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By M. S. Burton, J. E. Ritter

The sessile-drop technique was employed to study the effect of atmosphere and alloy additions of titanium and chromium on the surface tension and contact angle of nickel on sapphire substrates at 1500oC. Shear tests were conducted on the solidified sessile drops. The liquid-gas surface tension of pure nickel on sapphire was found to be 1747 ergs per sq cm, with a contact angle of 109.6 deg. The surface tension and contact angle were not affected significantly by the four atmospheres, vacuum, impure argon, pure argon, and pure hydrogen. Small additions of titanium and chromium decreased the contact angle and for the same alloy content, contact angles were lower in pure argon than in pure hydrogen. On the basis of shear-test results , the most probable cause for adhesion in the Ni-Al2O system is the formation of NiO:Al2O3 spinel at the interface; in the titanium alloy-Al2O3 system adhesion is thought to be due to a mechanical interlocking effect; in the chromium alloy-Al2O3 system adhesion is believed to be the result of solid-solution formation involving Cr2O3 and Al2O3 at the interface. In the last few years there has been considerable interest in reinforcing metals with ceramic whiskers. It has been postulated that, by reinforcing nickel with sapphire whiskers, high-temperature strengths su- perior to those of the best current nickel alloys can be achieved.' To fabricate a whisker-metal composite having optimum density and strength, understanding of wettability and adherence in the system is of prime importance. Although there has been some previous research in this a a need for further studies has been cited4-8 to understand better the effects of impurities, alloys additions, and atmosphere on the wetting and bonding of metals to metal oxides. The purpose of this research was to investigate the factors involved in the wetting and adherence of nickel/nickel alloys to sapphire (single-crystal a Al2O3). Sessile-drop experiments were conducted in vacuum, impure argon, pure argon, and pure hydrogen, to determine the effect of atmosphere on the contact angle of the metals on sapphire, and the liquid-gas surface tension of pure nickel. The solidified sessile drops were sheared from the sapphire substrate to measure the bond strength between the metal and ceramic. The alloy additions chosen were titanium and chromium since both enhance the wetting of nickel on sapphire.2, 3c Also, titanium is commonly used when brazing metal-to-ceramic seals to improve adherence. Since chromium forms an oxide that is completely soluble in sapphire, it was thought that the oxide could serve as a transition phase to promote bonding between the Ni-Cr alloy and sapphire. I) EXPERIMENTAL APPARATUS AND PROCEDURE The sessile-drop apparatus was a horizontal furnace, with an induction-heated, cylindrical molybdenum susceptor in a water-cooled Pyrex chamber. This apparatus was patterned after that of Williams and Nielsen.7 A flat Pyrex window at each end of the furnace allowed temperature measurements to be made at one

Jan 1, 1968

By P. S. Rudman

Crystal-structure occurrences in binary phase diagrams of fifth- and sixth-period elements, zirconium through palladium and hafniun through platinum, are surveyed with the conclusion that average .group number GN is the dominant correlative. This is interpreted in terms of curves of enthalpy differences between competitiue structures that are continuous func -tions of GN. It is further reasoned that the absolute formation energies may also be continuous functions of GN and if so can be simply obtained from the regatives of the heats of sublimation of the elements. It is shown that from such a heat of formation-GN plot the heats of mixing of alloy systems can be quantitatively predicted. For example, for sixth-period alloys very large exothermic heats of mixing are predicted for systems that span GN = 6 (i.e., Hf-Pt, Ta-Os, ...). Thermodynamic data with which to test these predictions do not appear to be available. If in the latter transition (A subgroup) elements we eliminate from consideration the fourth period where magnetic terms contribute to crystal-structure stability, as shown in Table I, there is a very regular sequence of structures. Using the group number (GN) assignments of Table I, which differ from the usual assignments of 8 to the elements listed as 8 through 10, it is perhaps trivial to say that the phase occurrence is a unique function of GN. However, the interesting aspect of alloys from among these elements is that the alloy structures also appear to correlate with GN. The GN for an alloy is given as GN = SixiGNi, where xi and GNi = atomic fraction and GN of component i, respectively. It is difficult to credit anyone in particular with having discovered this correlation, so many people have implicitly or explicitly employed it in the last 10 years. However, Bloom and Grant' in their correlation of s-phase occurrence with total number of d + s electrons were certainly one of the first to appreciate the correlation and Hume -Rothery2 appears to be responsible for the use of average GN as defined above. Only in the last few years have the phase diagrams of enough alloy systems been determined for this correlation to be surveyed with any degree of completeness. We shall here, in an abbreviated format, summarize the available phase-diagram literature and discuss some consequences of the GN correlation. BINARY DIAGRAM SURVEY In Figs. 1 to 3 the phase occurrences are summarized. In Fig. 4 the occurrence limits for the more common structures are summarized. That the GN of an alloy falls within the occurrence limits of a particular structure is a necessary but not a sufficient condition for the appearance of that structure. The preceding figures certainly illustrate that GN is a dominant correlative for structures of these elements. Many of the diagrams have complications, with ordering and other phase changes occurring in intermediate phases, that cannot be clearly accommodated in such a schematic survey and have hence been left out. Such omissions cannot, however, negate the GN correlations discussed here. Relative atomic size is also an important crystal-structure determinant and since atomic size varies quite regularly with GN for these elements it is possible that the apparent GN correlation is basically a size correlation. In Fig. 5 relative size occurrence limits are given for intermediate phases and extended terminal solutions. The relative volume, ?v/(v) - 2(vA - vB)/(vA + uB), has been taken as the measure

