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By William C. Sleppy

The nmgnetic susceptibility of heat-treatable aluminuin alloys is sensitive to chanyes such as solution or dissolution of solute and the precipitation of mew phases. By measuring the change in the magnetic susceptibility of aluminum alloys caused by various heat treatments, an empirical relation was found from which atomic arrangements in dilute binary alloys of copper, zinc, and magnesiutn in aluminum have been delineated. The relation predicts the ultimate formation of C1LA12 when copper is precipitated from solid solution in aluminum. Euidexce joy silovt- range order is found for copper in solid solution in aluminum in the sense that copper atoms avoid being nearest neighbors to an extent greater than would result from a purely random arrangertzeizt. Hume-Rothery has predicted such short-range order joy solid solution of copper in aluminum The Al-Zn system agrees with evidence obtained from X-ray scattering at small angles and predicts a tendency for zinc atoms to cluster in solid solution in aluminum. In the Al-mg system, the empirical relation indicates an approach to randor distribution of magnesium in solid solution in aluminum with a tendency for magnesium segvegation which increases with incveasing temperature. ThE magnetic properties of metals are complicated by the fact that contributions are made to them both by electrons of a "metallic" type which belong to the crystal as a whole, and by electrons in states localized on particular atoms. An expression1'2 for the bulk magnetic susceptibility of aluminum may be written as the sum of three contributions: where XA1 is the bulk susceptibility of aluminum per gram of material (in the cgs system, the units are those of reciprocal density); Xa1+3 is the diamagnetic contribution of the electrons localized in ion cores; Xa1 is. the paramagnetic spin contribution of conduction electrons often called Pauli paramag-netism: Xa1 is the diamagnetic contribution of the conduction electrons often called Landau diamag-netism. Ion core diamagnetism arises from the precession of the electron orbits which occurs when a magnetic field is applied to a system of electrons moving about a nucleus. Its contribution to the magnetic suscepti- bility is small, temperature-independent, and unaffected by alloying. The conduction electron diamagnetism is also temperature-independent and arises from the translatory motion of the electrons. For perfectly free electrons this contribution should be exactly one-third of the Pauli spin paramagnetism, but this relation is seldom even approximately true. Blythe2 determined the conduction electron diamagnetism in pure aluminum and found it to be extremely small. Any change in the conduction electron diamagnetism caused by alloying is neglected in this work. The Pauli paramagnetic contribution3 to the magnetic susceptibility of aluminum depends upon the number of electrons that occupy excited states and whose spins can be turned parallel to an applied magnetic field. The number of electrons free to turn in the field is proportional to the temperature and each spin contribution to the susceptibility is inversely proportional to the temperature. A slight temperature dependence of Pauli paramagnetism occurs when the number of electrons occupying excited states cannot increase sufficiently to balance the inverse dependence on temperature of each spin contribution. The decrease of the magnetic susceptibility of aluminum with increasing temperature is attributed to a temperature dependence of the Pauli paramagnetism. Estimates of the Pauli paramagnetism of aluminum have been made by several workers.2,4,5 All of the values are in reasonably good agreement with each other. In this work Xal at 17°C is taken as 0.761 X 10-8 cu cm per g. An expression similar to [I] can be written for the magnetic susceptibility of an aluminum base alloy containing a fractional weight percent x of solute:' Xa = (1 -x)XAl+3 +xXsoluteion * XaPauli +Xadia) [2] where X, is the magnetic susceptibility per gram of alloy, Xal'3and Xsolute ion are the ion core diamag-netic contributions, and xpauli and xdia are the Pauli and diamagnetic contributions of conduction electrons in the alloy. If the components of a mixture are not alloyed but simply mixed together in their pure states without producing a new phase, then the magnetic susceptibility of the mixture is given by the Wiedemann additivity law: Xm =x1X1 +x2x2 + ..xnxp [3] where X, is the susceptibility per gram of mixture and xnXp are the weight fractions and susceptibilities, respectively,-. for the pure components. The additivity law is not applicable to alloys because the outer electronic structures of the components are changed by alloying.' Both the Pauli paramagnetism and Landau diamagnetism are affected; hence the magnetic susceptibilitv of an alloy is usually different from that calculated using the additivity law. In this work the difference, X, -X,, is taken as a measure of the change caused by alloying.

Jan 1, 1968

By R. Grierson, L. J. Bonis

The high-temperature Strength oF TD nickel has been observed to be dependent upon the previons thermal and mechanical history of the material. Variations in both the level and the anisotropy of strength have been observed. 01 this paper- these variations are correlated with the storing of annealing resistant elastic strain energy in the matrix of the TD nickel. An x-vay line -broadening tecknique is used to measure the maLrTis elastie strain. THE inclusion of a finely dispersed second phase into a ductile matrix has long been recognized as an extremely effective method of strengthening the matrix both at high and at low homologous temperatures. It has been found, however, that the factors which determine the high-temperature strength are not the same as those which are important at low temperatures. Below 0.5 Tm the size and distribution of the second phase particles are of prime importance in determining the strength,')' while above this temperature the strength is mainly dependent upon the previous thermal and mechanical history of the alloy,3-7 This paper is primarily concerned with explaining the response of the high-temperature mechanical strength of one of these alloys (DuPont's TD nickel) to various thermo-mechanical treatments. It will be shown that this response is not associated with the occurrence of any form of dislocation substructure within the matrix of the alloy. It has been found, however, that a correlation does exist between the elastic strain level in the matrix and the previous thermomechanical history of the alloy and that the observed changes in elastic strain level parallel the measured changes in high-temperature strength. It therefore must be concluded that variations in high-temperature strength are a direct result of the variations in elastic strain level. MATERIAL TD nickel contains approximately 2 vol pct of Tho2 in an unalloyed nickel matrix. It is formed, as a powder, by a chemical technique and this powder is compacted to form ingots which are then extruded to give 21/2-in.-diam rod. Rod of smaller diameter is prepared from the as-extruded rod by swaging. In the studies reported in this paper, 1/2-in.-diam rod was used. This rod received an anneal of 1 hr at 1100°C prior to being used in any of these studies. EXPERIMENTAL TECHNIQUES Two methods were used to examine the structure of the nickel matrix of the TD nickel. These were: 1) transmission electron microscopy; 2) the analysis of the position and profile of X-ray diffraction lines obtained using the nickel matrix as the diffracting media. To prepare thin foils for electron-microscopical examination, slices of TD nickel approximately 0.050 in. thick were cut from the as-received 1/2-in.-diam rod. These were then chemically polished down to 0.045 in., rolled to 0.009 in., given a predetermined heat treatment, and thinned, using a modified Bollman technique, to provide the foils for observation. All observations were carried out at 100 kv, using a Hitachi HU-11 electron microscope. Specimens of the undeformed rod were prepared by grinding down the 0.050-in.-thick slices to approximately 0.015 in. and then thinning chemically and electrolytically to give the thin foils. The X-ray specimens were prepared by rolling 0.375-in.-thick rectangular blocks down to 0.075 in. The surfaces of the rolled material were ground flat, chemically polished to remove the layer disturbed by the grinding, and given a predetermined anneal in an inert atmosphere. They were then ground lightly to check their flatness and given a final chemical polish prior to being examined. The X-ray diffraction line profiles were measured using an automated Picker biplane diffractometer. A special specimen holder was built to allow a more accurate and reproducible positioning of the specimen. The line profiles were determined by carrying out intensity measurements at intervals of either 1/30 deg or 1/60 deg over a range of 3 deg on either side of the nickel peaks of interest. A piece of pure nickel which had been recrystallized to give a large grain size was used as a standard to give the X-ray line profile generated by a strain-free matrix. The analysis of the X-ray diffraction line profiles is a modification of that due initially to Warren and Aver-bach8and has been described elsewhere.3 This analysis gives a measurement of two parameters associated with the structure of the nickel matrix. These parameters are: 1) the size of the coherently diffracting domains within the nickel matrix; 2) the magnitude of the elastic strains in these domains. Both of these parameters are first determined in terms of a Fourier series. These series are obtained from other Fourier series which describe the measured profile of the X-ray diffraction lines. Thus, for both the coherently diffracting domain size and the elastic strain level, it is possible to plot Ft (the Fourier coefficient) against t (the term in the Fourier series), where t can be expressed in terms of a distance L and the Fourier coefficient Ft(S) (associated with elastic strain level) can be expressed in terms of the root mean square strain (e2)1/2. Thus a plot of (F 2)1/2 vs L can be obtained. Plots of this type are shown graphically in Figs. 6 and 8. Interpretation

