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By V. B. Kurfman

The temperature, strain rate, and orientation deDendence of defbrnzation of single-crystal MgAg has been examined. The crystals exhibit a tendency to single glide and little or no hardening at 25°C for many orientations. A much higher hardening rate is observed when multiple glide occurs, such as can be initiated by surface defects. The tendency for easy glide becomes less dependent on surface preparation and orientation as T — 100°C and bars so tested often fail after one-dimensional necking-. At T > 200°C (transition temperature for single-crystal notch sensitivity and poly crystalline ductility) single glide diminishes and two-dirnensionul necking begins. The crystals do not strictly obey a critical resolved shear stress law, but show the influence of {loo) cracks in determining the slip mode. The results are correlated with the difficulty of sciperdzslocation intersection and semibrittle behavior of this compound in single-crystal and poly crystalline form. Comparisons are made with the slip selection mode observed in tungsten, with the reported observations of easy glide in bee metals. and with the mechanical behavior of poly crystalline MgAg. PREVIOUS work on tensile deformation of polycrys-talline MgAgl and bending deformation of single-crystal MgAg2 has shown that the compound is semi-brittle (i.e., notch and grain boundary brittle). If this semibrittleness is supposed to result from the difficulty of multiple glide (associated with the problems of superdislocation intersection) one might expect single crystals deformed in tension to show pronounced single glide and strong orientation dependence of hardening rate. These experiments were done to examine this supposition and to study the tensile deformation of a highly ordered system which may be considered bcc if the difference between the two kinds of atoms is ignored (actual structure: CsC1). EXPERIMENTAL Single-crystal ingots were grown by directional freezing as previously described.' These ingots were sliced into a by a by 2 in, rectangular bars by electric discharge machining, then round tensile bars were conventionally machined to 1/8-in.-diam by 1-in.-long reduced section. The bars were typically tested without an anneal because of the problem of magnesium vapor loss and they were typically tested as mechanically polished. The analyses are within the same limits as those reported earlier; i.e., the average composition for each specimen is within 0.5 at. pct of stoichiometry, while the total range from end to end in a given specimen varies from 0.7 to 1.4 at, pct. There has been no indication in the results of any variation in slip or fracture mode attributable to the composition fluctuations. The slip systems were determined by two-surface analysis of the bars after testing to failure at room temperature. Single glide was so dominant that there was little difficulty in identification of the dominant slip system even though the tensile elongation to failure often approached 7 to 8 pct in room-tempera- ture tests. Elevated-temperature testing was done in a silicone oil bath and low-temperature testing was done in liquid Np or a dry-ice bath. All stress measurements are reported as engineering stress unless otherwise specified, and crosshead travel is used as the strain measurement. RESULTS The tendency toward single glide is best seen in the pictures, Figs. 1, 2, and 3, which depict deformation at fracture as a function of test temperature. While it is possible to find regions of secondary slip by careful microscopy, such regions are very small. The development of a ribbon-shaped configuration from an initially round section bar pulled at 100°C is typical, occurred by single glide, and illustrates the degree to which such glide continues. At temperatures =100°C the bars typically show elongation of 20 to 50 pct by predominently single glide. Despite the large elongation, fracture even at 150°C occurs in a brittle mode, Fig. 2, in the sense that it is an abrupt failure which shows no discernible necking in the second dimension of the bar's cross section (i.e., there is no appreciable action of any slip modes which would decrease the broad dimension of the cross section). Near 200°C the fracture mode changes slightly. Although most of the sample extension is by single glide, after the bar develops the characteristic ribbon shape it begins to neck in the second (i.e., broad) cross-sectional dimension. The bar becomes very thin in the "necked down" region, Fig. 3, and the reduction in area approaches 100 pct. Often there oc-

