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By C. P. Kempter, H. L. Brown

Recently Chang determined heat content values of tantalum monocarbide and tungsten monocarbide from 325" to985°Kand 326" to 912"K, respectively, and, using other published data, made certain solid-state calculations for these two compounds. Chang expressed his Cp values in units of cal per "g-atom alloy" OK. We consider this poor usage since l) tantalum monocarbide and tungsten monocarbide are not alloys, and 2) an atom of an alloy does not exist. However, one may convert his values to units of cal per mole OK by merely doubling them. For TaC he calculated a Nernst-Lindemann parameter of 9.07 x lo-' "g-atom per cal". We have refined the calculation of this parameter and have arrived at a much lower value. Rather than approximating the true coefficient of volume expansion, a,, as three times the true coefficient of linear expansion, a, we calculated u, from the TaCo.99, lattice expansion data of Fries and Wahman.38 At 25°C a, = 14.3 x 10s per OC. The molar volume was calculated to be 13.32 cu cm per mole at 25°C. From the lattice compression data of Champion and Drickamer~' for "TaC,.,," we determined the room-temperature compressibility to be 3.5 x 10-l3 sq cm per dyne by plotting l/Vo (aV/ap) vs applied pressure. (Since the lowest pressure at which Champion and Drickamer reported a relative volume was 20 kbars, one may calculate an approximate compressibility only. Chang calculated a compressibility of 3.175 x 10-l3 sq cm per dyne from the same data.) We also used twice Chang's value of Cp = 4.38 cal per "g-atom alloy" OK for the molar heat capacity at 25°C. From these four values we calculated a Nernst-Lindemann parameter of 5.8 x 10-l4 mole per erg or 2.4 x lo- ' mole per cal, and a Cdil value of 2.3 x 10' ergs per mole OK. In the case of tungsten monocarbide no isothermal compressibility has been reported; however, one may calculate an approximate Nernst-Lindemann parameter by using the adiabatic compressibility reported by Brown, Armstrong, and Kempter." Using the WC lattice expansion data of Mauer and Bolz~l we calculated a, to be 12., x l0-' per OC. The molar volume was calculated to be 12.5 cu cm per mole. We used twice Chang's value of Cp = 4.18 cal per "g-atom alloy" OK for the molar heat capacity at 25°C. From these four values we calculated an approximate Nernst-Lindemann parameter of 2 x lo-' mole per cal, which is much

Jan 1, 1969

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 P. J. Spencer, J. N. Pratt

The vapor pressure of manganese over liquid Mn-Sn alloys has been determined by a high-temperature torsion-effusion technique. Alloys containing from 8 to 100 at. pct Mn were investigated in the temperature range jrom 1280" to 1580" and the measured pressure values were used to calculate the partial and integral thermodynamic properties of the liquid alloys. The activities show small negative departures from ideality while the integral heats and excess entropies of mixing are asymmetric inform, changing from positive to negative with increasing manganese content. The possible contribution of various factors to the observed thermodynamic properties is discussed. COMPARATIVELY few thermodynamic data are available for manganese alloy systems.' Therefore, as part of a continuing program of studies of the thermodynamic properties of transition metal alloys, measurements have been made on various binary alloys involving this element. In recent publications,2~3 investigations of liquid Mn-Cu alloys and of the Mn-Au system in both solid and liquid states have been reported. For the first-mentioned system the work suggested that magnetic interactions may be responsible for the observed form of the thermodynamic properties, while in the second the influence of the electrochemical factor appears to be dominant. The present paper describes a similar study of liquid Mn-Sn alloys. Again the thermodynamic properties have been obtained from vapor pressure measurements made by use of a high-temperature torsion-effusion technique.4 A detailed description of the apparatus and of the experimental procedures used in alloy preparation and pressure measurement may be found elsewhere.2'4 EXPERIMENTAL RESULTS Sixteen alloys, ranging in composition from 8 to 100 at. pct Mn, were prepared from spectroscopically standardized manganese of 99.99 pct purity and tin of 99.999 pct purity, both supplied by Johnson-Matthey and Co., Ltd. One-gram samples of the alloys were obtained by carefully weighing appropriate amounts of the pure components into an effusion cell; this was then suspended in the apparatus and the metals melted together in situ by heating under vacuum to approximately 1550°K. After allowing sufficient time for a homogeneous liquid alloy to be formed, vapor pressure measurements were commenced. These were determined as rapidly as possible at a series of steady temperatures within the range of interest. The duration of experimental runs on individual samples was kept sufficiently short to ensure insignificant varia- tion of alloy composition during investigation. After completing pressure measurements, the alloys were rapidly cooled and their compositions checked by weighing or chemical analysis. All experiments were conducted using effusion cells machined entirely from boron nitride. Measurements were made using a variety of cells with orifice areas ranging from 0.0032 to 0.0075 sq cm and lengths of the order of 0.04 cm; the usual effusion correction factors for orifice geometry and molecular distribution were calculated using Freeman and Searcy's equation5 and had values between 0.6 and 0.75 for the orifices employed here. The vapor pressures of manganese over the alloys were measured at approximately 20°K intervals in the temperature range 1280" to 1580°K. In view of the close approximation of the measured pressures to Clausius-Clapeyron behavior in the experimental temperature range, the data for each alloy have been expressed by equations of the form: logp(atm) =-A/T + B A least-squares computer treatment was applied to the vapor pressure values in order to obtain the coefficients A and B with their associated error. The resulting equations are listed in Table I, together with the equation for pure solid manganese obtained from a previous study.4 To minimize the effect of possible apparatus calibration errors, the activities and partial free energies of manganese in the alloys were calculated by initial reference to the latter equation, obtained from identical torsion-effusion measurements. The immediately resulting thermodynamic quantities, based on a solid manganese reference state, were then converted to refer to the more appropriate supercooled pure liquid manganese standard; tabulated values of the free energies of solid and liquid manganese from Hultgren et al.' were used for this purpose. Partial entropies of solution of manganese were calculated from the temperature coefficients of the free energies and partial heats from the Gibbs-Helmholtz relationship.

Jan 1, 1969

By R. S. Rickard, M. C. Fuerstenau

Anodic polarization curves for iron dissolution and cathodic polarization curves for copper deposition and ferric and hydrogen ion reduction were studied. These results were used to predict the relative rates of the reactions: The rates of the first two reactions were found to be first order with respect to the reacting ion, and the rale-controlling step was diffusion of the ions to the callzode surface. The rate of hydrogen ion reduction in an oxygen-free solution is dependent on the reciprocal of the square root of the hydrogen ion activity. In solutions containing oxygen, the rate of hydrogen reduction becomes dependent on the square root of the partial pressure of oxygen. At equal concentrations copper precipitation occurs about twice as fast as ferric ion reduction. In an air-saturated solution containing 0.01 M cupric ion at pH 2, the rate of hydrogen ion reduction zs about 10 times slower than that of copper precipitation. At pH values below 3, the rate of hydrogen reduction in oxygen-free solutions is very slozu. COPPER cementation has been utilized industrially for many years as a means of recovering copper from aqueous solutions. There are many different types of cementation plants, but all simply provide a means of contacting iron with relatively dilute copper solutions. In the past little or no attention has been paid to rates or mechanisms of the reactions involved. As a result, this and other studies'-3 have been undertaken recently to establish the important parameters in this system. The reactions involved in copper cementation by iron are: Since transfer of charge is involved in every case, these reactions should be considered from an electrochemical point of view. In any electrochemical system involving electrolytic conduction, passage of electrons necessitates ion transfer to the respective electrodes according to Faraday's law. The current in the system will be proportional to the rate of ion transfer, and, therefore, when the current in the galvanic cell is known, the rates of the reactions involved can be determined. Galvanostatic electrode measurements5" are applicable for these electrochemical studies, in that with this technique polarization curves (current density vs electrode potential) are established by impressing a constant current through an electrode and measuring the electrode potential. Once the current density, electrode potential, and reacting area are known for each reaction in this cementation system, the rates of the iron-consuming reactions can be determined. EXPERIMENTAL MATERIALS Several metal electrodes were used in this investigation; they are shown in Table I. Solutions were made with reagent-grade salts and conductivity water. Air, nitrogen, and oxygen were employed. All of these gases were saturated with water and degreased prior to use. EXPERIMENTAL PROCEDURE The experimental work was divided into two general areas. The first area involved galvanostatic measurements, which were used to determine the rates of reactions as a function of various parameters. The second area comprised actual cementation experiments to check the rates predicted from the electrode measurements. Galvanostatic Electrode Experiments. Polarization curves were obtained using a standard galvanostatic technique5'= with the apparatus shown in Fig. 1. The various electrode polarization experiments were run the same way except for changes in solution composition, polarity, and type of measured electrode. The general procedure involved the following steps: 1) a solution was made 0.5 M in sulfate ion and to the desired cation concentrations; this solution was placed in a constant-temperature bath and saturated with the desired gas; 2) the electrodes were cleaned and placed in the electrode holder; 3) the previously cleaned apparatus was assembled and immersed in a constant-temperature water bath (temperature controlled to ± 0.05"C); 4) the electrode was then positioned; the solutions were introduced, and the polarization meas-

