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By W. C. T. Yeh, T. G. Oakwood, A. A. Hendrickson, R. H. Hammar

The objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for by the influence of the solute addition on the dislocation structure oj- the crystals. The additions of both tin and indium produced only small changes in the dislocation densities and arrangements in silver crystals. However, as found previously, small solute additions have large effects on the tensile properties; the inj-luence of the tin and indium additions on the temperature dependence of the flow stress and the easy-glide range is especially strong; It is concluded that the indirect strengthening effect of the solute due to variations in the dislocation density as proposed by Seeger is of minor importance and that solute atom-dislocation interactions are responsible for the observed strengthenirzg effects. The experimental results were combined with those of Rogausch to test the concenlvatiorz dependence of solute strengthening. Both the first and one-half power dependences of the critical resoleed shear stress on concentratiorz fail in very dilute solutions. THE objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for, at least in part, by the influence of the solute addition on the dislocation structure of the crystals. It is recognized that the addition of solute atoms may influence the strength properties of a metal through both "direct" and "indirect" effects. The former refer to the strengthening mechanisms that result from the interaction of solute atoms with dislocations; in the latter case, the strengthening effects arise as a result of solute's influence on quantities such as dislocation density, dislocation arrangement, stacking-fault energy, diffusivities, the elastic constants, and so forth. It is clear that the correct interpretation of solid-solution strengthening phenomena cannot be given until the importance of indirect strengthening effects is properly evaluated. In the particular case of close-packed metal crystals, Seeger showed that solute strengthening effects in dilute solutions of copper and silver might be accounted for by an increase in dislocation density due to the addition of the solute. Seeger's argument was that the strengthening effects extrapolated from more concentrated solutions indicate that small concentrations of impurities raise the critical resolved shear stress much more than is predicted by a concentration-independent dislocation density. The above idea was a very reasonable one. The dislocation theories of work hardening of Taylor,2 Cot-trell, 3 Mott, 4 and seeger5 had already associated the increased flow stresses with increased dislocation densities in deformed metals; investigations of the dislocation structure of metal crystals had provided a logical basis for expecting an increased dislocation density in crystals containing impurities (see for example, Ref. 6). The numbers involved seem reasonable, too. It can be expected that the flow stress of the crystal would increase as the one-half power of the dislocation density.' Solute additions of 1 at. pct to metal crystals result in strength increases by factors in the range of three to ten. If one assumes that the strengths of the pure metal crystals are determined by their dislocation densities, then dislocation-density increases of one to two orders of magnitude as a result of solute addition would be required to account for the observed strengthening—not an unreasonable expectation. In addition to the effect of the solute addition on dislocation density, one might also anticipate important strengthening contributions to result from the solute's influence on the dislocation arrangement. Parker and washburns have reviewed a number of experimental evidences which show important strengthening effects due to the presence of subboundaries. Further, lattice strains due to impurity segregation would be expected to influence the distribution as well as the dislocation density of the as-grown crystal. As pointed out in the reviews of Chalmers,6 Elbaum,9 and winegard,lo micro segregation of impurities occurs at all interfaces of crystals in cellular growth; the impurity gradient results in lattice strains which can be reduced with the presence of dislocation arrays in the region of the impurity gradient. Hence, one would expect the presence of a solute to favor the formation of dislocation subgrain structures and that the subgrains would have an important influence on the strength of the crystal. The experimental observations that concern the possibility of an important strengthening contribution through the influence of the solute on the dislocation density or arrangement are not in agreement. Haasen has reviewed the observations of Meakin and Wils-dorf,12 Howie,13 and Bocek 36 and concluded that the solute's influence on dislocation density is not sufficient to account for strengthening effects in concentrated solutions but might, as seegerl suggested, make an important contribution in very dilute solutions. On the other hand, Hendrickson and Fine 14 concluded that changes in the dislocation density and dislocation width accounted for the solid-solution strengthening effects observed in silver-based aluminum solid solutions. Goss et a 1.I5 observed dislocation arrays in Ge-6 at. pct Si, Ge-0.2 at. pct Sn, and Ge-0.2 at. pct B crystals that were not observed in germanium crystals of

Jan 1, 1968

By R. D. Pehlke, J. V. Gluck

A study was made of' the effects of up to five additional solutes on the thermodynamic activity of zinc in dilute solution with molten bismuth in the range 450" to 650°C. The experimental measurements were made in a multielectrode galvanic cell apparatus employing fused LiCl-KCl as the electrolyte. The solute additions included indium, lead, tin, cadmium, copper, silver, antimony, or gold. A range of positice and negative interactiotls with zinc was covered. The experinzer~tal observations were cowlpared with the activity coefficients calculated usitlg either Wagner's first-order Taylor series rnodel or a proposed second-order solution itrteraction model. hi general, the truncated first-order Taylor series proposed by Wagner gaue good results for "dilute" solutions (XBi > 0.90) contaitzing up to six solutes. The second-order model, which includes a second-order cross-interaction term, produced a slight improvement in predictions for solutions with XZn = 0.015 and a significant improvement for solutions with XZn = 0.050 hear the limit of Henry's law region). Seveval of the quaternary solutions studied contained a total solute content of 0.215 mole fraction, and fairly good success was achieved in predicting the activity coefficient 01- zinc. ThE study of thermodynamic interactions between dilute solutes in liquid metallic solutions has occasioned much recent interest. It is useful to recall in this respect that Wagner's well-known expression for the activity coefficient' is a practical application of the problem of representing a given function, i .e., In ?, by means of a sequence of polynomials. No specific physical model of a solution is involved in its use. As suggested by Wagner, a Taylor Series is used to expand In ? about a point of infinite dilution with respect to all solutes. The partial differential coefficients of the series have been termed "interaction parameters". Various authors'-6 have proposed formalisms for parameters, the definitions being designed to meet some specific experimental or physical condition. A usual assumption is that terms above first-order in the Taylor Series may be neglected. In that case, the logarithm of the activity coefficient is expressed as a linear function of solute concentrations. The resulting expression is presumed valid for any number of additional solutes as long as the solution can be regarded as "dilute". This assumption can be termed "the hypothesis of additivity". However, experimental tests of that hypothesis for quaternary or higher-order solutions have been extremely limited. Primarily such tests have been confined to studies of effects of added metallic elements on either the activity of carbon or the solubility of gases in liquid iron.7-13 The only known previous study of an all-metal system is the limited work of Okajima and pehlke14 on the effects of multiple solute additions on the activity of cadmium in liquid lead. The present investigation is a portion of the work to determine the effects of various solute additions on the activity of zinc in dilute solution with molten bismuth in the range 450" to 650C It was shown for such ternary solutions that second-order Taylor Series terms could be evaluated at the same time as first-order terms, with no additional experimentation required. A second-order solution model was described which, under certain conditions, is a rigorous representation of solute activity in a ternary solution. (In the sense employed in this paper, the term "model", as distinguished from "equation", is taken to mean an empirical correlation or formalism, but not a hypothetical physical system per se.) Presumably such a model could be extended to produce a better representation of In ? in solutions of even higher order. The feasibility of a generalized Taylor Series approach to solution interactions and inclusion of second-order terms also has been discussed recently by Lupis and Elliott in independent work concurrent with the present investigation. In addition, they discussed empirical means of estimating certain second -order coefficients.17 The utility of such solution models rests on the ability of a truncated series to represent adequately the experimental facts in multicomponent solutions. Questions that arise include: Do the second-order terms really make a significant contribution? How far away from "dilute" solution may such models be applied? Are the types and varieties of the additional solutes important? among others. In order to provide some answers to these questions, an experimental study was made of the effects of two or more additional solutes on the activity of zinc in dilute solution with molten bismuth. Comparisons were then made with calculated activity coefficients obtained using the previously determined ternary interaction parameters. INTERACTION MODELS As an example of the approach to defining activities in multicomponent solutions, consider the Taylor Series expansion for a quaternary system, i.e., three dilute solutes. Writing terms through second order, the result is:''

