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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

By W. R. Bacon

"MAGNETITE HAS BEEN found in many .parts of the coastal area of British Columbia, but the more important deposits are on Vancouver Island and Texada Island. The locations of these deposits are shown on Figure 1.Interest in the magnetite deposits dates back to the 1870s, when land was acquired on the southwest coast of Texada Island by the Puget Sound Iron Company. This ground included the Prescott, Paxton, and Lake deposits. During the years 1885 to 1903, and 1908, 28,898 tons of magnetite ore was shipped to the company's blast-furnace plant at Irondale, Washington, U.S.A. This production was almost entirely from the Prescott open-pits.In the years following the Texada Island discoveries, other magnetite deposits were found in the coastal area, and various plans were proposed to utilize the local ores in the establishment of a steel industry in the Pacific Northwest. None was carried to fruition but, in 1951, open-pit mining was begun at Iron Hill, Vancouver Island, to furnish iron concentrates for steel mills in Japan. In 1952 mining of the Texada deposits was resumed to supply the same market. Production figures for these recent operations are as follows:"

Jan 1, 1949

By Carroll C. Bailey, William F. Boericke

Mine financing, or providing adequate capital for developing and bringing a mining property into production, is an essential requirement for a successful operation. Today it presents a different picture than even twenty-five years ago. The day appears to be gone when a mining property could pay its own way from grass roots to production. The country has been quite thoroughly combed for surface showings from which sufficient initial profit could be immediately garnered to pay for further development and production facilities. The four M's for success in mining-mineral, market, management, and money-are still essential, but doubled or tripled wage costs and steep advances in cost of equipment and supplies throw increased emphasis on adequate capital funds for converting a prospect into a producer. Consequently, the old picturesque, although seldom rewarding, grub- staking procedure where a single venturesome citizen might advance funds to a prospector on a fifty-fifty basis for whatever discovery he might find, has largely disappeared. Its place, to some degree, has been taken by the small syndicate of venturesome members who band together for furnishing funds to a group of prospectors for the same general purposes. Such a syndicate has a definite organization and is usually assured of sufficient initial funds, or flow of funds, to carry on work for several years. It is usually headed by an engineer-promoter or an entrepreneur trader who has had considerable field experience as well as personal knowledge of his prospecting crews. For the owner of a potential mining property who has ample capital, the problem is to determine (1) justification for the necessary investment in exploration and development, and (2) the economics of the enterprise as to size and degree of integration of the ha1 operating entity. If the owner of such a property has little or no capital, he also faces these same basic problems but, in addition, must be able to present the findings of fact and persuade the prospective investor that the enterprise will produce

Jan 1, 1964

By Jameel Menashi

A process has been developed for recovering the refractory metal values contained in mixed secondary source materials such as contaminated grinding wastes, oxides and sludges. The wastes are calcined with sodium carbonate in air to convert the refractory metals to water soluble Na2CrO4, Na3V04, Na2Mo04 and Na2W04. The base metals, Fe, Ni, Co and Cu, are converted to water insoluble oxides. An aqueous leach of the calcine effectively separates the refractory metals from the insoluble base metals. Co, Ni and Cu can be recovered from the oxidic residue by conventional processing methods. The leach solution is purified and then treated to recover the refractory metals as Cr203, NH4VO3, (NH4)6Mo7024?4H2O and H2WO4. The purity of the products is sufficient for their use in many metallurgical applications. The Na+ values in the leach solution are recovered as Na2CO3(or NaHC03) and are recycled to the calcination step. It is shown that the process can accommodate a wide range of feed compositions and generates a minimum of aqueous effluents.

Jan 1, 1984

By J. C. Williams, M. J. Blackburn

In recent years examination of thin foils of metals and alloys has been widely used in studies of deformation and phase-transformation mechanisms. Applications of this technique to studies of titanium and titanium alloys have been infrequent. Therefore, as a large number of titanium alloys have been investigated in this laboratory, it is proposed to give an account of methods used. Particular emphasis will be placed on some of the artifacts introduced in thin foils of titanium and titanium alloys during preparation. Experimental Procedure. It has been found that a large number of titanium alloys can be electropolished in a solution consisting of 30 cu cm perchloric acid (60 pct), 175 cu cm n-butyl alcohol, and 300 cu cm methyl alcohol. Thin foils are prepared using the window method and the electropolishing conditions listed in Table I. Although this solution is not unique, it is attractive because of its low concentration of perchloric acid and the wide range of alloys for which it can be used. Electropolishing is conducted at below -25°C as above this temperature a brown anodic film is produced on the specimen surface. Temperatures above -25°C also accentuate preferential attack of the 0 phase in the two-phase alloys, which unfortunately occurs at all temperatures. Contamination. It is advantageous to reduce the specimen to a thickness of 25 to 50 p prior to electropolishing, since the low-temperature electropolishing technique results in a low rate of metal removal. Both chemical polishing and grinding have