Jan 1, 1968

By R. C. Padfield

Experience over a 3-year period in Bethlehem Steel Corporation's plants has demonstrated the reliability of open-hearth roofs of bonded sprung-arch constructzon with burned basic brick. The design principles lor constructing these roofs include a minimum hot-strength requirement for the basic brick, expansion allowances that extend the full roof thickness, structural members to control arch contour, and a specified minimum roof rise. The greater stability of bonded roofs is explained in terms of the basic stress patterns of ring constrution and bonded construction. PRIOR to the development of successful sprung-arch roofs of basic brick, the majority of open-hearth furnaces in the United States were operated with sprung-arch roofs built of silica brick. Although many silica roofs used on open-hearth furnaces were ring-arch construction, Bethlehem Steel Corp. used bonded-arch construction because of its greater stability. In ring construction, each ring of brick is separately keyed and comprises an independent arch with the straight joints between rings traverse to the longitudinal axis of the furnace. In bonded construction, the bricks are laid in rows starting from the skewbacks so that the straight joints run parallel to the longitudinal axis of the furnace. Each brick in a given row is laid so that it spans the joint between two bricks in the row beneath it. Thus, the transverse joints across the arch are broken and the arch rings are thereby interlocked or bonded. When basic roofs were first being developed, the basic brick that were available had low hot strength. Such brick could not be safely used in sprung-arch construction without some means of suspending them. With the development of higher firing techniques by brick manufacturers and the recently introduced direct bonded bricks with high hot strength, the use of burned basic brick in sprung-arch roofs became feasible. The availability of high hot strength basic brick coupled with the potentially lower cost and proven stability of bonded construction prompted Bethlehem's Research Department to study the possibility of using basic brick in bonded roofs. With the full cooperation of plant ceramic engineers and open-hearth superintendents, particularly in 3 years of fur-nace trials, we developed the design criteria for bonded roofs and the corresponding property requirements for the basic brick that are discussed in this paper. DESIGN PRINCIPLES OF SPRUNG-ARCH BRICK ROOFS Stresses in Fixed Arches. A sprung-arch open-hearth furnace roof is generally built on rigidly held skewbacks. The constraint of the fixed support at each end adds a bending moment to the horizontal and vertical reactions at the ends of the arch. Fig. 11 shows the positive direction of forces acting on an arch fixed at both ends. Fixed arches can be analyzed when the members are continuous and have elastic properties. However, brick are inelastic, and arches built with individual brick segments cannot carry tensile stresses. Therefore, for practical solution of brick arches, empirical formulas have been derived from elastic theory that place design restrictions on arch dimensions to avoid development of tensile stresses. McDowell2 cites three main conditions for stability in sprung brick arches: 1) the thrust line of the arch should be maintained in the middle third of the thickness to avoid tensile stresses and resulting open joints in inner and outer curves of the arch; 2) the angle between the line of thrust at any joint and a line perpendicular to the joint must not exceed the angle of repose between brick; and 3) the maximum pressure at any point must not exceed the strength of the arch materials at furnace operating temperatures. The first and third conditions are particularly important in designing sprung-arch basic roofs because of the comparatively low hot strength of basic brick. According to McDowell's equation, if the thrust line is maintained within the middle third of the arch thickness, the unit pressure is obtained as follows: where p = unit pressure in psi, F, = resultant thrust normal to skewback in pounds per foot, t = arch thickness in inches, and z = distance in inches of thrust line from arch axis. When the resultant thrust normal to the skewback acts along the arch axis, z equals zero and unit pressure is simply the thrust divided by the cross-sectional area. If the thrust line moves to the limits of the middle third of the arch thickness, beyond which tensile forces would develop, z then equals one-sixth of the arch thickness and the unit pressure is double that when the thrust line is acting

Jan 1, 1968

By Ray W. Carpenter, Ralph Hultgren, Raymond L. Orr

Heats of formation of Au-Zn alloys of compositions Au3Zn and AuZn were rneasured at several temperatures by liquid tin solution calorimetry. The data for Au3Zn show that much smaller heat and entropy effects are associated with the a2- a1 transformation than for the a1 - a transformation. This result is consistent with reported X-ray diffraction studies which indicate that the a1 and (a2 phases have ordered structures which only slightly differ, whereas the a phase is disordered. The heat of formation of AuZn(ß') does not change significantly between 322o and 8000 K, confirming that the ß' alloy remains highly ordered to high temperatures. Not many measurements have been made of the energies of order-disorder transformations in alloy phases. In many cases these energies may be conveniently determined by measuring heats of formation as a function of temperature. Many alloy phases approximately obey Kopp's law of additivity of heat capacities; as a consequence their heats of formation do not change with temperature. In ordered alloys, however, a decrease in degree of order with increasing temperature will contribute an endothermic component to the heat of formation. Thus, for ordered phases where other anomalous contributions to heat capacity in the alloy or its pure components are absent, a measured change in the heat of formation may be attributed to the energy of disordering. A portion of the Au-Zn phase diagram1" is shown in Fig. 1. The composition AuZn(ß') has a well-ordered superlattice structure of the CsCl type at room temperature. The alloy is considered to remain ordered to its melting point,1 although, from X-ray diffraction data and electromotive force measurements of zinc activities, Terpilowski3 concluded that considerable disordering began at -673°K. The Au3Zn composition is a disordered fee solid solution (a) at high temperatures. Between 693o and 543oK, the ailoy orders to form the a1 phase, having a structure based on the L12(AuCu3) type, but with a regular distribution of ordering faults in the c direction, making it tetragonal. Below 543oK, the alloy orders further by means of slight atomic shifts, without diffusion, yielding a complex long-period orthorhom-bic superlattice structure, a2.4-7 Heats of formation of Au3Zn(a2) and AuZn(ß') were measured at 363°K by Biltz et al.8 by aqueous solution calorimetry. Heat capacities of several alloys between 14.9 and 38.4 at. pet Zn in the range from 373" to 723°K were measured by Iwasaki ef al.6 Stoichiometric Au3Zn, however, was not included in the alloys measured, the nearest composition being 26.1 at, pet Zn. Also, the heating rate used for the measurements, 2 deg per min, may not have permitted equilibrium to be reached in the neighborhood of the transformations. Heat contents of solid and liquid AuZn were measured between 488o and 1138°K by Kubaschewski.9 It was decided to determine the ordering energies of Au3Zn and to check on the possible disordering of AuZn by measuring the heats of formation of these alloys at several temperatures. The present paper reports measurements by liquid tin solution calorimetry of the heats of formation of the three phases of Au3Zn at temperatures within their regions of stability, and of AuZn at a low (322°K) and a high (800°K) temperature. EXPERIMENTAL Alloy Preparation and X-Ray Examination. Ten-gram ingots of Au3Zn and AuZn were prepared by melting weighed amounts of gold (99.95 pct Au) and zinc (99.99 pet Zn) together in sealed evacuated Vycor tubes at 1060°K, followed by rapid quenching. The resulting ingots were homogenized at 900°K for 10 days. The Au3Zn alloy lost no weight in preparation, the loss from the AuZn alloy was enough to introduce an uncertainty of only 0.1 at. pet in its composition. Filings for X-ray examination were taken from various parts of each ingot and strain-annealed at 723°K for 20 min in vacuo. The Au3Zn filings were quenched rapidly to retain the disordered phase. Diffraction patterns were determined with an X-ray dif-fractometer using copper Ka radiation.

