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By J. B. Wagner, B. Swaroop

The atomic ratios of oxygen to iron in zlarious corn-posilions of wustite in the vicinity oj the reported p to n transformation were determined in the temperalure range between 950" and 1250°C. For these conditions, equilibrium vacancy concenrations have also been determined at vatious mixtures of C0,-CO. The data show a continuos introduction of iron vacancies as oxygen is introduced into wuistite. No phase change is observed with in the wuustite field. However, the value of n in the isothermal oxygen pressure dependence, the weight change shifts to 1ower values as the concentration of oxygen increases. WUSTITE is a metal deficit semiconductor with the majority lattice disorder being cation vacancies. Using the notation similar to that of Kroger and ink,' the dissolution of oxygen into wiistite using C02-CO mixtures is represented by, WHere v+! denotes a cation vacancy with k effective negative charges and kh • denotes k electron holes, h -. Applying the law of mass action and assuming a dilute solution of defects in the wiistite yields Where the square brackets denote concentrations. Furthermore, when k = 2 the cation vacancies are completely ionized, and both the concentration of cation vacancies and the concentration of electron holes are proportional to the third root of the ratio, PC /PCo. This analysis is valid for one particular mael based on an ideal solution at elevated temperatures (in this case t > 1000°C). At lower temperatures, it has been shown2 that the pressure dependence of the electronic conductivity changes in a manner which suggests that vacancies interact with or "trap" electron holes. At the very high concentrations of defects, 10'' to 10" per cu cm, these simple models no longer hold. Recently Tannhauser,3 Geiger et a1.' Bransky and Tannhauser; and Hillegas' have found an apparent p to n transformation in wiistite in the temperature range of 950" to 1300°C. This junction was found by thermoelectric and electronic conductivity measurements. Geiger eta1.' found that the electronic conductivity became almost independent of the oxygen pressure at high temperatures and oxygen concentrations within the experimental error. In addition, Vallet, Raccah, and coworkers6'7 have reported the existence of several "varieties" of wiistite which were reported to exist within what was heretofor presumed to be a

Jan 1, 1968

By C. S. Yust, Lida K. Barrett

The change in shape of the void in a sirzterir~g copper mass has been investigated as a juntction of' density. A serial sectioning' technique was used to eoaltrate the irregular shape of the void at two levels qf density. A measure of the void size and configuration, the proximity number, is defined and used to describe the progress of void removal. The process of. void removal deduced front the observations of this study contrasts with current sintering models in that it takes into account the irregularity of structure of a sintering mass and demonstrates that isolated Porosity does not occur first as spherical pores, but as large, definitely nonspherical sections of the void void volume. The process of sintering, about which there is much practical and theoretical knowledge, has evaded a direct and thorough analysis despite the intensity with which it has been studied for 60 years or so. This is due, of course, to the complex structure of a sintering mass and the inability to observe directly the development of a fully dense solid from the initial particulate arrangement. Extensive theoretical analyses have been based on the adoption of one or another of several model systems, that is, by visualization and analysis of some sort of regular assembly or arrangement of geometric "particles" approximating the conditions of a sintering mass. It seems appropriate at this time to try to examine experimentally in some detail the extent to which a sintering mass of irregular particles dlffers from these models. Many models deal with neck growth and the initial stage of sintering and follow the direction established by ~ucz~nski' in 1949 for the sintering of spheres to flat plates. Recently Johnson and cutler2 have adapted these models to sintering of powder masses. coble3 has presented a mathematical model for sintering that applies to the middle and final stages of the process. These papers, without exception, assume a regular geometry, generally spheres in contact in a regular array. Rhines~ and coworkers, however, are studying the sintering process by applying a model based on the topological concept of genus which permits them to consider an irregular structure. whites has described the various models with the exception of that of Rhines et al., and the assumptions on which they are based and their shortcomings. The present paper examines the geometric changes that occur in the powder mass during sintering by examination of the void. The method is to analyze a series of partially sintered structures and to propose from this analysis the sequence of events which occur in the removal of the void space as a sintering mass progresses from a collection of individual particles to a solid body. The irregular nature of the stacking of particles and of the particles themselves will be taken into account. The significant points derived from this study are: first, accurate reconstructions of the irregular void shapes are presented; second, it is clearly established that closed porosity occurs first as widespread volumes of interconnected porosity, definitely nonspherical in shape; and third, a new factor, the proximity number, is defined, which serves in this paper as a tool for describing the void shape changes observed, and which will be used in a later paper as part of the basis of a mathematical model for sintering. While the specific material studied is copper, the observations are thought to be relatively general as indicated by comparison of the results with partially sintered structures in other materials presented in the literature, both metallic and nonmetallic. EXPERIMENTAL PROCEDURE Four series of specimens representing progressive stages of the sintering process were prepared by sintering high-purity copper powder for various time periods. A relatively large particle size was used so that the void-solid interface could be readily distinguished at low magnification. In three series of specimens a loose stacking of particles was obtained by pouring powder into an alumina mold and lightly tapping the mold. The green density of such compacts was approximately 40 pct of theoretical density. Two of these three series utilized irregularly shaped particles in the size range -230 +325 mesh, one series sintered in vacuum and one in hydrogen at 950°C. The third series of loosely stacked particles consisted of spherical particles in the size range -270 +325 mesh, sintered in hydrogen at 950°C. A fourth series was prepared from compacted irregular particles sintered in hydrogen at 950°C. The specimens for this series were formed by lightly pressing the irregularly shaped particles in a steel die; the green density of the pressed pellets was approximately 60 pct. The irregularly shaped particles used in this study are shown in Fig. 1. The density of these particles, measured by a toluene picnometer technique, is 98.2 pct of theoretical density. Each particle is highly convoluted, and in some instances appears in cross section to contain internal porosity. The density measurement, however, indicates that completely enclosed porosity is very small so that the individual particles have a highly irregular surface but are essentially fully dense copper. Therefore, most of the void space that appears in two dimensions to be isolated within the particle is actually at the particle surface and connected to the external void in the dimension not included in the plane of the cross section. The void space that appears as void surrounded by the par -ticle or within folds in the particle w~ll be r~fc\r?