Jan 1, 1968

By H. Kreye, E. Hornbogen

An increase in electrical resistivity during aging or after quenching from high temperatures is known in a large number of alloys. Plastic deformation of alloys in this condition leads to a decrease in resistivity. This anomaly has been called the K effect. This effect has been reported in Ni-A1 alloys by several authors.'-4 The nickel-rich solid solution y is in equilibrium with Ni,A1 (y') with CkAu structure. With this alloy it is therefore possible to produce a homogeneous solid solution as well as a coherent mixture of y and y. The changes in resistivity should be determined for these two conditions. In the present literature on the K effect no distinction is made between them, because of experimental difficulties to determine small coherent particles. In the present work transmission electron microscopy and image formation by (100) and (110) superlattice reflection of the y' phase was employed for a detailed determination of the temperature dependence of solubility of aluminum in nickel and the resulting microstructures with alloys up to 15 at. pct Al. The solubility line follows the equation indicating a smaller solubility than given in the literature at temperatures below 700°C. X-ray scattering was used to get evidence for short-range ordering in the homogeneous solid solutions.5 Parallel to the determination of the microstructure electrical resistivity was measured as a function of aging tempera- ture, time, and aluminum content, which led to the following results: 1) Resistivity increases slightly during aging of a homogeneous solid solution which was quenched from a high temperature as a consequence of short-range order, Fig. 1, curve c,. 2) Resistivity shows a maximum during aging of all alloys which are heterogeneous according to the phase diagram, but which were obtained as a supersaturated solid solution by quenching, Fig. 1, curve c,. The increase in resistivity is mainly due to coherent precipitation of y'. In Fig. 2 the effects due to short-range order pN and due to precipitation of particles APT are shown for an aging temperature of 450°C and different aluminum contents. 3) The increase in resistivity depends on the size !f the coherent particles. A critical diameter of 15 5A for the maximum was found for all alloys and aging treatments by extrapolating particle sizes determined by electron microscopy. 4) The maximum of resistivity of the heterogeneous conditions does not occur if particles, larger than the critical size, have formed already during quenching. 5) Plastic deformation destroys short-range order as well as small coherent particles. Therefore a decrease in resistivity is observed if the increase in resistivity caused originally by these phenomena is

Jan 1, 1967

By Fred Witt, Milton Schwartz

ESTABLISHED methods for obtaining quantitative pole figures for flat sheets1"5 can be extended to apply to thin films on a substrate. The mode of scanning the sample is exactly the same as described in the references? but consideration is given to the fact that the scattered X-ray intensities are due to both the thin film and its substrate with appropriate attenuation factors. The purpose of this paper is to describe a method to obtain the scattered intensities from the film alone for subsequent pole-figure determinations. Fig. 1 shows the four possible general positions of the film (f) and its substrate (s) with respect to the incident X-ray beam (I,). In this paper it will be assumed that the plane of the sample is normal to the plane of the diffractometer. In the diagrams the line jV is the normal to the flat sample and the line P is the trace of the diffracting crystallographic planes in the plane of the diffractometer. The angle of tilt, a, is the positive acute angle measured from the line N to the line P; if this angle is measured clockwise then a is said to be in the positive a region; if this angle is measured counterclockwise then a is said to be in the negative a region. For the reflection cases, the total scattered intensity, at the proper Bragg angle for a particular set of planes, is due to that scattered by the film Vf) and that scattered by the substrate. The beam incident on