Jan 1, 1968

By D. S. Tannhauser, I. Bransky

Measurements of the electrical conductivity, the thermal electromotive force, and the deviation from stoichiometry by thermogravimetry were made on ferrous oxide (wüstite) single crystals as well as on poly-crystalline samples in the temperature range of -900" to 1330°C. In the region defined by T 2 1000°C and 1.05 5 O/Fe 5 1.10 the electrical conductivity was shown to be proportional to the sixth root of- the oxygen partial pressure and to be linearly dependent on the deviation from stoichiometry. The absolute Seebeck coefficient of single and polycrystalline wüstite was shown to be independent of temperature in the above region and a p to n transition of the Seebeck coefficient was observed at O/Fe = 1.09 in polycrystalline wüstite. Analysis of the results showed that the predominant defects in wüstite in the above region were doubly ionized cation vacancies. The analysis also ruled out the existence of complexes of the type postulated by Roth, except that below 1000°C there is some evidence of 'association of defects. Of the three oxides of iron (FeO, Fe3O4, Fe2O3) only FeO (wüstite) can exist within a wide range of the ratio O/Fe. This has been shown by several investigations of the phase diagram using for instance chemical analysis of quenched samples'-4 or thermogravimetric measurements. 5,8 Darken and Gurry's1 data for example in the temper- ature range 1100o to 1400°C show that the lowest O/Fe ratio obtainable for FeOl +. is about 1.045 and that the existence range extends to O/Fe = 1.20 at 1400oC. On the basis of detailed analysis of thermogravimetric measurements made by Vallet and Raccah6 the existence of three varieties of wüstite at elevated temperatures was suggested by these authors and by Kleman. It is well-established that wüstite has a NaCl structure with vacant cation sites.3, 8 From a neutron-diffraction study of wüstite samples quenched to room temperature Roth9 concluded that defects in wüstite are mostly complexes composed of two cation vacancies and one interstitial cation in a tetrahedral site. The atomic arrangement in the vicinity of such a defect is similar to that in magnetite, where each occupied tetrahedral site is surrounded by four vacant octahedral positions disposed at the corners of a tetrahedron, so arranged that each vacancy is shared by two tetrahedral cations. Thus there is an average of two vacancies per interstitial. Recent X-ray diffraction measurements made by Smuts10 on quenched wüstite samples confirmed the results of Roth's neutron-diffraction experiments. Roth's model of defects in FeO can be regarded as a solid solution of Fe3O4 in FeO; salmon1' used this defect model to calculate the activity of Fe3O1 in FeO at high temperature and claimed good agreement with the results obtained experimentally by Darken and Gurry.' Each missing cation in wüstite is accompanied by two trivalent cations, thus preserving charge neutrality. The "holes" which differentiate between the Fe 2+ and Fe3' states of the ions in octahedral positions can overcome the attractive field of the cation vacancies, and are then free to move through the crystal as charge carriers. A similar picture holds for COO, NiO, andMnO.l2, 13 Localization of the charge carriers in transition

Jan 1, 1968

By Harold M. Feder, Robert V. Schablaske, Irving Johnson, Ewald Veleckis

The stoichiometry, structure, and stability of the internzediate phases formed between zinc and some of the rare earth (RE) metals were systematically exarnined by means of a recording effusion balance and X-ray diffraction analyses. In the La-, Ce-, PY-, Nd-, and Y-Zu systems, at or below about 600 C, the following sequences of phases (REZnx) were found: La, x = 1, 2, 4.0, 5.25, 7.3, 17/2, 11, and 13.0;' Ce, x = 1, 2, 3, 11/3, 4.3, 5.25, 7.0, 17/2,* and 11; Pr,x = 1,2, 3, 11/3 ,* 4.3, 5.3(?), 7.0, 17/2,* and 11; Nd,x = 1,2, 3,* 11/3,* 4.3, 6.5, 8.5,* and 11; Y,x = 1,2,3, 11/3, 4.5, 5.0, 17/2,* and 12.* The structure types of all these phases were classified. In addition, lattice parameters were obtained for the first time for the pluses denoted by asterisks. In the absence of de tectable valency or electronegativity effects the systesnatic trends in the results have been ascribed to the effects of' the lanthanide contraction. For example, the maximum number of zinc atoms in the coordination polyhedron surrounding the RE atom decreases from twenty-four to twenty-two to twenty as the size of the RE atom decreases. THE structures and compositions of a great many intermetallic phases (e.g., the Laves phases) are known to be based primarily, but not exclusively, on the space-filling efficiency of various modes of packing together atoms of different sizes. The valencies and electronegativities of the constituent atoms are, however, also influential. In extreme cases hypothetical intermetallic phases which fulfill the efficient spacefilling requirements may not be present in the constitutional diagram because of thermodynamic instability brought about by the operation of valency or electronegativity factors. Hence, for a detailed study of the influence of atomic size on alloy structure and composition, it would be desirable to minimize variations of valency and electronegativity. The intermetallic phases formed by the rave earths (RE) with some common partner offer an excellent opportunity for isolating the effects of size from those of valency and electronegativity. The rare earths exhibit a large, but smooth, decrease in size (the lanthanide contraction) in the series from lanthanum to lutetium when inter comparison is made for a common valence state, e.g., isolated atoms or trivalent ions. The elements yttrium and scandium are frequently included as pseudo rare earths; their sizes place them in the vicinity of dysprosium and lutetium, respectively. The electronegativities of RE elements vary by less than 10 pet. The trivalent state is the most common; however, the well-known tendency of cerium, praseodymium, and terbium to achieve higher valencies, and of samarium, europium, and ytterbium to seek lower valencies, requires that caution be exercised in the assumption of equal valencies. In the present study the existence, constitution, and structure of each of the numerous intermediate phases formed by zinc with lanthanum, cerium, praseodymium, neodymium, or yttrium were examined systematically and in detail. The investigation was conducted by a recording effusion balance technique and by X-ray diffraction analysis. The results enrich our knowledge of the phase diagrams of these systems. In addition, they present some clear-cut evidences of the operation of the size factor alone. EXPERIMENTAL PROCEDURE Apparatus. The mode of operation of the recording effusion balance and its application to phase studies have been discussed in detail elsewhere.' In this work, an effusion cell containing a finely divided alloy was suspended within an evacuated tube from the beam of an analytical balance. The tube was immersed in a massive molten salt bath whose temperature was controlled to within 0.5o C during each experiment. The loss in weight of the alloy owing to effusion of zinc* was continuously recorded. Two effusion cells, 1/2 in. diam by 1 in. high, were machined from tantalum rods. Two orifices were drilled laterally into the walls of each cell. The orifice areas were determined by calibration with pure zinc: cell A had a total orifice area of 6.5 x 10-41 sq cm, and cell B an orifice area of 9.8 x 10-3 sq cm. By appropriate choices of orifice area and temperature the wide range of volatilities from pure zinc to pure rare earth metal could be investigated. X-ray diffraction powder photographs were made at room temperature with a 114.6-mm Debye-Scherrer camera with both filtered CuKa radiation and filtered CrKa radiation. Lattice parameters were refined by a computer-programmed least-squares analytical treatment which incorporated appropriate extrapolation techniques.2 Frequent use was also made of a special computer program3 designed to generate a powder pattern from an assumed structure in order to verify structural assignments. Materials. Lanthanum, neodymium, and yttrium were purchased from the Lunex Co., cerium from the Cerium Metals Corp., and praseodymium from the St.