Jan 1, 1968

By E. J. Ripling, S. I. Liu

IT has been shown in a number of recent publications that much information on the mechanical behavior of metals can be gleaned by first deforming test specimens under one set of conditions, and then evaluating the effect of this deformation by means of a subsequent tensile test. A straining procedure of this type has been applied to study the flow behaviors of a number of metals.1, 2 In these studies the prestraining and testing were both tensile strains, while the straining temperature was varied between the prestraining and testing steps. These data indicate that there is a more or less general flow behavior exhibited by all metals which are pre-stretched at one temperature and then tested in tension at a second temperature. Prestraining a metal at a high temperature produces a lower yield strength during the subsequent low temperature strain than would the same total strain at the lower temperature. On reversing the order of the strains, low temperature prestraining produces a higher yield strength during the subsequent high temperature straining than would a single high temperature strain of the same magnitude. Unlike the flow behaviors, the fracturing characteristics of metals when prestrained under one set of conditions and tested under a second set of conditions is quite material dependent. The fracture behavior of a number of steels2" as well as of a commercially pure zinc,4 have been investigated by these two-step tests and was found to depend upon the position of the transition temperature with respect to the prestraining and testing conditions. Since these fracturing phenomena are complicated by the appearance of the transition temperature, it has been difficult to reliably define the basic effect of a two-step straining procedure in fracturing. Metals crystallizing in the face-centered cubic system do not exhibit transition temperature effects so that the mechanical characteristics obtained on these materials could serve as a base for two-step straining behaviors. Consequently groups of specimens of the aluminum alloy 24s-T4 were prestrained various amounts at room temperature in either tension or compression after which these strained specimens were further strained to failure, or tested in tension, at either room or some lower temperature. Other groups of 24S-T4 specimens were prestretched at various low temperatures after which these were tested in tension at room temperature. These straining techniques then made it possible to compare the behaviors of aluminum with the behaviors previously presented for steels. Material and Procedure The commercial aluminum alloy 24S-T4 in the form of 3/4 in. rods was used in this investigation. The material was subjected to the following treatments before machining: 1—resolution treating at 920" & 10°F for 45 min, 2—quenching in water at room temperature, and 3—aging at room temperature for four days. The re-heat treated material was then machined to either of the specimen shapes shown in Fig. 1. Fig. la shows the threaded-end specimen used for prestraining in compression. Fig. 1b shows the specimen used for both prestrain in tension and final testing. The material subjected to precompression in the form of the specimen shown in Fig. la was re-machined to the specimen shape in Fig. 1b for final testing. Prestraining in tension and final testing were done without any intermediate machining. All straining was performed on a 10,000 1b Riehle tensile testing machine. Tensile strains were conducted in a specially designed concentric fixture which produced an eccentricity of less than 0.001 in." The change in diameter at the minimum section of

Jan 1, 1954

By Irving Cadoff, Kurt Komarek, Edward Miller

THE lead-telluride phase diagram as compiled by ansen' has one intermetallic compound, PbTe, with solid-solubility limits extending from 22 to 45 wt pct Te (31.4 to 57.1 at. pct). Pelzel2 redetermined the solubility limits on the lead-rich side of the compound by measuring the relative areas of the two phases in samples annealed in the liquid + compound region, and obtained data that agreed with that of Hansen. Recent studies of the semiconducting properties of PbTe3 however, have indicated that addition of either lead or tellurium to PbTe does not produce samples having carrier concentrations greater than about 10 19 cm-3. Assuming that each impurity atom results in one ionized charge carrier, this carrier concentration corresponds to a solubility range of less than 0.04 at. pct. Fritts and Karrar4 have also observed two phases in samples containing from 0.15 to 3.0 pct excess Pb. To resolve the discrepancy between these data, the solid solubility limits of the compound PbTe were reinvestigated, using several other techniques. Ten 25-g samples with compositions of 1/2, 1, 3, 5, and 10 wt pct excess Pb and Te and two 100-g samples of 15 and 65 wt pct Te were prepared, sealed in evacuated quartz capsules, and melted at 950oC. The 1 pct excess Pb and Te and the 15 and 65 wt pct Te alloys were homogenized for 96 hr at 450°C; the remaining specimens were annealed 50°C below the solidus temperature reported in Hansen. The specimens were polished and etched with dilute HNO,. All the samples were two phase, the second phase appearing at grain boundaries or as spheroidized inclusions in the grains. In the case of the tellurium rich specimens, the second phase could be identified as a eutectic. Debye-Scherrer powder diffraction patterns of the i, 1, 3, 5, and 10 pct excess samples were obtained using CuKa filtered radiation. The films were indexed as the B1 or NaCl structure. The calculated lattice parameter of PbTe was the same for all the specimens, with an average of a0 = 6.460 ± 0.0005A. Lines due to excess lead or tellurium were very faint but could be clearly seen in all the films. The relative areas of the two phases in the 15 and 65 wt pct Te samples were corrected for the differences in density of Pb, Te, and PbTe, and taken as proportional to the relative volumes of the two phases. The corrected relative volumes agreed with a phase diagram having negligible solubility of both lead and tellurium in lead tellurium. The density of the two specimens was obtained to give a third independent determination of the phase limits. The specimens were broken into small pieces to eliminate any internal porosity, and adherent air bubbles were removed by vigorous shaking under water for several hours. The density of lead (11.34 g per cm3) and of tellurium (6.25 g per cm3) was taken from the International Critical Tables and that of stoichiometric PbTe (8.25 g per cm3) calculated from the lattice parameter. For the 15 wt pct Te samples, the density assuming no solubility was calculated to be 9.89 g per cm3; the observed density was 9.86 g per cm8. For the 65 wt pct Te alloy, the density calculated for the case of no solubility was 7.24 g per cm3; the measured density wag 7.22 g per cm3. These results are consistent with those of planimetry and X-ray. SUMMARY Data have been presented which show that the solid solubility of both lead and tellurium in PbTe is

Jan 1, 1961

By M. Hansen, C. C. Wang

THE 6 phase of the Cu-Sn system (Cu,Sn, = 32.53 pct Sn) was considered to be stable down to room temperature until Owen and Iball showed by X-ray analysis that it undergoes a eutectoid decomposition into the a and e phases at a temperature near 300°C. Their findings have been confirmed by other investigators,2-5 a11 of whom used X-ray diffraction studies of powdered specimens. The transformation temperature has been reported by various authors as lying between 300" and 380°C. To our knowledge, no microscopic evidence of the eutectoid reaction has been published, as yet. It was in connection with other work that longtime annealings at 300°C were conducted with alloys containing 22, 32.6, and 35 pct Sn (nominal compositions) prepared from electrolytic copper and electrolytic tin and cast in a small iron mold. The specimens were first annealed at 700°C for 5½ hr and quenched from 400 °C after cooling to, and annealing at, that temperature for 9½ hr. After this treatment the sample with 22 pct Sn was cold worked for 15 pct reduction in thickness; the 32.6 and 35 pct alloys were too brittle to be cold worked. The final anneal at 300°C was done in a sealed pyrex glass bulb for 63 days. Fig. 1 represents the microstructure of the annealed alloy with 22 pct Sn. It shows primary a solid-solution crystals in a matrix of the (a + 8)-eutectoid formed at 520 °C. The a crystals contain 8 inclusions which precipitated from a due to the decrease in the solubility of tin in copper with fall in temperature. The decomposition of the 8 phase into a (light) and E (dark) can clearly be seen in some areas of the (a + 8)-eutectoid matrix. However, the decomposition is far from being completed, even after the long-time anneal used. Figs. 2 and 3 depict the microstructures of the annealed 32.6 pct alloy, which was intended to consist entirely of 6 phase. Due to some loss in copper on melting, the composition is slightly higher in tin. Accordingly, the sample after quenching from 400 "C consisted of grains of the 8 phase with the e phase arranged along the grain boundaries and as a Wid-manstatten precipitate within the 6 grains. After an annealing time of 63 days, the eutectoid decomposition, 6 + a + e, is still in its early, initial state. The pearlitic type of eutectoid is nucleated at the c crystals, preferably those surrounding the grain boundaries of the 8 phase. The appearance of the (a + €)-eutectoid in the 35 pct Sn alloy was very similar to that shown in Figs. 2 and 3. Again, the eutectoid decomposition nucleated at the 6 phase and proceeded from there into the 8 areas. As is evident from Fig. 2, the rate of decomposition of the 6 phase at 300°C is extremely sluggish: In the representative area shown only about 5 pct of the 8 phase has undergone the eutectoid trans- formation after annealing for 63 days. On the other hand, Owen and Williams2 have reported that X-ray photographs of powdered samples with between 17.5 and 34 pct Sn did not show 8 lines after annealing for only five to seven days at 300°C. This is in accordance with the fact that the rate of reaction in powdered samples is higher than in massive specimens, as a result of the excess free energy of the powder (due to its greater surface area). The authors wish to express their thanks to C. A. Johnson for preparation of the micrographs.

