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By E. P. Abrahamson

The effect of transition element binary solid solution additions upon the recrystallization temperature of titanium has been investigated. All additions, except columbium and tungsten, raised the recrystallization temperature. A correlation is obtained between the logarithm of the absolute rate of change of recrystallization temperature with atomic percent solute and the number of uuter d shell electrons attributed to the free atom of the solute element in its ground state. The work of Abrahamson, et aL.1-6 on dilute binary solid solution alloys indicated a correlation between the free atom ground state electron configuration of the solute and both the brittle-ductile transition and recrystallization temperature. It is shown in these studies that the number of outer s and d electrons in the solute are of prime importance in determining the absolute rate of change of recrystallization or transition temperature with composition. Furthermore, the limit of initial linearity (in the curve of recrystallization temperature vs at. pct solute) has been shown to be a function of the number of d shell electrons in the solute for dilute iron- and vanadium-base alloys. To date no complete systematic recrystallization study of dilute binary titanium base alloys has been made. This study together with that of zirconium base alloys 6 will provide the data for the comparison of the effect of the same solutes upon two solvents with the same number of outer d shell electrons.

Jan 1, 1962

By O. N. Carlson, S. A. Bradford

Discontinuous yielding in tensile tests was observed in V-O alloys in the temperature ranges of 150° to 175°C and also 350° to 400°C. The magnitude and intensity of the serrations were found to vary considerably with oxygen content. Maxima were observed in tensile and yield strengths and in the strain-hardening coefficient at the higher temperature only. The strain rate sensitivity was observed to be negative between 150° and 400°C. THIS investigation was undertaken to study the effect of oxygen on the tensile properties of iodide vanadium in the temperature range of 25o to 450°C. Brown1 observed an increase in strength between room temperature and 400°C in vanadium metal, and found that oxygen and nitrogen had a rather pronounced effect on the strength and ductility. A maximum in the tensile strength was observed by Rostoker et al.2 near 300oC and by Pugh3 around 450°C for calcium-reduced vanadium. Pugh also found a maximum in the yield strength and in the strain-hardening exponent, and minima in the elongation and strain rate sensitivity at the same temperature. Eustice and Carlson4 reported the appearance of serrations in the stress-strain curves between 140° and 180°C in iodide vanadium containing 600 ppm O. These anomalies in the mechanical properties indicate that strain aging occurs in vanadium, but the impurity or impurities responsible for the above-mentioned effects have not been identified. The phenomenon of strain aging is usually characterized by the return of the yield point after interruption of a strength test. In the temperature range where strain aging occurs, the yield and tensile strengths attain maximum values, elongation and strain rate sensitivity exhibit minima, and discontinuous yielding is generally observed in the stress-strain curve. Cottrell5, 6 has postulated that strain aging is due to the migration of solute atoms to dislocation sites to produce locking after the dislocations have broken free from their impurity atmospheres during the initial yielding. At the strain-aging temperature the process is a dynamic one in which the solute impurity atoms diffuse to the vicinity of the moving disloca- tion producing "locking" which gives rise to maxima in the tensile strength and serrations in the elongation curves. Cottrel17 has noted that discontinuous yielding in iron occurs when the diffusion coefficient of nitrogen, D, and the strain rate, i, are related by D = 10-9 €. EXPERTMENTAL PROCEDURE The vanadium metal employed in this study was prepared by the iodide refining process as described by Carlson and owen.8 A representative analysis of the vanadium used in this investigation was: 150 ppm O, <5 ppm N, <1 ppm H, 150 ppm C, 150 ppm Fe, 70 ppm Cr, <50 ppm Si, 30ppm Cu, 20 ppm Ni, <20 ppm Ca, <20 ppm Mg and <20 ppm Ti. Alloys containing from 200 to 1800 ppm O, all of which lie in the solid solution range of the V-O system, were prepared by arc melting vanadium together with portions of a high-oxygen master alloy. The master alloy was prepared by tamping pure V2O5 into holes drilled in a vanadium ingot and arc melting this five or six times in an inert gas atmosphere, inverting the button between each melting step. The oxygen content of the master alloy was then determined by vacuum fusion analysis. Vanadium containing less than 150 ppm O was prepared in the following manner. A bar of iodide vanadium was deoxidized by sealing it in a tantalum crucible with a few grams of high-purity calcium. This was held at 1100°C for 4 days to allow time for the oxygen to diffuse to the surface and to react with the calcium vapors. The calcium oxide product was later dissolved from the surface of the bar with dilute acetic acid. In this way vanadium containing from 20 to 50 ppm O was prepared. Sample Preparation. The are-melted ingots were cold swaged into 3/16-in. diam rods and these were machined into cylindrical tensile specimens with a reduced section of 1.00-in. length and 0.120-in. diam. The test specimens were annealed for 4 hr at 900°C in a dynamic vacuum of mm of Hg to remove hydrogen from the metal. This recrystal-lization treatment produced a uniformly fine-grained structure with a mean grain size of approximately 0.06-mm diam. The oxygen contents reported in this paper were determined by a vacuum fusion analysis of the tensile specimens after testing. Analyses for other interstitial or metallic impurities showed no significant changes from that of the original material. Tension Tests. Tension tests were performed on a screw-driven tensile machine at a constant cross-head speed of 0.01 in. per min. Tests at elevated temperatures were carried out by heating the

Jan 1, 1962

By K. M. Busen, J. Lindmayer

A heterojunction model is suggested for descrihzng the electronic conditions at oxide -semiconductor interfaces. Detailed study of the silicon oxide-silicon interface shows that the heterojunction model explains many experimental facts; however, it is necessary to assume that a transition layer exists at the interface. It will he demonstrated that ionic contrbution way also he present. Extended low-temperature heating stabilizes the oxide to a charge carrier density in the order of 10&apos; cln-: determined by the heterojuncton model. OXIDIZED semiconductor surfaces are widely used, since they offer technological advantages and "passivate" the surfaces of semiconductor devices. However, it has been recognized that there are always n-type inversion layers formed in the silicon oxide-silicon system, which must be regarded as a definite disadvantage. An added complication is the "instability" of these inversion layers;&apos; the inversion layer appears to vary with the processing and they change at temperatures as low as 100" to 200°C This paper will point out that the inversion layer is a result of the dissimilarity of the contacting materials and therefore must always be present. The dissimilarity is the essence of the heterojunction or electronic model and involves directly the structure of the materials involved. In addition, one finds the contribution from ions; this disturbance, however. can be eliminated for the case of silicon oxide-silicon interface. The strength of the inversion layer or channel will be expressed in terms of the density of elementary charges per square centimeter, N*, maintaining the channel. The next section contains the formulation of the heterojunction model by assuming a contact between two homogeneous materials. This calculation should not imply that silicon oxide is homogeneous; it serves only to point out the general properties of the electronic model. Following the electronic model, the practical case of the silicon oxide-silicon interface will be discussed. I) THE HETEROJUNCTION MODEL Contacting an oxide with a semiconductor, a work-function difference must be accommodated. Fig. 1 represents the oxide and the semiconductor before and after contact. When the contact has been made, one finds that qVi + qV, = A@; i.e., the work-function difference is distributed between the oxide and the semiconductor. Normally, the work-function difference appears on the wide-bandgap material, but in the present case the oxide is thin and far from being a single crystal. Accordingly, a significant fraction of the work-function difference must appear on the semiconductor. The work function of silicon2 is about 4.8 ev, but we shall not assign any particular work function for the oxide as it may vary. However, oxides usually have lower work functions and therefore the potentials must build up in the manner shown in Fig. 1. Such an argument predicts that the inversion layer must be n type, as opposed to the clean surface which is p type. Another important factor to be considered is that the oxide is disorderly and therefore contains many trapping levels. As a result, the charges in the oxide arise primarily from the change in trap occupation, while on the semiconductor side the space charge is composed of mobile free electrons. The consequence of this fact is that a change to another thermal equilibrium will require some time, dictated by the traps in the oxide. The conditions can easily be calculated on the semiconductor side. Assuming an intrinsic semiconductor, Poisson&apos;s equation is

