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By N. O. Gray, John Henderson

Hydrogen-reduction data for naturally occurring single crystals and Prepared polycrystals of dense hematite have been presented. Results cover the temperature range 400o to 1000oC, for particles from ten sources, ranging in size from 0.07 to 10 mm and in shape from spheres to cylinders, cubes, and thin slabs. A consistent pattern of behavior has been demonstrated for single crystals and the reduction mechanism shown to be temperature-dependent. Below 579oC reduction is a simple topochemical process but at higher temperatuves it is complex and occurs in two distinct stages. Prepared particles from these laboratories behave in a similar manner to the single crystals. Data from two investigators showing topochernical reduction of Prepared particles above 575°C are inconsistent with that for other dense hematites. It is concluded that topochenzical reaction should not be used as a model for generalized rate expressions for dense hematites. SINCE 1958, McKewan1-6 has brought to prominence a simple concept of dense hematite reduction. This model is that oxygen is lost from a hematite particle undergoing reduction only from an oxide-iron interface that recedes in such a way that the oxide remaining retains the original shape of the particle, i.e., reduction occurs topochemically. An adjunct to this concept is that any intermediate oxides in the transition from hematite to iron only form thin layers so that oxygen cannot be lost from the particle without movement of the oxide-iron interface. Further, the rate of oxygen loss from the particle is said to be proportional to the area of the receding interface so that the iron layer grows linearly with time and the over-all reduction process can be described by the equation where ro and do are the initial particle radius and density, respectively, R is the fraction of the original oxygen lost, i.e., the fractional reduction, at time t, and K is the rate constant. The idea of an underlying simplicity in hematite reduction is attractive because it gives a tractable basis from which general theories of hematite reduction can be developed and it has received wide support,7-14 based mainly on the large amount of data13 that can be fitted to Eq. [I]. However, despite the fact that this equation has been derived for dense materials, the bulk of the data that have been used to test it13 have been for materials of only about 90 pct of theoretical density (5.26 g cm-3) or less, so that its generality for dense hematites has not been demonstrated. In any case, as will be seen, adherence of reduction data to Eq. [1] does not necessarily imply that reaction occurs topochemically. In this work only data for hematites approaching theoretical density are considered and it will be shown that in only one study besides McKewan's is topochemical behavior observed over the whole range of temperature investigated. For the majority of materials a linear rate of interface advance is observed to complete reduction only when wustite is not a stable intermediate phase in the transition of hematite to iron, i.e., at temperatures below about 575°C. Above this temperature, reduction is an exceedingly complex series of reactions that takes place in two distinct stages and it is only in the first stage that reaction in any way resembles a topochemical process. This means then that, far from representing general behavior as has commonly been supposed, topochemical reaction for dense hematites is only a particular behavior that may be observed under some circumstances. EXPERIMENTAL Hydrogen-reduction data have been collected and cross-checked in these laboratories by three techniques, weight loss, collection of water evolved in the reduction reactions, and direct metallographic examination. Details of these techniques are discussed elsewhere," where it is shown that results obtained by the three methods are in close agreement. The weight-loss method, by which most of the results were obtained, consisted of hanging the sample in a platinum mesh basket from an Ainsworth Model AV-AU-1 vacuum recording balance inside a vertical l 1/4-in.-ID alumina tube furnace. Dry deoxidized hydrogen was flowed downwards through the tube at 2 to 4 liters min-1 (stp). Single crystals from two sources and artificial oxides from three sources have been examined. The single crystals were from hematite deposits at Yampi Sound, Western Australia, and Brazil, the latter being obtained from Gregory, Bottley and Co., London, U.K. The "Yampi Blue" crystals were hand-picked from washed, magnetically concentrated, sized fractions, -200 mesh BSS (mean diameter ca 0.07 mm) and —36 + 44 mesh BSS (mean diameter ca 0.4 mm) while 10-mm cubes were cut from the Brazilian crystals with a diamond saw. The starting materials for the prepared particles were hematites designated, respectively, "Specpure Iron Oxide", Laboratory No. S639 from Johnson Matthey & Co. Ltd., London, U.K., "Calcined Ferric Oxide" from B.D.H. Laboratory Chemicals Division, Poole, U.K., and "Pigment Grade Oxide", EPR-50, from C. K. Williams & Co., Easton, Pa., U.S.A. Approximately spherical particles were prepared from the artificial oxides by rolling the material, moistened if necessary, in a glass jar, and cylindrical compacts approximately 10 mm in diam and of approximately equal height were pressed in a steel die at 200 psi. These spheres and cylinders were subsequently fired in oxygen for 20 to 100 hr at 1370°C. The

Jan 1, 1967

By R. D. Carnahan, G. A. Stone, R. J. Arsenault

An experimental technique has been developed for carrying out a dynamic tensile stress-strain test in which plastic strain is measured continuously throughout the microstrain region extending through the macroflow region to total deformations of 5 pet. The tests were carried out on niobium, samples having interstitial impurity levels of 160 and -800 ppm at temperatures ranging from room temperature down to 100°K. A band spectrum of activation energies was obtained from calculations based on the measured activation volumes and temperature dependence of flow stress. The inability of a single rate-controlling process to predict such a phenomenon has led to the proposal that several sequential rate-controlling dislocation mechanisms are operative in the preyield micro-strain region. These are thought to be: the motion of geometrical kinks, the formation of double kinks in edges, and finally in the macrostrain region the formation of double kinks in screws. In less pure niobium the effect of interstitial impurities is shown to be dominant in the microstrain region, suggesting that a fourth probable mechanism is overcoming interstitial barriers instead of geometrical kink motion and the formation of double kinks in edge dislocations. THE principal fundamental aim of most mechanical properties studies of crystalline solids is to determine the dislocation mechanisms responsible for the plastic behavior. The extension of such studies to the region of preyield microstrain behavior has received renewed attention in the past few years as the details of macroscopic flow behavior have become better understood. For the most part, microstrain studies have been carried out using one of two variations of a single experimental technique.1 The first method involves loading the sample at a constant extension rate to a predetermined stress level (less than the macroscopic yield stress), instantaneously unloading, and then determining the extent of plastic deformation to a sensitivity of 10"6. The microscopic stress-strain curve is then constructed from the results of a repeated series of such individual measurements, each of which involves loading to an incrementally higher stress level, by relating the accumulated plastic microstrain for each step to the maximum applied stress in that step. The second variation, also carried out by step-wise increases in stress, measures the total strain to a sensitivity of ~10"6 and relates the maximum stress to the area of closed hysteresis loops that are generated under certain conditions (namely, prestrained samples). The foregoing methods have yielded interesting information about the nature of preyield deformation and plastic response to stresses below the yield stress, but they offer certain disadvantages for studying the dynamic behavior of dislocations. In the first method it is physically impossible to specify a plastic strain rate inasmuch as the test sample is reexposed, as it is loaded to its maximum stress in a particular step, to lower stresses at which flow will take place. The strain corresponding to a given stress level on the stress-microstrain curve thus generated will then always be greater than that at the corresponding stress level of a truly dynamic test carried out at the same extension rate. The second method has been used to obtain correlations with dynamic macroscopic flow parameters by applying dislocation damping theory to the hysteresis loop areas.2 The approach has had some success but suffers in that only samples that have been prestrained a few percent can be studied. Although the stresses