Jan 1, 1967

By George A. Roberts

The development of an alloy system, high-speed steel, is used as an example of the progress of physical metallurgy. Tracing the history of men and their thoughts as they studied and invented and modified these materials, the story of high-speed steel since the 1890's is seen to be a long, slow, but steady progression of achievements. Today's multiplicity of high-speed steels are the result. Data are presented on quantitative metallography of carbides in high-speed steel with high vanadium content using the QTM instrument. Grindability as well as mechanical properties are related to the content of excess MC and M6C carbides in a series of high-speed steels and the newer matrix steels. These emphasize the present state of knowledge and show the current stages of thought that may affect the development in succeeding years. It is a great thrill for me, an ex-research metallurgist and ex-practicing metallurgical engineer, to speak to an audience currently engaged in both pursuits on the occasion of the 43rd Howe Memorial Lecture before the Iron and Steel Division of the AIME. I shall not review Henry Marion Howe's distinguished career, so adequately reviewed in Maxwell Gensamer's contribution in the 1965 AIME History of Metallurgy, except to point out that, while leading the life of an intellectual, he worked as a practicing research metallurgist and a practicing metallurgical engineer for significant periods of time and contributed greatly in both areas. For those of you who believe, as I do, that in the intellectual activity of metallurgy we are blessed with an intimate mixture of science and engineering (see Mehl's 1960 Howe Lecture), we might recall that Howe, while pursuing a life of writing and teaching in later years, served as the first Chairman of the Division of Engineering of the National Academy of Sciences. That metallurgists were called upon then to lead an engineering recognition movement is perhaps related to the strong part played by the AIME and its members in the recent establishment of a National Academy of Engineering and to the fact that a metallurgist is its head, 47 years after Howe served. I stress these engineering aspects for I wish to talk about a metallurgical engineering subject today. Alloy systems, physical metallurgy, and steel blended with an historical perspective and a report on new techniques to improve the old will, I trust, be of sufficient interest to bring these lectures back to the physical-metallurgy banner from which they have departed for 4 years. Those process metallurgists, open-hearth fiends, and physical chemists among you will just have to be patient. The development of an alloy system is the engineering application of scientific thought and fact. There are many interesting alloy systems, developed to a high degree of technology and sophistication over the past 40 to 70 years. These systems are bound together and related by a similar set of characteristics. For example, stainless steels are a system in which the members are related by a high chromium content which gives a corrosion-resistant characteristic. A subfamily in this system would be austenitic steels

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.' 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'-= 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 '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'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.' 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'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,' 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.' 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.' 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.' 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,' 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.' 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 D. McLean

For many pu@oses uniform strength is desired over a long temperature range, coupled to a band of softness at the hot end for easy shaping. Various types of material fulfill such a requirement to different degrees, depending on the regularity of their atomic structure. In long-chain polymers and vitreous glasses the irregular structure leads to a steep temperature dependence of deformation resistance and the temperature band between the hard and brittle condition and the soft condition is only about 100 C. In crystals and especially metals the atomically regular structure leads to a much smaller sensitivity over a wide temperature band, thus approaching the ideal behavim. The reason for this insensitivity is that the regular crystalline structure deforms by the movement of dislocations and the elastic interactions of dislocations in- PLASTICS, GLASSES, AND CRYSTALS The ease or otherwise of deformation varies with temperature much more in some substances than in others. This is an important matter when service over a wide temperature range is needed, especially volve energies of several hundred electron volts compared with which the energy of thermal agitation is insignificant. However, temperature affects a metal&apos;s defmmation resistance through its influence on the annealing, m coarsening, of the three-dimensional dislocation network. This coarsening is a phenomenon very similar to grain growth and ideas about grain growth can be applied to it. Taking into account also the temperature dependence of the glide resistance from alloying additions, a reasonable account can be given of the overall effect of temperature on deformation strength and of stress and grain size on deformation rake. Special structures me described. some arising from these ideas and as yet untried, which may benefit metals and polymers but not ni-treous glasses. when in addition a degree of softness suitable for shaping is required at some stage. It would be nice if one could write on this subject in as much detail about plastics, glasses, and so forth, as about metals, but there has been far more study of this matter in metals than in other substances, which is one reason why most of this paper concerns metals. However, in Fig. 1 there are shown the deformation strengths of several nonmetallic substances as a function of temperature. In many tests the attempt at deformation caused breakage and the graph lines are then drawn dashed. Long-chain plastics, a glass, and a crystalline substance are included in Fig. 1. The notable feature of all of them is the sensitivity of the

