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By C. E. Richards, C. N. Reid

The influence of preferred orientation on the incidence of defbrtnation tuinning has been studied. High-purity iron with almost vandonz grain orientation was cotnpared uitll iron of the sa)ne grain size and composilion lza,ing a strong (110) fiber texture. As expected from published work on single crgslfls, /he ))lean stress for the onset of luitzning-, and the l,olu)nt. fraclion of twinned nzaterial obserlled in lension differed fron the 1-a1ue.s it2 co?nPression for tnolerial with a slrong texlure. The llinning stress of "rctndorrl " )zalerial did not 17ary with the sense of the aPPlied unin.via1 stress, but sirprisinglg the incidence of 1c)i)zning- was about three 1i))zes greater ill conzp?&apos;ession Illon in lension. These results (Ire attributed entirely to ovienbation and may be nderslood in ler?ns of the shear slresses acting on the allowed twinning syster)is. J. HE twins most commonly formed in bcc metals may be described as regions of the crystal in which a particular set of (112) planes is homogeneously sheared by 0.707 in the appropriate ( 111) direction. A similar twin-related crystal could be produced by a shear of 1.414 in the reverse (111) direction but twinning by this large displacement has never been reported. Thus, twinning is unidirectional and a shear stress which produces twinning does not do so when its sense is reversed. The sense of a shear Stress is reversed when the loading is changed from tension to compression, or vice versa. Consequently, for a given orientation of a crystal relative to a uniaxial stress, only a fraction of the twelve (112) twinning systems are geometrically capable of operating in tension, and the remaining systems may operate only in compression. Therefore, when twinning is involved, there are expected to be differences in behavior between crystals tested in uniaxial tension and those tested in compression. This has been verified experimentally by Reid et 01.&apos; and Sherwood el al.,&apos; although a critical stress criterion was not encountered. Furthermore, twinning stresses in colmbium," tungten, tantalum,&apos; irn,&apos; i-Fe,\ nd molybdenum7 single crystals have been shown to depend critically on orientation, although again twinning did not occur at a critical value of the macroscopic shear stress. However, when twinning occurs, it generally does so on the most highly stressed systems, 1--4&apos;6&apos;8&apos;9 implying that the stress level does have some relevance to twin formation. In view of the large orientation dependence of twinning in bee single crystals, it might be expected that such an effect would be present in poly crystalline material which possesses a recrystallisation texture. Indeed, riestner" showed that the twinning stress in tension is very orientation-sensitive it1 <&apos;grain-oriented, silicon-iron;" this material possessed a very strong t c m^ii a nnr x_____k . i-_ii__ ri_______j. _x r»i_._:__i preferred orientation obtained by secondary recrystallisation. Reid et a/.&apos; observed a marked difference in the tensile and compressive yield stresses of polycrys-talline columbium which was rationalised in terms of the effect of a preferred orientation on twinning. No other such illformation is known to the authors. Several investigations of twinning in polycrystalline bcc metals have been reported in which the possible existence of a preferred orientation was not even mentioned. It is the purpose of this paper to show that there is a strong effect of texture on twinning in polycrystalline iron, and to poilt out the difficulty in eliminating preferred orientation in recrystallised metals. 1. EXPERIMENTAL METHOD Material and Specimen Preparation. Low-carbon, high-purity iron was obtained from the National Physical Laboratory in the form of $-in. diam rod which had been cold-swaged from a diam of 1 in. The composition of the material is given in Table I. The as-received bar was cold-swaged directly to 0.185 in. diam from which cylindrical tensile and compression specimens were machined. Specimen geometry is illustrated in Fig. 1. The gage length was 0.30 in. long and 0.10 in. diam; it should be noted that, apart from the extra heads which are necessary for tensile loading, the geometry and dimensions of the two types of specimen are identical. The specimens were heat treated either by sequence A or B outlined in Table 11. The essential difference between these two treatments is that in one case the material was repeatedly cycled through the y- to a-phase change in order to produce grains of almost random orientation ("random" iron)

Jan 1, 1969

By A. S. Yue

The movphology of the Mg-32 wt pct Al eutectic has been studied as a function of freezing- rate and temperature gradient. At slow freezing rates a lamellar eutectic was formed; whereas, a rod-like eutectic was generated at fast rates. The inter-lamellar spacing increased as the freezing rate decreased in aggreement with theoretical predictions. Lamellar faults, morphologically similar to edge dislocation models in crystals, were responsible for the subgrain structures in the eutectic mixture. A linear increase in fault density with freezing rate was observed. Fault concentl-ations of the order of 10 per sq cm for a range of freezing rates from 0.6 to -3.0 x 10 cm per sec were estimated. The transformation from lamella?, to rod-like morphologies was determined experimentally to be dependent on the freezing rate and independent of the temperature gradient. Moreover, the number of rods formed per- unit cross-sectional area increased exponentiallv with increasing freezing rote. BRADY&apos; and portevin2 classified eutectic structures into lamellar, rod-like, and globular according to the morphology of the solid phases present. Although this classification is quite descriptive, very little has been reported on the details of the mechanism by which the eutectic structures are formed. Recent work by Winegard, Majka, Thall, and chalmers3 and by chalmers4 on lamellar eutectic solidification suggest that the maximum thickness of the lamellae decreases with increasing rate of solidification due to inadequate time for lateral diffusion. scheilS and Tiller&apos; have shown theoretically that the lamellar widths indeed depend on the solidification rate. However, there has been no experimental evidence to support the theory. Chilten and winegard7 have studied the interface morphology of a eutectic alloy of zone-refined lead and tin. They found that the lamellar width decreased as the freezing rate increased in agreement with the theoretical predictions of scheils and Tiller.&apos; More recently, Kraft and Albright&apos; have investigated the microstructures of the A1-CuA12 eutectic as a function of growth variables. They observed lamellar faults present in the lamellar eutectic, similar to edge dislocation models in crystals. Furthermore, Kraft and Albright reported that they could not designate which extra lamellar was responsible for the formation of a lamellar fault even under electron microscopic magnification. In this paper, the morphology of the Mg-A1 eutectic structure is described. The effects of freez- ing rate on the interlamellar spacing and on the lamellar fault density are presented in detail. The transformation from lamellar to rod-like eutectics is discussed in terms of the freezing rate and the temperature gradient. EXPERIMENTAL PROCEDURE The experimental details of alloy preparation, the decanting mechanism and the determinations of the freezing rate and the temperature gradient have been reported elsewhere. Measurements of plate-edge angles were made with a microscope. The true angles used to determine the interlamellar spacings were determined by a two surface analysis technique.&apos;&apos; Since the decanted interface structure does not represent the true eutectic morphology on the solid,g all measurements were made from an area in the solidified bar behind the interface. Measurements of the apparent interlamellar spacings between the two phases of the eutectic were made on a photographic negative by means of a calibrated magnifier. Each value listed in Table I represents the average of thirty measurements on one negative. In general, these measurements are approximately equal with an error of less than pct. The average rod diameter for each specimen was also measured on a magnified photomicrograph. Each value of the diameter represents the average of fifty measurements. RESULTS AND DISCUSSION The experimental observations and their discussion to be presented here are restricted to the morphology of the eutectic structure and to the effects of the freezing rate and the temperature gradient on the solidification of eutectics. INTERLAMELLAR SPACING It has been shown previouslyg that the micro-structure of the decanted interface and the longitudinal section of the Mg-A1 eutectic is characterized by the presence of both lamellar and rod-like morphologies. The lamellae become more regular as the freezing rate is decreased. A three-dimensional photomicrograph representing a perfect lamellar morphology is illustrated in Fig. 1. The lamellae of the top and longitudinal sections of the specimen are regularly spaced while those in the transverse section are not quite straight and parallel. Their parallelism is slightly distorted because fault lines producing a discontinuity are present. A method for calculating the interlamellar spacings A, is described in Appendix 1. The true