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 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,' 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 M. J. Blackburn

The phasal equilibria in TI':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's' 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's paper.' 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"2'4 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,' 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.' 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,' 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

Jan 1, 1967

Jan 1, 1968

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.' 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 M. J. Pool, P. J. Spencer, R. V. Miner

The partial molar heat of solution of rhodiunz in liquid lin and Rh-Sn alloys has been measured as a function of rhodium concentration at 700" , 725" , 750" , and 775°K. The values at infinite dilution are very exo thermic, ranging from -29,950 to -28,260 cal per g-atom Rh at 700" and 775"K, respectively. At the solubility limit the heat of solution becomes sharply nzore exothermic and has permitted the liquidus boundary to be accurately established at each temperature. From the measurements in the two-phase region of liquid Plus RhSn, the heat of formation of RhSn,has been determined. A large increase in the heat of formation between 725" and 750°K suggests the possibility of a phase transformation in this compound. V ERY few measurements have been made of the heats of solution of transition metals in liquid tin; yet those values that are available are of great interest because of their very large exothermic nature. For example, the heat of solution at infinite dilution of palladium in tin has been measured as about -26,000 cal per g-atom (625" to 800°~),' while the heat of solution at infinite dilution of platinum is even more exothermic at -28,591 cal per g-atom (914°K).' These values are of the same order of magnitude as the heat of formation of many intermetallic compounds and as such clearly indicate that very strong bonding must exist between the solute and tin atoms in the liquid solutions. Rhodium might be expected to display similar solution characteristics in tin in view of its close electronic resemblance to palladium and platinum. Since no thermodynamic data are available for Rh-Sn alloys, rhodium was chosen as an appropriate solute for further investigation of transition-metal systems with highly exothermic heats of solution at infinite dilution. EXPERIMENTAL The heat of solution of rhodium in dilute Rh-Sn liquid solutions was measured as a functlon of rhodium concentration at 700°, 725", 750°, and 775°K. The liquid-metal solution calorimeter used in this work has been fully described elsewhere. At the start of each series of measurements, the solvent bath consisted of about 0.5 g-atoms of 99.9+ pct pure tin. To this was made a number of small rhodium additions, about 0.0005 g-atoms each, and the heat of solution was measured for each. Rhodium of 99.9+ pct purity in powder form was used in order to promote rapid dissolution in the liquid tin. The powder specimens were contained in tin foil stated to be purified (lead-free). This foil was found to have no measurable heat of solution in pure tin so the effect of any impurities could be neglected. The energy equivalent of the calorimeter was experi- mentally determined by dropping tungsten and/or tin specimens at intervals during each series of rhodium drops. The tungsten and tin used were 99.95 and 99.999+ pct pure, respectively. The only heat effect due to a tungsten drop, or a tin drop at low rhodium concentrations in the bath, is the sensible heat of the specimen. The heat content of these materials is well-established and is presented in the compilation of Hultgren et al. 4 As the rhodium concentration in the tin bath increases a small heat effect arises from the reaction: Sn (liquid, T) — & (soln, T) where T is the temperature of the tin bath. Where necessary, this heat of solution of tin was determined by Gibbs-Duhem integration, and corrections were made to the heat effect of the tin calibration specimens and the tin foil containing the rhodium specimens. RESULTS AND DISCUSSION The calculated values of the heat of solution of rhodium in dilute Rh-Sn alloys as a function of composition are shown graphically in Fig. 1. The values have been corrected for the sensible heat of the specimens, initially at 273"K, and apply to the reaction:

