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By A. H. Larson, R. J. McClincy

ALTHOUGH arsenic has a very high vapor pressure and vacuum distillation appears to be a likely method for its removal from lead, the published literature contains virtually no information concerning the vacuum removal of arsenic from lead. Caldwell, Spendlove, and St. Claire1 mention arsenic in their investigation of the removal of volatile metals from lead by vacuum distillation. They do not, however, give any data for arsenic removal or refer to any actual experimental work involving arsenic dissolved in lead. Moriyama, Kozuka, and Miura2 have determined the activity of arsenic in dilute As-Pb alloys in the temperature range from 450" to 600°C using a closed galvanic cell. They found that the activities of both arsenic and lead showed a positive deviation from ideality at 600°C. In view of the lack of experimental data regarding the vaporization of arsenic from As-Pb alloys, a limited vapor pressure study was made on liquid alloys containing from 0.5 to 3.3 wt pct As in lead at 703°C. The pressure of As4(v) above the alloys studied was determined from weight-loss data collected by means of the inert-gas saturation method. The experimental apparatus and procedure used were similar to that discussed by Alcock and Hooper9 with modifications as described by the authors., The technique involved was one of passing a known volume of inert gas over the alloy to be studied in a known amount of time and determining the loss in weight of the sample. Because of the low vapor pressure of lead at 703"C, the observed weight loss could be attributed solely to the vaporization of arsenic as the tetratomic molecule AS43 Measurements of the apparent vapor pressure were repeated at different inert-gas flow rates until from three to five values were obtained which were independent of inert-gas flow rate. This value of the apparent vapor pressure was taken to be the equilibrium vapor pressure of the alloy under consideration. The vapor pressures measured in this investigation have been converted to the activities of arsenic in As-Pb alloys, Table I, by use of the data compiled by Elliott and Gleiser5 for the vapor pressure of pure arsenic. The standard state for arsenic was chosen as the pure, hypothetical, supercooled liquid. The activity of arsenic was calculated from the fourth root of the ratio PAs,/PAS,. The low magnitude of the vapor pressures given in Table I explains the difficulty en- countered by earlier workers in successfully vacuum distilling arsenic from very dilute As-Pb alloys. The data shown in Fig. 1 indicate that the As-Pb system behaves ideally. The apparent outlier represented by the alloy containing 1.43 mol pct As is a result of the fact that the pressure of As, above the alloy was barely detectable by the experimental procedure used in this investigation. Because of this, the apparent vapor pressure determined for this alloy could be in considerable error. Moriyama, Kozuka, and ~iura' have reported that arsenic shows a positive deviation from ideality in dilute solution in lead. However, details of their results have not been made available. This research was made possible by a grant from the National Science Foundation (GK-196) for which the authors are very appreciative.

Jan 1, 1970

By John D. Meahin

THE use of digital methods for generating crystallo-graphic data is well-established and many programs are now available. Transmission electron microscopy usually requires a knowledge of the electron diffraction pattern which is obtained by plotting a planar section through reciprocal space. With cubic symmetry these sections are very easily produced, but with hexagonal and lower symmetry systems considerably more labor is involved. Johari and Buchanan1 have written a Fortran program for generating standard projections and along similar lines we have produced a short but completely general program for generating any section through reciprocal space. The required inputs are the lattice parameters and angles for the real crystal. The Miller indices of the direction [U, V, W] parallel to the electron beam are then specified and the program will generate the Miller indices of the plane normals perpendicular to [U, V,, W] up to some specified integer. A subroutine can be inserted to test for forbidden reflections if desired. We have used such routines for fct and hcp crystals. As each permitted index is generated it is printed or punched out and no storage arrays are utilized in the computer. The normal diffraction pattern corresponds to the zero-order Laue zone, but with thin crystals or crystals of large lattice parameters the higher-order Laue zones may contribute to the diffraction pattern. Accordingly the program will generate successive Laue zones and project them onto the zero-order zone. The output of the program first lists the zone axis [C, V, W] and the Laue zone, and then gives a list of permitted reflections and the corresponding XP and YP coordinates of the reciprocal lattice point in angstroms-'. In addition, ZP, the perpendicular distance of the reciprocal lattice point from the (U, V, Ur) plane in reciprocal space is given, as is the reciprocal interplanar spacing. In the case of the zero-order Laue zone ZP is zero. A diffraction spot from the higher-order Laue zones will be very slightly displaced from the computed coordinates as its position in an actual pattern is given by projection along the diffracted beam2 and not along [u, V, w]. For any given electron wavelength this correction could be readily incorporated into the program, but as it only amounts to -1 pct it was decided to leave the program in its most general form, i.e ., a computation of points

