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By J. R. Mihalisin

Phase changes in as-cast alloys in the Ni2 CoCr-Ni, Ti-NSAl system containing 0.1 wt pct C were studied after heat treatment at 1650°F. It was found that a vegion of CrCo-type s was developed in this system after I1000 hr. The tendency for s formation was dePendent upon the aluminum and litanium content, the s -forming tendency generally becoming more pro-nounced as the latter two elements are increased. s lended to form in interdendritic regioues and was associated with solutioning- of- carbide phases. Electron- vacancy computations for prediction of s formation on these alloys mere in sufficient agreement with what was observed experimentally to indicate that the method should be of value in assessing a-forming potential in cast alloys. However, the correlation of electrotz- vacancy numbers may not be as favorable in cast as cormpared to wrought alloys. THE increasing use of high-temperature alloys for longer times at higher temperatures has resulted in a real need for obtaining information on the phase changes taking place in these alloys since these changes often have a direct effect on properties. This paper reports on a study of the phase changes in Ni-Cr-Co-Al-Ti alloys after prolonged heating at 1650°F. The alloys were selected from the pseudo-ternary system Ni2CoCr-Ni3Ti-Ni3Al and this system was chosen because it is the basis of many of the newer cast commercial superalloys. The attempt here was not to define accurately the boundaries of s formation in the NizCoCr-Ni3Ti-Ni3Al system but to delineate the phase transformations taking place upon heating alloys covering a wide range of chemistries in this system. An addition of carbon was made to all alloys to further simulate commercial alloys. It was hoped that the information generated in this manner would be of more direct use to superalloy designers than an equilibrium diagram approach since commercial alloys generally have outlived their usefulness when equilibrium is attained. EXPERIMENTAL PROCEDURE The alloys were vacuum-melted from carbonyl-nickel pellet, vacuum-grade chromium, electrolytic cobalt, high-purity aluminum and titanium, and spec-trographic-grade carbon.

Jan 1, 1968

By W. N. Miner, R. O. Elliott

Electrical-resistivity )measurments were made be-trueetz room temperatrive and 1.5 oK on five different stocks of cerium metal, and the results were correlated with the types, amounts, and distribution of the impurities present. Magnesium, which appeared to be distributed as a solute throughout the cerium matrix, was found to have a large effect on the residual resistivity, 1 at. pct Mg being sufficient to increase the residual resistivity by about 10 microhm-cm. The formation of ß by repeated thermal cycling between room temperature and liquid-helium temperature is attributed to the deformation and faulting that occurs during the ? D a transformation. In preparation for starting a proposed study of cerium-rich alloys, we examined samples from severa1 stocks of cerium metal in order to choose the purest stock for future use in making the alloys. Low-temperature electrical-resistivity data were used to gain initial information about the purities of the stocks. Additional information was subsequently obtained from chemical analyses, density measurements, optical metallography, and electron-micro-probe analyses. Cerium that has been annealed at high temperature and cooled to room temperature has the fee crystal structure (? phase) with a = 5.16Å. When cooled further, in the region between about 250" and 150°K, some of the fee phase transforms to the double hcp form (ß phase) with a = 3.68 and c = 11.92Å. The remainder of the room-temperature fee form (and perhaps some of the hexagonal phase) transforms electronically in the vicinity of 100° K to the more dense or "collapsed" fee form (a phase), a - 4.85A, by transferring about 0.5 electron per atom from the 4f level to the valence band. Very little work related specifically to the effects of impurities on the physical properties of cerium has been reported in the literature. Gaume-Mahn1, 2 has studied the effects of calcium, magnesium. iron, silicon, and tantalum on the electrical resistivity and magnetic susceptibility of cerium between 60o and 300°K. Gschneidner, Elliott, and McDonald3 have discussed the effects of total impurity content on the hysteresis of the a —? (reversible) transformation and on the formation of the 4 and "a-? intermediate" phases. Smith and Morrice* have reported the effect of total impurity content on the resistivity of cerium at 4 and 293°K. In none of these reports, however, is it apparent that the distributions of the impurities were determined, L.r., whether the impurities were present in inclusions or in solid solution in the matrix is not mentioned; nor does it appear that the phase purity of the cerium was always considered. In the present study, five different stocks of cerium were involved. One was represented by a single sample of electrowon cerium, which was all that had remained from a stock of high-purity material obtained from the U.S. Bureau of Mines, Reno, Nev., in 1959. The other four stocks were recently purchased from commercial sources and were specified to be 99.9 wt pct pure. EXPERIMENTAL Cerium stocks designated as #1, #2, #4, and #5 were obtained from commercial suppliers for the specific purpose of finding a reliable source of high-purity cerium. Although the purity level of the cerium was specified to be 99.9 pet, the specifications did not include limits as to the amounts of various impurities that would be acceptable. Consequently the chemical analyses of the different stocks varied widely. Stock #3, which had been obtained from the U.S. Bureau of Mines and which was the purest on the basis of chemical analyses, consisted of a single specimen of electrowon cerium. It was included in the examination for purposes of comparison. Table I contains the chemical and spectrographic-

