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By D. R. Uhlmann, T. P. Seward, O. Chalmers

A magnetic field has been used to damp out liquid convection during the solidification of castings. Ingots of Al-2 pct Cu were poured from various sperheats (10" to 65°C) into a room-temperature graphite mold located between the poles of an electromagnet. The effect on ingot structure of varying the strength and time of application of the magnetic field was investigated, and the results are interpreted in light 01- current theories of ingot structure. In the solidification of alloy systems, thermal gradients in the melt and differences in density of the constituents are expected to produce convective motion in the liquid. The thermal convection caused by temperature gradients should be present during the freezing of both alloys and pure materials, while the solute convection caused by density differences should be of concern only for alloys. The possible influence of this natural convection on the structure of castings has been discussed by Ruddle,' Chalmers, and Tiller. More recently, an experimental investigation of such effects was carried out by Cole and Bolling. These workers took stationary molds containing lead- and tin-based alloys and. using a brine solution. quenched them from various superheats above their respective liquidus temperatures. When grids were placed across the mold diameter to suppress convection, the grid region was later observed to contain a larger percentage of columnar grains than other parts of the casting or than similar castings poured without the grids present. From thermocouple measurements, they found the temperature in the grid region to be higher than that in the region outside the grids throughout the freezing process, and concluded that convection should be an important mode of heat transfer in normal castings. In addition to such convection arising from thermal gradients or differences in density of the constituents, a further source of convective motion, which we shall call "momentum convection", may be particularly important in small (laboratory-size) castings. By this term we refer to the convective motion produced in the initial pouring process, a motion which is damped out as the linear momentum and angular momentum of the liquid are dissipated. Besides these sources of convection, which are present to some extent in all castings. external influences may also be effective in producing convective motion. Examples of such "forced" convection which have been discussed in the literature include stirring the melt, shaking the mold, rotating the mold, and so forth The purpose of the present study was to examine the effect of convection on the structure of castings poured into a cold mold. In this work, a magnetic field was employed to damp out the convective motions within the liquid, and hence control the extent of con- The effect of a magnetic field on convective currents in a conducting liquid is to induce eddy currents which oppose and damp out the convective motion. vection. The technique of magnetic damping was previously used by Utech and F1emings" in their study of convective effects on impurity banding and other substructure in alloy crystals grown unidirectionally from the melt. In their investigation, fields as small as 200 gauss were found to be effective in damping the convection currents which influence the banding. I) EXPERIMENTAL TECHNIQUE In the present study, alloys of A1-2 wt pct Cu were poured into a room-temperature graphite mold. The mold, in the shape of a circular cylinder, 2 in. ID, 2-3/4 in. OD, 5 in. inside height, and 5-1/2 in. outside

Jan 1, 1967

By Wei-Kao Lu, G. Bitsianes

An improved general rate equation for a one-ditnensional gas-solid system has been derived. Fov the veversihle interfacial chemical reaction, there are concentrations of gaseous reactant and product at the reacting zone to be considered. They have been calculated with the velations fuvnished by the constraints on the system, namely, quasi-steady state and equimolal counterdiffusion of the gases. The results of the diffusiori study of Evans, Watson, and ,Mason based on the "dusty gas" model have been applied here. The interfacial chemical reaction is taken as first-order with respect to the concentration of the gases involved. The equation has proper dependence on gas composition and on solid structure through the relative values of Knudsen and normal diffusivities. The existence of the total pressure gradient inside the specimen has been predicted and confirmed experimentally. In a previous communication' we introduced a general rate equation for gas-solid reactions by considering the contributions of chemical reaction at inter- phase boundaries and diffusion through the solid product layer simultaneously. These equations, for one-dimensional and spherical specimens, take care of the whole range continuously from purely diffusion control to purely chemical reaction control. In this paper we study only the one-dimensional system. The corresponding rate equation is reproduced here: Of the two terms on the right-hand side of Eq. [I], the first represents the contribution of interfacial chemical reaction and the second that of gaseous diffusion. The shortcomings of Eq. [I] are that in its derivation the interfacial chemical reaction was assumed to be irreversible and the diffusion rate of gaseous product was not considered. Any pressure effects building up within the porous media were also neglected. Evidently. these simplifying assumptions will limit the general applicability of these equations. The rate of reduction of iron oxide by hydrogen, for instance, is very sensitive to the concentration of water vapor in the main gas stream, as has been reported by cewan' and by Quets et a1.3 Furthermore, the gaseous phase at the reacting interface will contain an appreciable amount of the gaseous product of reaction. If this were not true, a sufficiently high concentration gradient for the outward diffusion of the gaseous product could not be maintained. With these shortcomings in mind, Eq. [1I cannot be rigorously ap-

