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By F. G. Jones, R. D. Pehlke, H. E. Gardner

The solubility of nitrogen in liquid Fe-18 pct Cr-8 pct Ni-0. 7 to 2.3 pct A1 alloys has been measured up to the solubility limit for the formation of aluminum nitride in the temperature range 1600° to 1700°C uszng the Sieverts' method. The solubility of nitrogen in 18-8 stainless steel increases with increasing aluminum content. Based on a nitride composition, AlN, the standard free energy of formation of aluminum nitride from the elements dissolved in liquid 18-8 stainless-steel alloys has been determined to be: ?G° = -42,500 + 20. IT in the range from 1600° to 1700° C. EVANS and pehlke1 have measured the equilibrium conditions for the formation of aluminum nitride, AlN, in liquid Fe-A1 alloys. The present study extends that work to the more complex solvent, liquid 18 pct Cr-8 pct Ni (18-8) stainless steel. Recent work by Small and pehlke2 has dealt with the effect of fourth-element additions on the solubility of nitrogen in 18-8 base alloys. They found the effect of aluminum additions, up to 0.74 pct, on the solubility of nitrogen to be small. The present study covered the range from 0.74 to 2.28 pct aluminum, and by extending the composition range may be used to better define the effect of aluminum on the nitrogen solubility in these alloys. EXPERIMENTAL PROCEDURE The Sieverts' method was used to measure the equilibrium solubility of nitrogen gas in liquid 18-8 stainless steel alloys containing 0.74, 1.49, 1.93, and 2.28 pct Al. The solubility was measured as a function of the nitrogen gas pressure at temperatures of 1600°, 1650°, and 1700°C. The apparatus used is the same as described by Small and Pehlke.2 The 100-g melts were made from Ferrovac-E high-purity iron, Crucible Steel Co.; 99.95 pct Cr, Union Carbide Corp.; 99.9 pct Ni, International Nickel Co.; and 99.99+ pct Al, Aluminum Co. of America. The aluminum was charged at the bottom of the crucible, surrounded by nickel and iron. The chromium was packed into the interstices to minimize vapor transport of the aluminum during initial melting. The hot volume of the system, measured for each melt with argon, ranged from 45 to 55 standard cu cm with a temperature coefficient of —8 x 10-3 cu cm per °C. The melt temperature was measured with a Leeds and Northrup disappearing-filament type optical pyrometer sighted vertically downward on the center of the melt surface. The temperature calibration of the system by Small and pehlke2 was assumed. Two problems are involved in determining the solubility product of a solid, metal nitride phase in liquid iron alloys. These are: 1) establishing the point of departure from Henrian behavior at the solubility limit of the metal nitride phase; and 2) determining the composition of the solid nitride which is precipitated. Determination of the solubility product of AlN was made by admitting small amounts of nitrogen into the reaction bulb until the deviation from Sieverts' law was clearly evident in the form of a pressure halt. To obtain the solubility product at several temperatures during one run the following procedure was used: 1) add increments of nitrogen to determine the Sieverts' law line at the lowest desired temperature; 2) continue to add nitrogen to precipitate a small amount of the nitride phase; 3) increase the melt temperature 50°C to dissolve the precipitated nitride; 4) repeat step 2 until either a nitride formed or the system reached ambient pressure; if a nitride formed at 1650°C, the sequence was repeated at 1700°C. The composition of the precipitated phase was checked by an X-ray diffraction pattern obtained from powder scraped from the surface of the solidified 1.93 pct A1 melt. RESULTS AND DISCUSSlON Solubility Measurements. Fig. 1 is a typical nitrogen-absorption curve obtained from measurements on a 1.93 pct A1 alloy. Since the initial absorption of nitrogen follows Sieverts' law the nitrogen solubility is plotted as a function of the square root of the pressure of nitrogen gas in the reaction bulb. The results of the solubility measurements for all alloys studied are summarized in Table I. The slope of the Sieverts' law line for each alloy was determined. Since this is also the solubility of nitrogen at 1 atm pressure of nitrogen gas, the latter designation is used for the data. It should be noted. however, that in most cases the value lies above the solubility limit for AlN. Fig. 2 shows the effect of aluminum on the solubility of nitrogen at this reference pressure and as a function of melt temperature. The solid portions of the lines represent attainable solutions; the dashed regions lie above the limit for precipitation of AlN.

Jan 1, 1969

By R. L. Bell, T. G. Langdon

A technique was developed- for determining the grain strain, and hence the grain boundary sliding contribution, occurring during the high- temperature creep of a magnesium alloy, from the distortion of a grid photographically printed on the specimen surface. The results were compared with those obtained from measurements of grain shape, both at the surface and interrwlly, and it was concluded that the grain shape technique may substantially underestimate the grain strain and overestimate the sliding contribution due to the tendency for migration to spheroidize the grains. ALTHOUGH a considerable volume of work has been published on the role of grain boundary sliding in high-temperature creep, many of the estimates of Egb (the contribution of grain boundary sliding to the total strain) have been in error due to the use of incorrect formulas or inadequate averaging procedures.' One of the most easy and convenient measurements from which to compute Egb is that of v, the step normal to the surface where a grain boundary is incident. Unfortunately, this parameter is also the one associated with the treatest number of pitfalls. Values of v have been used to calculate Egb from the equation: egb =knrVr [1] where k is a geometrical averaging factor, n is the number of grains per unit length before deformation, v is the average value of v, and the subscript ,r denotes the procedure of averaging along a number of randomly directed lines. If the dependence of sliding on stress were assumed, it would be possible, in principle, to calculate k from the known distribution of angles between boundaries and the surface. This in itself is difficult because the distribution depends on the history of the surface,' but the problem is even further complicated by the fact that v depends on other factors such as the unbalanced pressure from subsurface grains.3 However, the great simplicity of the measurement procedure for v makes it highly desirable that this problem of k determination should be overcome. In the present experiments, this was achieved by the use of an indirect empirical method in which the grain strain, eg, at the surface was determined by the use of a photographically printed grid. The assumption here is that the total strain, et, is simply the sum of that due to grain boundary sliding, egb, and that due to slip or other processes within the grains, eg. SO that: Et = Eg + Egb [2] Thus k is given by: In practice, it is customary to indicate the importance of sliding by expressing it as a percentage of the total creep strain; this quantity is termed y (= 100Egb/Et). The determination of Eg from a printed grid within the grains avoids the difficulties due to boundary migration which should be considered when the grain strain is calculated from measurements of the average grain shape before and after deformation. As first pointed out by Rachinger,4,5 however, this latter technique has the particular advantage that it can also be applied in the interior of a polycrystal. Recently, several workers have produced evidence on a variety of materials6-'' to support the observation, first made by Rachinger on aluminum,4,5 that 7 can be very high, 70 to 100 pct, in the interior, even when the surface value, determined from boundary offsets, is very much lower.10'11 Although there have been criticisms both of the shortcomings of the grain shape technique'' and of the different procedures used to determine y at the surface,' it seemed important to check whether measurements of sliding by grain shape gave values of y which were truly representative of the material. In the present experiments, grain shape measurements were therefore made both at the surface and in the interior for comparison with one another and with the independent measurements of grain strain using the surface grid technique. EXPERIMENTAL TECHNIQUES The material used in this investigation was Magnox AL80, a Mg-0.78 wt pct A1 alloy supplied by Magnesium Elektron Ltd., Manchester. Tensile specimens, about 7 cm in length, were prepared from a 1.27-cm-diam rod, with two parallel longitudinal flat faces each approximately 3 cm in length. The specimens were annealed for 2 hr in an oxygen-free capsule, at temperatures in the range 430° to 540°C, to give varying grain sizes, and, prior to testing, the grain size of each was carefully determined using the linear intercept method. This revealed that the grains were elongated -0.5 to 5 pct in the longitudinal direction. Testing was carried out in Dennison Model T47E machines under constant load at temperatures in the range 150" to 300°C. At temperatures of 200°C and below, tests were conducted in air with the polished flat faces coated with a thin film of silicone oil to prevent oxidation; at higher temperatures, an argon atmosphere was used. To determine v,, each test was interrupted at regular increments of strain and the specimen removed from the machine. At the lower strains, when v, was less than about 1 pm, measurements were taken on a Zeiss Linnik interference microscope;