Jan 1, 1969

By R. W. Heckel, R. E. Trabocco

The recovery process in 400 Monel filings was followed, principally, by using the Warren-Averbach technique of X-ray peak profile analysis. The deformation fault probability, a, was 0.006 in samples of unannealed filings. a , the twin fault Probability , was approximately 0.002 in samples of unannealed filings. Both a and 0 were found to "anneal out" at 600°F. The effective particle size and mzs strain increased and decreased in the (111) direction, respectively, with increasing annealing temperature. The actual particle size was found to be almost equivalent to the effective particle size. Tile small values of deformation and twin fault probabilities accounted for the similarity in values of the effective and actual particle sizes. Stored strain energy and dislocation density calculations based on rms strain decreased with increasing annealing temperature. The dislocation density decreased from 10" per sq cm in the unannealed filings to 10' per sq cm in the partially re-crystallized filings. The square root of the dislocation density based on strain to that based on particle size indicated a random dislocation distribution in the unannealed filings. The dislocation arrangement changed to one with dislocations in cell walls with increasing annealing temperature. THE recovery processes which occur in metals are generally thought to be a redistribution and/or annihilation of defects.' Investigators' have shown that recovery processes can be characterized by X-ray line-broadening analyses. Michell and Haig4 measured the stored energy of nickel powder by calori-metry and found the value to be greater by a factor of 2.5 than that from X-ray data obtained by the Warren-Averbach technique.= Minor increases in particle size occurred up to 752°F (recovery), while above 752°F the particle size increased greatly due to recrystalliza-tion. X-ray microstrain values decreased between room temperature and 392"F, remained constant from 392" to 752"F, and decreased from 752°F to a negligible value at 1112°F. Faulkner developed an equation for calculating stored strain energy based on X-ray line-broadening data which gave a closer correlation of measured and calculated stored strain energy based on the data of Michell and Haig. The stored strain energy released during recovery is predominately dependent on the decrease in dislocation density which was p-enerated from cold work.7 Stored energy has been measured8 in alkali halides during recovery and recrystallization and 80 pct of the stored energy was found to be released during recovery. Dislocation distributions have been studiedg in a number of fcc metals by thin-film electron microscopy. Howie and Swann" found the stacking fault energy of copper and nickel to be 40 and 150 ergs per sq cm, respectively. ~rown" has pointed out that these stacking fault energy values should be corrected to 92 and 345 ergs per sq cm, respectively. The dislocation distribution of a metal is directly dependent on the stacking fault energy of the system. Metals of high stacking fault energy such as aluminum cross-slip readily and do not form planar arrays of dislocations. Metals of lower stacking fault energy such as stainless steels" do not cross-slip readily. Cold-worked nickel has been found to form a cellular dislocation structure after annealing.13 The relatively high stacking fault energy of nickel and copperlo to a lesser extent favor cellular structures of dislocations rather than planar arrays after deformation. The present study of recovery was carried out on a Ni-Cu alloy (Monel 400) to compare with prior studies for pure nickel and pure copper. X-ray line-broadening techniques were used to measure the effect of recovery temperature on rms strain and particle size and the results were compared with previous studies on copper'4-'7 and nickel., Calculations were also made on stacking fault probabilities, dislocation density, dislocation distribution, and stored strain energy as affected by temperature. EXPERIMENTAL PROCEDURE The nominal analysis of the Monel 400 used in this investigation was: 66.0 pct Ni, 31.5 pct Cu, 0.12 pct C, 0.90 pct Mn, 1.35 pct Fe, 0.005 pct S, 0.15 pct Si. The annealed material was cold-reduced in two batches, one 50 pct and the other 80 pct. It was originally planned to conduct line-broadening studies of these bulk samples; however, rolling textures that developed produced low-intensity peaks which were not suitable for line-broadening analysis. Filings were prepared at room temperature from both the 50 and 80 pct cold-reduced specimens, series A and series B, respectively, and were not screened prior to heat treatment or X-ray studies. Heating to the annealing temperature, 200" to 120O°F, was accomplished in a matter of minutes in a hydrogen atmosphere. Following heat treatment, some of the filings were mounted and polished for microhardness measurements with a Bergsman microhardness tester, using a 10-g load. A G.E. XRD-5 diffractometer using nickel-filtered Cum radiation was used to obtain all diffraction patterns. Only (111)- (222) line-broadenin data were used in the present study since the {400f peaks were too weak to use. The Fourier analysis of the (111) and (222) peak