Jan 1, 1967

By G. R. Love, M. L. Picklesimer

Aboue 950°C the Nb-Zr system consists of a completely miscible bcc solid solution, commonly called the phase. Between 950 and 600°C, and between 20 and 85 pct Nb, the phase deconlposes, after sunciently long times, into two bcc solid solutions. The pct Zr alloys are conveniently descibecl with T-T-T (time-temperature-transformation) curves having a nose at about 2 hr at 700°C. The reaction rate varies only slowly with zirconium content and negligibly with oxygen contanzination; it is speeded up by a factor of 10 to 15 by 90 pct cold ulork and slowed dou by n factor oj 10 to 30 by a two-hundrecljold increase in grain size. Nb-r alloys with compositions between 40 and 85 pct Nb have been the basis for the majority of commercially important superconducting materials. In part because of their commercial promise, more is known about these alloys than about most other high-field superconducting materials. At the same time, there is considerable disputed or incomplete metallurgical information. For example, although Rogers and tkins&apos; indicate a monotectoid reaction at approximately 600°C and a two-phase 01 + 0, field extending between 20 and 85 pct Nb and to a maximum of 95OGC, erhout&apos; has reported that this entire region would be a single homogeneous B were it not for oxygen contamination. Again, although it has been shown that relatively short-time heat treatments in the vicinity of 700CZ significantly improve the ability of short wire samples to carry high currents in high magnetic fields at 4.2K, these observations have never been fully correlated with the structural change or changes occurring during the anneal. We intend to investigate in detail the effect of metallurgical variables, including heat treatment, on the superconducting properties of hard superconductors. To verify that our experimental techniques are valid and to establish a relative standard against which other materials may be measured, we feel it advisable to know the behavior of the Nb-Zr alloys under a variety of processing conditions. As an initial step toward this goal, we have determined in detail the kinetics of the transformations in Nb-Zr alloys. EXPERIMENT A number of problems had to be solved before beginning any fruitful work on the reaction kinetics in this system. While solving some of these problems, either by chance or by design, small amounts of information were obtained about alloys containing 40, 50, 60, 65, 67, 70, and 75 pct Nb, bal. Zr. In addition, a large range of grain sizes and a range of temperatures considerably greater than the range indicated by Rogers and Atkins phase diagram were examined. We will, however, report in detail only the results obtained for the Nb + 33 pct Zr and Nb + 25 pct Zr alloys at three grain sizes, two levels of oxygen contamination, and the temperature range 550 to 950°C. These data are most complete, but the other data are sufficiently complete to indicate the kind and magnitude of the variation of the transformation kinetics outside this range. The first and most difficult problem encountered in this inquiry was one of sample homogeneity. When Nb-Zr alloys are arc- or electron-beam-melted on a cooled copper hearth, solidification is sufficiently slow that there is appreciable coring in the cast structure and a large variation of grain size across the button thickness. Both these factors significantly affect the apparent reaction rate in the system. A two-step solution to the problem was attempted; an arc-melting and drop-casting technique has been developed by conald that greatly reduces the as-cast grain size and virtually eliminates coring segregation. Ingots made in this way exhibited no detectable (3 pct maximum) zirconium segregation. Before it was evident just how good this technique was, we attempted to supplement it with rather long-time, high-temperature annealing of the cast ingots. This annealing was carried out in evacuated and sealed (seal-off pressures < 1.0 x 106 torr) quartz capsules lined with tantalum foil at 1400 to 1450 C for 8 to 72 hr. There were two principal effects of this treatment: the grain size increased to a fairly uniform 150 p, and the surface and all grain boundaries near the surface acquired a film of a second phase, tentatively identified as an oxide (possibly additionally contaminated with silicon). There was no evidence that this 1400 C treatment had affected the zirconium segregation. High-temperature annealing was subsequently used only for grain-size control, but anneals of longer than 4 hr at temperatures greater than 1000°C were performed in dynamic vacuums (pressure no greater than 1.0 x lo torr). Any contamination resulting from these treatments was well below the limits of detection of our techniques. All samples, as cast, were cold-swaged to at least 85 pct reduction in area. The samples called cold-worked were tested as swaged. The minimum re-crystallization anneal for these alloys was about 12 hr at 1050 C; this produced an equiaxed grain diameter of about 4 to 8 P. Annealing for 4 hr at 1450°C produced a grain size of about 80 to 150 p; and annealing for 4 hr at 1650aC, close to the melting point of many of these alloys, produced a grain size of 0.5 to 1.0 mm. At all temperatures, the larger grain size was

Jan 1, 1967

By Robert D. Pehlke, Robert G. Blossey

The solubility of nitrogen in liquid binary and ternary Fe-Ni-Co alloys has been measured by the Sieverts&apos; method between 1550°and 1700°C. Solubility data and standard free energzes and enthalpies of solution for nitrogen in the alloys are presented. Interaction parameters are discussed and presented for binary and ternary alloys. MOST of the studies of nitrogen solubility in liquid metals have been directed toward the dilute alloys of iron. Several of these investigations have included measurements of the nitrogen solubility in Fe-Ni al10s&apos;- and in Fe-Co alloys.435 There has been some work, however, that has extended across the e-i-" and F-CO" binaries. This investigation was undertaken to determine the nitrogen solubility in both binary and ternary alloys of the Fe-Ni-Co system. It was also hoped that the differences between earlier studies might be resolved. EXPERIMENTAL METHOD This investigation was made using a Sieverts&apos; apparatus described previously." The nickel (99.85 pct) and cobalt (99.9 pct) were obtained from Sherritt-Gordon Mines, Ltd., and the iron (99.95 pct) was Fer-rovac-E obtained from Crucible Steel Co. Recrystal-lized alumina crucibles were used throughout the entire investigation with no evidence of crucible-melt reaction. Melt temperatures were measured with an optical pyrometer and the temperature scale calibrated against the melting points of the three pure metals. The emissivity of the melt was assumed to be a linear function of composition for all alloys, as has been shown for Fe-Ni alloys.lZ The emissivity of the pure metals at 1600°C were taken as 0.43 for iron, 0.44 for cobalt, and 0.45 for nickel. Using these emissivities, the trans mis sivity of the system was found to be 0.51 i 0.01. The Sieverts&apos; method was used for this study and followed the procedures outlined previously.l&apos; The individual metals were weighed to give about 100 g of alloy. The alloys were melted in the crucible under a partial pressure of argon. The system was evacuated, and the "hot volume" was measured with argon. To avoid the errors caused by vaporization, the melt was held under vacuum only long enough to ensure that all of the gas in the system had been removed. The influence of any small amount of vaporization on the "hot volume" was shown to be negligible by measuring the "hot volume" after a run. This measurement agreed with that made at the start of the run within the implicit error, 0.2 cc, caused by the limitations in accurately reading the buret. The solubility-pressure relationship was measured in the pure metals and in several alloy compositions throughout the ternary system. These measurements were made by admitting measured amounts of nitrogen to the system, and then determining the equilibrium nitrogen pressure above the melt. This method has the distinct advantage of higher accuracy, particularly at lower pressures, than measurements made by withdrawing gas from the system to reduce the pressure after determining the solubility at 1 atm nitrogen pressure. This latter method has a practical lower limit of about 0.4 atm where an increased error is encountered because the buret must be emptied to permit further measurements at lower pressures. By determining the relation between apparent solubility and pressure, it was possible to make a good estimate of the initial nitrogen content of the metal from the intercept of the solubility curve extrapolated to zero pressure.11 DISCUSSION The solubility data corrected to 1 atm nitrogen pressure are summarized in Table I. The reported solubility has been corrected for the initial nitrogen content of the alloys. The initial nitrogen contents fell between 0.0002 and 0.0010 wt pct, and were lower in the iron and nickel than in the cobalt. Sieverts&apos; law was obeyed in all alloys at pressures up to 1 atm. Examples of this behavior are shown in Fig. 1. The reaction for solution of nitrogen is Taking the standard state as 1 wt pct N in the alloy and the reference state as nitrogen at infinite dilution in the alloy, and noting the adherence to Sieverts&apos; law, K becomes the solubility of nitrogen in the alloy at 1 atm pressure. Thus the solubility data of Table I were used directly to calculate the standard free energy for the solution reaction. These results are also presented in Table I. The enthalpy of solution is also summarized in Table I as calculated from a form of the van&apos;t Hoff relation: Iron-Nickel System. The data for the solubility of nitrogen in liquid Fe-Ni binary alloys is presented in Fig. 2 along the with data of aito, Schenck et al.,&apos; and Humbert and 1liott.l&apos; The data for studies of nitrogen solubility in Fe-Ni alloys containing less than 20 pc t i&apos;- are not presented in Fig. 2, although they are in good agreement with the present work. The results of this study are in good agreement with Schenck