Jan 1, 1952

By J. N. Butler, R. J. Morris

A series of organic collectors has been developed which successfully float synthetic secondary uranium minerals, such as autunite, carnotite, and torbernite. Recoveries up to 97 pct have been obtained. With cleaning of rougher concentrates, ratios of concentration as high as 15:1 are possible on head assays of 0.10 to 0.50 pct U 3 O 8. Additions of certain base metal salts aid in recovery and materially increase the rate of flotation and selectivity of the collectors for the synthetic minerals. Flotation tests on natural uranium minerals have not yet equaled results obtained on the synthetics, although these collectors do give better results than conventional collectors for nonsulfide minerals. RAPID increase in mining and milling uranium ores during the past seven years and the discovery of large tonnages of uranium-bearing material too low in grade to stand the cost of leaching have developed considerable interest in possible methods for beneficiating these marginal ores. Such ores are generally classed as those containing less than 0.10 pct U3O8. Development of a beneficiation method that would give both high recovery and high ratio of concentration would also make possible the beneficiation of higher grade ores and would provide higher grades of feed to existing leaching plants. Although considerable research and testing on physical or physico-chemical beneficiation of domestic uranium ores has been done in the past, to the best knowledge of the authors only a single application of physical beneficiation is now in operation on a commercial scale. Flotation has been attempted on the basis of mineral association rather than by direct concentration of the contained uranium minerals. Flotation studies conducted on this project on certain ores gave recoveries of 60 to 70 pct of the uranium by the use of conventional flotation agents such as oleic acid, but ratios of concentration were in the order of 1.5:1 to 2.5:1. Subsequent cleaning to upgrade the concentrates rapidly increased losses in the cleaner tailings, which were not later refloated in the rougher flotation. Selection of Collector: In selecting desirable organic collectors for these oxide systems, a thorough study was made of the relationship between structural characteristics and collector activity by an examination of the behavior of a number of different functional arrangements present in a variety of organic molecules, (see Fig. 1). It is generally accepted that a collector must have a relatively long-chain hydrocarbon radical and a chemically reactive elec-trophilic center. Such a requirement could be met by a large number of compounds, but steric effects at the uranium mineral surface, solubility, compat-ability with aqueous systems, air avidity, bond strength at the mineral surface, interfacial concentration of the collector, and diffusion rate of the formed complex from the air-water interface eliminated many as unsuitable for this purpose. Preliminary investigations were completed of possible collector designs consisting of aliphatic and aromatic hydrocarbon radicals attached to stable combinations of nitrogen, oxygen, sulfur, and halogen electrophilic centers, Fig. 1.Tests were made to determine melting point spans, solubility of mineral-collector combinations in various solvents, reactions with soluble uranium salts, contact angles, and floatability by semi-quantitative beaker methods.' Contact angle determinations were not too useful because of the fine particle sizes of available mineral samples. From the foregoing study it appeared that nitrogen-sulfur electrophilic centers coupled with straight-chain saturated alkyl hydrocarbon radicals would hold the most promise for floating secondary uranium minerals. As the dithiocarbamate compounds can be made to combine these attributes they were selected for further study. The dithiocarbamates form a parallel structure to the xanthates, with the fortuitous exchange of

Jan 1, 1957

By J. Jones-Parra, J. C. Calhoun

INTRODUCTION The purpose of this paper is to present the results obtained by solving the fractional flow' and frontal advance' equations to obtain oil recovery at water breakthrough as a function of the length of the system being flooded, the linear velocity of injection and the displacing phase viscosity. The method of solution makes use of the stabilized zone concept first presented by Terwilliger, et al3 when calculating saturation distributions in a gravity drainage system. In order to check the calculated results, the equations and method of solution were applied to the system on which Rapoport and Leas' reported experimental data. METHOD OF SOLUTION The solution of the fractional flow equation and the frontal advance equation is obtained by assuming that a water front forms to sweep the oil out ahead of it. There is ample evidence that under the proper conditions a water 'front does form. If this water front is not to dissipate, the water saturations which comprise it must have equal linear velocities. These water saturations are said to comprise the stabilized zone. Equation (2) indicates that for all these saturations and hence fw must plot as a straight line against saturation for those water saturations comprising the stabilized zone. The water saturations lying between the highest in the stabilized zone and the highest that can be achieved in the porous medium comprise the variable zone. Regardless of the numerical value of the length of the system, the variable zone must eventually span all of it, so that for long enough systems in Equation (1) will be small enough to be neglected. Hence, for the saturations in the variable zone Equation (1) can be simplified to In order to determine the composite fw function applicable to the entire range of saturations in the porous medium, it is necessary to find the water saturation which separates the stabilized zone from the variable zone. This dividing saturation must be on the curve defined by Equation (4), and a tangent curve at that point must pass through the initial water saturation to satisfy Equation (3). Hence, the valid fw curve is given by a straight line starting at the initial water saturation, tangent to the curve of Equation (4): and along the curve of Equation (4) from the point of tangency on. The point of tangency determines the water saturation dividing the zones. The length and shape of the stabilized zone can be found by solving Equation (1) for Integrating this expression numerically between any two saturations in the stabilized zone gives the distance separating these two saturations. By repeated integration, the saturation distribution of the stabilized zone can be determined. The total length of the stabilized zone is given by The integral appearing in Equation (5) is a function of the viscosity ratio, the capillary properties of the rockfluid system, the relative permeabilities, and the initial water saturation. Considering these variables fixed and designating the value of the integral by writing caw for and v/60 for q/A; Equation (5) becomes The saturation distribution of the stabilized zone can be integrated over its length and divided by the length to obtain the average water saturation The volume of water in the stabilized zone is then given by The average water saturation in the variable zone can be found by extending the straight line segment of (the segment joining Sw and Sw) until it intersects fw = 1.00. The saturation at the intersection is. This method of finding is nothing more than the graphical solution of the equation The volume of water in the variable zone at breakthrough is then given by Assuming no initial water saturation, the recovery at breakthrough expressed as percent pore volume is given by

