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By H. S. Wang, Y. P. Gupta

Diffusion of zinc and germanium in liquid silver is measured in the temperature range 975" to 1400°C by use of the capillary-reservoir technique. The ex-perinzental results are discussed in terms of the fluctuation and the "hole" theories of liquid diffusion, assunzing the solute as a point charge equal to the difference in the valences of the solute and solvent atoms. The additional coulombic interaction term due to the excess solute charge is evaluated in terms of the Thomas-Fenni approximation. The theoretical and experimental results agree with both the fluctuation and "hole" theories of liquid diffusion. No perceptible effect on solute diffusion in liquid silver of the size difference between the solute and solvent atoms/ions is apparent. DIFFUSION in liquid silver of electropositive solutes indium, tin, antimony, and homovalent gold has been previously reported by Leak and Swalin1 and Gupta,' respectively. These solutes have nearly the same atomic size but differ principally from one another in excess valence (+2, +3, +4, respectively). The observed differences in the temperature dependence and the rate of solute diffusion were explained in terms of an added coulombic interaction between the solute and the solvent atoms. In the case of diffusion of gold in liquid silver, the data were found to be consistent with an effective valence for gold of -0.85, as proposed by Le Claire.3 Recently, Wang and Gupta4 have reported a study of diffusion of ruthenium, iron, and cobalt in liquid silver. The results of diffusion of these solutes and their temperature dependence were found consistent with the hole theories and the fluctuation theories of liquid diffusion, if ruthenium, iron, and cobalt were diffusing in liquid silver with relative valences -2, -1.3, and -0.5, respectively, instead of -3, -3, and -2 as suggested by the relative position of these elements in the Periodic Table of Elements. Furthermore, the predicted valences for these solutes were observed to be consistent with the sparsely available information on the magnetic properties of some of the dilute alloys of copper and silver with these solutes. In theoretical calculations of solute diffusivity, the solute was assumed as a point excess charge equal to the difference in the valences of the solute and solvent atoms. Both the assumption of a point excess solute charge and the use of the Thomas-Fermi approximation to calculate the potential of a solute charge are less precise for the case of electronegative solutes. Therefore, it was not possible to infer from the data on ruthenium, iron, and cobalt an effect, if any, on solute diffusion of the relative differences in either the Period or the size of the solute and solvent atoms or the solute atoms themselves. A study of the diffusion of Period 4 elements, specifically zinc and germanium was, therefore, undertaken since zinc and germanium, respectively, have relative valences of +1 and +3 in liquid silver and the data obtained on diffusion of these solutes could be compared with the available data on diffusion of Period 5 electropositive solutes, indium, tin, and antimony in liquid silver. From such a comparison, it was hoped to learn something about the effect, if any, of the ion size or the structure of the ion core on impurity diffusion in liquid silver. EXPERIMENT The diffusion of tracer zinc and germanium in liquid silver was studied by the capillary reservoir technique, modified adequately for use at high temperatures. In principle, capillaries containing liquid silver

Jan 1, 1970

By M. C. Flemings, T. S. Piwonka

Pore formation is examined analytically in cellu-larly solidified single crystals, in cylindrical castings of pure metals and alloys, and in unidirectionally solidified castings. Effects are considered of fluid flow. dissolved gas, and surface tension. Experimental results show that flow through a partially solid "mushy" aluminum alloy obeys relations similar to those applicable for flow through other types of porous beds. Flow rate is proportional to the square of the fraction liquid (fL) for fL less than 0.3. Results indicate models chosen for mathematical description of pore formation in alloy solidification are valid. ONE of the solidification variables which is influential in determining mechanical properties of castings and of wrought material produced from cast ingots is porosity. This porosity may result from shrinkage, dissolved gases, or a combination of both, and may take the form of either macroscopic pores in localized areas of the casting or microporosity evenly distributed throughout large areas of the casting. In alloys which freeze over a range of temperatures some microporosity is generally found after solidification. There has been much discussion as to whether the micropores are caused primarily by shrinkage, by gas, or by a combination of both.'-3 There has, however, been little experimental or analytical work performed to delineate the relative contributions of shrinkage and gas in causing microporosity or to quantitatively describe the influence of processing variables on microporosity. Porosity other than microporosity (e.g., center line shrinkage) has also received only limited quantitative treatment.495 The aim of this work is to examine analytically the general problem of pore formation in solidification and to perform limited confirmatory experiments. Consideration is first given to shrinkage porosity in pure and nearly pure metals (shrinkage in cellular growth, centerline shrinkage in cylinders). Next, a discussion is given of formation of shrinkage-caused microporosity in unidirectional solidification and in "mushy" solidification. Finally, influences of dissolved gas and surface tension on microporosity are examined. Numerical results are given for aluminum and an aluminum alloy. Typical examples of microporosity are shown in Figs. 1 to 3, for 1) cellularly solidified aluminum, 2) sand-cast aluminum alloy, and 3) low alloy steel. SHRINKAGE POROSITY IN PURE AND NEARLY PURE METALS 1) Cellular Growth. In cellular freezing of an impure liquid, liquid grooves may exist over a considerable length of the growing crystal.6 The cross-sectional area of the grooves decreases with increasing distance from the cell tips; the root of the groove is blunt if the liquid at this point reaches eutectic composition. As a result of volume contraction during solidification, flow occurs down the groove, parallel to the growth direction; hence, there must be a pressure drop from the groove entrance to points within the groove. The geometry of the groove is simplified to that of a circular cylinder of radius r and length L, Fig. 4, L » r, and a simple and useful limiting case is obtained. This is that, in the circular cylinder freezing at constant velocity, the pressure at the root of the groove is lower than that pressure at radius r in grooves of other geometries where r decreases continuously to a lower limit at L. As discussed below, a pore resulting from a given pressure difference

Jan 1, 1967

By David Cornell, Yusuf K. Sukkar

The fundamental differential equation for fluid flow has been rearranged, integrated numerically for natural gases, and the results presented in tabular and graphical form suitable for the direct calculation of vertical gas flow problems. The integration is rigorous except for the use of a constant average temperature. Both static and flowing bottom-hole pressures may be calculated by (his method without resort to trial and error procedures. INTRODUCTION Bottom-hole pressures can be determined either by direct measurement with a bottom-hole pressure gauge or by calculation. Since measurement with a bottom-hole pressure gauge is costly, calculation of bottom-hole pressures is to be preferred when possible. Calculation involves knowledge of the wellhead pressure, the properties of the gas, the depth of the well, the flow rate, the temperature of the gas, and the size of the flow line. These quantities must be combined in a suitable equation for vertical flow. Several equations have been developed for the purpose of calculating gas flow through both horizontal and vertical pipes1,2,4,5,6,7,8,9 These equations all have the basic differential equation for flow as their starting point. They differ only in the assumptions which are made in order to simplify the integration step. The bottom-hole pressures calculated using any of the better known equations are in good agreement with bottom-hole pressures calculated by a more rigorous but considerably more tedious stepwise integration method. All of these methods, however. require a trial and error solution for the calculation of flowing bottom-hole pressures. The purpose of this paper is to present a method which provides a direct solution of static and flowing bottom-hole pressures without use of a trial and error solution. At the same time the method involves fewer simplifying assumptions than any of the previous methods used, except lor the lengthy stepwise method. The derivation of any practical flow equation begins with the basic differential equation which is rigorous for almost all flow problems. The five terms in Equation 1 represent the potential energy, the potential energy of position, the kinetic energy, the shaft work done, and the energy losses due to motion of the fluid respectively. Equation 1 reduces to Bernoulli's theorem for the case of horizontal flow of an incompressible fluid, no work done, and no energy losses due to friction. In the present case, the term (v) (dv)/(g,.) can be shown to be quite negligible compared to the other terms, and is therefore neglected in the derivation. The term — dws includes work done by a pump or turbine in the system and is zero in this case. The frictional losses in the pipe are included in the term — d(lw) which is expressed in terms of the Moody friction factor as in Equation 2. (f) (v2) (dL) d(lW) = (f)(V2) (dl)/(2) (g) (d) The specific volume of a gas can be expressed in terms of the temperature, pressure, molecular weight, and compressibility factor. The velocity of the gas can be expressed in terms of the weight rate of flow, the specific volume, and the dimensions of the pipe.The reduced pressure Pr is to be used because z can be expressed as a function of Pr and Tr alone for most natural gases:

Jan 1, 1956

By E. Swartzman, G. C. Behnke

THE free-swelling index, a numerical value for the free-swelling properties of coal, is being used to an increasing extent in specifying coal for burning in various types of equipment. The empirical standard ASTM method for determining this index uses, as a source of heat, a gas burner which requires frequent calibration because gas pressures are not constant, relatively small changes in gas pressure resulting in rather wide variations in the temperature attained in a crucible and thus in the resultant size of the coke button. Furthermore, the quartz crucibles specified for the test are not standard equipment, and relatively small variations in dimension and wall thickness from those specified often result in rather wide variations in the resultant size of the button. A method of analysis to be satisfactory not only for a scientific laboratory but also for use in industrial control laboratories under varying conditions should employ equipment which is rugged, easily calibrated, and readily replaceable by standard materials. Gas is not universally available as is electricity, and it is generally easier to calibrate and control a simple electric furnace or heater than a gas burner, the voltage not usually fluctuating to the degree that gas pressure does. Quartz crucibles are fragile, and the size specified in the test is not normally used for any other purpose in the laboratory. Although more expensive, the 15-cc platinum crucible, available in all laboratories where volatile matter in coal is determined by the standard ASTM method, is sturdy and standard and easily replaced. Because of these considerations, a modification of the standard method has been developed which employs a standard laboratory 350-w cone heater and standard 15-cc platinum crucibles. The results of numerous tests conducted with such apparatus show conclusively that the free-swelling index values as judged by the buttons produced with this equipment are exactly the same as those obtained by the standard gas burner method. Thus it is suggested that this electric cone heater method employing standard 15-cc platinum crucibles be considered as an alternative to the ASTM method, Designation: D720-46. The free-swelling index of coal is determined by means of the ASTM method, D720-46. This method, which is an adaptation of the crucible swelling test for coal of the British Standards Institution, consists of heating 1 g of coal in a special covered quartz crucible in a regulated gas flame for a period of not less than 2.5 min in which time the temperature of the inner surface of the bottom of the crucible reaches a temperature of 82025°C. The residual coke button is then compared in size and shape with a series of standard profiles shown in Fig. 1 and designated by number from 1 to 9 in increasing order of size. As the method is empirical, it requires rigid standardization of the apparatus and repeated calibration of the gas burner. The dimensions of the low form quartz crucible recommended must be rigidly adhered to as small variations in diameter or wall thickness result in variations in the rate of heat transmission and thus in the resultant size and shape of the coke button. The gas burner must be calibrated almost every time a new set of determina-

Jan 1, 1952

By B. A. Shaw

Historically, microwave tubes have been fabricated from massive metal and ceramic components. The current trend is to lighten tibes for airborne applications. The reqciiremenls of light weight and also reduced cost have created a novel approach to tube structure in which thin-film technology plays a major role. Although the electrical requirements of thin-film circuits in microwave tubes differ from those required or se,niconductor integrated circuits. the technology is basically similar. The stringent requirements of the micvowave tube have created sophisticaled thin-film techniques thut are of interest to the integrated-circuit industry in general. This paper describes a nunzber of thin-jilm techniques recently developed and discusses in detail the application of the technology in microwave tubes. The particular areas of interest are: 1) ceramic mounted thin-film slow-wave structures; 2) thin-film secondary emitters; 3) suppression of tube environnental multipactor by semiconducting' thin films; and 4) age-hardenable and dispersion-hardened thin metal films. SEVERAL thin-film techniques specifically applied to microwave power tubes are discussed in this report. There are two reasons for this work. One is the necessity of reducing weight and cost of microwave tubes and the other is related to overcoming problems in the tube operation by the use of applied thin-film technology. The major emphasis of this work has been on tube slow-wave structures. Other work in the area of secondary emission, either its suppression or its enhancement, is continuing; the most satisfactory results to date have been by utilization of thin-film technology. The requirements of high thermal and electrical conduction together with greater strength than normally obtained with elemental materials have led to the development of dispersion-hardened films. The paper will discuss: 1) ceramic-mounted delay-line microwave tubes; 2) multipactor and secondary emission; 3) hardened films. I) CERAMIC-MOUNTED THIN-FILM SLOW-WAVE STRUCTURES In a conventional crossed-field microwave tube, the slow-wave or delay-line structure is produced from two carefully machined components. One half of the structure is shown in Fig. 1. The other half is the mirror image of the first but is rotationally offset by a half a period. The combined structure now forms an interdigital type of slow-wave structure and is the anode of the tube as shown in Fig. 2. The period and finger length of an interdigital slow-wave structure are prescribed by the desired dispersion characteristics. The typical design is as shown in the first figure; it can be noticed that the finger width is several times greater than the finger thickness. Even assuming that it were mechanically possible to produce free-standing fingers of extremely small cross-sectional dimension, for example, 0.002 in. thick by 0.005 in. wide by 0.500 in. long, decreasing this finger width would increase the tube efficiency but would also decrease the thermal-conduction path, causing an increased temperature rise from intercepted rf current which in its extreme could easily cause finger melting. Hence, for free-standing lines of this type, the design is a compromise between mechanical capabilities, tube efficiency, and thermal dissipation. These structures are also expensive and tend to be heavier than purely electrical considerations would demand. In the present approach, we have transposed the three-dimensional structure previously shown into an essentially two-dimensional structure as shown in Fig. 3. The linear structure is used here for clarity of detail. The support member is a ceramic material and the line is deposited copper. The final tube design is shown in Fig. 4. Because of the backwall sup-

