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By Irving B. Cadoff, Ernest Levine

The fracture path in a Cu-4 pct Ag alloy wet with mercury was found to he dependent on the heat treatment used prior to tensile testing. Both quenched and slow-cooled alloys were embrittled by the mercury.. For quenched alloys, which were single -phase, the crack path was intergranular. Slowly cooled alloys, which contained precipitate platelets, exhibited transgranular fracture. By comparing stress-strain data for these alloys with similar data on mercury -embyittled solid-solution alloys, it was found that the role of the precipitate and that of the grain boundary in the fracture process were equivalent . THE fracture path which results when metals are strained in a liquid environment appears to be dependent upon the nature of the specific system. Mixed transgranular and intergranular cracking has been observed in the 2024 T4 aluminum alloy when wet with a Hg-Zn amalgam.' Transgranular fracture was induced in an A1-4 pct Cu alloy by masking off the grain boundaries from the liquid Hg-Zn amalgam.' The embrittlement of solid-solution alloys of copper in mercury results in intergranular fracture.' The effect of a precipitated phase on the fracture path in copper alloys is the subject of the present investigation. Cu-4 pct Ag was chosen so that its behavior could be compared with previous work on embrittlement of copper alloys. PROCEDURE High-purity copper (99.999 pct) was used as a base metal, along with 99.999 pct purity silver. Melting was carried out in graphite crucibles with manual agitation to get adequate mixing. The ingots were homogenized by means of vacuum annealing, chemically cleaned, and cold-rolled with intermediate vacuum anneals, to the desired thickness of 0.025 in. The rolled sheets were sheared to the final specimen size of 1 by 0.025 by 0.1 in. The specimens were then electropolished in phosphoric acid (concentrated) and heat-treated in an evacuated capsule at the solution temperature of 770°C. One batch was slow-cooled and the other quenched in water. The thermal etching which occurred during heat treatment was sufficient to permit grain boundary and precipitate delineation. Tensile tests were carried out in air and in mercury on a Table-Model Instron at a pulling speed of 0.2 in. per min. Wetting was accomplished by electro-polishing in phosphoric acid, rinsing in alcohol, and immersing in a pool of mercury. Once wet the coating was stable throughout the mechanical tests. In our studies it was found that wetting the surface or total immersion in mercury produced identical results. For convenience, the wetting technique was used for the experiments described. The crack pattern was observed directly on the surface by removing the mercury after testing. De-wetting was accomplished by flame heating the samples in a vacuum after testing and before observation of the surface. No etchant or polishing was used so as not to obscure the crack pattern on the surface. The mercury removal, however, resulted in a pitted surface but otherwise left the pertinent features visible. Photomicrographs were taken in this condition so as not to disturb the structure associated with the crack pattern. The average precipitate spacing was measured previous to coating the sample with mercury by use of an optical eyepiece micrometer. RESULTS The microstructure of the quenched specimens was single-phase while that of the slow-cooled specimens contained thin platelets of a second

Jan 1, 1964

By M. E. Wadsworth, J. R. Lewis, J. M. Quets

Samples of snythetic magnetite were reduced in hydrogen at various partial pressures and temperatures. The reaction mas found to be surface controlled and directly proportional to hydrogen partial pressure over the temperature range studied (400° to 1000°C). A transition in the mechanism occurred at approxirnately 590°C. This has been attributed to a change in the slow step of the reduction reaction resulting from the presence of stable wüstite at higher temperatures. Below 590°C the heat of activation for the reduction was found to be 14,700 cal per mole and it was 3,200 cal per mole above 590°C. THE reduction of the oxides of iron has been a subject of study and interest for many years. Edstrom1 has reviewed the work up to 1953 and his findings provide much basic information concerning details of the reduction of hematite (Fe2O3 ) and magnetite (Fe3O4) with both H2 and CO. He concluded that below 600°C the reduction of both hematite and magnetite was essentially identical, since the rate was controlled by a surface reaction at a magnetite gas interface and the iron formed was very porous. The decrease in the reduction rate for both hematite and magnetite immediately above 600°C was attributed to the formation of a stable wüstite phase across which diffusion was very slow. The wide difference in reduction kinetics for hematite and magnetite above 600°C was explained in terms of the character of the wüstite formed. The rate of magnetite reduction increased slowly with temperature beyond the minimum immediately above 600°C and rates equivalent to those observed at 550°C were not obtained until the temperature was increased beyond 850oC. Edstrom and Bitsianes2 studied the solid-state reduction of magnetite, the reaction of which can be written (4x-3)Fe + Fe3O4—4 FexO [1] where x is between 0.83 and 0.95. The rate was found to be controlled by the kinetics of transport of iron ions through the wüstite phase. Bogdandy and Riecke3 studied the kinetics of reduction of small grains of iron oxide in hydrogen and qualitatively attributed the slow step in the reduction process to the diffusion of hydrogen and water vapor through pores. McKewan4 has analysed the data of Joseph,5 Stalhane and Malmburg,6 and Lewis7 and has demonstrated that the kinetics of reduction of both hematite and magnetite are controlled by surface reactions and also that the variation in surface area during reduction must be accounted for. McKewan was able to correlate the reduction data by the equation rodo[1-(1-R)1/3] = Kt [2] where ro is the initial particle radius, do is the density of the iron oxide, R is the fraction reduced at time t, and K is a rate constant. The applicability of Eq. [2] for temperatures above 600°C where a stable wüstite phase is present, indicates the slow step in the over-all kinetics does not result from diffusion unless diffusion occurs laterally along the oxide metal interface or through a wüstite layer of constant thickness. Diffusional control through a layer of wüstite is unlikely, however, in view of the pressure effects demonstrated by Tenenbaum and Joseph,' Diepschlag,9 McKewan,10 and the results of the present study. McKewan has demonstrated a linear rate dependence on the hydrogen partial pressure over the temperature range 400" to 1050°C for the reduction of hematite.

