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By William C. Hagel

Oxygen-18 exchange between gaseous oxygen, held at a pressure of 125 mm Hg in a PL-IORh chamber, and splzeres of a Fe2O3 containing three or less grains was determined from 9000 to 1250°C. Isotope equilibrum on crystal surfaces appears to be quickly established, and the rate-determining factor is self-difiusion confbvrning to the relation D = 2.04 esp(- 77,900/RT) sq cin sec-'. Changing sphere diameters caused no detectable variation in diffusion coefficients. Oxygen ions diffuse faster than cations at low temperatures, but a crossover may occur at about 1150°C. INVESTIGATIONS by Davies et al.' and Himmel et al2 have suggested that the mechanism of iron oxidation above 600°C involves a predominance of cation migration in the wüstite (FeO) and magnetite (Fe301) layers and oxygen-ion migration in the hematite (a Fe2O3) layer. Evidence for little cation migration during hematite growth consists of: 1) the disappearance of radioactive-silver markers, presumed to vaporize from the oxide-gas interface, and 2) a large discrepancy between parabolic rate constants for magnetite oxidation and those calculated from Lindner's3 data for cation self-diffusion, D:, using Wagner's theory.4 Reversing the calculations gave anticipated self-diffusion coefficients, D:, for oxygen ions of 3.6 x 10-9 sq cm sec-1 at 1100°C and 5.9 x 10-10 sq cm sec-1 at 1000°C. Since then Kingery et a1.5 reported three values for oxygen-ion diffusion in polycrystalline, sintered hematite. These were obtained near 1200°C, at an oxygen pressure of approximately 150 mm Hg, and could be represented by the Arrhenius expression, Dg = 1 x 10 11 exp(-146,000/RT) sq cm sec-1. Extrapolation to temperatures below 1100°C infers that oxygen ions are less mobile than cations. This contradicts the aforementioned oxidation evidence and also coble7s study of the initial sintering of hematite. From the latter, apparent diffusion coefficients for the slowest rate-controlling species could be calculated, and fair agreement was found with an extension of Lindner's data for cation diffusion. Fig. 1 depicts such comparisons graphically. Three points have been included for the determinations of Himmel et al. on cation diffusion in large, natural hematite crystals surrounded by pure oxygen at atmospheric pressure. No dependence on crystal log raphic direction was noted. Since the value of 10-l4 sq cm sec-' at 1000°C actually represents an upper limit, one might interpret that there is a small decrease in D: when single crystals are employed. On the whole, however, cation diffusion appears relatively well-defined,* while the few results tension to lower temperatures. After having gained experience measuring oxygen-ion diffusion in certain glasses7 and in the corundum oxide, a Cr2O3, the purpose of this work was to determine D; values for hematite and thus possibly assist a mechanistic understanding of the kinetics of the oxidation and reduction of solid iron oxides. I) EXPERIMENTAL PROCEDURE A) Material. Hematite powder of moderately high purity was received from the Columbian Carbon Co. An accompanying lot analysis listed 0.03 H2O, 0.008 weight percents, with the remainder Fe2O3. Subsequent treatments were ball milling, drying, prepressing, and hot-pressing for 60 min at 1350°C under 5000 psi. Since graphite dies coated with a slurry of alumina were used for hot-pressing, the surrounding atmosphere at temperature was sufficiently reducing to form some magnetite on the outer surface of each cylinder. After removing any attached alumina, a stabilizing anneal of 50 hr at 1300°C in oxygen was added. The final product was nonmagnetic and exceeded 97 pct of the density (5.24 g cm-3) usually given for FezO3. On polishing cylindrical ends, counts were made of the number of grain boundary intercepts per

