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By John W. Cahn

Tile avevage value of the mean curvature of surfaces in a specimen can be precisely delermined by sitrlple measurements performed on random sections or on 1 vojectiotzs of these surfaces. For surjaces enclosing particles, the quanlity is sllown to be velated to the probable tlurrrhev ot particles intevcepted by a random platne and, under certain conditions, to the perimeter of their Projected image and to the increuse in surjace area when the particles grow. Many of the velalionsl~ips are valid for any shape or size of the particles. THE recent growth of the field of stereology or quantitative microscopy is largely the result of the discovery of a limited number of rigorously defined geometrical parameters that can be precisely measured on random sections or projections of a structure without assumption about particle shape.' Such parameters have been the volume fraction and surface area and line length in a unit volume. The present paper introduces the average of the mean curvature of surfaces in a volume, and shows that it can be rigorously measured by counting methods alone. AVERAGE CURVATURE ON A PLANE Consider a curve y = v (x) on the xy plane. The curvature Kp in the plane at any point is given by Kp = (dZy/dx2)/[1 + (dy/dx)2]3/2. The average curvature along the curve may be defined as Kp = (1/L) fKpdl |1] where dl = [(dx)' + {dy)2]1/2 is the length of an element of the curve and .(dl = L is the total length of the curve. The integral on the right-hand side of Eq. [l] will be called the total curvature, It is dimensionless and readily evaluated by substituting d = arctan (dy/dx) to give ah which is the change in direction of the tangents to the ends of the curve, Fig. 1. Hence, Kp = (1/L)(?h) [2] It can also be seen that Eq. [2] is applicable in the limit of sharp corners. Even though the curvature is infinite at a corner, f Kpdl remains integrable and equal to the change of angle. The signs of the quantities Kp and dl are arbitrary and, if the areas adjoining the curve are equivalent, there seems to be no compelling reason to fix the signs. For a closed curve, however, it becomes worthwhile to use the signs to distinguish among different types of areas or phases enclosed. For such a closed curve AO = t2r and As a convention, we shall take the direction of the integration along the curve in such a way that the area or phase under consideration (henceforth called a) is kept to the left side of the curve, Fig. 1. Then Kp is positive where the curve is concave and negative where the curve is convex. For a closed curve Ad - +2n if the curve encloses a, and Ad = —2n if the curve is surrounded by a. PLANAR SECTIONS OF THREE-DIMENSIONAL STRUCTURE OF ISOLATED a PARTICLES Consider next a planar section of a microstructure containing particles of a in a matrix. We place no restriction on shape of connectedness of these particles, and begin by considering the curvature of only the boundary between a particles and matrix' Clumps of contiguous a particles are then treated as a single a particle. The two-dimensional section will show in a unit area na simple closed curves enclosing a particles and nh closed curves of holes, in-

Jan 1, 1968

By John Chipman, Raymond L. Orr

Recently reported high -temperatlnre thermal data have been incorporated in a reuieu' of the therinody-r~ar,zic propesties of iron. The recent data permit mot corlsisterlt and reliuble choices to be made for many of the pvoperties, resnlling in bettev eslablished tabrtlations of the thermodynamic functions. Values of Cp, h°t- - H°298. s°t - S2sa, and (G°T -H298/T are tabulated for -the solid and liquid phases of iron in both stable and melastable regions. Consistency of the tabulations has been maintained to the precision necessr~vg to yield the Gibbs energy change belween the bcc (a, 8) and fcc (y) phases of iron at temperatures pertinenl to alloy studies. THE importance of the metal iron has stimulated many investigations of its thermodynamic properties at elevated temperatures. Reviews and summaries of the data have appeared from time to time. Among these the 1951 paper of Darken and smith' deserves highest recognition for the quality of its criticism and for the precision and thermodynamic consistency of its tabulations. These and the more recent table of Kaufman, Clougherty, and weiss2 reproduce the Gibbs energy of the (a, 6)--Y transformation with sufficient sensitivity for alloy studies. Other recent compilations of equal validity3-' make no attempt to do this. Since this Gibbs energy change is not greater than 22 cal per g-atom over the temperature range 1100° to 1800°K, it is obviously desirable to tabulate values of (G°t - H298)/T to four places of decimals even though the absolute accuracy would not warrant such precision. The necessity for reconsideration of the problem is emphasized by the recent publication of several important researches on the enthalpy and heat capacity of iron. The older work is well-covered in the reviews cited and will be mentioned here only when actually employed in the tabulations. GAMMA IRON Transition temperatures are taken from the selec -tions of Elliott and Gleiser,5 based on the work of Boulanger7 and earlier workers. For the a-y (A3) transition at 1184°K we retain the value 215 cal per g-atom adopted by Darken and smith.' It has received confirmation in the recent work of Dench and Kubaschewski,' and of Braun8 using adiabatic calori-metry, and of Wallace, Sidles, and Danielson10 using a pulse heating technique. The enthalpy data of Olette and ferrier" and of Anderson and Hultgren12 at higher and lower temperatures may be extended to 1184°K to give the following values which are adjusted to the required value of ? 1184 Ha,1184 Ha 298 = 8030 cal per g-atom [11 hr,1184-ha298 = 8245 cal per g-atom [2]