Jan 1, 1965

By A. H. Daane, W. J. Wunderlin, B. J. Beaudry

The solid solubility of holmium in copper, silver, and gold, determined using metallographic techniques, was found to be a maximum of 0.06, 2.4, and 3.2 wt pct, respectively, nt the eutectic temperatures. The temperatures of these eutectic horizontals, determined by differential thermal analysis, were found to be 868", 787", and 778"C, respectively. The first compound on the silver-rich side of the Ag-Ho system was found to be A&Ho2. In a study by Gold et al.,&apos; on the effect of small amounts of soluble impurities on the electrical resistance and thermoelectrical properties of copper, traces of iron were shown to have drastic effects on the thermoelectric power due to the magnetic scattering of the conduction electrons. Since little is known about the state of the iron ion when dissolved in copper, Gold had hoped to repeat these experiments using certain rare earths as the magnetic scattering centers; because of the tightly bound 4f electrons it is not expected that their spectroscopic state would be affected by alloying. In such an experiment the sole role of the trace rare-earth impurity would be to magnetically scatter the copper conduction electrons without producing appreciable distortions in the otherwise pure copper matrix. Since holmium was chosen for such a study because of its high magnetic moment, it was necessary to establish precisely its solid solubility in copper. The study was extended to include the solvents silver and gold, so that an evaluation of the data using classical solubility parameters could be made. No previously reported work on the systems of holmium with copper, silver, or gold was found in the literature. Information on the solubility of other rare earths in these three metals is also very meager. The solubility limit of yttrium in copper was reported as less than 1 wt pct2 and the solubility of praseodymium in gold as 0.35 wt pct,3 while no references were found on solubility studies of rare earths in silver. EXPERIMENTAL Materials. The materials used in this investigation were distilled holmium prepared in this Laboratory, OFHC* copper, electrorefined silver (99.9 *OFHC = oxygen-free high conductivity. pct), and gold with the analyses given in Table I. Sample Preparation. Samples weighing 1 to 2 g were prepared by arc-melting the components together on a water-cooled copper plate under purified argon atmosphere. The samples, turned and remelted at least five times to ensure homogeneity, showed weight changes of less than 0.1 wt pct after melting. Samples containing less than 0.7 wt pct Ho were prepared by diluting 1 to 2 wt pct Ho alloys with the pure solvent, while samples with concentrations greater than 0.7 wt pct Ho were prepared directly from the metals. The samples were wrapped in tantalum foil, sealed in outgassed Vycor tubing under helium, annealed at the desired temperature for at least 24 hr, and then quenched by shattering the Vycor tube in cold water. Metallographic Methods. Standard mechanical polishing methods were used in preparing the silver and gold alloys for examination, while the copper alloys were electropolished using a 40 pct solution

Jan 1, 1963

By J. F. Enrietto

Internal friction measurements were used to determine the effect of manganese on the solubility and precipitation kinetics of nitrogen. Manganese, in concentrations up to 0.75 pct, has little effect on the solubility at temperatures above 250°C. On the other hand, at Concentrations as low as 0.15 pct, manganese inhibits the formation of iron nitrides, especially Fe4N, even though it may not form a precipitnte itself. The precipitation and solubility of carbides and nitrides have been extensively investigated in the pure Fe-C and Fe-N systems.1-3 In recent years, some effort has been ispent in studying the influence of substitutional alloying elements on the behavior of carbon and nitrogen in ferrite.4 -7 In particular Fast, Dijkstra, and Sladek have investigated the effect of 0.5 pct Mn on the internal friction and hardness during the quench aging of Fe-Mn-N alloys.&apos;, &apos; They found that at low temperatures (below 200°C) the presence of 0.5 pct Mn greatly retarded quench aging. For example, after 66 hr at 200°C very little precipitation had taken place in the iron alloyed with manganese, whereas precipitation was complete after a few minutes in a pure Fe-N alloy. The effect of varying the manganese content and the details of the precipitation process were not mentioned in these papers. Fast&apos; postulated that manganese causes a local lowering of the free energy of the lattice with a resulting segregation of nitrogen atoms to these low energy sites. The segregated nitrogen atoms are bound so tightly to the manganese atoms that they cannot form a precipitate. The internal friction measurements of Dijkstra and Sladek tended to confirm the concept of segregation of nitrogen around manganese atoms, and the increase in free energy on transferring a mole of nitrogen atoms from a segregated to a "normal" lattice site was computed to be - 2800 cal. Dijkstra and Sladek9 distinguished between two types of precipitates: ortho, a nitride of appreciably different manganese content than that of the matrix, and para, a nitride with a manganese content essentially that of the matrix. With each type of precipitate a solubility, again designated ortho or para, can be associated. Since the internal friction maximum in alloys which were aged several hours at 600" C dropped almost to zero, Dijkstra and Sladek9 concluded that the ortho solubility must be very low. The effect of temperature on the ortho and para solubilities has no1: been investigated. There are obviously several gaps in our knowledge concerning the influence of manganese on the behavior of nitrogen in a-iron. It was the purpose of the experiments described in this paper to determine the following: 1) The ortho and para solubilities of nitrogen as a function of temperature. 2) The details of the precipitation process at elevated temperatures. 3) The effect of varying the manganese concentration on the above phenomena. EXPERIMENTAL PROCEDURE Internal friction is conveniently employed in studying the precipitation of nitrides and/or carbides from a -iron because it is one of the few parameters, perhaps the only one, which is not affected by the presence of the precipitate itself. For this reason, internal friction techniques were heavily relied upon in the present experiment. A) Preparat of -. All specimens were prepared from electrolytic iron and electrolytic manganese. Alloys containing 0.15, 0.33, 0.65, and 0.75 wt pct Mn were vacuum melted and cast into 25 lb ingots. After being hot rolled to 3/4 in. bars, the ingots were swaged and drawn to 0.030 in. wires. The wires wen? decarburized and denitrided by annealing at 750° C for 17 hr in flowing hydrogen saturated with warer vapor. To obtain a medium grain size, - 0.1 mm, the wires were then heated to 945oC, allowed to soak for 1 hr, furnace cooled to 750°C, and water quenched. Subsequent internal friction measurements showed that this procedure reduced the nitrogen and carbon concentrations of the alloys to less than 0.001 wt pct. The wires were nitrided by sealing them in pyrex capsules containing anhydrous ammonia and annealing them for 24 hr at 580°C, the nitrogen being retained in solid solution by quenching the capsule into water. Immediately after quenching, the wires were stored in liquid nitrogen to prevent any precipitation of nitrides. By varying the pressure of ammonia in the capsule, it was possible to produce any desired nitrogen concentration. B) Internal Friction. The internal Friction measurements were made on a torsional pendulum of the Ke type,&apos;&apos; a frequency OF 1. or 2 cps being used. For