Jan 1, 1968

By J. C. Bokros, A. S. Schwartz

The irradiation-induced densification of pyrolytic carbon has been shown to take place by a simple first-order rate process. The values of the densification constant, kd, for isotropic carbons are 1.0 x 10-22, 1.4 X 10-22 and 2.8 X 10-22 (nut)-1 at irradiation temperatures of 520o, 670°, and 1000oC, respectively. The apparent activation energy obtained from the temperature dependence of kd for isotropic carbons is about 0.2 ev. Estimates of the maximum stresses that develop in isotropic carbons owing to shrinkage onto an unyielding support show that stresses in excess of 15,000 psi may be avoided during irradiatian at 600" and 1000°C if the initial coating density is kept above 1.5 and 1.9 g per cu cw, respectively. If a carbon coating on an unyielding support is not completely isotropic, stresses may continue to build up at high neutron exposures after densification is complete because of continued anisotropic distortion. Stresses in excess of 15,000 psi from this source may be avoided during irradiation at 1000°C if' the Bacon anisotropy factor is kept below 1.3. A variety of applications of carbon and graphite in nuclear technology has stimulated numerous studies of the effect of neutron irradiation on these materials One of the most interesting problems associated with the use of carbons and graphites in the high fast neutron fluxes of nuclear reactors arises as a consequence of the neutron-induced dimensional changes that occur during irradiation. Energetic neutrons displace car- bon atoms from their lattice positions; and, depending on the temperature, the interstitials and vacancies produced migrate to form clusters, recombine, or are annihilated at dislocations or crystallite boundaries. The competition of various sinks for the point defects results in structure-sensitive bulk-dimensional changes that vary with temperature in a complicated way. This paper deals with the neutron-induced dimensional changes in turbostratic carbons that are being used as coatings on nuclear fuel particles. Details of the structure of these carbons and the variations of their structure with deposition conditions have been reported.'-3 It has been shown in previous work that the neutron-

Jan 1, 1968

By W. Bonfield

The microstrain characteristics of a polycrystal-line Cu 1.9 wt pet Be precipitation-hardening alloy have been determined for various conditions of aging. The friction stress remained constant for all the conditions investigated, whereas the microscopic yield stress (the stress to produce a plastic strain of 2 x 10-8 in. per in.) and the three-stage stress-strain curve in the microstrain region were sensitive to changes in dislocation and precipitate distribution. Correlations between the measurements of microplasticity and electron-nzicroscope observations of substructure are considered. ALTHOUGH the macroscopic mechanical properties of Cu 1.5 to 2.0 wt pet Be precipitation-harden ing alloys were established' in some detail, there has been no previous investigation of the nature of microyield-ing in these alloys. This paper describes a high-sensitivity extensometer determination of microplasticity in polycrystalline Cu 1.9 wt pet Be, in which the friction stress, the microscopic yield stress (the stress to produce a plastic strain of 2 x 10-6 in. per in.), and the rate of strain hardening in the micro-strain region were measured for various conditions of precipitation. The structural changes accompanying aging in this alloy were examined using transmission electron microscopy, a study which differed from previous investigations as, in order to minimize grain boundary precipitation effects,' the solution-treated alloy was cold-rolled to 40 pet reduction prior to aging. Hence the extent of recovery and recrystalliza-tion, as well as the variation of precipitate morphology and distribution, were assessed. From these results possible correlations between the microstrain characteristics and the observed precipitate and dislocation structure are considered. EXPERIMENTAL PROCEDURE The material investigated was a commercial copper beryllium alloy (Berylco 25), which had a com- position of 1.9 wt pet Be and 0.2 wt pet Co. The alloy was solution-treated at 800°C, quenched in water, and then cold-rolled to 40 pct reduction. Tensile specimens of gage length 1 in. and rectangular cross section of 0.18 by 0.06 in. were prepared from the solution-treated, cold-rolled material and aged for 15 min, 2, 24, and 100 hr at 315°C and 24 hr at 425°C to produce a range of precipitate structure. The hardness values associated with these conditions are listed in Table I. It can be seen that a maximum value is obtained after 2 hr at 315oC, which decreases with continued time at temperature to a minimum after 24 hr at 425°C. For comparison some as-solution-treated specimens were also aged for 2 hr at 315°C. The specimens heat-treated to a given condition were examined in two ways. First, the nature and distribution of the precipitate and dislocation structure was characterized using transmission electron microscopy. Thin foils were obtained from the specimens by electrolytic polishing in a 30 pet nitric acid-alcohol solution at -20oC, and were examined in an RCA EMU 3 electron microscope. Second, the mi-croplastic behavior of the specimens was measured with a Tuckerman strain gage, using the load-unload technique previously described2, 3 to determine the friction stress, the microscopic yield stress, and the variation of plastic microstrain with stress. RESULTS 1) Structural Changes During Aging. a) Annealing Processes. The solution-treated, cold-rolled Cu 1.9 wt pet Be had an irregular dislocation-cell structure,

Jan 1, 1968

By R. D. Pehlke, J. V. Gluck

A study was made of the effect of small additions of metallic solutes on the thermodynamic activity of zinc in dilute solution with molten bismuth in the range 450o to 650°C. The experimental measurements were made in a multielectrode galvanic cell using. a fused LiCl-KCl electrolyte. The activity of zinc in binary solution exhibited a strong positive deviation from Raoult's law and obeyed Henry 's law to at least 0.050 mole fraction. The ternary addition of lead, gallium, or indium increased the activity of zinc. Cadmium or tin additions slightly decreased the zinc activity. Copper, mercury, silver, or antimony caused moderate decreases, while gold strongly decreased the zinc activity. The results are expressed in terms of Wagner's interaction parameter ejZn and a second-order cross-interaction parameter. The interactions for copper, gold, silver, and antimony showed a linear dependence with reciprocal absolute temperature, while the other interactions were essentially independent of temperature over the experimental range. Since tin and antimony decreased the zinc activity, the hypothesis of a purely periodic variation with atomic number was rejected. A semiquantitative explanation was possible with a free-electron model when relative electronegativities were used to express changes in the electron/atom ratio caused by the solute addition. Random solution and quasi-chemical models correctly predicted the majority of the interactions for which binary data were available to apply them. A knowledge of the thermodynamic interactions in liquid (and solid) metallic solutions is of considerable theoretical and experimental interest in the formulation of quantitative thermodynamic relations for metallurgical processes. The approaches to defining the interactions may be either phenomenological (i.e., "What mathematical function adequately describes observed behavior and permits extrapolation to new situations?") or theoretical, such as a specific model