Jan 1, 1968

By H. I. Aaronson, H. A. Domian

ELectvon-probe analgsis has been used to in7:estigatr the partition ot alloying- elements between aus-tenite and proeutectoid ferrite (or the Jerritic component of bainite) in high-purity Fe-C-X alloys, lsuully at tzco levels of carbon content fca 0.1 and 0.4 pct in ntost steels) at temperatures between the M, and the Ae3 in Si, mn, Ni, mo, Co, Al, Cr, Cu, and PI steels. No partition ous found during the early stages of transformation at any temperature studied in the Si, ,mo. Co, Al, Cr, and Cu steels. Partition did take place, Jrowel'er, in Ihe Mn, ATi, and Pt steels, occurring in lewtperature. regions below the Ae3 of ca 130°, 65", UNDERSTANDING the mechanisms through which alloying elements influence the kinetics of austenite decomposition reactions which proceed by nucleation and 35c respectively. A break was discovered in the TTT curve for the initiation oj the proeutectoid ferrite reaction in the latter steels at the temperature at which partition began. The alloy content in ferrite at the a:y bondavy remained at constart lecels, shown experimentally to be significantly above those corresponding to eqiilib+iu??l, e'en at the longest reaction times investigated (ca 1o6sec). The partition and the TTT curve observations foere rationalized on the basis of the thermodynamic treatment developed in an accompany ing paper. and diffusional growth has been a major research objective of physical metallurgy since the latter part of the 19th century. The measurements made on the dif-fusivities of carbon and of substitutional alloying elements in austenite during the 1930's and 1940's seemed to provide a useful clue as to the nature of these mechanisms. These measurements showed that the diffu-sivity of carbon is several orders of magnitude higher than that of the alloying elements at a given tempera-

Jan 1, 1967

By Marius S. Darrow, William B. White, Rustum Roy

The PbS-PbTe systen has been studied by quench-ing and D.T.A. techniques f?om 400' to 1150°C. Runs were made in evacuated silica tubes so that all equilibria are at the vapor pressure of the system. Lattice parameters of the quenched salnples , measured by X-ray diffraction, show a complete crystalline-solution series existing over a narrow temperature range between approximately 805" and 871°C. An exsolution dome extends from a maximum of about 805"C (approximately 30 mole pct PbTe) to 1 and 96.5 pet PbTe at 400°C. A narrow melting region, deternined by D.T.A., extends form 918c (mp PbTe), The shapes of the liquides and solidus curves imply the existence of a minimum at 871°C at approximately 65 pct PbTe. THe exact composition of the minimum could not be established due to the very narrow two-phase region. At compositions containing less than 50 pet PbTe, liquidus temperatures begin to increase, while the solidus remains almost flat to about 15 mole pet PbTe before beginning to vise toward the mp of PbS (1075 C). LEAD sulfide and lead telluride are isostructural (NaC1 type) semiconductors whose electrical and optical properties have been extensively studied and used in recent years. If appreciable crystalline solution exists between these compounds, the variation of physical properties with composition could be of interest. The purpose of this investigation was to determine the extent, if any. of crystalline solution, and to obtain the phase diagram for the system. To the knowledge of the authors, only three studies of the system PbS-PbTe have been reported, and, in chronological order, each investigation found an increasing amount of crystalline solution. In 1956, Yamamoto reported finding no evidence of crystalline solution between the compounds. Sindeyeva and Godov-ikov,' in 1959, found very limited crystalline solution. but only under conditions of excess tellurium concentration. Finally Melevski s3 investigation in 1963 indicated that one solid phase exists in the region from PbS to 7 pct PbTe and from 82 pct PbTe to PbTe at 886'C, with an eutectic at 55 pct PbTe at that temperature. Detailed data on the solvus boundary were not given. EXPERIMENTAL EQUIPMENT AND MATERIALS Commercially produced PbTe and PbS powders were used as starting materials. Batches of specific mole percent composition were accurately weighed and mixed in a plastic bottle, in a shaker mill. An analy- sis of impurity content is given in Table I for pure PbS and PbTe and for two randomly selected batches after the powders were mixed. Individual samples, ranging in weight from 0.2 to 0.5 g, were sealed in evacuated silica tubes which had been thoroughly washed and rinsed with acetone and distilled water. Thus all data taken were at the pressure of the system. Subsolidus relations were studied down to 400°C by heating the samples in a vertical tube furnace for 24 hr. The sealed tubes were quenched in water with quench time from the hot zone not exceeding 1 sec. Temperatures were measured by a chromel-alumel thermocouple and controlled to 53°C for most runs. The number and composition of phases present were determined from powder X-ray diffraction patterns taken at room temperature on a Norelco diffractome-ter, using silicon as an external standard. Above 850°C quenching techniques were, in general, found to be unsatisfactory, and differential thermal analysis (D.T.A.) was used to determine melting relations. The evacuated tubes were recessed about 1 cm at one end to accommodate the differential thermocouple. Al203 was used as the reference material in a similar tube containing the other side of the differential couple. For temperature measurements, a separate thermocouple was placed in the recess of the tube containing the sample to be measured, thus providing an opportunity to obtain thermal, as well as differential, analysis. All thermocouples for these measurements were Pt-Pt 10 pct Rh. Temperature and differential curves were recorded separately on synchronized strip-chart recorders. Thermocouples and recording equipment were calibrated using NaCl and gold standards, using the melting points 801" and 1063 C, respectively, which span most of the temperature range of interest. Heating and cooling rates generally were from 4 to 7°C per min. It was found, in fact. that rates ranging from 1.5 to 25°C per min did not significantly change the data obtained.