Jan 1, 1961

By W. D. Brown

Newell1 has shown that hydrogen is removed from steel in a vacuum at a temperature of 500° to 900° C. within 136 hr. Holm and Thompson2 also state that, especially when the hydrogen is high, the results obtained by extraction at 800°C. agree with those obtained by vacuum fusion. In this laboratory, an apparatus was designed (Oct. 1940) and used wherein the piece of steel was heated at 100°F. in a Torricellian vacuum (Fig. I). This vacuum was produced by raising and lowering a "leveling bottle or bulb" containing mercury. Extensive tests were made with this apparatus. The weakness of the procedure was the possibility of leakage of air into the tube around the rubber stopper at the bottom. The present plan is to raise and lower the mercury by applying vacuum from a mechanical pump, to the top of the tube and then to a bottle of mercury in which the bottom of the tube is immersed. The Apparatus The extraction is made in a Pyrex tube A, I in. i.d. It is drawn down at the top at N and an 8-mm. i.d. tube is welded on it. To this a Pyrex stopcock E, 4-mm. bore, is welded. The tube between N and E is preferably 8 in. long and is graduated in milliliters. The total length of A to the stopcock is 28 inches. Heat is supplied by a split-tube furnace. 0 in. long by 6 in. in diameter, hinged on the side. A short pyrometer couple P is inserted through the walls of the furnace. In use this is standardized by comparison with a standard couple in a I-in. tube, just opposite this short couple. In the I-in. tube A a glass rod R, flattened at one end, supports the sample S and the length of R is so adjusted that the sample is in proper place. (It may float in the mercury.) The tube A is inserted in a large rubber stopper to fit the bottle B and extends nearly to the bottom. It is so placed that the handle of the stopcock faces the operator. In this stopper also is a short tube D bent at right angles for the application of vacuum. Also in this stopper is an 8-mm. tube C reaching nearly to the bottom; this is bent so as to miss the heater and again bent to bring it in line with and as near as possible to the upper and reduced part of tube A. On this tube C is welded a 4-mm.-bore stopcock H. In order that the two tubes may be as near as possible, the handle of stopcock H faces the back, or is the reverse of stopcock E. The total height of II above the bottom is 28 in. As explained later, this is the pressure-measuring tube C. The bottle B is about half full of mercury. The mercury must cover the ends of A and C by about I in. when they are evacuated. By tees T and rubber tubing RT the tubes A, C and D, the latter through the three-way stopcock M, are connected to the vacuum pump. A sheet of asbestos at K prevents the stopcocks E and H from becoming so hot that they leak. A good grade of vacuum lubricant prevents leakage of E and H. In order to measure the pressure of the

Jan 1, 1945

By Carlos G. Valenzuela

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

Jan 1, 1965

By Donald Ofte, L. J. Wittenberg

The absolute viscosity coefficients and activation energies for viscous flow of bismuth, lead, and zinc are reported. The viscosities were measured in an oscillating cup viscosimeter from nearly 1000°C to within 1 deg of the melting point of zinc; 2 deg of the melting point of lead; and in the supercooled condition of bismuth, 9 deg below the melting point. Two methods of relating the change in the viscosity coeflicient with temperature were compared. From the plot of the logarithm of viscosity (77) as a function of reciprocal absolute temperature (1/T), the equations of the lines which fit the data are: AS a part of the Reactor Fuels and Materials Research program at Mound Laboratory, precise measurements of the physical properties of liquid metals are of interest because the desirability for a low vapor pressure liquid coolant in high-temperature nuclear power plants has focused attention on the properties of the liquid metals.' Also, a clearer understanding of the liquid metal state can be achieved when better measurements are available. For these reasons, the viscosity values of certain liquid metals have been determined. The viscosities of the liquid metals, bismuth, lead, and zinc are measured in an oscillating cup viscosi-meter. In this apparatus the liquid is sealed in a right-circular cylindrical cup which is attached to a torsion fiber so that the system forms a torsion pendulum. The damping effect of the molten metal upon the normal oscillations of the torsion pendulum is a function of the viscosity of the liquid. This method is advantageous because of the small amount of sample required (8 to 10 cc), the ease of remote operation of the apparatus in a vacuum system, and the containment of the liquid metal in a hermetically sealed, nonreactive, tantalum crucible. With the liquid metal sealed in the crucible, loss of liquid by vaporization and chemical reactions with atmospheric gases are prevented. Additionally, an absolute viscosity determination is obtained which avoids the sources of possible error in a relative measurement. The difficulties in a relative method include the repetitious cup calibrations, and the uncertainty inherent in the practice of calibration of the apparatus at room temperature and extrapolation to the high temperatures necessary for the investigation of most liquid metals. The oscillating cup viscosimeter was first described by Meyer in 1891.2 The first complete mathematical treatment offering an absolute measurement of viscosity with this type of apparatus was proposed by Andrade and chiong3 in 1936 for an oscillating sphere filled with a liquid. This solution was modified to include a right circular cylinder by Hopkins and Toye4 in 1950, and R. Roscoe5 in 1958. Roscoe's treatment for the calculation of the viscosity of a liquid at a particular temperature from the logarithmic decrement and period of oscillation of the torsion pendulum was used in this investigation. A detailed description of the method of calculating the viscosity from these measurements has been reported earlier.' This calculation has been programmed for the IBM 704 and IBM 1620 computers for expedition of the otherwise laborious calculations. APPARATUS The cutaway view of the apparatus in Fig. 1 shows the suspension system within the high vacuum enclosure. The low residual gas pressure. maintained between 1 x 10-4 and 5 X 10-6 mm Hg during a determination, avoided both air drag on the pendulum and