Jan 1, 1967

By L. H. Wolfe, J. O. Thieme

The tensile and shear strengths of frozen soil and the compressive strengths of ice and frozen soil were measured These tests showed that the strength of ice and of frozen soil increased as the temperature was decreased. A method is presented for the measurement of thermal conductivity and specific heat of earth and ice. Using the parameters thermal conductivity, specific heat and density, the thermal diffusivity was calculated. Results of thermal property tests establish water as the major variable contributing to thermal property values. INTRODUCTION During the last few years, a considerable interest has developed in underground storage of cryogenic liquids such as liquid natural gas. Because of its economy and safety, underground storage is being used. Before underground caverns could be seriously considered, however, the strength and thermal characteristics of the soil had to be obtained. Methods are presented herein for measuring tensile, compressive and shear strengths, specific heats and thermal conductivities. The tests were performed on two soils at temperatures from ambient to -195C. Because it is difficult to find data in the literature that pertain to a particular soil, ice was used to evaluate some of the experimental procedures. Some of our ice data are compared to the published values. PHYSICAI, PROPERTIES SOIL SELECTION AND SAMPLE PREPARATIONS The physical and thermal tests were performed on recompacted samples of two typical soils that might be encountered in underground caverns: a gray, fire clay that had been pulverized and mixed with water into a pliable mud; and a brown, sandy silt that was dug from a dry river bank and subsequent1y mixed with tap water. The moisture content of the test specimens was 17 to 22 per cent (based on the wet weight of the soil). This amount of water nearly saturated the silt, but the clay was well below the saturation point. The soils are partially described by the sieve analyses (Fig. 1) which show the particle size distribution of the coarser than 44 micron portion of the soils. The curves also show that approximately 75 per cent of the clay and 20 per cent of the silt are finer than 44 microns. The particle size seems to affect some of the physical properties, and the finer than 44 micron portion is important in the thermal conductivity test. Physical specimens were cut with a bandsaw from frozen blocks of the soil. The specimens were then sanded and kept frozen until after they were tested. They were stored at the approximate test temperature for several hours. Then, to equilibrate the samples to the test temperature, they were stored at the temperature at least an hour before they were tested. TEST EQUIPMENT An Instron, which is a constant speed gear-driven instrument, applied force to the samples and drew stress-strain plots of the test. All of the samples were strained at 0.02 in./min. All of the physical tests were conducted in a temperature cabinet that controlled the temperature to 1C. TENSILE STRENGTH Briquette or "dog-bone" shaped tensile specimens were pulled with suitably shaped jaws. This shape of specimen, which is usually used for tensile tests of concrete, is satisfactory for testing frozen soils except that the samples tend to

Jan 1, 1965

By H. R. Thresh, A. F. Crawley

THIS paper reports the results of viscosity measurements on cadmium and indium undertaken as part of a continuing program of liquid metals research at the Mines Branch, Department of Energy, Mines and Resources, Ottawa, Canada. For several years this work has continued with support from the Canadian Zinc and Lead Research Committee and the International Lead and Zinc Research Organization. In the literature, existing viscosity data for cadmium are conflicting and for indium are scarce. To achieve reliable viscosity values, further work was deemed desirable. Viscosities were measured using an absolute technique applied to an oscillating closed right cylinder of liquid metal. The apparatus, constructed in this laboratory, and the techniques involved in its use have been described in an earlier paper.' In calculating viscosity coefficients from the experimental data. Roscoe's2 mathematical analysis was used. Because accurate viscosity determinations are dependent on accurate density data, and since the available data in the literature are conflicting, the densities of liquid cadmium and indium were also determined in this laboratory by a pycnometric technique. This increased the control exercised over all the variables contributing to the accuracy of viscosity measurements. For both density and viscosity determinations, cadmium and indium of 99.999 pct purity were used. These materials were obtained from Cominco Ltd. In order to suppress excessive evaporation losses and help prevent oxidation, a technique developed in measuring the viscosity of zinc' was used for cadmium. This involved maintaining an atmosphere of purified hydrogen in the viscosimeter during the rela- tively long periods while the experimental temperature was changed and stabilized between individual determinations of the logarithmic decrement. Then, immediately prior to a decrement measurement. the viscosimeter was rapidly evacuated to a pressure of about 2 X 10-6 torr. On the other hand. with indium. no difficulties arise from vaporization or oxidation. In this case. therefore. the apparatus was held under a constant vacuum of about 2 x 10-6 torr. When all sources of random and systematic error have been evaluated, the technique is considered to yield data accurate within 10.5 pct. The viscosity of cadmium was measured to a maximum temperature of 451.8°C and that of indium to 346.5°C. These temperatures are. respectively. 130° and 190°C above the melting points. Two separate runs were made on indium. The results are given in Table I and, when plotted. yield the smooth curves evident in Figs. 1 and 2. Values of A and C to fit the well-known Andrade1 equation were determined by a regression analysis. The equation is: where n = coefficient of viscosity. i = specific volume. T = temperature in °K Despite its empirical nature. Andrade's equation has been shown by many workers to describe accurately the temperature dependence of viscosity. During the current research program, this equation has been found to fit the data precisely for all the metals and alloys that have been studied.5,6 The A and C' values for cadmium and indium are given in Table 11. Comparing the magnitude of the present data with those of previous workers,7-10 as has been done in Fig. 1, it is evident that the results of Fisher and Phillips10 deviate markedly from the rest. With the exception of one point from Gering and Sauerwald,7 all other data agree within ±2.5 pct. However, the agreement between the present results and the work of Menz and sauerwald9 is especially good over the entire experimental temperature range. Such agreement may be expected since Menz and Sauerwald's

Jan 1, 1970

By K. R. Janowski, A. B. Chase, E. J. Stofel

Ruby crystals of exceptional optical quality have been grown from fluxes composed of Bi2O3 + PbF2 or Bi2O3 + BiF3. Careful control of growth conditions was required to minimize the number of growth defects consisting primarily of dislocations, occluded flux, and growth twins. Slow growth rates coupled with the addition of small amounts of La2O3 as a flux dopant were helpful in producing nearly perfect crystals. Chromium concentrations up to 1 pet were incorporated into these crystals without adversely affecting their perfection. Crystals up to 10 mm in diameter having as few as one to ten dislocations per crystal were typical of those produced under optimum growth conditions. Under these same conditions the occlusions were eliminated, and growth twins were either eliminated or reduced to one to three twin boundaries per crystal. INTEREST in the nature of lattice imperfections produced during the growth of ruby crystals (Al2O3-corundum structure) has been stimulated recently by the need for ruby lasers of good optical uniformity. As a result, ruby crystals grown by the flame-fusion (Verneuil) process have been studied in detail and have been found to contain high densities of dislocations (106 to 107 dislocations per sq cm) and mosaic structures that impair their optical quality.'-3 Attempts to improve the quality of Verneuil-grown crystals by controlling the growth variables have not been entirely successful. On the other hand, rubies grown by the flux process have received little attention even though their more nearly equilibrium growth conditions suggest that they would have fewer growth defects. Nelson and Remeika have shown recently that small flux-grown rubies can indeed be made into very low-loss lasers. However, they did not report information on crystalline imperfections in these crystals.4 Stephens and Alford have reported briefly on defects found in a flux-grown corundum crystal but they neither described these defects in detail nor related them to the method of growth.5 The present investigation was undertaken to establish the relationship between growth conditions and crystalline perfection of flux-grown rubies, sapphires, and other crystals of the corundum family. EXPERIMENTAL PROCEDURE The corundum crystals used in this study were grown by slowly cooling solutions of A12O3 in molten-salt solvents of PbO + PbF2, Bi2O3 + PbF2 or Bi2O3 + BiF3. The materials employed were Linde A (a Al2O3 powder) with reagent-grade chemicals as solvents. Some of the solutions also contained small additions (1 pet or less) of one or more of the transition metal elements chromium, manganese, iron, and titanium as crystal dopants. La2O3 was added to some of the solutions to alter the growth habit of the crystals. The La2O3 promoted the occurrence of growth facets parallel to (0112) and {1011} planes, where the indexing system is the morphological system described in detail by Kron-berg6 and used throughout this paper. The melts from which the crystals were grown were prepared by mechanically mixing the various constituents and placing them in platinum crucibles. The covered 50- and 100-ml platinum crucibles were heated in muffle furnaces at 1250°C for short periods of time (1 to 4 hr) and then program-cooled at either 2° or 4°C per hr to 1000°C. At this lower