Jan 1, 1968

By R. T. DeHoff

In any structural transfortnation which is driven by surface tension, the geometric variable of fimdamental importance is the local value of the mean surface curvatuve. Acting through the suvface free energy, this quantity determines the magtnitude of both the pressure and the chemical potential that develops in the neighborhood of an arbitrarily curved surface. A metallographic method which would permit the quaniitatiue estinzation of this propevty is of fundarnerztal irztevest to studies of such processes. In the present paper, it is shoun that the average value of the mean surface curvature in a structuve can be estimated from two simple counting measuretnents made upon a vepresentative metallograpIzic section. No simplifyirlg geonzetric assurmptions are necessary to this deviuation. It is further shoum that the result may be applied to parts of interfaces, e.g., interparticle welds in sintering, or the edge of growing platelets in a phase transformation, without loss of validity. In virtually every metallurgical process in which an interface is important, the local value of the mean surface curvature is the key structural property. This is true because the mean curvature determines the chemical potential of material adjacent to the surface, as well as the state of stress of that material. The theoretical description of such broadly different processes as sintering,1,2 grain growth,3 particle redistrib~tion4,5 and growth of Widmanstatten platelets8 all have as a central geometric variable the "local value of the mean surface curvature". The tools of quantitative metallography currently available permit the statistically precise estimation of the total or extensive geometric properties of a structure: the volume fraction of any distinguishable part:-' the total extent of any observable interface,10,11 and the total length of some three-dimensional lineal feature:' and, if some simplifying assumptions about particle shape are allowed, the total number of particles.'2"3 The size of particles in a structure, specified by a distribution or a mean value, can only be estimated if the particles are all the same shape, and if this shape is relatively simple.14-16 The relationships involved in converting measurements made upon a metallographic section to properties of the three dimensional structure of which the section is a sample are now well-established, and their utility amply demonstrated. In the present paper, another fundamental relationship is added to the tools of quantitative metallography. This relationship is fundamental in the sense that its validity depends only upon the observation of an appropriately representative sample of the structure, and not upon the geometric nature of the structure itself. It involves a new sampling procedure, devised by Rhines, called the "area tangent count". It will first be shown that the "area tangent count" is simply related to the average value of the curvature of particle outline in the two-dimensional section upon which the count is performed. The average curvature of such a section will then be shown to be proportional to the average value of the Mean surface curVature of the structure of which the section is a sample. The final result of the development is thus a relationship which permits the evaluation of the average value of the mean surface curvature from relatively simple counting measurements made upon a representative metallographic section. The result is quite independent of the geometric or even topological nature of the interface being studied. QUANTITATNE EVALUATION OF AVERAGE CURVATURE IN TWO DIMENSIONS The Area Tangent Count. Consider a two-dimen-sional structure composed of two different kinds of distinguishable areas (phases), Fig. l(a). If the system is composed of more than two "phases", it is possible to focus attention upon one phase, and consider the remaining structure as the other phase. The reference phase is separated from the rest of the structure by a set of linear boundaries, of arbitrary shapes and sizes. These boundaries may be totally smooth and continuous, or piecewise smooth and continuous. An element of such a boundary, dA, is shown in Fig. l(b). One may define the "angle subtended" by this arbitrarily curved element of arc, dO, as the angle between the normals erected at its ends, Fig. l(c). Now consider the following experiment. Let a line be swept across this two-dimensional structure, and let the number of tangents that this line forms with elements of arc in the structure be counted. This procedure constitutes the Rhines Area Tangent Count. Suppose that this experiment were repeated a large number of times, with the direction of traverse of the sweeping lines distributed uniformly over the semicircle of orientation.' Those test lines which ap- proach from orientations which lie in the range O to O + dO form a tangent with dA; those outside this range do not, see Fig. l(c). Since the lines are presumed to be uniformly distributed in direction of traverse, the fraction of test lines which form a tangent with dA is the fraction of the circumference of a semicircle which is contained in the orientation range, dO; i.e., vdO/nr or dB/n. If the number of test lines is N, the number forming tangents with dA is N(d0/n). Since each test line sweeps the entire area of the sample, the total area traversed by all N test lines is NL2. The number of tangents formed with dA, per unit area of structure sampled, is therefore

Jan 1, 1968

By C. B. Alcock, M. G. Hocking

The kinetics of the growth of sulfate layers on blocks of Cu20 has been studied between 688" and 800°C. At 788c the over-all weight increases followed the parabolic rate law, with k = 216 30 sq mg per cm4 min, using a 1:1 entering gas mixture of SO2:02. At 757 after an initial linear period the parabolic rate law was followed, with k = 57.8 10 sq mg per cm4 min. The gas mixture required a platinum catalyst to produce the maximum SOs pressure. The sulfation rate at 757' and 788c was high until all the CUZO had changed into a core of CuO, when it became very much lower. At 757°C marker experiments showed that the sulfates (CuO. CuS04 and CuSO4) grow outwards from the oxide surface, but CuO. CuS04 mixed with CuO was found beneath the markers. At 688 markers were found at the CuO. CuS04/CuS04 interface. Visual observations at 757 showed a liquid eutectic moving beneath the sulfate surface. causing very rapid sulfation and extruding to solidify as thick 'needles" up to 8 mm long. Marker experiments have shown conclusi.cely that CuO grows on Cu20 in air by the outward migration of copper. ThermODYNAMIC measurements on the sulfate and basic sulfate of copper, reported recently,' are followed here by measurements of the rates of formation of these sulfates on cuprous oxide, in order to provide a background for the understanding of roasting processes. peretti2 and McCabe and Morgan3 have shown that the phase Cu20 lies next to Cu2S when the sulfide is roasted under conditions where sulfates will be formed. Since this would present too complex a system for kinetic study, the present work4 has been based on the kinetics of sulfation of the oxide phase. The results of a study of the kinetics and mechanism of the sulfation of cobaltous oxide have recently been reported.4,5 Results on the sulfation of cuprous oxide have also appeared,6 but are at variance with those to be reported here. This seems to be because the previous workers6 did not obtain constant SO3 pressures from the SO2/O2 sulfating gas mixtures used, as will be discussed later. Wadsworth, Leiter, Porter, and Lewis found that the sulfates produced when SO2/O2 mixtures are passed over Cu20 at red heats are CuS04 and the basic sulfate CuO.CuSO4. When the decomposition of CuS04 was followed' by differential thermal analysis, a stage corresponding to CuO .CuS04 was reached before decomposition into the oxide occurred. APPARATUS The vertical furnace used for quantitative studies was a conventional resistance-heated and propor- tionately controlled furnace with an even zone (1 deg) which was 4 cm long. The gas mixtures of SO2 and 02 were made by mixing measured flows from capillary flowmeters and drying over phosphorous pentoxide before passing them into the Pyrex top-piece of the furnace assembly. A mullite tube of bore 2% cm was used as reaction vessel and at the bottom of this tube was a trap for SO3, which condensed as a colorless liquid. The residual gas was led into a fume cupboard for ventilation to the atmosphere. The furnace used for visual observations of needle growth and other phenomena consisted of a transparent silica reaction tube of bore 3 cm, having an optically flat silica window sealed into its wall. The reaction tube was clamped vertically, inside a mullite tube of bore 4 cm and length 42 cm which was heated by Kanthal windings. The window in the silica reaction tube was arranged opposite a hole 3 cm wide and 2 cm tall which had been cut in the wall of the mullite winding tube 19 cm from its top end. A binocular microscope was used to look through the window, illumination being provided by a focusing microscope-lamp offset sideways and downwards. The oxide block to be sulfated was suspended from the removable Pyrex top-piece to the reaction tube, by means of which it was inserted at the start of the experiment, and through which entered the S02/02 gas mixture. The variation of the temperature inside the reaction tube with horizontal and vertical displacement from the window was investigated, and, while it can be said that the temperature was constant 1 deg, its value at a given position was known only to 12 deg. In both furnaces, the oxide block to be sulfated was suspended from a small silica hook immediately downstream from a platinum thimble used as catalyst, which was held on a long silica rod from a Pyrex spring attached to the removable Pyrex top-piece of the furnace. The spring was only included in the quantitative sulfating furnace; its sensitivity was 1.4 cm per g and it was found to be free from creep in a 16-hr test when carrying the working load. The extensions were followed by a cathetometer which could be read to 0.001 cm, corresponding to i0.7 mg. Extensions of the spring were measured on adding weights between 5 and 500 mg to the working load (thimble + oxide block), and Hooke's law was closely obeyed. SAMPLES Cuprous oxide blocks were prepared by oxidizing Johnson Matthey "Specpure" copper sheet of 1 mm thickness (impurities: iron at 3 ppm, silver at 2 ppm, lead, nickel, sodium, and silicon each at 1 ppm, calcium, chromium, magnesium, and manganese each at less than 1 ppm) for 6 days in air at 1000°C in a re-crystallized alumina boat. It has been reported7 that when Cu20 is prepared by heating copper sheet for 1 day the central plane of the blocks produced consists