Jan 1, 1967

By S. R. Goodman, Hsun Hu

The formation of secondary - recrystallization tex-tlires in cube-textured 18-8 stain less steel (Type 304) Ilas been studied at three temperatures. Prolonged annealing at 100°'C protluces a PredoninanGly (520) [OOZJ-type texture, which is related to the cube te.ture of the primary lnatrix by a rotation of approxivzately 22 deg around the [001] axis in the rolling direction. Annealing at 1200 or 1300°C facers the formation of the (123)[272/-type texture, which is related to the matrix texture by a [111] rotation of app.voxiniately 40 deg. These observations suggest that in the secondary recrystallization of cube-texlut-ed stainless steel an apparent actilation energy for growth is higher for grains related to the tncrtuix Og [111] rotations thun those reloted by [100] rotations. THE formation of secondary-recrystallization textures in cube-textured primary matrices of fcc metals has been studied widely by various investigators. For Fe-40 pct Ni alloys, Pawlek' and wassermann2 reported that the orientations of secondary grains were related to the cube texture by rotations of 30 and 38 deg around [001] in the rolling direction. However, Rathenau and custers3 found that, while in one Fe-48 pct Ni alloy, most of the secondary grains were oriented with respect to the cube-textured matrix by rotations around [001] of 26.5 deg, in another alloy of a different origin, the orientations of secondary grains were related to the cube texture by rotations of approximately 35 deg around a [lll] axis. Similar orientation relationships were also observed between the secondary grains and the cube-textured primary matrices of copper.4"a No attempt was made to differentiate these two types of orientation relationships; reorientation by either a [111] or a [100] rotation was considered to be equally favored. The present investigation consisted of a study of the secondary recrystallization textures in cube-textured stainless steel. It was noted that the secondary grains formed in stainless steel were considerably smaller than those of Fe-Ni alloys or copper. This offered the advantage that the secondary recrystallization texture could be determined by the texture-goniometer technique, and a more detailed study of the textural development during the course of secondary recrystallization could be made. The effect of annealing temperature on the formation of secondary-recrystallization textures was also investigated. MATERLAL AND METHOD It was shown earlier"-" that a strong cube texture can be obtained in 18-8 stainless steels by rolling at 800°C to produce the copper-type deformation texture, followed by annealing at 800" to 1000°C for recrystallization. To improve the cube texture for the present study, a commercial-grade 18-8 stainless steel (Type 304) was rolled at 800°C first to 5 mm (0.2 in.) thick plates. Three of these plates were then stacked and welded together along the edges into a sandwich assembly. After annealing at 900°C for 20 min: the assembly was finally rolled at 800'C to 90 pct reduction in thickness with reheats and end-for-end reversals after each pass. Only the central strip, which was reduced from 5.0 to 0.50 mm (0.7 in. to 0.020 in.) thick, was used. The chemical composition of the steel in weight percent was as follows: C, 0.06; Mn, 0.38: Cr, 18.71; Ni, 9.56: P, 0.011; S, 0.009; and Si, 0.39. The purpose of rolling the strip in a sandwich assembly was to prevent direct contact between the central strip and the rolls. It was observed earlier" that, when the strip was rolled at 800°C without being enclosed in a sandwich assembly, the cube texture obtained by subsequent annealing at 900" or 1000° C for recrystallization was largely confined to the central section of the strip, while most of the recrystallized grains formed in the surface section of the strip were not cube-textured. This was obviously due to the fact that the actual temperature at the strip surface during rolling, as a result of direct contact between the strip and the cold and massive rolls, was considerably lower than 800°C. By using a sandwich assembly for hot rolling, the cube texture obtained upon subsequent annealing for recrystallization was found to extend through the entire thickness of the strip. After rolling, the central strip was taken from the sandwich assembly. and cut into specimens. Prior to annealing. the specimens were etched to 0.25 mm (0.010 in.) thick. A tube furnace provided with a purified, dry argon atmosphere was used for annealing. Textures were determined by the reflection technique. using a Siemens automatic texture-goniometer and ZrOz-filtered MoKa radiation. With a time constant of 4 sec. the preferred orientation of the secondary grains could be measured satisfactorily by the integrated intensities. Both (111) and (200) reflections were measured, and corresponding pole figures were constructed according to the techniques described previously.10 The agreement between results deduced from these two reflections was excellent. RESULTS AND DISCUSSION Secondary-Recrystallization Texture due to Prolonged Annealing at 1000°C. Fig. 1 shows the primary-recrystallization texture of a specimen annealed at 1000°C for 30 min. A substantial improvement in both sharpness and intensity of the cube texture, owing to the present processing method, can be noted readily by comparing Fig. 1 with similar pole figures shown earlier in Refs. 9 and 11. Secondary recrystallization