Jan 1, 1953

By W. F. Hosford

A series of aluminum single crystals was subjected to axially symmetric flow by drawing through dies. The orientation dependence of the drawing stress, which indicates the resistance to this type of flow, compares reasonably with predictions of Taylor and of Bishop and Hill. Measured lattice rotations likewise are generally consistent with theory. The most successful analyses of the plastic behavior of polycrystalline metal and its relationship to single crystal behavior are those of Taylor1-3 and of Bishop and Hill.4-6 The purpose of this paper is to provide a critical test of some of the basic assumptions involved in these theories. Both treatments apply to fcc metals and assume the shape change of each grain in a polycrystal to be the same as that of the polycrystal as a whole. Thus for a randomly oriented polycrystal extended under uni-axial tension each grain is assumed to undergo axially symmetric flow. dey = dez = -1/2dex, deyZ = dezx = dexy = 0 [l] where x, y, and z are a set of orthogonal axes, x being the tensile axis. Although [011.] oriented grains in bcc and fcc metals may depart markedly from this ideal behavior,7,8 the assumption is probably quite reasonable for most grains. Under a uniaxial tensile stress, ox, the work dW per unit volume expended in producing an increment of axial strain dex is, dW=oxdex [21 Since this work is expended in slip, dw =STi dyi 131 where Ti and yi are the shear stress and shear strain on the active slip systems. In both analyses Ti is taken to be the same on all slip systems, and dependent only on the total prior shear strain on all systems, so dw = Tdy [41 where t is the shear stress required for slip and y is the sum of the shear strain yi on all slip systems. Combining 121 and [4] and defining M = oX/T The ratio M is a generalized Schmid factor. It relates the tensile stress required for axially symmetric flow, ox, to the basic shear stress, 7, and it also expresses the ratio of crystallographic strain, y, to the tensile strain, Ex It depends only on the orientation of the crystal. Taylor evaluated M for various orientations by finding the least value of dy/dEx which could satisfy the shape change. Bishop and Hill, on the other hand, found M by considering the relative work (1/T)dW/dEx expended by stress states which could activate enough slip systems to produce the shape changes. The results of both methods appear to be equivalent, although certain omissions were made in Taylor's original work. The orientation dependence of M, calculated by the second method,9 is shown in Fig. 1. Taylor used the average 2= 3.06 for all possible orientations to predict the tensile stress-strain curve (oxvs Ex) for a random polycrystal from the shear stress-strain curve (t vs y) of a single crystal. Changes in M from lattice rotation were neglected so points on the ox vs ex curve were simply taken at ox = 3.06t and e = y/3.06 from corresponding points on the t vs y curve. Recent extension of the analyses of Taylor and of Bishop and Hill to crystallographically textured metals has been used to relate plastic anisotropy to textures, and to predict the potential texture hardening that could result from texture control.9 Unfortunately there have been relatively few experimental tests of the underlying theory. Taylor found that the tensile stress-strain curve of polycrystalline aluminum did agree reasonably well with that predicted from a single-crystal T-y curve. Had the single crystal undergone easy glide, how-

Jan 1, 1965

By D. L. Martin

THAT small amounts of impurities have a harm-J- ful effect on the malleability of metals and alloys is well-known. One common type of em-brittlement involves the formation of a small quantity of eutectic at the grain boundaries, and is typified by sulfur embrittlement of nickel. Another example of eutectic embrittlement—sulfur embrittlement of cobalt—is described in this report. In the preparation of specimens for a study of Co-Pt alloys, it was observed that the hot swagabil-ity of the alloys appeared to be influenced by the grade of cobalt used as melting stock. The cause of the hot-shortness was not traced to any particular impurity, although sulfur was suspected.' The damaging action of sulfur on the malleability of cobalt has not been generally recognized,'; in spite of the fact that the Co-S phase diagram8 eveals the same basic conditions—low solubility and eutectic formation—responsible for sulfur embrittlement of iron and nickel.7, 8 Apparently sulfur embrittlement has not been a serious problem in the fabrication of cobalt alloys. One related factor is likely the limited commercial experience with high cobalt alloys, since the predominant use of cobalt has been in alloys containing less than 75 pet Co. A series of Co-S alloys was prepared and studied to establish the effect of sulfur on the hot working characteristics of cobalt. Specimens, 5/8 in. diam by 4 in. long, were prepared by vacuum melting in magnesium oxide crucibles and casting in a copper mold. Two grades of low sulfur electrolytic cobalt were used as the basic material for the study, one from Johnson, Matthey and Co. and the other from the International Nickel Co. Each contained about 99.5 pet Co and had a nominal sulfur content under 0.005 pet. The sulfur was added initially as cobalt sulfide powder. Later, some low sulfur alloys were prepared by diluting the high sulfur alloys with cobalt. Trouble was experienced in controlling the sulfur content. Apparently much of the cobalt sulfide powder was lost during melting, as most of the samples contained a lower sulfur content than was added. The alloys were evaluated for hot brittleness by heating to 1000°C in a hydrogen furnace and swaging in air. The results of these tests are summarized in Table I. All the alloys containing less than 0.008 pet S were successfully hot swaged to 1/4 in. diam. The bars containing more than 0.015 pet S could not be swaged because of the formation of intercrystal-line cracks similar to those illustrated in Fig. 1. Examination of the microstructure of the cast bars revealed cobalt sulfide eutectic at the grain boundaries, Fig. 2. The sulfide was not always continuous at grain boundaries in bars that were hot embrittled but, in general, the particles did form a network that could account for the brittleness above the eutectic temperature, 880°C. There is no question about the brittle nature of a specimen exhibiting a continuous sulfide network such as is shown in Fig. 2b, though a sulfide distribution similar to that in Fig. 2a is marginal. This particular bar cracked when hot-swaged. However, other bars with lower sulfur content but with some sulfide phase at grain boundaries were successfully worked. The reduction of area of a hot tensile test specimen was also found to be a sensitive indicator of sulfur embrittlement. The variation of reduction of area with sulfur content is shown in Fig. 3 for specimens fractured at 900°C in an evacuated capsule. The ductility of cobalt is greatly reduced when the sulfur content exceeds 0.005 pet. Similar results were obtained for alloys tested at 800°C, below the eutectic temperature. The upper sulfur embrittlement limit of 0.015 pet, Table I, agrees with the observation of Kalmus8 hat

Jan 1, 1957

By M. T. Hepworth, T. P. Papazoglou

Hydrogen diffusion in hcp and bcc titanium in the temperature range 610° to 900°C was measured by reacting cylindrical specimens of high-purity titanium at constant temperature with small constant pressures of hydrogen of the order of a few Torr. In the range 0 to 6.7 at. pct H in hcp titanium, the diffusion coefficient D in sq cm per sec is given by: where T is in °K and R in cal per g-atom OK. Only three measurements of diffusivity in bcc titanium were made: at 900' : the diffusivity in ß titanium was found to be 1.8 x 10-4 sq crn per sec. McQUILLAN1 has studied the constitution of the Ti-H system and reported the concentration of hydrogen as a function of pressure of hydrogen and temperature. He found hydrogen absorption was reversible and rapid at temperatures above 500°C in both crystallographic modifications, the a (hcp) phase and the ß (bcc) phase, with the latter phase stabilized by hydrogen additions. Wasilewski and Kehl 2 measured the diffusivity of hydrogen in hcp and bcc Ti-H alloys. For bcc alloys, they reacted cylindrical specimens of titanium with hydrogen gas at 1 atm pressure. They measured the rate of absorption of hydrogen isothermally on specimens ranging from zero hydrogen content when above the transformation temperature to hydrogen contents sufficient to stabilize the bcc phase when below the transformation temperature. By integrating Fick's second law for a cylindrical geometry, assuming a diffusion coefficient independent of composition, they calculated diffusivities as a function of temperature. In the range 650" to 1000°C their results in bcc titanium yielded the expression: where D is in sq cm per sec, T in OK, and R the gas constant in cal per g-atom-OK. Their studies on the hcp a phase were conducted by exposing long cylindrical titanium specimens to hydrogen at a sufficiently high pressure to establish a surface layer of fl phase 80 to 120 u thick for the duration of an isothermal experiment. Concentration profiles were then determined by hydrogen analysis from chips obtained upon machining quenched specimens. The diffusivity of hydrogen was then calculated yielding the expression: The present investigation was undertaken principally to redetermine the diffusivity data on a titanium by a direct absorption from the gas phase at sufficiently low hydrogen pressures to avoid the presence of a surface bcc phase and also to check the diffusivity data at low hydrogen concentrations in the bcc stmcture. EXPERIMENTAL PROCEDURE High-purity electrolytic sponge titanium (99.9 pct) of BHN 91 was arc-melted, forged, rolled, and machined into cylinders of final hardness, upon annealing, of BHN 92. Cylindrical specimens of two sets of dimensions were used: 1.524 by 2.931 cm and 1.905 by 3.663 cm diam and length, respectively. The experimental apparatus used for annealing specimens and for admitting known amounts of hydrogen at constant pressure is shown in Fig. 1. In a typical experiment, a specimen was lightly abraded with fine-grain silicon carbide, washed with water and detergent, and then thoroughly degreased with reagent-grade tri-chlorethylene and acetone. The specimen was suspended by a Chrome1 wire in the center of a quartz furnace tube, without contact with the tube, and heated to 925°C (as measured by a thermocouple adjacent to the specimen, outside the tube) for a period of at least 4 hr under a vacuum of from 10-6 to -7 Torr as measured by an ionization gage. The furnace temperature was then adjusted to the temperature chosen for the particular diffusion study and the specimen allowed to equilibrate thermally. Hydrogen was then ad-

