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By L. D. Lash, J. R. Ross

Discovery of scandium in the Vitro solvent extraction plant for uranium led to commercial recovery of the byproduct. Micro amounts of scandium were extracted with uranium by dodecyl phosphoric acid, but failed to follow ura-niuminto the hydrochloric acid strip solution and were eventually concentrated in the organic extractant. A fluoride strip system was developed to recover scandium from the solvent in concentrated form. High purity scandium oxide was then prepared in multi-pound lots by chemical separation techniques. The plant recovery operation, final product purification, and analytical procedures are described. Scandium is a pseudo-rare earth which is truly rare and expensive. It has special properties which may make it desirable even at the present price of $2750 per lb. Recently the price was lowered from $5000 per Ib which had prevailed since 1952, and it is anticipated that usage will be stimulated because of the lowered price. This metallic element is distributed widely in trace amounts in the rocks of the earth's crust. In addition to micro-amounts found in most uranium ores, concentrations of 50 to 100 ppm have been found in Colorado ferberite ore, lateritic nickel ore, heavy sandstone from Utah, Wyoming, and New Mexico, and various zircon sands and monazites from the western part of the U. S. Scandium has been found as an essential constituent of very few minerals, the most important being thortveitite, a scandium silicate. At the present time, this mineral commands a price more than twice that of gold. Chemically, scandium is in group 3A of the periodic table. It is closely associated with yttrium and the rare earths which it strongly resembles in its reactions. It has a valence of three and will form an insoluble hydroxide, fluoride, or oxalate under proper conditions, similar to the rare earths. Eight years before its discovery, scandium was predicted by Mendeleef who ascribed his eka-boron with properties nearly identical to the actual properties of scandium. Its position as the element with Atomic No. 21 and Atomic Weight 44.96 places it between calcium and titanium in Period 4 of the chart. The successful commercial application of scandium must depend on unique properties to justify use of this high cost substance. Greater consumption would allow additional price reductions, but scan- dium will remain a relatively high-priced commodity because of its inherent scarcity. Research reportedly has been oriented toward use of scandium as an agent to achieve high-temperature, low-density alloys with magnesium and tantalum.' Also, the U.S. Air Force sponsored a project for production of research amounts of pure scandium metal.' The oxide has been used experimentally in electronics, ceramics, and metallurgy. The various aspects of scandium are well covered in recent publications.s-5 CONCENTRATE RECOVERY Small amounts of scandium exist in uranium ores and are dissolved during an acid leach yielding up to 0.001 gpl Sc2O9. When Vitro converted their uranium plant from phosphate precipitation to solvent extraction: scandium was found to follow the uranium into the dodecyl phosphoric acid solvent (DDPA). However, scandium did not strip with uranium from the DDPA in hydrochloric acid, but remained in the solvent. Therefore, a concentration of scandium built up in the organic phase. Residues from the solvent were spectrographed by the U.S. Bureau of Mines and found to contain scandium. As a result of this discovery, provisions were made in the plant for recovery of scandium-bearing concentrates. Solvent extraction of uranium was added to a conventional acid leach process in a typical installation? The ore was crushed and ground, and then leached with dilute sulfuric acid. Addition of an oxidant such as sodium chlorate insured conversion of uranium minerals to a soluble form. At this point, the slurry was chemically reduced by a sulfide, such as sodium hydrosulfide, to remove substances such as ferric iron and molybdenum which were partially extracted by the solvent. The solids-liquid separation was accomplished by a four-stage counter cur rent decantation (CCD) thickener circuit. The uranium was extracted from pregnant liquor with 0.1M DDPA in kerosene and stripped with ION

Jan 1, 1961

By L. D. Mullins, W. R. Bartlett, R. H. Barham, W. L. Wahl

This paper describes an electrical model and its applicution to the analysis of four reservoirs in Saudi Arabia. The model has 2,501 mesh points and represents 35,000 sq miles of the Arab-D member. Details of modeling such as mesh size, control problems and standards of performance in matching reservoir history are discussed. The particular performance match achieved for the Arab-D rnember is presented. Details such as permeability barriers, aquifer depletion and iwerference between oil fields are given. The performance match realized in the Abqaiq pool is presented in detail. INTRODUCTION The resistor-capacitor network and associated control equipment described in this paper comprise an electrical analog of a reservoir system. Similar equipment has been used to study the transient response of reservoirs for many years. The unique feature of the model and application to be described is the extremely large size of the model and reservoir system, and the detail observed in simulating the reservoir with the model. The Arabian American Oil Co. first became interested in analog computers for simulation of oil reservoirs in 1949. Since that time, several models have been developed, each more elaborate and refined so that the reservoir system might be more closely simulated. The current model is the latest in a series designed, built and operated by the Field Research Laboratory of Socony Mobil Oil Co. in collaboration with Aramco. It has been and continues to be used to study the regional performance of the Arab-D member limestone reservoir. The Arab-D member is one of the Middle East's most prolific producing horizons.. THE MODEL The theory of simulating a reservoir system with an electrical system has been presented in the literature.1-5 Therefore, this paper will not discuss the theoretical aspect of the problem except to point out the correspondence between the fluid system and electrical system, as shown in Table 1. In general, the complete model is made up of input devices, output devices, central control and a resistance-capacitance (RC) network. At times, the RC network alone is referred to as the "model". However, it should be evident from the text which meaning is attached to the word "model". A discussion of the equipment follows. THE RESISTANCE-CAPACITANCE NETWORK The RC network consists of 2,501 capacitance decades interconnected through 4,900 resistance decades. The components are arranged to form a rectangular network of 2,501 mesh points in a 41- X 61-mesh array. Imposing the mesh grid system on the continuous reservoir system divides the reservoir into discrete areal segments. These discrete segments may be of various sizes. More precisely, the mesh size need not be uniform throughout the model. The RC network is fabricated in two sections which are connected at the top. An inside view of the "tunnel" formed by the two sections is shown in Fig. 1. The height and width of the tunnel are shown in the figure. Numerals appear along the bottom and along the back opening of the tunnel. These numbers denote the x and y co-ordinate positions of mesh points. Fig. 2 presents a rear view of one-half the model. The length dimensions of the model, as well as a rear view of the capacitor decades, are shown in this figure. The control dials used in adjusting the resistance and capacitance values on the model can be seen in the enlarged portion of the model shown in Fig. 3. The electrical capacity at any mesh point can range from 0 to 1.0 microfarads set to the nearest tenth of a microfarad. The electric resistance connecting any two mesh points can range from 0 to 9,990,000 ohms set to the nearest 1,000 ohms. External capacitors may be added to any or all mesh points if the need arises. The values of electrical resistance and capacitance are adjusted manually by manipulating the two types of decade units. INPUT EQUIPMENT A considerable quantity of equipment is used to control the input to the RC network. These input devices are