Jan 1, 1967

By H. M. Davis, T. S. Jones

A methodfor accelerating the reduction of a metal oxide by carbon monoxide is to incorporate in the reduction system a nonreducible oxide which has a strong affinity for carbon dioxide and will remove it from the product gases. The effectiveness of this method was investigated by veduction experiments on specially prepared powder mixtures of SrO-ZnO ("active'.) and SrCO3-ZnO (reference). Measurements at 750o and 677°C showed that the rate of reduction of ZnO by CO was as much as an order of magnitude greater in the presence of SrO. Under the experimental conditions at least as much CO2 as generated by veduction was absorbed when SrO was present. Enlzancernent of the veduction rate by SvO resulted from modification of' gaseous djfitsion processes. THE specific question posed in this investigation was whether the reduction reaction CO + ZnO - Zn(g) + COa [1] could be accelerated by incorporating strontium oxide into the oxide charge undergoing reduction. Provided the strontium oxide was active enough, it could remove carbon dioxide from the product gases of ( 11 and form strontium carbonate, thus modifying Reaction [ 1] to CO + ZnO + SrO = Zn(g) + SrCO3 [ 2] This study of the comparative rates of Reactions [ I] and [2] can be considered as a particular case of a general scheme for increasing the rates of reduction of metal oxides by carbon monoxide. The limits of applicability of this scheme are indicated in the simple thermodynamic analysis presented in the appendix. This analysis primarily dictated the choice of the system, CO-ZnO-SrO, employed in this investigation. In addition, it was thought that a study of this scheme by use of the CO-ZnO-SrO reaction system would be of special interest in view of indications in the literature1-3 that the gaseous reduction of zinc oxide is prone to rate control by diffusion in the gas phase. The distinction should be pointed out between this and other efforts to increase the rates of reduction reactions through the use of addition agents. Additions of a wide range of chemicals have been tried with de- grees of apparent success varying from slightly negative to highly positive. The reasons for making additions have included the use of salts to produce effects akin to catalysis,4, 5 the alteration of the microstruc-tural details of the reduction process (including solid-state diffusion),6-8 and the conversion of an en-dothermic reaction into one that is exothermic or autogenous.9-12 The means used to attempt alteration of the enthalpy change has commonly been to incorporate lime into the charge, so that heat is generated by reaction with either of the reaction products, carbon dioxide or water. The use of lime in this way makes endeavors such as that of Edstrom and Wiberg similar to the present one. Furthermore, the basic principle behind the present work has previously been set forth.13 However, a detailed investigation of the type of reaction described in this work does not appear to have been conducted. EXPERIMENTAL PROCEDURE From both conceptual and physical standpoints, Reaction [2] is to be considered as the sum of two reactions:

Jan 1, 1968

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

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 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 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 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 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

By A. Mitchell, T. Bagshaw

A recent paper by Thomas1 has presented new data on the solubility of hydrogen in solid silver at 1 atm pressure in the temperature range 600° to 963°C. However, no data is reported in the literature on hydrogen solubility in liquid silver. The Sieverts technique which has been described previously2,3 was used in the present work. Charges of approximately 160 g were melted in Morgan "purox" recrystallized alumina crucibles and purified helium was used for the determination of the "hot volume" during each experiment. A chemical analysis of the silver indicates that the impurity content (Cu + Al) is less than 0.02 wt pct. Hydrogen solubility in the temperature range 963° to 1200°C was investigated. The results of three experiments are shown in Table I. Fig. 1 shows an Arrhenius plot of the present work together with the solid-state data of Thomas, Steacie, and johnson,4 Eichenauer et al.,5 and Siegelin et al.6 The following expression has been derived from the Arrhenius plot of the present data: log (solubility of hydrogen, cm3 per 100 g) = 2.154-3512.0/ToK The heat of solution derived from Fig. 1 is 31,150 cal per g mole H2 compared with the value of 33,020 cal per g mole H2 obtained by Thomas and 12,000 cal per g mole H2 obtained from the data of Steacie. It was observed that hydrogen evolution took place when the silver melts were solidified under 1 atm of hydrogen, which would not be expected from an extrapolation of the results of Steacie. Schenck and Lange7 have observed that, for several transition metals at their melting points, the ratio of the hydrogen solubility in the liquid to that in the solid lies in the range 2.1 to 3.1. The present results and those of Thomas are in accord in this respect having a ratio of 2.8. &apos;C. L. Thomas: Trans. TMS-AIME, 1967 vol. 239, pp. 485-96. 2T. Bagshaw and A. Mitchell: I. Iron Steel Inst., 1966, vol. 204, p. 87. &apos;M. Weinstein and J. F. Elliott: Trans. TWS-AIME, 1963, vol. 227, p. 382. &apos;E. W. R. Steacie and F. M. G. Johnson: Proc. Roy. Soc. (London), Ser. A, 1928, vol. 117, pp. 662-79. &apos;W. Eichenauer et al.: Z. Metallk., 1958, vol. 49, pp. 220-25. 6W. Siegelin et al.: Z. Elektrochem., 1957, vol. 61, pp. 359-66. &apos;H. Schenck and K. W. Lange: Arch Eisenhuettenw., 1966, vol. 37, no. 9, pp. 739-48.