Jan 1, 1967

By C. M. Sellars, F. Maak

Electvomotie -force measurements hazle been made on ten Au-Ni alloys at temperatures 7754 825O, 900O, and 935°C using galvanic cells with solid electrolyte. Partial and ivtegral thermodynamic functions are derived from the determined activities. which show la9,ge positive deviations jvom Raoult&apos;s law. The enthalpies of mixing- are in close accord with calorinletric data and are of comparable accuracy. The results are used to determine the miscibility gap and the spinoidal curL1e, and are qlalitaticely interpreted in terms of the large size difference and electvonic interactions between gold and nickel. Tabulated nalues of the actielities and partial and inteqal free energies, entropies , and enthalpies of mixing are given in the appendix. The Au-Ni binary alloys are of particular interest thermodynamically as despite the large size difference between gold and nickel atoms they have a simple phase diagram.&apos; This shows complete solid solubility above a miscibility gap with a maximum at about 71 at. pct Ni and 810°C. Activity measurements (over a range of temperature) have been made previously on this system using an electrolytic-cell method with a liquid chloride eletrolyte. The accuracy of this data has, however, been queried3&apos;4 as it leads to values for the enthalpy of mixing which are too high when compared with calorimetric measurements.46 Also, the entropy of mixing is too high when compared with the values derived from specific-heat measrements. It was therefore considered worthwhile redetermining the activity data using a galvanic cell with a solid electrolyte (0.85 ZrO, 0.15 CaO). This method is based on a technique introduced by Kiukkola and aner&apos;&apos; and has been used to determine the thermodynamic data for Cu-Ni alloys.&apos; THE ELECTROLYTIC CELL The cell used to determine the activity of nickel in Au-Ni alloys was: The cell reaction, which is discussed for a similar cell by Rapp and Maak, gives a direct measurement of the activity of nickel in the alloys as where aNi(alloy) is the activity of nickel in the alloy, 3 is Faraday&apos;s constant, E is the measured electromotive force, R is the gas constant, and T is absolute temperature. For the valid application of this type of cell the arrangement must be ther modynamic ally stable, which means that: 1) The free energies of formation of the oxides fulfill the relation 2) The vapor pressures or dissociation pressures of each component must be so small that during the time of the experiment the amount of any material transported by the gas is negligible. 3) Side reactions which change the alloy composition must be negligible. These reactions are possible both with the surrounding gas atmosphere and with neighboring solid material. The first two conditions are fulfilled by the above cell.&apos; The third condition is approached by care in the experimental technique. The factors which control the attainment of equilibrium in this type of cell have been considered by Rapp and aak, who conclude that metallic diffusion in the alloy is the rate-control ling step. A lower temperature limit for the practical application of this cell is therefore set by the condition that equilibrium must be attained in reasonable times. EXPERIMENTAL MATERIALS AND TECHNIQUE The starting materials were mint gold (99.99 pct Au) and Mond nickel (99.9 pct Ni). Alloys, nominally 5 at. pct Ni and then each 10 at. pct across the system, were produced by vacuum-levitation melting compacts of mixed drillings of the pure metals. The nickel used for the reference tablets in the cells was melted in a similar manner. The alloy ingots, cast in boron nitride molds, were cold-forged and

Jan 1, 1967

By V. B. Tare, H. Schmalzried

The use of solid electrolytes for determining kinetic paraneters at elevated tevnperatures is pointed out. The reaction rate constant k1 of the phase-boundary reaction during oxidution of iron to wiistite by CO2-CO gas mixtures has been deternined between 850 nnd 975C, using ZrOz(+CaO) as an electrolyte. Values are between 1.4 x 10-a and 5.2 x 10 ole per sq ctn atm. The tzain difficulty is due to mixed potentials arising from side reactions at the electrolyte inteyface. In a number of papers the calcium-doped zirconia electrolyte has been used for the determination of thermodynamic data from measured differences in oxygen activities (or potentials) between two electrodes. The purpose of this note is to suggest the use of this solid electrolyte for kinetic measurements as well. The principle can be seen from Fig. 1. A thin and compact phase II (electron conductor) is fixed on a plate of gas-tight, polished ZrO2(+CaO) (I), which separates two compartments with different oxygen potential. p, is a constant reference pressure of oxygen (1 atm). The electromotive force of this galvanic cell is given by E = RT5 In pep, and pe is the oxygen partial pressure at the interface electrolytephase 11. If phase I1 is in equilibrium with the surrounding gas phase, p, = DR. If pg changes sud- denly to a value pi, p, and therefore the electromotive force, E, change as a function of time according to the phase-boundary reaction rate at the gas phase I1 interface and the transport processes inside phase 11. It is assumed that local equilibrium is established at the boundary electrolytephase 11, that the gas phase shows no concentration gradients, and that the con-