Jan 1, 1962

By A. K. Csazar, L. W. Holm

This paper describes our investigation of a post-water-flood, oil recovery process which consists of injecting a slug of propane followed by water. Also described are the results obtained by applying a modification of the process in which gas was injected ahead of the water. Under the conditions of the latter experiments, misci-bility was not achieved between the propane and gas. Preliminary experiments or) uniform, watered-out sandstone cores showed that an oil bank could be formed and produced by applying this recovery process. However, since reservoirs are not uniform in structure, the process also was applied to porous media containing irregular porosity and to stratified sand systems. As a supplenzerrt to the experinlental work, a mathernatical procedure was developed for calculating the performance of the recovery process in a bounded, layered, porous system with crossflow between layers. As a specific example, the method was applied to predict the perforrnance of the recovery process in a 6-ft long, two-layer, stratified, unconsolidated sand model for comparison with experinlental data. The calculations were programed for the ZBM 704 computer. The equations and calcula-tional procedure presented can be extended to systems containing any number of randomly distributed permeability variations or any number of parallel layers. INTRODUCTION The problem of recovering the oil that remains in a reservoir which has been waterflooded is receiving considerable attention now as an increasing number of water floods reach an economic limit. A large number of the waterflood projects are in shallow reservoirs which are at pressures below 1,000 psi. It has been demonstrated in the laboratory that post-waterflood oil can be recover-ered by miscible displacement, but the LPG-gas, miscible flood and the enriched gas drive cannot be applied effectively at pressures below 1,000 psi. Only a few reports have appeared in the literature2-4 on low pressure, partially miscible recovery methods. However, it is possible to use LPG in a partially miscible displacement process in a reservoir where pressures of 200 to 1,000 psi can be achieved. Under these Pressures and at normal reservoir temperatures, propane is miscible with the oil; but, of course, gas or water used to drive the propane slug would not be miscible with the propane. Because of the lack of complete miscibility, it has generally been concluded that excessive amounts of propane would be required to recover oil and that such a recovery method would not be economical; however, we have found that under conditions present in certain reservoirs, an imrniscible recovery process can be applied effectively. The oil saturation in reservoirs at the economic limit of waterflood projects is usually in the range of 20 to 35 per cent of the pore space." A certain portion of this oil is left trapped by water in various size pores of the rock, but a good part of this so-called "residual" oil can be present in the less permeable lenses or layers of the reservoir rock which were by-passed to some degree by the water. The oil in these permeability traps can be produced only if favorable pressure gradients are formed in the reservoirs between adjacent zones of high and low permeabilities. A low viscosity liquid, miscible with the oil in place, which is driven by water through a stratified or heterogeneous porous system can aid in the development of these favorable pressure gradients. The oil that is released thereby from the permeability traps can be recovered by the subsequent water flood. Studies were made to determine how much oil could be recovered from homogeneous and stratified cores and models, which had been water flooded, by injecting a slug of propane and driving it with water. The effect of injecting a slug of gas ahead of the water was also determined. Most of the work described herein was done with the propane-water combination; unless otherwise specified, no gas was injected. The principal objectives of the investigation were to determine (1) if an oil bank could be formed and (2) what ratio of oil recovered to propane injected would be obtained. A further objective was to develop a method for calculating fluid-flow performance in stratified systems which would account for fluid transfer between zones in hydrodynamic communication but of different permeabilities. THEORETICAL ANALYSIS In a theoretical study of the recovery process, analytical expressions were derived to calculate the pressure distribution, the fluid flux in longitudinal (parallel to layers) and transversal (across the layers) directions, and the fluid distribution at any point in the system. The equations were developed for a two-layer porous system in which it was assumed that the fluids in the system were incompressible and that capillary and gravity effects were

By S. L. Craig, C. Orr, H. G. Blocker

WITHIN recent years gas adsorption methods have been developed for measuring the surface area of finely divided materials and have become extremely valuable in research on the corrosion and the catalytic activity of metals. Rather elaborate apparatus is required, and a single determination is so time-consuming that these methods have not been utilized to the fullest extent; the methods are un-suited for most routine control work such as that encountered in powder metallurgical operations and in processes employing metal catalysts. These difficulties are largely eliminated, and surface area is reduced to a routine determination if the liquid-phase adsorption of a surface-active agent such as a fatty acid can be used. When the affinity of the fatty acid carboxyl group for the solid surface is greater than its affinity for the solvent, a unimolec-ular layer of orientated fatty acid molecules will be formed at the solid-liquid interface in a manner similar to that of a compressed fatty acid film on a water surface. The measurement of surface area is then reduced to a measurement of fatty acid adsorption. This propitious circumstance, first investigated by Harkins and Gans,¹ has been employed with somewhat inconclusive results by a number of investigators in evaluating the surface properties of metals, metal catalysts, and metal oxides. The specific surface area values for nickel and platinum catalysts, determined from the adsorption of a number of fatty acids from various solvents, were found by Smith and Fuzek² to agree with values calculated by the gas adsorption technique of Brunauer, Emmett, and Teller," he so-called BET technique. And recently Orr and Bankston4 have also reported good agreement between nitrogen gas and stearic acid adsorption results in the measurement of the surface areas of clay materials. On the other hand, Ries, Johnson, and Melik5 found only order-of-magnitude agreement between these two methods in studying supported, cobalt catalysts having specific surface areas as great as 420 sq m per g; the reason is partially attributable to the very porous nature of the materials. Greenhill,6 investigating the adsorption of long-chain, polar compounds in organic solvents on a number of metal powders, concluded that a uni-molecular layer of stearic acid was formed on exposure of the solid to the acid solution and that the presence of an oxide or another film did not alter this result. Furthermore, the adsorption process appeared to be the same whether or not the sample was degassed prior to exposure to the solution. Greenhill estimated the surface area of one of the powders he investigated from microscopic diameter measurements, and obtained a rough check with surface area evaluation. Russell and Cochran7 found moderate agreement for alumina surface area results by fatty acid and gas adsorption methods. In addition, they also found that the prolonged heating and evacuating pretreatments previously used by investigators were unnecessary. The present work, however, considerably extends these previous investigations, shows that fatty acid adsorption can be used to determine the surface area of a variety of metals and metal compounds, offers further confirmation of the correctness of gas adsorption methods, and presents a simplified technique for the determination of the metal surface area which is suitable for routine work. Experimental Technique Basically, the fatty acid adsorption method is quite simple. It consists of exposing a sample of the material of which the surface area is desired to a fatty acid solution of known concentration. By analysis of an aliquot of the solution, the concentration after adsorption has occurred may be determined. The difference between the initial quantity of acid in solution and the final quantity is that quantity of acid adsorbed by the sample. The specific surface area of the adsorbent material may be calculated from the quantity adsorbed and the weight of the sample. In agreement with the findings of others as outlined above, it was found entirely unnecessary to degas or pretreat the nonporous materials employed other than by drying them thoroughly. However, precaution was necessary so that the dried sample entered the fatty acid solution with little exposure to moisture. The effect of moisture on the interaction of stearic acid with finely divided materials has been thoroughly investigated by Hirst and Lancaster." They found the presence of water merely reduced the amount of acid adsorbed by powders such as TiO2, SiO2, Tic, and Sic. With reactive materials such as Cu, Cu2O, CuO, Zn, and ZnO, however, water was found to initiate chemical reaction. Only with ZnO was reaction observed when the solid and the solu-

Jan 1, 1953

By F. E. Werner, B. L. Averbach, Morris Cohen

THAT bainite formed near the M, temperature bears a striking r esemblance to martensite tempered at the same temperature has been shown by the electron microscope.&apos; By means of electron diffraction,&apos; it has been established that carbide and cementite are present in bainite formed at 500°F (260°C); these carbides are also found in martensite tempered at 500°F (260°C).&apos; The investigation reported here is concerned with an X-ray study of the matrix phases in lower bainite and tempered martensite. These phases have turned out to be dissimilar in structure; the matrix of bainite is body-centered-cubic while that of tempered martensite is body-centered-tetragonal. A vacuum-melted Fe-C alloy containing 1.43 pct C was studied. Specimens of 16 in. diam were sealed in evacuated silica tubing and austenitized at 2300°F (1260°C) for 24 hr. One specimen was quenched into a salt bath at 410°+7 °F (210°+4°C), held for 16 hr, and cooled to room temperature. The structure consisted of about 90 to 95 pct bainite, the re: mainder being martensite and retained austenite. A second specimen was quenched from the austen-itizing temperature into iced brine and then into liquid nitrogen. It consisted of about 90 pct martensite and 10 pct retained austenite. The latter specimen was tempered for 10 hr at 410°+2°F (210°+1°C). The specimens were then fractured along prior austenite grain boundaries (grain size about 2 mm diam) by light tapping with a hammer. Single aus-tenite grains, mostly transformed, were etched to about 0.5 mm diam and mounted in a Unicam single crystal goniometer, which allowed both rotation and oscillation of the sample. Lattice parameters were measured by the technique of Kurdjumov and Lyssak. This method takes advantage of the fact that martensite and lower bainite are related to austenite by the Kurdjumov-sachs orientation relationships Thus, the (002) and the (200) (020) reflections can be recorded separately, permitting the c and a parameters to be determined without interference from overlapping reflections. According to these findings, the matrix phase in bainite is body-centered-cubic and, within experimental error, has the same lattice parameter as ferrite (2.866A). On the other hand, martensite, tempered as above, retains some tetragonality, with a c/a ratio of 1.005t0.002. Most workers in the past have assumed that bainite is generated from austenite as a supersaturated phase, but the nature of this product has not been established. The question arises as to whether bainite initially has a tetragonal structure and then tempers to cubic, or if it forms directly as a cubic structure. If it forms with a tetragonal lattice, it might well be expected to temper to the cubic phase at about the same rate as tetragonal martensite. The martensitic specimen used here was given approximately the same tempering exposure, 10 hr at 410°F, as suffered by the greater part of the bainite during the isothermal transformation. About 50 pct bainite was formed in 6 hr at 410°F. On tempering at this temperature, martensite reduces its tetragonality within a few minutes to a value corresponding to 0.30 pct C.&apos; Further decomposition proceeds slowly, and after 10 hr the c/a ratio is still appreciable, i.e., 1.005. Thus, even if the bainite were to form as a tetragonal phase with a tetragonality corresponding to only 0.30 pct C, which might be assumed to coexist with e carbide, it would not be expected to become cubic in this time. It seems very likely, therefore, that bainite forms irom austenite as a body-centered-cubic phase and does not pass through a tetragonal transition. The carbon content of the cubic phase has not been determined, but it could easily be as high as 0.1 pct, within the experimental uncertainty of the lattice-parameter measurements. It has been postulated that retained austenite decomposes on tempering into the same product as martensite tempered at the same temperature. There is now considerable doubt on this point. The isothermal transformation product of both primary and retained austenite at the temperature in question here is bainite," and the present findings show that bainite and tempered martensite do not have the same matrix. Acknowledgments The authors would like to acknowledge the financial support of the Instrumentation Laboratory, Massachusetts Institute of Technology, and the United States Air Force.