Jan 1, 1969

By P. S. Kotva

Dislocation substructures in superalloy matrices of varyzng co)npositions have been studied. In general, it has been found that the alloys can be classified into ''high", ''medium", and "low" stacking fault energy classes based on the type of dislocation substructure observed in the matrix and that the substructure can be correlated to the stacking fault energy. The effect of different types of dislocation substructure and dislocation reactions on the intragranulur precipitation of carbide phases has been studied. In a Ni-Cv-Mo-Fe matrix, precipitation of MC carbides in association with stacking faults has been observed. In most superalloys, solid-solution strengthening and precipitation hardening are the chief mechanisms employed to achieve strength. The latter contribution to strength is usually achieved by the precipitation of / in certain wrought alloys. Insufficient attention has been given to the problem of obtaining strength in su-peralloys by controlling precipitation of carbides on imperfections within the matrix. The present work was undertaken to investigate the dislocation substructure in various superalloy matrices, to study the effect of such substructure on subsequent precipitation of carbides in the matrix, and to investigate whether certain modes of precipitation of carbide phases found in austenitic stainless steels2"4'6 would occur in nickel-base alloy matrices with dislocation substructures of the same type as those found in austenitic steels. 1) EXPERIMENTAL TECHNIQUES Five-pound heats of the various alloy compositions reported here were vacuum-cast. The ingots were given light deformation by rolling to break up the as-cast structure and then homogenized for 24 hr. HASTELLOY alloy X (nominal composition: Ni-2OCr-17Fe-8Mo-0.05C) was homogenized at 2150°F and In-cone1 625 (nominal composition: Ni-20Cr-5Fe-8Mo-3.5Cb-0.05C) was homogenized at 2280°F. Fabrication of 0.004-in. sheet was achieved by cold rolling with intermediate annealing treatments being carried out at the same temperature as those used for homogeniza-tion. Each solution anneal was followed by quenching. The aim of this procedure was to redissolve as much of the primary carbide phase as possible. Samples of the 0.004-in. sheet were cut and encapsulated in quartz capsules and then heat-treated in the tube furnaces. Thin foils were prepared using an ethanol-10 pct perchloric acid bath at 32°F and at a voltage of 22 v. A "window" technique was employed. Observations were made on a JEM-7 electron microscope operating at 100 kv. 2) EXPERIMENTAL RESULTS a) Types of Dislocation Substructure. Fig. 1 shows a schematic correlation between stacking fault energy, SFE, and the type of dislocation substructure observed in various matrices of nickel- and cobalt-base alloys. A precise quantitative determination of stacking fault energy is not implied in the figure but the correlation between stacking fault energy and the type of dislocation substructure obtained allows alloys to be divided into three classes in analogy with the classification employed by Swann and ~uttin~' for binary alloys of copper. Class I alloys are associated with a "high" SFE and show a cellular substructure of dislocations as typified by the micrograph of a thin foil of pure nickel deformed 4 pct at room temperature in Fig. 2. With decreasing SFE the tendency toward cell formation is lessened and dislocations tend to be arranged in coplanar groupings. Examples of this class of alloys with "medium" SFE are provided by the mi-crostructure of solution-heat-treated, quenched, and deformed thin foils of HASTELLOY alloy X, "Waspaloy" (prior to any aging), and Inconel 625. Fig. 3 shows a thin-foil micrograph of an alloy of Inconel 625 composition, solution-heat-treated, quenched, and deformed 5 pct at room temperatures. No evidence of any cell structure can be obtained in materials of "medium" stacking fault energy, Fig. 3, even after severe deformation. The stacking fault energy of the alloy shown in Fig. 3 is, however, not low enough to make the dissociation of dislocations visually obvious. As stacking fault energy decreases further, with successive addition of solute in the matrix, there is an increased tendency toward dissociation of dislocations and cross slip becomes progressively more difficult. Eventually, when the stacking fault energy is "low" enough, complete dissociation of dislocations is seen to occur as shown in Figs.

Jan 1, 1969

By J. M. Oblak, W. A. Owczarski

A cellular appearing recrystallization product formed by annealing a cold-worked nickel-base super-alloy at 1800°F has been studied by electron nzicroscopy. Prior to deformation, an equilibrium micro-structure of fcc matrix y and cuboidal ,,', Ni (Al, Ti), precipitates of CuzAu structure had been established by an age at 1825°F. The strain-free recrystallization cells consist of very large rodular y' particles in a y matrix. They precipitate is oriented and coherent both before and after recrystallization. The results showed that y' coarsening accompanies recrystallization at 1800°F. However, it does so as a secondary effect and does not necessarily take place at lower temperatures. The structural similarity of this reaction to cellular precipitation in other systems indicates that lattice strain may also play a significant role during some cellular precipitation reactions. THERE have been numerous microstructural investigations of recrystallization in single-phase materials but two-phase systems have received much less attention. The second phase can either remain inert or be altered along with the matrix during recrystallization. If the second phase is an oxidelm3 or a relatively inert pre~ipitate,~, recrystallization is retarded when the interparticle spacing is less than 1 p. Prior to the onset of recrystallization, these materials show a well-polygonized substructure with the subgrain size limited by the interparticle spacing. Since recrystallization by the motion of preexisting grain boundaries6 is not observed, retardation has been related to particle pinning of the subboundaries. This pinning prevents coalescence' or growth8 of subgrains to a critical size (formation of a high-angle boundary) necessary to initiate recrystallization. In a material such as a nickel-base superalloy both y matrix and y' precipitate are altered by the recrystallization reaction. Haessner et al.' studied the recrystallization of a cold-rolled Ni-Cr-A1 alloy by electron microscopy. The material was initially cold-rolled in the supersaturated condition. upon annealing at 750°C, immediate precipitation of 7'occurred. Presence of this 7' greatly retarded the onset of recrystallization which eventually took place by the development of randomly oriented, strain-free grains. The original •/ was dissolved at the recrystallization interface and reprecipitated as oriented, coherent par-tiles in the new grain. Recrystallization caused a refinement of .)' particle size. Recently ~hillips'' investigated recrystallization of Ni-12.7 at. pct Al. Reduction by cold rolling presumably elongated the p' precipitate into lamellae that remained coherent with the matrix. After recrystallization at 600" to 750°C, there was no unusual change in y' particle size al- though there was a tendency toward clustering along the prior rolling direction at 750°C. Above 750°C, the recrystallized grains were generally free of precipitate. Studies in the somewhat analogous Cu-3.23 wt pct CO" and Cu-2 wt pct'2 systems demonstrated that the coherent cobalt-rich fcc precipitate in these alloys obstructed softening, initiation, and completion of recrystallization. The precipitates were deformed into lam~llae during rolling and those of diameter less than 250A remained coherent. Recrystallization took place by the growth of new grains into the recovered or poly-gonized material. In the first study," both matrix and precipitate reoriented in the same manner upon passage of the recrystallization interface. There was no change in particle size or morphology. Tanner and ~ervi,~ on the other hand, observed that motion of the recrystallization fronts was strongly hindered by the pinning action of coherent precipitates in the deformed material. Particles in contact with a pinned boundary coarsened and coalesced leaving a denuded zone in the unrecrystallized region. When the number of pinning points was sufficiently reduced by coalescence, the boundary swept past these particles and through the denuded zone. The authors1' considered this as a variation of discontinuous precipitation with both chemical driving force and deformation strain energy contributing to recrystallization. Preliminary observations by the present authors had revealed that recrystallization in Udimet 700, a nickel-base superalloy, occurred in an entirely different manner. Optical metallography showed that the recrystallized product formed as cellular colonies containing coarse y' particles elongated in the direction of cell growth. In this investigation the structural features of this reaction were investigated by transmission electron microscopy. EXPERIMENTAL PROCEDURE As-received I$-in. rounds of Udimet 700* were (wtpct) 18.4 15.2 4.95 4.42 3.43 0.06 0.031 0.14 Bal. solution-annealed for 4 hr at 2150" and then fast air-cooled. An initial y-~' structure was established by a 4-hr age at 1825°F followed by a fast air,cool. Essentially the equilibrium volume fraction of ?' at 1825°F is precipitated within 4 hr. Microstructural examination showed no measurable increase in the amount of precipitate after longer aging times. Deformation consisted of swaging to 52 pct RA with 6 pct reduction per pass at room temperature. To reduce the precipitation potential to a negligible amount, recrystallization anneals were conducted at 1800"~ (982"~). Microstructures were investigated by optical and transmission electron microscopy. To prepare foils for electron microscopy, the material was first sliced into 30-mil slabs parallel to the swaging direction. Discs were dimpled and electrolytically cut from