Jan 1, 1967

By C. A. Wert, M. G. Coleman

The Zener relaxation in alloys in the a! solid-solution region of the Cu-Ni-Zn ternary system has bear investigated. Of the binary solid solutions that bound this region, Cu-Zn and Ni-Zn exhibit measurable Zener peaks whereas Cu-Ni does not. At constant atomic percent copper, the Peak height drops uni.forinly from the value in the Cu-ZTL binary to zero in CIA-Ali. The cariation of peak ternperatuve with composition is linear. At constant atomic percent zinc, the peak height in the ternary alloys goes through a large maximum as compared with the binary values. The temperature of these peaks varies smoothly with composition. The half-width of the peaks in the ter nary alloys, however, are much larger than those in the binaries. A large enhancement of the relaxation strength of the Zener relaxation in ternary Au-Ag-Zn alloys as compared to the relaxation strengths in Au-Zn and Ag-Zn binary alloys was observed by Firson and ert.&apos; Since this effect was unexpected, the present study was devised to investigate whether enhancement of the Zener relaxation in ternary alloys is a general feature or is particular to the Au-Ag-Zn system. We have chosen the Cu-Ni-Zn alloy system for this investigation. Measurable Zener relaxations are observed in both the Cu-Zn and the Ni-Zn binary systems, but not in the Cu-Ni binary system. A large solid-solution region extends to large concentrations of zinc, making it possible to vary composition of the alloys over a wide range without crossing phase boundaries. EXPERIMENTAL PROCEDURE Two series of alloys were prepared. the first at constant atomic percent copper, the second at constant atomic percent zinc. The compositions of these alloys are shown by the circles in Fig. 1. The alloys were prepared by melting the individual components, each of which had previously been vacuum-melted, in an evacuated quartz capsule in an induction furnace at 1500 C. The capsules containing the molten alloys were quenched in water to reduce coring. Any individual melt which exceeded 0.001 pct weight loss was discarded. The ingots were swaged to a 50 pct reduction of area and annealed for 1 week in an evacuated quartz capsule to aid homogenization. The alloys were then

Jan 1, 1967

By W. M. Yim

Experimental results are presented which indicate that transverse striations in horizontal zone-leveled Bi-Sb alloy crystals are due to irregular growth rate resulting from thermal fluctuations in the melt (Iring gowth. Thc thermal fluctutations arose from two different sources. The first type was brought about by periodic fluctuations in the furnace temperature. The second type can be attributed to turbulent therrrol conlcclion in the trzelt near the solid-liquid inteyace. Tile arrzplitlcde ond fvequency of the tetiperaticre fluctlrations vesultity from llle lhevnal con1,ecrrell. The striation spacings in Lhe crystals covvelale well with the periodicity 0.f the tempevature flueluatiors. Altliough the strialiors represenl corrlpositiozul inhoiHogeneity oh a rzicroscule, less than f.z cil. be1 S6 in Best&apos;s as deterrirzed by electron-pro be chalq&apos;sis, the slriations roerre fbund to ILUL&apos; no rrleusuanble effect on electical vesistirity rwr on weak field macgnetoresistance of. the Bi-Sb a1lu.y in the ternpevutue ),unge 4.Polo 300°K. DURING the course of an investigation on the horizontal growth of semimetals,&apos; it was found that crystals of Bi-Sb alloys contained many closely spaced parallel arrays of striations. These striations occurred perpendicular to the growth direction and parallel to the solid-liquid interface. We shall refer to them as transverse striations, or just striations&apos;&apos;, to distinguish them from lineage substructures or longitudinal striations which form parallel to the growth direction and have been known to be associated with cellular structures.&apos; Similar transverse striations have been reported previously to occur in other materials prepared by horizontal growth: metals,4 semiconductors,5 as well as their alls. - Various methods of crystal preparation have apparently little effect on the occurrence of the transverse striations. They form whether the crystals were grown by the vertical Czochralski technique, withe1&apos; or without&apos;3- rotation, or by the horizontal zoning methd.- Thus, the transverse striations are not limited to any one class of materials, nor to any particular method of preparation. It is likely, therefore, that all of the observed transverse striations may have some common cause. Previously, workers agreed that periodic changes in the growth rate bring about the striations. However, no agreement exists as to the origin of the growth-rate fluctuations. Some attributed the discontinuous growth to a purely external cause, such as fluctuations in the furnace temperature, jerky motions in the crystal pulling mechanism, or a nonsymmetrical temperature distribution in the melt (in the case of crystals grown by the Czochralski technique with rtation). Others looked for the cause in some fundamental property of the growth process itself. For instance, a certain degree of supercooling is required to initiate growth from the melt. But, with further growth, the degree of supercooling decreases because of the liberation of the heat of solidification at the solid-liquid interface. Thus, crystal growth would be brought to a halt until sufficient supercooling is resotred and the cycle begins again.3&apos;11 According to this model, periodic fluctuations in the melt temperature should exist at the solid-liquid interface. Since the periodic fluctuations in growth rate would result in changes in the segregation coefficient of solute atoms, crystals containing the transverse striations may, in some cases, show a periodic impurity fluctuation along the length, resulting in a degradation of electrical properties. The resistivity striations in doped germanium&apos;9-10 or lnsbB are well-known examples of this microsegregation. The present work was undertaken to explain the exact origin of the transverse striations, and to assess the extent of their effect on chemical homogeneity as well as on electrical properties of Bi-Sb alloy crystals. Results from our previous study of the crystal growth of Bi-Sb alloys1 indicated that the transverse striations may arise from the temperature fluctuations in the melt during growth. This paper will show that the melt temperature fluctuations are indeed responsible for the occurrence of the transverse striations. I) EXPERIMENTAL Although the transverse striations have been observed in all slow-grown Bi-Sb alloys across the entire compositional range, we selected a composition, Big3Sbs, for the present study in view of the extensive data available on the crystal growth of this alloy from a previous study.&apos; High-purity bismuth and antimony, both a 6-nine grade by the manufacturer&apos;s emission spectrographic analysis, were used throughout. Independent mass-spectrographic analysis showed, however, that the starting materials were more nearly a 5-nine grade. each containing metallic impurities of approximately 10 ppm atomic. In zone-leveled Big5Sb5 alloys, the total metallic-impurity content was slightly lower, about 7 ppm atomic, indicating that some degree of purification was achieved during the growth. None of the electrically active impurities, such as tin and lead (acceptors) and tellurium and selenium (donors), were present in significant quantity in undoped Bi95Sb5. Typical analysis of the undoped Bi95Sb5 alloy is shown in Table I. Nonmetallic impurities, such as carbon and oxygen, were detected, sometimes as much as 100 ppm, in both the starting materials and the zone-leveled alloys: but the data were only qualitative. Temperature fluctuations in the melt were monitored over 1 or more days by means of a 5-mil chromel-

