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By V. G. Leak, R. A. Swalin

The dilhsion of silver and trace concentrations of tin in liquid silver has been rrzeasured in the temperature range from about 975° to 1350°C. The difBsion dala. fil lhe following equations: fov self-diffusion of silver The ratio of DSn to DAg is found to be about 1.34. The higher diffusivity of tin is interpreted in terms of the coullombic repulsion which results from the fact that tin dissolved in silver has a valence of +3 relative to silver. THE phenomenon of diffusion has been well-described theoretically for hard-sphere gases and solids and found to be in good agreement with experimental data for certain gases and solids. Liquid-diffusion phenomena have not been well described theoretically and there is generally a lack of good experimental data. In this investigation self-diffusion and solute diffusion in liquid silver were studied. Silver was chosen as a solvent for two main reasons. First, silver is a noble metal and the atoms are considered to have a spherically symmetric charge field; hence the liquid may be considered to be a random array of approximate hard spheres. Mercury, gallium, and other lower-melting metals were eliminated from consideration since it appears possible that in their liquid states there is some residual long-range order and directional bonding. Second, silver behaves as a monovalent solvent and, while cadmium, indium, tin, and antimony all have nearly the same atomic size, they have chemical valences relative to that of silver of +1, +2, + 3, and +4, respectively. Slifkin, Lazarus, and coworkers1-5 investigated the diffusion of these solutes in solid silver and found that their diffusion rates increased with an increase of the excess valence of the solute. In the solid state the diffusion-rate increase was calculated to be due to a change in local modulus of the solvent caused by the excess valence of the solute.1"3 For the present investigation it was planned to determine the effect of valence upon solute diffusion in liquid silver. It was deduced that a coulombic repulsion between solute and solvent might be responsible for larger volume fluctuations in the vicinity of the solute thereby enhancing the diffusion of the solute atoms. Tin was the first solute investigated and was chosen for experimental convenience. If an excess-valence diffusion effect exists in the liquid state, the solute tin with its excess valence of + 3 might show a large enough effect to distinguish it from the self-diffusion of silver in silver. The silver self-diffusion data were obviously required as a base line for comparison. In addition silver self-diffusion was investigated with a view toward examining the data in connection with the Sutherland- Einstein: Coheen-Turnbull,7 and swalin8 theories of diffusion in liquids. I) EXPERIMENTAL TECHNIQUES The diffusion coefficients for tin and silver in liquid silver were determined in separate experiments using the capillary-reservoir method of Anderson and saddingtono but following closely the experimental techniques outlined by Ma and Swa1in. The radioactive alloy bath was prepared by plating either tin-113 or silver-110 m isotope* onto 99.999 *Isotopes obtained from Oak Ridge National Laboratory. pct Ag rods.* The silver and isotope were melted *Silver obtained from Cominco Co. and mixed in a graphite crucible under a purified argon atmosphere, then outgassed for capillary filling. Some of the fused-silica capillaries were filled individually as reported by Ma and Swalin, but most were filled in a different manner. A long piece of capillary tubing was sealed off on one end and held in the system so that the open end was just above the surface of the molten alloy. The system was evacuated, the open end submerged into the alloy, and argon was admitted into the system up to atmospheric pressure. The molten alloy was forced up the capillary several inches where it solidified and was subsequently cut into segments of the proper length for diffusion annealing. The apparatus for diffusion annealing was the same as that used for capillary filling except that a Pt—Pt, 10 pct Rh therinocouple was placed in the solvent bath in order to accurately measure the temperature during the run. A diagram of the dif-

Jan 1, 1964

By W. D. Ludemann, J. E. Dor, L. A. Shepard

Recovery of the creep resistance of 99.99 pct pure Al was studied at temperatures 540°, 573°, 600°, and 611°K. Poly-crystalline specimens crept under a stress of 950 psi to a strain of 5.5 pct were allowed to recover for periods of from 1 min to 16 days under a residual stress of 4.4 psi. Increased creep rates upon reapplication of the 950 psi stress evidenced softening of the material. The activation energy for the recovery process was found to be 64,000 cal-per mol. THREE major observations have clearly revealed that the creep of polycrystalline aluminum above about 510°K is controlled by the rate of climb of jogged edge components of dislocations past the barriers impeding their motion: 1) Extensive polygonization, characteristic of climb, takes place during creep.'9' 2) The activation energy for creep equals the estimated activation for self-diffusion. 3) The stress law for creep coincides with theoretical predictions based on the climb mechanism.4,5 The decreasing rate during the primary stage of creep must be ascribed to the introduction of additional barriers to the glide of dislocations. During secondary creep the density of barriers must remain constant, the rate at which new barriers are formed being equal to the rate at which they recover. For this reason the nature of the barriers, and their rates of formation and recovery, are significant to a complete understanding of creep. It is proposed here to study the kinetics of the recovery of barriers to creep of high-purity polycrystalline aluminum in the climb range. The technique will consist of creeping a series of tensile specimens under a prescribed stress to given state following which the specimens will be recovered for various times and temperatures under approximately zero stress. The amount of recovery will be determined by comparing creep curves following the recovery. EXPERIMENTAL PROCEDURE The material used for this investigation was a 99.99 pct pure Al supplied by the Aluminum Co. of America in sheets of 0.001-in. thickness having an H-18 temper. The spectroscopic analysis of impurities gave Cu-0.004 wt pct, Fe-0.002 pct, Si-0.001 pct, others-0.000 pct. Creep specimens were machined with their tensile axes in the rolling direction of the sheets. Annealing in a molten potassium nitrate-potassium nitrite bath for 1 hr at 686K, followed by air-cooling, resulted in a grain diameter of from 0.22 to 0.27 mm. Creep machines were equipped with constant stress lever arms of the type suggested by Fullman, Carreker, and Fishher,' which maintained the applied stress to within 0.04 pct of the reported value of 950 psi. Creep strains were calculated from extensions over a 6-in. gage section to the nearest 3 X 10"5. The temperatures of testing, 540°, 573", 600°, and 611°K, were obtained by immersing the specimen and extensometer assembly in a molten KNO2-KNO3 bath. Temperatures during the periods of creeping could be maintained constant to within better than ± 1°K. Correlation of creep data at different temperatures of testing demanded the use of an appropriate temperature-compensated time 8. Previous investigations have shown that the creep of pure metals at temperatures above about 0.55 of their melting temperatures can be correlated by the functional relationship3" e=f(0), s= const. [1] where e = total plastic strain during creep f = a function that depends on stress a = stress 6 = te-Q/RT = a temperature-compensated time t = time under test Q = 35,500 cal per mol = activation energy for creep R = gas constant, and T = absolute temperature In the present series of tests all of the creep was conducted under the same stress of 950 psi. To provide identical initial conditions for the recovery all specimens were first crept to a temperature-compensated time of = 47 X 10-14 min which resulted in a creep strain of 0.055 + 0.005 regardless of the creep temperature. During recovery, a small stress (4.4 psi) was permitted to remain upon the specimens to maintain tautness in the pulling assembly and to prevent mechanical damage to the soft specimen. After each recovery period, the full stress was reapplied and