Jan 1, 1969

By M. Bevis, A. F. Acton, P. C. Rowlands

Defor~nation twinning and transformation twinning modes most likely to be operative in Fe-Ni and Fe-Ni-C martensites have been determined using a new theory of the crystallography of deformation t~inning.~ This analysis shows that potentially important conventional and nonconventional twinning modes1 have been omitted in previous analyses. Discussion is given on the relevance of the predicted twinning modes to the lattice invariant shear associated with the martensite transformation in steels and to anomalous deformation twinning in Fe-Ni-C martensites. THE two most important criteria which appear to govern operative twinning modes in metallic structures1 are that the magnitude of the twinning shear should be small and that the twinning shear should restore the lattice or a multiple lattice in a twin orientation. The latter criterion ensures that the shuffle mechanism required to restore the structure in a twin orientation is simple. These criteria have been adhered to in the prediction of twinning modes2"6 in bcc and bct single-lattice structures with axial ratios in the range y = 1 to 1.09 as, for example, encountered in martensite occurring in steels. Refs. 2 and 3 in particular consider the martensite transformation in steels and the twinning modes in these cases relate to transformation twinning, and hence the lattice invariant shear associated with the martensite transformation. The list of twinning modes which can be compiled from these sources is incomplete and the ranges of magnitude of shear considered could be unrealistically small, particularly in the case of deformation twinning. The latter consideration is supported by the fact that twinning modes with magnitudes of shear large compared with the smallest shear consistent with a simple shuffle mechanism have been established in, for example, the single-lattice structure mercury7 and the multiple-lattice structure zirconium.&apos; In addition the anomalous deformation twins reported by Ftichrnan4 to occur in a range of Fe-Ni-C martensites still remain unexplained. It is clear that a comprehensive analysis of twinning modes likely to be operative in martensite In steels is required. The results of the application of a new theory of the crystallography of deformation twinningg to these structures are presented in this paper. The theory has been used to determine all shears which restore the lattice or a multiple lattice in a new orientation with magnitude of shear up to a required maximum. The orientation relationships between parent and twinned lattices are not restricted to the classical orientation relationships of reflection in the twin plane or a rotation of 180 deg about the shear direction. PREDICTED TWINNING MODES Twinning modes which restore all or one half of lattice points to their correct twin positions will be referred to as m = 1 and m = 2 modes, respectively. These modes are the most likely to describe operative modes in single lattice structures. The bcc m = 1 and m = 2 modes which have magnitudes of shear s in the range s < 2 and s < 1, respectively, have been given10 and are reproduced here in Tables I and 11. Detailed discussion of the crystallography of these modes and cubic modes in general will be discussed elsewhere (~evis and rocker, to be published). The four twinning elements Kl, &,ql,7)2 as well as the magnitude of shear s are given for each twinning mode, and the twinning modes are given in order of increasing shear. Two twinning modes are given in each row of the tables, the twinning mode Kl, Kz, ql, q2 and the reciprocal twinning mode with elements Kl = K,, Ki = Kl, q: = q2, and 17; = ql. The m = 1 and m = 2 twinning modes which describe twinning shears with small magnitudes of shear and simple shuffle mechanisms in bct crystals with -y = 1 to 1.09 are given in Tables I11 and IV, respectively. On increasing the symmetry of the tetragonal lattice to cubic, that is making y = 1, all modes listed in Tables 111 and IV must reduce to crystallographically equivalent variants of the modes given in Tables I and 11, respectively, or become twinning modes with both shear planes as symmetry planes in the cubic lattice and hence not considered in Tables I and 11. With the exception of this last type of mode only those tetragonal twinning modes which reduce to modes 1.1, 1.2, 2.1, and 2.2 of Tables I and I1 are considered in Tables 111 and IV. For values of y in the range -y = 1 to 1.09 the tetragonal modes and the corresponding cubic twinning modes have approximately the same magnitude of shear. The twinning modes listed in Tables 111 and IV are therefore by the criteria given above the most

Jan 1, 1969

By Werner Engelmaier

Constant-strain rotating-bending fatigue tests were conducted on 2024-T3 aluminum alloy constant-strain McAdams-type specimens in ultrahigh vacuum, 10-lo Torr, and in atmospheric air. In the elastic strain range the ratio of vacuum-to-air fatigue life varied from about 10 at a maximum bending stress of 37 ksi to near unity at the endurance limit. After 10 pct of the fatigue life, intergvanular microcracks appeared on the surface which did not appreciably propagate further until the last 5 pct of the fatigue life, where trans-granular cracks propagating first in slip-plane cracking and then in the stress-dominated mode led to failure. No reduction in residual tensile strength resulted from the fatigue of the specimens short of fracture. The mechanism governing the fatigue life operates between the occurrence of the intergranular microcracks and the initiation of the trans granular cracks. MORE than forty years ago, Mc Adam&apos; and Haigh2 published the first systematic studies showing that the fatigue properties of metals were greatly affected by environments. Gough and sopwith3 found in a later study that the fatigue life of metals subject to corrosion can be substantially increased by reducing the atmospheric pressure. This and their later work4&apos;5 was, however, done in a vacuum of only 10~3 Torr. Subsequent studies6-&apos; at a vacuum of 10- Torr showed that water vapor is the primary agent affecting the fatigue properties of aluminum alloys. Only recently was ultrahigh vacuum used for fatigue studied.l Various theories have been put forward to explain this phenomenon. Wadsworth and Hutchings12 postulated that cracks form very early in the test and that the chemical attack by the corrosive components of the atmosphere at the root of the cracks enhances the speed of the crack propagation. They also noted that chemisorbed layers of gas on the fresh crack surfaces prevent cold welding of the crack and make the separation irreversible. Ham and Reichenbach, on the other hand, reported that their specimens showed no cracks after a run in vacuum, even though the runs were long enough to have caused the specimen to fracture in atmospheric air. They also reported that in argon at 0.14 Torr the fatigue life was about 5 times longer than at 7 X lo-&apos; Torr. Jacisinll reported that fatigue tests in dry nitrogen showed results close to those obtained in ultrahigh vacuum. The present experiment was designed to determine the extent to which cumulative fatigue damage, i.e., the accumulation of length of fatigue cracks, reduces the residual static tensile strength of an aluminum alloy in both ultrahigh vacuum and atmospheric air and to obtain fatigue-life data for this aluminum alloy at various strains. It was also hoped that information ex- tracted from these data might support one of the previously mentioned theories. 1) EXPERIMENT Test Specimens. The material tested was commer-cial 2024-T3 aluminum alloy. In addition to aluminum, this alloy contains approximately 4.4 pct Cu, 0.5 pct Fe, 0.5 pct Si, 0.6 pct Mn, 1.5 pct Mg, plus smaller amounts of other elements.13 Some typical mechanical properties of this aluminum alloy are listed in Table I.&apos;~ The material was used in the as-received condition, i.e., solution-treated and cold-worked. Mc Adam-type1&apos; constant-stress specimens and notched fatigue specimens were machined from 4 -in. -diam rods, Fig. 1. The critical section of the McAdam-type samples was polished with a 45-deg spiral motion to a No. 8 microfinish. The notch in the notched specimens was machined on a lathe with a forming