Jan 1, 1970

By Frank A. Crossley

The work described has one serious shortcoming: grain size was not monitored during heat up to the temperature (1675°F) of isothermal anneal. The chief obstacles to p grain growth in titanium a-ß structures are the a grains. Heating a structure such as that shown in Fig. 1 to a temperature close to ß transus causes dissolution of a grains in order to adjust the a/ß ratio, compare Figs. 1 and 2. During this process there is a concomitant growth of the ß grains—otherwise ß grains would have to be nucleated in order to adjust the a/ß ratio. When the annealing temperature is reached the a/ß ratio stabilizes and this initial phase of ß grain growth ceases. After an incubation period growth resumes as described. Some 0 grain boundaries can be clearly seen in Fig. 1. (Skilled metallography commonly produces photomicrographs which show more structural detail than direct observation.) These boundaries suggest that the average ß grain size is approximately 0.002

Jan 1, 1970

By R. G. Vardiman, M. R. Achter

THERE has been interest recently in the conditions under which dislocation pipe diffusion may be observed. In order to extend the measurements to temperatures below Tm/2, where pipe diffusion becomes more important, a chemical sectioning technique was developed for silver single crystals which makes possible the removal of layers of 100A or less. The procedure is briefly as follows. Silver single crystals of 99.995 pct purity were cut in the form of discs t by 4 in., electropolished, and electropolated with Ag110 to about 1000A thickness. The thickness was determined by calibrating the activity with the weight of heavier platings, up to 10,000A. Both diffused and undiffused samples were sectioned in a two-step process. Reaction with a solution of iodine in alcohol formed a thin, even layer of AgI, which was then dissolved in a KCN solution. The reaction rate of the iodine solution varied slightly over a period of time, so that the thickness of the stripped layers, while quite even and regular for a given specimen, ranged from 65 to l00W for different specimens. This variation was checked by using a thickly plated standard with each run. Layer thickness was determined from undiffused samples by the point where the layer activity drops to half the maximum. This maximum intensity also provides, with appropriate corrections, the initial concentration per layer co. Because of the small penetration distances, it is necessary to use the exact solution of Fick's law for a source of finite thickness.' For a plating of thick- where c is the concentration at depth x. flj the error function, D the apparent diffusion coefficient, and t the time. The diffusion coefficient was obtained from the concentration-penetration data by extrapolating to x = 0 where c/co = erf h/2(Dt)1/2 Enough points were taken to impart confidence in the accuracy of the intersection, generally about ten layers. Four temperatures were used as in Table I. For best accuracy, t and h were chosen to give values of the parameter (Dt)1/2/h between 1.0 and 1.7. A typical concentration-penetration curve is shown in Fig. 1. The diffusion coefficients calculated from Eq. [I] are plotted in Fig. 2. For comparison, the high-temperature data of Tomizuka and sonder 2 which go down to 630°C are plotted as the solid line 2(a) from their expression D = 0.40 exp (-44,090/RT). Also for comparison, the lowest temperature point of Hoffman and Tumbull3 is plotted. It is apparent that our data diverge appreciably from the high-temperature extrapolation by 373°C. A better straight line fit for the low-temperature portion is obtained by subtracting the extrapolated volume diffusion coefficient from the apparent. or measured coefficient, and plotting the difference, curve (h) of

Jan 1, 1970

By J. Kittl, D. Arias

THE decomposition on cooling of the high-temperature ß bcc phases in copper- or silver-based binary systems usually takes place by a martensitic. massive, bainitic, or pearlitic reaction depending upon the particular conditions of each system. The AgAl system is one of these systems in which a massive or a martensitic transformation can occur upon cooling from the 3 phase field. Recently Hawbolt and Brown1 observed both massive and martensitic transformation products in a 22.7 at. pct A1 alloy. In the present work the massive and the martensitic transformations were investigated in a number of alloys for the composition range between 23.2 and 27.9 at. pct Al. The alloys were prepared using high-purity silver, 99.999 pct, supplied by ASARCO and aluminum, 99.999 pct, supplied by ALCOA. The metals were melted using a graphite or a sintered alumina crucible which was sealed in quartz tubes under an argon atmosphere. The alloys Were remelted to reduce segregation and homogenized in the 13 phase field for 24 hr. The weight of the alloys after homo-genization compared with the initial weight indicating the alloy composition to be within k0.1 pct of the in- tended composition. Chemical analysis of several samples confirmed the estimated alloy composition. All metallographic observations were performed on samples electropolished with ac current using a 10 pct solution of KCN and a stainless-steel electrode. The samples were cut into -1-mm-thick slices, polished, heat-treated in the ß phase field, and quenched in air, ice water, or iced brine. Some heat treatments consisted of a 2-min anneal carried out in air to allow maximum quenching speeds. Other samples were heat-treated in a vacuum of 10"4 torr and quenched using a helium blast in a quenching apparatus described elsewhere.&apos; In both cases, no appreciable losses of silver or aluminum were noted at the sample surface by sectioning and electropolishing. Table I summarizes the microstructure resulting from the various quenching treatments. The composition of the alloys investigated is also indicated on the equilibrium diagram in Fig. 1. The <, hcp phase, typical of a massive ß — cm, transformation, was observed in all alloys. A minimum temperature of 450°C was estimated for this transformation based on preliminary cooling experiments. the results being included in Fig. 1. In these