Jan 1, 1969

By Erwin Pink

It has been pointed out in a previous publication' that, for a given strain rate, serrated yielding can be observed only at certain test temperatures. Fig. 1 shows the results obtained for polycrystalline and re-crystallized tantalum, Va group in the periodic table of elements, where serrations in the course of deformation match the decrease of total elongation. However, there was no evidence of repeated yielding when testing molybdenum or tungsten, VIa group, at similar conditions, i.e., annealed and air-cooled samples (serrations have been found in quenched tungsten2). The reason for the observed serrations in the stress-strain curve are dissolved impurities on interstitial sites of the lattice. Of importance is the concentration of oxygen, carbon, and nitrogen, which are in random solution. Two methods to calculate the limiting concentrations for serrated yielding have been evaluated and applied with more or less success in estimating the role of carbon and nitrogen in mild steel.3 J. Friedel4 has given two equations, which determine the upper and lower strain rates i for the appearance of serrations at a certain test temperature: W denotes the binding energy of the interstitial atom, -1 ev for refractory metals;5 e' the portion of continuous strain in the discontinuous stress-strain curve, measured as -3x10-3; b the Burgers vector, c the concentration, see Table 11, in atom fractions; p the dislocation density, -2 X l09 per cm2 at an average stress ?, -15 kp per mm2 at medium strain. k stands for the Boltzmann constant, T for the absolute temperature, and D for the diffusion coefficient. Table I. Eq. [1], for a given strain rate, determines the minimum temperature, and [2] the maximum temperature, below or above which no "dynamic strain-aging" can occur. According to the calculation, which uses the given quantities, serrations should only be observed within the cross-hatched temperature regions in Fig. 1, and this is in good agreement with the experiment. The effect of varying impurity concentrations is indicated schematically in Fig. 2: only Eq. [I] is affected. Setting Eq. [I] equal to [2], one can calculate the limiting concentration cmin which first causes serrations. The second method uses the aging condition by Cottrell and Bilby6,7 \£i/ \ n. a / where n(t) is the number of impurity atoms, which segregate at a dislocation line of 1 cm length after the time t (t in our case is the time between "repeated yield drops" in the serrated curve, or, the time until the above mentioned strain E' is obtained, i.e., -1 sec for medium intensity or serrations). no is the number of impurity atoms in 1 cm3 and A = Qb4ep[(1 + v)/(l - v)], derived from equations given in Ref. 7. p is the shear modulus, 18,800 kp per mm2 for tantalum, 12,200 for molybdenum, AE the tetragonal distortion caused by interstitial impurities in a bcc lattice (approximately 0.4 for both tantalum and molybdenum) and v Poisson's ratio (0.35 for tantalum, 0.30 for molybdenum). From Eq. [3], combined with the condition for a pronounced yield drop as formulated by cottrel16 (at least one impurity atom segregated at the unit length of a dislocation), again a no min, and hence the concentration Cmin can be calculated.

Jan 1, 1970

By O. N. Carlson, D. G. Alexander

THE hardness anisotropy of metals and alloys has been of increasing interest in recent years but silicon ferrite,1 niobium,2 and tungsten3,4 are the only bcc metals about which this type of information has been reported. This investigation was carried out on vanadium and chromium single crystals in an effort to determine to what degree the hardness variations observed in these metals are due to orientation effects and to compare their behavior with other bcc metals. In earlier work the authors had observed a small angular dependence in the Diamond Pyramid Hardness of single crystalline vanadium on the (100) plane but no anisotropic effects were noted on either the (110) or (111) planes. At the suggestion of R. G. wheeler5 it was decided to investigate this effect in greater detail using the more asymmetric Knoop indentor. The vanadium metal used in the study was prepared by the aluminothermic reduction of V2O5 followed by electron beam melting.6 The principal analyzed impurities were 230 ppm C, 230 ppm O, 65 ppm N, 90 pprn Al, Cr not detected, 50 ppm Fe, 60 ppm Ni, and 200 ppm Si. The chromium was an iodide-refined product obtained from the Chromalloy Corporation. Analysis of this material showed the following amounts of impurities present: 10 ppm C, 9 ppm O, 2 ppm N, 0.4 ppm H, 3 ppm Al, 2 ppm Ca, 2 ppm Cu, 20 ppm Fe, 1 ppm Mg, 0.3 ppm Mn, 1 ppm Mo, 3 ppm Ni, 10 ppm Si, and 1 ppm V. Single crystals of both metals about 1 cm in diam and 10 cm in length were grown by an arc-zone melt- ing technique.7 The chromium crystal was annealed at 1600°C for 6 hr in a purified argon atmosphere to remove any strains or inhomogeneities, but the vanadium was tested in the as-grown condition. The crystals were oriented by the Laue back-reflection method and then sectioned with a spark cutter into individual specimens with a (loo), (110), or (111) plane parallel to the crystal surface. They were mounted in Lucite and carefully ground to a flat surface. The vanadium specimens were then electropolished in a 6 pct perchloric acid-methanol mixture while the chromium specimens were mechanically polished on a Syntron vibratory polisher using an alumina abrasive. The orientation of each crystal was then rechecked by the back-reflection X-ray method. All of them were found to lie within 2 deg of the desired orientation with the exception of the (110)-Oriented chromium crystal which was within 4 deg. Microhardness impressions were taken at 10 deg intervals from the common (110) direction by rotating the crystal in the plane of the crystal surface. A Knoop indentor was used with a 400-g load on the vanadium crystals and an 800-g load on the chromium. The hardness values are averages of 6 impressions and standard deviations were calculated for each set of data. The values reported for the (111) plane of vanadium are based on from 10 to 15 measurements for each point. The microhardness results for vanadium and chromium are plotted as a function of the angular rotation of the long axis of a Knoop indentor from the (110)

Jan 1, 1970

By S. S. Lisnyak, B. D. Lichter

An important question in the study of the "hot corrosion" phenomenon (i.e., accelerated oxidation of Ni-Cr-base and Co-Cr-base "superalloys" in the presence of sulfur) is the condition of formation and physico-chemical properties of different sulfides in the system Ni-Co-Cr-S. seyboltl has observed the presence of ((chromium-rich" sulfides of compositions M3S4, and M2S3 in the scales of superalloys after hot corrosion; however, as he points out, much confusion exists as to the identity of sulfides found on Ni-Cr and Co-Cr alloys. According to the literature,&apos; ternary sulfides, e.g., NiCr2S4, (monoclinic structure) and CoCr2S4 (spinel structure) exist in these systems. Therefore, it is likely that these compounds are found in the scale of alloys undergoing hot corrosion. At present this possibility has not been discussed in the literature. Accordingly, we have begun investigation on the properties of ternary sulfides and their mutual interaction. The magnetic and electrical properties of pure NiCr2S4 and pure CoCr2S2 have been previously determined."-&apos; In the present work we have studied the interaction between these sulfides at high temperatures by means of X-ray diffraction and magnetic susceptibility. The measurements were carried out at room temperature after appropriate thermai treatment of samples at high temperatures. For alloys containing the three elements nickel, chromium, and cobalt this interaction may be of importance in the study of the hot corrosion phenomenon. The compounds NiCr2S4 and CoCr2S4 were prepared from stoichiometric amounts of the elements and CoS in the case of CoCr2S4. Samples were mixed and sealed in evacuated silica tubes, slowly heated to 900&apos; to 100O°C, and held at temperature for a total of 120 hr (NiCr2S4) or 80 hr (CoCr2S4) with intermediate re-grinding~. X-ray diffraction showed a pure spinel structure for CoCr2S4 and a monoclinic structure for NiCr2S4. Samples of mixtures of the two ternary sulfides were prepared with different compositions, see Table I. Samples were heated for a total of 80 hr at 900&apos;C in evacuated silica tubes, with one intermediate regrind-ing. The capsules were slow-cooled to room temperature in the furnace. Samples for X-ray diffraction were prepared by placing powder on a glass slide with vaseline. Dif- fractometer traces were obtained on a G.E. XRD-5 diffractometer using a chromium tube and vanadium filter (40 kv and 31 ma). The size of the spinel unit cell was determined from the eight highest angle peaks (80 deg < 2b < 160 deg). Calculated lattice parameters were plotted vs cos B . ctn 0 and extrapolated to 6 = 90 deg. Measurements of the magnetic susceptibility were carried out at room temperature using the Faraday method in a magnetic field of 3000 G and using a Cahn RG automatic microbalance. The system was calibrated from the well-established susceptibilities of platinum and palladium: (Xpt = 0.968 x 10-6 g-1 and Xpd 7 5.04 x 10~6 g-1). The weight of samples were approximately 0.200 g. X-ray diffraction patterns for unsintered mixtures showed Bragg peaks from both the spinel (CoCr2S4) and monoclinic (NiCr2S4) structures. After sintering no monoclinic peaks were observed in samples containing up to 40 mol pct NiCr2S4. However, the spinel peaks were displaced to higher angles with increasing