Jan 1, 1965

By J. L. Martin, W. M. Campbell

A new electric logging method, called displacement logging, often gives a direct indication of the presence of mobile hydrocarbons in hydrocarbon-bearing formations. This method is based on the detection of a bank of connate water which is formed between the invading mud filtrate and virgin formation fluids in these cases. The existence of this phenomenon has beer, verified by laboratory studies and by actual field logs taken in known oil sands. INTRODUCTION During the past decade increasing use has been made of conventional electric logs to determine the amount of oil or gas in formations traversed by a borehole. This determination requires knowledge of several factors, such as true resistivity of the formation, formation factor, and water resistivity. Sometimes all of the factors necessary to make a reliable saturation calculation are not available. Also, the computations and corrections which are necessary in such a study often require the services of an experienced log analyst. It has long been the desire of exploration people to have a logging device which will locate hydrocarbon-bearing formations directly without requiring complex interpretation methods. The displacement log, while not completely fulfilling this desire, appears to be a Step in that direction. Basis for the Device The basis for this device stems from a phenomenon which occurs when mud filtrate invades a formation which contains displaceable hydrocarbons. As the mud filtrate invades the formation, most of the oil or gas is pushed out of the invaded zone, leaving residual oil. However, in addition to displacing most of the oil or gas, the connate water is also swept out, since the originally irreducible water is mobile in the presence of a water phase.1,2,3 Tonsequently, this irreducible water piles up as a bank between the virgin oil zone and the invading filtrate. If the mud filtrate is of higher resistivity than the formation water— as is commonly the case—the resulting annular zone, containing the bank of formation water, will be of lower resistivity than either the virgin oil-bearing formation resistivity or the invaded zone resistivity. This resistivity configuration, going from high to low to high again as the distance from the borehole increases, is found only in those zones which contain displaceable hydrocarbons. A device which would reliably detect this low resistivity zone would give a direct indication of mobile hydrocarbons. Illustrations This phenomenon is illustrated in Fig. 1 and 2. Fig. 1 shows a sketch of a zone containing salty connate water plus displaceable hydrocarbons, along with graphs showing fluid content and electrical resistivity vs distance from the borehole, before invasion occurs. Fig. 2 shows this zone, together with fluid content and resistivity graphs. after invasion by a fresh water mud. The resistivity pattern on moving away from the borehole is high: low: high. The absence of the low zone phenomenon in water zones is illustrated in Fig. 3 and 4. Fig. 3 shows a sketch of a zone containing salty formation water and residual oil, along with graphs showing fluid content and electrical resistivity vs distance from the borehole, before invasion occurs. Fig. 4 shows this water zone, together with fluid content and resistivity graphs, after invasion bv a fresh water mud. In this case the resistivity pattern on moving away from the borehole is high: low since there is no change in water saturation at the head ol

Jan 1, 1956

By J. G. Kura, P. D. Frost, L. W. Eastwood

THE preparation and general properties of mag-nesium-lithium base alloys have been described in earlier papers.l,2 Lithium forms solid solutions with pure magnesium, lowers its density, and improves its formability. The improved isotropy and better formability of these alloys are attributed to the ability of lithium to convert the magnesium lattice from hexagonal (alpha phase) to body-centered-cubic (beta phase) structure. This change in structure is, however, accompanied by some limitations which make it difficult, if not impossible, to combine all the desirable properties in one composition. The most important of these limitations is the tendency of the high-strength alloys to overage and lose strength at temperatures of the order of 150" to 200°F. A study was made of the effects of composition and heat treatment on the age-hardening character- istics of the alloys. Stability of properties was determined by hardness and tensile testing of the alloys at room temperature after various periods of exposure to elevated temperatures. Precipitation-hardening curves are shown for a number of magnesium-lithium-zinc alloys in fig. 1. All the alloys were solution treated at 700°F and aged at 200°F. The reason for using the drastic quench, toluene at —105°F, was to reduce the rapid precipitation of the hardening phase which takes place at room temperature. Previous experience has shown that a hardness of about 90 to 95 Rockwell E is indicative of yield strengths in the range of 35,000 to 40,000 psi. This is a desirable strength level for magnesium-lithium base alloys with specific gravities of the order of 1.65 or less. Although the hardness level is raised by large zinc contents, a corresponding decrease in the cold formability of these alloys occurs with increasing zinc content. Thus, alloys containing up to about 10 pct Zn and having hardnesses of the order of 70 to 75 Rockwell E may be bent over a very small radius; however, the 16 pct Zn alloy requires a bend radius of more than 8T. The hardness relationships illustrated in fig. 1 can be explained by the partial phase diagram shown in fig. 2. The zinc-free magnesium-lithium alloys are entirely body-centered cubic (100 pct beta phase) when the lithium content of the binary is 10.3 pct or higher. When zinc is added, the boundary between the beta and alpha-plus-beta fields at 700°F is shifted to lower lithium contents. In addition, the solubility of zinc at 700°F decreases with decreasing lithium content. It is shown by a study of micro-structures that the limit of solid solubility of zinc in the 6Mg/Li* matrix at 700°F is about 19 pct. It is believed from a study of the aging curves that this limit is about 2 to 3 pct at 200°F. Zinc additions up to about 2 pct increase the hardness and strength of the magnesium-lithium base solid solution. Larger additions of zinc effect further hardness increases, but precipitate during prolonged aging at 200°F. Alloys having 14 to 20 pct Zn precipitation harden extremely rapidly during quenching, even when quenched in toluene at —105° F. The high-zinc alloys overage at 200°F but are capable of maintaining reasonably high hardnesses for periods up to 1000 hr.