Jan 1, 1963

By R. V. Colligan

[CONTENTS PACE Educating and Training Economic Geologists of the Future. By C. H. BEHRE, JR. (TP 2278, Min. Tech., Nov. 1948. Discussions by R. V. COLLIGAN and EVAN JUST) ....... I Mercury Industry in Italy. By EDWIN B. ECKEL. (TP 2292, Min. Tech., Jan. 1948. Discussion .............................. by C. N. SCHUETTE) 3 Chert in the Kingsport Formation at Mascot, Tennessee. By ARTHUR T. ALLEN. (TP 2299, ............... Min. Tech., Jan. 1948. Discussion by M. M. BUTLER) 5 Wall Rock Alteration at Butte, Montana. By RENO H. SALES and CHARLES MEYER. (TP 2400, Min. Tech., May 1948. Djscussions by C. D. HULIN, W. D. JOHNSTON, JR., and L. C. ................................... GRATON) 5] Educating and Training Economic Geologists of the Future R. V. COLLIGAN*-I can best illustrate my opinions by drafting another five year plan (Table 2). This plan is set up following the same stipulations outlined by Dr. Behre, namely: (I) the student is preparing himself for commercial work as a mining geologist; (2) he is attending an institution with a sufficiently broad curriculum (that is, engineering school and mining school as well as liberal arts college) to furnish the courses listed; and (3) he is not planning to continue his studies through to a doctor's degree before going into commercial work. A comparison of my study plan (Table 2) and that submitted by Dr. Behre (Table I) will at once point up the basic similarity, due to the obvious fact that there are so many essential courses which must be included in any outline of study. However, a more detailed analysis will show up certain differences, which, in fact, are only certain refinements on Dr. Behre's program. These I plan to discuss in order of their importance. The first and most important change is the addition of 12 hr of optional subjects, making a total of 24 hr of optional subjects as against a total of 12 hr under Dr. Behre's schedule. This of course entails the elimination of certain courses, which I shall discuss later. However, I wish to make it clear that I suggest eliminating these courses not because I feel that they are unnecessary, but rather because I feel the optional courses are more necessary to the complete education of the individual. I appreciate that Dr. Behre recognizes the importance of the cultural side of education, but I take issue with his thesis that the student will get it without credit and in his spare time. I do not think that the average college student, and certainly not the college freshman, is mature enough to know what he needs and where to get it in his spare time. I think it must be "spoon-fed"; he must be oriented through specific courses. University life (or should I say "college life") is too full of athletics, fraternity activities, dances, "bull sessions," and countless other enjoyable distractions, all of which contribute to the "full man." I fail to see how the average young American male can possibly sandwich in a necessary complement of "cultural activities" in his spare time. Since these latter activities do not fall within the pattern set by the "group," and show less promise of immediate return in enjoyment, or increased social status on the campus, they are bound to suffer in competition with the more popular, "group" activities. No doubt much of the criticism levelled against arts colleges, namely, that the cultural courses are useless, is well taken, for the culture

Jan 1, 1947

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

THE Annual Fall Meeting held in Chicago in conjunction with the celebration of a Centennial of Engineering brought forth a round of field trips and symposiums which did much to add to the store of information of the 240 who registered for the gathering. Instead of a scattered program, technical papers were grouped together in organized symposiums, where the particular importance of each report was enhanced by presentation in context. Despite the heavy accent on technical papers and informative field trips, those attending the meeting had ample time to enjoy the benefits of a visit to Chicago. The AIME dinner dance was held at the Palmer House, in the Red Lacquer Room. The Chicago Section played host Friday evening at dinner. The MBD held four sessions at the meeting headquarters, the Palmer House, September 4 and 5. Featuring the meetings was a review of taconite concentration and new theories on comminution. The first session opened with a paper on the Structural Features Which Effect the Concentration of Iron Formations, presented by F. J. Tolonen. The paper was centered upon the various members of the low grade iron formations of the separate Michigan districts. The study correlated macrostructure, microstructure, and concentration tests. [ ] Beneficiation Characteristics of Michigan Low Grade Iron Ores, presented by F. X. Tartaron, cochairman of the session, reviewed the work of his laboratory on the beneficiation of low grade ore taken from various strata of a deep shaft on the Marquette Range. The paper included data on flotation, gravity separation, magnetic separation, and combinations of these processes. The economics of low grade ore treatment generated great interest. Ty. Maki offered a compilation and correlation of field results with magnetic separators in ferrosilicon and magnetite medium recovery circuits. Following the morning session, 130 persons attended a luncheon, followed by a brief business meeting. Later, a film illustrating the grinding, separation, and pelletizing steps investigated by the Mines Experiment Bureau, was presented by H. H. Wade. T. E. Ban, and L. J. Erck gave a report on pelletizing which evoked much discussion. R. A. Limons presented a paper on the Mineralogy of Blast Furnace Sinter, for its author, H. M. Kraner. Friday sessions featured a new hypothesis for high speed drill rod milling and a new technical approach to comminution. Jack Myers commented that Consolidated's large rod mill was a hammer mill turned inside out. Steve Erickson described the use of Cyclones for Heavy Media Concentration of Iron Ore Fines. Bob Meaders gave a Progress Report on the Aerofall Mill. Shiou-Chuan Sun described an improved high frequency analyzer for studying the conductivity of suspensions of various minerals. L. A. Roe discussed a magnetic reflux condensor which enabled him to determine the degree of liberation of magnetic iron ores. Roy A. Johnson described a function of the hydroscilator in which the fan rake was eliminated in favor of a conical bottom. The Industrial Minerals Division sessions held September 5 and 6 and were well attended. The Friday morning session was particularly concerned with developments and advances in industrial minerals with special emphasis on the Chicago area. The first two papers dealt with transportation on the Great Lakes and fuel movement into the Chicago area. The third paper proved to be of great interest, turning the spotlight on the fairly new hydraulic mining methods introduced by a silica company in the Ottawa, Ill. field.

Jan 1, 1952

By S. J. Rothman, L. T. Lloyd

S. J. Rothman and L. T. Lloyd (Argonne National Laboratory)— Hagel's paperz0 discusses the question of the mechanism for self-diffusion in bcc transition metals. Recent work21"23 has led us to agree with him in reabandoning the ring mechanism in favor of a defect mechanism, most likely vacancies. On the other hand, we think that Hagel's attempt to group together all self-diffusion in bcc transition metals is wrong. We prefer the scheme of Peart, Graham, and omlin," who separate them into two groups. One group contains the anomalously behaved metals P titanium,', y uranium, and perhaps zirconim.' The other group contains a iron," this alloy was held at 1800°C for 2 hr before quenching, its structure was all a. B. C. Giessen, I. Rump, and N. J. Grant (Authors' reply)—We very much appreciate the discussion by Deardorff and Kato regarding the a to /3 transformation temperature of hafnium. In the W-Hf program, as well as in a current study of the system Cr-Hf, standard precautions were exercised against contamination, including vacua of less than 10"5 mm Hg and a weight control check of all specimens to insure an impurity rise of less than 100 ppm. Following receipt of the above discussion, a revision was made in the annealing process. Arc-cast specimens were etched with a 10 pct HF-90 pct HNO solution until 1 mm of surface, including a possible oxide film, was removed. Annealing was done in a hafnium container which provided a long diffusion path for gaseous contaminants. Finally, the heat treating time was shortened. Structural changes were noted to occur quite slowly. A 99.5 at. pct Hf alloy showed 70 pct /3 after 30 min at 1700°C and was 100 pct /3 after 10 min at 1715°C. After 24 hr at 1740C, the alloy was found to be 10 pct/3. This change is due to contamination; it was estimated that it corresponds to an increase of 60°C in the transformation temperature over a 24 hr period. The corresponding change in 30 rnin would be slight. Using the same hafnium as in the above publication, and three new alloys at 98, 99, and 99.5 at. pct Hf, the transformation temperature was indicated to be 1715" 15°C. Since this hafnium contained 4.4 at. pct Zr, a correction of 40 5C, based on an assumed approximately linear transformation temperature curve, must be made for pure hafnium. This yields a value of 1755 20°C in good agreement with Deardorff and Kato's value. Because the slope of the boundary is small, this permits a good extrapolation, and we regard the W-Hf alloys as well suited to check the Hf transformation temperature. niobirn,'' and molybdenum,22 whose activation energies correlate with the melting temperature and whose Do values follow Zener's predictions.28 We have no quarrel with Hagel's placing chromium into the second group; we disagree with his interpreting our data to make uranium fit into that group. Hagel considers that the measurements of self-diffusion in uranium below about 950°C represent combined volume and grain boundary diffusion. This contention is based on the curvature of the penetration plot for our 891°C run,4 which also has a nearly straight line plot of log c vs x. Hagel has extrapolated these characteristics to our 803.5C run and fitted his Arrhenius plot for self-diffusion in y uranium to our four highest temperature points only. We think this is wrong for the following reasons.