Jan 1, 1957

By D. E. Spiller

Introduction Precious metals recovery from ore can generally be accomplished using gravity concentration, flotation, and/or hydrometallurgical (leaching) techniques. The objective of this paper is to show why gravity concentration can be an important part of recovery systems that employ leaching as the primary unit operation. A brief discussion of modem gravity concentration equipment is also presented. Discussion Gravity concentration of ores has generated increasing interest in recent years. Reasons for this interest include: • Gravity concentration is environmentally attractive. There is little or no use of reagents. Hence, it is relatively nonpolluting. • The cost of cyanide has continued to increase. Therefore, cost savings may be realized whenever leaching feed tonnage can be reduced by preconcentration. • Compared to flotation and leaching, gravity equipment costs are low per processed ton. Field installation costs for gravity circuits usually are less because many&apos; units are supplied as self-contained modules. Also, the cost required to supply services, particularly power, to a gravity plant site are also less. In situations where preconcentration at coarse particle size is applicable, significant grinding equipment savings may be possible. • Gravity circuit operating costs are also relatively low compared to typical flotation and leaching circuits. Reagents, power, maintenance, and manpower savings in a well-engineered gravity plant may be realized. Again, if grinding is reduced, significant power and steel (media and liners) savings are possible. •In recent years, more efficient gravity concentrating devices have been developed. Benefits to Precious Metal Leaching Gravity beneficiation can complement precious metal leaching in two ways. First, the recovery of coarse liberated values before leaching may reduce leach time requirements and may reduce reagent consumption. Second, gravity preconcentration can reduce the size of a leach plant by decreasing the quantity of material to be leached. Coarse gold and silver have been shown to leach rather slowly. Kameda (1949) and Habashi (1967) have investigated the kinetics of cyanide leaching systems. They concur that in a heterogeneous reaction, the rate of gold and silver dissolution is directly proportional to the surface area. Thus, the instantaneous rate of dissolution for spherical 0.37 mm (400 mesh) gold is theoretically -25 times faster than for the same amount of gold at .841 mm (20 mesh), based on data from Fuerstenau, Chander, and Abouzeid (1979). Conversely, coarse liberated, +.841 mm (20 mesh), gold is more readily recovered by gravity concentration than is fine, -.037 mm (400 mesh) gold. Therefore, it is apparent that the two recovery systems complement one another. Figure 1 data demonstrates the potential synergism. A sample of - 3.327 mm (6 mesh) Nevada gold-bearing ore was cyanide leached using conventional bottle-roll test procedures. Gold extraction was determined as a function of leaching time. A second sample split from the same leach feed material was hand jigged to remove a coarse heavy mineral fraction, including virtually all of the +.210 mm (65 mesh) liberated free gold. This second sample, with the coarse gold and heavy minerals removed, was subjected to an identical cyanide leach procedure. Figure 1 presents the resulting comparative extraction data. Note that the percent gold extraction for the sample containing no +.210 mm (65 mesh) free gold includes the coarse gold recovered by gravity. The data show that the sample containing coarse gold required about 72 hours of leaching time to achieve 80% extraction. This compared to about 22 hours of leaching time for 80% gold recovery from the sample that contained only -.210 mm (65 mesh) free gold. Thus, there was a 69% reduction in leaching time. The improved extraction data is not wholly attributable to coarse gold removal, but rather it was the combination of gold removal and rejection of other heavy mineral cyanide consumers or leach retardants. Further investigation was not warranted at this time. Preconcentration is the second manner in which leaching systems can benefit from gravity concentration. The premise is that preconcentration can reduce the quantity of leach feed, which, in turn, may reduce leaching costs. Figure 2 presents preliminary data developed by CSMRI for US Minerals Exploration (USMX). Centennial Exploration Inc., in agreement with USMX, is proceeding with evaluations to determine the suitability of various processing schemes for recovery of gold values from the Montana Tunnels property. The data shows how the ore can be preconcentrated by gravity techniques to result in a reduced feed tonnage to secondary extraction techniques, presumably flotation or cyanide leaching. Testing has shown that Reichert cones, followed by treating the cone concentrate on spirals, can deliver about 88% gold recovery in about 13% weight, that is, 87% weight rejection. Consequently, fine grinding and reagent costs are attributable to only 13% of the plant feed rate. Cost data is not yet available, but the potential exists for significant cost savings.

Jan 1, 1985

By V. F. Zackay, W. A. Goering

ALLOYS of iron and aluminum up to 35 wt pct aluminum are single-phase solid solutions, and are of potentially wide applicability.1-3 In spite of early and continued interest1-4 little progress has been made until recently in the preparation and evaluation of sound alloys containing more than 6 wt pct aluminum. Vacuum-melting techniques for the production of ductile Fe-A1 alloys have been described recently.1-7 A. procedure for air melting these alloys is presented here. Low-carbon iron is induction melted without a slag in a rammed magnesia crucible. At the beginning of melt-down, aluminum pig (99.95 pct Al), charged in a clay-graphite bottom-pouring crucible is placed in a pot furnace at 1800°F. The primary deoxidation of the molten iron after melt-down is effected by the addition of 0.1 pct aluminum and 0.5 pct manganese. (Hilty and Crafts" have reported a significant increase in the deoxidation efficiency of the aluminum and manganese combination over that of the aluminum alone.) A more drastic deoxidation designed to reduce the oxyen content to the lowest possible level is accomplished by plunging metallic calcium to the bottom of the melt. This is done by wiring small cubes of the metal to a steel rod. A circular shield larger than the diameter of the crucible opening is attached to the rod so that any spa&apos;ttering of the molten metal will not endanger the operator. Since the temperature of the molten metal is above the boiling point of calcium, the bath is vigclrously purged by calcium vapor. It is believed that the calcium-vapor treatment permits a homogeneous distribution of calcium in the melt. Owing to the vigor of the reaction the temperature of the molten metal should be kept below 2900°F prior to the calcium addition. A total of 0.05 pct calcium is added in two stages in this manner. The second calcium deoxidation is made just before charging the molten aluminum into the iron, in order that an excess of calcium be present for the remainder of the melt. The aluminum, which has been removed from the holding furnace, is then hydrogen degassed by bubbling chlorine through a quartz tube immersed in the molten aluminum. The hydrogen-chlorine reaction is an exothermic one preventing the solidification of the aluminum during the 5-min chlorination. Approximately 0.1 pct calcium, based on the amount of aluminum, is then added to the aluminum. A further excess of calcium is introduced into the melt in this manner. The oxide dross is removed, fluorspar is added to the molten iron, and the molten aluminum is poured through the fluorspar slag. The fluorspar should be dried thoroughly prior to its use, as any water present will react with the aluminum. Aluminum oxide formed during the pouring operation reacts with the fluorspar slag to form gaseous aluminum fluoride and calcium oxide. A forced-draft ventilating system is required for this operation as aluminum fluoride is toxic. As soon as the molten aluminum has been added, vigorous manual stirring of the melt is required because the slag-aluminum oxide reaction is highly exothermic and tends to take place near the top of the melt. The combination of high temperature and the slagging action of the fluorspar quickly erodes the crucible at the slag line if the aluminum is not stirred uniformly into the melt. It has been found that at least 4 min of manual stirring combined with induction stirring are necessary to ensure homogeneity. The power is shut off 1 min prior to pouring to allow metal and slag to separate. As much slag as possible is removed from the melt, which is then poured directly into cast-iron molds. A mold wash of aluminum oxide is used to prevent ingot sticking. For slab ingots which are to be rolled into sheet, a carbon-tetrachloride vapor atmosphere or a chlorinated-pitch mold wash is desirable, as the aluminum oxide formed in the pouring operation is subsequently removed by the chlorine in the presence of carbon." As in vacuum melting, a pouring temperature of about 2900°F is recommended. Adequate hot-topping is important as iron-aluminum ingots are subject to very deep piping. Ingots are removed from the molds and buried in vermiculite, where they are allowed to cool slowly to room temperature. The ingots are radiographed,