By T. E. Leontis

Data are presented in this paper to show that addition of zirconium to sand-cast Mg-Th alloys effects a marked decrease in the grain size of these alloys which is accompanied by a significant increase in the mechanical properties over the entire range of thorium content investigated. The beneficial effect of zirconium on the strength properties is maintained at elevated temperatures up to 700°F. In addition the alloys exhibit exceptionally high creep resistance at temperatures up to 600°F. Zirconium does not greatly improve the strength or creep characteristics of extruded Mg-'Th alloys. Cerium is not a desirable addition to Mg-Th-Zr alloys. IN a previous paper,' it was shown that addition of thorium to magnesium imparts exceptionally high resistance to creep at elevated temperatures both in the sand-cast and in the extruded states. The large grain size of the sand-cast alloys, however, renders them of questionable value as engineering materials. Sauerwald² showed that the grain size can be reduced effectively by the addition of zirconium. Results of a detailed study of the properties of Mg-Th-Zr alloys over a wide range of thorium content are presented in this paper. In accordance with the preliminary findings of Sauerwald,² it is shown here that Mg-Th-Zr alloys possess the unusual combination of fine grain size and a high level of strength and creep resistance at elevated temperatures. Some information on the effect of cerium on the properties of Mg-Th-Zr alloys is presented also. Effect of Th on Solubility of Zr in Molten Mg Sand-cast test bars and 3 in. diam extrusion billets of Mg-Th-Zr and Mg-Th-Ce-Zr alloys* were pre- pared according to the procedures described in the previous paper.' The zirconium was added in the form of sponge metal as supplied by the Bureau of Mines.' The maximum amount of zirconium that usually can be introduced into magnesium at the customary alloying temperature of 1350° F is about 0.7 pct. The analyses in Table I clearly show that thorium in- creases the solubility of zirconium in liquid magnesium. The tabulated zirconium contents are designated as "acid soluble;" this serves to distinguish these values from the small amount of zirconium that is not dissolved when the alloy is subjected to the action of a dilute acid solution. The "acid-insoluble" zirconium is believed to be ineffective as an alloying ingredient. The acid-insoluble zirconium contents ranged between 0.03 and 0.16 pct in the present alloys, the tendency was toward higher values in alloys with higher thorium content. In contrast to the effect of thorium, cerium decreases the solubility of zirconium in magnesium. This is shown by the three Mg-Th-Ce-Zr alloyst in- cluded in Table I and stands in agreement with the observations of Nelson and Stricter".' on Mg-misch-metal-Zr alloys. Effect of Zr on Grain Size of Mg-Th Alloys The potent effect of zirconium as a grain refiner has been demonstrated for many types of magnesium alloys.3-8 Of greatest importance to date are Mg-Zn-Zr alloys5,6,8 and Mg-mischmetal-Zr alloys.3,4,7 Zirconium has also been found to exert a marked grain-refining action on Mg-Th alloys. All the Mg-Th-Zr alloys cast in the form of ½ in. diam test bars have an exceedingly fine grain size (Table I). Reference to the previous paper' will show that binary Mg-Th alloys containing up to 6 pct Th are almost completely columnar even in the M in. diam reduced section of a test bar, and that 10 to 50 pct Th alloys have an equiaxed grain structure of 0.03 to 0.08 in. The data in Table I also show that addition of cerium to Mg-Th-Zr alloys has no effect on the grain size. In addition to increasing the strength properties, the fine grain size of Mg-Th-Zr alloys

Jan 1, 1953

By W. M. Robertson

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

Jan 1, 1965

By P. G. Shewmon

Radioactive MgZA has been used to study the rate of self-diffusion in oriented single crystals of magnesium in the temperature range 468O to 635OC. The diffusion coefficients parallel and perpendicular to the c-axis are: Dl, = 1.0 exp (—32,200IRT) cm2 per sec and Dl = 1.5 exp (—32,500IR T) cm Qer sec. The ratio Dl/Dll was found to vary from 1.13 at 468 to 1.24 at 575 C. Assuming a vacancy mechanism, an explanation of this aniso-tropy of diffusion follows from a consideration of the difference in the saddle points for diffusion in and out of the basal plane. RECENT discovery of radioactive Mg2"'-' has made possible the study of self-diffusion in magnesium. The experimental procedure and the results of a study of diffusion in polycrystalline magnesium have been described in an earlier paper.V he present work is an application of the same techniques to the study of self-diffusion in oriented single crystals of magnesium. In the general diffusion problem the diffusion coefficient is a second order tensor relating the two vectors, the diffusion flux, and the concentration gradient. In a hexagonal lattice, such as magnesium, the complete determination of the diffusion coefficient D as a function of direction in the lattice requires a knowledge of D,, and D,, i.e., the diffusion coefficients parallel and perpendicular to the c-axis, respectively. It can be proven quite generally that in a hexagonal lattice D is independent of direction in the basal plane, and that out of the basal plane it varies with 0, the angle between the c-axis and the direction of diffusion, according to the equation D(B) = D,,cos2B + D,sin2B. [I] The proof of Eq. 1 depends only upon the symmetry elements of the hexagonal lattice and upon the transformation properties of a second order tensor." Therefore, Eq. 1 holds for any mechanism of diffusion and any c/a ratio. Experimental Procedure The experimental procedure used with polycrystalline specimens can be briefly outlined as follows. Radioactive Mg" was produced by bombarding a NaCl crystal with 350 mev protons and was chemically separated from the target as MgO. The Mg" was then vapor deposited on a specially cleaned magnesium specimen by heating the MgO on a tantalum ribbon in a vacuum. During the diffusion treatment, oxidation and vapor loss of the radioactive material were minimized by annealing the samples in pairs with the active faces in contact, each pair being inside a magnesium container, which was in turn surrounded by an argon atmosphere in a sealed Pyrex tube. The distance-activity profiles were obtained by measuring the activity of thin sections cut parallel to the original interface with a lathe. The only technique which was peculiar to this work was the preparation and orientation of the single crystal specimens. The single crystals used in this work were grown by E. C. Burke of the Dow Chemical Co., using a modified Bridgman method, in which the furnace and specimen were stationary while the temperature gradient moved.' In growing these crystals the starting material was distilled magnesium, the crucibles were machined from Acheson electrode graphite, and the furnace atmosphere was tank argon. The crystals were grown from sublimed magnesium with the following analysis: 0.0002 pct Al, 0.0017 pct Fe, 0.0009 pct Mn, 0.0001 pct Ni, 0.0006 pct Pb, and less than 0.01 pct Ca, 0.0001 pct Cu, 0.001 pct Si, 0.001 pct Sn, and 0.02 pct Zn. The two crystals used were roughly lh in. diam and eight in. long. The c-axis made angles of about 7" and 78", respectively, with the specimen axes. If the values of D obtained by the use of these two crystals are taken equal to D,, and D,, respectively, the error introduced by this assumption is less than 1 pct. This can be shown by combining Eq. 1, the identity sin% + cos'8 = 1, and the experimental fact that DJDn in magnesium was always less than 1.25.