Jan 1, 1969

By R. W. Jordan, J. Winter, A. J. Goldman

Kirkendall diffusion of copper and nickel atoms across the bond interfaces, as well as oxygen diffusion in the core to the interfaces, are the mechanisms which control the variation in bond strength with annealing time at 1600°to 1800°F in the cupro-nickel clad copper Mint composite. The unequal mass transfer resulting from the high diffusion rate of copper in cupro-nickel compared with that of nickel in copper caused void formation in the core. Small voids also formed in the cladding after short annealing times. These may have been nucleated by nickel oxide particles which are formed by the dissociation of the cuprous oxide in the core and the movement of oxygen to the cupro-nickel interfaces. The bond strength drops to very low values for annealing time up to 3 hr when the void density is greatest. The increase in bond strength after 16 to 72 hr at 1600°F is a result of the decrease in the void density in the cupro-nickel cladding and the growth of grains across the interface. The void density decrease is attributable to grain boundary diffusion of vacancies to the surface. The abnormally large grains in the copper preclude a similar process from taking place in the core. THE solution to many engineering materials problems that cannot be satisfied by using a single metal or alloy is often attained by combining two or more metals in such a way that each component performs a different function, while the composite meets the overall requirements. The Coinage Act of 1965 authorized a changeover from the traditional 90 Ag-10 Cu dimes and quarters to a bimetallic laminate of 75 Cu-25 Ni clad on a copper core. Economic considerations as well as physical, chemical, and mechanical properties provided a basis for the selection of this composite as a substitute for the silver-bearing alloy. An extensive survey of alloys suitable for use as coinage was prepared by Battelle Memorial Institute for the U.S. Mint.1 It was found that the cupro-nickel/cop-per/cupro-nickel composite satisfied the required color, density, mechanical properties, corrosion resistance, electrical properties, and magnetic properties to make it completely acceptable to the general public and the vending machine industry. This investigation is part of a program to determine the feasibility of reclaiming composite scrap by thermally degrading the bond strength of the cupro-nickel clad copper laminate. The composite exhibits bond degradation and subsequent bond improvement during annealing in the temperature range 1600" to 1800°F. A study of the operative diffusion processes and the resultant structural changes was made in order to explain the observed variations in bond strength with annealing time. EXPERIMENTAL PROCEDURES AND RESULTS Bond Degradation. A measurement of the forces required to peel the cupro-nickel cladding from the

Jan 1, 1969

By T. Leffers, A. Grum-Jensen

The development of texture in copper and brass (15 pct Zn by weight) rolled at room temperature and in copper rolled at -196°C has been followed by determination of pole figures for various degrees of reduction. The concurrent development in microstructure has been investigated by transmission electron microscopy. For low deformations, the texture in brass, and in copper rolled at -196°C, is the same as the texture in copper rolled at room temperature. The difference in texture does not show until 50 pct reduction. At the same reduction at which the difference in texture appears, mechanical twinning starts in brass and low-temperature rolled copper. Nevertheless, Wassermann&apos;s twinning theory is found to be incompatible with the present resulls. All fcc metals and alloys develop, by heavy rolling, one or the other of two types of texture, classified for convenience as copper type and brass type, or possibly a &apos;(mixed" texture representing an intermediate stage between the two types. The pure fcc metals, except silver, develop copper-type texture by rolling at room temperature. Silver and many alloys, including brass with more than 10 pct Zn, develop brass-type texture.&apos; By rolling at low temperatures a transition in texture from copper type to brass type has been observed for copper of commercial purity.2&apos;3 It is generally accepted that there is a correlation between the type of texture developed and the stacking fault energy. Metals and alloys having fcc structure develop brass-type texture when rolled at room temperature if the stacking fault energy is low, whereas those with higher stacking fault energies have copper-type texture.2 Thus, the difference in stacking fault energy must cause a difference in deformation mechanism responsible for the difference in texture. Of the numerous theories advanced concerning the nature of this difference in deformation mechanism, four seem to be of current interest. Smallman and Greeen,2 Dillamore and Roberts,4 and Dillamore5 refer to the fact that cross slip more easily takes place in a material with a higher stacking fault energy and suggest that the copper-type texture is developed by deformation with extensive cross slip whereas the brass-type texture is developed by deformation without cross slip. Haessner6 has advanced the theory that the copper-tye texture is developed by a combination of normal {111} slip and slip on other planes, mainly 1100). Thus his theory, like the theory above, proposes an additional deformation mode for the formation of the copper-type texture. Contrary to this, wassermann7 and Ahlborn et al.8 believe that the copper-type texture is obtained by normal slip. In their opinion mechanical twins will change a copper texture into a brass texture. For this reason it is suggested that the brass-type texture is developed when, in addition to normal {111}(110) slip, mechanical twinning is present. None of these theories are, however, supported by direct experimental evidence. In a recent experiment Hu et al.9 have followed the development of rolling texture in copper and brass. The texture of copper and brass was found to be es-

