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By Eugene A. Mizikar

A mathetnatical model of heal transfer in continuously cast steel slabs is described. The model, consisting of a unidimensional transient conduction equation and boundary condition equations, has been pvogrammed for computer solution. Temperatuve and solidification profiles calculated for a 6-in. slab, being cast under several conditions of secondary cooling, are presented and compared. Calculated solidification profiles are in agreement with reported expevinle~ztal values. For the mold zone, the predicted slab shell thickness can be described by: Resuilts of the study indicate that multibank spray cooling followed by radiant cooling should be employed when solidifying thick slabs with minimum surface temperature of 1600°F. Under these conditions, a 6-in. slab can be expected to solidify in about 8.3 min. Computer results also indicate that radiant cooling can replace spray cooling during solidification of the final 30 pct of slab with little increase in overall solidification time. CONTINUOUS casting has come to the forefront of the steel industry in recent years because of economic advantages resulting from increased yields and elimination of several processing steps. Considerable work, however, remains to be done regarding modifications to the process and operating procedures. Both a lack of operating plants in this country and the experimental difficulties associated with direct measurements on moving castings have made determination of solidification rates and temperature distributions difficult. An alternate approach is to mathematically simulate heat transfer in a continuously cast section, and then calculate the temperature distributions as a function of the controllable variables of the process. Simulation of heat transfer during solidification requires that a nonlinear mathematical problem be solved. As pointed out by Ruddle,' there are two mathematical approaches to the problem- the analytical approach and the numerical approach. While the analytical approach is certainly the more elegant of the two, it does require a number of inexact assumptions because of the complexity of the problem. For example, noteworthy analytical treatments of heat transfer in continuous casting have been developed by Savage Hills,3 and pehlke4 only by making one or more simplifying assumptions such as invariant thermophysical properties, constant heat-transfer coefficients in the mold, and linear temperature profiles in the shell. Simplifying assumptions such as these can introduce considerable uncertainty in the validity of results calculated with analytical solutions. Numerical solutions, which are considerably more versatile, appear to be better suited for solving solidification problems. Complex variations in the boundary conditions and variable thermophysical properties can be handled readily with this technique. Whereas numerical computations can be long and tedious when done by hand, results can now be obtained quite rapidly with the use of either the digital or analog computer. Several numerical models of heat transfer in continuous casting have been published. In 1963, Adenis, Coats, and Ragones published a numerical model used to calculate temperature distributions in direct-chill-cast magnesium billets. More recently, Donaldson and Hess 6 presented results obtained with a numerical computer model of heat transfer in continuously cast steel billets. In the present study, a model of unidimensional heat transfer in continuously cast slabs is presented. The method of solution on a digital computer is also included. Calculated temperature distributions and solidification profiles for various schemes of secondary cooling along with attempts to verify the model are also discussed. MATHEMATICAL MODEL The schematic representation of the slab continuous casting process in Fig. 1 illustrates that the slab passes through three distinct zones of cooling. Accordingly, the mathematical model consists of three parts: 1) solidification in the mold; 2) solidification in the spray cooling zone ; 3) solidification in the radiant cooling zone. Heat-Transfer Equations. The model was developed bymaking a heat balance on a horizontal slice of slab over the time period required for the slice to proceed from the liquid metal meniscus in the mold to the cutoff station. As shown in Fig. 2, the imaginary slice extends from the center line to the surface of the slab. As the slice moves downward, heat is conducted from the center line to the surface of the slab at a rate governed by the surface boundary condition and thermophysical properties of the metal in the slice. The following partial differential equation describes the conduction of heat in a medium moving at velocity U in direction Z:

Jan 1, 1968

By L. C. Michels, O. G. Ricketts

The disorientations between s?nall grains, whose growth has been arrested at an early stage of recrys-tallization, and the deformed matrix in cold-rolled aluminum single crystals were determined using transmission Kikuchi line and electron diffraction patterns. The orientations of the recrystallized grains were found to be random, and the disorientations of these grains with the matrix weve found to be intermediate to large. This leads to the conclusion that the observed vecrystallization began in small areas of large disorientation present in the cold-worked structure. heavily cold-worked thin sections of aluminunz single crystals and of polycrystalline aluminum and nickel were produced directly by a mechanical technique. The specinlens thus prepared were heated with the electron beam to bring about vecrystallization during observation in the electron microscope. Motion pictures taken du.ring heating and the electvon, microg.raphs taken both before and aftev heating allowed the recrystallization process to be traced to its ovigin. Re cvystallized grains originated in very s,mall regions of the cold-worked structure and developed through rapid migration of high-angle boundaries. The boundaries either were present as such in the matrix or were formed out of dense dislocation networks. SIGNIFICANT advances have been made in recent years in the study of nucleation of recrystallization using the technique of transmission electron microscopy of thin metal foils. Bollman1 in a study of heavily rolled polycrystalline nickel found support for the Cahn-Cottrell2,3 theory of nucleation. According to this theory nuclei form by the initially slow growth of subgrains formed through polygonization. During this initial period of slow growth (the incubation period) the migrating boundary of the subgrain increases its disorientation with the cold-worked matrix and thereby increases its mobility to become a rapidly migrating high-angle boundary. Bailey4,5 investigated the annealing behavior of several metals deformed both in tension and by rolling and concluded that recrystallization took place through the migration of high-angle boundaries. With low deformations these boundaries were present in the metal before deformation. With high deformation it was not possible to tell whether the boundaries were pieces of the original grain boundaries or were produced either during deformation or by polygonization during ameal- ing. Direct observation during heating of metal foils indicated that subgrains form by polygonization and grow at an uneven rate. The grain size obtained decreased with decreasing foil thickness indicating that the foil surface resists boundary motion. Votava,6 in heating stage experiments on rolled copper, observed nuclei to appear suddenly and grow in jumps of differing magnitude. However, he found no special dislocation configurations where the nuclei appeared. Fujita,7 as a result of a study of subgrain growth in heavily worked aluminum, concluded that the boundary of a recrystallized grain initially forms from the boundary of a group of subgrains. This occurred by a process of deposition of vacancies and dislocations in the group boundary as the boundaries within the group disappear. HU8,9 directly observed a similar process in heating stage experiments on 70 pct rolled Si-Fe single crystals. The growth of subgrains appeared to proceed by a coalescence mechanism. The observed fading away of the boundary between two subgrains was explained by the moving out of dislocations from the disappearing boundary into the connecting or intersecting boundaries around the subgrains. The subgrain size and degree of disorientation with the surrounding structure were thus increased. With the increase in disorientation occurred a corresponding increase in boundary mobility, which eventually allowed the boundary to migrate rapidly. This process was observed to occur within "microbands" consisting of parallel narrow segments disoriented by a few degrees present in the as-rolled structure. The conclusion of Rzepski and Montuelle10 that growth is preceded by the coalescence of blocks through disappearance of their common boundaries supports this view. In contrast to Hu's coalescence model for nucleation were the conclusions of Walter and ~och.""~ Working with the same material as Hu, of the same orientation and rolled to the same reduction, they concluded that nucleation occurred by the Cahn-Cottrell mechanism. They observed, in agreement with Hu, that recrystallization began in the "microband" regions which they referred to as "transition" bands. Bartuska13 studied subgrain growth in heavily rolled nickel using a beam heating method in the electron microscope. He concluded that nuclei for recrystallization form from the largest most perfect subgrains present in the cold-worked structure by rapid intermittent migration of parts of subboundaries. In rare instances he observed subgrain growth by coalescence. EXPERIMENTAL PROCEDURE The materials used in this study were 99.999 pct A1 supplied by A.I.A.G. Metals, Inc., and 99.999 pct Ni supplied by Johnson and Matthey and Co., Ltd. The Hitachi HU-11 electron microscope, with uniaxial