Jan 1, 1963

By C. F. Weinaug

In recent years, several methods have been proposed for correlation of physical properties and behavior of hydrocarbon systems. These correlations were found to be unsatis. factory for predicting differential gas liberation and shrinkage data now obtained experimentally. To achieve the desired accuracy, methods were developed to adjust the correlations with two experimental pieces of data. The required data are the saturation pressure at reservoir temperature and the specific volume or density at these conditions. The saturation pressure is used to adjust the vapor-liquid equilibrium-ratio correlations. The density measurement is used to determine the apparent density of liquid methane. With these adjustments, differential gas liberation and shrinkage are predicted within the experimental error. EQUILIBRIUM RATIOS Equilibrium ratios published by the National Gas Assn. of America' were used as a basis for the calculation. The convergence pressure for the sample was determined by using a hypothetical binary system, with methane as one component and the remainder of the system lumped together to form the other component. For the critical temperature of the heavy constituent, the weight average of the critical temperatures of the ethane and heavier components was used. The correlation of pseudo-critical temperature, density and molecular weight of Matthews, Roland and Katzl was used in this calculation for the hexane and heavier fractions. Points for the critical properties of methane and the hypothetical heavy constituent were placed on a chart of the critical loci of hydrocarbon systems. A critical loci for the hypothetical binary system was drawn, and the critical pressure of this system was determined at the reservoir temperature. This critical pressure became the convergence pressure for which equilibrium ratios were read from the NGAA4 charts. The NGAA equilibrium constants for C, through C, were used for the C,; through C, fractions since they were separated on the bases of normal paraffin boiling points. The correlation of Hoffman, Crump and Hocott5 as used to estimate the equilibrium constant for the C fraction. The NGAA eauilibrium-ratio charts are based primarily on paraffin systems and have to be corrected for the presence of naphthenes and aromatics. The correlations in the literature proved too unsatisfactory for determining these corrections. EXperimental data, the saturation pressure, is used with the correlation of Soloman2 to make this adjustment. The correction factors of Soloman were cross-plotted so that the factors for ethane and heavier components were made a function of the factor for methane. a2 = 0.7927 at + 0.1646 .........(1) where a, = correction coefficient for for methane NGAA equilibrium ratio, and a2t = correction coefficient for ethane and heavier NGAA equilibrium ratios. This equation and the equation for the bubble point are solved simultaneously for the correction coefficients. The bubble-point equation is anKnXn = 1.0 . . . . (2) The equilibrium constant for the saturation pressure at reservoir temperature is used. This procedure not only corrects for the relative volatility between components, but also assures that the results will be directly related to the experimental saturation pressure. METHANE DENSITY After determining a set of equilibrium ratios, the apparent density of condensed methane at 60°F and 14.7 psia was estimated. This was found to be necessary because the correlations of Standing3 ere found to be unsatisfactory. The law of additive volumes was employed to make this calculation.

By Kenneth A. Moon

Kenneth A. Moon (U.S. Army Materials Research Agency)—The authors are to be congratulated for a very interesting and valuable paper. Their discussion of the structural implications of the results shown in their Fig. 5, however, requires a small correction. The model of Speiser and Spretnak with 0 = 1 and z' = 2 is perfectly reasonable for the Ti-O a phase, but Eq. [3] is valid only for solutions sufficiently dilute that the number of empty sites excluded by more than one filled site is negligible. The composition at which intrinsic saturation occurs therefore cannot be deduced from Eq. [3], but but must be decided by consideration of the structural details of the phase in question. In this case, intrinsic saturation is expected not at the composition Ti3O but at Ti2O, because Ti2O has the anti-Cd structurel4 for which each filled octahedral site has two nearby empty sites, one in the hexagonal plane immediately above it, and one in the similar plane below it. The other two models, with ?=1/3 and 1/2, imply a distinction between octahedral sites in pure titanium which is not easy to justify. The problem of extending Speiser's and Spretnak's treatment in a general way to more concentrated solutions will be the subject of a forthcoming publication by the writer. M. T. Hepworth and R. Schuhmann, Jr. (authors' reply)—The authors wish to thank Dr. Moon for calling to their attention the paper by Holmberg which presents the results of X-ray studies of Ti-O solutions ranging from 0 to 33 at. pct 0 and quenched from various annealing temperatures between 400" and 1800°C. Within these ranges, Holmberg found three types of phases: 1) At high oxygen contents (above 25 at. pct) and low annealing temperatures, he found the anti-Cd(OH)2 structure referred to by Dr. Moon. In this structure each titanium atom is in contact with 3 oxygens and each oxygen is in contact with 6 titaniums, the "available" oxygen sites corresponding to every other layer of octahedral sites in the titanium matrix. The limiting composition is Ti2O. However, this anti-Cd(OH)2 structure was not observed for samples containing 25 at. pct 0 or less. 2) For the specimen containing 25 at. pct 0 annealed at 400°C an ordered Ti3O structure was observed. This structure is related to the anti-Cd(OH)2 structure but differs from it by providing only two oxygens adjacent to each titanium atom and thus is consistent with the model represented by Eq. [5] in our paper, with 6 = 1/3, z' = 0. 3) For dilute solutions and for more concentrated solutions annealed at higher temperatures, the structure corresponds to that of the metal with random distribution of oxygens among all the octahedral sites. Thus, it is interesting to observe that the thermo-dynamic indications of ordering in the vicinity of Ti3O can now be supported qualitatively at least by Holmberg's X-ray evidence of the existence of an ordered phase of the composition Ti3O. That is, for solutions with oxygen contents close to that of Ti3O, both the thermodynamic data and the X-ray data are more consistent with models based on the ordered structure of Ti3O than they are with the model which Dr. Moon suggests corresponding to "intrinsic saturation" at Ti2O.