Jan 1, 1959

By R. H. Gautschi, F. C. Langenberg

Rare-earth additions were made to laboratory heats of Type 310 stainless to observe their effect on as-cast ingot structure, nitrogen and sulfur contents, and nonmetallic inclusions. Lanthanum had a grain-refining effect in 30-lb ingots, but results with 200-lb ingots were inconsistent. Cerium, lanthanum, and misch metal lowered the sulfur content when the sulfur exceeded 0.015 pct and the rare-earth addition was greater than 0.1 pct. The rare-eardh content in the metal dropped very rapidly within the first few minutes after the addition. The size, shape, and distribution of nonmetallic inclusions was not changed in 30-lb ingots, but changes were noticed in larger ingots. RARE-earth* additions have been made to austenitic Cr-Ni and Cr-Mn steels to improve their hot workability. The high alloy content of these steels often results in a considerable resistance to deformation and inherent hot shortness at rolling temperatures, particularly in larger ingots. Rare earths in the metallic, oxide, or halide form are usually added to the steel in the ladle after deoxidation although they can be added in the furnace prior to tap or in the molds during teeming. The literature- indicates that the effects of rare-earth treatments on these stainless steels are not consistent, and sometimes even contradictory. Since no mechanism has been presented which satisfactorily accounts for the claimed improvements, the effects of rare earths are a qualitative matter. The work described in this paper was initiated to expand the knowledge of the effects of rare-earth additions on melting variables such as ingot structure, chemical analysis, and nonmetallic inclusions. REVIEW OF LITERATURE Ingot Structure—Rare-earth additions to stainless steels have been reported to cause a change in primary ingot structure in that there are fewer coarse columnar grains. However, the results are inconsistent. While one investigation1 has shown a large reduction in coarse columnar crystals, another2 has been unable to observe this effect, particularly when small ingots were poured. Post and coworkers3 observed ingot structures for a number of years and found that the columnar type of structure is not definitely a cause of any particular trouble in rolling or hammering, provided the alloy is ductile. Knapp and Bolkcom4 found rare-earth additions to be quite effective in preventing grain coarsening in Type 310 stainless steel. Chemical Analysis—Many effects of rare-earth treatment on chemical analysis have been claimed in the literature. Russell5 observed that some sulfur is removed by rare-earth metals, and that a high initial sulfur content improved the efficiency of sulfur removal. Lillieqvist and Mickelson6 report that rare-earth treatment causes sulfur removal in basic open-hearth furnaces, but not in basic lined induction furnaces. Knapp and Bolkcom found no sulfur removal in acid open-hearth and acid electric furnaces, probably because the acid slag can not retain sul-fides. snellmann7 showed that sulfur could be lowered apprecfably with rare-earth additions; however, a sulfur reversion occurred with time. Langenberg and chipman8 studied the reaction CeS(s) = Ce(in Fe) + S(in Fe), and found the solubilit product [%Ce] [%S] equal to (1.5 + 0.5) X 10-3&apos;at 1600°C. Results in 17 Cr-9 Ni stainless were about the same as those in iron. Beaver2 treated chromium-nickel steels with 0.3 pct misch metal and observed some reduction in the oxygen content. He also noted an inconsistent but beneficial effect of rare earths when tramp elements were present in amounts sufficient to cause difficulty in hot working. It is not known whether rare earths reduce the content of the tramp elements or change the form in which these elements appear in the final structure. No quantitative data are available concerning a possible effect of rare-earth treatment on hydrogen and nitrogen contents. However, Schwartzbart and sheehan9 stated that additions of rare earths had no effect on impact properties when the nitrogen content was low (0.006 pct), but served to counteract the adverse effects of high nitrogen content (0.030 pct) on these properties. Knapp and Bolkcom4 analyzed open-hearth heats in the treated and untreated conditions and found the nitrogen content (0.006 pct) to be unaffected. These two results lead to the speculation that rare-earth additions can reduce the nitrogen content to a certain level. Decker and coworkers10 have observed that small amounts of boron or zirconium, picked up from magnesia or zirconia crucibles, increased high-tem-

Jan 1, 1961

By C. Richard Tinsley

Like most minerals, coal is inherently a demand-limited commodity. The very sedimentary nature of its occurrence implies greater availability potential than demand. But this situation is overridden by economics among fuels, between coals, and within coal blends. Such considerations make coal forecasting a very hazardous profession indeed. THERMAL COAL If one thought that the lead times involved with a mining project were very long, one has obviously not been exposed to the planning process in the electric generation business - a process seriously confounded by shifts in load growth, environmental pressures, capital intensity, security of fuel sourcing, inter-fuel economics, and so on. But as a general rule, the near-term forecasts for thermal coal can reliably be based on a bottom-up, plant-by-plant analysis. Cement plant conversions can also be reasonably estimated next in order of reliability, although they have a much wider spectrum of coal qualities and fuel sources to choose from with a notably higher tolerance for sulfur and ash. Finally, industrial demand can be assembled from the estimates for conversions by pulp/paper plants, chemical plants, etc. The industrial sector is harder to estimate, since it may involve small boilers or dual-fired units. Assessing demand in the Pacific Rim is relatively a straightforward process in the near term because the major importing countries are all located on the Asian continent with either negligible or very minor (yet stable) indigenous coal production, (itself often operated on a subsidized basis). Furthermore, all imports are seaborne. These major importers are Japan, Korea, Taiwan, and Hong Kong with Thailand, Singapore, and Malaysia up-and-coming consumers. The suppliers to this market all have substantial reserves to back up decades of exports to these countries. Australia, the US, Canada, South Africa, China, and the USSR dominate the supply side. The second oil-shock of 1979/1980 has convinced the importers that reliance on oil can be expensive and eminently interruptible. Thus, they are determined to diversify away from oil&apos; to nuclear and coal for generating electricity and for coal for other purposes where possible. This trend is seen to continue even in the face of the oil glut worldwide and oil-price reductions in early 1982. But the importers are also convinced that reliance on one coal source and, in particular, one infrastructure route for the coal chain from mine to consumer can be equally expensive and interruptible. Strikes in the US and Australia; excessive demurrage at certain ports; relegation of coal to a lower priority on multiple-use railroads in the USSR and China; and concern over escalation on high-infrastructure or high-freight coal chains are among the risks worrying the importers. As a consequence, Pacific Rim thermal coal purchases are being allocated among supplier nations, between ports, and within each country. An example of Japan&apos;s shift away from Australia and toward the US and Canada is shown in the estimates in Table 1. But the confidence of the import estimates deteriorates sharply beyond the plant conversion timetables and construction schedules in the near term. If part of the second generation of coal-fired power plants can handle lower-energy coals, the field of suppliers could widen to accept sizeable tonnages from Alaska, Wyoming, Alberta, or New Zealand resources. These supply sources generally have some infrastructure or freight advantage to compensate for their lower quality and to compete on a delivered energy-unit basis. These also offer diversification in sourcing. And the possibility of coal liquefaction in Japan further widens the sourcing network. A great number of Pacific Rim coal forecasts have been generated, especially for Japanese thermal-coal imports which are expected to grow strongly in the 1980&apos;s. Since the Japanese themselves have not yet settled their energy policy, the exact numbers are hard to call. Nevertheless, at 50 million tonnes of imports in 1990, Japan would consume 50-60% of the total Asian thermal coal imports as shown on Tables 2 and 6. The next most important consumers are the "island" nations of Korea, Taiwan, and Hong Kong (see Tables 3-5). All three are embarking on power plant developments usually with captive unloading facilities, capable of accepting more than 100,000-dwt vessels. Korea, with no-indigenous bituminous coal, is not especially enamoured with US coals, which are deemed too heavily loaded by freight and infrastructure costs -- up to 70% of the delivered price. Thermal coal contracts are presently split to Australia (70%) and to Canada (30%). Korea Electric Power Co. is already considering second-generation boilers capable of burning lower-quality coals than the present standard. Korea does burn domestic anthracite.

Jan 1, 1982

By L. Delisle

This work represents the first step of an attempt to test the applicability of the electron microscope to the study of subgrain structures in copper. Observations on annealed and deformed single crystals and polycrystalline samples of copper are described. IN the course of study of the structure of fine tungsten wires and tungsten rods with the electron microscope, well defined subgrain structures were observed. The size, size distribution, and orientation uniformity of the etch figures varied widely in different samples. Figs. 1 and 2, electron micrographs of a tungsten wire and of a tungsten rod, respectively, are illustrations of the difference in size and size distribution of the etch figures in different samples of the same metal. The observed differences, as pointed out in a previous paper,&apos; appeared to be related to the heat and mechanical treatments of the samples. They were also consistent with the results reported in the literature on the mosaic structure of metals.&apos; For that reason a program of research was initiated in an effort to obtain more systematic evidence of the possible relation of heat and mechanical treatments to the subgrain structure of metals as observed in the electron microscope. The purpose of this paper is to present observations made on the effect of cold work on the subgrain structure of copper. Procedure Starting Materials: Copper was the metal studied because it can be obtained in a high degree of purity, much information is available in the literature on its properties and its response to cold work and heat treatment, it shows no allotropic change, and it is sufficiently hard to be handled without great difficulty. Two groups of specimens were used: 1—single crystals cast from spectroscopically pure copper and 2—polycrystalline samples of oxygen-free high conductivity copper. Single crystals were studied because it was hoped that the elimination of a number of variables, such as grain boundaries, orientation differences, degree of purity, would simplify the problem and perhaps permit a better understanding of the phenomena that would be observed. The polycrystalline samples were designed to give a general picture of the changes considered. The single crystals were made of copper which analyzed spectroscopically to better than 99.999 pct Cu. They were cast in vacuum, by the Bridgman method, in crucibles made of graphite with a maximum ash content of 0.06 pct. The mold design is shown in Fig. 3. It permitted casting crystals of the size and shape required for the experiments, so that the danger of introducing cold work in the original samples by cutting or other machining would be eliminated. The polycrystalline samples were pieces, 3/4 in. long, cut from a rod of oxygen-free high conductivity copper, % in. in diameter. A flat surface, 1/4 in. wide, was milled along the rods, polished, and etched. The samples were then annealed in vacuum at 850°C for 1 hr. Polishing and Etching: Work previously done on tungsten,&apos; polished mechanically and etched chemically," had shown that: 1—the general appearance of the etch figures of a given sample was not altered by repeated polishings and etchings under similar conditions; 2—variations in the time of etching and the concentration of the etchant changed the definition of the etch figures, but did not alter their general size nor orientation distribution within the limits of observation. Further work confirmed the reproducibility of the subgrain structures observed in, 1—single crystals and polycrystalline samples of copper when polishing and etching were repeated under similar conditions, and 2—specimens of tungsten and polycrystalline copper when electrolytic polishing and etching were substituted for mechanical polishing and chemical etching, respectively. On the strength of these observations, it was felt that, if conditions of polishing and etching were kept constant, changes observed in the subgrain structure of a sample upon deformation and annealing would be attributable to such treatments. For that reason the conditions of polishing and etching were kept as constant as possible. The single crystals were polished electrolytically in a bath of orthophosphoric acid in water, in the ratio of 1000 g of acid of density 1.75 g per cc to 1000 cc of solution, under a potential drop of 1.6 to 1.8 V. Electrolytic polishing was selected to prevent the formation of distorted metal in polishing. The same samples were etched by immersion in a 10 pct aque-