Jan 1, 1969

By J. J. Frawley, W. J. Childs

The dynamic nucleation of supercooled bismuth and Bi-Sn alloys has been studied over a frequency range of 15 to 20,000 cps. For low-frequency vibration, a minimum vibrational energy was required for enhancement of nucleation. Above this critical energy, the dynamic supercooling was less than static supercooling showing that vibration promoted nucleation. The amount of dynamic supercooling continued to decrease with increasing vibrational energy until a minimum or threshold value was reached. This minimum value of supercooling for nucleation remained constant joy all further increases in vibrational energy. For higher frequencies, similar results were observed. This behavior has been related to the necessity of cavitation for dynamic nucleation. When a liquid is cooled to a temperature below its equilibrium melting point, the solid phase is more thermodynamically stable. However, for solidification to occur, a two-step process, nucleation and subsequent growth of the solid phase, must occur. When a liquid is supercooled, that is cooled below the equilibrium melting point, the controlling process for solidification to begin is the rate of nucleation. Once nucleation has occurred, the solidification process is controlled by the rate of growth. Nucleation can be induced by two factors: either by a catalyst or by the use of mechanical shock. Numerous investigators1-4 have studied the effect of nucleation catalysis but much less systematic study has been made of nucleation by mechanical shock waves. The influence of vibrations on grain size in castings and ingots has been studied by many authors but no clear understanding of the mechanism or accurate prediction of the effect has been presented.5 It would be intuitively expected that the further the departure from equilibrium (i.e., the greater the supercooling), the easier it would be to induce nucleation. This has been quantitatively demonstrated both by walker6 and later by Stuhr,7 that the greater the degree of supercooling the easier it is to nucleate by a shock wave. Stuhr also attempted to obtain the mechanical energy required for nucleation of bismuth as a function of supercooling. He vibrated a crucible containing supercooled metal at low frequencies and various amplitudes and noted the corresponding dynamic supercooling obtained. The amount of supercooling was inversely proportional to the mechanical energy applied. Limitation of his experiment was the problem of the confinement of the liquid in the crucible without splashing and minimizing other unwanted modes of vibration. Tiller et al.8,9 did similar work on tin and Sn-Pb alloys using an electromagnetic stirring device. Their conclusions were that the magnitude of the magnetic field strength did not affect the amount of undercooling at which nucleation was initiated. While conclusive experimental results have been lacking to explain this effect of mechanical vibration on inducing nucleation, a number of theories have been proposed. Two of these theories are discussed below. 1) The Change in Melting:- Point Locally Due to the Change in Pressure (Clapeyron Equation). According to Vonnegut10 the most plausible explanation for the nucleation of a supercooled melt by cavitation is the effect of changing the melting point by a change in pressure. For materials where the volume decreases on solidification, an increase in pressure raises the melting point; for materials which expand on solidification, the melting point is raised for a decrease in pressure, i.e., rarefaction. Using the Clapeyron equation, the melting point of a metal can be calculated as a function of pressure. If it is assumed that the equation can also be used to calculate the temperature of nucleation of a supercooled melt as a function of pressure (i.e., the temperature of heterogeneous nucleation will increase with pressure at the same rate as the melting point), the amount of supercooling required for nucleation will be constant at all pressures as shown in Fig. 1. It is obvious that an isothermal change which results in an increase in melting point results in an equal increase in supercooling. This increase in supercooling may now be sufficient for nucleation. A pressure of 80,000 atm was calculated, using the Clapeyron equation, as the pressure required to increase the temperature of nucleation of nickel by 200°C. According to Lord Rayleigh,11 this very large pressure could be generated for a very brief period of time by the collapse of a cavity. This pressure wave is radiated in all directions from the collapsed cavity. If the temperature of the melt is slightly below its equilibrium melting temperature at atmospheric pressure, stable growth can follow; that is, once nucleation occurs, growth becomes the main driving force of the solidification process. This proposal has been extended to water which expands on freezing by assuming that nucleation occurs during rarefaction following the pressure pulse. This negative pressure pulse should follow immediately after the positive pressure pulse with its magnitude approaching the critical tensile strength of the liquid. The negative pressure developed during this period would raise the melting point of water and thus promote nucleation. Hunt and jackson12 have suggested this for water. Similarly, it could be postulated that bismuth which also expands on freezing could be nucleated during the negative pressure pulse. 2) Nucleation by a High-pressure Phase. An extension of the Clapeyron equation to systems where density decreased on freezing at atmosphere pressure has been proposed by Hickling.13 The phase diagram for water initially shows the well-known decrease in

