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By W. F. Laverty

Two recent papers in this journal1,2 contain experimental evidence for an anomaly in the concentration gradient for tracer diffusion. In both papers, the authors suggest that this anomaly is due to a Gibbs' absorption effect. Their hypothesis is that surface active tracer elements tend to remain in or near the surface adsorption layer, thereby altering the diffusion flux and concentration gradient. It is not clear how the anomaly can be explained in terms of an adsorption effect. Surface tension forces act parallel rather than perpendicular to a surface and therefore should affect only the rate of spreading of surface active agents tangentially across a surface. Frenkel3 has given a short treatment of surface tension as a driving force for surface diffusion. While the equilibrium concentration of a surface active agent at the surface of a solution is known to be higher than in the bulk, its chemical potential is necessarily the same. It is difficult to see how adsorption can result in an anomaly in the chemical potential gradient, which is the driving force for diffusion. A more detailed explanation by the authors of the adsorption mechanism is in order. A similar anomaly does not seem to arise where

Jan 1, 1970

By T. J. Fabiniak, R. A. Dodd, R. Balow

ALTHOUGH the (111) slip direction in pure bcc metals is well established, the information on operative slip planes is less unambiguously interpreted. So far, (110) {112), and (123) slip planes have been identified, but it is not certain whether glide on (112) and (123) really occurs or if it is composite slip on non-parallel (110) planes. The second of these possibilities is supported by the work of Chen and Maddin on niobium and molybdenum, and a subsequent analysis by these same workers of slip in bcc metals generally.3 The alternative possibility is exemplified by the work of Opinsky and smoluchowsky4 who concluded that slip in Fe-Si crystals can occur on any one of the systems {110}(111), {112}(111), and {123)(111), depending on which system the resolved shear stress is highest. Allen et alS5 also found that glide in ar iron could occur on any of these three systems, the operative system being determined principally by orientation. By an analysis of crystal rotation, slip lines, and X-ray asterism Harris6 concluded that niobium also deforms on these same systems, but if one of these glide planes does not coincide with the plane of maximum resolved shear stress, composite slip on nonparallel (110) planes may occur giving a macroscopic high indices slip plane. Earlier work on iron by Vogel and Brick reached the same conclusion.7 The analysis of slip in bcc metals is made more difficult by the fact that the slip lines may be quite wavy. In fact, the generality of wavy slip lines suggests that screw dislocations slip readily from one plane to another in the (111) zone ("pencil glide") although, as noted, it is not certain whether planes other than (110) really contribute to the slip. If planes of higher indices than {110} do operate, there is a possibility they may do so more readily at higher temperature Argon and Maloof9 observed {100}{211}(111) slip in tungsten single crystals plastically strained at low temperatures, but the results were interpreted in terms of an orientation-dependence rather than temperature-dependence. Therefore, at the present time corroborative evidence for the operation of higher indices slip planes at higher temperatures is lacking. The present results were obtained during the course of an investigation into the effect of cathode and anode surface crystallography on the prebreakdown currents of vacuum insulated devices. In the experiment of particular interest, the 1/8-in.-diam anode and the in.-diam cathode were tungsten crystals (total impurities -230 ppm) with (110) and (100) faces respectively. The faces were electrolytically planed and examined for initial perfection by plastic/carbon replicas and a study of Kikuchi lines in reflection electron diffraction patterns. They were aligned precisely parallel in an insulating holder incorporated into the electron microscope, the measured microscope vacuum being 2 x 10-5 torr, and the electrode spacing 0.01524 cm. The anode structure shown in Fig. 1 was obtained

Jan 1, 1970

By Anwar-ul Karim

In one of our recent papers, Cheng, Karim, Langdon, and Dom1 analyzed the creep mechanisms in a Fe-4 pct Si alloy. The experimental results of apparent ac-

Jan 1, 1970

By W. W. Gerberich, P. L. Hemmings, V. F. Zackay

ThE strain-induced martensitic transformation may be used to attain desirable combinations of strength, ductility, and fracture toughness. One of the parameters is the relative stability of the austenite. For example, it has been shown by Zackay et al.1 that the volume percent of strain-induced martensite is related to the combination of strength and elongation obtained. It has also been shown that the degree of transformation is an important factor in the crack propagation resistance of metastable austenitic steels.2 Considering both tensile and crack-propagation tests, it was of interest to see if there was any functional relationship between the amount of strain and the volume of strain-induced martensite. Previously,9 it had been shown that at room temperature, there was a relationship between uniaxial tensile strain and the volume percent of resulting martensite given by The data were obtained by plastically elongating tensile samples to a certain strain and then measuring the field strength to determine the strain-induced ferromagnetic volume. This was accomplished for two conditions having yield strengths of 229 and 233 ksi. The nominal composition of this material was 9Cr-8 Ni-3 Mo-2 Mn-2 Si-0.25 C-0.09 N. In evaluation of the strain-induced martensite at a crack tip: the question arose as to whether Eq. [1] would also be valid under triaxial stress conditions. Tests were conducted on 1/2-in. thick plate material having a composition of 9 Cr-8 Ni-4 Mo-2 Mn-2 Si-0.27 C. It was found that sectioning, polishing, and etching of fractured specimens could reveal the strain-induced martensite occurring at a crack tip. Care had to be taken to minimize the final polishing steps so as to avoid a smeared layer of strain-induced martensite. The method for taking metallo-graphic samples from fractured crack-line loaded type samples is shown in Fig. 1. Observations of the strain-induced martensite occurring at room tem-

Jan 1, 1970

By A. J. Ardell

SASS and cohenl (S-C) have recently reported some transmission electron microscope observations of an interesting effect which they call "veining". They observed veining in thin foils of solution-treated and (in certain cases) aged samples of a Ni-10.3 at. pct Ti-0.6 at. pct A1 alloy (assumed equal to 10.9 at. pct Ti). S-C suggest that veining in solution-treated samples is due to the selective electrolytic etching of titanium-rich regions in alloys which are otherwise homogeneous. They associate the veins with the discrete titanium-rich regions detected in a magnetic study of aging in this system by Ben Israel and Fine,' and they also suggest that the initial strengthening of aged Ni-Ti alloys is due to these titanium-rich regions, rather than the formation of the coherent precipitate (Ni3Ti, L12 crystal structure).