Jan 1, 1969

By Gordon W. Hodgson, Edward Tipman

INT'RODUCTION An appreciable number of the oil fields in Western Canada are accumulations of heavy black oils in more or less unconsolidated sandstones. When the crude oils are produced by conventional means, they are frequently contaminated with both sand and oilfield water. The water is usually present as emulsified water, and the sand and other solid materials are suspended in the emulsions. The presence of the solid material in the crude oils is troublesome and, in general, little is known about the behavior of suspended solid particles in emulsions. The Stokes equation describes the behavior of suspended particles in homogeneous fluids in terms of particle size, density differential, and fluid viscosity. In the case of an emulsion, particle size and density differential introduce no difficulties, but considerable doubt centers around the viscosity term. It has been reported1 that the viscosity of an emulsion is related to the viscosity of the continuous phase by an expression of the type: n = a, (1 + a C) where n is the viscosity of the emulsion, n,, is the viscosity of the continuous phase, a is a constant, C' is the volume concentration of the disperse phase. The value of 17, the coefficient of the concentration term, has been determined for various systems, and has been found to vary from a value of 1 to 4.75. The value of 2.5 has been found to be applicable to a large number of systems, and this is the value that is widely used in the equation which then becomes the Einstein equation for the viscosity of emuls~ons. It is of considerable significance that neither the particle size nor the viscosity of the disperse phase enters the expression; the expression for the viscosity of the enlulsion is based solely upon the viscosity of the continuous phase and the concentration of the disperse phase. For crude oil emulsions the Simha equation and the data presented by Fukushima and lchimurai show a non-linear dependence of the viscosity ratio on the water concentration. While it is undoubtedly reasonable to use these data for predicting the viscosity of a specific emulsion, and while it is equally reasonable to expect the calculated viscosity to predict the settling rate of a solid spherical particle in the emulsion by means of Stokes equation, there seems to be no direct evidence that this calculation is indeed sound for describing the settling rates of solid particles in emulsions of water in crude oils. PROCEDURE A direct approach to the problem was thus indicated. Laboratory equipment was designed and built for the direct determination of the rate-of-fall characteristics of solid particles in emulsions of water in oil. Although the apparatus incorporated the basic design of conventional falling-ball viscometers, the study was concerned directly with the rate-of-fall characteristics of particles in emulsions, rather than with the viscosity of the emulsions as such. The crude oil used in this study was a very heavy black crude oil—the McMurray oil obtained from oil-soaked sands outcropping on the Athabasca River in northeastern Alberta. It was produced from the sands by strip mining followed by hot-water separation of the oil in the separation plant of the Alberta Government at Bitumount'. The primary plant product was a wet crude oil containing about 5 per cent solids and 35 per cent water. The final plant product was only slightly different from the native oil, having lost only about 4 per cent of its bulk as light ends during dehydration distillations. In the present investigation two kerosene dilutions of the McMurray oil were used in addition to the dry plant product. The McMurray oil contained 1.92 per cent solids. Analysis of the solids by X-ray diffraction showed the presence of kaolinite, pyrite, and illite as major constituents. with lesser amounts of quartz. Particle size of the pyrite and quartz was less than 10

Jan 1, 1957

By F. W. Jessen, C. A. Johnson

The effect of treatment with ferrochrome lignosul-fonate on both sodium and calcium bentonites has been examined. In the early stages of treatment it appears that some base exchange of iron and chromium for sodium may occur with the sodium bentonite. Such exchange appears specific for exchange of sodium ions when the calcium ion concentration represents 40-5.5 per cent of the total exchangeable cations, and when additions of lignosulfonate are less than 1 lb per bbl. Adsorption appears entirely physical above 1 lb per bbl treatment level for all concentrations of calcium studied. Gel strength and plastic viscosity of both calcium and sodium bentonite systems were reduced with treatments of ferrochrome lignosulfonate up to 2 Ib per bbl, the greatest reduction occurring within a range of calcium concentration of 40-5.5 per cent of the total exchange capacity of the clay. INTRODUCTION The problem of control of viscosity and gel strength of drilling fluids by the action of thinners or dispersants has been studied by many investigators.1-7 In addition, much work has been done on formation of gel structure in clay suspensions. However, gel formation and structure still are incompletely understood, and the use of the various dispersing chemicals is based, to a large extent, on data almost entirely empirical in nature. In recent years the lignosulfonates have become increasingly important in the treatment and control of drilling fluids. More specifically, ferrochrome lignosulfonate has found rather wide acceptance, particularly in calcium systems.5-7 Lignosulfonates are refined lignin products made from spent sulfite liquor from which the fermentable sugars have been removed.15 The exact structure of lignin is not known; however, it is believed to be a phenolic propane type polymer which may exist as a branched chain or cross linked structure. The molecular weights of lignosulfonates probably range from 300 to 100,000 or more.15 A better understanding of the mechanism of adsorption of dispersants is essential before improvement and development of characteristics of drilling fluids and drilling fluid control is possible. This investigation was undertaken to determine the action of ferrochrome lignosulfonate on sodium and calcium montmOrillonite' LABORATORY INVESTIGATION A Stormer viscosimeter and Fann V-G meter were used to measure viscosity and gel strength. A Zeiss spectrophotometer was used for analysis of Fe and Cr and the flame attachment was employed in the analysis of Na, Ca and Mg. A General Electric X-ray diffraction unit utilizing Copper Ka radiation and a Ni-filter was utilized in the X-ray studies. PROCEDURE Two systems were studied. Predominately sodium clay, obtained from Wyoming, and a predominately calcium clay from Texas were used. These particular samples were chosen because of the extensive work of characterization completed by Mungan. Ionic base exchange capacity determined by flame photometry and total exchange capacity by the Kjehldahl method were obtained experimentally. A 7-per cent suspension of the sodium clay and a 20-per cent suspension of the calcium clay in distilled water were prepared by mixing with a high-speed mixer. The suspensions were allowed to stand for two weeks for complete hydration. Calcium chloride was added to portions of the sodium and calcium cla suspensions to obtain suspensions varying in Ca++ concentration as shown in Table I. A series of treatments was run with 500-ml portions of the original suspensions using a ferrochrome lignosulfonate. Treatment was carried out in the same way with each of the suspensions of varying Ca concentration. Viscosity and gel strength were measured and a filtrate obtained at each treatment level. Ten ml of filtrate were diluted to 50 ml, and aliquot portions of the 50 ml were taken for the Na, Ca, and Mg analysis by the flame photometer. The pH of these filtrates ranged from 7 to 7.3. Standard

