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By F. O. Shuck, F. E. Butler

A diaphragm diffusion cell suitable for use with liquid metals was designed and tested by measuring the diffusion coefficients for a Hg-10 pct In alloy at 25°C. The binary diffusion coefficient and the coefficients for In and Hg tracers were measured at this composition. The measured coefficients for both tracers were less than the binary diffusion coefficient. When these coefficients were combined with the activity correction term of Darken, the predicted binary coefficient was somewhat higher than the experimental value. In recent years a number of investigators have been studying diffusion of liquid metals in order to gain a better understanding of the liquid state and to examine possible applications to liquid metal processing. The bulk of this work has involved either self-diffusion or diffusion of low concentrations of solute metals in an essentially pure solvent metal. The most common experimental technique employed has been the capillary-reservoir method of Anderson and saddington1 since it is well-suited to measurements involving low concentrations of solutes. As an expansion of previous studies, an investigation of the variation of diffusion coefficient over large composition ranges has been undertaken in this laboratory. Although it is possible to modify the capillary-reservoir method for such measurements, the technique loses its principal advantage of requiring only small quantities of solutes. Therefore, it was felt desirable to investigate other possible experimental techniques applicable to measurements over large composition ranges. A technique which has been used widely in measurements of other liquid systems and seemed potentially applicable to studies of liquid metals was the diaphragm cell. This method has been found to combine relative simplicity of operation with accurate and reproducible results. In use with normal liquids, the tyiical diaphragm cell utilizes a porous glass disk. However, because of the high surface tension, it is not possible to use a diaphragm of such fine pore structure with liquid metals. Furthermore. projected use at high temperatures makes the use of glass undesirable. Consequently, the first problem was the search for an appropriate cell design. EXPERLMENTAL Diaphragm Cell. A number of possible cell designs were examined. Prototypes of several were constructed and tested. The final design is shown in an exploded view in Fig. 1. The cell consists of two identical chambers, one on either side of a 0.20-in.-thick partition. The chambers are 0.15 in. deep and have a volume of 3.45 cu cm. Each chamber is provided with two small threaded holes for filling and emptying. The filling holes may be sealed with stainless-steel screws. Drilled lengthwise through the center partition is a 0.250-in.-diam hole. Inserted into this hole is a rod having seven 0.059-in.-diam holes drilled radially through it. The total "hole" volume is 0.078 cu cm. When the rod is properly aligned, the holes in it constitute the "diaphragm" through which diffusion occurs. The center section was of Teflon and the rod and face plates were of Plexiglas. Four such cells were constructed and used in this study. Subsequent to this investigation, a similar cell constructed entirely of iron was fabricated and tested at higher temperatures. Several considerations led to this final design. It is desirable to minimize the volume of the cell chambers to decrease the time required for a measurement. However, the total volume of metal in the diaphragm must be small in comparison with that in the chambers. To facilitate filling and emptying it is desirable to have a diaphragm which may be closed.

Jan 1, 1970

By M. J. Marcinkowski, D. B. Crittenden, A. S. Sastri

A study co.mbining stress-strain .measurements in conjunction with transmission electron microscoPy has been made with near equiatomic Fe-Cr alloys which were aged for various times at 500°C. Associated with this aging is a marked increase in deformation twinning. The outstanding feature of these twins is that they generate stress fields sufficiently great so as to give rise to spontaneous dislocation loop nucleation nearly normal to the propagating twin. This observation is in agreement with the theoretically predicted elongation of the stress field of a dislocation Perpendicular to its direction of motion as it moves near the speed of sound. Dislocation loop nucleation is more difficult in the longer aged alloys so that this energy absorption mechanism is not effective in hindering twin propagation. Since crack nucleation can readily occur near the tip of a twin, the aged alloys become extremely brittle when deformed in tension. Iron-chromium alloys in the vicinity of the equiatomic compositions become severely embrittled when aged at about 500°C. Fisher et 01.' have shown that this embrittlement is related to the decomposition of the original random Fe-Cr solid solution into a chromium-rich and an iron-rich phase. In addition, Mar-cinkowski et a1.' have shown that twinning becomes an increasingly more important mode of deformation as the aging time is increased. These results have been recently corroborated by the transmission electron microscopy study of Mima and amauchi . The Fe-Cr alloy thus seems ideal for verifying the predictions made in Parts I4 and 115 of this investigation where the behavior of large static or blocked twins and those of large dynamic or propagating twins, respectively, were investigated numerically. It was thus decided to measure the stress-strain curves generated by embrittled alloys that were aged for various times and to examine sections by transmission electron microscopy. EXPERIMENTAL PROCEDURE Electrolytic iron and electrolytic chromium were vacuum-melted and poured into ingot form. The composition of the resulting alloy was found to contain 46.0 wt pct Cr (47.8 at. pct), the remainder being iron. The resulting ingot was swaged above 850°C into 0.250-and 0.400-in.-diam rounds. Compression samples of 0.250 in. diam and 0.400 in. long were cut from the smaller-diameter rounds. These samples were then sealed in evacuated quartz tubes and annealed for 30 min at 1150°C to produce a uniform and equiaxed grain size of mean diameter equal to 1.73 mm. They in turn were rapidly quenched from 850°C so as to preserve the condition of random solid-solution characteristic of the elevated temperature. The samples were then aged for various times up to 300 hr at 500°C in a massive Pb-Bi alloy bath. The samples were next polished and tested in compression at room temperature as described in Ref. 6 using an Instron tensile testing machine. The strain rate used was 0.05 in. per in. per min. The remaining larger round was converted into compression specimens of 0.325 in. diam and 0.500 in. long. This larger diameter enabled wafers of sufficient size to be prepared for examination by trans-mission electron microscopy techniques after subjecting them to a suitable strain. Foil preparation is described in some detail in Ref. 6. All foils were examined in a type HU-11A Hitachi electron microscope operating at 100 kv. RESULTS AND DISCUSSION Fig. 1 shows the effect of aging at 500°C on the room-temperature stress-strain curves of the FeCr alloys. For greater clarity the origin of each curve has been displaced upward. The same origin has been used for both the 0 and the 0.1 curves. It is apparent that with increased aging times a sharp drop in load is observed at the yield stress which becomes more pronounced as aging proceeds. A loud sonic burst accompanies this drop and subsequent metallographic examination shows the sample to contain numerous twins. For intermediate aging times, a number of smaller twin bursts follow the initial large one. The total plastic strain associated with the twinning mode of deformation can be obtained by adding up the contributions AE~ from all i twin bursts, i.e., £,¦££,-, in the manner illustrated schematically in Fig. 2. The contraction of the specimen, as measured from the strip chart of the Instron, after suitably correcting for the elasticity of the machine, was converted into true strain using the assumption that there was no volume change and that the sample remained cylindrical. The dashed lines are all drawn parallel to the