Jan 1, 1970

By P. Niessen, S. J. Bercovici

RECENTLY Aust et al.&apos; proposed a model of non-equilibrium grain boundary segregation based on a vacancy gradient induced uphill diffusion process of solute to grain boundaries. According to their proposal, solute atoms which are attracted to vacancies would, during the cooling of a sample, migrate with vacancies toward grain boundaries (vacancy sinks) and thereby enhance the solute concentration in boundary regions. For solute atoms which are not attracted to vacancies no such boundary solute enrichment would be expected. These concepts were given experimental support by boundary and bulk mi-crohardness measurements of various thermally treated dilute zinc and lead alloys and also doped aluminum oxide. The underlying assumption in their work was that solute enrichment in boundary regions is indicated by higher microhardness values. From thermodynamic considerations1&apos;2 it appears that the solid-liquid solute distribution coefficient (K), defined as the concentration of solute in the solid to the concentration of solute in the liquid at equilibrium, indicates whether attractive or repulsive forces exist between vacancies and solute atoms. K < 1 indicates a solute-vacancy attractions, K > 1 indicates no, or a repulsive, vacancy-solute interaction. This note is to report on observations of different grain boundary etching phenomena in high purity zinc alloys. These phenomena appear to depend on whether a K < 1 or K > 1 solute is present. In experiments designed to measure directly the solute enrichment in grain boundary regions, samples of zone refined zinc with 0.1 at. pct solute additions were cooled from 380°C at a rate of 3°C per min. A surface layer of approximately 50 was then removed from the samples by chemical polishing. The samples&apos; surfaces were then protected by a chromating treatment such that in a subsequent etch only grain boundary regions were dissolved. The dissolved regions were approximately semicircular troughs, 10 µ in width. The grain boundaries were usually in the middle, i.e., at the bottom, of this trough. For zinc containing the K < 1 solutes cadmium and aluminum, the grain boundary was always indicated by a ridge as shown in Fig. 1. For pure zinc, and zinc containing the K > 1 solutes copper and gold, a groove at the bottom of the trough indicated the boundary position, Fig. 2., To test if these different grain boundary etching behaviors were possibly connected with the segregation process discussed above, the Zn-Cd alloy was again heated to 380°C and quenched into brine. After surface protection and etching it was found that this specimen no longer exhibited the grain boundary ridges but rather grain boundary grooves as shown in Fig. 2. It would appear, therefore, that the boundary ridge is a consequence of a process occurring during the slow cooling of the samples. From absorption spectrophotometric analysis it was found that for slowly cooled samples containing K < 1 solutes, the solute/zinc ratios of the material from the boundary trough were consistently considerably higher than the solute/zinc ratios of the bulk alloys. This boundary region solute enrichment was not observed in quenched samples. It is concluded therefore, that the boundary ridge shown in Fig. 1 is directly or indirectly connected with nonequilibrium solute segregation.

Jan 1, 1970

By R. G. Aspden, D. A. Colling

THE {120}(001) texture has been reported in near 50 pct Ni-Fe alloys <0.004 in. thick1,2 and in copper 0.014 in. thick.3 This texture is one of two types of secondary recrystallization textures observed to replace a cube texture matrix and is desirable in Fe-Ni alloys because of its unique magnetic characteristics.1,2 However, the conditions for and mechanism of the {120}(001) formation are not well understood.3 During an investigation of the influence of alloying elements on the magnetic characteristics of 49 pct Ni-Fe alloys with a sheet thickness of 0.014 in., we have observed the growth of {120}(001) secondaries when strong deoxidizers such as aluminum and calcium were present. It is believed that this observation in unique and provides additional insight with regard to the mechanism for {120}(001) texture formation. Three alloys were prepared with electrolytic iron and nickel and contained a nominal 49 wt pct Ni. Alloy A was a straight binary Fe-Ni alloy, whereas intentional additions of 0.013 wt pct Ca to alloy B and of 0.59 wt pct A1 to alloy C were made. Ingots were forged at 1100 C, hot-rolled to 0.150 in. gage, pickled, and cold-rolled to 0.014 in. Standard U-shaped magnetic test specimens were punched, deburred, sprayed with MgO, and annealed in ~50°C dew point hydrogen. Textures were identified with the aid of etch pits, the

Jan 1, 1970

By H. W. Kerr, B. Soutiere

THE possibility of using unidirectionally solidified eutectic alloys as high-strength composite materials has been investigated by several workers. Unidirectionally solidified lamellar and fibrous eutectics have been shown to have good short-time structural stability at temperatures close to the eutectic melting temperature.&apos;-4 Several investigations of both short-time high temperature tensile properties and creep properties of eutectic alloys have been carried out,3-" with promising results. Little work has been reported, however, on the thermal stability of eutectic alloys which have been unidirectionally solidified and subsequently deformed in compression. Since processes such as rolling and grinding introduce compressive stresses, and since the properties depend on the spacing and perfection of the composite structure10,11 this aspect is of definite importance if unidirectionally solidified eutectic alloys are to be considered for commercial use. A Cd-Zn alloy made from 99.999 pct starting materials was cast into a graphite boat and zone levelled12 to obtain a completely lamellar structure at one end of the bar. Sections from this region of the bar were removed, recast into 6.5 mm I.D. Pyrex tubing, and solidified unidirectionally upwards at a rate of 2.8 cm per hr. Specimens were cut from the solidified rods, heated in air at 200°C (0.88 of the eutectic melting temperature) for various lengths of time, and examined metal-lographically. Compression specimens were also cut from the solidified rod carefully machined to a length of & in., and deformed with the compressive axis parallel to the original growth axis to produce a total longitudinal strain of 12 pct. Some of these specimens were examined metallographically; others were heated in air at 200°C for various lengths of time and then examined. Metallographic examination of the deformed specimens showed the two types of deformation previously described; slip lines13 (smoothly bent lamellae) and kinks13,14 (sharply bent lamellae). Very close to the specimen ends there were a large number of deformation bands, but at a distance of about -re- in. the deformation was very localized, as shown in Fig. 1.

