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By David T. Peterson

Calcium metal was found to deoxidize thorizcm at 1000° to 1200° C. The reaction kinetics were determilled and related to the diffusion coefficients of oxygen in thorium. The solubility of oxygen in thorium, the minimum oxygen concentration, and the diffusion coefficient were determined from 1000° to 1200°C. This firocess results in the lowest oxygen concentrations zohich have been reported for thorium metal. FOR many years it has been known that calcium metal will reduce thorium oxide to thorium metal. This reaction has been the basis for several methods of preparing thorium metal. From the equations giv-by Kubaschewski and vans, ' AF" for the reaction Cao, + Tho,(,) - CaO(,, + Th(,) was calculated and found to be -3.4 kcal at 1000°C, -2.5 kcal at llOO°C, and -2.0 kcal at 1200°c. Thorium is very slightly soluble in liquid calcium, and the solubility of calcium in solid thorium is very low. Consequently these metals would be in essentially their reference states. If thorium containing oxygen were equilibrated with liquid calcium between 1000° and 1200°C, the oxygen content of the thorium would have to be below the solubility limit in thorium. Oxygen is one of the impurities most difficult to remove from thorium and is the most abundant impurity in metal prepared by almost all known methods. Fortunately, oxygen does not have a large influence on the properties of thorium because the solubility in solid thorium is very low. EvenT in thorium containing 100 ppm of 0, particles of thorium oxide can be observed in the microstructure. In view of the incompatibility of thorium oxide and liquid calcium and the low solubility of thorium oxide in thorium, the deoxidation of thorium by this method was investigated. For thorium containing an amount of oxygen well in excess of the solubility limit, the reaction should proceed in the following sequence. The oxygen content of the thorium matrix near the surface would be depleted by the diffusion of oxygen to the surface. At the surface, the oxygen would react with calcium to form calcium oxide. To maintain equilibrium within the thorium, thorium oxide would dissolve to keep the matrix saturated. Consequently, the thorium-oxide particles would disappear first at the surface and then the particle-free rim would grow in thickness. If the rate-controlling step were the diffusion of oxygen through this layer of thorium which was growing in thickness in direct proportion to the amount of oxygen removed, the well known parabolic time law should be observed. If the oxygen concentration at the surface of the thorium and at the inner surface of the deoxidized rim were known, the diffusion coefficient of oxygen in thorium could be calculated from the parabolic rate constant. EXPERIMENTAL PROCEDURE The thorium metal used in this study was prepared by calcium reduction of ThF, by the method described by Wilhelm.' The analysis of this metal is given in Table I. The carbon was determined by combustion, the oxygen by the HC1-insoluble residue method, nitrogen by the Kjeldahl method, and the other elements by emission spectroscopy. A section of this ingot was hot rolled at 600°C to 1/4 and 1/8-in. thick plates. Specimens approximately 7/8 in. square were cut from these plates, and all surfaces of the specimens were cleaned and smoothed by filing with a clean file. Individual specimens were placed in 1-in. diam by 2-in.-long tantalum capsules. Approximately 1 g of clean, high-purity calcium was placed in the capsules and an end closure arc-welded in place. The tantalum capsules were sealed in Inconel crucibles to protect the reactive metals from oxidation. The entire loading procedure was done in a glove box filled with pure argon. The loaded crucibles were placed in a muffle furnace, controlled within 2OC of the desired temperature, for a measured length of time. After the specimen had cooled to room temperature, it was sectioned perpendicular to the large faces and through the mid-point of two of the sides. The sectioned specimen was mounted and polished through Linde A abrasive. The rim which was free of thorium-oxide particles could be clearly observed microscopically as mechanically polished. Twenty measurements of the thickness of the rim were made at equally spaced points far enough from the end of the

Jan 1, 1962

By Klaus Detert

Fifteen and 18 pct Ni maraging steel and several binavy and ternary alloys of the iron-rich corner of the Fe-Co-Ni system have been studied. After annealing in the austenite range, these alloys were deformed slightly by cold rolling and subsequently aged. Compavison of experimental measurements at various processing stages indicates that small degrees of deforn~ation (5 to 10 pct reduction in thickness) do not influence hardness and strength or the aging kinetics. Electrical resistivity and ductility are somewhat redu]ced and the coercive force is substantially lower when compared to identical samples which were not deformed. The results are explained in terms of retained austenite which transforms into martensite with the small amount of deformation. RECENTLY there has been increasing interest in maraging steel for applications in electric power generators requiring a high ratio of power to weight.' Fifteen pct Ni maraging steel has been investigated to evaluate its properties and performance for application as high-strength magnetic rotor steel,' and a thorough investigation of the precipitation and transformation processes in this alloy has been conducted in this laboratory.3 The influence of deformation, which preceded the aging treatment, was also studied. It was found that a small deformation in the order of 5 pct has a rather striking effect in reducing the coercive force. Other interesting effects on the properties caused by such deformation have led to the more detailed studies reported herein. EXPERIMENTAL METHOD The methods used to produce the samples from 15 pct Ni maraging steel have been described elsewhere.3 The general procedure of hot forging and cold rolling to sheet has been followed. The composition is included in Table I which also contains the composition of the 18 pct Ni maraging steel grade 250 studied. More data about the material and the processing of the 18 pct Ni maraging steel have been recently reported.4 The experimental alloys of binary and ternary Fe-Ni-Co alloys were made by levitation melting in an argon atmosphere and casting into rod-shaped ingots 7 mm thick weighing 20 g. From these ingots 25-mm-long rods were machined to study the phase transformation by a dilatometer. These rods were then cold-rolled to strips, 2.4 mm thick. Annealing for austenitizing was done in tube furnaces in an argon or helium atmosphere followed by cooling in the water-cooled portion of the tube. Aging was done in a salt bath containing a neutral blend of Alkali nitrates and nitrites. Vickers hardness was measured using a load of 50 kg for 15 sec. Tensile tests were carried out on a hard beam tensile tester at a strain rate of 5 X lo-' per sec using flat samples with a gage length of 37.5 mm and a cross section of 1.25 by 6.25 mm. Estimated sensitivity was 5 K x strain and 0.35 kg per sq mm stress. Magnetic saturation was determined on small cylindrical samples, 2.5 mm in length and diameter, by measuring the force exerted by the gradient of a magnetic field of 1000 oe per cm in a mean field of 11,500 oe. The measured values could be reproduced within *1 pct. Coercive force was measured by a precision-type magnetic field probe in a magnetic coil as described by Foerster.5 The magnetizing field was 1300 oe. The samples were 5 cm long, 1 cm wide, and 2.4 mm thick. he coercive force was measured to within +0.1 oe. Electrical resistivity was measured by using a potentiometer on flat strips with a gage length of 100 mm and a cross section of 2.5 by 0.5 mm. The accuracy of the measurement was 0.1 pct but the reproducibility of the measured specific resistivity among different samples was in the order of 1 pct. The method used to prepare the samples for electron transmission has been reported elsewhere.3 RESULTS Fig. 1 shows the influence of deformation after annealing on the resistivity, hardness, and coercivity. The samples were annealed for 30 min at 1000"C,