Jan 1, 1968

By E. Furubayashi, T. Taoka, S. Takeuchi

Recrystallization textures developed from artificial nucleation around indentations were compared with spontaneously recrystallized textures in two rolled 3 pet Si-Fe single crystals with (111)[112] and (100) [011] orientations. Orientation of individual grains in some stages of their growth was also directly determined by a microetch-pit method. In both the crystals, the recrystallization texture was characteristic of each orientation regardless of any nucleation conditions, artificial or spontaneous, though artificially nucleated grains were more randomly oriented in finer stage. These results support the concept that the process of selection of growing grains controls the formation of the prejerred recrystallization texture. Discussion is given on the factors controlling the mobility of grain boundaries. Recrystallization textures are formed through a number of stages which are customarily called by the terms recovery, nucleation, and grain growth. Many experiments have been done to clarify the mech- anism of formation of recrystallization texture but no fully successful explanation has been proposed. The texture consists of oriented grains which nucleate at many sites of the deformed matrix and grow at the expense of the matrix during annealing. The current theories on the formation of recrystallization texture are based on the following two extreme hypotheses: 1) the oriented nucleation theory by Burgers et al.;1, 2 2) the oriented growth theory by Beck et al.3-5

Jan 1, 1968

By J. H. Swisher

The solubility of sulfur and rate of solution of sulfur in pure Lron were measured in H2S + H2 and H2S + H2 H2O gas mixtures. The solubility and diffusivity of sulfur at 1410°Care 0.13 pet S and 1.0 x 10-5 sq cm per sec, respectively. The solubility iS the same, but the rate of sulfurization is slower in the presence of H2O in the reacting gas. Under these conditions, the over-all rate is controlled jointly by a slow surface reaction and by solid-state diffusion; the mechanism for the surface reaction has not been identified. KNOWLEDGE of the behavior of sulfur in solid iron is desirable for the metallurgy of such products as free machining steel, where a high sulfur level is required, and inclusion-free high-strength steels, where the sulfur specifications are very low. The present investigation was undertaken to check previously reported values for sulfur solubility and diffusivity in 6 iron, and to study the poisoning effect of chemisorbed oxygen on sulfurization kinetics in H2-H2S-H2O gas mixtures. All of the experiments were performed at 1410°C. The thermodynamic behavior of sulfur in 6 iron was the subject of a paper by Rosenqvist and Dunicz.' The sulfur solubility at 1400" and 1500°C was determined by equilibrating pure iron specimens with H2-H2S gas mixtures. The maximum solubility of sulfur in 6 iron was alsc determined by Barloga, Bock, and parlee2 by reacting iron wires with sulfur in sealed capsules. In another investigation, the diffusion coefficient of sulfur in 6 iron at temperatures up to 1450°C was measured by Seibel.3 The method used was to measure sulfur concentration profiles in diffusion couples containing radioactive sulfur EXPERIMENTAL Apparatus. A vertical resistance furnace wound with molybdenum wire and containing a recrystallized alumina reaction rube was used for the experiments. The hot zone in the furnace was approximately 2 in. long with a temperature variation of ±3oC. The hot zone temperature was automatically controlled to within ±2°C, and the test temperature was measured with a pt/Pt-10 pet Rh thermocouple before and after each experiment. Flow rates of the reacting gases were obtained using capillary flow meters. Materials. The source of H2S in the gas train was a premixed cylinder containing 5 pet H2S in H2. This mixture then was diluted with additional hydrogen and argon. In some experiments, water vapor was introduced by passing hydrogen and argon through a column containing 10 pet anhydrous oxalic acid and 90 pet oxalic acid dihydrate. The vapor pressure of water above this mixture is well-known.4 Argon was used as a diluent to minimize thermal segregation of H2S in the furnace5 and to reach higher H2O:H2 ratios than could be obtained in mixtures of H2 and H2S alone. Argon was purified by passage over copper chips at 350°C and subsequently over anhydrone. Hydrogen was purified by passage over platinized asbestos at 450°C and then over anhydrone. The H2-H2S mixture was purified by passage over platinized asbestos and then over P2O5. The specimen stock was made by melting and vacuum-carbon deoxidizing electrolytic "Plastiron" in a zirconia crucible. The principal impurities are listed in Table I. In some of the equilibrium experiments, six-pass zone-refined iron was used to minimize impurity side effects. This zone-refined iron had a total impurity level of about 25 ppm. Procedure. Specimens were annealed in hydrogen for a period of at least 2 hr at the beginning of each experiment. The specimens were held in the reacting gas for times varying between 10 min and 17 hr, and cooled to room temperature in a water-cooled stainless-steel block at the bottom of the furnace. The pH2S/pH2 ratios reported are those for gas equilibrium at 1410°C. Calculations based on available thermodynamic data8 showed that the only other gaseous8 species that formed in significant amounts in the furnace were S2 and S. Even when water vapor was introduced into the gas mixture, the concentrations of SO2, SO, and so forth, were negligible. The initial partial pressure of H2S was therefore corrected for its partial dissociation to S2 and S in determining the equi-

Jan 1, 1968

By D. Dever, E. S. Fisher

Measurements of the temperature dependence of the elastic moduli in single crystals of hep ruthenium, rhenium, cobalt, dysprosium, and erbium were carried out for various temperature ranges so as to investigate the correlation, suggested by prior work, between the shear anisotropy ratio, A = C44/C66, and the occurrence of the hcp — bee phase transformation. These measurements confirm the suggestion that A has a positive temperature dependence in that group of hcp metals that undergo thermally induced transfornzations to the bee structure and a negative or zero temperature dependence in the other hcp metals. It appears, from indirect evidence, that the hcp -fee transformation in cobalt is preceded by a highly negative temperature dependence of A. These results indicate that elastic anisotropy is an important factor in determining the temperatures at which martensitic phase transformations occur. Two possible roles for elastic anisotropy are proposed: 1) the shear-modulus ratio within the habit planes must be nearly similar for the two phases and 2) a large anisotropy decreases the stress necessary for the movement of the transfornzation dislocations. FUCHS' calculations of the elastic moduli in the alkali metals have shown that the high shear-anisotropy ratios, c/c', in certain bee metals and alloys are the result of large negative contributions to c' = (c11 - c12)/2 arising from the nearest-neighbor repulsive forces.' On this basis, and following Zener,2 the association between high c/c' ratios and the martensitic phase transformations that occur upon cooling certain bee metals is explained as a unique characteristic of the bee structure. Recent measurements of the elastic moduli in hcp titanium and zirconium show, however, that a high elastic anisotropy also exists in these hcp structures at the temperatures at which they transform to bee upon heating3. If there exists a direct and consistent correlation between the elastic anisotropy in close-packed structures and the occurrence of transformations to the bee phases then there is evidently a need to re-examine the conclusions of Zener theory. Elastic anisotropy may also be the result of the effects of temperature on the stability of the low-temperature close-packed structures or it may play an important role in the mech- anism of the martensitic transformations. The present measurements were aimed at establishing the phenomenological correlation between elastic shear anisotropy in hcp structures and the thermally induced hcp —bee transformations that occur in the majority of the twenty-three hcp metals, as shown in Table I. Prior to the present work the temperature dependence of the anisotropy ratio, A = c44/c66, was known at various temperatures for nine of the metals listed. The data showed a negative temperature dependence of A for cadmium, zinc, magnesium, and cobalt, which do not transform to bee, and a positive temperature dependence of A for thallium, zirconium, titanium, hafnium, and yttrium. The correlation was, however, ambiguous in that these two groups of metals are also separated with respect to the c/a ratios as noted in Table I. There remained the possibility that the temperature dependence of A is a function of c/a and not consistently associated with the transformation. The measurements of the elastic moduli in rhenium and ruthenium, in which hcp —bee transformations do not occur, were needed to help decide this question. The studies of dysprosium and erbium were undertaken to determine whether the correlation holds for the heavy rare earth metals.