Jan 1, 1962

By M. E. Nicholson

The solubility of carbon in Ni-Cu alloys was determined at 1000°C. The factors which limit solid solubility are discussed with particular reference to the influence of electronic factors. The results indicate the extent of solid solubility is a function of the density of states at the Fermi surface. THE solid solubility of an interstitial element is primarily limited according to Seybolt and Fullman1 and Speiser and Spretnak2 by (a) the strain energy produced when the solute atom takes its interstitial position, and (b) the partial molal free energies of the solid solution and the coexisting phases. In several binary systems of a transition and a noble metal, where there are no abrupt changes in strain energy or free energies of coexisting phases, the solid solubility of an interstitial third element drops abruptly to a negligible value at a composition corresponding to a complete filling of the "d-band." Such a decrease occurs in the case of hydrogen in the Pd-Ag system at 60 pct Ag.3,4 The solubility of carbon in Ni-Cu alloys seems to vary in a similar manner as indicated by the embrittling effect of carbon on these alloys. These al- loys are embrittled by slow cooling due to the precipitation of graphite. This embrittlement can be removed by heat treatment if the carbon content is less than the solid solubility limit at the heat-treating temperature. If the carbon content of the alloy exceeds the solid solubility at the heat-treating given temperxture, the embrittlement cannot be eliminated by solution heat treatment.&apos; Since pure nickel has a carbon solubility of 0.25 wt pct6 at 1000°C, embrittlement is easily removed from commercial nickel and nickel-rich alloys, which may contain of the order of 0.10 wt pct C. Embrittlement due to carbon cannot be removed from Ni-Cu alloys containing 70 to 80 wt pct Cu by annealing unless: the carbon content is of the order of 0.04 wt pct CL or less."&apos; Thus, it appears that the

Jan 1, 1962

By B. C. Allen

Liquid surface tensions of copper and 18 Group IV-A to VIII transition metals (Ti, Zr, Hf, V, Cb, Ta, Mo, W, Re, Ru, Rh, Pd, Os, Ir, Pt, Fe, Ni. Co) have been measured by the static pendant-drop and dynamic drop-weight methods on the same rod sample. The drops were formed by electron-bombardment heating in high vacuum. Application of necessary corrections enabled determination of surface tensions to k2 pct and agreement between methods to * 1 to 4 pct for all the metals studied. Evidence is presented that the liquid surface was well screened by metal vapor, suggesting negligible adsorption of gaseous impurities and that the surface tensions measured are characteristic of the metals involved. Correlations between liquid surface tension and melting point, molar volume, heat of vaporization, and atomic number are presented and discussed. Temperature coefficients of surface tension were calculated using Eötvös&apos; law. SURFACE tension and interface energies of metals are the result of incomplete atomic coordination resulting in a force perpendicular to the boundary, tending to minimize its area. These energies are important in many phases of metallurgy, including microstructure, sintering, joining, electronic emission, and lubrication, which in turn affect many physical and mechanical properties of metals. Liquid surface tension refers to the interface between the liquid and its own vapor or nonreactive atmosphere, and is considered a physical property of the liquid. Since equilibrium shapes can be readily obtained with liquids, the units of surface tension (force per length) and interface energy (energy per area) are interchangeable. Thermo-dynamically, the surface tension ?LV is given by the change in free energy F with surface area A at constant pressure P, temperature T, and composition N: for commercially important refractory metals, vanadium, columbium, tantalum,13,14 molybdenum,14 and tungsten,l5 and none for the rare platinum-group metals and rhenium. Measuring the surface tensions of transition metals is difficult because of their high reactivity and melting points. Of the many techniques available,16-18 the pendant-drop 19-21 and drop-weight methods17,22 are considered superior because they can be modified to eliminate persistent sources of contamination such as supports and capillaries necessary in the popular sessile drop, capillary rise, and maximum-bubble-pressure techniques. The necessary modification is to melt a drop on the tip of a vertical rod, which provides support through a solid of the same composition.13,15 The object of the work was to study the surface-tension behavior of copper and transition metals, having reasonably low vapor pressures. Liquid surface tension of each pure metal was systematically determined by using a combination of the static pendant-drop and dynamic drop-weight methods on the same rod. Liquid drops were formed by electron-bombardment heating in high vacuum. EXPERIMENTAL WORK As indicated in Table I, the metals studied were high purity and generally were obtained in rod form. The exceptions were titanium and zirconium, which were machined from crystal bars, and molybdenum (tot 11, osmium, and ruthenium, which were sintered and arc cast into rods. All the metals were ground or swaged to desired sizes between 1- and 7-mm diam, and centerless ground round and smooth to a finish better than 50 µ in., rms. Each rod was thoroughly cleaned with steel wool, degreased, acid etched, and dried. In a typical run, the rod was vertically clamped in a modified floating-zone electron-bombardment furnace designed after Calverley23 and Carlson.24 The specimen was outgassed and maintained positive at several kilovolts in a dynamic vacuum of 10-5 to 10-7 mm. The bottom end was enclosed by a tantalum pillbox and heated by electrons emitted from a hot concentric tungsten filament mounted on a movable bracket. The bombardment power was slowly raised until melting was observed. Power requirements ranged from 30 w for copper to 1300 w for 4-mm tungsten. The stabilized and out-gassed drop of near-maximum size was photographed at 4. 1X on panchromatic film at desired time inter-

