenitizing temperature of 1600°F. The hardenability curves, shown in Fig. 1, indicate that boron treatment resulted in considerable increase in hardenability of the steels. Any such change in hardenability must result from a change in the transformation rate of the austenite, and these rate changes can be established readily by isothermal transformation studies. Isothermal transformation studies were conducted on these steels as follows: specimens were austeni-tized at 1600°F for 15 min, transferred to a lead bath operating at a constant subcritical or intercritical temperature, held for various lengths of time, and water quenched. The specimens were sectioned for metallographic examination to determine the amount and the type of transformation products present. In order to determine the effect of boron on the formation rate of ferrite, isothermal transformation tests were made on the 0.20 pct C steel in both the boron-treated and boron-free condition at an intercritical temperature of 1375°F where ferrite is the only decomposition product of this low carbon austenite. The results of these tests are shown in Fig. 2, where the percentage of ferrite formed is plotted as a function of time at temperature. It is apparent that boron markedly decreased the transformation rate of austenite to ferrite at this temperature.

Jan 1, 1956

By H. N. Hall

Various factors must be considered in an engineering evaluation of gravity-drainage reservoirs. Among these are: (1) the effect of producing rate on total oil recovery; (2) the effect upon well productivity and ultimate recovery of the pressure level maintained during the producing life of the reservoir; (3) the economic advantage of full or partial pressure maintenance; and (4) estimate of the rate of gas production and injection and the possible purchase of gas under conditions of full pressure maintenance to ascertain compressor facilities needed. All of these factors can be evaluated only when a reliable method is employed for determining reservoir performance in gravity-drainage reservoirs. The purpose of this paper is to present a general method for calculating the performance of a gravity-drainage reservoir. This method is applicable for conditions of complete pressure maintenance, partial pressure maintenance and normal pressure depletion. Provisions are made to take into account variations throughout the reservoir of reservoir configuration, changes in permeability and fluid composition. Based on the method presented in this paper, an IBM 650 computer program has been developed. The past performance of an actual gravity-drainage reservoir producing under conditions of declining pressure and no gas injection was duplicated using this program. INTRODUCTION In tilted reservoirs the production of oil is influenced by drainage of oil from upstructure to downstructure locations. When this downstructure drainage of oil is sufficient to cause effective segregation of the gas and oil in a reservoir, the reservoir is usually classified as a segregation drive or gravity-drainage reservoir. (Discussion will be restricted to gravity-drainage reservoirs which have no encroachment of edge water.) The important feature in gravity-drainage reservoirs is the density difference between reservoir oil and gas. These phases tend to segregate in the reservoir with the result that in the gas cap the oil saturation is maintained at a higher level by drainage of oil from the gas-cap area. Oil can be produced from the oil zone at a low gas-oil ratio and reservoir energy is thereby conserved. The standard material balance in not adequate for predicting gravity-dramage reservoir performance because it does not take into account the difference in saturation above and below the gas-oil contact. Several authors'.' have presented methods for calculating the performance of gravity-drainage reservoirs in which reservoir pressure is maintained constant by gas injection into the gas cap. Using some simplifying assumptions, these methods can be employed with a desk calculator to give acceptable results. The problem of predicting the performance of gravity-drainage reservoirs under the conditions of declining reservoir pressure is many time more complex than that of constant pressure. fierefore, attempis to develop a method suitable for desk calculation have required excessively simplified assumptions. In the past several years, highspeed digital computers have become more widely available for reservoir engineering problems. These corn puters are well suited to problems such as the prediction of the performance of gravity-drainage reservoirs with pressure decline. Many of the simplifying assumptions necessary for hand computation can be eliminated so that a realistic approach to the gravity-drainage process can be made. CONCEPTUAL PICTURE OF OIL MOVEMENT IN GRAVITY-DRAINAGE RESERVOIRS Before attempting to develop an analytical treatment for conditions occuring in a gravity-drainage reservoir, a concept should be formed concerning the movement of fluids in the reservoir as oil is produced. A review of the literature'.' shows that it is customary to classify gravity-drainage operations into two categories—(1) with complete pressure maintenance, and (2) with declining pressure. The same line of reasoning will be followed in presenting the concept of the movement of fluids in the reservoir because it is easier to visualize the movement of fluids under conditions of complete pressure maintenance. After discussing complete pressure maintenance, an analogy will be made between that and the case of declining pressure. It should be kept in mind throughout that the final aim for the problem of solving gravity-drainage performance with digital computers will be to develop a general program for any kind of gravity-drainage reservoir. COMPLETE PRESSURE MAINTENANCE One feature which is generally common in gravity-drainage reservoirs is a gas cap located at the top of the structure. This is shown in Fig. 1(a). Fig. l(b) shows oil saturations that might occur through the reservoir. In the gas cap, oil saturation is lower than