Jan 1, 1967

By Merton C. Flemings, Harold D. Brody

Analyses that include diffusion of solute in the solid phase are formulated to describe solute redistribution in dendritic solidification of metallic alloys. The analyses are based on conditions that include negligible undercooling before nucleation of solid phases, negligible increase of solute in advance of the tips of growing dendrites, complete diffusion within the liquid over distances the order of dendrite spacings, and a plate-like dendrite morphology. The classical nonequilibrium freezing equation, Cs = kCo(I - fS)k-l accurately describes solute redistribution between dendrite arms for the solidification processes considered, provided diffusion in the solid is negligible. To account for the effect of diffusion in the solid, an analytic expression is given which is similar inform to the classical expression. 172 addition, a numerical-analysis procedure is etnployed to examine in more detail the effect of diffusion both during and after solidification. The analyses are intended for application to solidification of castings and ingots to describe a) final solute distribution after solidification and cooling to room temperature (microsegregation) and b) local fraction solid as a function of ternperatcre within the solidifying casting or ingol. SOLUTE redistribution in cellular and dendritic solidification has been discussed quantitatively in recent papers'-3 and in a series of earlier work.4-6 However, none of the analyses developed have permitted close correlation of theory with final solute distribution (microsegregation) observed in castings and ingots. In this paper, discussion is given of approximations which may reasonably be made in mathematical treatment of microsegregation, and analyses are presented based on these approximations. Numerical results are given for Al-Cu alloys. In a second paper the analyses will be compared with exeriment.7 CLASSICAL ANALYSIS The classical quantitative treatment of solute redistribution within a closed "volume element" has been derived repeatedly, for example by Gulliver,4 Scheil,' and Pfann.' This "classical nonequilibrium solidification equation" is written for constant partition ratio: where Cs = interface composition of the solid when the weight-fraction solid within the "volume element" is fs (weight fraction, wt pct); k = equilibrium partition ratio; Co = initial alloy composition within the volume element (weight fraction, wt pct). Assumptions of Eq. [11 are: 1) There is negligible undercooling before nuclea-tion, or from curvature or kinetic effects. 2) There is no mass flow in or out of the volume

Jan 1, 1967

Jan 1, 1967

Jan 1, 1968

By G. P. Conard, E. H. Rennhack

The generation of fibers composed of individual TiZn15 compound particles and their influence on crystallographic orientation in chill-cast, hot-rolled hypoentectic Zn-Ti alloys were explored. Metallo-graphic examination and X-ray diffraction data show that such fibers form a planar network after 50 pet reduction which eventually tends to suppress twinning at some critical reduction level (-90 pct) where the grain size approaches the interfiber, spacing. This leads to the development of a duplex-type projerred orientation through slip rotation consisting of an al-most ideal (0001)(2iiOj texture and a (0001) (1010) rotated component. Correlations between basal-plane rotation and secondary- creep rc11e sugg-est, however that prejerred orientation does not contribute in a major way to the creep resistance of these alloys. EFFORTS to improve the creep resistance of zinc through alloying without incurring a loss in fabricating properties have achieved only minor success with the exception of the very effective addition of titanium. Anderson, Boyle, and Ramsey,l for example, demonstrated that increasing the amount of thiselement from 0.05 to 0.23 wt pct produced a progressive, 45-fold increase in the inverse creep rate of hot-rolled