Jan 1, 1968

By B. F. Oliver, C. W. Haworth

Pure tin and Sn-0.5pct Pb ingots have been frozen unidirectionally from the base. For quiescent melts that were initially undercooled, a transition from lower eqlciaxed structure to an upper columnar structure is found in the alloy ingots. Columnar to equi-axed back to columnar transitions are observed in superheated alloy ingots, but no such equiaxed band is observed impure tin. The reproducible equiaxed band is associated with a thermal undercooling followed by a recalescence. This undercooling is <5"C, whereas the critical (maximum obtainable) under-cooling for both the pure tin and the alloys used is -20°C. A similar undercooling is observed at the same position in the pure tin ingots, although in this case no clear transition in structure can be seen. The structure of the pure tin ingots is either entirely columnar or mixed columnar-equiaxed. A consideration of the detailed thermal history of the ingots indicates that the ingot macrostructures are determined by the occurrence of a local therlnal undercooling in conjunction with nuclei multiplication and transport mechanisrris. GENERALLY it is found that a pure metal ingot solidifies so as to produce an entirely columnar structure. Frequently an alloy ingot is found to have a columnar outer zone and an equiaxed central portion. Early systematic work to examine the factors controlling the formation of the equiaxed structure was reported by Northcott&apos; who showed that, for copper alloys frozen unidirectionally with a given ingot practice, the alloying element influenced the length of columnar crystals and the extent of the equiaxed structure. Northcott showed that alloys with a wider freezing range more readily produced the equiaxed structure. The nucleation process can be important in producing equiaxed structures; frequently an alloy which readily solidifies with an entirely columnar structure will produce an entirely equiaxed structure when a nucleating agent is added to the melt.&apos; The formation of the equiaxed structure was attributed by Winegard and chalmers3 to the presence of constitutional supercooling; that is, a region of liquid in front of the growing solid could have a temperature below its equilibrium liquidus temperature. Thus, with a small enough temperature gradient in the liquid, it was suggested that the presence of constitutional supercooling may be sufficient to bring about the nuclea-tion necessary for the formation of an equiaxed structure. Although this explanation is plausible, and may be relevant in many ingots, Walker has described an experiment&apos; for which constitutional supercooling seems to be an unlikely cause of nucleation. A Ni-20 pct Cu alloy, repeatedly undercooled more than 50"C, was crystallized and found to show the typical colum-nar-equiaxed structure. The separation between the liquidus and the solidus for the alloy is 40°C. Thus, in this experiment the nucleation required for the formation of the equiaxed structure must have come about in some other way than by the nucleation catalysis constitutional supercooling hypothesis. Chalmers has suggested more recently5 that nuclei (in a typical ingot) are present immediately after pouring and are prevented from redissolving by the constitutional supercooling effect. More recently Uhlman, Seward, Jackson, and ~unt&apos; have shown direct evidence using ice and organic materials that freeze dendritically that the "remelt mechanism" may be an extremely effective crystal multiplication process during the freezing of ingots under conditions involving dendritic growth. JSlia" experimentally demonstrated the detachment of dendrite arms. chernov14 has analyzed the dendrite arm detachment process as a coarsening phenomena driven by the minimization of interphase area. Katta-mis and ~lemings" working with undercooled steel melts give evidence supporting this mechanism. Mechanisms of dendrite arm detachment such as those assisted by convection are believed to be the origin of the macrostructures obtained in this study. This study makes no attempt to distinguish the relative contributions of these mechanisms. The object of the present work was to obtain accurate temperature measurements during the solidification of an ingot and to correlate these measurements with the formation of equiaxed grains in the resulting ingot structures. Similar previous work is very limited. The measurements carried out by Northcott are neither sufficiently extensive nor sufficiently accurate for any interpretation. Plaskett and winegard7 carried out experiments on A1-Mg alloys in which they observed values of the temperature gradient, G, in the liquid and rate of freezing, R (for a given alloy solute content Co), at the transition from a columnar to an equiaxed structure. They reported that equiaxed crystals were produced at values of G/G approximately proportional to the solidus composition. Similar experiments using Pb-Sn alloys carried out by £111011" showed a linear relation between G/R and the solidus composition. However, the thermocouples were in the mold wall rather than in the melt and, in one case, ingot surfaces were examined. There is ambiguity in the meaning of the values of G and R measured in all these experiments. APPARATUS AND EXPERIMENTAL PROCEDURE Alloys were prepared by induction melting 99.999 pct Sn and 99.999 pct Pb to form a Sn-0.5 wt pct Pb alloy in air in a graphite crucible and casting into a cylindrical graphite mold 6 in. long, 1 in. in diarn , and with a & in. wall thickness. This mold was mounted on a copper base through which cooling water could be

Jan 1, 1968

By B. H. Kear, B. J. Piearcey

The orientation and temperature dependence of the tensile and creep propevties oj Mav-M200 crystals halle been determined. Crystals oriented for single slip exhibit ,maximum ductility, minimum work hardening, and least creep resistance, whereas crystals in multiple slip orientations show nzinimu~n ductility, strongest work hardening, and greatest creep resistance. At 1400" and 1600°F there is a marked improzlenzent in creep strength for orientations approaching [001] and [111], indicating that interactions between dislocations gliding in intersecting octahedral slip systems play an important role in creep resistance. At 1800°F the creep strength is much less dependent on orientation, which is rationalized in terms of slip in cube planes as well as octahedral A frequent mode of failure in high-strength cast nickel-base superalloys is by intergranular fracture, particularly along those grain boundaries oriented transverse to the major stress axis. VerSnyder and ~uard&apos; demonstrated that this problem could be overcome by eliminating transverse grain boundaries through unidirectional solidification. Piearcey and versnyder2 made use of this principle in the development of unidirectionally solidified gas turbine blades and vanes, where the growth direction of the columnar grain structure coincides with the axis of principal stress under operating conditions. The present investigation was undertaken to determine if further improvement in properties may be obtained by eliminating grain boundaries altogether, so as to take advantage of the well-known dependence of mechanical properties of single crystals upon the orientation. 1) EXPERIMENTAL PROCEDURE Single crystals of Mar-M200* were grown from the melt under vacuum by a modified Bridgman method. The melt was poured into a preheated alumina mold, and crystal growth was promoted from one end by appropriate gradient cooling. Tensile and creep specimens (2 in. diam by $ in. gage length) were prepared by a series of operations involving electrical discharge machining, precision grinding, and electropolishing. The orientations of the specimens were determined by the Laue X-ray back-reflection method. Tensile tests were carried out in aWiedemann machine with furnace attachment, using a strain rate planes. In all orientations imzpvouement in the strength charactevistics of the material can be induced by heat treatment. Creep ad stress rupture data for (001) oriented crystals are compared with similar data obtailted previously joy random polycvystalline material, and also columnar grained material having a prejevved (001) orientation. The single-crystal )material exhibits both longer rupture life and lower minimum creep rate at all temperatuves, and the rupture elongation is comparable with that in the columnar grained material. From these results it is concluded that single crystals should and useful application in gas-turbine blades and tanes. The optimum orientation for a blade is considered to be with its axis of principal stvess parallel to (001) ou (111). of 0.0001 sec-&apos;. Load and extension were recorded directly on an X-Y recorder. The strain measuring device consisted of extension arms attached to the grips at one end and leading out of the furnace to an LVDT (linear variable differential transformer) at the other. Creep tests were performed using a standard constant load creep frame. 2) DISCUSSION OF RESULTS 2.1) Structure of Alloy. The structure and segregation in as-cast and heat-treated Mar-M200 has been described in detail else where.~ The main features are as follows: the as-cast material is heavily cored, due to pronounced dendritic segregation during solidification; the dendrites are rich in tungsten and cobalt whereas the interdendritic regions are rich in chromium, titanium, nickel, and carbon. The structure consists of -60 vol pct coherent precipitate of y&apos;, basically Ni3(A1,Ti), in a matrix of y (nickel-base solid solution), interspersed in the interdendritic regions with minor MC carbides and -y&apos; eutectic. The y&apos; particles, and y-y&apos; eutectic, contain more titanium, aluminum, and nickel, and less tungsten, cobalt, and chromium than the y matrix. Heat treatment partially removes segregation, eliminates the eutectic, refines the y&apos; dispersion in y, and gives additional partially coherent M23Cs carbide. An as-cast crystal, therefore, is composed primarily of two oriented phases (y + y&apos;), whereas the normally heat-treated crystal consists of three oriented phases (y + y&apos; + MZ3Cs). Typical electron transmission micrographs of the y + y&apos; structure are shown in Fig. 1. Crystals grown in the (100) orientation develop a simple unidirectional dendritic structure, Fig. 2, since (100) happens to be the preferred direction of growth for dendrites in this material. Crystals grown in the {110) and (111) orientations, however, tend to promote equal growth, generally in separate colonies, in the two and three geometrically favored (100) growth directions, respectively. In other orientations of growth, a single (100) dendrite direction generally pre-