Jan 1, 1968

By Craig R. Barrett

The influence of the stress dependence of the dislocation density on the overall stress dependence of The steady-state creep rate is discussed. Experimental measurements of dislocation densities and creep rates jor an Fe-3.1 pct Si alloy tested over a wide range of stress are presented which indicate a close correlation between the two quantities. EXPRESSING the stress dependence of high-temperature steady-state creep rates has been the subject of numerous investigations over the past decade. From these investigations have emerged a few general equations which fit most of the available data reasonably well. Garofalo 1 has proposed that for a wide range of stress and temperature the creep rate, i, can be expressed by a relationship of the form: where A, ß, and n are temperature-dependent and is the applied stress. Eq. [I] gives a stress dependence of a at low stresses and exp(nßo) at high stresses, both consistent with experimental observation where n = 5. A number of other investigatorshave proposed a similar expression where: where m and w are in general functions of temperature. Theoretical justification for Eqs. 111 and [2J comes from two different approaches, theories based on dislocation glide3-5 and theories based on the balance between work-hardening and recovery.' Dislocation glide theories predict where p is the mobile dislocation density and V is the activation volume. In order for Eq. [3] to predict a on stress dependence at low stresses with n = 5, it is necessary for p to be a strong function of stress, about proportional to u3 or u4.436 Recovery models of creep start with the general expression:' where r is the recovery rate and h is the work-hardening rate, and then employ a detailed model to determine the stress dependencies of r and h. As example, weertman2 has described a model based on pile-up hardening which results in an expression similar to Eq. [2] with m = 2 and p = 2.5. A recent, seemingly more general approach suggested by McLean is to use Friedels dislocation network growth expression to calculate the stress dependence of r. This model predicts r = p 3,2 and, as h is taken to be a relatively weak function of stress, the stress dependence of i should be about proportional to p3, 2. Once again, it is required that p be a strong function of stress to yield i This recovery model is by no means complete as the stress dependence of network growth is calculated in the absence of an applied stress meaning that r should probably be a stronger function of stress than given by p3, 2 and also some recent work by Mitra and McLean8 suggests that the stress dependence of h may be as large as Because of the importance of the stress dependence of p in determining the overall stress dependence of the strain rate it seems reasonable to examine this relationship in some detail. Measurements made on dislocation densities present during high-temperature steady-state creep generally obey the following relationship a =o0 + aGVWp [5] where uo is usually called a friction stress, a is a numerical constant about equal to unity, G is the shear modulus, and b is the Burgers vector. Depending on the magnitude of uo, data obeying Eq. [5] can give rise to a range of stress dependencies of p. For example, if we assume that the expression where 6 is some constant, adequately represents the stress dependence of p over a range of o, then from Although Eq. [6] obviously breaks down when u 5uo for uo 6 can vary over a wide range of values. In particular, if u > a, > 0 then 6 will be greater than 2. As an example the data of Ishida and McLean are plotted in Fig. 1 showing excellent agreement with dynes per sq cm) and also showing good agreement with a p cc u3 dependence when plotted on a log-log basis. As oo increases 6 tends to increase and correspondingly the stress dependence of the predicted creep rate should also increase,* as-

Jan 1, 1968

By Paul A. Farrar, Sanford Adler

The Tz-Zr system was reinvestigated using both metallographic and X-ray diffraction techniques. It mas found that titanium and zirconium are soluble in all proportions in both the a and 0 phases. The minimum in the transformation was found at 50 at. pct and 535°C. THE Ti-Zr system has previously been the subject of several investigations.1-6 A study by Hayes et al.5 using magnesium-reduced titanium and zirconium melted in graphite crucibles indicated that the system was a continuous series of solid solutions in both a and 0 phases with a minimum at approximately 545°C and 65 pct* Zr. These conclusions were substantiated by the work of Duwez4 as well as by the limited data of Craighead et al.,3 Fast,2 and deBoer.1 However, a more recent investigation of the titanium-rich region by Ence and Margolin6 indicated that the solubility of zirconium in a, titanium at 500°C is approximately 22 pct with the a + 0 field extending to approximately 47 pct Zr. Therefore in order to resolve this discrepancy the following investigation was initiated. EXPERIMENTAL PROCEDURES The alloys used in this investigation were prepared as 20- to 30-g buttons by nonconsumable electrode melting in a helium atmosphere. The starting materials were Bureau of Mines titanium BHN 71 and Foot Mineral iodide crystal bar zirconium. The titanium was premelted before the alloys were prepared to avoid excessive weight losses in the final melting. The compositions of the alloys prepared were as follows: Ti-12.0, 22.2, 29.0, 39.6, 50.0, 58.0, 72.4, 83.5. and 90.8 pct Zr. Prior to heat treatment the alloys were cold-worked 10 to 20 pct, stopping at the first signs of cracking. Specimens for heat treatment were wrapped in molybdenum sheet and annealed in argon-filled quartz capsules for the following times and temperatures: 750°C-40 days, 675°C-61 days, 600°C—109 days, 575°C-112 days, 550°C-112 days, 525°C—127 days, and 450°C —153 days. Quenching was accomplished by breaking the capsules in an iced-brine solution. The standard techniques used for polishing the specimens involved belt grinding, grinding on emery paper, polishing electrolytically, and etching with Remington "A" etch7 or "R" etch 8 Debye-Scherrer X-ray powder photograms were obtained for a number of samples using a 114.6-mm camera and CuK, radiation. Exposure times were from 19 to 23 hr. The powder samples were obtained by filing to 270 mesh size. After filing the samples were wrapped in molybdenum foil capsuled in quartz and reannealed at the temperature of original heat treatments; following the heat treatment the samples were quenched into iced brine without breaking the capsules. RESULTS AND CONCLUSIONS On the basis of the microstructural examinations of the heat-treated samples and of the X-ray diffraction data, the Ti-Zr system shown in Fig. 1 was constructed. The data indicate that a, and 0 titanium form a complete series of solid solutions with a, and ß zirconium. The minimum was found to occur at 65 pct (50 at. pct) Zr and 535°C, in excellent agreement with the earlier investigations,1-5 see Fig. 2. Typical microstructures are shown in Figs. 3 to 7. Figs. 3, 4, and 5 show the 22.2, 39.6, and 50.0 pct Zr alloys after heat treatment at 675°C for 61 days with the 22.2 pct Zr showing equiaxed a, and the 39.6 pct Zr alloy a + transformed ß, while the 50 pct Zr alloy shows only transformed B. Figs. 6 and 7 show the 29.0 and 39.6 pct Zr alloys after heat treatment for 109 days at 600°C. The 29 pct Zr alloy has an equiaxed a structure while the 39.6 pct alloy has a partially recrystallized a+ß structure. X-ray diffraction data obtained from the 50 pct Zr alloys after heat treatment at 525° and 450°C as well as from the as-cold-rolled material showed only those lineos which couid be indexed a: a titanium, good agreement with the previously published values. 2,4,5,9 Chemical analysis* of the 50 pct Zr alloy

Jan 1, 1967

By K. W. Smith, E. A. Thomas

Various grades of synthetic mullite have been developed in recent years to replace or supplement natural sources of mullite deriued from the mullite group of minerals consisting of sillimanite, kyanite, and andalusite. Raw materials and heat treating processes used in making synthetic mullite are described. Chemical and physical data are given for typical grades and crystalline structure is illustrated with micrographs. Use of synthetic mullite as a refractory material in the glass and metallurgical industries is discussed. Mullite (3A12O3.2siO2), the only stable compound formed in the alumina-silica system, is usually present to some degree in all aluminum silicate ceramic products. The formation of mullite is considered beneficial to give rigidity to the structure and is dependent upon the ratio of Al2O3 to SiO2 in the original composition, particle size, degree of mixing, firing temperature, cooling rate, and the presence of auxiliary glass-forming fluxes. Mullite may also be formed at the reaction interface of fire clay or alumina-type refractories in contact with glass or slag melts. The term synthetic mullite is commonly used today to identify a class of sintered and fused aggregates or grains in the alumina-silica system having a highly developed mullite structure but derived mainly from raw materials other than the sillimanite group of minerals. Within the past 15 years extensive research has been done to develop economical processes to form sintered synthetic mullite aggregate to replace calcined Indian kyanite in super-refractories. Severa1 brands of such mullite are now being produced in commerical quantity and finding extensive use in refractories. Based on the service results of such refractories in many applications throughout the metallurgical, ceramic, and glass industry these developments have been considered successful and suitable substitutes for Indian kyanite now appear assured. EARLY DEVELOPMENT The conversion of kyanite, sillimanite and anda-lusite minerals of the sillimanite group to mullite and their use in refractories and porcelain have been discussed quite extensively in the literature by peck,' Grieg,' Riddle and Foster,3 Bowen and Grieg,4 and others and will only be mentioned here for reference to compare properties with synthetic mullite. In 1928, curtis5 reported on the development of a high temperature gas-converter process for forming synthetic mullite. The raw materials were derived mainly from lumps of high alumina clay of the correct natural composition or blends of clays and alumina that was interground and briquetted to form a suitable charge to maintain a surface combustion firing within the converter. Curtis was, no doubt, the first to illustrate by micrographs in natural color the crystalline structure of mullite derived from kyanite and mullite derived by sintering clay and alumina mixtures at temperatures above cone 32 (3123°F) and by electric fusion. In 1937, sei16 was issued a patent covering the use of a mixture of alumina-silica minerals and alumina in the proportion to form a mullite-yielding material at temperatures in excess of 3100' F. During the period from 1930 to 1940, economic conditions were not favorable for the production of synthetic mullite mainly due to an adequate supply of good grades of Indian kyanite ore suitable for conversion to mullite. Uncertain conditions on availability of the Indian kyanite during the early stages of World War II fostered further study on the development of synthetic substitutes. In 1943, McVay and wilson7 reported on an extensive investigation of domestic substitute materials. Their work covered essentially the use of mixtures of electric furnace mullite, calcined topaz, and calcined domestic kyanite. Compositions were found that gave equivalent or better hot load strength than Indian kyanite in mullite-type brick compositions; however, the calcining of the topaz presented certain physical and chemical problems on the disposition of silicofluoride and hydrofluoric acid while the high cost of electric furnace mullite was a limiting factor. In this work it was pointed out that water-quenched fused mullite was found to be unstable on reheat and gave poor hot load strength due to excessive glass present whereas the slow cooled or annealed mullite contained large crystals of mullite and corundum with little glass and gave superior results.