Jan 1, 1961

By H. L. Gilbert, W. W. Stephens

Production of anhydrous zirconium tetrachloride by direct chlor- ination of a zirconium oxide carbon mixture in a silica-brick-lined chlorinator is described. Theory and thermodynamics of reactions are discussed. A pilot-model chlorinator and full-scale production equipment are described and operating data are included. ANHYDROUS zirconium tetrachloride required as a starting material in the Kroll process for production of ductile zirconium has been produced in this country principally by chlorination of the carbide or "carbonitride" made by reduction of zircon sand concentrates with carbon in the arc furnace. This process and the equipment used have been fully described.'.' It is well known that zircon or badde-leyite ores may be chlorinated directly with chlorine in the presence of carbon, and this one-step approach would seem at first glance to be preferable to the two steps involved in the carbide-chloride operation. As previously discussed1 considerations leading to adoption of the longer process were: 1—Chlorination of the carbide proceeds rapidly at temperatures below 500°C, whereas temperatures above 900°C were considered necessary for chlorination of zircon-carbon mixtures. 2—The highly exothermic nature of the carbide-chlorine reaction makes it self-sustaining, while heat must be supplied continuously in direct chlorination of the ore. 3—Silicon was thought to be chlorinated along with zirconium in the direct chlorination of zircon, leading to high chlorine consumption. In production of carbide in the arc furnace, silicon is driven off as silicon monoxide and does not enter the chlorinator. 4—For efficient direct chlorination, the ore must be finely ground and intimately mixed with carbon, and the mixture briquetted. 5—Direct chlorination requires a much larger chlorinator for a given production capacity than chlorination of carbide. Recently it has become necessary to produce large quantities of zirconium metal from a chemically purified zirconium oxide. Since the cost of the latter is high, the relatively high losses encountered in production of carbide in the arc furnace could not be tolerated, and a graphite resistor furnace5 was developed for production of carbide, which was then chlorinated in equipment previously used for chlorinating arc-furnace carbide. This method of operation was quite satisfactory, and losses in the carbid-ing step were minimized. However, operating costs were relatively high, and the process did not lend itself particularly well to large-scale operation because of the multiplicity of small units required and the hand labor needed to load, unload, and maintain the furnaces. To chlorinate the carbide, a vertical-shaft chlorinator was used in which the charge was heated with a central split graphite-rod resistor.' Operation of this chlorinator was somewhat less satisfactory with the resistor furnace carbide than it had been with the arc-furnace carbide due, principally, to the differences in physical properties of the carbide. The arc-furnace carbide is obtained as a fused metallic-appearing mass which can be crushed to -1/4 in. with production of a minimum of fines, whereas the resistor-furnace product is lightly sintered and produces a large proportion of fines in crushing and handling. These fines tend to pack in the chlorinator and promote channeling. which results in poor chlorine efficiency and low capacity. Data based on production of 22,000 lb of chloride from resistor-furnace carbide in this equipment are shown in Table I. Necessity for increasing production of chloride from about 2,000 to 15,000 lb per week led to further investigation of possible methods for direct chlorination of the oxide or oxide-carbon mixtures. Direct chlorination of the pure oxide presents much less difficulty than chlorination of zircon sand or oxide ores. The oxide is easily ground to —200 mesh, and no silica is present to cause excessive consumption of chlorine or contamination of the product. Theoretical Considerations The principal chemical reactions involved in chlorination of mixtures of zirconium oxide and carbon may be written as follows: ½ ZrO2 (c) + C(c) + Cl2(g) = ½ ZrCl,(g) + CO(g) [I] 1/2 ZrO, (c) + CO(g) + Cl2(g) = ½ ZrCl,(g) + CO2(g) 121 ½ ZrO2 (c) + ½ C(C) + Cl2(g) = 1/2 ZrCl4(g) + ½ CO2(g) [3]

Jan 1, 1953

By E. T. Turkdogan, L. E. Leake

A number of measurements have been made on the vapor pressure of pure iron at 1600°C. Experiments were carried out by the transportation method in which a sample of iron is exposed in a furnace to a stream of pure argon, metered at a predetermined flow rate for a specified period of time. The vapor pressure was obtained from the weight loss of the sample. A detailed diagram of the apparatus used for the experiments is given in Fig. 1. It consisted of a horizontal molybdenum-wire-wound furnace fitted with a recrystallized alumina tube 1 1/8 in. internal diam. The boats, 1 by 3/16 by 1/8 in., were fired in argon at 1600°C to constant weight before use. After this treatment, subsequent heating of the boats to 1600°C gave little or no further change in weight, e.g. ±0.05 mg in 24 hr. The furnace and reaction tube were separately fed with argon from two independent flowmeters. These were connected to a common supply source via an argon purification furnace containing metallic titanium sponge at 700°C, and an anhydrone drying-tower. A rotary displacement-type meter was included in the gas train to provide a direct means of measuring the total volume of gas passed through the reaction tube. The material used was vacuum melted high-purity iron in the form of wire 2mm in diam. The following impurities were present in the iron: 0.008 pct C, 0.002 pct Si, 0.005 pct Mn, 0.008 pct S, 0.001 pct P, 0.01 pct Ni, 0.001 pct Cr, 0.006 pct Cu, and 0.001 pct Al. Samples consisting of three small pieces of this wire were laid end to end in a recrystallized alumina-combustion boat, and were separated by small fragments of alumina. The wire samples were then melted in argon to form spherical beads 2 to 3 mm in diam. After weighing, the boat with its contents was placed on the boat carrier and introduced into the cool end of the reaction tube. The entire furnace system was then flushed with argon for 30 min. At the end of this period, the flow of argon to both furnace and reaction tubes was adjusted to the desired level; then the boat was slid rapidly into the hot-zone of the reaction tube. After a known volume of gas had passed through the reaction tube, the boat was withdrawn quickly to the cool end of the furnace. When quite cool, the boat was removed from the fur-mace and placed in a desiccator for subsequent re-weighing. The semi-micro balance used in these experiments had a sensitivity of 0.005 mg. The above procedure was repeated at several flow rates within the range of 25 to 300 ml per min. The flow of argon in the annular space between the two tubes was at a rate of 300 ml per min in all experiments. During all the experiments the furnace temperature was maintained at 1600° ± 5°C by means of a temperature controller. The temperature of the reaction zone was measured with a Tinsley high precision disappearing filament pyrometer which was initially calibrated against a Pt-13 pct Rh/Pt thermocouple; the errors due to temperature measurements were within * 5°C. RESULTS Assuming that the iron vapor is in the monatomic state, the vapor pressure can be calculated from the weight loss of the sample and the volume of the carrier gas. The results obtained are plotted in Fig. 2 against the rate of flow of argon through the chamber containing liquid iron beads. At low flow rates, the thermal diffusion of iron gives an apparent high vapor pressure, but at high gas flow rates, the carrier gas is not saturated with the vapor, and therefore, low vapor-pressure values are obtained. This is now a well-known phenomenon. There is a distinct inflexion of the curve at about 120 to 160 ml per min rate of argon flow and the vapor pressure of iron within this