Jan 1, 1970

By J. H. Swisher

Two recent papers in this journal1,2 contain experimental evidence for an anomaly in the concentration gradient for tracer diffusion. In both papers, the authors suggest that this anomaly is due to a Gibbs' absorption effect. Their hypothesis is that surface active tracer elements tend to remain in or near the surface adsorption layer, thereby altering the diffusion flux and concentration gradient. It is not clear how the anomaly can be explained in terms of an adsorption effect. Surface tension forces act parallel rather than perpendicular to a surface and therefore should affect only the rate of spreading of surface active agents tangentially across a surface. Frenkel3 has given a short treatment of surface tension as a driving force for surface diffusion. While the equilibrium concentration of a surface active agent at the surface of a solution is known to be higher than in the bulk, its chemical potential is necessarily the same. It is difficult to see how adsorption can result in an anomaly in the chemical potential gradient, which is the driving force for diffusion. A more detailed explanation by the authors of the adsorption mechanism is in order. A similar anomaly does not seem to arise where

Jan 1, 1970

By Derek J. Fray, John Chipman

THE solubility of graphite in y-iron has been determined by several workers'12 with reasonable agreement. With the increasing use of more complex steels, it is necessary to understand more fully the thermodynamics of the austenite phase. The activity of carbon in a number of alloys is known but the maximum solu- bility of graphite has only been measured by Sohnchen and piwowarsky3 for Fe-Ni and Fe-Si alloys. Recently, Chipman and Brush reviewed the published data on the activity of carbon in binary and ternary austenite and also obtained expressions for calculating the solubility of graphite in Fe-Ni, Fe-Co, and Fe-Si alloys. On comparing the theoretically derived solubilities with the limited results of Sahnchen and Piwowarsky, it was found that the agreement for Fe-C-Si was excellent but there was considerable discrepancy for Fe-C-Ni and no data for Fe-C-Co. It was therefore decided to measure the solubility of graphite in a series of Fe-Ni and Fe-Co alloys. The alloy samples were made up by induction melting a high-purity master alloy under an inert atmosphere in an alumina crucible and drawing the molten metal into four-bore alumina tubes. Using this technique, it was possible to form alloy rods approximately 2 in. long and 1/18 in. in diam. Sixteen lengths of fine rod could be made without solidifying the master alloy. These were then allowed to cool under the inert atmosphere before being sectioned. The samples were packed in a graphite crucible with spectroscopic graphite powder, together with a piece of pure iron foil. Dry hydrogen, which had been saturated with isopropyl alcohol at room temperature, was passed over the crucible at 1000°C for 72 hr. At the end of the 72 hr argon displaced hydrogen in the reaction tube and the crucible was quickly pushed to the water-cooled end. The samples were thoroughly cleaned of the adhering graphite and analyzed. The pure iron samples always contained 1.5 0.02 pct C, which compares favorably with the data of smith2 and

Jan 1, 1970

By William G. Fricke

MaCROSEGREGATION, as distinct from microseg-regation, is often inverse in nature. That is, the eu-tectic solute elements, which are expected to be con-

Jan 1, 1970

By C. Feng, W. E. Krul

A study was made of the development of texture and the anisotropy in plastic flow of Ti-8Al-1Mo-1V alloy. Based on Pole figure determinations, the shifting of texture induced by rolling at approximately 400°C was found to be due primarily to slip rotation for the major Portion of the material. Grain boundary shear is believed to be an important factor. The anisotropy of the textured alloy was examined in terms of the variations of yield stress under tension and the ratio of bi -axial strain increments µp, in the temperature range 25" to 290°C. The results were related to Hill&apos;s theory on plastic anisotropy. The Schmid factors of (1100)[1120], (1101)[1120/, and (1101)[1120] slip systems were analyzed and found to be compatible with the observed anisotropy. Cross-slip between these planes was proposed as a possible deformation mode. In a number of published articles, considerable interest has been directed to the possible achievement of texture hardening in hcp metals. Following Backofen, Hosford, and Burke,&apos; this phenomenon was related to the yield criteria of the material and was expressed in terms of the biaxial strain ratio, r = d?w/d?l. The higher the value of r, the greater is the expected potential for texture hardening under certain loading conditions. For a given material, r varies with direction. Such variation can be traced to the anisotropy in plastic flow and can be explained within the framework of the various modes of deformation. Hatch2 found that a high r value coincides with a texture whereby the (0001) pole is closely aligned with the surface normal for sheet materials, Based on the analysis of the slip on the {1010}, {1011}, and (0001) planes, Lee and Backofen3 and Avery, Hosford, and Backofen4 concluded that the resistance to thinning is reduced by the operation of the (0001) <1120> slip system; with this reasoning they were able to explain the low r values (i.e., r « 1) observed in magnesium alloy sheets in the rolling direction and in commercially pure titanium in the transverse direction. The general equation, dealing with plastic flow in a polycrystalline aggregate has been used to correlate the plastic anisotropy and texture. In this expression, T and s are shear and normal stresses, and dri and d? are shear and normal strain increments, respectively. Assuming that five slip systems are operative within each grain and applying the principle of maximum work,5,6 one can determine the m value among the available systems. On this basis, Hosford7 and Chin, Nesbitt, and Williams&apos; were able to correlate m with yield stress under plane-strain compression, and Svensson9 was able to predict the variation of yield stress in textured aluminum. These workers made their analyses from materials in which slip operation is known to be associated with plastic flow. Questions remain regarding the derivation of Hill&apos;s theory on plastic anisotropy,10,11 since it was formulated on von Mises&apos; yield criterion.&apos;&apos; Its ability to deal with other forms of deformation has been in doubt.13 Others have discussed the validity of Hill&apos;s quadratic equation relating strain and yield stress.14&apos;15 For hcp titanium, deformation by various modes of slip and twinning operations has been reported.16-20 If all possible modes of deformation operate and contribute substantially to the plastic flow, it is difficult to imagine how the quadratic expression can suitably describe the anisotropic plastic flow of titanium alloys. Backofen and Hosford15 considered that Hill&apos;s is a macroscopic theory and implied that the major mode of deformation by slip mechanism will adequately describe anisotropy of the material. In the present investigation, slip operation will be shown to play the major role in the development of sheet texture induced by rolling of a commercial titanium alloy. Although twinning and other modes of deformation may also operate, their operation is believed to be secondary. The anisotropic properties of the sheet, which can be expressed in terms of directional variation of r, µp = -d?w/d?l and the yield stress will be shown to be governed primarily by slip operation. MATERIALS AND EXPERIMENTAL TECHNIQUES The titanium alloy chosen for the present investigation had a nominal composition of 8 wt pct Al, 1 wt pct Mo, 1 wt pct V, and 0.1 wt pct interstitial impurities. Sheets varying between 0.1 and 0.15 in. thickness were used. The alloy was received in a condition which was prepared by rolling at 900°C and annealing at 700°C. Subsequently, the sheets were subjected to further reduction in thickness by rolling at 400°C. A total reduction in thickness of 65 to 70 pct was obtained by a series of quick passes in a rolling mill with intermediate reheating. Further reduction in thickness was not possible due to cracking developed at the edges of the sheets. X-ray measurements were conducted in a Siemens and a Norelco unit to determine the texture of the sheets. Reflection techniques were used exclusively with CuK, radiation and a nickel filter. The loss of X-ray intensity due to geometric defocusing was calibrated with a technique described previously." The (0001), (1010), and (1071) pole figures were plotted from 0 to 80 deg, and to present the texture elements quantitatively, inverse pole figures were constructed following the technique described by Jetter, McHargue, and Williams.22 Tensile experiments were carried out at 25", 175",