Jan 1, 1970

By J. P. G. Farr, R. Brownsword

THE role of solute segregation in the formation of cellular solidification substructures in tin and its dilute alloys is well-established, see, e.g., Ref. 1. Segregation has been shown to persist during cooling, enabling solidification structures to be studied from sections taken at some distance behind the interface. In the present work, a single crystal of commercial nickel, 99.965 pct, was examined in this way. The crystal was cut from the center of a rod given a single pass in an electron beam floating zone melter. Polished sections of a nickel specimen taken normal to the growth direction showed a very fine precipitate phase, the distribution of which varied over the section. The identification of the phase proved difficult because of the small amount present and the small particle size, about 1 p: but it was shown by probe microanalysis to contain only nickel and oxygen in detectable concentrations and was probably nickel oxide, NiO. Bulk analysis of the material before melting showed there to be only 3 to 4 ppm of oxygen present, thus demonstrating a very considerable segregation concentration effect. In some areas of the section the precipitate formed a discontinuous hexagonal network suggesting decoration of the cellular boundaries known to be present in the sample2 whereas in a restricted region the precipitate formed small clusters. Occasionally it could be seen that the clusters were at the intersections of an hexagonal network of cellular dimension. It was suggested3 that this was the result of enhanced segregation to the cell boundary intersections whereas general cell boundary segregation was insufficient to give a precipitate. Enhanced nodal segregation has since been demonstrated in a number of systems.1, 4-8 The development of a suitable electrolytic etching technique (perchloric acid 20 pct v/v; ethyl alcohol 70 pct; glycerol 10 pct; current below electropolishing plateau; 1 to 2 sec etching) suggested the association of the phase with regions of solute segregation (where ko < 1); in these regions anodic attack produced grooves or depressions. In a study of the variation of solidification substructures with degree of constitutional supercooling, Biloni et a1.&apos; appear to have used standard growth conditions and varied the solute concentration. They were able to produce in a series of individual tin crystals examples of substructure ranging from planar interface through various cellular structures to den- Fig. 1—Electroetched section taken normal to the rod axis; the center of the rod lies to the left and the periphery to the right of the micrograph. The variation of structure across the section is evident. Magnification 60 times. drites. It was possible in the present nickel crystal to observe a continuous range of substructures varying with degree of supercooling across a single section as shown in Fig. 1. Growth rate, 13 mm per min, and temperature gradient were essentially constant; the variation in structure is thought to be due to a radial gradient in solute concentration ahead of the solid interface. The liquid at the interface is likely to have been richer in solute toward the periphery of the zone, the result of curvature of this interface. The type of substructure was seen to vary with increasing constitutional supercooling as follows: a) region free of precipitate. top left, Fig. 1: 6) region of nodal precipitates which became arranged in hexagons on passing from the center of the rod: c) irregular hexagonal cells with incomplete boundary precipitation; d) regular hexagonal cells of decreasing size with complete boundary precipitation. Fig. 2 shows the transition from stage 6 and Fig. 3 shows the structure in stage d. Within stage 0, the range of conditions over which irregularly positioned nodes occur appears to be small and the nodes are soon recognizable as taking up positions at the intersections of an hexagonal network as the supercooling increases.

Jan 1, 1970

By P. T. Gallagher, W. A. Oates

THE partial excess entropy of interstitial solutes in metals, SXS , has usually been interpreted as being principally vibrational ever since the initial statistical treatment of hydrogen in metals by Fowler and Smith-ells. The vibrational entropy is considered being due to the optical modes of the light interstitial atom. Little attention has been given to the magnitudes of the values of SXS&apos;. Leiser and Witte2 and Ebisuzaki and O&apos;Keeffe3 have noted that for hydrogen in metals Si is approximately constant for different metals. On the other hand if it is assumed that the interstitial solute is an isotopic defect then, as shown by McLellan, SXS should vary from metal to metal as follows: where S is the standard entropy of the solvent and Mi, M, are the masses of the interstitial and solvent atoms. respectively. Fair agreement with this equation was found for oxygen in silver and nitrogen in iron4 and for carbon in iron.= Ln a subsequent analysis of metal- hdrogen systems McLellan&apos; found a variation of $&apos; from metal to metal but not in a manner expected from the isotopic impurity equation. However, a possible correlation between the energy of solution, Ei, and sf was noted. Similar correlations have been noted for certain dilute substitutional solid Solutions 7, 8 and recently Kubaschewski 9 has demonstrated a correlation between integral heats and ex-