Jan 1, 1957

By R. M. N. Pelloux

This study of aluminum-copper alloys had two aims: 1) To determine the effect of the amount and distribution of a second phase, CuAl2, on the creep-rupture strength, ductility, and fracture characteristics of the alloys. The work of Gemmell and grant' on single-phase aluminum-copper alloys provided a basis for the present study. 2) To attempt to provide a relation between the microstructure and strength of two-phase alloys deformed at comparatively high temperatures (greater than 0.45 T,). The creep behavior of the two-phase magnesium alloys Mg;Ce and Mg-A1, has been treated by Roberts. 9 In work reported by Sully and Hardy4 and by Underwood, Marsh, and Manning~ on A1-Cu two-phase alloys, and also in a portion of the work of Gemmell and grant,' aging took place during the creep tests. 'In the present work, overaged aluminum-copper alloys were subjected to creep deformation at two temperatures, 500 and 700OF. The overaging treatments to produce the precipitate dispersions were performed prior to the test, at temperatures which were the same as the ultimate respective test temperatures. Hence, the present study is concerned with the creep behavior of stable (in contrast to "underaged") two-phase A1-Cu alloys, i.e., alloys in which no depletion of the solid-solution matrix occurred during: creep. MATERIALS AND PROCEDURE A 2 and a 3 pct Cu alloy, supplied by Alcoa, were studied; Table I shows the compositions. The grain size of the specimens, 0.9 to 1.0 mm, was achieved by annealing the machined test bars for 2 hr at 1000°F, followed by furnace-cooling to 900°F, and homogenizing for 4 hr. Both compositions are in the single-phase condition at 900°F. Two types of overaged dispersions, termed "over-aged I" and "overaged 11" were prepared after the grain size and the homogenization anneals. The overaged I alloys were prepared by quenching to room temperature after homogenization, aging at either 500' or 700°F for 72 hr, and air-cooling to room temperature. The overaged I1 alloys were prepared by furnace-cooling after homogenization, to either 500' or 700°F, and holding at the necessary temperature for 72 hr. The times for furnace-cooling from 900°F to 700° and 500°F were, respectively, about 2 and 3.5 hr. The structures of the A1-2 pct Cu alloys are shown in Fig. 1 (overaged I) and in Fig. 2 (overaged 11). A comparison of Figs. 1 and 2 shows that in the overaged I alloys the precipitate particles along the grain boundaries are much more closely spaced and the grain boundaries are straighter than they are in the overaged I1 alloys. Further, the particle size and spacing in the grains are smaller than in the overaged I1 alloys. Microstructures of the A1-3 pct Cu alloys have not been shown; the structures of these alloys differed from those of the A1-2 pct Cu alloys only in that the distribution density of the particles was greater. The creep specimens had a gage section 1 in. long with a diameter of 0.155 to 0.195 in. Before testing, specimens were electropolished in a solution of 100 cc glacial acetic acid, and 30 cc of 60 pct perchloric acid, at 40' to 50°F, at 24 v. The specimens were kept refrigerated prior to testing to avoid precipitation at room temperature. Constant stress creep tests were conducted; the load was applied 75 min after heating of the specimens to test temperature had begun. EXPERIMENTAL RESULTS Creep-Rupture—Fig. 3 shows the log stress-log rupture life plotfor the overaged alloys studied, and also for the underaged A1-2 pct Cu alloy.' At 700°F, the stress-rupture life relationship is nearly independent of both the amount of precipitate (i.e., composition) and of the type of overaging treatment (i.e., precipitate dispersion). At 500°F it is apparent that the increase in rupture life that was ex-

Jan 1, 1960

By H. M. Otte, A. L. Esquivel

A new leasl-squares method is Presented for determining lattice parameters of hexagonal or tetragonul structures. The method is adapted for use on electronic computers and involves a reiterative procedure. The correction factor employed raries linearly with the lattice parameter, a (determined from the Brag, angle). In contrast, Cohen's method and recent modifications of it use a correction factor that varies incersely as the squure of the lattice paramneter, a. While the recent modifications attempt to improve the precision of the extrapolated lattice parameter, a, (or-cu). by stressing the importance of the weighting factor. the present approach emphasizes the need for choosing the correct extrapolation function. A comparison between the present method (the Linear method) and Cohen's method indicates that the Linear method may be more appropriale in certain cases. through a priori no critertion appears to he available for making a chorce between the methods. The size of hexagonal and tetragonal crystal lattices is determined by two parameters, a, and c,. Although in principle the two lattice parameters can be determined independently from reflections for which h - k = 0 and 1 = 0, respectively, in practice this may be inconvenient (because of the angular positions at which these reflections may occur) or not easily possible (because of low intensity). Furthermore, if a high precision or accuracy is required, the limited number of reflections of this type available, particularly in the high-angle region, is not sufficient for the necessary corrections (mainly due to absorption) to be determined with accuracy. Several methods1-7,11-13 have been proposed employing all reflections, to obtain the optimum values, a. and co, either by a trial and error procedure or a least-squares fit. Of the latter method, cohen's5 is the best known one since it provides explicit expressions for the optimum a. and c,. However, Cohen's method is only strictly valid if an extrapolation function is used that varies linearly with l/a2 or lie2 (see Section 3), a requirement that does not appear to be generally appreciated. On the other hand, all the better known and more widely used A recent trial and error method was proposed by Massalski and King8,7 who computed extensive auxiliary tables of axial ratios vs the functions A = [(4/3)(h2 + hk +k2) + l2+(a/c)2] and C = A(c/a)2 used in computing a and c values from the observed Bragg angles. These values of a and c were then plotted against a function which permitted linear extrapolation. As a criteria; for the "optimum" values, Massalski and King rely upon a visual fitting of the line through points representing reflections of low 1-index points to compute the extrapolated value of ao and high 1-index reflections to obtain CO. The successive computations and graphical plotting required to reach the "optimum" value are quite lengthy and tedious even on a desk calculator and no quantitative assurance is obtained of having in fact selected the optimum value.* If the method of Massalski and King is used on an electronic computer, then their published tables become redundant and a least-squares fit becomes a natural selection for the choice of optimum values. Such an approach will be called the Linear method. For work now in progress on the effect of certain physical variables on the lattice parameters of hexagonal crystals, it has become essential to determine the confidence limits of small changes in the lattice parameters. Since extrapolation functions that varied linearly with a and c actually also appeared to vary linearly with l/a2 or l/c2 when tested against published as well as our data, a comparison of Cohen's method and the Linear method was considered desirable (Sections 3 and 4). For the latter method an electronic computer was required since a reiterative procedure to obtain the optimum ao and co values had to be employed. The purpose of this paper is to describe the principles of the Linear method, illustrate its application, and compare it with Cohen's method. 1) THE LINEAR METHOD The standard practice in obtaining the lattice parameters in the Debye-Scherrer method is to

Jan 1, 1965

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

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

Jan 1, 1965

By D. A. Elgillani, S. Atak, D. A. Rice, M. C. Fuerstenau, R. B. Bhappu

Quartz and feldspar cannot be floated with sulfonate at any pH; spodumene floats over a narrow acid pH range, while beryl responds moderately over a broad pH range. After wet-grinding in a steel mill, beryl, quartz, and spodumene float well with sulfonate below about pH 7, whereas the improvement in the response of feldspar is not so marked. A mechanism by which iron can be adsorbed on these minerals is presented. Also, the responses of leached, natural, and wet-ground beryl to amine, sulfonate, and oleate flotation are shown and related to the measured zero-points-of-charge of these materials. Earlier work with leached beryl showed that good flotation could be obtained with alkyl aryl sulfonate over a rather wide pH range using a Fagergren flotation cell.' When a similar response was observed with leached quartz, it was decided that unintentional activation was being obtained from the metallic components of the Fagergren cell. To obviate this difficulty, a microflotation cell was designed, and an experimental technique was devised. These have been described elsewhere. Experiments conducted with the small cell showed that leached quartz could not be floated at any pH with any sulfonate addition,3 which is in agreement with the observations of Kraeber and Boppel.4 Similarly, it was also found that leached beryl responded to sulfonate flotation only over a narrow pH range rather than the broad range reported earlier.1 This early work,1 however, revealed the important effect that wet-grinding in a steel mill has on the flotation response of certain silicates. That is, it was found that quartz and especially beryl floated well over an unusually wide pH range after wet-grinding in a steel mill. Microcline, however, floated poorly below pH 4, even though wet-ground under the same conditions. The work of Eigeles6 on adsorption of oleic acid on leached quartz and iron-contaminated quartz at constant pH is in agreement with these flotation data. Other research has shown that ferric iron, added as a salt to the system, functions as an activator in the narrow pH range in which Fe +++ iron hydrolyzes to its hydroxy complexes.3,5 These phenomena indicate that iron functions differently in flotation systems depending on its method of introduction. The object of this paper is to determine the mechanism by which iron is adsorbed on certain minerals, the mechanism of collector adsorption after iron abstraction, and the role that Fe++ and Fe+++ assume in the selective separation of these minerals. EXPERIMENTAL MATERIALS AND METHODS Sodium alkyl aryl sulfonate, mol wt 450,7 pure potassium oleate, and pure dodecylamine were used as collectors. All other chemicals were reagent grade in quality, i.e., n-amyl alcohol as frother; HC1, H2SO4, and KOH for pH adjustment; and ferric chloride as activator. Conductivity water, made by passing distilled water through an ion exchange column, was used in the experimental work. All minerals used in the investigation were hand-picked specimens. Sample Preparation: Each of the minerals was crushed through 8 mesh, and the product was divided into two groups, one to be ground dry and the other wet. Dry grinding was accomplished with an alumina mortar and pestle. The product was dry-screened to 48 x 150 mesh, cleaned magnetically, deslimed in conductivity water, and dried. Preparation of the samples by wet-grinding involved grinding a 200-g charge of the mineral (-8 mesh) at 60% solids with natural water in a mild steel rod mill for four minutes. This charge was then wet-screened immediately with natural water to 48 x 150 mesh, dried, and cleaned magnetically. Some experiments were also conducted with leached beryl and quartz. These products were prepared by leaching the sized sample (48 x 150 mesh) with concentrated HC1 with a percolation technique until no iron could be detected in the leach liquor. Following this step, the sample was rinsed with conductivity