Jan 1, 1961

By H. G. Papacharalambous, S. C. Sun

Experimental results indicate that wet cyclones could be effectively used for the preliminary classification of the tested synthetic abrasive materials, thus supplementing the currently used sedimentation method. An empirical formula is also proposed on the basis of the test data to calculate the particle size of separation. One of the basic operations in the abrasive industry is the classification of the crushed and ground materials into different sized products. The relatively coarse grains, plus 325 mesh, are commonly sized by dry screening with satisfactory results. On the other hand, however, the currently used grading tank, for classifying grains finer than 325 mesh, is intermittent. Consequently, it is difficult to operate efficiently and keep pace with erratic market requirements. Little success was made in an attempt to substitute air settling and continuous hydraulic settling for the grading tank, because size specifications1 for abrasive powders are very stringent and difficult to meet. Finally, a wet cyclone was chosen for experimentation. Even though wet cyclones have not been extensively used in the classification of abrasives; however, their performance as a classifier has been verified by Driessen2,4 on coal, McCarrel5 with manganese, and Herkenhoff6,7 on iron ore. Experimental work on silicon carbide, boron carbide, and fused alumina has shown that the cyclone

Jan 1, 1963

By Arch. B. Johnston, Carle R. Hayward

The effect of copper on steel has been studied by numerous investigators. Before modern testing methods had been developed, blacksmiths noted red shortness in iron, the cause for which was ascribed to the presence of copper. Numerous papers have been published on the corrosion of steels containing various amounts of copper, and a few writers have discussed the effect of copper on the mechanical properties of steel. The purpose of the investigation described in the following paper was to obtain additional data on the mechanical properties of medium-carbon steel containing small quantities of copper. Among those who have published results of mechanical tests on copper steels are Ball,' who states that copper increases the tensile strength and hardness but lowers the elongation. Stead2 states that copper steels closely resemble nickel steels containing equivalent percentages of nickel, as regards tensile strength, resistance to shock, corrosion and hardness. Wigham3 found that copper in small amounts had no injurious effect on steel. Breui14 found that with 1 per cent. carbon, copper lessened the brittleness of steel and in low-carbon steel it increased the tensile strength and lowered the ductility slightly. H. H. Campbell5 states that copper up to 0.25 per cent. slightly raises the elastic limit, elongation and reduction of area.

Jan 1, 1918

By G. L. Kehl, Emilo Jaraiz F., J. S. Brett

The transformation of eutectoid beryllium bronze has been quantitatively investigated at 550° and 592°C, the temperature region where the products of p decomposition are a fine lamellar eutectoid and a coarse lamellar aggregate which replaces the fine eutectoid with prolonged annealing. Metallographic evidence indicates that the coarse lamellar aggregate forms preferentially in the most densely lamellated regions of the fine eutectoid and favors the hypothesis that the development of the coarse lamellar aggregate in the fine eutectoid is due to the occurence of a cellular segregation reaction. WHEN eutectoid beryllium bronze (Cu-94 pct, Be-6 pct) is isothermally transformed at high temperatures in the and y region after quenching from the fl field, the principal initial decomposition process is G one of growth of approximately spherical nodules composed of a number of lamellar colonies of the a and y phases. After the initial reaction has proceeded substantially or completely, depending on the transformation temperature, a second reaction occurs wherein the fine lamellar eutectoid is replaced by a coarser lamellar aggregate composed of the same oand yphases.' This reaction is not simply a spheroidization of the initial fine eutectoid but the nucleation and growth of a coarser, structurally different, and more stable distribution of the @and yphases. Fig. 1 illustrates the replacement of the initial fine lamellar structure by a coarse lamellar aggregate. The a phase is the dark mottled constituent; the light constituent the y phase. The phase diagram for the copper-rich end of the Cu-Be system2 is shown in Fig. 2. The a phase has the face-centered cubic structure characteristic of copper-rich solid solutions. The B phase is a disordered body-centered cubic structure, while the y phase is body-centered cubic, ordered (CsC1, B2 type). A. viswanathanS investigating Debye patterns of Cu-6 pct Be discovered that a transitory phase appeared on very rapid quenching from the /3 region which was absent when the quenching velocity was moderate. The phase could be assigned a body-centtred cubic structure with a lattice parameter of 2.876. Tempering at 100°C for 2 hr after quenching resulted in complete disappearance of the phase. The work of Fillnow and Mack' is the only previously published study of the isothermal transformation of eutectoid beryllium bronze. Their study elucidated the nature of decomposition at various subcritical temperatures in an exploratory fashion. The purpose of the research reported in this paper was principally to obtain quantitative information on the isothermal decomposition of the fl phase and to clarify the relationships existing between the fine lamellar eutectoid and the coarse lamellar aggregate. EXPERIMENTAL PROCEDURE The material used in this investigation was an almost eutectoid Cu-Be alloy bar furnished by D.J. Mack. The alloy had been melted under a protective carbon cover and centrigugally cast into a graphite mold preheated to 490 "C. Segregation was minimized by violent agitation during melting and pouring. The analysis of the casting was 93.85 pct Cu, 5.60 pet Be with traces of Si, Mg, Mn, Co, and Al. To determine the minimum soaking time necessary to insure specimen homogeneity, a number of specimens were held in the P region at 788OC for times fron 1 min to 12 hr and isothermally transformed at 550°C. Specimens betatized less than 12 min exhibited partial transformation at times shorter