Jan 1, 1967

By A. Raman

The Nb-Co system was nuestigated in the range 10 to SO at. pct Co with X-rays. A pt phase with the W6Fe.r-type structure occurs in the system between 46 and 52 at, pct Co. Its unit-cell dimensions are nearly identical to those of the p Phases found in the Nb-Fe and Nb-Ni systems. Two Laves phases, one having the MgZnz-type structure and the other the MgCuz-type structure, already t-eported in the literature, are found to exist in the system. The ,l.IgZnz-type phase occurs between 62 and 64 at. pct Co. A MgNi2-type Laves phase, reported in the literature, is no! obtained. A binalry phase is found to exist belozv I000C around 82 at. pct Co. THE cobalt-rich side of the system Nb-Co has been repeatedly investigated by previous inestiators" and the following intermediate phases are known to occur: NbCo, which crystallizes in the MgCu2-type structure and Nbc03,&apos; reported originally by Wall-bam, which has the MgNiz-type structre. Jordan and uwez&apos; as well as lliott&apos; were unable to find the MgNiz-type phase. Two phases, designated as x and y, were reported by Saito and eck.&apos; The phase x was inferred to have a narrow composition range near 77 at. pct Co. No published work is known to the author which reports the investigations in the niobium-rich portions of the system. This paper presents the results of an investigation in the Nb-Co system between 10 and 80 at. pct Co. EXPERIMENTAL PROCEDURE Two or three grams of the alloys under investigation were prepared using niobium (99.9 pct +) and cobalt (98.8 pct + with 0.14 pct Fe and and 0.03 pct C) in a tungsten-electrode arc furnace under commercial argon atmosphere. They were then wrapped in molybdenum sheets and annealed for a period between 5 days and 1 week at 1300°C in high vacuum (10-" orr) or in evacuated quartz amules for 2 weeks at 1000°C. Powders of -325 mesh size were prepared for X-ray work by crushing and grinding the specimens. Subsequent reannealing of the powders was not undertaken since most of the alloys were brittle and broke easily. X-ray powder patterns of the as-cast and annealed samples were prepared in a Siemens cylindrical camera (57.3 mm radius) with Cr-K, radiation. A Siemens diffrac to meter was used to get the X-ray patterns of some new phases. Metal log raphic examination of the alloys supplemented the X-ray findings. RESULTS The results of the X-ray and microstructural analysis Of the alloys are in in Table I. The lattice parameters of the phases are listed in Table 11 for quick reference. A set of micro photographs in Fig. l(n) to (j) show the microstructures of some alloys. A probable equilibrium diagram is drawn in Fig. 2

Jan 1, 1967

By Ashok K. Kakar

THE occurrence of superplasticity in Al-Zn alloys is of interest because of its possible industrial exploitation.&apos; The eutectoid composition (78Zn-22A1) has been the most extensively studied;&apos;-= neck resistant flow and high strain rate sensitivity of flow stress (characteristic of superplasticity) are associated with a micron-size grain conferred on the alloy by an homo-genization and quench.5&apos;6 Compositions away from the eutectoid have received comparatively little attention, especially from the viewpoint of relating the structural

Jan 1, 1969

By H. Morgolin, M. A. Greenfield, P. A. Farrar

In attempts to correlate mechanical properties with microstructure, it is desirable to determine the effect of ß grain size. Determination of 6 grain size is not a problem where a has precipitated at ß grain boundaries. However, in alloys which have been processed to produce an equiaxed a +ß structure the ß grain size is difficult to determine because ß grain boundaries do not etch. The ß grain size can sometimes be laboriously determined by searching for grains which have some a! outlining the 6 grains. This difficulty of ß grain size determination in equiaxed a + ß alloys can be overcome by heating below the ß transus temperature for a short time and water quenching. Fig. 1 shows the starting equiaxed a + ß structure of the Ti-5.25A1-5.5V-0.9Fe-0.5Cu alloy used in this investigation, and Fig. 2 shows the microstructure of the same sample water-quenched after heating 1 min at 1675"F, which is 25°F below the 0 transus. The heavily etched microstructure consists of some equiaxed a! in a structure showing considerable amounts of transformed ß. The ß grain

Jan 1, 1969

By George L. Montgomery

In a recent article Heckler, Elias, and woods1 have described an automatic computer technique for plotting of pole figures. To anyone who has constructed pole figures manually from raw X-ray data, the development of computer plotting techniques has been a very welcome development. The purpose of the present note is to describe an alternative computer plotting method which, if somewhat less precise than the method described by Heckler et al., has the advantages of being faster and of not requiring the availability of a plotter. The plot is made directly by the printer of the terminal system and, by its nature, has a good deal of visual impact. Each character of output symbolizes a level of intensity. For example the numerals 1 to 9 might represent intensities referred to some reference obtained from a randomly oriented sample. Should more levels be required (this is seldom necessary) alphabetic or other characters may be used in addition. When these are arranged in the proper fashion, the result is a pole figure such as is shown in Fig. 1. It is the purpose of the computer program to transform the data and carry out the arrangement in a suitable manner. The computation is carried out on a line by line basis in order to reduce the amount of storage required and thus keep the program "small". It is, thereby, well within the limitations of the time-sharing systems which are becoming increasingly available. The inaccuracies introduced are slight and the plot can easily be made as precise as the technique used to collect the data. Comparison of pole figures produced by this method with those constructed manually shows a high degree of equivalence. To the present, the technique has been applied to reflected X-ray data only. X-ray data are collected in a manner identical to that described by Heckler et al. That is, as the goniometer rotates the specimen, a series of counts, accumulated over a preset time, is recorded. The method by which the proper symbol, representing an intensity level, is assigned to each print position is up to the ingenuity of the programmer. Perhaps the simplest method is to section the stereograph in the fashion of a polar net, and to assign all print positions lying within each segment a symbol representing the level of intensity recorded at the data point nearest to the center of the segment, see Fig. 2. The number and arrangement of the segments are selected to conform more or less with the number of accumulated counts and the geometry of the goniometer path used to collect them. Since the angular distance between accumulated counts is usually not infinitely controllable, it is impossible to locate one reading within each segment and, at the same time, maintain symmetry in the sectioning of the stereograph. This latter requirement is essential to keep the computer program simple and flexible. As an expedient it was found that the number of data points could be increased to conform with the number of segments, with very little loss of