Jan 1, 1961

By J. J. Stokes

Literature on the electrolysis of aluminum from cryolite melts and on the structure of these melts is surveyed critically. Data on density, freezing point, and other properties are reviewed. Theories of the electrolysis are examined in the light of these data. Two theories are presented which account equally well for the observations. ALTHOUGH the production of aluminum is a large-scale industrial process, consuming approximately 3 pet of all of the electric current generated in this country, the mechanism of the Hall Process remains a 70-year-old mystery. It is a remarkable fact that the aluminum industry, which was established largely through research and owes much of its growth to research, still employs as its basic process the one developed by Charles Martin Hall while he was still a young man working in a woodshed. There are, of course, modifications in detail and a tremendous expansion of the size of the units used, but basically the process employs carbon anodes and a carbon-lined iron vessel as a cathode for the electrolysis of alumina dissolved in molten salt. Of the almost infinite variety of salts available, the relatively minor Greenland mineral, cryolite, 3NaF.A1F3, is still the only one which gives good performance in the electrolysis. In the early days, the process was thought of as a simple one. The dissolved alumina dissociated and, during the electrolysis, the aluminum was carried to the cathode where it was discharged and collected in a pool of metal. The oxygen was carried to the carbon anode where it reacted to form primarily carbon dioxide together with some carbon monoxide. About the only virtue that can be claimed for this hypothesis is that of simplicity. The actual mechanisms must be tremendously more complex. This paper is devoted to a rather narrow part of the whole subject, namely, what ions are present in the bath, and by what mechanism the current is carried. The complexity of the literature on this system is demonstrated in Table I, which shows the ions postulated as being present during the process. This system is not easy to investigate. Cryolite melts at about 1000°C, so that all the investigations are at relatively high temperatures. Molten cryolite fumes in air, particularly if excess aluminum fluoride is present. The cryolite changes composition on heating at 1000°C, principally by reaction with moisture in the air, but apparently also by reaction with oxygen. Cryolite reacts with most of the customary materials of construction, and those that are not attacked by cryolite seem inevitably to react with molten aluminum. Graphite is the only common material that is inert to the electrolytic bath. Pure cryolite can be held in platinum. There is hope that some of the newer refractories will stand up in bath, and their development for this purpose would be a major advance in the field. The techniques to be discussed, then, are not the most advanced ones. Rather, they are examples of old standardized methods applied under difficult conditions. The principal methods that shed real light on the mechanism are density, electrical conductivity, freezing-point lowering, transport number, viscosity measurements, and reactivity of bath with carbon dioxide. The first measurement to be discussed is density. This procedure is relatively straightforward. A hollow platinum bob is suspended by fine platinum wire from an analytical balance into the melt being investigated. Density1-4 of the system sodium fluoride-aluminum fluoride is shown in Fig. 1. There is a maximum in the density near the cryolite composition, but actually the maximum is on the NaF-rich side of cryolite, close to the composition NaF - Na3AlF8. Density measurements are also useful in giving a clue to the nature of cryolite-alumina melts.1, 4 On the first addition of alumina, density decreases, Fig. 2, although the density of alumina, either solid or liquid, is higher than that of cryolite. These density results indicate that the systems are not simple. A great deal of effort has been spent in measuring the electrical conductivity of molten cryolite and of cryolite with various additives. Conductivity measurements are quite easy for fused salts that can be measured in a dip cell, but no successful dip cell has been made available yet for cryolite. Recourse is had

Jan 1, 1959

By G. T. Hahn, C. N. Reid, A. Gilbert

An evaluation is made of the possible cautsal relationship between twinning and fracture in molybdenum. For both single and poly crystalline material no instance of twin-induced fracture was observed. Instead brittle fracture was found to be slip-induced at heterogeneities. For single-crystal material, the yield stvess in compression and the fracture stvess in tensiow obey a similar angular- relationship which follows approximately a 1/cos2 ? law. where 0 is the angle between the specimen axis and the nearest (100) plane. This sittlilarity between yield and fracture behavior casts doubt on the interpretations made previoltsly that a 1/cos2? relationship supports a critical normal fracture stress criterion. SINCE fracture in brittle materials takes place at stresses an order of magnitude lower than the theoretical strength of the lattice, it must be postulated that some stress-concentrating effect is operative during the fracture-initiation process. Several mechanisms have been proposed whereby the necessary stress concentrations could be produced. The well-known Cottrell mechanism1 describes a dislocation interaction which can lead to the formation of an incipient cleavage crack on a cleavage plane, and both zener2 and stroh3 have discussed models which predict the stress concentration at the intersection of a slip band with a grain boundary. When twinning occurs twin/twin intersections and twin/grain boundary intersections represent another possible means of fracture initiation. Although still controversial, the concept of twin-induced fracture is supported by a weighty mass of evidence, which has been reviewed in a recent paper.4 This investigation was conducted in order to assess the extent to which the brittleness of molybdenum can be ascribed to this cause. Emphasis was placed on seeking direct metallographic evidence for twin-induced fracture such as arrangements of twins located at the fracture origin. EXPERIMENTAL PROGRAM Materials. The experimental materials are described inTable I. From the chemical analyses and estimates of the amounts of interstitials likely to be retained in solution,5 it is concluded that all were mul-tiphased systems. X-ray diffraction experiments6 showed no evidence of preferred orientation in the polycrystalline materials. Single crystals were grown from Molybdenum X and Y using the floating-zone technique,' in a vacuum of better than 3 x 10-5 Torr. However difficulties were experienced with Molybdenum X due to violent gas evolution from the molten zone, and additional crystals (Crystals 3 to 6) were produced by annealing for 5 1/2 hr at 2300°C under a vacuum of 10-4 Torr. Techniques. A series of tension, compression, and bend tests was conducted. Tension tests were used to demonstrate brittle behavior, to measure brittle-fracture stresses, and to provide fractured specimens for metallographic inspection. Compression tests were employed in order to obtain some ductility and a measure of the yield stress. Furthermore, it was considered that compression loading would permit the study of crack nucleation in the absence of propagation. The bend tests were conducted to facilitate identification of the fracture origin, which would be expected to be at, or near, the tensile surface of the sample. Tests were carried out at temperatures between 78" and 298°K attained by means of a liquid-nitrogen evaporator of modified Wessel design.' Specimens were fashioned by mechanical grinding, and, prior to heat treatment, were electropolished at 10 v in a 3:l mixture of ethyl alcohol and sulfuric acid, using a stainless-steel cathode. Except where noted, a strain rate of 4 pct per min was used. All specimens had a gage section 0.75 in. long; diameters of 0.10 and 0.20 in. were adopted for the tension and compression specimens, respectively, the former of single shoulder design, the ends being gripped in split collets with a conical bearing surface. In the bend test, electropolished specimens measuring 0.080 by 0.25 by 1.25 in. were deformed at 78°K by four-point loading. The bending device had spans of 1 in. between the outer and 4 in between the inner fulcra; it was stressed between the compression anvils of the Instron machine at a constant deflection rate. EXPERIMENTAL RESULTS Polycrystals. Tension and Compression Tcsls. It is apparent from Fig. 1(a) that above 170°K fracture of Molybdenum X takes place at stresses equal to or greater than the compressive yield stress whereas