Jan 1, 1961

By A. E. Dwight, A. F. Berndt

ThE published U-Ru equilibrium diagram indicates the existence of six intermetallic compounds in this system.' The structure of only two of the compounds, u2Ru2,3 and URU3,4 have been identified. This communication reports on the crystal structure and density of Uau3, which is formed by a peritectoid transformation at 1025° ± 5°C: U3Ru4 + U3Ru5 = U2Ru3. An alloy with the stoichiometric formula U2Ru3 was prepared by arc melting electrolytic uranium and ruthenium of 99.9 pct purity on a water-cooled copper hearth under an argon atmosphere. After homo-genization at 1000°C for 3 days, a metallographic examination revealed that the peritectoid transformation was complete and less than 5 pct of a second phase was present. A powdered sample, obtained by crushing the brittle compound, was annealed for 1 hr at 1000°C and air-cooled. Debye-Scherrer patterns were obtained with filtered CrKa, FeKa, CoKa, or CuKa radiation. The X-ray patterns of U2Ru3 weFe indexed as an fcc structure with a. = 12.895 0.00lA. The unit-cell constant and its standard deviation were calculated by a computer program described by Mueller, Heaton, and Miller.5 The density, measured by an immersion method, was 14.45 g cm-3. A calculated density of 14.48 g cm-3 was obtained on the assumption that twenty-four formula units (120 atoms) comprise a unit cell. The space group is either oh7 Fd3m, or the less symmetric, T4h, Fd3, since reflections indexed as hk0 with h + k + 4n are absent. All values of h2 + k2 + 12 permitted by both space groups are listed in Table I together with dc, do, and I. values. The calculated d spacings were obtained by the computer program of Mueller, Meyer, and simonsen.6 The observed d spacings above 0.77A were obtained from X-ray" patterns prepared with CuKa radiation, above 0.90A with CoKa radiaaion, above 0.98A with FeKa radiation, and above 1.16A with CrKa radiation. An attempt was made to identify the crystal structure of U2Ru3 by comparison with published data on other A2B3 compounds. A recent compilation7 of intermetallic compounds lists thirty-two structure types with the A2B3 stoichiometry. Only two of the structure types are fcc and they are Sb2O3(r), senarmontite, with 16 Sb2O3 per unit cell, and In2Te3 for which several structures have been proposed.8 However, the two cases cited do not have twenty-four formula units in the unit cell. We therefore, cannot identify UPRU3 with any of the other known A2B3 compounds. Ternary alloys were made in which 5 at. pct Os, Rh, or A1 were substituted for 5 pct of the Ru in U2Ru3. The osmium substitution increased the unit cell constant to 12.899 * .001A, which is to be expected since the atomic volume of osmium is slightly larger than

Jan 1, 1969

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

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

Jan 1, 1958

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

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

Jan 1, 1964

By P. Dayal, L. S. Darken

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

Jan 1, 1951

By D. J. Schmatz

DISCUSSION OF RESULTS The qualitative correlation between low-temperature ductility and prior high-temperature creep strain in nickel obtained in this investigation confirms the result obtained on high-purity brass by Chen and Machlin. However, the quantitative effect is much smaller in nickel. Comparison can be made on the basis of a prior high-temperature strain that is a certain percentage of the total high-temperature elongation to rupture. In the research of Chen and machlin, the prior high-temperature strain of 1/2 pct equaled 8.5 pct of the total high-temperature elongation at rupture. For nickel, in our experiments, 8.5 pct of 21.2 pct equals 1.8 pct. For eh = 1.8 pct, the loss in ductility in percent equals x 100 = b.5 pct. That is, for equivalent bo Formation of Beta Manganese-Type Structure in Iron-Aluminum-Manganese Alloys D. J. Schmatz IRON-aluminum alloys have gained much interest in the past few years for use as a base material for elevated-temperature alloys because of their excel- high-temperature strain the loss in low-temperature ductility is 8.5 pct for nickel as compared to 60 pct for pure a, brass. It is also interesting to note the observation that in nickel the low-temperature fractures, even at the most extreme high-temperature pre-strain, were partly trans crystalline and partly intercrystalline. In the case of a brass, these fractures were completely intercrystalline. According to the data on the percent of the grain boundary area that is cracked, at 22 pct high-temperature elongation, about 12.5 pct of the grain boundary area does not carry load. Thus, the inter-crack areas are carrying a stress that is about 11 pct higher than the nominal stress. A simple model predicts that the overall elongation, which is primarily the elongation in the bulk of the specimen, will correspond to the nominal stress when the stress in the intercrack area equals the tensile strength. Quantitatively this model predicts the equation The form of this equation will agree with that found if the strain-hardening exponent, n, equals unity. Actually this model is too gross an approximation to yield good quantitative results. The question naturally arises as to whether in ordinary hot-working, such as hot-rolling, intercrys-talline cracks are introduced that affect the low-temperature properties. It appears that the answer is that such a possibility cannot be overlooked, if the hot-working induces tensile stresses at temperatures above the equicohesive temperature and if the material tends to be notch sensitive at low temperature. ACKNOWLEDGMENT This research was supported by the Aeronautical Research Laboratory, Directorate of Research, Wright Air Development Center, United States Air Force. REFERENCES lC. Zener: Fracturing of Metals, 1948, Cleveland, ASM. 'H. C. Chang and N. J. Grant: Mechanism of Intercrystalline Fracture. AIME Trans., 1956, voL 8, p. 544; lownal of Metals, May, 1956. 'E. S. Machlin. CreepRupt ure by Vacancy Condensation, AIME Trans., 1956, vol. 8, p. 106; lownd of Metals, February, 1956 'C. Chen and E. S. Machlin: On a Mechanism of High-Temper at ure Inter-crystalline Cracking, lownd of Metals, July. 1957. p. 829. Alloys lent oxidation resistance. Binary alloys of aluminum in iron are ferritic and consequently have poor hot strength. Alloys of iron-aluminum-manganese were made in an attempt to produce an austenitic alloy containing sufficient aluminum to retain the oxidation resistance of binary alloys of iron-alumi-