Jan 1, 1970

By R. Kerby, T. R. lngraham

The rates of cadmiuln cementation from buffered solutions were studied on both the cylindrical and circular faces of a rotating zinc disk. The activation energies are equivalent on both surfaces, but the rate is more rapid on the cylindrical face. At higher temperatures and at pH values above 6.4, the rate of deposition increases because of an increase in the cathodic area of the deposit. The rate may also be increased by decreasing the thickness of the diffusion layer by rapid stirring. The presence of small amounts of copper, cadmium, lead, iron, or aluminum in the zinc does not affect the cementation rate, but when srnall amounts of copper, cobalt, and arsenic were present in the solution cadmium deposition ceased shortly after it started. Small amounts of copper in solution become cemented with the cadmium to form a coarse deposit of Cd3Cu. When zinc ores containing cadmium are processed for electrolysis, the cadmium appears with the zinc in the leach liquors. Because of the discharge potential of the cadmium ion and the hydrogen overvoltage on metallic cadmium, the cadmium ion must be removed prior to zinc electrolysis to prevent its codeposition. Cadmium is usually removed from acidic zinc sulfate solutions by cementation on zinc. When zinc sheets are used with the appropriate conditions of pH and temperature, a finely divided, high-purity cadmium powder is obtained; it floats to the surface with attached hydrogen bubbles and, after careful washing, may be processed directly to a marketable product.' The reaction on zinc sheets is relatively slow because of the limited amount of exposed cathodic area on the sheets. A much more rapid reaction is obtained when zinc powders are stirred into the solution, but this procedure does have a potential disadvantage: some unreacted zinc may be trapped in the cemented cadmium and thus lower its grade.1 The equilibrium constant at 25°C for the displacement of cadmium by zinc is of the order of lo", which indicates that at equilibrium the displacement would be essentially quantitative and no back reaction need be considered. This indication is not entirely true, however, because in the presence of oxygen any loose cadmium which is out of contact with metallic zinc tends to redissolve after cementation.' The overall effect is much the same as that to be expected if the equilibrium constant were much smaller. Previous experimental work on cementation reac- tions3 is in general agreement that the rates of cementation usually follow first-order kinetics. The metal on which cementation occurs is considered to consist of anodic areas from which metal dissolves and cathodic areas onto which the reactive metal is cemented. For the reaction to continue, the cemented deposit must remain open and porous for the removal of ions. Usually, the deposited metal influences the rate of cementation; when it blocks the pores in the deposit, the rate of cementation will be decreased. Alternatively, when the cemented metal grows as den-drites or as coarse powder the cathodic area is correspondingly increased and the rate of cementation increases,3 Thus, it is only during the initial stages of cementation, prior to the development of deposit effects, that the kinetic behavior of the reaction may be studied without ambiguity. In this paper, experiments will be described for cementation of cadmium from dilute solutions onto the surface of a rapidly spinning zinc cylinder. The effects of ionic concentration, disk rotation speed, temperature, and impurities will be described. APPARATUS AND PROCEDURE The apparatus used for the experiments was described in a previous paper.4 It consisted of a 2-liter vessel in which the contents were protected, against oxidation, by a stream of prepurified nitrogen. The vessel was immersed in a water bath which controlled

Jan 1, 1970

By R. M. Hudson, P. E. Perry

Weight-gain data obtained by nitriding low-carbon sheet steel in an amrnonia CNH,) atmosphere indicated that the process obeyed a parabolic rate law. The calculated actization energy for nitriding in the range 964" to 1268°F agreed reasonably well with published data. At 1358"F, rate data indicated that the activation energy decreased. Weight-gain data obtained by uszng mixtures of NH3 -Nz at 1268°F containzng jrom 10 to 100 zol pct NH3 also obeyed a parabolic rate law. The rate of 'nitriding increased with an increase in the NH3 content of the gas Mixture. It is well-known that steel heated in gas mixtures containing ammonia (NH3) takes up much larger quantities of nitrogen than steel heated in nitrogen, both gases having a total pressure of 1 atm;' this phenomenon can presumably be attributed to the catalytic decomposition of NH3 on the steel surface to furnish nascent (monatomic) nitrogen. This process was studied bv Brunauer. Jefferson, Emmett, and Hend-ricks at furnace temperatures of 752" and 831°F2 using mixtures of NH3 in Hz. Englehardt and wagner3 reported that, at a furnace temperature of 914°F and under their experimental conditions, both nitriding and denitriding were controlled by the rate of gas-metal reactions at a steel surface rather than by the rate of diffusion of nitrogen in iron. The present study was undertaken to obtain information on the kinetics of nitriding low-carbon steel strip at higher temperatures so that practical rates for short-time strip-annealing treatments could be estimated. Variables studied included time: temperature, and NH, content in the annealing atmosphere. Mechanical and chemical characteristics of steel nitrided in this manner will not be considered in the present article. MATERIALS AND EXPERIMENTAL WORK The samples used were from a commercial low-carbon steel, 0.0244 cm thick, in the cold-reduced condition. The chemical composition of this steel is given in Table I. Panels were cut to 5.1 by 17.8 cm, degreased in toluene, and weighed just before treatment. Four specimens were nitrided under each of the experimental conditions. A study was made of the nitriding rate of steel in a 100 vol pct ammonia atmosphere, 740 mm pressure, at five specific temperatures within the range 964" to 1358°F. The nitriding rates of steel in ammonia-nitrogen gas mixtures containing 10, 18, 26, 50, and 100 vol pct ammonia, 740 mm total pressure, at 1268°F were also determined. All atmospheres used were dried by successively passing them through drying towers packed with soda lime and with Linde Molecular sieve Type 4A. Quoted gas compositions refer to those entering the furnace. Specimens were held in the constant-temperature zone of a vertical annealing tube furnace for times of 14, 3, 5, 10, or 15 min. Gas flow rates were maintained at 3.8 cu ft per hr, which was nineteen volume changes per hour for the system used. The rate of flow was selected to provide a high level of free NH3 for cracking on the steel surface where the ammonia gas is most effectively used as a nitriding agent. The vertical annealing tube furnace consisted of a Hevi-Duty tube furnace with a 2 1/2-in.-ID mullite ceramic high-temperature tube. The constant-temperature zone (controlled within 10°F) was about 10 in. long. After each specimen was degreased, a hole was punched in one end, for attaching the specimen by hook to a chain so that it could be lowered into or raised from the high-temperature portion of the tube by means of a power-driven winch. A stainless-steel access port with O-ring seals was connected by suitable glass-to-metal seals to the cool upper portion of the furnace tube. After the weighed specimen was placed in the access port, the furnace tube was evacuated to approximately 10"3 torr, and then the system was flushed thoroughly with the atmosphere under study. When the gas flow rate and constant-temperature zone of the furnace were established, the specimen was lowered into the constant-temperature zone. The atmosphere flowed from the top to the bottom of the vertical furnace tube and was then vented. For all these runs, during the first 3 min of the time the specimen was in the constant-temperature zone of the furnace the specimen was heating up to the tempera-

Jan 1, 1970

By A. Ghosh, T. B. King

The kinetics of the discharge reaction: 20'- (in silicate melt) = O,(g) + 4e- at a platinum anode in lithium silicate melts have been studied al 1350°C by galvanostatic methods. Plots of the sleady-state overpotential, q, as a function of the logarithm of the current density, i, showed injlections and were linear only at high current densities. The value of the overpotential was influenced by bubbling gas through the electrolyte. The ocer potential was also studied as a function of time. The rise and decay of overpotential were very slow processes. At low current densities transport is the likely rate-controlling process but at high current densities passivation of the electrode, Presumably by an oxide film on the surface, seems to be a contributory functor. IT is well-established that molten silicates behave as electrolytes'5 and, except in a few cases,6 conduction is entirely ionic. Moreover, it is supposed that a possible, and perhaps predominant, mechanism for phase boundary reactions between metals and slags is similar to that in corrosion whereby anodic and cathodic processes occur at unrelated sites, the metal serving to conduct electrons.1'8 Thus electrochemical studies of some slag-metal reactions would seem to be a useful way to diagnose the rate-controlling steps in the overall reaction. The electrochemical method is, in principle, a better diagnostic tool than the direct chemical method for the following reasons: 1) The partial electrochemical reactions, which are simpler than the overall reaction, may be studied individually. 2) The rate of reaction can be controlled at will and independently of the concentrations of reactants. 3) Fast reactions can be studied by relaxation methods.' Esin and his coworkers5'10"12 have pioneered such studies in silicates and have deviloped some ingenious techniques. Not all of their findings, however. can be accepted without a good deal of further work. In this investigation, the kinetics of the oxygen discharge reaction: 202- (in silicate melt) = Oz(g) + 4e- [I] at a platinum electrode were studied by both steady-state and transient galvanostatic techniques. Interest in this reaction was first developed as a result of the findings of Fulton and chipman13 that the reduction of silica, in a silicate slag, by carbon, dissolved in liquid iron, is a very slow reaction. Subsequent work, for example, by Rawling and ~lliott,'~ has demonstrated that the reaction under these conditions must be slow, because the rate is limited by diffusion of oxygen in the iron to the metal-crucible phase boundary at which a CO bubble may be nucleated. Further work by Tarassof,'~ in which the reduction of silica by aluminum dissolved in copper was studied, has shown that under these conditions, where carbon monoxide evolution is not involved, control of the reaction rate resides in diffusion of silica in the slag phase. However, there is no practical way of inducing sufficient convection in the system to make it clear that the phase boundary reaction is indeed fast. The overall reaction of silica reduction involves the discharge of silicon ions at cathodic sites and oxygen ions at anodic sites. In the examples cited, the discharged ions are dissolved in a liquid metal. In the present study of oxygen ion discharge, gaseous oxygen may be evolved at high current densities or oxygen may simply dissolve, possibly as oxygen molecules, in the silicate at very low current densities. The discharge of an oxygen ion at an anode must, in silicates less basic than the orthosilicate composition, be preceded by a reaction in the vicinity of the electrode, such as: which makes oxygen ions available. Platinum was chosen as the working electrode since it is comparatively inert to oxygen and is, therefore, expected to come rapidly into equilibrium with the electrolyte and with gaseous oxygen. Minenko, Petrov, and Ivanova16 have measured the electromotive force at a platinum electrode in molten silicates as a function of the partial pressure of oxygen in the atmosphere, the concentration of oxide ions in the melt, and the temperature. They found platinum to behave as a reversible oxygen electrode. At two different oxygen pressures, Po2 (I) and Pq (11). the electromotive force is given by: where F is the Faraday constant, equal to 23,060 cal per v equivalent, indicating that the electrode reaction is as written in Eq. [I.]. Platinum has been similarly used in molten silicates by other inve~ti~ators. "'~~ In this investigation platinum was used only as an anode, since a current deposits other elements on its surface and changes its characteristics.