Jan 1, 1969

By John P. Hager, Igor A. Wilkomirsky

The thermodynamic properties of the Pb-Ag system have been determined between 775° and 950°C by the cell: Electrotransport measurements on silica-saturated PbO-SiO2 melts established that the conduction was entirely ionic and that lead is present only in the divalent state. The activities of lead and silver exhibit Positive deviations from ideal behavior. In dilute solutions the activities of lead and silver follow Henry&apos;s law. The values obtained for yhb and yig at 1200°K are 1.49 and 1.69, respectively. Determination of a portion of the liquidus curve agrees well with the established phase diagram. provides an accurate means for the thermodynamic study of liquid alloy systems. However, Wagner and wernerl have shown that cells of type I are limited to alloy systems for which the reaction at the alloy-electrolyte interface will be extremely small. The traditional electrolyte for cells of type I has been a low melting point mixture of group IA chlorides, to which a small amount of the compound ACIZa has been added. However, the choice of a chloride electrolyte may not always be practical, in that the Gibbs free energies of formation of the compounds ACIZ, and BCIZb may not be sufficiently different to minimize Reaction [I]. On the other hand, the Gibbs free energies of formation of the oxides of metals A and B may be sufficiently different to minimize Reaction [I]. In this case, the use of molten oxide electrolyte would be clearly advantageous. In the present study, the thermodynamic properties of the Pb-Ag system have been investigated using the cell: Previous galvanic cell studies on the Pb-Ag system2&apos;= are not reliable due to the displacement reaction between the alloys and the chloride electrolyte. Wagner and ~erner,&apos; using Laitinen and Liu&apos;s&apos; value at 450°C for the standard electrode potential of Reaction 111, have estimated the percent error in the activity of lead bPb) when using a chloride electrolyte. At 1000°C the error for xpb = 0.10 is 12 pct. Taking the Gibbs free energies of formation for PbClz and Ag cI,&apos; and the equations of Wagner and Werner,&apos; the error in apb at 1000°C and Xpb =0.10 was calculated to be 140 pct. However, using the Gibbs free energies of formation for Pb O&apos; and an estimated value for Ag 20, the error in apb when using a molten oxide electrolyte at 1000°C was estimated to be less than 1 pct for The virtual reaction of cell I1 for the passage of n Faradays of positive electricity from left to right in the cell is: where 5 is the Faraday equivalent (23,063 cal per v equivalent), E is the electromotive force of the cell in volts, and n is the number of Faradays of electricity required for the transfer of 1 g-atom of lead through the cell. The value of n should be equal to 2 since lead is generally divalent in oxide melts. However, the presence of either tetravalent lead ions or electronic conductivity through the molten oxide electrolyte will result in a value of n greater than 2. Bockris, Kitchener, and Davies&apos; have determined the amount of ionic conductance in a liquid PbO-SiO2 mixture (xPbO= 0.50) at 920°C by measurement of the volumes of CO and C& evolved at a carbon anode during electrolysis. From their data a value of 2.13 * 0.16 was calculated for n. Although their measurements indicate the possible presence of multivalent lead ions and/or electronic conductivity, their measurements were not at silica saturation and no definite conclusions can be drawn. However, as a result of the electrotransport measurements described in the next section the ;due of n can be taken as equal to 2.

Jan 1, 1969

By J. Campbell

Various models are discussed for the evaluation of the negative pressures which may occur in solidifying materials which exhibit various deformation modes: elastic-plastic, Bingham, viscous, or creep flow. The inadequacy of the previously proposed elastic-plastic solution for solidifying metals is revealed by comparison with the more reliable creep results which are given graphically for aluminum, copper, nickel, and iron. The maximum tensions experienced in the liquid phase of solidifying spheres ranging in size from large castings to submicron powders are in the range from —10&apos; to —105 atm for these metals. THERE has been much recent interest in the negative pressures associated with the volume change on solidification and in the possibility of the occurrence of cavitation. Considering the freezing of a highly supercooled liquid, an attempt to evaluate the stresses in the liquid ahead of the rapidly moving solidification front has been made by Horvay1 on a microscale and by Glicksman2 on a macroscale. In a casting of a wide freezing range alloy, the pressure differential due to viscous flow of residual liquid through the pasty zone has been discussed by Piwonka and Flemings,3 In a previous publication4 the author has attempted to estimate the negative pressure occurring in the residual liquid of a spherical casting, employing an elastic-plastic model to describe the collapse of the solidified shell under the internal tension. An earlier model assuming a rigid shell was shown to be inaccurate by many orders of magnitude. The elastic-plastic model is critically reviewed here, and other models are developed which are thought to be more closely related to metals and other materials near their melting points. The spherical geometry (Fig. 1) is chosen because the highest shrinkage pressures would be developed, although the analyses are readily adaptable to cylindrical geometry. A parallel sided casting experiences little internal tension because of the relatively easy dishing inward of the sides. (This commonly observed phenomenon has previously been attributed solely to atmospheric pressure.) Furthermore, small regions of confined liquid in a large solidified volume of a casting approximate reasonably well to spherical geometry. ELASTIC-PLASTIC MODEL The author has shown4 that as solidification proceeds the internal hydrostatic tension builds up until the elastic limit of the shell is exceeded. At this point the internal pressure is closely -2Y/3. Subsequently a plastic zone spreads from the inner surface toward the outer surface of the shell. When the whole casting is deforming plastically a rather more generalized analysis taking account of the externally applied pressure PA + 2y/b gives the internal pressure as: P = Pa + 2y/a + 2ys/b - 2 Y In(b/a) [1] The 2y/a and 2ys/b terms result from the tendency of the liquid-solid and solid-vapor interfaces to shrink, reducing their energy, and thereby helping to collapse the solid phase and compress the liquid phase. The 2y/b term would be important only for powders. The last term arises because of the plastic restraint of the solid, resisting collapse and so effectively expanding the residual liquid. From Eq. [I] it is easily shown that there is a minimum in the pressure at the radius amia= y/Y [2] which is of the order of 103K for the metals aluminum, copper, and iron, and corresponds to the minimum pressure Pmin = 2 Y[l-ln(bY/y [3] The results of a fully worked out elastic-plastic solution are given in a previous reporL4 The main criticism which may be leveled at this analysis when applied to metals at their melting points is the strong dependence of the yield stress on the strain rate. The strain rate varies with both solidification conditions (e.g., whether chill-cast or slowly cooled) and during solidification, as is indicated in the following section. Thus an appropriate choice of Y is very arbitrary. Before proceeding to a discussion of models which are strain-rate-dependent, it is necessary to evaluate the strain rate as a function of the rate of solidification. SOLIDIFICATION RATE Various empirical relations have been deduced5 for the rate of thickening of the solid shell by pour- out tests on partially solidified spheres. These, however, are unsatisfactory for our purposes since they become very inaccurate when the liquid core is very small. A theoretical approach is therefore necessary, and some solutions are set out below. Making the assumptions of constant surface temperature of the casting during freezing, no superheat, and a material freezing at a single temperature, Adams8 deduces the approximate solution: which becomes when b » a: Employing a semiempirical approach vallet6 finds:

Jan 1, 1969

By W. Jolley

Decarburized iron and Fe-3.28 pct Ni alloys were impact and tension tested in the temperature range of ambient to 4°K. It was found that alloying with nickel improves the fracture properties of the ferrite matrix. The improvement in toughness of iron alloyed with nickel is attributed to the effect of the nickel addition on the temperature and strain rate dependence of the yield stress as well as on slip behavior. The Fe-Ni alloy exhibits wavy slip when strained at temperatures down to at least 50°K. This behavior contrasts with that of the unalloyed iron where a change It is a generally accepted fact that of the common alloying elements of steel only nickel and manganese improve both the room-temperature yield strength and the notch impact properties. It has been argued for a number of years that manganese refines the ferrite grain size, the pearlite spacing, and the grain boundary carbides in medium- and low-carbon steels and thereby increases resistance to brittle fracture.&apos;&apos;&apos; This hypothesis recently was confirmed for a 0.04 pct C iron containing manganese, but at the same time from wavy to planar slip occurs at about 120°K. The observed lower temperature and strain rate dependence of the lower yield stress in the Fe-Ni alloy as compared to the unalloyed iron may be attributed to this difference in slip behavior. In contrast to suggestions published previously, transmission electron microscopy showed that the uniform dislocation distributions and the lack of dislocation tangles which are produced by low-temperature straining of bcc materials cannot be attributed to the absence of cross slip at these temperatures. no increase in notch toughness was observed in a decarburized Fe-Mn alloy.3 It thus appears that manganese only increases the toughness of Fe-Mn-C alloys by refining grain boundary carbides and has no toughening effect in carbon-free iron. On the other hand, the mechanism whereby nickel improves toughness has not been established. Hodge et a1.4 have clearly shown that a 3.28 pct Ni addition lowers the impact transition temperature of 0.02 pct C steel approximately 35°C when the grain size is maintained constant. Recently, Wullaert and Tetelman6 stated that nickel refined the grain boundary carbides of an Fe-C alloy and consequently increased the toughness. They also observed the previously reporteda-&apos;