Jan 1, 1963

By Frank Woolley, John F. Elliott

The high-temperatzrre solulion calorimeter has been modified and an extension dynamic analysis of i/s transient behavior has provided an improved basis for interpretation of the experimental data. The partial molar heats of mixing, Him, of aluminum, copper, and silicon in the corresponding binary liquid-iron alloys haz,e been measured directly at 1600°C. The resulls in kcal per g-alom are: THE high-temperature1,2 solution calorimeter was planned and designed to obtain directly the partial molar heat of solution of solute elements in a variety of liquid metals that might serve as solvents. Results obtained in the temperature range of 1000° to 1200°C were described in the two earlier publications. However, a long-term goal in the program has been to obtain measurements at 1600°C of the heats of solution of elements in liquid iron. Hence, subsequent to the work last reported,2 and based on the experience of the first two studies, the calorimeter system has been modified and operated at 1600°C to obtain measurements on the Fe-Si, Fe-A1, and Fe-Cu systems. This paper reports the results of the work. THE MODIFIED SYSTEM It was clear from the earlier results that the most precise measurements can be obtained with the high-temperature solution calorimeter when the solution time is less than approximately 30 sec. This can be achieved only when the bath temperature, Tb, is above the melting (liquidus) temperature of the solute material being dropped. A second point of importance is that the refractories used earlier liberated considerable water so that, although the oxygen potential of the atmosphere in the system was satisfactory for work with nickel and copper, it was too high for work with iron, silicon, and so forth. Third, for work at 1550" to 1650°C, an improved temperature-sensing unit is needed. The modified calorimeter in its latest form is shown schematically in Fig. 1. The refractory brick and the Kanthal-Super heating elements which formed the furnace for heating the solute addition have been replaced by a smaller resistance-heated tube furnace which is insulated with bubble-grain alumina. A more elaborate gas purification system was installed to maintain a satisfactorily low oxygen potential in the atmosphere of the calorinieter chamber and of the solute addition furnace. As was the case in the earlier work, at the beginning of a run the calorimeter chamber is evacuated and then filled with purified argon so that a total pressure slightly in excess of 1 atm is maintained during the run. When either of the furnaces within the enclosure attains a red heat, 6 pct H2 is added to the atmosphere. Throughout the run, gas from the calorimeter is circulated through a de-oxidation system at the rate of approximately 5 standard liters per min; the changeover time for the gas within the calorimeter enclosure is approximately 1 hr. The essential stages of the deoxidation system are: a copper furnace at 600°C, a drying tube of anhydrite, and a titanium furnace at 800°C. The oxygen potential of the gas stream in the purification system can be monitored at several points by a stabilized zirconia oxygen cell. This cell is invaluable in detecting the development of leaks in the container vessel and the gas circulating system. The installation of the solute-addition furnace allowed either of two types of temperature-sensing units to be mounted on a water-cooled probe. The first was a small optical device using a silicon diode that was

Jan 1, 1968

By W. A. Backofen, M. L. Ebner

SINCE the early work of Gough with Hanson and Wright,l-3 the study of fatigue has been characterized by experiments on single crystals only in recent times.9-10 Now, increasing attention is given to this aspect of fatigue research for the insight that it may provide into details of mechanism. The investigations have concentrated to a large extent on the development of deformation markings on fatigued crystals, and have shown the cracks to originate in slip bands possibly preceded or accompanied by slip-band extrusions. Experiments of special interest to the present work were conducted by paterson5 on copper crystals and involved both metallographic examination and measurement of change in flow stress. Crystals were cycled in alternating tens ion-compress ion with a constant plastic shear-strain amplitude of approximately 0.8 pct, and were particularly revealing for their demonstration of hardening with accumulated strain similar to that in unidirectional straining, through an easy-glide stage I followed by a stage II of rapid hardening; deformation was not continued beyond 40 cycles, however, so that the eventual course of the hardening curve could not be decided. For the conditions used by Paterson, surface slip markings were similar to those observed in unidirectional straining, but there were no X-ray asterisms and no deformation bands on the surface. In current thinking about the nature of fracture in fatigue, two views relative to mechanism are generally acknowledged, with the reservation that both could apply simultaneously in some measure. As one possibility, fracturing across a slip plane is regarded as a result of loss of cohesion from the creation of many point defects by dislocation movement under the cyclic loading.'' On the other hand, fracture has also been taken to follow as a consequence only of the geometry of slip at a free surface, consisting of offsets and crevices which eventually become fatigue cracks.12, l3 The work of McCammon and Rosenbergl4 showing fatigue in polycrystals at 4.2oK makes clear that any long-range diffusion of point defects is unnecessary, yet studies such as those of Forsyth and stubington15 show that accelerated diffusion may be a characteristic of deformation under fatigue loading. Interest in obtaining data of possible use for resolving such questions led to the experiments described below. Copper crystals were conveniently loaded in alternating four-point bending at constant deflection, a test condition shown to approximate a constant plastic strain amplitude for a wide range of axial orientations. The method of testing was not readily adapted to extensive study of temperature effects, but an investigation of the geometry of crack formation could simply be made by orienting,the slip direction at different angles to the surface. EXPERIMENTAL PROCEDURES Single crystals were grown by a modified Bridgman method in a stationary gradient furnace under an atmosphere of purified dry nitrogen. Purity of as-grown crystals was 99.999 pct as determined by spectrographic analysis plus vacuum fusion and gravimetric analyses for oxygen and sulfur, respectively. Crystals were of reasonable perfection as evidenced by a critical resolved shear stress at 10 deg from (110) of 60 g per sq mm and half-width of a (400) X-ray diffraction line from one crystal of