Jan 1, 1951

By D. M. Boulin, E. S. Greiner

Single crystals of vanadium were bent at 293" and 77°K to a maximum fiber strain of about 1 pct. Analysis of slip line and etch markings of- crystals deformed at either temperature show the slip planes are {112}. The slip directions at 298° and 77°K, deterwined from the asterism axes of rotation of crystals compressed in a {110} direclion, were (111). Etch pits, associated with dislocations, were observed in the plastically deformed vanadium. There was no evidence of mechanical twinning. THIS paper presents results on single crystals of vanadium plastically deformed by bending and compressing at 298° and 77°K. Bcc metals have been observed to slip on {110}, (1121, and (123) planes while the slip direction has invariably been found to be ( 111) 1 Lindley and smallman2 have studied the deformation intension of polycrystalline vanadium between 298° and 20°K and reported that at and above 77°K the deformation is predominantly by slip, but at 20°K the deformation is associated with twinning. Later, Edington and smallman3 found that single crystals of vanadium compressed in a (111) direction at 77°K deformed by twinning on { 112}( 111) systems. Clough and pavlovic4 have reported that mechanical twins were observed in vanadium loaded by impact at 77°, 173°, and 195°K, respectively. PREPARATION OF SINGLE CRYSTALS The vanadium single crystals were made from commercial vanadium reported to contain 0.03 pct C, 0.03 pct 0, 0.02 pct N, 0.0X* pct Ca, 0.0X pct Si, proximately 0.8 cm diam, 4 cm long and were grown in (100) and (110) directions. A crystal for studies of etch pits was gound to have a face parallel to a {l00} plane by the Bond crystal-orienting technique.7 In order to avoid straining, the crystals were placed on the steel mount with a low-melting organic compound (glycol phthalate) before grinding. Crystals for the bending experiments were ground to have the four side faces parallel to ( 100) planes. The crystals were electropolished8 in 10 pct H2So4 using a current density of about 3 amp per sq cm to remove the strained surface material. The crystals were bent slowly by three-point loading in a stainless-steel jig designed by Sylwestrowicz.9 The end rollers of the jig were 3.8 cm apart. DEFORMATION AT 298°K The bent vanadium crystal, after removal from the jig, had a radius of curvature of 20.4 cm over the 2-cm length close to the center loading roller, where the maximum bending moment occurred. This radius of curvature corresponded to a maximum fiber strain of 0.9 pet. The side faces contained slip bands as shown in Fig. 1. These bands are straight where the strain is high, top and bottom of micrograph, but are curved on either side of the neutral axis in the center. This curvature of the slip bands in the low-stress area may be due to cross slip. The plastically deformed crystal was subsequently electropolished and then electroetched in 10 pct H2SO4 solution, using a current density of 0.25 amp per sq cm. The structure is shown in Fig. 2. The directions of the traces on two adjoining faces were plotted stereo graphically, Fig. 3.* Since there were two sets of

Jan 1, 1968

By A. A. Bauer, H. A. Saller, F. A. Rough, J. R. Doig

among uranium alloy systems are the U-Zr, U-Ti,and U-Mo binary systems, in that an intermediate phase, of limited solubility range, exists in each system. These intermediate phase alloys offer a promising field of investigation, both as binary alloys and as ternary alloy combinations. While a limited amount of work has been done on the binary alloys, none has been done on ternary combinations of these alloys. As a possible prelude to more intensive investigation of these systems, a study of the phase relationships between the 6 phases of the U-Zr and U-Ti systems was undertaken. The solid-state portions of the binary constitutional diagrams for the U-Ti,1 Zr-Ti,2 and U-Zr3 systems are shown in Fig. 1. The solid to liquid transformations are not shown, as these transformations were not studied in the ternary system. The phase designations employed are based upon those shown in the uranium constitutional diagrams. The crystal structures of the various phases are given in Table I. Experimental Materials and Methods The ternary section presented is based upon the results of thermal, metallographic, and X-ray analyses of a series of alloys ranging in composition between the phases of the U-Zr and U-Ti systems (U-74 atomic pct Zr to U-35 atomic pct Ti). After preparation of the alloys, thermal data were obtained. On the basis of these data, specimens were heat treated and examined metallographically. Specimens were then selected from those heat treated for X-ray determination of the phases present in what were considered critical phase regions. Alloy and Specimen Preparation—Alloys for this investigation were prepared from selected as-reduced uranium and crystal-bar zirconium and titanium. For nominal compositions, see Table 11. Charges were arc melted from five to seven times under a helium atmosphere, finally being cast into wire-bar form for fabrication. A zirconium getter button was used to clean the furnace atmosphere prior to melting. The alloys were homogenized 20 hr at 900 °C and furnace cooled. A portion of each bar was then removed for thermal analysis; the remainder was saved for fabrication. Alloys 8 through 14 were placed in steel tubes along with zirconium getter chips and, after flushing with argon, the tubes were welded shut and rolled at 1500 °F to a 50 pct reduction in diam. The remaining alloys were annealed 24 hr at ll00°F to insure transformation of the ? phase to the 8-U2Ti phase and were then hot rolled from a salt bath. Attempts to roll alloys 6 and 7 at 1100 °F were unsuccessful. Following this, attempts were made to roll pieces of alloys 1 through 5, which had cracked rather severely during casting, at 1200 °F, but these efforts were also unsuccessful. These alloys were, therefore, further treated in their cast and homogenized condition. All alloys were pickled to remove oxide formed during rolling. Thermal data were obtained on these alloys by conventional differential thermal analysis at a heating rate of 30C per min, and by a high-speed heating method at rates of approximately 10°C per sec. For the latter method of analysis, a 36-gage Chromel-Alumel thermocouple is spot welded between two slivers of alloy, the sandwich being en-

Jan 1, 1958

By T. J. Whalen, S. M. Kaufman

Surface-tension measurements for liquid Fe-C-Co and Fe-C-Ni alloys were performed by the sesszle-drop technique at 1350o and 1425°C. Cobalt was shown to he more effective than nickel in lowering the surface tension of Fe-C alloys A minimum value for surface tension of 1640 dynes per cm was found in the Fe-C-Co system at a concentration of 1.5 pet C and 12pet Co. Analysis of these measurements in terms of adsorption and desorption behavior indicated that cobalt and nickel lower surface tension in Fe-C alloys by replacing carbon at the liquid-vapor interface. Comparison of results to date for Fe-C liquid alloys has shown that most substitutional-type elements having about the same atomic diameter as iron also have relatively the same influence on surface tension when present in dilute amounts. It has been shown previously that surface-adsorption behavior in liquid Fe-C ternary alloys is related to the manner in which the ternary addition affects the activity of carbon in the bulk solution.' Certain ternary additions, such as chromium, tending to decrease carbon activity cause adsorption of carbon and chromium to the liquid-vapor interface. Additions, such as silicon, increase the carbon activity, resulting in a desorption of carbon and an adsorption of silicon. Both cases were shown to cause a decrease in surface tension due to adsorption. It is the object of this paper, as part of the writers' continuing interest in the effect of alloying additions on the surface tension of Fe-C alloys, to present and discuss surface-tension data on solutions in the ternary systems Fe-C-Co and Fe-C-Ni. Available activity measurements for these systems in the solid state indicate a strong increase in carbon activity when either nickel or cobalt is added to Fe-C alloys.2, 3 EXPERIMENTAL PROCEDURE The alloy compositions used are shown in Table I. These alloys were prepared by vacuum melting in stabilized zirconia crucibles and then vacuum casting into cold-steel molds. The nominal analyses for the alloys used in this investigation are given in Table I. Surface tensions and densities were measured by the sessile-drop method4,5 in conjunction with the tables of Bashforth and bdams.' Specimens were prepared by slicing 1/4-in. cubes from the center of the vacuum-cast ingots and grinding the edges of these cubes until their shapes approximated spheres with flat bottoms. Proper handling techniques, including an acetone rinse immediately before use, assured minimum contamination from sources extraneous to the actual melting. For each experimental run a sample was placed on a BeO plaque and positioned and leveled inside a vacuum induction heating apparatus. The sample and plaque arrangement sat inside a molybdenum tube which acted as the susceptor. Diagrams of this apparatus may be found in the literature.= After heating to temperatures just above the liquidus at pressures of the order of 10-4 to 10- 5 mm Hg, photographs of the drop profile were made using its natural thermal radiation as a light source. Some measurements were made with partial pressures (-1 cm Hg) of a mixture of H2 and He gases. The H2-He atmospheres proved to be necessary at higher nickel contents to retard excessive vaporization losses. Chemical analysis for carbon and the ternary addition was performed for each alloy sample after completion of the experimental run.