Jan 1, 1967

By R. W. Vieth, S. A. Bradford

THE orientations of tetragonal tin crystals are commonly examined by either the transmission Laue method or the back-reflection Laue method. The predominant planes and zone axes of the pattern are plotted on a Wulff net and indexed by measuring the angles between planes and directions. The problem of identifying the Laue spots has been approached in several different ways. Nicholas 1 tabulated interplanar angles for ten planes but did not relate the angles to permutation of indices or sign. A table of angles between adjacent planes and of angles between adjacent zones was published by Chandrasekhar and veal.' These tables are very helpful, provided the film shows all the low-order zones that occur within about 20 deg of each other. Frounfelker and Hirthe's compilation3 of angles between the (001) plane and twenty-nine other planes is useful for the indexing, only if the (001) spot can be found on the film. For all but the simplest orientations, however, more information is needed to index the diffraction spots. Standard stereographic projections, such as those published by Bicelli, 4 provide part of the information required. By their nature, these projections show the positions of only a few zone axes. In the tetragonal system many low-order zone axes are not normal to the planes having the same indices. Consequently, planes and directions can have entirely different positions on a stereographic projection. For example, the [011] zone axis is 33 deg from the normal to the (011) plane. The crystallographic orientation usually has to be deduced from a combination of the predominant zone axes and a few low-order planes that appear on the film. In addition to a standard stereographic projection of the planes, a stereographic projection of the directions is needed. Such a projection can be constructed from the angles given in Table I. To provide more information about angles between planes and directions, we have calculated interplanar angles up to (332) and angles between planes and directions up to [332] on an IBM 1620 computer. The angles are differentiated according to permutations of sign and indices. Those doing research on tin single crystals are welcome to request a copy of these tables from the authors.

Jan 1, 1967

By F. Haessner, M. Wilkens, U. Jakubowski

ThOUGH at present there is a wide range of possibilities for the quantitative determination of preferred orientations, pole figures of identical specimen material have not been determined by different methods as yet.''' In this paper a comparison of (Ill), (200), and (220) pole figures is presented which were obtained from a 95 pct cold-rolled high-purity cop- per sheet (99.9998 pct Cu), by three different methods. The three methods are: a) The combined X-ray reflection-transmission technique of plane samples by schulz3 and Decker, Asp, and Harker. 4 A Siemens texture goniometer was used. The experimental details are described elsewhere. 6 b) The X-ray reflection technique of spherical samples by Jetter and Boric.' A Siemens texture goniometer with some modifications was used. The samples were prepared by sticking 140 polished sheets together with an adhesive and machining a sphere (20 mm diam).* Additional

Jan 1, 1967

By J. E. Hanlon, J. D. Wolf

The relaxation peaks observed in plastically deformed materials at low temperatures have been reviewed by sack1 and Niblett and wilks. 2 In particular, the dislocation-relaxation in columbium has received considerable study.3-6 The present work deals with the lower-temperature dislocation-relaxation peak (referred to by Chambers and Schultz as the a peak) in columbium and Cb-5 pct Zr. The columbium and Cb-5 pct Zr specimens were machined to 3/8-in.-diam by 7-in.-long rods from bars hot-extruded at 1200°C. The internal friction and resonant frequency of the samples were measured in torsion at kilocycle frequencies at a maximum strain amplitude of -10-6. The interstitial content of both materials was approximately 70 ppm N and 200 ppm 0. The dislocation-re laxation peaks were measured in the hot-extruded state and after successive anneals. Fig. 1 is a compilation of the data. The resonant frequencies for the columbium and Cb-5 pct Zr samples were, respectively, 5.5 and 6.5 kc. Other workers have noted that the dislocation-relaxation peaks in columbium are not characteristic of a single relaxation time. As can be seen in Fig. 1, the zirconium addition further broadens the spectrum of relaxation times. The magnitude of the modulus defect as computed from resonant-frequency data also reflects this extension. The occurrence of the low-temperature a peak at a position 20°K higher in Cb-5 pct Zr as compared to pure columbium, in the hot-swaged state, suggests a decrease in the average dislocation mobility for the alloy. The authors do not feel that these data are sufficient to permit an interpretation in terms of any detailed models.

Jan 1, 1967

By Nicholas J. Grant, John S. Benjamin, Bill C. Giessen

In the course of a study of hard particle-duc tile binder composite alloys, interest arose in the nature of the products of the reaction between the inter metallic compound NiAl and the binder niobium. No published information was then available. A program to