Jan 1, 1968

By A. J. Stosick, J. R. Hoffman, E. Rudy, St. Windisch

The binary alloy system Mo-C zoas investigated by means of X-ray, metallog/aphic, thermoanalytical, and melting-point techniques on chemically analyzed specimens. The system, Fig. 39, is characterized by three congruently melting, intermediate phases, Mo2C, n MoCi-x, and aMoC1-,, of which only Mo,C is stable at temperatures below 1650°C. Substoichio-metrzc (~32.5 at. pct C) dimolybdenum carbide undergoes a homogeneous sublattice order-disorder transformation at temperatures of approximately 1400°C, whereas hyperstoichiorrletric compositions undergo a discontinuous Phase change. The order-disorder transitions in the Me, C phases are discussed in terms of the structural changes involved in the transformation processes and the absence of long-range sublattice coherency in stoichiometric or hyperstoiclziomet-ric compositions attributed to the impossibility of obtaining long-range order in a linear chain of alternating carbon atoms and vacancies. From the experimental phase relutionships and the known thermody-namic data for Mo2 C, limits for the free energies of formation for the high-temperature phases r) MoC1-, and aMoC1-, are deriued and found to be in good agreement with data previously obtained from phase equilibria in ternary metal-carbon systems. IN the course of studies of the high-temperature phase relationships in ternary systems of refractory transition metals with carbon,&apos; a number of inconsistencies found in previous work necessitated a reex-amination of some of the related metal-carbon binaries. A reassessment of the binary system data also seemed

Jan 1, 1968

By B. E. Terkelsen, B. J. Piearcey

A study has been made of the effect of unidirectional solidification on the creep behavior, stress-rupture properties, and thermal shock resistance of four nickel-base superalloys. The alloys Mar-MZOO, B-1900, IN 100, and TRW 1900 show improved rupture ductility and thermal shock resistance when tested with the columnar grains parallel to the major stress axis during test. The relative improvement in creep-rupture properties depends on the intrinsic strength of the alloy, a property which depends on composition, heat-treatnient, and crystallographic orientation. The data clarifies some of the factors affecting the properlies of the cast nickel-base superalloy. COMPONENTS designed for high-temperature use have, in recent years, been fabricated by precision casting techniques using nickel-base alloys developed specifically for use in the conventionally cast condition. This development was a result of both the increasing complexity of the component and the recognition that high-temperature strength was incompatible with workability. The use of castings can be economically favorable, but, more important, the recent complex designs of air-cooled gas turbine blades and vanes in alloys which possess the necessary high-temperature strength cannot be forged. Common modes of failure of high-temperature components are excessive creep, creep rupture, and thermal fatigue. If rupture occurs then the mechanism is usually by inter crystalline cracking along those grain boundaries oriented transverse to the major stress axis. In the stronger alloys, rapid propagation of intercrystalline cracks result in apparent premature failure demonstrated by the absence of third stage creep in a creep-rupture test and low rupture ductility. Tensile ductility shows a similar trend, that is, decreasing ductility with increase in strength. It is not surprising, therefore, that increases in creep strength have only been obtained with a loss in resistance to thermal shock, a property which shows a dependence on tensile ductility. VerSnyder and ~uard&apos; showed that the application of unidirectional solidification to a brittle Ni-Cr-A1 alloy both improved the rupture life of the alloy and increased rupture ductility. Since this casting method results in columnar grains, it appeared that the solution to the lack of ductility in nickel-base alloy components was the elimination of the source of failure, namely the transverse grain boundaries. This concept was recently developed2 to produce cast-to-size gas-turbine blades and vanes consisting entirely of columnar grains oriented parallel to the major stress axis of the component. Not only did the process impart increased rupture life and ductility to the components, but it also increased their resistance to thermal shock. During this development, the effect of unidirectional solidification on the properties of several alloys was investigated. The resulting data allows certain conclusions to be drawn regarding the factors affecting the creep and stress-rupture properties of the cast nickel-base superalloy and also its resistance to thermal shock. Detailed information was obtained on the alloys Mar-MZOO, B-1900, In 100, and TRW 1900. The composition of the alloys studied are shown in Table I. MATERIAL PREPARATION AND TESTING The conventionally cast alloys are cast as +-in.-diam bars in innoculated shell molds under conditions designed to maintain control of grain size. Unidirec-tionally solidified casting were produced in the form of 3-in.-diam ingots. Specimens from the latter were machined such that the axes of the columnar grains were parallel with the axis of the test bar, except in certain cases where the transverse properties of the material were being evaluated. The specimens were tested in an axial loading creep machine.&apos; Temperatures were measured with thermocouples, attached just outside each end of the gage length, to assure uniform temperature along the entire specimen. Chromel/alumel thermocouples were used up to 1800"F and Pt/Pt-10 pct Rh thermocouples above 1800"F. The specimen temperature was recorded and maintained within i2"F throughout the test. Creep extensions were measured automatically with extenso-meters attached to ridges on the specimen and recorded continuously using linear variable differential transformers and multipoint recording equipment. MICROSTRUCTURE The microstructures of transverse sections of the four alloys studied are shown in Figs. 1 and 2. Fig. 1 shows optical micrographs of the alloys, both in the conventionally cast and unidirectionally solidified conditions. Each alloy displays a cored dendritic structure, a distribution of MC carbide, and the presence of the y — y&apos; eutectic constituent.~ In the case of IN 100 and B-1900, Fig. 1 indicates that in these specimens the eutectic is degenerate. That is, it consists only of y&apos; pools indicating that the y constituent has been solutioned during the cooling period after solidification. The major effect of unidirectional solidification on the microstructures of the alloys is a tendency to promote a more dendritic form of MC carbide and an increase in dendrite arm spacing, both effects being a result of the slower solidification rate in the unidirectional solidification technique. V, lec tron micrographs of transverse sections of the four alloys in the two cast conditions are shown in