Jan 1, 1970

By M. J. Pool, R. K. Saxer, J. R. Myers, D. S. Dickson

ThE equilibrium phase diagram of the Mo-Cr system, described by anssen,&apos; indicates that chromium and molybdenum form a continuous series of solid solutions above 1673K. The liquidus and solidus have been reported to have a minimum at about 12 at. pct Mo and 2133°K by Bloom and Grant2 and by Putnam, Potter, and Grant.3 X-ray studies by Trzebiatowski and ploszek4 and Baen and Duwez&apos; revealed no indication of solid solution decomposition after long anneals at 1473", 1273", 923", and 873°K. However, Bloom and rant&apos; by means of cooling and heating curve analysis of alloys containing up to 45 at. pct Mo found thermal effects at temperatures approximately 100" * 30°K below the liquidus. The only previous thermodynamic study of the Cr-Mo alloy system was made by Laffitte and Kuba-schewski6 who used the Knudsen effusion method at 1471°K. These investigators reported the possibility of a miscibility gap because they observed positive deviations from ideality in their chemical activity

Jan 1, 1970

By A. H. Larson, R. J. McClincy

The activity of Sb,03 in PbO-Sb,03 slags containing less than 50 mol pct Sb,03 was determined by the inert-gas saturation method at 700°C. In this composition range, the activity gf SbzO3 shows a strong negative deviation from ideality. The activity of PbO in these slags was calculated by application of the Gibbs-Duhem iniegration to the Sb203 activity data. The calculated activity of PbO in slags containing more than 63 mol pct PbO was found to deviate in a positive direction from ideality uthile a negative deviation was found for slags containing less PbO. The standard Gibbs free energies of formation of Sb,03 and PbO. Sb203 have been calculated and compared with existing data in the literature. The activity of Sb203 in PbO-Si0,-Sb203 (PbO/SiO, = 2) slags containing less than 25 mol pct Sb,03 was also determined by the inert-gas saturation method at 700°C. In this composition range, the activity of Sbz03 shows a very large negative deviation from ideality. VERY little experimental work has been published in the past to determine equilibrium data in the oxide systems connected with the refining of lead. These data are of value since impurities such as antimony, arsenic, and tin must be removed from lead and recovered for further treatment. Equilibrium studies on antimony and arsenic systems are also of interest for the design of new processes for lead refining and lead dross treatment. Maier and ~incke&apos; first determined the liquidus curves for the PbO-Sb203 system and identified the compound PbO . Sb203. They found the phase diagram for this system to be two simple eutectics located on either side of the congruent melting compound. They also determined a very limited amount of vapor pressure data for Sb406 abbve PbO-Sba3 melts at 697"~. A second phase diagram investigation on this system was reported by Hennig and Kohlmeyer&apos; who confirmed the existence of the compound PbO . Sb203 as well as the form of the diagram. A disagreement was noticed, however, in that their liquidus temperatures over nearly the entire composition range were higher than those reported by Maier and Hincke. Barthel~ and pelze14 redetermined the liquidus curve at the PbO-rich end of the PbO-Sb@, system and agreed very closely with the results of Maier and Hincke. None of the investigators mentioned above reported any mutual solid solubility in the PbO-SbD3 system. Zunkel and Larson5 have determined the phase diagram for the PbO-rich end of the PbO-Sb203 system by slag-metal equilibrium studies in the Pb-PbO-Sb203 system and by thermal analysis studies in the PbO-Sbz03 system. A maximum solid solubility of 5.6 mol pct Sb203 in PbO was observed at the eutectic temperature of 604°C. Their results for the phase diagram agree favorably with those of Maier and Hincke. The vapor pressure of Sb2O3 in the temperature range from 470" to 800°C has been determined by Hincke, using a modification of the transportation meth~d.~ His results for temperatures below the melting point of Sba3 are the only data reported in the published literature. The predominant vapor species has been shown to be Sb,06 by Norman and staley.? Myzenkov and Klushin,8 using the boiling-point method, have determined the pressure of Sb406 above liquid SbD3 in the temperature range from 715" to 1025°C. The agreement between these two studies is not very close. A portion of the discrepancy lies in the fact that Hincke used silica crucibles, which were attacked by the liquid Sbz03 at high temperatures. This fact does not account, however. for the large difference observed at the melting point. ~aier&apos; gives a brief summary of vapor pressure data for Sb,O, above pure liquid Sbz03 which agree quite well with the data of Myzenkov and Klushin at temperatures near the melting point. This paper describes the determination of Sb2O3 activity data in the PbO-Sb203 and Pb0-Si02-Sb203 (PbO/SiOz = 2) systems by the inert-gas saturation method. These activity data are compared with the data calculated by Zunkel and arson. EXPERIMENTAL Materials. The materials used in this investigation were analytical reagent-grade PbO (99.8 pct PbO, 0.14 pct insoluble in CHsCOOH, 0.02 pct not precipitated by HB, 0.1 pct CaO, and 0.08 pct SiOz), Sbf13 (99.6 pct Sb203, 0.004 PC~ C1-, 0.005 PC~ SO;-, 0.15 p~t AS, 0.001 pct Fe, and 0.03 pct other heavy metals such as Pb), and SiOz (chromatographic grade). Apparatus for Vapor Pressure Determinations. The apparatus used in this investigation consisted of a transportation reaction system with two separate gas trains. The argon transporting gas was first mixed with a small amount of hydrogen, metered, and dried by passage through silica gel and anhydrone drying tubes arranged in series. After this preliminary drying, the argon was passed through copper wool at 500°C to convert the residual oxygen to water vapor which was removed by three anhydrone drying tubes. A second stream of argon was metered and dried and then passed around the outside of the alumina reaction tube to flush away the volatile species to pre-