Jan 1, 1969

By J. J. Jonas, J. L. Uvira

Equipment was constructed which permitted the hot compression of 99.8 pct Armco iron and 2.8 pct Si steel at constant true strain rates of 0.05 to 1 per sec over the temperature range 600" to 1000°C. A maximum true strain of 1.9 could be attained, followed by immediate quenching or by isothermal annealing. True stress-true strain curves were obtained, and the steady-state flout stress, a, strain rate, i, and temperature, T, were found to fit the following expression: The constants A, a, n&apos;, and AH were determined for the two ,materials. The activation energies obtained for Arrnco iron and silicon steel are 66 and 80 kcal per mole, respectively, and approximate those for seu- diffusion and for creep. This indicates that hot compression is a diffusion-controlled thermally activated process. THE hot compression of iron and steel is usually carried out in the austenite temperature range,1"7 as this is the one of greatest interest with respect to industrial hot working. However, a disadvantage of testing in the austenite range is that the hot-worked structure is destroyed by the phase transformations taking place during cooling. The present study was therefore carried out in the ferritic temperature range, and the hot-worked substructures were preserved by rapid quenching after deformation. The substructural results will be described in a separate paper, and the present communication is restricted to the strain rate/stress/temperature relationship observed during hot working. The results of hot-compression testing are usually given in the form of true stress/true strain curves, with a different curve for each temperature/strain rate ~ornbination.&apos;,~,~ Sometimes simple algebraic equations are fitted to the curves, so that certain extrapolations or interpolations can be performed.1&apos;2&apos;5 These equations are, however, devoid of mechanistic interpretations. The present study was undertaken to show that hot compression can be described by an equation of the type used in creep studies. That is, it will be shown that the temperature dependence of the strain rate in hot working is well-represented by an Arrhenius term, with an activation energy similar to that for creep. Also it will be seen that the stress dependence of the strain rate is similar to that for creep EXPERIMENTAL METHOD AND MATERIALS The investigation was carried out with the following three ferrous materials: 1) Armco iron; 2) Armco iron with 0.26 pct Mn; 3) 2.8 pct Si steel. The first two materials were utilized for investigations performed in the temperature range 600" to 800°C; the last one was used for tests at temperatures from 600" to 1000°C. The materials were of commercial purity,* as shown in Table I. Cylinders of five different sizes were prepared by strain annealing. The resulting mean grain diameter was 3 mm in the 1-in. Armco iron and 2 mm in the other sizes and grades. Different ratios of diameter/height were used to enable the determination of the coefficient of friction. The specimen faces were provided with concentric grooves, which acted as lubricant holders during compression, as recommended by English and ~ackofen&apos; and others.2&apos;9 Powdered glass lubricants were applied to the samples before hot compression to decrease friction and barreling, following the practice of previous investigator~.~~~~~~~~ Different mixtures of glass powder were used for each temperature, after the determination of suitable compositions by experiment.&apos;&apos; Equipment for Hot Compression. Hot-compression tests were carried out on an adapted 150-ton vertical hydraulic extrusion press and also on a modified high-temperature creep machine. The modified extrusion press was used for temperatures up to 800°C. The following items were added to the press: a) a high-temperature furnace with built-in upper and lower platens; and b) a transmission assembly, which permitted the attainment of logarithmically decreasing crosshead speeds. These accessories are described in detail in Ref. 11.

Jan 1, 1969

By R. H. Hopkins, R. W. Kraft

X-ray and metallographic analysis reveal that the preferred cryslallograPhic relationships in direc-tionally solid~fied Pb-Sn eutectic specimens can be stated: interface growth direction, Experiments in which tin single-crystal seeds were used to nucleate the eutectic demonstrate that the normal lamellar structure observed at steady state can be forced to break down initially to a semide-generate structure when the crystallograPhic direction of the tin seed does not lie within the preferred eutectic interface plane. A normal structure eventually develops by preferred grain growth. X-ray topo-graphs and rocking curves substantiate that the perfection of eutectic samples increases as growth proceeds until steady-state conditions prevail. RECENT years have seen substantial progress made in the understanding of eutectic solidification through both intensive theoretical1&apos;&apos; and experimental investigations (see Ref. 7 for a review and extensive bibliography of both aspects). Several important observations concerning the nucleation and growth aspects of binary eutectic solidification have been brought to light. Briefly some of these include the nonrecipro-cal nucleation of one phase upon another,&apos;j9 the tendency for a specific low-index direction of one or both phases of the eutectic to be aligned in the growth direction during unidirectional solidification,&apos;0711 and the production of lamellar microstructures having a preferred interface plane between "11-13 phases. Questions quite naturally arise as to the mechanism by which preferred grain growth evolves during eutectic solidification and what relationships (if any) connect the initial nucleation of one phase upon another with the preferred growth directions and interface planes observed after a few centimeters of growth in many systems. This study was initiated in an attempt to answer these questions. An experiment was devised in which both the nucleation and growth steps in the crystallization of a binary eutectic, Pb-Sn, could be correlated with subsequently developed eutectic morphology and crystallography. This was accomplished by nucleating the eutectic upon a tin single crystal seed and then causing the eutectic to grow from the seed by directional freezing. The morphology of the structures produced in this manner was then monitored metallographically and the orientation relationships and substructural perfection determined by X-ray analysis. The information thus ob- tained was correlated to the growth history of the samples. EXPERIMENTAL DETAILS The eutectic of composition 38.1 wt pct Pb and 61.9 wt pct sn14 was prepared by accurately weighing lead and tin of 99.999+ (from ASARCO and Lytess Metals and Chemicals, respectively), melting in a clean Pyrex beaker under an argon blanket, and casting into the proper crucible for resolidification as described below. Tin seeds were grown by the method of ~halmers," saw-cut, oriented by the Laue method, and soldered to the pull rod of the Czochralski puller. All seeds were given a final electropolishing (to assure the removal of any deformed material from the cutting operation) and acetone degreasing immediately prior to the nucleation experiment in which they were to be used. Eutectic samples were unidirectionally solidified in a horizontal graphite boat1&apos; or by pulling from the melt16 with tin (or graphite) seeds. A flowing argon atmosphere was employed in all experiments and growth rates and temperature gradients, constant for a given run, varied from 2 to 4 cm per hr and 8" to 15°C per cm over the course of all the experi-