Jan 1, 1960

By G. J. W. Kor, F. D. Richardson

The sulfide capacities a1 1500°C of slags in the systern CaO + CaF, +Al2O3 have been measured by bringing samples into equilibrium with gas mixtures made from CO + CO2 + SO, + N2. The capacities are negligzble both JOY CaF, and CaF, + Al2O3 melts but when lime is present even at 20 wt pct capacilies as high as 30 x lom3 can be obtained. The results have yielded information concerning the liquidus at 1500°C and fluoride-oxide melts in general. The slags used in electroslag refining contain substantial amounts of calcium fluoride. Robinson and Grainger' report that good results can be obtained by using slags of the approximate composition 70 wt pct CaF2 + 30 pct Al2O3. It has also been reported2 that a mixture of 50 pct CaF2 + 30 pct A12O3 + 20 pct CaO makes a good slag for general use. In view of the fact that very low sulfur contents are claimed for ingots produced by the electroslag process. studies have been made of the sulfide capacities [c, = wt pct S (PO2/Ps2)1/2 at 1500°C. of slags consisting of pure calcium fluoride, and of its mixtures with lime and/or alumina. These studies have also provided information on the phase diagrams. The slags were brought into equilibrium with gas mixtures prepared from NZ + CO + CO2 + SO2. Because CaFz is volatile and also easily hydrolyzed. measurements were made of its loss in weight in various flowing gas mixtures. EXPERIMENTAL Procedure. The apparatus and procedure were the same as described previously. Both platinum and iridium crucibles were used (height and inner diameter about 1 cm), but those made from iridium were stronger and able to withstand a greater number of experiments. In each experiment two crucibles were set in an alumina support and 1 g of slag mixture was divided between them. The materials from each crucible were analyzed separately after being brought to equilibrium with the gas, and then quenched in the water-cooled end of the reaction tube. Materials. Alumina and lime were prepared as de-scribed previously.4 Calcium fluoride was obtained by igniting Analar calcium fluoride in a platinum boat at about 800°C in a stream of pure dry nitrogen: the product was cooled in a desiccator. The slags were produced from mixtures of the powdered constituents, these being melted together in the course of each equilibrium experiment. The sulfur analyses and the X-ray diffraction meas- urements on the solidified slags were made as described previously.4 From the latter it appears that the CaF2 contained less than 0.5 mol pct CaO. RESULTS Values of (ps2/po2) for the Gas Mixtures. The re-sults have been represented in terms of (ps, /Po,)"? for the various gas mixtures used. The va1;es of this function at 1500°C are listed in Table I: they were calculated from the data cited previously for calculations at 1350°C 4 Weight Losses with CaF, and CaF, + CaO. The re-sults of the weight loss measurements* at 1500°C for

Jan 1, 1970

By T. J. Koppenaal, M. E. Fine

A yield point effect attributed to short-range ordevi?g (SRO) occurs in Cu base Al. At at 296°K varies with heat treatment, decreasing as the annealing ternperature is raised .from 433Oto 598°K. Davies aid Cahn' observed a corresponding decrease in SRO. (523 °K anneal, measured at 77°K) is approximateZy proportional to the variations of A7 with strain rate and testing temperature are also Consistent with the idea that is associated with SRO. A preliminary investigation of the tensile properties of a Cu-Al single crystals showed the presence of a rather strong yield-point effect (drop in flow stress after initial yielding). The object of this research was to investigate its origin and behavior. a Cu-Al alloys are particularly interesting because diffuse X-ray scattering measurements by Davies and Cahn,' Houska and Averbach,' and Borie established the presence of short-range order. The degree of local order may be changed with heat treatment.' cottrel14 suggested that the presence of local order might result in a yield-point effect, and thus the possibility exists here for experimentally ascertaining the importance of short-range order with respect to yield points in these alloys. Since a 12 pct difference exists between the atomic sizes, elastic or Cottrell locking5 must also be considered. Further, Howie and swanne have shown that the stacking fault energy of copper is reduced by aluminum additions. The width of extended dislocations should thereby increase. hus the conditions appear attractive for Suzuki locking.' Finally, the possibility of stress-induced order at dislocations, schoeck locking,' must also be examined, EXPERIMENTAL PROCEDURE Alloys up to 14 at. pct Al were prepared by induction melting high-purity (99.999 pct) Cu and (99.996 pct) Al in a graphite boat under a dynamic vacuum of 5 X 10o mm of Hg. After homogenizing the ingots at 900°C for at least 24 hr under vacuum, they were rolled with intermediate anneals to strips 1.55 mm thick. Single crystals 10 in. long were grown by lowering strips, contained in a split graphite mold sealed in fused quartz at 5 X lo-' mm of Hg, through a single coil induction heater at a constant rate of 1/2 in. per hr. Tensile specimens 1.25 in. long were cut from the single crystal strips and reduced cross sections about 0.7 in. long and 3.0 to 3.5 mm2 in area were introduced by filing and abrading.8 To remove the worked portion about 10 pct of the cross-sectional area was removed by etching. Back-reflection Laue photographs of a filed and etched specimen were taken before and after annealing at 900°c for 24 hr. Small, well defined Laue spots were obtained with no visual difference in the two photographs. Further, specimens with and without the reduced sections began yielding at about the same stress. Hence, for our purposes, filing and abrading did not affect the structure of the specimens. Each single crystal specimen was annealed at 900° c in vacuum for at least 24 hr and furnace cooled; while cooling through the range of 250o to 200°c, the rate was about 55°C per hr. Orientations were determined by the usual back-reflection Laue

Jan 1, 1962

By W. B. Hickman, J. J. Pickell, B. F. Swanson

Many physical properties of the porous media-immiscible liquid system are dependent upon the distribution of fluids within the pores; this in turn, is primarily a function of pore structure, liquid-liquiri interfacial tcnsion and liquid-solid wetting conditions. The cnpillary pressure hysteresis process provides a means of investigating the influence of pore structure upon fluid distribution for consistent sur/acc conditions. Invcstigntiot2s indicate that residual non-wetting-phase saturations /ollozuir,g the imbibition process (i.e.,wetting phase displacing nor2-wctting phase) are dependent upon both pore structure and initial non-raetting phase saturation and suggest that residual fluid is distributed as Discontinuous ,globules, one to a few pore sizes in dimension, thrnugh the entire range 01 pore sizes originally occupied. It clppears that air-mercury capillary pressure dala adequntely rellect the distribution of fluiris in a water-oil system when strong wetting condition preliczil. An oil-air counter-current imbibition technique has also been found to provide a rapid rneans of obtaining residual-initial saturation data. In a majority of cnses, rcsidual saturations detf-rniinecl from the oil-air or air-mercury process reasonably approximate residual oil saturation following water drive of a strongly water-wet medium. INTRODUCTION A reliable estimate of recoverable reserves depends not only on the amount of original oil-in-place but also on pore geometry and distribution of fluids within the pores. A critical parameter determining the recovery from a reservoir under waterflood, for example, is the amount and distribution of residual oil within the various rock types present. The purpose of this paper is to investigate the mechanism of capillary trapping and assess its importance in laboratory measureqents of residual oil saturation. The degree of wettability of a reservoir rock is recognized as an important factor in waterflood or imbibition experiments. In this paper, however, only the water-wet case has been considered. Considerable experimental evidence1 suggests that for water-wet rocks, capillary forces predominate in tile distribution of fluids and that viscous forces in the range normallv of interest in the reservoir have a minimum influence on residual oil saturation. It follows that if the ultimate recovery is controlled by pore geometry, a unique residual non-wetting phase saturation should exist for a given set of initial conditions. Two laboratory procedures.found to be extremely useful in the study of pore structure and degree of fluid interconnection at various saturations are decribed. Although air-nercury capillary injection curves have been used2 previously to characterize the drainage case, the withdrawal or imbibition case can provide valuable supplementary data. The air-mercury process, however, has several disadvantages; it is difficult to run in a sufficiently accurate manner, mercury does not always act as a strongly non-wetting liquid and in the air-mercury process the sample is rendered unsuitable for future analyses. An alternative process is described in which air is the non-wetting phase and naptha, hentane, octane or toluene is the wetting phase. INTERFACIAL TENSION AND CAPILLARY PRESSURE Interfacial tension between immiscible fluids is due to the difference in attraction of like molecules as compared with their attraction to molecules of the neighbouring fluid. This net attraction results in a tension at the interface. To extend the interface; thus, interfacial tension s can also be thought of as free surface energy. Interfacial tension is normally expressed as dynes/cm, and interfacial energy is measured in ergs/cm2 hence, both have dimensions ml A 2 and are numerically equal.