Jan 1, 1970

By John R. Low

A number of cases of low-temperature, intergranu2ar brittle fracture of metals containing small amounts of certain impurities, have now been identified. Some degree of understanding of this phenomenon exists for the simpler binary systems of a metal and a single impurity, but the profound effects of other impurities and alloying elements in modifying this type of behavior remain unexplained. Current research in this area is reviewed and some of the newer techniques of investigation which should make possible a more quantitative study of the structure and composition of grain boundaries in impure metals are described. To indicate the subject matter of this lecture, we may begin by reviewing the experimental observations concerning low-temperature intergranular brittleness in impure metals, particularly those examples in which the embrittlement appears to result from what has been called "equilibrium grain boundary segregation."&apos; These are the systems in which it has been impossible, at least up to now, to detect the presence of any second phase film at the brittle interfaces. When second phase films are present they are usually readily detectable by fractographic methods, often appearing as epitaxial films in geometric or dendritic patterns. An example is shown in Fig. 1 for the case grain boundary carbides in a sensitized stainless steel which failed by intergranular brittle fracture at 78?k2 In contrast to this type of embrittlement there are numerous examples of low-temperature intergranular embrittlement in which the fractographs are essentially featureless, for example, that of an oxygen-embrittled iron shown in Fig. 2. The only second phase particles visible are the small, widely separated, round oxide particles typical of the bulk material. The fracture surface is extremely smooth and the fracture path appears to follow the intergranular interface without deviation. This type of fractograph also implies that crack propagation has occurred without plastic deformation at the crack tip, since localized slip or twinning ahead of the crack would be expected to distort the interface and be readily visible in the fractograph. Such indications are occasionally seen in these fractographs, but are not characteristic. A second example of this type of fractograph is shown in Fig. 3, which is from a temper-embrittled, carbon-free, Fe-Cr-Ni alloy containing Sb, broken at 1OO?C.3 The similarity to the oxygen embrittled iron case will be apparent. In the case of the temper embrittled Cr-Ni ferrite containing antimony, it is possible to remove the embrittlement by suitable thermal treatment. The grain boundaries may then be examined by thin film transmission in the electron microscope for the material in both the nonembrittled condition and in the embrittled condition. Two boundaries are shown in dark-field transmission in Fig. 4, one in the nonembrittled

Jan 1, 1970

By H. B. Huntington

Some of the basic problems in understanding elec-tromigration in metals are discussed, along with the attempts that are being made to handle them. One such problem is the effect of the electrostatic forces. It is now acknowledged that the momentum exchange with charge carriers plays generally a dominant role in the driving force but the question remains to what extent the electrostatic force may still be effective. The electromigration of interstitial impurities is also an area which presents some intriguing questions. For the substitutional impurity, moving by the vacancy mechanism under the influence of an electric field, the correlation considerations are somewhat more complex than have been previously recognized. Another problem of basic importance in the calculution from first principles is the strength of the "electron friction" force, say for a simple one-band metal. A related problem growing out of the preceding is the prediction of the direction of the "electron wind" force for metals with band structure involving both holes and electrons. THE term electromigration has come to be used to describe the flow of matter in condensed phases carrying high electronic currents such as metals and alloys, whereas one usually reserves the term electrolysis for situations where the current is largely ionic, particularly in the liquid state such as molten salts. It follows that the mass transport number in electromigration is always very small, of the order of 10-7. Studies of electromigration date back some 30 years but the modern period would appear to date from the work of Seith and Wever1 who in the mid 1950&apos;s first incorporated markers to display mass motion relative to the lattice and first suggested that the direction of the mass flow was primarily determined by the sign of the charge carriers. Since that time interest in the field has grown steadily and more rapidly recently as certain technological applications became apparent. Chief of these is certainly the deleterious effects that electromigration can cause, even at relatively low temperature, to current-carrying elements in integrated circuitry.2 These phenomena have been the subject of intense study and considerable ingenuity. On the constructive side electromigration has proved a useful tool in the purification of certain metals.3 The interest of this paper is, however, centered more on the basic aspects of the subject than on its technological applications. That high electric currents should give rise to mass flow in metals and that the driving force should be more directly associated with momentum exchange with the charge carriers than with the electrostatic field are ideas that no longer cause surprise or particular interest. The field has matured to the point where the general concepts are widely accepted and continued progress in basic understanding rests on more detailed and quantitative exploration. It is the purpose of this paper to point out what are some of the current problems. As a result, we expect to raise more questions than we answer. The first of these will be the role of electrostatic forces, if any, in electromigration. A second section will deal with the electromigration of interstitials. A third and final section treats with electromigration of substitutional impurities or of the matrix atoms themselves. ELECTROSTATIC DRIVING FORCE In the conceptual treatments of electromigration it has been customary to write the driving force in terms of an effective charge number Z* and to divide it into two terms F = e£Z* = e£[Zel- z(pd/Nd)(N/p)(m*\m*\)] [1] The first of these represents the electrostatic force under immediate consideration in this section and the second and usually dominating term for metals arises from momentum exchange with charge carriers, commonly called the "electron drag" term. As can be seen it is set proportional to the electrons per atom, z, and the ratio of the specific resistivity of the moving entity to the corresponding resistivity per matrix atom. The (m*/Im*I) factor takes into account the fact that the sign of the charge carrier determines the sign of the driving force. The specific resistivity of the moving entity is averaged over its path. In the case of motion of the matrix atoms by vacancies this gives rise to approximately one-half the resistivity at the saddle point since the scattering power of the atom at its equilibrium position bordering the vacancy differs only slightly from that of a normal matrix atom. Although the formulation of the "electron drag" term in Eq. [I] is based on a highly simplified model for electron defect scattering, the essential features implicit in the expression are common to all the theoretical approaches that have so far appeared in the literature.4-6 As for Zel, most treatments of electromigration have included the quantity as the parameter which measures the direct interaction of the electrostatic field with the ion and equated it to the nominal valence of the latter. However, there has been considerable discussion whether this interaction may not be 0 in many cases.6 If the moving ion is always enveloped by the same distribution of shielding charge, then clearly its motion will not involve any work done by the electric field and one can expect there will be no electrostatic force exerted on such a neutral composite. From this point of view the shielding charge around the ion would be said to be complete and hence the entity within the Debye shielding sphere would be unaffected by the electrostatic field per se. There is, however, the prospect that, as the moving ion progresses, new charge comes in to participate in the shielding action

Jan 1, 1970

By S. Floreen, R. M. Pilliar, H. W. Hayden

The fracture behavior of a 50 pct Cu-50 pct Fe mi-croduplex alloy, laminated composites of copper and iron and an extruded 50-50 Cu-Fe elemental powder composite was studied. Very low ductile-brittle transition temperatures were achieved in all cases, but for different reasons. In the microduplex alloy both the initiation and also the propagation of cleavage fractures appeared retarded by the very small in-terphase distances. In the composites, crack propagation through the sumples was prevented in most cases by delamination fractures perpendicular to the advancing cracks. These delaminations occurred at different regions and by different mechanisms in the various composites. In the extruded powder composite, de-lamination appeared to take place along preexisting flaws. In the crack arrest geometry of the laminated plates, delamination took place by localized shear fractures within the copper near the Fe-Cu interfaces. In this case delamination was enhanced by thicker laminate layers, and by having the resistance to shear failure of the copper sufficiently low compared to the toughness of the iron. BRITTLE fracture in engineering materials has long been a problem, and many different ways of preventing it have been considered. One method that has been of growing interest lately is to prevent crack propagation by the introduction of mechanical discontinuities into the structure. These discontinuities may act in several ways. They may simply act as crack stoppers. They may introduce secondary fractures such as de-laminations that deflect the initial crack into new, less damaging directions. Alternatively, they may subdivide a fairly large bulk sample that would have been loaded in plane strain, for example, into a number of subunits that are individually loaded in plane stress and thus are more resistant to fracture. Other mechanisms, or combinations of mechanisms, are also feasible. A number of methods exist for introducing mechanical discontinuities into a structure. Composites by their nature have discontinuities in structure, and numerous studies have shown that fracture propagation in materials of this type can be radically changed by suitable control of the composite parameters. Of particular significance to the present work are recent investigations of layered composites made by joining high strength steel sheets by various means.&apos;-4 These studies have shown that through proper control of the mechanical properties of the bonds joining the sheets it was possible to introduce delamination fractures that markedly improved the overall toughness of the composites and in some cases completely prevented through-the-thickness fractures. Another technique for introducing structural discontinuities is simply to use a two-phase alloy. It has been recognized for many years that a small amount of a second phase may improve toughness either by homogenizing plastic flow and thus preventing localized stress concentrations that nucleate fracture, or by interacting with an advancing crack. In most of these studies of two-phase materials, the decreases in ductile-brittle transition temperatures produced by the second phase were relatively small. More recently, work on two-phase stainless steels having a very fine grain microduplex structure has shown that the presence of on the order of 40 to 50 pct of a tougher second phase may lower the ductile-brittle transition temperature of the brittle phase by approximately 300°F. 5-7 In these alloys delaminations were seldom observed. The tougher second phase appeared to minimize the ease of both the initiation and the propagation of cleavage fractures. These results show that both the composite approach and the microduplex alloy approach are effective methods of preventing brittle fracture. Therefore, it was of interest to compare the fracture behavior of a microduplex alloy with composites made from the two-phases that were present in the alloy. To simplify this comparison the 50 pct Cu-50 pct Fe system was selected for study. At low temperatures the equilibrium tie line phases in this system are essentially pure ferrite and pure copper. A 50-50 alloy was cast and hot worked to produce a microduplex structure. Two types of composites were studied; laminated structures prepared by roll bonding iron and copper sheets of the tie line compositions, and an extruded powder composite made from high purity elemental powders. The fracture behavior of these materials was then compared. EXPERIMENTAL PROCEDURE Alloy Preparation. The 50-50 Fe-Cu alloy and the components for the roll bonded composites were prepared by vacuum induction melting 30-lb heats using electrolytic grades of iron and copper as charge materials. A carbon boil was used to deoxidize the melts. Small additions of copper and iron were made to the iron and copper heats, respectively, to approximate

