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By Thomas O. Ziebold, Robert E. Ogilvie

Experimental analysis of diffusion samples covering the entire Cu-Ag-Au system at 725°C has been carried out. Experimental coefficients are computed at twenty-eight points in the lermary system. It is found that the direct coefficienl for copper is nearly independent of the silver, content for 1ow-silver alloys and that the cross coefficient for silver correlates with the ther-nzodynatnic properlies. This lalter observalion leads to the conclusion that the mobililies of copper and gold are nearly equal. Thermodynarmic actiuilies for Cu-Ag-Au were computed from binary data and adjusted to be consistent with neasured tie lines across the two-phase region which extends into the ternary diagram at 725°C. Application of these therknodynarnic calculaliorls to the dijftcsion data terifies the Onsager reciprocal relations to the extent that experimental uncertainlies will allow. It is jound that diffusion neav the critical point of the 1200-phase field in the isothermal section at 725°C causes the composition gradients for copper and silver to approach infinity while the direct and cross coeficients become equal. From the standpoint of experimental Procedures, it has been shown that microanalysis of ternary samples may be carried out using a simple expression for the conversion of X-ray zntensily to composilion. The accuracy of' this method has been demonstrated by the analysis of standard alloys and by the reproducibility of composition determinations using differed X-ray lines. DIFFUSION in a ternary alloy system is basically and significantly different from diffusion in binary alloys. When only two elements are present there is just one independent composition variable, and the diffusion profile of composition vs distance across a sample must change monotonically through all solid solutions bracketed by the terminal alloys. If two-phase regions are stable for compositions between the terminal values, these must appear as planar interfaces in the diffused sample, with the composition profile exhibiting sharp discontinuities. Adding a third element may alter this picture completely. Because of the additional degree of freedom in the composition, we may see composition profiles which do not change monotonically through solid-solution ranges, and stable, nonplanar phase interfaces. Even though two-phase regions may lie between the terminal compositions of a diffusion sample on the constitution diagram, they will not necessarily appear in the diffusion profiles. In binary diffusion only one coefficient is needed to describe the interdiffusion process. From Fick's law this coefficient relates the diffusive flux of one component to its own composition gradient. In ternary diffusion we must allow for cross interaction between the two independent species. By a linear extension of Fick's law we introduce "cross" or "off-diagonal" diffusion coefficients which relate the flux of one component to the composition gradient of the other independent constituent. Thus, we require four interdiffusion coefficients to describe the transport process in a ternary system. In its most general form,1,2 the rate equation for mass transport by isothermal diffusion in a system of s components states that the diffusive flux of component i, Ji, is a linear summation of all driving forces, Xk, each force being multiplied by an appropriate compliance coefficient:

Jan 1, 1968

By J. H. Swisher

In measuvements of the solubility of nitrogen in fer-rilic Fe-P alloys, tile nitrogen solubility is found to be Less in pIrospliorus-bearing alloys than in pure iron. The reduction in solubility is about 20 pct in a 1.0 wt pct P alloy at 1300°C and about 30 pct in a 0.23 wt pct P alloy at 440°C. Diffusion coefficient measurements at 1150 and 585°C show that phosphorus also decreases the nitrogen diffusivity in iron. In previous work on the Fe-P-N system, phosphorus was found to reduce the nitrogen solubility in liquid iron slightly.&apos; Indirect evidence for similar behavior in a Fe at low temperature was obtained by Dickenscheid and Brauner.&apos; These authors found that phosphorus reduces the height of the internal-friction peak due to dissolved nitrogen. The results of Dickenscheid and Brauner were confirmed by J. C. Swartz of this Laboratory in a single internal-friction experiment using the same specimen stock as in the solubility measurements described below. In the present investigation, the solubility of nitrogen in a fer rite-stabilized Fe-1.0 wt pct P alloy was measured in the temperature range from 800" to 1300°C. Additional experiments were performed in the temperature range from 440° to 585°C, using an Fe-0.23 wt pct P alloy and NH3-H2 gas mixtures. EXPERIMENTAL The experiments were performed in a vertical tube furnace wound with platinum wire. For experimental temperatures of 800°C and above, a mixture of 5 pct Hz in N2 was used as the reacting gas. The gas mixture was prepurified from oxygen by passage over platinized asbestos at 450°C, and subsequently over anhydrone to remove water. Flow rates of the gases were measured with capillary flow meters. The temperature was measured before and after each experiment with a Pt/Pt-10 pct Rh thermocouple. The specimens used for the high-temperature solubility measurements were in the form of rectangular plates, 0.534 by 1.6 by 3.8 cm. The specimens were cleaned in trichloroethylene and annealed for 2 hr in hydrogen at the beginning of each experiment. In measuring the nitrogen solubility, the specimens were held in the reacting gas until equilibrated, then cooled in a water-cooled copper block at the bottom of the furnace. The time needed for equilibration at 1150°C was determined by measuring the average nitrogen content of the 1.0 pct P alloy as a function of reaction time. As will be described, the nitrogen diffusivity in the alloy at 1150°C is only slightly less than its calculated diffusivity in pure iron. At temperatures other than 1150°C, the reaction time used in measuring the nitrogen solubility was about twice the calculated equilibration time for pure iron at the same temperature. With a few exceptions, the procedure for the low-temperature solubility measurements was the same as that described above. The compositions of the NH3-H2 gas mixtures were determined by collecting gas samples from the gas train and analyzing them for NH3 by titration with HC1. The specimen thicknesses were less than those used for the high-temperature experiments, eg., 0.124 and 0.051 cm for measurements at 585° and 440°C, respectively. Nitrogen concentrations were obtained by chemical analysis, using the Kjeldahl method. The Fe-P alloys were made by adding ferrophos-phorus to electrolytic Plastiron (Type 104 A). Commercial ferrophosphorus, containing 3 pct Mn and 0.35 pct Si as the major impurities, was first purified by melting under an FeO slag. In a separate heat, the electrolytic iron was melted and vacuum-carbon-deoxidized prior to making the ferrophosphorus addition. The principal impurities and their concentrations in weight percent in the 1.0 pct P alloy are as follows: Mn, 0.01; Si, <0.01; C, 0.01; 0, 0.003; and N, 0.0012. The impurity levels in the 0.23 pct P alloy are con-