Jan 1, 1967

By C. J. McHargue, J. C. Ogle

Lightly deformed columbiun single crystals which contained only parallel hoins or purullel and intersecting trains were annealed at 1000' and 1600"C. No re-crystallizntion occurred in specimens hawing only parallel twins. Only noncoherent twin boundaries nzipated at 1000°C but both coherent and noncoherent ones moved al 1600°C. Recrystallization occurred within a few minutes at twin intersections at 1000°C. The orientation 01 the recrystallized grains differed front that of both the matrix and deformation twins, but could he derired by (110) and/or(112) rotations. ALTHOUGH twinning in metals has been extensively studied, there have been no definitive studies of the annealing behavior of crystals containing deformation twins. Some effects observed after annealing deformation twins have been summarized by Cahn1 and Hall2. Any or all of these phenomena are observed: 1) The twins may contract so that the sharp edges of the lens become blunted, and eventually the twin may disappear entirely. 2) The twins may balloon out at an edge, giving rise to a large grain having the same orientation as the twin. 3) The specimen may recrystallize; i.e., new grains are nucleated and grow at the expense of the twins and the crystal immediately adjoining the twin. Such grains have orientations which are not present before. Contraction has been observed in iron,3 titanium,3, 4 beryllium,5 zinc,8, 7 Fe-A1 alloy,' and uranium.9 Long anneals at high temperatures are required to have any appreciable effect in these metals and only thin twins are absorbed. Lens-shaped twins are absorbed from the edges: the thin, almost parallel-sided twins are usually punctured in several places and each piece contracts independently. Absorption is very gradual and no sudden cooperative jumps have been observed. The expansion of a twin into a larger grain of identical orientation is unusual, but such growth has been observed in iron,"'" zinc,6 and uranium." Crystals which have been deformed simultaneously by slip and twinning recrystallize first in the area adjacent to the twin. New grains appear faster where the twins intersect: but isolated twins, especially if thick, can also give rise to new grains. This type of recrystallization occurs in zinc.6, 7, 12, 13 and beryllium.14 Reed-Hill noted, in a single crystal of magnesium, the nucleation of a recrystallized grain at a twin intersection which had the same orientation as the second-order twin and which grew into the highly strained matrix.15 Short-time annealing has been reported to cause no change in the deformation twins in vanadium,16 columbium, 17, 18 tantalum,19 tungsten,'' and zinc.7 The purpose of this investigation was to note the effects of annealing on the coherent and noncoherent boundaries of deformation twins in columbium and to locate the nucleating sites for recrystallization. The orientation relationships, which the new recrystallized grains have with the parent crystal and the deformation twins, were also determined. EXPERIMENTAL PROCEDURE Single crystals of columbium were obtained by cutting large grains from electron-beam-melted buttons which contained 10 to 50 ppm C, 10 to 100 ppm O,, 1 to 10 ppm H2, and 10 to 15 ppm N2. The crystals were hand-ground and chemically polished until all grain boundaries were removed. The specimens were mounted in an epoxy resin and a face of each crystal was mechanically polished on a Syntron polisher using Linde A and then Linde B polishing compounds. After all faces were mechanically polished, the crystal was electrolytically polished to remove all distortion due to cutting and grinding. Laue photographs were taken of all faces of the crystals to determine the quality and orientation of each crystal. The crystals were compressed about 10 pct at -196 C in a specially constructed compression cage with an Instron tensile machine. Each crystal was separated from the top and bottom anvils by teflon films which acted as a lubricant. With the specimen crystal in position, the entire cage was cooled to -196°C by being submerged in a Dewar containing liquid nitrogen. The crystals were compressed at a rate of 0.02 in. per min and the load was recorded on a strip-chart recorder. After deformation the crystals were mechanically polished on 600-grit paper and Pellon cloth with Linde A and Linde B polishing compounds. The crystal faces were chemically polished and then etched. The twin planes were identified metallographically from an analysis of the twin traces on two surfaces. Annealing was carried out by placing each crystal in a columbium bucket made from the same electron-beam-melted material as the crystal itself and suspending the bucket by a tantalum wire in a quartz tube. After a vacuum of 10-7 Torr was attained, a furnace at 1000" or 1600 C was raised into position and the crystals held for various lengths of time. The crystals were repolished and etched after annealing to remove any surface contamination. Approximately 0.010 in. was removed during this process. The resulting surface was examined metallographically for microstructural changes due to annealing. A microbeam Laue camera mounted on a Hilger Micro-focus X-ray unit was used to determine the Orientstions of the recrystallized grains. This X-ray micro-beam camera had a 0.002-in.-diam collimator and incorporated the ideas of both and and chisWik21 and Cahn.22