Jan 1, 1970

By E. R. Buchanan, R. E. Reed-Hill

A transmission electron microscope study was made of magnesium single crystals deformed in torsion using the basal pole as the forsional axis. While this type of deformation is predicted to result in the formation of hexagonal networks of screw dislocations, these networks were not observed. The basic dislocation arrangement consisted of arrays of nearly parallel and approximately equally spaced dislocations. The average dislocation density was over an order of magnitude higher than that required to account for the torsional deformation. The observed high rate of work hardening in these crystals is consistent with both their high dislocation densities and the arrangement of dislocations in pile-ups. The experimental observations are also in agreement with the assumption that dislocation sources are activated not only at the surface but at interior locations as well. In considering torsional deformation, Amelinckx and Dekeyser1 postulated that when a torque is applied to a crystal oriented with a glide plane normal to the specimen axis, deformation occurs by the following steps: 1) Nucleation of dislocation sources at or near the specimen surface in areas where the shear stress, resolved along a slip Burgers vector, is a maximum; 2) the screw orientations of the dislocations accommodating the twist move inwards towards the specimen center. If two glide directions lie on the glide plane, the geometry shown in Fig. 1 should result; 3) the screw dislocations that pile up in the central part of the specimen cross-slip to form a grid. At the same time, screws of opposite sign and most edges leave the specimen. Tinder,2 using zinc crystals twisted about the basal pole, independently reached essentially the same conclusions. He suggested a mechanism involving nucleation of ?(1120) screw dislocations at the six points of highest resolved shear stress that lie on the cross-section near the surface. Under the applied shear stress these dislocations were assumed to move inward and interact so as to form a hexagonal network of screw dislocations. Today it is often accepted that rotational slip occurs by a mechanism of the above type, but to our understanding this has never been experimentally proved. This paper reports an experimental study of rotational slip, using magnesium single crystals, that indicates that in this metal rotational slip does not conform well to this mechanism. EXPERIMENTAL PROCEDURES Mechanical Testing. Specimens with a (0002) axis were prepared from magnesium crystals of 99.95 pct purity grown by Jillson&apos;s3 modified Bridgman technique. The crystals were acid machined into cylindri-

Jan 1, 1970

By C. H. P. Lupis, Henri Gaye

There are m -I conditions for the stability of a solution of m components with respect to infinitesinzal flucturations. However, in most cases, only one of these conditions has to be considered to determine the domain of instability and the existence of this more restrictive condition greatly simplifies the calculations. It may be used advantageously for the prediction of miscibility gaps and the method is illustrated in details for the case of the Ag-Pb-Zn system. THE thermodynamic conditions for the formation of a miscibility gap may be viewed as a necessary consequence of the conditions for spinodal decomposition. A previous article1 has examined in detail the form of these conditions for multicomponent systems. There is only one condition for the stability of a binary system (with respect to infinitesimal fluctuations), but there are two conditions for a ternary system, and m — 1 conditions for an m-component system. The probability of violating a stability condition, and thus forming a miscibility gap, obviously increases with the number of components, a result which is rather intuitive since the atoms of the solution have now many more ways of redistributing themselves and introducing complexities in the form of the free energy hy-persurface. It is of interest to take advantage of this possibility of precipitating new phases and to examine which stability condition is the likeliest to be violated, that is, which stability condition is thermodynamically the most restrictive. The finding of such a condition would greatly simplify the application of the stability criteria since only one condition could then be considered, instead of m - 1. In Ref. 1, coherency strain energy terms were neglected, thus restricting the applications of the treatment to solutions where they are negligible, such as liquid alloys. In the following study the same assumption will be made. To generalize the treatment to systems where the strain energy terms are sizable, the reader is referred to Cahn&apos;s classical article on spinodal decomposition.2 Let us designate by Gij the second derivative of the Gibbs free energy with respect to the number of moles ni and n j. There are several equivalent sets of m — 1 stability conditions.&apos; The one considered here expresses that the successive diagonal determinants of order 1, 2, ... m — 1, associated with the symmetric Gij matrix (for 2 5 i, j 5 m) are positive.&apos; For a binary solution 1-2, the condition for stability is: O(u=G22^0 [1] For a ternary system 1-2-3, the condition [I.] is re- tained (the value of G22 will differ, of course, according to the concentration of 3) and another condition is introduced: £>(21 = G22G33 - Gl3 ^ 0 [2] In a composition diagram, these two conditions define two domains of instability. Starting at a point where the solution is stable (for instance at a point where the solution is very dilute) we gradually change the composition until the condition [I] or [2] is violated. As already noted in the literature, e.g., in the work of Prigogine and Defay,3 it is the boundary of the domain (2) which is first crossed. For if we assume that the boundary of the domain (1) is reached first, at this point G22 = 0 and the second condition is necessarily violated (D(2) = -& 5 0), in contradiction with our original assumption. An exhaustive study of the ternary regular solution case may be found in the work of Meijering.4 Moreover if the boundaries of the two domains have a common point, they also have a common tangent. For if the two lines were to cross each other as is illustrated in Fig. 1(a) any point M in the line QP would be such that £> = 0 and 0"&apos; > 0 which, as shown above, are incompatible results. Thus, the two lines must be tangent at their common point Q as illustrated in the example of Fig. l(b). The reasoning of Fig. l(a) implies that the point Q is not a "singular" point for either boundary line. This singularity may be of two types. First, the lines meet without crossing each other and without being tangent. Second, the tangent at Q for D"&apos; or 0"&apos; is not single-valued. Other types of singularity are unlikely because of the usual analytical forms of D"&apos; and 0"&apos;. The exception to the common tangent requirement due to the first type of singularity was pointed out by John Morral;5 it occurs when the common point, Q&apos; or (3" in Fig. l(b), is located at a boundary of the composition diagram, e.g., at the line X3 = 0. It may also be noted that at the common nonsingular point Q of D(1) and D(2), Fig. 1(b), G23 is necessarily equal to zero, whereas at a point such as Q&apos; or Q", this conclusion is no longer valid because the product G22G33 is now indefinite (of the form 0. a). The exception to the common tangent requirement due to the second type of singularity occurs when two branches of the same boundary line intersect, for example when D(1)or D(2) decomposes into a product of functions, at a point which belongs to the boundary of the other condition. It is possible to show by a simple analytical calculation that, in this case, if Q is a singular point of D(1), then it is necessarily a singular point of D(2), and that the reciprocal is true except if G33 = 0 at Q. For the present article, however, more elaboration on these singularities appears to be unwarranted. To generalize the previous results to an m -component system, we use the mathematical theorem stating that if the diagonal determinant D(r) = 0, then