Jan 1, 1968

By B. C. Allen

The solubility of chromium in liquid silver and that of molybdenum and tungsten in liquid tin have been determined by equilibrating Ike Liquid in a crucible of the solule metal. Generally the weight of solute in solulion was delermined both chemically and from crucible weight losses. The resulting weight percent solubilily of chromium in silver as a function of absolule temperature T is given by log w = -6660/T + 4.02 in the range 960° to 1445°C, and that of molybdenlttrl in tin by log w = —5050/T + 1. 79 in the range 1200° to 2200°C. The values appear unaffected by minor changes in solute composition. Calculations aye made of the parlial molar heal and excess entropy of mixing. The estimated solubility of tungsten in tin is 0.001 pct at 2000°C. Evidence is presented that molybdenwm dissolves in tin without compound for mation and that tungsten and tin form W10Sn. RECENT developments in coatings, heat transfer, and brazing require a knowledge of equilibrium solubilities in a variety of systems at elevated temperatures. Of particular interest are solid-liquid interactions in metal systems involving dilute solutions. This investigation was undertaken since little is known about the phase relations or solubility of chromium in liquid silver or of molybdenum and tungsten in liquid tin.1,2 EXPERIMENTAL WORK As indicated in Table I, high-purity metals or those of known impurity levels were used. Crucibles were machined from chromium, molybdenum, and tungsten bar stock 1.3 cm diam and 2.2 cm long. Chromium rod was prepared by arc melting and extruding iodide process crystals.3 The five chromium impurity alloys were in the form of 0.6-cm-diam swaged rod. A Cr-0.06N* alloy was prepared by exposure to NH3 at 1150°C in a closed quartz capsule for 24 hr. Because significant nitrogen was lost during annealing in argon at 1600°C,4 the estimated level was 0.01 pct N. Chromium and Mo,W crucibles were outgassed at 1200" and 1600°C, respectively, at 3 X 10-5 mm. The solvent was placed In crucibles of the solute metal- 6 g Ag in chromium, 0.4 g Ag in the five chromium impurity alloys, and 4 g Sn in Mo,W crucibles. The silver and tin series were outgassed at 900" and 110O°C, respectively, and held at the desired solution temperature in a tantalum resistance furnace under 1.05 atm 99.995 pct Ar. An equilibration time of 0.5 to 1 hr was chosen since 0.3-, I-, and 4-hr anneals at 1235°C for Cr-Ag yielded similar results. Temperatures were measured optically to +10°C under essentially black body conditions which were checked against the melting point of silver. The Cr-Ag and Mo-Sn,W-Sn series were respectively equilibrated at 990° to 1400°C and 1200" to 2000°C. Vaporization losses were generally held to <1 pct by the argon. In the 1800" and 2000°C anneals for 0.5 hr, the crucibles were placed in tightly sealed tantalum cans which kept tin losses to <5 pct. After the anneals, the specimens were furnace-cooled. One anneal was made on small Mo-0.02 C, Mo-0.5Ti-0.lZr, and tungsten crucibles containing tin at 2200°C. The metals were sealed in an electron-beam-welded tantalum can of minimum volume. After the anneal, tin was still present in each crucible, none of which was severely attacked. After equilibration, the saturated solvent metal was selectively removed from the crucible by acid leaching. Weight losses sustained by the crucibles were determined from the initial weight minus the final blank-corrected weight after acid leaching. Chemical analyses were performed on some of the samples. Hot 1:l HNO3-H2O removed silver from chromium with the blank running <0.1 mg or <0.002 pct on measured solubility. Tin was removed from molybdenum and tungsten by hot concentrated HC1 with the respective blanks amounting to -0.004 and -0.0004 pct in the presence of tin. The insoluble residues were weighed and checked for composition. The leaching solutions contained traces of the solute metals which were analyzed by colorimetric methods, Diphenyl Carbazide for chromium, Thiocyanate for molybdenum, and Dithiol for tungsten. The total of the two percentages found from the residue and leaching solution minus the blank gave the desired solubility values. On the basis of annealing empty molybdenum and tungsten crucibles, weight losses due to MoO3 or WO3 volatilization were found to be generally 10.4 mg and affect measured solubilities by <0.01pct. RESULTS AND DISCUSSION Chromium-Silver . Since no intermediate compounds are reported to form in the Cr-An system,&apos; crucible weight losses and chemical analysis of the entire melt should provide reliable measures of the chromium in solution. Values obtained by the two methods are in agreement as shown by the results for unalloyed chromium in Table II and plotted in Fig. 1. Furthermore, the results are consistent with those previously determined by melting equilibrated silver out of the crucible and analyzing calorimetrically for chromium.&apos; On the basis of limited thermal analysis data, the solubility of chromium in silver has been quoted as 8 pct at the monotectic temperature of -1445°C.1 This investigation indicates an extrapolated solubility of 1.38 pct which is believed to be more reliable. At the eu-

Jan 1, 1968

By Donald T. Hawkins, Ralph Hultgren

The lorsion effusion method has been used to measure the vapor pressure of lead over pure lead and eight Pb-Sn alloys ranging from 9.1 to 87.9 at. pct Pb in the temperature range 950° to 1125°K. The resulting ?H°y 298 = 46,630 ± 200 cal per g-atow for pure lead is in excellent agreement with previous work. Deriued ?Gph values for the alloys were smoothed and correlated with previous heat of formation data to obtain entropies for the liquid alloys. values for the tin component were calculated by Gibbs-Duhem integmtion. Surfhce depletion of these liquid alloys was found to be absent, as shown by the fact that the measured pressure remained substantially constant with time in contrast with previous measurements on iron-rich solid Fe-Mn alloys. The activities and Gibbs (free) energies of the liquid Pb-Sn system are not well known although the heats of formation have been accurately determined by K1eppa.l Vapor pressure determinations of the activity of lead by Voronin and Evseev2 disagree with those of Predel.3 Elliott and chipman4 measured activities by the electromotive -force technique in the ternary Pb-Sn-Cd system. From the resulting values of the activity of cadmium, they were able to calculate the activities of lead and tin for the binary Pb-Sn system at the compositions xsn = 0.33 and 0.67. Atarashiya, Uta, Shimoji, and Niwa5 determined the activity of tin from Hz-H2O equilibrium measurements, but their results are subject to question due to uncertainty in the final state of their samples. To resolve these differences, measurements of the activity of lead were made using a torsion-effusion apparatus. Among other advantages, this apparatus rapidly detects errors caused by surface depletion, which tends to reduce the apparent vapor pressure of the more volatile component. If the measured torques remain nearly constant with time, only bulk depletion is occurring. This contrasts with the rapid decrease in torque found in solid Fe-Mn alloys at high temperatures and low manganese contents.6 EXPERIMENTAL 99.999+ pct Pb was obtained from the American Smelting and Refining Co. and 99.999 pct Sn from Vulcan Detinning Co. Eight Pb-Sn alloys were prepared by melting together weighed amounts of the pure metals in evacuated Pyrex tubes and quenching the melts in water. Loss of weight in preparation was less than 0.02 pct in all cases. The effusion cells were made from high-purity, nonporous graphite. Graphite was chosen because of its resistance to reaction with lead and tin and because it can be accurately machined with precision orifices. Two cells were used with overall dimensions as shown in Fig. 1. The orifices of cells 1 and 2 were, respectively, 1 and 1.5 mm in diam.

Jan 1, 1968

By Mark J. Klein

The precipitation of nitrogen in quenched and aged CY-35 at. pct Re was followed by internal-friction and electrical-resistivity measurements. It is shown that the precipitation kinetics of nitrogen from solution are many orders of magnitude lower in this alloy than in chromium. The reluctance of nitrogen to precipitate from sol~ction can be attributed to the composilional r-eadjustnzents required in the z.icinity of a chromium nitrade particle for gowth to occur. AS part of an investigation of the mechanism by which rhenium increases the low-temperature ductility of chromium and other Group VI-A metals, it was of interest to compare the concentration of interstitial elements retained in solution in chromium with that of a ductile Cr-Re alloy. The presence of certain interstitial elements in chromium has been shown to decrease its ductility1-5 and, of these interstitials, nitrogen is believed to have the most detrimental effect on mechanical properties. Thus, a comparison of the disposition of nitrogen in chromium with that in a ductile Cr-Re alloy might provide information about the mechanism whereby rhenium enhances the ductility of chromium. In previous internal-friction studies it was shown that the equilibrium solubilities of nitrogen in chromium and Cr-35 at. pct Re did not differ greatly.= However, results indicated that the actual concentration of nitrogen retained in solution at ambient temperatures is likely to be considerably greater in the alloy than in chromium because the precipitation kinetics of nitrogen are greatly retarded by the addition of rhenium. The objective of this investigation was to study the kinetics of nitrogen precipitation in Cr-35 at. pct Re in greater detail and to obtain information concerning the mechanism of nitrogen precipitation in this alloy. The properties studied were internal friction and