Jan 1, 1967

By K. J. Anusavice, R. T. DeHoff, A. G. Guy, T. B. Lindemer

As one oi the approacizes to understanding multicorn-ponent dimsion, an expevinzental sturly is being jnade of tracer diffusion in the copper corner of the CLI-Ni-Zn syste?n, out to 30 at. pct each of nickel and zinc, and in the 150°C range oJ temperature just below tlze solidts te?rlperature. The reslts obtained using the Znm isotope are reported heve, while studies with nickel and copper isotopes are planned for a future paper. The fifteen alloys investigated were melted in sealed wear lubes, sroaged, homogenized, and then analyzed, using the conventional isotope-plating plus lathe- sectiorzing teclzniqlte. The data obtaiued show that the difJusion coeflcient of the zinc isotope increases titlz increase in zinc content, and decreases t'itlz incease in nickel content. The correlation xith solidus temperature is particularly strong. Diffirsiui-ties ranged fro u sq cm per sec nt tlze Iiigh-zinc, low-nickel compositions. The activation energy /or tracer diffusion ravied j.or 31.000 to 54,000 calper mole. It is now generally recognized that diffusion data and theories are needed for multicomponent systems, where extensive practical developments and even some theoretical studies have already been made. For example, much recent work on precipitation from solid solution has been concerned with ternary solid solutions such as A-M-Z' while Zener relaxation has been studied on Au-Ag-Zn alloys,' although adequate diffusion data are available for neither of these systems. Actually, the only ternary systems for which systematic diffusion studies have been begun, in addi- tion to the one reported here, are CO-i-cr3 and Cu-A-Au. Since the theory of multicomponent diffusion is still in the stage of active development5 it is important to distinguish the various kinds of diffusion data that can be determined. An oversimplified approach, widely used prior to 1950, was to determine the influence of a third element, such as nickel, on the diffusion behavior of a binary alloy, such as CU-Z. Later it was recognized7 that four diffusion coefficients can be used to describe ordinary interdiffusion in a ternary system, while as many as six coefficients may be required to include the Kirkendall effect. It is likely that the number of independent coefficients will be shown to be less than four and six, respectively, through the application of the thermodynamics of irreversible processes.5 The simplest type of diffusion in a multicomponent system is tracer diffusion, since each component is characterized by its own tracer-diffusion coefficient in an alloy of a given composition. Thus, in a ternary alloy there are three tracer-diffusion coefficients, each a function of composition and temperature. The present research program is a study of tracer diffusion in the copper corner of the Cu-Ni-Zn system out to 30 at. pct each of Ni and Zn in a 150°C range of temperature just below the solidus temperature. The

Jan 1, 1967

By C. E. Coleman, D. Hardie, A. E. Wraith

A photoguaplric method of measuring crack velocities has been applied to an examilzation of- the effect of hydrogen on the impact properties of zirconium. Results indicate that the crack in hydrided zirconit travels at about 26 m per sec whereas that in the uacuum -annealed is dependent on the speed of the hammer. RECENT work on the effect of hydrogen on zirconium reveals that when hydrided zirconium is tested in slow bending the crack producing failure can be unstable. The mode of fracture seems to involve the crack linking up broken hydrides by a ductile mechanism in the zirconium matrix.2" In order to compare the fracture of zirconium with that of other metals which show unstable crack propagation, notably steel, the rate of the crack spread must be known. As the methods previously used for measuring crack growth are either unsuitable for the present work5-'' or very costly," a simple technique has been devised in which the maximum crack velocity is derived from a series of crack position-time measurements. EXPERIMENTAL PROCEDURE The experimental arrangement is shown schematically in Fig. 1. The flash unit12 was triggered when the Charpy hammer touched the specimen and the 6-psec flash of the lamp delayed by a preselected time interval in the range 100psec to 10 msec. The camera was left on open shutter during the test. From direct measurement on a calibrated photographic print, Fig. 2, the position of the crack and the specimen was found at a known time after impact and, from a series of such tests using an appropriate range of flash-delay times, the crack velocity was estimated. Preliminary experiments were carried out on mild steel above and below its transition temperature. Vacuum-annealed zirconium, and zirconium hydrided to 100 ppm H were then tested at 20" and 150°C. For comparison, Zr-2.6 pct Nb alloy (in the 0 + transformed /3 condition), vacuum-annealed or hydrided to 100 ppm H, was tested at 20 C. The chemical analyses of these materials are given in Table I. For the high-temperature tests a fine chromel-alumel thermocouple was spot-welded onto each specimen close to the notch. The test piece was heated up to 200°C to allow enough time for preparing the apparatus while the specimen cooled to the testing tem- perature. It was assumed that the specimen cooled uniformly. The accuracy of the flash-delay time was better than i2 pct i 5 psec. The crack length was taken as its maximum distance traveled normal to the length axis of the specimen. Errors in these measurements arise as a result of the uncertainty in the location of the crack tip and the difficulty in defining the exact position of the crack starting point. The latter was due to the bonding and large amounts of deformation at the hammer contact point, especially in the vacuum-annealed specimens tested at 150°C. The maximum error in the measurements was however estimated to be about 5 pct. DISCUSSION OF RESULTS From the trial experiments using mild steel above its transition temperature it can be seen from the plot of crack length against time after impact, Fig. 3. that a reasonable estimate of the maximum crack velocity at the surface of the specimen may be made. Other features of note are the initiation time before the crack is first seen and the slowing down period