Jan 1, 1967

By H. I. Aaronson, H. A. Domian, G. M. Pound

The thernodyna,nics of I the Proeutectoid ferrite re-action ha1.e been investigated on the bases of three diifevent descviptions of the statistical thernzodynamics of interstitzal solid solutions. Especially at low ternperatures, substantial dijeretzces are found in the valltes of the extrapolated y/y + a and cr/a + y equilibriurn curls, and in the To- co7nposilion metastable eqliilibriunz curl-es thus co,npited. Although neither actiztity nor phase-diagram date are able to distingrish udeqiutely among the various descviptions, the statustics of Lacher, Fouller, and Guggenheinz provide the ?nost conplete epresentation az3ailable of the single carbon-ctrbon interaction energy (w) nzodel of an intevstitiril solid solution, and the relationships deduced frojrl then2 are accordingly pre.ferred. The findings tlzut w in austenite 'aries significu?ztly uith tenpevntrue and that phase-diagawr data arc not accurately con?palible usith eqcrctions deduced on the basis of actility infoation indicate, hou'e13er, that a wzore cornplex nlodel of the uustenite , und pvobably of the .feyrite, solirl solutions will have to forn the basis of f4tuve statistical t1.eat1nents. Some suggestions for such a ruodel arc advanced. Althoug11 w represents a vepltlsio energy in austozite, it was found to corvcsporzd in ferrite to a binding energy, in qualitatit.e accord zc,itlz the internal-friclion results of Keefer and wert. ThE transformation of austenite to proeutectoid fer-rite is becoming recognized as an exceptionally useful vehicle for quantitative studies of the kinetics of phase transformations.'" Reasons for this popularity include well-characterized microstructures which develop on a convenient scale with acceptable kinetics within a considerable temperature-composition region, the absence of great sensitivity to common impurities, and, especially. the availability of a unique wealth of the ancillary information indispensable for the quantitative interpretation of kinetic measurements, including phase diagram,3 crystallographies diffusivity,5 inter-facial energy,=17 elastiit," specific vlume, ''' and ativity'-' data. Development of considerable amounts of additional thermodynamic information from activity data is of particular importance with respect to kinetic studies, since much of this information is needed in temperature-composition regions not directly accessible to presently available techniques for the measurement of equilibrium properties. A generally useful approach to the thermodynamics of solid solutions, which is of especial value in this situation, is based upon the formulation of the free energy of such solutions as a function of temperature and composition. The free energy of solid solutions has been resolved into many components. Particularly in the case of interstitial solutions, with which we shall be concerned in the present study, however, only the positional entropy component has been intensively studied. The other components are conventionally taken into account by fitting equations for the activity of the interstitial species or the temperature-composition path of phase boundaries, derived principally from positional entropy considerations, to experimental information on these quantities through adjustment of one or more constants in the equations. A number of studies of the thermodynamics of interstitial solid solutions have been made primarily on this basis,'"25 but only Kaufman, Radcliffe, and cohenZ2 (hereafter KRC) and ener''% ave applied the results of such studies to develop relationships for the thermodynamic quantities of interest in the austenite —- proeutectoid ferrite transformation. KRC made use of a model developed by cheil'' (on the basis of a previous study by ohansson'), and subsequently rede-rived correctly by Speiser and retnak,' in which a carbon atom is considered to inhibit occupancy of a certain number of its nearest-neighboring interstitial sites. schei120 determined the number of sites in austenite thus excluded by matching calculated and experimentally measured curves for the variation of carbon activity with the mole fraction of carbon. zener17 used a different approach. He assumed that the positional entropy of carbon is ideal both in austenite and in ferrite (i.e., no excluded interstitial sites), and included all other contributions of carbon in a temperature-independent "free-energy change" accompanying the transfer of 1 mole of carbon between the two phases. This quantity was determined by "pinning" an equation derived for the boundaries of the a + y region to experimental data on the compositions of these boundaries at a single temperature. In the present investigation, three different approaches to the thermodynamics of the proeutectoid ferrite reaction are examined comparatively: I) the method of Zener; 2) the model employed by KRC and predecessors; and 3) the more detailed statistical thermodynamic treatment of the same model developed by acher and Fowler and uenheim, ' in which the problem of overlapping regions of influence of individual interstitial atoms is resolved. In order to make these comparisons, it is necessary to undertake an extension of one aspect of Zener's method; since the Lacher- Fowler -Guggenheim (LFG) treatment has not been previously used in the present context, the necessary thermodynamic "superstructure" for this treatment will be developed in parallel