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 A. F. Giamei, E. J. Freise

A discussion of the various factors affecting the accuracy of volume fraction determination by the direct comparison X-ray diffraction method is presented. To minimize errors introduced by nonrandomization effects such as preferred orientation and large grain size, as well as errors introduced by statistical effects, an iterative mathematical analysis is introduced. This analysis is applied to all observable diffractio~ spectra from a given specimen by means of computer techniques and is statistically superior to the standard direct comparison technique which utilizes only one or tm sets of intensity spectra. The computer program also presents a graphical interpretation of- the results which enables the investigator to visualize and readily assess the scatter in volume fraction estimates caused by deviations from randomness. Finally, the iterative analysis is applied to experimental data collected from a series of plain carbon steels in both the as-received and spheroidized conditions to determine the volume fraction of cemen-tite present in each case. The results show markedly good agreement with chemical analyses for all spheroidized specimens. In theory, quantitative X-ray diffraction is a power-ful analytical technique for precise determination of the volume fractions of various phases present in a multiphase poly crystalline aggregate. There are two generally used methods; both utilize the fact that the intensity of a diffraction line of a particular phase is a function of volume fraction of that phase present in the aggregate. The more common method is the so-called internal standard technique where a known amount of standard substance is mixed with the aggregate containing the unknown. The resulting ratio of the intensity of a particular diffraction line of the unknown to the intensity of a diffraction line from the standard is used to find the weight fraction of unknown material by reference to the intensity data obtained from a previously prepared set of standards containing the same amount of standard material. The details of this technique are outlined in standard works on X-ray diffraction.' The disadvantages of the technique are that it requires the use of powder specimens and that the powder mixture must be homogeneous near the surface to the maximum effective beam depth. The alternative technique is the direct comparison method in which the ratio of the intensity of a diffraction line of a phase in the aggregate to the intensity of a second-phase diffraction line yields the ratio of the volume fractions of each phase present. This method has been applied most extensively to the determination of the percentage of retained austenite in martensitic steels and to determining the amounts of hcp and fcc allotropic modifications in pure cobalt5 and the amounts of hexagonal and rhombohedra1 modifications in graphite.8 This method is applicable to bulk as well as powder aggregates and is the technique which will be considered in the following text. It is the purpose of the present communication to show that by combining the results of X-ray diffrac-tometry with the use of high-speed digital computers the results of the direct comparison quantitative X-ray analysis technique can be optimized by using all of the data available on a diffraction pattern. THEORETICAL DISCUSSION In optimizing any quantitative X-ray diffraction experiment, the problem of accuracy vs time to collect and analyze the experimental data arises. For any method to be practical, it is required that both experimental and analytical procedures are reasonably short. In most of the previous work performed by the direct comparison method, intensity data from only one or two sets of peaks were used to calculate the volume fraction of phases present in the aggregate. Consequently, rather long-time experimental measurements are required to assure that the intensity data are sufficiently accurate to justify the use of one or two sets of data. By using computer techniques to analyze the experimental data it becomes feasible to use all of the available data on a diffraction pattern. By so doing, the time spent in measuring any one diffraction maxima can be appreciably reduced. Although this results in poor counting statistics for any one maxima, the number of data points available for analysis is greatly increased. Based on the above discussion, it will be assumed that a continuous scanning counter-diffractometer technique will be used to collect intensity data from a two-phase mixture. The integrated intensity of the ith diffraction line from the a phase in the aggregate is given by:'" where is the volume fraction of the a phase, The various quantities in Eq. [la] are angular independent while those in [lb] depend on the hkl spectrum of a particular phase. The meaning of the individual quantities in Eqs. [la] and [lb] are given in Appendix 1. It is convenient at this point to outline briefly the factors which will affect the measured intensity of any one hkl spectrum. a) Extinction effects arise from two independent experimental conditions. Primary extinction arises from a high degree of crystal perfection and results in spectra having lower intensity than predicted by Eq. [I]. Any treatment, such as powdering, which reduces