Jan 1, 1970

By G. R. Belton, R. J. Fruehan

The Knudsen cell-mass spectrometer combimtion has been used to study the Fe-Al and Ag-Al liquid alloys. By application of the recently developed integration technique to the measured ion-current ratios, activities have been derived for the Fe-A1 system at 1600° C and for the Ag-Al system at 1340"C. The results are partially represented by the following equations: Internal consistency between the data on silver-rich and iron-rich alloys is demonstrated by application of the literature measurements on the distribution of aluminum between the nearly immiscible liquids iron and silver. The usual restrictions on the ratio of the mean free path of the escaping atoms to the orifice diameter of the Knudsen cell are shown not to be limiting in this technique. DESPITE the importance of a knowledge of the activity of aluminum in understanding deoxidation equilibria in molten steel, no direct studies have been made of activities in liquid Fe-A1 alloys at steel-making temperatures. Lower-temperature direct studies have, however, been carried out on aluminum-rich liquid alloys by Gross, Levi, Dewing, and Eilson' at 1300°C and by Coskun and Elliott' at 1315°C. Apart from phase diagram calculations by Pehlke, other determinations have been indirect and were made by measurement of the distribution of aluminum between iron and silver475 and combination of these data with extrapolated activities in the Ag-A1 system.~-% ecently, however, Woolley and Elliott have made a significant contribution by directly measuring heats of solution in the Fe-A1 system at 1600°C. The present authorslo have recently employed a Knudsen cell-mass spectrometer technique in a study of activities in iron-based liquid alloys. In this technique activities and heats of solution are determined from a series of measurements of the ratio of ion currents of the components; and since ion-current ratios are used, problems caused by changes in instrument sensitivity or cell geometry are overcome. Results obtained for the Fe-Ni system were found to be in excellent agreement with previous work, thus demonstrating the reliability of the method. The present paper describes a similar study of activities in the liquid Fe-A1 and Ag-A1 systems, this latter system being included in order that a meaningful comparison can be made with the above-mentioned indirect studies. INTEGRATION EQUATIONS A detailed derivation of the equations used to determine the thermodynamic properties from the measured ion current ratios has been given elsewhere;'' however it is useful to summarize them here. By the combination of the Gibbs-Duhem equation with the direct proportionality between ion-current ratios and partial pressure ratios, it was shown that for a binary system at constant temperature and pressure: where al is the activity of component 1 with pure substance as the standard state, N, is the atom fraction of component 2 in the solution, and I; and t'2 are ion currents of given isotopes of the components. The activity coefficient is given by: this latter equation being more suitable for graphical integration. Combination of Eq. [l] with the Gibbs-Helmholtz equation gives an expression for the partial molar heat of mixing: EXPERIMENTAL A Bendix Time-of-Flight mass spectrometer model 12! fitted with a 107 ion source and a M-105-G-6 electron multiplier, was used to analyze the vapor effusing from the Knudsen cell. The arrangement of the Knudsen cell assembly was essentially that of the commercial instrument (Bendix model 1030) but with several modifications. Instead of heating with a single tungsten filament, a cylindrical tantalum-mesh heater was employed. Up to 1400°C simple resistance heating was used but above this temperature electron bombardment between the tantalum mesh and the tantalum cell susceptor was necessary. The temperature was measured by means of a Leeds and Northrup disappear ing-filament type optical pyrometer sighted on an essentially black-body hole in the side of the cell. Details of the temperature control, temperature measurement, and in situ calibration of the optical pyrometer can be found elsewhere.I0 In the investigation of the Fe-A1 system the Knudsen cells were constructed of thoria crucibles with fitted thoria lids (Zircoa). The cells employed in investigating the Ag-A1 alloys were made up of high-purity alumina crucibles (Morganite) with lids of recrystal-lized alumina (Lucalox). The cells were 0.370 in.

Jan 1, 1970

By W. A. Oates, J. A. Lambert, P. T. GaIIagher

Monte Carlo methods have been used to compute the arrangements of interstitial atoms dissolved in tetrahedral sites in bcc lattices. It is assumed that the presence of an interstitial atom "blocks " a certain number of neighboring sites and prevents their occupancy. Sites "blocked" by more than one filled site are allowed for. The computed values of. the mean occupation number (defined as the ratio of the total number of sites blocked to the number of solute atoms are used to calculate the configurational entropies of the solutions. These entropies are compared with those resulting from previous theoretical studies of this problem and also with available experin~ental data for the p Zr-H, Nb-H, V-H, and Ta-H systems. Evidence is also given that the "blocking" explanation of low limiting compositions in these systems, rather than this being due to initial limitations on the number of sites available, is probably correct. THE ideal partial configurational entropy of mixing of an interstitial solute in a metal is given by: where p is the number of interstitial sites per metal atom and Xi is the atomic fraction of the interstitial. For the bcc lattice. which we shall be concerned with in this paper, the interstitial positions are shown in Fig. 1. It can be seen that for the tetrahedral sites, p=6. whereas for the octahedral sites, p = 3. Different emphasis has been placed on the relative importance of energy and entropy effects in determining deviations from ideality in interstitial solid solutions. In some cases the same system, e.g., Fe-C, has been described by the contradictory regular and athermal solution models indicating that the enthalpy and entropy functions, derived from equilibrium data, are frequently not accu.rate enough to differentiate between these treatments. However, for certain metal-hydrogen solutions the equilibrium data is available over sufficiently wide ranges of temperature and composition to permit a reasonably accurate determination of the compositional variation of the heats and entropies. Hoch&apos; has attempted to interpret the results of interstitial solid solutions in terms of a regular solution model. In the case of the Ta-H system where 13 = 6, this model entails fitting the experimental relative partial entropies of solution, asH, to the equation: where ASgs is the relative partial excess entropy of solution of hydrogen. Hoch found that the results of Mallett and Koeh1 could be fitted to this equation with an approximately constant value of AF up to XH = 0.25. However, it is apparent from the solubility isotherms in this system which become asymptotic to the composition TaH that, since (Xh /6 - ~Xh ) becomes infinite only at TaH6, it is necessary that AS<&apos; tends to infinity at TaH. In other words, the low saturation composition of TaH, instead of the anticipated TaH,, eliminates the possibility of applying regular solution theory to such systems. Rather large negative excess configurational entropies must exist at higher hydrogen concentrations in order to explain the lower saturation values. To account for these low limiting compositions and excess entropies two distinctly different approaches have been followed. Rees and many others1-l2 have assumed that not all interstitial sites are crystallographically equivalent with respect to the interstitial addition; that is, in Eq. [I] p is less than the value anticipated from geometrical considerations. To describe, say, a bcc metal-hydrogen system with a limiting composition of MH by this approach one would consider that p = 1 in the first instance instead of p = 6.&apos;j3 In some cases, nonintegral values of B have been taken in order to improve the fit with the experimental data over limited ranges of composition. The other approach which has been used to explain the low saturation compositions is to assume that, although all sites are available for occupancy, strong repulsive interactions exist between the neighboring interstitial atoms, and hence occupancy of any site excludes or blocks a certain number of neighboring sites from being occupied. Earliest treatments of this concept considered the exclusion of an integral number, of nearest-neighbor sites from being occupied at all concentrations. In this case, the partial configurational entropy is given by: These early treatments failed to allow for the overlap of the blocked sites which will arise at all but the very lowest concentrations. More recently attempts have been made to calculate the effect of this decrease in the number of blocked sites on the configurational entropy. Using the quasichemical treatment of interstitial solid solutions as given by Lacher and assuming that an infinite repulsive interaction energy existed between the solute atoms. atom obtained an approximate configurational entropy applicable to the blocking with overlap case:

Jan 1, 1970

By H. Y. Hunsicker

A graphic method has been devised for three-di-mensional analysis of hot deformation and for correlating the amount and directionality of the deformation with resulting directional properties. Deformation is evaluated in terms of dimensional change ratios referred to three orthogonal axes. Since all combinations of the three ratios can be represented in a triangular coordinate field with logarithmic scales, a two-dimensional chart of extent of deformation and degree of asymetry is possible. The entire gamut of shape changes from upsetting through flat-rolling to rod-rolling is accommodated. The resulting coordinate system is a base upon which can be represented the properties of the wrought products measured in the directions of the axes employed fir evaluating the deformation. When property data are available for many types and amounts of deformation, a three-dimensional figure can be constructed, and the projection of this figure is referred to as a &apos;&apos;3d&apos;&apos; chart. Experience in using such charts to plan fabricating operations for a variety of thick-section forged and rolled products of heat-treated aluminum alloys has verified its practical value for optimizing directionality relationships. MechANICAL anisotropy of thick section products of heat-treatable aluminum alloys is recognized by producers and users of these products, and the extent of the directional differences is apparent in property tabulations included in handbooks, standards, and specifications.&apos; Attention has also been directed to the existence of important directional differences in the resistance of these products to stress-corrosion cracking. Metallurgical structure factors responsible for these directional differences include, among other possibilities, shape and alignment of grains, voids and nonmetallic inclusions (when present), volume fraction and spatial distribution of secondary phase particles and solid-state precipitates, crystal-lographic textures, and Bauschinger effect. The contributions of the individual factors vary with alloy composition, heat-treated temper, type of working process (forging, rolling, extrusion), and the amount and directional nature of the deformation. In general, the cast ingot used as the starting material for producing these wrought products exhibits only a modest degree of directionality. A monotonic and continuous transition from this nearly isotropic state with progressive hot deformation would appear probable, assuming that the working temperature is sufficiently high to cause continuous dynamic recovery. Several years ago a project was undertaken to evaluate the effects of hot deformation and metallurgical structures on the directionality of thick wrought aluminum alloy products, and the method to be described was developed as an analytical tool in this investigation. DIRECTION NOMENCLATURE The nomenclature system adopted by industry for the three mutually perpendicular directions employed in testing aluminum alloy products includes four terms: "longitudinal", "transverse", "long transverse", and "short transverse". These terms are conventionally related to the external geometry of the product but also by implication to the deformation and resulting metallurgical structure. Occasions arise in which through use of unusual fabricating methods, intentional or otherwise, the structure does not have the usual relationship to external geometry or may be very complex because of inhomogeneity of deformation throughout the piece. The longitudinal direction is generally parallel to the primary rolling direction or to the direction of extrusion. In the case of forging, it is parallel to the direction of maximum extension (not maximum "working" or "flow", as frequently stated). The term transverse is applied to any direction perpendicular to the longitudinal direction in a product having symmetry about the longitudinal axis, and generally, although not always, the deformation to produce these forms is nearly symmetrical in the transverse plane. This term then may be applied to a round, square, hexagon, or other polygonal, symmetrical shape produced by extrusion or rolling or by forging, if produced by a simple, symmetrical drawing procedure. The type of microstructure generally associated

Jan 1, 1970

By J. B. Cohen, S. L. Sass

The nucleation process for y&apos;, Ni3Ti, is shou&apos;n to change from heterogeneous to uniform as the undercooling within the phase boundary increases. As unifornz nucleation beconres copious, (100) alignment is observed in the early stages of aging; howecer. whether or not the alignment is due to spinodal decomposition could not be determined. The presence oi a large-scale reversible segregation of titanium and not the intermediate precipitate y&apos; may be the cause of the initial strengthening in this alloy system and the discrete regions detected magnetically by Ben-Israel and Fine. Evidence is presented for the role of dislocations in the formation at long aging tines oJ the equilibrium precipitate . ThE nickel-rich portion of the Ni-Ti phase diagram consists of a terminal fcc solid solution of titanium in nickel called y.&apos; For temperatures below 1290°C if the solubility limit is exceeded and the temperature is high enough, the excess titanium will combine with nickel to form q, Ni3Ti, a four-layer hcp ordered structure with stacking sequence ABAC."~ Since a change in structure is involved, formation of q is slow and a metastable precipitate referred to as y&apos; forms. This metastable precipitate is an ordered cubic phase in the unconstrained state having a structure similar to Cu3Au (LIZ) with the composition Ni,Ti."&apos;5 From X-ray studies,8, 7 the following sequence is indicated for the precipitation reaction at low temperatures: 1) The appearance of satellites around low-index diffraction spots and splitting of high-index spots, indicating the formation of a slightly tetragonal phase in an imperfectly periodic arrangement. The tetragonal phase is y&apos; or the depleted matrix, depending on the volume fractions of matrix and precipitate (and hence, the alloy composition); tetragonality apparently arises from coherency strains. 2) The appearance of diffraction spots from the equilibrium second phase, q. Ben-Israel and Fine&apos;" used magnetic methods to measure the changes in matrix composition during aging, and to estimate the precipitate composition in a Ni-10.1 at. pct Ti alloy. They observed that the alloy, solution-treated at 1270°C and quenched, contained heterogeneities with discrete compositions which gradually vanished upon aging. It was suggested that y&apos; may initially form as a defect structure with several possible compositions deficient in titanium as compared to Ni3Ti; the composition Ni3Ti develops with prolonged aging. The initial composition was Ni6Ti which would require a very large deviation in stoichiometry for y&apos;. It was noted that at 700°C the precipitation reaction was 80 pct complete after 2 hr and that the volume fraction of second phase was 0.2 after 1 hr. Mihalisin and Decker&apos; suggested that the equilibrium precipitate, besides being nucleated at grain boundaries, could also form at stacking faults. ~errick" examined the formation of in Ni-Cr-Ti, and suggested that a collapsed vacancy cluster within y&apos; acted as a nucleus for intragranular q at high temperatures, 820" and 900°C. After long aging times at lower temperatures, 650" and 750°C, diffraction patterns taken from regions containing ribbons of stacking faults showed spots associated with q. Aging greatly enhances the mechanical properties of these alloys, even at high temperatures, and the metastable precipitate y&apos; is thought to be responsible.&apos; At 600°C the hardness of a Ni-10.1 at. pct Ti alloy increases rapidly during the first 20 hr of aging and continues to increase slowly thereafter.&apos;" At 700°C the hardness reaches a maximum at 1 to 2 hr and then decreases.l1 In this paper the kinetics of formation of y&apos; and the mechanism of transformation to in a Ni-Ti alloy are described. Evidence is presented that suggests that large-scale regions of titanium segregation are present initially and these may have an important influence on the initial strengthening of the alloy: these regions may be the heterogeneities detected by Ben-Israel and Fine. I) EXPERIMENTAL TECHNIQUES The Ni-10.3 at. pct Ti-0.6 at. pct A1 alloy was prepared by vacuum melting. Its chemical analysis is given in Table I. A 0.007-in.-thick strip was sandwiched between foils of the alloy and placed in an open Vycor tube with titanium chips (to get oxygen) and solution-treated for ; hr at 1150°C in a Globar Furnace under a flowing argon atmosphere. Following a quench into an ice-brine mixture at -5" to -2"C, a sample to be aged at temperatures up to and including 700°C was sealed in an evacuated Vycor capsule before being put into a fused salt bath. Aging above 700°C was carried out on bare samples in a salt bath. When removed from this bath and quenched into an ice-water mixture, the sample was normally coated with a thin layer of oxide easily removed with emery