Jan 1, 1967

By H. I. Aaronson, H. A. Domian, G. M. Pound

Zener's two-parameter theory of the y a reaction in Fe-X alloys is extended to encornpass austenite-stabilizing as well as fewite-stabilizing elements, and is then cottzbitzed with statistical thermodynamic theories of Fe-C alloys to permit development of a ther-modynamic description of the proeutectoid fewite reaction in Fe-C-X alloys. Equilibrium tielines are calculated for tile a + y rep'on from experimental data and frort extrapolations of the y/y +a equilibrium surface. Sectzovs of the y/y + 0 surface are calculaled for the tzetastable sstuation LYL u-kich alloyrtg eleitzents do not partition betzseen azrstenite andfer-rite. The finding that the metastable y/a + y curves Lie close to their equilibriuwz counterparts when X = Si, .Vo, Co, Al, and Cu but well below them when X = A/ln or Ari pr-elides a thermodunamic explanation for the expcri1?7e?ztally obserted absence of partition during the proeutec toid ferrite reartlon in the fortner alloys and for the occurrence of partition at hzgher ternperatures in the latter alloys. Cotarison ofno- patitzoa free-energy changes and y/y i a curr,es in Fe-C-X alloys with the equilibrium 11al1es of these quantities in Fe-C alloys furnishes additional qualitative insight into the irqluence of allojling elements upon the kinetics of the proeutectoicl ferrite reaction. THE introduction of a substitutional alloying element, X, appreciably complicates calculation of the thermodynamics of the formation of proeutectoid ferrite from austenite. As noted in the preceding paper,' the positional entropy of the interstitial species is the principal component of the free energy of an interstitial solid solution with which theory has so far been able to deal. One would expect, however, that other components of the free energy of this type of solid solution may be significantly altered by the addition of a substitutional alloying element. Even if the assumptions are made, by analogy to the case of Fe-C alloys,' that changes in the positional entropy of carbon represent a significant part of the thermodynamic effects of an alloying element, and that the remaining effects can be taken into account by fitting the equations developed on this basis to experimental data on Fe-C-X phase diagrams or on the activities of carbon in alloyed austenite and ferrite, the experimental information available on either of these quantities is not yet sufficiently accurate or extensive, respectively, to make such an approach useful. An attempt made by Zener on the former basis to explain the effects of alloying elements on the thermodynamics of Fe-C alloys in terms of a temperature-independent "free-energy change" (actually enthalpy hane') required to transfer 1 mole of an alloying element from austenite to ferrite, in which the "free-energy change" was determined by fitting the theoretical relationships developed to Fe-C-X phase diagrams, thus proved inadequate in part because of deficiencies in the available ternary-phase-diagram data.= Other difficulties of a more fundamental nature, however, also indicated the desirability of a different approach to the problem.3y4y6 zener6 subsequently proposed that the free-energy change associated with y — a transformation in pure iron can be decomposed into magnetic and nonmagnetic components. Alloying elements were assumed to affect those components separately. One parameter was used to describe the quantitative effect exerted on each component. These parameters were evaluated from Ms (martensite-start) temperature data and from other experimental information usually either readily available or measurable with acceptable accuracy. Zener applied this treatment only to the calculation of Fe-X phase diagrams in which X is a ferrite-stabilizing element. In the present study, this treatment is extended to include austenite-stabilizing elements, and then combined with treatments previously considered for Fe-C alloys1 to permit calculation of the thermodynamic quantities of interest in the austenite - proeutectoid ferrite transformation in Fe-C-X alloys, where a number of representative, and commonly used alloying elements are chosen for X, including Si, Mn, Co, Mo, Al, Cr, and Cu. The results are used to explain important features of the partition of alloying elements between austenite and proeutectoid ferrite, as reported in a companion paper7 on the basis of electron-probe analysis, and to provide some additional understanding of the influence of alloying elements upon the kinetics of nucleation and growth of proeutectoid ferrite. Portions of this treatment6 have been clarified in the course of a review by Kaufman and Cohen.3 The consolidated summary of these developments with which this section is begun provides a basis for further clarification of the treatment, from which extension to include austenite- as well as ferrite-stabilizing elements is a natural consequence. The division of the free-energy change associated with the 7 - a transformation in pure iron, into two independent components is formally stated as:

Jan 1, 1967

By A. Karim, T. G. Langdon, C. Y. Cheng, J. E. Dorn

The effect of changes in temperature and stress on the creep behavior of Fe-4 pct Si was investigated over the temperature range from 650° to 1175K Over the temperature range of 799° to 110l°K, the shear strain rate, ?', obeys the relationship: where K is a constant, 7 the applied shear stress, G the shear modulus, g the free activation energy for diflusion, R the gas constant, and T the absolute temperature. The results strongly suggest that the creep in this alloy is controlled by a dislocation climb mechanism. In a recent investigation, Ishida, Cheng, and Dorn1 observed that the apparent activation energy for creep of a! Fe from 480" to 775°K corresponded to that for self-diffusion. Over the magnetic transformation range (775" to 1045"K), the apparent activation energy for creep increased steeply with increasing temperature in agreement with the known decrease in the free activation energy for self-diffusion. Passing through the Curie temperature, the apparent activation energy decreased abruptly following which it then increased mildly as the temperature further increased. Inasmuch as the apparent activation energy for creep of a! Fe below the Curie transformation range of temperatures appeared to decrease with increasing values of the stress, the data were analyzed in terms of a model based on the nonconservative motion of jogged screw dislocations. But since the observed creep rate was much higher than that which could be accounted for on the basis of usual models, the authors found it necessary to assume that pipe diffusion became significant over the lower temperature range. Furthermore, the abnormally high activation energy for creep above the Curie temperature was attributed to grain boundary migration which became prevalent in this temperature range. It was thought that a number of the interesting issues that arose in the creep of a Fe might be resolved by investigating the creep of Fe-4 pct Si alloy: This alloy has about the same Curie range and therefore should give creep results that closely parallel those for a Fe and in this way provide comparable data for analysis of creep mechanisms. Furthermore, it can be annealed at higher temperatures which could provide some stabilization against grain boundary migration. In addition, it might serve to illustrate the possible effects of short-range ordering on creep.

Jan 1, 1969

By Matti J. Saarivirta

The relative machinabilities of the precipitation-hardenable Cu-0.9 pct Cr, Cu-0.25 pct Zr, and Cu-0.9 pct Cr-0.25 pct Zr alloys are improved from 18 to 80 pct by 0.75 to 1.25 pct Pb. The Lead also improves the tensile strength, hardness, ad resistance to softening of the Cu-Cr and Cu-Cr-Zr alloys. When the alloy containing 0.7 to 2.2 pct Cr, 0.10 to 0.25 pct Zr, 0.75 to 1.25 pct Pb, and balance copper is solution-annealed at 1000°C (1830°F) and then aged at 525°C (Y75°F), tensile strength of 65,000 psi, 16 pct elongation, 62Rb hardness, and 84 to 87pct IACS electrical conductivity are obtained. The copper base Cu-Cr, Cu-Zr, and Cu-Cr-Zr alloys have high electrical and thermal conductivities, high strength and resistance to softening at elevated temperatures, but their machinability is poor, i.e., close to that of the pure copper. In the manufacture of various components such as welding electrodes or electrical and thermal conductors it is ofter desirable that the alloy have good machinability for high production rates and long tool life. Thus, alloys that combine these properties may be used not only for existing applications, but for new ones where good machinability is a requirement. This investigation was undertaken to improve machinability without impairing other desirable characteristics of the Cu-Cr, Cu-Zr, and Cu-Cr-Zr alloys. These commercial alloys contain about 0.4 to 1.2 pct Cr, 0.10 to 0.25 pct Zr, and balance copper. Lead was selected as an element that should improve the machinability and possibly other characteristics of the alloy. WORK PROCEDURE This investigation began with a study of the effect of lead on the hardness, tensile strength, electrical conductivity, and machinability of the binary alloy containing 0.10 to 1.30 pct Cr and balance copper. This was followed by an investigation of the effect of lead on the Cu-0.1 to 0.4 pct Zr and Cu-Cr-Zr alloys. The alloys were made from initially oxygen-free copper and for comparison some castings were made from phosphorus-deoxidized Lake Copper. Commercially pure chromium, zirconium, and lead were used for alloying. In melting the chromium was added to molten copper at 1400°C (2550°F), the heat held for 15 min at temperature, and the temperature then lowered to 1350°C (2460°F) when the other elements were added. The alloys were held for 15 min at this temperature and cast into a cast-iron mold. One-kilogram, 3-in.-diam castings were made. An argon cover was maintained during melting and casting to prevent oxidation. The chemical compositions of the alloys are shown in Table I. The micro structure and properties of the alloys were studied in the cast and wrought conditions prior to and after various solution-annealing and heat-treating cycles. The relative machinability was determined as a function of the lead content and compared with the free-machining Cu-lpct Pb alloy. To determine the machinability, 13/16-in.-diam cast specimens were cut by a machine hack saw using a constant cutting speed of 50 fpm, a fixed feed force, and a new blade for each alloy specimen. Molybdenum highspeed steel saw blades, 0.032 in. thick with 14 teeth per in., were used in all tests. No cutting fluid was used. Five tests were made on each specimen and the average elapsed time per test was taken as a measure of the relative machinability for that alloy. The variation of cutting time for each alloy was less than 110 pct.