Jan 1, 1968

Jan 1, 1967

Jan 1, 1968

By J. L. Swedlow, M. L. Williams

Two standard techniques for assessing fracture initiatlon in sheet specimens involve measurements of 1) the applied load of fracture which, via linear fuacture mechanics, is used to find the fracture tough/less SC (or SIC), and 2) the velative displacement of fracture of the opposite free faces of the crack (COD). In the past, the quantitative association between these two parameters has not been determined in detail, owing to the mathematical difficulties of computing. the stress and strain fields in the combined elasto-plastic flow near the crack. Using a numerical technique Irecently developed and applied to a 7075- TO' aluminum plane stress specimern, the two parameters noted have been determined and associated quantitatirely. CONSIDERABLE effort has been expended in selecting a rigorous yet practical manner for predicting fracture. The usual point of departure is the modified Griffith criterion in which the mechanism of energy dissipation is reflected in Sc (or SIC), the parameter of "fracture toughness". Sc. differs from the surface energy used by Griffith in perfectly brittle fracture in that it includes the effect of plastic flow in the vicinity of the crack tip. Because plastic flow alters the stresses and displacements predicted from the usual linear theory of fracture mechanics, and because analysis of the nonlinear stress-strain field has presented great obstacles: only estimates of several pertinent quantities have heretofore been available. Nevertheless, two parameters have often been measured experimentally althougll usually just at the point of fracture. These are the energy release rate, or fracture toughness 9, (or I,), and the crack-opening displacement (COD). Such observations have been used in connection with frarture criteria and have been most helpful in design, although their application requires care with respect to changes in geometrical configuration from that upon which the criteria were based 1,2 Recently, however, a reasonably accurate and comprehensive method for analyzing the elasto-plastic flow has been devised and applied to plane stress specimens having arbitrary octahedral stress-strain curves.3 It thus becomes feasible to compute, albeit numerically, both the fracture toughness and crack opening as functions of the applied tensile loading on a typical specimen geometry. As a result, it is now possible to associate these two parameters quantitatively, and thereby to associate data obtained by one method with data pertaining to the other. ELASTIC ANALYSIS For the case of linear elasticity, it is relatively easy to deduce the connection between various measures of crack deformation. Using, for example, the singularity analysis, it is found that the leading term of the Airy stress function x f°r symmetrically applied loadings on an isotropic medium is

Jan 1, 1968

By R. E. Hook, R. L. McGaughey, A. M. Adair

The initial yielding characteristics of a vacuum-melted iron have been measured as a function of thertnal history after slow cooling or quenching from a 700°C recrystallizntion anneal. A thermal history favoring the segregation of interstitials to grairz boundaries results in a material having high values of upper and lower yield stress and long, irregutar Luders' plateaus, wheueas specimens treated to minimize grain boundary segregation have significantly lower values of these yielding characteristics. The struc- ture of typical grain boundary areas as revealed by electron transmission microscopy is consistent with these findings. The grain boundaries in iron are considered to be principally responsible for the release of dislocations during macroscopic yielding and it is suggested that strong locking results when a substantial amount of grain boundary segregution is present; it follows that weak locking results from a more random distribution of interstitials to grown in dislocations. RECENT years have seen an increased emphasis placed on a more quantitative study of the influence of grain boundaries on the yield behavior of bcc metals. The earlier picturk of dislocation pileups at grain boundaries building up a sufficient stress concentration to unlock dislocations in neighboring grains1

Jan 1, 1967

By I. S. Levy, J. L. Brimhall, B. Mastel

Specimens of' Hastelloy X-280, a low-cobalt version of the solid-solution- hardened nickel-base alloy Hastelloy X, were given a series of thermomechanical treatttzents. They were then Lensile-tested at room temperature and 1350°F. The Microstructures of the specimens tested at 1350°F were studied by electron Microscopy. Microscopy showed that dislocation tangling, caused by the cold working, mas still in evidence after aging-for 24 hr to temperatures as high as 1550oF. (Cr, Mo)23 C6, (Fe, Mo)6 C'. as well us an unidentifiable phase precipitale due to the combination of the thermomechanical treatments and subsequent tensile strain. The room -temperature and 1350°F tensile properties show a general increase ill strength and decreccse in ductility with increusing cold-work level. This is due to the dislocation taangling-. PerLurbatiot~s to this general trend occur- due to solid-solution weakening at the higher cold-work levels as a direct result of the preciplitation reactions. THE requirements for corrosion resistance and high-temperature strength place nickel-base alloys among the more promising materials for advanced nuclear reactor applications. However, when these alloys are irradiated at service temperatures, they generally suffer severe embrittlement'" and reduction in rupture life.3 Certain experimental treatments resulted in improvements in the tensile and stress-rupture properties of Hastelloy X-280, a solution-hardened nickel-base alloy.' To provide a basis for understanding these improvements, unirradiated tensile specimens were examined by electron microscopy. The results are reported in this paper. EXPERIMENTAL DETAILS Material. Hastelloy X-280, a low-cobalt version of Hastelloy X, is a member of the solution-hardened class of nickel-base alloys. The Hastelloy X-280 was obtained from 4- and 1-in: thick plates in the mill -annealed condition. Table I gives the chemical composition of the material as reported by the National Spectrographic Laboratories. ~x~erimental Treatments. Plates of suitable size, 12 by 3 by 1 in., or by + in., were cut under a water jet from the stock material and examined ultrasonic -ally for homogeneity of grain size and absence of voids. The acceptable plates were solution-treated at 2150°Ffor 1 hr and air-cooled. These plates were then reduced in thickness by cold rolling 0, 10, 15: or 20 pct along the original rolling direction. The plates were machined into buttonhead tensile specimens with a gage diameter of 0.125 in., with a gage length of 1.125 in., and with their tensile axes parallel to the rolling direction. The specimens were examined for quality of finish with a penetrant dye, ultra son ically checked for voids, and finally given a dimensional tolerance check with an optical comparator. The acceptable specimens were aged for 24 hr at either 1000" or 1500 F and air-cooled. These specimens were then held at 540°F in a water loop for approximately 18 days to qualify as controls for similar specimens irradiated under the same conditions of time, temperature, water chemistry, and flow rate. Table U summarizes the treatments. These treatments were investigated to establish whether prior precipitation and stabilization of carbide phases at strain sites within the matrix could reduce the amount of carbides available for precipitation at grain boundaries during service. Tensile-Test Conditions. Specimens were tested to fracture at room temperature or 1350 F in air on an Instron tensile-testing machine at a crosshead speed of 0.05 in. per min. The time for the furnace to reach equilibrium at 1350°F was approximately 30 min; soak time prior to testing was 15 min; and test duration was approximately 5 min.