Jan 1, 1967

By T. W. Watson, D. R. Flynn

Measurements have been made of the thermal conductivity and electrical resistivity of two specimens of 0.005-cm (2-mil) Be-Cufoil over the temperature range -140° to +200°C. The thermal cmductivity of Be-Cu Alloy 125 was found to be significantly higher than that of Alloy 25, which had a higher impurity content. The thermal conductivity and electrical resistivity values obtained were in concordance with the Smith and Palmer relation for copper alloys which states that ? = 0.0239 (T/p) + 0.075 where A is thermal conductivity (W cm-' deg-'), p is electrical resistivity (microhm-cm), and T is absolute temperature (OK) , indicating that the Smith and Palmer relation can be used to predict the thermal conductivity of this type of Be-Cu alloy over the temperature range -140" to + 200°C to within an accuracy suitable for most engineering applications. THE National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, Md., requested the National Bureau of Standards to measure the thermal conductivity of 0.005-cm Be-Cu foil which was to be used to fabricate antennae for use in Radio Astronomy Explorer space craft. It was felt that measurements had to be made on the actual antenna material, rather than on a thick bar of similar material, since the cold-working and age-hardening properties of the alloy would make it very difficult, if not impossible, to place a thick bar in the same metallurgical state as the 0.005-cm material. As discussed in Section 111 of this paper, the thermal conductivity of many copper alloys can be computed rather accurately from electrical resistivity data using an empirical relation developed by Smith and palmer' and further confirmed by owell.' However, there has been very little work done on correlating thermal and electrical conductivities on Be-Cu alloys. We were reluctant to assume the validity of the Smith-Palmer relation on Be-Cu alloys because of the very large mass difference between beryllium and copper. As will be seen, however, our experimental results indicate that the Smith-Palmer relation is valid for the two alloys on which we made measurements. I) DESCRIPTION OF SAMPLES Samples of Be-Cu Alloy 25 and Be-Cu Alloy 125 were furnished to NBS in the form of rolled strip material, 0.005 cm thick by 5.08 cm wide. The Be-Cu Alloy 25 was purchased by NBS in the form of a continuous length of flat strip. The Be-Cu Alloy 125 was furnished to NBS by Goddard Space Flight Center in the form of two lengths of strip that had been formed into "tubing" of about 1.2 cm diam, with one side of the strip overlapping (but not connected to) the other side by about 90 deg. This "tubing" had been opened up to be flat and then rolled onto spools of about 3 cm diam. When unrolled, the strip would spring back into tubular form. Samples of both of the Be-Cu alloys were chemically analyzed by the NBS Analytical Chemistry Division. The beryllium content was determined quantitatively by the phosphate-gravimetric method to be 1.83 wt pct for Alloy 25 and 1.80 wt pct for Alloy 125. The two alloys were also examined by a general qualitative spectrochemical method for metallic elements. The Alloy 25 specimen contained between 0.1 and 1.0 wt pct Al, Co, Fe, and Si and between 0.01 and 0.1 pct Ni. The Alloy 125 specimen contained between 0.1 and 1.0 pct Co and between 0.01 and 0.1 pct Al, Fe, and Si. Other metallic elements present were in amounts less than 0.01 pct. The NBS Engineering Metallurgy Section measured the tensile strength, elongation, and Knoop hardness of both the Be-Cu Alloy 25 and the Be-Cu Alloy 125. These are given in Table I. The NBS Engineering Metallurgy Section also prepared photomicrographs of the two alloys; these are shown in Figs. 1 and 2.

Jan 1, 1969

By C. J. Leith

A study of the effect of rock composition, rock structure and degree of weathering on the stability of cut slopes is being sponsored jointly by the U.S. Bureau of Public Roads and the North Carolina Highway Commission. In 58 mountain and piedmont counties of North Carolina the percentage of failed cut slopes is greatest in micaceous metasediments, gneisses, and schists, and in saprolite and soil derived from these rock types. Soil slope failures outnumber rock slope failures by two to one. Joints and similar planes of separation exert a strong influence on size and shape of the sliding mass. They may or may not act as failure surfaces, depending on their orientation with respect to the active forces. Climatological data, though indicative of weathering conditions, do not correlate well with slope failure frequency. Because of the presence of joints and similar planes of weakness in soil and rock materials, conventional methods for analyzing slope stabilities are not directly applicable. Empirically derived modifications of these methods are being investigated. A study of the stability of highway cut slopes, sponsored by the U. S. Bureau of Public Roads and the North Carolina State Highway Commission, began in 1962 at North Carolina State of the University of North Carolina at Raleigh. As part of this study all slides, rockfalls and other types of cut slope failures on Federal and State highways in the 58 mountain and piedmont counties in North Carolina were located and described, and the data catalogued in a punched card file system. A major objective of the project is to relate slope failures to properties and physical conditions of the geological units in which the slopes were constructed, and to correlate soil type and/or geological unit with type and frequency of slope failure. The complexities of the problem of slope stability and the limitations which these complexities impose on methods for analyzing slopes have been recognized for many years. A great variety of factors and processes may lead to slides, often making it almost impossible to analyze theoretically the conditions required for stability of slopes. One of the principal factors determining maximum safe slopes is the shear strength of the material in which the slopes are cut, but unfortunately there are very few data available concerning shear strengths of residual soils. Vargasl tested clay derived from gneiss and granite in southern Brazil; the properties of decomposed granite occurring near Hong Kong were determined by Lumb.2 These data are being used, when applicable, to supplement the test data obtained in the present study by Yorke.3 The locations of the North Carolina slope failures, more than 400 in number, are shown on Fig. 1. This map, adapted from the Geological Map of North Carolina,4 suggests the possibility of a relationship between frequency of slide occurrence and rock type. However, the evaluation of this possibility requires consideration not only of the type of rock, but also of its large and small scale structural features, its susceptibility to and degree of weathering, and the composition and structure of the weathering products. Soil slope failures in thoroughly weathered soil material and saprolite outnumber rock slope failures two to one. INFLUENCE OF ROCK TYPE The agricultural soil type involved in each soil slope failure was identified and each failure was catalogued in terms of the parent material from which the soil was derived. These data indicate that most of the slope failures, whether in the rock or in the derived soil, are associated with metamorphic rocks (see Fig. 2a). The data may be skewed somewhat because of the relative sizes of the total areas underlain by the various rock types, but Leith and Gupton5 have demonstrated that the preponderance of failures in metamorphic rocks is of much greater magnitude than could be accounted for by the areal factor alone. The dominance of metamorphic rocks is emphasized when soil slope failures are considered in terms of the specific rock types from which the soils were derived (see Fig. 2b). In particular, mica schists and mica gneisses account for more slides