Jan 1, 1970

By C. S. Giggins, F. S. Pettit

The oxidation of Ni-Cr alloys in 0.1 atm of oxygen has been studied at temperatures between 800" and 1200°C. For alloys with 30 wt pct or more Cr, continuous layers of Cr2O3 are formed during oxidation. In the case of alloys with chromium concentrations between approximately 5 to 30 wt pct, external scales of Cr203 are formed over grain boundaries whereas internal precipitates of Cr2O3 and external layers of NiO are formed at other areas on the alloy surface. When such conditions are present on the alloy surface, chromium diffuses laterally from those areas covered with a continuous layer of Cr2O3 to areas where a Cr2O3 sub scale exists and it is possible for the sub-scale zone to become separated from the alloy by a continuous layer of Cr2O3. Whether such a state will be attained depends upon the initial grain size of the alloy and the oxidation time. When the concentration of chromium in the alloy is less than 5 pct, Cr2O3 is formed internally both at grain boundaries and within the interior of grains and the alloy is covered with an external layer of NiO. MECHANISMS which describe the growth of oxide scales on nickel-base superalloys are complex and the effects produced by the various elements in these alloys on the oxidation behavior of superalloys are not clearly understood. In order to determine the influence of the different elements on the oxidation behavior of superalloys, it is first necessary to examine the oxidation properties of binary nickel-base systems which contain the principal elements present in the superalloys and then progressively more complex systems until compositions typical of the superalloys are attained. Chromium is present in virtually all nickel-base superalloys and the purpose of the present studies was to examine the selective oxidation of chromium in Ni-Cr alloys. The oxidation characteristics of Ni-Cr alloys have been extensively studied1-" to date principally as a result of the high oxidation resistance exhibited by some of these alloys. Ni-20Cr* has long been known *All compositions are given as wcight percent unless specified otherwise. to be oxidation resistant and is commonly used as resistance heating elements for service temperatures up to 1100°C. This alloy cannot be used for extended periods of time at higher temperatures because of the apparent reaction of the external scale with oxygen to form gaseous CrO3. In spite of the considerable work cited above some important aspects of Ni-Cr oxidation still remain unresolved. Virtually all of the previous studies agree that small additions of chromium to nickel, e.g., <10 wt pct Cr, result in increased oxidation rates as compared to that of pure nickel, whereas larger additions, e.g., 20 to 30 wt pct Cr, form alloys with substantially lower oxidation rates. The controversial aspects of the oxidation mechanisms for these alloys that still remain unresolved are as follows: 1) A description of the oxidation mechanism for the low chromium alloys. 2) A description of the oxidation mechanism for the high chromium alloys, particularly with respect to the composition of the external scale which results in the lower oxidation rates. 3) The specific alloy compositions at which the oxidation mechanism changes from that obtained for low chromium contents to that of the high chromium alloys and the reason for this transition. EXPERIMENTAL The Ni-Cr alloys listed in Table I were prepared from high purity metals by nonconsumably arc melting and casting as buttons. These alloys were then given a preliminary annealing treatment in argon at 815°C for 100 hr to promote homogeneity. Each button was cut into 0.250 in. thick sections that were subsequently cold-rolled to 0.050 in. thicknesses and annealed in argon at 815°C for 48 hr to provide a twinned, equi-axed grain structure. The grain size for these alloys was not uniform and the limits, within which the average grain size lies, are given in Table I for the single-phase alloys. All the alloys were single phase with the exception of the Ni4OCr alloy in agreement with the Ni-Cr phase diagram.&apos;&apos; Rectangular specimens were cut from the sheet to provide surface areas of approximately 2.5 sq cm. Exact areas were determined with a micrometer after surface preparation was completed. All of the specimens except the Ni-40Cr alloy and pure chromium were polished through 600-grit Sic abrasive paper, ultrasonically agitated in ethylene trichloride, rinsed with ethyl alcohol, and electro-polished. The specimens were electropolished in a 10 vol pct H2SO4 (conc), 6 vol pct lactic acid, methyl alcohol solution at 70" to 80°C for 2 min at a current density of 0.8 to 1.2 amp per sq cm. This electro-polishing procedure did not produce acceptable surfaces on the Ni-40Cr alloy nor on pure chromium and the oxidation properties of these materials were obtained for specimens polished through 600-grit Sic

Jan 1, 1970

By R. O. Williams

Analytical representation of the thermodynamics of solutions is highly desirable from the standpoint of accuracy, compactness, and numerical manipulations. In particular, computer calculations are greatly implemented. Mathematical considerations show that previous expressions have one or more serious defects. This investigation shows a Fourier series to be satisfactory but that it is also possible to derive a new series which fits certain additional conditions. Included examples show the value of analytical expressions in giving a simple characterization of each system using some two to five parameters, the elimination of the Gibbs-Duhem integration, and the es timation of the error for the experimental function as well as derived functions. It is further shown that the present characterization provides easy comparison between systems. IN the past, thermodynamic calculations have depended to a considerable extent on tabular and graphical methods. As the volume and precision of such data increase such methods become less satisfactory. Specifically, the selection of the optimum representation and the estimation of errors require statistical methods which in turn require analytical representation. The utilization of such data require further manipulations which are best done analytically for maximum precision. For example, phase equilibria are determined by common tangents to free-energy curves: a graphical determination is normally of low accuracy. As computers are increasingly used analytical representations become almost mandatory. Insufficient mathematical consideration has been given previously to the selection of empirical expressions. Those expressions having some theoretical justification are generally too inflexible and mathematically unattractive. We consider the problem in some detail and show that a Fourier series can be effectively used. Also a new series is defined which has certain advantages. ANALYSIS We wish to consider the analytical representation of the heat of mixing, AH, the excess free energy, ?Gxs, and the excess entropy, ?sXS, as a function of composition, X, for binary solutions relative to the pure components in the same state. When a distinction is not required, we use W to denote any one of the above functions. One may use a Taylor expansion around X = 0 to generate a power series. As the derivatives are un- known we represent the series as W = A + BX + CX2 + DX3 + EX4 + ... [l] where the constants A , B, C , ..- are to be selected to provide some optimum fit. For the extremes of composition W is necessarily zero so it follows that A = 0 [2a] B +C + D + E +••• = 0 [2b] Nonelectrolytes, which we are considering, appear to satisfy the condition that d3W/dx3 = 0 [3] in the terminal regions. This is the basis of the a, ß, and Q functions used by Hultgren et al.&apos; and others. While this condition does not have a strong theoretical basis it does appear desirable that any analytical relation should satisfy this condition. Darken2 and Turk-dogan and Darken3 have shown that many systems exhibit this behavior over an extended range from each terminal region, departure being restricted to a limited intermediate region. Since we have no a priori knowledge as to where this transition occurs we can require that this condition be satisfied only as a limit at the extreme compositions as a general condition. We will show later how more restricted conditions can be included in specific solutions. Darken2 has called this behavior the quadratic formalism; we call our application the limiting quadratic formalism, LQF. This condition applied to the above power series requires that D = 0 [4a] 4-3-2E +5-4-3_F + 6 • 5 . 4G + ••• =0 [4b] The form of the power series normally used, due to Margules,4 is W=X(1-X)(A + BX + CX2 + DX3 + EX4 + •••) [5] where A, B, C, --. are a new set of constants. (Guggenheim5 has given a variation of this expression in a more desirable form. Since, however, it is contained in the above expression it does not require separate consideration.) This form is precisely what results by incorporating the conditions in Eq. [2] into the power series and regrouping the constants. The LQF requires that B =C [6a] and 4.3.2(D-C) +5-4-3(E-D) + ••• =0 [6b] Thus, the correct form of the Margules expression with two adjustable parameters is w =X(1-X)[A + B +X2-2/3x3)] 171 and the EX4 term must be included before three adjustable parameters are permitted.