Jan 1, 1970

Jan 1, 1970

By Shiro Ban-ya, John Chipman

The effects of many alloying eletnents on the acticity coefficient of sulfur in liquid iron have-been studied by the equilibriutn in the reaction Sfin Fe) + Hz = HzS at 1550°C&apos;. Results are expressed in terms of a concentration variable for a nonmetallic or for a substitutional metallic solute. Activity coefficient of sulfur, defined as increased by B, Al, C, Si, Ge, Sn, P, As, Sb, Mo, W, Co, and PI. It is decreased by Cu,Au, Ti. Zr, V, h&apos;b, Ta, Cr, ,23n, and Ni. Irulues oj. the interaction coejficient 0i = 6 In are labulated. The same interactions are expressed also in terms of atom fraction and of weight percent. The thermodynamic properties of sulfur in liquid iron have been fairly well established. Our recent paper1 reported new determinations of activity coefficient up an atom fraction of 0.12 and equations based on a careful review of all published data. The effects of alloying elements on the activity of sulfur have been studied by several investigators,2"11 especially by Morris and Williams for silicon,&apos; by Morris and Buehl for carbon,~ and by Sherman and Chipman for manganese. phosphorus, and al~minum.~ However, the effects of some important alloying elements remain to be determined. The purpose of this investigation was to determine the effects of many alloying elements on the activity of sulfur in Fe-S-j ternary systems. EXPERIMENTAL METHOD This study was based on experimental determination of equilibrium in the reaction at 1550°C: The same apparatus and procedure as described in our previous paper have been retained, and the same corrections were applied for dissociation of H2S. The alumina crucibles used in the experiments consisted of four separate compartments. In a given experimental run. kach of three alumina crucibles held four different samples of about 3 g each which reached equilibrium in the same gas atmosphere and temperature. The charges were made up of electrolytic iron, pure iron sulfide, and desired alloying elements, which were pure metal or master alloys made in the laboratory. The weighed samples were held for 4 to 12 hr in the prepared atmosphere at 1550°C. They were then low- ered to be cooled as quickly as possible. The quenched metal beads were crushed to avoid the errors of segregation in the ingot. The sulfur content was determined gravimetrically and alloy content by appropriate chemical analysis. CALCULATIONS The apparent equilibrium constants of Eq. [I] are expressed as follows from the corrected gas ratios and sulfur concentrations: The term K" is the observed equilibrium constant in any given ternary solution, K&apos; is the value for the Fe-S binary solution. and the limiting value of K&apos; in the infinitely dilute solution is designated by K, which is the true equilibrium constant in Eq. [I]. In the thermodynamic treatment of nonmetallic elements in a metallic solution, it has been suggested1&apos; that the lattice ratio has certain advantages over other variables to express the concentration of solute. In interstitial solid solutions the lattice ratio zj is proportional to the ratio of filled interstitial sites to those which remain unfilled. The equations derived for the activity of the solute using zj as the concentration variable are found also to be applicable to liquid solutions containing nonmetallic solutes when the nonmetal is treated as if it were interstitial. For this purpose we adopt the following definitions: The quantity vj which is negative for interstitial solutes is taken as -1 for nonmetallic and +1 for metallic solutes. For purposes of calculation however ; j may be assigned a value which results in a linear relation such as shown in Figs. 1 to 15. The activity coefficient of sulfur, Qs, and equilibrium constant. K(z). are defined as follows: According to a Taylor series expansion. the logarithm of the activity coefficient of sulfur in Fe-S-j ternary system is: However, the value of 6 In */6zi remains constant through a broad range of dilute solutions and the terms of higher order are negligibly small. As a consequence, Eq. [6] is simplified as follows:

Jan 1, 1970

By R. M. Rose, K. A. Jones

Resistive measurements ulere made on superconducting niobium single crystals in transverse magnetic fields. Crystals were grouln in both high and ulfrahigh vacua, doped with stnall quantities of oxygen, and annealed in ultrahigh vacua at temperatures from 900&apos; to 1350°C. Maxima in the fluxoid pinr~ir~g force were observedfor the [100] and [210] directions. The increase of the critical current density with dissoved oxygen was seen to saturate at relatively low concentration. This behavior, and the variation of J, and residual resistivity (as a function of oxygen content and annealing) of both clean and dirty gassy) crystals, is seen as a consequence of the formation of clusters with (210)~b habit planes and (200)ffo common boundaries. These suboxide clusters are apparenlly stable at high temperatures and very low oxygen concentrations. It is generally known that dissolved oxygen at concentrations well below the solubility limit sharply increases the critical current density of superconducting niobium.&apos; Such a result would not be expected if Nb-0 solutions were random, not even as the result of segregation on the scale usually encountered in solid solutions. According to the Kim-Anderson theory of flux creep,&apos; the critical transport current density is determined by the pinning force Fp associated with some feature of the microstructure. As the Lorentz force. a or (J X R), of the transport current in the magnetic field approaches Fp, flux creep and then flux flow occur. The pinning force is expected to be quite small if the heterogeneity involved is significantly smaller than tte range of coherency which for niobium is circa 250~.~ Although the strain field of an individual oxygen atom in the niobium lattice is relatively large, it does not seem plausible that individual atoms could be so effective as to account for the data. Also, ~ramer~ found that straining and strain aging specimens containing small amounts of oxygen on occasion decreased the residual resistivity. A possible explanation for the above behavior may be found in the work of van Ooijen and van der Goot,= who found that annealing changed J, for niobium foils containing oxygen, and they attributed the changes to ordering of the oxygen atoms. This phenomenon has been observed by other investigators using X-ray and PROCEDURE Cylindrical 4-in.-diam niobium single crystals with axial orientations [ill], [110], [112], and [oo~] were grown from pure niobium, see Table I for analysis, in an ion-pumped ultrahigh-vacuum system using the electron beam floating zone technique. Total pressure during growth was lo-&apos;9 torr: the oxygen partial pressure was less than lo-" torr, as determined by a mass spectrometer. These crystals will be referred to as the "clean" crystals. Similar crystals were also grown in another system at a pressure of 5 X 10"6 torr. These crystals will be referred to as the "dirty" crystals. Specimens 14 in. long were cut from the as-grown crystals and one end was polished down to no. 600 carbide paper smoothness. A back-reflection Laue photograph was then taken in order to fix the crystallo-graphic directions transverse to the crystal. The critical current density J,, the current density necessary to produce a voltage drop of 1.0 pv between voltage leads placed a in. apart, was determined as a function of the magnitude and direction of the transverse magnetic field and of the oxygen concentration. The technique and experimental arrangement was essentially similar to that of Tedmon et al.&apos; In the remainder of this paper, the azjmuthal angle $ for the field H is referenced to the [ I101 direction in all four crystals, and oxygen was added in small equal increments by anodization and annealing.7 The resistivity ratio, RR, of the resistance at room ternperature to that at 4.2"K (H =7.00 kG) was determined as well.