By A. L. Labbe

SOON after the Cottrell treater was placed in operation in the Murray plant in 1918 to treat combined lead sinter and Wedge roaster smoke, it was noticed that the power flowing through the treater did not remain constant. This was indicated by the varying milliamperes and also by the total amount of power consumed by the rectifiers. At times, for then unknown reasons, the treater current fluctuated through a wide range of from 40 to 300 milliamperes. Fortunately, these variations in power did not affect the treater's overall recovery, as this installation consisted of three independent units in series, a feature which made the Murray Cottrell an outstanding installation over many years of operation. Water conditioning of the smoke as a means of improving recovery was already known, but was not adaptable to this installation for reasons of excessive corrosion, which had been the case with other treaters using water as a conditioner exclusively. Tests conducted on the smoke had proved conclusively that water vapor played no part in the fluctuation of power, and the same was true of the SO2 contents and dust burden of the smoke. Neither did temperature variations of from 150 to 400°F have any effect on the power. Finally it was noticed that the variation in power taken by the treater, and the efficiency of recovery, had some definite relation to the number of Wedge roasters operating, and particularly to the sulphur contents of the charge. This observation soon led to the discovery that free sulphuric acid was the conditioner for Murray smoke and that variations in acid contents of smoke accounted for fluctuations of treater power. Analysis of recovered dust revealed that only a few hundredths of a per cent free acid was necessary to maintain a very efficient recovery. Once this knowledge was available, the roaster charge was adjusted as to sulphur contents to produce the necessary acid conditioner. For a number of years this practice was followed, but with improvements in the field of flotation, excess pyrites were eliminated from the smelting picture, so with a change in metallurgical practice we were confronted with the problem of providing the deficiency in acid by some other means. The situation was aggravated and our problem of acid conditioning made more difficult by the increase in the lead contents of concentrates roasted resulting from better flotation methods. The first step towards introducing acid vapors into the smoke stream by accessory means was accomplished by boiling sulphuric acid in cast iron pots placed in an open fire box. Acid fumes evaporated from the pots together with the combustion gases from the fire box were discharged into the flue through a cast iron pipe. Capacity of the iron pots was quite limited because of the comparatively slow rate of evaporation and the use of lump coal as a fuel, which did not lend itself to practical temperature control. This method of firing resulted in frequent pot failures due to overheating. In spite of these incidental difficulties, encountered in any new venture, the pot evaporator demonstrated the practicability of fuming sufficient acid to make up the deficiency in that naturally evolved in the Wedge furnace operation. As time progressed, less and less high sulphur material was available for Wedge roasting, and the necessity for accessory acid conditioning reached a climax when the supply of this material was entirely eliminated. Since the cast iron pots could only evaporate a few hundred pounds of acid per day, and were costly to replace, the logical thought presented itself of spraying the acid in a heated chamber. This new type of acid evaporator was simpler and more economical to operate and had sufficient capacity to fume several thousand pounds per day. The attached fig. 1 presents the outstanding features of the new furnace. A is the vaporizing drum, which is heated by the combustion gases of coal stoker fire box, B. Acid is sprayed into the hot gas stream within the drum through a number of air-acid atomizers, C, and the acid vapor, together with combustion gases, is introduced into the smoke stream through two cast iron pipes extending to different points in the flue. The operation of this type of furnace requires control of temperature inside the drum to prevent overheating, which dissociates the acid vapor to SO, and eventually to SO2, with resulting loss of acid. The dissociation to SO, at elevated temperatures is comparatively high, and in some cases accounts for as much as 60 pct of the acid sprayed into the drum. To reduce the loss of acid, through dissociation, some Cottrell plants, where the rate of acid sprayed reaches at times 9 ppm, use two evaporating units. Fuming the acid into the smoke stream is only

Jan 1, 1951

By Ikuya Takase

INTRODUCTION Since the occurrence of the first oil crisis, coun-tries of the world, especially oil-importing countries have made sustained and vigorous efforts to lessen the dependency on oil as a source of energy supply. The adoption of "Principles of Coal Policy" by the IEA Ministerial Governing Board Meeting in May, 1979 was the first formal action taken by major energy consuming countries. At the Venice Summit in June, 1980, it was agreed that production and use of coal should be doubled over the next ten years. In fact, the world coal use in 1980 showed around a 10 percent increase over the previous year. Recently, we have seen an indication that the balance of oil supply and demand in the short term have eased. But I believe that it remains vital that we continue to encourage the development and introduction of alternative energy sources. Because, from the medium and long range viewpoint the recovery of the worldwide economy will lead us to increased oil requirements and thus we will be faced with the cyclical, structural tightening situation between the supply and demand of oil. Moreover, we are still convinced that the constraint of the supply capabilities of the Middle-East nations may be increasing in the long-term, since there still remains political uncertainties among these nations. Consequently, above all, coal is viewed as an alternative energy resource available for immediate expansion of use and is given as high a priority as nuclear power. In Japan, we regard coal as the most reliable alternative energy resource to replace oil. According to the "Alternative Energy Supply Targets" approved by the Cabinet in November, 1980, the level of coal imports is estimated to approximately double by 1990, while our domestic coal production will remain nearly at the same level. The transition from oil to coal is found in the recent import levels of coal---73 mil¬lion tons in 1980, a 23 percent increase over the 59 million tons imported in 1979. There was an upsurge in steaming coal imports, reflecting the transition in feedstocks---7.2 million tons in 1980, four times over the previous year's amount. Henceforth, from the medium to long range view, the demand for coal, especially that of steaming coal is forecast to continue to grow. The timely expansion of supply capabilities is our utmost concern and should be one of the most significant goals of our comprehensive policy. The Overseas Coal Investigative Committee, a privately organized advisory panel to the Director-General of the Natural Resources and Energy Agency of the Ministry of International Trade and Industry (MITI), investigated means to secure a stable supply of overseas coal. The panel presented its interim proposals in August, 1981, recommending the diversification of coal import sources, extensive use of low rank coal, as well as enhanced international cooperation between coal producing and importing countries. THE CONTENTS OF THE COMMITTEE'S REPORT Four Points for Major Consideration In order to ensure a stable supply of overseas coal, Japan needs adequate policy measures consistent with the characteristics of coal resources and environmental requirements, giving consideration to Japan's status and the role she is expected to play in the areas. From the above, great importance should be attached to the following four points: All the components of the "Coal Chain" (Namely, the development of mine sites, construction of railroads, port loading facilities, coal shipping vessels, port receiving facilities, including coal centers and international transport facilities etc.) should be reviewed and reformed with steps taken to assure efficiency consistent with the entire coal chain system. The complete formation of a coal chain system requires such lengthy lead times and huge amounts of investment that necessary measures should be undertaken well in advance utilizing long-range projections of future demands and various economic surveys. Policy planning should be conducted taking into account of harmonizing stability and economics of the supply structure. For ensuring the long-term stability and expansion of the coal trade, international cooperation on a bilateral and multi-national basis should be encouraged. Mutual understanding and close relationships are essential to facilitate the formation of the supply system and to promote the extensive use of coal. Direction and Problems Related to Supply Stability Expansion of Supply Capabilities. World coal imports in 1979 amounted to 229 million tons, of which Japan's share amounted to 59 million tons, or one fourth of the entire amount. The imports of European and Asian countries accounted for 83 million tons and 7 million tons respectively. According to the examination of the Investigative Committee, Japan's coal requirement is estimated to be between 140-150 million tons by 1990, nearly the same level as announced in the Provisional Long-Term Energy Supply and Demand Outlook in 1979. This fore¬cast is-to be revised in April, 1982. Japan's demand is expected to be met through fiscal 1985; however, by 1990, the supply is estimated to fall short of demand, particulary, in the field of steaming coal. For the expansion of supply capability, first, mine development should be accelerated. The proposed