Jan 1, 1965

By J. L. Bray, S. T. Ross

The paper provides electrometallurgical data on the problem of germanium removal from zinc sulphate solutions. Germanium traces have caused much concern to the zinc refiner. Confirmatory evidence of interaction between germanium and cadmium is presented. Statistical analysis of data expands its significance and enhances its value. Further research is outlined. THE literature contains many references to the effects of trace amounts of germanium in the production of electrolytic zinc. One of the authors had experience with this troublesome element as early as 1917 at Trail, B. C. In 1929, Tainton and Clayton' reported that concentrations of as little as one part per million of germanium were sufficient to cause serious losses in current efficiency. Liddell2 reported that trace amounts of germanium cause marked lowering of the hydrogen overvoltage of electrolytic zinc cells, so that commercial production was impaired. Bray3 recorded the history of germanium in relation to electrolytic zinc production, noting that concentrations below 10 ppm have been found to yield low current efficiencies and copious hydrogen evolution. Koehler' stated that germanium "when present to the extent of a small fraction of one part per million per liter, causes serious evolution of hydrogen with a corresponding reduction in current efficiency." Recently, however, S. W. Ross" reported, from Risdon, Tasmania, that "in the course of leaching . .. dissolved traces of germanium... if not removed almost completely ... increase the reversion of cadmium during the filtration of the copper-cadmium precipitate and reduce the current efficiency during subsequent analysis." The copper-cadmium precipitate referred to is the residue from the zinc-dusting purification of zinc sulphate leach solutions. In the face of such conflicting testimony and with the increasing industrial importance of pure germanium and zinc it was decided to investigate the relationship between cadmium and germanium. Furthermore, other work by the authors showed certain discrepancies to exist in the theories of Tainton, et al. In the laboratory, without marked efficiency decreases, the authors have deposited zinc successfully from solutions containing as high as 1 g per liter of germanium. This could be done only when there was no cadmium present. Preliminary investigations of the suspected rela- tionships were carried out by means of emission spectrographic analysis using a beryllium internal standard. Several solutions containing 100 g per liter of zinc, as zinc sulphate, and 1 g per liter of cadmium, as cadmium chloride, were prepared. These concentrations were on the order of those obtained during a commercial low-acid leaching process. Varying concentrations of germanium were added to these solutions so that the range of 0.0000 to 0.5000 g per liter of germanium was covered. A 250 ml sample of each solution was agitated with 2.5 g of zinc dust for 30 min, filtered, and the filtrates were examined spectroscopically. Qualitative evidences of cadmium traces were found in those filtrates which originally contained above 10 ppm of germanium. Reliability of the analytical method did not permit quantitative investigations since cad-Table I. Current Efficiencies Obtained at 0.0000 and 1.5000 G per Liter Cadmium Concentrations Ge Concentrastion,* Cd Concentration,* EtBclenoy, G per Liter G per Llter Pot 0.0000 0.0000 84.270 0.0010 0.0000 94.849 0.0050 0.0000 92.649 0.0075 0.0000 94.039 0.0100 0.0000 96.084 0.0000 1.5000 93.460 0.0010 1.5000 95.158 0.0050 1.5000 92.148 0.0075 1.5000 91.260 0.0100 1.5000 84.546 • Cd and Ge concentrations shown are those existing before zinc-dust purification. mium determination in the concentrations present in zinc-dusted solutions lacks sufficient sensitivity for reproducible results. As a consequence of the inability of the investigators to obtain acceptable results through direct quantitative analysis, an indirect approach was devised. This indirect method involved a study of the current efficiency, in a model zinc cell, as a function of the concentrations of cadmium and germanium. Variables such as cell temperature, voltage, current density, anode spacing, relative electrode area, degree of agitation, cathode preparation technique, time, acid concentration, and solution volume were held constant. Fig. 1 shows the cell used. The current was fur-

Jan 1, 1952

By R. H. Olds, B. H. Sage

The transient flow of gases in long pipe lines is a problem of industrial interest. The present discussion deals with the application of the conservation of momentum and material to the transient flow of gas in conduits which are long with respect to their diameter. Solutions of the resulting equations include consideration of variations in friction and specific volume of the fluid as functions of time and position along the conduit. The changes in state along the pipe line are established as a function of time. The methods proposed may be extended to other situations. The flow of compressible fluids under steady conditions' has been considered in detail. Primary emphasis was placed on the development of simple means of taking into account the non-uniform flow' realized in long conduits under such conditions. Binder2 discussed the essential differences between the flow of compressible and uoncompressible fluids. Bonilla" proposed direct methods of solution for equations describing isothermal flow in long pipes. Similar considerations limited to steady flow have been discussed by Ruth.' Palsgrove 5 sugrested a graphical means of solving specific problems relating to the flow of gases in conduits of uniform section. Some of the basic concepts of the flow of a compressible viscous fluid in straight tubes have been described by Kuo.6 Problems of this type require knowledge of the equation of state of the fluid. In many cases it liar been convenient to assume that the fluid follows the relationship ascribed to a perfect gas. The treatment of unsteady flow of compressible fluids is less complete. This state of affairs result* from the fact that the differential equations relating pressure and flow rate with time and position for unsteady flow are nonlinear in character.' Muskat and Wyckoff presented an excellent treatment of the situation in laminar Bow where inertia forces were not of controlling importance. Somewhat earlier Hurst9 discussed the uncteady flow of fluids in petroleum reservoirs. Helhering-ton. MarRoberts. and Huntington'" established experimentally the pressure distribution and accumulative flow rate of natural gas through an unconsolidated sand. Recently Joffe11,12 conhitlcretl the specific problem of the flow of natural gas in relatively long.,. pipe lines for unsteady conditions with emphasis upon the economic feusibility of the storage of gas in such a reservoir. These discussions were based upon approximations of the partial differential equations applying to the condititons of flow. The results were descriptive of the physical situation and indirated the effertiveness of large pipe lines as cyclic storage facilities for natural gas. The advent of analog computers" has increased materially the practicality of solving nonlinear partial differential expressions. Several iterative numerical and graphical methods14,15,16 have been developed to solve nonlinear equations. However, it appears that the pair of simultaneous nonlinear partial differential equations involved in problems of this nature are not directly susceptible to solution by presently available analog computer or formal iterative numerical techniques. Nevertheless. graphical analyses afford a means of obtaining data of engineering value without special equipment. MATHEMATICAL CONSIDERATIONS Since the length of the conduit is large in comparison to the cross section in the cases to be considered, it is possible to treat the characteristics of the flow as independent of position in the cross section of the conduit. This possibility follows since the energy- connected with the velocity profile is small compared to that required to overcome the friction associated with its movement throughout the length of the line. Average values of the pressure. velocity. kinetic energy. momentum, and specific volume may he assigned to the fluid at any particular cross section. From a mathematical viewpoint this may be expressed in the following way for velocity: µ = µ(?X)..........(1) The uncertainties introduced by such assumptions usually are negligible when the ratio of length to diameter is greater than the order of 1.000. On this basis a volume element ma!. be considered to occupy the entire cross section of the conduit. Such an element is presented in Fig. 1.