Jan 1, 1970

By Peter Beardmore, Michael B. Bever

The effects of the temperature of deformation and the degvee of deformation on the annealing spectrum of a Au-Ag alloy have been determined by vesistance measurements. Specimens were deformed in torsion at 4°, 78K and room temperature up to strains nd/l of about 1.0 and were isochronally annealed. Discrete annealing stages similar to those found for pure metals were observed. Stage A occurred below room temperature; the decrease in reszstance associated with this stage increased as the temperature of deformation was lowered or the strain was increased. Stage B manifested itself as an increase in resistance; this is attributed to the restoration of short-range order promoted by vacancy or vacancy aggregate migration. At temperatures above 48S0K, recrystallization or Stage C occurred. Stages A, B, and C in the annealzng curves of this alloy may be considered to correspond to Stages II, Ill, and V, respectively, in the terminology used to describe the annealing spectrum of pure metals. ThE annealing behavior after deformation below room temperature has been thoroughly investigated on pure metals, in particular gold and copper. The occurrence of several discrete stages in the annealing spectrum of these metals has been established, but the interpretation of some of these stages in terms of specific mechanisms is still controversial.&apos; The annealing of alloys deformed below room temperature has been the subject of only a few investigations. In the investigation reported here, a Au-Ag alloy was annealed after deformation at and below room temperature. This continues a research program on the deformation and annealing behavior of Au-Ag alloys.2-8s EXPERIMENTAL PROCEDURE An alloy rod of composition 82.6 wt pct Au-17.4 pct Ag was reduced to wire, 0.0428 in. diam, by swaging and drawing. After a recrystallization treatment, the grain size was 0.031 mm, as obtained from the average linear intercept.7 The ends of wires about 6 in. long were flattened and sealed into short brass tubes with cold setting cement to form the grips of the torsion specimens. The equipment used for deformation has been described elsewhere.6 The specimens were deformed at room temperature, 78", and 4°K to various strains nd/l, where n is the number of turns, d the diameter of the specimen, and 1 its length between grips. The strain rate ?max was 0.1 min-&apos; at the sur- face of the specimen except where noted otherwise. The specimens were annealed isochronally for 30 min at intervals of approximately 30°K from the temperature of deformation to approximately 800°K, except that after deformation at 4°K the lowest annealing temperature was 78°K. A potentiometric method was used to measure the resistance: all measurements were made at 78°K with the exception of some measurements at 4°K mentioned below. Data obtained with a single specimen yielded a complete annealing curve: in several cases duplicate specimens were used to confirm the reproducibility of the curves. Since the surfaces of the specimens were rough after deformation, their diameters could not be measured accurately. The resistance increments after deformation and annealing are therefore reported as percentages of the resistance of the same specimen measured after completion of the annealing, that is, after full recrystallization. The corresponding resistivity values can be calculated by obtaining the effective diameter of a deformed specimen from the ratio of its resistance after recrystallization to the true resistivity, which was determined with a smooth specimen of known dimensions. This method of calculation was used to obtain data shown in several of the figures. RESULTS AND DISCUSSION The isochronal annealing curves after deformation to various strains at 4", 78K, and room temperature are shown in Figs. 1, 2, and 3, respectively. The resistance increment of the as-deformed specimens as a function of strain is shown in Fig. 4. For the specimens deformed at 4°K. values measured at 78°K are plotted with the exception of those for the as-deformed

Jan 1, 1970

By S. K. Tarby, A. E. Rathke

A series of 0.21 pci carbon steel melts was processed under conditions which sinzulated industrial vacuum degassing practices. The results indicated that the efliciency of carbon deoxidation was not significantly increased by vacuunz degassing at chamber pressures below 100 torr. The two common phenomena of vacuu?rz carbon deoxidation, i.e.,an unaccountable carbon loss and nonequilibrium deoxidation, were observed in this study. Oxygen from adsorbed and chenzically combined water of certain refractory structures was probably responsible for the unaccourttable carbon drop. The nonequzlibrium deoxida-tion phenomenon was adequalely correlated by a bubble nucleation )mechanism. Although the major limiting factor in oxygen removal from these melts contained in alumina crucibles could not be eslablished with certainty, there was some evidence that melt-refractory interactions were not the most imp-portant limiting factor. CONSIDERABLE attention has been given to the use of carbon in conjunction with vacuum degassing* as a deoxidation technique. An advantage of utilizing the reaction: for deoxidation purposes is that the reaction product is gaseous and hence can be effectively removed from the melt. The pressure dependency of Eq. [I] is illustrated by the expression for the thermodynamic equilibrium constant, K: where pco is the partial pressure of carbon monoxide, and hc and ho are, respectively, the Henrian activities of carbon and oxygen in molten steel. The thermodynamic aspects of the C-0 reaction in molten Fe-C-0 alloys have been investigated extensively. Theoretical predictions based on Eq. [2] indicate that, at the chamber pressures reached in most vacuum degassing units, carbon is the most effective deoxidizer that can be obtained. ~ornak&apos; has compared industrial values of carbon and oxygen contents with values calculated from theory, and has shown that on a commercial basis vacuum carbon deoxidation has not achieved the degree of success that is predicted from theoretical considerations of the C-0 reaction. The use of industrial units to determine the reason for this deviation is limited by economics and the difficulty in controlling critical process variables. Therefore laboratory-sized experiments in this area should yield valuable information. Investigations on vacuum carbon deoxidation have been made in experiments conducted under vacuum induction melting conditions where pressures in the low micron range, long treatment times, exposure to highly dynamic vacuum conditions, and relatively quiescent bath conditions have been maintained. Inve~ti~ators~~~ utilizing vacuum induction melting for the production of high-purity iron by carbon deoxidation have concluded that, under high vacuum conditions, melt-refractory interactions constantly supply oxygen to the melt. Thus, it has been suggested that refractory dissociation rather than the C-0 reaction establishes the lowest possible oxygen content of a melt. Thomas and Moreau4 and Bennett, Protheroe, and ward5 have studied carbon deoxidation of Fe-C alloys melted in magnesia crucibles under reduced pressures. The results of both studies differed considerably from those predicted by theory, and the limiting factor for lower oxygen contents was attributed to melt-refractory interactions. Because the refractory material used in both investigations was magnesia, no quantitative measure of crucible reaction could be made and the amount of carbon consumed during treatment was utilized as an indirect indication of the extent of crucible reaction. Studies concerned with the determination of the minimum oxygen content attainable in pure iron and Fe-C alloy material vacuum-induction-melted in various crucible materials have also been conducted."&apos; The suitability of a crucible refractory for use under vacuum conditions appears to depend upon the major refractory constituent, the amount and type of impurity oxides, and the composition of the melt. Meadowcroft and Elliott9 have presented a theoretical review of the type and extent of various refractory reactions which should be considered in vacuum refining. ~eadowcroft&apos;~ considered the vacuum degassing process to be dependent upon the "carbon boil" and has proposed that a part of the difference between the experimental and theoretical results for vacuum carbon deoxidation may be explained by the fact that the pco term in Eq. [2] is not the chamber pressure. Instead, the pressure necessary for carbon monoxide

Jan 1, 1970

By Eckhard Nembach

The phase diagram of the system Pb-In has been investigated between -27° and + 40°C, using nzainly X-ray dijfraction. In accordance with t her mo dynamic measurements by Heumann and Predel, a segregation occurs at low temperatures, though not in the form of a nziscibility gap. THE phase diagram of the system Pb-In has been the subject of extensive investigations,1&apos;1 but recently Heumann and prede13 concluded from their thermodynamic data that a new feature should occur below room temperature. These authors observed that the maximum values for the enthalpy and entropy of mixing, which occurred at a composition of 50 at. pct Pb, were +400 and —1.7 cal per g-atom deg, respectively. From this the authors estimated that a miscibility gap should occur below 30°C, centered at 50 at. pct Pb. Resistivity measurements seemed to support this view. These authors proposed the phase diagram outlined in Fig. 1. Three phases exist at 30°C: the tetragonal indium phase with c/a > 1, the tetragonal intermediate phase a, with c/a < 1, and the fcc lead phase. During an investigation of the superconducting properties of Pb-In alloys. it has been observed4 that aging a specimen with 50 at. pct Pb for 14 days at -18°C decreased the superconducting transition temperature about 0.13"K and tripled the transition width. In this paper, the results of an investigation of the Pb-In phase diagram in the temperature range from — 2T to +40°C are reported. Superconductivity and X-ray methods have been used. 1) SPECIMEN PREPARATION The materials were provided by the American Smelting and Refining Co. According to the manufacturer their purity was 99.999 pct. The weighed amounts of the constituents were sealed in quartz tubes under an atmosphere of 10 torr helium, mixed for 24 hr in a rocking furnace at 380°C, quenched in ice water, and homogenized at 20" to 30°C below the solidus line, established by Heumann and Predel. The annealing times were 144 hr for specimens containing Less than 30 at. pct Pb and 36 hr for the remainder. 2) SUPERCONDUCTIVITY EXPERIMENTS The specimens were quenched from the homogeniza-tion treatment into ice water and their superconducting transition temperatures T, measured. The procedure used has been described in Ref. 4. The transition was detected by the change of the mutual induc- tance of two coaxial coils containing the sample. T, was defined as the temperature at which 50 pct of the total change in inductance had occurred. The repro-ducibility with which T, could be measured was i0.002"K. Then the specimens with lead contents between 38 and 75 at. pct were aged for 7 days at temperatures between -30" and 40°C. If this treatment caused T, to change by more than 0.005"K or the width of the transition to increase by more than 0.002"K, it was concluded that the specimen had undergone a phase change and no longer consisted only of the fcc lead phase: as it did immediately after homogenizing. The result is shown in Fig. 2. From this one can estimate at what temperatures and concentrations phase changes occur. The X-ray measurements were based on these preliminary results. 3) X-RAY EXPERIMENTS Because of the softness of the material, relatively coarse powders. 75 p, had to be used, which were filed in a helium atmosphere from homogenized specimens. The powders were annealed at least 30 min at temperatures between 120" and 16OJC, depending on their concentration, and quenched in ice water. Then their X-ray patterns were taken at -178°C with a Picker diffractometer, model 3488K, and a cold stage. on which the specimen was in thermal contact with a liquid-nitrogen reservoir. In this way the following relation was established for the fcc lead phase: a = 4.697 + 0.00247C for 40 5 C 5 75 11 where n is the lattice constant (A) and C is the at. pct of lead. The coarseness of the powder made it impossible to use lines with 0 > 75 deg; therefore n was averaged from lines with 45 deg 5 0 5 75 deg. The results were reproducible to within i0.05 pct. Relation [I] is very similar to the one found by Heumann and Predel at room temperature. Following this, homogenized specimens with compositions between 15 and 56 at. pct Pb were aged for at least 10 days at temperatures between -27" and