Jan 1, 1968

By E. N. Aqua, C. M. Owens

The microstructure in cold-rolled Zircaloy-4 sheet has been characterized by transmission electron microscopy and X-ray diffraction line-broadening techniques. The rate of work hardening is measured in terms of microstrains, particle sizes, micro hardness, the tensile yield strength. The tensile yield strength of Prestrained (less than 10 pet) Zircaloy-4 sheet is found to be a linear function of the square root of the dislocation density, us predicted by work-hardening theories. ZIRCALOY is one of the most important structural alloys for nuclear reactor applications.''2 In order to understand the effects of the nuclear environment on Zircaloy structural members, the preirradiation microstructure must be characterized. This report will describe the substructure existing in cold-rolled Zircaloy-4 sheet as observed by electron microscopy and by X-ray diffractometry. I) EXPERIMENTAL PROCEDURE Commercial Zircaloy-4 strip was cold-rolled and annealed in argon at 760°C for 1 hr. The annealed sheet was again cold-rolled to a maximum of 50 pct reduction in thickness with segments of the strip being retained after 2.5, 5, 10, and 20 pct reductions. One-inch-square portions were chemically polished (50 parts HNO3, 50 parts H2O, 10 parts HF) and mounted onto lucite blocks using double-sided tape to prevent bending during handling. Thin foils suitable for transmission electron microscopy were prepared from each of the sheet samples. The sheets were mechanically polished through 600-grit paper to a 3 to 4 mil thickness and were chemically polished by immersion for 1 to 2 min in a solution containing: 50 parts HNO3, 50 parts H2O, and 10 parts HF, and rinsed in distilled water. The final metallographic procedure was to electropolish for less than 10 sec with an electrolyte of 10 parts perchloric acid and 90 parts glacial acetic acid, at 20 v, at room temperature using stainless-steel point cathodes and a vigorous stirring action. These foils were examined in a Philips EM 200 electron microscope using a 100-kv accelerating voltage.