Jan 1, 1969

By W. A. Backofen, G. Mayer

Single crystals of iron, copper, and a Cu-7 wt pct A1 alloy were pulled through conical dies to simulate the constraint in a polycrystalline aggregate undergoing axisymmetric reduction. With Taylor-type hardening, dependence of the drawing stress, od, on the Taylor orientation factor, M, is predictable from the polycrystal stress-strain curve; in particular, for a power-law relationship, it should follow that d log od/d log M = (1 + n). A first-order agreement with analysis was found in the data from iron. For copper, the implied n from the observed d log od/d l°g M was -0, while for Cu-7Al it was negative. The trend was in the direction of random polycrystal behavior. Thus the idea of hardening only in response to the amount of prior slip loses validity as stacking fault energy (SFE) is lowered. Two possible explanations have been suggested: as stacking fault ribbons are widened, barriers from dislocation reactions become increasingly effective in dispersing slip and reducing the orientation dependence of the total glide strain dm that appears in alternatively, or conjointly, the polyslip shear stress, 7, acquires an orientation dependence of a kind which has the same leveling effect on M. The problem of relating the strain hardening of polycrystalline material to that of an isolated single crystal is still largely unsolved. In a new experimental approach from recent work, single crystals of different orientations have been deformed under the constraints found in an aggregate while measuring their deformation resistance. Procedures have involved drawing cylindrical crystals through conical dies1 and compressing slab-shaped crystals in plane strain.2'3 Predictions for the outcome of such experiments were made first by Taylor~ and later, in more general form, by Bishop and Hill.5'6 Taylor's example was the axisymmetric extension of an fcc crystal slipping on the usual {111}(110) systems or, equivalently, a bcc crystal undergoing 'kestricted" slip on {110}(111). In his solution, the deformation work supplied was equated to that dissipated internally in slip on all active systems. With o the single applied tensile stress, dc the resulting axial strain, and dyT the total glide strain on systems operating at resolved shear stress, 7: The orientation dependence of M was found by minimizing dyT for each orientation while activating five independent systems, Fig. l(a).? The Bishop and Hill analysis, based on a principle of maximum work, leads to essentially the same conclusion; the need for at least five active systems is recognized in the finding that either six or eight are actually brought into operation. The mean value from the entire stereo-graphic triangle in either case is M - 3.06. More recently, Hutchinson8 made a Taylor-type analysis for pencil glide in a bcc structure, from which piehlerg prepared Fig. l(b) as the counterpart in Fig. l(a); here M = 2.75. The obvious weakness in such analyses is the indifference to slip-system interactions. A condition of what might be termed "independent"

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 M. Bevis, E. O. Fearon, P. C. Rowlands

Fe-Ni and Fe-Ni-C martensite specimens have been deformed in compression at room temperature and the habit planes of operative deformation twins determined by two-surface optical trace analysis. The full orientations of the martensite crystals were determined from divergent X-ray beam diffraction patterns. The experimental results are in excelled agreement with predicted twinning modes. In particular, the habit planes of some deformation twins in bcc martensites are consistent with a "Type XI compound&apos;&apos; twinning mode with Kl, Kz, 71, 77~ elements given by {5, 8, 11) {ioi}, (33) (ill) Tetragonal derivatives of this mode are operative in bct martensites. UnUSUAL deformation twinning modes have been reported by Richman&apos; to occur in Fe-Ni-C martensites with bcc and bct structures. The twin habit planes were determined by single-surface trace analysis (pole locus method) and the remaining twinning elements were determined from the geometry of twin-twin intersections. The indices assigned to the observed habit planes are (3 101, "(089)" and "{0, 1,13)" or "{1,2,7} ", and only in the first case do the twinning elements correspond to a predicted twinning mode. This is mode 1.4 in the paper by Bevis et al. The results presented in Ref. 2 indicate that previously unpublished bcc and bct modes should be operative in preference to the (130) mode and anomalous modes reported by Richman. In view of these results and the uncertainties involved in determining habit planes from single-surface trace analysis and twinning elements from twin-twin intersections5 a two-surface trace analysis of deformation twins in Fe-Ni and Fe-Ni-C martensites has been carried out. EXPERIMENTAL PROCEDURES Two alloys with compositions Fe-23 pct Ni-0.6 pct C and Fe-30.4 pct Ni were prepared from 4N pure materials by induction melting under a vacuum of 10"5 mm Hg. The alloys were homogenized at 1350&apos;~ for 5 days. Both of these alloys are austenitic at room temperature with M, temperature - — 50"C. The aus-tenite grain size of the Fe-Ni-C alloy was approximately 300 to 400 p. The Fe-Ni alloy was remelted in a vertical tube furnace and the melt lowered slowly from the hot zone of the furnace to produce s ingle -crystal austenite specimens. Specimens approximately 10 by 5 by 5 mm were cut from the ingots and quenched to various temperatures below the Ms temperature. The specimens were elec-tropolished in a 10 pct perchloric acetic electrolyte before being deformed in compression at room temperature. Martensite plates which exhibited profuse deformation twinning were selected for analysis and the specimen polished on a second surface such that the two surfaces which contained the martensite plate enclosed an obtuse angle of approximately 145 deg. The specimens were then electropolished to reveal the traces of the deformation twins on both surfaces. The full orientations of the martensite crystals were determined using a divergent X-ray beam technique (Kossel line technique) employing an AEI SEM2 electron probe microanalyzer. Details of this technique which include a detailed description of the Kossel camera attachment to the microanalyzer used in the present experiments have been discussed elsewhere.3 Only additional details relevant to this investigation are discussed here. The specimens were mounted with one surface normal to the incident electron beam as illustrated schematically in Fig. 1. The martensite plates to be analyzed were located using the normal scanning equipment of the microanalyzer. The position of the electron beam and hence the position of the source of divergent X-rays generated within the crystal could be located to within 1 p. Exposure times of approximately 8 to 10 min were required for back-reflection Kossel patterns and it was found that useful diffraction patterns could be obtained consistently from heavily deformed martensite plates. A reference line (carbon contamination mark) produced on the two surfaces of the specimen by scanning the electron beam in a direction having a known relationship with the reference !ine in the X-ray camera enabled the full orientation of the crystals to be determined. Martensite plates with widths as small as 8 p could be oriented using this procedure. The Kossel line patterns were interpreted using the charts developed by Rowlands and ~evis~ as generally

Jan 1, 1969

By C. E. Violet, R. J. Borg, E. M. Howard

The miscibility gap in the Au-Ni system has been determined by Mossbauer spectroscopy, with used as a probe. The phase boundaries were determined from the compositional dependence of both the isomer shift and Curie temperature. X-ray diffraction measurements were also used to confirm the Mossbauer results. 1 HE purpose of this research is to demonstrate the application of Mbssbauer spectroscopy to the determination of phase boundaries and to redetermine the miscibility gap by an independent and novel technique. The techniques evolved in this study are readily applicable to other polyphase systems and are generally as quick and accurate as the more conventional methods, e.g., metallography, X-ray diffraction, thermal analysis, and so forth. To be sure, not all polyphase systems will lend themselves favorably to Mijssbauer investigations, but this is a problem met in the use of conventional methods as well. The Mbssbauer spectrum responds to a different set of physical parameters, and consequently provides an entirely independent method of analysis. It is especially useful if the system has either a ferromagnetic or an antiferromagnetic transition. The Au-Ni system was selected because alloys containing more than -60 at. pct Ni become magnetically ordered at low temperatures; also the miscibility gap is quite well established (see Ref. 7 for a compilation of pertinent references, also Fig. 11, and thus provides a reliable test of this novel procedure. As Fe is the most commonly used Mijssbauer isotope, there exists a wealth of information concerning its behavior in iron-containing alloys and compounds. However, as yet there have been relatively few experiments using it as a probe to investigate nonferrous systems. By choosing a nonferrous alloy system, we are able to demonstrate that its use is not restricted to systems containing iron as one of the major constituents. Wertheim and ~ernick&apos; have used the same method to investigate Cu-Ni, and demonstrated that one can obtain a systematic variation in the isomer shift and magnetic hyperfine field. However, we believe this to be the first time these techniques have been used to establish phase boundaries. Two hyperfine interactions were measured and used to determine the phase boundaries, viz., the magnetic hyperfine splitting and the isomer shift which in this alloy system are both strong functions of composition. Calibration curves were established based upon single-phase solid solutions obtained by quenching from temperatures well above the maximum of the miscibility gap, see Fig. 1. Solid solutions containing 25, 50, 65, 75, 85, 92, and 96 pct Ni as well as pure nickel were used in the calibration procedure. Fig. 2 shows the Curie temperature, TC, and the isomer shift, v,, as determined from the Mbssbauer spectra, and variation in lattice parameter as determined by X-ray diffraction, as functions of composition. The compositions of the two-phase systems quenched from temperatures within the miscibility gap are obtained by comparing their respective values of TC and v0 with the calibration data. I) EXPERIMENTAL Mbssbauer sources were made by fusing the component metals in a tungsten arc melter, which has a water-cooled copper hearth. Both nickel and gold were 99.999 pct pure, and the melting was done in an atmosphere of purified argon. The alloys were rolled, diced,