Jan 1, 1970

By Barry D. Lichter, Pierre Sommelet

High-temperature heat contents of InSb, GaSb, and AlSb were measured over the temperature range 400" to 1450°K using a diphenyl ether drop calorimeter. Smoothed ualues of the thermal properties, H$ - H:9s, have been derived and are tabulated at even temperature intervals. The heats of fusion of the three compounds were determined as, respectively, 5707 *100, 7780 * 100, and 9800 5 3011 cal per g-atorn at the determined melting points of 797" l°, 985" * , and 1330" * 5°K. The calculated entropies of fusion are, respectively, 7.16 0.12, 7.90 * 0.11, and 7.37 * 0.23 cal per deg per g-atotn. The heat capacities increase substantially on tnelting in contrast to the behauior of structurally related germanium and silicon. Deriations from the Kopp-Neumann rule are negative for solid compounds and positive for the liquid phases. Previously obsevrrd "post melting" in InSb is confirmed. The high-temperature thermal properties of 111-V compounds are presently not well-established, despite the technical importance of these semiconducting cbmpounds. Uncertainties in available heats of fusion and heat contents have seriously hampered thermo-chemical evaluations&apos; and thermodynamic analyses of phase equilibria2"" in these systems. This paper reports results of high-temperature heat content investigations of InSb, GaSb, and AlSb measured in the range 400" to 1450°K employing a diphenyl ether drop calorimeter. Similar measurements for InAs and GaAs will be reported in a following publication.~ EXPERIMENTAL PROCEDURES Samples. High-purity samples of the compounds InSb and GaSb were supplied in the form of crushed crystal fragments by Dr. Carl Thurmond of the Bell Telephone Laboratories and in the form of single crystals by Dr. A. Strauss of the M.I.T. Lincoln Laboratory. Single-crystal samples of semiconductor-grade AlSb were supplied by Dr. W. P. Allred of the Bell and Howell Research Center. Chemical analyses indicated that all compounds were stoichiometric to *0.1 at. pct, which is within the experimental uncertainties of the analyses. Samples were crushed, weighed, and encapsulated in evacuated, thin-walled, fused silica capsules. The capsules were nearly identical in external shape, 2 cm by 2 cm diam, but varied in weight due to differences in wall thickness. One sample of AlSb was contained in a thin-walled, high-purity alumina cup encapsulated in silica and used for heat content determinations of liquid AlSb. The capsule materials showed no visual evidence of reaction with any of the compounds. The sample and capsule weights are given in Table I. Calorimeter. A Bunsen-type calorimeter, similar in design to a previously described instrument6 but employing diphenyl ether (C6H5)&apos;0 as the calorimetric substance, was used for measurements of heat contents above 300.0°K, the melting point of diphenyl ether. Heat input to the calorimeter caused isothermal melting of diphenyl ether, and the resulting increase in volume was measured by displacement of mercury from the calorimeter into a 200 cm horizontal, calibrated capillary, 1.25 * 0.01 mm diam, or into a weighed beaker. The advantages of diphenyl ether over water have been previously pointed out7 and include: i) an increase by a factor of 3.5 in sensitivity as measured by the ratio of the volume change to the enthalpy change on fusion, ii) the smaller required extrapolation from the melting point to the standard temperature of 298.17"K, and iii) the positive volume change on fusion of diphenyl ether in contrast to the contraction which occurs on fusion of ice. Diphenyl ether was purified by fractional crystallization to 99.95 mol pct as determined from the melting point depression with fraction crystallized. During assembly of the calorimeter, the ether was repeatedly outgassed under high vacuum to remove dissolved air. The calorimeter receiving vessel consisted of an 8-in.-long by 1:-in.-diam copper tube with twelve horizontal 3-in.-diam radiator "fins" for dissipating heat to the surrounding mantle of diphenyl ether. Before forming the mantle the chamber surrounding the receiving vessel contained 3300 cu cm of liquid diphenyl ether above 250 cu cm of mercury which was

Jan 1, 1970

By M. J. Pool, with Appendix by Larry Kaufman, R. W. Krenzer

Thermodynmic properties of the Cu-Mn system have been deterrrzined in the temperature range 973" to 1273°K by measuring the vapor pressure of manganese in equilibrium with alloys of compositions varying from 0.13 to 0.91 rnole fraction manganese using the Knudsen effusion technique. Activities of manganese calculated from the measured vapor pressures show large positive deviations. Calculated heats and entropies of mixing are positive with a maximum occurring at approximately 0. 7 mole fraction manganese. ThE investigation of thermodynamic properties of binary systems involving transition metals is of considerable interest at the present time. The incomplete subvalency electron levels of transition metals lead to unusual behavior in some alloys, and considerable information can be obtained by determining the thermodynamic characteristics of these systems and relating the thermodynamic behavior to observed physical properties. The Cu-Mn system, shown in Fig. 1,&apos; provides an example of an alloy system in which the determination of the equilibrium phase diagram and various physical properties has received considerable attention, but very little work has been done on measurement of the thermodynamic properties. Elemental copper and manganese have comparable electronegatives, atomic sizes, and cohesive energies, but differ in crystal structure. They form a continuous series of solid solutions only at high temperatures and the structure varies in a continuous manner from fcc at the copper-rich end to fct at the manganese-rich end.&apos; The purpose of this investigation was to measure the vapor pressure of manganese over a series of Cu-Mn alloys and from these values determine the thermodynamic properties of the binary system. Vapor pressure measurements were made in the temperature range 973" to 1273"K, remaining within the solid-solution region for each alloy studied. EXPERIMENTAL PROCEDURE The relative thermodynamic properties of solid Cu-Mn alloys were determined from vapor pressure measurements by means of the Knudsen effusion tech- nique. Several discussions of the theory can be found in the literature. In the case of copper and manganese, it is assumed that manganese is the only component subliming, so the vapor pressure of manganese over the various alloys can be determined directly by measuring the weight loss of the effusion cell. This is a valid assumption since the vapor pressure of manganese is about four orders of magnitude higher than the vapor pressure of copper in the temperature region of interest. The vapor pressure of manganese over the alloys at any given temperature is then related to the weight loss of the effusion cell per unit area per unit time. An upper limit of 1.5 x 10"s has been measured for the ratio of polyatomic to monoatomic molecules for manganese vapor in equilibrium with solid manganese at 1180°K, so it was assumed that manganese vapor is monoatomic. The effusion cells, fabricated from high-purity alumina, are 26 mm high, 18 mm OD, and have a wall thickness of 1 mm. Three different sized holes of 2.03, 2.54, and 3.18 mm diam were drilled in the lids from the inside face to minimize chipping, and the lids were then slip-cast onto the cells to provide a gas-tight seal. Alumina was selected for this particular application both because of its resistance to thermal shock and reaction with manganese vapor. In the ideal case, the orifice of the effusion cell should have a knife edge so that effusion through the orifice