Jan 1, 1968

By Y. C. Liu, G. A. Alers

measurements of the anisotropy in Young's modulus produced in copper by rolling 95 pct reduction in thickness below room temperature have been carried out in order to study the dependence of the texture on rolling temperature. The results clearly show the transition from a copper-type texture to a brass-type texture as the temperature of rolling is lowered. The intermediate textures observed can be described very well as a simple mixture of the two terminal textures. These results cormbined with other texture measurements make possible afresh review of the experimental facts velating to rolling textures in fee metals and, as a consequence, a critical examination of the current theories is presented. PREVIOUS experiments have shown that the transition from the copper- to the brass-type rolling texture is clearly displayed and can be quantitatively analyzed by measurements of the anisotropy of Young's modulus.' Application of this method to the Cu-Zn alloy system showed that the description of the texture transition as a gradual rotation of the grains from the orientation characteristic of the copper texture to the {110}(112) texture of brass2 was inconsistent with the data. Instead, the data suggested that the texture within the transition region could be described as a simple mixture of the two terminal textures.5 Unfortunately, it was difficult to establish this point conclusively because of the inadequacy of corrections for the composition dependence of the single-crystal elastic constants. Since a rigorous establishment of the nature of this texture transition is essential to our understanding of the formation of rolling textures in fee metals, it is clearly important to undertake an investigation in which the composition dependence of the elastic constants would not enter. A suitable composition-independent texture transition is provided by the well-established variation in the rolling texture of copper with rolling temperature. This temperature-dependent texture transformation has been studied by smallman' in several fee alloys and by Müller5 and others"' in copper. They observed that the texture characteristic of copper rolled at room temperature changed to a brass-type texture when the rolling temperature was lowered to 77°K. Although it is not possible to decide unequivocally from the published pole figures whether or not the 77°K rolling texture of copper is entirely of the brass type,' this complication does not affect the main purpose of the present investigation. In addition to establishing the nature of the texture within the transition region, the modulus data should also provide a determination of the temperature at which the transition occurs as well as the temperature range over which the transition extends. This information when combined with the modulus data on Cu-Zn alloys would then provide a considerable body of new information on textures in fee metals. Since these modulus results and the data obtained from pole-figure studies must be internally consistent, it is appropriate to compile a brief summary of the experimental observations based on all available methods rather than on the pole-figure data alone as has been done in the past. The primary purpose of such a summary would be to yield a more precise definition of the experimental facts on the rolling textures of fee metals, and thus greatly facilitate our evaluation of various proposed theories in this field. The final section of this paper is devoted to this compilation of consistent, experimental facts and their application to the various theories. EXPERIMENTAL PROCEDURE Two 18-lb ingots of cathode copper of 99.99 pct purity were induction-melted under a nitrogen atmosphere in a graphite crucible and chill-cast into a steel mold. The ingots were repeatedly cold-rolled and annealed (I hr at 500°C) into slabs about 1 1/8 in. thick. Blocks 3 1/4 in. wide, 2 1/4 in. long, and 1.000 in. thick were machined from each slab. The rolling schedule used was the same as in the previous investigation1 and the final thickness of the sheet was 0.050 in. with a rolling reduction of thickness of 95 pct instead of 97.5 pct as in the previous work.' The compositions and temperatures of the cold baths used for the low-temperature rolling were as shown in Table I. After each pass the rolled strip was immediately immersed in the cold bath for about 1 min or until the bubbling of the bath had subsided. The modulus data were taken within 2 hr after the rolled strip was warmed to room temperature for the first time, so that effects due to recrystallization were minimized. The modulus specimens were in the shape of flat bars, 3 in. long, 4 in. wide, and 0.050 in. thick, cut with their long dimensions oriented at 15-deg intervals between the rolling direction and the transverse direction. The values of Young's modulus were deduced from measurements of the frequency at which these long narrow bars were set into longitudinal, resonant vibration as previously described.9 To excite the mechanical vibrations in the specimen, an electromagnetic drive similar to that employed by Thompson and lass" was used. The maximum in the amplitude of

Jan 1, 1968

By Robert E. Green, Edmund G. Henneke

Expressions are derived for the orientation factors associated with dislocation damping due to dislocation motion in the basal slip plane. The results of the calculation of these factors for zinc crystals aye pvesepzted and the relevance of these results to ultvasonic-attenuation measuvements is discussed. In this paper expressions are derived for the orientation factors associated with damping of sound waves due to dislocation motion in the basal slip plane of hexagonal crystals. For zinc crystals, the orientation factors for dislocation motion in one slip direction only, as well as for simultaneous motion in all three basal slip directions, have been calculated at 1-deg intervals. The results of these calculations are presented in the form of contour diagrams in a sector of a standard polar coordinate graph. The calculations have been carried out for both the traveling- and the standing-wave conditions. The relevance of these results to ultra sonic-attenuation measurements is discussed. Associated with the calculation of the orientation factors, the modes of elastic-wave calculation were also evaluated, according to the procedure previously employed by Hinton and Green.' The results of these calculations are not presented here since similar results have been reported earlier by Mus-grave.2 However, it should be mentioned that, although the qualitative features of Musgrave's results are preserved, the quantitative values are somewhat altered since different values for the elastic constants of zinc were used. ORIENTATION FACTORS It is convenient to refer to three different sets of coordinate axes, Fig. 1, in the following calculations. First, there are the Miller-Bravais axes which are used in describing the Miller-Bravais indices of planes and directions in a hexagonal crystal. These axes are denoted in the conventional manner by a,, a,, a,, and c. The second set of axes used is a rectangular Cartesian coordinate system located as shown in Fig. 1. Note that the x axis coincides with the close-packed direction al [2110], the z axis coincides with the c axis [0001], and the y axis is orthogonal to these two lying in the [0110 ] direction. Finally, a form of Eulerian angles is used to locate the position of the specimen axis. The angle between the specimen axis and the c axis is denoted by 0 and the angle between the projection of the specimen axis on the basal plane and the a, direction is denoted by ø. The majority of observations on plastic deformation of metal crystals indicates that such deformation is caused by the motion of dislocations on a limited number of crystalline planes and in a close-packed direction. In crystals with hexagonal symmetry the most prominent slip plane is the basal plane (0001) and the slip directiops- are one of the close-packed directions, [2110], [ 12101, or [ 1120]. To properly set the stage for the following work, several points must be clarified. First, we want to consider the contribution to the attenuation of elastic waves by dislocations only. While the Granato-Lucke, model for dislocation damping is presently the one most quoted, it is not necessary to refer the present work to it. The only assumption that need be made is that the motion of dislocations absorbs energy from the elastic wave and therefore attenuates it. It is immaterial here how this energy absorption occurs. However, because dislocations have been observed to move most freely on the (0001) plane for hexagonal crystals undergoing plastic deformation, it will be assumed that it is the dislocation motion on this plane which attributes to the observed attenuation. The basic orientation factor, Ok, is essentially the same as that used by Green and Hinton for fee crystals,4 defined by the equation