Jan 1, 1963

By A. J. Shaler, H. Udin, J. Wulff

In the study of the sintering of meta powders, we have come to the conclusion in this laboratory that further progress requires a more basic understanding of the operating mechanisms. This is emphasized in detail by Shaler. He has shown that a knowledge of the exact value of the surface tension is imperative for a solution of the kinetics of sintering. This force plays a principal role in causing the density of compacts to increase.2 Furthermore, a knowledge of the surface tension of solids is also applicable to other aspects of physical metallurgy. C. S. Smith3 points out the relation between surface and interfacial tension and their function in determining the microstructure and resulting properties of polycrystal-line and polyphase alloys. This paper describes one group of results of an experimental program designed for the study of the surface tension in solid metals. As a by-product of this work, considerable information has been obtained on the rate and nature of the flow of a metal at temperatures approaching the melting point and under extremely low stresses, a field of mechanical behavior heretofore scarcely touched by metallurgists. The importance of this additional information to students of powder metallurgy need not be stressed. Theoretical Considerations Interfacial tension arises from the condition that an excess of energy exists at the interface between two phases. Gibbs proves that this energy is a partial function of the interfacial area; thus: ?F/?s = ? where ?F/?s is the rate of change of free energy of the system with changing surface area, at constant temperature, pressure and composition, and ? is the interfacial tension, or interfacial free energy per unit area. If one of the phases is the pure liquid or solid, and the other the vapor of the substance, ? may properly be termed "surface tension," and is a characteristic of the solid or liquid. The attempt of a body to lower its free energy by decreasing its surface gives rise to a force in the surface which is numerically equal in terms of unit length to the free energy per unit area of the surface. Thus ? may be expressed either in erg-cm-² or in dyne-cm-1. Similarly, surface tension may be determined either by a thermo-dynamic measurement of the surface energy or by a mechanical measurement of the surface force. We have chosen the latter approach. Tammann and Boehme4 determined the surface tension of gold by measuring the amount of shrinkage or extension of thin weighted foil at various temperatures and interpolating to zero strain. The method is of questionable accuracy because of the tendency of foil to form minute tears when heated under tension. Their assumption of F = 2W?, where W is the width of the foil, is unsound, as the foil can decrease its surface area by transverse as well as by longitudinal shrinkage. Although their experimentation was meticulous, the paper does not include details of the sample configuration required for recalculating ? on a correct basis, even if such a calculation were possible. In the experimental procedure chosen here, a series of small weights of increasing magnitude are suspended from a series of line copper wires of uniform cross-section. This array is brought to a temperature at which creep is appreciable under extremely small stress. If the weight overbalances the contracting force of surface tension, the wire stretches; otherwise, it shrinks. The magnitude of the strain is determined by the amount of unbalance, so a plot of strain vs. load should cross the zero strain axis at w = F?. If balance is visualized as a thermodynamic equilibrium, the critical load is readily calculated. At constant temperature, an infinitesimal change in surface energy should be equal to the work done on or by the weight: ds = wdl [A] For a cylinder, s = 2pr2 + 2prl [2] If the volume remains constant, r = vV/pl [31 s = 2vpl+2V/l [4] ds = vpv/l - 2V/l²) dl [5] Substituting [5] into [I] gives for the equilibrium load, w = ?(z/rV- 2V/12) [6] and, again expressing V in terms of r and l, w = pr?(1 - 2r/l [7] Here the end-effect term, 2r/l, is neglected for thin wires in subsequent work. Eq 7 can be confirmed by means of a stress analysis. If the x-axis is chosen along the wire, then the stress is 2pr? - w pr² pr2 [8] A cylinder of diameter dis equivalent to a sphere of radius r, insofar as radial surface tension effects are concerned.³ Thus xv = 2?/d = ?/r = sz [9] For the case of zero strain in the x direction, the strain will also be zero in the y and z directions. Since the wire is under hydrostatic stress, Eq 8 and 9 are

Jan 1, 1950

By B. G. Reisdorf

This paper describes the microstructural changes that occur when quenched ultrahigh-strength steels containing OA pet C and various amounts of nickel, silicon, and cobalt are tempered. The changes that occur in hardness, yield strength, and martensite diffraction-peak widths when these steels are tempered are related to the precipitation of the carbide phases. An unea$ectedly high silicon content (about 30 pct) was found in the E -carbide phase in a steel containing only 1.5 pct Si. TEMPERED martensitic steels have such wide-spread utility that they have been the subject of numerous investigations, and a sizable amount of literature has developed on this subject.M This investigation, which is a part of a larger program to correlate microstructure with mechanical properties at a variety of strength levels, is limited to the microstructural changes that occur when a quenched 0.40 pct carbon steel (USS Airsteel X-200 steel) is tempered, and to the effects of the alloying elements—nickel, cobalt, and silicon—on these microstructures. Used in this investigation were electron microscopy, electron-diffraction identification of the carbide phases, electron-probe micro-analysis of the carbides, X-ray determinations of retained austenite, and measurements of martensite X-ray diffract ion-peak widths. MATERIALS AND METHODS The chemical analyses of the eight heats examined eats No. 30 through 37) are shown in Table L Heat No. 30 has the chemical com~osition of Airsteel X-200, and the remaining seven heats contain various amounts of nickel, chromium, cobalt, and silicon. The heats were air-melted in an induction furnace and cast into 8 by 8 in. ingots that were subsequently heated to 2300 and rolled to 1-in.-thick plate. Oversize 0.505-in.-diam tensile specimens were rough-machined from the plates and austenitized in air at 1700° F for half an hour and oil-quenched. The specimens were then tempered in air at temperatures of 400° to 1000 for tempering times of 1, 4, and 16 hr, and finish-machined to 0.505-in.-diam tensile specimens. Electron micrographs were prepared from Formvar replicas of the midthickness of tensile-specimen shanks that had been electrolytically polished and etched in nital. Electron-diffraction patterns were obtained from carbon-extraction replicas. The replicas were prepared by etching the sample surface in the same manner as for microscopy, evaporating carbon on the etched surface, and re-etching the sample to free the carbon film and the precipitate particles. Electron-probe microanalysis was performed on some of the extraction replicas. To obtain adequate fluorescent X-ray intensities, several thicknesses of replica were exposed to the electron beam so that the results represent an average composition of the extracted particles rather than an analysis of single precipitate particles. The retained austenite contents of the specimens were determined by an empirical X-ray diffraction

Jan 1, 1963

By D. D. Pollock, G. P. Conard II

Equations of the form of the Mott and Jones equations for the absolute thermoelectric powers of metals are derived primarily from a thermodynamic approach. The behaviors of transition thermoelements in common use are then examined and compared with this simple theory. MOTT and ones&apos; derived a general expression for the absolute thermoelectric behavior of metals and alloys using the approach of the solid state physicist. This expression was then applied to specific cases.1,2 The present work develops equations of the same form principally by a thermodynamic approach. These relationships are then employed to gain some insight to the behavior of the transition thermoelements in common use. I) DERIVATION OF AN EXPRESSION FOR ABSOLUTE THERMOELECTRIC POWER First consider a metallic conductor which is maintained in a temperature gradient with no current flowing. At constant pressure, there will be a gradient of the free energy (F,) given by:

Jan 1, 1963

By R. S. Wagner, W. C. Ellis

A new mechanism of crystal growth involving oapor, liquid, crnd solid phases explains many observations of the effect of implurities in crystal growth from the vapor. The role of the impuuitq is to form a liquid Solution with the crystalline tnalerial to be grown from the vapor. Since the solution is n prefevred site for deposition firorti the uapor, the liquid becorrles supersaturated. Crystal growth occurs by precipitatzon from the supersaturated liquid crt tlie solid-liquid zntevfnce. A crystalline defect, such as a screw dislocation, is not essetztial for VLS (vapor -liquid-solid) growth. The concept of the VLS mechanism is discussed in detail with reference to tire controlled growth of silicon crystals using gold, platinum, palladium, nickel, silver, or copper as an implurity agent. RECENTLY a short communication&apos; described a new concept of crystal growth from the vapor, the VLS mechanism. In this paper we present a detailed description of the process and its application to the growth of silicon crystals and we discuss its relevance to existing concepts of .&apos;whisker" crystal growth. Crystal growth from the vapor is usually explained by a theory proposed by Frank2 and developed in detail by Burton, Cabrera, and Frank.3 In this theory a screw dislocation terminating at the growth surface provides a self-perpetuating step. Accommodation of atoms at the step is energetically favorable, and is possible of much lower supersatu-ration than required for two-dimensional nucleation. Crystals of a unique form resulting from aniso-tropic growth from the vapor are "whisker" or filamentary ones. Such crystals have a lengthwise dimension orders of magnitude larger than those of the cross section. For most filamentary crystals both the fast-growth direction and directions of lateral growth have small Miller indices. The special growth form for a whisker crystal implies that the tip surface of the crystal must be a preferred growth site. sears4 proposed that, according to the Frank theory. a whisker contains a screw dislocation emergent at the growing tip. Such an axial defect provides a preferred growth site and accounts for unidirectional growth. The hypothesis was extended by Price. Vermilyea. and Webb," still implying the presence of a dislocation at the whisker tip. They postulated that impurities arriving at the fast-growing tip face become buried while those arriving on the surface of slow-growing lateral faces accumulate and thereby hinder growth. These considerations led to a whisker morphology. There is increasing evidence that most whisker crystals grown from the vapor are dislocation-free. Webb and his coworkers6 searched for an Eshelby twist7 in zinc? cadmium, iron. copper, silver, and palladium whisker crystals. They found unequivocal evidence for an axial screw dislocation in only one element, palladium. However, not every palladium crystal examined contained a dislocation. Observations with the electron microscope have failed to show dislocations in whisker crystals of zinc, silicon.9 and one morphology of AlN.10 Since many whiskers are completely free of dislocations, an axial dislocation does not appear to be required for whisker growth of many substances. A significant advance in understanding whisker growth has been a recognition of the need for impurities. This requirement has been clearly demonstrated for copper,11 iron,13 and silicon9-1 whiskers. For silicon, detailed studies proved conclusively that certain impurities, for example, nickel or gold, are essential. Another pertinent phenomenon which has received little attention is the presence of a liquid layer or droplets on the surface of some crystals growing from the vapor. Crystals in which this has been observed include p-toluidine,14 MoO3,15 ferrites,16 and silicon carbide.&apos;" The liquid layers or globules were considered to be metastable phases, molecular complexes, or intermediate polymers originating from condensation of the vapor phase. The possibility has been suggested that the halide being reduced is condensed at the tip18 or adsorbed on the surface11 of a growing metal whisker, for example copper. The literature on whiskers discloses illustrations of rounded terminations at the tips. These appear. for example, on crystals of A12O3,19,20 sic,21 and BeO.22 For BeO, Edwards and Happel suggested that during growth of the whisker the rounded termination consisted of molten beryllium enclosed in a solid shell of BeO. A recent paper9 on the growth of silicon whiskers contains many observations pertinent to an understanding of the mechanisnl of whisker growth. These observations are summarized as follows. 1) Silicon whiskers are dislocation-free. 2) Certain impurities are essential for whisker growth. Without such impurities the silicon deposit is in the form of a film or consists of discrete polyhedral crystals.

Jan 1, 1965

By W. F. Chiao, R. B. Gordon

Tile sharp-yield point found in magnesium crystals in the solulion-treated and aged condition is studied by dislocation internal-friction experiments. The results show that the sharp yield is not file to the sudden release of pinned dislocations hut is movc likely due to the rapid multiplication of an initially small number of dislocations. Recovery or the dislocation internal friction after deformation is also studied. This yecovery results from the re-pinning of dislocations by a solute, presumably nitrogen, which moves with a relatively small activation energy. SHARP-yield points, when they occur, are a striking feature of the stress-strain curve generated during a tensile test. Although commonly associated with steel, sharp yielding has been found in a variety of metallic and nonmetallic crystalline materials. In particular, sharp-yield points have been found in zinc"&apos; and cadmium3 containing nitrogen. With this background, Geiselman and Guy4 investigated the tensile properties of magnesium single crystals containing nitrogen to see if sharp yielding also occurs in this system. They found that sharp yields did indeed occur in solution-treated and aged specimens tested at elevated temperature but were not able to give conclusive proof that the sharp yield was caused by nitrogen, a yield drop being observed even in their purest crystals. Sharp-yield points have also been found in various polycrystalline magnesium alloys.7&apos;8 In the study of the sharp-yield phenomenon it is desired to observe the behavior of dislocations in the earliest stages of the deformation process. Internal-friction experiments are useful for this purpose because dislocation damping is sensitive to the mobility of free-dislocation segments. At low strain amplitudes the damping, A, due to the the forced vibration of dislocation segments of average length L is ? =KAL4 [1] where A is the dislocation density and K, if the applied frequency is well below the resonant frequency of the dislocation segments? is a constant for the sample under observation.5 Dislocation damping, because of the fourth-power dependence on L, is particularly sensitive to the creation of free-dislocation segments during deformation. Since sharp yielding is associated with the sudden release of pinned-dislocation segments, marked changes in the dislocation damping are expected at the yield point.6 The use of the dislocation-damping observations to help elucidate the incompletely understood mechanism of yielding in magnesium is the primary objective of the experiments reported here. PROCEDURE Many investigations have shown that very marked and rapid changes occur in the dislocation damping of of a deformed material as soon as the straining is stopped.5 It was quite essential, then, for the purpose of this investigation, to make the damping measurements during the deformation of the samples. This can only be accomplished through the use of the ultrasonic-pulse method. In this method traveling sound-wave pulses are used and, in contrast to resonating-bar methods, only the sample ends are set in vibration. Thus, the sample can be gripped along its sides in the tensile-test machine without disturbing the damping measurements. In the pulse method, the decrease in the amplitude of a sound pulse is measured as it travels back and forth through the sample. If A is the amplitude after traversing a distance x and A. is the initial amplitude, A=Aoe-ax [2] and a is called the attenuation. It is commonly measured either in units of cm-I or as db per µ sec. The observed attenuation in a metal sample is due to a number of causes. These include scattering by grain boundaries and impurity particles, thermo-elastic damping, diffraction effects, stress-induced ordering of solute atoms, and dislocation damping. The total observed attenuation in a given sample usually cannot be resolved into these various components, but changes in a due solely to changes in dislocation damping can be accurately determined, provided the experiment is arranged so that all other sources of damping are held constant. It is desired to reduce the extraneous sources of attenuation to a minimum and for this reason the experiments are done on single crystals of high purity. Magnesium crystals offer the further advantage that, when properly oriented, only a single set of slip planes is active during deformation. Crystal Preparation. The method of sample preparation is similar to that of Geiselman and Guy.4 The starting material was high-purity, sublimed magnesium rod supplied by the Dow Chemical Co. Melting under Dow 310 flux was used to reduce the nitrogen content of the starting material: the fluxing was done under an argon atmosphere and the