Jan 1, 1970

By S. G. Cupschalk, J. J. Wert, R. A. Buchanan

The uniaxial deformation of thermally ordered and disordered polycrystalline Cu3Pt was studied by means of the X-ray line - broadening analysis according to Warren and Averbach and the extension of this analysis to ordered fcc materials by Mikkola and Cohen. Because of the heat treatment history, extinction had a pronounced effect on the X-ray spectra of ordered and disordered C%Pt at small plastic strains. After an appropriate correction for extinction, the long-range order in thermally ordered ChPt was found to decrease at a slow constant rate with plastic strain. Furthermore, the antiphase domain probability increased at a constant rate to 17.5 pct strain. The effective particle size behavior indicated that the stacking fault energy is lower in ordered than in disordered Cu3Pt. Analysis of the stress-strain curves shouled that ordered Cuzt has a slightly lower yield Point but a much higher work-hardening rate than disordered Cu3Pt. THE presence of long-range order in a solid-solution alloy has a marked effect on its mechanical properties. While this effect has been known qualitatively for many years, it was not until recently that detailed investigations have been performed to determine the exact role long-range order plays in this strengthening mechanism. The development of an advanced, quantitative. X-ray diffraction analysis by Warren and Averbachl and the extension of this analysis to the L1, type super lattice by Mikkola and cohen2 have greatly accelerated research in this field. The research reported in this paper consisted of two primary phases. The first phase was to determine the effect of long-range order on the tensile properties of polycrystalline Cu3Pt. This objective was accomplished by comparing the stress-strain behavior of thermally ordered CusPt to that of thermally disordered CusPt. The second phase of the research was to determine the difference between the atomic arrangements in thermally ordered and thermally disordered Cu3Pt as a function of uniaxial deformation and thereby gain a deeper insight into the mechanism by which long-range order affects the tensile properties. This second objective was accomplished by applying the Warren-Averbach method of peak profile analysis to the X-ray diffraction patterns obtained from ordered and disordered Cu3Pt after given amounts of uniaxial deformation. EXPERIMENTAL PROCEDURE The Cu3Pt was prepared by vacuum melting and casting. After a homogenization anneal, the ingot was cold-rolled to sheet form. Two tensile specimens with gage sections of 2.50 by 0.500 by 0.115 in. were carefully machined from the sheet. The specimens were polished with a final step of 600-grit paper to insure smooth diffracting surfaces. Finally, one specimen was heat-treated to yield an average grain diameter of 0.016 mm and an initial degree of long-range order, S, of 0.825. The other specimen was water-quenched from above the critical temperature, 645"C, to yield an average grain diameter of 0.017 mm and zero long-range order. The heat treatment history of each specimen is shown in Table I. The tensile tests were performed utilizing a Research Incorporated Model 900.95 Materials Testing System. This unit employs a closed-loop feedback system which maintains a constant strain rate through an extensometer clipped to the gage section of the tensile specimen. A strain rate of 1.32 i0.02 x 10"4 sec-&apos; was employed in testing both specimens. In the X-ray diffraction analysis, a General Electric XRD-5 diffractometer equipped with a pulse-height analyzer set for 90 pct efficiency was employed. The goniometer speed selected was 0.2 deg, 20, per min. Filtered Cu radiation was used for all peaks and all peaks were chart-recorded. Because of nonuni-form grain size. it was necessary to spin the specimens during X-ray analysis in order to obtain reproducible integrated intensities. The spinning rate was 2000 i100 rpm. The application of the Warren-Averbach method of peak broadening analysis to a diffraction pattern is very time consuming if done manually. In this research, the calculations involved were performed with the aid of a computer program by wagner.3 As reported by Wagner, the program is written in Fortran TV computer language. It was modified to Fortran I1 so as to be handled by the IBM 7072 computer at Van-derbilt University. In the X-ray diffraction analysis of uniaxially deformed Cu3Pt, the 100, 200. 400. 111, and 222 reflections were recorded from the initially ordered sample after &apos;plastic strains of 3.0, 6.0, 9.0, 12.0,