Jan 1, 1964

By C. S. Smith, L. H. Beck

KNOWLEDGE of the Cu-Zn constitution diagram was critically examined in 1944 by G. V. Ray-nor,1 who suggested the diagram reproduced in Fig. 1 as the best evaluation of available data. No pertinent work on the constitution has been published since that time, although a number of authors have discussed transformation kinetics and theory. Despite the large amount of work that has been done on the constitution of these industrially important and scientifically interesting alloys, minor uncertainties still exist. For example, it is still not possible to say definitely whether a two-phase region exists between the ordered and disordered forms of the 8 phase. A careful re-examination of the phase boundaries in this part of the diagram was therefore undertaken. Two methods were selected for the new investigation—quantitative metallography for the higher temperatures and precision lattice parameter measurement for lower temperatures. Because of the relatively narrow two-phase regions flanking the ß phase in these alloys, quantitative metallography is particularly suited for their examination, since the relative amounts of the two phases are very sensitive to their compositions. The method, however, is useless below about 350°C because of the inadequate resolution of the two constituents. Below 400°, however, the X-ray diffraction method is applicable, although it is of somewhat lower sensitivity in this system. The changes of composition that occur during quenching from above about 500°C entirely vitiate X-ray measurements at room temperature though they do not affect metallographic area measurements. The two methods overlap and supplement each other admirably. Both methods depend on the attainment of equilibrium composition of the two phases in a more or less intimate mixture and thus avoid the difficult problems of nucleation and long range diffusion involved in the conventional metallographic bracketing method. The alloys were melted from a master alloy made from re-electrolyzed cathode copper and Horsehead 99.99 pct Zn. Melting was done under a cover of either borax or charcoal and the alloys cast into a 7/8 in. sq graphite mold for the a-ß alloys or a 3/8 in. diam cylindrical graphite mold for the ß-? alloys. The a-ß alloys were rolled at 750°C to 5/8 in. sq; annealed for 24 hr at 800°C and quenched; then rolled and swaged at 200°C to 3/8 in. diam rods, annealed 24 hr at 200°C, quenched and cold rolled 2 pct reduction. This treatment was intended to obtain a small grain size and to produce many nuclei of the minor phase for growth on subsequent heat treatment. The unworkable ß-? alloys were given preliminary treatment by sealing in Vycor tubes in vacuum and annealing for 4 hr at 800°C followed by cooling in air. Samples of homogenized alloys were checked spectrographically for impurities, but the principal components were determined on samples subsequent to heat treatment. The impurities analyzed averaged approximately as follows: Ag, 0.0002 pct; Fe, 0.004; Si, 0.0008; Cd, 0.005; Mg, 0.0002; and Pb, 0.002. For metallography, samples of appropriate composition were cut into rods 5/8 in. long, sealed in pyrex tubes in vacuum and annealed for eight weeks at temperatures of 470°C and below, two weeks at 480°, 500°, and 600°C, and 4 hr at 700°C, followed by quenching in cold water. Temperatures were accurate to ±2°C. The cylinders were then machined to 8.7 mm diam and a slice weighing 1.5 g cut with a thin saw transversely from the center of each. This

Jan 1, 1953

By S. R. Goodman, Hsun Hu, R. S. Cline

The quenching technique has been used to study phase relations in the composition area 2FeO.SiO2-FeO-SiO2-MnO.Si02-ZMnO.SiO2 of the system iron oxide-manganese oxide-silica under strongly reducing conditions such as exist in a gas mixture consisting of equul parts of carbon dioxide and hydrogen. Liquidus and solidus temperatures of most mixtures in the composition area studied are in the range of 1173° to 1345°C. EQUILIBRIUM relations existing among the oxides of iron, manganese, and silicon are of particular interest in two areas of steelmaking: slags and ingot inclusions. Mixtures of these oxides represent about 90 pct of the slag in the acid steelmaking process, and so dominate the chemistry of the whole refining process. These constituents also play an important role in the early slags existing at the time of the "lime boil" in the basic open hearth process. If these slags are liquid, they "wet" the lumps of lime rising from the bottom of the bath, and react with them. A liquid slag rich in CaO is then formed at the very beginning of the refining. Because the temperature is still low, all conditions for a good dephosphoriza-tion are fulfilled at this stage of the operation. Metal deoxidized with ferromanganese or silico-manganese is likely to contain, as inclusions, phases made up from among the oxides of iron, manganese, and silicon. A knowledge of stability relations existing among the phases present in this system, therefore, enables one to predict the hardness of the inclusions encountered. Moreover, because the shape of the inclusions in steel has a profound influence on the physical properties of the metal, it is important to establish whether or not the oxidic material is present as liquid or crystalline phases during heating and rolling of the steel (-1150 to 1350°C). A knowledge of melting relations in synthetic mixtures of iron oxide, manganese oxide, and silica will give a clue to these problems. Methods for determining such relations and the results obtained are described iln this paper. I) PREVIOUS WORK A number cf previous studies have dealt with the three "binary"* systems bounding the system iron oxide-mangar,.ese oxide-silica. The system iron oxide-silica was studied by Bowen and shairerl in 1932. Their data were obtained by equilibration of mixtures in contact with metallic iron. Phase relations for the system iron oxide-silica ill atmospheres of different oxygen pressures car1 be derived from data on the system FeO-Fe2O3-SiO2 as determined by Muan.2 The diagram shown iri Fig. l is a section of this system in an atmosphere of CO2 and H2 in ratio 1:l. The system manganese oxide-silica has also been the subject of several investigations. Most of the early studies suffered from a lack of proper control of the atmosphere under which the equilibrations were carried mt. Phase diagrams for the system at two well defined levels of oxygen pressures have been determined recently. Glasser3 determined stability relations in an atmosphere consisting of carbon dioxide and hydrogen in ratio 5:1, diagram Fig. 2, and Muan4 studied phase relations in the system in air.