Jan 1, 1965

By C. Hays, R. E. Swift, E. G. Kendall

Investigations of the Zr-Pt system, by metallography, incipient melting, and X-ray diffraction, determined the phase relationshifis from 0 to 50 at. pct Pt. Phase fields in the Pt-~ich region were outlined, and three intermetallics (ZrPt, Zr2Pt, and ZrPtd were located. A eutectic between Zr and Zr2Pt, and a eutectoid veaction between Zr and a Zr + Zr2Pt, were established. The maximum solubility of Pt in P Zr was approximately 13.5 wt pct, as opposed to less than 1 wt pct solubility in a Zr. EARLIER work on the Zr-Pt system was limited to an X-ray study on the intermetallic compound, ZrPt3, by H. J. Wallbaum,1 It was reported that ZrPt3 existed at 86.52 wt pct Pt, and had a hexagonal structure, isomorphous with TiNi3. Wallbaum&apos;s data revealed the following structural particulars: a = 5.633A, c = 9.21A, and c/a = 1.635A. Other studies allied to Zr-Pt alloys concerned only 1) Pt-rich alloys (0.05 to 5.0 pct Zr) for corrosion resistance,2 2) a Zr-base alloy with 5 pct Pt and 0.124 pct C for oxidation resistance,3 and 3) electroclad-ding of Zr with Pt for in-pile corrosion resistance of Zr to uranyl sulphate. 4 Metallographic, incipient melting, and X-ray diffraction techniques were applied to accurately resolve the phase relationships in the 0 to 50 at. pct (68.2 wt pct) Pt region, and to outline the phase fields in the Pt-rich area. Three intermediate phases: Zr2Pt, ZrPt, and ZrPt3, were also established by the same methods. PROCEDURE Melting stock for this program was of the highest purity obtainable. The Zr was iodide crystal bar with a low hafnium content of about 0.05 wt pct (Westinghouse "Grade 3"). The as-received Zr was treated to remove the surface film of corrosion product that resulted from a standard autoclave grade designation test. Next, the bars were processed to yield material suitable for arc melting and free of contaminants. Sheet platinum metal (Baker and Co. "Grade 2") was used for alloying additions. This material con-

Jan 1, 1962

By David Turnbull

IN isothermal recrystallization processes, new crystals generally grow into the matrix until they impinge upon other new crystals or an external surface, at constant linear rates G. Before impingement the perceptible course of growth can be described by the equation: 1 = G(t-7) C1I where, G = dl/dt, 1 is a crystal dimension measured in a constant direction, t is the time, and 7, the nucleation period, is a positive intercept on the time axis. Fig. 1 is a schematic representation of I as a function of time for a recrystallizing grain. G is dependent upon temperature, driving energy (strain or surface energy), relative grain and boundary orientations, but is generally independent of time. The frequency of nucleation, fi, (time" volume") can be defined by the equation: N = 1/fV [2] where ? is the mean nucleation period and V is the volume of the specimen that has not recrystallized. The kinetics of primary and secondary recrystallization generally can be described satisfactorily in terms of the parameters N and G only.&apos;-" After recrystallization is complete the average grain size 7 increases with time by "normal grain growth;" didt, the average rate of grain growth, is strongly time dependent and has not yet been precisely related to G for the motion of the individual grain boundaries constituting the system. It has been suggested4* " that the elementary act in grain boundary migration is closely related to the elementary act in grain boundary self-diffusion. Although the distance of atom movement in the two processes may be somewhat different, there is reason to expect that the activated states may be very similar, so that the free energy of activation for grain boundary migration should be of the same order of magnitude as for grain boundary self-diffusion. Therefore, it is desirable to develop a satisfactory basis for comparing data on self-diffusion and grain boundary migration and to make such comparisons where possible. Theory The formal theory of grain boundary migration rates is analogous to the theory for the rate of growth of crystals into supercooled liquids reviewed elsewhere 6-8. Boreliuss has shown that the latter theory describes, within the theoretical uncertainty, the growth of selenium crystals into supercooled liquid selenium. Motto and more recently Smolu-chowski" have derived expressions for the rate of boundary migration in recrystallization. The treatment to be presented is similar to Mott&apos;s excepting that the formalism of the absolute reaction rate theory will be used. The atomic mobility, M, in grain boundary migration is defined by: G = -M6p/6x where p is the chemical potential per atom and x is the coordinate measured in the direction of grain boundary movement. Let AF be the free energy difference per gram atom on the two sides of the boundary and k the thickness of the boundary. For RT>>AF the potential gradient across the boundary (6p/6x) is essentially linear and it follows that: SF/8x = - aF/N\ [4] where N is Avogadro&apos;s number. According to the Nernst-Einstein equation, M is related to a diffusion coefficient, Do, for matter transport in grain boundary migration by the equation: M = Da/kT [5] Substituting eqs 4 and 5 into eq 3 gives the basic relation between Do and G: G = DoaF/\RT [6] Do values may be calculated from experimental values of G from eq 6 and directly compared with the coefficient of self-diffusion within the crystal, DL, or the grain boundary self-diffusion coefficient D,. However, a more convenient, though equivalent, basis for comparing atomic mobility in grain boundary migration and self-diffusion is through the constants of the absolute reaction rate theory. According to this theory diffusion coefficients may be written:" D = k2(kT/h) exp [-AF,/RT] 171 aFa, the free energy of activation, is related to the measured energy of activation, Q, by the equation: AFA = Q - T aSx - RT [8] where aSa is the entropy of activation. Substituting eqs 8 and 7 into eq 6 gives: G = ek(kT/h) (aF/RT) exp [(AS,,)C/R] exp C-Qc/RTI C91 where the subscript G refers to boundary migration. The relationship between the driving free energy and the free energy of activation in boundary migration is indicated schematically in Fig. 2. Experience indicates that the variation of G with temperature can be described by: G= Go exp [- Qc/RT] [10] where Go and Qc are generally temperature independent over wide ranges of temperature. Comparison of eq 9 with eq 10 gives:

Jan 1, 1952

By O. D. Gonzalez, R. A. Oriani

A thermo-osmosis technique has been used to measure the heat of transport, Q* , of hydrogen and of deuterium dissolved in a iron and in nickel, and of hydrogen in Feo.6Nio.4 in the tempevature range 400° to 600°C. For all these systems, Q* is negative and has a large temperature coefficient; an isotope effect can be established for the solutes only in nickel. The magnitude of Q* is considerably larger than the activation energy, E , for migration in the case of these isotopes in a iron, so that all variants of the Wirtz model must be rejected. The phenomenological definition of Q* is developed to show that Q* is related to the mechanisms by which the activation energy is dissipated back into the lattice, and that Q*/E is a function of the ratios of the mean free paths of electrons and of phonons to the distance of jump of the diffusing atom. A correlation is shown to exist between the sign of Q* in thermal diffusion and that of the effective charge in electro migration, and may be understood as due to the large ratio of the mean free path of electrons to that of phonons. THE study of nonisothermal diffusion in the solid state is of interest because certain aspects of the mechanism of diffusion are made manifest which remain concealed though still present in the isothermal case. The thermodynamics of irreversible processes characterizes nonisothermal diffusion, known as thermal diffusion or as the Ludwig-Soret effect, by a quantity, Q*, called the heat of transport, which essentially measures the sign and the magnitude of the steady-state concentration gradient produced by the imposed temperature gradient. The problem then is to understand the quantity Q* at the atomistic level. There does not exist a theory for the atomistic interpretation of the heat of transport. There are, however, two classes of simple models which seem to afford some physical insight into Q*. Wirtz&apos;s model1, z and its subsequent generalizations partition the activation energy, E, for the migration of the atom spatially about the region of the migrating atom, so that Q* is the difference between the portion of the activation energy centered about the original site of the jumping atom and that portion about the arrival site. Clearly, the magnitude of Q* cannot on this model be larger than the activation energy for migration. The model of Oriani3 also considers the spatial distribution of E not only before but also after the atomic jump, and Q* is related to the variation of the spatial distribution of E that is produced by the jump. The simplest kind of system with which to compare the consequences of these ideas is the interstitial solid solution, since one may easily choose a temperature at which only the interstitial component moves, the solvent lattice serving as a completely satisfactory frame of reference. Thus, one avoids complications arising when both species in a binary system move. In addition, one avoids the necessity of knowing the energy for the formation of a vacancy, something which is needed for the analysis of thermal-diffusion data on metals which diffuse by the vacancy-exchange mechanism. However, the number of well-measured interstitial systems is extremely small, and, in particular, there are almost no data in the published literature for the temperature dependence of the heat of transport. If one works with solutes which are gases in the pure state at ordinary temperatures, one may use the technique of thermo-osmosis4 which permits thermal diffusion to be measured over a small temperature difference so that the temperature dependence of Q* can be more easily determined. The choice of dissolved hydrogen in iron and nickel was based on these considerations as well as on the desire to look for an isotope effect associated with localized

Jan 1, 1965

By J. F. Butler, H. W. Paxton

The vapor pressures of manganese in equilibrium with several alloys in the iron-manganese-carbon system between 1200° and 1275°K have been measured using the Knudsen effusion technique in conjunction with a vacuum microbalance. The effect of orifice area of the effusion cell upon the measured pressure has been determined. The binary iron-manganese system shows small negative departures from ideality, and the system of mixed carbides, (Fe, Mn)7C3, in equilibrium with graphite behaves ideally. THIS work is a continuation of the investigations in which the Knudsen effusion method has been used to determine thermodynamic activities in systems and at temperatures of interest to metallurgists. In a previous publication,&apos; the free energy of formation of Mn7C3 was determined and some preliminary work on the solution behavior of this carbide with the hypothetical "Fe7C3" was reported. The present work deals with this latter topic and also includes data on the binary ir-on-manganese system. EXPERIMENTAL METHOD The Knudsen effusion method was used to measure the vapor pressure of manganese in both the alloy and carbide sections of this investigation. This dynamic method of vapor pressure measurement presents a problem when studying solid alloy systems in which one of the components has a much larger vapor pressure than the others. Over-all depletion of the alloy in the most volatile component will occur during evaporation so that the pressure of that component will decrease. Even more serious than the over-all concentration change is the surface depletion of volatile component in the alloy brought about by the slow rate of diffusion of this component from the interior to the surface of the solid particle. Since knowledge of this surface composition is necessary in order to relate it to the activity determined through the measurements, changes in surface composition from the analyzed bulk composition are to be avoided in dynamic vapor pressure studies of solid alloys. The system under investigation in this study presents the problem of surface depletion of manganese since its pressure at 1230°K is 105greater than iron and 1020 greater than carbon. Since the existence of a volatile manganese carbide had been ruled out previously,&apos; the high manganese pressure relative to iron and carbon insured that the only species leaving the effusion cell was manganese. Therefore, the effusing species required no analysis so that the manganese pressure was determined directly from the weight loss of the effusion cell. In order to detect small weight losses near the beginning of effusion, a vacuum microbalance was used to weigh the cell continually. These initial weight loss data allowed the rate of manganese effusion to be determined before the surface of the alloy became depleted in manganese. The apparatus used in this investigation is shown in Fig. 1. Temperature was measured using chro-

Jan 1, 1962

By P. A. Farrar, M. D. Silver, K. L. Komarek

Thermodynamic properties of Hf-0 alloys have been determined from 0 to 25 at. pct 0 between 1000" and 1200°K by equilibrating specimens with alkaline metal oxide-metal vapor combinations. Partial molar-free energies, enthalpies, and entropies of oxygen have been obtained and are conzpared with similar results for the Ti-0 and ZY-0 In continuation of a thermodynamic investigation of the Ti-O and Zr-O systems1 activities of oxygen and lattice parameters of Hf-0 alloys have been deter- system. The positional entropy in all three systems corresponds to an ideal random interstitial solution with one interstitial site per one metal atom. The lattice parameters of hafnium and Hf-O solid solutions have been determined in the range 0 to 20 at. pct O from measurements of Debye powder patterns. mined. All three metals dissolve large quantities of oxygen to form interstitial solid solutions. The phase diagram of the Hf-O system is shown in Fig. 1.&apos; The maximum solubility of oxygen in the cph a phase is considerable (up to 25 at. pct O). The solubility in the high-temperature phase is much smaller. The only stable compound in the solid state is HfO2 which may exist with a certain oxygen deficiency. The low partial pressure of oxygen of Hf-0 alloys required the application of an indirect method. As the most suitable procedure a method, first applied by Kubaschewski to the V-O system,3 was combined with a principle developed by Herasymenko for the

Jan 1, 1963

By L. L. Seigle

Free energies, heats, and entropies of mixing of solid Fe-Au alloys have been measured by the galvanic cell method between 800° and 900°C. A positive deviation from Raoult&apos;s law and a large excess entropy of mixing were observed, both attributable to lattice distortion caused by the disparity in component atom sizes. Since the terminal solid solutortiontions are not regular, thermodynamic properties computed from the location of the mis-cibility gap do not agree well with measured quantities. The electromotive force data suggest some changes in the existing Fe-Au phase diagram. ALTHOUGH a considerable amount of information has been accumulated about the thermodynamic properties of metal solid solutions which exhibit negative deviation from Raoult&apos;s law, particularly those in which ordering occurs, relatively few experimental measurements have been made on solutions with positive deviation. This is due to the infrequency of broad homogeneous regions suitable for experimental measurement in solutions of this type, since any marked positive deviations from ideality lead to restricted solubility and the formation of miscibility gaps. Thermodynamic data reported in the literature for such systems have usually been calculated from the location of the miscibility gap boundaries under the assumption that the entropies of mixing are ideal, i.e., the terminal solutions are regular.&apos; One of the few binary systems with both positive deviation and a wide homogeneous range in the solid is the Ni-Au system. A recent investigation of solid Ni-Au alloys&apos; revealed that the entropies of mixing were much larger than ideal and consequently thermal data computed from the phase boundaries assuming regular solutions were seriously in error. Theoretical considerations put forward by Zener indicated that high entropy values should generally be associated with systems possessing a miscibility gap in the solid, when this is due to differences in the size of component atoms. These facts suggest that the regular solution assumption is a poor approximation for many solid solutions with positive deviation and that reliable thermodynamic data generally cannot be obtained by conventional methods from the location of miscibility gap boundaries. The Fe-Au system, Fig. 1, resembles the Ni-Au system in certain respects. The presence of a miscibility gap in the solid indicates a large positive deviation from ideality, but there is nevertheless an extensive single phase region suitable for experimental measurement. The following investigation of solid Fe-Au alloys was carried out in order to obtain additional data on the thermodynamic properties of metal solid solutions with positive deviation from Raoult&apos;s law and to further compare thermodynamic data computed from miscibility gap boundaries with those measured experimentally. Experimental Method The thermodynamic properties were derived from measurements of the potential developed between pure solid iron and Fe-Au alloys in a high temperature galvanic cell. The experimental apparatus and technique were the same as those used for the Ni-Au alloys and described in a previous report.&apos; Cell electrodes were 1/16 in. diam rods swaged from chill-cast ingots and annealed for one week at 850°C. The alloys were prepared by melting fine gold granules under argon with pure iron obtained from the National Research Co. The cell electrolyte was