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 M. A. Dayananda

Based on the Kirkendall frame of reference, a method is proposed for the determination of atomic mobilities of all the diffusing species in a multicorn-ponent system with a single diffusion couple. The method is based on an atomic mobility model developed on the concept of negligible interactions among the intrinsic fluxes. It is shown in the model that mobilities can be obtained directly from the cumulative intrinsic fluxes past the Kirkendall interface. The proposed method replaces the need for a prior determination of interdiffusion coefficients far the calculation of mobilities. Relations between intrinsic diffusion coefficients and mobilities are derived and the mobility calculations are illustrated with diffusion data in Cu-Zn-Mn alloys at 850°C. ThE concept of "intrinsic flux" with respect to a fixed lattice was introduced "i Darken1 to explain toa Kirkendall effect2 demonstrated by the motion of inert markers during isothermal diffusion in single-phase binary solid solutions. Based on this concept, intrinsic diffusion studies have been made in various binary metallic systems3,4 employing such a lattice frame of reference, commonly referred to as the Kirkendall interface. Similar approaches, both theoretical and experimental, have been presented5"10 to study intrinsic diffusion in multicomponent systems. Based on the direct integration of Fick&apos;s law extended to multicomponent diffusion, Philibert and Guy8 proposed a method for the determination of intrinsic diffusion coefficients. For an n-component system, this procedure requires an experimental study with (n — 1) diffusion couples, all having their Kirkendall interfaces at the same compositio;, where n(n — 1) intrinsic diffusion coefficients are defined. This technique has been employed for ternary diffusion studies by Dayananda and Grace" and Guy and Leroy.11 A different approach is recommended by Ziebold and Cooper,12 who have derived relations between interdiffusion coefficients and atomic mobilities employing fluxes referred to the local center of volume. Their analysis is based on the simplifying assumption of negligible interactions among intrinsic fluxes. This assumption has been considered satisfactory for dilute solutions.5"7 The use of this analysis for the calculation of mobilities requires an initial determination of interdiffusion coefficients with a set of diffusion couples having intersecting diffusion paths. It is the purpose of this paper to propose a method that would permit a direct determination of mobilities of all components of a multicomponent system from a single diffusion couple. This method is based on a mo- bility model developed with diffusion fluxes referred directly to the Kirkendall interface, generally identified by inert markers. gen erall, like that of Ziebold and Cooper,12 employs the simplifying assumption that the flux of each component relative to a fixed lattice is caused only by the driving force of its own chemical potential gradient. THE KIRKENDALL INTERFACE Inert markers are employed in diffusion couples to locate experimentally the position of the Kirkendall interface. They are initially placed at the weld interface for "sandwich" couples, or at the original vapor-solid interface for vapor-solid couples. Studies of marker motion in binary systems3&apos;4 with both types of couples indicate that markers remain in a plane of constant composition and move with this plane para-bolically with time. Parabolic marker movements were also observed in ternary Cu-Zn-Mn couples by Dayananda and Grace.10 It is reasonable to expect a similar marker behavior even for diffusion couples with a higher number of components.