Jan 1, 1968

By H. C. Fiedler

The solubility of sulfur in Si-Fe was determined by the metallographic examination of heat-treated and quenched samples. In the absence of manganese, the solubility in 3.1 pct Si-Fe was found to be about 0.010 pct at 1000o C, 0.015 pct at 11000C, and 0.020 pct at 1150°C, which is substatntially less than hitherto reported. Increasing the silicon content was found to decrease the solubility of sulfur, which is consistent with the increase in the activity coefficient of sulfur with increasing silicon content that has been reported for Fe-Si alloys. Manganese additions were studied in alloys containing 3.1 pct Si and between 0.013 and 0.015 pct S. At low manganese levels the solubility product of manganese sulfide was found to be lower than previously reported. THE solubility of sulfur in pure polycrystalline iron has been reported by Rosenquist and Dunicz1 and by Turkdogan et al.2 Samples were equilibrated in atmospheres containing different ratios of H2S/H2. Both groups of investigators found a solubility limit in y iron of 0.013 pct at 1000oC and 0.031 pct at 1200°C. In addition, Rosenquist and Dunicz1 found a solubility limit in a iron of 0.020 pct at 900°C. Ainslie, Hoffman, and seybolt3 found significantly higher sulfur contents in polycrystalline iron samples than in single-crystal samples after heating at 890°C in a sealed tube containing a mixture of powdered iron and FeS made with s35. Whereas the single crystals contained 0.013 and 0.016 pct S (± 0.005 pct), the polycrystalline samples contained between 0.016 and 0.026 pct S. Autoradiographs suggested that the excess sulfur in the polycrystalline samples was due to the segregation of sulfur in solution at grain boundaries. Ainslie and seybolt4 have reported on the solubility of sulfur in 3 pct Si-Fe. Their samples were sealed in capsules containing hydrogen and sufficient sulfur as cobalt sulfide to saturate the sample. After heat treating, the sulfur-rich phase on the surface was removed by abrading, and the sulfur content of the sample was taken as the equilibrium value for that temperature. Before the equilibrating heat treatment, the samples were heated to 1300°C to coarsen the grains. The resulting grain size, which was about 3/18 in. in diam, was considered sufficiently large to preclude a sensible increase in sulfur solubility due to grain boundary segregation. They reported the solubility to be 0.029 pct at 900oC, 0.063 pct at 1000oC, 0.076 pct at 1100°C, 0.122 pct at 1200°C, and 0.098 pct at 1300°C.

Jan 1, 1968

By J. N. Maycock, P. W. M. Jacobs

Previous measurements of the thermoelectric power of ionic crystals are reviewed briefly. It is concluded that, while extensive measurerements are available on systems in which the electrode M has a cation in cornon with the sall MX, there is as yet little modern work on systems in which the metal electrode M' does not haue a calion in common with the salt. We haue now measured the thermoelectric power of- single cryslals of KC1 and of KC1 + SrCl2 between plati.nu?n electrodes over a much wider range of temperature than before. individual ionic heats of transport, which, while probably not very accurate, are of a reasonable order of magnitude, are obtained from this data on the basis of an assumption that charge carriers do not cross the electrode/salt interface. RELATIVELY little work has been done on thermal diffusion in ionic crystals. Reinhold and coworkers1-I measured the thermoelectric power and Soret effect in silver and cuprous salts and their mixed crystals. One electrode was kept at constant temperature and electromotive force was measured as a function of the temperature gradient. This is not a satisfactory technique if the results are to be compared with theory; rather should the electromotive force be measured for small temperature differences as a function of the mean temperature of the two electrodes. They used electrodes having the same cation as the salt. Patrick and Lawsons measured the thermoelectric power of AgBr and of AgBr containing 0.25 mole pct CdBr2 using silver electrodes and temperature gradients of 10°C in the temperature range 100° to 400°C. The results were analyzed using the Teltow9 values of the ratio of the mobility of the two types of charge carrier (cation vacancies and interstitials) found from conductance measurements and the wagnerlo estimate of the heterogeneous contribution to the thermopower, Ohet They obtained values of qi = 0.017 ev and q$ = -0.385 ev for the heats of transport of interstitial Ag ions and cation vacancies, respectively. Their data has been reanalyzed by Haga using the corrections to the Wagner formula for ehet given by Howard andLidiard; Haga found ev. Christy et a1.14 have measured the thermopower of AgBr containing 0.01 to 1.0 mole pct CdBr,. They analyzed their results in terms of the theory of Howard and Lidiard and found that excellent agreement with the theory was obtained if q5 + : + hF was set equal to 0.70 ev at 175°C and equal to 0.58 ev at 250°C. Since Teltow's value for hF, the enthalpy of formation of a Frenkel defect pair, is 1.27 ev, this means that qt + q: increases in magnitude from -0.57 ev at 175°C to -0.69 ev at 250°C. This result is in poor agreement with Patrick and Lawson's value of -0.37 ev for pure AgBr (for which the corrections to the Wagner estimate for ehet are very small). christy1' has also reported thermopower measurements for pure silver halides and for the systems he finds that qr + qt for AgBr increases in magnitude from about -0.55 ev at 150°C to about -1.1 ev at 400°C. The temperature dependence of the sum of the heats of transport in AgCl is very similar in magnitude. The sum qi + q cannot be decomposed into the individual interstitial and vacancy heats of transport without a knowledge of the entropy contribution from the change in the lattice vibrational frequencies around the interstitial and vacancy. Despite this it seems an inescapable conclusion from Christy's analysis that and -6 = Q Ag are quite strongly temperature-de pendent and that -q: is much greater in magnitude than the corresponding activation energy for vacancy migration, +0.37 ev. It remains a mystery as to why the data for pure AgBr are fitted so well by the assumption of temperature-independent heats of transport if association of impurity ions and vacancies is neglected.l The values for q$ and q: so obtained are also much more in line with those expected from a simple kinetic interpretation of the heats of transport due to wirtz.17 Christy and Hsueh have also measured the thermopower of CuCl between copper electrodes; 0 for pure CuCl is comparable with that for the silver halides but, owing to the limited solubility of divalent cation impurities it was not found possible to deduce values for the heats of transport. In contrast to these extensive measurements on cells of the type M MX 1 M, there have been relatively few attempts to measure the thermoelectric power of cells of the form M' 1 MX I M'. (We specifically exclude from discussion cells of this type in which the metal electrodes M' are in contact with gas containing a controlled partial pressure of either M or X,, since in these cells the electrochemical reactions are analogous to those of the first type.) The thermoelectric power of Pb12, PbC12, TlC1, TlBr, TlI, NaNO3, and KNO 3 between platinum electrodes was measured by Thie1e.l3 In discussing these measurements Holtan20 asserts that the thermopotential initially fluctuated wildly and even changed sign before approaching a steady value. A high degree of irreproducibility is also evident in the work of Nikitinskaya and Murin21 who first studied the thermopower of NaCl and KC1 between platinum electrodes. Much better reproduci-bility was achieved in our earlier measurements on KC1;22 these were, however, confined to a relatively narrow temperature range and one of the objects of the work reported in this paper was to extend the temperature range of the measurements of the thermoelectric power 8 of KC1. The only other published