Jan 1, 1968

By M. J. Blackburn

The phasal equilibria in TI&apos;:Al alloys has been studied Ry transmission electron microscopy, electron diffraction, and X-ray diffraction. It is shown that three-phase fields exist below the transformation, viz.: a disordered hexagonal solid solution a; an ordered hexagonal phase based on Ti3Al, aa; and a two-phase region. (a + (YZ) , occurring between the single-plzuse fields. The size. disiribution, and morphology of- the a, phase in the two-phase region is shown to be dependent upon the alloy composition and heat treatement. The ordering process in the a, phase leads to the formation of anliphase domain boundary networks; the contrast and stability of these networks is shown to be dependent on alloy composition. A new and relatively simple phase diagralil for the systemm is constructed. The phasal equilibrium at the titanium-rich end of the Ti:Al system has long been the subject of considerable controversy. crossleyl has recently reviewed the phase diagrams that have been advanced for the system and in his turn proposed yet another one. There would seem to be general agreement that a phase exists at a composition at or near Ti& with an ordered hexagonal DO,,-type structure. However, several other phases have been proposed; for instance, Ence and ~ar~olin&apos;s&apos; diagram includes two phases, Ti2A1 and Ti3A1, in the region up to 25 at. pct Al. The position of the proposed phase boundaries varies over a considerable compositional and temperature range, a point graphically illustrated in Fig. 1 of Crossley&apos;s paper.&apos; It is perhaps germane to briefly examine the techniques used by other workers in the establishment of the phase structure. These fall into three categories: 1) X-ray diffraction, the only limitation of which is the rather low intensity of superlattice reflections in this system.3 Thus, superlattice reflections become increasingly difficult to detect in the more dilute aluminum alloys. 2) A considerable amount of optical microscopy has been performed"2&apos;4 and it will be shown in a later section that many of the obscure mi-crostructures that have been observed can be attributed to hydrogen contamination. It is concluded, therefore, that such observations should be interpreted with considerable care. 3) The variation of some physical property with aluminum content has been measured.5"7 These methods are a useful indication of the existence of a transformation, but are usually insufficient in themselves to identify the transformation. The results using these techniques will be considered in more detail in the discussion. In this paper, the phase structure of alloys containing up to 25 at. pct A1 has been studied by transmission electron microscopy and X-ray techniques, and the results are used to generate a new and relatively simple diagram for the titanium-rich end of the Ti:Al system. EXPERIMENTAL A series of alloys containing 5.05, 10.16, 13.39, 13.99, 14.40, 20.83, and 25.05 at. pct A1 were obtained in the form of hot-rolled sheet 0.02 in. thick. These alloys contained 0.10 to 0.15 pct 0. Thirty-gram arc-melted buttons were prepared from iodide titanium and 99.99 A1 which contained 16.1, 16.9, 18.2, 19.0, 21.6, 22.2, 23.0, and 23.9 at. pct A1 and had an average oxygen content of 0.03 pct 0. The differences in oxygen content did not appear to influence the nature of the phase transformations which were found. Oxygen content may affect the temperature of these transformations, but insufficient samples of the high-purity alloys were examined to answer this question. The heat treatment of alloys was performed in dynamic atmosphere and vacuum furnaces or in helium -filled silica capsules. A special vacuum furnace was constructed to provide a high quenching rate in which rates of 4000°C per sec were obtained using water as the quenching medium. As pointed out by Crossley,&apos; it is important to avoid heat treatment in the a - [} phase field as the resultant segregation of the alloy into the two phases containing different amounts of aluminum can persist through subsequent treatments leading to ambiguous results. It will be demonstrated later that step cooling of specimens from the a phase region can also lead to anomalous effects. Thus, all solution treatments were carried out in either the a or 3 phase fields followed by water quenching and subsequent isothermal annealing at various temperatures. X-ray analyses were performed on a diffractometer on fine-grained bulk specimens. The value of long-range order parameter, S, wa_s calculated from the integrated intensity of the (1211) reflection. In general, the intensity of the (1011) superlattice reflection was compared with that of the (2021) fundamental reflection to correct for experimental differences between measurements. Thin foils for electron microscopical examination were produced by electropolishing using the technique described in an earlier paper.8 Dark-field techniques were employed to a large degree in this investigation using the gun-tilt method. Finally it should be noted that the lattice parameters of the D01,-type superlattice are approximately related to the disordered hexagonal phase parameters by Crf - c, and 2ad - a, where the subscripts s and d refer to the ordered and disordered unit cells, respectively.

Jan 1, 1968

By G. B. Craig, B. Ramaswami

The temperature and strain rate dependence of the flow stress ratio and the stvain rate dependence qi the flow stress of annealed polycrystalline a zirconiur were determined over the temperature range 30 0" to 1000°K. Some evidence was found for strain aging and discontinuous flow in the temperature ranges 520" to 650°Kand650" to 760°K, respectively. The Cottvell-Stokes relationship was obtained when deformation occurred by twinning as well as slip. The flow stress ratio showed a strong dependence on temperature and strain rate above 800°K. The expevirnental evidence indicated that the rate-controllitzg mechanism for the deformation of a zirconium above 800°K was dislocation climb, and that the deformation was not thermally activated in the range 520" to 800°K. The stacking-fault energy of a zirconium was estimated to be about 250 ergs per sq cm. A knowledge of the temperature and strain rate dependence of the applied stress necessary to deform a crystalline solid is essential for understanding the thermally activated processes occurring during deformation.&apos; Several experimental techniques have been developed for studying these processes.273 One of the techniques is the deter mi nation of the strain rate dependence of the flow stress at constant temperature. In close-packed crystals, it has often been observed that the change in stress due to a change in the strain rate varies linearly with the flow stress, (~1,&apos; This relationship, known as the Cottre ll-Stokes law, is obeyed when deformation occurs by glide alone. However, when deformation occurs by twinning as well as glide, there is disagreement among different investigators on whether the Cottrell-Stokes law is observed. Whereas Thornton et ~1.~find departures from Cottrell-Stokes law when twinning occurs in copper, ~avis~ and sasinski? find that Cottrell-Stokes law is obeyed when deformation occurs by twinning as well as slip in cadmium and magnesium, respectively. One of the main objectives of this study is to determine whether the Cottrell-Stokes law is obeyed when deformation occurs by twinning as well as slip. The second technique that has been used extensively to study the thermally activated deformation of crystals is the determination of the ratio of the flow stresses, at identical dislocation structures and con-

Jan 1, 1968

By E. Miller, R. Geffken, K. L. Komarek

The thermodynamzc properties oJ liquid Cd-Sb alloys were investigated using the cell arrangement measurments were obtained every 2°C at a heating and cooling rate of 12°C per hr and at equilibrium every 2O0C frorn 500°C down through the stable liquidus. The S-shaped asCd US composition curve was used in the cotnposition regzon near Cd,Sb, to calculate a tempeerture-dependent inleraction coefficient from quasichemical theory. Rapid changes in a scd were observed at a transition temperature varying from 400" to 465°C depending on con/kosition. It could not be determined if the changes in aScd were discontinuous, but tlze composition dependeke of the magnitude of the change is indicative of a second-order phase transformation in the liquid. The values of the experimental changes in ASCd are in agreement with calculations from the slope of the transition temperature, using the concept that a second-ovdev phase transition occurs in liquid Cd-Sb alloys. II is suggested that the transformalion is associated with the formation of Cd4Sb3 molecules in the liquid. ThE structure of liquid alloys is the subject of many investigations. X-ray, resistivity, and thermody-namic data have been interpreted as indicating varying degrees of short-range order in the liquid in alloy systems forming inter metallic compounds. In general, the melting process is not a transition from an ordered to a completely disordered state, but some degree of order is retained in the liquid. Maximum ordering in the liquid state occurs close to the melting temperature of the compound and the arrangement of atoms becomes more random at higher temperatures. Of special interest in this respect is the Cd-Sb system. It is one of the few metallic systems which form both stable and metastable compounds when liquid alloys are cooled at normal rates. The stable system exhibits an intermetallic compound, CdSb, melting at 459"c.l A second compound, CdrSbs, has also been reported,&apos; melting close to this temperature. The metastable system has one compound, CdsSbz, melting at 420"c.I Resistivity measurements on liquid Cd-Sb alloys close to the liquidus temperatures have been interpreted in terms of a complex ordering behavior which changes rapidly with increasing temperature.3 The resistivity-composition curve is characterized by two maxima corresponding in composition to CdSb and CdsSbz. The resistivity-temperature plots show sharp breaks for alloys in the composition range of 45 to 70 at. pct Cd on cooling through a transition temperature close to the stable liquidus. Fisher and phillips4 investigated the influence of temperature and composition on the viscosity of liquid CdSb alloys. The viscosity of some alloys increases sharply on supercooling below the stable liquidus. A maximum in the viscosity-composition curve occurs at the composition CdSb. The thermodynamic properties of liquid Cd-Sb alloys have been investigated by Seltz and ~e~itt&apos; and Elliott and chipmane by the electromotive-force method and their results are in good agreement. However, these investigations were carried out at temperatures well above the liquidus temperatures of the alloys, and the temperature coefficients of the electromotive force, dE/dT, were obtained from experimental points for each alloy at a few temperatures considerably above the liquidus temperature. Scheil and ~aach&apos; investigated the thermodynamic properties of this system by the dew point method in the temperature range from about 100°C above the stable liquidus down into the supercooled liquid region. They reported several anomalies, i.e., the activity of a melt on heating differed from that on cooling, and the activity increased sharply in the limited temperature interval immediately above the liquidus temperature of the stable alloy, followed by a sudden decrease below the liquidus. Values obtained on heating and cooling were not in agreement. A reinvesti-gation of a few alloys by Scheil and Kalkuhl&apos; by the electromotive-force method failed to confirm these observations. The authors concluded that the anomalies were due to inhomogeneities in the starting alloys and they discarded their previous results. The present investigation was undertaken in order to obtain thermodynamic data close to the liquidus temperature and in the supercooled region where the anomalies were originally reported, employing the electro motive-force method. This method is quite precise and will most easily permit observations of small changes in activity and partial molar entropy with temperature. Measurements were taken every few degrees so that the dE/dT values could be calculated over the entire temperature range and small changes in the thermodynamic properties close to the liquidus temperature could be observed. I) EXPERIMENTAL PROCEDURE Specimens were prepared from 99.999+ pct Cd and Sb (Cominco). Surface oxide was removed by scraping and then melting the metals under vacuum and filtering through Pyrex wool. Appropriate amounts of the metals were weighed on an analytical balance to k0.1 mg, sealed in double Pyrex capsules under vacuum,