Jan 1, 1951

By Tibor Stefansky, John E. Dorn

MOTT and Nabarro1-5 were first to illustrate the importance of the flexibility of dislocations in accounting for the strengthening that metals undergo due to the presence of internal-strain centers. Such strain-centers might arise from a number of causes such as radiation damage, the presence of semicoherent and coherent precipitates and clusters, as well as individually dispersed interstitial and misfit substitutional solute atoms. Each strain-center induces positive and negative shear stress fields on the slip planes of the surrounding alloy matrix. In order to effect plastic deformation, therefore, the alloy must be subjected to sufficiently high applied shear stresses to push dislocations past all such internal stress fields. If dislocations were inflexible and moved as rigid lines, they would be equally pushed and pulled by internal stress fields. At this extreme the strengthening would be vanishingly small. Dislocations, however, are not rigid; they are flexible and extensible. They wiggle between positive and negative strain-centers, thus increasing their line energy at the expense of their interaction energy with strain-centers. cottrel16 and Friedel7,8 have independently presented lucid reviews of the significance of the Mott-Nabarro dislocation-flexibility concept to the strain-center strengthening of alloys. Their analyses however were only semi-quantitative. There is evidence in the recent literature of renewed interest in a more rigorous analysis of flexibility. Thus, Gleiter9 and Gerald" have shown that the calculated strain-energy interaction between a dislocation and the stress fields of coherent precipitates can be seriously in error if the flexibility of the dislocation is not taken into account. This report will be concerned with a more detailed analysis of the problem based on the following approximations: 1) Although many types of strain-centers exist, the following analysis will be limited to the case of solute-atom strain-centers in fcc substitutional alloys. 2) To facilitate the analysis by avoiding statistical considerations, the strain-Centers are assumed to be in regular arrays on the slip plane. Although the quantitative results are somewhat dependent on the type of array that is assumed, the qualitative trends are similar for various arrays that were studied. 3) An adjustment of the results from those for square arrays to those for the more realistic case of a random distribution of strain-centers is accomplished by adopting the interesting statistical theory first introduced by Kochs,11,12 elaborated on by Dorn, Guyot, and stefansky,13 and analyzed by Foreman and Makin14 in their computerized experiments. 4) For simplicity the dislocation lines are taken to wiggle about their edge orientation and no correction is applied to their line energy for deviations from edge configurations or for the elastic interaction between segments of the now curved dislocation. It will be shown that for extremely low concentrations of atomic strain-centers the strengthening increases with the square root of their concentration. For slightly higher concentrations the strengthening rate becomes less rapid. At a critical concentration a maximum strength is obtained and a decrease in the strengthening takes place as the concentration of solute atoms is further increased. These trends are a direct consequence of dislocation flexibility. They arise from changes in the amplitude of the waviness of the dislocation line at the yield stress with solute atom concentration. Despite the simplifying assumptions that were made, the results agree qualitatively with appropriate experimental data. I) STRESS FIELDS ON SLIP PLANES Internal stresses are introduced in a lattice whenever a host atom of radius ro is replaced by another that has a different atomic radius. According to the classical theory of linear elasticity,15 the stress field about a solute atom at the origin of a spherical coordinate system is given by arr=-4G€(?_0)3 ffflfl ="W =2G€{t) f°rr^ro(l+e) UJ where G is the shear modulus of elasticity and Y, = ro(l + E) is the radius in situ, of the substituted atom. As shown by ~shelb~,'~ this approximation assumes that the bulk modulus of elasticity of the substituted atom is identical with that of the host species. ~abarro'~ suggested that the strain E can be deduced

Jan 1, 1970

By R. H. Olds, B. H. Sage

The transient flow of gases in long pipe lines is a problem of industrial interest. The present discussion deals with the application of the conservation of momentum and material to the transient flow of gas in conduits which are long with respect to their diameter. Solutions of the resulting equations include consideration of variations in friction and specific volume of the fluid as functions of time and position along the conduit. The changes in state along the pipe line are established as a function of time. The methods proposed may be extended to other situations. The flow of compressible fluids under steady conditions' has been considered in detail. Primary emphasis was placed on the development of simple means of taking into account the non-uniform flow' realized in long conduits under such conditions. Binder2 discussed the essential differences between the flow of compressible and uoncompressible fluids. Bonilla" proposed direct methods of solution for equations describing isothermal flow in long pipes. Similar considerations limited to steady flow have been discussed by Ruth.' Palsgrove 5 sugrested a graphical means of solving specific problems relating to the flow of gases in conduits of uniform section. Some of the basic concepts of the flow of a compressible viscous fluid in straight tubes have been described by Kuo.6 Problems of this type require knowledge of the equation of state of the fluid. In many cases it liar been convenient to assume that the fluid follows the relationship ascribed to a perfect gas. The treatment of unsteady flow of compressible fluids is less complete. This state of affairs result* from the fact that the differential equations relating pressure and flow rate with time and position for unsteady flow are nonlinear in character.' Muskat and Wyckoff presented an excellent treatment of the situation in laminar Bow where inertia forces were not of controlling importance. Somewhat earlier Hurst9 discussed the uncteady flow of fluids in petroleum reservoirs. Helhering-ton. MarRoberts. and Huntington'" established experimentally the pressure distribution and accumulative flow rate of natural gas through an unconsolidated sand. Recently Joffe11,12 conhitlcretl the specific problem of the flow of natural gas in relatively long.,. pipe lines for unsteady conditions with emphasis upon the economic feusibility of the storage of gas in such a reservoir. These discussions were based upon approximations of the partial differential equations applying to the condititons of flow. The results were descriptive of the physical situation and indirated the effertiveness of large pipe lines as cyclic storage facilities for natural gas. The advent of analog computers" has increased materially the practicality of solving nonlinear partial differential expressions. Several iterative numerical and graphical methods14,15,16 have been developed to solve nonlinear equations. However, it appears that the pair of simultaneous nonlinear partial differential equations involved in problems of this nature are not directly susceptible to solution by presently available analog computer or formal iterative numerical techniques. Nevertheless. graphical analyses afford a means of obtaining data of engineering value without special equipment. MATHEMATICAL CONSIDERATIONS Since the length of the conduit is large in comparison to the cross section in the cases to be considered, it is possible to treat the characteristics of the flow as independent of position in the cross section of the conduit. This possibility follows since the energy- connected with the velocity profile is small compared to that required to overcome the friction associated with its movement throughout the length of the line. Average values of the pressure. velocity. kinetic energy. momentum, and specific volume may he assigned to the fluid at any particular cross section. From a mathematical viewpoint this may be expressed in the following way for velocity: µ = µ(?X)..........(1) The uncertainties introduced by such assumptions usually are negligible when the ratio of length to diameter is greater than the order of 1.000. On this basis a volume element ma!. be considered to occupy the entire cross section of the conduit. Such an element is presented in Fig. 1.