Jan 1, 1967

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 D. W. G. White

The surface tension of zinc has been determined by the sessile-drop method in a progvam emphaszzing detailed experimental care. The surface tension oj. the pure metal was measured over a range of ternperature from the melting point (419.6"C) to 540°C. At the melting point, the suvface tension of zinc was found to be: 1) 99.99+ pct Zn - 757.0 5 dynes per cm 2) 99.999+ pct Zn - 761.0 5 dynes per CI 3) 99.9999 pct Zn - 76'7.5 5 dynes pev cna From experiments carried out in a closed, isothermal cell, the temperatuve coejyicient of the surface tension (6y/6T)p, , of zinc xas found not to be negative but to be postiue. A positive tenzperatre coefficient indicates a greater depee of order in the surface than in the body of the lquid. Houlezer, by delibevately inducing continuous zaporization, a temperature coefficient of su)face tension with a negative slope can be produced. The work reported herein was undertaken as part of a larger program of fundamental research on the properties of molten zinc and zinc alloys. This program grew out of a continuing interest at the Mines Branch in the behavior of liquid metals in the foundry and of a desire on the part of the zinc industry for reliable basic data. The work was originally begun in cooperation with the Consolidated Mining and Smelting Co. Ltd., Trail, B.C., and was subsequently continued from 1960 to date in association with the Canadian Zinc and Lead Research Committee and the International Lead and Zinc Research Organization. Although the surface tension of liquid zinc has of course, been measured before, as Table I and Fig. 1 demonstrate, there is not good agreement among the existing values. Such disparities arise because sources of experimental error are insufficiently controlled. This situation places the reader in doubt. One result may be correct within narrow limits—even fortuitously—yet, because there is not agreement between several values, none can be accepted with conviction and all become suspect. It seemed, therefore, in the circumstances, that there was room for further work embodying considerable emphasis on experimental care in order that, within a small margin of error, an accurate value might be obtained. It was in this spirit that the work was undertaken. METHOD The sessile-drop method -as adopted for this work. In this method, when applied to liquid metals at elevated temperatures, the outline of the meridional section through a drop resting freely on a horizontal surface is recorded photographically. Certain parameters

Jan 1, 1967

By T. F. Archbold, P. G. McCormick

Silica fiber 11arkevs and hardness irzdentatiozs have been used to study the thermal diffusion of racancies in zinc placed in temperature gradients of 460o and 706oK per Cm All markers mored toward the higher temperatures, and the data show that the heat of trarlsport Q is greater than the eizthalpy of z,acancj3 forrjalion E by an amount equal to 3.5 kcal per mole. These results ore not in agreement with those obtained in either of the two previous studies with zinc. The problem is discussed in terms of experimental differences and racancy source and sink efficiencies. THE general interest in thermal-diffusion phenomena over the past several years has prompted a number of marker movement studies using pure metals. In order to understand better the relationships between thermal and mass flow, a general goal of the experiments has been to obtain values for the net enthalpies carried by the diffusing atoms. For self-diffusion by means of the vacancy mechanism, the determination of relative marker positions before and after an anneal in a temperature gradient permits a calculation of a value for (Q - Ef). Q is the transferred enthalpy, and Ef is the enthalpy of vacancy formation in the metal being investigated. The initial experimental study of thermal diffusion in pure metals was accomplished by Shewmon who found essentially no movement of surface-hardness indentation markers in single and bicrystals of zinc held for 20 days in a temperature gradient of 310°C per

Jan 1, 1967

By A. C. Losekamp, J. B. Conway

Thermal-expansion data for, tungsten, rhenium, tantalum, .molybdenum, niobium, W-25 pct Re, Ta-10 pct W, ant1 Mo-50 pct Re are presented covering the range from room tempature to 2500°C. In these measureMents, made in a resistively heated tungsten tube furnace operating in a helium atmosphere, data for rod and sheet specimens were found to be identical; in addition, arc-cast and sintered tungsten were found to yield essentially identical results. Optical rneasurenlents of thermal expansion .made in any atmosphere other- than vacuum are subject to a refraction error which can be quite substantial. Specimens tested in helium appear shorter than when tested in racuum and hence a special correction factor must be applied to the helium data in order to obtain accurate results. WHILE it is true that linear thermal-expansion data for many of the refractory metals have been measured to very high temperatures, it is also true that except in a few instances the data from various investigators are not in good agreement. This is particularly evident in the case of tantalum and niobium although some tungsten data have been reported which differ by as much as 40 pct from the data of other investigators. Due to the sensitivity of both tantalum and niobium with respect to impurity absorption during exposure to high temperatures, it is probable that this single factor accounts for the majority of the discrepancies in the thermal-expansion data for these metals. However, this same factor can probably not be employed to explain the existing differences in the tungsten data. In all probability, these are due to errors in the measurement technique, to material composition variations, or to changes which take place in the material during the heating process (e.g., additional densifica-tion resulting from heating a sintered specimen above the original sintering temperature). In view of the discrepancies which exist in the linear expansion data reported for many of the refractory metals, the current study was initiated in an attempt to resolve such differences. Also, no high-temperature linear thermal-expansion data were found to be available for several refractory metals. Providing such data was another objective of the current investigation. MATERIALS In this study test specimens were employed in either rod or sheet form and in several instances both arc-cast and sintered material were employed. Material compositions are presented in Table I. Helium gas was fed to the furnace at a rate of about 0.5 SCFH and no special purification procedures were employed. However, the helium contained less than 50