Jan 1, 1960

By G. S. Upadhyaya, A. D. McQuillan

HERE would appear to be a simple relationship between the group number in the periodic table of the early transition metals and the maximum amount of hydrogen which they can absorb.' Thus group IIIA metals (Sc, Y, and La) yield a trihydride in which the metal atoms are on a fcc lattice and the hydrogen atoms occupy both tetrahedral and octahedral interstices. Group IVA metals (Ti, Zr, Hf) form dihy-drides in which the metal atoms are on either a fct or cubic lattice, but in which only the tetrahedral interstices are occupied by hydrogen atoms. In group VA (V, Nb, Ta) the hydrogen-saturated metal attains a composition slightly below that of a monohydride under normal conditions. Finally the metals of group VIA (Cr, Mo, W) do not dissolve appreciable quantities of hydrogen. The manner in which hydrogen solubility disappears on alloying a group VA metal with one from group VIA has previously been investigated.2 It is necessary, in order to obtain a general picture of the reactions of alloys of the early transition metals with hydrogen, to examine a system containing metals from groups IVA and VA in which there must be a change from a fcc to a bee hydride phase. The system chosen for investigation was the pseudobinary system between titanium hydride and niobium hydride. Metallic alloys were prepared by melting iodide-prepared titanium with zone-refined niobium in an argon-atmosphere are-furnace. To ensure homogeneity each alloy was cold-swaged and then heated at 1250°C in a high-vacuum furnace until metallo-graphic examination confirmed its complete homogeneity. Small weighed specimens of the alloys were charged with hydrogen using gaseous hydrogen generated by heating titanium hydride. The apparatus has been described elsewhere.3 Throughout the charging process the hydrogen pressure was kept at about 1 atm while the specimen, initially at 800 °C, was slowly cooled to 150°C over a period of days. The total amount of hydrogen absorbed by each specimen and the room-temperature crystal structure of the hydride powders were determined. The X-ray investigation indicates that the fee hydride phase arises from alloys extending in composition from titanium to 67 at. pct Nb. After a two-phase field lying between 67 and 74 at. pct Nb in which the fee and bee hydrides coexist, all alloys richer in niobium yield a distorted bee hydride. Data derived from parameter measurements are presented in Fig. 1. The atomic volume per metal atom has been plotted against the composition of the initial metallic alloy in order to facilitate comparison of the effects of hydrogen addition in the two phases of different crystal structure. The amount of hydrogen absorbed by each alloy at saturation in terms of the hydrogen to metal ratio and alloy composition is given in Fig. 2. Over the whole range of the fee hydride phase the hydrogen content remains constant, while in the distorted body-centred hydride phase, the hydrogen content increases with increasing titanium content reaching a hydrogen/metal ratio of 1.4 at the boundary of the two-phase region. It seems likely, therefore, that the maximum hydrogen content of the fee hydrides is limited to a hydrogen/metal ratio of 2 because hydrogen atoms

Jan 1, 1962

By Philip R. Strand, O. F. Stewart

Vermiculite is the name generally applied to the group of hydrated ferromagnesian aluminum silicates that are characterized by the ability to expand when heated. This process, called exfoliation, results in a lightweight product of commercial value. Most uses of vermiculite are for the expanded material. The chief markets are in construction, agriculture, and horticulture, with lesser uses in general industry. Composition and Properties Vermiculite, in its natural state, has the characteristic micaceous habit, a perfect basal cleavage which causes splitting into thin laminae that are soft, pliable, and inelastic. The structure of vermiculite is basically that of a talc. The prominent monoclinic crystal faces are often marked by lines at 60° and 120°. Hardness varies from 1.5 to 2 or more; specific gravities are between 2.1 and 2.8; color varies from almost clear to amber, bronze, brown, green, or black. Vermiculite feels like talc, especially when wet. Although much research has been performed on the chemical and structural composition, there is not yet complete agreement on the exact formula. This is to be expected when different workers have examined the many different varieties. Vermiculite is not considered to be a single mineral species but a family of related minerals. The structural formula for a trioctahedral vermiculite may be written: (H20)-(Mg,Ca,K)-(A12,Fe,Mg)-(Si,A1,Fe)4O10 (OH) 2 Hydrobiotite also occurs with vermiculite and is usually considered a vermiculite for commercial uses. When heated quickly to elevated temperatures, vermiculite expands by exfoliating at right angles to the cleavage into wormlike particles. The name vermiculite is derived from the Latin vermiculare, to breed worms. This characteristic of expansion is the result of the mechanical separation of the layers by the rapid conversion of contained water to steam. The decrease in bulk density of commercial grades is usually approximately 10 times, from 50 to 5 lb/ft3, but varies depending on the quality, size, and furnace efficiency. Individual flakes may expand up to 30 times. Vermiculite may also be expanded by soaking in chemicals such as hydrogen peroxide, weak acids, and other electrolytes. Color change during expansion is dependent upon the type of vermiculite and furnace conditions. Heating in an oxidizing atmosphere produces a dull gray or tan color, whereas a reducing atmosphere can produce a bronze or gold color. The expansion of the vermiculite crystal results in large pores being formed between the platelets. Thus, exfoliation makes available a large increase in void volume which is important in the application of vermiculite as a chemical carrier. Mathieson and Walker (1954) state vermiculite must be regarded as a true clay mineral. The characteristic properties of the mineral, such as high cation exchange capacity, organic complexing ability, and variable interlamellar distance are very similar to those of montmorillonite. The cation exchange capacity of vermiculite is one of the highest of all the clay minerals. The interplatelet space is accessible to penetration by some electrostatically neutral molecules. Water and glycerine are two common substances whose molecules may be so imbibed. In the natural state and under normal atmospheric conditions, water occupies the spaces between the silicate layers. The crystal d-spacing is near 14.2A. By differential thermal analysis, it has been determined that the water