Jan 1, 1969

By E. A. Steigerwald, G. L. Hanna

The influence of work-hardening exponent on the variation of fracture toughness with material thickness was studied for high-strength steel, aluminum, and titanium alloys. The results indicate that, when materials are compared at similar fracture toughness to yield strength ratios, the material with the lower work-hardening exponent undergoes the transition from flat to slant fracture at a larger thickness than material with a high work-hardening exponent. In the thickness range where complete slant fracture is obtained the reverse is true and a lower work-hardening exponent results in a lower fracture toughness. The influence of work-hardening exponent on fracture toughness is, therefore, dependent on the particular fracture mode. In the transition region a low work-hardening exponent is beneficial for fracture toughness while in the 100 pct slant region it is detrimental. THROUGH the use of fracture mechanics analyses, the influence of geometric variables on the crack propagation resistance of structures can be interpreted with reasonable consistency. However, in order to gain a more complete understanding of the fracture process, the influence of material parameters on crack propagation must be defined and coupled to the macroscopic fracture mechanics approach. The work-hardening exponent, which characterizes specific material behavior, may serve as an effective parameter to allow some degree of coupling to be accomplished. In the extension of a crack in a specimen of suitable dimensions the propagation process occurs in a stable manner when the crack extension force is balanced by the resistance to crack extension, which exists in the material at the crack tip. As the applied stress, and therefore the crack extension force, on the specimen increases, the resistance also increases primarily because the effective plastic zone at the crack tip, which is the main energy absorption process, becomes larger. Since the work-hardening rate of a material influences the stress-strain relationship, it will also influence the energy absorption process in the plastic enclave at the crack tip and hence should have an effect on crack propagation. A number of studies have been made correlating the strain-hardening exponent or the strain to tensile instability with the ability of a material to resist fracture. Gensamer1 concluded that a low-strain-hardening exponent would result in a steep strain gradient at the base of a notch. He reasoned that a large work-hardening coefficient would result in high-energy ab- sorption due to the increased area under the stress-strain curve. Larson and Nunes2 experimentally observed in Charpy tests on steels heat-treated to below 200,000 psi yield strength that the energy to failure in the fibrous mode, i.e., above the brittle-to-ductile transition temperature, was logarithmically related to the strain-hardening exponent. In order to avoid the complicating effects present in studying materials which undergo a brittle-to-ductile transition, Ripling evaluated the notch sensitivity of a variety of fcc metals with varying work-hardening exponents.3 The results indicated that the relative notch sensitivity, as determined from tests on specimens with a sharp notch, decreased with increasing values of strain hardening. Although the energy required for ductile or fibrous fracture increases with increasing work hardening, high-strength steels often exhibit improved crack propagation resistance when heat-treated to obtain low values of strain hardening.4,5 An analysis of whether low strain hardening is beneficial or detrimental to crack propagation resistance must depend on the particular fracture criterion involved. At temperatures where the material is relatively ductile and the development of a critical strain is required for fracture, high strain hardening increases the energy required to produce failure. In the transition region and below, however, a critical stress law appears to be valid6 and a low rate of work hardening may produce superior resistance to semibrittle crack propagation. The experimental program is aimed at studying these possibilities and determining the specific influence of strain hardening on the crack propagation resistance of several high-strength materials. MATERIALS AND PROCEDURE The alloys, chosen as representative of various classes of high-strength materials, are summarized in Table I. The heat treatments evaluated along with the smooth tensile properties are presented in Table 11. Pin-loaded sheet tensile specimens were employed to determine the smooth tensile properties. A strain gage extensometer (measuring range 0.200 in.) was used at a strain rate of 0.02 in. per in. per min. The work-hardening exponents were determined from the stress-strain curves generated in the smooth tensile tests and the assumption that the portion of the stress-strain curve beyond the yield point can be described by the power relationship: where a is the true stress, P is the true plastic strain,

Jan 1, 1969

By Arnt Solbu, Jomar Thonstad

The reaction between CO, and aluminum in cryolite-alumina melts in contact with aluminum has been studied by passing CO2 over the melt. In unstirred melts a homogeneous reaction between dissolved metal and dissolved CO2 was observed. In stirred melts in which convection was induced by bubbling argon through the melt, the dissolved metal apparently reacted mainly with gaseous CO2. The rate of formation of CO increased slightly with increasing depth of the melt, and it did not depend on whether CO2 was passed over or bubbled through the melt. The rate of formation of CO increased with increasing area of the metal/melt interface and with the application of anodic current to the metal. It is concluded that the dissolution of metal into the melt is the rate-determining reaction. THE current efficiency in aluminum electrolysis is determined by the rate of the recombination reaction between the anode gas and the metal: 2A1 + 3CO2—A12O3 + 3CO [1] as originally stated by Pearson and waddington.1 The occurrence of this reaction in cryolite-alumina melts in contact with aluminum was first verified experimentally by Schadinger.2 Thonstad3 has shown that the reaction may proceed further to give free carbon: 2A1 + 3CO— A12O3 + 3C [2] Normally only a few percent of the CO formed undergoes such reduction. The mechanism of these reactions has not yet been clarified. Aluminum, as well as CO,, is soluble in the melt. The solubility of aluminum in cryolite-alumina melts at around 1000°C corresponds to 75 x 10- 6 mole A1 per cu cm,4 while that of CO2 is only 3 x 10-6 mole CO, per cu cm.5 Taking into account the stoichiometry of Reaction [I], the ratio between dissolved aluminum and dissolved CO2 available for the reaction in a saturated melt is about 40. Therefore, as will be shown in the following, the reaction probably mainly occurs between gaseous COa and dissolved aluminum. The dissolved aluminum presumably consists of subvalent ions of aluminum and sodium.4&apos;6 Since the interpretation of the present results is not dependent upon the nature of this solution, the dissolved metal will be designated solely as Al+ in the following. The reaction can then be divided into four steps: A) dissolution of metal, e.g., 2A1 + Al3 — 3A1+ [3] B) diffusion of dissolved metal through a boundary layer; C) transport of dissolved metal through the bulk of the melt; D) Reaction [1]. If dissolved CO, takes part in the reaction, three additional steps embodying the dissolution and transport of CO2 must be added. schadinger2 observed, when bubbling CO2 through the melt, that the rate of formation of CO (in the following designated rfco) did not depend on the distance from the metal surface. The results also indicate that the rate of bubbling did not affect the rfco. When passing CO, over the melt, Revazyan7 found that the loss of metal did not depend on the depth of the melt above the metal or on the flow rate of CO2, and concluded that Step A is rate-determining. In an unstirred melt, however, Gjerstad and welch8 found that the rfCo decreased with increasing depth of the melt, indicating that step C was rate-determining. It thus appears that the rate control of the process depends on the experimental conditions, particularly on the convection. In the present measurements the reaction has been studied in unstirred as well as in stirred melts. EXPERIMENTAL AND RESULTS The experiments were carried out at 1000°C in a Kanthal furnace with a 10-cm uniform temperature zone (±0.l°C). The melts were made up of "super purity" aluminum (99.998 pct), hand-picked natural cryolite, and reagent-grade alumina. In experiments where alumina crucibles were used, the alumina content in the melt was close to saturation (13.5 wt pct9); otherwise it was 4 wt pct. Pure Co2 (99.85 pct) was passed over the melt, and the exit gas was analyzed for CO2 and CO by the conventional absorption method.3 From the weighed amount of CO (as CO2) the rfco was calculated as the number of moles of CO formed per min per sq cm of the surface area of the melt. The amount of carbon formed by Reaction [2] was not determined. As already indicated the rfco is much higher than the rfC, by Reaction [2]. Since the rfC probably is proportional to the rfco, the measured rfco should then the proportional to, but slightly lower than, the total rate of Reactions [I] and 121. In general the scatter of results obtained in duplicate measurements was ±5 to 10 pct, while within a given run a precision of ±3 to 5 pct was obtained. The various crucible assemblies that were used will be described below. Measurements in Unstirred Melts. When carrying out aluminum electrolysis in small alumina crucibles. Tuset10 observed that after solidification the lower part of the electrolyte was gray and contained free metal, while the upper part near the anode was white and contained no metal. One may test for the presence of free metal by treating with dilute hydrochlorid acid.