Jan 1, 1969

By G. R. Love

i\ program has been written which allows fully automatic conversion of data for X-ray intensity, as a function of time, to finished conventional pole figures. The program accepts input data in the serial order in which they are taken and is therefore immediately compatible with automatic data-acquisition devices. From these data taped instructions are prepared for the Calcomp plotter to construct ink-on-paper drawings. Because both Siemens and Norelco pole figure goniometers are used in this laboratory, the program was written for pole figure data obtained from one or more interpenetrating spiral scans during which both the polar angle, @, and the equatorial angle, a, are varied simultaneously and continuously. The reference direction for a scan, that is the point @ = 0 deg, may be chosen coincident with either the normal direction (N.D. figures) or the rolling direction (R.D. figures). In either case the plotted figures are drawn with the transverse direction (a = 0 deg) at the right and the rolling direction at the top. The full, circular, pole figure is drawn as two semicircular figures labeled "front side" and "back side". As presently constituted, the program will also accept data from circular scans taken at constant values of @. In every case the angular coordinates of each intensity entry are generated in the computer from a relatively small number of auxiliary data. The X-ray intensity data are corrected for background scattering by direct subtraction of the intensity measured with 28 set appropriately "off" the Bragg angle. It is possible to enter this correction as an additional spiral scan through the a, @ space; because the background correction does not normally vary rapidly enough to warrant this detailed a determination, the background corrections are entered as one or more auxiliary data. All data are normalized to a multiple of random intensity. The data taken in this laboratory for N.D. figures are normally taken in a reflection geometry from from sheet samples and do not extend beyond <p = 75 deg; for these data random intensity must be determined from separate experiments and entered as auxiliary information. When the auxiliary information is not available, a number is chosen to give intensity values normalized to a scale of 1 to 10. In this laboratory, R.D. figures are based upon hemispherical samples for which data are taken out to @ = 90 deg; for these data random intensity is calculated by direct numerical integration of . sin @ d@ using the trapezoidal rule and the background-corrected values of the input data. Points necessary to the construction of the pole figure are identified by simple linear interpolation between adjacent data points to determine the loci of contour lines. Points lying on a given contour are connected to one another with straight-line segments and the search-calculation-drawing sequence is patterned to assure that different contour lines do not cross, that a single line does not branch, and that lines do not end in space. However, so that there be no ambiguity in the data presentation, all contour lines end at the limits of the input data. Since the curves are constructed of straight-line segments, they are not continuous in their derivatives. However,

Jan 1, 1969

By Fritz Wald, Martin Weinstein, Herbert E. Bates

ONE of the methods for preparing a fiber-reinforced composite is that of directional solidification of a eutectic melt. Its major drawback lies in the fact that the matrix in this case is a pure constituent (or a terminal solid solution of fixed concentration) and the ratio of fiber to matrix volume is fixed. Only very few, if any, pure metal matrices possess technically useful properties, and the necessity for alloying is the inevitable consequence of this fact. Nevertheless, structures similar to binary eutectic ones can be obtained in higher-order systems by pseudoeutectic reactions of a type where crystallites and a solid-solution matrix are simultaneously precipitated from a liquid.1"3 Trials to solidify such alloys directionally—the matrix consisting of a solid solution of chromium, nickel, and silicon and the reinforcing phase being Cr3C2— will be reported elsewhere.4 This note describes constitutional studies carried out primarily to determine -the position of the pseudoeutectic and further to insure that no undesirable reactions between the reinforcing phase and components of the matrix occur in the solid state at elevated temperatures. In the investigation it was specifically desired to reinforce a matrix which is as close as possible to the 80/20 Nichrome composition with Cr3C2 to insure good oxidation resistance and improve the strength at high temperatures. No konstitutional information on the quaternary C-Cr-Ni-Si svstem in the range of interest was found in the literature. Nevertheless, the two most important ternaries c-cr-Ni5 and have been completely investigated. On C-Cr-Si some investigations have been conducted,7"9 and C-Ni-Si was studied with a few alloys in the course of the present investination 9 Eight alloys were prepared to investigate the changes in the constitution of the ternary C-Cr3Ce-yNi eutectic5 with silicon contents up to 10 wt pct. Five alloys were made with varying chromium and carbon contents around compositions containing -60 to 70 wt pct Ni and 5 to 6 wt pct Si. The latter alloys were designed to locate the y(Ni-Cr-Si-C)-Cr3C2 pseudoeutectic reaction and to determine the maximum chromium content in solid solution compatible with a two-phase equilibrium between y and Cr3C2 only. The alloys were prepared from electrolyte nickel, semiconductor-grade silicon, high-purity chromium (99.999 pct pellets), and semiconductor-grade graphite. They were melted inductively in high-purity alumina crucibles under flowing argon. Twenty-gram charges were prepared and investigated by optical microscopy (including hot-stage investigations), X-ray powder methods, and electronmicroprobe analysis. The alloys were studied in the as-cast condition and also after a homogenization annealing treatment of 48 days at 900°C in evacuated quartz ampoules. The structures of all alloys based on the ternary eutectic plus silicon in the as-cast state consisted generally of an inhomogeneous solid solution and at least two other phases. Annealing of the alloys showed that the solid solution was homogenized but that an incomplete solid-state reaction had taken place in all alloys with silicon contents over 5 wt pct. This reaction is clearly visible in Fig. 1 around the large Cr3C2 crystals (gray areas). Below this concentration, the alloys consisted of a homogeneous matrix and precipitates of Cr3C2 plus graphite, Fig. 2. The Cr3C2 was entirely unreacted here. From these observations and subsequent X-ray and microprobe investigations, it was deduced that the