Jan 1, 1967

Jan 1, 1967

By D. L. Albright, R. W. Kraft

High-purity materials have been used in producing as-cast, controlled, colony, and degenerate solidification structures in the Fe-FeS eutectic. Experiments disclosed that this eutectic can be classified as normal and has a natural morphology composed of rodlike iron particles dispersed in a matrix of iron sulfide. The metallography of the various structures was studied, and a preferred crystallography was revealed in the controlled specimens produced by unidirectional solidification. The orientation effects found in these latter specimens are an [001] fiber texture in the -mowth direction of the bcc iron bhase and a texture corresponding to bicrystalline behavior in the hexagonal iron sulfide, with the growth direction near to (2111) poles. The observed texture of the iron phase is considered as indirect evidence that the alloy un-dercooled by at least 75°C before solidification. The unidirectional solidification of binary eutectic alloys has produced materials which exhibit a structure and properties markedly dependent upon the solidification process. In many cases a controlled microstructure with pronounced metallographic and crystallographic anisotropy can be experimentally achieved by proper regulation and balance of the growth rate of the alloy, the chemical purity of the starting materials, and the thermal gradient in the liquid at the liquid-solid interface. The purposes of this investigation were to produce various micro-structures in the Fe-FeS eutectic for subsequent study of their magnetic properties and to correlate the different structures with the solidification conditions in order to obtain a better understanding of the structure of eutectics. The Fe-S equilibrium diagram exhibits a eutectic composed of nearly pure iron and stoichiometric iron sulfide (FeS1.00), with the eutectic reaction occurring at 988°C and 31.0 wt pct S.1 Calculations indicate that this eutectic should solidify with about 9.5 vol pct Fe and 90.5 vol pct FeS, which in turn suggests2 that the micros tructure will consist of a rodlike iron constituent dispersed in a matrix of FeS. This characteristic has in fact been revealed some years ago.3 Thus, controlled solidification of this alloy might yield a material whose micromorphology would consist of very small ferromagnetic iron particles, rod-like in shape and aligned parallel to one another, supported in a matrix of antiferromagnetic FeS. Such specimens, because of the magnetic characteristics of the two phases, would be interesting subjects of study as magnetic materials. Hence the magnetic properties were considered in detail and are reported elsewhere.4 EXPERIMENTAL PROCEDURE The specimens of Fe-FeS eutectic were prepared from ultrapure iron (99.99+ pct) and high-purity sulfur (99.999+ pct). The iron was estimated to contain 60 ppm impurities (99.994 pct Fe) after zone purification.5 The ingots of iron were cut into chips, and the lumps of sulfur were ground into powder. In order to redice any nometallic impurities which might have accumulated during handling, the iron chips were annealed for 5 hr at 750° ± 10°C in a dry hydrogen atmosphere. Immediately after this treatment the chips were blended with the sulfur powder in eutectic proportions; the mixture was tamped into transparent fused quartz tubing and then vacuum-encapsulated under a pressure of 40 to 60µ of Hg. Because FeS expands upon solidification it was necessary to re-encapsulate the initial capsules so that oxidation reactions would be avoided when the inner tube cracked during solidification. For purposes of homogenizing the blended mixtures before solidification, the double capsules were heated to 750° ± 20°C and held for 20 hr; after this treatment the reacted product was weakly agglomerated. Each sample was then loaded into an apparatus for very rapid melting and freezing; this was accomplished by passing a molten zone through the specimen, using induction heating and a traverse mechanism. The resulting specimens solidified in the shape of the quartz tubing. Two sizes of specimens were used in this work, 18 mm diam by 100 mm long and 5 mm diam by 30 mm long. Metallographic examination of several ingots of both sizes after the above consolidation indicated no lack of compositional homogeneity and a random "as-cast" structure, because the travel rate was so rapid that unidirectional solidification was not achieved. Unidirectionally solidified specimens were resolidified in the apparatus shown schematically in Fig. 1, This equipment consisted of a kanthal resistance furnace mounted on the carriage of a zone-melting unit so that the heating element could traverse the length of the sample at a selected rate of speed. Large specimens were solidified with the mechanism tilted at ap-

Jan 1, 1967

By J. A. Bailey, J. H. Tundermann

The dihedral angles of the solid-liquid interfaces were measured at various temperatures above the solidus and the interfacial energies calculated when small additions of copper, indium, lithium, magnesium, antimony, and silicon were made to an aluminum alloy containing 3 pct Sn. When the results were compared with those of the Al-Sn alloy some differences were found which could be interpreted in terms of the ability of the added element to enter into solution or form intermetallic compounds with the aluminum and tin. It was shown that in some cases considerable changes in the shape of intergvanular liquid films can be brought about by comparatively small compositional changes in the alloy. DURING the melting or solidification of an alloy a temperature range is usually found where the presence of a liquid phase may be detected at the grain boundaries of a solid. It is believed that the presence of this liquid phase is responsible for hot tearing in castings and welds and hot shortness in the working of some alloys at elevated temperatures. Rosenberg, Flemings, and Taylor1 in a study of the solidification of aluminum castings have indicated the importance of intergranular liquid films and shown that their shape and distribution at the end of solidification effect the hot tearing characteristics of the material. The shape of such intergranular liquid films are determined largely by the ratio between the solid-liquid interfacial energy (yLS) and the grain boundary energy (ySS). A measure of this ratio (yLS/ySS , relative interfacial energy) is the dihedral angle 8. The dihedral angle 0 is related to the relative interfacial energy by the following expression: Rogerson and Borland 2 have also suggested that the shape of the intergranular liquid is an important factor in determining the susceptibility of a material to hot shortness. They showed that on a comparative basis materials having the lowest dihedral angles at a given temperature gave the greatest severity of cracking. They stated that liquid in the form of globules should be less harmful than liquid in the form of extensive films as more intergranular cohesion should be possible. Rogerson and Borlland 2 also showed that the susceptibility of an A1-Sn alloy to hot cracking can be reduced by small additions of cad- mium. It was found that the cadmium gave an increase in the dihedral angle at all temperatures. Ikeuye and smith3 investigated changes in the dihedral angle and relative interfacial energy with temperature for a number of ternary alloys formed when small additions of bismuth, cadmium, copper, lead, and zinc were made to an A1-Sn alloy. They found that in most instances changes in the dihedral angle were caused by compositional changes in the liquid phase; as the composition of the liquid approached that of the solid the dihedral angle decreased. They noted that the addition of a third element which was soluble in both the liquid and solid phases at a given temperature may decrease the dihedral angle (e.g., the addition of copper or zinc) but otherwise the ternary alloys formed exhibited dihedral angles between those of the A1-Sn binary alloy and those of the binary alloy of aluminum with the added element. Dwarakadasa and Krishnan4 investigated the changes in dihedral angle and relative interfacial energy with temperature when small additions of magnesium, iron, silicon, manganese, sulfur, cobalt, and silver were made to a copper alloy containing 3 pct Bi. They found that in all cases the added elements gave an increase in the dihedral angle and relative interfacial energy when compared with the values obtained for the simple binary alloy at the same temperature. It was noted that an increase in temperature gave a decrease in dihedral angle and relative interfacial energy in each of the ternary alloys studied. Similar results have been obtained by Ramachandran and Krishnan5 for the addition of small quantities of lead. This paper describes the application of dihedral angle measurement to the determination of the shapes of liquid phases at various temperatures above the solidus when small additions of copper, indium, magnesium, lithium, antimony, and silicon are made to an aluminum alloy containing nominally 3 pct Sn. An attempt is made to correlate the measurements with the relative solubility of the added elements in tin and aluminum. The work was undertaken to provide more data concerning the effects of temperature and composition on the shape of liquid films above the solidus. EXPERIMENTAL PROCEDURE In the present work ternary aluminum alloys containing nominally 3 pct Sn and small additions of high-purity copper, indium, lithium, magnesium, antimony, and silicon were made. The alloys were melted in a graphite crucible under an inert atmosphere of argon and cast into ingots 6 in. long by 0.5 in. diam. The ingots were then cut into rods 1.5 in. long, given a 50 pct cold reduction, and machined into test pieces 0.5 in. long by 0.5 in, diam for heat treatment. The alloy samples were annealed at the various test temperatures between the liquidus and solidus for approxi-