Jan 1, 1969

By H. E. Cook

The Ising model for the internal energy of a binary alloy has been used to obtain a general equation for the critical resolved shear stress of partially ordered crystals. The equation expresses the stress in terms of the Warren "alphas " and can be used to estimate the variation in strength with order without the assumption, present in the original formulation of this problem in terms of domain size, that order is complete within each domain and that the domains are of ungorm size and shape. In addition, it is the general equation, according to the Ising model, for strengthening by short-range order. Two applications of the equation are considered: One is an estimate of the variation in strength of CkAu with long-range order. The other is an estimate of the variation in strength of FeCo with quench temperature. Reasonable agreement is found with the variations reported in the literature. When the internal energy of an alloy crystal depends upon the distribution of solute, the strength of the crystal will also depend upon it because a portion of the applied stress for plastic deformation will be: where V is the volume of the crystal and E(E) is the energy change associated with the solute redistribution caused by the plastic strain, E. We expect T to equal zero for a crystal having a random arrangement of solute because the arrangement would remain random after plastic deformation. Likewise, we expect it to equal zero when the crystal is perfectly ordered because the motion of paired dislocations found in such crystals does not disrupt order. However, when short-range order exists or when long-range order is incomplete, plastic deformation will decrease the amount of order and additional work, proportional to the ordering energy, will be expended. Fisher&apos; estimated T for crystals having short-range order by assuming an interaction energy between neighboring atoms and estimating the change in the number of unlike neighbors as a dislocation moved through the crystal. (His analysis was limited and several workers2"6 have since given more complete ones.) Fisher minimized the importance of a strengthening mechanism of this type for paired dislocations in a structure having long-range order. ~ottrell,&apos; however, pointed out that T could be appreciable for ordered crystals having antiphase domains. He attributed the strengthening to the increase in surface energy of the domains as they were cut by paired dislocations. Ardley,&apos; in his test of Cottrell&apos;s theory, found that r for Cu3Au crystals obeyed the equation: for 1 > t where 1 is the domain size, t is the domain wall thickness, and y is the surface energy of an antiphase boundary. His experiments represent the classic confirmation of the strengthening mechanism proposed by Cottrell. However, the assumptions involved in using Cottrell&apos;s theory are valid only for large domain size in CU~AU,~"~ i.e., when Eq. [2] reduces to: For small domains, ~linn~ has questioned Ardley&apos;s assumption that order was complete, and, indeed, Stoloff and ~avies" fpnd it incomplete until a size of approximately lOOA was reached. Even when the order within a domain is complete, it is not obvious how one determines the appropriate value for I in a structure where domains vary in size and are irregularly shaped. The purpose of this paper is to estimate T without restrictions upon the degree of order and domain shape. Our major assumption will be the use of a generalization of the model proposed by Bethe" (the Ising model) for the internal energy. This will in fact allow us to combine the theories for strengthening by short-range order and by antiphase domains into a single, general formalism. We will use the results to estimate the variation in strength of Cu3Au crystals with long-range order8 and the variation in flow stress of FeCo crystals with quench temperature.12&apos;13 INTERNAL ENERGY For simplicity, we restrict our considerations to those binary solid solutions which can be described as an arrangement of atoms on a Bravais lattice. An atom site will be indexed by three numbers (PI, pz, p3) determined by the vector: from the origin fixed at atom (0, 0, 0) to the atom site where a&apos;, an, and a, are the lattice translation vectors. We write: For the energy of the crystal where pi(p) is the probability (either zero or one) of finding an atom of type i (i = 1, 2) at site (p), which is shorthand for (pl, pz, p3) and pj(p + r) is that for an atom of type j (j = 1, 2) at the site (p + r), which is shorthand for (pl + rl, The coupling parameter, resents the energy associated with the pair Pi(p), Pj(p + r). The crystal is assumed large enough so that surface effects can be neglected; therefore, trans-lational and inversion symmetry require the coupling parameters to obey the relations