Jan 1, 1967

By J. F. Breedis

The stabilization of austenite in Fe-Ni alloys against martensitic transformation after reversion has been attributed' to the lattice imperfections remaining from previous transformation. More recently, however, such stabilization has been associatedzy3 with compositional changes which occur in martensite during slow heating. Dislocation arrangements in deformed austenitic stainless steels strongly influence transformation to martensite on quenching.4 Therefore, it is of interest to observe the transformation behavior of stainless steel after reversion, especially since previous studies have been confined to Fe-Ni alloys. The transformation-product morphology also differs in the two iron-alloy systems;6 plate martensite forms in the latter while stainless steel transforms to lath-type martensite. Samples of Fe-16 wt pct Cr-12 wt pct Ni (maximum C + N = 0.005 wt pct, 0 = 0.02 wt pct), prepared by vacuum melting and casting from high-purity components, were annealed at 900°C for 24 hr, after cold rolling to produce a 40-p grain diameter. The M, temperature of this alloy is -80°C and samples are fully austenitic after annealing. The amount of martensite present after quenching, annealing, and requenching was determined magnetically, to within 0.01 wt pct, using a vibrating specimen magnetometer. Nearly 14 pct of martensite forms during the initial quench in 1 min at -196°C. Two-min and 2-hr anneals were done in air and in evacuated quartz capsules, respectively. All specimens were electro-polished before making the magnetic measurements.

Jan 1, 1967

By H. U. Schutt, J. M. Toguri

REGARDLESS of the degree of purification effected during the electrorefining of copper, a danger of re-introducing impurities exists in the operation of melting and casting of the refined copper. Logically only a combination of the purification and casting operation would remedy the situation. A well-known method of metal purification is the "Gross"-type process, whereby a volatile halide is produced, purified, and decomposed.' In the present case, this concept was used to remove the impurities rather than to form possible volatile copper halides. The object was to produce volatile halides of the impurities present and distill these away, leaving high-purity copper. It is interesting to note that such techniques are used in spectrographic procedures in order to shorten exposure time and enhance the density of impurity lines.' In the present investigation, copper hydroxy fluoride was used, since the temperature of decomposition of copper hydroxy fluoride and the melting point of copper nearly coincide. The fluorine released by the thermal decomposition of copper hydroxy fluoride purges the molten copper. Copper hydroxy fluoride was prepared by dissolving high-purity copper in nitric acid and adding hydrofluoric acid and ammonium hydroxide in the required proportions. The melt was made in a high-purity graphite crucible heated by an induction furnace. Trial experiments showed that impurities can be introduced from the crucible material. Therefore, preceding each cast, the crucible itself was cleaned by decomposing copper hydroxy fluoride and discarding the residual copper. Best experimental conditions were obtained by adding 30 g of copper hydroxy fluoride to 500 g of nor-

Jan 1, 1967

By M. R. Louthan, C. L. Angerman

In polycrystalline Zircaloy-2 the orientation of zirconium hydride precipitates is influenced by an applied stress during hydride precipitation; hydride platelets are oriented nearly parallel to a compres-sive stress and perpendicular to a tensile tress. 1,2 A similar effect has been observed in the Ti-H system, where precipitation of the low-density hydride platelets occurred on habit planes made energetically favorable by the application of stress. 3 Recently, stress activation of hydride habit planes in zirconium and Zircaloy-4 was also demonstrated. The hydrides precipitated on {101l), {112l} and (2131) planes in both zirconium and Zircaloy-4; however, no platelets were found near the prism-plane positions in the Zircaloy-4 samples. Investigations at the Savannah River Laboratory, using polycrystalline Zirc_aloy-2 samples, have confirmed the (101l) and (1121) habit planes but also showed that the prism planes were active hydride habit planes. Using single-surface stereographic analysis and back-reflection Laue techniques, most of the previously reported habit planes for a zirconium were observed.4"1 and one additional plane, the (1013) plane, was noted, Table I. All the habit planes observed had the form (101l) or { 112l) indicating that these planes are the habit planes for hydride precipitation in poly-crystalline Zircaloy-2. The specimens used in these studies were cut from large-grained weld areas of seam-welded tubing and were hydrided in either a static steam autoclave at 400°C and 1500 psig or in a modified Sieverts apparatus at 400°C.