Jan 1, 1970

By D. B. Jugle, J. B. Darby

The equilibrium solubility limits of the transition elements Ti, V, Cr, Fe, and Co in liquid tin were determined in the temperature range from 827" to 1211°K. Since the equilibrium concentration of Ti, V, or Cr in liquid tin is moderately dilute in the temperature range investigated, the solubility data were employed to estimate the partial molar enthalpy and the partial molar excess entropy of solution for the three solutes in liquid tin. The reference state s for titanium or vanadium were selected relative to the solute in an intermetallic compound. The thermodynamic quantities for chromium were calculated relative to pure chromium. RECENT experiments1 have shown that the rate of solution of several transition elements in liquid aluminum can be qualitatively predicted from a knowledge of the temperature dependence of the solvent-rich liquidus. In order to extend the analysis to binary tin systems,&apos; it was necessary to know the equilibrium solubility of several of the first-long-period transition elements in liquid tin. Since solubility data for the tin-rich portion of binary systems are meager, the present investigation was undertaken to determine the equilibrium solubility limit of Ti, V, Cr, Fe, and Co in liquid tin in the temperature range from 850" to 1200°K. EXPERIMENTAL PROCEDURE A useful technique3 to determine the equilibrium solubility of a solute in a liquid-metal solvent consists essentially of placing a pure solute in contact with a pure solvent and allowing sufficient time for equilibrium to be attained at the temperature of interest. Subsequently, the solvent is removed and the equilibrium solute concentration in the solvent is determined by an appropriate analytical procedure. The technique can be applied very successfully to relatively simple systems such as the copper-germanium system.3 However, in many binary systems of transition elements with tin, several intermediate phases are known to exist and precipitation of the phases from solution, in solubility experiments, can lead to an erroneously large solubility. The difficulty was avoided in the present work by equilibration of the most solvent-rich intermediate phase with the pure solvent over a range of temperatures. The compounds employed in this investigation, and the temperature range over which each compound is in equilibrium with liquid tin are listed in Table I. No stable intermediate phases are reported in the chromium-tin system4 and, therefore, pure chromium was utilized as the solute. The stoichiometric compounds were prepared by arc-melting on a water-cooled copper hearth in a helium-argon atmosphere. The elemental tin employed in.this investigation was 99.998 pct pure, and typical lot analyses of the transition elements were reported elsewhere.&apos; A sample of an appropriate solute, in the form of a button and in sufficient quantity to exceed the equilibrium solubility, and the pure tin solvent were placed in a high-purity recrystallized-alumina crucible. The crucible and contents were placed in a horizontal furnace under a high vacuum (10-6 torr) and held at temperature for periods varying between 24 and 72 hr. A water-cooled quench tank, partially filled with diffusion-pump oil, was attached close to one end of the

Jan 1, 1970

Jan 1, 1970

By G. R. Speich

The distribution of carbon and the type of substructure in iron-carbon martensites containing 0.02 to 0.57pct C has been studied in the as-quenched condition and after tempering at 25" to 700°C by using electrical resistivity, internal friction, hardness, and light and electron microscope techniques. in marten-sites containing less than 0.2 pct C, almost 90 pct of the carbon segregates to dislocations and to lath boundaries during quenching; in martensites containing greater than 0.20 pct C, appreciable amounts of carbon enter normal interstitial positions located far from defects. Tempering martensites with carbon contents below 0.20 pct at temperatures below 150°C results in additional carbon segregation to dislocations and to lath boundaries but no carbide precipitation whereas -carbide precipitation occurs in martensites with carbon contents exceeding 0.2 pct. Above 150°C, a rod-shaped carbide (either Fe3C or Hagg) is precipitated in all cases. At 400°C, spheroidal Fe3C precipitates at lath boundaries and at former aus-tenite grain boundaries. At 400" to 600"C, recovery of the martensite defect structure occurs. At 600" to 700°C, recrystallization of the martensite and Ost-waW ripening of the Fe3C occur. The effects of the carbon segregation that occurs during quenching and the subsequent substructural changes that occur during tempering on martensite tetragonality, hardness, and precipitation behavior are discussed. A mathematical analysis of carbon segregation during quenching is presented. RECENT studies of the strength of low-carbon martensitel-4 emphasize the importance of carbon segregation to the martensite lath boundaries and to the dislocations contained between them during quenching. Unfortunately, very few studies of the tempering of low-carbon martensites have been conducted, so the exact nature of this segregation is poorly understood. In fact, most early tempering studies5,6 were restricted to carbon contents greater than 0.20 pct. Moreover, these studies did not determine the amount of carbon segregated to the martensite substructure during quenching so that the initial state of the martensite was not established. Aborn7 studied the precipitation of carbide in low-carbon martensite during quenching but did not establish whether carbon segregation occurs prior to carbide precipitation, nor did he study the subsequent tempering sequence in detail. In the present work we have used electrical resistance and internal friction measurements, supplemented by electron transmission microscopy to establish the carbon distribution in as-quenched specimens. Specimens thin enough to avoid carbide precipitation (but not carbon segregation) were employed. The redistribution of carbon on subsequent tempering below 250°C was followed by measurements of elec- trical resistance. Additional studies were made on specimens tempered at 250" to 700°C to elucidate the overall tempering behavior of low-carbon martensites, including the formation of cementite and recrystalli-zation of the martensite. EXPERIMENTAL PROCEDURE Eight iron-carbon alloys with 0.026, 0.057, 0.097, 0.18, 0.20, 0.29, 0.39, and 0.57 wt pct C were prepared as 8-lb ingots by vacuum melting. Typical impurities in wt ppm were 40 Si, 20 Mn, 30 S, 10 P, and 10 N. These alloys were hot rolled to 3 in. plate at 1095°C) (2000°F). The hot-rolled plates were surface ground to remove scale and the decarburized layer, then cold rolled to 0.010 in. sheet. Specimens cut from the sheet were austenitized for 30 min at 1000°C (1830°F) in a vacuum tube furnace in which the pressure did not exceed 2 x 10-3 torr. Chemical analysis of specimens after austenitization indicated no decarburization at this pressure. Immediately before quenching, the furnace was filled with prepurified helium. The specimen was then pushed rapidly through an aluminum foil gasket, which sealed the bottom of the furnace, into an iced-brine bath (10 pct NaC1, 2 pct NaOH). The quenching rate at the M, temperature is about 104&apos;c per sec for 0.010 in thick specimens, as calculated from Newton&apos;s law of heat flow2 using a heat transfer coefficient of 25 ft-&apos;. This quenching rate is sufficiently high so that all the alloys transformed completely to martensite throughout the entire 0.010 in thickness and no carbide precipitation occurred in the martensite. All specimens were immediately transferred to liquid nitrogen after quenching and stored there until needed. Tempering below 250°C (480°F) was done in silicone oil baths thermostatically controlled to *;"C. Tempering above 250°C was done in circulating air furnaces or lead pots with the specimens contained in evacuated silica capsules. Electrical resistance was determined by measurement of the potential drop across both a standard resistance and the specimen, connected in series. All resistance measurements were made in liquid nitrogen (77K, -196°C) to minimize thermal scattering of electrons and thus maximize the contribution of impurity scattering to the resistance. Specimen dimensions were 5.10 by 0.19 by 0.025 cm. Although the precision in the electrical resistance measurements was +0.1 pct, the electrical resistivities could only be measured with an accuracy of +5 pct because of uncertainty in the specimen dimensions. Internal friction measurements were performed in an inverted pendulum apparatus at vibration frequencies of either 1.9 or 66 Hz. The specimen dimensions were 5.10 by 0.375 by 0.025 cm. Hardness measurements were made with a Leitz-Wetzlar microhardness machine with loads of 100 g. Specimens were examined by light microscopy after etching in 2 pct Nital and by electron transmission microscopy after preparation of thin sections by electrolytic thinning in a chromic-acetic acid solution.