By S. S. Lisnyak, B. D. Lichter

An important question in the study of the "hot corrosion" phenomenon (i.e., accelerated oxidation of Ni-Cr-base and Co-Cr-base "superalloys" in the presence of sulfur) is the condition of formation and physico-chemical properties of different sulfides in the system Ni-Co-Cr-S. seyboltl has observed the presence of ((chromium-rich" sulfides of compositions M3S4, and M2S3 in the scales of superalloys after hot corrosion; however, as he points out, much confusion exists as to the identity of sulfides found on Ni-Cr and Co-Cr alloys. According to the literature,&apos; ternary sulfides, e.g., NiCr2S4, (monoclinic structure) and CoCr2S4 (spinel structure) exist in these systems. Therefore, it is likely that these compounds are found in the scale of alloys undergoing hot corrosion. At present this possibility has not been discussed in the literature. Accordingly, we have begun investigation on the properties of ternary sulfides and their mutual interaction. The magnetic and electrical properties of pure NiCr2S4 and pure CoCr2S2 have been previously determined."-&apos; In the present work we have studied the interaction between these sulfides at high temperatures by means of X-ray diffraction and magnetic susceptibility. The measurements were carried out at room temperature after appropriate thermai treatment of samples at high temperatures. For alloys containing the three elements nickel, chromium, and cobalt this interaction may be of importance in the study of the hot corrosion phenomenon. The compounds NiCr2S4 and CoCr2S4 were prepared from stoichiometric amounts of the elements and CoS in the case of CoCr2S4. Samples were mixed and sealed in evacuated silica tubes, slowly heated to 900&apos; to 100O°C, and held at temperature for a total of 120 hr (NiCr2S4) or 80 hr (CoCr2S4) with intermediate re-grinding~. X-ray diffraction showed a pure spinel structure for CoCr2S4 and a monoclinic structure for NiCr2S4. Samples of mixtures of the two ternary sulfides were prepared with different compositions, see Table I. Samples were heated for a total of 80 hr at 900&apos;C in evacuated silica tubes, with one intermediate regrind-ing. The capsules were slow-cooled to room temperature in the furnace. Samples for X-ray diffraction were prepared by placing powder on a glass slide with vaseline. Dif- fractometer traces were obtained on a G.E. XRD-5 diffractometer using a chromium tube and vanadium filter (40 kv and 31 ma). The size of the spinel unit cell was determined from the eight highest angle peaks (80 deg < 2b < 160 deg). Calculated lattice parameters were plotted vs cos B . ctn 0 and extrapolated to 6 = 90 deg. Measurements of the magnetic susceptibility were carried out at room temperature using the Faraday method in a magnetic field of 3000 G and using a Cahn RG automatic microbalance. The system was calibrated from the well-established susceptibilities of platinum and palladium: (Xpt = 0.968 x 10-6 g-1 and Xpd 7 5.04 x 10~6 g-1). The weight of samples were approximately 0.200 g. X-ray diffraction patterns for unsintered mixtures showed Bragg peaks from both the spinel (CoCr2S4) and monoclinic (NiCr2S4) structures. After sintering no monoclinic peaks were observed in samples containing up to 40 mol pct NiCr2S4. However, the spinel peaks were displaced to higher angles with increasing

Jan 1, 1970

By J. Pinto, F. Galasso

THE current emphasis in preparing boron fibers by reduction of gaseous boron compounds on a resistively heated metal wire substrate has renewed interest in the borides of those metals which have relatively high melting points and are available as fine wires. A knowledge of the structures and properties of the borides, which are formed when boron diffuses into the metal core during boron deposition, can be of assistance in the understanding of the boron fiber formation process and the fiber properties. Many of these borides are well-known and their properties have been measured. However, when an unidentified boride is found in the core, it may be difficult to establish its composition because of the small amount of material available, the preferred orientation effects on the reflections in its X-ray pattern, and the possible overlap of X-ray reflections if several borides are present in the core. For example. the proper indexing of the X-ray pattern of WB4, which was formed in the tungsten substrate core during boron fiber formation, was accomplished only after small single crystals of this boride were grown and X-ray precession investigations were conducted.&apos; This note presents the results of a study of the phases formed in the core when tungsten, tantalum, and molybdenum metal wires were used as substrates in the boron fiber preparation process with particular emphasis on the identification and characterization of a higher boride of molybdenum analogous to WB,. Boron was deposited on resistively heated stationary 0.0012-in.-diam tantalum, tungsten, and molybdenum wires at 1050°C for various times up to 60 sec using boron trichloride and hydrogen as the reactant gases. After 60 sec of boron deposition the fibers were approximately 0.006 in. in diam. Examination of photomicrographs of fiber cross sections showed that the boron had diffused nearly to the center of the tungsten and molybdenum cores in 15 and 30 sec, respectively, and only halfway to the center of the tantalum core in 60 sec. X-ray diffraction photographs of the fibers indicated that it was also after 15 and 30 sec deposition times that the tungsten and molybdenum metal reflections, respectively, had disappeared from the X-ray patterns of the fibers. The patterns of the boron fibers produced using tantalum wire as a substrate showed that amorphous boron, TaB2, and tantalum metal were present after a few seconds deposition time and remained even after deposition times of 60 sec. Until a deposition time of 15 sec was reached, the tungsten substrate fibers contained amorphous boron,273 6WB, W2B5, and WB4 as well as tungsten metal, while the molybdenum substrate fibers contained amorphous boron, MoBa, Mo2B5, and molybdenum metal for deposition times up to 30 sec. Just before the molybdenum metal pattern disappeared, a pattern similar to that of WB, appeared, suggesting that a phase, MOB,, isomorphous with WB,, was present in the fiber. This same pattern was obtained from the product formed by heating a mixture of molybdenum metal and excess boron powder in a boron nitride crucible at 1960°C in an argon atmosphere. As was the case with the WBn pattern, this pattern could best be indexed on the basis of a hexagonal unit cell rather than the tetragonal unit cell Chrktien and Helgorsky reported for ~0~4,~ see Table I. The unit cell parameters for MoB4 were calculated to be a, = 5.214A, co = 6.358A. Assuming the space group P63/mmc and positions5 2M01 in 2b and 2MoII in 2c found for tungsten in WB~,&apos; a logical structure for MOB, was determined using geometrical considerations to place the boron

Jan 1, 1969

By Dwight H. Seely, Louis R. Records

A process for low-temperature dehydration of natural gas utilizing Joule-Thomson effect in expansion through a throttling orifice has been tested in a full-scale field installation. The results of these tests are presented in the form of performance curves from which the process may be easily evaluated. The effect of separation temperature on condensate recovery from the process is also shown. INTRODUCTION The transportation of natural gas from producing well to the consumer has always encountered the problem of hydrate prevention. This problem has become increasingly important in the past ten years due to the rapid increase in produced gas volumes, production pressures, transportation pressures and distance from producing wells to consumer. Natural gas, as normally produced from gas or gas-condensate wells, is saturated with water vapor at well-head conditions of temuerature and pressure. The solution of the hydrate problem require; but one basic process — dehydration of the gas to a water content which will result in a water dew-point below the minimum temperature to be encountered from the producing well to the point of consumption. Much of the recent development of gas and gas-condensate reserves in the Gulf Coast Area has been in locations which are accessible only by water. High well-head pressures, pipeline construction and maintenance costs and the desirability of final central gas-condensate separation facilities have stimulated the development of dehydration equipment which can be installed at each well and which will permit hydrate-free transportation of both gas and condensate in the same line to central facilities. There are four types of natural gas dehydration processes now used: 1. Adsorptive processes. 2. Absorptive processes. 3. Chemical reaction processes. 4. Refrigeration processes. The first three of these processes are indirect in that they require use of adsorbents, absorbents or reactive chemicals. These materials require regeneration and part of the total gas stream is consumed in the regenerative process. Indirect processes have a wide range of flexibility as defined by allowable operating pressure and temperature, but most are not easily adapted to automatic operation. The refrigeration process described in this paper was designed for installation at the producing well-head. It requires no regenerative cycle and with normal well-head temperatures no external source of heat. The flexibility of this process is limited only by the pressure drop which may be allowed between well-head and transportation line. THEORY There are three basic physical concepts involved in the low temperature dehydration process. These are: 1. Formation of hydrocarbon hydrates. 2. Joule-Thompson effect resulting from the expansion of gaseous mixtures through a throttling orifice. 3. The equilibrium composition characteristics of water vapor and gaseous hydrocarbon mixture.. The chemical composition and physical structure of hydrate; have been described by several investigators.3,4,5,10 Specific conditions of temperature, pressure and composition as well as the requirements for turbulence and presence of free water necessary for hydrate formation have been described by Katz.6 Natural gas hydrates, as they are found in plugged gas pipe lines, have the appearance of packed snow. The mass of these hydrates has low continuous porosity and permeability. Joule-Thomson effect. or the reduction in temperature which occurs when natural gas is throttled throusll a restrictive orifice, is the basic phenomenon which permits efficient use of refrigeration for the purpose of dehydrating natural gas. Joule-Thomson coefficients for gafeous mixture; of methane with ethane and with butane have been reported by Buder.-I~olzer, Sage and Lacey.2 Brown1 predicted temperature drops for pressure drops from enthalpy-entropy calculations. Aside from this work there were no fundamental data found which would be applicable to natural gas mixtures of varying spe-