Jan 1, 1951

By G. A. Vissac

MoIstuRe in coal must be considered as an impurity, just the same as ash, from the standpoint of utilization of the coal. Being incombustible, it reduces directly the heating value of the coal, and in addition absorbs heat for its evaporation. Its presence means useless expenditures in handling and transportation. In coke plants, extra moisture reduces capacity and may cause damage to brick work and equipment. Accordingly, the removal of extra moisture can be considered just as important as the removal of other impurities, such as ashes, in the modern coal preparation plant. Moisture, which can be removed by heating the coal up to a temperature of 100°C, may be retained in various forms: 1. As a film, on the surface of each coal particle, and in the interstices between particles, retained by capillary forces. 2. Or "occluded" inside the coal particles. This occluded moisture may be either free moisture (as in a sponge), or hygroscopic moisture which varies with atmospheric conditions, (also called "regain"). These latter forms of moisture are particularly common in "young" coals (subbituminous and lignites); bloom coals (seam outcrops); fusain; and carbonized products. In our study of coal drying, we shall consider only the removal of free moisture, exclusive from hygroscopic moisture. Dewatering If we reserve the name of drying to the removal of water by evaporation, we must consider the initial phase of the mechanical removal of free moisture as a distinct operation covered by the term dewatering. In all cases the free water carried over the surface of the coal particles or in their interstices, or in their pores, is retained by capillary forces. Dewater-ing is accomplished by breaking or counteracting these capillary forces; removal of as much water as possible by dewatering methods is usually advisable, as the cost of these operations is generally much less than by evaporation. The most common methods of me-chanical dewatering are: 1. "Pressure piling," which reduces the interstitial spaces, accomplished in dewatering bins or over dewatering screens. 2. Or dynamic methods, such as used in centrifuges or over vibrating screens. We shall only mention the " preferential wetting" method, in which surface water can be displaced by hydrocarbons, as offering possibilities, but which, to our knowledge, has not reached yet a practical development. But we must point out that the capillary forces retaining water on the coal surfaces, decrease considerably with increased temperatures. This is the principle used in all modern dishwashing machines; by using very hot water, dishes are extracted almost dry. In line with this development, we favor the type of dryers including a dewatering section; as the coal enters the dryer and is gradually brought up to higher temperatures, its dewatering ability is increased and advantage can be taken of this conditioning, resulting in increased drying efficiencies and reductions in drying costs. Heat Drying In the final phase, the remaining moisture must be evaporated. Coal and water must be brought up to the chosen temperature of evaporation, and heat must be supplied to fill the requirements of the latent heat of evaporation of the water to be removed. Accordingly, drying becomes largely a problem of heat transfer, and drying methods can be classified accordingly, namely: 1. Radiant transfer. 2. Transfer by surface contact and conduction. 3. Transfer by hot gas contact. The first method is not applicable to coal drying; the second method is used in the old type rotary dryer. The third method, the most commonly used in modern coal dryers, will be the only one considered here; and, of course, we shall deal with continuous types of dryers only. The mechanism of complete drying is really very complex-—several phases are involved: 1. The constant rate period. 2. The uniform falling rate period. 3. The varying falling rate period. As most of our practical coal drying problems deal with wet coals (over 6 pct of moisture), and do not require complete drying (under 1.5 pct), we shall deal with the first condition only, namely the constant rate drying. Dryer Calculations Instead of presenting the algebraic formulas, we believe a concrete example will provide a clearer illustration. Assume a feed of wet coal at the rate

Jan 1, 1950

By Paul J. Fopiano

SOME relationships between the flow characteristics of iron single crystals of 99.9 pct purity and the behavior of imperfections have been investigated. X-ray rocking-curve measurements and etch-pit counts were made as a function of plastic strain, and compared to the stress-strain curve obtained on a modified Polyani tensile machine. Crystals grown from rolled strips of vacuum-melted iron by the strain-anneal method1 had a high preference for a (110) longitudinal direction and a (211) face normal. The tensile specimens were prepared from 2 by i by 0.040 in. single crystals having a gage area of 3 by \ in. Rocking-curve measurements were carried out with a highly perfect germanium monochromating crystal in which the dazz spacing was matched to that of the dZl1 in the ir0n.l Well-collimated CuKal radiation was used throughout. These procedures practically eliminated errors due to geometrical and wavelength resolution. Inasmuch as the rocking-curve half breadth may vary markedly from point to point in the specimen being irradiated, the crystals were strained in place by mounting a hydraulic loading device on the double-crystal spectrometer. The rocking curves were taken after each increment of strain in the unloaded condition, since no observable difference was found in the rocking-curves between the loaded and unloaded states. The rocking-curve half breadths of the as-grown specimens were in the range 90 to 120 sec of arc when the beam irradiated an area of about -£ by -& in. on the specimen. DeMarco and weiss3 have shown that, for a well-colli- mated X-ray beam, irradiating about 10"! sq in. of the very same material, half breadths within 10 pct of the Darwin natural half breadth were observed. Since the rocking-curve specimens were stressed by the load-unload technique, the strain achieved at any given stress depended on the time of holding because of low-temperature creep. Fig. 1 shows the rocking-curve half breadth (also area/peak height) as a function of plastic strain for a relatively short holding time (2 to 5 min) at each stress level. For strains less than 0.1 pct the rocking-curve breadth is essentially constant; it is only for larger strains that there occurs a significant increase in this breadth. Where the holding times at each stress level were longer (by well over an order of magnitude) there occurs a significant increase in the rocking-curve breadth only after plastic strains of the order of 0.6 pct had been introduced into the specimen. This observation is related to the time dependence of creep phenomena and emphasizes the difficulty in comparing data obtained by two such different straining methods. Etch-pit results were obtained using a 2 pct nital etch on specimens strained in the range of 0 to 1 pct. Prior to etching, all specimens were annealed for 3 hr at 150°C, the carbon content being sufficient to decorate the dislocations for strains of at least 1 p~t.~ The data points were all taken from parts of the same single crystal which had been strained with short holding times at stress in increments of strain of the order of tenths of 1 pct. The (211) plane is particularly difficult to etch-pit in vacuum-melted iron and therefore it is felt that these values are as much as an order of magnitude low. Fig. 2 shows the etch-pit density as a function of plastic strain. The smooth curve passing through the data points is not meant to infer a quantitative correlation with the rocking-curve data. What is of interest, however, is the change in etch-pit density in the region of 0.2 pct plastic strain. The first three increments in strain (points 2,3, and 4) did not produce a measurable change in the etch-pit density while subsequent increments did produce a measurable change. While the absolute values of these results do not appear to be cor-

Jan 1, 1967

By F. W. Archibald

The American Smelting and Refining Co. has standardized its copper converting practice to attain a maximum unit blister production with a minimum of refractory consumption by careful location of the tuyeres and by applying magnetite coatings on the hard-burned magnesite brick linings. THE American Smelting and Refining Co. operates four primary copper smelters in the United States with a total of 17 Peirce-Smith type converters; 15 of them are 13 ft in diameter by 30 ft long, and two are smaller. Some details of operations vary with locale; however, fundamentals of design, operation, and maintenance are common to all plants. All converter shells are l-in. thick except for one new converter with riding rings on the ends which has a shell thickness of 1 1/2 in. More tuyeres can be installed with rings on the ends and hence more air can be used. Welded construction is replacing riveted. Minor shell repairs are made after each campaign. Principal causes of complete shell replacement are warpage and cracking resulting from localized over-heating. A 13x30 ft shell is being replaced after 34 years of operation and a total production of approximately 750,000 tons of blister. Converters are driven by 80 hp DC motors through company-designed worm gear reducers. Rotation is 0.38 rpm which permits the skimmer to spot the converter quite accurately for skimming slag. At three of the plants, protection against unscheduled air or power failures is afforded by the installation of emergency drives, consisting of auxiliary air motors or storage batteries. In order to avoid excessive splash out of the converters, the converter mouths are located as far back on the shells as existing flue facilities will permit. At one plant, the back of the mouth is only 13" to the rear of the vertical center line of the converter,. whereas it is 28" at another plant. Newly-lined mouth areas vary from 36 to 44 sq ft with effective operating areas about 25 pct less. It is important to keep the converter mouths as clean as possible. Dirty mouths create back pressures in the converters and as a consequence the tuyere air volumes are reduced. Mouths are generally cleaned by bumping with an empty ladle. Small mouth-cleaning rams have been used but unless extreme care is exercised the brickwork may be damaged. After considerable experimentation, the plants standardized tuyere elevations at 4 to 4% in. below horizontal center line at the shell with a downward pitch of about 13/16 in. per ft of length. Tuyeres are spaced at 6 in. centers except at the riding rings where there are no tuyeres. With this tuyere location, several of the plants now freeze magnetite slag in the bottoms, fronts, and backs up to the bottom of the tuyeres to control the internal shape of the converter. This has the effect of improving the agitation and mixing so that there is a marked increase in converting speed besides affording protection to the brick lining. Currently, the trend is to increase tuyere diameters from 1% to 2 in. to increase the air flow. At present, all converters are hand-punched but one converter is being equipped with a set of mechanical tuyere punchers. Rods for punching are % in. hexagonal smelter bar upset to ll/s in. and rods for cleaning tuyeres are upset to about 1% in., or larger, depending upon the tuyere diameter. Two of the plants use pneumatic reamers for cleaning the tuyeres between charges to minimize disturbing the coating on the inside of the refractory lining. Most of the puncher's platforms are pneumatically or hydraulically mounted so that a convenient punching position can be maintained regardless of tuyere position. For normal operations, tuyere air pressures vary from 15 to 13.5 psi, although some cycles such as magnetiting require pressures down to 8 psi. Air requirements vary from an average of 25,000 cfm on the newer installations down to 12,000 cfm on the older ones. Converter hoods are designed to protect the punchers from sparks, splash or hood accretions as well as to prevent the escape of objectionable