Jan 1, 1962

By A. D. Schwope, L. R. Jackson, A. M. Hall

In the course of an extensive investigation of the comparative properties of several types of copper, data were obtained on the cold working and subsequent recovery and recrystallization of the copper. In this paper, relations between the degree of cold work and the course of re-crystallization are developed. In particular, it is shown that the course of recrystallization over long periods of time and at low temperatures can be predicted with reasonable accuracy from short-time high-temperature recrystallization data. Materials Used in The Investigation Three types of copper were used in this investigation; these were tough pitch, OFHC, and OFHC copper with 15 oz per ton of silver added identified herein as Lots C, D, and F, respectively. The material was supplied by the American Metal Co. Ltd., and processed by the Rome Cable Co. The analyses of the three types of copper are given in Table I. Originally, it started as wire bars 4 X 4 X 54 in. These bars were heated to 871° C in air and hot rolled to % in. rod. This rod was cold drawn to 0.204 in. rod (70 pct reduction) in three passes and annealed at 427°C for 4 hr. A portion of the 3/8 in. rod was saved for more detailed cold-drawing experiments. Starting with the annealed 0.204 in. rod, hard-drawn wires were produced by cold drawing to 0.081 in. wire in 7 passes (84.4 pct reduction in area). Half-hard wires were made by cold drawing the 0.204 in. rod to 0.102 in. wire, (75 pet reduction) in 6 passes and annealing at 427'C for 4 hr. This annealed wire was then drawn to 0.081 in. wire, (37.1 pet reduction) in 2 passes. Square rod was made by hot rolling wire bars to Re in. rod in 8 passes. This rod was then cold drawn to 0.445 in.-diam rod and annealed for 346 hr at 538°C. It was then cold drawn to 0.325 in. rod and again annealed at 538°Cf or 3 1/2 hr Hard square rods were then made by cold rolling this material to 0.257 X 0.257 in. rod, a reduction in area of 20.5 pct. Half-hard square rods were made by cold rolling to 0.268 x 0.268 in. square, annealing for 3 1/4 hr at 538°C and cold rolling to 0.257 x 0.257 in., a reduction of 8.5 pct. Soft wire or rod was made from all types of copper by annealing the hard-drawn material at 343°C for 3 hr in steam. The grain size of the annealed 0.081 in. wire varied slightly among the three lots: from o.o15+.oz5 mm in the silver-bearing OFHC to 0.035-0.045 mm in the OFHC copper. The annealed 0.257 in. wires were more uniform in grain size, averaging about 0.035-0.045 mm. Representative structures are shown in Fig I. Effect of Cold Drawing and Tensile Strain on Strength of Copper Conventional tensile tests were performed on the three types of copper in the various degrees of hardness described above. Results of these tests are tabulated in Table 2. The results in Table 2 are 6

Jan 1, 1949

By P. Dayal, L. S. Darken

THE migration of carbon in austenite under the influence of an electric current has been observed qualitatively several times.14 Lebedev and Guterman5 recently have reported quantitative measurements; their method consisted of welding a low-carbon to a high-carbon wire, passing current, and later estimating the carbon distribution metal-lographically. We believe the method reported in this paper is superior in principle since electrolytic migration and ordinary diffusion are not necessarily coupled as in the weld method; also for the first time the extent of migration is determined by combustion analysis for carbon. A uniform tubular specimen (S.A.E. 1045 or 1095) was mounted as illustrated in the figures. the whole assembly being in an atmosphere of purified nitrogen. Direct current (129 to 226 amp at 0.65 to 1.0 v) served as source both of heat and of potential gradient for carbon migration. The duration of experiment was 7.5 to 12 hr, during which time the temperature was controlled (±10°C) manually. The experimental conditions are indicated in the first five columns of table I. With this experimental arrangement, the temperature initially has a maximum value at the central plane. Also, in this vicinity (by virtue of the symmetry), the carbon entering any volume element is equal in quantity to that leaving; the loss or accumulation of carbon occurs near the electrodes since the carbon moves uniformly near the center and is "frozen" at the cold ends. Hence, providing the time of experiment is not sufficiently long to seriously influence the conditions at the central plane, carbon crosses this plane only under the influence of the electrical potential gradient and not under the influence of temperature or concentration gradient. The amount of carbon which has crossed this plane was determined by combustion analysis of the two halves of the specimen. The results of these analyses are shown in the sixth and seventh columns of table I. It will be noted that substantial amounts of carbon migrated from the anode portion to the cathode portion (except at 920°C, which temperature was too low to exhibit the effect in the allotted time). In spite of precau-tions taken, considerable decarburization occurred as may be seen by comparing cols. 8 and 5. In three cases (indicated by asterisks in table I) the specimen was ground on one side, polished, and examined metallographically before analysis. One specimen was normalized and re-examined. Micrographs of selected areas in specimens 4 and 6 are shown in figs. 1 and 2, respectively. Evidence of carbon migration from the anode toward the cathode is quite apparent. Fig. 2 shows abundant graphite as well as cementite in a region near the cathode. The temperature of this zone is estimated at about 800°C. In fig. 1, particularly in the micrograph on the extreme right (the right side of which is of unaltered carbon content), there is evidence of slight depletion of carbon in the immediate vicinity of the cathode as contrasted to the general increase in carbon of the cathode half of the specimen. Although this may be attributed in part to decarbur-ization, it is believed that it is occasioned also by thermal diffusion—migration (of carbon) from a cool to a hot zone4—a phenomenon superimposed upon the electrical migration. Evidence of carbon migration was visible particu-larly during the course of the high-temperature,

Jan 1, 1951

By R. L. Perrine

This paper presents results obtained by consider ation of unstable miscible displacement within a porous medium as a quasi-turbulent displacement process, that is, a process characterized by fluctuations around a simpler, mean flow behavior. The instability usually results from the miscible displacing fluid having a viscosity lower than that of the displaced fluid. Such instability is evidenced in suitable experiments by the presence of viscous fingering. A unified theoretical relationship applicable to both stable and unstable displacement is derived. Parameters in the theory are obtained by empirical means. Although the theory describes an idealized conceptual model, agreement with experiment is quite reasonable up to moderately adverse viscosity ratios, such as 17:1. INTRODUCTION Many experimental studies of miscible displacement in porous media have been conducted with prediction of reservoir displacement efficiency as the ultimate objective. Most such studies have utilized lower displacing than displaced fluid viscosity, scaled to potential reservoir fluid pairs. Theoretical approaches have been largely limited to unit viscosity ratios, however, in spite of the necessity for an understanding of the mechanism of the unstable, adverse viscosity ratio displacement process. An obvious reason is the difficulty of describing in mathematical form the viscous fingering characteristic of these conditions. Observation of experiments conducted with dyed fluids in transparent systems suggests an analogy between unstable miscible displacement and turbulent flow in a pipe. In both cases there are fluctuations around a simpler, mean flow behavior. An important difference is that flow behavior of interest in the porous medium is entirely transient, contained within a transition zone between displacing and displaced fluids. Transient behavior complicates description in that coefficients in the equations become variables rather than constants. In the study reported here, the analogy with turbulent flow has been used in treating unstable miscible displacement as a quasi-turbulent displacement process. The purpose has been to derive, even if restricted to an idealized conceptual model, a unified theoretical relationship applicable to both stable and unstable displacement. A relationship meeting these specifications up to moderately adverse viscosity ratios, such as 17:1, is presented. One fluctuation parameter in the theory and dispersion coefficients are obtained by empirical means. The idealized theory is compared with experimental results. UNSTABLE MISCIBLE DISPLACEMENT AS QUASI-TURBULENT DARCY FLOW The miscible displacement of one fluid by another within a porous medium is considered in this study. Flow conditions are such that Darcy's law is applicable. It is further assumed that, by the stability criterion proposed by perrine,1 initial flow conditions lie well within the regime of instability. Thus substantial viscous fingering is assured. We wish to show how this flow regime can be represented as quasi-turbulent. That is, the Reynolds number for the established flow conditions is below that for inertial or turbulent flow within a porous medium, and lies within the regime for which Darcy's law is valid. Yet flow behavior can be described as the combination of some relatively simple average result, and characteristic fluctuations that are superimposed on the simpler behavior. Stated another way, flow behavior includes the movement of layers of fluids with different velocities past or over one another. Such descriptions are characteristic of turbulent pipe flow. The fluctuations in the present case are a direct consequence of the local viscous fingering which accompanies the unstable displacement process. Should displacement become stable, fluctuations would die out. It is of particular importance to note that fluctuations such as these can interact in a way that contributes to material transport by the basic flow. The basic transport equations required for engineering calculations must be modified to reflect this fact.