Jan 1, 1967

By J. C. Uy, A. A. Burr

A quantitative relationship between the allotropic phase boundaries of zirconium-base binary systenzs and the solute metallic valence is shown through an intermediate thermodynamic parameter. A simplified equation relating this parameter to the phase boundaries is briefly reviewed, and data from the literature are used to show the relationship of this parameter to the solute metallic valence. It has been reported that the solute metallic valence can be used as an index of phase stabilization in zirconium-base binary alloys.&apos; It was shown that the algebraic sign of the slopes of the hcp/bcc phase boundaries of zirconium alloys correspond to the algebraic sign of the metallic valence of zirconium minus the metallic valence of the solute, or, in other words, a solute whose metallic valence is higher than that of the solvent tends to stabilize the high-temperature phase while one whose metallic valence is lower than that of the solvent tends to stabilize the low-temperature phase. Further analysis of the zirconium binary systems has revealed a quantitative relationship between the solute metallic valence and the relative slopes of the two-phase allotropic boundaries. This relationship involves a thermodynamic quantity whose significance can be seen in the following section. PHASE-STABILIZATION PARAMETER Let Qb be the difference between the partial molar heats of mixing of a given solute in the two allotropic phases of the solvent which are in equilibrium with each other at a given temperature, thus A relationship between this term Qb and allotropic phase boundaries has been employed by several au-thors&apos;-= in the evaluation of phase diagrams, and can be briefly derived as follows. Referring to Fig. 1, consider the general case of two allotropic phases, each having a small mole fraction (Xa,Xb) of the solute, in equilibrium at temperature T and atmospheric pressure as represented by the reaction. solute in ß phase =solute in a phase If now a reaction occurs such that an infinitesimal amount of the solute is removed from the ß phase and added to the a phase, there would be a partial molar

Jan 1, 1967

By C. E. Lundin

The Ce-H system was investigated in the temperature range, 573° to 1023°K, and the pressure range, 10-3 to 630 Torr, as a function of &apos;composition up to 72 at. pct H. Families of isothermal arid isopleth curves were plotted from the pressure-terr~perature-composition relationships. From these curves the solubility relationships were determined for the system. The isopleths are analytically represented by equilibrium dissociation pressure equations. The relative partial molal enthalpzes and entropies of solution of hydvogen in the systerrz were calculated fronz the dissociation pressure equulions and are tabulated. The integral free energies, enthalpies, and entropies of mixing in the Ce-H system were determined from the relative partial quantities and are also tabulated. The standard free energy, enthelpy, and entvopy of reaction of the dihydride phase at kcal per kcal per mole H2, and ?S° = -34. 1 cal per deg mole H2, respectively. The equilibrium dissociation pressure equation in the two-phase region is: UNTIL recently very little was known of the detailed solubility and thermodynamic relationships of the Ce-H system. Two previous investigations1,2 are noteworthy. However, significant discrepancies and omissions exist on analyzing them. The work of Mulford and Holley1 on cerium did not clearly delineate the boundaries of the two-phase region, Cess - CeH2-x. The plateau partial pressures were not thoroughly defined and were considerably displaced in pressure compared to those from the work of Warf and Korst.2 These latter authors concentrated their studies primarily from 823° to 1023°K in the pressure range of 1 to 760 Torr. No data were determined to outline the regions of primary solid solubility and the hydride phase. Also the establishment of the plateau partial pressures was rather limited in scope. In neither work was a treatment conducted of the relative partial molal enthalpies and entropies of solution of hydrogen in the single-phase regions and the integral thermodynamic quantities of mixing throughout the system. Therefore, it was the objective of this research to determine the complete equilibrium solubility relationships and thermodynamic data for the system by pressure-temperature-composition studies. EXPERIMENTAL PROCEDURE The cerium metal for this study was donated by the Reno Metallurgy Research Center of the Bureau of Mines. Total impurity content was 0.13 pct with only 60 ppm O. The metal was checked metallographically and contained only minor amounts of second phase compared to cerium from other sources. Specimen preparation was done in a dry box flushed with argon gas. The surface of a small rectangular piece of cerium (about 0.2 g) was filed with a clean, mill file. Final weighing was done in a tared enclosed vial containing argon gas. The specimen was then loaded quickly into the reaction chamber which was purged several times with high-purity hydrogen gas and then allowed to pump to about 10-6 Torr. The furnace was heated to the reaction temperature and the run started. The equipment used to conduct the hydriding was a Sievert&apos;s-type apparatus. Basically it consisted of a source for pure hydrogen, a precision gas-measuring burette, a heated reaction chamber, a McLeod gage, and a mercury manometer. Pure hydrogen was supplied by the thermal decomposition of uranium hydride. The 100-ml precision gas burette was graduated to 0.1-ml divisions and was used to measure the quantity of gas and admit it to the chamber. The reaction chamber was a quartz tube. Prior to each run, the cerium specimen was wrapped in a tungsten foil capsule to prevent reaction of the cerium with the quartz. Control of the temperature was achieved within ±1°K. Pressures in the manometer range were measured to ±0.5 Torr and in the McLeod range (10-3 to 5 Torr) to ±3 pct. The compositions of hydrogen in cerium were calculated in terms of hydrogen to cerium atomic ratio. These compositions were estimated to be ±0.01 H/Ce ratio. The technique used to study the equilibrium pressure-temperature-composition relationships of the Ce-H system was to develop experimentally a family of isothermal curves of composition vs pressure. The range of pressure through which each isotherm was developed was from 10-9 to about 630 Torr in the temperature interval, 573° to 1023°K. RESULTS AND DISCUSSION The hydriding characteristics of cerium are iso-morphous with those of the elements of the light-rare-earth group (lanthanum, cerium, praseodymium, and neodymium) wherein the region from the dihydride to trihydride is continuously single phase.&apos; The structure of this phase is fcc.3 The heavy rare earths form a trihydride,2 which is hcp, separated by a two-phase region from the fcc dihydride phase. The Ce-H system is represented by the family of experimental isotherms in Fig. 1. Due to the small scale required to draw the curves, the experimental points are omitted; however, a total of 240 experimental data points were taken to prepare these curves. The solubility relationships can be deduced therefrom. Three distinct regions of partial pressure and composition can be seen. The region of cerium solid solution is represented by the rapidly rising isotherms in the dilute composition range. In accordance with Gibbs Phase Rule only one solid phase, the cerium solid so-