Jan 1, 1982

By W. M. Robertson

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

Jan 1, 1967

By Anton Sawatzky, Erich Vogt

By means of mathematical solutions to the appropriate diffusion equations, we describe the kinetics of the thermal diffusion of hydrogen in Zircaloy-2 for the various temperatures and concentrations encountered in a heavy water moderated reactor. When the hydrogen concentration is below terminal solid solubility only the a Phase is present. Redistributions are then described in terms of the characteristic functions of the difhsion equation. For higher concentrations both the a and 6 phases are present. We assume the two phases to be always in equilibrium. For moderately small hydrogen concentrations exact solutions of the two-phase equation approach the the approximate solutions derived by Sawatzky and for all concentrations the exact solutions exhibit the qualitative features of his result: the two-phase concentration increases with time, everywhere; in the absence of a hydrogen current at the hot end of the sample an a-phase region always exists there; the interface of the a + 6 , a-phase boundary moves toward the cold md of the sample and the hydrogen concentration is discontinuous at the interface. Simultaneous solulions of the a and a + 6 hydrogen distributims and of the concomitant interface motion are obtained and compared to the observations of Sawatzky and Markowitz. The kinetics of the hydrogen diffusion process are shown to lead to m apparent heat of transport of the a phase which is lower than the actual value (even for samples with long anneals) thus resolving at least partially the disparity between experimental measurements of this quantity. A number of recent papers1"4 have reported measurements on the diffusion and redistribution of hydrogen in Zircaloy-2 under temperature and concentration gradients. These studies were instigated by problems arising from increasing use of Zircaloy-2 as a fuel element cladding material in pressurized-water power-reactors. The Zircaloy-2 picks up hydrogen during the operation of the reactor: the consequent precipitation of zirconium hydride in the Zircaloy-2 has pronounced effects on its mechanical properties. The Purpose of the present Paper is to describe the kinetics of the thermal diffusion of hydrogen in Zircaloy-2 for the various hydrogen concentrations and temperatures likely to be encountered in reactors. When the hydrogen in the Zircaloy-2 is entirely in the solid solution phase (a phase), the differential equation for thermal diffusion is well known and the redistribution can be described by standard mathematical methods some of which are given in Section 11 below. The treatment of the a + 6 (hydride) region differs from the earlier treatment of sawatzky3 by taking into account several modifications of the two-phase diffusion equations as suggested to us by Markowitz4 and Kidson.5 Even with the modifications the results obtained in our more complete treatment are substantially the same as those found by Sawatzky. As we show, the difference between the results of sawatzky3 and kIarkowitz4 is largely due to the difference in the geometry of their experiments. In the next section we derive the modified two-phase equation for arbitrary geometry. The exact solution of this equation is given in Section III for linear and cylindrical geometry. It is shown that Sawatzky's approximate solution is quite accurate for almost all the temperatures and hydrogen concentrations which are actually encountered. In Sawatzky's approximate theory the hydrogen concentration everywhere in the two-phase region increases continuously. As his paper pointed out, this result, together with hydrogen conservation, implies that in a sample with no hydrogen current flowing into the hot end a two-phase region is always accompanied by a single-phase region at the hot end of the sample. The net hydrogen gain in the two-phase region is supplied by the decrease of hydrogen in the single-phase region and by the movement of the (a, a + 6) boundary toward the cold end of the sample. Hydrogen conservation at the (a, a + 6) boundary leads to a discontinuity in the concentration and its derivative there. In Section IV it is shown how these qualitative features of the thermal diffusion kinetics arise from the simultaneous solution of the a-phase differential equation and a + 6 phase equation. Methods derived by us previously for the solution of the redistribution in both phases and the accompanying motion of the boundary are used to obtain approximate solutions valid for large times. The solutions account well for the observed redistributions of Sawatzky and Markowitz. It is shown how the continuing motion of the (a, a + 6) boundary leads to measured values of the heat of transport lower than the actual value, even for specimens with relatively long anneals.