Jan 1, 1968

By T. O. King, Y. P. Gupta

The self-diffusion of sodium in two sodium silicate liquids was measured in the temperature range 850" to 1500°C by the capillary-reservoir technique. Radioactive Na 22 was used as the tracer. The total count and autoradiographic methods were used for determination of the total Na 22 depletion and diffusion profiles of the dqy-used specimens. The diffusion coefficients obtained by the autoradiographic technique are slightly smaller than those obtained by a total count method. Error analysis of the two methods suggests that more confidence be placed in the results of the total count method. The experimental results were analyzed in terms of the existing activated rate process theory. The activation energy for diffusion was shown to decrease markedly as the temperature increased. This was attributed to a variation in the heat of activation with temperature, probably related to a change in the distribution of anions associated wilh the cation. In terms of a model, suggested for diffusion in liquid silicates, differences in the aclivation energies for diffusion and electrical conduction may arise from the effect of the electric field applied in conduction measurements. It is generally accepted that liquid silicates consist of cations and an equilibrium distribution of complex anions determined by temperature and composition. Transport properties in molten silicates are of interest, not merely because of their relevance to the kinetics of pyrometallurgical reactions and glassmak-ing processes, but also because they are useful to development of the theory of such ionic liquids. Self-diffusion is one such transport process that may, if studied for liquid silicates of widely varying compositions, indicate structural changes through changes in the activation energy for diffusion. The self-diffusion of calcium, silicon,' sulfur: aluminum, 4 and oxygenS in lime-alumina-silica melts and of iron6 in molten iron silicates have been measured. Unfortunately, the errors in some of the reported activation energies for diffusion are too large to allow firm conclusions concerning structure and the mechanism of the diffusion process to be drawn. The research reported here was a study of the self-diffusion of sodium in liquid sodium silicates. The soda-silica system was chosen since: i) a reasonable composition range can be covered in the binary system at moderate temperatures; ii) suitable isotopes of sodium (radioactive Na 22 and NaZ4) can be obtained; iii) data on the electrical conductivity and viscosity of sodium silicate liquids are available. However, the range of composition actually used in diffusion experiments was limited, to 20 to 35 wt pct soda, by the relatively high viscosity of silica-rich compositions and by evaporation of soda from basic melts. EXPERIMENTAL PROCEDURE The capillary-reservoir technique was used, wherein a radioactive tracer, Na 22, incorporated in the capillary melt, was allowed to diffuse out of the platinum capillary tube into a large reservoir of silicate liquid containing a chemically identical melt, but without radioactive tracer. After a specific diffusion time, both the total depletion in the tracer concentration and concentration-distance profiles of the diffused samples were measured by procedures to be described later. The diffusion cell assembly was similar to that used by Koros and King.' The temperature of the diffusion cell was measured with a calibrated Pt, Pt-10 pct Rh thermocouple located at the center of the liquid reservoir. The same thermocouple was used to obtain the temperature profile in the reservoir. The temperature at the top of the reservoir was slightly higher (2°C) than that at the bottom, to minimize convection in the capillary tubes, which were placed, open end up, in the reservoir. Convection was not expected to be a problem since the length-to-diameter ratio of the tubes was about 12:1 and the maximum capillary diameter was 1 mm. The diffusion cell was heated in a molybdenum-wire resistance furnace, previously used by Koros and King, but somewhat modified. A Pt, Pt-10 pct Rh thermocouple enclosed in an alumina tube and located near the furnace winding was used in conjunction with a preamplifier and Micromax proportional controller for temperature control, within 4°C, at temperatures near 1500°C. Before starting a diffusion run, the furnace was heated to the desired temperature and an alumina guide assembly for the capillaries was slowly lowered to within 2 cm of the liquid reservoir. The capillaries were thus heated to about the temperature of the bath. The run was started by lowering the assembly till the open ends of the capillaries were about 1 cm below the surface of the liquid. The run was ended by raising the assembly to about 15 cm above the liquid bath. Later, the sample assembly was slowly withdrawn from the furnace. Six diffusion samples were usually run at the same time. Three runs made with the open ends of the capillaries down were discarded because in the majority of these samples air bubbles trapped at the open end were observed. Some glass adhered to the outside of the capillary on withdrawal. This was carefully removed and used to check that the Na 22 activity in the sink remained at a low level. Materials. Nonradioactive sodium silicates were prepared by melting, in a platinum crucible, weighed quantities of sodium carbonate and powdered silica. To prepare radioactive sodium silicates, Na2 obtained in HC1 solution, was first checked for radioactive impurities by obtaining a y-ray energy spectrum, then the chloride ions were removed by anion-ex-

Jan 1, 1968

By A. D. Zunkel, A. H. Larson

Equilibrium arsenic contents of Pb-As alloys in contact with PbO-As2O3 slags containing less than 30 mol pct As2O3, were determined at 650°, 700: and 750 C in an inert at?rzosphere. In this temperature range, the arsenic content of the alloy increased with increasing temperature in the single-phase liquid slag region and decreased with increasing temperature in the two-phase slag region and the single-phase solid-solution slag region. The PbO-As2O3 phase diagram below 22 mol pct As2O3 was determined by thertrzal analysis and by application of a log ?As2O3/?PbO vS log XAs2o3 /x3pbO plot determined from the equilibrium actiuity data. The resulting phase diagram was not well-defined since the eutectic temperature was not detected in the thermal analysis experiments, although a region of terminal solid solubility of As2O3 was found. Results from the phase diagram determination are compared with an existing diagram in the literature. THIS experimental investigation is an extension of a study by the authors1 on the slag-metal equilibria in the systems concerned with commercial lead refining processes such as softening and dross fuming. The first part of this investigation was a study of the slag-metal equilibria in the Pb-PbO-Sb2O3 system. The only experimental work previously done on the Pb-PbO-As2O3 system was by Pelzel2,3 in which the phase diagram for the PbO-As2O3 system was determined below 50 wt pct As2O3 and the equilibrium constant for the reaction 3Pb + As2O3 + 3PbO + 2As was determined as a function of temperature. No slag-metal equilibrium data have been determined. It is due to the scarcity of information regarding the Pb-PbO-As203 system that this work was undertaken. This paper describes the determination of the slag-metal equilibria in the Pb-PbO-As203 system by equilibrating Pb-As alloys with PbO-As2O3 slags in an inert atmosphere, the effect of 1 wt pct additions of bismuth and copper on the slag-metal equilibria, and the PbO-As2O3 phase diagram both by thermal analysis and the use of the slag-metal equilibria data. EXPERIMENTAL Materials. The materials used in this investigation were analytical reagent-grade and assayed as follows: 1) 99.8 pct PbO (0.014 pct insoluble in CHJCOOH, 0.02 pct not precipitated by H2S, 0.1 pct CaO, and 0.08 pct SiO2); 2) 99.95 pct As2O3; 3) 99.99 pct Pb; 4) 99.0 pct As; 5) 99.99 pct Cu; and 6) 99.97 pct Bi. Room-temperature X-ray patterns revealed no detectable impurities in any of these materials. Apparatus for Equilibrium and Thermal-Analysis Determinations. The resistance-heated crucible furnace used in this investigation employed nichrome elements and was mounted so that it could be raised to surround the reaction tube during each experiment and, subsequently, lowered. A schematic diagram of the apparatus is shown in Fig. 1. Each charge was heated in a 3+-in.-OD by 31/2-in.-high 416 stainless-steel crucible placed in a 41/4-in.-1D by 18-in.-long fused-silica reaction tube which was closed at one end. On a shoulder around the crucible was placed a 3: -in.-OD by 12-in.-long open-end fused-silica condenser tube. The open end of the reaction tube was covered by a water-cooled brass cap with ports for 1) admitting an inert atmosphere to the system through a stopcock, 2) introducing a stainless-steel, motor-driven, paddle stirrer into the crucible, 3) evacuating the system with a mechanical vacuum pump, and 4) sampling the melt with Vycor sampling tubes. The brass cap was fitted to the open end of the reaction tube with a silicone gasket and collar clamp. The furnace temperature was controlled by a Barber-Coleman Capacitrol controller and a chromel-alumel thermocouple. Due to the corrosiveness of the melt, the controlling thermocouple also served as the measuring thermocouple. The temperature of the melt was calibrated against the controller temperature and was checked periodically during each test with a Vycor-enclosed calibrated chromel-alumel thermocouple. The temperature measurement and control can be considered accurate to ±3°C. Procedure. The charge placed in the crucible for each experiment consisted of 1000 g of Pb-As alloy and 300 g of PbO-As2O3 slag. The crucible was then placed in the reaction tube, the condenser tube was placed on the shoulder of the crucible, the silicone gasket and brass cap were fitted on the open end of the reaction tube, and the entire system was evacuated and filled with argon ten times. After the last flushing, a positive argon pressure of 1 psig was impressed on the system. The furnace was then raised to sur-