Jan 1, 1967

By David R. Poirier

THE activity of carbon in Fe-C-Cr liquid solutions has been measured by Richardson and Dennis,1 Fuwa and chipman,2 and Goto et aL3 Fuwa and Chipman2 have presented their data along with data of Richardson and Dennis1 and utilized an interaction parameter. However, the interaction parameter is only valid for dilute solutions of carbon, because, as indicated, the same interaction parameter does not apply to more concentrated solutions of carbon (i.e., the effect of chromium on the saturation of graphite in liquid iron). Ohtani4 has attempted to account for the effect of carbon concentration on the interaction parameter; however even his analysis does not apply to the saturation data. Also, the effect of temperature on interaction parameters must be taken into account. Therefore, in any process where the concentration of carbon and/or the temperature changes (such as solidification), the use of an interaction parameter is not adequate to know the activity of carbon. The purpose of this communication is to make use of the existing data on the effect of chromium on the activity of carbon in liquid iron solutions in such a way that the activity can be described as a function of both composition and temperature. The method is an extension of Rist and chipman's5 analysis for the binary Fe-C solutions. As in Rist and Chipman's analysis, the activity coefficient is assumed to obey the relation: log y1 = at(l -X1)2 + It [1]

Jan 1, 1969

By M. A. Quader, D. Kuhlmann-Wilsdorf, R. A. Dodd

STACKING fault tetrahedra were first observed in quenched and aged pure gold by Silcox and Hirsch1 and identified as defects originating in the collapse of vacancy discs on {111} planes. It was supposed that sessile loops are the first product of the collapse, and that by a dislocation dissociation/glide sequence these are converted into tetrahedra. Although the tetrahedra can be mechanistically accounted for in this way, recent investigations indicate that their growth occurs by the absorption of individual vacancies on small nuclei involving perhaps as few as six vacancies.2-7 Besides stacking fault tetrahedra, triangular and crystallographic shaped Frank loops, although fewer in number, have always been observed in quenched and aged gold.19798 It is not known definitely whether these loops form from collapsed tetrahedra. The fact that the Frank loops are usually larger than the accompanying tetrahedra might indicate that the loops grow independently by absorbing vacancies, but this does not rule out the possibility of the collapse of tetrahedra into loops under all circumstances. Silcox and Hirsch1 have actually observed under the electron microscope tetrahedra collapsing into loops, probably due to stresses set up by the heating of the specimen by the electron beam. The energy residing in the stacking faults of a tetrahedron is proportional to the square of the edge length, while the energy of a triangular perfect dislocation loop depends on its edge length, L, as const L ln(L/ro). Therefore, beyond some critical size tetrahedra must become unstable with respect to collapse into triangular loops.1,3,8-11 However, it seems that in the absence of strong stresses tetrahedra usually decay by the