Jan 1, 1970

By J. P. Hirth, A. H. Clauer

A simple graphical method is presented for the determination of climb forces on dislocations exerted by uniaxial stresses. In conjunction with standard stereographic projections, the technique is applicable for any crystal system. Climb forces on glide dislocations in bcc crystals are determined as an application. In connection with a study1 of elevated temperature creep of molybdenum single crystals, a detailed analysis of the climb force on a dislocation was necessary. In general, such forces can be calculated for an arbitrary dislocation segment from the Peach-Koehler equation2 (or one of its variants3"6) where Fk are the components of the force per unit length of dislocation line, ?i of the unit sense vector tangent to the line, ojl of the stress tensor, bl of the dislocation Burgers vector, and is the Einstein permutation operator with components ?123 = ?231 = ?321 = —?132 = — ?321 = —?—213 = unity, and all other components zero. It is understood in the suffix notation of Eq. [I.] that repeated indices are to be summed over 1, 2, and 3. For the most general coordinate system, the matrix manipulations required to solve Eq. [I] are fairly complex. However, a simplification can be achieved by specifying a coordinate system based on the dislocation in question. The pertinent system involves cartesian coordinates xi, x;, xi, with attendant unit vectors e&apos;i; ei being parallel to the Burgers vector b, and e&apos;3; being parallel to the climb directions (b x ?), i.e., normal to the slip plane. In this coordnate system b = (bi, 0, 0) and ? = (?&apos;1,?&apos;2, 0). Hence, Eq. [I] yields for the climb force per unit length F3 = ?&apos;2s&apos;11b&apos;1—?&apos;1s&apos;12b&apos;1 [2] The first term on the right side of Eq. [2] is the climb force on the edge component of the dislocation, while the second is the (cross-slip) force normal to the glide plane acting on the screw component. Thus, the problem of determining the climb force reduces to that of resolving the stress components —il and s&apos;12 in the xi coordinate system. Several authors7- l0 have shown, for the glide case, that such stress resolution can be performed most readily by graphical methods. Therefore, we present a similar method for the climb case. Of the suggested methods, we follow that of Hartley and Hirth,9 which can be performed directly with a standard stereographic projection for the crystal system in question. We treat the case of simple tension, or compression, this being the most common creep test in which climb is important. A set of cartesian coordinates (x1, x2, x3) is fixed with x3 parallel to the specimen axis. This set is connected to the x&apos;i set by the factors defined in Table I. A perspective view of the coordinate systems relating them to the glide ellipse, is given in Fig. 1, while a stereographic projection of the coordinate systems is presented in Fig. 2. The transformation matrix connecting the xi and xi coordinates is x&apos;i =aijXj [3] where an a11 a13 aij = a21 a22 a23 a31 a23 [4] s The corresponding transformation for the stresses is i [5] The only nonzero component of okl for the simple tension case is s33,. Hence, using Eqs. [4] and 151, we find that Eq. [2] becomes F3 = b&apos;1s33 sin2 cos ?[cos ? sin a - sin ? cos a] [6] = m1b&apos;1s033 sin a- rn2b&apos;s33 cos a where sin a = 5: and cos a = ?i, with a the angle measured from b to ?, i.e., a polar angle in the x1, x2 plane. The same equation with a sign change applies for compression. A graphical plot of the "Schmid" factor m1, relating to the climb force on the edge component, is presented in the stereographic projection of Fig. 3. In this projection the glide plane normal points toward the top of the page and the glide direction points normal to the plane of the page. To use the graph, one

Jan 1, 1970

By Ashok K. Sinha

The quasi-binary systems "VFe3"—VCo,—VNi,— "VCu3"and "TiFe3"—TiCo3,—TiNi3-"TiCu3"have been studied by a combination of microscopic and X-ray methods. Of the Phases encountered, eleven had close-packed ordered layer structures. Within each system, there is an approximately linear variation of the degree of hexagonality of the stacking arrangement with electron concentration, e/a. A study of eighty -four known examples of AB3 structures in transition metal alloys indicates that at e/a = 8.65 the ordered structure of the close -packed layers changes from "triangular" (AuCu3 type) to "rectangular" (SbCu3 type). At e/a < 8.65, the slope of hexagonality us e/a line increases with the group number of the A component. An interesting series of close-packed ordered structures is known to exist at the composition AB3; however, their alloy chemistry has not yet been fully understood. Dwight and Beck1 observed a correlation between position of the components in the periodic table and the type of crystal structure of the binary AB2 structures formed by transition metals. No consistent effect due to atomic size was noted and they proposed that electron concentration* predominates in In the present paper, the AB3 structures are characterized by a symbol describing the stacking and a symbol specifying the ordered layer. The stacking symbol used was introduced by Zhdanov,7 and later used in the International Tables,8 and by Beck9 in his survey of possible layer stacking structures. Alternating positive and negative integers are used to represent the number of positive (e.g., in abcabc...) and negative (e.g., in cbacba...) stacking sequences. T denotes the triangular ordering found in close-packed planes of the AuCu3 structure and R the rectangular ordering found in close-packed planes of the SbCu3 structure, Figs. 3(a) and (b). The present structure symbols are listed in Table I alongside the prototypes, where known, and other structural characteristics of AB3 phases found in the present investigation. EXPERIMENTAL The starting materials were metals of 99.9+ purity. The alloys were prepared by arc melting under argon atmosphere using a nonconsumable tungsten electrode and water-cooled copper hearth. The total weight loss upon melting and subsequent annealing was always less than 0.5 pct and hence the alloys will be referred to by their intended (unanalyzed) compositions. The alloys were homogenized and annealed at suitable temperatures in the range 750" to 1200°C, the annealing periods varying from 3 days at 1200°C to 10 days at 750°C. The heat treatments were carried out in sealed silica capsules under argon atmosphere and with a molybdenum foil cover between the alloy and the walls of the capsule. The quenched alloys were microscopically examined and reduced to powder by crushing or filing. The powders were, whenever necessary, given a stress-relieving anneal at the original annealing temperature. X-ray powder patterns were obtained with an asymmetrical focusing camera, a Guinier-deWolff focusing camera, or a Debye-Scherrer camera. Cr, Co, or Cu radiations were used. In some cases, to ensure the minimum degree of contamination, the deeply etched specimens were mounted in the asymmetrical focusing camera to obtain an X-ray pattern. Internal silicon standards were employed for lattice parameter determinations. The intensity calculations were made by using a Fortran IV program