Jan 1, 1968

By Y. Baskin

Solid-solubility relationships in the Pseudobinary systems UAS-UP, UAs-US. UAS-UC, aid UAs-UN were investigated. The first two systems exhibit complete mutual solubility, whereas the component compounds in the other two systenzs are immiscible. The above information, together with solid-solubility data joy six additional pseudobinary systems , were analyzed for compliance wilh the Hurrze-Rothery rules for rnetallic systems. The relative size difference of the component nonmetal atoms was found to be the dopainant jactor determining the extent of solid solubility between the NaC1-type uranium compounds. The anionic and covalent radii of the nonmetal atoms appear to be inadequate for these systems, but compuled radii based on rare earth compounds yield consistent results for the uranium compounds. THE actinide elements, like metallic elements of the transition and rare earth series, readily form binary compounds with nonmetallic elements of groups IV, V, and VI of the periodic table. Of particular importance are the NaC1-type equiatomic compounds with carbon, nitrogen, sulfur, phosphorus, and arsenic. The uranium members of this family of compounds have high melting points, are essentially stoichiometric, and exhibit various amounts of mutual solubility. Thus, they are of interest for investigating the factors governing the extent of solid solubility. Previous investigators have determined the solid-solubility limits in the pseudobinary systems between the compounds UC, UN, US, and UP. Anselin et a1 .' reported complete miscibility in the system UC-UN. Baskin and shalek 2 and Allbutt et a1.3 reported that UP and US exhibit complete mutual solubility. Shalek and white4 reported partial miscibility in the system US-UC. At 1800°C the maximum solubility of UC in US is 40 mol pct, but that of US in UC is 4 rnol pct. shalek5 found limited solubility in the system US-UN; the maximum solubility of UN in US is 11 rnol pct at 1800°C, while that of US in UN is only 0.3 mol pct. White and askin 6 found very limited miscibility in the system UP-UC at 1800°C. Approximately 7 mol pct UC is soluble in UP, but there is no solubility of UP in the monocarbide. Phase relations in the pseudo-binary system UN-UP were investigated by askin.' Approximately 0.7 mol pct UN is soluble in UP at 1800°C, while UP is immiscible in UN. The present study was carried out to explore the extent of terminal solubility in the systems UAs-UC, UAs-UN, UAs-US, and UAs-UP. This information, combined with existing data, provided a sufficient basis on which to determine the factors governing solid solubility in pseudobinary systems containing NaC1-type uranium conpounds. I) EXPERIMENTAL 1) Materials. The compounds UC and UN were obtained from the Kerr-McGee Corp. and United Nuclear Co., respectively. The US, UP, and UAs were synthesized by reacting finely divided uranium with H2 S, pH3, or AsH3 gas at low temperature (300° to 500°C), followed by homogenization in a vacuum at moderately high temperatures (1400° to 1700°c).8-10 The materials were essentially stoichiometric, with the exception of UC, which exhibited a C/U ratio of 1.05. Oxygen was the major contaminant in these compounds, ranging from 0.05 wt pct in US to 0.30 wt pct in UC, and it was generally combined with uranium to form UO2. The UO2 content in these materials was usually of the order of 1 wt pct, and did not exceed 2 wt pct. Furthermore, no evidence was found for a high-temperature reaction between uranium dioxide and any of the compounds. Chemical analyses of equilibrated compositions in the systems UAs-UP and UAs-US showed that the non-metal atom to uranium ratios averaged about 1.01, and that the oxygen contents ranged from 0.06 to 0.22 pct. However, the small deviations from stoichiome-try or the presence of minor oxygen impurities do not invalidate the conclusions to be drawn from this study. 2) Experimental Procedures. The component compounds in powdered from were blended in the desired proportions for 5 hr in the ball mill that consisted of stainless-steel balls in a plastic container. Chemical analyses indicated very little metallic pickup from the blending operation and virtually no increase in oxygen content. The pellets were pressed in a 0.270-in.-diam steel die under 40,000 psi pressure. One wt pct of stearic acid dissolved in CCl 4 served both as a binder and as a die lubricant. Chemical analyses revealed that the stearic acid left no carbon residue in the sintered samples. The pellets were sintered in vacuum in an unsealed tantalum crucible. The temperature, measured with a calibrated optical pyrometer, was maintained at 1800" + 30°C for 3 hr. This was sufficient time for attaining equilibrium as no change occurred in either the lattice parameters or the sharpness of the X-ray patterns when samples were annealed for longer periods of time. The pellets were cooled with the furnace. Debye-Scherrer powder patterns were taken at room temperature with a 114.59-mm-diam Norelco powder camera and CuKor radiation (CuGI = 1.5405A). Unit cell dimensions were determined from a Nelson-Riley extrapolation to the high-angle reflections. The values for were precise to k 0.001A. 11) RESULTS X-ray and met allographic investigation revealed that complete mutual solid solubility exists in the pseudobinary systems UAs-UP and UAs-US. The lattice parameter vs composition plots, Fig. 1, show a