Jan 1, 1954

By H. R. Thresh

An oscillational vis cometer has been constructed to measure the viscosity of liquid metals and alloys to 800°C. An enclosed cylindrical interface surrounds the molten sample avoiding the free surface condition found in many previous measurements. Standardization of the apparatus with mercury has verified the use of Roscoe&apos;s formula in the calculation of the viscosity. Operation of the apparatus at higher temperatures was also checked using molten lead. Extensive measurements on five different samples of zinc, of not less than 99.99 pct purity, indicate i) impurities at this level do not influence the viscosity and ii) the apparatus is capable of giving reproducible data. The variation of the viscosity ? with absolute temperature T is adequately expressed by Andrade&apos;s exponential relationship ?V1/3 = AeC/VT , where A and C are constants and V is the specific volume of the liquid. The values of A and C are given as 2.485 x 10-3 and 20.78, 2.444 x 10-3 and 88.79, and 2.169 x 10-3 and 239.8, respectively, for mercury, lead, and zinc. The error of measurement is assessed to be about 1 pct. Prefreezing phenomena in the vicinity of the freezing point of the zinc samples were found to be absent. AS part of an over-all program of research on various phases of melting and casting nonferrous alloys, a systematic study of some physical properties of liquid metals and their alloys was undertaken in the laboratories of the Physical Metallurgy Division.1,2,3 The most recent phase of this work, on zinc and some zinc-base alloys, was carried out in cooperation with the Canadian Zinc and Lead Research Committee and the International Lead-Zinc Research Organization. One of the properties investigated was viscosity and the present paper gives results on pure zinc; the second part, on the viscosity of some zinc alloys, will be reported separately. Experimental interest in the viscosity of liquid metals has virtually been confined to the past 40 years. The capillary technique was already established as the primary method for the viscosity of fluids in the vicinity of room temperature; all relevant experimental corrections were known and an absolute accuracy of 1 to 2 pct was possible. Ap- plication of the capillary method to liquid metals creates a number of exacting requirements to manipulate a smooth flow of highly reactive liquid through a fine-bore tube. Consequently, the degree of precision usually achieved in the high-temperature field rarely compares with measurements on aqueous fluids near room temperature. However, the full potential of the capillary method has yet to be explored using modern experimental techniques. As an alternative, many investigators in this field have preferred to select the oscillational method. Unfortunately, the practical advantages are somewhat offset by the inability of the hydrodynamic theory to realize a rational working formula for the calculation of the viscosity. In attempting to overcome this restriction many investigators have employed calibrational procedures, even to the extent of selecting an arbitrary formula for use with a given shaped interface. However, where calibration cannot be founded on well-established techniques, the contribution of such experiments to the general field of viscometry is questionable. A critical appraisal of the viscosity data existing for pure liquid metals reveals a somewhat discordant situation where considerable effort is still required to establish reproducible and reliable values for the low-melting point metals. The means of rectifying this situation have gradually evolved in recent years. Here, the theory of the oscillational method has undergone major advances for both the spherical and cylindrical interfaces. The basic concepts of verschaffelt4 governing the oscillation of a solid sphere in an infinite liquid have been adequately expressed by Andrade and his coworkers.5,6 Employing a hollow spherical container and a formula, which had been extensively verified by experiments on water, absolute measurements on the liquid alkali metals were obtained. The extension of this approach to the more common liquid metals has been demonstrated by culpin7 and Rothwel18 where much ingenuity was used to surmount the problem of loading the sample into the delicate sphere. Because of the elegant technique required to construct a hollow sphere, the cylindrical interface holds recognition as virtually the ideal shape. On the other hand, loss of symmetry in one plane increases the complexity of deriving a calculation of the viscosity. The contributions of Hopkins and Toye9 and Roscoe10 have markedly improved the potential use of the cylindrical interface in liquid-metal viscometry. The relatively simple experi-

Jan 1, 1965

By T. S. Lovering

The use of geothermal energy is expanding very rapidly. This type of energy has proven commercially profitable for generation of electricity, for space heating, process heating, auxiliary heating of water in conventional steam power plants and for recovery of chemicals contained in natural hot water and steam. Two types of geothermal energy sources are recognized: 1) hot springs in regions of nearly normal heat flow that tap a deep reservoir through which water moves slowly to a hot springs conduit and then rapidly to the surface; 2) hyperthermal areas in which the water is heated by a relatively concentrated heat source related to volcanicity. If there is a geologic trap that provides a geologic analog to a steam boiler, as at Larderello, Italy, the hyperthermal area will have a convecting system that develops superheated water at relatively shallow depth and may provide natural steam in large quantities. If a hyperthermal area is to be productive for a long time, the underflow into the reservoir should be slow enough to allow the heat source and convective system to heat the underflow to the working temperature, and the production rate must not exceed this rate of underflow. A model based on a typical aquifer suggests that the rate of movement of water through the reservoir be such that a few years are spent in transit between isotherms that are spaced about 2°F apart. The possibility of finding blind geothermal areas is illustrated by discussion of the techniques developed in evaluating the subsurface temperatures in the East Tintic district of Utah where a map of isotherms at water level (2000 to 2000 ft below the surface) shows that a hyperthermal area may exist a short distance southeast of the mining district. Very nearly all of the energy that man currently uses comes ultimately from the sun&apos;s radiation. This includes water power, fuels such as wood, peat, coal and petroleum, the wind and all our animal power. In the paper summarizing a conference on solar energyl6 the average amount of solar energy received daily on the earth is taken at about 1 cal per m2 per min or slightly less than 2 pcal per cm2 per sec; this is almost exactly the amount of energy on the average that the earth liberates in regions of normal geothermal gradient due to its own internal heating. In many places, however, the energy released is many times the average and in some of these hyperthermal areas, geothermal steam is used for generation of electricity, and hot springs are used for heating buildings and private dwellings, process heating, auxiliary heating of water in conventional steam power plants, and chemicals may be recoverable from both hot water and steam. The use of hot springs waters for heating houses goes back hundreds of years but until recently was confined to a few dwellings close to the hot springs. In Korea, some houses had hot spring water channeled through conduits in the floor centuries ago and thus the Koreans can be credited with pioneer development of radiant heating. In Iceland at present nearly a third of the population uses natural thermal water for domestic heating." The Reykjavik system pipes hot spring water at about 94°C throughout the city and has devised insulated double pipes that allow the water to be piped for some 25 km with a drop of only 1°C for every 5 km. The actual cost to the Icelandic consumer is only one-third the cost of heating by imported coal and yet the industry is one of the most profitable in Iceland. The most profitable use of geothermal energy has been its conversion into electricity which can be transmitted economically much greater distances than hot water. The largest installation at the present time is that at Larderello, Italy, where the Count of Larderello began to experiment in the production of electricity from geothermal steam 60 years ago — in 1904. He installed his first steam turbine, with a capacity of only 250 kw, in 1912 as the result of a local quarrel with the power company which furnished the current required in the Larderello chemical industry - an industry that then dated back nearly a century. As experience was gained in drilling deep holes to tap geothermal steam and in converting it to electric power, the capacity of the installation of Larderello gradually increased, but was all destroyed by the Germans during their retreat from Italy in the closing

Jan 1, 1965

By W. O. Philbrook, K. Natesan

The oxidation kinetics of spherical pellets of zinc sulfide made from Santander concentrates were studied using a thermogravimetric technique. The experiments covered a temperature range-. of 740" to 102O°C, 0-N mixtures varying from 20 to LOO pct O2, and pellet diameters between 0.4 and 1.6 cm. Mathematical models were formulated to Predict the reaction rate on the assumption that a single transport or interface reaction step was rate -controlling. Analysis of the data indicated that the process of oxidation was predominantly controlled by transport through the zinc oxide reaction-Product layer. ROASTING processes, which are reactions between solids and gases, are very important because they are employed in the production of a number of basic metals. These processes are highly complicated, and one needs to consider the transport phenomena of heat and mass between the solids and gases in addition to the kinetics of various chemical reactions involved. Because of such complications there is a lack of knowledge concerning the rate-limiting factors, which may strongly depend on temperature, particle size, gas composition, and solid structure. The oxidation of zinc sulfide, which is of commercial importance in zinc production, falls into this class of reactions. The major goal of this work was to elucidate the roles played by different process variables, such as reaction temperature, gas composition, pellet size, and pellet porosity, on the kinetics of oxidation of single pellets of zinc sulfide. Roasting of zinc sulfide single particles has been a subject of both experimental and theoretical investigations.&apos;-&apos; The reaction is exothermic and may be considered to be irreversible. Such a reaction has been found to proceed in a topochemical manner. In other words, as the reaction proceeds, a progressively thicker outer shell of zinc oxide is formed, while the inner core of unreacted sulfide decreases. It has been found experimentally, both in the present work and in the previous investigations,1-9 that the particle retains its original dimensions and the process requires transport of gaseous oxygen across the porous product layer for continued reaction. The reaction may be represented by ZnS(s) + 3/2 O2(g) = ZnO(s) + SO2(g) [1] The solid product considered here is only zinc oxide, since the diffraction patterns of zinc sulfide pellets oxidized partially at &apos;798" and 960°C showed K. NATESAN, Junior Member AIME, formerly St. Joseph Lead Fellow, Department of Metallurgy and Materials Science, Carnegie-Mellon University, Pittsburgh, Pa., is now at Argonne National Laboratory, Argonne, Ill. W. 0. PHILBROOK, Member AIME, is Professor of Metallurgy and Materials Science, Carnegie-Mellon University. This paper is based on a them submitted by K. NATESAN in partial fulfillment of the requirements for the Ph.D. degree in Metallurgy and Materials Science at Carnegie-Mellon University. Manuscript submitted December 2, 1968. EMD lines corresponding to original zinc sulfide and the newly formed zinc oxide. OXIDATION MODEL The generalized model for gaseous oxidation of zinc sulfide is illustrated in Fig. 1. This depicts a partially oxidized sphere of zinc sulfide in a gas stream surrounded by a laminar film of gas. The spherical sample of zinc sulfide of unchanging external radius r0 is suspended in a flowing gas stream of total pressure PT and composition specified by the partial pressures of the individual components. Partial pressures of the gaseous species in the bulk gas phase, at the exterior surface of the pellet, at the ZnS/ZnO interface, and at equilibrium for Reaction [I] are identified by the superscripts b, o, i, and eq, respectively. The overall reaction involves the following ~te~s:&apos;~&apos;~&apos; Step 1. Transfer of reactant gas (oxygen) from the bulk gas stream across the gas boundary layer to the exterior surface of the pellet and the reverse transfer of the product gas (sulfur dioxide). Step 2. Diffusion and bulk flow of oxygen from the pellet surface through the product shell (ZnO) onto the ZnS/ZnO interface and the reverse transfer of sulfur dioxide. Step 3. Chemical reaction at the interface, which results in consumption of oxygen gas and generation of sulfur dioxide gas and heat; at the same time the _________ PARTICLE SURFACE / x^^^^n^X / MOVING INTERFACE core-----/ sJSNxy " /T^T^02 \ V\V$\ ^NWX/ "*/— GAS BOUNDARY x. \\ZnO SHELLV/ / \^ . / &apos; ^ BULK GAS --------N_______ _____,------p£ w \ P« / (f> \ / a \ <i) / <----------------- _(o) ^^--------------(b) °- pso, pso2 ro ri 0 ri ro RADIAL POSITION Fig. 1—Generalized model for oxidation of a sphere of zinc sulfide.