Jan 1, 1970

By Kun Li, Alex Simkovich

The rate of dissolution of alumina in carbon-saturated liquid iron has been studied experimentally in a system where alumina was in the form of a cylindrical rod immersed in an iron bath contained in a graphite crucible. Data obtained consisted of the concentrations of aluminum in the melt as a function of time. In the case of static experiments, the data are shown to agree with theoretical prdictions based on the diffusion of aluminum.. The rate of dissolution was greatly increased by the rotation of the alumina rod. It is concluded that the diffusion of aluminum from the alumina/metal interface is the rate-controlling step. In the past, thermodynamic investigations of systems encountered in ferrous process metallurgy have received widespread attention. More recently, considerable work has been devoted to the study of kinetics associated with these systems in an effort to determine their rate controlling mechanisms. The alumina-iron system is of great importance in ferrous metallurgy. Yet information concerning kinetics of reaction in this system is seriously limited. The present study was made in order to establish the rate-controlling step for dissolution of solid alumina in liquid iron. LITERATURE REVIEW A number of papers concerning dissolution of solid metals in liquid metals have been reported in the literat~re. Generally, for these simple systems, dissolution is controlled by mass transfer of the dissolving species. Complex systems involving dissolution of solid metal carbides and oxides in liquid metals and slags have been studied to a much lesser extent. Skolnick5,6 reported on the reaction between liquid cobalt and poly-crystalline cylinders of tungsten carbide, in which the cylinders were dissolved while being rotated about their longitudinal axes at various speeds and temperatures. As a result of unexpected preferential grain boundary attack by the liquid cobalt, large errors in the measured dissolution rates occurred because of loss of tungsten carbide grains to the liquid cobalt. Nevertheless, it was possible to establish that the liquid Co-W carbide reaction was not controlled by mass transfer. In a similar approach, cooper7 was able to show that artificial sapphire rods, (alumina single crystals) dissolving in lime-alumina-silica slags obeyed a mechanism of mass transfer control. Here, again, the rods were rotated at various speeds and temperatures, and the process was followed as a function of these variables. Forster and Knacke8 took a practical approach to reaction between slags and refractories. By blowing argon through refractory cylinders of silica, silli-manite, or dolomite and directing the gas to rise along the slag-refractory interface, it was possible to increase the rate of mass transfer. Although the method was admittedly crude, it nevertheless permitted an evaluation of the relative stabilities of refractories with respect to slag attack. Data were interpreted on the basis of mass transfer control. EXPERIMENTAL TECHNIQUE Apparatus. An illustration of the apparatus used in this study is shown in Fig. 1. The furnace consisted of a Morganite recrystallized alumina tube wound with a molybdenum coil. A secondary molybdenum heater was mounted around the upper half of the primary coil to aid in controlling the thermal gradient within the furnace. The primary heater tube was 3 in. in ID and 30 in. long. A reducing mixture of 95 pct N and 5 pct H was maintained around the heating elements. Thermal insulation was provided by alumina powder. The chamber within the primary combustion tube contained a boron nitride block near the top to assist in controlling the thermal gradient to the furnace and also to provide a bearing surface for the rotating graphite shaft. The outside diameter of the graphite shaft was $ in. A separate threaded graphite specimen holder was screwed into the end of the shaft. The holder contained a tapered hole drilled into the end to guide the oxide specimens as they were pressed into it for mounting. Additional guidance for the rotating graphite shaft was furnished by a water-cooled bronze bushing attached to the top of the furnace. A steel clamp was fastened to the upper end of the graphite shaft and rested on a thrust bearing; the shaft and clamp were driven by a dc motor through a set of gears. Two O-rings located immediately above the bronze bushing maintained a gas-tight seal about the graphite shaft. The lower half of the alumina tube housed the crucible and charge, which were placed on a 3/4-in. diam movable alumina support tube. With this arrangement, charges could be inserted into or removed from the furnace while the hot zone was maintained at or above 1000°C. To control the temperature of the furnace, the thermocouple was mounted inside the support tube and in contact with the crucible bottom. Stray electric fields in the furnace were of sufficient intensity to cause erratic indications by the thermocouple. By enclosing the thermocouple protection tube in a molybdenum sheath and grounding this shield, the problem was eliminated. Output of the thermocouple went to an automatic continuous balance controller. Procedure. A typical run was as follows. First, electrolytic iron was premelted in graphite crucibles and cast into graphite molds with the same configura-

Jan 1, 1970

By G. L. Kulcinski, R. D. Leggett

Irradiated uranium containing 635 ppm of carbon, mostly in the form of UC precipitates, was annealed at temperatures from 650" to 900°C under hydrostatic pressures of 0 to 1000 bars. Postirradiation examination revealed that the carbide particles are not stable in the r phase of irradiated material but are stable in unirradiated material annealed under identical conditions. The degree of carbide dissolution appears to be connected with the fission product concentration and independent of annealing pressure. THIS paper describes the change in appearance of carbide particles in irradiated uranium after the uranium has been postirradiation-annealed. It has been proposed by several investigators&apos;-5 that fission gas-induced swelling in irradiated uranium may be reduced by incorporating a fine dispersion of second-phase particles into the metal. Because of the low solubility of carbon in uranium6 and the apparent stability of UC precipitates at high temperatures,6-8 this system has received some attention. The stability of UC particles to low-temperature irradiation has been demonstrated many times, as well as their stability during postirradiation anneals in the high a or B phases.9 Unirradiated uranium containing UC particles has been annealed high in the r phase, and the solubility of carbon was found to be only -115 ppm at 1050ºC.6 Vacuum annealing of irradiated uranium to the same temperature produces a spongelike sample, due to the formation and growth of fission gas bubbles."14 This highly disrupted lattice has made any determination of the stability of UC at these temperatures impossible. Nevertheless, it has always been tacitly assumed that the UC particles were still present. Recently, postirradiation, high pressure-high temperature tests have been performed on irradiated uranium containing a secondary phase of UC. 14 Examination of these samples after 100-hr, 900°C tests revealed that the carbides are not stable, and the results of these tests are presented here. 1) EXPERIMENTAL PROCEDURE The samples, high-pressure equipment, and subsequent analytical techniques are the same as those described elsewhere.14,15 Briefly, cylindrical samples of commercial-purity uranium that had been irradiated at <350°C to 0.37 at. pct B.U. were subjected to 90O°C, 100-hr anneals in NaK at pressures ranging