Jan 1, 1969

By Richards R. Vandervoot

T HE creep behavior of many polycrystalline metals at moderate stresses can be described by the empirical relationship: where Em is the minimum creep rate, A is a constant, a is the applied stress, E is the average elastic modulus at the test temperature, and D is the self-diffusion coefficient.&apos; This equation is generally applicable for strain rates of less than around 10-5 per sec and temperatures greater than about one-half the melting point in absolute units. Under these conditions atomic mobility plays an important role in the deformation process, and steady-state creep occurs when a dynamic equilibrium is reached between the generation and recovery of dislocation substructure. Although several theoretical mechanisms have been proposed to explain the creep of polycrystalline solids,2"4 the dislocation climb model2 is in accord with most experimental observations. The majority of creep data used to develop Eq. [1] came from metals with either the fcc or hcp crystal structures. However, on the basis of results for a and 7 iron as well as those for a and a thallium, Sherby concluded that the high-temperature deformation behavior of close-packed metals and bcc metals is probably the same.&apos; The greater creep resistance of fcc and hcp metals and alloys on a relative temperature scale was attributed to lower diffusivities in the close-packed structures. To further compare the creep properties of fcc, hcp, and bcc metals, creep data for all six bcc refractory metals were analyzed according to Eq. [I]. The results are shown in Fig. 1. The sources of information for the quantities used to prepare this figure are listed in Table I, except for high-temperature elastic moduli. The latter data were obtained from Refs. 28 and 29. The dashed lines in the figure represent the range and breadth of data analyzed by Sherby for fcc and hcp metals. In general, the deformation behavior of all of the refractory metals, ex- cept possibly that of tungsten, can be represented by Eq. [1]. This correlation is strong evidence of the similarity that exists between creep of pure close-packed metals and creep of pure bcc metals. At (Em/D) < 108, the results of Flagella and Tarr on tungsten (W-1 in Fig. 1) agree with the five-power stress law, while those of Green (W-5 in Fig. 1) show a seven-power stress dependence. Where (Em/D) > 108, the stress exponents for other data on tungsten were in the range 10 to 15. It is possible that the creep rate dependence on stress in this region is not a power law but exponential (i.e., Em - eßo). However, it was not feasible to differentiate between these two cases because of the steep slope and scatter in the data. Note the inflection point in the curve for the data of Flagella and Tarr (W-1 in Fig. 1). The slope of the line changes from 5 to around 10 at Em/D = 108. The breakdown of the fifty-power stress law at high stresses is not uncommon in other metals, and this phenomenon may result from nonequilibrium conditions in the material such as excess lattice vacancies produced by rapid straining.30 The mechanical strength of a polycrystalline metal is related to its microstructure. Attempts to establish the influence of grain size on the creep rate of metals and alloys have led to a wide variety of results. For example, the following effects have been observed: creep rate decreases as grain size increases;31&apos;32 creep rate decreases as grain size decreases;&apos;,33 creep rate is a minimum at some critical grain size and increases with either an increase or decrease in

Jan 1, 1969

By William J. Gillich, Gerald L. Moss

PREVIOUS studies of the shock loading of randomly oriented polycrystalline aggregates have firmly established that, after rather short load duration, hydrostatic compression closely approximates the shocked state.&apos; However, McQueen deduced from pressure measurements with good time resolution that, during shock loading, metals begin to undergo a stress relaxation at the yield stress. He suggested that the relaxation is due to plastic deformation accompanying the change from a one-dimensional compression to a three-dimensional, hydrostatic, compression.&apos; Stress relaxation may occur faster as stress is increased above the yield stress, but the existence of unidirectionally compressed states for finite times suggests that the concept of a unidirectionally distorted lattice should furnish considerable insight into the mechanical behavior of materials subjected to shock loading. Here, a crystallographic analysis is presented for the hypothetical situation where atom motion may be considered as unidirectional which, as indicated above, is a useful extension of the macroscopic concept of shock loading to the microscopic domain. Only motion caused by the com-pressive forces is treated; i.e., lattice vibrations upon which this motion is superimposed, as discussed by Fitzgerald, are ignored.3 The purpose of the analysis to be presented is to develop a description for single crystals of the lattice rotations that occur for idealized uniaxial strain deformation. The usefulness of such an analysis in realistic deformation is to give a method of specification of those properties of an initially distorted lattice which would affect the subsequent deformation. Non-axial complications that arise experimentally, such as off-axis rarefaction waves, must be treated in proper context. Consider the material element shown in Fig. 1 and let the compression be uniform at all regions of the element. Then, any interior point of the element is displaced in proportion to its distance from the base of the element. Accordingly, if the top of a unit element is displaced by an amount, (-K), with respect to the base, a point P(X, Y) will be displaced by (-KY). Crystal planes are, therefore, rotated by the compression. Analysis of this rotation may be accomplished from the geometry shown in Fig. 1 where the line OP is the edge of the plane {hkl} and N is its normal. The orientation of the crystal plane with respect to the shock direction is specified by the angle, before deformation. After deformation the edge of plane {hkl}