Jan 1, 1967

By M. M. Rao, P. G. Winchell

The growth rates of bainitic plates were measured at 400°C in Fe-Ni-C alloys containing 0.10 atom-fract~on nickel and 0.0012 to 0.0075 atonz-fraction carbon. The growth rates are adequately represented by where xc is nearly the atom fraction carbon of the bulk austenite and PXCy is nearly the carbon atom fractlon in the ferrlte of radiids p In equilibrium with austetzite. The form of the equation is that predicted by a model in which carbon diffusion in austernite controls the gvowth, but the numerical constatnt is two orders of magnitude below that suggested by the model. THE growth of bainitic plates in steel is often assumed to be controlled by the diffusion of carbon away from the advancing plate tip. This hypothesis predicts that the growth rate will increase as the carbon content of the austenite, xCz, is reduced toward the carbon content of the saturated ferrite comprising the plate tip, PxCY The growth rate should vary approximately as (xCg- pxCy)-1. Experimental observation of the growth behavior at low carbon levels should provide a significant test of this model. An alloying element in addition to carbon is required so that low-carbon austenite can be experimentally observed while undergoing bainitic transformation. Nickel was selected. The presence of nickel complicates the interpretation of the data in two ways: First, diffusion of nickel during the transformation would make analysis very difficult. Nickel is assumed immobile during the transformation. Second, nickel affects the solubility of carbon in ferrite and austenite in equilibrium. This effect has been evaluated.' At the completion of our experimental work Goode-now et al.2 published data in essential agreement with the observations to be reported here. Since their discussion is abbreviated and their data are scanty in the region of interest, we believe the present work is of significance. I) THE MODEL OF BAINITIC PLATE GROWTH The rate of lengthening of a plate is assumed to be controlled by the diffusion of carbon from the advancing ferrite-austenite interface into the surrounding austenite. The precipitation of carbides is assumed to be a secondary process. For ease of analysis the carbon-atom ratio,* pxCy, of austenite in equilibrium with ferrite which is convex with minimum curvature radius p, and the carbon-atom ratio, PxCY, of that ferrite in equilibrium with austenite are assumed independent of location on the ferrite-austenite interface. Since these carbon contents vary with the radius of curvature of the ferrite, p, their assumed positional independence must be held as an approximation. The consequences of these assumptions have been developed approximately by zener3 and Hillert,4 and the resulting equation for a platelet has been applied to bainite by Speich and cohen5 and Kaufman, Radcliffe, and Cohen.8 The Zener-Hillert equation* for plates is: The analysis of Hillert is supported by that of Hor-vay and cahn7 which involves no mathematical approximations but does include the assumption that the a/y interface coincides with an isoconcentration line. The solutions of Horvay and Cahn for elliptic paraboloids are replotted in Fig. 1. The shape of the paraboloid is expressed in terms of the ratio of the principal radii of curvature at its tip, A =p1/p2, which is also the ratio of the minor to the major axis of the elliptic cross section. The Zener-Hillert equation for plates is also plotted. The agreement is within a factor of two for (pxyaCr - xyC )/(xyC - PxCaY) between 0.5 and 100. This is the range of interest here and in most other work on bainite. The original form of the Zener-Hillert equation was the form given above with the right-hand side replaced by (pxCya -xCy)/(PxCya). This replacement is not appropriate here. 11) THE EXPERIMENTAL PROCEDURE Alloys were prepared and three kinds of experiments carried out. Continuous-cooling-transformation experiments were carried out on wires by measuring temperature and resistance during continuous cooling. Isothermal-transformation experiments were carried out on wires by measuring electrical resistance as a

Jan 1, 1968

By P. L. Rittenhouse, M. L. Picklesimer

A rapid and seniquantitative method of determining prefered orientation on large numbers of. Zircaloy-2 specimens was desired. knoop microhardness measurerrzetzls were irvestigated as a solldtion to this pro6lem. The variation of Knoop microhardness measurerlerzts on selected planes as a function of 'irzdenle axis relutilje lo cryslallograplzic or fabrication divectals were used to corzstrrcl a polar coordinate hardness contour map. With use of an empirical relationslip between the single-crystal hardnesses and those of the polycrystalline material conentional pole figures could be constructed which compare favorably also obtained. To determine preferred oriention qualitatively from hardness data requires a minimum of twelve measurements per plane on three, preferattention to grain size, specimen prepartion, and in-rreinetzt, and analjlsis is of the order of- 45 to 60 rrin. THE design of structures from Zr alloys requires consideration of preferred orientation and the resulting anisotropy of mechanical properties. Rapid and semi-quantitative methods of evaluating anisotropy and of determining preferred orientation are needed for quality control and for examining the large number of test specimens required in development programs. The variation of Knoop microhardness with indenter orientation has been studied in single crystals of several hcp metals including titanium.' beryllium,' magneium, and zinc.4 The maximum hardness observed on any crystallographic plane other than the basal plane invariably occurred when the long axis of the Knoop indenter was either parallel or perpendicular to the projection of the [ OOOI.] direction on the plane of examination. When the major slip mode was (0001)(i2i0j the maximum hardness occurred at the parallel positio! but when the operating slip system was {10i0) (i210) the hardness was a maximum perpendicular to the [0001] projection. A minimum hardness was always observed at a rotation of 90 deg from the maximum. It follows that the orientation of the projection of the [0001] can be determined on any non-basal plane by making hardness measurements at a number of indenter orientations. The determination of the orientation of the [0001] projection on two non-parallel, preferably orthogonal, surfaces of the specimen will allow location of the [0001] direction in the specimen. It seems possible that such measurements could be used to examine, at least qualitatively, the preferred orientation existing in polycrystalline hcp materials. An investigation of the microhardness anisotropy in Zircaloy-2 was undertaken to ascertain whether these measurements could be used for this task. EXPERIMENTAL PROCEDURE Single crystals of Zircaloy-2 were grown by an a-8-a annealing sequence using electron-beam heating.= The orientation of the crystals was determined by a conventional back-reflection Laue technique. The crystals were then mounted on a goniometer head and the desired crystallographic faces were milled and chemically polished. Polycrystalline Zircaloy-2 specimens were prepared from fabricated sheets or plates. Inverse pole figures for these materials were obtained using the X-ray diffraction techniaue described by Jetter, McHargue, and illiams.' A Wolpert-Greis Micro-Reflex hardness-testing machine was used to make the Knoop microhardness measurements. The single-crystal and polycrystalline specimens were loaded to 0.5 and 2.0 kg, respectively. Determination of the scatter of hardness numbers as a function of applied load for several indenter orientations on several specimen surfaces showed that the loads selected were the lightest consistent with minimum scatter. Heavier loads did not appreciably decrease the scatter and produced hardness impressions too large to be conveniently measured with the equipment used. Seven crystallographic planes of the single crystals were examined, while six planes of examination were used in studying Zircaloy-2 polycrystals. The specimens were rotated 10 to 15 deg after each measurement and from four to eight impressions were made at each angle of rotation. RESULTS The two angles which were used to relate crystallographic directions and planes in the hcp cell to the planes of examination of the single crystals are shown in Fig. 1. 8 is the angle between the c axis. [0001]. and the normal, N, to the plane of examination. a is the angle between the long diagonal of the Knoop indenter and the projection of the c axis on the plane of examination. For exampIe, if P = 90 deg and a = 0 deg, the plane of examination is of the family