Jan 1, 1968

By A. E. Wraith, N. J. Petch, J. D. Embury, E. S. Wright

The two most important parameters controlling the fracture behavior of a solid are its intrinsic properties, e.g.,grain size, and the operative stress system. The latter may be modified in laminates by the presence of weak interfaces. This is studied in notch-impact tests on a mode1 system of mild steel laminates containing a variety of interfaces. The effect of these is evaluated in terms of the ductile/cleavage transition. Two laminate geometries are distinguished, here called "crack-arrester " and "crack-divider". In both, cleavage is inhibited. This arises because of relaxation of a state of triaxial tension. In the crack-avrester laminates, cleavage initiated at a notch is confined to the layer containing the notch. In crack-cliuider laminates, a thick specimen behaves as the Sum of a number of thinner ones. Additional benefit may derive from improved intritnsic propevties of- the lanlinate layers arising from greater deformation in their manufacture. It has long been recognized that the two most important parameters controlling the fracture behavior of solids are their intrinsic properties (e.g., grain size friction stress,3 distribution of second phase particles4) and the operative stress system under which fracture occurs. In solids that show a ductile/cleavage transition, cleavage is favored by the presence of a notch. This is because triaxial tensions, generated by the localized plastic constraint at the notch, are operative when fracture occurs.= Anything that suppresses these triaxial tensions will be unfavorable to cleavage. Such suppression may possibly occur in laminates containing weak interfaces and the purpose of the present paper is to explore this possibility. Two basic laminate geometries, here termed "crack-avrester" and "cvack-divider", are examined. They are illustrated in Fig. 1. With the crack-arrester laminates, there is the possibility that, when the fracture crack approaches the interface, this, if weak, may delaminate due to the tensile stress acting parallel to the plane of the crack.= If this happens, energy will be used in delamination, the crack will be completely blunted, and the triaxial tension associated with the crack will be relaxed. To fracture the second portion of the laminate, crack reinitiation will be necessary and, because of the relaxation of the triaxial tension, this reinitiation will occur under conditions of nearly uniaxial tension, which are unfavorable to cleavage. Thus there is the possibility of cleavage suppression in the second and subsequent subunits of a crack-arrester laminate. With the crack-divider geometry, there is again the possibility of delamination at the interfaces. This will divide the crack into a series of cracks propagating through the individual laminate subunits. If these are sufficiently thin, the triaxial tension will be relaxed towards a state of biaxial tension in each of them. Thus, with the crack-divider laminates, there is again the possibility of cleavage inhibition. In the present work, these possibilities are explored using a notched impact test on mild steel laminates bonded with soft solder, silver solder or copper. Even if delamination does not occur, it is still possible that cleavage may be inhibited in laminates. With the crack-arrester geometry, the cleavage crack in the first layer may be blunted and arrested by plastic deformation in the laminate bond, if this is ductile. Partial relaxation of the stress transmitted ahead of the crack into the second layer will then result and this will reduce the significance of this stress in the fracture of the second layer. With the crack-divider geometry, there cannot be much effect in the absence of delamination unless a large amount of energy is absorbed in rupturing the ductile material. EXPERIMENTAL DETAILS The composition of the mild steel (wt pet) was: 0.04 C, 0.29 Mn, 0.01 Si, 0.006 P, 0.008 S. "As-received" plate was annealed for 2 hr at 900°C and slowly cooled to give a grain size of 0.04 mm. The laminates were made by brazing or soldering together mild steel plates 8 by 3 in. by various thicknesses. These were obtained from the annealed plate by machining, so that the intrinsic material properties were .kept constant. Laminates containing two to six steel layers were studied using standard Charpy V-notch specimens cut from the bonded plates. Standard homogeneous specimens from the annealed plate and subsize ones from the laminate components

Jan 1, 1968

By Donald L. Ball

The equilibrium of boron nitride, gaseous nitrogen, and solute boron was investigated in Fe, Fe-C, and Fe-Si rnelts by the Sieverts technique. The free ellergy of dissociation of boron nitride, involving -the implied standard states, was evaluated in the range 1400" to 1600°C as: ?Fo = 38,000 - 23.5T, cal ber mole The solute-solute interaction coefficients eBB, ecB , and eg were determined as 0.058, 0.22, and 0.078, respectively. BORON is an important ingredient in some types of steel and cast iron. It was employed at a particularly high level, 0.01 wt pet, in the as-cast malleable iron "CentraSteel".1 In this material, the boron concentration was critical in order to assure graphite, and avoid primary cementite, in the as-cast structure. One possible function of the boron in this alloy was the nucleation of graphite through the agency of boron nitride, which, conceivably, precipitated from the melt during cooling. A research program was instituted to assess the validity of this proposed mechanism. The first undertaking, reported here, was a determination of the thermodynamic possibility of boron nitride precipitation. Data available in the literature on the activity coefficient of solute boron in iron-base melts are inadequate for the present purpose. They will be reviewed briefly, however, so that comparison can be made, when