Jan 1, 1969

By Charles R. Simcoe

The stress-strain curves in the microyield region for various Fe-C solid solutions shown by Davies and Ku are typical examples of parabolic curves defined by the expression a = kEn 111 These data, when replotted on log-log coordinates, as shown in Fig. 9, exhibit three essentially parallel straight lines. It is apparent that carbon increases the flow stresses, but does not affect the exponent n. In other words, the only factor in Eq. [1] affected by in in carbon content is the constant k. As Eq. [1] is written k is the stress at a strain of 1.0. This is unsatisfactory for examining data in the microyield region. Therefore, the equation can be altered to the form: to permit the use of the authors&apos; microyield stress at a strain of 10-6 as k. Extrapolating the curves in Fig. 9 to a strain of 10-6 gives stress values of 2000, 3200, and 5400 psi for 0.008, 0.014, and 0.02 pct C, respectively. These values do not agree exactly with the authors&apos; measured values, but this will not affect the following discussion. The effect of carbon content on the slopes of the stress-strain curves shown in Fig. 2 of the paper by Davies and Ku can be analyzed by differentiating Eq. [2] with respect to strain. Thus: where n is always less than 1.0. Since n is essen- tially constant as a function of carbon content for the data under discussion, the slopes of the stress-strain curves depend only on k and E. If the slopes are examined at various selected Plastic strains. i.e., 10-6, 10-5, and so forth, it follows from Eq. [3] that the dif-ferent slopes for the different carbon contents depend only on the different values of ke=10-6. Thus, the larger ke=10-6, the steeper the linear stress-strain curve will rise with increasing plastic strain. This

Jan 1, 1969

By S. W. Zehr, G. S. Murty, W. A. Backofen

AN observation by Squires, Weiner, and phillipsl has stimulated interest in a mechanism of deformation at high temperature (above -0.5 of the absolute melting point) that is not usually thought to be involved in the creep of metals. They found precipitate-free or "denuded" zones along grain boundaries normal to the stress axis in tensile specimens of a hydrided Mg-1/2 wt pct Zr alloy after slow straining at 450° and 500°C. Their suggestion that the zones were a result of directional diffusion of magnesium atoms was supported with calculations from Harris and Jones2 which also tended to identify the process as Nabarro-Herring (N-H) creep3,4—a process that is characterized by Newtonian viscosity, with stress (o) directly proportional to strain rate (C), and one that proceeds by lattice diffusion. Material transport by diffusion along grain boundaries is an alternative basis for Newtonian viscosity, as demonstrated by Coble,5 and is favored over N-H creep for fine grain size and lower temperature.6 In either case, the strain rate sensitivity of flow stress, defined as m = d log o/d log E (which commonly appears in the empirical a = KEW), is unity. The experiments to be described here gave metallo-graphic indications of diffusional creep which were no less clear than those just cited, but the associated m (as measured by the method of Ref. 7) was much more like that of a Bingham material. For true Bingham behavior, (a — ao) E, where oo is an initial yield stress. Therefore, even if flow after yielding should occur by diffusional transport, m must increase from 0 as < is raised to reach unity only in the limit as One result is that the resistance to tensile necking conferred by Newtonian viscosity is lost, which would become increasingly apparent through the formation of more sharply defined necks as 6 is lowered. That trend appeared in these experiments. Most of the work was done on an extremely finegrained alloy of magnesium with -6 wt pct Zn and ½ wt pct Zr (Mg ZK60); the initial mean-intercept grain diameter, L, was 0.55 µ. Shown in Fig. l(a) is a germanium-shadowed carbon replica of the surface of a specimen that was coated with silicone oil,* heated to 270°C under a helium atmosphere, and then stretched locally -200 pct at an initial E = 3.3 x 10-5 sec-1. Under

Jan 1, 1969

By W. C. Coons, E. H. Rennhack, R. A. Perkins

THE constitution of Ti-N alloys containing up to 17.5 wt pct N has been investigated by Palty, Margolin, and Nielsen.1 Their results, which confirmed earlier work

Jan 1, 1969

By H. A. McKinstry, F. F. Lange

A vector analysis of orientating single crystals using the Laue back-reflection X-ray technique is given. Briefly, the analysis involves using a few data taken from a Laue photography and defining the crystal co- ordinate axes in a reference coordinate system. After a few matrix multiplications, the proper goniometer angles can then be determined to orient the crystal coincident with the reference frame. This analysis is easily programed for a digital computer to provide a fast, precise, and efficient method of orienting many crystals which are identical. The general procedure is as follows. The crystal is mounted on a goniometer. Laue photographs are taken until an array of diffraction spots is observed that includes a Laue spot that represents a rotational axis of symmetry. The rotation angles of goniometer are recorded. These angles are defined as positive for a counterclockwise rotation. When the axis of symmetry is located on the Laue photograph, the crystal coordinate axes can be defined in the reference coordinate system* as follows. Two Laue spots are chosen, one of which corresponds to the rotational axis of symmetry and the other to a set of planes whose zone axis is a known crystallographic direction and normal to the rotation axis of symmetry. The Laue spots are used to determine these two crystal directions in the reference coordinate frame. This is done by placing the Laue photograph on a sheet of polar coordinate graph paper and determining the polar coordinates (r, o) of these two diffraction spots in the reference coordinate frame. Their third coordinate is the distance between the crystal and the film (-D). The coordinates Xni of the two crystal directions Nn, (n = 1, 2) in the reference frame are then calculated by the following equations: Xn1 = -D X2n = Ancos on X3n = A, sin on where -tan- 1 rn/D An =Dtan(tan-1rp/D/2) By taking the proper cross products of these two directions (normalized to unit vectors), the crystal coordinate axes 3 (i = 1, 2, 3) can be determined in the reference frame. This is illustrated in Fig. 1. The next step is to determine the relation between

Jan 1, 1969