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 &apos;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;&apos; 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 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&apos; at 1300°C and by Coskun and Elliott&apos; 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;&apos;&apos; 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&apos;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 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 M. S. Burton, J. E. Ritter

The sessile-drop technique was employed to study the effect of atmosphere and alloy additions of titanium and chromium on the surface tension and contact angle of nickel on sapphire substrates at 1500oC. Shear tests were conducted on the solidified sessile drops. The liquid-gas surface tension of pure nickel on sapphire was found to be 1747 ergs per sq cm, with a contact angle of 109.6 deg. The surface tension and contact angle were not affected significantly by the four atmospheres, vacuum, impure argon, pure argon, and pure hydrogen. Small additions of titanium and chromium decreased the contact angle and for the same alloy content, contact angles were lower in pure argon than in pure hydrogen. On the basis of shear-test results , the most probable cause for adhesion in the Ni-Al2O system is the formation of NiO:Al2O3 spinel at the interface; in the titanium alloy-Al2O3 system adhesion is thought to be due to a mechanical interlocking effect; in the chromium alloy-Al2O3 system adhesion is believed to be the result of solid-solution formation involving Cr2O3 and Al2O3 at the interface. In the last few years there has been considerable interest in reinforcing metals with ceramic whiskers. It has been postulated that, by reinforcing nickel with sapphire whiskers, high-temperature strengths su- perior to those of the best current nickel alloys can be achieved.&apos; To fabricate a whisker-metal composite having optimum density and strength, understanding of wettability and adherence in the system is of prime importance. Although there has been some previous research in this a a need for further studies has been cited4-8 to understand better the effects of impurities, alloys additions, and atmosphere on the wetting and bonding of metals to metal oxides. The purpose of this research was to investigate the factors involved in the wetting and adherence of nickel/nickel alloys to sapphire (single-crystal a Al2O3). Sessile-drop experiments were conducted in vacuum, impure argon, pure argon, and pure hydrogen, to determine the effect of atmosphere on the contact angle of the metals on sapphire, and the liquid-gas surface tension of pure nickel. The solidified sessile drops were sheared from the sapphire substrate to measure the bond strength between the metal and ceramic. The alloy additions chosen were titanium and chromium since both enhance the wetting of nickel on sapphire.2, 3c Also, titanium is commonly used when brazing metal-to-ceramic seals to improve adherence. Since chromium forms an oxide that is completely soluble in sapphire, it was thought that the oxide could serve as a transition phase to promote bonding between the Ni-Cr alloy and sapphire. I) EXPERIMENTAL APPARATUS AND PROCEDURE The sessile-drop apparatus was a horizontal furnace, with an induction-heated, cylindrical molybdenum susceptor in a water-cooled Pyrex chamber. This apparatus was patterned after that of Williams and Nielsen.7 A flat Pyrex window at each end of the furnace allowed temperature measurements to be made at one