Jan 1, 1969

By M. A. Rigdon, R. E. Grace

The dissociation of cupric oxide to cuprous oxide and oxygen was studied with a microbalmce technique at 700" to 750°C. In this temperature range the dissociation pressure of the reaction 2CuO= Cu2O + 1/2 O2 was: The theory of near-equilibriwm reaction rates predicts a linear relationship between reaction rate and the Gibbs free-energy change for small values of AF/RT. This correlation is found to be valid for AF/RT = -0.1 or approximately 200 cal per mole away from equilibrium. THE theory of reaction rates near equilibrium as developed from classical thermodynamics suggests a small range of linear behavior between the overall reaction rate and the free-energy change accompanying the process. The extent of this linear correlation is generally unknown, even to the order of magnitude. The idea of linearity is also found in the formal mathematics of coupled transport phenomena, e.g., chemical diffusion, thermal diffusion, thermoelectricity, and so forth. The linear array of forces and fluxes which leads to various main and cross coefficients is predicated upon linearity between reaction rates and the bulk thermodynamics which govern the process. The general case in reaction kinetics is well-known: the magnitude of the free-energy change does not cor- relate with observed reaction kinetics, irrespective of whether the process occurs by diffusion or chemical reaction or both. The real need is to investigate specific reaction paths near equilibrium in order to learn of the limitations in attempting to correlate reaction rates and thermodynamics. It is the main purpose of this paper to examine the dissociation kinetics of cupric oxide under conditions of known driving force where the dissociation process is likely to occur by chemical reaction. A secondary objective is to obtain equilibrium data for the CuO-Cu20-O2 system. In a prior paper Edmiston and race' investigated reduction kinetics of wustite in H2-H2O gas mixtures. The present study was carried out in oxygen according to the following reaction:

Jan 1, 1969

By Claude H. P. Lupis, John F. Elliott

The classic Siez~erts' technique has been employed to determine the solubility of oxygen in liquid pure silver and the effect on the oxygen solubility of solute metal additions to liquid silver. The results indicate that oxygen deviates slightly from Sieverts' law in pure silver as = 3.9. Gold, platinum, md palladium decrease the solubility of oxygen in silver. First-order free energy, enthalpy, md entropy interaction coefficients are determined from the data. An important aspect in the establishment of the formalisms to be applied to represent the thermody-namic behavior of components of solutions is the accuracy of the experimentally determined thermody-namic properties. Wagner developed the first-order free energy interaction coefficient.' Recent papers2'3 extend the treatment formally to other thermodynamic properties and define the second- and higher-order interaction coefficients. A current communication4 considers in some depth the requirements and limitations imposed because of experimental error on the use of several formalisms now under active consideration in the field. This communication reports the results of an experimental study of the behavior of oxygen in liquid silver alloys that was carried out concurrently with the development of Refs. 2 and 3 with the hope of providing sufficiently precise information so that enthalpy and entropy interaction coefficients could be determined. THE EXPERIMENTS The Sieverts technique was employed using an improved design of the reaction bulb over that developed originally by Humbert5 and subsequently improved by pehlke6 and Weinstein.7 The Vycor reaction bulb as shown in Fig. 1 was air-cooled and contained a port for the thermocouple angling off to one side and a vertical port for connections to the gas supply and

Jan 1, 1969

By Owen F. Devereux

Two discrete types of microstructure me seen in cermets formed by the reaction: 4Al (liquid) + 3SiO2 (glass) — 2A12O3(a) + 3Si (solid) Relatively coarse-grained macroscopically isotropic specimens resulted from reaction with aluminum containing appreciable silicon, while macroscopically anisotropic fine-grained specimens were formed by reaction with aluminum low in silicon. Optical microscopy, electron microscopy, and X-ray diffraction suggest that the anisotropic material contains gross areas in which submicroscopic grains of a A12O3 are oriented along radial lines drawn from the specimen surface. These lines are presumed to originate at defects in an otherwise protecting surface layer. A unique cermet is formed by the reduction of high-silica glass by molten aluminum according to the reaction: 4A1 (liquid) + 3SiO2 (glass) — 2A12O3 (a) + 3Si (solid) The free-energy change accompanying this reaction is -150 kcal at 800°C; the volume change (volume of A12O3 and silicon minus volume of SiO2) is +6 pct. The reaction product, however, contains aluminum metal as well as Al2O3 and silicon because some of the product silicon is dissolved in the aluminum bath and is replaced by aluminum in the structure. The product is a hard gray solid that retains the external dimensions of the original silica article. The system has been studied in the past, the investigations culminating in patents to George1, 2 and Saw-chuk., The former emphasize that this reaction is but one of a relatively broad class of such systems, while the latter demonstrates that a marked improvement in the gross physical properties of the cermet can be obtained by dissolving appreciable quantities of silicon in the aluminum reactant. The system has also been studied by workers at Rolls Royce Ltd.,4-6 who have patented the addition of small quantities of arsenic, antimony, bismuth, or phosphorus to the reactant bath to SO impede the reaction that glass fibers may be metal-coated by immersion in molten aluminum.

Jan 1, 1969

By Shiro Ban-ya, John Chipman

Equilibrium in the reaction was investigated at temperatures of 1500°, 1550°, and 1600°C for sulfur concentrations up to 7.2 wt pct. Multisample crucibles contained the liquid alloys in a resistance-heated furnace using a technique especially designed for the study of more complex alloys to be reported separately. Modern free-energy data are used to correct the H2S:H2 ratio for dissociation of H2S and calculalion of the partial pressure of S2. Published data on the equilibrium are similarly corrected. Thermodynanzic treatment of the data employs the composition variable zs = nS/(nFe — nS) and the activity coefficient Gs = as/zs The data at 1500" and 1550°C are fitted by the equation log s = —2.30zs. Within the limits of experimental error the same coefficient is applicable to the data at higher temperatures. Equations are given for the free-energy change in Reaction [I] as well as for the solution of S, gas in the metal. The heat of solution of 1/2 s2 is -32.28 i2.5 kcal. Uncertainty in the free energy is very much smaller. For dilute solutions of interest in steelmaking, the activity coefficient of sulfur is unchanged from that listed in Basic Open Hearth Steel-making. DETERMINATIONS of the thermodynamic properties of sulfur in liquid iron by Morris and williams1 and by Sherman, Elvander, and chipman' provided a basis for control of sulfur in steelmaking processes. From the standpoint of understanding the chemistry of metal plus nonmetal in liquid solution they left several questions unanswered. The activity of sulfur in dilute solution at about 1600°C was well-established but temperature coefficients were uncertain, due at least in part to the use of the optical pyrometer and uncertainty regarding the effect of sulfur on emissivity. It appeared that deviation from Henry's law increased with increasing temperature, a most unusual behavior requiring either confirmation or disproof. These studies were based on experimental determination of equilibrium in the reaction: At high temperatures H2S is partially dissociated so that the gas mixture contains HS, S2, and S in addition to HS. At the time of the earlier studies the free energies of these constituents were unknown and it was therefore impossible to make adequate correction for dissociation. Observations on the effects of alloying elements by Morris and coworkers1, 3 and by Sherman and Chip-man4 enable us to assess the effects of alloying elements on the activity and to make corrections for incidental impurities in the binary liquid. These studies as well as a number of more recent investigations will be reviewed in detail after out own experimental results have been presented. It was our purpose in planning this study to avoid uncertainties regarding the emissivity of alloys and the errors of thermal diffusion which plagued some of the early attempts,5 by using a resistance furnace and thermocouple in preference to induction heating and optical pyrometer. Modern data on free energies of the gaseous species are to be applied to our data and to those of other investigators to obtain corrected values of K1 and of the activity coefficient and ultimately to relate the sulfur content of the bath to the equilibrium partial pressure of S,. Extension of the study to include ternary and complex solutions will be described in a later section. EXPERIMENTAL METHOD a) Preparation and Calibration of H2-H2s Gas Mixture. The source of hydrogen sulfide was a preparer mixture of 43 pct H2S, balance hydrogen, contained in a large aluminum cylinder. This was passed through anhydrone and through a microflowmeter. Hydrogen was passed through platinized asbestos, ascar-ite, and anhydrone, and through a capillary flowmeter. Argon was passed through copper wool at 500°C, then through ascarite, anhydrone, and a flowmeter. The flow rate of hydrogen was kept constant at 200 ml per min, to which an arbitrary amount of the hydrogen-hydrogen sulfide mixture was constantly added and then the prepared gas mixture was introduced into the reaction tube through a gas mixer. In certain experiments 200 ml per min of argon was added to the hydrogen-hydrogen sulfide gas mixture to increase the total flow rate of gas. The ratio of hydrogen-hydrogen sulfide in the inlet gas was checked for each run by chemical analysis. A sample of the gas taken from a bypass was bubbled through zinc and cadmium acetate solution (4 pct zinc acetate, 1 pct cadmium acetate, and 1 pct acetic acid) to remove hydrogen sulfide from the gas mixture, and the flow rate of the remaining hydrogen was measured by a soap bubble method to determine the volume of hydrogen. The amount of hydrogen sulfide absorbed in solution was determined by titration with iodine against sodium thiosulfate, with starch used as the indicator. The ratio of hydrogen sulfide to hydrogen in the inlet gas could be kept within ±2 pct in the range from 10-2 to 5 x 10"4 which corresponds to from 0.2 to 7.0 wt pct sulfur in liquid iron. b) Furnace Arrangement. Fig. 1 shows the furnace arrangement and the shape of the alumina crucible used in this experiment. A vertical-tube silicon carbide electric resistance furnace contained the reaction tube which consisted of two parts, the gas-tight