Jan 1, 1968

By D. D. Pollock

Many constitution diagrams do not indicate the limits oJ solid solubility of the silver-rich solid solutions below 200°C. Thermoelectric measurements were employed to determine this limit in the nieighborhood of room temperature. The appearance of a second phase causes a discontinuity to occur in the tkevtrroelectric power as a function of cornposition at constant temperature and pressure. This discontinuity was employed to determine the limits of the silver-rich terzinal solid solutions of the Ag-A l, Ag-As, Ag- Bi, Ag--Ge, Ag-In, Ag-Pb, Ag-Sb, and Ag-Sn systenls at 30°C. CONSIDERABLE work has been done on the constitution of binary alloys of silver. The available data have been compiled by Hansen1 and Elliott.2 However, many of the binary diagrams do not show the limits of solid solubility of the silver-rich solutions below about 200° C. This work was undertaken in an attempt to extend these limits to the neighborhood of room temperature . PREPARATION OF ALLOYS All of the alloys were made with silver containing less than 0.014 pct (by weight) of impurities. The materials were weighed out into 225-g heats and melted in a high-frequency induction furnace. The indium, tin, and antimony alloys were melted in A1203 crucibles, under a boric anhydride cover, and were poured into split graphite finger molds. The aluminum, germanium, arsenic, lead, and bismuth alloys were melted in machined graphite crucibles; they were also covered with boric anhydride and poured into split graphite finger molds. The $-in.-diam ingots were heated to 750°C and were forged and hot-rolled down to 0.1 by 0.1 in. The wires were pickled in a 25 pct HNO3-75 pct H2O solution to remove any oxygen-rich surfaces. The wires were then annealed at 550°C for 2 hr in a dissociated ammonia atmosphere. They were then furnace-cooled for 20 hr to room temperature in this atmosphere. The wires were cold-drawn to 0.0808 in. diam. The finished wires were again annealed at 550°C in the same manner as in the first anneal. Thermoelectric Power. The thermoelectric power of a single specimen of each alloy was determined against pure silver which contained a maximum impurity content of 0.014 pct by weight. The wire specimens were straightened and then cleaned with ethyl alcohol. They were then reannealed in the same way as the finished wires to assure that any residual stress would be at a minimum level. Previous work has shown that the presence of small amounts of stress has the effect of decreasing the thermoelectric power. The alloy specimen was soldered to the pure silver wire to form the measuring junction. A standard set of copper leads was then soldered to the reference junctions of the thermocouple. These junctions were maintained in separate dewar flasks which contained finely shaved melting ice during the test. The thermal electromotive forces of the thermocouples were measured at four temperatures between 15° and 45°C. A known source of electromotive force was balanced against the output of the thermocouple until a null balance was reached. The data were then expressed in terms of the thermoelectric power at 30°C. The results were then converted to absolute thermoelectric power, s303.3 These data have an average error of less than ±0.2 pct. RESULTS AND DISCUSSION All of the experimental data are given in Table 11. Since the electromotive forces of the binary alloys of silver were determined against the pure silver from which they were made, the resultant thermoelectric powers are only a function of the intentionally added binary elements at the constant test temperatures. This provides a direct measure of the effects of the alloying elements. The absolute thermoelectric power of an alloy of silver is given4 by:

Jan 1, 1968

Jan 1, 1968

By A. W. Schlechten

The proposition is advanced that edutcation specifically for exlractive metallurgy is desirable not because the course content is cmique but rather as a means of indoctrinating the student with a backgrocmd that will give him an interest and pride in the profession. Factors that have caused the decline in enrollment in metallurgical engineering courses emphasizing extractive processes are being overcome. There is a need to distinguish between the sciences of metallurgy and the engineering applications to avoid confusion both in and out of the profession. AS a first step in preparing the 1967 EMD Lecture I searched the literature to determine what my predecessors had done hoping thereby to gain some clues for my own performance. The Transactions of the Metallurgical Society show that the first EMD Lec- turer in 1959 was Dr. W. J. Kroll, known chiefly today for his pioneering work on the production of titanium and zirconium, but equally respected by an earlier generation for his contributions to lead refining. He has been followed by a series of well-known and competent metallurgists all possessing specialized knowledge that has served as a basis for their lectures. The EMD Lectures have in general been a review of the development of a certain aspect of the extractive metallurgical industry or a preview of a particular area of science or technology that has applications in extractive metallurgy. The usual format is to describe developments of the past, summarize the present state of knowledge, and make predictions for the future. There has been great variation in the relative amount of time devoted to these three subdivisions, the past, the present, and the future. For example, Professor Gaudin, the 1961 EMD Lecturer, in speaking of Separation Engineering on the Moon, did not have too many examples of past practice and so had to emphasize the future. It is cheering to observe that all of these authorities were optimistic in their predictions. Despite the fact that four of the previous EMD Lecturers have been educators, Professors Gaudin, Pidgeon, Schuhmann, and Kellogg, none of them discussed the subject of education for extractive metallurgists. I might say parenthetically that lecturers in other divisions, such as B. M. Larsen, J. B. Austin, F. D. Richardson, John Chipman, and R. F. Mehl, have commented with concern on the present state of training for extractive metallurgy. What can you say that is new about extractive metallurgy education? Certainly nothing new can be said about the educational process itself. Professional educators do have new approaches to teaching and learn-

Jan 1, 1968

By C. Graeme-Barber, R. L. Bell, T. G. Langdon

An analysis is made of the formulas and ,methods used to estimate the contribution of grain boundary sliding to the overall strain of a polycrystal. The errors involved in the approximations and/or ,mistakes in earlier work are assessed quantitatively so as to make possible the critical use of previously published data. SINCE it has been found that, under conditions of very slow creep, the strain due to grain boundary sliding (?gb) may contribute as much as 80 pct of the total creep strain,1,2 it is obviously important to have reliable methods for estimating this grain boundary strain. In two recent papers Stevens3,4 has drawn attention to the pitfalls encountered in assessing ?gb. He criticizes 1) the assumptions made in the derivation of some of the formulas for ?gb, and 2) the indiscriminate averaging procedures used for obtaining the quantities substituted in these formulas. These and further criticisms of earlier work are mostly valid. Unfortunately the only formulas and procedures recommended are either impossible or very difficult to apply in practice. Furthermore no attempt is made to assess the errors involved by the earlier approximations or mistakes, and so it is not possible to make critical use of any of these early dab. The present article attempts to improve on these shortcomings by reference to empirical verification of easily applied formulas whose theoretical derivations involve some otherwise unjustifiable assumptions, and by a quantitative assessment of the errors in previous work. DEFINITIONS First it is necessary to define the terms and symbols to be used. The choice of symbols preferred here is a logical combination and extension of the v introduced by McLean5 and the u by Brunner and rant.' In Fig. 1 the two grains X and Y are displaced by the sliding vector AC. u is the component of sliding resolved along the stress axis, v is that measured perpendicular both to the stress axis and to the specimen surface, and w is that measured perpendicular to the stress axis but in the plane of the surface. Two angles define the orientation of the grain boundary: 8, between the stress axis and the surface trace of the boundary, and +, the internal angle on a longitudinal section cut perpendicular to the surface. In computing the strain resulting from the boundary displacement at all the in- dividual boundaries in a polycrystal the components u, v, or w are sometimes averaged along a longitudinal line (i.e., parallel to the stress axis), sometimes along a transverse line, and sometimes at randomly chosen boundaries. Averages obtained in these three ways are given subscripts 1, t, and r, respectively. Stevens rightly calls attention to the possibility of non-equiaxed grain shapes either at the start or at the end of deformation. In this article all values of numbers of grains per unit length will refer to measurements made before deformation. The subscripts 1 and t will be used for the number of grains per unit length obtained along longitudinal and transverse lines, r for that obtained by averaging along a number of randomly directed lines. FORMULAS FOR ?gb ?gt, as a Function of u. An obvious truth is that cgb can, in principle, be obtained by summation of all the v components at the boundaries intersected by a longitudinal line of known length I, viz.: where nl is the number of grains per unit length, parallel to the stress axis, in the unstrained specimen. There are assumptions in the analytic derivation of Eq. [I] due to Brunner and rant' but ~achinger' arrived at Eq. [la] by a rigorous method. Unfortunately the experimental procedure required by Eq. [ la] proves very difficult as boundary migration tends to obscure the points at which the longitudinal line meets the grain boundary and the errors on such measurements tend to be large, see Fig. 2. For example, on a specimen of Magnox AL 80 at a creep strain of 9.7 pct, 300 measurements of u obtained from the points of intersection of a longitudinal line with the grain boundaries gave ul = 8.95 ± 3.58 pm, or an error of ±40 pct, at the 95 pct confidence limit. These large errors due to migration may be avoided by measuring u from the separation of the segments

