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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.' 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'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'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.' 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' 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'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.' 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 J. Eldridge, K. L. Komarek

Activities of aluminum in solid Fe-Al alloys have been determined between 0 and 75 at, pct Al and 1100" and 1400°K by an isopiestic method in which iron specimens, heated in a temperature gradient, are equilibrated in a closed all-ceramic system with aluminum vapor. The activity of aluminum in these alloys shows a strong negative deviation from Raoult's law at low concentrations but increases rapidly above 40 at. pct Al. The enthalpy and entropy of mixing me both negative. For an alloy with equiatomic composition the values are: HM = -7300 cal and SM = -0.85 eu. Sodium chloride has been added at lower temperatures to accelerate the evaporation of aluminum. Equations have been derived to calculate activities of aluminum from experimental data. THE Fe-Al system has been the object of a great number of investigations.' Most of these studies have been concerned with the phase diagram and specifically with the order-disorder reactions in the range of solid solutions of aluminum in iron. The results have been compiled by Hansen2 and presented as a complete phase diagram, Fig. 1. More recently, Taylor and ones' have found that both ordered and disordered alloys can exist in the a field up to the solidus curve separated by a line starting at 18.75 at. pct Al at room temperature up to 37 at. pct Al at 1375°C. Chipman and coworkers4-7 have studied repeatedly the activity of aluminum in liquid dilute Fe-Al alloys. They have measured the distribution equilibrium of aluminum between liquid iron and

Jan 1, 1964

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'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's law, namely, those exhibiting superlattice or compound formation. The results of previous investigations are summarized in recent publications.'-' 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'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'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

By John P. Huger

me phase diagram for the system Ag-Si has been established by thermal analysis. The diagram is a simple eutectic type with a eutectic at 3.0 pct Si and 840°C. From the liquidus curve and with the aid of regular solution theory, the thermodynamic properties of the liquid Ag-Si system at 1420 °C have been determined. Silicon exhibits positive deviations from Raoultain behavior at all compositions, while silver exhibits both positive and negative deviations. MEASUREMENTS of silicon activities in liquid iron alloys by means of distribution studies between the immiscible liquids silver and iron have been reported by Chipman, Fulton, Gokcen, and caskey.' The applicability of this technique is dependent, however, on the accuracy of the silicon activity values in the Ag-Si alloys, particularly in the dilute silicon region. Darken and Gurry2 have shown that log ?si/(1-xSi)2 is approximately linear with composition, but uncertainty exists in the extrapolation to dilute solutions. Their calculations are based on the old Ag-Si phase diagram of Arrivaut3 and any variation in the position of the liquidus curves will strongly influence the extrapolation. The purpose of this study is to redetermine the Ag-Si phase diagram and calculate the associated thermodynamic properties. EXPERIMENTAL The Ag-Si phase diagram was determined by thermal analysis of liquid alloys. The alloys were contained in a 35 mm alumina crucible under a protective stream of purified argon. The crucible was placed inside a 64 mm alumina tube fitted with a gas-tight, water-cooled, copper head. The tube and assembly were heated in a manually controlled globar furnace. The temperature was measured with a Pt, Pt + 10 pct Rh thermocouple in a high-temperature porcelain protection tube. The thermocouple calibration4 was checked against the melting point of pure silver at the start and during the course of the experiments, and against both gold and silver at the completion of the experiments. The alloys were prepared from granular silver analyzing 99.95 pct Ag and powdered silicon analyzing 99.88 pct Si and 0.026 pct Fe. Approximately 150 g of alloy were used for each run. The composition of the alloy was determined by withdrawing samples of the liquid alloy with a vycor tube-aspirator bulb device. Analysis of solidified samples agreed, for alloys containing less than 23 pct Si, within ±0.3 pct Si of the calculated composition. Duplicate samples showed a variance within 50.05 pct Si of the mean analysis. The alloy was heated to 100' to 20pC above the estimated liquidus temperature and then the furnace was adjusted to give an average cooling rate of 2" to 7°C per min. A cooling curve was obtained by taking potentiometer readings at 15-sec intervals. Several analyses were made by recording the thermocouple output on a high-speed, Stip-chart recorder, with the exception of run NO. 11, a minimum of two thermal analyses were made for each alloy and the cooling curves then obtained duplicated the liquidus and eutectic temperatures to about 1°C. RESULTS The results of the thermal analysis are given in Table 1, and are represented as the Ag-Si phase dlagram, Fig. 1. The eutectic composition was found