Jan 1, 1983

* Kennecott Copper Corp. gets Charles R. Cox as president on Jan. 1. Mr. Cox is resigning his position as president of Carnegie-Illinois to take the new post with Kennecott, left vacant by the death of Mr. Stannard in September. •The ECA signed a contract in December to advance X3,600,000 to Newmont Mining Corp. to aid development of lead and zinc mines in French Morocco. The funds are to be repaid in lead and zinc for the United States' stockpile over a period of seven years. The mines are owned by the Societe des Mines de Zellidja, with which organization Newmont is associated. • Under the direction of John M. Brooks, Jr., general manager, the Matahambra mine in Cuba, will probably produce sufficient tonnage to make 4 million lb of copper per month during 1950. The grade is presently running between 7 and 10 pet. •S. H. Ash reports that the fatality rate per million-man-hr for the anthracite industry for 1949, through November, is 0.78. This is 15 pct better than that achieved during 1948, which was the lowest fatal injury rate in coal mining history. The first full year on record without a major disaster was recorded in 1949 (p. 34). •The Atomic Energy Commission has authorized the production of 200 lb of uranium metal for use under AEC license in non-Commission research projects. •A national survey of projected 1950 purchases of new machine tools, machine tool accessories, materials handling equipment, etc., just completed by the American Society of Tool Engineers reveals that, of the companies reporting, 80 pct state that they plan to buy either more equipment or the same amount as in 1948. • Armour Research Foundation is conducting investigations for the use of clay and shale deposits to make lightweight aggregates. The material is heated until it expands and forms material suitable for mixing with cement which it is hoped will be lighter, stronger, have better insulating qualities and will lower the cost of concrete. •In the first six months of 1949 the bituminous coal miners' average hourly earnings were $1.94 -as compared with X1.392_ national average for all manufacturing. Average annual earnings of full-time employees in the bituminous coal mines in 1948 were $3387 as compared with $2809 for all industry. •LaSalle Business Bulletin reports: "year ends on a rising trend in industry and trade ... nearly record-breaking demand from almost all sources keeps business high... most indicators but little below postwar peak... forces keeping activity high arestill powerful--changes in general business conditions likely to be slow and moderate." •Office of Internal Trade of the Commerce Department requests that technical data significant to the national security which is to be sent outside of the United States be submitted to it for an official opinion on the desirability of transmitting such information. This voluntary compliance program is part of our national security control. • Blast furnace slag reduced to 12 to 16 mesh is being used for sanding track at the Mont Coal mines of Armco. The slag replaces silica sand which caused silicosis. It has proved so effective and cheap that tests are being made to use the slag for rock dusting.

Jan 1, 1950

By T. L. Berger, M. C. lnman, M. F. Rose

AFTER shock loading, mechanical twinning has been observed by several authors1-4 for a variety of fcc metals and alloys. It has been shown2,3 that low stacking fault energy materials deform primarily by the formation of mechanical twins and stacking faults during dynamic loading. Further, Inman, Murr, and Rose2 have shown that a correlation exists between the average hardness and the volume percent of mechanically twinned material in stainless steel. It has been observed in nickel' that mechanical twins are produced during shock deformation if the peak pressure associated with the shock wave is greater than 350kbar. It is the purpose of this work to discuss shock-hardening mechanisms in nickel and to determine to what extent the initial condition influences the final response. The "flying plate technique" was used to generate planar shock waves with peak pressures as high as 710 kbar. The details of the technique5" have been discussed elsewhere and will not be repeated here. The material used in this study was polycrystalline nickel of 99.98 pct purity and had an initial grain size of 0.18 mm. Prior to any deformation, all samples were given a stress-relief anneal of 6 hr at 600°C in a vacuum furnace. After annealing, the initial condition of the samples was changed by cold rolling individual samples from 0 pct to a maximum of 80 pct reduction in thickness. This provided samples with controlled initial histories for shock deformation. Immediately after shock loading, the specimens were slowed and quenched by suitable arrangement of buffer material and water bath. This technique minimized specimen damage and the effects of shock heating on the samples. Since deformation twins in high stacking fault energy fcc metals are only produced at high stress levels, the initial defect configuration prior to mechanical twinning should greatly influence the number of twins formed. In fact, Zukas and Fowler7 have found that prestraining in iron and steel greatly suppresses the formation of mechanical twins during the shock deformation process. Following the methods of Warren and warekois8 and Cohen and Wagner,9 X-ray diffraction profile analysis was performed to determine the incidence of stacking faults and mechanical twins in the deformed nickel. Analysis was made on samples in the annealed, cold-rolled, shock-loaded, and cold-rolled—shock-loaded states. The estimated accuracy of the peak position measurements is *0.01 deg in 2?. Therefore the accuracy in the measurement of the relative peak shifts between the (400) and (222) diffraction line profiles is on the order of *0.04 deg in 2?. None of our measurements indicated peak shifts greater than 0.04 in 28. This would correspond to a fault density of -1 pct and sets the limit on the sensitivity of our instrument. Similarly, analysis of the shift in the center of gravity of the diffraction line profiles yields the minimum measurable value of the twin fault probabilitya to be -0.002. Fig. 1 shows mechanical twinning in nickel shock-loaded to 400 kbar. In this photograph, fault intersections are clearly visible. The thickness of the individual fault lamellae was determined from the image widths of their lines of intersections by the