Jan 1, 1970

By H. A. Wriedt

At 500°C (932°F) the range of y&apos; iron nitride is from 5. 77 + 0.03 wt pct N (in coexistence with a iron) to 5.88 * 0.03 wt pct N (in coexistence with E iron nitride). Stoichiometric "Fe,N" (5.900 wt pct N) is near the upper extreme of possible compositiom. The depe-dence of nitrogen activity (expressed as pnh,/Ph,) on nitrogen content is described satisfactorily by a "Langmuir" isotherm: At even the highest nitrogen concentrations, less than 0.18 pct of&apos; the nitrogen atoms present are impositions of disorder. Past investigations1-4 of the Fe-N system have left only details of the thermodynamic behavior of the y&apos; nitride, "Fe,N9&apos;, to be studied. The present investigation was made to establish more precisely than hitherto the limits of composition and the relation between composition and nitrogen activity at 500°C. EXPERIMENTAL TECHNIQUE The compositions of nitrides in equilibrium with various NH, + Hz mixtures at 500°C were determined from the weights gained by 0.02-in.-thick (4.0 to 4.5 g) strips of purified iron* when the nitrides were formed A description of the gas generation and furnace system has been published.5 Cracking and blistering during conversion of the original solid iron at 550°C injected considerable porosity into the strips without causing their disintegration. The time for complete conversion was significantly lowered by periodically reducing partly nitrided specimens in hydrogen and then reexposing them to the nitriding gas. Gas mixtures producing single-phase were used in the equilibrations at 500°C. Equilibrium was regarded as existing when the specimen weight was not detect-ably affected by further exposure to the same conditions. The gas compositions and nitrogen activities at which y&apos; transformed to a iron (lower activity limit) and to E iron nitride (upper activity limit) were redetermined during the investigation. A specimen was equilibrated in an NH, + Hz mixture at 500°C and then exposed to a s1ightly different gas. When equi- librium had been reestablished the gas was again changed slightly. At each stage of this repeated process, while the specimen was reacting with the gas, the variation of its weight with time was observed. The onset of phase transition was marked by an abrupt change in the amount and rate of weight gain or loss. The specimens were weighed outside the furnace, in air and at room temperature, on a balance with 0.05 mg precision. When it was found that the specimens were oxidizing at a significant rate during the weighing, a series of timed weighings was made with each specimen, starting 1 min after its exposure to air. RESULTS AND ANALYSIS The gain in specimen weight from oxidation during weighing was linear in the logarithm of time between 1 min and about 2 hr, Fig. 1, later becoming linear in the cube root of time. In the logarithmic period, nitride specimens oxidized two to three times as fast as

Jan 1, 1970

By J. Serra, M. Turpin, R. Alberny

A new method is proposed to obtain automatically an unbiased estimate of the interdendritic spacing A. It is shown that the structure can be built by a random distribution of a rectangular basic unit. The usual definition of the interdendritic spacing yields a value 1 which, coupled with A, gives the shape of the basic rectangular unit. A study of the relationship between dendrite arm spacing and solidification rate was conducted as a part of a research program on dendritic solidification. For any comparison between theory and experiments to be meaningful, it is necessary to measure reproducible and clearly defined spacings. Fig. 1 shows clearly that even in a fairly simple structure such measurements are difficult. if we compare photos (a) and (b), we can hardly assess which one shows the larger spacing. Moreover, the quantity to be measured can be defined in several ways. On a small scale, dendrites seem to be distributed in a very regular and ordered way. However, on a larger scale, this regularity no longer exists. The usual way to measure spacings is to pick up some rows of dendrite stalks; such measurements are obviously biased since less orderly regions are not taken into account. A more objective method is to section the picture with randomly oriented straight lines and average the measured interdendritic spacings. The purpose of this paper is to show that such measurements, which can be conducted automatically, yield objective and reproducible results which are directly related to characteristic features of the dendritic structure. I) THEORETICAL ANALYSIS 1-1) Mathematical Morphology and Function of Co-variance. Matheronl and Serra2 enlarced- the definition and geometrical meaning of the notion of covariance to encompass problems in mathematical morphology. A brief review of part of their theory can be stated as follows. Let A&apos; be an isolated particle, and let us consider a group of two scanning points h is the vector joinlng these points, h its modulus, and a its direction. Let us also define a boolean function, k(x), whose value is 1 if x lies inside the particle and 0 if it 1s outside. The total number of events in which both points are inside A&apos; IS the covariance Ii&apos;,(h): is the measure of the intersection of A&apos; with the particle ALh obtained by translating A&apos; of -h Obviously K,(O) is the volume of the particle A&apos;, or its area if A&apos; is a two-dimensional body. The average value of K,(h), when the direction of a vector h of constant modulus is rotated, is: An important property of the covariance is illustrated on Fig. 2: if the shape of a particle shows some regularity along a direction a, K,(h) generally presents a maximum. We now consider a group A, made of many particles A&apos; distributed in space; then k(x) is taken as the realization of a stationary random f~nction.~ The volume fraction (or fraction of area if the problem is two-dimensional) occupied by A equals the average value q of k(x): meaning "average value of"). We also replace

Jan 1, 1970

By K. Tangri, B. Swaroop

Simultaneous measurements of lattice (elastic) strain by X-ray line shift method and total strain with an electrical strain gage have been carried out on polycrystalli,ne nickel with the help of a specially designed tensometer attachment for the X-ray dif-fractometer. During the initial stages of deformation, the rate of increase in lattice strain closely follows the total strain until the plastic strain sets in. From then onwards, the two strains deviate from each other and with further increase in afiplied stress the rate of increase of lattice strain eventually decreases. Depending upon the mode of unloading, both compressive and tensile strains have been observed in nickel deformed up to 0.29 pct strain. These results have been explained on the basis of the effects of clustering of dislocations and also the production and behavior of point defects during loading and unloading, respectively. POLYCRYSTALS deformed plastically in a uniaxial tension test show residual lattice strains (hereafter referred to as RLS), which broaden the X-ray line profiles and shift their peak positions.&apos;&apos;4 It is known that uniform straining of a crystal lattice (macrostrain) produced movement of ddfraction line peaks, whereas nonuniform straining (microstrain) causes line broadening.= Though the nature and origin of RLS in deformed metals is not yet clearly understood, these are believed to be due to the presence of some form of a locked-up stress system. Several possible detailed interpretations6&apos;" of the stress system have been proposed by various workers and common to all these interpretations is the assumption that different parts of the aggregate have different tensile yield stresses; e.g., that a part A yields under a lower applied stress than a part B. Therefore, during the deformation process, the elastic strain in A will be less than that in B, and, after completion of deformation, B will tend to contract further than A but will be prevented from doing so by the restraining influence of A. Thus, when equilibrium is reached, A will be in compression while B is in tension. Although there is general agreement on the correctness of this argument, controversy still exists as to the exact nature of the parts A and B in a deformed metal. In an alternative approach to the creation of parts A and B, many other investigators have assumed that the RLS observed in unloaded specimens are in some way connected with the lack of proportionality between lattice strain and applied stress in the region above the yield stress." cullity13 has prepared a schematic summary of the results of previous workers, mainly Smith and Wood,2&apos;11 which suggests that, above the elastic limit, the lattice strain may increase less rapidly with respect to strain, or may even decrease with increase in applied stress. If the applied stress is then decreased, the lattice strain would decrease along a line parallel to the loading line in the elastic region and thus produce a compressive residual lattice strain after unloading. At equilibrium, to balance these compressive stresses? there would have to be regions under tensile stress which may well be the grain boundaries or the substructure walls formed during deformation. The present investigation was undertaken to gain a better understanding of the nature and origin of RLS and also to experimentally verify the salient features of this hypothesis. EXPERIMENTAL Stress and strain determinations were made with a specially constructed tensometer attachment for the X-ray diffractometer, Fig. 1: which permits the following measurements simultaneously on a sheet specimen under uniaxial tension at various stress levels during loading and unloading: a) lattice strains, E=. in a direction perpendicular to the direction of pulling (x direction) from shifts in X-ray line peak positions; b) the total strain, ex, in the direction of pulling. with the help of an electrical strain gage affixed to the back of the specimen directly below the area irradiated by X-rays: and c) the applied stress, with the help of a load cell which consisted of a calibrated stainless-steel sample of dimensions identical to those of the specimen under investigation, and to which it was coupled. Because of its high stacking fault energy.I4 nickel

Jan 1, 1970