Jan 1, 1967

By L. Messulam, A. S. Appleton

Iwo major studies of the Fe-Cr-C system are available in the literature. The earlier one of Kinzel and crafts' forms the basis for the data most commonly quoted in works of reference (e.g., Metnls HandDook) though the later work of Bungardt el a1.' is more extensive and amenable to analysis in terms of isothermal sections and so forth. However it is evident from examination of either of these studies that the delination of phase boundaries on the basis of the data obtained can only be very approximate. Indeed in several instances the data are so inconclusive that this delineation is a matter of opinion. This note is to report an analysis of experimentally determined carbon activity data in this system, which, originally intended as a means of checking the self-consistency of the data for a number of alloys, enables some conclusions to be drawn concerning the 10503C isothermal section of the iron-rich corner of the system as deducible from the data of Bungardt

Jan 1, 1967

By Rodney P. Smith

The solubility of niobium carbide in y iron has been determined for the temperature range 1000" to 1300°C from the carbon content of a series of Fe-Nb alloys equilibrated with hydrogen-methane mixtures. The method is similar to that used by Darken, Smith, and Filer 1 to determine the solubility of aluminum nitride in y iron and by smith2 to determine the solubility of niobium nitride in y iron. The samples* were strips 1.2 by 3 by 0.035 cm. The niobium oxide.* For samples of composition slightly

Jan 1, 1967

By Eugene S. Machlin

A classical theory of solid solutions involving neavest-nergkbor intevactions with both central and linked-central forces between atoms has been developed. It has been found that the theory, where it can be checked quantitatively, is in ageement with experiment. The theory encompasses a description of many diverse pkenomena, such as antiphase shift structures, size effect, relative stabilities of various solutions, lattice para,neters, and order-disorder transitions. In particulav. a quantitative prediction not involving adjustable pavameters is made concevning the deviation of the Au-Cu interatonlic distance in long-range ordered (Ll,) Cu-Au I fronl the average distance based on the distances in pure gold and copper. This prediction, which is in agreement with expel-intent, has not been encompassed by any preuious theory. The theory of order-disorder is fragmentary. That is, no one theory exists that can explain the variety of qualitative phenomena observed. Further, many theories are not in good quantitative agreement with experiment. This subject has been reviewed by Muto and Takagi, Tuttman, and Oriani.3 There exists no doubt that the quasi-chemical approximation is not a complete description and that the inclusion of strain energy using macroscopic elasticity theory concepts leads to results in disagreement with experimenL4 The observation of antiphase domains and ordering systems such as Cu-Pt has led to Brillouin zone treat-ment of the order-disorder transition as opposed to the classical Ising model. The objective of this paper is to demonstrate that it is possible to develop a pairwise approximation model that can explain many of the observed order-disorder phenomena that have puzzled investigators in the past. This theory is based upon an empirical model due to ergmman' for the elastic constants of metals. This model is generalized for multicomponent systems. As will be shown, the theory yields a short-range ordering energy for the disordered solution which differs from the ordering energy calculated from the differences in energy of disordered and long-range ordered solutions. It will be demonstrated that there is no necessary correlation between heats of formation and the tendency to order or between size effect and the tendency to order. Also, the existence of antiphase domains and iso-short-range-order systems that form superlattices (Cu-Pt) is predicted on the basis of the theory. Further, the relative stability of competing superlattices is calculable from the theory. If single-crystal elastic-moduli data are available for the pure components and one superlattice then there exists but one adjustable parameter in the calculation of lattice parameters for both the disordered and ordered solid solutions. In one special case, no adjustable parameters are required and a quantitative prediction is made. For the calculation of energies and partial order, there exists but one additional adjustable parameter, the pair-exchange energy V used in the quasi-chemical approximation (or the Ising model.) However, in these calculations, much more precise values are required for the single-crystal elastic moduli than available if the quantitative uncertainties in the predicted values of the energies are to be sufficiently small. THEORY ~er~man' has developed a model with which he was able to obtain fair agreement with experiment for the relations between the elastic constants for metals. This model which we shall call Bergman's model is a linear combination of his models I and 11. In effect, Bergman, in this model, considers that each interatomic distortion is composed of two components: a classical central force distortion with an associated central force constant and what we shall call a linked-central force distortion with an associated linked central-force constant. The linked-central force distortion component obeys the constraint that the sum of such distortions over all the bonds equals zero. No constraint is imposed on the classical central force distortion component. Bergman' derives the constraint on the linked-central force distortion on the basis of application of Pauling's relation between bond distortion and bond number to metals.ga This assumption is not logically necessary, however, and the Bergman model may be taken as a mathematical model for elastic constants, e.g., a purely empirical model without a physical basis. In the present work, the method of Bergman has been applied to two-component systems (solid solutions). In place of an external strain—which would allow a calculation of the elastic constants for the two-component system—it is considered that internal interatomic distortions exist as a consequence of having three potentially unequal distortion-free interatomic distances and but one "average" interatomic distance. It is assumed that the distortion-free interatomic distances between atoms of the same element are those found in the pure element having the same undistorted crystal structure as the solid solution. The distortion-free interatomic distance between unlike atoms is in general not measurable except in the probably nonexistent