Jan 1, 1968

By W. A. Oates, J. A. Lambert, P. T. GaIIagher

Monte Carlo methods have been used to compute the arrangements of interstitial atoms dissolved in tetrahedral sites in bcc lattices. It is assumed that the presence of an interstitial atom "blocks " a certain number of neighboring sites and prevents their occupancy. Sites "blocked" by more than one filled site are allowed for. The computed values of. the mean occupation number (defined as the ratio of the total number of sites blocked to the number of solute atoms are used to calculate the configurational entropies of the solutions. These entropies are compared with those resulting from previous theoretical studies of this problem and also with available experin~ental data for the p Zr-H, Nb-H, V-H, and Ta-H systems. Evidence is also given that the "blocking" explanation of low limiting compositions in these systems, rather than this being due to initial limitations on the number of sites available, is probably correct. THE ideal partial configurational entropy of mixing of an interstitial solute in a metal is given by: where p is the number of interstitial sites per metal atom and Xi is the atomic fraction of the interstitial. For the bcc lattice. which we shall be concerned with in this paper, the interstitial positions are shown in Fig. 1. It can be seen that for the tetrahedral sites, p=6. whereas for the octahedral sites, p = 3. Different emphasis has been placed on the relative importance of energy and entropy effects in determining deviations from ideality in interstitial solid solutions. In some cases the same system, e.g., Fe-C, has been described by the contradictory regular and athermal solution models indicating that the enthalpy and entropy functions, derived from equilibrium data, are frequently not accu.rate enough to differentiate between these treatments. However, for certain metal-hydrogen solutions the equilibrium data is available over sufficiently wide ranges of temperature and composition to permit a reasonably accurate determination of the compositional variation of the heats and entropies. Hoch&apos; has attempted to interpret the results of interstitial solid solutions in terms of a regular solution model. In the case of the Ta-H system where 13 = 6, this model entails fitting the experimental relative partial entropies of solution, asH, to the equation: where ASgs is the relative partial excess entropy of solution of hydrogen. Hoch found that the results of Mallett and Koeh1 could be fitted to this equation with an approximately constant value of AF up to XH = 0.25. However, it is apparent from the solubility isotherms in this system which become asymptotic to the composition TaH that, since (Xh /6 - ~Xh ) becomes infinite only at TaH6, it is necessary that AS<&apos; tends to infinity at TaH. In other words, the low saturation composition of TaH, instead of the anticipated TaH,, eliminates the possibility of applying regular solution theory to such systems. Rather large negative excess configurational entropies must exist at higher hydrogen concentrations in order to explain the lower saturation values. To account for these low limiting compositions and excess entropies two distinctly different approaches have been followed. Rees and many others1-l2 have assumed that not all interstitial sites are crystallographically equivalent with respect to the interstitial addition; that is, in Eq. [I] p is less than the value anticipated from geometrical considerations. To describe, say, a bcc metal-hydrogen system with a limiting composition of MH by this approach one would consider that p = 1 in the first instance instead of p = 6.&apos;j3 In some cases, nonintegral values of B have been taken in order to improve the fit with the experimental data over limited ranges of composition. The other approach which has been used to explain the low saturation compositions is to assume that, although all sites are available for occupancy, strong repulsive interactions exist between the neighboring interstitial atoms, and hence occupancy of any site excludes or blocks a certain number of neighboring sites from being occupied. Earliest treatments of this concept considered the exclusion of an integral number, of nearest-neighbor sites from being occupied at all concentrations. In this case, the partial configurational entropy is given by: These early treatments failed to allow for the overlap of the blocked sites which will arise at all but the very lowest concentrations. More recently attempts have been made to calculate the effect of this decrease in the number of blocked sites on the configurational entropy. Using the quasichemical treatment of interstitial solid solutions as given by Lacher and assuming that an infinite repulsive interaction energy existed between the solute atoms. atom obtained an approximate configurational entropy applicable to the blocking with overlap case:

Jan 1, 1970

By C. Atkinson

A method is described for the numerical solution of the diffusion equation with a composition-dependent diffusion coefficient and applied to the radial growth of a cylinder; the radial growth of a sphere, and the symmetric growth of an ellipsoid. Sample applications of the method are made to the growth of particles of proeutectoid ferrite into austenite. RECENTLY&apos; we described a method for numerical solution of the diffusion equation with a composition-dependent diffusion coefficient for the case of the growth of a planar interface. In this paper we extend this method to describe the radial growth of a cylinder, the radial growth of a sphere, and the symmetric growth of an ellipsoid. In the latter case, limiting values of the axial ratios of the ellipsoid reduces the problem to one of a cylinder, a sphere, or a plane depending on the axial ratio. A check on these limiting values is made in the results section. In all of these cases we consider growth from zero size. A natural consequence of this assumption as applied to the sphere, for example, is that the radius of the sphere is proportional to the square root of the time. This is consistent with the condition that the radius is zero initially, i.e., grows from zero size. It may be argued that it is more realistic to consider particles which grow from a nucleus of finite initial size; even in this case the analysis of this paper is likely to be applicable. This can be seen if a comparison is made of the work of Cable and Evans,2 who consider a sphere of initially finite size growing by diffusion in a matrix with a constant diffusion coefficient, with the results of Scriven3 for growth from zero size. This comparison shows that the rates of growth in each case differ trivially by the time the particle has grown to about five times its initial size." This investigation is a generalization of those of Zener,4 Ham,5 and Horvay and cahn6 to the situation often encountered experimentally, in which the diffusion coefficient varies with concentration. First let us consider each of the cases separately. I) GROWTH OF SPHERICAL PARTICLES FROM ZERO SIZE In this case the differential equation in the matrix depends only on R, the radius in spherical coordinates, and can be written: ? 1 <^\ ^13D . , dt U\dRz + R 3Rj + dR dR [ J where C is the composition, t is the time, and D is the diffusion coefficient which depends on c. The boundary conditions will be: c = c, at the moving interface in the matrix, c = c, at infinity in the matrix (and at t = 0, everywhere in the matrix), c = X, is the composition in the spherical particle. Each of the above compositions is assumed constant. In addition there is the flu condition at the moving interface which can be written: , dR0 ~/3c dt \dR/H =Ra where R,, which is a function of t, is the position of the moving interface. We make the substitution q = RI~ in [I] reducing this equation to: & - m - *ws) »i where we have written D = D,F(c) or simply D,F, and Do = D(c,). Thus F[c(q0)] = 1 where q, = ~,/a is the value of the dimensionless parameter q evaluated at the interface. Multiplying Eq. [2] by dq/dc and integrating, we find: where the lower limit of the integral has been chosen so that dc/dq — 0 as c — c,, thereby satisfying the boundary condition at infinity. We require, then, to solve Eq. [3] subject to the condition c = c, when q = q, (this follows from putting R = R, at the interface) together with the flux condition which can be rewritten in terms of q as: Eqs. [3] and [4] together with the condition c = c, at q = q0 enable us to find 77, and the concentration profile c = c(q). Numerical Method. We treat Eq. [3] in the same way as we did the corresponding equation for the planar interface problem&apos; i.e., by dividing the interval c, to c, into n equal steps so that: cr = ca -rbc [5] where r takes the values 0, 1, ... n and we call no,, q1, ... nn the values of n corresponding to the compositions c,, c,, ... c,.