Jan 1, 1951

By Dwight H. Seely, Louis R. Records

A process for low-temperature dehydration of natural gas utilizing Joule-Thomson effect in expansion through a throttling orifice has been tested in a full-scale field installation. The results of these tests are presented in the form of performance curves from which the process may be easily evaluated. The effect of separation temperature on condensate recovery from the process is also shown. INTRODUCTION The transportation of natural gas from producing well to the consumer has always encountered the problem of hydrate prevention. This problem has become increasingly important in the past ten years due to the rapid increase in produced gas volumes, production pressures, transportation pressures and distance from producing wells to consumer. Natural gas, as normally produced from gas or gas-condensate wells, is saturated with water vapor at well-head conditions of temuerature and pressure. The solution of the hydrate problem require; but one basic process — dehydration of the gas to a water content which will result in a water dew-point below the minimum temperature to be encountered from the producing well to the point of consumption. Much of the recent development of gas and gas-condensate reserves in the Gulf Coast Area has been in locations which are accessible only by water. High well-head pressures, pipeline construction and maintenance costs and the desirability of final central gas-condensate separation facilities have stimulated the development of dehydration equipment which can be installed at each well and which will permit hydrate-free transportation of both gas and condensate in the same line to central facilities. There are four types of natural gas dehydration processes now used: 1. Adsorptive processes. 2. Absorptive processes. 3. Chemical reaction processes. 4. Refrigeration processes. The first three of these processes are indirect in that they require use of adsorbents, absorbents or reactive chemicals. These materials require regeneration and part of the total gas stream is consumed in the regenerative process. Indirect processes have a wide range of flexibility as defined by allowable operating pressure and temperature, but most are not easily adapted to automatic operation. The refrigeration process described in this paper was designed for installation at the producing well-head. It requires no regenerative cycle and with normal well-head temperatures no external source of heat. The flexibility of this process is limited only by the pressure drop which may be allowed between well-head and transportation line. THEORY There are three basic physical concepts involved in the low temperature dehydration process. These are: 1. Formation of hydrocarbon hydrates. 2. Joule-Thompson effect resulting from the expansion of gaseous mixtures through a throttling orifice. 3. The equilibrium composition characteristics of water vapor and gaseous hydrocarbon mixture.. The chemical composition and physical structure of hydrate; have been described by several investigators.3,4,5,10 Specific conditions of temperature, pressure and composition as well as the requirements for turbulence and presence of free water necessary for hydrate formation have been described by Katz.6 Natural gas hydrates, as they are found in plugged gas pipe lines, have the appearance of packed snow. The mass of these hydrates has low continuous porosity and permeability. Joule-Thomson effect. or the reduction in temperature which occurs when natural gas is throttled throusll a restrictive orifice, is the basic phenomenon which permits efficient use of refrigeration for the purpose of dehydrating natural gas. Joule-Thomson coefficients for gafeous mixture; of methane with ethane and with butane have been reported by Buder.-I~olzer, Sage and Lacey.2 Brown1 predicted temperature drops for pressure drops from enthalpy-entropy calculations. Aside from this work there were no fundamental data found which would be applicable to natural gas mixtures of varying spe-

Jan 1, 1951

By A. S. Yue

Small-angle tilt boundaries have been observed in a lamellar eutectic structure. These boundaries are morphologically similar to a theoretical till boundary originally proposed by Burgers. The production of a small-angle tilt boundary in the lamellar eutectic structure is attributed to the formation of an indentation on a planar solid-liquid interface during growth. Constitutional supercooling due to the accumulation of impurity atoms ahead of the interface is primarily responsible for the generation of an indentation. The distance between two faults of like sign, designated as lamellar fault distance, is calculated by the Burgers equation for small-angle boundaries. It was found that the lamellar fault distance decreases exponentially and the tilt angle increases exponentially with freezing rate. SMALL-ANGLE tilt boundaries have been observed in many crystals in the as-grown states by etching techniques. However, a detailed substantial proof for revealing the presence of dislocations in the form of etch-pits was recently accomplished by Vogel. These boundaries are described as an array of dislocations of like sign. The angle of tilt associated with a boundary is treated theoretically by Burgers3 and is given by 0 = b/D for small tilt-angle where b is the Burgers vector of the dislocations and D is their average spacing. During the course of experimentation on the solidi fication of the lamellar Mg-32 wt pct Al eutectic a microstructure which was strikingly similar to a dislocation tilt boundary was observed. An example of the type of microstructure is given in Fig. 1, which shows a combination of transverse and top sections of the lamellar eutectic structure. The lamellae of the top section on one side of the apparent tilt angle are not parallel with those on the other side. Consequently, some lamellae must be terminated somewhere. Fig. 1 shows that the termination of lamellae is analogous to a dislocation tilt boundary in a crystal lattice originally proposed by Burgers. This work represents a closer look at such structures. The factors governing the production of the small-angle tilt boundary are discussed in terms of the freezing condition and impurity distribution in the melt. The effect of freezing rate on the distance between two faults, designated as lamellar fault distance, and the tilt angle is also described. In addition, the lamellar fault distance is determined by means of the Burgers equation for small-angle tilt boundary. EXPERIMENTAL PROCEDURE The slightly impure Mg-32 wt pct Al eutectic rods, 5/8 in. in diam and 12 in. long, were made from 99.99 wt pct Al and 99.98 wt pct Mg and were cast in a high-purity graphite mold. Some of these rods were purified by zone-refining the eutectic using direct-radiation helical-coil furnaces5 A molten zone about 2 in. long was passed through the cast rods at a speed of 5.3 x 104 cm per sec for ten passes of the molten zone. Before the freezing experiment was begun, 2-1/2 in. of the material from the head and tail ends of the zone-refined eutectic were removed from the rod to eliminate any impurity. The freezing experiments were carried out under controlled conditions,8 using a protective atmosphere of purified argon. At the end of each run, observation of the tilt boundary was made throughout the entire length of the rod with a light microscope on the top, longitudinal, and transverse sections (three mutually perpendicular sections) of the lamellar eutectic solid. The experimental data used for the determination of interlamellar spacing and tilt angle were taken from the middle portion of