Jan 1, 1970

By K. Tangri, M. Chaturvedi

The addition of 0.5 wt pct Cu to Zr-2.5 Cb alloy increases the as -quenched hardness of the hexagonal martensitic a&apos; phase, produced by water-quenching bccß-Zr phase, by about 35 pct. This strengthening has been attributed to the solid -solution hardening of the matrix. On aging ternary martensite, a&apos; phase reverts to equilibrium a and Zr2Cu and ß-Cb precipitate out, mainly at the twin and grain boundaries, causing a secondary hardening of the matrix. COLD-worked Zircaloy-2 pressure tubes have been in use in power reactors for a considerable period of time. The search for a better material led to the development of Zr-2.5 wt pct Cb alloy which in the quench-aged condition develops 50 pct more strength than that of cold-worked Zircaloy-2, however, its corrosion resistance in water and steam in the temperature range of 316" to 400°C, in absence of neutron flux, is inferior to that of zircaloy-2.&apos; Work carried out by Ells et al.1 and Dalgaard2 has shown that the corrosion properties of Zr-2.5 wt pct Cb alloy can be considerably improved by the ternary addition of 0.5 wt pct Cu. This paper is concerned with the effect of 0.5 wt pct Cu on the formation of martensitic a and its aging characteristics in a Zr-2.5 wt pct Cb alloy. MATERIALS AND EXPERIMENTAL TECHNIQUES Zr-2.5 Cb-0.5 Cu (referred to as the ternary alloy) and Zr-2.5 Cb (referred to as the binary alloy) alloys, supplied by the Chalk River Nuclear Laboratories of the AECL were used. The detailed chemical analysis is given in Table I. Cold rolling and swagging with frequent intermediate anneal of 1000°C were used for the initial fabrication of the alloys. All the heat treatments were carried out after the specimens were wrapped in zirconium foils and encapsulated in silica tubes under a vacuum of 5 x 10-6 mm of Hg. For optical metallography and hardness measurements specimens were mechanically and then chemically polished in a 45 pct HNOj, 45 pct HzO, and 10 pct HF solution. Hardness was measured on a Vickers hardness tester using a 10-kg load. For each specimen at least fifteen indentations were made in order to obtain a representative value. The phase identification and structural analysis were carried out using X-rays and electron diffraction techniques. Wires of 1.5 mm diam reduced to 0.12 mm diam by chemical etching were used for making Debye-Scherrer powder patterns using Cu Ka radiation in a 114.6 mm diam camera. Carbon extraction replicas were prepared by etching the specimens, after depositing a layer of carbon on the metallographic specimen, in one part HF and thirty parts ethyl alcohol. Thin films were prepared by electropolishing heat-treated 3/4 by 1/2 by 0.005 in. thick strips using a modified Bollman-Window technique. The 10 pct perchloric acid-90 pct methyl alcohol bath was kept at -50°C and polishing was done at 5 to 10 V. The thinned specimens were washed in ethyl alcohol at -30º to -40°C and dried between filter papers. Replicas and thin films were examined in a Phillips 300 G electron microscope. For resistivity measurements thin strip specimens 0.02 by 0.3 by 10.0 cm long were used. The potential leads were spot welded to the specimens in order to maintain a fixed length for the initial and the final resistivity measurements. The resistivity was measured by a Kelvin bridge in a temperature controlled room. The temperature was maintained at 72º ±1°F and the accuracy of the resistivity measurements was 0.03 µa-cm. RESULTS As-Quenched Structures. In order to produce a homogeneous matrix to study the precipitation reaction the solution-treatments of both the alloys were carried out in the -field region. From the Zr-Cb phase diagram due to Lundin and cox3 ß/a + ß phase boundary for Zr-2.5 wt pct Cb alloy is 820°C. Ells et al.1 have reported this boundary for Zr-2.5 Cb alloy containing 1100 ppm 0 to be at 920°C. Also, the addition of 0.5 wt pct Cu reduces this temperature by 50°C. Therefore, the solution-treatments were carried out at 1000°C to ensure that the alloys were in ß-phase region. The soaking time was 1 hr and the specimens were water-quenched. The as-quenched hardness of the binary alloy was 245 Vpn whereas, that of the ternary alloy was 330 Vpn. The X-ray diffraction studies indicated that the as-quenched structure of both the alloys consists of martensitic hexagonal phase a&apos;, with a c/a ratio of 1.591, and some retained ß-Zr. The presence of a&apos; phase was further confirmed by thin film electron microscopy. Electron micrographs of typical ß-quenched structures of the ternary and the binary alloys are shown in Figs. 1 and 2, respectively. Fig. 3 shows the diffraction pattern from an area similar to that shown in Fig. 1. Although, the as-quenched hardness of the ternary alloy is about 35 pct greater than that of the binary alloy, the structure of both the alloys seems to be the same. The matrix of both alloys is heavily twinned and shows very few dislocations. Furthermore, there is no evidence of any precipitation taking place in either of the two specimens during quenching from the solution-treatment temperature. Aging Behavior of Martensitic a&apos;. The aging kinetics of the ternary alloy were followed by resistivity and hardness measurements. The as-quenched values