Jan 1, 1967

By T. R. Ingraham

The thermal decomposition of Nickel (II) sulfate was examined by determining the total pressure of SO3, SO2, and O2 developed over a sample when it was heated in an evacuated system fitted with a Pyrex-bellows mercury manometer. The equilibrium pressures were combined with previously published data on the oxide and sulfide systems to establish a predominance volume diagranz for the Ni-S-O system over the normal range of roasting temperature and gas composition used in the treatment of nickel minerals. The protective coating of NiSO4 which forms on the oxide during roasting, and which causes the sulfation reaction to almost cease, may be disengaged readily by temperature cycling. When nickel sulfide is roasted in air, either nickel sulfate or nickel oxide may be formed by altering the experimental conditions. Because of the differing stabilities of various metal sulfates and oxides, possibilities exist for separating some of the constituents of mineral mixtures by the technique of selective sulfation and oxidation roasting. The experimental information required to make reasonable predictions of the possibilities of this technique is incomplete and, in some cases, in conflict. As part of a general program of providing some of the required information, a study EXPERIMENTAL Materials, Apparatus, and Procedure. Fisher certified reagent-grade nickel sulfate hexahydrate was used in the source material for both nickel sulfate and nickel oxide. The manufacturer&apos;s analysis indicated: 0.001 pct Fe, 0.005 pct Cu, 0.003 pct Co, 0.001 pct C1, other 0.15 pct. The material was dehydrated, before use, by heating at 420°C for 5 hr. The oxide was prepared by roasting the sulfate in an open tray in a muffle furnace for 10 hr at950°C. Preliminary experiments which were made by thermogravimetric analysis and X-ray diffraction analysis established that only one crystal form of nickel oxide and one of nickel sulfate were involved in the equilibrium shown in Eq. [I]. The apparatus used in the experiments was described previously.1,3 The main feature is a corrosion-resistant, flexible Pyrex bellows which is used to protect the mercury in a u-tube manometer. Before a run was begun, the apparatus was washed thoroughly with hot hydrochloric acid and water and dried by heating under vacuum. The mixed sulfate -oxide sample was contained in a platinum bat rest-

Jan 1, 1967

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

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

Jan 1, 1967

By C. N. J. Wagner, E. N. Aqua

The bee alloys of the terminal solid solution of rhenium in niobium were investigated by X-ray diffraclion methods. The analysis of the broadening of the powder pattern peaks from the niobium-rich alloys, cold-worked by filing, showed evidence for faulting on (211) planes. The alloys with larger rhenium concentrations were brittle, and fractured when filed. The analysis of the shapes of the diffraction profiles from powders produced by hammering with steel plates) of these brittle alloys indicated that the broadening was due predominantly to platelets bounded by clibe planes. This result was consistent with the Laue patterns from single-cleazlage facets which showed evidence for clearage fracture on {100} planes. The influence of faulting on the mechanical properties of face-centered cubic (fcc) metals and alloys, i.e., how faulting affects the various dislocation configurations in fcc metals, is well-known.&apos; The important question is whether or not faulting occurs in body-centered cubic (bcc) metals and alloys, and, furthermore, if faulting does occur, to what extent it affects the mechanical properties. Theoretical calculations indicate that the stacking-fault energy is rather high in most bcc metals.2 The results of sev-eral studies using transmission electron microscopy have indicated that faults are present in well-annealed and lightly deformed bcc metals and alloys, such as tungsten,3 vanadium,4 and Mo-Re alloys.5,6 These faults, as have been observed, may be stabilized by the presence of interstitial (C,N,O) atom segregation to the extended dislocations. In addition, there is considerable X-ray diffraction evidence for faulting in bee metals,7-8 using the same techniques that were successful for the study of faulting in fee metals and alloys.7 This X-ray diffraction method is currently the only technique applicable for the investigation of faulting in metals with high stacking fault energies, i.e., when severe amounts of deformation are required to produce sufficient amounts of faulting to be detectable by X-rays. The thinned films of heavily deformed metals will become opaque in the electron microscope due to the high dislocation densities present. In a previous investigation of faulting8 in bee metals of group Vb and VIb, the authors observed that niobium was ductile when filed at room temperature, and showed the highest density of faults on the (112) family of planes. A niobium-base alloy system was therefore chosen to study the effect of alloying on the occurrence of faults in a bcc alloy. There is a large range of terminal solid solubility of rhenium in the alloys of the bee refractory metals. All of the Group VIb-rhenium alloys, i.e., Cr-Re, Mo-Re, and W-Re, exhibit solid solution hardening without loss of ductility.9 In fact, the ductility reaches a maximum for alloys with compositions near to the limits of solubility. This enhanced ductility has been attributed to the lowering of the stacking-fault energy in the alloy; i.e., the increased amounts of twinning provide an additional mode of deformation, resulting in the observed high ductility.&apos; Because of this demonstrated effect of rhenium in bee alloys, it was decided to study a series of alloys of Nb-Re. Using the same X-ray diffraction methods as described in the previous investigation,&apos; one is able to identify the possible causes of broadening of the powder pattern peaks, e.q., particle size, microstrains, stacking faults, and/or twin faults. The separation of these various contributions to the measured peak shape is accomplished by the Warren-Averbach analysis.7 I) EXPERIMENTAL PROCEDURE A series of seven bee solid solution alloys containing from 2.5 to 21.5 at. pct Re (remainder niobium) were prepared at the General Electric Research Laboratory. Buttons, weighing 25 g, were alloyed from electron-beam-melted niobium chips and random rhenium sheet by arc melting in a water-cooled copper crucible, under an argon atmosphere. The buttons were inverted and completely remelted to promote homogenization. The nominal alloy compositions are listed in Table I. Samples of the cold-worked alloys were obtained by filing to produce a powder for the X-ray study. Alloys too brittle to be filed were hammered with steel plates. The resultant filings or brittle impactings were screened through 150-mesh classifiers and compacted to the required shape for the diffractometer holder. The X-ray diffraction peaks were automatically recorded by fixed time counting at uniform 28 intervals, or by continuous registration with a ratemeter. In all cases, the (110)-(220) and (200)-(400) pairs of peaks and the (211), (310), (222), and (321) reflections were measured on a GE-XRD5 diffractometer using CuKa radiation with nickel filter or MoKct radiation and a LiF monochromator in the diffracted beam. The first part of the data reduction, completed with the aid of a series of programmed computations,10 was the analytical resolution of the Kol component of the diffraction profile. Subsequent computations were then made with reference only to the resolved Kol peak shape. These included the measurement of the