Jan 1, 1963

By Robert J. De Angelis, James H. Barker

An improved method for solving dynawzical dislocation problems using a digital computer is described in this paper. Interactions between two distinct types of dislocations were studied: attractive screw dislocations; and Lomer lock forming dislocations. One dislocation is positioned in the lattice and is initially at rest, while the other dislocation is moved through the lattice on an intersecting slip plane at a constant velocity in the range 0.5 to 0.999C. (C is the transverse velocity of sound.) The results obtained from these computations indicate that screw dislocations account for a small fraction of the total strain over a wide portion of the range of velocities studied. They further indicate that mixed dislocations mainly repel other dislocations in the neighborhood of the active glide plane. From this a possible explanation for cell formation is put forth. The density of Lomer locks expected to exist after a strain of 0.2 was found to be 1.4 x 106 cm-2 which is in good agreement with indirect experimental estimates. IN the past, predictions of favorable or nonfavorable dislocation reactions were based on the associated changes in elastic strain energy. Such considerations take no account of the probability of the two dislocations coming into contact to react. Venables1 was the first to approach these probabilities by considering the interactions between two moving screw dislocations on perpendicular glide planes. Because of the restrictive types of dislocations and glide plane geometry employed, his results have limited application to metallic crystals. The work to be presented here develops a general approach to solving dynamical dislocation problems; either dislocation-dislocation interactions, presented here in detail, or dislocation interactions with any other suitably defined stress field. Two types of dislocation-dislocation interactions common to face centered cubic (fee) materials are considered: those between pure screw dislocations of opposite sign on intersecting slip planes and those between mixed dislocations on intersecting slip planes, that can react to form a perfect dislocation. This latter reaction, referred to as the Lomer reaction, produces a locked product dislocation that finds it energitical favorable to disassociate into two Shockley partials and a stair-rod dislocation. This partial configuration known as a Lomer-Cottrell (L-C) lock plays a major role in work hardening of fee crystals. seeger2 names the L-C lock as the prime contributor to Stage II hardening while Kuhlmann-wilsdorf3 and Meakin and Wils- dorf4 also state that it is a significant contributor to work hardening. However, with a few notable exceptions,5-7 direct observations of the Lomer lock and the L-C lock by electron transmission microscopy are scanty, and even these are subject to other interpretations.5,6 In a study of partial dislocations present in austenitic stainless steel, whelan8 did not observe any L-C locks at the head of pile-up groups. This result contradicted existing work hardening theories and led him to postulate an alternate theory based on the stress required to break away dislocations intersecting a pile-up group, from their stacking fault nodes. Due to the importance of the Lomer reaction in producing L-C locks which are an essential feature in current work hardening theories and because there exist no data giving direct quantitative values for the density of locks, and because there has even been some doubt expressed as to whether this important reaction occurs at all, a study of the dynamic behavior of the mixed dislocations which form the Lomer lock was undertaken. Due to their ability to cross-slip with relative ease, screw dislocations play an important role in the deformation of fee crystals. For this reason, the second type of reaction considered here is between screw dislocations of opposite sign. In addition, computations in volving screw dislocation interactions are relatively simple, thus providing a convenient check on the cornputational scheme employed. DEFINITION OF PROBLEM The force exerted on a dislocation due to a generalized stress field is given by the Peach and Koehler9 equation: Here t2 and b2 are respectively the tangent and Burgers vectors of the dislocation, and T1 is the stress dyadic defining the local stress field. The stress field may be externally applied or generated internally by the presence of a lattice defect, such as a second dislocation, as is the case in this work. Frank10 has shown that an equivalent momentum, P, of a screw dislocation can be defined by: Here, EST is the total energy of a screw dislocation and ESo is its rest energy. The left side of Eq. [2] is the time derivative of momentum and the right side is the position derivative of the energy due to the dynamical nature of the dislocation. The total energy of a dislocation is the sum of the potential and kinetic energies. Weertman11 has developed the expressions which were used here; these give the potential and kinetic energies of uniformly moving edge and screw dislocations in an isotropic medium.

Jan 1, 1969

By R. W. Raymond

PROF. HENRY Louis, of Armstrong College, Newcastle-on-Tyne, England, a distinguished member of this Institute and other technical societies, has recently sent to the Institution of Mining Engineers, and to the Institution of Mining and Metallurgy, in Great Britain, a communication, the substance of which is as follows Prof. Louis calls attention to the absence of any recognized English term for the definite description of a frequent phenomenon-namely, the oblique position of an ore-body in the plane in which it. lies. In this connection, Prof. Louis says that in America the term " pitch " has been occasionally applied to this relation, and proposes that, in the literature of ore-deposits, it shall be hereafter restricted to this particular meaning, the angle of the pitch, like that of the dip, being always measured from the horizontal, and the dip being always taken at right angles to the strike, while the pitch is taken on the plane of the dip, in the direction of the strike. Thus, for example, in a vein or bed striking N-S., and dipping, say, 45° E., there might be an ore-body, the axis of which pitched northward, at an angle of 45° below the horizontal line, as measured on the plane of the inclosing vein or bed. If the term " pitch " had this universally recognized meaning, the situation could be simply and perfectly expressed by its use, in connection with the general data of strike and clip. As Prof. Louis says ?This suggestion has a certain practical value, and is not merely academic. Every mining engineer of practical experience in such types of ore-deposit will have met with cases, in which a vertical shaft has been sunk with the object of cutting the deposit, but has missed it, because the dip alone has been taken into account, while the pitch has been overlooked." He adds the acute observation that such an oversight is much likelier to occur with regard to a condition not definitely desig-