Jan 1, 1967

By A. J. Griest, P. D. Frost, H. A. Robinson

The flow characteristics and uniform elongation of alpha-beta titanium alloys in the solution-treated condition were shown to be markedly affected by the solution temperature. Two classes of alpha-beta alloys were distinguished, based on the effect of solution temperature on the uniform elongation. Martensitic alpha-beta alloys, which are relatively weakly beta-stabilized, showed decreasing values of uniform elongation as the solution temperature was initially increased. However, after solution-treatment at still higher temperatures in the alpha-beta field, the uniform elongation of these alloys was again high, and often attained its maximum value. Nonmartensitic alpha-beta alloys, which are more heavily beta-stabilized, showed a continuous decrease of uniform elongation with increasing solution temperature. The behavior was rationalized in terms of the alpha-beta ratio and the alloy content of the beta existing at the solution temperature. The data indicate that in commercial practice close temperature control may be required to get maximum uniform elongotion, and hence, maximum potential formability, in solution-treated sheet. Bend-test data also were obtained for the solution-treated conditions. A MOST important objective of current titanium research is the development of age-hardenable alloys with superior formability in the solution -treated condition. Alpha-beta titanium alloys have been shown to be amenable to high-strength aging treatments after solution-treatment in the alpha-beta field.' However, heat-treatment data on the properties of solution-treated sheet, such as uniform elongation, minimum bend radius, and flow properties, which have a bearing on the potential formability, have not been widely available. This paper presents only the most significant results of a research program conducted at Battelle for the Air Force in an effort to develop sheet alloys that can be formed readily as solution-treated and subsequently aged to very high strengths. Data for 10 compositions representative of the more than 25 alloys studied in this program are presented. A primary objective of the paper is to demonstrate the pronounced dependence of the flow characteristics and uniform elongation on solution-treatment temperature. This effect is believed to be vitally important in the commercial heat-treatment of age-hardenable titanium sheet alloys. Experimental Procedures Melting and Fabrication—The nominal and actual compositions, beta transi temperatures, and rolling temperatures of 10 of the 30 alloys studied are presented in Table I. Stock :€or two of the alloys, E (Ti- 8Mn) and J (Ti-6A1-4V) was obtained from commercial heats. The remaining heats, except D and I, were double melted as 10-lb heats in a consumable-electrode furnace. Melting stock was 120 Brine11 hardness sponge. The oxygen and hydrogen analyses spotted throughout the heats indicate the range of interstitial levels resulting from the melting practice used. Heats D and I were melted as 20-lb ingots with the same grade of sponge. These ingots were cut in half and one portion used in the present evaluation. The ingots, which were about 4 in. diam and 4 in. in height, were upset forged and drawn at 1750°F to sheet bar 5/8 in. thick by 2 1/2 in. wide in such a manner that the top of the ingot corresponded to the top of the sheet bar. Slabs of the sheet bar, 5 1/2 in. in length were scalped to 1/2 in. thickness and rolled at the temperatures indicated in Table I to approximately 0.055 in. sheet. Elongation during rolling took place at 90" to the original forged length. The fabrication procedure used is described in some detail since the experimental heats showed considerable directionality in mechanical properties. The rolling procedures for the commercial heats were unknown, but were such as to produce essentially isotropic properties. All heats, as rolled, showed microstructures typical of alpha-beta alloys worked in the alpha-beta field; that is, the structures consisted of equiaxed alpha particles in a beta matrix. Heat Treatment— The effects of solution and aging heat-treatments on the properties of the alloys were evaluated uSing longitudinal and transverse tensile and bend coupons sheared from the sheet. Two or three solution-treated conditions were evaluated for each alloy. In addition, the alloys were also tested after annealing at 1200°F for 4 hr and furnace cooling. The solution-treated and annealed conditions were those in which the alloys might be expected to

Jan 1, 1959

By M. E. Wadsworth, T. L. MacKay

Sintered UO, samples were leached in sulfuric acid solutions of various concentrations. A pressurized system was used so that it was possible to investigate the kinetics of the reaction to 270°C with oxygen overpressures as high as 900 psi. The rate was observed to be a function of the concentration of hydrogen ions and directly proportional to the partial pressure of oxygen. Evidences are presented which indicate that a UO2 surface site reacts with a molecule of water to form a hydroxyl complex which in turn can dissociate with the characteristics of a weak acid. A rate determining step has been proposed which involves the reaction between an oxygen molecule and the hydroxyl complex on the surface of UO,. ThE 2 principal methods for uranium dissolution are carbonate and acid leaching. The sulfuric acid leach is the more popular and is used for the treatment of the majority of the ores of Africa, Canada, and the United States. Low recoveries in basic leach circuits led investigators at the University of British columbia1 to study leaching of uranium ores in pressurized vessels. Early in the study of dissolution of uranium it was found that only uranium in the hexava-lent state could be leached in acid or basic circuits. Therefore, the use of oxygen over-pressure in an autoclave offered an interesting approach to solving the low recovery problems of carbonate leaching. UO, was used in this study because it could be obtained in high purity and also because it is representative of the most refractory of the primary uranium minerals. A pressurized system was used to provide a means whereby important temperature and pressure parameters could be varied for the evaluation of the kinetic processes. The mechanism for the dissolution of UO2 should be similar for any of the uraninite type minerals. At the present all of the kinetic studies that have been conducted have been in carbonate media. Peters and Halpern2 carried out a kinetic study of the leaching of pitchblende. Their specimens were pitchblende ores selected on the basis of high grade and homogeneity. Pearson and wadsworth3 conducted a kinetic study of the dissolution of UO2 in carbonate solutions with results very similar to those obtained by Peters and Halpern. EXPERIMENTAL The UO2 as received* was found by spectroscopic *Mallinckrodt reagent, supplied by the Atomic Energy Commission. analysis to have a purity of 99.94 pct 0.03. It was ground in a mechanical agate mortar and screened through a 400-mesh sieve. Thin flat disks of UO2 were prepared by pressing the sized powder in a specially constructed die at a total pressure of approximately 25 tons per sq in. The pressed disks were approximately 0.25 cm thick, 1.6 cm diam, and 3.5 g in weight. As pressed, the samples were approximately 65 pct of theoretical density. It was essential that a binder such as poly-vinyl alcohol be added before pressing to prevent formation of cracks when fired. It was found by trial and error that pressed disks sintered close to 1870°C in a hydrogen atmosphere, reach densities between 91 and 91.5 pct of the theoretical density. At this density the samples had no measurable porosity based upon a 2-hr emersion in boiling water. An X-ray examination of these sintered UO2 disks showed them to be identical with the original UO2 received. Reaction of UO2 with the alundum furnace core was prevented by placing molybdenum between the samples and the core according to the method of Corwin and Eyerly.4 Leaching studies were carried out in a specially designed autoclave, the details of which have been presented e1sewhere.6 The main features of the equipment as applied to a kinetic study are: 1) solution samples may be removed during the course of a single run; and 2) temperature and agitation are carefully controlled. Two-ml samples removed from the autoclave during the course of a run were analyzed for U3O8 content with a Beckman model DK-2 spectrophotometer by the method of

Jan 1, 1959

By J. B. Cohen, O. F. Kimball

Aging of specimens of Au-20 at. pct Ni and Au-40 at. pct Ni has been followed with electron microscopy, resistance, magnetic measurements, and X-ray diffraction. The periodic structures observed by electron microscopy in Au-Ni alloys by Fisher and Embury are shown to be due to nickel-rich prepre-cipitates. Assuming this alloy system undergoes spinodal decomposition, our observations and available data on thermodynamic properties and elastic constants indicate that the gradient energy coefficient in this system is of the order of 10-5 ergs cm-1 . Shifts of X-ray peaks in this system have been found to be due primarily to residual stresses, not faulting. A large effect of applied stress during aging was detected by X-rays and electron microscopy for the Au-20 at. pct Ni alloy. The presence of a preprecipitation stage during aging of gold-rich Au-Ni alloys for short times below 300°C has been indicated by several previous investigations. Changes in electrical resistivity,1"3 elastic modulus,4 superparamagnetisrn,5 positions of X-ray diffraction peaks,6 and hardness7 have been studied. Electron diffraction and microscopic studies by Fukano8 and Fisher and Embury9 respectively showed that the precipitation process resulted in the formation of periodic composition fluctuations—perhaps spinodal decomposition. MOSS10 detected a satellite with X-rays in quenched specimens, but the wavelength was much smallerthan that found by Fukano. Recently Woodilla and Averbac11 detected a modulation similar to that found by Moss, but with electron diffraction. They suggested that the microstructures observed by Fisher and Embury may be simply due to a Moir'e effect from a back deposit of gold during electropolishing. Satellites in electron diffraction can be enhanced by small bends or tilts of a foil. Even if this were not the case, asymmetric satellites, as are found in Au-Ni are difficult to analyze. They are principally influenced by the large differences in atomic size in this system, and obtaining information on the associated composition fluctuations depends on assumptions as to whether or not there are isolated clusters or composition "waves", and in the latter case whether or not the entire specimen has decomposed. Assuming that decomposition was complete in alloys aged at low temperatures, Woodilla and Averbach suggested that the satellites indicated a composition which varied about the average value by only± 5 pct, much less than that predicted from the phase limits, Fig. 1; they attributed this small variation to a cessation of the reaction caused by the loss of mobile vacancies. In Ref. 12 it was shown that vacancies are trapped by the preprecipitate in this system. Furthermore, after reversion, aging proceeds at a much slower rate than immediately after a quench from the solution temperature,5'11,13 indicating the importance of vacancies in the kinetics. In some senses Au-Ni is a favorable system for studying preprecipitation and reversion mechanisms because of the simplicity of the equilibrium diagram14 and the availability of good thermodynamic15 and diffusion data.16,l7 The calculations necessary to relate the decomposition process to classical nucleation and growth or to spinodal decomposition, as well as those necessary for understanding reversion mechanisms, can, therefore, be made. As an example, the position of the chemical spinodal, calculated from the thermo-dynamic data of Sellars and Maak15 with the method described by Rundman and Hilliard,18 is included in Fig. 1. It is compared to the chemical spinodal calculated from the equilibrium miscibility gap by Cook and Hilliard's method.l9 Included is the coherent spinodal suggested by Golding and MOSS," using measured elastic constants for their calculations and the same ther-modynamic data. The spinodal estimated by Woodilla and Averbach,11 by determining the temperature limits for the observation of the satellites discussed above, is also given. Actually this last curve is open to question on the following grounds: As a phase boundary is approached the spacing of particles or the wavelength