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 R. G. Garlick, M. Garfinkle

It was observed for several bcc metal crystals that the Knoop hardness anisotropy was dependent essentially on the direction of the lung axis of the indentor alone and not on the plane of indentation. The generality of this observation was tested for an fcc md an hcp metal and an ionic crystal. For cubic crystals, this observation was valid; for the hcp structure, however, the planes of indentation did have an effect on the hardness anisotropy, although this was not nearly as significant as the direction of indentation. Because the direction of indentation is the only significant crystal-lographic parameter necessary to describe the hardness anisotropy, it is possible to represent the anisotropy of single crystals on the standard stereographic triangle. THE commonly observed1, 2 periodic variation of indentation hardness with crystallographic direction on the high-symmetry planes of various single crystals has been inadequately related to the physical or mechanical properties of the crystals examined. In fact, the hardness anisotropy curves for the various planes of a particular metal crystal, as is illustrated in Fig. 1, are uncorrelated and appear in the literature3, 4 as unrelated observations. Attempts to correlate hardness anisotropy curves with specific physical properties can be generally divided into either mechanistic or nonmechanistic approaches. A nonmechanistic approach would be to devise a mathematical expression that could describe the various hardness anisotropy curves. Such a relation could then be compared with the known anisotropy of various physical properties to determine which contribute to the observed hardness anisotropy. No such mathematical expression has been found in the literature.

Jan 1, 1969

By R. Fawley, M. A. Quader, R. A. Dodd

Stacking fault energies and annealing twin frequencies have been measured for austenitic stainless steels having a) constant 20 wt pct Cr and varying nickel contents, and b) constant 20 wt pct Ni and varying chromium contents. The effect of nitrogen has also been studied and, to a lesser extent, so has the effect of carbon. All measured stacking fault energies plot linearly against the corresponding annealing twin frequencies, suggesting that, for constant prior deformation and grain size, twinning frequency can be used to estimate stacking fault energy. Compositions low in nickel possess the lowest fault energy, while the maximum fault energy within the investigated composition range occurs mound 20 pct Cr-20 pct Ni. Nitrogen has practically no effect on stacking fault energy when increased from 0.005 to 0.05 wt pct, although Planar dislocation glide is associated with higher nitrogen contents; this may be a short-range order effect. Carbon may raise the stacking fault energy a little, and causes pronounced dislocation tangling in deformed alloys. The basically different dislocation structures promoted by nitrogen and carbon, respectively, are not associated with large variations in stacking fault energy, and the reason for the difference remains unknown. INTEREST in the dislocation configurations developed in plastically deformed alloys arises principally from a desire for an understanding of mechanisms of plastic deformation and fracture. Comparatively little basic work has been concerned with austenitic stainless steels, although considerable interest has developed in the fundamental aspects of deformation of these alloys since the suggestion that those compositions deforming essentially by planar glide are particularly prone to transgranular stress corrosion cracking.' Certain facts are well-established. An 18 Cr-8 Ni steel (type 304) has a low stacking fault energy which is increased by higher nickel contents, and the structure of these steels when moderately plastically deformed changes concomitantly from planar to less planar to distinctly tangled dislocation configurations. These changes are thought to relate to changes in stacking fault energy, and considerable effort has been expended in measuring stacking fault energies of austenitic stainless steels through the determination of node curvatures2"4 even though the method has limitations due to formula approximations,5 an upper limit of measurement of 50 erg cm-2 at the most,5 and the necessity of an extremely meticulous experimental technique. Therefore, it is not surprising that only qualitative agreement between different investigators is generally to be found.'-' At high energies where node radius measurements are inappropriate, some use has been made of annealing twin frequencies to estimate relative stacking fault energies, although a recent critical evaluation of the method suggests that it should be used cautionsly with due regard to effects of grain size and prior deformation.6 Finally, there is a question as to whether the structures of some deformed steels are due to ordering effects. In particular, the role of nitrogen in promoting planar dislocation motion has been suggested to be due to ordering,' but similar suggestions have been made for steels having low interstitial contents.4 EXPERIMENTAL Small ingots of austenitic stainless steels (-50 g) were prepared from components exceeding 99.99 pct purity, the nickel and chromium being Johnson Matthey "Specpure" metals. Carbon was added as pure graphite, and nitrogen as CrN. The components were accurately weighed, and it was assumed that the final composition was the same as the nominal composition

Jan 1, 1969