Mar 1, 1908

By A. J. Lena, M. F. Hawkes

Changes in hardness, tensile properties, microstructure, electrical resistance, and X-ray diffraction effects indicate that lattice strains are necessary for the embrittlement of ferritic stainless steels when heated for relatively short times at 475°C (885°F). It is suggested that 475°C (885°F) embrittlement is due to the accelerated formation of an intermediate stage in the formation of s under the influence of these strains. FERRITIC stainless steels (low carbon alloys of iron with more than 15 pct Cr) are subject to two forms of embrittlement when heated in the temperature range of 375° to 750°C. The embrittlement which occurs after long time heating between 565" and 750°C is well understood; it is caused by the precipitation of the hard, brittle s phase. Sigma is an intermetallic compound of approximate equi-atomic composition with an extended range of formation in Fe-Cr alloys. The maximum temperature at which this form of embrittlement can occur is dependent upon chromium content; and is approximately 620°C for a 17 pct Cr steel and 730°C for a 27 pct Cr steel. The other form of embrittlement occurs after relatively short heating periods in the range of 375" to 565°C; in the higher chromium steels, hours may be sufficient as compared to months for s embrittlement. This phenomenon is not at all well understood and several controversial theories have been proposed. The rate and intensity of embrittlement increase with increasing chromium content but the maximum rate occurs at 475°C re-gardless of chromium content. As a result of this, the phenomenon has been termed 475°C (885°F) embrittlement. The effect of 475°C embrittlement on the properties of ferritic stainless steels has been thoroughly reviewed by Heger.1 The embrittlement causes a pronounced decrease in room temperature impact strength and ductility, a large increase in hardness and tensile strength, and a decrease in electrical resistivity and corrosion resistance. Microstructural changes accompanying embrittlement are minor and difficult to interpret with a general grain darkening, appearance of a lamellar precipitate, grain boundary widening, and precipitation along ferrite veins having been reported at various times. With the exception of reported line broadening, X-ray diffraction studies by conventional Debye analysis of solid samples have been of little value. BY making use of electron diffraction methods, Fisher, Dulis, and Car-roll' have recently shown the existence of a chromi-um-rich, body-centered cubic phase in 27 pct Cr steels which had been aged at 482°C (900°F) for as long as four years. Two types of theories have been advanced to account for the embrittlement. The first of these requires the precipitation of a phase not inherent in the Fe-Cr system with various investigators suggesting a carbide,3 nitride,3 phosphide,4 or oxide." Theories of this type have difficulty accounting for the influence of alloying elements on the embrittlement and for the facts that a minimum chromium content is necessary for embrittlement and the intensity of embrittlement increases with increasing chromium content. The second type of theory that has been proposed relates 475°C embrittlement to s phase formation which is inherent in the Fe-Cr system. An assumption of this kind can adequately explain the influence of alloying elements, for they exert an effect on 475°C embrittlement similar to that on s phase for-mation as can be seen in Table I. The minimum chromium content is essentially the same for both phenomena and it has been shown12,13 that s is a stable phase in the embrittling temperature range. In addition, it has been reported14,15 that pure alloys embrittle to the same extent as commercial type alloys. There are, however, several factors which have prevented complete acceptance of a s phase theory. Foremost of these is that the embrittlement can be removed by reheating for short time periods above 600°C, which in the higher chromium steels is within the stable s region. No s has ever been observed after one of these curing treatments, nor has any s been found as a result of embrittlement at 475°C. In addition, the simple precipitation of s cannot explain the time-temperature relationships for reactions between 350°and 750°C. This behavior is shown schematically in Fig. 1. Newell 16 and Ried-rich and Loib4 have shown that 475°C embrittlement follows a C-type curve as illustrated, while Short-

Jan 1, 1955

Allan Gibb, Queensland, Australia (communication to the Secretary*):—It is gratifying that Mr. Edward Keller,' who has clone so much work elucidating the principles of copper-metnllurgy, should have subjected only that portion of our investigation relating to magnetic iron oxide to anything like adverse criticism. Situated as we were on a rnining-camp, it was impossible to undertake work that would cover all the intricate possibilities connected with the materials commonly classed as matte. We therefore began the investigation on matte produced from ores that contained no other components than the sulphides of copper and iron that would be likely to enter into the composition of matte. We were, accordingly, free from ally possibility of magnetic iron oxide entering the matte, unless it were formed in the operation itself. The work done on this subject was incomplete, and the results thereof recorded as giving only negative evidence as to the absence of magnetic iron oxide. It would have been better to have left the matter open, as " not proven." The trend of the investigation was to account for the insufficiency of sulphur in matte to satisfy the requirements of ferrous and cuprous sulphides. So far as our deductions are correct, it was unnecessary to consider the (in our samples) somewhat doubtful constituent, magnetic iron oxide. The mattes that mere investigated were among those mentioned by Mr. Keller, " which scarcely show ally magnetic property." The samples showed no such property. There was no unaccountable variation in the specific gravity, which only varied, as would be expected, with the proportion of ferrous sulphide. I have had experience in smelting ores of which the gangue was a siliceous magnetite, both in blast- and rever-beratory furuace. The mattes so produced contained magnetic