Jan 1, 1970

By D. A. Elgillani, M. C. Fuerstenau

With either sulfonate or oleate as collector, quartz responds to flotation with moderate additions of calcium only at moderately high pH, where some portion of the activator has hydrolyzed to caOH+ . Calculations of the concentrations of various ionic and precipitated species of calcium and collectors suggest that the products of [(CaOH+) (RSO3)] and [(CaOH+)(01-)] determine whether flotation is obtained under specific conditions. Ion products on the order of 10-12 were calculated for both the sulfonate and oleate systems. The activating effect of calcium ion in nonmetallic flotation systems is of considerable interest because of the normal presence of calcium in natural water. As a result, this phenomenon has received quite some attention in the past. Kraeber and Boppel1 showed that quartz could be activated by calcium above pH 10 with sulfonate as collector. The feasibility of selectively separating quartz from hematite with calcium activation at relatively high pH was demonstrated by Clemmer, Clemmons, Rampacek, Williams, and stacy.2 Cooke and Digre3 showed with a bubble pick-up method that the minimum quantity of calcium ion required as activator for complete pick-up of particles occurs at pH 11.5 for an addition of 20 mg per liter sodium oleate. They also showed that larger additions of calcium (10-fold increase per unit decrease of pH) must be added for complete bubble pick-up as the pH is reduced. Schuhmann and Prakash,4 using a vacuum flotation technique, found that quartz could be floated with moderate additions of calcium chloride and oleic acid at neutral pH, providing the metal ion was present in stoichiometric excess over the quantity needed to form the normal soap with oleic acid. They also reported that calcium will function as an activator only in basic media. More recently, Eigeles and volova5 have shown that essentially complete flotation of quartz is obtained with 6 x 10-4 mole per liter calcium chloride and 1.7 x 10-5 mole per liter sodium oleate at pH 11.6. while no flotation is obtained at about pH 10.9 and below. The importance of adsorption of activator and collector at the air-liquid interface is also demonstrated in these systems. The important role that metal ion hydrolysis assumes in quartz activation systems was also demonstrated recently.6-8 A detailed investigation of metal activation in sulfonate flotation of quartz was undertaken in one system7 and yielded a number of interesting and important observations. Quantification of the data of this system7 to the extent desired was not possible, though, because certain species could neither be ignored nor accounted for accurately. These difficulties can be circumvented when calcium is involved as activator. This detailed analysis was undertaken to obtain a more quantitative explanation of calcium and metal ion activation in quartz flotation. EXPERIMENTAL MATERIALS AND METHODS Sodium alkyl aryl sulfonate9 mol wt 450, and pure potassium oleate were used as collectors. All other reagents used were reagent grade in quality, i.e., n-amyl alcohol as frother, KOH for pH adjustment, and calcium chloride. Conductivity water, made by passing distilled water through an ion exchange column, was used in the investigation. Quartz was prepared by leaching the sized sample (48 x 150 mesh) with HC1 until no iron could be detected in the leach liquor. The experimental equipment and procedure were the same as that described previously.6,10 EXPERIMENTAL RESULTS As the presence of precipitates was noted in all of the systems to which ca++ and collector were added, experiments were undertaken to determine the solubility products of calcium sulfonate and calcium oleate using a nephelometer. With this technique, collector is titrated into a known solution, which in this case was 5 x 10-5 mole per liter CaCl2 at pH 5.5. Upon precipitation of the calcium-col lector salt, e.g., calcium oleate, light is scattered and detected

Jan 1, 1967

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 N. J. Themelis, P. Spira

The efficiency of the reverberatory furnace operation in producing. slags of 1020 copper content depends on the mixing and flow conditions in the bath. Radioactize-tmcer tests have indicated the jkaction of bath volume engaged inflow and the mixing conditions in the bath. The factors controlling the flow pattern of slag have been classified as laminar transfer flow, natrsral convection, and flou, due to the rapid addition or removal of slag.. Similarity criteria for model studies have been developed. The pyrometallurgical processing of copper begins with the smelting of either flotation concentrates, or direct-smelting ores which have been partially roasted to calcines. These materials are generally smelted in a reverberatory furnace, Fig. 1, and separate into two liquid phases, a sulfide matte and an iron silicate slag. he matte is tapped and subsequently reduced to metallic copper in a converter, while the reverberatory slag is usually discarded without any further treatment. Molten slag from the converting operation is returned intermittently to the reverberatory in order to recover its high copper content (1 to 3 pct Cu). The reverberatory furnace is about 115 ft long by 30 ft wide. In general, the solid charge is fed at intervals through openings along the sides of the roof and forms sloping banks from which the molten materials trickle down into the bath; the charge banks extend over a length of about 70 ft from the firing wall. The depth of the slag and matte layers varies from smelter to smelter; in the Noranda furnaces, the slag depth is 24 to 30 in., while the depth of matte at the taphole is about 20 in. Apart from smelting, the functions of the reverberatory are to recover most of the copper content in the converter slag by physical and chemical interaction with the furnace bath, and to provide adequate time for optimum separation between matte and slag. The efficiency of these operations depends on the mixing and flow conditions in the bath and is reflected on the copper losses in the slag. In the present study, the reverberatory furnace is considered as an open-channel chemical reactor and the driving forces for material transport through the bath are examined by means of flow and mathematical models. FLOW CONDITIONS IN THE REVERBERATORY FURNACE To facilitate the study of mixing conditions in continuous-flow reactors, two idealized patterns of flow have been accepted by workers in this field.' The term "backmix" flow is used to describe complete and instantaneous mixing in the reactor (perfect mixing); all particles have the same chance of leaving the system, independently of their time of entrance, and the fluid is uniform in composition throughout the vessel. On the other hand, "plug" flow, or "piston" flow, assumes that a fluid element moves through the reactor without overtaking or mixing with fluid entering at an earlier or later time. In addition to the two idealized patterns of flow, "deadwater" flow accounts for that portion of the fluid which is moving so slowly that it may be assumed to be stagnant. According to the definition by evensppiel,' the cut-off point between active and stagnant fluid may be taken as material which stays in the vessel for a period twice the mean residence time. The flow patterns in real vessels may be approximated by a combination of the above flows. Thus, the vessel is assumed to consist of interconnected flow regions with various modes of flow existing between them. The flow pattern may be determined directly from the flow paths of fluid through the essel. -However, the difficulty of obtaining and interpreting such information has led to the alternate approach of determining the residence time distribution of fluid elements by means of stimulus-response studies. The stimulus is provided by introducing a tracer in the inlet stream and the response by the record of the change in tracer concentration in the exit stream from the reactor. Such tests have been conducted in glass tank furnaces using either chemical7"9 or radioactive tracers1'-'' and, in one case, experiments have been reported for a metallurgical furnace.'"