By R. F. Domagala, M. Hansen, D. J. McPherson

On the basis of metallographic analysis, incipient melting data, thermal analysis work, and X-ray diffraction, phase relationships in the 0 to 50 atomic pct Cr region were carefully resolved. Phase relationships in the 50 to 100 atomic pct region were outlined. A single intermediate phase, ZrCr,, was established in the system. A eutectic and a eutectoid were found in the zirconium-rich region of the system, while a eutectic was located in the chromium-rich region. Limited solubility of chromium in both a and a zirconium was observed. THIS is another in a series of papers on zirconium-base binary phase diagrams based on a program sponsored by the Atomic Energy Commission. The Zr-Sn,' Zr-Si,' and Zr-Mo and Zr-W" systems have already been published. Previous work on the Zr-Cr system includes a partial diagram by Hayes, Roberson, and Davies' and a complete diagram by McQuillan." The phase relationships reported by these authors were determined with magnesium-reduced zirconium, whereas those reported herein are based on iodide metal. Some X-ray work on the intermediate phase in this system was also reported by Hayes et al., as well as by Wallbaum.' Comparisons with these data are made in the appropriate sections. Thermal analysis, metallographic and incipient melting techniques were employed to accurately resolve phase relationships in the 0 to 50 atomic pct Cr region, while the remainder of the diagram is outlined on a basis of cast structures and thermal analysis. A description and analyses of the metals used in the preparation of alloys for this study are included in Table I. A "low-hafnium" zirconium crystal bar (Westinghouse "Grade 3") was used. This material was produced by the decomposition of a volatile iodide onto a hot zirconium filament. The as-received crystal bar was coated with corrosion product from a standard autoclave test by which its grade designation is determined. A sand-blasting and subsequent HF-HNO, pickling treatment was employed to remove this contamination. The bars were cold-rolled to approximately 1/32-in. sheet, pickled again, sheared to 1/4-in. squares, washed with acetone, and stored for use. Ingot chromium metal from National Research Corp. and electrolytic chromium flakes from Johnson, Matthey and Co., Ltd., were available as alloy additions. The ingot chromium was received in granular form. The large granules were sized by crushing, treated for iron removal, rinsed with acetone, and stored. The flakes were broken to approximately 1/8 in. with mortar and pestle, cleaned with acetone, and stored for charging. Experimental Procedure A nonconsumable electrode arc furnace identical to that described by Hansen, Kessler, and McPher-son,' was used in this work. A 400 amp dc welding generator was the source of power. To insure homogeneity, ingots were melted in a water-cooled spun copper crucible, a total of four times without opening the furnace. No difficulties were encountered in the preparation of these binary alloys. Analyzed chromium contents were found to agree very well with the intended content. Melts of pure zirconium were interspersed in the course of preparing the alloys and their hardness was measured to keep a constant check on the melting technique. Vycor and quartz bulbs were used to contain the samples for isothermal annealing treatments. Vycor bulbs were employed for temperatures up to 110O°C, while quartz was used above this temperature. For treatments up to 950°C the bulbs were evacuated before sealing, but for higher temperatures a partial pressure of argon was admitted to the

Jan 1, 1954

By W. T. Olsen, R. Ulcer

WHEN a liquid alloy freezes, the solid first formed usually differs widely in chemical composition from that last formed, so that there is segregation in the alloy as cast. For example in the copper-nickel system (fig. 1) the first solid formed from a liquid containing 55 atomic pct Cu may contain as little as 38 pct Cu, while the last must contain well over 55 pct. Three factors may act to decrease segregation from the maximum possible. 1. Diffusion in the cooling solid tends to make the phase homogeneous, decreasing segregation. This may be important at slow rates of cooling. 2. Segregation is impossible without diffusion in the liquid. At extremely rapid rates of cooling there may not be enough time to allow maximum segregation. 3. Supercooling delays nucleation to temperatures well below the liquidus thereby decreasing segregation. Hence the first nucleus in the copper-nickel system may contain well over 38 pct Cu. At sufficient supercooling the first nucleus may form below the solidus, in which case there is no reason to expect any segregation whatever. From these considerations, we could predict that at sufficiently low rates of cooling the alloy would be unsegregated because of factor 1 and at sufficiently high rates of cooling there should also be no segregation because of factors 2 and 3. Considerable segregation should occur only at intermediate rates of cooling. We have demonstrated experimentally that segregation can be completely suppressed by rapid rates of cooling. For the alloys studied, however, these rates are too great to be attained in any commercial practice. An alloy of 55 atomic pct Cu, 45 atomic pct Ni was frozen by cooling at varying rates. The degree of segregation in the solid was determined by X-ray diffraction photographs. Slow rates were obtained by slowly cooling the furnace containing the liquid alloy; fast rates by pouring or ejecting droplets of the alloy into water or iced sodium hydroxide solutions. The cooling rate of the droplets can be cal-culated from their dimensions by assuming reason- able values of thermal conductivity.' The experi-ments were repeated with an alloy of 16.5 pct Cu and 83.5 pct Au. A single experiment also showed a 50 atomic pct Bi-Sb alloy had no segregation at the most rapid quench. The position of back-reflection X-ray diffraction lines is a highly sensitive function of the lattice constant, which in turn depends on the chemical composition of the phase. A phase of varying composition will give broad diffraction lines. By measuring the edges of these lines and making suitable corrections for intrinsic line width, it is possible to determine the range of lattice constants represented. These can be converted to chemical compositions from a lattice constant vs. composition curve. Results are shown in table I. In the copper-nickel system the greatest segregation is found at the slowest cooling rates, where the lowest percentage of copper theoretically possible is found. In the copper-gold system, on the other hand, the degree of segregation is decidedly less at the slowest rates of cooling, being greatest at 11,100°C per sec. At no rate is the theoretically lowest percentage of copper (12 pct) found. At the rates of cooling found in sand and die castings the degree of segregation is large and depends little on the rate of cooling. Acknowledgment Most of the material in this paper is abstracted from a thesis presented by William T. Olsen, Jr. in 1948 in partial fulfillment of the requirements for the degree of Master of Science at the University of California.

Jan 1, 1951