Jan 1, 1908

By F. M. Smith, R. H. Moore, J. R. Morrey

Electrodiffusion in y cerium reported by Henrie has been confirmed and a Preliminary estimate made of the relative rates of electrodiffusion of iron, cobalt, and nickel. These diffuse to the anode at rates decreasing in that order. In addition, copper and manganese exhibit slow, but detectable, diffusion to the anode and molybdenum exhibits detectable diffusion to the cathode. The electrodiffusion of carbon, .zirconium, antimony, magnesium , and silicon in y cerium could not be detected. Iron and cobalt diffuse in y cerium at rates proportional to the current density and with no apparent dependence on temperature. Decreasing polarization of iron and cobalt with increasing temperature, which cancels the expected rate increase, would account for this behavior. The electrodiffusion rate of iron in y uranium and in E plutonium has been measured. Diffusion of iron is anode-directed. Tin was found to diffuse to the cathode, in y uranium, at an appreciable rate. In all of these solvent metals, negative ions diffuse to the anode and positive ions to the cathode. The potential field effect appears to account satisfactorily for these results. FROM early experimental work summarized by Jost1 and Seith,2 the driving force for electrodiffusion was attributed to the potential field acting on ions in a metal. More recently, Heuman,3 Wever,4 and Huntington5 have shown that momentum interchange between conduction electrons and mobile entities in the metal contributes to electrodiffusion. Electron momentum interchange is anodically directed and the direction of diffusion resulting from the field force is dependent upon the charge on the diffusing entity. These two effects may either reinforce or oppose each other. Glinchuk6 has pointed out that momentum transfer in defect conductors should be cathode-directed and this appears to be the case as demonstrated by wever's4 work on iron. Barnett's7 work, on the other hand, indicates that, even in defect conductors, electrons show a negative E/m ratio when accelerated with respect to the lattice and should lead to anode-directed momentum transfer. In discussing this problem, Wever and seith8 suggest that defect electrons interact preferentially with activated ions so as to allow a net movement toward the cathode while still maintaining an electron momentum transfer in the anode direction. Williams and Huffine9 and Henriel0 have demonstrated that electrodiffusion may be useful for purification of yttrium and cerium. In yttrium, Williams and Huffine note that movement of several metallic impurities toward the anode is in keeping with observations in most other metallic systems and indicates that yttrium remains a normal electronic conductor at least to 1230°C. Close inspection of their data shows, however, that oxygen, nitrogen, and the transition elements diffused toward the anode, while nontransition elements diffused toward the cathode. This suggests that potential field effects may have been appreciable. The present work was concerned with the applicability of electrodiffusion as a technique for purification of plutonium, but, because of the obvious hazard inherent in work with this metal, experiments to develop the technique were carried out using cerium and uranium. The results of electrodiffusion measurements on these metals and on plutonium are reported here. EXPERIMENTAL The metal specimens prepared for this work were 6 in. long, 1/4 to 1/2 in. wide, and 1/16 to 3/32 in. thick. The uranium specimens were machined from a bar which analyzed 310 ppm Fe and the electrodiffusion of iron was followed by spectrographic and by chemical analysis. Cerium and plutonium specimens were cut from sheet rolled from ingots obtained from molten salt-metal equilibrations during which radioactive tracers were introduced. The electrodiffusion of the tracers was subsequently determined by counting methods. The specimens were electrolyzed between nickel electrodes containing resistance heaters used to equalize the specimen and electrode temperatures, thereby reducing thermal gradients. The temperature of the electrodes adjacent to the ends of the specimen was measured with chromel-alumel thermocouples which were connected to the heater controls. The surface temperature of the specimen at a point midway between the electrodes was measured with a sapphire rod pyrometer, the output of which controlled the dc power supply. This assembly was enclosed within an evacuable chamber containing a quartz viewing window. The temperature of the specimen over its entire length could be scanned with a portable pyrometer through

Jan 1, 1965

By A. K. Mukherjee, J. E. Dorn, J. D. Mole

Investigations were carried out on the effect of polyslip on the strain hardening of aluminum single crystals. The orientations investigated were those lor which the tensile axis was in the [001], [111], [112], and [012] directions plus another for which the Schmid angles for {111}(110) slip were 1 deg. The experimental data were analyzed on a model based on the intersection of dislocations with particular emphasis on the effect of polyslip on the activation volume for inter-section. It is shown that the rate of strain hardening inreases for those orientations wherein attractive dislocation intersections occur and that those orientations which produce the greater number of such intersections exhibit the greater strain hardening. Good correlation of the data is obtained with the concept that attractive junctions, as proposed by Saada, Play an important role in accounting for the rate of strain hardening. EXISTING concepts on the nature and cause of strain hardening in fcc metals have been deduced principally from experiments on the deformation of single crystals under single slip. The effect of crystal orientation on the shapes of the stress-strain curves for single slip have been summarized by seegerl and more recently by Clarebrough and Hargreaves.2 Tensile specimens whose axes fall near the center of the [001]-[011] line of the standard triangle of the stereographic projection exhibit the longest range of easy glide (Stage I) and the lowest rates of linear hardening (Stage 11) whereas specimens whose axes lie near fie [001]-[111] line of the standard triangle have limited or no easy-glide range and exhibit somewhat higher linear strain-hardening rates. Specimens whose axes lie near the [001] or the [ill] poles do not exhibit easy glide and have the highest rates of linear hardening. Kocks3 has shown that the highest rates of linear hardening Occur under Polyslip when the tensile axis coincides with the [111] or the [ 001] pole. Since the rate of strain hardening is sensitive to specimen orientation and the incidence of polyslip, these relationships might help to discriminate between various dislocation models for strain hardening in fcc metals. Previous attempts to analyze the effect of orientation on strain hardening,1"3 however, did not provide a unique answer to this problem. Consequently the present investigation was undertaken wherein additional data, particularly that for the effect of polyslip on the activation volume for intersection, was also determined in order to provide more complete information on the details of strain hardening. Whereas analyses of these data reveal that several recommended models for strain hardening are at variance with the facts, good correlation of the data is obtained with the concept that attractive junctions4 play an important role in accounting for the rate of strain hardening. I) EXPERIMENTAL APPROACH seegerl demonstrated that slip in fcc crystals at low temperatures is dependent on thermally activated intersection of glide dislocations with forest dislocations. This has been confirmed by tests on single crystals of aluminum by Mitra, Osborne and Dorn5 and on polycrystalline aluminum by Mitra and Darn.' Thus in accord with Seeger's theory, the shear strain rate, ?, below a critical temperature, T, is where .V is the number of points of contact per unit volume between forest dislocations and glide dislocations, A is the area swept out per successful intersection, b is the Burgers vector, v is the frequency of vibration of the segment of the glide dislocation undertaking intersection, U is the activation energy for intersection, k is Boltzmann's constant, and T is the absolute temperature. For aluminum, which has an extremely high staeking-fault energy, the constriction energy is negligibly small and therefore the activation energy decreases practically linearly with the stress according to as will be recomfirmed later, where Uo is jog energy at the absolute zero, G and Go are the shear moduli at the test temperature T and O°K, respectively, L is the spacing of the forest dislocations, t is the applied shear stress for slip, and tGo is the stress field that must be surmounted athermally.