Jan 1, 1970

By A. U. Seybolt, J. L. Walter

The effects of the addition of 0.5 pct ThO2 (by volume) on the grain structure and texture of heavily rolled tungsten sheet were studied. Powder metallurgy ingots were rolled to sheet, 0.001 in. thick, and samples were annealed at temperatures from 1200" to 2500°C. The heating rate to the anneal temperature was varied from 3°C per min to 6500°C per min. The orientations of the largest grains were determined by X-ray diffraction. The disposition and loss of the ThO2 particles were determined by electron transmission microscopy and the activation energy for remozlal of the thorium was measured by mass spec-troscopy. Heating rates below about 800 C per min produced large, highly elongated grains. Higher heating rates produced much smaller, less elongated grains. The grain structure and texture of the slowly heated samples were identical to the structures and textures of heavily rolled tungsten foil conventionally doped with aluminum, silicon, and potassium but the recrystallization temperature was about 200°C lower. There was stringer-like dispersion of larger ThO2, particles superimposed on a uniform dispersion of fine particles. The particles increased in size and decreased in number with time at temperature. The loss of particles was accompanied by formation of grain boundary voids and surface pits. The activation energy for removal of the ThO2 was about 40 kcal per mole. THE addition of small amounts of aluminum, silicon, and potassium to tungsten has a profound effect on the grain structure of heavily rolled sheet1 or drawn wire."4 Thus, "doped" tungsten sheet, rolled to 0.001 in. and recrystallized, develops a structure consisting of large, highly elongated grains of a specific preferred orientation.&apos; It has been shown that the elongated grain structure was caused by a dispersion of particles, identified as mullite (Al6si2O13),1,4 in strings parallel to the rolling direction in sheet or to the wire axis. Identical results were obtained for iron which was doped with glass and rolled to 99 pct reduction of thickness and recrystallized.5 Again, the glass particles were disposed in strings parallel to the rolling direction. The strings retarded boundary migration in the lateral direction but grain growth was able to proceed relatively unhindered along the direction parallel to the strings.1,5 In both the doped tungsten and the glass-doped iron, the particles were highly plastic during the high-temperature deformation. Since mullite melts at about 1800°C and the glass employed melts at about 810ºC, the particles were probably molten during the recrystallization anneals (above 1800°C for the doped tungsten and 850°C for the glass-doped iron). There are indications in the literature that particles not plastic at hot-working temperatures (up to about 1550°C for tungsten) may also impart elongated grain structures by primary recrystallization of worked alloys. Examples are dispersions of tantalum carbide in chromium,6 and ThO2 in nickel where elongation ratios of recrystallization grains of up to 20:l were obtained.7 Strings of ThO2 particles in W-ThO2 wire have been seen by Rieck.8 In view of the available evidence, it was of interest to extend the previous studies of doped tungsten and glass-doped iron to include W-ThO2 sheet materials. Of specific interest was the grain structure, preferred orientation, recrystallization temperature, and disposition of the thoria particles. EXPERIMENTAL PROCEDURE A) Material Preparation. About 380 g of blue tungsten oxide (approximate composition WO3) was wet with a sufficient amount of aqueous solution of Th(N03)4 to provide 0.5 vol pct ThO2. The wet mixture was stirred to distribute the doping material uniformly throughout the powder. Stirring was continued while the mixture was heated until it was completely dry. The dried, doped mixture was then reduced to tungsten powder by heating at 850°C for 2 hr in a stream of dry hydrogen. The doped tungsten powder was hydropressed in a rubber sack at pressures of 50,000 psi to produce an ingot approximately 2 cm diam by about 5 cm long. Next, the pressed cylinder was heated in hydrogen for 2 hr at 1350°C to render it strong enough for machining. The cylinder was machined to a square cross section of 1.6 by 1.6 cm with rounded corners. Finally, the bar was heated for 2 hr at 2150°C in hydrogen to provide a sufficiently dense mate rial to withstand the hot-rolling operation. Prior to rolling, the ingot was reduced in thickness by about 20 pct by forging at 1550°C. This served to increase the density of the material and to widen it slightly for better rolling characteristics. The forged ingot was then rolled at 1550°C to a reduction of 45 pct of thickness, following which the rolling temperature was reduced to 1300°C and the slab rolled, with several reheats, to 0.050 in. Further reduction was accomplished at 800°C in tungsten sheet packs to a total reduction of about 99.85 pct. B) Annealing Treatment and Observation of Structure. Small samples of the rolled foil were annealed in one of two ways. Some of the samples were suspended in a covered tungsten can and annealed at temperatures from 1200" to 2200°C for various times in vacuum of l0-7 to 10-6 mm Hg. The can was heated by induction and temperatures were determined by optical pyrometry

Jan 1, 1970

By M. B. Bever, A. K. Jena

Equations for the heat effects of additions of mixtures of multicomponent phases to a solution have been derived in terms of the enthalpy interaction coefficients. By these equations and the measured composition dependence of the heat effects on addition of mixtures of Ag-Cd solid solutions and elemental gold to liquid tin-rich solutions, values of the enthalpy in-teraction coefficients in tin-rich solutions at 541°K have been obtained. Analysis of these results in terms of the regular solution theory and the quasichemical theory suggests that near the melting point of the solvent association in the solution becomes important. SEVERAL recent papers have discussed the nature of dilute solutions on the basis of measured enthalpy interaction coefficients. l-3 These coefficients contribute to the understanding of the constitution of solutions and can be used for the evaluation of thermo-dynamic data of multicomponent systems. Their experimental determination, however, is laborious. This communication reports values of the enthalpy interaction coefficients of silver, cadmium, and gold in liquid tin-rich solutions obtained from the measured heat effects of additions of mixtures of Ag-Cd solid solutions and elemental gold to liquid tin-rich solutions. These measurements were made in the course of the determination of the heats of formation of Ag-Cd solid solutions reported in a concurrent publication.4 THE HEAT EFFECT OF AN ADDITION TO A SOLVENT This analysis is concerned with the addition of a mixture of multicomponent phases from the temperature To to a solvent of known composition at temperature T. If Nmixture << Nsolvent, where N designates the gram-atoms involved, the heat effect per g-atom of mixture added can be expressed as (HT - HT )i = difference in heat contents of component element i in the mixture at T and To Q = heat effect on solution of the mixture at temperature T Also1 Q = S Xi [2] where ?Hi ,T,x = relative partial enthalpy per g-atom of i in solution at temperature T and composition of the solution x x = average of the atom fractions of the added material in solution before and after the addition The relative partial enthalpy ?Hi per g-atom of an element i in a dilute solution composed of a solvent 1 and the solutes j = 2, ... m is related to the interaction coefficients by the following equation5 ?Hi - ?Hi-?Hi,x1-1 + S n1ixj+ . . . +S...S...S nrixn2... Xnji...Xnmm+... [3] vhere Xj = atom fraction of solute j in the solution nri = the rth order enthalpy interaction coefficients, which can also be represented by the more general designation5 L(i)n2,n3...nm and nj may have any positive integral value or zero. For identification of various rth order interaction coefficients, nri is written as nn2i2,...nij,...nmm. Eqs. [1], [2], and [3] combine to give the following general equation for the heat effect on addition of a small quantity of a mixture to a large quantity of a dilute solution n = _?ga ?Ha,To + ? Xi(HT - HT o)i a. i + ?xi?Hi,X,i?1 + ??xnjixj + . . . + ???. . .?. . .?xinrix2n2. . . xnji. . . xnmm+ . . . [4] The first term on the right-hand side of this equation is the heat of decomposition at the addition temperature of the phases present in the mixture, the second term is the heat required to raise the temperature of