Jan 1, 1969

By S. K. Asunmaa, W. D. English, N. A. Tiner, W. A. Cannon

This paper discusses the reaction of metal surfaces with fluorine. Fluorination reactions result in the formation of metal fluoride films which are "passive" toward further reaction of the metal with fluorine. These films are very adherent, and do not easily detach from the substrate metal by mechanical flexing or thermal shock. Exposure of passive films to a humid atmosphere produces hydrated metal fluorides which cause secondary fluorination reactions upon reexpo-sure of the metal surface to fluorine. The surface films formed range from 10 to 30A in thickness and they pow at the expense of surface oxide films. The apparent film formation is completed rapidly in 15 to 30 min on stainless steel and nickel surfaces. On copper and on Monel surfaces, the film at first grows rapidly, then increases slowly over an extended period of time. Passive films are formed at all fluorine pressures in the range from 0.1 to 1.4 atm at room temperature. ALL metals react when exposed to fluorine. These reactions generally produce surface films which consist of metal fluorides. The rate of reaction is largely determined by the extent to which these films are protective. Although there is an extensive literature concerning reactions of oxygen with metals, there are very few investigations reported concerning fluorine-metal reactions. Brown, Crabtree, and ~uncan&apos; investigated the kinetics of the reaction of gaseous fluorine with copper metal which had been freshly reduced in hydrogen. The reaction rate was independent of pressure over the range from 6 to 60 torr. A logarithmic rate law was obeyed in the temperature range from 25" to 300" ~. There was some deviation at higher temperatures which could have been the onset of a parabolic law. The calculated film thicknesses ranged from about two molecular layers, 10A, for 5 hr exposure at room temperature to thirty-five molecular layers for 5 hr exposure at 200" . The authors concluded that no single mechanism could explain all the observations. O7Donnell and spatkowski2 studied the reaction of fluorine with copper at 450°C at pressures from lo to 133 torr. The reaction was found to be pressure -dependent and followed a logarithmic rate law. It was not entirely diffusion-controlled, and fluorine was thought to be the migrating species in the reaction. Miscellaneous metal-fluorine reactions were investigated by Haendler et ~1.~ Reaction products were identified but no rate data were determined. Air Prod- ucts and Chemicals, Inc., have conducted an investigation of reactions between fluorine and various metal powders at room temperature and 85° C. Fluoride film thickness as a function of time of exposure was reported on the assumption that the reaction takes place between fluorine and metal to form the normal metal fluoride. Surface areas of the powders were only estimated so the relative film thicknesses may not be exact. The data showed reaction rates which were generally logarithmic in character, the rate of film growth virtually ceasing after a few hours exposure time for some alloy powders. The effect of moisture on fluoride films was also investigated by measuring additional reaction with fluorine after exposure of passivated powders to atmosperic moisture. The fluorination of iron was studied by 0&apos;~onnell~ at temperatures from 225" to 525" ~ and at pressures ranging from 20 to 200 torr. In all ranges, the reaction followed a logarithmic rate law and was dependent on the square root of the gas pressure. The author concluded that fluorine gas passes through pores in the film. As the film grows, the blocking of pores leads to a rapid decrease in reaction rate; hence a logarithmic rate law is observed. Jarry, Fischer, and Gunther&apos; investigated the mechanism of the reaction of fluorine with nickel at about 600" to 700°C. On the basis of the metallographic examination of fluoride scales growing on the nickel and from separate radioautographic data, it was claimed that fluorine is the migrating species in the reaction. This is in sharp contrast to the growth of oxide films on nickel where it has been shown that nickel ions migrate through the scale to the gas-solid interface to react with oxygen. Few investigations have been reported of the reaction of fluorine with metal oxides. Such investigations should be of great significance for a better understanding of passivation in view of the ubiquitous oxide films on technical alloys. Haendler et al.3 studied the reaction of fluorine with oxides of copper, tin, titanium, zirconium, and vanadium. Copper (I) oxide reacted as follows in the temperature range 150" to 300"~: temperature above 300" ~ was required for the CuO to react to form additional copper fluoride. Ritter and smith7 also investigated the reaction of fluorine with copper (11) oxide. An oxide powder comprised of spherical particles with a fairly high surface area was reacted with fluorine, starting at room temperature and increasing to 100° C over a period of 3 or 4 hr. The initial reaction was slow until the fluoride film thickness reached about to or 15R at which time the reaction rate accelerated, then decreased again. Most of the kinetic data was obtained during this final phase of reaction. The authors conclude that the film grows slowly at first until the stresses developed in the distorted lattice are sufficient to rupture the initial

Jan 1, 1969

By K. P. Gupta, A. K. Pal, L. Chandrasekaran, U. P. Singh

The Mn-Sn binary system, investigated at the high-manganese end and between 500° and 1000° C, shows four phases at temperatures below 727"C, namely the u Mn, the p Mn, the Mn3 Sn, and the Mn, Sn phases, while at higher temperatures only the last three phases remain stable. The solubility of tin in a Mn is very small and the maximum solubility of tin in P Mn phase appears to be abollt 10 at. pct Sn. The solubility range of the Mn,Sn and the Mn, Sn phases is 23.0 to 26.0 and 37.0 to 40.0 at. pct Sn, respectively. The lattice parameter of the 13 Mn phase increases with increasing tin content. The Mn, Sn thase is hexagonal with and appears to be basically of the Ni3 Sn type structure except that for quite a few X-ray diffraction lines the calculated and observed relative intensities do not agree well. The Mn-Sn binary system has been studied by several investigators.&apos;&apos;~ Their results indicate that three intermediate phases, namely, the Mn3Sn, Mn,Sn, and MnSn, phases, exist at high concentrations of tin. However, so far the proper phase equilibrium has not been established at the manganese-rich end and very little data is available for the composition range between pure manganese and Mn3Sn. Moreover, earlier investigators differ in their opinion about the exact composition range at which the Mn3Sn and Mn,Sn phases appear and some doubt has been cast by some investigators3 regarding the structure of Mn3Sn phase which has been reported to be isotypic with Ni3Sn (Mgscd type) structure. In this investigation an attempt has been made to establish the proper phase equilibrium between pure manganese and Mn + 50 at. pct Sn composition in the temperature range of 500" to 1000°C. PROCEDURE The raw materials used were from three different sources. For exploratory work five alloys containing 5, 10, 15, 20, and 25 at. pct Sn were prepared using 99.9 pct pure manganese and tin supplied by E. Merck & Co., Germany. The rest of the alloys and one more 25 at. pct Sn alloy were prepared using 99.9 pct Mn supplied by Gallard Schlesinger Chemical Mfg. Corp., U.S.A., and 99.999 pct Sn supplied by Semi Elements Inc., U.S.A. Weighed amounts of manganese and tin were melted in recrystallized alumina crucibles in an inert gas (argon) high-frequency induction melting furnace. By careful control of temperature and time of melting the losses were reduced to below 0.2 pct in all cases. Since the losses were very small, no attempt was made here to analyze the samples chemically. Alloys were wrapped in molybdenum foil and sealed in small evacuated fused silica capsules. The alloys were annealed at different temperatures, controlled within + l°C, for sufficiently long periods to attain proper phase equilibrium, and subsequently quenched in cold tap water. The annealing periods used at different temperatures were 15 days at 500°C, 7 days at 600°C, 5 days at 700" and 750°C, 3 days at 800°, 850°, and 900°C, 2 days at 968"C, and two alloys annealed at 968°C were reannealed for 10 hr at 1000° C. From each annealed specimen, a part was utilized for metallographic study while another piece was used for X-ray diffraction study. 1.0 pct HNO, solution and oxalic acid solutions of concentrations 0.05 to 1.0 pct were used for etching Mn-Sn alloys above and below the MnsSn composition, respectively. Since all alloys were brittle, X-ray specimens were prepared using the as-crushed -325 mesh alloy powders. Only one 25 at. pct Sn alloy powder was reannealed in an evacuated silica capsule at 800°C for 5 min and water-quenched. X-ray diffraction patterns . for the Mn3Sn phase with the as-crushed and the reannealed powders did not show appreciable change. Un-filtered iron radiation at 25 kv, 15 ma was used with either Norelco 114.6-mm-diam Debye Scherrer Camera (for phase identification) or Norelco 12-cm-diam symmetrical focusing camera (for lattice parameter determination of the 6 Mn phase). The estimated accuracy of lattice parameter determination for the focusing camera was * 0.001A. RESULTS AND DISCUSSIONS The results of metallographic and X-ray diffraction study made with different alloys are shown in Fig. 1. The variations in lattice parameter with composition for the p Mn and the Mn3Sn phases are given in Tables I and 11, respectively, and the lattice parameter as a function of composition for the p Mn phase is shown in Fig. 2. The lattice parameter of the p Mn phase increases with increasing tin content while for the Mn,Sn phase the data obtained from two two-phase alloys and one single-phase alloy indicate increase in a,, and decrease in c, parameters with increasing tin content. The results, Fig. 1, indicate that the solubility of