Jan 1, 1969

By Louis A. Rosales, Kanji Ono

The anomalous behavior of hydrogen in iron is examined and a new model is proposed It is postulated that hydrogen single and di-interstitials are in equilibrium with each other. When the binding enthalpy of the di-interstitial, B, is assumed to be about 10 kcal per mole, the predicted temperature dependence of the solubility agrees reasonably well with the reported data. Effective diffusiuity is calculated assuming the di-interstitials to be immobile. Since the number of mobile single interstitials is greatly reduced at lower temperatures, the effective diffusivity is decreased. A good agreement in the temperature dependence of diffusivity between theory and experiment is provided with B - 10 kcal per mole. The predicted diffusivity is also a function of total concentration of hydrogen and this appears to be Partly responsible for the large scatter in the reported data. HYDROGEN is known to form an interstitial solid solution with iron.&apos;&apos;&apos; At elevated temperatures, it has been well-established that hydrogen enters iron in the dissociated form and occupies the interstices, and that diffusion of hydrogen in iron is via the interstitial mechanism. The concentration, c, permeability, P, and diffusivity, D, of hydrogen in iron have been separately determined and are consistent with each other under the steady-state condition for temperatures above approximately 400°C; that is, the relationship P = c-D holds. At lower temperatures, however, anomalous behavior of hydrogen in iron has been observed by many investigators. The results of experimental studies4-&apos;&apos; of the diffusion of hydrogen in iron are summarized in Fig. 1, in which the values of D are plotted against the reciprocal temperature. Although there is an increasing divergence in observed values of D with decreasing temperature, the values of D at temperatures below approximately 200°C are definitely small as compared with the extrapolation from high-temperature data. The lines shown bracket the region containing the most probable data. The observed values of c6," are plotted against the reciprocal temperature in Fig. 2, where the dashed lines represent Geller and sun&apos;s&apos;&apos; most probable isobars at 1 and 100 atm. At high external hydrogen pressure and low temperatures, the values of c observed are higher than those expected from high temperature data. It is generally accepted that certain trapping mechanism is responsible for the anomalies, but the nature of the trapping mechanism has not been clarified. Various types of hydrogen traps were suggested in the literature, such as "rifts" in the lattice dislocations, voids, microcracks, and so forth. However, no quantitative account of the observed behavior has been given in terms of these trapping mechanisms. Formation of methane in hydrogen-charged steel was found by ~odgurski." This appears to explain the existence of the so-called "residual" hydrogen,4 but not the observed anomalies of hydrogen in iron. McNabb and Foster&apos; proposed a mathematical analysis in terms of a trapping mechanism. However, the physical significance of the traps was not clarified. The necessity of evaluating five parameters in their theory made comparison with experiment difficult. In the present paper, a model is proposed in which the anomalous behavior of hydrogen is attributed to the formation of hydrogen di-interstitials at lower temperatures. In this model, it is postulated that single and di-interstitials are in equilibrium with each other. (The hydrogen di-interstitial is to be distinguished from a hydrogen molecule which may exist in voids.) It can then be shown that most of the anomalies can be explained by assuming that the di-interstitials are virtually immobile and that the binding enthalpy of the di-interstitial, B, is approximately 10 kcal per mole. Predictions of the theory agree with the available experimental data reasonably well. THEORY The basic postulate of the present analysis is that single and di-interstitials are in equilibrium with each

Jan 1, 1969