Jan 1, 1968

By J. C. Swartz

Measurements of the effect of precipitation stresses on the solubility of cementite (Fe3C) precipitates in a iron are reported. Solubilities were determined from measurements of the Snoek relaxation due to interstitial carbon after quenching from various equilibrium treatments. Stress-free precipitates were obtained by a spheroidizing treatment of vacuum-melted Fe 0.06 wt pet C. Subsequent equilibration treatments were designed to suppress nucleation of other precipitates. The results for stress-free cementite give a heat of solution of 14.8 i 0.2 keal per mole and an entropy change of 1.1 i 0.2 eu in the temperature range 400" to 715°C. Comparison with previous data indicates that the heat of solution increases about 6 keal per mole as temperature increases from 700" to 1000°C. Data on self-stressed cementite in quench-aged specimens of Fe 0.013 wt pet C indicate 1) an apparent heat of solution of 12.1 i 0.4 keal per mole in the range 280" to 690°C, 2) a strain energy of- 1.1 keal per mole Fe3C accompanying precipitation at 280°C, and 3') a gradual decrease in the strain energy of precipitation with increasing equilibration temperature. In com-parison with 2 and 3 the strain energy calculated for an isotropic model is 1.7 keal per mole Fe3C. The lower values obtained from the experiment indicated substantial stress velaxation by dislocation motion. WHEN a supersaturated solution of carbon in a iron is aged at temperatures in the range 200o to 700oC, the carbon clusters by interstitial diffusion and forms cementite (Fe3C) precipitate particles. Unstressed cementite has a volume per iron atom 9 pet higher than that of a iron;' hence, cementite precipitate particles are usually under pressure from the iron matrix. The pressure would tend to increase the solubility of cementite in iron.' This report describes anelastic measurements of the solubilities of self-stressed and stress-free cementite in a iron. Previous determinations of the cementite solubility are summarized in Table I. The method of cementite formation for each reference was studied to ascertain the state of stress of the cementite. The results judged to be for stress-free and stressed cementite are distinguished in the table. In the next section an estimate of the stress effect is obtained which is clearly too small to account for the large difference between the previous results in parts A and B of the table. THEORETICAL Let AGO be the standard free-energy change of the reaction Fe3C (eem.) = 3Fe (a) + C (in a) [1] in the absence of stresses. Since cementite precipitates appear to be rather pure10 and the carbon is so dilute in the iron,8 the cementite and iron of Eq. [ I] for the stress-free case have essentially unit activities and the activity of carbon equals its atom fraction xoC Then the stress-free equilibrium is expressed by RT In XoC = -?GO 121 To first approximation the change in the chemical potential of carbon due to the precipitation stresses equals the elastic strain energy W accompanying precipitation of a mole of cementite.2 Hence, in the presence of the precipitation stresses the equilibrium is described by RT In x sq = -?G° + W [3] where xsC is the mole fraction of dissolved carbon in the stressed case. An approximate value of W can be obtained from analysis of the inclusion problem in elasticity theory. The inclusion is a small portion of the matrix phase which has suffered a transformation while still imbedded in the matrix. In the absence of the constraint of the matrix the transformation would be equivalent to a uniform dilational strain eT. Both the matrix (a) phase and inclusion (0) phase are assumed to be homogeneous, isotropic materials. When the a and 0 phases have the same elastic moduli, which is approximately true for iron and cementite,11 the total strain energy per mole ß is12 2µVß(eT)2(3 +4 µx)-I [4]

Jan 1, 1968

By B. R. Hollebone

The chemical action of molten anhydrous pyridinium chloride (pyridine hydrochloride) on oxy salts and ores of some Group IV and V metals are discussed-in particular zirconium, hafnium, niobium (columbium) , and tantalum. Laboratory-scale experiments are described whose results suggest that this reaction might provide a practicable means of converting ores of these metals to the anhydrous metal chlorides. Experimental results are given which provide some insight into the nature of the reactions and some of the compounds which could be present at intermediate stages. The treatment of ores of the more refractory metals is difficult and expensive and often demands the use of gaseous chlorine, hydrogen fluoride, or other reagents which are, if nothing else, expensive and dangerous to use. This situation is, of course, due to the strong metal-oxygen affinity resulting from the high charge and the small size of the metal ion which combine to produce such high lattice energy in the metal oxide as to defeat standard reduction methods. Thus, the characteristic of these metals which leads to one of their most important properties—corrosion resistance—is the main hurdle in obtaining the metal. Many common methods' for treating ores of zirconium and niobium (columbium), for example, proceed as directly as possible to the preparation of anhydrous halides. These halides are purified by now standard processes of solvent extraction, fractional distillation, and so on. This paper reports on preliminary stages in the development of a method of treating these ores—particularly of niobium—so as to prepare the anhydrous, volatile halides by the use of chemical reagents which are much more easily handled than those used at present. CHEMICAL PRINCIPLES The solvent action of aminium halides has been referred to periodically in the literature over several decades. The chemistry of pyridinium chloride has been discussed particularly by Audreith2 and Starke.3 However, since this is not familiar chemistry in its nonaqueous setting, it is perhaps well to point out some general metallurgical principles and applications. One can use, as point of departure, the fact that HC1 dissolved in pyridine is an acid very much the same as aqueous HC1. It thus gives essentially all the reactions of the HC1 with which we are familiar. However, when the ratio of HC1:pyridine reaches 1:l (a ratio far higher than is possible with H2O) the solution becomes solid C5F5NHC1, pyridinium chloride.* Inter- estingly, the acidic properties of HC1 persist in this medium, although they are manifest only in the molten state of the compound. Some typical reactions of divalent metal compounds which we have carried out in our laboratories are the following: 2PyHCl + Zn — (ZnCl2) + H2 + 2Py 2PyHCl + MnO — (MnCl2) + H2O + 2Py 2PyHCl + CuS — (CuCl2) + H2S + 2Py 2PyHCl + CaCO3 — (CaCl2) + H2O + CO2 + 2Py In these equations, the parentheses indicate a solvated compound which in water would be predominantly a hydra ted cation but which in molten PyHCl will more likely be a complex chloro-anion of the type MC14-. Some important physical properties of pyridinium chloride (PyHCl) are given in Table I. One sees from the data in Table I that at the temperature of molten pyridinium chloride both water and pyridine will boil away. Thus the system will be kept anhydrous. For this reason the reaction 2NbCl5 + 5H2O— Nb2O5 + 10HC1 has no counterpart in molten PyHCl. Instead, the chloride is made even more stable by the formation of a hexachloro complex: Nb2O5 + 12PyHC1 — 2PyHNbC16 + 5H2O + 10Py One interesting property of these complexes is their thermal instability which for the case of niobium can be illustrated as PyHNbCl6 — PyHCl + NbCl5 With a view to possible use of this chemistry in ore treatment, we have attempted to dissolve Pyrochlore (essentially FeO - Nb2O5) and recover the NbC15 from it.