Jan 1, 1968

By H. A. Wriedt

Zinc-vapor pressures in equilibrium with bcc solutions of zinc and iron at 703.5", 757", 793", and 900°C were measured by an isopiestic method. Thermody-na?nic properties of zinc in these solutions were derived directly and those of iron with a Gibbs-Duhem integration. Zirzc and iron exhibit large, positive, and moderately temperature-sensitive deviations from ideality. Excess enthalpies and Gibbs energies are positive in the ranges studied. It has been establzshed in relating published phase equilibria to the Gibbs energies of forming solid solutions that positive departures from ideality also exist in the fcc solutions. Tlze stability, as defined by Darken, of the bcc solutions is small but positive at 703.5"C. Its decrease with decreasing temperature indicates that a miscibility gap may exist in the stable or metastable bcc solutions at lower temperatures. The changes of thertnodynanlic properties relatable to changes in magnetic state are minor compared to other changes due to alloying. The accuracy with which the relation between lattice parameter and composition of the bcc solutions is known has been improved. Zinc increases the lattice parameter of a iron by O.ZOZA per unit atom action zinc to at least NZn = 0.25. TO our knowledge, only Ciganl has previously investigated thermodynamic properties of the bcc solutions of the Fe-Zn system. He measured zinc-vapor pressures in the temperature range from about 320" to 360°C by an effusion technique. We have measured the vapor pressures of zinc in equilibrium with bcc solutions of zinc and iron at 703.5", 757", 793", and 900°C by an isopiestic technique. This investigation and the pursuant thermodynamic computations are part of a program for studying several properties of these solid solutions. In the appendix we report a remeasurement of the relation at room temperature between the lattice parameter and zinc content. Related work not reported herein embraces measuring the diffusivity2 of zinc in ferrite at 700" to 900°C and the Curie point temperature3 as functions of composition. EXPERIMENTAL METHOD AND APPARATUS Purified iron at a series of constant temperatures was saturated with zinc at a series of constant zinc-vapor pressures, the range of conditions being so limited that the equilibrated solid solutions were ferri-tic. The equilibration was conducted in long capsules, Fig. 1, that had been evacuated, gettered with titanium, and sealed. The purified iron, part of a vacuum-melted ingot of electrolytic-iron stock (Glidden Co. 1044-grade), had the impurity contents listed in Table I. It was used in the form of millings about 0.001 in. thick. A zinc of 99.999 pct purity (United Mineral and Chemical Corp.) and later one of 99.9999 pct purity (Cominco Products, Inc.) were used, with no observed difference in results. Sufficient zinc was placed in the capsule (separate from the iron and kept at a different temperature) to supply the vapor phase and the iron alloy, while leaving a pool of pure liquid zinc throughout the run. The imposed temperature of the residual zinc pool fixed the vapor pressure of zinc throughout the capsule; condensation was avoided at other locations by making this the lowest temperature in the capsule. Two common complications of nonisothermal systems were, we believe, effectively absent from ours: first, molecular species other than monatomic have no appreciable concentration in zinc vapor at 700" to 900~~: second, the development of zinc-pressure differentials in the capsules was suppressed by use of relatively large-diameter tubing and the absence of diluents in the zinc vapor other than desorbed impurities. The specimens and zinc pool were located at two isothermal zones (each ranging within 1°C over several inches) of a wire-wound, 37-in.-long vertical-tube furnace. The required temperature distribution was achieved by external adjustment of the currents in three electrically isolated windings. The temperatures of the isothermal zones were controlled independently by ther-

Jan 1, 1968

By S. J. Burns, W. W. Webb

The dislocation arrangements formed during unsteady propagation of cleavage fractures on (010) planes in LiF have been investigated by high-resolution etch-pit techniques and by X-ray diffraction topogvaphy. In impurity-hardened crystals, cracks propagating in any direction on (010) planes at velocities of about 103 cm per sec are usually accompanied by light plastic deformation which is enhanced wherever the crack is allowed to hesitate. Dislocations with [011] type Burger&apos;s vectors are often formed looped around the crack tip. They are dragged along with the crack tips leaving edge dislocations lying nearly parallel with the clearage surface about 5µ from it. These dislocations are easily overlooked since they may initially intersect with the cleavage surface infrequently and later may disappear from the crystals due to image forces during aging at room temperature. Although the plastic work associated with these dislocations is only comparable with the reversible (010) surface energy, an instability in crack propagation appears due to a limit of the velocity with which dislocations can be dragged along with the crack. Transition to a fully brittle nonplastic fracture mode occurs when the crack velocity exceeds the velocity with which dislocations can be moved by the stress field of the crack. TRANSITIONS between brittle and ductile modes of fracture appear to be common processes in the behavior of materials in which the flow stress is close to the stress at which brittle cracks can propagate. High-strength engineering alloys fit into this category and the transition from ductile to brittle modes of crack propagation may be associated with catastrophic failures in these important materials. The methods of theoretical mechanics indicate the geometrical conditions in which these processes may occur but the detailed mechanisms controlling the generation of dislocations in the initiation of the plastic mode and the process by which the loss of plasticity occurs on transition to the brittle mode are not yet clear. Since these mechanisms are not amenable to direct observation in engineering alloys we have chosen a semi-ductile alkali halide LiF as a model system in which to observe transition mechanisms between plastic and brittle modes of crack propagation. Cleavage cracks in this system are known to undergo a plastic-elastic transition at velocities between 103 to 104 cm per secl and dislocation configurations in LiF are amenable to study by optical-microscopic observation of dislocation etch pits2 and by X-ray diffraction topography.3 We have been able to identify a dislocation mechanism responsible for the transition from brittle to slightly plastic modes of crack propagation in LiF. A model based on this mechanism permits calculation of the critical crack-propagation velocity for this transition and indicates the importance of the stress dependence of dislocation velocity in determining the critical crack velocity. Of course, this model cannot be carried directly over to more complex materials but it is quite possible that its qualitative features are generally applicable. Dislocations intersecting fresh cleavage surfaces in LiF were reported by Gilman,4 by Forty,5 and by Wash-burn et a1.6 Such dislocations were construed to have been nucleated where the cleavage crack hesitated or stopped, near stress concentrators, such as cleavage steps, on the crystal face. The loci of such dislocations deposited On the cleavage plane in bands were called "stop lines" or "deformation zones". Gilman, Knudsen, and walshl measured the velocity of cleavage cracks in lithium fluoride by evaporating thin resistive strips on the crystal side and recording