Jan 1, 1968

By P. S. Rudman

Crystal-structure occurrences in binary phase diagrams of fifth- and sixth-period elements, zirconium through palladium and hafniun through platinum, are surveyed with the conclusion that average .group number GN is the dominant correlative. This is interpreted in terms of curves of enthalpy differences between competitiue structures that are continuous func -tions of GN. It is further reasoned that the absolute formation energies may also be continuous functions of GN and if so can be simply obtained from the regatives of the heats of sublimation of the elements. It is shown that from such a heat of formation-GN plot the heats of mixing of alloy systems can be quantitatively predicted. For example, for sixth-period alloys very large exothermic heats of mixing are predicted for systems that span GN = 6 (i.e., Hf-Pt, Ta-Os, ...). Thermodynamic data with which to test these predictions do not appear to be available. If in the latter transition (A subgroup) elements we eliminate from consideration the fourth period where magnetic terms contribute to crystal-structure stability, as shown in Table I, there is a very regular sequence of structures. Using the group number (GN) assignments of Table I, which differ from the usual assignments of 8 to the elements listed as 8 through 10, it is perhaps trivial to say that the phase occurrence is a unique function of GN. However, the interesting aspect of alloys from among these elements is that the alloy structures also appear to correlate with GN. The GN for an alloy is given as GN = SixiGNi, where xi and GNi = atomic fraction and GN of component i, respectively. It is difficult to credit anyone in particular with having discovered this correlation, so many people have implicitly or explicitly employed it in the last 10 years. However, Bloom and Grant&apos; in their correlation of s-phase occurrence with total number of d + s electrons were certainly one of the first to appreciate the correlation and Hume -Rothery2 appears to be responsible for the use of average GN as defined above. Only in the last few years have the phase diagrams of enough alloy systems been determined for this correlation to be surveyed with any degree of completeness. We shall here, in an abbreviated format, summarize the available phase-diagram literature and discuss some consequences of the GN correlation. BINARY DIAGRAM SURVEY In Figs. 1 to 3 the phase occurrences are summarized. In Fig. 4 the occurrence limits for the more common structures are summarized. That the GN of an alloy falls within the occurrence limits of a particular structure is a necessary but not a sufficient condition for the appearance of that structure. The preceding figures certainly illustrate that GN is a dominant correlative for structures of these elements. Many of the diagrams have complications, with ordering and other phase changes occurring in intermediate phases, that cannot be clearly accommodated in such a schematic survey and have hence been left out. Such omissions cannot, however, negate the GN correlations discussed here. Relative atomic size is also an important crystal-structure determinant and since atomic size varies quite regularly with GN for these elements it is possible that the apparent GN correlation is basically a size correlation. In Fig. 5 relative size occurrence limits are given for intermediate phases and extended terminal solutions. The relative volume, ?v/(v) - 2(vA - vB)/(vA + uB), has been taken as the measure

Jan 1, 1968

By R. C. Padfield

Experience over a 3-year period in Bethlehem Steel Corporation&apos;s plants has demonstrated the reliability of open-hearth roofs of bonded sprung-arch constructzon with burned basic brick. The design principles lor constructing these roofs include a minimum hot-strength requirement for the basic brick, expansion allowances that extend the full roof thickness, structural members to control arch contour, and a specified minimum roof rise. The greater stability of bonded roofs is explained in terms of the basic stress patterns of ring constrution and bonded construction. PRIOR to the development of successful sprung-arch roofs of basic brick, the majority of open-hearth furnaces in the United States were operated with sprung-arch roofs built of silica brick. Although many silica roofs used on open-hearth furnaces were ring-arch construction, Bethlehem Steel Corp. used bonded-arch construction because of its greater stability. In ring construction, each ring of brick is separately keyed and comprises an independent arch with the straight joints between rings traverse to the longitudinal axis of the furnace. In bonded construction, the bricks are laid in rows starting from the skewbacks so that the straight joints run parallel to the longitudinal axis of the furnace. Each brick in a given row is laid so that it spans the joint between two bricks in the row beneath it. Thus, the transverse joints across the arch are broken and the arch rings are thereby interlocked or bonded. When basic roofs were first being developed, the basic brick that were available had low hot strength. Such brick could not be safely used in sprung-arch construction without some means of suspending them. With the development of higher firing techniques by brick manufacturers and the recently introduced direct bonded bricks with high hot strength, the use of burned basic brick in sprung-arch roofs became feasible. The availability of high hot strength basic brick coupled with the potentially lower cost and proven stability of bonded construction prompted Bethlehem&apos;s Research Department to study the possibility of using basic brick in bonded roofs. With the full cooperation of plant ceramic engineers and open-hearth superintendents, particularly in 3 years of fur-nace trials, we developed the design criteria for bonded roofs and the corresponding property requirements for the basic brick that are discussed in this paper. DESIGN PRINCIPLES OF SPRUNG-ARCH BRICK ROOFS Stresses in Fixed Arches. A sprung-arch open-hearth furnace roof is generally built on rigidly held skewbacks. The constraint of the fixed support at each end adds a bending moment to the horizontal and vertical reactions at the ends of the arch. Fig. 11 shows the positive direction of forces acting on an arch fixed at both ends. Fixed arches can be analyzed when the members are continuous and have elastic properties. However, brick are inelastic, and arches built with individual brick segments cannot carry tensile stresses. Therefore, for practical solution of brick arches, empirical formulas have been derived from elastic theory that place design restrictions on arch dimensions to avoid development of tensile stresses. McDowell2 cites three main conditions for stability in sprung brick arches: 1) the thrust line of the arch should be maintained in the middle third of the thickness to avoid tensile stresses and resulting open joints in inner and outer curves of the arch; 2) the angle between the line of thrust at any joint and a line perpendicular to the joint must not exceed the angle of repose between brick; and 3) the maximum pressure at any point must not exceed the strength of the arch materials at furnace operating temperatures. The first and third conditions are particularly important in designing sprung-arch basic roofs because of the comparatively low hot strength of basic brick. According to McDowell&apos;s equation, if the thrust line is maintained within the middle third of the arch thickness, the unit pressure is obtained as follows: where p = unit pressure in psi, F, = resultant thrust normal to skewback in pounds per foot, t = arch thickness in inches, and z = distance in inches of thrust line from arch axis. When the resultant thrust normal to the skewback acts along the arch axis, z equals zero and unit pressure is simply the thrust divided by the cross-sectional area. If the thrust line moves to the limits of the middle third of the arch thickness, beyond which tensile forces would develop, z then equals one-sixth of the arch thickness and the unit pressure is double that when the thrust line is acting