Jan 1, 1965

By R. V. Whetsel, V. R. Garfias

For some time the writers have been compiling and analyzing statistics of consumption and production of petroleum, its products and related fuels, in order to arrive at a fairly accurate picture of the world-wide situation of the petroleum industry. In production, crude oil, natural gasoline, benzol and alcohol blended with motor fuel have been considered. In consumption not only refined products, but crude consumed as fuel, refinery losses, ships' bunkers and blended fuels have been taken into account to obtain a true balance between supply and demand. Statistics from practically every country and territory have been studied, and where actual figures were not available the estimates have been based on all the data available. The figures in Table 1 indicate that during the last five years the world's production has exceeded demand every year and that the aggregate difference is some 207,150,000 bbl. The supply in the United States exceeded consumption by 111,401,000 bbl. over the same five-year period and in 1931 and 1932 the demand exceeded supply, while outside the United States the excess of output over demand was 95,749,000 bbl. Table 2 combines the excess production in the United States with its favorable balance of exports over imports, showing that the United States has reduced its storage over the five years by about 136,-595,000 bbl., while in Table 3 it is shown that, including its excess of imports from the United States, the rest of the world has added 343,-745,000 bbl. to storage during the period in question, the greatest accumulation coming in 1934. Table 4 shows the world's consumption classified by countries according to the principal products. These tables also indicate that at the end of 1934 the statistical position of the petroleum industry outside the United States was decidedly unstable, a situation that probably will become more acute as a result of the added Iraq production; and that the present favorable statistical position of the industry in the United States, which is partly due to the excess of exports over imports, may be to some extent jeopardized by the unstable situation in the foreign market.

Jan 1, 1935

By W. L. Mamme, G. Y. Chin

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain was analyzed by Taylor and by Bishop and Hill in terms of a minimum (internal) and a maximum (external) work criterion, respectively. These two criteria have now been generalized to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (noncrystallographic) pencil glide. The generalized treatment also takes into account the possibility of a Bauschinger effect and of unequal hardening among the shear systems, which were considered in the Bishop and Hill work. Optimization techniques of linear and nonlinear programming are shown to be applicable for the numerical calculation of the minimum or maximum work. In the case of crystallographic shear, the constraint functions are linear and hence the optimal work is obtained as the saddle value of the lagrangian function Wi(y) e minimum and W,(u) + (a) for the maximum, where Wi is the (internal) work, We is the (external) work, Y is the crystallographic shear strain, u is the applied stress, and and are constraints. It is shown that the Lagrangians are functionally the same and the saddle value of one problem is identical to the saddle value of the other, proving that the two analyses are completely equivalent. In the case of pencil glide, although the constraint functions are nonlinear and neither convex nor concave, the equivalence of the optimal values to the saddle value of the Lagrangian (which is again identical for both problems) is still valid. WHEN a crystal deforms plastically by crystallographic shear, five independent shears are generally required to accommodate five independent strain components specifying the deformation. Assuming slip as the only shear mechanism, Taylor1 in 1938 analyzed the deformation in terms of a minimum work criterion. He hypothesized that of all combinations of five slip systems which are capable of accommodating the deformation, the active combination is that one for which the internal work C is a minimum, where 1 TI is the critical resolved shear stress for slip on the 1-th slip system and is the corresponding simple shear. By further assuming equal 72 for all equivalent slip systems and no Bauschinger effect, Taylor re- duced the minimum work problem to one of minimum and applied the analysis to the case of axisym- Metric flow by {111}(110) slip in fcc crystals. However, he did not consider the question of whether the resolved shear stress has in fact attained the critical value for slip on the newly found active systems without exceeding it on the inactive systems. In 1951 Bishop and ill' put forth the maximum work analysis in which slip is again assumed as the only deformation mechanism. In this analysis, the work o1 done in a given strain ij by a stress ujj not violating the yield condition is maximized. In addition, the analysis takes into account the possibility that the critical resolved shear stress for slip may not be equal among the slip systems and that the slip behavior may exhibit the Bauschinger effect. As with Taylor, a single set of slip systems—{111)(110) — was analyzed numerically. It thus appears that the Bishop and Hill treatment is on a more sound physical basis than the Taylor treatment. However, Bishop and Hill showed that where there is equal hardening among all slip systems and when there is no Bauschinger effect, Eq. [11 ] of Ref. 2, as assumed by Taylor, the results of their maximum work analysis are the same as those of Taylor's minimum work analysis. Hence at least under those conditions there is an implication that the Taylor analysis does lead to a critical resolved shear stress for slip on the predicted active systems without violating the yield condition on the inactive systems. Recently, the Taylor analysis was applied for numerical solutions of the axisymmetric flow problem, for slip on {110}(111), {112}(111). {123)(111) systems as well as a mixture of all three sets of svstems."1 Computational techniques based on the optimization theories of linear and nonlinear programming4 were employed in these solutions. The same techniques were employed in the solutions of an axisymmetric flow problem of deformation by slip on (111) (110) systems and twinning on (111)(112) systems5 which had been considered theoretically from a modified Taylor approach. The utilization of these techniques has led to the realization that the solutions of Taylor's minimum work problem imply the solutions of Bishop and Hill's maximum work problem. The two problems turn out to be dual problems in the well known sense of mathematical programming. It is thus the purpose of this paper to first generalize the minimum and maximum work analyses to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (non-crystallographic) pencil glide, as well as the possibility of a Bauschinger effect and of unequal hardening