Jan 1, 1969

By Charles E. Lundin

Pressure-temperature-composition data were obtainedfor the Er-H system. Measurements werecar-ried out in the temperature range of 473° to 1223°K, the composition range of erbium to ErH,, and the pressure range of 10-5 to 760 Torr. Solubility relationships were established from these data throughout the system. Three solid-solution phases were delineated: metal solid solution, dihydride phase, and trihydride phase. The trihydride Phase decomposes at about 656°K and 1 atm pressure. The dihydride phase is stable to about 1023°K, but becomes more deficient in hydrogen above this temperature. The equilibrium decomposition pressure-temperature relationships in the two-phase regions, erbium solid solution plus dihydride and dihydride plus trihydride, were deter- The differential heats of reaction in these two regions are AH = - 52.6 * 0.3 and - 19.8 i 0.2 kcal per mole of Hz, respectively. The differential entropies of reaction are AS = - 35.2 * 0.3 and - 30.1 * 0.4 cal per mole HZ.deg, respectively. Relative partial molal and integral thermodynamic quuntities were calculated in the system to the dihydride phase. RARE earth metal-hydrogen systems have been the subject of general survey,1"4 and all have been found to form hydride phases. The heavy rare earths, of which erbium is a member, form dihydride and trihydride phases with different crystal structures, whereas the light rare earths form only a single-phase dihydride which expands without structure change, as hydrogen is added, to the trihydride composition. These materials are of interest primarily because of their theoretical properties, such as bonding, defect structure, and thermodynamic and electronic characteristics. Erbium has been studied in several previous investigations.5, 6 It was deemed desirable to more thoroughly and accurately define the system, both for the phase equilibria and the thermodynamic properties. I) EXPERIMENTAL PROCEDURE A Sieverts&apos; apparatus was employed to conduct the experimental measurements. Briefly, it consisted of a source of pure hydrogen, a precision gas-measuring buret, a heated reaction chamber, a mercury manometer, and two McLeod gages (a CVC, GM 100A and CVC, GM 110). Pure hydrogen was obtained by passing hydrogen through a heated Pd-Ag thimble. The hydrogen was analyzed and found to have only a trace of oxygen and nitrogen. A 100-ml precision gas buret graduated to 0.1-ml divisions was used to measure and admit hydrogen to the reaction chamber. The reaction unit consisted of a quartz tube surrounded by a nichrome-wound furnace. The furnace temperature was controlled by a recorder-controller to ±1°K. An independent measurement of the sample temperature in the quartz tube was made by means of a chromel-alumel thermocouple situated outside, but adjacent to, the quartz tube near the specimen. Pressure in the manometer range was measured to ±0.5 Torr and in the McLeod range (10-4 to 10 Torr) to ±3 pct. The hydrogen compositions in erbium were calculated in terms of hydrogen-to-erbium atomic ratio. These compositions were estimated to be ±0.01 H/Er. The erbium metal was obtained from the Lunex Co. in the form of sponge. The metal was nuclear grade with a purity of 99.9 pct +. The oxygen content was reported to be 340 ppm and the nitrogen not detectable. Metallographically the structure was almost free of second phase (<1 vol pct). A quantity of sponge was arc-melted for use as charge material. The solid material was compared with the sponge in the pressure-temperature-composition relationships. They were found to be identical. Therefore, sponge material was used henceforth, so that equilibrium could be attained more rapidly. The specimen size was about 0.2 grain for each loading of the reaction chamber. The procedure employed to obtain the pressure-temperature-composition data was to develop experimentally a family of isothermal curves of composition vs pressure. First, a specimen of erbium was wrapped in a tungsten foil capsule to prevent contact with the quartz tube. After loading the specimen, the system was evacuated to less than l0-6 Torr, flushed several times with high-purity hydrogen, and evacuated again ready for the start of the experiment. The furnace was then brought to the desired temperature. A measured amount of hydrogen was admitted into the chamber. Equilibrium was allowed to be attained, the pressure read, and the process then repeated many times until 1 atm of gas pressure was finally reached. Other isotherms were then developed in the same manner. The partial pressure plateaus were determined by another manner. In the solid solution-dihydride region a composition of approximately 1.0 H/Er was selected on the plateau. The temperature was varied throughout the range of interest. At each temperature level, equilibrium was achieved, the pressure read, and the next temperature attained. The temperature was cycled both up and down. In the dihydride-trihy-dride region, the plateaus were determined in the 473" to 651°K range only by heating to the desired temperature and not by both heating and cooling. The data were much more reproducible in this manner. Equilibrium required long periods of time. Specimens were initially hydrided to 2.8 H/Er, so that at the higher

Jan 1, 1969

By T. S. Lundy

Anand and Agarwala recently determined diffusion coefficients by the residual activity (Gruzin) method for several tracers in large-grained, high-purity aluminum. D values at any particular temperature in the range of 400" to 630°C were about four orders of magnitude lower for cd115, 1n114, sn113, and pdlm than for Ag. Corresponding values for Do and Q in the Arrhenius equation were also quite small. It was pointed out previously that unusually low diffusion coefficients within the region of a specimen near a free surface may be the major cause of such anomalous results for impurity diffusion in silver and in aluminum.44 Anand and Agarwala considered this possibility but rejected it because their penetration profiles were "homogeneous" and "yielded diffusion coefficients obeying the Arrhenius plot". Neither of these two criteria satisfactorily prove or disprove the presence of a near-surface effect. Such can be accomplished only by direct serial sectioning in which the chips ground from the specimen are assayed for tracer content. In fact, such experiments always should be done prior to use of the somewhat indirect Gruzin method where the finer details of the transport process cannot be determined. There have been several other reports of unusually low D, Do, and Q values for impurity diffusion in silver and aluminum.1"4 It is interesting to note that all of these studies made use of the Gruzin method. Also, in all cases where the same systems were examined by use of a direct serial sectioning technique, large near-surface effects were observed. One must conclude therefore that the reported anomalous diffusion parameters for cd, In114, sn113, and pd in aluminum are due to some near-surface effect, while the results for Agl10 indicate that no such effect was encountered for this system.