Jan 1, 1964

By J. Szekely, G. P. Martins

A formulation is given and a general analytical solution is presented for the problem of spherical phase growth in multicomponent systems. The results are valid for describing the rate of bubble growth in the absence of translational motion and, therefore, should be relevant to heterogeneous nucleation processes. Typical worked examples are given, which include bubble growth due to the simultaneous diffusion of hydrogen and nitrogen in molten steel, and the growth of CO bubbles in steel, due to the reaction: C + 0 = CO. The calculations predict that the presence of additional components would enhance the growth rate and also increase the absolute rate at which the individual components are transferred into the bubble. These findings should be relevant to degassing processes. THE problem of spherical bubble growth in the absence of translational motion is appropriate to the description of the heterogeneous nucleation and subsequent growth of gas bubbles while attached to a solid surface. Such problems are of considerable practical relevance to various vacuum degassing and steelmaking processes where bubble nucleation and subsequent growth play an important part in the overall reaction mechanism. A definitive formulation of spherical phase growth has been given in the now classical paper by Scriven1 and the analogous problem for solid phase growth has been discussed by Horvay,2 furthermore a thorough review of the relevant literature has also become available.3 All this previous work was concerned with one component or binary systems. The purpose of this paper is to show that the technique developed by Scriven may be generalized to alow the consideration of multicomponent systems. The results of this generalization would be particularly relevant, as gas bubble nucleation in the metallurgical systems previously mentioned frequently involves the simultaneous diffusion of several components. In the following a general formulation is given and typical worked examples are presented. FORMULATION Consider the growth of a spherical gas bubble due to diffusion in a quiescent liquid of infinite extent, as sketched in Fig. 1. The formulation of such problems requires the statement of the following conservation equations relating to the liquid phase: Equation of continuity Equation of motion Conservation of the diffusing species—Diffusion Equation. The following assumptions are made: a) The fluid is incompressible, quiescent, and of infinite extent b) The bubble is stationary, i.e., it undergoes no translational motion c) Spherical symmetry is observed throughout d) The mass diffusivity is constant e) Chemical equilibrium exists at the surface of the bubble, and any reactions occurring there are fast compared to the diffusion process f) Inertia and surface tension effects are neglected. Equations derived on the basis of these assumptions by previous investigators were found to provide a reasonable representation of bubble growth while attached to a surface in organic and aqueous systems4,5 For gas bubble growth in molten metal systems assumptions a) to d) chould hold reasonably well. The exclusion of chemical kinetics as a possible rate limiting step may not be universally valid, but should hold for many systems operating at high temperatures. The effect of hydrodynamic inertia may be neglected for moderate growth rates; finally, the assumption neglecting the effect of interfacial tension on the bubble growth was made for the sake of mathematical convenience; its inclusion would have required the use of quite cumbersome numerical techniques. While surface tension effects could be appreciable on the initial values of the overall growth rate, especially at low absolute pressures and in case of small bubbles, they are not thought to modify the relative effects present in multicomponent systems, the study of which is the objective of this paper. Within the framework of the above assumptions

Jan 1, 1970

By H. E. Cline

A criterion for stability of a lamellar structure in two-phase alloys ulas derived froflr perturbation analysis of the steady-state solutions for eutectic growth. Both the mass and thermal diffusion were considered with boundary conditions for coupled lamellar growth. The concept of an effective liquidus slope was introduced. Excellent agreement was found with the experiments of Mollard and Flemings and the theory predicted a range of compositions on one side of the eulectic composition in which stable growth may occur with zero temperature gradient. The lamellar structure was found to be more stable than predicted by simple constitutional supercooling. The effect of impurity additions was also considered. DIRECTIONALLY solidified eutectic alloys may have a structure consisting of parallel plates or rods. It is important to know the range of composition and growth conditions that produce this ideal composite structure. Breakdown of the planar solid-liquid interface during growth may lead to a dendritic or cellular structure as in single-phase alloys. In the case of single-phase alloys, the concept of constitutional supercooling1 may explain breakdown, but in two-phase alloys the concept is no longer valid because the melting point is not given by the liquidus of one phase. Both phases must be considered in the mass and thermal diffusion problem. In the following theory a boundary condition at the solid-liquid interface was determined by using the steady-state equations of Jackson and ~unt&apos; to relate the average temperature and composition of the liquid at the interface. Then a sinusoidal perturbation in the shape of the interface was introduced to test for stability as in the analysis of Mullins and ~ekerka.~ The wavelength of the important perturbation was assumed to be much larger than the lamellar spacing, h, and the perturbation was assumed not to change the lamellar spacing, A. Both the mass and thermal diffusion equation were used with averaged quantities at the boundary to determine whether the perturbation grows or shrinks in time. A stability criterion was determined by considering the case in which the perturbation remains stationary. An example of Pb-Sn alloys was used to illustrate the validity of this theory. I) THEORY A) Temperature at the Interface. The temperature of the interface in coupled two-phase growth is close to the eutectic temperature TE even for alloys off eutectic composition. It is assumed that the interface is in local equilibrium and one expects the temperature at the intersection of the liquid phase and the solid phases a and 0 to be near the eutectic temperature. The interface is undercooled because of curvature and the deviation of the composition in the liquid from the eutectic composition. The average interface temperature Ti for steady-state growth of a lamellar eutectic with a plane interface was determined by Jackson and Hunt&apos; as given in their Eq. [17c]. Instead of using the ratio of the lamellar widths hp/h, as a parameter, the volume fraction of the 0 phase, +, will be used as it simplifies the algebra. The average interface temperature using this notation becomes: The average temperature of the interface depends on the volume fraction of the 0 phase, +, which may be related to the composition of the solid or the bulk composition of the liquid Co by: where C, and Cp are the average compositions of the solid phases. In steady-state growth, the composition of the solid is equal to the composition in the liquid far from the interface. The variation of the average interface temperature with composition is illustrated in Fig. 1 for the case of Pb-Sn alloys with a 10"4 cm lamellar spacing as calculated from Eqs. [I] and [2]. The interface temperature goes through a maximum at a composition near but not exactly at the eutectic composition. There is no reason why the composition corresponding to the maximum temperature should be equal to the eutectic

Jan 1, 1969

By F. G. Tahmoush, N. J. Grant, E. P. Abrahamson

The effect of grain size on the brittle -ductile transition temperature of pure iron and three dilute Fe-W alloys has been investigated by slow bend tests. The brittle-ductile transition temperature for pure iron increased with increasing grain sizes from 8000 to 500 grains per sq mm where the transition temperature then decreased with further increase in grain size. The dilute additions of tungsten lowered the transition temperature for fine grain sizes, suppressed a reversal of the curve in the coarse grained portion, and raised the transition temperature for this region. The frequency of twin occurrence increased with increasing grain size and decreasing temperature. The object of the present investigation was to re-examine the effect of grain size on the brittle -ductile transition of pure iron and several dilute Fe-W alloys. Current literature normally presents a simple relationship between grain size and the brittle-ductile transition temperature, namely, that the transition temperature increases with increasing grain size. Heslop and etch&apos; have studied the transition temperature of mild steel by V-notch Charpy impact tests for the grain size range between 200 and 6000 grains per sq mm. The result was a linear plot of In 1-1/2 vs brittle-ductile transition temperature, where 1 is the grain diameter. Recent experiments by sipos2 revealed the possibility of a reversal in the slope of the grain size vs transition temperature plot for pure iron; however, his investigation was limited in scope, and the data obtained were insufficient to permit a definitive curve. The present investigation was undertaken in an effort to confirm or extend the grain size effect observed in iron by Sipos. PROCEDURE All alloys were vacuum induction melted, using 99.95 pct Fe containing 0.03 pct 0 and 0.004 pct C. Four ingots were made, ranging from pure iron to iron with 0.035 pct W. The chemical composition of each alloy, after processing, is given in Table I. The four alloys were prepared as 45 lb heats and cast into 4 in. diam by 16 in. molds. They were then extruded into 3/4 in. rods at 1800oF. Specimens for chemical analysis, taken from various positions along the rods, revealed no variation in tungsten content along the length. The extruded rods were reduced to 0.156 in. diam stock by a series of cold swaging operations involving intermediate vacuum annealing treatments. This procedure yielded a final cold reduction in area ranging from 10 to 90 pct. The swaged rods were chemically cleaned, cold pressed to a cross section of 0.10 by 0.18 by 1.0 in. long (2.54 by 4.73 by 25 mm). The specimens were wrapped in iron foil and vacuum sealed (10-4 mm Hg) in quartz. Various heat treatments at temperatures from 700" to 1300oC were utilized to produce grain sizes from 8000 to 1 grain per sq mm. Grain sizes were determined by measuring the average area of grains in a polished section. In specimens with grain size greater than 20 grains per sq mm, the total number of grains in the cross section was counted and then divided by the area to yield grains per sq mm. Grain size was measured both for longitudinal and transverse cross sections. The average of the two measurements was plotted vs transition temperature. An Instron Table Model testing machine was used to determine the transition temperature of specimens tested in three point horizontal bending. The specimen was supported by two 1/4 in. dowels one in. apart. Bending was accomplished with a push rod, the end of which had an 1/8 in. radius. The head speed was 50 in. per min. Temperatures were established through the use

Jan 1, 1963