Jan 1, 1967

By Nicholas J. Grant, Hanna Ibach, Bill C. Giessen

The system Ta-Rh was investigated over the entire comnposition range using metallogvaphic and X-ray techniques as well as thermal analysis. Terminal solubility limits, solidus temperatures, and the crystal structures of two new intermediate phases were determined. There are five intermediate phases: o, tetragonal, isostructural with o(Fe-Cr); a1, orthorhomnbic : a2, orthorhombic, isostructural with CozSi; 0 3, a high -temperature phase of unknozun structure; and a TaRh3, cubic, AuCu3 structure. a, aL, a,, and a melt peritectically; and a TaRh, has a maximum melting point. Five peritectic and one eutectic reactions occur. THE Ta-Rh phase diagram has not been fully treated in the literature; however, two inter metallic phases have been described.&apos;-&apos; This study attempts to work out the diagram covering the details of phase boundaries as well as the crystallography of the intermediate phases. EXPERIMENTAL METHODS Starting materials were tantalum powder of 99.8 pct purity, supplied by National Research Corp., Cambridge, Mass., and rhodium powder of 99.9 pct purity, supplied by Bishop Co., Malvern, Pa. Analyses as given by the manufacturers are presented in Table I. In addition to the spectroscopic analysis, an oxygen analysis has been made of the tantalum powder. After preliminary trials, the standard procedure employed in making the alloys was as follows (see Ref. 4 for further details). The powders were weighed, mixed manually, compacted under 16,000 psi, and arc-melted at not more than 500 amp under thoroughly titanium gettered welding-grade argon of 400 mm Hg pressure. The gettering process was repeated after each melt. It had been shown previously5 that under these conditions no oxygen pick-up exceeding 0.001 pct in a hafnium button could be detected. The buttons, ranging from 5 to 10 g in weight, were inverted or, if possible, crushed and remelted three times. Melting presented no difficulty, except for tantalum-rich al- loys, which showed considerable spashing during melting. The average weight loss of 1 wt pct rose to 2.5 wt pct in these cases. Subsequent melting, however, resulted in losses of less than 0.1 wt pct. The melts obtained frequently showed small in-homogeneities, mostly in the tantalum-rich part of the system below 25 at. pct Rh. This was not due to insufficient blending of the elements, but to crystallization taking place from the cooled bottom. This condition was not improved by further re-melting; therefore the following precautions were taken. Cross sections of as-cast buttons were made. For the investigation only buttons were used where these inhomogeneities did not exceed 1 at. pct (estimated from the amounts of haSeS resent). In addition, only the center portions of such buttdns were utilized to minimize errors. Smaller buttons showed smaller concentration gradients and were used as a check. Finally, all alloys were homogenized to eliminate coring (see below). After this, the error in alloy composition due to inhomogeneity was cl at. pct. In order to confirm the concentrations of the alloys and to provide an impurity check, wet-chemical analyses and oxygen-fusion analyses of four key alloys were carried out. The results, together with the concentrations as calculated with the weight balance method, are presented in Table 11. It was found that for three alloys the agreement is very good (< 0.2

Jan 1, 1964

By A. E. Worthington, R. F. Meldau

An analog computer study was made of the reduction of the magnitude of the SP by formation geometry and resistivity effects. Practical field .situations were studied. The analog data were converted to the form of departure charts. These charts may he used to determine the reduction in the SP due to the above eflects pith good precision Quantitative interpretation of the SP log in terms of formation water resistivity is presently based on the premise that the observed SP is equal to the electrochemical potential developed across a shale between the mud filtrate and the formation water. This procedure inherently assumes that, first, no electro kinetic (streaming) potential is present, and, second, that the SP is not reduced by resistivity or geometry effects in the formation. When, however, such a reduction of the observed SP does occur, one may write, SP = b,E, b, E, (1) where SP is the observed self-potential opposite the center of the bed under consideration. In this case, E, is the electrochemical potential, E, is the electrokinetic potential, b, is the electrochemical reduction factor, and h, is the electrokinetic reduction factor. The first assumption above is equivalent to assuming E, = O in Eq. 1 and the second assumption is equivalent to h, = b, = 1. Examination of electric logs shows that for many formations of interest the observed SP is reduced below its maximum value. The object of this work is to aid quantitative SP interpretation in at least some of these situations by obtaining values for b, and b, in Eq. 1 as functions of realistic combinations of bed thickness, depth of invasion, and formation resistivity. The only previously published work in this field known to the authors is by H. G. Doll&apos; in 1948. He evaluated b, under conditions permitting exact analytical solution. His work clearly established the importance and qualitative nature of formation geometry and resistivity effects upon the SP, but the necessity of obtaining analytical solutions restricted his study to situations of limited practical interest. In order to extend such studies to practical combinations of formation parameters which do not lend themselves to feasible analytical solutions, the results reported in this paper were obtained by use of a special analog computer. THE ANALOG MODEL The analog model used for this study was the Guyed Analog Computer which originally was designed and built for resistivity log departure curve studies. It consists of a two-dimensional mesh of resistors, with the vertical mesh corresponding linearly to vertical distance along the borehole, and the horizontal mesh corresponding to radial distance from the borehole axis. By proper choice of horizontal resistor values, a three-dimensional, axially symmetric, borehole-formation problem can be modeled with this two-dimensional array. These and other details of the model are contained in a paper by H. Guyod&apos;. The geometry used for the SP studies with the analog is depicted in Fig. 1. This configuration has a horizontal plane of symmetry, and, hence, the model, and the following discussion, need only to be concerned with one quadrant such as shown in Fig. 2. A further simplification arises by considering that both the natural potential sources and those used in the model have fixed internal impedance. Therefore, the current flows produced by these sources can be separated and studied independently ( i.e., the superposition theorem can be applied). SP = SP, i SP, = h,E, + b,E, ,(7)