Jan 1, 1967

THE increased demand for titanium alloys with improved high-temperature creep strengths has stimulated interest in silicon as an alloying addition to titanium. Silicon is a potent solid-solution strength-ener and, if added in sufficient concentration and properly heat-treated, can also dispersion-strengthen titanium by eutectoid decomposition.&apos; However, better understanding of the nature and distribution of the resulting silicide dispersion in more highly alloyed titanium matrices is necessary for the development of useful titanium alloys which utilize the latter strengthening mechanism. This note describes the chemical and crystallographic characteristics of the silicide phase as it occurs in a typical high-temperature near-a titanium alloy matrix. Several Ti-6A1-3Sn-3Zr a11oys containing various amounts of silicon ranging from 0.1 to 1.0 pct were melted as 10- to 20-lb ingots and processed into 1/2-in.-diam bar stock. The microstructures of specimens annealed at various temperatures were conveniently summarized by the (Ti-6Al-3Sn-3Zr)-Si pseudobinary phase diagram illustrated in Fig. 1. Comparison with the Ti-Si equilibrium diagram indicates the substitutional solutes (Al-Sn-Zr) increase the eutectoid temperature and decrease the a terminal solubility. Annealing at temperatures sufficiently high to dissolve the silicon in a ß solid solution and cooling rapidly enough to preclude coarsening generally produced a uniform dispersion of fine silicide particles, whereas annealing at temperatures near but below the ß transus produced relatively coarse silicide particles. Annealing in the limited a, plus 3 region produced a duplex coarse and fine silicide array. Several a-annealed specimens were examined by X-ray diffraction to determine the crystallographic identity of the precipitate phase. Copper Ka X-ray diffraction patterns of bulk specimens which contained 0.5 and 0.8 pct Si were virtually identical to that of the silicon-free Ti-6Al-3Sn-3Zr base alloy except for a slight shift in some of the high-angle diffraction lines. Apparently the silicide volume fraction was too low to be detected in bulk specimens. X-

Jan 1, 1969

By M. B. Bever, A. K. Jena

In the investigation reported here, calorimetric measurements have been made to determine the heat of formation of the compound AuSb2 and the partial gram-atomic enthalpies of antimony and gold in dilute solution in liquid tin and their enthalpy interaction coefficients. In order to interpret the behavior of antimony and gold in dilute solution in tin, nonzero values are assigned to the energies of bonds between like solute atoms relative to the pure solute state. Sa.mples of the compound AuSb2 were prepared by melting stoichiometric amounts of antimony and gold (99.999 pct pure) in evacuated and sealed Vycor tubes, which were shaken vigorously and quenched in water. The ingots were annealed in evacuated and sealed tubes at approximately 700°K for 2 weeks. Metallo-graphic and X-ray examinations gave no indication of second phases or microsegregation. The samples were added from 273°K to tin-rich solutions in a solution calorimeter1 maintained at 623°K. The calorimeter was calibrated with tin; the heat content of tin, H623°K- H273°K, was taken as 4.08 kcal per g-atom.2 In each calorimetric run at least four additions were made. The total concentration of solutes in the bath at the end of any run did not exceed 1 at. pct. The measured heat effect of an addition was plotted against the average of the atom fractions x of Sb + Au in solution before and after that addition. From this plot the heat effect at infinite dilution h,,, and the composition dependence of the heat effect dh/dx in the composition range 0 < x < 0.01 were obtained. The results for the additions of antimony, mixtures of antimony and gold, and the compound AuSb2 are listed in Table I. The heat effect h on addition of a sample of the compound AuSb2 or a mechanical mixture of antimony and gold at 273°K to a tin-rich solution at 623°K can be expressed as:

Jan 1, 1969

By R. H. Tien

The accuracy of the method of steady-state approximation applied to the problems of heat transfer involving phase change (London and Seban&apos;s solution) is improved by defining a "modified heat of fusion" which accounts for the effect of specific heat. An analytical expression for this modified heat of fusion is derived in terms of the actual heat of fusion, specific heat, and surface temperature. Numerical solution for the freezing of iron indicates that the ratio of the modified heat of fusion to the actual heat of fusion increases from 1.04 to 1.4 as the surface temperature decreases from 2700° to 1600°F. The heat transfer process accompanying solidification is complicated owing to the moving solid-liquid interface where the latent heat of fusion is released. Exact analytical solution is available only for a few special cases of freezing problems such as Stefan&apos;s1 problem. In a commonly used steady-state approximation method, London and seban&apos;s2 solution, the effect of specific heat is neglected. This approximation, however, may introduce some degree of error in mathematical analysis when the temperature of the solid surface is much lower than the freezing temperature, as in the case of freezing metals. In a recent work by Robertson and Schenck,3 the problem of freezing a semi-infinite region with finite surface conductance was programed in a digital computer through the finite difference method. A family of curves for the correction of the London-Seban solution was given in a dimensionless plot for different ratios of heat of fusion and specific heat effect; it was shown that the London-Seban solution when applied to the freezing of a mild steel slab under some particular conditions gave results in error by about 10 pct in the solidification rate. Although the Robertson-Schenck computer result has improved the London-Seban solution to a great extent, lack of generality and the tedious computing procedure have restricted its application. In this paper a "modified heat of fusion" which accounts for the effect of specific heat is defined, and is used instead of the actual heat of fusion in the London-Seban solution. An analytical expression of this modified heat of fusion in terms of the specific heat, surface temperature, and actual heat of fusion is derived by comparing the solutions of Stefan and London-Seban for the case of freezing of a semi-infinite region with constant surface temperature. It can also be extended to the case with finite surface conductance, and the results show good agreement with the Robertson-Schenck computer solution. The expression of the modified heat of fusion, the accuracy of the London-Seban solution, and the temperature distribution within the solid are presented graphically in dimensionless form. Numerical solution for the freezing of iron indicates that the ratio of the modified heat of fusion to the actual heat of fusion increases from 1.04 to 1.40 as the surface temperature decreases from 2700° to 1600°F.