Jan 1, 1970

By C. Laird, C. E. Feltner

May different kinds of dislocation structures have been observed in strain-cycled metals and alloys. In order to understand their pattern and causes, an experimental program has been carried out to determine the influence on the dislocation structures of the three variables: 1) slip character of the material, 2) test temperature, and 3) strain amplitude. The results show that at high strain amplitudes cell structures me formed when the slip character is wavy, and that these are progressively replaced by uniform distributions of dislocations as the stacking fault energy is decreased. At lower strains, dislocation debris is formed which consists primarily of dipoles in wavy slip mode materials and multipoles in planar slip mode materials. Temperature merely acts to change the scale of the structure, smaller cells, and clumps of dislocation debris being associated with lower temperatures. It is shown that the results for many metals fit this pattern, which Parallels that occurring in unidirectional deformation. DISLOCATION structures produced by cyclic strain (fatigue) have been examined in a number of metals by transmission electron microscopy. These studies have produced a variety of interesting and often seemingly conflicting results. For example, different investigators have reported such structural features as cells.le4 bands of tangled dislocations,4&apos;5 dense patches or clusters of prismatic dislocation loops, planar arrays,4&apos;10 and various combinations or mixtures of these different structures. Most of these observations have been made on materials which were initially annealed and cyclically strained at low amplitudes resulting in long lives. Recently we have reported observations of the dislocation structures produced in copper and Cu-7.5 pct Al cycled at large amplitudes, resulting in lives of less than 104 cycles.4 These results, examined in combination with those in the literature, have suggested that a common or consistent structural pattern exists. Variations in this pattern appear to be determined chiefly by the three variables, namely, the slip character of the material,4,11 test temperature. and the strain amplitude. To verify this interpretation, we have studied [he influence of the above three variables (in different combinations) on the resultant structures in cyclically strained metals. Copper, fatigued at room temperature, was chosen as a reference state to which all other observations can be compared. The effect of slip character has been investigated by employing fcc metals of different stacking fault energy. Thus aluminum which has a more wavy slip character than copper, and Cu-2.5 pct A1 having a more planar slip char- acter, have been examined. The aluminum samples were fatigued at 210°K thus making their homologous temperature equal to that of copper at room temperature. The influence of temperature has been evaluated by examining the structures in copper at room temperature and 78°K. Finally the effect of strain amplitude was studied by looking at the structures at amplitudes giving lives ranging from 104 to 107 cycles. All of the specimens were examined at the 50 pct life level at which stage the structures have reached a stable configuration.12 I) EXPERIMENTAL PROCEDURE Strip specimens, 0.006 in. in thickness, were prepared from base elements of 99.99 pct purity or greater. Specimens were fatigued by cementing the strips to a lucite substrate which was subjected to reverse plane bending. This method of testing has been described e1sewhere.7 After fatiguing, specimens were thinned and examined in a Philips EM 200 which was equipped with a goniometer stage capable of ±30-deg tilt and 330-deg rotation of the specimen. On the basis of separate calibrations,13 allowances were made for the relative rotation and inversions between the bright-field images and the diffraction patterns. II) RESULTS AND DISCUSSION The life behavior of the materials under different test conditions is shown in Fig. 1 in the form of plots of total strain range vs cycles to failure. Comparisons of structures produced in the different materials were made at amplitudes which produced equal numbers of cycles to failure. The influence of strain amplitude on the structures produced in the reference state material (copper tested at room temperature) is shown in Fig. 2. At the 104 life level the structure produced comprises cells similar to those previously observed.3,4 They are approximately 0.5 p in diam and the cell walls are generally more regular or sharper than those produced by unidirectional deformation.14 At the 10&apos; life level the

Jan 1, 1969

By C. W. Beattie, R. L. Solter

ALUMINUM-KILLED, low carbon steel sheets are used extensively for severe deep drawing and other difficult forming operations. They usually, but not always, have a characteristic grain structure in which the grains are elongated both in the lengthwise and in the transverse direction. As described by Burns and McCabe,&apos; a typical grain in the plane of the sheet has its two axes in that plane from 1 Y2 to 4 times as long as the axis normal to the plane of the sheet. Rickett, Kalin, and MacKenzieZ have also reported on the recrystallization behavior of such steel. The contrast in grain structures of fully processed sheets of aluminum-killed and rimmed steel is illustrated by Figs. 1 and 2. The elongated grain structure of the aluminum-killed sheet is not developed on all heats or lots of this metal, and studies of the factors controlling and influencing its formation are reported in this paper. Jeffries and Archerb tate that unstrained grains are normally equiaxed, but exceptions are common. For example, if a metal containing a material mechanically obstructing grain growth is subjected to considerable working followed by thorough annealing, it may exhibit grains consistently elongated in the direction of working. Our experiments demonstrate that aluminum-killed, low carbon steel is such a metal, and that the substance mechanically obstructing grain growth is aluminum nitride. The effectiveness of aluminum nitride in inhibiting grain growth has been found to be influenced by the degree of cold reduction, the rate of heating in annealing, the thermal history of the sample before cold reduction, and the residual aluminum content. A correlation between grain shape and austenitic grain coarsening temperature also was indicated and additional experiments demonstrated that aluminum nitride is also the principal cause for the fine grain characteristic of aluminum-killed steels. Manufacture In conventional practice, aluminum-killed sheet steel is manufactured from a low carbon steel containing approximately 0.02 to 0.07 pct residual (HC1 soluble) Al. With the exception of certain samples containing greater or lesser amounts of aluminum, the steels used in these investigations were within the following composition range: C, 0.03 to 0.06 pct; Mn, 0.28 to 0.38; S, 0.017 to 0.032; Al, 0.03 to 0.06; P, <0.01; and Si, <0.01. Properly heated ingots are rolled to slabs about 4 in. thick. After surface conditioning, the slabs are reheated to about 2300°F and hot rolled continuouslv to strip about 1/10 in. thick. The strip rolling is completed at a temperature of 1550°F or higher, and the strip is coiled, usually at a temperature near the lower critical transformation. After cooling, the strip is pickled to remove oxide, cold reduced 40 to 70 pet to final thickness, then annealed to 1250° to 1350°F in 20 to 80 ton charges, the size of which results in slow heating and cooling rates. Effect of Cold Reduction According to Sachs and Van Horn,&apos; the deformations of the individual grains in rolling are similar to those of the total volume. Thus individual grains would elongate in rolling according to the amount of cold reduction imposed. This is true theoretically, but as cold reduction increases the individual grains tend to fragment, and measured grain elongations become less than theoretical. The amount of grain elongation may be described by a numerical rating based on grain counts made by the intercept method. Specimens are polished normal to the plane of the sheet, with the polished surface extending parallel to the rolling direction. After etching, grain intercepts are counted along a 50 mm line on a micrograph of suitable magnification. In random locations parallel to the plane of the sample 20 counts are made and 20 are made in the thickness direction of the sample the average count in the thickness direction divided by the average count parallel to the plane of the sample gives a numerical rating of the grain shape called grain elongation. For example, a grain elongation of 2.00 means that the average grain is twice as long as it is thick. The average of both counts may be converted to grains per sq mm by a nomograph relating intercept counts and grain count. By the same procedure the grain elongation in the plane of the sheet but transverse to the rolling direction may be determined, using transverse metallographic samples. A comparison of theoretical and measured grain elongation was obtained on an aluminum-killed

Jan 1, 1952