Jan 1, 1968

By I. R. Kramer

The effect of the specimen diameter, d, on the flow stress, cra of polycrystalline aluminunz (99.997) was studied. The increase in the flow stress could be accountedfor by the increase in the surface layer stress, with decreasing specimen diameter. Both , and a, were found to be proportional to For the smaller-dianzeter specimen (< 0.033 in.) at strains less than aboul 0.1, the work hardening of the surface layer was greater than that associated with the bulk of the specimen. At higher strains the work hardening due to the bulk appears to be independent of the specimen diameter. THE increase in the strength of metals with decreasing diameter is well-known; however, an adequate explanation for the cause of the size effect is still lacking. The earliest systematic investigation of size effect appears to be that of Onol who reported that for aluminum monocrystals the resistance to slip at low strains increased as the specimen diameter decreased. A change in the stress-strain curve beyond 0.001 strain was not found. However, Suzuki et a1 .&apos; reported for monocrystals of a brass and copper having diameters in the range of 2 to 0.12 mm that the entire stress-strain curve was raised as the specimen diameter was decreased. The effect of size was most apparent when the diameter of the specimen was less than 0.5 mm. In the discussion of this paper Honey-combe reported a size effect in copper crystals as large as % in. diam. These results are in agreement with those of paterson3 and Garstone et al.4 While the majority of the investigations on size effects was conducted in terms of the variation in the diameter of the specimen, several investigators studied the influence of the specimen geometry. For example, Wu and smoluchowski 5 reported that in aluminum monocrystals the slip system was a function of the specimen dimension in the slip direction. King-man and Green 6 studied the influence of size on the compressive stress-strain relationship of aluminum monocrystals when the ratio of length to diameter was constant. Their specimen diameters ranged from to & in. For specimens oriented for single slip the critical resolved shear stress for the smaller-size specimens increased with decreasing diameter. No effect was observed in the large-size specimens. Specimens having an orientation near the corners of the stereographic triangle did not exhibit a size effect. Apparently, the increase in strength with decrease in the diameter of the specimen is a general phenomenon and has been observed in a brass |T and cadmium as well as in aluminum and copper.&apos; In a series of investigations (for example Ref. lo), it was shown that during deformation a surface layer was formed which imposes a back stress, a,, on the moving dislocations. It is reasonable to predict that this surface layer stress, as, should be a function of the specimen diameter and could possibly account for the flow stress size effect. In fact, experimental evidence will be presented to show that this is the case; i.e., the increase in flow stress with decreasing size is equal to the increase in the surface layer stress, as, with size. In addition, data will be presented on the variation with size of and a* where is the back stress associated with the generation of dislocation obstacles in the bulk of the specimen and a* is the net effective stress acting on the mobile dislocations. A limited investigation was carried out on gold specimens to determine the influence of an oxide film. EXPERIMENTAL PROCEDURE The aluminum specimens were prepared from -in. bar stock (99.997 pct purity). The 0.350- and 0.150-in.-diam specimens were machined directly from the bars while the specimens having a diameter of 0.033, 0.020, and 0.015 in. were prepared by swaging and drawing to 0.04 in. and electropolishing almost to final size. The specimens were prepared with a 2-in. gage length. The specimens were annealed in vacuum (-10-4 Torr) at 350°C for 8 hr. The grain diameter of the specimens in the various specimen diameter groups was 0.08 ± 0.02 mm. Gold specimens of two diameters, 0.14 and 0.03 in., were prepared in a similar way and annealed at 650°C for 8 hr. The grain diameter of the gold specimens was 0.2 mm. After annealing the specimens were electrochemically polished to the final size and tested in an Instron tensile machine at a strain rate, E&apos;, of 10- 3 per min. While it was possible to determine the surface layer stress, a,, in the larger-size specimens by measuring the difference, Aa, between the stress before unloading the specimens and the initial flow stress after removal of the surface layer as outlined in detail in Ref. 10, this method is not applicable for small wires because of the difficulty in obtaining a sufficiently accurate measure of the diameter. The values at the various strains were therefore determined by measuring after the specimen had been annealed at 35°C for 4 hr. It has previously been shown" that the two methods give the same results for a provided that the annealing temperature is low enough to affect only the surface layer and not the dislocation barriers in the bulk of the specimen. For the gold specimens a treatment at 150°C for 16 hr was found to be satisfactory for the determination of by the low-temperature annealing method. EXPERIMENTAL RESULTS Determination of a,, and a,. The stress-strain curves for the various diameter aluminum specimens, plotted in terms of the logarithms of the true stress, and true strain, are given in Fig. 1. These curves represent the average data taken from at least ten specimens at each size. Over the range of strains investigated the curves follow the empirical equation

Jan 1, 1968

By D. F. Stein

In spite of the apparent usefulness of autoradiography in demonstrating segregation, it has had very limited success in demonstrating grain boundary segregation. Because of this limited success, a model system amenable to mathematical analysis was devised to determine which variables in the experiment are most important. As a result of these calculations, it was concluded that autoradiograPhy is a rather insensitive technique to measure grain boundary segregation. The range (energies) of the emitted particles (ß and a) must be low, and the concentration of the radioactive speczes at the grain boundary must be (in general) two or three orders of magnitude greater than the concentration within the grain. Because of these very restricted conditions , the limited success of the technzque is not surprising. In spite of the apparent usefulness of autoradiography in demonstrating segregation, it has had very limited success in demonstrating grain boundary segregation. Sulfur segregation in iron1 and possibly polonium segregation in Pb-5 pct B1 2 alloys are the only autoradi-ography experiments that have demonstrated segregation to grain boundaries in metals without the formation of a second phase. Segregation to a boundary without the formation of a second phase is often called Gibbs&apos; absorption and is discussed by McLean in Chapter 5 of Ref. 10. There are several394 experiments showing grain boundary diffusion of a radioisotope, but this type experiment is not representative of equilibrium between the concentration of an element at a grain boundary and that in bulk, so it will not be discussed in this paper. In an attempt to determine if temper embrittle ment of low-alloy steels was associated with segregation of antimony to grain boundaries, a program to use auto-radiography (using Sb-125) was initiated. Even though other measurements strongly suggest that segregation is occurring during embrittlement, no evidence of grain boundary segregation was observed in the auto-radiography experiments. An attempt was also made to detect segregation of carbon (using C-14) to grain boundaries in iron during slow cooling. There is again strong indirect evidence7 that segregation occurs during such a treatment, but the autoradiography experiment gave no evidence of such segregation. Because of the failure of these experiments and the general lack of success by our metallographic unit in measuring grain boundary segregation using autoradi-ography, a model system amenable to mathematical analysis was devised to determine which variables in the experiment are most important. MODEL SYSTEM The model system is illustrated in Figs. 1 and 2. It is a semi-infinite bicrystal with a single grain boundary perpendicular to the top face. The width of the grain boundary, W, is defined as the region to which segregation has occurred and it is assumed that this region is of constant composition. The assumption of an infinite dimension is for mathematical reasons but the results of such an analysis (as will be demonstrated later) are valid for even very small specimens. It also is assumed that the measurement is not limited by means of detecting the radiation (photographic emulsions, counters, and so forth) but that the means of detecting radiation is linearly sensitive to the radiation and has infinite resolving power. The distance y is the perpendicular distance from the center of the grain boundary to the point at which the background radiation is measured and x is the integration variable. CALCULATION FOR BETA PARTICLES Two values of the intensity of radiation will be calculated, the intensity at the center of the grain boundary and the intensity far from the grain boundary. The radiation at the center of the grain boundary can be calculated in the following way. Assume a grain boundary of width W having a uniform concentration equal to Cgb + Cb where CGb is the excess concentration of the element under consideration at the grain boundary and Cb is the bulk concentration. The intensity of radiation, IgB, at the center of the grain boundary, is a consequence of the amount of radioactive material, decay rate, absorption, and geometrical factors which can be represented mathematically by the following expression:

Jan 1, 1968

By G. E. Pellissier, P. H. Salmon Cox, B. G. Reisdorf

Banding that occurred in plates rolled from the early production heats of 18Ni(250) maraging steel is described and related to the segvegation of certain alloying elements (nickel, molybdenum, titanium), the extent of which was quantitatively evaluated by means of electron-microprobe analysis. The effect of banding on mechanical properties is discussed, with particular reference to observed directional differences in plane-strain fracture toughness of plates. It is shown that banding originates as interdendritic segvegation during ingot solidification and persists in some degree through normal soaking and hot reduction to plate. The results of the study showed that heating sections of small laboratory-cast ingots at 2200°F for 4 hr was sufficient to markedly reduce microsegregation and to considerably improve mechanical properties. Hot rolling of 7-in.-thick ingot sections to 1/2-in.-thick plate effected a similar reduction of microsegregation, but resulted in even greater increases in ductility and toughness than that obtained by homogenization treatment alone. DURING the past few years, considerable attention has been directed towards the low-carbon, high-alloy maraging steels and in particular towards the 18Ni-8Co-5Mo-0.4Ti alloy. The steels of this group, having an excellent combination of high strength and toughness, have a number of advantages over their more conventional medium-carbon low-alloy, quenched-and-tempered counterparts. In the annealed condition, the maraging steels are in the form of a ductile marten-site; aging at a relatively low temperature, typically 900°F for 3 hr, increases greatly the strength through the precipitation of intermetallic compounds. One problem in the early production heats of maraging steel was that the finished plate frequently displayed a banded structure. Previous work on other steels1-&apos; had established that banding in wrought products is either a direct or an indirect consequence of chemical segregation, which occurs during solidification and persists to some extent through normal thermal and mechanical treatments. For example, Smith and others: in a study of low-alloy steel, were able to correlate the severity of banding in the wrought product with the degree of interdendritic segregation of nickel and chromium in the as-cast ingot. The effect of banding on the mechanical properties of steels is usually considered to be detrimental, although there is only limited evidence to suggest that a marked improvement in properties can be obtained with less heterogeneous structures. Comparison of the longitudinal and transverse tensile properties of banded and of homogenized 4340 steel showed that only the transverse ductility was improved by homogenization, but even then the improvement was not commercially significant.&apos; Conversely, homogenization of through-the-thickness tension specimens of quenched-and-tempered steel plate, containing 1.47 pct Mn, increased the strength by as much as 10 pct and the tensile ductility by at least a factor of twos5 This improvement was related to the elimination of manganese-rich bands, which also are one of the factors responsible for cold cracking in the heat-affected zone of metal-arc welds.7 In the present study the nature and severity of banding in early commercial 18Ni(250) maraging steel plate and in laboratory-melted 18Ni(250) maraging steel plate was determined. The effects of banding on plane-strain fracture toughness and the effects of thermal homogenization treatments on the strength, tensile ductility, and toughness of 18Ni(250) maraging-steel as-cast ingots and rolled plate were evaluated. In addition, the effects of hot deformation by rolling on the mechanical properties of ingots were determined. 1) STUDIES OF BANDING IN EARLY PRODUCTION PLATE The chemical composition of the steel (A) used in this part of the investigation is shown in Table I. Banding was not clearly evident in either as-rolled or annealed* plate, but annealed and agedc** plate had a banded structure. The typical banded condition, Fig. 1, consists of layers of unetched austenite (white) and dark-etching martensite in a light-etching martensitic matrix. X-ray diffraction measurements showed that this steel contained more than 6 pct austenite. An electron-probe X-ray microanalyzer (using a focused beam of electrons) was used to determine the composition of the bands and of the material between the bands with respect to the main alloying elements— nickel, molybdenum, titanium, and cobalt. The recorded X-ray intensities were converted to concentration values with the use of a standard of similar composition. To facilitate probe positioning, all analyses were conducted on specimens that had been given a light etch. The influence of this etching on the analytical results was negligible; analyses made on the identical area before and after etching yielded essentially the same concentration values. The results of the electron-microprobe analyses at selected points revealed that the layers of austenite and adjacent dark-etching martensite contained greater amounts of nickel, molybdenum, and titanium than did the surrounding matrix, Table 11. The austenite layers

Jan 1, 1968

By Harold R. Larson, John F. Elliott

The standard free energies of formation of several nzetallic sulfides have been measured by a reversible electromotive-force cell employing stabilized zir-conia as the electrolyte. The oxygen potential at the cathode was fixed by the use of pure oxygen gas at 1 atm. It was established at the anode by bringing to equilibrium the reaction between the sulfide and oxide species present. Thus, Gf: for the sulfide could be obtained from the cell potential and the standard free energies of formation of the oxides participating in the reaction. The results in calories per cam rnole for the temperature range 850" to 1100°C are: Use of the reversible electromotive-force cell having an oxide-ion electrolyte to obtain the standard free energies of formation of some of the more stable metallic sulfides offers a convenient experimental method that is very productive. It also avoids some of the problems inherent in the experimental methods&apos; for such studies which rely on precise determination of gas compositions, particularly if these compositions lie near the limits of our capabilities for accurate chemical analyses. The reaction equilibrium between the lowest sulfide of a metal, SO2 at a fixed pressure, and an oxide of the metal has a characteristic oxygen potential. For example: and for metals whose lowest sulfide is much more stable than the oxides of the metal, the equivalent reaction might be:

Jan 1, 1968

By N. B. Gray, R. V. Culver, W. S. Boundy, N. W. Stump

The kinetics of sulfation of single crystals of lead sulfide to lead sulfate have been studied between 969" and 1073°K in gas atmospheres of known composition using a thermobalance technique. The data are described by an equation derived on the basis that diffusion outward through the Product layer is the major controlling step. The rate of sulfation is linearly related to the logarithm of the sulfur trioxide partial DESPITE its industrial significance the oxidation of lead sulfide has received limited attention. The oxidation reactions have been studied using beds, briquettes, single crystals, or thin films of lead sulfide. Lead oxide and lead sulfate (PbSO,) were formed when Mclntoshl and Gardner2 roasted beds of galena pressure and the temperature coefficient of reaction is 40 ± 5 kcal per g mole. Gold marker experiments show that the sulfate layer grows by outward movement of ions through the sulfate layer. Initially the PbSO, adheres to the PbS but later forms an irnpewious spheroidal envelope; PbS vaporizes and pb2&apos; ions diffuse through the envelope to react at the external surface. in air at temperatures up to 800°C. In a more extensive investigation, Tchizhykov3 obtained Pb, PbO, and PbS04 in accordance with Eqs. [1] to [4], when a bed of -200 mesh galena was oxidized in O2-N2 mixtures at 700° to 900°C.

Jan 1, 1968

By Y. A. Chang

Heat content values of tantalum monocarbide and tungsten monocarbide have been determined from 325" to 985°K by means of a drop-type diphenyl ether calorinzeter. Based on the values obtained in the present study and those available in the literature, best values lected and computed from 298. 15°K to temperatures close to their respectiue melting points. At temperatures higher than 1700°Kfor TaC and 27000 K for WC, values of Cp and related thermodynamic quantities were extrapolated based on the two Debye parameters: one corresponds to the metal sublattice and the other to the carbon sublattice. The contrzbutzon In the total specific heat due to lattice dilation was evaluated using the Nernst-Lindemann relalionship. The calculated values of Cp were in good agreement with the In view of their refractoriness, tantalum monocar-bide (TaC) and tungsten monocarbide (WC) are of con- experimentally determined ualues. Furthermore, the calculated values of the absolute entropies at 298.15"K were 5.03 and 4.15 in comparison to the experimental values of 5.05 and 4.15, all expressed in the unit of cal per degg-atom. Using the same Debye parameters, values of the linear coefficients of ther mal expansion for TaC and WC were calculated from absolute zero to their respective melting points using the Grüneisen equation. The calculated values are in excellent agreement with the experimental values available in the literature. Finally, the values of the bulk modulus of TaC from room tenzperature to temperature near its melting Point were also calculated using the equation recently derived by Anderson. No cot~ipari-son between the calculated and experimental values can be made due to lack of experimental data. siderable practical interest. In order to completely define these materials, it is necessary to know their thermal properties as a function of temperature. Tantalum rnonocarbide having a NaCl structure (B-1 type) melts congruently at 4250PK,1 while tungsten monoearbide with a simple hexagonal structure (Bh type) melts per itectically at 3049°K into melt and graphite.2 In the present study, the heat content values (from which

Jan 1, 1968

By Colin M. Sargent

THE electron diffraction pattern as seen in the electron microscope represents an approximately plane section of the reciprocal lattice. Identifying the zone axis of a diffraction pattern is often laborious for a crystal of low symmetry, especially if several crystal orientations are present. A program has been written in FORTRAN II (Version 2) for the IBM 1620 which will assist in plotting out reciprocal lattice sections. The calculation is performed by choosing a zone axis [uvw] and determining the d spacings and angle between the planes (Ow - v) and (wO - u). (This procedure is varied slightly for zone axes with Miller indices equal to zero.) Cartesian coordinates for the reciprocal lattice points are then calculated for these planes and for (ww— [u + v]). Any reciprocal lattice points within the parallelogram formed by the origin and these three points are then computed. The input and output are best described by use of an example (Monoclinic ZrO2) used in the author&apos;s work. Input consists of two cards: 1) The crystal parameters: a, b, c, a, 8, y, e.g., 5.1477, 5.2030, 5.3156, 90.000, 99.380, 90.000. 2) Three numbers, D, E, F, e.g., 5, 3, 3.0710-the first is the limit of the sum (u + v + w) considered; the second limits the absolute value of u, v, and w to (E- 1), e.g., 2, so that zones (221) would be the highest order considered in this example; the third, F, is the required constant, yL. Output is in the format shown in Table I. The reciprocal lattice sections may then be plotted on standard graph paper and compared with the unknown diffraction pattern. (Note that no attempt has been made to deal with systematically absent reflections.) A card deck for the program is available from Colin M. Sargent, ARZ, W-PAFB, Dayton, Ohio, 45433.

Jan 1, 1969

By Stephen D. Antolovich

RECENTLY, much interest has been generated in materials that undergo martensitic phase transformations on straining.&apos;)&apos; While it is undoubtedly true that a large amount of ductility can be obtained at rather high strength levels, the question of the general way in which the phase transformation affects the plane strai fracture toughness, as measured by the parameter KIC, has yet to be answered. Let us consider a material that contains a sharp crack as shown in Fig. 1, and is subjected to a tensile stress 00. It is known that the presence of a crack tends to multiply the stress in the area of the crack according to the following equations:3

Jan 1, 1969

By J. K. Abraham

In recent years there has been interest displayed in the precipitation phenomena occurring in austenitic alloys based on the binary Fe-Ni system.1&apos;2 Previous communications have been extended covering the kinetics of clustering in the Fe-Ni-Ti system and the effect of cluster size on subsequent mechanical properties.3&apos;4 To a great extent the question of coherency, which has a dominant role in determining the mechanical properties, is dictated by the degree of misfit between the precipitate and matrix. Thus, the change in lattice parameter of the matrix with composition is an important variable that should be examined. The lattice parameter, ao, of austenite was determined for Fe-29.75 Ni-1 to 6 Ti and Fe-27 Ni-1 to 10 Ti alloys in this study. The alloys used in this investigation were melted in a vacuum induction furnace from a starting stock of plast iron (99.95), electrolytic nickel (99.9), and ti- tanium sheet (99.5) in a MgO crucible. The alloy compositions in atomic percent are given in Table I and their relative position in the Fe-Ni-Ti ternary is indicated in Fig. 1. The chemical analyses were taken from the homogenized bulk materials treated in a manner related earlier.3 A diamond file was used to obtain powder from the bulk. To remove the stresses induced by filing, the powders were austenitized at 1875°F for

Jan 1, 1969