Jan 1, 1969

By George V. Smith, Daniel E. Sonon

Various mechanical properties of the Ni-Co-C alloy system were investigated to delineate the strengthening effect of carbon. Carbon concentration, cobalt concentration, vain size, temperature, and strain rate were varied so that thermal activation analysis and the Hall-Petch analysis could be used to evaluate the strengthening effect of carbon. Increasing carbon increased the strength of nickel and a Ni-60 pct Co alloy , with the effect becoming more pronounced at lower temperatures. Yield stress depended linearly on carbon concentration in nickel, but it depended on the square root of carbon concentration in the Ni-60 pct Co alloy. The Hall-Petch slope of nickel increased with carbon concentration; however, that of the Ni-60 pct Co alloy did not. The yielding behavior of these alloys was sensitive to composition, grain size, and temperature. Cobalt eliminated serrations in the flow curve of carbon-containing nickel at 300&apos; and weakened them severely at higher temperatures. Pairs, or clusters, of carbon atoms appear to be responsible for the observed strengthening behavior. FLINN&apos; conducted several experiments with carbon in nickel in an effort to provide information on the strengthening effect of interstitial impurities in solid solution in fcc metals and alloys. Strengthening which increased with decreasing temperature led him to conclude that carbon causes Cottrell locking in nickel. Fleischer2 analyzed Flinn&apos;s data and calculated that the strengthening effect of carbon in nickel was smaller by a factor of fifty than the strengthening effect of carbon in a! iron. Fleischer2 termed the magnitude of strengthening of carbon in nickel "gradual" and that of carbon in a! iron "rapid". He attributed "gradual" hardening to hydrostatic strains and localized changes in modulus of elasticity around solute atoms, whereas he attributed "rapid" hardening to tetragonal strains around solute atoms. Sukhovarov et a1.3-7 reported strain aging and serrated plastic flow in nickel, both of which they attributed to the presence of carbon. Serrated plastic flow has been rationalized by a process involving a series of dislocation pinning and multiplication steps.8, This process is more probable when screw dislocations are strongly pinned. Screw dislocations cannot be pinned by pure hydrostatic forces from the symmetrical strains of an interstitial impurity in an fcc lattice, except for small, second-order effects. However, they might be pinned by localized changes in modulus of elasticity around solute atoms,&apos; by the pinning of the edge components of the partial dislocations of an extended screw dislo~ation,&apos;~ or by clustered groups of solute atoms whose net elastic stress field is unsymmetric. The purpose of the present work was to investigate various mechanical properties of the Ni-Co-C a1loy system which are sensitive to pinning effects in order to delineate the specific pinning mechanism of carbon. Carbon concentration, grain size, temperature, and strain rate were varied so that thermal-activation analysis and the Hall-Petch analysis could be used to evaluate the pinning mechanism. Cobalt was added to lower stacking fault energy so that the number and extension of split, screw dislocations would be increased in order to test the possibility of pinning by carbon at extended screw dislocations. EXPERIMENTAL PROCEDURE Nickel and cobalt (both 99.98 pct-. pure) were melted with graphite in stabilized zirconia crucibles and cast at lo-&apos; Torr to form Ni-C and Ni-60 pctCo-C alloys. Two ingots were heated to 1250°C and were forged to 1-in.-sq bars. These bars were machined to 4-in.-round bars, and then swaged cold to 0.144-in. -diam rods. Reductions in area of approximately 75pct were used with intermediate anneals at 900°C for 1 hr. The carbon content of batches of 0.144-in.-diam rods from each ingot was reduced to two levels by annealing 5-in. lengths in palladium-purified, dry hydrogen at 1100°C for 25 and 100 hr. The remaining material from each ingot was annealed at 10"5 Torr for 1 hr at 1100"~. These treatments gave a total of three carbon levels for both the nickel and the Ni-60 pct Co alloy. The 0.144-in.-diam rods were swaged to 70-mil wire, cut into test specimens, and then re crystallized at lom5 Torr in capsules for 1 hr at temperatures ranging from 760" to 1050" ~. The capsules were broken and the specimens were immediately quenched into water. Average grain size was measured using Hilliard&apos;s method of circular intercepts." Annealing twin boundary intercepts were counted in addition to grain boundary intercepts to establish an average grain size. Average grain sizes ranged from 5 to 140 p depending on the cobalt concentration and re-crystallization temperature. Tension tests were made in duplicate at various temperatures at a crosshead speed of 8.34 x 10"4 in. per sec with an Instron Universal Testing Machine. Specimens of 1-in. gage length with soldered ball ends were used at atmospheric and cryogenic temperatures. Pinch grips were used on specimens at elevated tem-

Jan 1, 1969

By N. J. Grant, Per Knudsen, J. T. Blucher

The fatigue behavior of three SAP alloys was studied in ternzs of strain rate and temperature, at high strains. The k values in the modified Manson-Coffin equation, Nk4 = C, were less than 0.5 under all test conditions, and change with strain amplitude for the lower-oxide alloys at about 2 pct strain. Lowest k values were near 0.25. Strain rate had no effect on life at 80 F, but had an increasingly greater effect with increasing temperature above 500". Life decreased with decreasing strain rate, above 500"F, and with increasing temperature. Ductility at fracture in a tension test was indicated to be an important factor in determining 1ife in these big+-strain tests with the SAP alloys. INEVITABLY, in the course of mechanical tests at elevated temperatures, particularly if significant time at temperature is involved, there are large changes in structure; these changes make it difficult to relate behavior patterns over ranges of temperature or strain rates at high temperatures. Such changes are to be expetted in low cycle fatigue at low strain rates and high temperatures. Accordingly, it was of great interest to examine the low cycle fatigue behavior of SAP / an aluminum oxide dispersion-strengthened aluminum, a type of alloy which had shown unusual structure stability to temperatures as high as 1000" to 1150°F and resisted recrys-tallization essentially to the melting temperature.&apos;j3 Since the matrix is pure aluminum, there are no complications of averaging, agglomeration, or phase solution. It was also desirable to check the Manson-Coffin equation4?&apos; for the SAP alloys, namely N~E~ = , where ep is the total plastic strain amplitude, k and C are constants, and N is the number of cycles to failure. Here, too, was an opportunity to check the roles of temperature and strain rate with a very stable material. Tavernelli and coffin6 had concluded that k had a value of about 0.5 for many alloys and C was equal to ~/2, where E is the fracture ductility determined from a static tension test. The results were obtained from low-temperature tests where creep and diffusion processes are unimportant. Manson7 found k = 0.6 fitted his data reasonably well; however, in later analyses of a large amount of low cycle fatigue data generated at room temperat~re@"~ he found k to vary from 0.6 for short lives to 0.21 for long-life fatigue tests. In the latter studies,89g Manson separated the total strain range into elastic and plastic components when he found that k was influenced by the nature of the strain. The use of EL (total strain) instead of EP (total plastic strain)4&apos;5 makes a difference in the resultant k value. The ratio of changes with temperature, strain rate, and strain; further, there are the problems in the determination of the elastic strain. Based on these considerations, and the improved fit of points in a plot of by Wells and Sullivan,&apos; is also utilized in these studies. Anderson and wahl,14 using commercial 1100 aluminum, and Blucher and Grant,15 using 99.99 pct pure aluminum, found an increase in life with increasing test temperature. Anderson and Wahl were the first to report low cycle fatigue results from SAP materials. With increasing temperature, the role of strain rate becomes more important. In this regard, care must be exercised to differentiate between frequency (wherein strain rate may vary from zero to a maximum in each cycle, sinusoidally, for example), and constant strain rate, as used in the present study, in a saw-tooth type cycle; in the latter case, the frequency is not specified but can easily be calculated from the strain and strain rate data. It has generally been found that life in low cycle fatigue tests decreases with decreasing frequency16 or with decreasing strain rate at elevated temperatures.15 Coffin,17 reviewing Eckel&apos;s work,16 also reported that k increased with decreasing frequency for acid lead, yielding values from 4.0 at a frequency fo 6.6 cycles Per day to 1-46 at a frequency of 7440 cycles per day; the value of k decreased to 0.58 at a frequency of 2.38 x lo6 cycles per day. EXPERIMENTAL PROCEDURE Three SAP alloys, of two nominal compositions, were tested. Alcoa supplied XAP 005 as 2-in.-diam extruded bar, of nominal composition A1-7 wt pct A1203. The Danish Atomic Energy Commission supplied SAP 930 (A1-7 wt ~ct Ala3) and SAP 865 (A1-13 wt pct Al&) manufactured by Swiss Aluminium Ltd., in the form Of $-in.-diam extruded rod. Metallographic comparison of the structures of XAP 005 and SAP 930 showed the former to have a more uniform oxide distribution. Button-head specimens were machined in the longitudinal direction of the bar with 0.4 in. gage length by 0.2 in. diameter, with a fillet radius of j-B in. After machining, the specimens were electropolished in a 1 to 4 mixture of perchloric acid to methanol to remove all machining marks. All test bars were in the as-extruded condition. The fatigue tests were performed on a hydraulically activated, axial strain machine, with complete reversal of strain.15 Test conditions were:

Jan 1, 1969

By E. S. Fisher, L. C. R. Alfred

The elastic anisotropy factors, c4,/c6,, c3,/cll, and c12/cl,, for hcp metal crystals vary significantly among the dgferent unalloyed metals. Significant variations with temperature are also found. The effects of elastic anisotropy on the dislocation in an elastic continuum with hexagonal symmetry have been investigated by computing the elasticity factors for the self-energies of dislocations in fourteen different metals at various temperatures where the elastic moduli have been reported. For most of the metals the effects of the orientation of the Burgers vector, dislocation line, and glide plane are small and isotropic conditions can be assumed without significant error. Significant effects of anisotropy are, however, found in Cd, Zn, Co, Tl, Ti, and Zr. The elasticity factors have been applied in the calculations of dislocation line tensions, the repulsive forces between partial dislocations, and the Peierls-Nabarro dislocation widths. It is predicted that the increase in elastic anisotropy with temperature in titanium and zirconium makes edge dislocations with (a), (a + c), and (c) Burgers vectors unstable in basal, pyramidal, and prism planes, respectively. The probability of stacking faults forming by dissociation of Shockley partials in basal planes also decreases with increasing c4,/c6, ratio, when the stacking fault energy is greater than 50 ergs per sq cm. The widths of screw dislocations with b = (a) in titanium and zirconium increase very significantly in prism planes and decrease in basal planes as c4,/c6, increases. The effects of elastic anisotropy on various dislocation properties in cubic crystals have received considerable attention during the past few years. In the case of cubic symmetry the departure from isotropic elasticity depends entirely on the shear modulus ratio, A = 2c4,/(cl, —c12); i.e., the medium is elastically isotropic when A = 1. Foreman1 showed that an increase in the ratio A produces a systematic lowering of the dislocation self-energy for a given orientation and Poisson&apos;s ratio. ~eutonico~, has shown that large anisotropy can have a marked effect on the formation of stacking faults by the splitting of glissile dislocations in (111) planes of fcc and (112) planes of bcc crystals. ~iteK&apos; made similar calculations for (110) planes of bcc metals. Both studies of bcc metals showed that the large A values encountered in the alkali metals tend to reduce the repulsive forces between Shockley partial dislocations. In fcc metals, however, A does not vary over the large range encountered in bcc metals; consequently, the effect of A on the forces between Shockley partials is masked somewhat by the differences in Poisson&apos;s ratio between metals. The effect of A on the line tension of a bowed out pinned dislocation has also been investigated for cubic crystals, first by dewit and Koehler5 and more recent- ly by Head.6 In both cases the line energy model is applied and the core energy is not taken into account, thus making the conclusions somewhat tenuous with regard to the physical interpretation. Nevertheless, the fact that a large A decreases the effective line tension is clearly evident and the tendency for large A to produce conditions that make a straight dislocation unstable (negative line tensions) also seem evident. Head, in fact, shows visual microscopic evidence that stable V-shaped dislocations occur in 0 brasse6 For hcp metals the definition of elastic anisotropy is more complex and, furthermore, significant deviations from an isotropic continuum are found among a number of real hcp metals, especially at higher temperatures. The present work was carried out to survey the effects of elastic anisotropy on the elasticity factors, K, that enter into the calculations of the stress fields around a dislocation core. Some isolated analytical calculations have previously been carried out for several hcp metals but they are restricted in the dislocation orientations and temperature.8&apos;9 The present computations are based on single-crystal elastic moduli that have appeared in the literature and consider various orientations requiring numerical computations. The results are then applied to survey the effects of temperature on the dislocation line tension and dislocation splitting in hcp metals. PROCEDURE Anisotropy Factors. The degree of elastic anisotropy in hcp crystals cannot be described by a single parameter, such as the A ratio in cubic crystals. The following three ratios must be simultaneously equal to unity in order to have an elastically isotropic hexagonal crystal: The magnitudes of these ratios at several temperatures, as computed from the existing data for the elastic moduli of unalloyed hcp metals, are given in Table I. There are no cases of complete elastic isotropy, but the large anisotropy ratios encountered in the cubic alkali metals are also missing. There are, however, several significant differences among the hcp metals, the most notable being the relatively small A and B ratios in zinc and cadmium and the differences in the magnitudes and temperature dependences of A. It has been noted that the temperature dependence of A has a consistent relationship to the occurrence of the hcp — bcc tran~formation. For cadmium, zinc, magnesium, rhenium, and ruthenium, A is less than unity at 4&apos;~ and, with exception for rhenium, decreases with increasing temperature. In the case of rhenium, A has essentially no temperature dependence between 923&apos; and 1123"~, so that it is clear that A does not approach unity at higher temperatures. Cobalt is similar to the above-mentioned group of metals in that it also does