Jan 1, 1969

By O. P. Arora, I. L. Caplan, H. von E. Doering

ThE interpretation of X-ray and electron diffraction data obtained in plastic deformation studies of hcp a titanium requires knowledge of angular relationships between crystallographic planes and directions. Rarey el 01.&apos; have calculated both interplanar angles and angles between directions for a number of c/a ratios. This information, although useful for approximate applications, does not provide exact data for specific hcp metals. Recently, Hu2 has tabulated interplanar angles specifically for hcp titanium. The present study augments the existing data on titanium by providing the angles between plane normals and rational crystallographic directions in addition to interplanar and interdirectional angles. These angular relationships were calculated on an IBM 360 Computer using a Fortran IV program.* Cal-

Jan 1, 1969

By Y. Nakada, E. J. Fasiska, A. S. Keh, L. Zwell

DURING an investigation of solid-solution hardening of nickel by carbon,&apos; we found that there were no reliable data on the dilating effect of dissolved carbon on the unit cell of nickel. Bernier2 reported an increase in lattice parameter of nickel (3.523A) when an unknown amount of carbon was introduced into solid solution (3.536A). Similarly KG, Tsien, and Misek3 found an increase from 3.523 to 3.531A when nickel was carburized. strong4 studied the variation of nickel lattice constant as a function of dissolved carbon. However, in his case carbon was introduced into nickel by solidifying the melt at 65 kbar. Therefore, his carbon concentrations were much above the highest equilibrium solubility limit5 (2.7 at. pct C at 1 atm). Knowledge of the lattice mismatch between solute and solvent is essential in understanding the mechanism of solid-solution hardening. Therefore, we decided to determine the dilation of the nickel lattice by carbon under the more usual conditions of atmospheric pressure. The material used was Inco Electrolytic Nickel of 99.95 pct purity, as specified by the supplier. The impurity contents in wt pct were: Fe, 0.01; Cu, 0.01; Co, 0.03; 0, 0.005; C, Si, S, N, trace. To this base material various amounts of AUC-grade high-purity carbon were added during vacuum induction casting. Ingots, 2 in. in diam, were heated in a muffle furnace at 1000°C for i hr., hot-rolled to 1/2-in. thickness, and quenched into brine. All ingots with carbon concentration greater than 0.98 at. pct were enclosed in a cast iron box during the heating to minimize decar-burization. Small pieces were then either swaged down to 0.028-in.-diam wire or cold-rolled to 0.010-in.-thick sheets. After the final cold reduction in area of 50 pct, the specimens were recrystallized by heating in evacuated capsules at 1100°C for 60 to 80 sec and then quenched into brine. The final grain size was 50 to 100 µ. The carbon contents of the alloys, Table I, were determined by a combustion method

Jan 1, 1969

By Y. Mishima, R. Shiromizu

THE equilibrium y phase in Cu-Be alloys forms by discontinuous precipitation, the new phase nucleating at the grain boundaries and growing into grains on both sides of the boundary. When the alloy is aged above 500°C, however, growth may take place into only one of the grains.1&apos;2 In A1-Ag alloys it is known that the precipitate has the same orientation as the grain in which no growth takes place.3, 4 This was confirmed in the present investigation on a Cu-Be alloy. A Cu-1.79 wt pct Be alloy was solution-treated at 810°C for 2+ hr, quenched into water at O°C, and aged at 600°C for 1 hr in a salt bath. The specimen was thinned by chemical polishing and electropolishing at room temperature in a solution of H3PO4 saturated with CrOs. The foil produced was examined in a JEM 150 electron microscope operating at 150 kv. Fig. 1 shows precipitates growing on only one side of the grain boundary. The black platelike precipitates were identified as the y phase. Electron dif-

Jan 1, 1969

By H. I. Aaronson, W. L. Winterbottom, G. M. Pound

On the basis of a statistical thermodynamic treatment of the data of smithz2 on the activity of carbon in austenite, a Darken and smith23 deduced that the interaction energy, wy, between carbon atoms occupying nearest-neighboring interstitial sites is repulsive. Aaronson, Domian, and pound 24 (ADP) have applied two different statistical thermodynamic analyses to the same data. One analysis, a composite of the treatments of Darken and Smith,23 Speiser and Spret-nak," and Kaufman, Radcliffe, and Cohen,26 primarily takes account of the positional entropic effects of wy in dilute solutions. The other, due to Lacher 27 and Fowler and Guggenheim," is also applicable to more concentrated solid solutions. The equations which both analyses produce for a,, can be rearranged so that, when In a,, is plotted against the appropriate function of the carbon content of the austenite, the plot will have a slope of unity when the correct value of wy is employed. Since no other constant need be simultaneously evaluated in order to make this determination, ascertaining the most probable value of wy from Smith&apos;s data on the bases of these analyses was an elementary problem in least-squares statistics. ADP demonstrated that the wy&apos;s obtained from both analyses vary with temperature in a statistically significant manner. McLellan, Gerrard, Horowitz, and sprague 29 (MGHS), on the other hand, have recently made a new statistical thermodynamic study of a,, and have concluded from this study that wy is independent of temperature. The equation which they derived for a,, is: where 0 = ratio of the mole fraction of carbon atoms to that of iron atoms, z = number of sites from which occupancy is excluded by the presence of a carbon atom and the repulsive character of its interaction with nearest-neighboring carbon atoms (z = zb in Ref. 24), and x = a geometric parameter taking account of overlapping of the exclusion shells of nearby carbon atoms. z is 1 when wy = 0 and 13 when wy = Q. For a given value of z there is a definite value of X . In the absence of an equation connecting z and X, MGHS computed geometrically the value of x at several integral values of z; x increases from 0.47 to 8.67 as z is increased from 2 to 5. MGHS fitted Eq. [I] to the a,, data of Ellis, Davidson, and Bodsworth30 at 925° and 1050°C and to the data of smithz2 at 1000°C. Confining z to integral values in the range 4 to 6, and also somewhat restricting AG, the values of z, X, and AG were sought which would minimize the average root mean square percent deviation, D, of the calculated a,, values from those obtained experimentally. Finding that D was almost always smallest when z = 5, they concluded that z is independent of temperature. Since:23, 26 where R = gas constant and T = absolute temperature, and w,, was considered to be similarly invariant, this statement cannot be strictly true. The temperature range employed, however, was small and the interval between the values of z tested was sufficiently large so that the results could still be consistent with a constant The statistical treatment of the a,, data applied by MGHS is clearly quite approximate. Since more than three values of a,, are available at each temperature, z, and X, and AG have actually been over deter mined, rather than underdetermined as their treatment implies. In order to make more complete and exact use of the a,, data, we shall employ the Legendre Method of Least Squares, as described by Whittaker and Robinson. This technique permits conversion of the overdetermined system of equations produced by the substitution into Eq. [I] of the available pairs of a,, and 0 data at a given temperature into an even determined system. Solution of the latter system yields the most probable value of each of the three constants. This procedure will allow a statistically rigorous test to be made of the conclusion drawn by MGHS in respect of the temperature dependence of In order to obtain linear iiequations of conditions" from Eq. [I], the exact values of the three unknown constants are replaced by G/RT = =/RT + y, where z, i, and aG are estimated values of the constants. This allows the conditional equations to be written in the form:&apos;l where fi -f6, i, =/RT) = the right-hand side of Eq. [I] for a given pair of ayi and values. When applied to Eq. [I], these relationships become: The i equations of condition are reduced to three "normal equations" in the manner discussed by Whittaker and Robinson. The normal equations are then solved for a, ß, and y. Both of these operations are most conveniently performed by means of the computer technique of Winterbottom and Gjostein.32 This technique was used iteratively until the value of 0 (the most sensitive of the three correction factors) became 10.01. (Until they became small, a, 8, and y