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

By J. E. Hilliard

A procedure is described for determining, from measurements on a section, the moments of any degree n (i.e., the mean value of Dn, where D is a linear dimension) of the size distribution of particles (or grains) in an opaque sarnple. The analysis is applicable to particles of alnzost any shape and to any mixture of shapes. However, if absolute values of the wloments are required, it is necessary to know what shapes are present and the relative frequency of their occurrence. In addition, certain shape-dependent parameters have to be evaluated before the formulas can be used. The measurement required is the distribution of intercept lengths. This can be determined either visually or with an automatic scanning instrument. Corrections me derived for the bias due to instrumental end effects. The proposed analysis has the following advantages over existing ones: 1) Confidence limits are easily estimated for the measured properties or, conversely, the number of counts required to achieve a given accuracy can be determined. 2) The analysis is not restricted to particles of a special shape. 3) The error resulting from any known degree of departure of the actual from the assumed particle shape can be estimated. 4) The computations are simple and, apart from a change in constants, are independent of particle shape. 5) The number of particles per unit volume can be determined by a simple counting procedure. MANY procedures have been described for determining the size distribution of particles from measurements on a section (or plane of polish). They differ from one another in the property measured on the section (radius, intercept length, profile area) and in the method used for the numerical solution of the integral equation relating the property to the particle size distribution. However, all existing analyses share at least two of the following disadvantages. 1) They are limited to a particular shape of particle (usually spherical). 2) It is very difficult to determine how the statistical sampling error is propagated into the computed size distribution. The investigator thus has no means of knowing the reliability of his result and, what is of equal concern, he is unable to estimate how many measurements are required to obtain a result of the required accuracy. 3) It is also difficult to assess the error resulting from any deviation between the actual and assumed particle shape. The foregoing limitations stem from the complex relationship between the particle size distribution and the distribution of the property measured on the section. As will be shown, they can be avoided by defining the size distribution in terms of discrete parameters

Jan 1, 1969

By K. R. Carson, J. Weertman

An attempt is made to ascertain the mechanism of tangle and cell formation and its dependence upon dislocation-interstitial carbon interactions. The strain-hardening behavior of single crystals of 3.25 pct Si-Fe was determined at 300° and 425°K and under conditions of both continuous and interrupted tensile strain. Significantly enhanced hardening was observed in crystals deformed at the elevated temperature, and it was further accentuated by interrupted straining. Transmission electron microscopy was used to study the resultant dislocation structures. Strain aging was found to aid tangle and cell formation at 425°K, but at both temperatures embryo tangles formed solely from primary glide dislocations, presumably by a process involving cross slip and "mushrooming". IN the course of plastic deformation all bcc metals and alloys develop a dislocation structure characterized by loose-knit groups of tangled dislocations. With increasing strain the tangles become more tightly knit and grow larger; finally a three-dimensional cellular substructure is formed:1 This process has been observed with the transmission electron microscope.&apos;-l7 However, most investigations were confined to the study of nearly pure polycrystalline metals at relatively low temperatures. At intermediate temperatures, 0.17 to 0.14 Tm where T, is the melting temperature in degrees absolute, the mobility of interstitial impurities such as carbon is high enough to permit migration to nearby glide dislocations but is still low enough so that a significant drag force is exerted.18,19 it is also in this temperature range that a hump occurs in the curve of work-hardening rate vs temperature for iron. Analogous plots for tantalum" and columbiumzo show a definite upward trend in the work-hardening rate. Keh and Weissman1 have pointed out that this behavior may be explained solely on the basis of changes in the dislocation configuration: at low temperatures the dislocations tend to be relatively straight and uniformly distributed, but at intermediate temperatures tightly knit tangles and cellular substructure appear. The interference of these tangles with glide dislocations causes the observed increase in the work-hardening rate. This explanation appears reasonable, yet one might ask what factors cause tangle formation to be so favorable at intermediate temperatures. It seens likely that the strong dislocation-interstitial interactions which are known to occur in this temperature range are at least partly responsible," with the magnitude of the effect being proportional to the interstitial concentration. The purpose of the present work is to study the relationship between tangle formation and strain hardening in a bcc metal in the temperature range 0.17 to 0.4 Tm. Particular emphasis was placed upon a study of the effects of interstitial-dislocation interactions. Single crystals of 3.25 pct Si-Fe containing about 200 ppm of C in solid solution were used in the investigation for the following reasons: 1) The mobility of interstitial carbon in 3.25 pct Si-Fe is negligible at 300°K but increases rapidly at slightly elevated temperature22. Hence, differences between the flow curves and dislocation structures of crystals deformed at 300°K, 0.17 T,, and crystals deformed, say, at 425°K, 0.24 Tm, should be appreciable because of the enhanced dislocation-carbon interactions at the elevated temperature. This effect was accentuated in some samples by interrupted straining, thereby introducing a certain amount of aging. 2) Near room temperature, slip in suitably oriented 3.25 pct Si-Fe single crystals is largely confined to the (110) planes.23&apos;24 Dislocation structures formed under conditions of single glide are the least complicated and their method of formation is the most easily discernable. 3) Dislocations in Si-Fe can be tightly locked with carbon atmospheres by a low-temperature aging treatment. The subsequent thinning of samples to foil thicbess causes little or no rearrangement in the dislocation structure.25 EXPERIMENTAL PROCEDURE Large single-crystal sheets of 3.25 pct Si-Fe were donated by Dr. C. G. Dunn of the General Electric Research Laboratory, Schenectady, N. Y. The orientations of the sheets were determined and slabs 1.0 by 0.25 by 0.05 in. were cut such that the desired tensile axis corresponded to the long dimension. The slabs were mechanically polished and subsequently decar-burized by heating at 1000°C for 3 days in a flowing wet-hydrogen atmosphere. A carbon content of about 200 ppm was introduced by heating at 805°C for 25 min in a flowing atmosphere of dry hydrogen containing heptane vapor. Shaped copper tools were then used to spark-machine at 0.125 by 0.50 in. gage length onto each slab. Vacuum annealing at 1225°C for 2 days followed by a quench into the cold end of the furnace to retain carbon in solid solution concluded the soecimen preparation. Continuous tensile flow curves for crystals of severa1 orientations Were obtained both at 300&apos; and 425°K. A strain rate of 6.67 x 10-4 Per set was used in these and all other tests. Crystals oriented for single glide, B and D in Fig. 1, were subjected to a 3.5 pct plastic elongation to insure uniform slip along the gage length; they were then immediately subjected to interrupted strain cycling as indicated in Fig. 2(a). Each cycle consisted of unloading to 1.5 kg per sq mm, holding