By D. F. Kelsall

The hydraulic cyclone, in simple or modified form, is finding increasing application in metallurgical processing. In this article, the author considers several aspects of conventional applications, less conventional applications and some potential uses of modified cyclones. Information concerning the mechanism of separation within a cyclone and the effect of the major variables is summarized. During the past twenty years, and especially in the last decade, hydraulic cyclones have found increasing application in metallurgical processing as classifiers and, under special circumstances, as thickeners. To a more limited extent cyclones have been used to extend heavy, or dense, medium separation into the finer size ranges, and several attempts have been made to separate dispersions of immiscible liquids with a view to use in the field of liquid-liquid extraction. A large proportion of published work reports incomplete data, applicable only to particular systems. The more useful papers, covering data of relatively wide significance, have been reviewed recently in considerable detail1,2 and no attempt will be made to cover the same material in the present paper. However, before considering several aspects of conventional application, less conventional applications and some potential uses of modified cyclones, it is considered pertinent to summarize information relating to the mechanism of separation within a cyclone and the effect of the major variables. LIQUID FLOW PATTERNS At any point within a simple cyclone the liquid velocity may be resolved into three components, i.e., the tangential or swirling velocity (v), the vertical velocity (w), and the radial velocity (u). The relative values of these components at selected positions within a typical cyclone have been established for water. 3 The extent to which similar flow patterns exist in systems of considerably higher viscosity, or apparent viscosity, operating under conditions of reasonable pressure drop, is not known with precision, but indirect evidence indicates that up to approximately five centipoise there is no marked change. Beneath the bottom of the vortex finder, envelopes of constant tangential velocity are cylinders coaxial with the cyclone, and, at any horizontal level, starting from near the conical wall, this component of velocity increases with decrease in radius (r) according to the relationship vrn = constant (where 0 < n < 1) This holds to regions near the center of the cyclone where v reaches a maximum value at a radius somewhat smaller than that of the inside wall of the vortex finder. At this point, the centrifugal acceleration, v2/r reaches a maximum value. As the radius is further decreased the tangential velocity decreases so that v = r. Above the bottom of the vortex finder there is a tendency for the first relationship to persist to near the outside wall of the vortex finder, until v reaches a maximum and then decreases rapidly as the wall is approached. The two most significant features of the vertical velocity distribution are an approximately conical Table I. List of Symbols v = liquid tangential velocity at any point in the cyclone w = liquid vertical velocity at any point in the cyclone u = liquid radial velocity at any point in the cyclone r = radius from cyclone axis to any point ? = half angle of conical portion of the cyclone ?= fluid viscosity d = particle diameter s = liquid specific gravity p = particle specific gravity d50 = the particle diameter which distributes 5090 to overflow, 50% to underflow e = overflow diameter, in. b = feed diameter, in. G = gpm of feed slurry

Jan 1, 1963

By John P. Huger

me phase diagram for the system Ag-Si has been established by thermal analysis. The diagram is a simple eutectic type with a eutectic at 3.0 pct Si and 840°C. From the liquidus curve and with the aid of regular solution theory, the thermodynamic properties of the liquid Ag-Si system at 1420 °C have been determined. Silicon exhibits positive deviations from Raoultain behavior at all compositions, while silver exhibits both positive and negative deviations. MEASUREMENTS of silicon activities in liquid iron alloys by means of distribution studies between the immiscible liquids silver and iron have been reported by Chipman, Fulton, Gokcen, and caskey.&apos; The applicability of this technique is dependent, however, on the accuracy of the silicon activity values in the Ag-Si alloys, particularly in the dilute silicon region. Darken and Gurry2 have shown that log ?si/(1-xSi)2 is approximately linear with composition, but uncertainty exists in the extrapolation to dilute solutions. Their calculations are based on the old Ag-Si phase diagram of Arrivaut3 and any variation in the position of the liquidus curves will strongly influence the extrapolation. The purpose of this study is to redetermine the Ag-Si phase diagram and calculate the associated thermodynamic properties. EXPERIMENTAL The Ag-Si phase diagram was determined by thermal analysis of liquid alloys. The alloys were contained in a 35 mm alumina crucible under a protective stream of purified argon. The crucible was placed inside a 64 mm alumina tube fitted with a gas-tight, water-cooled, copper head. The tube and assembly were heated in a manually controlled globar furnace. The temperature was measured with a Pt, Pt + 10 pct Rh thermocouple in a high-temperature porcelain protection tube. The thermocouple calibration4 was checked against the melting point of pure silver at the start and during the course of the experiments, and against both gold and silver at the completion of the experiments. The alloys were prepared from granular silver analyzing 99.95 pct Ag and powdered silicon analyzing 99.88 pct Si and 0.026 pct Fe. Approximately 150 g of alloy were used for each run. The composition of the alloy was determined by withdrawing samples of the liquid alloy with a vycor tube-aspirator bulb device. Analysis of solidified samples agreed, for alloys containing less than 23 pct Si, within ±0.3 pct Si of the calculated composition. Duplicate samples showed a variance within 50.05 pct Si of the mean analysis. The alloy was heated to 100&apos; to 20pC above the estimated liquidus temperature and then the furnace was adjusted to give an average cooling rate of 2" to 7°C per min. A cooling curve was obtained by taking potentiometer readings at 15-sec intervals. Several analyses were made by recording the thermocouple output on a high-speed, Stip-chart recorder, with the exception of run NO. 11, a minimum of two thermal analyses were made for each alloy and the cooling curves then obtained duplicated the liquidus and eutectic temperatures to about 1°C. RESULTS The results of the thermal analysis are given in Table 1, and are represented as the Ag-Si phase dlagram, Fig. 1. The eutectic composition was found

Jan 1, 1963