Jan 1, 1970

By B. J. Shaw, R. Kossowsky, W. C. Johnston

High purity (99,95) Ni-51 wt pct cr eutectic alloy was unidirectionalty solidified at rates of 0.1 to 8 in. per hr. The resulting material was characterized by large grains, approximately 0.5 mm in cross section and extending through almost the entire length of the specimen, parallel to the growth axis. The eutectic structure of specimens the growth at -1/3 The per hr consisted of a continuous nickel-rich phase and chrome -rich lamellae approximately 2 thick, spaced about apart. Specimens were tested in compression at temperatures ranging from —196 to 850"C over which range the 0.2 pet yield strength dp -creased from 160,000 p si to 35,000psi, respectively. Swaging to 40 pet reduction in area, followed by a 30-min anneal at 1000c to remove residual cold work, increased the 0.2 pet yield to 260,000 psi at -196°C, dropping to 35,000 psi at 850°C. The increase in strength was attributed to a residual cell structure. The strength of the alloy could be rationalized by the simple rule of mixtures if one assumed that additional strength is derived front a size effect characterized by is petch equation IN recent years there has been increasing interest in dispersion and second phase strengthening in materials needed for high-temperature applications. inm role of structure on the mechanical The of such alloys has been well established of such some extent accounted for theoretically. and to of how the strengthening mechanisms due to fibers and lamellae operate has been reduced to its fibers form by the fabrication of composites of strong rods unidirectionally aligned in a From work on tungsten-fiber-reinforced copper, for example, it was established that the "Rule of Mixtures" could explain the strengthening.12 " some what more sophisticated technique for introducing strong fibers into copper matrix was used by Hertzberg strong Kraft3 who unidirectionally solidified the copper-chromium eutectic. The use of unidirectionally fied eutectics has advantages in that there are no matrix-fiber wetting problems and fine fibers are automatically aligned and uniformly fiber However, one Is restricted to a specific volume fraction of the second phase. Nevertheless, even though the volume fraction is fixed, the rod or lamella thickness, , can be varied by controlling the freezing interface velocity. Alternatively, the grown material may be worked down by swaging or rolling. Embury and Fisher, " using this approach, drew down pear lite in iron and studied the mechanical properties iron and that the yield strength, oy, was properties.proportional They that d was the wire diameter. It could be inferred that was also proportional to but the work hardening had to be taken into consideration at the same time. By varying the growth rate of the cadmium-zinc lamellar eutectic, Shaw'1 showed that was proportional to without the introduction of work hardening and suggested that the lamellar interface itself contributed to the strengthening of the composite. In this investigation we have evaluated the mechanical properties of the unidirectionally solidified fec-bec eutectic Ni-Cr. This eutectic was selected because it presented the possibility was selected beca temperature, and high corrosion resistant alloy, and also represented a hard-soft phase combination with two completely different slip systems. Specimens were tested in compression and tension up to 850°C and a detailed study of the micro structure as a function of plastic strain and temperature was carried out by light and electron microscopy. It was shown that the composite strength tested in compression can be accounted for by the simple rule of mixtures if one allows for an additional term representing the effect of Intereprese EXPERIMENTAL PROCEDURE 1) Unidirectional Solidification. Fig. 1 is a schematic drawing of the apparatus used to produce 0.2 in. diam by 12 in. long alloy ingots. The crucible tube is alumina, containing the charge which has been is swaged, or machined to 0.195 in. diam. The lower end of the tube is immersed to 0 .195in in.d iam. The upper end is supported by a 10 mil nichrome wire which lowers the crucible mil nic hr the] wire at a prescribed rate. Surrounding the furnace is a graphite susceptor into which a control thermocouple is inserted. The furnace is insulated with fiberfrax and enclosed in a quartz tube. There is a sliding seal at the bottom around the crucible and one on the top so that an atmosphere may be used for the sample and suscep tor. The power for the furnace is supplied from a 10-kw, 450 kc generator. The skin depth (the skin depth at which the field falls to l/e of its value at the outer surface) for graphite (p = 10 (j-ohm-cm) is 0.1 in. at this fre-

Jan 1, 1970