Jan 1, 1969

By Niels Hansen

Dispersion-strengthened aluminum products consist of an aluminum matrix containing finely distributed ceramic or intermetallic particles. Examples of the two types of product are SAP, in which the dispersed phase is aluminum oxide, and materials made from atomized aluminum alloy powder, in which the dispersed phase can be FeA1, particles.&apos; A fundamental difference between the two types of product is that the elongation of aluminum/aluminum oxide products decreases with increasing temperature, whereas the elongation of aluminum- FeA13 products, like that of aluminum alloys, increases with increasing temperature. As regards the structural stability, aluminum/aluminum oxide products are stable to temperatures above 600° C as aluminum oxide does not react with aluminum, whereas prolonged heating at above 400°C of aluminum-FeA1, products leads to coarsening of the intermetallic phase and loss of strength.&apos; On the basis of these results it is supposed that a dispersion-strengthened product combining strength, ductility, and stability at elevated temperatures may be obtained if the dispersed phase reacts with the matrix in such a way that the reaction does not proceed at any significant rate at the application temperature. Different ceramic or intermetallic compounds may be selected as the dispersed phase, and, as alloying of the matrix phase may also influence the reaction, many possibilities exist for each metal. In the present study, aluminum products containing different oxides have been examined. For a reaction to take place between the dispersed oxide and the aluminum the free energy of formation of the oxide (MeO) must be greater than that of aluminum oxide; the difference should, however, not be too great in order to limit the reaction rate. Furthermore the aluminum alloy formed when aluminum reacts with the dispersed oxide should have a melting point near

Jan 1, 1969

By E. S. Tankins

The main purpose of this work was to study the effect of gold on the activity coefficient of oxygen in the liquid Fe-Au alloy and to determine how copper and silver change the activity coefficient of oxygen. A preliminary investigation has been made of equilibrium in the reaction of hydrogen with oxygen in some of the liquid gold alloys. The experimental method, which has been described in detail elsewhere,&apos; consisted of bubbling accurately known H-A-water vapor mixtures through the Fe-Au alloys contained in alumina crucibles within a vertical closed furnace. When equilibrium was reached, the samples were quenched by rapidly lowering the crucible under an atmosphere of argon to a water cooled brass fixture at the bottom of the furnace tube. The melts were found to freeze from the top in less than 4 sec. The heats were carefully prepared for oxygen analysis. The oxygen content was determined by vacuum fusion analysis.&apos; Only high purity electrolytic materials were used in this investigation. The activity and free energy of oxygen in the liquid iron alloys were studied by means of the reaction; The data for the 80 Fe-Au alloys, obtained as a function of temperature, are summarized in Table I and presented in Fig. 1, where log is plotted against . The results can be expressed by: The data were obtained using water vapor-hydrogen ratios between 0.04 and 0.30, and a 25 pct H2-75 pct A mixture. An oxygen content between 0.030 and 0.060

Jan 1, 1970

By David L. Holt, Walter A. Backofen, Anwar-ul Karirn

ANNEALING the binary alloy, Mg-0.5 wt pct Zr in a hydrogen atmosphere results in extensive precipitation of zirconium hydride. The morphology of these precipitates has already been investigated.lm3 Squires, Weiner, and phillips4 found, following creep testing of the hydrided alloy at 450" and 500°C, that hydride denuded zones formed along grain boundaries that were aligned approximately normal to the tensile axis. Zone formation was attributed to diffusional creep by magnesium transport down the prevailing stress gradients.4&apos;5 Recently, electron microprobe analysis by Karim, Holt, and Backofen6 showed the zones indeed to be zirconium-free and furthermore it was shown that in compression, zones formed along boundaries approximately parallel to the stress axis. Thus it was confirmed that the zones are formed by diffusional creep. Typical zone-formation is shown in Fig. 1. Karim, Holt, and Backofen also measured the con- tribution to the total strain, from diffusional flow, slip creep, and grain boundary shear: results showed that diffusional strain tends to saturate with increasing imposed strain, while grain boundary shear eventually becomes the dominant deformation mode. It was suggested in explanation that the precipitate-denuded zones are soft and easily sheared, such deformation contributing to the grain boundary shear measurement. A point to be emphasized is that the Mg-0.5 Zr alloy was not superplastic for the index of strain rate sensitivity of flow stress, m = a log log 6 was only 0.25. It was recognized that diffusional creep in a poly crystalline aggregate must be accompanied by boundary shearing.&apos; The suggestion was that the non Newtonian-viscous character of diffusional creep in the Mg-0.5 wt pct Zr alloy is due to resistance to sliding of boundaries lying approximately parallel to the tensile axis.= The work described in the present note should be seen against the above background for it represents initial efforts to observe in a similar way diffusional creep in a superplastic alloy. Previous work with the ternary-alloy Mg-6 Zn-0.5 Zr, pellet extruded, showed it to be superplastic however it does not contain resolvable precipitates to act as internal markers for diffusional creep. Also the fine grain size of the alloy (0.5 p) made conventional metallography rather difficult. Solubility relationships in the Mg-Zn-Zr system are not well known, however making reasonable guesses about the probable phase diagram of the ternary, Mg-Zn-Zr, various heat treatments were attempted to produce hydride precipitation. Finally a 16-hr anneal at 495&apos; in hydrogen was found to pro-

Jan 1, 1970

By R. Schuhmann, G. W. Powell

The concept of local equilibrium is examined and, in particular, the applicability of the concept to two-phase binary diffusion couples is discussed. It is concluded that, if binary solid solutions are treated thermodynamically as ternary solutions, vacancies being the third component, then recent experimental observations of nonequilibrium interface compositions (i.e., compositions different from the phase diagram values) are consistent with a state of complete dynamic equilibrium at the interface. CLASSICAL approaches to diffusion and to other irreversible processes often utilize a postulate of "local equilibrium". That is, one assumes even in the presence of gradients, fluxes, and time changes of properties, a) that the Second Law can be formulated locally, and b) that thermodynamic equations of state among intensive properties are identical with those for equilibrium phases. A direct consequence of this assumption, for example, is that one would calculate the total entropy of a nonequilibrium phase simply by integrating the entropy density (eu per unit volume) over the volume of the phase, assuming that entropy density is the same function of energy and particle density as for equilibrium phases. In the study of diffusion and of diffusion-controlled phase transformations, metallurgists take this concept of local equilibrium for granted and utilize it automatically. In fact, experimental evidence of all kinds is overwhelming that "local equilibrium" is a valid limiting law, approached more and more closely as gradients and rates of change approach zero. On the other hand, we have neither experimental nor statistical thermodynamic proof that this principle of "local equilibrium" should remain rigorously valid at high gradients and for rapid processes. Theoretically, in fact, one would expect deviations because interactions between adjacent volume increments of material affect the evaluation of entropy. Also one observes experimentally structural and small energetic differences between equilibrium and nonequilibrium phases. The purpose of this paper is to present a thermodynamic framework for the study and correlation of deviations from strict local equilibrium in isothermal diffusion and related processes. This procedure, in effect, preserves the principle of local equilibrium by thermodynamically assigning the deviations from static equilibrium properties to a defect component. Although this theory is entirely phenomenological, the possibility does exist of correlating the theory with experimental observations of defects under favorable circumstances. The most immediate application appears to be to the equilibria at the interfaces in two-phase binary diffusion couples. A recent pertinent work by Eifert et al.1 has shown that the concentrations of aluminum in the a(fcc) and B(bcc) phases at the 0-8 interface in Cu:Cu-12.5 wt pct A1 diffusion couples are greater than those given by the phase diagram. It is postulated by these authors that the supersaturation of the o phase at the interface provides the driving force for the a-to-B lattice transformation; the excess free energy of the a phase, ?Gaxs, arising from the greater-than-equilibrium aluminum concentration is about 3 cal per g-atom. On the basis of the schematic free energy-composition diagram shown in Fig. 1, Eifert et al. concluded that the thermodynamic situation at the interface is one of the partial equilibrium; that is, = for the more mobile aluminum whereas will be reexamined in the latter part of this paper. THERMODYNAMIC PROPERTIES OF DEFECTS A rigorous analysis of the thermodynamics of defects requires an added degree of freedom in the Phase Rule sense, because the standard formulations of solution thermodynamics (partial molal properties of components, free energy minimization, equality of chemical potentials, and so forth) involve the implicit