Jan 1, 1967

By M. C. Flemings, T. S. Piwonka

Pore formation is examined analytically in cellu-larly solidified single crystals, in cylindrical castings of pure metals and alloys, and in unidirectionally solidified castings. Effects are considered of fluid flow. dissolved gas, and surface tension. Experimental results show that flow through a partially solid "mushy" aluminum alloy obeys relations similar to those applicable for flow through other types of porous beds. Flow rate is proportional to the square of the fraction liquid (fL) for fL less than 0.3. Results indicate models chosen for mathematical description of pore formation in alloy solidification are valid. ONE of the solidification variables which is influential in determining mechanical properties of castings and of wrought material produced from cast ingots is porosity. This porosity may result from shrinkage, dissolved gases, or a combination of both, and may take the form of either macroscopic pores in localized areas of the casting or microporosity evenly distributed throughout large areas of the casting. In alloys which freeze over a range of temperatures some microporosity is generally found after solidification. There has been much discussion as to whether the micropores are caused primarily by shrinkage, by gas, or by a combination of both.&apos;-3 There has, however, been little experimental or analytical work performed to delineate the relative contributions of shrinkage and gas in causing microporosity or to quantitatively describe the influence of processing variables on microporosity. Porosity other than microporosity (e.g., center line shrinkage) has also received only limited quantitative treatment.495 The aim of this work is to examine analytically the general problem of pore formation in solidification and to perform limited confirmatory experiments. Consideration is first given to shrinkage porosity in pure and nearly pure metals (shrinkage in cellular growth, centerline shrinkage in cylinders). Next, a discussion is given of formation of shrinkage-caused microporosity in unidirectional solidification and in "mushy" solidification. Finally, influences of dissolved gas and surface tension on microporosity are examined. Numerical results are given for aluminum and an aluminum alloy. Typical examples of microporosity are shown in Figs. 1 to 3, for 1) cellularly solidified aluminum, 2) sand-cast aluminum alloy, and 3) low alloy steel. SHRINKAGE POROSITY IN PURE AND NEARLY PURE METALS 1) Cellular Growth. In cellular freezing of an impure liquid, liquid grooves may exist over a considerable length of the growing crystal.6 The cross-sectional area of the grooves decreases with increasing distance from the cell tips; the root of the groove is blunt if the liquid at this point reaches eutectic composition. As a result of volume contraction during solidification, flow occurs down the groove, parallel to the growth direction; hence, there must be a pressure drop from the groove entrance to points within the groove. The geometry of the groove is simplified to that of a circular cylinder of radius r and length L, Fig. 4, L » r, and a simple and useful limiting case is obtained. This is that, in the circular cylinder freezing at constant velocity, the pressure at the root of the groove is lower than that pressure at radius r in grooves of other geometries where r decreases continuously to a lower limit at L. As discussed below, a pore resulting from a given pressure difference

Jan 1, 1967

By P. G. Winchell, R. J. Russell

The distribution of displacements of originally plane surfaces by an invariant-plane strain has been analyzed statistically. The displacement ratio (the magnitude of the displacement of a point originally a unit distance from the invariant plane) can be determined from an analysis either of tilts of random surfaces or of displacements of random scratches scribed on a randowz surface. In either case the mean of the tangent of the observed displacement angle is related to the displacement ratio, and the number of observations used in determining the mean is related to the confidence limits placed on the estimate of the displacement ratio. In estimating the effect of applied stress on a phase transformation whose displacement effects can be approximated as an invariant-plane strain,* the dis- placement ratio of the invariant-plane strain is of primary importance. Two procedures for determining such displacement ratios are considered here. In the tilt method the measured quantity is taken to be the angle through which a random polish plane is rotated by the invariant-plane strain. In the scratch method the measured quantity is taken to be the angle between the original direction of a random scratch in a random polish plane and the projection of its final direction in the polish plane. In order to obtain precise results from either of the methods, it is necessary to measure the relative volume change associated with the strain in a separate experiment. TILT METHOD A locally homogeneous invariant-plane strain, P, with displacement ratio, S, may be written&apos; where ; and < are unit vectors indicating the displacement direction and invariant-plane normal, respectively, as pictured in Fig. 1. Eq. [I] describes a uniaxial strain if the direction of displacement is parallel to the invariant-plane normal and a pure shear strain if the displacement direction is perpendicular to the invariant-plane normal. The original orientation of the random polish plane relative to the invariant plane and to the displacement direction is shown in Fig. 2. The angle 03 between < and u is related to the relative volume change, ?V/V, and to the displacement ratio by As a result of the invariant-plane strain, the polish plane is rotated about its intersection with the invariant plane by the angle y, which is always taken to be positive. The tangent of this angle in terms of the above parameters is

Jan 1, 1967

Jan 1, 1967

Jan 1, 1968

By B. E. Sundquist

The various methods based on solution models for obtaining free energies of mixing from miscibility-gap data have been applied to a number of binary-alloy systems. For nine of these systems there exist experimental thermodynamic data that permit a comparison of the results to experiment. It was found that the method of van der Toorn and Tiedema almost invariably leads to results that are physically unacceptable and that vary drastically with small changes in the miscibility-gap parameters. The subregular solution model is found in all cases, except the Al-Zn, Fe-Cr, and Cu-Pb systems, to exaggerate the free energy of mixing by 30 pct or more. The model developed by Lumsden is found to give results that are often in excellent agreement with experiment and which exaggerate the free energy of mixing by no more than 30 pct. These results and others give evidence that the Lumsden treatment of the effect of unequal atomic sizes and of imperfect configurational randomness due to deviations of AB bond energies from the mean of AA and BB bond energies is adequate for most systems. ANALYTIC expressions are frequently proposed for the dependence on composition of the activities of the components of a solution. Because the development of solution theory is incomplete, these expressions contain parameters which must be determined by experiment. The measurement of activities is often difficult and consequently such measurements are less readily available than are measurements of phase equilibria which, under certain conditions, can also be used to evaluate these parameters. For example, suppose it is known that two structurally dissimilar phases, each of known composition, in an n-com-ponent system are at equilibrium at a given temperature and pressure. n equations can be set up in terms of these parameters expressing the equality of the chemical potential of each component in the two phases. In addition, one can write the Gibbs-Duhem equation for each phase that also contains these parameters. Thus, if these n + 2 equations contain n + 2 parameters, these parameters can be determined (at the temperature in question) from the phase diagram alone. If the average number of parameters in each expression for the activity of a given component in a given phase is V then there will be 2nV parameters involved. Equating 2nV to n + 2 shows that, for n + 2, V = 1. If the temperature dependence of each parameter were to be expressed in some explicit form one could use equilibrium conditions at a number of temperatures to increase V. The situation is much improved when the two phases in equilibrium are structurally similar. It can then be assumed that, stably or metastably, two phases will become one at higher temperatures. Thus the number of parameters involved becomes nV instead of 2nV. Hence, V = 2 for n = 2 using only one temperature. (It is implied here that the activity expressions used are valid over the entire composition range.) In this investigation only the equilibrium of two structurally similar, two-component phases (miscibility-gap systems) will be considered. The various proposed solution models will be applied to a number of these systems and the results compared with available experimental results. All of the analytic expressions that have been proposed for the free energy of mixing of a two-component system are of the form where ?Gmix is the free energy of mixing per mole of solution, N1 and N2 are the mole fractions of components 1 and 2, respectively, and f(Ni, T) is some function of composition and temperature. In the "ideal" solution model f = 0. In the "regular" solution model f = a constant. Since these two models permit only a symmetric equilibrium diagram they will not be considered further here. The simplest model that permits a nonsymmetric miscibility envelope is the so-called "subregular" solution model proposed by Hardy.1 This model gives where the Ci(T) are functions of temperature only. The same expression for f is obtained from the "linear a function" model proposed by Darken and Gurry2 and applied to miscibility-gap systems by Wriedt.3 This model requires that the a function defined by be a linear function of composition (yi is the activity coefficient of component i). This model is not purely hypothetical for it has been found2 to hold true for a number of systems. It is readily shown3 that the f(Nl, T) obtained from this model is of the form given in Eq. [2]. It will be noted that the subregular solution model contains only two parameters and hence both of them can be determined at any desired temperature below the critical temperature, Tc, for a miscibility-gap systems in the manner described previously. At T, the two constants can be determined by equating the second and third derivatives of ?Cmix with composition to zero. Another two-parameter model was proposed by Lumsden4 who set