Jan 1, 1969

By T. Watanabe, S. Karashima, H. Oikawa

Creep tests of a! iron and its solid-solution Fe-Mo, Fe-Co, and Fe-Si alloys with bcc structure were conducted under constant stresses in ferromagnetic and paramagnetic temperature regions above 0.5T,(T, is the absolute melting temperature). It was found their high-temperature creep behavior changed in the vicinity of the magnetic transformation temperature, that is Curie temperature, TC. In the ferromagnetic region below the steady-state creep rates were lower than those expected from the extrapolation of the data in the paramagnetic region, the amount of decrease being affected by solute addition. Also, activation energies for steady-state creep were different in the two temperature regions. The observed changes were concluded to be due to the effect of ferromagnetism on diffusion. It is well-known that plastic deformation of metals and alloys in the temperature region where mobility of atoms becomes high enough is controlled by atomic diffusion." Many experimental results394 on fcc and hcp materials have been reported to confirm this view. In bcc metals and alloys, not much basic investigation of creep deformation has been performed. In particular, experimental work on iron5-&apos; and its alloys, covering a quite wide temperature range is extremely scarce. On the other hand, the effect of ferromagnetism on diffusion has recently been demonstrated in a iron and its alloys;&apos; it has been made clear that diffusion rates in ferromagnetic temperatur~e region are significantly lower than those expected from diffusion measurement in the paramagnetic region. Therefore, it is concluded that the magnetic effect influences the high-temperature creep behavior in a! iron and in its alloys. The present authors have conducted creep experiments on a iron and its solid-solution alloys over a very wide temperature range, and have demonstrated the magnetic effect. A part of the result has already been reported elsewhere.26 In this paper, the experimental results will be described in detail. While the manuscript was in preparation, a similar magnetic effect on creep deformation of a iron was reported by Ishida . Though their experiments covered an extremely wide temperature range, the creep stresses varied from several thousand psi to several ten thousand psi with decreasing temperature. Consequently, it may be said that there remain some questions concerning their results. I) EXPERIMENTAL PROCEDURE The materials used in the experiments were pure iron and its alloys; they were prepared by vacuum melting (10"" mm Hg) electrolytic iron (99.9 pct), molybdenum powder (99.9 pct), ultrapure silicon, and cobalt pellet (99.5 pct) in alumina crucibles. The ingots were hot-forged to plates 10 mm thick and 50 mm wide, and then were hot-rolled at about 700°C into sheets 1 mm thick. Creep specimens, 5 mm in width and 15 mm in gage length, were machined from the sheets. They were annealed at temperatures which were well above their respective recrystallization temperatures. The chemical compositions of the metal and alloys are shown in Table I together with their heat treatments. High-temperature creep tests by the use of a lever-type creep testing machine were carried out in argon atmosphere under constant tensile stress. In order to keep &eep stress constant within about *0.5 pct, stress change due to specimen elongation was compensated by tensile force of a stainless-steel bellows which was inserted between the loading lever and lower specimen grip with the assumptions of a linear relationship between change in cross section and strain and uniform strain along the section. Beyond the limit of compensation by the bellows, small amounts of load were removed after appropriate strains. The testing temperatures were maintained to within i2"C of the reported values. Creep deformation was auto-graphically recorded at the upper (moving) specimen grip using a linear differential transformer which was held by a stainless-steel rod mechanically connected to the lower specimen grip. It was also directly measured with a dial-gage reading to -& mm. 11) EXPERIMENTAL RESULTS AND DISCUSSION 1) Creep Curves of a Iron and Its Alloys. Creep curves of a! iron, Fe-Si, Fe-Co, and Fe-Mo (<2 at. pct Mo) alloys usually consisted of three stages, that is transient (primary), steady-state (secondary), and accelerating (tertiary) stages. An example is illustrated in Fig. 1 for a! iron. However, in Fe-Mo alloys with more than 2 at. pct Mo, an inverse transient creepZ8 was observed as indicated in Fig. 2. The inverse behavior, which varied with the amount of molybdenum, may be due to the substructure* in the annealed specimen as was sug-