Jan 1, 1970

By S. Kobayashi, A. E. Armenákas, C. Mylonas

Earlier work1-4 has shown that commercial mild steels under static loading at the lowest natural operating temperatures fracture in a brittle manner only when damaged by a suitable history of straining. Notched and then compressed plates have fractured in subsequent tension at loads as low as 10 pct of the limit load and precompressed smooth bars at a subsequent extensional strain as low as 0.01. The comparison of the average net fracture stress with the flow limit stress was shown to be an excellent criterion of brittle or ductile behavior of mild steel structures when only loads and general stress levels are known. The present investigation shows that the deformation at fracture is a far more sensitive measure of brittleness than the fracture stress. Both criteria, deformation and stress, are used to determine the amount of uniform precompression of two mild steels, ABS-B and Project E-steel, resulting in brittle fracture under the strong constraint of a subsequently machined severe circumferential groove. The fracture stress equaled or exceeded the theoretical flow limit Ól = 2.680., (&apos;based on the elevated yield stress at each prestrain) up to prestrains of about 0.20 and then fell off to about 1 at prestrains of 0.60. Yet a prestrain of only 0.05 reduced the elongation at the shoulders by a factor of about 4. The total plastic elongation of a region surrounding a sharp notch in prestrained steel deternines whether or not fracture will be initiated in large structures, hence is a direct and realistic measure of the remaining ductility and provides an excellent test of the material&apos;s resistance to embrittlement. ALMOST all engineering structures of mild steel which failed in service in a so-called "brittle" manner exhibited appreciable local plastic deformation (more than 1 pct) and a mixture of "cleavage" and "shear" fracture surfaces. Furthermore, the peak local stress in an advancing crack is always high. Such simple criteria as pure cleavage, absence of plasticity, or fracture stress, so useful in other fields, are insufficient to characterize brittleness in engineering structures at ordnary temperatures. The "brittle)&apos; behavior of engineering structures is caused by the limited ductility at cracks or notch regions, as shown by recent work at Brown University summarized and extended in Refs. 1 to 4. It was also shown that the local ductility of mild steel may be catastrophically reduced by a suitable strain and temperature history similar to those which may occur in real structures. Localized yielding begins at the notch roots at low loads but is contained by surrounding elastic regions. The plastic strains are hence small. They increase slowly with the load up to the flow limit or limit load for an ideally plastic material. Unrestricted plastic flow then occurs. At such strains the real material locally st rain-hardens and fractures. With work-hardening materials no flow limit exists, and the transition from low to high plastic strains is gradual but increases more rapidly at loads close to the flow limit of an equivalent perfectly plastic material. When the available ductility is sufficient for reaching the limit load, the behavior is normal or "ductile". With insufficient ductility, fracture will occur at a low load and will be defined as "brittle". Accordingly the sufficiency or not of the ductility at a notch is reflected in the magnitude of the fracture load or average net stress as compared with the limit load or flow limit. The application of this criterion gave surprising results. Service failures under semistatic loading occurred mostly below the limit load, hence were "brittle". On the contrary all static tests with undamaged commercial mild steels reached the limit load in spite of the deepest notches and temperatures below Charpy impact transition (say about -30°F or higher). Notched bars showed no brittleness even under fully dynamic axial loading up to 1.5 x107 psi per sec at -23°F and about 2.5 x l06 psi per sec at -ll0°F, but broke in a brittle manner at -200°F and l03 psi per sec.&apos; To propagate a fracture at low load, experimenters had to trigger it by superimposing a strong dynamic impact at a notch cooled by liquid nitrogen as in the Robertson5 or Esso tests.&apos; Once started the cracks would run through warmer regions of smaller stress. Obviously the ductility of the apparently undamaged commercial steels was "sufficient" in the laboratory tests but not in the service fracture, where it must have been reduced by some embrittling procedure of fabrication or service. These conclusions were confirmed by the achievement of low static stress (brittle) fracture initiation in unwelded steel after a local reduction of ductility by simple prestraining. Symmetrically notched plates of undamaged mild steel cooled below the Charpy V-notch transition range were tested in central static tension: Undamaged plates withstood loads of limit intensity, but when subjected to prior in-plane com-pressive prestraining perpendicular to the notch axis and to accelerated aging, the plates fractured completely or partially at very low static loads, as low as one-tenth of the flow limit.2-4 However, damage could not be easily related to the strongly variable prestrain around a sharp notch. To obtain easier strain measurements, it was decided to use axially precom-pressed bars and bent bars. Final testing was done by