Jan 1, 1967

By R. G. Ward, D. R. Gaskell

Using the maximum bubble pressure technique, the densities of iron silicates at 1410°C have been measured blowing helium, nitrogen, and argon. By ensuring equilibrium between the melt and the blowing gas with respect to oxygen potential and by minimizing tempcrature cycling of the furnace, iron precipitation in the melt has been prevented. Thus the previously reported effect of blowing-gas composition on the densities of the melts has been eliminated. Consideration of the oxygen densities of the melts gives an indication of the structural changes accompanying composition change. The density-composition relationship of iron oxide-silica melts in contact with solid iron has been the subject of several investigations1-7 and considerable disparities exist among the various results obtained. Of these investigations, all except one5 have employed the maximum bubble pressure method. In the most recently reported of these investigations1 the density-composition relationship obtained blowing nitrogen differed from that obtained blowing argon. The measured densities obtained under nitrogen were greater than those obtained under argon, the difference being a maximum at the pure liquid iron oxide composition and decreasing with increasing silica content. This observation rationalized the disparities existing among the results of the earlier investigations, showing that two lines, one for nitrogen and the other for argon, could be drawn to fit all the earlier results. No explanation for this phenomenon could be offered. Chemical analysis of rapidly quenched samples of melt for dissolved nitrogen, and direct weighing measurements, excluded solution of nitrogen in the melt from being the cause of the increase in density. The range of blowing gases was extended by Ward and Hendersons who measured the density of liquid iron oxide bubbling helium, nitrogen, neon, argon, and krypton. The measured density was found to decrease smoothly with increasing atomic number of the bubbling gas. The work reported here is a continuation of the program initiated by Ward and Sachdev7 to study the densities in multicomponent melts in which the iron oxide-silica system is the solvent. As such it is necessary to explain or eliminate the anomalous densities of iron silicates under different atmospheres, and the present rede termination was carried out towards this end. EXPERIMENTAL The maximum bubble pressure method of density determination was again employed and the experimen- tal apparatus used was essentially the same as that used by Ward and Sachdev.7 A molybdenum-wound resistance furnace heated an ingot iron crucible of internal diameter 1 in. containing a 2-in. depth of melt. The bubbling gas was blown through a 1/4 -in.-diam mild steel tube onto the end of which was welded a 2-in. extension of 1/4 -in.-diam ingot iron rod, drilled out to 5/32 in., and chamfered to an angle of 45 deg. The blowing tube was introduced to the furnace through a sliding seal and its position was controlled by a vertically mounted micrometer screw which allowed the depth of immersion to be determined with an accuracy of ± 0.01 cm. A Pt/Pt-10 pct Rh thermocouple was located below the crucible and temperature control was effected initially by means of an on-off controller and later by a saturable core reactor. The bubble pressure was determined by measurement of a dibutyl phthalate manometer using a cathetometer. PREPARATION OF MATERIALS Iron oxide was produced by melting ferric oxide in an inductively heated iron crucible in air. The liquid was quenched by pouring onto an iron plate. Silica was prepared by dehydrating silicic acid at 650°C for 12 hr. RESULTS Before any measurements of the density of a melt were made, the density of distilled water at room temperature was measured bubbling helium and argon. Both gases gave the density as 1.00 ± 0.01 g per cu cm which showed that the density of the manometric fluid (dibutyl phthalate) was not affected by contact with the blowing gas. With the furnace controlled by an on-off temperature controller an attempt was made to measure the density of pure liquid iron oxide by bubbling argon. The furnace atmosphere gas and bubbling gas were dried over magnesium perchlorate and deoxidized over copper turnings at 600°C. It was found that the pressure required to blow a bubble at a given depth increased slowly with time, and thus it was impossible to obtain a unique value for the density of the melt. Inspection of the blowing tube after removal from the furnace showed that rings of dendritic iron had precipitated from the melt onto the immersed part of the tube. This is shown in Fig. l(a) where the various "steps" correspond to different depths of immersion. The precipitation of iron was considered to be due to one or both of two possible causes: i) The composition of the liquid iron oxide is that of the liquidus at the temperature under consideration and can be expressed by the equilibrium

Jan 1, 1968