Jan 1, 1969

By V. Koump, T. F. Perzak, R. H. Tien

A series of experiments were carried out in which the rates of propagation of the liquidus and the eutectic fronts Mere measured during essentially one-dimensional freezing of Al-Cu alloys. The dimensions of the ingots were 3 by 5 by 6 in. Three different alloys containing 0.1, 4.5, and 17 pct Cu were used in these experitments. For each alloy the rate of heat removal was varied to give a total jreezing time in the range 3 to 30 min. The results of these measurements cowlpared favorably with the theoretical model of freezing of binary alloys with time-dependent surface temperature. IN engineering analysis of solidification of commercia1 steels and nonferrous alloys it is a common practice to assume that an alloy freezes by propagation of an isothermal solidification front, i.e., essentially as a pure metal. In two recent theoretical investigations&apos;j2 the present authors explored the possibility of a more realistic approach to the problem of solidification of alloys. In the proposed model the freezing of an alloy is assumed to take place by propagation of two isothermal fronts, i.e., the liquidus front and the solidus (or eutectic) front. The region between the two fronts contains both liquid and solid and is referred to as the solid-liquid region. The width and the solid content of the solid-liquid region vary with alloy type, solute concentration, and cooling rate. For a given alloy system, initial concentration of solute, and the mode of heat removal, the proposed model yields the temperature distribution within the solid skin, temperature, solid fraction, and concentration distributions with the solid-liquid region, and the rates of propagation of the liquidus and the solidus fronts. This model is obviously of considerable practical importance in engineering analysis of solidification processes, since it gives a more realistic estimate of skin strength during solidification and a better estimate of the total freezing time. Before the new model can be used with confidence, however, it is necessary to test this model experimentally. The experimental testing of the proposed model is a relatively simple matter since the effects to be measured are large and a relatively simple experiment will suffice. The theoretical model predicts, for example, that during freezing of an alloy containing substitutional type solute (negligible diffusion in the solid during freezing) the solid-liquid region occupies an appreciable portion of the ingot, even at low concentration of solute.&apos; Another prediction of the theo- V. KOUMP, formerly with U. S. Steel Corp., is now with Research and Development Center, Systems and Process Division, Westinghouse Electric Corp., Pittsburgh, Pa. R. H. TlEN is Senior Scientist, Fundamental Research Laboratory, U. S. Steel Corp., Research Center, Monroe ville, Pa. T. F. PERZAK, formerly with U.S. Steel Corp., is now with Fiber Industries, Greenville, S. C. Manuscript submitted March 6, 1968. IMD retical model, easily verifiable by experiment, is that the rate of propagation of the solidus (or eutectic) front increases as the solidus front approaches the center of the slab. This prediction is contrary to well-known behavior of the solidification front during freezing of pure metals, where the rate of propagation of the solidification front decreases with time and freezing is completed at the lowest rate. A rather severe test of the proposed model is provided by comparison of theoretical predictions and experimental measurements of the effects of cooling rate and composition on the rates of propagation of the liquidus and the eutectic fronts. In order to test the soundness of the formulation and the method of solution of the problem of solidification of alloys a series of experiments were carried out in which the rates of propagation of the liquidus and the eutectic fronts were measured during essentially one-dimensional solidification of A1-Cu alloys. The A1-Cu system was chosen strictly as a matter of convenience. Three different alloys containing 0.1, 4.5, and 17 pct Cu were used in these experiments. For each alloy the rate of heat removal was varied to give the total freezing time in the range 3 to 30 min. The results of these measurements are compared with the predictions of the theoretical model of solidification of binary alloys, with time-dependent surface temperature.&apos; Before the experiments described in this paper were undertaken, a serious attempt was made to utilize the measurements of previous investigators to test the theoretical model. In the course of this preliminary study a careful review was made of experiments of Pellini and coworkers3 and Doherty and Melf~rd.~ The measurements in Pellini&apos;s work were carried out using a steel containing at least four major components. Evaluation of the solid fraction-temperature relation for this steel (required in the theoretical model) is difficult and uncertain. Doherty and Melford, on the other hand, measured the solid fraction-temperature relation experimentally, but did not give sufficient data to explore the effects of composition and the cooling rates on solidification. Hence it was not possible to utilize these measurements to test our theoretical model. EXPERIMENTAL METHOD The experimental technique used in this investigation differs somewhat from the more conventional techniques employed in solidification studies. This technique was developed primarily to eliminate con-vective mixing in the molten metal caused by pouring of molten metal into the mold. In our experiments A1-Cu alloys were melted directly in the mold. The mold assembly used in solidification experiments is shown in Fig. 1. The mold was fabricated from *-in. stainless-steel sheet. The dimensions of

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 A. Phillips, D. H. Killpatrick, V. Kerlins

The tensile failure of two dispersion-strengthened Ni-20 Cr alloys was studied and compared to the fracture of a similar alloy with no dispersoid. The fracture characteristics were studied using electron fruc-tography and transmission electron microscopy. In all three cases, the mode of failure was found to be microvoid coalescence. The failure in the dispersion-strengthened alloys was found to have initiated at the particles. The size of the dimples in the fracto-graphs was found to be related to the spacing of the particles, but not to the total elongation before failure. The elongation before failure was found to be related only to the amount of dispersed phase. These results are compared to those predicted by a theoretical model of ductile failure. THE continually increasing strength requirements for creep-resistant materials capable of long life at service temperatures above 1600"F (875"C) have developed considerable interest in dispersion-strengthened nickel-base alloys. The high yield strength of these alloys results from the presence of a dispersion of fine particles of thoria which act to impede the normal motion of dislocations. Many theories have been presented to explain the role of the dispersion in the strengthening of these alloys. A good review of these theories is presented by Ansell.&apos; The ultimate strength of such alloys is not only related to mechanisms raising the yield strength, but also to the amount of work-hardening which occurs. This work-hardening is determined by the work-hardening rate and the amount of plastic strain before failure. Since fracture limits the amount of plastic strain, a study was undertaken to gain a better understanding of the fracture mechanisms in these alloys. Electron fractography and transmission electron microscopy were used to study the fracture characteristics in two dispersion-strengthened alloys and one similar alloy containing no dispersoid. These results are related to the tensile properties of the dispersion-strengthened alloys at room temperature and at 2000°F (1095°C). The results are also related to a theory for ductile fracture. 1) PROCEDURE Standard tensile specimens were made from 0.020-in. (0.051-cm) sheets of three different Ni-Cr alloys. The alloys had nominal compositions of Ni-20Cr, Ni-20Cr-2Th0,, and Ni-2OCr-4Th0,. All alloys were supplied in an annealed condition. The specimens were fractured in tension at room temperature to determine the effect of the dispersed thoria on the fracture appearance. The tensile properties were determined from the average of a minimum of three ten- sile specimens for each condition tested. The fracture surface of all of the alloys was examined by electron microscopy using standard two-stage plastic-carbon replica techniques. Thin foils of the dispersion-strengthened alloys were used to investigate the size and spacings of the dispersion particles, and to investigate sections of the 2 pct thoria alloy taken from areas of the specimen adjacent to the fracture surface. The thin foils were mechanically ground to 0.010 in. (0.025 cm) and then chemically polished to approximately 0.001 in. (0.003 cm) in a solution of 29 g of ferric chloride and 10 ml hydrochloric acid in a liter of water. The polishing solution was maintained at 150"F (65°C) during the thinning operation. The final thinning of the foil was done electrolytically using a solution of 700 ml ethanol, 100 ml 2-butoxy eth-anol, 120 ml distilled water, and 78 ml perchloric acid (70 pct). The potential was maintained at 15 v and the bath temperature at -20°~ (-29°C) during the thinning operation. The final thickness of the foil was approximately l000A as determined from the width of twins boundaries observed in many of the foils. 2) RESULTS AND DISCUSSION The electron fractographs of the fracture surfaces of the alloys are shown in Figs. 1, 2, and 3. The normal interpretation of this type of fractographz is that, as a result of the difference between elastic and plastic properties of the matrix and the particles or other inhomogeneities in the alloy, microvoids are formed