Jan 1, 1968

By Ray W. Carpenter, Ralph Hultgren, Raymond L. Orr

Heats of formation of Au-Zn alloys of compositions Au3Zn and AuZn were rneasured at several temperatures by liquid tin solution calorimetry. The data for Au3Zn show that much smaller heat and entropy effects are associated with the a2- a1 transformation than for the a1 - a transformation. This result is consistent with reported X-ray diffraction studies which indicate that the a1 and (a2 phases have ordered structures which only slightly differ, whereas the a phase is disordered. The heat of formation of AuZn(ß&apos;) does not change significantly between 322o and 8000 K, confirming that the ß&apos; alloy remains highly ordered to high temperatures. Not many measurements have been made of the energies of order-disorder transformations in alloy phases. In many cases these energies may be conveniently determined by measuring heats of formation as a function of temperature. Many alloy phases approximately obey Kopp&apos;s law of additivity of heat capacities; as a consequence their heats of formation do not change with temperature. In ordered alloys, however, a decrease in degree of order with increasing temperature will contribute an endothermic component to the heat of formation. Thus, for ordered phases where other anomalous contributions to heat capacity in the alloy or its pure components are absent, a measured change in the heat of formation may be attributed to the energy of disordering. A portion of the Au-Zn phase diagram1" is shown in Fig. 1. The composition AuZn(ß&apos;) has a well-ordered superlattice structure of the CsCl type at room temperature. The alloy is considered to remain ordered to its melting point,1 although, from X-ray diffraction data and electromotive force measurements of zinc activities, Terpilowski3 concluded that considerable disordering began at -673°K. The Au3Zn composition is a disordered fee solid solution (a) at high temperatures. Between 693o and 543oK, the ailoy orders to form the a1 phase, having a structure based on the L12(AuCu3) type, but with a regular distribution of ordering faults in the c direction, making it tetragonal. Below 543oK, the alloy orders further by means of slight atomic shifts, without diffusion, yielding a complex long-period orthorhom-bic superlattice structure, a2.4-7 Heats of formation of Au3Zn(a2) and AuZn(ß&apos;) were measured at 363°K by Biltz et al.8 by aqueous solution calorimetry. Heat capacities of several alloys between 14.9 and 38.4 at. pet Zn in the range from 373" to 723°K were measured by Iwasaki ef al.6 Stoichiometric Au3Zn, however, was not included in the alloys measured, the nearest composition being 26.1 at, pet Zn. Also, the heating rate used for the measurements, 2 deg per min, may not have permitted equilibrium to be reached in the neighborhood of the transformations. Heat contents of solid and liquid AuZn were measured between 488o and 1138°K by Kubaschewski.9 It was decided to determine the ordering energies of Au3Zn and to check on the possible disordering of AuZn by measuring the heats of formation of these alloys at several temperatures. The present paper reports measurements by liquid tin solution calorimetry of the heats of formation of the three phases of Au3Zn at temperatures within their regions of stability, and of AuZn at a low (322°K) and a high (800°K) temperature. EXPERIMENTAL Alloy Preparation and X-Ray Examination. Ten-gram ingots of Au3Zn and AuZn were prepared by melting weighed amounts of gold (99.95 pct Au) and zinc (99.99 pet Zn) together in sealed evacuated Vycor tubes at 1060°K, followed by rapid quenching. The resulting ingots were homogenized at 900°K for 10 days. The Au3Zn alloy lost no weight in preparation, the loss from the AuZn alloy was enough to introduce an uncertainty of only 0.1 at. pet in its composition. Filings for X-ray examination were taken from various parts of each ingot and strain-annealed at 723°K for 20 min in vacuo. The Au3Zn filings were quenched rapidly to retain the disordered phase. Diffraction patterns were determined with an X-ray dif-fractometer using copper Ka radiation.

Jan 1, 1968