Jan 1, 1957

By B. L. Averbach, Morris Cohen, L. L. Seigle

Free energies, enthalpies, and entropies of mixing of Ni-Au solid solutions containing 5 to 95 atomic pct Ni have been determined by the electromotive force method at 700° to 900°C. The thermodynamic activities exhibit large positive deviations from Raoult&apos;s law, and the entropies of mixing are almost twice those of ideal solutions. The enthalpies of mixing are positive (heat is absorbed) and are attributable to the lattice distortional energy resulting from the size difference between the nickel and gold atoms. This factor appears to be responsible for the miscibility gap at lower temperatures. IN the thermodynamic study of metallic solid solutions, most interest has been directed toward systems with negative deviation from Raoult&apos;s law, namely, those exhibiting superlattice or compound formation. The results of previous investigations are summarized in recent publications.&apos;-&apos; Relatively little experimental work has been carried out on solid solutions which manifest a positive deviation, possibly because the range of solubility in such cases is usually quite limited. Nevertheless, the relationship of the thermodynamic properties of these solutions to diffusion, nucleation, and precipitation in the solid state are of considerable importance. The binary Ni-Au alloys are particularly suited to an investigation of these relationships. Despite the presence of a miscibility gap at lower temperatures, Fig. 1, indicating a large positive deviation from Raoult&apos;s law, complete solid solubility is found above 840°C. Moreover, the difference in the atomic scattering powers of nickel and gold is sufficiently great to permit X-ray diffraction studies of atomic arrangements and pre-precipitation phenomena. Radioisotopes of both nickel and gold are available for diffusion work, and finally, a large difference in nobility between the two elements facilitates measurement of the thermodynamic properties. The present paper describes the experimental determination of the free energies, enthalpies, and entropies of mixing of solid Ni-Au alloys. Table I gives a list of the symbols used in the paper. Experimental Method The stability of nickel chloride relative to gold chloride" indicated that the galvanic cell method could be used for determining the thermodynamic properties of Ni-Au alloys. An electrolytic cell (Fig. 2) was constructed, similar to that of Weibke and Matthes,7 in which the electrodes were solid nickel and Ni-Au alloys, and the electrolyte was a fused mixture of alkali chlorides containing NiCl,. The cell electrodes were made from fine gold granules and carbonyl nickel shot melted together under argon, chill cast, swaged to 1/16 in. diam rod, and annealed for one week at 850°C. Commercial reagent and chemically pure grade salts, purified by dehydration, were used for the electrolyte. The cell, operating in an atmosphere of purified argon, was heated in a resistance-wound cylindrical furnace whose temperature was controlled to within ±0.5ºC. The potential developed between the pure nickel and the alloy electrodes, which is related to the thermodynamic properties of the alloys by standard equations to be presented later, was measured with a potentiometer and a mirror galvanometer sensitive to 10-7 v. Dehydration of the electrolyte was carried out in the assembled cell by evacuating at 100°C for about

Jan 1, 1953

By A. T. Aldred, K. M. Myles

The vapor pressure of chromium over solid V-Cr alloys has been measured by the torsion-effusion method in the temperature range 1450" to 1650°K. The chemical activities as well as the free energies, entropies, and enthalpies of formation of the alloys have hem computed from the vapor-pressure data. The activities of both chromium and vanadium exhibit fairly small negative deviations from Raoult&apos;s law over the entire composition range. The values of the excess entropies and the enthalpies of formation found at 1550°K are considered in terms of the changes in the clzaracteristic properties of vanadium and chromium that occur upon alloying. RECENT interest in the theory and properties of transition-metal alloys has shown the need for relevant thermodynamic data. The present investigation of the V-Cr system was undertaken as part of a more general study of thermodynamic properties of transition-metal alloys. The system was chosen because of the reported complete solid solubility of the components at all temperatures1 and because the difference in magnitude of the vapor pressures of vanadium and chromium allowed a simple effusion technique to be used. The torsion-effusion method was employed to minimize compositional changes in the alloys during the experiments. EXPERIMENTAL Equipment. The torsion-effusion apparatus, shown diagrammatic ally in Fig. 1, consists of a torsion system suspended inside a vertical vacuum chamber whose lower end is surrounded by a high-temperature vacuum furnace. An auxiliary optical lever and screen are used to determine the angle of rotation of the effusion cell. The torsion fiber is an annealed, high-purity, tungsten wire usually between 0.003 and 0.007 cm in diameter and about 43 cm long. The wire supports a concave mirror and a rigid tantalum connector tube. The effusion cell is fastened to the lower end of the connector tube by a dovetailed yoke and har- ness arrangement. The cells, which are 1.27 cm in diameter and 4.4 cm long, were made by electron-beam welding tantalum endcaps onto a 0.025-cm-wall tantalum tube. The two orifices, formed by drilling, have similar areas ranging from 0.011 to 0.031 sq cm. The noninductive sheath-type furnace consists of a single-phase tantalum heating element 6.35 cm in diameter, 15 cm high, and 0.013 cm thick; the element is completely surrounded by radiation shields in an evacuated chamber. The power system includes a 17-kva self-saturating saturable core reactor with an integral magnetic amplifier and a water-cooled, 15-kva, step-down power transformer with a multitap secondary. Temperatures are controlled to within ±1/2o at 1600°K by means of a unit that includes a reference voltage source, a dc electronic null detector, a current-adjusting proportional band relay, and the self - saturating reactor. At 1650°K the temperature variation within the cell, vertically and horizontally, is 3/4oK. Unwanted motions of the torsion system are damped by the movement of an aluminum vane, which is mounted on the connector tube, between the poles of an electromagnet. When not in use the magnet is withdrawn and rotated 90 deg to prevent its interaction with the rotation of the system. Measurements. The vapor pressure, p, is re-

Jan 1, 1964