Jan 1, 1968

By John Chipman

Published data on the equilibria of carbon in binary Fe-C austenite with H2-CH4 and CO2-CO gas mixtures are used to obtain the constants of an equation repre -senting the activity coefficient of carbon throughout the stable austenite range of temperatutre mid compositiotl. Calculated values for the solubility of graphite are found to be in agreement with the best-published direct observations. Its heat of solution is 10,680 calper g-atom. The free energy of formation of cementite is culculated from the equilibrium compositions of austenite and of gas. Its entropy and heat of formation are also obtained. BASIC knowledge of the high-temperature properties and treatment of steels is contained in the Fe-C diagram and its extensions for the effects of alloying elements. The application of thermodynamics to the Fe-C system, with addition of alloying elements, can serve to simplify and systematize this knowledge. The points of beginning are the binary fee solution, austenite, concerning which our information is reasonably complete, and the binary carbide, cementite. Further studies must include the other phases of the binary system, a and liquid, and for these an accurate knowledge of the ? phase boundaries is essential. These studies should provide a firm base for systematic study of the effects of alloying elements on all phases of the system, their transformations, and precipitation phenomena. With the aid of the simplifying thermodynamic concepts of activity coefficients and interaction parameters it is to be hoped that the results of these studies will be amenable to computer solution thus making the information on multicomponent systems more readily available than would be possible in multidimensional diagrams. Studies of the thermodynamic properties of austenite have utilized equilibrium measurements on the reactions:

Jan 1, 1968

By L. S. Darken

Measurements of the electrical conductivity, the thermal electromotive force, and the deviation from stoichiometry by thermogravimetry were made on ferrous oxide (wüstite) single crystals as well as on poly-crystalline samples in the temperature range of -900" to 1330°C. In the region defined by T 2 1000°C and 1.05 5 O/Fe 5 1.10 the electrical conductivity was shown to be proportional to the sixth root of- the oxygen partial pressure and to be linearly dependent on the deviation from stoichiometry. The absolute Seebeck coefficient of single and polycrystalline wüstite was shown to be independent of temperature in the above region and a p to n transition of the Seebeck coefficient was observed at O/Fe = 1.09 in polycrystalline wüstite. Analysis of the results showed that the predominant defects in wüstite in the above region were doubly ionized cation vacancies. The analysis also ruled out the existence of complexes of the type postulated by Roth, except that below 1000°C there is some evidence of 'association of defects. Of the three oxides of iron (FeO, Fe3O4, Fe2O3) only FeO (wüstite) can exist within a wide range of the ratio O/Fe. This has been shown by several investigations of the phase diagram using for instance chemical analysis of quenched samples'-4 or thermogravimetric measurements. 5,8 Darken and Gurry's1 data for example in the temper- ature range 1100o to 1400°C show that the lowest O/Fe ratio obtainable for FeOl +. is about 1.045 and that the existence range extends to O/Fe = 1.20 at 1400oC. On the basis of detailed analysis of thermogravimetric measurements made by Vallet and Raccah6 the existence of three varieties of wüstite at elevated temperatures was suggested by these authors and by Kleman. It is well-established that wüstite has a NaCl structure with vacant cation sites.3, 8 From a neutron-diffraction study of wüstite samples quenched to room temperature Roth9 concluded that defects in wüstite are mostly complexes composed of two cation vacancies and one interstitial cation in a tetrahedral site. The atomic arrangement in the vicinity of such a defect is similar to that in magnetite, where each occupied tetrahedral site is surrounded by four vacant octahedral positions disposed at the corners of a tetrahedron, so arranged that each vacancy is shared by two tetrahedral cations. Thus there is an average of two vacancies per interstitial. Recent X-ray diffraction measurements made by Smuts10 on quenched wüstite samples confirmed the results of Roth's neutron-diffraction experiments. Roth's model of defects in FeO can be regarded as a solid solution of Fe3O4 in FeO; salmon1' used this defect model to calculate the activity of Fe3O1 in FeO at high temperature and claimed good agreement with the results obtained experimentally by Darken and Gurry.' Each missing cation in wüstite is accompanied by two trivalent cations, thus preserving charge neutrality. The "holes" which differentiate between the Fe 2+ and Fe3' states of the ions in octahedral positions can overcome the attractive field of the cation vacancies, and are then free to move through the crystal as charge carriers. A similar picture holds for COO, NiO, andMnO.l2, 13 Localization of the charge carriers in transition

Jan 1, 1968

By L. S. Darken

A quadratic formalism is developed lor the representation of the excess free energy, and of the activity coefficients of each component of a ternary system in the vicinity of a single component selected as solvent. This formalism, in contrast to the e formalism, is thermodynamically consistent at .finite concentrations. Numerous specific systems are used as illustrations, with cross checks where possible; these systems are Fe-C-X systems in the vicinity of 1600°C and include practically all those for which reliable data are available. It is shown that this formalism is usually quite adequate to rebresent available data up to a solute concentration of 20 to 30 at. pet. It is hoped that the formalism here presented may prove useful for the treatment and tabulation of data on ternary and multi-component solutions. SINCE, as discussed in a prior paper,' we do not as yet have an adequate basic understanding of the nature of binary metallic solutions, we cannot hope to be in better position for ternary and multicomponent systems. However, the accumulation of thermodynamic data on ternary and multicomponent metallic solutions has led to an urgent need for a rational formalism for the presentation and use of such data. Notable attempts to represent the isothermal isobaric thermodynamics of ternary solutions were made by Benedict et 01.' and by Wohl.3 These attempts were directed toward developing an analytic expression adequate to encompass the entire ternary triangle, primarily for organic systems; they generally involve the power-series approach, which has been shown' to be inappropriate, in general, even for binary metallic systems. On the other hand, interest in the thermodynamics of ternary and multicomponent metallic solutions has tended to focus either on general thermodynamic relations4-10 over wide compositional ranges, or on cases where one or more components have been at rather low concentration. This latter approach has been followed by Wagner,= by chipman,11 and by Alcock and Richardson,12 and more recently in many publications by the same and other authors. It has already been shown' that the thermodynamic behavior of binary metallic systems is, in general, relatively simple only in the terminal regions. Hence, it would appear that any approach, at this time, to a simple formalism for ternary and multicomponent systems must, a fortiori, be limited to the vicinity of the major component or solvent. The present treatment is aimed to be useful for a given solvent with moderate solute concentrations ranging up to 20 or 25 at. pet and in exceptional cases to considerably higher concentrations. In order to achieve even this modest objective, it is necessary that any appropriate formalism have built into it 1) a thermodynamic consistency (at least within the desired degree of approximation), and 2) an approach at infinite dilution to Raoult's law for the solvent and to Henry's law for each solute. Let us first formulate the condition of thermodynamic consistency for a ternary system. Under isothermal isobaric conditions, we may write for the molal value G of any extensive function dG - C1 dN1 + G2 dN2 + G3 dN3 [l] where the G's are the corresponding partial molal quantities and the N's are the atom fractions. Taking component 1 as the solvent, this relation may be rewritten in terms of the independent variables N2 and N3

Jan 1, 1968

Jan 1, 1968