Jan 1, 1969

By R. M. Douthwaite, G. Birkbeck

The effect of grain size and specimen dimensions on the occurrence and magnitude of a yield point drop in pure iron has been examined. The tests were done at room temperature. The results indicate that gain size is the critical factor determining whether a yield drop occurs. The specimen diameter:gain size ratio does not influence the magnitude of the yield drop for the range of gain size and specimen diameters investigated. HUTCHINSON,&apos; petchY2 and worthington3 have investigated the grain size dependence of the upper yield stress (uUYP) and the yield point drop, ouyp - aLYP, in Armco iron, mild steel, and Si-Fe, respectively. These authors used center-annealed wires to avoid stress concentration from specimen shoulders and to ensure uniformity of the applied stress. Coarsegrained specimens show no yield point drop; the yield point drop then increases as d-&apos;I2 increases (where d is the grain diameter). These results can be understood in terms of Petch&apos;s analysis2 in which the magnitude of amp depends on the strain rate in the (limited) number of grains deforming plastically at the upper yield point. If N grains per unit volume are undergoing plastic deformation, the strain rate in the deforming grains is l/Nd3 times higher at the upper yield stress than when the whole specimen deforms homogeneously. If N is constant and independent of grain size at uUyp, then all the grains are deforming when ~d~ = 1, so there is no yield point drop. At finer grain sizes, the yield point drop is given by: where AU, is the friction stress increase corresponding to a tenfold strain rate increase. Christ, Smith, and Burton studied the upper yield point in 0.050-in.-diam wire specimens prepared from zone-refined iron. Each end of the 2; -in. specimens was soldered to a & -in. diam steel ball and the load applied through the two balls. There was a yield point drop in specimens with grain diameters less than 0.1 mm; no drop was observed in specimens of grain diameter greater than 0.1 mm that were free from veining substructure, but specimens of grain diameter 0.129 mm, annealed in the y range, showed an upper yield point. and this was associated with the presence of a veining substructure in these specimens. Christ et al. suggested the upper yield point occurs when more than a specific number of grains fill the specimen cross section so a multiplicity of slip is required to initiate plastic deformation. Table I summarizes the published data on the grain size at which the yield drop disappears. On the basis of this data the ratio of specimen diameter:grain diameter = 5 to 27 appears to be the critical value for the occurrence of a yield point drop. Thus, petch2 interprets the appearance and magnitude of the yield point drop in terms of the limited number of grains deforming plastically at uuyp, whereas Christ et a1. consider that the occurrence of the yield drop depends on the ratio specimen diame-ter:grain diameter. The published data cover a wide variety of materials so some variation between the results is to be expected, but the size range covered in the data of Table I is rather limited. In an attempt to discover whether the specimen diameter:grain size ratio or the grain diameter is critical in determining

Jan 1, 1969

By K. M. Myles

The vapor pressure of palladium over a series of Rlz-Pd alloys has been measured by the torsion-effusion method. The thermodynamic properties of the alloy system at 1575=K have been calculated from the vapor pressure data. The activities and the free energies of formation exhibit large positive deviations from ideal behavior. The enthalpies of formation are endother-mic. The entropies of formation are positive and larger than the ideal entropy of mixing. All of the thermodynamic properties suggest that a strong tendency toward phase separation exists in the solid solutions. The possible origin of the phase instability and the various factors that influence the thermodynamic properties are discussed. RECENT studies of the thermodynamic properties of alloys of palladium with nontransition elements have indicated that a significant contribution to the enthalpy of formation is related to the redistribution of the conduction electrons upon alloy formation.&apos;-&apos; The present work was undertaken to ascertain the importance of this contribution in Pd/transition-metal alloys. The Rh-Pd system was chosen for this investigation for several reasons: 1) The thermodynamics of the system were unknown. 2) Rhodium and palladium are completely soluble at high temperatures; below 1118OK the solid solution becomes immiscible.&apos;, 3) The difference in magnitude between the vapor pressures of rhodium and palladium permitted the use of an existing effusion apparatus. 4) Additional information was known about the alloy system that would facilitate the interpretation of the thermodynamic results. EXPERIMENTAL PROCEDURE The thermodynamic properties of the Rh-Pd alloy system were calculated from the vapor pressure of palladium over solid palladium and over several solid Rh-Pd alloys. The vapor pressure was measured by means of the torsion-effusion apparatus that has been described previously. In this method, an effusion cell is suspended from a tungsten filament inside a high-temperature furnace. Two orifices are located eccentrically such that the effusion of the vapor creates a rotational torque in the filament. The angle of rotation is directly related to the total vapor pressure within the cell. As the vapor pressures of rhodium and palladium are approximately five orders of magnitude apart," the total vapor pressure was considered to be effectively equal to the equilibrium vapor pressure of palladium. The effusion cells were made from high-purity alumina since auxiliary experiments indicated that essentially no reaction occurs between alumina and solid Rh-Pd alloys. Unfortunately, because the orifices were irregular, an accurate calculation of the Free- man-Searcy correction factors" could not be made. The constants were determined in an independent experiment where the vapor pressure of copper, as measured in the alumina cell, was compared with an accurate value of the vapor pressure, which had been determined previously.4 Depletion of palladium from the surfaces of the specimens was minimal as the deflection of the cell remained constant, for at least 15 minutes, at each of the experimental temperatures. Lattice parameter measurements of the postrun alloys also indicated that no changes in the composition of the surfaces had occurred. The alloys were prepared by arc melting the requisite amounts of the 99.99 pct pure elements. The four most palladium-rich alloys were remelted in a levita-tion furnace since complete melting of the components had not occurred in the arc furnace. All of the alloys were subsequently homogenized at elevated temperatures in sealed alumina thimbles. After heat treatment, the alloys were analyzed chemically and were in essential agreement with the nominal compositions. The thermal histories and nominal compositions of the alloys are given in Table I. Lattice parameters of the heat-treated alloys were computed, by means of the method described by Mueller et a1. ,I2 from X-ray diffraction powder patterns obtained with filtered copper radiation in a 114.6-mm-diam Straumanis-type Debye-Scherrer camera. The results, which are tabulated in Table I, exhibit a slightly greater negative deviation from Vegards&apos; law than the values reported by Raub et al.13 The diffraction lines were sharp and well-resolved and thus indicated that the alloys were homogenous. RESULTS The logarithms of the individual values of the vapor pressure of palladium were fit, by the least-squares method, as a linear function of the reciprocal of the absolute temperatures. The constants of the equations are given in Table I along with the temperature range over which the data was accumulated. The latent heat of vaporization at 298.15"K for pure palladium, calculated by the third-law method,14 showed no systematic temperature dependence. The average value of 88,920 * 20 cal per g-atom agrees favorably with the average of the results obtained in the most reliable previous investigations.15"19 The activities of palladium were computed from the vapor pressure data at 1525&apos;, 1575", and 1625OK. Consistent with the mass spectrometric study of the atomicity of palladium vapor,lg the vapor was assumed to be monoatomic. The activities of rhodium were determined by integrating the Gibbs-Duhem equation with the aid of the a function.20 In the calculations, the activities of the pure solid metals were assigned the value of unity. From the activities, the partial and integral free energies, entropies, and enthalpies of formation at 1575° K were computed; they are assembled in Table 11.

Jan 1, 1969