Jan 1, 1967

By J. D. Verhoeven

The effectiue distriblltion coefficient has been Measured in a series of vertical, normal freezing experirtzents with large current densities passing through the solid-liquid interface. The results indicate that the effect of the current on solute redistribution is due to electvotransport in the liquid. The high currents produced extensive mixing in the liquid which was considerably reduced by solidifying in small lubing. Analysis of the convection indicates that it probably vesulls from a horizontal temperature gradient produced by the Joule heating- of the electvic crirver~t. Due to the strong dependence of this convection upon the specimen radius, it is conclnded that only for specit~ens with radii of less than somewhere between 1 and 2 mm wilt electric field freezing be getlerally effec-tire at enhancing the purification of zone-melting experittierats in loe-melting alloys. Experiments on 0.8-mm lubes illustrate some interesting potential applications of this techniqne as a means of solute control on smcrll specimens. In a number of papers published within the last few years'-4 it has been found that passage of large dc currents through the solid-liquid interface of a freezing alloy produces a change in the solute redistribution accompanying the solidification. It had been predicted theoretically by Hucke et al.s and by Pfann and Wagner that such an effect would occur as the result of electrotransport within the liquid boundary layer at the solid-liquid interface. These authors independently derived the following relation between the effective distribution coefficient and the variables of the process: Where k0 is the equilibrium distribution coefficient, V is the mobility of the solute relative to the solvent, E is the electric field intensity, D is the solute diffusion coefficient, R is the rate of interface motion, and 6 is the boundary layer thickness. Both groups of authors show that this equation predicts the possibility of extending the purification ability of zone-melting experiments by the addition of an electric current. However, there are other effects in addition to electro-transport which could be produced by the high dc current and might, perhaps, invalidate the applicability of Eq. [I]. For example, high electric current might affect the interface reaction or perhaps the equilibrium distribution which was assumed to exist at the interface. It was the purpose of this work to determine the applicability of Eq. [I] by systematically investigating a simple system for which all of the necessary parameters were known. It was of particular interest for speculating on the potential usefulness of this technique to determine the maximum practical field intensities obtainable, and the effect of these high fields upon convective mixing in the liquid. The initial work in this study was published in a previous paper3 which will be referred to as I. In that work, a current density of 2000 amps per sq cm was used with specimen diameters of 5 mm. The results gave a qualitative confirmation of Eq. [I.], and also showed that a large amount of convective mixing was produced in the liquid by the current. The present study is an extension of that work to smaller specimen diameters and higher current densities. Two points were overlooked in I and will be emphasized here: a) the value of ko has not been well-established in the Sn-Bi system and b) the observed convection could be due to thermal convection produced from the Joule heating. EVALUATION OF k0 To evaluate Eq. [ I.] it is necessary to know the value of the equilibrium distribution coefficient, k,. Tn I the value of k, was taken as 0.3 from a published phase diagram.7 According to ansen' the best data on the phase boundaries of the Sn-Bi system are those of Davidson.5 The data of Davidson give a k, value ranging from 0.21 to 0.25 for the compositions studied in this work, or an average value of around 0.23. In a recent publication, Rigaud and Tougas'10 determined ko by means of a solidification technique. For an alloy of approximately the same composition as that used in this work they obtained a ko value of 0.39. Hence, there is considerable uncertainty in the value of ko and, consequently, a series of experiments were made to determine k, more accurately.

Jan 1, 1968

By M. P. Tixier

In several log interpretation methods, water saturation is evaluated by use of the ratio of the readings of a short spacing resistivity device and a long spacing resistivity device plus information on the mud filtrate and connate water resistivities, which is often derivable from the SP. These methods are valid over a certain range of conditions, usually specified by moderate invasion and R.. greater than R,. Since these methods involve no explicit evaluation of the formation factor, F, the saturafiion so found may be used in the standard Archie equation to derive a computed formation factor which, as a check, may be compared with the formation factor known from other independent measurements. Discrepancies in the two values of formation factor generally indicate that the ratio method is not within its range of applicability. If the computed F is too low, the corresponding S, is too low; if the computed F is too great, the corresponding S, is too great. By means of this "porosity balance" check, and some knowledge of the probable conditions of invasion, the interpretation can often be improved. The poqosity balance check is discussed for the cases of the Induction-Electrical Log Interpretation Method, the Rocky Mountain Method, and the R.,/R, Method. For the first method, a discussion is also given for the case of shaly sands. INTRODUCTION Al though many logging tools are available to obtain a practical value of porosity, the only logging method reflecting the water saturation is electrical logging. Water saturation is commonly computed from electrical log data by means of the basic Archie formula, Where F is the formation factor, R, the resistivity of the formation water, and R, the true resistivity of the formation. One difficulty in this procedure is a possible error in the evaluation of R, from the logs— for example, in the case of very deep invasion. There is no possibility, inherent in the procedure, which would provide a check of the accuracy of R, and, hence, of the computed saturation. Other approaches have been proposed which are based essentially on the ratio of the readings made with two dzerent devices: one device, with a short radius of investigation, provides a value close to the resistivity of the invaded zone; the second device, with a long radius of investigation, gives a value close to the true resistivity of the bed. By these methods, the determination of saturation is made independently of any direct knowledge of the formation factor. Therefore, if the formation factor (or porosity) is known from other sources (core analysis, neutron log, MicroLog . . .), it becomes possible to take advantage of this additional information in order to check the value of saturation derived from these latter methods. Inasmuch as this proposed check procedure relies on a knowledge of the value of formation factor or porosity, it has been deemed appropriate to call this verification a porosity balance. The purpose of this paper is to discuss the principle and the application of the porosity balance, depending on the method of interpretation being used. Basis of the Method There are in existence three interpretation methods by means of which the water saturation can bc found without a knowledge of the formation factor (or porosity). As just stated, they are based on the fact that the ratio of the two resistivities (one measuring the resistivity close to the hole, the other measuring the resistivity far from the hole) is independent of the formation factor since it affects the two resistivity measurements in the same way. Chronologically, the resistivity ratio methods are: (1) the Rocky Mountain Method, which has been used since 1943 and was explained in a paper in 1949;' (2) the R../R, Method or Shaly Sand Method, presented in 1954, which permits the calculation of the water saturation in both clean and shaly sands2; and (3) the Induction-Electrical Log Method, presented in 1957 for the interpretation of the induction-electrical log combination." Each method requires certain definite conditions in order for the interpretation to be reliable. The porosity balance method will let us know whether these conditions are fulfilled. In clean formations we know that the fundamental Archie relation (Eq. 1) must always be verified. This relation can be rewritten:

By K. F. Veith, R. L. Marovelli, T. S. Chen

An analytical study is made of thermal stress distribution in a thin circular disc subjected to a peripheral thermal shock at various rates of heat transfer. The problem is of importance in predicting the thermal shock response of a rock body of finite size. The theoretical analysis is based on radial heat flow by conduction in the disc and heat exchange by convection between the disc and the surroundings. The case of constant properties and plane stress is treated. Solutions of the stress distribution are presented for both cooling and heating shocks and an average stress theory is formulated. Preliminary experimental verification was obtained from the results of shock tests on thin rock discs insulated on both flat end faces so that heat exchange took place through the exposed peripheral surface. Physical properties vital to the analysis are Young's modulus, tensile strength, coefficient of linear thermal expansion, thermal diffusivity and thermal conductivity. Plots of these properties are presented. Historically, thermal energy has been used for primary rock removal throughout the ages. Although it is not widely known, the fire-setting method of thermal rock fragmentation was still in use 100 years ago in systematic underground mining operations in Scandinavia.' There, the availability of cheap labor and abundant wood fuel made the method competitive with the early blasting powders. By 1880, as high explosives replaced powder, use of the method declined and it was finally abandoned about 1885. Only 40 years ago, some experimental fire-setting methods were used for rock removal underground at Pribram and Zinnwald in Central Europe.2 Compressed air-oil burners replaced the earlier wood fuels. About 15 years ago, gaseous oxygen-oil burners were introduced in the United States and gained acceptance for difficult blasthole drilling and some quarry opera- tions. At present, there is renewed interest in the compressed air-oil burner designs. The literature included information on thermal secondary processes for rock weakening or particle liberation3,4,5,6,7,8 on thermal spallation of rock 9,10,11,12,13 and on the thermal fracture of materials other than rock. The 1955 Symposium on Thermal Fracture14 and the later work of Hassel-man, cover recent developments in thermal shock investigations on brittle ceramics. Although the number of published analytical and experimental investigations conducted on ceramic and refractory materials is large, the literature reveals that there is a lack of information on both the theoretical and actual response of rock to thermal shock. Many of the thermal shock studies on ceramic and refractory bodies are based on the case of heat transfer at the solid's surface by convection in either liquid or air. A similar heat transfer situation was adopted for a theoretical analysis of the thermal stresses in a thin circular disc subjected to a peripheral thermal shock. Experimental thermal shock tests were then conducted on rock specimens to check the analytical results. Specially insulated quartzite, basalt and taconite discs were shocked in either liquid or still air bath at various rates of heat transfer. The work was done in order to resolve the question as to whether theoretically determined tensile stresses are actually realized in a finite rock body undergoing thermal shock. Specifically, if theory predicts that the tensile strength of a rock should be exceeded in a particular type of controlled thermal shock, will fracture occur? This information is needed by Bureau researchers working on thermal and electrical rock fragmentation methods. The object of this paper is to present the main features of the theory and procedure being used in the authors' approach to quantitative prediction of rock response to a thermal shock. THEORETICAL ANALYSIS In the analysis to follow, simple geometry of a thin circular disc is considered. The disc is assumed to be isotropic, homogeneous and perfectly elastic, and to have constant thermal and mechanical properties. The effect of radiation is neglected so that heat is transferred by conduction inside the disc and by convection with its surrounding. In addition, the end