Jan 1, 1970

By Robert E. Green, Wolfgang Sachse

Simullaneous ultrasonic attenuation measurements of both quasishear waves propagating in single cryslals of aluminum indicate that, in the undeformed annealed state, the dislocation density is generally not uniform on all slip systems. Change oof attenuation measurements made during plastic defortnation of crystals , which possessed specific orientations ideal for studying the orientation dependence of dislocation damping, indicate that, for low strain levels, dislocation motion occurs on additional slip systems besides the primary one, even for crystals oriented for plastic deformation by single slip. THE sensitivity of internal friction measurements permits such measurements to be used successfully in studying the deformation characteristics of metal crystals. On the basis of experimental observations, T. A. Read1 was the first to associate internal friction losses with various dislocation mechanisms. Since that time further work2-&apos; has been performed and a dislocation damping theory has been formulated by Granato and Lucke.6 In the amplitude independent region, this theory predicts the attenuation a to be dependent on an orientation factor O, a dislocation density A, and an average loop length L. if is a constant, independent of crystallographic orientation. For a given crystallographic orientation, changes in dislocation density and loop length give rise to the observed attenuation changes accompanying plastic deformation. The Granato-Liicke theory suggests the investigation of the orientation dependence of attenuation measurements in hopes of obtaining information to separate dislocation motion losses from other losses.7 An experimental study of the orientation dependence of attenuation in undeformed annealed single crystals should yield an insight into the uniformity of dislocation distribution throughout the entire specimen. A similar study on crystals plastically deformed in a prescribed fashion should give information about the alterations in the dislocation distribution on the slip systems activated during plastic deformation. The possible modes of elastic waves which can be propagated in aluminum,8 copper,9 zinc,10 and other hexagonal metals" have been calculated. Associated with each mode of wave propagation are dislocation damping orientation factors, which are based on the resolution of the stress field of that particular elastic wave onto the various operative slip systems in the material. These orientation factors have also been calculated as a function of crystallographic orientation in the papers cited above. Einspruch12 obtained agreement between predicted and observed attenuation values of longitudinal and shear waves in (100) and (110) directions of two undeformed aluminum crystal cubes. He ascribed the slight deviations between predicted and observed values to a nonuniform dislocation distribution, or to other loss mechanisms. In shear deformation of zinc crystals, Alers2 found that the attenuation of shear waves having their particle displacements in the slip plane was very sensitive to the deformation, while the longitudinal wave attenuation was affected only when the wave propagation direction was not normal to the slip plane. Using aluminum single crystals oriented for single slip, Hikata3 et al. found that during tensile deformation the change of attenuation of the shear wave (actually quasishear) having particle displacements nearly perpendicular to the primary slip direction exhibited the easy-glide phenomena, while longitudinal waves did not. Similar results were reported by Swanson and Green5 during compressive deformation of aluminum crystals. These results are in qualitative agreement with the calculated orientation factors for specimens of this orientation. In well-annealed, undeformed aluminum crystals, the damping is expected to be due to dislocations vibrating on all twelve slip systems. The orientation factors associated with this initial damping will be designated by O2 and O3, where a, represents the average orientation factor for the slow shear (or quasishear) wave and O3 represents the average orientation factor for the fast shear (or quasishear) wave. The calculation of these values for aluminum crystals by Hinton and Green8 shows that they vary very little as a function of crystallographic orientation—at most, by a factor of 2.47. If the dislocation density and loop length are uniform, then in the initial undeformed state, Here the subscript zero refers to the initial value of the attenuation. Also for aluminum, the calculations8 show that the orientation factors for primary slip only, associated with each shear wave, exhibit a sharp minimum for particular crystallographic orientations. A composite plot of the two shear wave orientation factors for primary slip only is shown in Fig. 1. Since these orientation factors are associated with dislocation motion occurring on the primary slip system only, the proper condition to check these factors might be attained by slightly deforming a single crystal oriented for primary slip. For dislocation motion on the primary slip system only,

Jan 1, 1969

By J. F. Martin, L. M. Melnick, R. Rapp, R. C. Takacs

Recent studies on the determination of hydrogen in steel have shown that the hot-extraction method for removing hydrogen from a solid sample is preferable to its removal from a molten sample by vacuum fusion or by fusion in vacuum with tin. A number of techniques are available, however, for determining the hydrogen so extracted. They include: thermal conductivity, gas chromatography, pressure measurement before and after catalytic oxidation of the hydrogen to water and removal of the water, and pressure measurement before and after diffusion of the hydrogen through a palladium membrane. These techniques have been evaluated on the basis of initial cost, maintenance, speed and accuracy of analysis, and applicable concentration range. The results of this study showed that the palladium-membrane technique is best suited for routine use. FOR some time investigators have been concerned with the origin, form, and effect of hydrogen in steel. In such stdies&apos;, the analysis for hydrogen constitutes one of the most important phases. It is quite apparent that the results for hydrogen concentrations in a given steel are dependent on the method of obtaining the sample, storage of the sample until analysis, preparation of the sample, and analysis of the sample, including all the facets inherent in the calibration and operation of an apparatus for gas analysis. There are a number of means available for determining hydrogen. This is a critical study of some of the more common techniques in use today. In most conventional melting and casting methods, hydrogen concentrations of 4 to 6 parts per million (ppm) in steel are quite common. Because of the undesirable effects of hydrogen on steel there has been increased use of techniques such as vacuum melting,&apos; vacuum casting, and ladle-to-ladle stream degassing, which lower the hydrogen content to levels on the order of 1 to 2 ppm. Therefore, the method used for determining hydrogen in steel must be sensitive and precise. In any analytical procedure for gases in metals there are two distinct operations—the extraction of the gas from the metal and the analysis of the extracted gas. To extract the gas from the steel, three methods have been employed: 1) fusion of the sample with graphite at high temperature; 2) fusion with a flux, such as tin, at a lower temperature; and 3) extraction of the hydrogen from the solid sample at a temperature below the melting point of the steel. Fusion with graphite is the least-acceptable method. The blank in this method is higher and more variable than in either of the other two methods. The hydrogen fraction of the total gas composition usually is between 10 and 50 pct; thus, a larger analytical error is possible. The vacuum-tin fusion4 extraction of hydrogen is probably the most rapid method in use today; the extraction time is usually about 10 min. However, with this system a bake-out of the freshly charged tin for 2 hr is necessary and a change of crucible and a charge of fresh tin are required after each day of operation whether one or thirty samples have been analyzed. In addition, frequent checks of blank rates are required since CO and Na are continually being given up by the steel samples dissolved in the tin bath. The composition of the gas in this method lends itself readily to analysis; although the hydroge concentration may fall to as low as 50 pct, more often it is above 90 pct, thus allowing a more precise analysis (because of less interference from other gases). In 1940 ewell&apos; published the hot-extraction method for extracting hydrogen from the solid sample, comparing analysis for hydrogen extracted at 600°C with similar analysis for the gas extracted at 1700°C by fusion with graphite. Good agreement for hydrogen was obtained between these two methods, provided sufficient time was allowed for extraction at the lower temperature. carsone obtained good results in his comparison of this hot-extraction method with vacuum-tin fusion. Subsequent work by Geller and sun7 and Hill and ohnson&apos; has shown that steel samples should be heated to at least 800°C to effect the release not only of the diffusible hydrogen but also of the "residual" hydrogen that may be present as methane. Since the rate of evolution of hydrogene9l0 depends on such factors as sample size and composition, thermal history, and extent of cold work, a fixed extraction time is not possible. Extraction times of 30 min are normal, but 2 hr are not unusual. Induction or resistance heating may be used in the hot-extraction method. With resistance heating the