Jan 1, 1969

By O. F. Walker, W. C. Hahn, V. A. Johnson, J. D. Wood

The diffusion coefficients of zinc in single-crystal zinc and carbon in single-crystal and poly crystalline nickel were measured by means of radioactive tracer techniques both with and without the application of ultrasonic vibrations under conditions such that the temperature of the sample was closely controlled. The results of this investigation indicate no enhancement of diffusion in any of the samples. It is suggested that previously reported enhancement may have been due either solely to temperature increases caused by ultrasonic vibrations or in combination with changes in the boundary conditions. A number of observations have been reported in the literature in which it has been implied or inferred that the application of ultrasonics enhances diffusion (see, for example, Refs. 1-5). The present study was undertaken in an attempt to observe this effect under carefully controlled conditions, particularly with regard to measurement and control of the temperature of the sample. Two different types of systems were studied; these were the self-diffusion of zinc and the diffusion of carbon in nickel. EXPERIMENTAL For diffusion with ultrasonic energy applied, the samples were included as part of a resonant ultrasonic system operating at 58.5 kcps. The ultrasonic generators used were rated at 100 and 250 w and could be tuned over a frequency from 10 to 100 kc. A PZT (lead titanate/lead zirconate) ceramic transducer provided the driving vibration. This system requires no metallurgical joining of the specimen to the acoustical transmission line since the ultrasonic driver and the follow-up section clamp the specimen in position by means of a constant pressure of 50 lb developed by an air cylinder. The ultrasonic driver and follow-up section, both made of titanium, were 4 in. in length from clamping point to the end in contact with the specimen. Using the relationship given by Mason,6 A = V/f, the resonant wavelength, A, in titanium is calculated to be 3.3 in. at a frequency, f, of 58.5 kc, taking the velocity of sound in titanium, V, as 1.95 X 105 in. per sec. The 4-in. driver and follow-up section, therefore, are each 4.0/3.3 =1.21 times the resonant wavelength. Clamping pressure must be applied at stress nodes of the transmission line in order to preserve resonance. Therefore, a specimen length of 0.58 times the wavelength in the specimen was required to place the clamping pressure application points at stress nodes exactly three wavelengths apart. A stress antinode was contained in the center 3 in. of the specimen. A small PZT ceramic disc attached to the follow-up section provided an output voltage proportional to the intensity of the standing wave. This output voltage was monitored on an oscilloscope and the ultrasonic system was tuned to resonance by varying the frequency until the output signal was a maximum amplitude. The amplitude of the output signal was maintained constant throughout the diffusion anneal. A split cylindrical stainless-steel chamber, which was purged with argon prior to and during the runs, was placed around the specimen. The chamber in turn was surrounded by a movable furnace whose temperature could be controlled to 7C. Heat exchangers were used to cool the driver, follow-up section, and ultrasonic transducer. Great care was taken to obtain the true specimen temperature in all cases. Several different methods were tried; the most successful was that in which the thermocouple was held in contact with the midlength of the specimen by means of an asbestos insulating pad and wire straps. In the case of zinc, single-crystal specimens of 99.999 pct purity were used. The samples were 0.25 by 0.25 in. square and of the proper length for resonance, that is 1.1 in. long with the c axis parallel to the long dimension of the specimen for the case of diffusion perpendicular to the c axis and ultrasonic motion parallel to the c axis, and 1.9 in. long with the c axis perpendicular to the long dimension of the specimen for the case of diffusion parallel to the c axis and ultrasonic motion perpendicular to the c axis. In each case, one of the rectangular faces was electroplated with a thin film of zinc containing Zn The constant pressure used to clamp the specimen in place in the ultrasonic system caused some deformation in some of the samples. For these samples the deformation was concentrated in either end of the specimen; thus, for all samples (both zinc and nickel) the center in. was cut from the specimen after the diffusion anneal to be used for sectioning and counting. The nickel single-crystal samples, of 99.999 pct purity, were used in the form of rods 0.25 by 0.187 by 2.07 in. long with the (100) direction parallel to the rod axis. The polycrystalline nickel samples of 99.97 pct purity had an average grain diameter of 0.007 in. and were used in the form of rods 0.25 by 0.125 by 1.87 in. long. The direction of ultrasonic motion was parallel to (100) direction (bar axis) for the single-cqstal samples and parallel to the bar axis for the polycrystalline specimens. A thin film of c14 suspended in methanol was applied to the diffusing face of the specimen. Two specimens were butted together lengthwise for each diffusion anneal to minimize oxidation. After diffusion, a precision lapping device similar to the one described by Goldstein7 and a radiation detector were used to obtain a plot of specific activity vs penetration distance for each specimen. (A scintil-

Jan 1, 1969

By G. R. Speich

The interlarnmelm spacing, growth rate, and degree of segregation that accompany cellular precipitation in four Fe-Zn alloys containing 9.7, 15.2, 23.5, and 30.5 at. pct Zn have been determined in the temperature range 400" to 600°C. The chemical free-energy change for the reaction was calculated from the available thermodynamic data and the known compositions of the phases. The fraction of the chemical free-energy change for equilibrium segregation that is converted into interfacial free energy decreases from 0.43 to 0.08 as the magnitude of this free-energy change increases from 35 to 270 cal per mole. At constant temperature the cellular growth rate is proportional to the cube of the dissipated free energy. At 600°C newly 100 pct of the equilibrium segregation is achieved during cellulm precipitation whereas at 400°C only 85 pct of the equilibrium segregation is attained. During cellular growth, mass transport of zinc occurs by grain boundary diffusion; excess zinc remaining in the a! phase after the completion of growth is removed slowly by volume diffusion. A modified Cahn theory of cellular precipitation predicts the observed interlamellar spacing within a factor of two. In cellular precipitation reactions such as pearlite formation or discontinuous precipitation, the basic problem is to predict the variation of growth rate G, interlamellar spacing S, and degree of segregation P with composition and temperature. To accomplish this we need three independent equations relating these quantities. One of these equations comes from the diffusion solution. To obtain two additional independent equations, some assumptions must be made. cahnl has suggested recently that two plausible assumptions are 1) that growth rate is proportional to the dissipated free energy and 2) that the spacing which occurs is that which maximizes the dissipated free energy. According to the first assumption, this spacing also maximizes the growth rate and the rate of decrease of free energy per unit area of cell boundary. The present work was undertaken to test these assumptions. To test the first assumption it is necessary to study a cellular reaction over a wide range of supersatura-tions to establish a relationship between G and the dissipated free energy at constant temperature. This is possible only in discontinuous precipitation reactions since in pearlite reactions constituents other than pearlite form if the composition of the parent phase deviates even slightly from the eutectoid composition. The Fe-Zn system was chosen for study because 1) discontinuous precipitation proceeds to completion over a wide temperature and concentration range, 2) the degree of segregation within the cell can be measured by lattice parameter measurements,2 and 3) the thermodynamics of this system have recently been determined by Wriedt.3 In this system the cells consisting d alternate lamellae of a and r phases form from supercooled iron-rich a phase. The a phase within the cells is bcc as is the original a phase, cia, but has a different orientation and a slightly lower zinc content than the original a phase. The r phase has a zinc content of about 70 at. pct and a crystal structure isomor-phous with T brass. EXPERIMENTAL PROCEDURE Four Fe-Zn alloys with 9.7, 15.2, 23.5, and 30.5 at. pct Zn were prepared from carbonyl-iron powder (400 mesh, 99.8 wt pct Fe) and zinc powder (200 mesh, 99.99 wt pct Zn). The powders were ball-milled together and cold-pressed under 60,000 psi to discs $ in. thick by $ in. diam. The cold-pressed discs of the alloys with 9.7 and 15.2 at. pct Zn were sealed in evacuated silica capsules and heated slowly to 1100°C over a period of 1 week (3 days at 600°C, then 3 days at 80O°C, then 1 day at 1100°C). The alloys with 23.5 and 30.5 at. pct Zn were treated similarly except that the final homogenization temperatures were 1000" and 85O°C, respectively, to prevent melting. The alloys were quenched in iced brine from the final homogenization temperature. Specimens of each alloy were subsequently aged in salt pots at temperatures of 400°, 450°, 500°, 550°, 600°, and 650°C for times that varied from a few minutes to several hundred hours. At a late stage of this work, an alloy containing 11.2 at. pct Zn was prepared by vapor-impregnation of iron foil with zinc vapor at 890°C. This alloy proved useful for electron microscope studies because it was free of porosity. The homogenization and aging conditions were based on the recent Fe-Zn phase diagram of Stadelmaier and Bridgers4 rather than the earlier diagram of ansen.5 They consist of a homogenization heat treatment in the homogeneous a field followed by an aging treatment in the two-phase a + r field. The aged specimens were metallographically polished and etched in 2 pct nital and the radius of the largest cell in the microstructure determined. This radius plotted vs time gave a straight line whose slope is the boundary migration rate or growth rate G of the cell. To determine the interlamellar spacing, specimens were examined by surface-replica and thin-section electron microscope techniques. Because of the irregular nature of the lamellae within the cell, the average interlamellar spacing S .of the cell was measured by the method of Cahn and Hagel,6 where S is defined by:

Jan 1, 1969

By R. A. Meussner, C. T. Fujii

Chromium solution in wustite depresses the oxygen activity in a nonideal manner and expands the lattice slightly. Gravimetric measurements of the equilibrium compositions of wustite containing 0.00 to 1.38 wt pct Cr define the oxygen potential (CO2-CO atm) and the limits of the phase field at 1000°C. These data extrapolate to a maximum solubility of 2 wt pct Cr. The lattice parameter data, room-temperature measurements of quenched samples, differ significantly from those in the literature. Both pure and chromium wus-tites contract at uniform and equal rates as the oxygen content (metal deficit) increases. The a. US metal deficit relationships are straight lines showing none of the curvature previously reported. At constant metal deficit, the a. expands by 0.002? on alloying with 0.4 to 0.5 wt pct Cr but is insensitive to further chromium additions: a small expansion rather than a marked contraction. These results require a modification of the accepted alloying mechanism. IN the high-temperature oxidation of Fe-Cr alloys in Ha-H,and CO2-CO atmospheres the vapor transfer of oxygen from the continuous wustite outer scale to the porous inner scale/alloy interface sustains the high oxidation rates.1"3 The driving force for this transport is the difference in the oxygen activity of the outer wustite and that at the inner scale/alloy interface. In pure CO2, as well as in CO2-CO atmospheres, carburization of the alloy accompanies this oxidation. Current efforts to evaluate the parameters controlling this carburization have shown that the process is not simple; i.e., the carbon concentration in the alloy initially increases rapidly, reaches a maximum, and then decreases slowly as the oxidation time is extended. This is the same pattern reported by McCoy for the more complex oxidation-carburization of stainless steels and an Fe-Cr alloy in CO2 at lower temperatures.4 These changes in the carburization process occur while the overall oxidation rate and the lattice parameters of the scale layers remain constant. If this invariance of the lattice parameter is assumed to indicate a constant scale composition and thus a constant oxygen potential, the carburization results are not easily explained. Electron microprobe traces across the thickness of these outer scales, however, have revealed distinct chromium gradients penetrating 10 to 50 µ from the inner surface where the chromium concentrations were estimated at a few tenths percent. The variation of the chromium cmcentration on the inner surface of the scale, and the resulting change of the oxygen activity, during the oxidation process is considered to be important in defining the carburization process. Thus, to gain an understanding of the complex oxidation-carburization proc- ess, it was necessary to measure the properties of wustite containing known amounts of chromium (chromium wustite). Although the general features of the Fe-Cr-0 equilibrium diagram between 900° and 1300°C have been fairly well established by Richards and white: Wood-house and White,6 Seybolt,7 and Katsura and Muan,8 there have been no detailed studies of the limits of the chromium wustite phase field or the properties of these alloyed wustites. The recent results of a limited study of chromium wustite by Levin and wagner9 indicate that more than 0.67 wt pct Cr is soluble in wustite above 850°C and that this alloying is accompanied by a substantial lattice contraction. This change in the lattice parameter was not evident in the X-ray diffraction patterns of wustite layers from the oxidation experiments;1,3 the lines were sharp even though a chromium gradient existed in the scale. The present paper describes gravimetric equilibrium experiments which delineate the boundaries of the chromium wustite single-phase field at 1000°C and define the changes in the oxygen activity and the lattice parameter of wustite as functions of chromium and oxygen contents. The lattice parameter data of chromium wustite obtained from these equilibrium and special quenching experiments differ considerably from those reported.9 Those for pure wustite show significant differences from the widely accepted data of Jette and Foote.10 Since the causes of these differences are not easily assignable, and since the literature contains many sets of data on wustite which if not in conflict are at best not in harmony, the experimental procedures are discussed in the present paper. EXPERIMENTAL Oxide Preparation. The specimens used in these studies were porous pellets compacted from high-purity (Fe,Cr)2O3 or Fe2O3 powders. These powders were prepared from electrolytic chromium (99.8 pct purity) and electrolytic iron purified by consumable-electrode, vacuum arc-melting processing (299.9 pct purity).11 The oxides were produced by standard analytical procedures: solution of the metals in acids (HC1, then HNO3 added), coprecipitation of the hydroxides (NHaOH), and filtering and washing these precipitates. Initial dehydration of the coprecipitated hydroxides was done in a porcelain evaporating dish heated by a Meker-type burner, final dehydration by firing in a recrystallized alumina crucible at 1000" to 1050°C for 20 hr in an electrically heated furnace. Spectrographic analysis detected the following impurities: silicon, 0.01 pct or less; aluminum, 0.001 pct to trace; manganese and copper, 0.0001 pct to none. Each of these levels is at least one order of magnitude lower than in commercially available CP grade ferric and chromic oxides. Fluorescence analy-

Jan 1, 1969

By W. D. Forgeng, R. E. Grace

The rate of copper corrosion in liquid lead was studied as a function of flow rate and temperature in a closed isothermal loop system between 350" and 500°C. Kinetic data were interpreted with the Nernst-Brunner equation and the Chilton-Colbum mass transfer analogy to heat transfer. Over the range of temperatures and flow rates employed the solution rate constant varied from 2 x 10-3 to 20 x 10-3 cm per sec. The rate constant was found to vary with the 0.76 power of the Reynolds number in the range 7500 < Re < 40,000. The results of this investigation indicate that the Cu-Pb corrosion process is controlled largely by diffusion across a boundary layer. particularly at the higher temperatures. The effective boundary layer for diffusion is found to be approximately three to four times smaller than the momentum boundary layer. CORROSION by liquid metals has long been a problem during melting, static containment, and casting. Recently, considerable emphasis has been placed on the understanding of liquid metal corrosion mechanisms in an effort to prevent mass transfer and eventual failure in liquid metal heat exchangers and in liquid-metal-fueled nuclear reactors. The present investigation was conducted to determine the relationships which exist between corrosion kinetics and hydrodynamic conditions in an isothermal loop containing a simple liquid metal-solid metal corrosion system. The Cu-Pb system was chosen for its simplicity and ease in handling. Previous isothermal Cu-Pb corrosion studies1-3 have been conducted in both static and dynamic systems but not under conditions which allow easy "scale-up" to engineering systems, such as liquid metal heat exchangers. On the other hand, most liquid metal loops which have been used to evaluate mass transfer rates4 have been driven with temperature gradients under conditions of natural convection and unknown flow rates. The primary contributions of this research are twofold: 1) to evaluate the design of a simple isothermal loop corrosion system and 2) to investigate liquid metal corrosion behavior under well-defined hydrodynamic conditions. MATERIALS AND EXPERIMENTAL WORK The apparatus used to measure the Cu-Pb corrosion rates is shown schematically in Fig. 1. The loop system consisted of 1) a reservoir made of Type 316 stainless steel containing a centrifugal pump and 2) stainless-steel tubing containing a removable copper test section. The copper test section was OFHC hard-drawn tubing, 11.0 0.05 cm in length and 0.775 ±0.005 cm ID. A Type 316 stainless-steel venturi meter* was inserted in place of the copper test sec- tion in order to determine the lead velocity as a function of pump speed at each temperature. The Cu-Pb system was chosen for this study because the solubility of copper in liquid lead is large enough to measure accurately but small enough that the diameter of the copper tubing was not changed significantly by corrosion. There are no intermediate phases formed in the system, and the solid solubility of lead in copper is vanishingly small so that back-diffusion cannot occur. Molten lead (corroding grade; 99.94+ pct Pb, 0.0015 max pct Cu) was charged from an auxiliary melting furnace into the system under an argon cover to minimize oxidation. The lead was then maintained at constant temperature by a stirred molten salt bath in which the loop was immersed to a depth just above the lead level in the reservoir, Fig. 1. The total volume of lead in the system was 320 2 cu cm.

Jan 1, 1969