Jan 1, 1969

By D. A. Woodford

A number of observations have now been reported where the steady-state creep rate is apparently linearly dependent on the applied stress at high temperature and low stresses. This results in a creep rate greater than that predicted by extrapolation of high-stress data and has obvious practical implications. However, some of these observations are open to question. For example, the analysis by Harris and Partridge17 of the data of Greenfield et a1.18 was dependent on strain rates which, according to the original authors, were too low to be measured. Dr. Bernstein appears to have demonstrated a linear stress dependence at low stresses in two zirconium alloys. There are, however, a number of discrepancies in his treatment of the data and the subsequent theoretical analysis which require clarification. 1) It is incorrectly stated that steady-state conditions are revealed by a slope of unity on a plot of log i vs log (time). This objection is trivial if the author meant to say a slope of zero, although it is unclear how subsequent extrapolation was made to determine the steady-state creep rates at low stresses for the zircaloy-2. If the plot used was actually log c vs log (time), it is unlikely that a slope of unity would represent a constant creep rate. A plot of log (c - co) vs log (time), where c0 is the extrapolated intercept sf the steady-state creep rate on the strain axis, would have a slope of unity during steady-state creep. However, eo cannot be determined unless is is already known. 2) The author chooses to interpret his results based on the equation: where A, and B, are structure-sensitive parameters, Ql and Q, are the activation energies for the particular creep process, and n describes the sensitivity of the creep rate on stress. The first term represents a slip creep process and the second a diffusion creep process. However, it is stated later that "two distinct processes acting in parallel are involved". Eq. [I] surely represents two processes in series since each reacts to the total applied stress and t, is the sum of the individual creep rates. If the processes are acting in parallel, then the effective stress in each would be less than the applied stress. The component stresses would be given by sl + s2 = a but it is not clear how the magnitude of either, or the corresponding stress exponent, could be determined.

Jan 1, 1969

By J. R. Cahoon, W. V. Youdelis

In a recent publication by Flemings and Nereo, equations for the calculation of the solute distribution in castings were developed, and the solute distributions for unidirectionally solidified A1-4.5 pct Cu ingots cast under various thermal conditions were calculated. The equations derived by Flemings and Nereo for the dendrite "expansion" and "steady-state" zones are essentially equivalent to those previously published by Kirkaldy and Youdelis, 16 for, although the flow velocity cooling rate, and temperature gradients appear in the fundamental differential equations, calculation of the solute distribution requires that the above be explicitly related to the assumed or measured solid-liquid mass distributions during solidification. In the treatment of Kirkaldy and Y-oudelis the mass distributions are simply assumed or measured without any prior and explicit association of the mass distributions to a velocity parameter. The treatment of Flemings and Nereo permits solidification conditions more complicated than the simple unidirectional case to be considered (although in principle the treatment of Kirkaldy and Youdelis could also be extended to include the more general solidification case); however, we note some limitations in the treatment of Flemings and Nereo, and the purpose of this discussion is to point these out and also to indicate those points of similarity in the mass distribution models used which make the two treatments equivalent. Both the Kirkaldy-Youdelis and Flemings-Nereo treatments consider a zone of dendrite "expansion" followed by a "steady-state" zone. However, Flemings and Nereo have failed to consider a zone of "collapse" which begins at the base of the first dendrites to reach the top of the ingot. The omission of this zone of "collapse" results in too high a value for the solute concentration in the latter portion of the ingot to solidify and the conservation of total solute is not possible. In the zone of "collapse" the solute concentration rapidly decreases, which may be accounted for as follows: consider a mushy zone of length X,, shown schematically in Fig. 11 (a), which develops at the chill face and then moves as a steady-state configuration along the length of a solidifying ingot. The solute distribution in this zone, when it first attains the steady state, is shown qualitatively in Fig. 11(b). The segregation is positive (above Co) in the region ab because this region contains primary dendritic solid, ranging from kco to kcE in composition (where k is the partition coefficient and CE is the composition of the eutectic liquid), and liquid metal near eutectic composition. The segregation is negative (below Co) in the region bc because it contains primary dendritic solid only slightly above kco in average composition and liquid metal only slightly above Co in composition. As the zone X, moves as a steady state

Jan 1, 1969