Jan 1, 1970

By R. M. S. B. Horta, W. T. Roberts, D. V. Wilson

Evaluation of results obtained by the Harris method for inverse pole figures is discussed. Two existing analyses and a new approach are compared. In the most frequently used analysis, different reflections are accorded equal weight. A second method involves area-weighting of reflections, mainly to take account of nonuniformity of Pole distribution. In the new method, reflections are weighted according to their multiplicity factors. Intensity ratios obtained from a sample of steel sheet by the three methods are compared. INVERSE pole figures offer a convenient method of depicting the proportions of material with various orientations referred to a unique specimen axis. The technique was first applied to fiber textures, but it is now frequently used as a description of texture in sheet metal, the unique axis in this case usually being the sheet normal. The Harris method&apos; for the determination of inverse pole figures has the great merit of simplicity. It suffers certain intrinsic limitations, but provided that these are borne in mind, the results allow useful conclusions to be drawn regarding the effects of texture components on certain mechanical properties. Much thought has been given to alternative methods of texture description, aimed at eliminating the ambiguity in the simpler methods.2"6 Refinements in the method of description are obtained at the price of increasing complexity, and it seems clear that a simple method, such as that of Harris, will continue to find application. The original derivation by Harris1 has been corrected by Morris7 and later by Mueller, Chernock, and Beck.2 Since the latter reference is more accessible, it is referred to more frequently than the work of Morris. Most users of the inverse pole figure method present their results on the basis of the treatment by Mueller et al., and it is the purpose of the present communication to comment on this treatment and to suggest a simple modification to the method of presentation which enhances the meaningfulness of the results. It will be convenient first to summarize the Mueller analysis as follows: The intensity Ihkl of a hkl reflection from a textured specimen is: Ihkl=CI0AL\Fhkl\2NhklPhkl [1] where C is a constant for a given sample I, is the intensity of the incident beam A is an absorption factor. With usual diffrac-tometer geometry and a flat specimen, A is inversely proportional to the density of the specimen. L is the Lorenz polarization factor Fhkl is the structure factor for the hkl reflection Nhkl is the multiplicity factor phkl is the fraction of crystals in the polycrystal-line aggregate with any particular (nkl) plane parallel to the surface. The corresponding equation for a specimen with randomly oriented grains is lR,hkl=CRl°ARL\fnkl\2Nnklk [2] the subscripts R indicating the factors that are different for the random sample, which will, in general, have a density different from that of the textured one. The intensity ratio is hkl , c A Phkl [3] IR,hkl CR AR PR The constants are eliminated by summing over all the measured reflections ^iRMi °R AR PR ljPkkl and from Eqs. [3] and [4] T IR,hkl The only unknown in Eq. [5] is Yj phkl and before this can be evaluated, it is necessary to adopt some form of normalizing procedure. Mueller et al. assume that when a large number, n, of reflections is used, the average value of p as defined by Eq. [6] below will be unity ? = £j**l3l [6] and the final result of their analysis follows: hkl Pkkl = i I&Jf~ [7] ±y* Ihkl ^ in,hki The normalizing procedure used by Mueller et al. involves an unrealistic assumption since it gives equal weight to each of the hkl reflections. Other normalizing procedures can now be examined with a view to selecting a more appropriate one. For an infinite number of reflections, the function p can be averaged over a continuous range of orientations covering the complete solid angle 4p by the integral relation: p =1 jp(a)dQ = l [8] This is the only exact procedure, but in practice a

Jan 1, 1970

By C. S. Giggins, F. S. Pettit

The oxidation properties of Ni-Cr alloys with fine grains, coarse grains, and deformed surface layers have been studied at temperatures of 900" and 1100°C in 0.1 atm of oxygen. The oxidation rates of alloys containing between 10 and 30 wt pct Cr have been found to be dependent upon the grain size of the alloy. Finegrained alloys had smaller oxidation rates than coarsegvained alloys because of the selective oxidation of chromium at alloy grain boundaries. In this compositional range alloys with deformed surface layers behaved similar to fine-grained alloys due to recrys-tallization of the deformed surface layer. In the preceding paper1 it was found that during the oxidation of Ni-Cr alloys, the volume fraction of precipitated Cr2O3 could be greater at alloy grain boundaries than at other areas of the alloy surface. In the case of alloys with chromium concentrations equal to or greater than 30 pct,* the volume fraction of Cr2O3 *AIL compositions are given as weight percent unless specified otherwise. precipitated at grain boundaries and within grains on the alloy surface both exceeded the critical amount required for lateral growth of the Cr2O3 particles and the surfaces of these alloys were completely covered with a continuous, external layer of Cr203 during oxidation. However, in the case of alloys with chromium concentrations between approximately 5 to 30 pct, the volume fraction of precipitated Cr2O3 exceeded the critical value required for external scale formation only at grain boundaries.but not within the interior of the grains. Consequently, the surfaces of these alloys had external scales of Cr3O3 over the grain boundaries but internal Cr2O3 subscales with external scales of NiO away from the grain boundaries. Under these latter conditions, it was found that chromium could diffuse laterally in the alloy from those areas covered with an external layer of Cr2O3, i.e., grain boundaries, to areas where the Cr2O3 was present as a subscale. This diffusion of chromium resulted in an increase in the volume fraction of Cr2O3 precipitated in the sub-scale zone and continuous layers of Cr2O3 could be formed at the subscale front in these regions. For the alloys used in the previous studies,&apos; continuous layers of Cr2O3 were formed on Ni-20Cr alloys in the subscale regions after approximately 30 hr of oxidation at 900°C. For shorter periods of oxidation, the Cr2O3 layer was semicontinuous with the continuous portion at the subscale front emanating from points where the Cr2O3 had been formed as an external scale over alloy grain boundaries. Some lateral growth of a Cr2O3 layer in the subscale region was observed on Ni-15Cr and even Ni-10Cr alloys but this layer was never continuous after 30 hr of oxidation. These results indicate that the selective oxidation of chromium in Ni-Cr alloys with chromium contents between 5 to 30 pct may be dependent upon the grain size of the alloy. Fine-grained specimens in this compositional range should have a larger fraction of the surface covered with external Cr2O3 than coarsegrained specimens and the subscale areas required to be sealed via lateral diffusion of chromium should be smaller. It is therefore to be expected that a continuous layer of Cr2O3 can be formed on alloys in this compositional range after short periods of oxidation providing the alloy grain-size is sufficiently small. bo studieS2,3 have established that the oxidation behavior of alloys can be significantly influenced by pretreatments which produce mechanically deformed surfaces. It has been found that deformed surfaces usually promote the selective oxidation of elements in alloys and it is believed that these effects are due to rapid diffusion of elements in the deformed layer. In view of the previous results,&apos; which showed that alloy grain boundaries may play an important role in the selective oxidation of chromium in Ni-Cr alloys, deformed surfaces may promote the selective oxidation of elements in alloys as a result of the numerous grain boundaries formed on the alloy surfaces via recrys-tallization during heating to the oxidation temperature. The purpose of the present studies was to determine the effect of alloy grain size and surface deformation on the selective oxidation of chromium in Ni-Cr alloys at temperatures of 900" and 1100°C in 0.1 atm of oxygen. EXPERIMENTAL The average grain diameter of the alloys used in the previous studies1 was not less than 0.04 mm and alloys with compositions between 5 and 30 pct chromium had average grain diameters between 0.04 and 0.14 mm. Since the oxidation kinetics were already available for these relatively coarse-grained alloys, it was desirable to use these same alloys in the present studies. The surfaces of the alloys listed in Table I of the previous paper were deformed by using a Model F S.S. White Industrial Airbrasive Unit, which delivered a controlled mixture of 25 µ Al2O3 particles in a stream of dry air at high velocity against the surface of a specimen. The amount of surface deformation produced by this treatment was not determined but a re-crystallized layer about 15 µ thick was formed upon annealing deformed specimens. The grain size at the surface of the specimens was reduced to an average grain diameter of 0.01 mm by annealing the deformed specimens, i.e., grit-blasted,

Jan 1, 1970