Jan 1, 1969

By D. R. Packard, J. D. Verhoeven

The resistivity us atom fraction relationships for dilute solutions of cadmium, mercury, and tin in molten sodium have been determined. With these data and the resistivity capillary-reservoir technique, the electro-transport mobilities, effective valences, and the diflusion coefficients of the three solutes have been determined. The mobilities are found to be higher than in other molten alloys by a factor of around 20. The results are compared to the Mmgelsdorf model for electrotrmtsport. The high values found for the mobility to diffusion coefficient ratio indicate that small quantities of the alkali metals should be susceptible to purification from many solutes by means of electrotransport. PASSAGE of a direct electric current through a liquid metal containing a solute will usually cause a relative motion between the solute and solvent atoms of the alloy. This electrotransport phenomenon may be described experimentally in terms of the mobility of the solute atoms, i.e., the drift velocity of the solute relative to the solvent per unit electric field. In dilute solutions of liquid alloys this relative mobility becomes a measure of the velocity of the solute with respect to the observer since the motion of the solvent is negligible. The mobility is a significant parameter in evaluating the potential usefulness of electrotransport for such things as purification or solute control upon solidification. Prior to around 1958, quantitative data for the mobility of solutes in liquid metals were restricted to some solutes in liquid mercury. Since that time ad- ditional data have been reported for the mobility of solutes in liquid mercury, bismuth, tin, and lead, as shown in Table I. In 1963 Drakin et al.11 reported some values of a transport number for mercury and thallium in molten sodium and potassium. When these values were converted to mobilities, it was found that the mobilities were higher than any of the previously reported values by a factor of around 20, as shown in Table I. Drakin&apos;s experimental technique did not eliminate the presence of back-diffusion and consequently his data were expected to be lower than the true values. The purpose of the present investigation was to determine the mobility of a number of solutes in molten sodium with an experimental technique which eliminates back-diffusion errors. EXPERIMENTAL The technique used to determine the mobility was a resistivity capillary-reservoir technique which had previously been used with a high degree of precision on Sn-Bi alloys.4 This technique consists of dipping the vertical Pyrex capillary cell shown in Fig. 1 into a molten bath of alloy while the bath and capillary are under vacuum. The capillary is then filled by intro-

Jan 1, 1969