Jan 1, 1964

By D. Atkinson, C. Bodsworth, I. M. Davidson

A geometric model of interstitial solid solutions, which has been used previously as a basis for the prediction of carbon activities in Fe-C austenite, is shown to serve also for the calculation of nitrogen activities in Fe-N austenite. The model has been developed to enable predictions to be made of the activities of an interstitial element in the presence of two host atom species. The activities calculated via the model are shown to be in satisfactory agreement with the measured values in the austenite phase for carbon in Fe-C-Co, Fe-C-Cr, Fe-C-Ni, Fe-C-~n, Fe-C-Si, and Fe-C-V alloys and for nitrogen in Fe-N-Ni alloys. The effect of the second substitu-tional solute on the logarithm of the activity of the interstitial element is expressed as the product of a constant mad the atomic concentration of that solute. The constants so derived we related to the thermo-dynamic interaction coefficients which describe the effect on the activity coefficient of carbon of an added solute element. In recent years the thermodynamic activities of carbon and nitrogen in the single-phase austenite field have been determined for iron binary alloys and for several iron-base ternary alloys. In order to extend the use of these measurements, it is desirable to be able to predict with reasonable accuracy the activities of the interstitials at compositions and temperatures other than those which have been measured experimentally. In all the systems studied to date, the interstitial elements do not conform to ideal behavior. Hence, the available data cannot be extrapolated or interpolated using the simple thermodynamic concepts of solutions. Several models have, therefore, been formulated for the purpose of predicting the activity of an interstitial element in the presence of one species of host atom. These models can be divided into the geometric1"5 and energetic6-&apos; types. The former group is based on the assumption that at low concentrations the activity of the interstitial species is determined by a composition-dependent configurational entropy term and an excess free-energy term which is temperature-dependent but independent of composition. The purpose of this paper is to show that the treatment, based on a geometric model, can be extended to enable predictions to be made of interstitial activities in the presence of two substitutional host atom species. THE CONFIGURATIONAL ENTROPY OF MIXING ICaufman5 has shown that the configurational entropy, S,, for a binary solution comprising of a host atom species, A, and an interstitial species, I, can be expressed as: where NI is the atom fraction of the interstitial species, R is the gas constant, and (2 - 1) is the number of interstitial sites excluded from occupancy by the strain field around each added interstitial atom. The number of interstitial sites per host atom, p, is unityg for the fcc austenite solutions considered here. The configurational entropy of mixing for a ternary solution comprising two substitutional atom species, A and B, and one interstitial species, I, can be derived similarly. Let the number of atoms per mole of each of these species in the solution be represented by «a, ng, and nI. From geometric considerations, it is improbable that the addition of a few atom percent of a second host atom species will change the type of sites (i.e., octahedral) in which the interstitial atom can be accommodated in the austenite lattice. At higher concentrations (determined largely by the relative atomic radii of the atomic species present and any tendency to nonrandom occupancy of the host lattice sites) other types of interstitial sites may become energetically favorable. Restricting consideration to compositions below this limit, for 1 = 1 the number of suitable interstitial sites is given by (n + nB). However, if each interstitial atom excludes from occupancy (Z - 1) additional sites, the total number of sites available for occupation is reduced to (n + ng)/Z. The number of vacant interstitial sites is given by: The total number of recognizable permutations of the atoms must include the recognizable, different configurations of the A and B atoms on the host lattice. Assuming that these arrangements are purely random, and are not affected by the presence of the interstitial species, the total number of recognizable permutations in the ternary alloy is given by: The configurational entropy is obtained by expanding, using Stirling&apos;s approximation, and collecting like items, as:

Jan 1, 1969

By W. F. Chiao, R. B. Gordon

Tile sharp-yield point found in magnesium crystals in the solulion-treated and aged condition is studied by dislocation internal-friction experiments. The results show that the sharp yield is not file to the sudden release of pinned dislocations hut is movc likely due to the rapid multiplication of an initially small number of dislocations. Recovery or the dislocation internal friction after deformation is also studied. This yecovery results from the re-pinning of dislocations by a solute, presumably nitrogen, which moves with a relatively small activation energy. SHARP-yield points, when they occur, are a striking feature of the stress-strain curve generated during a tensile test. Although commonly associated with steel, sharp yielding has been found in a variety of metallic and nonmetallic crystalline materials. In particular, sharp-yield points have been found in zinc"&apos; and cadmium3 containing nitrogen. With this background, Geiselman and Guy4 investigated the tensile properties of magnesium single crystals containing nitrogen to see if sharp yielding also occurs in this system. They found that sharp yields did indeed occur in solution-treated and aged specimens tested at elevated temperature but were not able to give conclusive proof that the sharp yield was caused by nitrogen, a yield drop being observed even in their purest crystals. Sharp-yield points have also been found in various polycrystalline magnesium alloys.7&apos;8 In the study of the sharp-yield phenomenon it is desired to observe the behavior of dislocations in the earliest stages of the deformation process. Internal-friction experiments are useful for this purpose because dislocation damping is sensitive to the mobility of free-dislocation segments. At low strain amplitudes the damping, A, due to the the forced vibration of dislocation segments of average length L is ? =KAL4 [1] where A is the dislocation density and K, if the applied frequency is well below the resonant frequency of the dislocation segments? is a constant for the sample under observation.5 Dislocation damping, because of the fourth-power dependence on L, is particularly sensitive to the creation of free-dislocation segments during deformation. Since sharp yielding is associated with the sudden release of pinned-dislocation segments, marked changes in the dislocation damping are expected at the yield point.6 The use of the dislocation-damping observations to help elucidate the incompletely understood mechanism of yielding in magnesium is the primary objective of the experiments reported here. PROCEDURE Many investigations have shown that very marked and rapid changes occur in the dislocation damping of of a deformed material as soon as the straining is stopped.5 It was quite essential, then, for the purpose of this investigation, to make the damping measurements during the deformation of the samples. This can only be accomplished through the use of the ultrasonic-pulse method. In this method traveling sound-wave pulses are used and, in contrast to resonating-bar methods, only the sample ends are set in vibration. Thus, the sample can be gripped along its sides in the tensile-test machine without disturbing the damping measurements. In the pulse method, the decrease in the amplitude of a sound pulse is measured as it travels back and forth through the sample. If A is the amplitude after traversing a distance x and A. is the initial amplitude, A=Aoe-ax [2] and a is called the attenuation. It is commonly measured either in units of cm-I or as db per µ sec. The observed attenuation in a metal sample is due to a number of causes. These include scattering by grain boundaries and impurity particles, thermo-elastic damping, diffraction effects, stress-induced ordering of solute atoms, and dislocation damping. The total observed attenuation in a given sample usually cannot be resolved into these various components, but changes in a due solely to changes in dislocation damping can be accurately determined, provided the experiment is arranged so that all other sources of damping are held constant. It is desired to reduce the extraneous sources of attenuation to a minimum and for this reason the experiments are done on single crystals of high purity. Magnesium crystals offer the further advantage that, when properly oriented, only a single set of slip planes is active during deformation. Crystal Preparation. The method of sample preparation is similar to that of Geiselman and Guy.4 The starting material was high-purity, sublimed magnesium rod supplied by the Dow Chemical Co. Melting under Dow 310 flux was used to reduce the nitrogen content of the starting material: the fluxing was done under an argon atmosphere and the

Jan 1, 1965

By J. D. Mote, J. E. Dorn

This investigation was undertaken to study the effects of piledup arrays of dislocations on inducing slip, twinning, and fracturing in magnesium bicrystals. A series of variously oriented bicrystals of magnesium having a vertical grain boundary were prepared and tested in tension. It was found that piled-up arrays of dislocations at the grain boundary could, under appropriate conditions, induce slip, twinning- and cracking. The results that were obtained substantiate, at least qualitatively, the general dislocation mechanism for transmission of strain across grain boundaries and the Petch-Stroh concept of fracturing. WHEREAS single crystals of magnesium generally exhibit extensive deformation, coarse-grained poly-crystalline magnesium at subatmospheric temperatures fractures after a few percent elongation.&apos; Although a small amount of ductility is obtained, several features of this fracturing are characteristic of typical brittle behavior. Over a rather broad temperature range the fracture stress is insensitive to the test temperature and the fracture stress increases linearly with the reciprocal of the square root of the mean grain diameter. The course of fracturing is predominantly intergranular, but small fragments of adjacent grains frequently adhere to the fractured surface.2 The brittle behavior of polycrystalline magnesium is attributable to the limited number of facile deformation mechanisms it exhibits at low temperatures. For a general deformation of a randomly oriented polycrystalline aggregate, each grain must exhibit at least five independent mechanisms of deformation to permit accommodation of the imposed deformation from grain to grain.= Although minor amounts of prismatic slip occur in corners of grains where stress concentrations are known to be high, glide in polycrystalline magnesium at low temperatures takes place almost exclusively by basal slip.&apos; The common type of twinning, which takes place on the (1012) pyramidal planes, can under the most favorable orientations, lead to a. strain of only 6.9 pet; the contribution of twinning to the tensile strain would indeed be much less than this in a randomly oriented polycrystalline aggregate of magnesium. Since the three mechanisms of basal slip are coplanar, they are equivalent to only two independent mechanisms, a number insufficient for a general deformation. Consequently, once the permissible twinning has taken place in conjunction with basal slip, no further plastic deformation is possible because of interference to slip at the boundaries of dissimilarly oriented grains. At this stage brittle fracturing takes place due to high stress concentrations at the juncture of slip bands with the grain boundaries; the predominance of intergranular fracturing in magnesium, in preference to transcrystalline fracturing which is prevalent in zinc, has not yet been rationalized. A more atomistic description of the plastic behavior and fracture characteristics of magnesium follows from the analyses made by stroh4 on the stresses induced by piledup arrays of dislocations. Slip first takes place by dislocation motion in the most favorably oriented grains. As the dislocations approach the boundary of a dissimilarly oriented adjacent grain they begin to form an array of dislocations with its attendant stress field. Piledup arrays of screw and edge dislocations introduce high localized shear stresses at the spur of the array; piledup arrays of edge dislocations also induce high tensile stresses localized in the vicinity of the grain boundary. Whereas the shear stresses can induce slip to take place, the tensile stresses, if sufficiently high, can cause fracturing. The localized shear stress will be relieved if sufficient numbers of mechanisms of deformation become operative in the original and the adjacent grain to permit accommodation of the dislocations in the grain boundary. In this event a ductile behavior will be obtained. But if the number of deformation mechanisms is insufficient for complete migration of dislocation arrays into the grain boundary, the tensile stresses due to the edge components of piledup dislocation arrays will continue to increase with increasing applied stress until fracturing takes place. Whereas face-centered-cubic metals have a sufficient number of mechanisms of slip for accommodation of dislocations in their grain boundaries to exhibit ductile behavior, hexagonal-close-packed metals, in general, do not. Consequently, hexagonal-close-packed metals are usually brittle except when conditions such as alloying or temperature permit facile slip by a number of mechanisms. The arguments presented above suggest that the mechanical behavior of magnesium depends on whether or not dislocation arrays in adjacent grains can enter the grain boundary. When such accommodation is possible, ductile behavior is expected; but when such accommodation is impossible, fracturing will ensue. To further test the validity of these arguments it was considered advisable to study the