Jan 1, 1969

By N. Standish

Heat transfer coefficients have been measured in beds of various packings irrigated with mercury and molten fusible alloy countercurrent to hot gases. The measured coefficients for both systems were found to increase with gas velocities and liquid rates. Correlations were determined which show this dependence and also indicate that heat transfer in these systems is influenced by the liquid flow characteristics and the thermal conductivity of the gas and the solid packings. A heat transfer model has beer2 proposed which explains the various features of the experimental results. On the basis of this study, which gives an insight into the heat exchange in the melting zone of the blast furnace, it was concluded that by comparison with the furnace stack heat transfer coefficients are about 1.5 times higher in the melting zone. EACH year large tonnages of metal are produced in operations which, in part, involve liquid metal irrigation of "packings" countercurrent to hot gases. The melting zone in blast furnaces and in cupolas is a good example of packings irrigated with a liquid melt countercurrent to gases. In all instances of this kind large amounts of heat are exchanged and it is desirable to have some knowledge of heat transfer phenomena involved in these systems. So far the most common method of analyzing furnace efficiencies, fuel requirements, and the general thermal state of the furnace has been through the use of heat balances. As heat balances are essentially statements of the first law of thermodynamics they give no real indication of the factors which govern heat transfer between phases in the various zones of blast furnaces. Hence, rational improvement in production efficiency and the development of theoretical models is only possible if the heat transfer characteristics are known at every stage of the process and related to the important variables involved. This has been generally recognized for some time but it was only recently that Kitaev et al.&apos; have produced a comprehensive treatment of heat transfer in solid-gas countercurrent systems such as the blast furnace stack and the packed bed regenerator. Using their treatment it is now possible to predict the effect of particle size, thermal conductivity, bed porosity, and the flow rates of both the gas and the solid material on the heat transfer in the blast furnace stack. However, the stack of a blast furnace is only one part of an integral unit for which the heat transfer analysis cannot be complete without also considering the heat exchange in the melting zone. The complexity of heat transfer processes in this region of the furnace has so far escaped quantitative description. Yet, the melting zone accounts for a greater amount of heat exchange than all the other zones of the furnace put together. Moreover, if the reduction of oxides in the melting zone proceeds in part in the liquid state the importance of heat transfer on furnace productivity and on the metal and slag temperatures is obvious. THEORY Heat transfer for two-phase flow in packed beds is a complex problem involving a number of heat exchange paths for which interphase areas are not known with any degree of certainty. Analytical solution is, therefore, difficult. This difficulty is emphasized by noting that Rabinovich~ and Luck have only recently solved the steady-state heat transfer for simplified two-phase heat exchangers of known area. However, useful progress can be made for the system considered by making a not unreasonable assumption that the usual heat transfer considerations apply and restricting treatment to the steady state. For these conditions the rate of heat transfer dq in a height dz of a packed bed of unit area is: dq = UaATdz [I.] Integration of Eq. [I] then gives the total heat transferred: assuming both U, the overall heat transfer coefficient, and a, the interphase area, to be independent of bed height. Since a, in these systems, is unknown it is convenient to combine this term with U. The group U, then represents the overall heat transfer coefficient on a volumetric basis. If AT is linear with q, then for a bed of unit volume Eq. [Z] can be integrated to give: is the log mean of terminal temperature differences. From Eq. [3] U, can be readily calculated as q and {AT)im are experimentally obtained quantities, but a difficulty arises in interpreting its meaning. Two approaches are possible depending on whether the effect of packing in the transfer of heat is neglected or not. If the packing is thermally decoupled then the resistance concept gives the relationship: which states that the overall resistance is the sum of the gas phase and the liquid phase resistances (assuming areas are equal throughout). Because the resistance to heat transfer in liquid metals is negligible by comparison with that of the gas,4 Eq. [4] can be simplified, i.e.:

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 E. T. Turkdogan

The activity of sulfur was determined as a function of composition of ferrous sulfide by equilibrating with hydrogen sulfide-hydrogen gas mixtures at 670° , 800°, and 900". The present results supplement the available data over the composition range from 36.6 to 39.5 pct S. The X-ray lattice spacing measurements made are in accord with the available data and indicate that the limiting composition FeSl.008 may be taken for the iron-iron sulfide equilibrium. The growth rate of ferrous sulfide on iron was measured by reacting iron strips or blocks in hydrogen sulfide-hydrogen gas mixtures. Owing to the slow approach to equilibrium between the gas phase and the surface of the sulfide layer, The sulfidation experiments were carried out for several days. It is shown that the growth rate ullimately proceeds in accordance wilh the parabolic rate law. From the parabolic rate constants and the thermodynamic data on iron sulfide the self-difiusivity and chemical diffusivity of iron in ferrous bisulfide are evalualed. The self-diffusivity of iron thus derived zs found to increase with increasing sulfur content. THE ferrous sulfide known as "pyrrhotite" is a non-stoichiometric phase having a wide composition range from about 50 to about 58 or 60 at. pct, depending on the sulfur activity. RosenQvistl studied the thermodynamics of this phase over wide ranges of temperature and composition. Hauffe and Rahmel&apos; and Meussner and ~irchenall~ studied the parabolic rate of sulfidation of iron in sulfur vapor. By using markers, these investigators showed that the iron cations were the predominant diffusing species in iron sulfide. This is confirmed decisively by the self-diffusivity measurements of condit4 who showed that the self-diffusivity of sulfur in ferrous sulfide is several orders of magnitude lower than the self-diffusivity of iron. Although much has been learned from these studies about the Fe-S system, further research on this subject was considered desirable for better understanding of the physical chemistry of iron sulfide. This work was confined to the study of the kinetics of sulfidation of iron in hydrogen sulfide-hydrogen gas mixtures. The results of this study are given in two consecutive parts. Part I, the present paper, is on the parabolic rate of sulfidation of iron and the diffusivity of iron in ferrous sulfide. The second paper, Part 11, is on the kinetics of the surface reaction between hydrogen sulfide and ferrous sulfide. EXPERIMENTAL Three types of experiments were carried out: i) equilibration of ferrous sulfide with gas of known E. T. TURKDOGAN, member AIME, is Manager,Chemical Metallurgy Division, Edgar C. Bain Laboratory for Fundamental Research, U. S. Steel Corp., Research Center, Monroeville, Pa. Manuscript submitted March 6. 1968. ISD sulfur potential; ii) X-ray studies of ferrous sulfide; and iii) measurements of the parabolic rate of sulfidation of iron. Equilibrium Studies. About 1 g of iron powder or foil. contained in a small recrystallized alumina crucible ind suspended from a calibrated silica spring, was reacted with a hydrogen sulfide-hydrogen mixture of known ratio until no further change in weight was observed. %hen the gas composition was changed and the new state of equilibrium was established after several hours of reaction time. The composition of the sulfide was obtained from the initial weight of the sample and the weight after equilibration. X-Ray Studies. The lattice parameters of some of the equilibrated samples were determined using the General Electric XRD-5 diffractometer with a cobalt tube (no filter) set at 40 kv apd 10 ma; the CoK, radiation was taken as 1.79020A. Observed 220 and 311 diffraction peaks of silicon served as an internal comparison standard to correct for possible misalignment of the goniometer. The lattice parameters of the sulfide phase were calculated from the corrected Bragg angles of the 110 and 102 peaks. Rate Studies. In the initial experiments attempts were made to measure the parabolic rate of sulfidation by measuring the gain in weight of a thin iron strip, -0.05 cm thick, suspended from a silica spring in the reacting atmosphere. The preliminary experiments showed that this technique was not reliable for the measurement of the parabolic growth rate of the iron sulfide layer. In the subsequent experiments the data on growth rate were obtained by measuring, on a microscope stage, change in the thickness of the sample after reaction for a specified time in a hydrogen sulfide-hydrogen mixture of known sulfur activity. For each reaction time a new sample was used. Precision-machined iron blocks, 0.5 by 2 by 5 cu cm, were de-greased and annealed in hydrogen for several hours prior to the sulfidation rate measurements. The experiments were carried out at 670°, 800°, and 900°C in gas mixtures having the ratios, and 1.0 for periods of times from a few hours up to 8 days. Apparatus and Materials. A vertical globar tube furnace with a 3-in.-long uniform temperature zone was used. The glass tube fittings were fused on the zircon reaction tube, 1.5 in. diam. The temperature was measured with a Pt-10 pct Rh/Pt thermocouple placed in the hot zone of the furnace inside the reaction tube (an alumina thermocouple sheath was used). A separate thermocouple was used for the temperature controller which maintained the furnace temperature constant within about 2°C. Anhydrous liquid hydrogen sulfide and oxygen-free dry hydrogen from gas tanks were used in preparing the gas mixtures by the constant head capillary flow-meters. In all cases volume flow rate was 1000 cu cm per min at stp, corresponding to a linear velocity of about 6 cm per sec at 800°C; under these conditions

Jan 1, 1969