Jan 1, 1967

By A. J. Shaler, H. Udin, J. Wulff

In the study of the sintering of meta powders, we have come to the conclusion in this laboratory that further progress requires a more basic understanding of the operating mechanisms. This is emphasized in detail by Shaler. He has shown that a knowledge of the exact value of the surface tension is imperative for a solution of the kinetics of sintering. This force plays a principal role in causing the density of compacts to increase.2 Furthermore, a knowledge of the surface tension of solids is also applicable to other aspects of physical metallurgy. C. S. Smith3 points out the relation between surface and interfacial tension and their function in determining the microstructure and resulting properties of polycrystal-line and polyphase alloys. This paper describes one group of results of an experimental program designed for the study of the surface tension in solid metals. As a by-product of this work, considerable information has been obtained on the rate and nature of the flow of a metal at temperatures approaching the melting point and under extremely low stresses, a field of mechanical behavior heretofore scarcely touched by metallurgists. The importance of this additional information to students of powder metallurgy need not be stressed. Theoretical Considerations Interfacial tension arises from the condition that an excess of energy exists at the interface between two phases. Gibbs proves that this energy is a partial function of the interfacial area; thus: ?F/?s = ? where ?F/?s is the rate of change of free energy of the system with changing surface area, at constant temperature, pressure and composition, and ? is the interfacial tension, or interfacial free energy per unit area. If one of the phases is the pure liquid or solid, and the other the vapor of the substance, ? may properly be termed "surface tension," and is a characteristic of the solid or liquid. The attempt of a body to lower its free energy by decreasing its surface gives rise to a force in the surface which is numerically equal in terms of unit length to the free energy per unit area of the surface. Thus ? may be expressed either in erg-cm-² or in dyne-cm-1. Similarly, surface tension may be determined either by a thermo-dynamic measurement of the surface energy or by a mechanical measurement of the surface force. We have chosen the latter approach. Tammann and Boehme4 determined the surface tension of gold by measuring the amount of shrinkage or extension of thin weighted foil at various temperatures and interpolating to zero strain. The method is of questionable accuracy because of the tendency of foil to form minute tears when heated under tension. Their assumption of F = 2W?, where W is the width of the foil, is unsound, as the foil can decrease its surface area by transverse as well as by longitudinal shrinkage. Although their experimentation was meticulous, the paper does not include details of the sample configuration required for recalculating ? on a correct basis, even if such a calculation were possible. In the experimental procedure chosen here, a series of small weights of increasing magnitude are suspended from a series of line copper wires of uniform cross-section. This array is brought to a temperature at which creep is appreciable under extremely small stress. If the weight overbalances the contracting force of surface tension, the wire stretches; otherwise, it shrinks. The magnitude of the strain is determined by the amount of unbalance, so a plot of strain vs. load should cross the zero strain axis at w = F?. If balance is visualized as a thermodynamic equilibrium, the critical load is readily calculated. At constant temperature, an infinitesimal change in surface energy should be equal to the work done on or by the weight: ds = wdl [A] For a cylinder, s = 2pr2 + 2prl [2] If the volume remains constant, r = vV/pl [31 s = 2vpl+2V/l [4] ds = vpv/l - 2V/l²) dl [5] Substituting [5] into [I] gives for the equilibrium load, w = ?(z/rV- 2V/12) [6] and, again expressing V in terms of r and l, w = pr?(1 - 2r/l [7] Here the end-effect term, 2r/l, is neglected for thin wires in subsequent work. Eq 7 can be confirmed by means of a stress analysis. If the x-axis is chosen along the wire, then the stress is 2pr? - w pr² pr2 [8] A cylinder of diameter dis equivalent to a sphere of radius r, insofar as radial surface tension effects are concerned.³ Thus xv = 2?/d = ?/r = sz [9] For the case of zero strain in the x direction, the strain will also be zero in the y and z directions. Since the wire is under hydrostatic stress, Eq 8 and 9 are

Jan 1, 1950

By N. A. Gokcen, J. Chipman

Aluminum and oxygen dissolved in liquid iron were brought into equilibrium with pure alumina crucibles and atmospheres of known H2O and H2 contents to study the reactions: 1—Al2O3(s) = 2 Al + 3 0; 2—Al2o3(s) + 3H2(g) = 2Al+ 3H2o(g); and 3—H2(9) +O = H2O(g). Aluminum strongly reduces the activity coefficient of oxygen and similarly oxygen reduces that of aluminum. Values of the product [% All" • [% O]3 are much smaller than those found in previous experimental studies and are of the order of magnitude of the calculated values. ALUMINUM is the strongest deoxidizer commonly A used in steelmaking, but the extent to which it removes dissolved oxygen has been debatable. The relationship between aluminum and oxygen has not been determined reliably not only on account of the usual experimental difficulties at high temperatures but also because of uncertainties in the analyses of very small concentrations of oxygen and aluminum. The earliest experimental attempt of Herty and coworkers' was followed by a more systematic study of Wentrup and Hieber.' These authors added aluminum to liquid iron of high oxygen content in an induction furnace and considered that 10 min was sufficient to remove the deoxidation products from the melt. Parts of the melts thus obtained were poured into a copper mold and analyzed for total aluminum and oxygen (soluble plus insoluble forms), assuming that the insoluble parts were in solution at the temperatures from which samples were taken. It is conceivable that the furnace atmosphere in their experiments, consisting of mainly air at 20 mm Hg pressure, was a serious source of continuous oxidation and therefore that their oxygen concentrations were correspondingly high. Scattering of their data was explained to be well within the maximum inaccuracy of 10°C in the temperature measurements and errors of ±0.002 pct each in the oxygen and total aluminum analyses. Maximum and minimum deoxidation values, i.e., values of the product [% All' . [% O] differed by factors of 10 to 15; mean values of 9x10-11 and 7.5x10-9 ere reported at 1600" and 1700°C, respectively. Hilty and Craftsv determined the solubility of oxygen in liquid iron containing aluminum, using a rotating induction furnace. Pure alumina crucibles used in their experiments contained the liquid iron which in turn acted as a container for slags of varying compositions consisting mainly of Al2O3, Fe2O3, and FeO. The furnace was continuously flushed with argon, and additions of aluminum and Fe2O3 were made in the course of each experimental heat. The inner surfaces of their alumina crucibles were covered with a substance other than pure Al2O3, containing both iron oxide and alumina. Although frequent slag additions can change the composition of slag in the liquid iron cup formed by rotation, the inner surface of the crucible must depend upon the transfer of oxygen or aluminum through the liquid iron for any adjustment in composition. It is not clear that their metal was in equilibrium with the crucible wall, but it is clear that it was not in equilibrium with Al2O3. Their deoxidation product, [% A].]" • [% O]3, varied by a factor of more than 50; the average values of 2.8x10- and 1.0x10-7 were selected for temperatures of 1600" and 1700°C, respectively. Aside from the experimental determinations, attempts have been made to calculate the deoxidation constant for aluminum indirectly from thermody-namic data. Schenck4 combined the thermodynamic data for Al2O3 and dissolved oxygen in liquid iron by assuming an ideal solution. His calculated values are 2.0x10-15 and 3.2x10-13 at 1600" and 1700°C, respectively. Later, Chipman5 attempted to correct for the deviation from ideality and derived an expression which led to deoxidation values of 2.0x10-14 and 1.1x10-12 at 1600" and 1700°C, respectively. The errors in these treatments originate mainly from inaccuracies of thermal data and uncertainties regarding the activity coefficients of dissolved oxygen and aluminum. The purpose of this investigation was to study the equilibria represented in the following reactions in the presence of pure alumina: Al2O3(s) = 2Al + 3O K = aAl2.ao3 [1] Al2O3(s) + 3H2(g) = 2Al + 3H2O(g) H2O K2 = aAl2(H2O/H2 ) [2] H2(g) +O = H2O(g) K3 = 1/ao (H2) [3] The experimental method consisted of melting pure electrolytic iron, usually with an initial charge of aluminum, in pure dense alumina crucibles under a controlled atmosphere of H,O and H2 and holding

Jan 1, 1954