Jan 1, 1970

By P. Shahinian, H. H. Smith, M. R. Achter

Crack growth rates are measured at elevated temperature in a resonant fatigue machine from vibration frequency decreases calibrated in terms of crack depth. Crack growth rates in Type 316 stainless steel at 500º and 800°C show a sharp increase with oxygen pressure in an intermediate pressure range and little or no change at high and low pressures. At 500°c, I torr of oxygen reduces the fatigue life by almost a factor of 100 in comparison to that in vacuum and raises the growth rate of shallow cracks by the same At At 800°C the effects are smaller. Changes in slope in the crack growth rate curves are discussed in terms of a model in which rates of surface production and of surface coverage by gas are compared. The use of a calculation method in which the surface exposure time is equal to X/v, where x is the interatomic spacing and v is the growth rate, makes it possible to obtain order of magnitude agreement at 500°C between the observed pressure and the predicted pressure at these slope changes. At 800°C oxidation becomes a .factor and the data cannot be treated by simple adsorption theory. THE decrease in the fatigue life of metals as a function of gas pressure usually follows a stepped curve with virtually all of the decrease concentrated in a sharp drop in a transition zone at intermediate pressures and little or no change at low and high ranges. A number of models, differing in the details of the mechanism, have been offered to explain the shape of the curve. Measurements of crack growth in aluminum as a function of gas pressure by Bradshaw and Wheeler&apos; and Hordon2 demonstrated opportunities for quantitative comparison to evaluate the proposed models. Since comparable data were lacking at high temperatures, in the present work rates of crack propagation were measured in Type 316 stainless steel at 500" and 800°C as a function of oxygen pressure. Choice of this material was dictated by two considerations; it is stiff enough at these elevated temperatures to resonate with the regenerative drive on our fatigue machine and it is known to display a large effect of environment. A new method of calculation is described to predict the gas pressure at the critical point. EXPERIMENTAL PROCEDURE Because of the difficulty of measuring crack depths directly at high temperatures, an indirect method was developed based on the decrease in the resonant frequency with the growth of a crack. A reversed bending, constant amplitude fatigue machine, described previously,3 vibrates a specimen at its resonant frequency, automatically records any changes in it and shuts itself off after it has reached a preset value of frequency decrease. The record of frequency change is used to determine the rate of crack growth. Sheet type specimens of Type 316 stainless steel, Fig. 1, incorporated a sharp, shallow notch to localize the formation of a single crack. After machining, they were annealed in a vacuum of l0-6 torr either at 1066" (lot A) or 871°C (lot B) and then electropolished in an acetic-chromic acid solution. Bending strains were measured at 500" and 800°C by an optical technique4 and reported as total strain without correction for the notch. At 500°C, the 0.141 pct strain was 0.085 pct elastic and the remainder plastic. At 800°C the 0.062 pct strain was all elastic. To convert frequency decrease to crack length, calibration curves were obtained by interrupting the vibration at stated intervals of frequency decrease. The crack depth was measured microscopically at a magnification of X400 and reported as the average of the measurement on each edge. Some specimens were sectioned for crack measurement while others were returned to the machine and fatigued further. There was good agreement between the two methods. Before beginning the vibration, the vacuum chamber was first evacuated cold to 1 x 1O-6 torr, then heated to the operating temperature and held there until the pressure was again reduced to 1 x10-6 torr at which time oxygen was introduced to the desired pressure. In this investigation the vibration frequency was nominally 10 cps and a decrease of 0.6 cps was taken as the failure point. The choice of the frequency decrease to represent failure has no appreciable effect on the fatigue life because the crack is growing very fast at this point.

Jan 1, 1970

By M. J. Richards, A. Szirmae, G. R. Speich

The formation of austenite from ferrite, ferrite plus retastable carbide, spheroidite, and pearlite has been studied in a series of irons, Fe-C alloys, and plain-carbon steels using fast heating techniques. In the absence of carbide, austenite nucleates at ferrite/ferrite grain boundaries; nucleation is followed by the rapid growth characteristic of a massive transfornation. The trarnsformation occurs at 950°C at heating rates of 106º C per sec and cannot be suppressed. Metastable carbide dissolves before austenite forms and does not influence the transformation kinetics. For spheroidite structures, austenite nucleates preferentially at the jinction between carbides and ferrite grain boundaries. Growth from these centers proceeds until the carbide is completely enveloped; subsequent growth occurs by carbon diffusion through the austenite envelope. For pearlite structures, austenite nucleates preferentially at pearlite colony intersections. Carbide la)?zellae dissolve at the advancing austenite interface but complete solution of carbide does not occur; the residtial carbide is eventually dissolvled or spheroid-ized depending on the carbon cuntent. The magnitude and temperature dependence of the austenite growth rate into Fe-C pearlite when incomplete carbide dissolution is assumed are satisfactorily explained by an approximate colume diffusion model. The impurities present in plain-carbon steel reduce the growth rate of austenite in comparison to that jound in an Fe-C alloy. The formation of austenite has been studied in much less detail than the decomposition of austenite. This is primarily a result of the importance of harden-ability in determining the mechanical properties of steel. Recently, more interest in the kinetics of austenite formation has resulted from the discovery by Grange1 that rapid heating techniques strengthen steel by refining the austenite grain size. Although the strengthening effect is not large, it is accompanied by no loss in ductility. In addition, interest continues in rapid heat treatment of low-carbon steel sheet for tin plate applications.2,3 Among the few systematic studies of austenite formation are the early work of Roberts and Mehl4 on formation of austenite from pearlite and recent work of Molinder5 and of Judd and paxton6 on formation of austenite from spheroidite. Also, Boedtker and Duwez7 and Haworth and paar8 have recently studied the formation of austenite from ferrite in relatively pure iron, Kidin et al.9,10 have studied the formation of austenite in 8 pct Cr steels, and Paxton has recently discussed various aspects of austenite formation in steels." The present work was undertaken to determine the kinetics of austenite formation for a variety of starting structures including ferrite, ferrite plus metastable carbide, ferrite plus spheroidal cementite, and ferrite plus pearlitic cementite. Emphasis was placed on determining the active sites for austenite nucleation, determining the temperature and time range of austenite formation, and in the case of pearlite a careful study of the growth rate of austenite was made in the absence and presence of impurities. By using a variety of heating techniques including laser-pulse heating, it has been possible to study austenite formation in an isothermal fashion over a wide range of temperatures. EXPERIMENTAL PROCEDURE The alloys studied in the present work are a zone-refined iron with 4 pprn C, an Fe-C alloy with 130 pprn C, 2 Fe-C alloys with 0.77 and 0.96 wt pct C, and a plain carbon steel with 0.96 wt pct C. The zone-refined iron and Fe-C alloys contained 60 pprn and 200 pprn total substitutional impurities, respectively. The plain carbon steel contained 2400 pprn Si, 2000 pprn Mn, and 900 pprn Cr. Various heat treatments were given to these alloys to produce different starting structures of equiaxed ferrite, ferrite plus metastable carbide, fine pearlite, and spheroidite. These heat treatments are given in Table I. A wide range of heating rates were employed in this work because many of the reactions occur so quickly at temperatures in the austenite range that they are completed during the initial heating cycle unless very fast heating rates are used. Essentially the same heating techniques employed by Speich et a1.12 and Speich and Fisher13 were used in this work. For time intervals of 2 sec to 20 hr, simple hand immersion of 0.010-in. thick specimens in a Pb-Bi bath was employed. These specimens were quenched in a 10 pct NaC1, 2 pct NaOH aqueous bath. For time intervals of 100 m-sec to 2 sec, an automatic dunking and quenching device was employed with 0.002-in. thick specimens. Again, liquid Pb-Bi baths were used for a heating medium but now helium gas quenching was employed. For time intervals of 2 to 100 m-sec a laser heating device was employed with 0.002-in. thick specimens; a helium plus fine water-droplet spray was now used for quenching. Additional information on heating times shorter than 2 m-sec was obtained by study of the zones around the centrally heated laser spot. Here diffusion of heat from the centrally heated zone raises the temperature of the specimen locally to all temperatures between ambient and the peak temperature, but for times of the order of microseconds. All the heat-treated specimens were examined by

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