Jan 1, 1967

By Rodney P. Smith

The diffusivity of carbon (0.1 wt pct C) in Fe-Nz alloys (0 to 100 pct Ni) has been determined for the temperature range 860° to 1100°C. As a function of nickel content, the diffusivity has a maximum near 60 pct Ni (the maximum diffusivity being about 1.3 times that in the absence of nickel); the activation energy has a maximum between 40 and 50 pct Ni and a maximum between 80 and 90 pct Ni. The difference between the minimum activation energy and that in iron is about 3000 cal pev g-atom; Do has a minimum between 40 and 50 pct Ni and a maximum between 80 and 90 pct Ni. The results cannot be rationalized by an approximate thermodynamic treatment. THE diffusivity of carbon has been determined in a number of iron alloys over a limited concentration range. It seemed desirable to investigate a system which allows an extended range of alloy composition within a single-phase region. The Fe-Ni system is ideal in this respect, in that all alloys from 100 pct Fe to 100 pct Ni are fee in a convenient temperature range.&apos; The carbon diffusivity was determined by a decar-burization method. The experimental procedure was identical with that used to determine the diffusivity of carbon in y Fe-Co alloys.2 The experimental data are given in Table I. A small correction (order of a few percent) has been made to the measured carbon loss to correct for the carbon lost from the ends of the cylinders.&apos; Since the diffusivity of carbon varies with carbon content the measured diffusivity is an average value for a carbon content between zero (surface) and that at the center of the sample at the end of the decarburization periods. In making the correction in D to 0.1 wt pct C it is assumed that the measured D corresponds to the arithmetical mean of the carbon content at the surface and at the center of the sample at the end of the decarburization period.3 Since this correction is small (<4 pct in D) and since for our decarburization times the changes in carbon content at the center of the sample was small the mean carbon content could have been taken as half the initial value. It is further assumed that the change in D with carbon content for the alloys is the same as that for the diffusion of carbon in iron. From the data of Wells, Batz, and Mehl4 and of smith5 the correction of D from the mean carbon content to 0.1 wt pct C is 0.3 (0.1 - mean wt pct C). The results for iron are given in Ref. 2. Within the experimental error log Do.l%C for each alloy is a linear function of 1/T; the constants for the equation determined by the method of least squares are given in Table I. The deviations of the experimental points from the least-squares line are of the order of 2 pct in D. A comparison of our results for the diffusivity of carbon in nickel with those of other investigations is shown in Fig. 1. The lower curve in Fig. 1 is a linear extrapolation of values calculated* from the equation of Diamond6 for the relaxation time (temperature range 100° to 500°C). The results indicate a small increase in the activation energy over the temperature range 100° to 1400°C; however, it is difficult to say whether the change in Q is real or experimental error. Certainly the change in Q is less than the variation of 5 kcal per g-atom in the diffusivity of carbon in a iron.6 The experimental data for all the alloys are plotted in Fig. 2. As a function of nickel content the diffusivity has a maximum near 60 wt pct Ni at all temperatures investigated and possibly a minimum between 80 and 90 wt pct Ni for temperatures below 1000°C. The activation energy, Q, and log Do are plotted as a function of the nickel content in Fig. 3. Due to the limited temperature range of our experiments neither Q nor Do can be determined precisely; the activation energies appear to be consistent to ±0.3 kcal per g-atom; however the deviation from the absolute values may be considerably larger, see Table II. The Do values probably have little significance. The solid line for Do in Fig. 3 represents the values required to reproduce the experimental values for D when Q has values represented by the upper solid line The diffusivity of carbon may be expressed in terms of the mobility B22, the activity coefficient r2,

Jan 1, 1967

By Klaus Schwerdtfeger

The rate of formation of silicon monoxide from silica spheres has been measured at 1500°C in H2, H2-H2O, H2-He, H2-Ar, and CO-CO2 gas mixtures. Indications are that in the hydrogen-containing gases the reaction rate is mainly determined by convective diffz~sion. In the CO-CO2 mixtures the rate approches a constant value which is independent of sphere diometer (and gas velocity). This suggests that a surface reaction becomes rate controlling in CO-CO2 gas. WHENEVER silica is exposed at elevated temperature to a strongly reducing atmosphere there occurs, inevitably, a volatilization of silica by the formation of gaseous silicon monoxide. Because of the importance of this reaction in metallurgical processes and laboratory experiments, its kinetics were studied in the present work. EXPERIMENTAL The spheres made of vitreous silica were suspended by a molybdenum wire in the hot zone of a gas-tight high-purity recrystallized alumina furnace tube of 3.1 cm internal diam and 100 cm length. Molybdenum wire resistance heating was used. A purified H2, H2-H2O, H2-He, H2-Ar, or CO-CO2 gas mixture was passed through the tube, from top to bottom. The amount of silicon monoxide formed was determined by weighing the silica balls before and after the experiments. The silica balls were made from commercially available translucent fused quartz glass. In experiments with hydrogen-containing gases the silica stayed vitreous during the experiment, whereas in experiments with CO-CO2 mixtures, which were performed over longer times, the balls were always crystallized to cristobalite (as determined by X-ray examination) at the surface. Constant-pressure head capillary flowmeters were used to control the composition of H2-He, H2-Ar, and CO-CO2 gas mixtures. The oxygen and water vapor were removed from the gases containing hydrogen by passage through columns containing platinized asbestos (450°C) and an-hydrone. The CO was purified from O2 and CO2 by passing it through activated copper (200°C) and through ascarite. The H2-H2O gas mixtures were prepared by passing purified Hz through a mixture of oxalic acid dihydrate and anhydrous oxalic acid held at a constant temperature in a water bath. The equilibrium water vapor pressures of oxalic acid dihydrate-anhydrous oxalic acid mixtures were taken from the available data.1 The furnace system was checked for sufficient gas tightness at regular intervals. As an additional check, the H2O and CO2 contents were measured in the exit gas and were found to agree closely with the metered contents when H2-H2O or CO-CO2 mixtures were used. When purified H2 was used, H2O pressures found in the exit gas were always below 0.1 mm Hg. These contents originate either from an incomplete reoxidation of silicon monoxide in the cold part of the furnace or from small leaks which cannot be avoided. If the latter is the case, such small uncontrolled H2O contents decrease the partial pressure of SiO in equilibrium with SiO2 by less than about 7 pct, which is considered small in comparison to other experimental uncertainties. The temperature of the furnace was controlled automatically in the usual manner. The reported temperature was measured with a Pl-Pt/l0pct Rh thermocouple and was accurate to ± 5°C. TRANSPORT-CONTROL LED RATE OF REDUCTION The gaseous convective diffusion from the surface of a sphere can be predicted from the semiempirical relationship obtained by Ranz and Marshall2 in a study of the evaporation of water and benzene drops in air. The following equation applies:

Jan 1, 1967

By N. N. Breyer

A specially built "hard" tensile machine with characteristics permitting the precise detertnination of the drop of the load at the yield point has been used to study the magnitude of the yield-point phenotnenon in prestrained martensitic 4340 steel. A new phenonzenon, the appearance of a secondary yield point, has been observed by holding the specimen at constant strain in the plastic region. Furthermore, it has been found that a series of yield-point drops could be introduced by successive constant strain holds in the plastic region. The isothermal kinetics of the development of the secondary yielding point lave been studied at four temperatures: 24° 0° -18°, and -79°C. From the results of the kinetic investigation, equations for the In a previous investigation1 it was shown that, contrary to generally held opinion, steels of medium carbon content, such as 4340, 4140, and 86B30, in the as-quenched martensitic condition, can be cold-drawn through a die with reductions in area of up to 10 pct without cracking. Tensile specimens of 4340 machined from bars quenched and prestrained in this manner exhibited tensile strengths of about 400,000 psi coupled with 30 pct reductions in area. In addition, it was found that each sample of such steels exhibited a yield point in the quenched, cold-drawn condition. Since these studies were conducted on a commercial hydraulic testing machine of a type which is not well-suited to detailed study of yield-point behavior, it was decided to study this phenomenon more thoroughly on a rigid straining machine. In this new investigation, use of such a "hard" machine not only allowed study of the magnitude of the yield-point drop but also revealed a new phenomenon—secondary yielding of the martensite introduced by stopping crosshead motion after plastic deformation of the sample had begun. The present paper is a report of these findings. MATERIALS AND PROCESSING The material used was a commercial 4340 steel of the composition shown below: 0.41 0.80 0.013 0.019 0.31 0.85 1.76 0.28 1 0.42 0.77 0.015 0.024 0.30 0.84 1.69 0.28 0.08 2 1 = Ladle analysis. 2 = Laboratory analysis. Bars of this steel were processed in the following way: 1) machined to predetermined diameters; 2) austenitized at 870°C for 1 1/2 hr; 3) oil-quenched; 4) cooled to -115°C for 1/2 hr; onset and increase in magnitude of the secondary yielding in this temperature region have been found to fit the relationship ?Ys = Atn where ?Ys is the magnitude of the secondary yield Point in psi, t is the time in seconds, and A and n are parameter characteris-tics of the material. Although the occurrence of the primary and secondary yield points could be rationalized qualitatively on the basis of stress-induced ordering of carbon atoms in the stress fields of dislocations, as postulated in an earlier paper, the kinetics of the secondary-yield-point development were interpreted to indicate that the ordering involves more than just single jumps of carbon atoms from high-energy to neighboring low-energy sites. 5) pickled and lime-coated; 6) drawn through a carbide die. The predetermined diameters were chosen so that drawing through the same die gave the various reductions desired. Tensile specimens of 0.252 in. diam with a 1 1/4 in. gage length were then prepared from the drawn bars and tested. In order to study the stress-strain behavior at the yield point in detail, a rigid tensile machine with a high spring constant was constructed. Columns of large cross section (relative to the specimen cross section) constituted the machine frame. A dc motor was used to drive a screw via a gear reducing train and a "crane" thrust bearing. In this relatively simple device small deformations could be observed un-blurred by the slow response and lower spring constant inherent in hydraulic machines.&apos; A strain-gage dynamometer permitted load changes as small as 8 lb to be read. RESULTS Tensile test samples machined from bars in the as-quenched condition with no subsequent drawing and samples from bars with 3.8 pct reduction after quenching gave stress-strain curves typified by those shown in Figs. I and 2. The time lapse between predrawing and tensile testing varied but usually ranged between 3 to 6 days at room temperature. The strain rate during testing was 0.003 in. per in. per min. The as-quenched curve is seen to have a broad serrated maximum whereas the stress on the specimen prestrained 3.8 pct rose linearly to point A, Fig. 2, fell abruptly to B, and then gradually to C. The abrupt drop to B was accompanied by evidence of incipient necking. The drop of the stress at the yield point in the prestrained samples (A to B in Fig. 2) changed with the percent prestrain, as illustrated on Fig. 3. Although the tensile strength increased continuously with the amount of previous cold drawing, the magnitude of the yield point drop first increased—up to about 6 pct prior reduction—and then decreased. Specimens from bars predrawn more than 8 pct broke in a brittle fashion in the elastic portion of the stress-strain curve.

Jan 1, 1967

By D. A. Koss, R. O. Gordon

Changes in the ultrasonic attenuation in steel specimens have been observed during tensile tests. Samples of AISI 1020, 1045, and 1095 steel quenched and tempered to a spheroidized condition have been used. Both attenuation and microstrain measurements fail to reveal preyield dislocation motion in the as-tempered specimens. Upon reapplication of the load to samples in the strain-aged condition there is a large preyield attenuation increase but no observable micvostrain up to 90 pct of the flow stress. These and other observed changes can be related to changes in the free disloca-tion density and the average dislocation segment length. The results show that the increase inflow stress in the strain-aged condition is caused by increased fric-tional stresses rather than by dislocation pinning. Strain aging is found to proceed through three distinct stages. The second of these follows the t2,3 law and is characterized by an activation energy of 20 kcal per mole. RECENT years have seen substantial progress in the understanding of the sharp yield-point phenomenon in metals; the influence of solute atom pinning of dislocations, of dislocation multiplication, and of the stress dependence of dislocation velocity on the stress-strain curve has been investigated. Evaluation of the relative importance of these factors in the various metals and alloys is not complete, however, because observation of the stress-strain curve alone is not sufficient to determine the yield mechanism. In the experimental study of the sharp yield point it would be desirable to be able to directly observe the dislocations in a bulk specimen. Ideally, the observations should be made during deformation because of the rapidity of recovery processes in lightly strained metals. While direct observation of dislocations under these conditions is not possible, certain physical properties sensitive to the dislocation structure can be observed while a test specimen is undergoing deformation. Of these properties, one of the most useful is the ultrasonic attenuation. The total observed attenuation, a, is due to a number of causes: acoustic diffraction, scattering by inhomogeneities in the structure, heat flow, magnetostriction, and dislocation damping. Satisfactory measurements of the absolute a are difficult to make because all of these factors cannot be evaluated in any given specimen, but changes in a due to changes in the dislocation contribution alone can be reliably observed by appropriate technique. Because dislocation damping is sensitive to small concentrations of long, free dislocation segments, observation of acoustic attenuation due to dislocations is particularly useful in the study of the early stages of plastic deformation. In the experiments to be described, acoustic-attenuation measurements have been made on steel samples as these were pulled through their yield in tension. While many details of dislocation-damping phenomena in the bee metals remain obscure, the main characteristics of this type of internal friction are established. At low strain amplitudes and at frequencies well below that of dislocation resonance (the conditions of these experiments) the dislocation contribution to a is given by1 where A is the density of freely oscillating dislocation segments, L is the average segment length, B is the damping constant for a moving dislocation, w is the frequency, O is an orientation factor, C is the dislocation line tension, and t is a numerical factor relating average segment length to the distribution of lengths. Because of its fourth-power dependence on L, a is highly sensitive to changes in dislocation free segment length such as might arise from unpinning, recovery, jog formation, or dislocation intersection. The above equation is not valid near the resonant frequency of dislocations, but the segment length in steel is believed to be much too short to cause over-damped resonance near 10 Mc; this will be discussed later. In the present experiments plastic-strain measurements with a sensitivity of 2 x 10-5 were also made during the early stages of loading in order to detect preyield strain. The general plan of the experiments is to observe

Jan 1, 1967