Jan 1, 1955

By Lyman H. Hart

Some of the significant facts that will affect the supply and demand for metals during the next few decades are given in this presentation. This is important because the only hope for intelligent guidance of the national destiny depends upon presenting a consistent and accurate picture of basic problems. The metals problems now fomenting are only slightly less important than those precipitating the energy crisis. Admittedly, it is difficult to generate serious thinking on this subject when the world is enjoying easy access to all metals at modest prices. This is possible because of the current world capacity to over-produce, and United States credit standing, at least up to now, has permitted buying freely on world markets. Although both these vital conditions are subject to change, there is little doubt that if the U.S. financial house is kept in order, we can muddle along for a while on a generally expanding, metal-based economy. But should our credit standing be permitted to collapse, or should there be a tightening of world supplies of metals, the nation would immediately find itself in trouble. Unfortunately, clear signals indicate that both of these conditions are threatening. The metal age started many centuries ago, and with the exception of the noble metals, barely a dent was made in world reserves until the present century. Then, as a result of the pioneering ideas of D. C. Jackling and Paul Gemmel, and the willingness of the McNeals, Penroses and Guggenheims to back ideas with money, a virtual explosion of metal production was propagated throughout the world. It is important to examine the causes of this expansion to determine whether it is a trend that may be sustained or whether it is anomalous and therefore attributable to circumstances not likely to be repeated or continued. This period of plenty is a once only phenomenon. Vast metal resources have been sitting around here for eons, while the world was unaware of or unconcerned with their existence. But when population began to grow exponentially, and ways were discovered to use metals to develop machines to do the work of men and animals, the exploitation of raw materials increased at a staggering rate. And now the realization is dawning that minerals are a wasting asset and are beginning to present supply problems that should begin to be of concern. Two main factors have caused this condition; One is the population growth, and the other is the expanding demand for irreplaceable raw materials as nations become more developed. A group of systems analysts, at Massachusetts Institute of Technology in a book Limits of Growth, has warned that at present rates of population growth and resource consumption together with environmental constraints, a point will be reached within 100 years when the world population will become totally incapable of supporting itself. The authors conclude that this end result could be avoided if a planned equilibrium could be established at a lower rate of population growth and resource consumption. Fortunately, there is evidence that the population problem is moderating. The growth rate in the U.S. has decreased from 2.3% per year in 1900 to 1.1% in 1970. But, even at the lower rate, population will double in 70 years. The world rate is greater, and if it continues, world population will rise from 3.5 billion to nearly 10 billion in 50 years. All of these projections are questionable because the dangers of growing population are now being recognized. A marked decrease in growth rate has been noted in the more developed countries-in fact, it was zero in the U.S. in 1972. The other factor affecting consumption of raw materials is the increase in per capita use of most items as individuals become more affluent. Many economists believe that developing countries such as China and India represent a vast future potential market; but there are others, with whom the author agrees, who believe over-population tends to stagnate development. Nevertheless, it is a fact that vigorously developing societies increase consumption at a rate far above their population growth rate.

Jan 1, 1974

By R. E. Reed-Hill

A simple accurate graphical method for orienting fcc crystals using (111) slip traces on a single surface is described. Solutions placing the pole of the surface in a unit stereographic triangle are obtained using a Wulffnet, a (111) standard projection showing the four (111) planes, and a (111) standard projection ruled into unit stereogmphic triangles. The multiplicity of solutions is described in relation to this method. AN accurate, rapid single-surface technique for orienting fcc crystals, using (111) slip or twin traces, has been a matter of continuing interest, as evidenced by the periodic appearance of papers on this subject.'-4 This note presents a new method possessing some advantages over those previously reported. It is an analog to the technique for hcp metals5 where the solution is based upon a stereographic rotation of the specimen surface on a (0002) standard projection that contains the planes of the possible features that might account for the observed traces. In the hexagonal solution, the axis of rotation is the basal-plane trace in the surface. In the fcc case, the axis of rotation is one of the observed ( 111) slip or twin traces. It has been observed that the solution is greatly facilitated if the indicated movements of the (111) traces during the rotation of the surface are plotted directly on a paper copy of a Wulff net as shown schematically in Fig. 1. The trace selected to represent the axis of rotation is assumed to fall at the north-south poles of the Wulff net. The directions of the other traces are then plotted as points at the proper angles around one-half of the basic circle of the net. The loci of points corresponding to the movements of these traces (directions) during a 90-deg rotation of the surface, about the polar axis of the net, are then easily and accurately drawn by following the appropriate small circles on the Wulff net. The solutions to the problem are obtained with the aid of a (111) standard projection of the (111) planes, see Fig. 2. This is normally a Xerox copy of a carefully drawn master made on high-quality tracing paper. The (111) standard projection is superimposed over the Wulff net and rotated about its center until the points of intersection of the loci of surface traces, drawn on the Wulff net, and the great circles representing the (111) traces, all lie along a common meridian of the Wulff net as demonstrated in Fig. 3. This latter great circle represents a possible position of the surface. The pole of this plane is then plotted on the (111) standard projection. Its location in a unit stereographic triangle may be readily obtained by superimposing (over the standard projection) another tracing paper (111) standard projection subdivided into unit stereographic triangles. The result of this last operation is shown in Fig. 4. MULTIPLICITY OF THE SOLUTIONS The maximum possible number of (111) traces on a single grain surface is four. Any one may be selected as the axis about which the surface is rotated. Corresponding to each such choice are three possible surface-pole orientations, related to each other by a simple 120-deg rotation about the pole of the (111) basic circle. This is a direct result of the threefold symmetry of the (111) standard projection. Since each of the four rotations will normally give a different set of three-pole positions, there are, accordingly, twelve possible solutions. Each of these twelve solutions places the surface pole in the same relative position in a stereographic triangle so that all are crystallo-graphically equivalent. Accordingly, only a single solution is required to obtain a basic orientation of the crystal. It should be noted, however, that the orientations obtained by reflecting* any of these twelve orien- *The reflected orientations may be obtained by a 90-deg rotation of the opposite sense to that shown in Fig. 1. This rotation places the correspond-ing trace loci in the lower hemisphere of the Wulff net rather than in the upper hemisphere. tations through the surface are also possible orientations that could account for the surface traces. Thus, a given set of four traces always corresponds to a pair of basic orientations related by reflection through the specimen surface. This ambiguity can only be re-

Jan 1, 1967