Jan 1, 1961

By C. R. Barrett, N. N. Singh Deo

The high-temperature steady-state creep behavior of a series of dilute copper-silicon alloys was studied to determine the effect of stacking fault energy on the creep-rate. The steady-state creep rate is, when taken at equivalent diffusivities decreases with decreasing stacking fault energy. The stress and temperature dependencies of is suggest that creep is a difusion controlled dislocation climb process. Electron microscopy studies of the creep substructure revealed: 1) the subgrain size is not a function of the stacking fault energy in these alloys, 2) the dislocation density not attributed to the subgrain walls seems to be higher during primary creep and decreases to a lower steady value during steady-state creep, and 3) the dislocation density during steady-state creep decreases with decreasing stacking fault energy. In the past few years numerous investigators have studied the influence of stacking fault energy on high-temperature creep strength. Most of these investigators have confined their attentions to studying the relationship between steady-state creep rate, is, and stacking fault energy, ?, when samples are tested under conditions of comparable stress and temperature. For the case of fcc metals, it was initially shown by Barrett and Sherbyl and since confirmed by many others2"4 that is decreases with decreasing ?, often following an empirical relation of the form i ?m where m is a constant about equal to 3. The application of theory to explain this observation has not been entirely successful. One of the main difficulties has been the almost complete lack of structural information (dislocation density, subgrain size, and so forth) for samples with different stacking fault energies, tested under high-temperature creep conditions. weertman5 has attempted to explain the stacking fault energy dependence of is on the basis of a dislocation climb mechanism. Assuming that both the rate of dislocation core diffusion and the ease of athermal jog formation decreases as ? decreases Weertman has argued that the rate of dislocation climb and hence the creep rate should also decrease as ? decreases. One questionable aspect of Weertman&apos;s analysis is the assumption that core diffusion down extended dislocations is slower than core diffusion down unextended dislocations. The only experimental work done in this area, by Birnbaum et al.6 on nickel and Ni-60 Co, has shown the core diffusivity to increase with decreasing ?. Theories of steady-state creep based on the diffusive motion of jogged screw dislocations often seem unable to predict even the qualitative nature of the es- relationship. Assuming that Weertman is correct in his assumption that the dislocation jog density decreases with decreasing ? then the jogged screw theories predict an increasing dislocation velocity with lower ?. It is usually assumed that the increase in dislocation velocity implies a corresponding increase in creep rate. However, two other factors must be considered before such a statement can be made. That is, we must know how both the mobile dislocation density and the effective stress (the difference between applied stress and internal stress) vary with ?. Significant changes in either one of these factors could outweigh any change in dislocation velocity accompanying a change in ?. And with the slower rates of recovery expected in low stacking fault energy materials it seems likely to expect both mobile dislocation density and effective stress to be dependent on ?. Sherby and Burke7 have suggested that stacking fault energy influences the creep rate in an indirect way. These authors cite evidence that the steady-state subgrain size generated during high-temperature creep is a function of ? decreasing with decreasing ?. Assuming the creep rate to be proportional to the area swept out by each expanding dislocation loop and that subgrain boundaries are good barriers to dislocations, then the creep rate should be proportional to subgrain area, hence increasing as ? increases. A critical evaluation of any of the above theories requires more quantitative information concerning the dislocation substructure generated during high-temperature creep. Accordingly this investigation was undertaken with an aim of studying the influence of stacking fault energy on tbe steady-state creep characteristics of a series of dilute copper-silicon alloys. Special emphasis was placed on studying the strain dependence of both the dislocation configuration and density. MATERIALS AND PROCEDURE Dilute copper-silicon alloys of the compositions shown in Table I were tested in tension at constant stress. The relative stacking fault energy of these alloys has been determined and is shown in Table 11. An Andrade-Chalmers lever arm was used to maintain constant stress and testing was carried out in a water

Jan 1, 1970

By J. Campbell

Various models are discussed for the evaluation of the negative pressures which may occur in solidifying materials which exhibit various deformation modes: elastic-plastic, Bingham, viscous, or creep flow. The inadequacy of the previously proposed elastic-plastic solution for solidifying metals is revealed by comparison with the more reliable creep results which are given graphically for aluminum, copper, nickel, and iron. The maximum tensions experienced in the liquid phase of solidifying spheres ranging in size from large castings to submicron powders are in the range from —10&apos; to —105 atm for these metals. THERE has been much recent interest in the negative pressures associated with the volume change on solidification and in the possibility of the occurrence of cavitation. Considering the freezing of a highly supercooled liquid, an attempt to evaluate the stresses in the liquid ahead of the rapidly moving solidification front has been made by Horvay1 on a microscale and by Glicksman2 on a macroscale. In a casting of a wide freezing range alloy, the pressure differential due to viscous flow of residual liquid through the pasty zone has been discussed by Piwonka and Flemings,3 In a previous publication4 the author has attempted to estimate the negative pressure occurring in the residual liquid of a spherical casting, employing an elastic-plastic model to describe the collapse of the solidified shell under the internal tension. An earlier model assuming a rigid shell was shown to be inaccurate by many orders of magnitude. The elastic-plastic model is critically reviewed here, and other models are developed which are thought to be more closely related to metals and other materials near their melting points. The spherical geometry (Fig. 1) is chosen because the highest shrinkage pressures would be developed, although the analyses are readily adaptable to cylindrical geometry. A parallel sided casting experiences little internal tension because of the relatively easy dishing inward of the sides. (This commonly observed phenomenon has previously been attributed solely to atmospheric pressure.) Furthermore, small regions of confined liquid in a large solidified volume of a casting approximate reasonably well to spherical geometry. ELASTIC-PLASTIC MODEL The author has shown4 that as solidification proceeds the internal hydrostatic tension builds up until the elastic limit of the shell is exceeded. At this point the internal pressure is closely -2Y/3. Subsequently a plastic zone spreads from the inner surface toward the outer surface of the shell. When the whole casting is deforming plastically a rather more generalized analysis taking account of the externally applied pressure PA + 2y/b gives the internal pressure as: P = Pa + 2y/a + 2ys/b - 2 Y In(b/a) [1] The 2y/a and 2ys/b terms result from the tendency of the liquid-solid and solid-vapor interfaces to shrink, reducing their energy, and thereby helping to collapse the solid phase and compress the liquid phase. The 2y/b term would be important only for powders. The last term arises because of the plastic restraint of the solid, resisting collapse and so effectively expanding the residual liquid. From Eq. [I] it is easily shown that there is a minimum in the pressure at the radius amia= y/Y [2] which is of the order of 103K for the metals aluminum, copper, and iron, and corresponds to the minimum pressure Pmin = 2 Y[l-ln(bY/y [3] The results of a fully worked out elastic-plastic solution are given in a previous reporL4 The main criticism which may be leveled at this analysis when applied to metals at their melting points is the strong dependence of the yield stress on the strain rate. The strain rate varies with both solidification conditions (e.g., whether chill-cast or slowly cooled) and during solidification, as is indicated in the following section. Thus an appropriate choice of Y is very arbitrary. Before proceeding to a discussion of models which are strain-rate-dependent, it is necessary to evaluate the strain rate as a function of the rate of solidification. SOLIDIFICATION RATE Various empirical relations have been deduced5 for the rate of thickening of the solid shell by pour- out tests on partially solidified spheres. These, however, are unsatisfactory for our purposes since they become very inaccurate when the liquid core is very small. A theoretical approach is therefore necessary, and some solutions are set out below. Making the assumptions of constant surface temperature of the casting during freezing, no superheat, and a material freezing at a single temperature, Adams8 deduces the approximate solution: which becomes when b » a: Employing a semiempirical approach vallet6 finds:

Jan 1, 1969