Jan 1, 1970

By R. F. Lynch, J. D. Wood

The Al-1.0 pct Mg alloy 565 7 was studied using optical microscopy and electron microprobe X-ray analysis. Constituent particles were found to exist inter-dendritically in the as-cast material in a region of precipitate free a -aluminum. Five phases besides a fine precipitate and a-Al were identified in the cast structure: Fel3, Fe2Al7, Mg2Al3, CUMgAl2, and Cu2FeAl7. Thermal treatments conducted for 100 hr at 1180°, 1130°, 1080°, 1030°, 980°, and 880° F revealed a general dissolution and spheroidization of the in-terdendritic constituent network observed in the cast structure. The principal constituents present in the thermally treated structures were FeAl3 and Fe2Al7 with the relative amount of Fe2A17 to FeAl3 increasing with a decrease in the treatment temperature. The phases Present in the wrought structure were identical to those observed after the thermal treatments, with the constituent particles strung out in the direction of rolling. ALLOY 5657 is a nonheat-treatable commercial purity Al-1.0 pct Mg alloy utilized extensively because of its bright finishing characteristics. This investigation was conducted to determine the constituents present in 5657 alloy, and to study the effect of extended thermal treatments on morphology. Numerous studies have been carried out to establish the equilibrium diagrams for various aluminum systems,1-3 with phase identification based on X-ray analysis, morphology, and the etching response of relatively large particles. Phragmen4 conducted a study of the phases in aluminum eutectic systems and compiled a "corrected" table of etching responses, drawing on his work plus that of Schrader,5 Keller and Wilcox,6 and Mondolfo.7 A review of the original work of Keller and Wilcox, and Mondolfo, which was concerned with the constituents found in commercial alloys, reveals that in numerous cases their etching responses differ from those reported by Phragmen and from each other. These inconsistencies may occur because a specific constituent will react to a given etch in a varying manner depending upon its size, the elements dissolved in the phase, the other constituents surrounding a phase, and the solute content of the matrix. Work with a commercial orientation was conducted on alloys 2024 and 3003 by Sperry8,9 and on alloy 3003 by Barker,10 where the relationship between the phase diagram and the nonequilibrium structure of an alloy was examined. Backerud11 investigated the A1-Fe binary system and found that at high cooling rates the equilibrium eutectic reaction forming a-A1 and FeA13 is replaced by another lower temperature eutectic reaction forming a-A1 and metastable FeAl6, a constituent first identified by Hollingsworth et al.12 Most of the above mentioned studies were conducted on materials having a significantly greater alloy content than 5657 alloy, where the relatively small size and sparse distribution of second phase particles hinders the process of identifying constituents. EXPERIMENTAL PROCEDURE Material with a composition as given in Table I was examined in the as-direct chill cast, hot rolled and cold rolled conditions, and after thermal treatment of the cast structure. Thermal treatments were terminated by a water quench. Microscopic examination was conducted under various lighting conditions following the application of standard etchants as specified in Table 11. A semi-quantitative electron microprobe X-ray analysis was conducted for Al, Mg, Fe, Cu, Si, Zn, and Ti. RESULTS AND DISCUSSION Microstructure of the As-Cast Material. Particles of second phase material were found to exist inter-dendritically, principally in regions of precipitate free a-Al, as illustrated in Fig. 1. Adjacent to the ingot edge was a region of inverse segregation, resulting in an increased amount of second phase material containing large sized particles which aided in phase identification. Phase Identification. Cast Structure. Five phases besides a-Al and a fine precipitate were identified using optical microscopy and electron microprobe X-ray analysis, as presented in Tables II and III, respectively. FeA13 and Fe2A17 are often found with Fe2A17 forming a sheath around the core of FeAl3, resulting from an incomplete peritectoid reaction. These phases have a nearly identical appearance under white light, although they are easily differentiated under crossed polarizers, as characteristically illustrated in Figs. 2(a) and 2(b), respectively. Microprobe analysis con-

Jan 1, 1970

By N. J. Olson, G. W. Toop

A series of equations previously derived for calculating ternary thermodynamic properties using binary data has been applied to the problem of predicting ternary phase diagrams and quaternary excess free energy. The methods are considered to be rigorous for regular ternary and quaternary systerns and empirical for nonregular systems. The equations have been used to predict ternary phase boundaries in the Pb-Sn-Zn system at 926°K and the Ag-Pd-Cu system at 1000ºK. Calculated quaternary excess free-energy values are presented for the Pb-Sn-Cd-Bi system at 773°K. A method for predicting the location of ternary phase boundaries would be a useful supplement to experimental measurements in ternary systems. This has been recognized with the considerable work that has been done to find models to predict or extend thermodynamic properties and phase diagrams in binary and ternary systems1-18 for which direct experimental measurements are limited. With the access to highspeed digital computers and mechanical plotting devices, it is currently rather easy to compare mathematical models with experimental data. The regular-solution model is consistent with systems which exhibit negative heats of mixing, positive heats of mixing, and miscibility gaps, and therefore it is applicable to simple phase diagrams. The purpose of this paper is to illustrate the use of regular-solution equations to predict, empirically, phase equilibria in some types of nonregular ternary systems. Corresponding equations for regular quaternary systems are given and used to calculate empirical quaternary excess free-energy data. METHOD FOR PREDICTING THE LOCATION OF TERNARY PHASE BOUNDARIES USING BINARY DATA Meijerin1,6 has used the regular-solution model to calculate common tangent points to ternary free energy of mixing surfaces and hence to determine phase boundaries in ternary systems involving miscibility gaps. He used the following equation to calculate ternary excess free energy of mixing values: stants characteristic of the binary solutions, and Ni is the mole fraction of component i. An alternate expression which gives for regular solutions as a function of binary values of along composition paths with constant N1/N2, N2lN3, and N1/N3 may also be derived:15 ternary r xs 1 ?c-*n.Ti*.U*. This expression for is more useful for the empirical calculation of ternary excess free-energy values for nonregular systems because actual binary AFXS data may be used in the expression rather than attempting to find suitable constants for Eq. [I]. The results of this feature of Eq. [2] are illustrated in Table I where calculated excess free-energy values for the Ni-Mn-Fe system at 1232°K are compared with experimental data of Smith, Paxton, and McCabe.19 Although regular-solution equations have been shown to give calculated thermodynamic quantities which agree quite well with experiment for single-phase nonregular ternary systems,14,15 care should be exercised in the use of the equations to predict thermo-dynamic properties of multiphase ternary systems in which strong compound formation is suspected. This precaution is consistent with the simple regular-solution model which for negative values of ai_j will indicate a tendency toward compound formation but even for very large negative values of ai-jwill not give multiphase binary or ternary systems involving a distinct stable compound. Hence, calculated ternary free-energy data using Eq. [2] might be expected to vary between being rigorous and poor, in the following order, for ternary systems which are: a) regular solutions, b) nonregular single-phase liquids in which random mixing is nearly realized, c) nonregular single-phase solids, d) nonregular multiphase systems exhibiting miscibility gaps, e) nonregular multiphase systems with binary compounds but no ternary compounds, f) nonregular multiphase systems with highly stable binary and ternary compounds. The calculated data will be expected to be least accurate for the last two cases. The general method adopted in this paper involves two-dimensional plots of ternary activity curves. The principle used is that tie lines indicating two-phase equilibria join conjugate phases a and B for example, for which a1(a) = a1(B), a2(a) = a2(B), and a3(a) = a3(B). Tie lines may be determined by plotting the ternary activities of two components along an isoactivity line for the third component and the unique points where the above equalities hold may be found graphically.

Jan 1, 1970