Jan 1, 1963

By M. T. Hepworth, R. Schuhmann

Hydrogen solubility measurements were made on a series of Ti-O alloys, and a portion of the 800°C isotherm for the Ti-O-H system was determined. Activities of oxygen and titanium were calculated from the experimentally measured activities of hydrogen, using ternary Gibbs-Duhem integrations. The data were extrapolated to obtain thermo-dynamic properties of binary Ti-O solutions. The thermodynamic properties of a Ti-0 solid solutions thus determined were compared with properties predicted from interstitial models. The Gibbs-Duhem equation, long used to calculate activities in binary systems, has been extended. recently to ternary systems.1"3 When the activity of one component in a ternary system is known as a function of composition, the activities of the other two components can be calculated from that of the first by an integration procedure, provided certain restrictions are observed on the path of integration. Often the activity of one component in a ternary system can be measured readily, while the activities of the other two components are difficult to measure. Gibbs-Duhem calculations are especially applicable to such systems. The further possibility arises of developing a new and indirect approach to activity measurement in binary systems. The proposed new method for binary systems consists of adding varying amounts of a third component whose thermodynamic behavior is easily measured. The activity of this added component is determined experimentally as a function of composition. Then the activities of the two components of the original binary system are calculated by Gibbs-Duhem integrations and extrapolations. For the work to be described in this paper, the Ti-0-H system was selected as a promising system for evaluating this approach. Investigations of the Ti-H system have shown that the activity of hydrogen can be measured precisely with little difficulty. Pure titanium transforms from a low-temperature a form (hcp) to a higher-temperature /3 firm (bcc) at 882.5"~ The phase transformation occurs in a temperature range where hydrogen pressures are easily measured. Also, the diffusivity of hydrogen at temperatures above 600" or 700"~ is large enough that equilibrium can be reached within a reasonable time.

Jan 1, 1962

By J. M. Toguri, K. Grjotheim

It is known 1,2 that the equilibrium between titanium metal, TiCl2 , and TiCl3, in a solvent of molten metal chlorides, is influenced both by the total amount of dissolved titanium and by the type of solvent. Assuming that the trivalent titanium forms the complex ion Ti111 Cl4, the equilibrium reaction may be expressed by the following equation, (Me) TiIII cl4+ 1/2 Ti = 3/2 TiII cl2+ (Me) Cl The ideal ionic equilibrium constant for this reaction is, Where the N's are the molar ionic fractions in the equilibrium melt, and (Me) the different types of cations present in the equilibrium mixture. The following thermodynamic relation is derived between Kand the concentration of cations in the equilibrium melt, mix The N"S are the equivalent ionic fractions, and so forth are constants corresponding to the standard changes in free energy for reactions in melts where only the cation indicated is present, and f (y1) is a function of the activity coefficients in the equilibrium mixture. When this term vanishes, a simplified linear relationship between In Kideal and the concentration is obtained. The simplified relationship has been applied with satisfactory results to the experimental data of Mellgren and pie,' and Kreye and Kellogg.2 MANY existing methods for the production of light metals involve the reduction of their respective metal halides in the presence of salt melts composed of alkali or alkaline earth chlorides. In such a solution phase, the light-metal halide may undergo stepwise reduction from a higher, to a lower valence, and finally to a zero valent state. In this connection, the disproportionation equilibrium is of great interest. In the case where the higher valence is three and the lower valence is two, the disproportionation equilibrium may be written as follows, 3 Me11 = 2 Me111 + Me [I] If this equilibrium occurs in a salt melt containing a large excess of alkali chlorides, a typical ionic melt is obtained. It is then possible to formulate the cation equilibrium: 2 Me+h' + Me = 3 Me++ [II] Reaction [11] is analogous to a cation exchange reaction. It has been shown thermodynamically that the equilibrium constant for such a reaction in 2

Jan 1, 1960

By James C. M. Li

The thermodynamics of the set of functions including the activation enthalpy. the activation free energy, and the activation entropy for the motion of dislocations at low temperatures is formulated without a specific model or a mechanism. The behniiior near absolute zero of all these functions and of other relevant quantities related to dislocation mobility Is examined in the light of the third law of thermodynamics. The velocity measurements of Stein and Low for edge dislocations in Si-Fe are used .for illustrotion. In the plastic deformation of crystalline materials, a fundamental assumption, which is supported by direct measurements using etch-pit techniques,'-4 is that the average velocity of a certain mobile dislocation is a single-valued function of temperature and the effective shear stress exerted on the mobile dislocation: Sometimes under certain assumptions, even without direct dislocation-velocity measurements, an activation volume can be obtained from a change in strain rate in a simple tension test. Similarly an ac tivation enthalpy can be obtained by changing the temperature in a creep test. However, the assumptions involved should be studied carefully before using the results of these tests. Consider, for example, a tensile specimen at some stage of deformation with a distribution of mobile dislocations. Let the total length of dislocations of type i be pi per unit volume. The Burgers vector of these dislocations is hi which makes an angle ?i with the tensile axis. With respect to the same tensile axis, let the normal of the slip plane of these dislocations

Jan 1, 1965

By Kenneth A. Moon

An exact statistical treatment of a one-dimensional model is used as a basis for evoluating the reliability of certain simplified expressions for the activity of the solute in interstitial solutions, including one obtained from the exact expression by setting the repulsive interaction equal to infinity. The latter approximation is found to be satisfactory at low and moderate concentration if the repulsive interaction is large, even though not infinite. A similar expression (identical if the co-odination number is two) is derived from the quasichemical expression of Lacher, and is recommended as the best available expression for the excess configurational entropy of interstitial solutions with excluded sites. Some reasonable models are discussed, and the nature of the saturated solutions is determined by inspection. Some of the models reduce to the one -dimensional case. An analysis is given of the excess partial entropy of hydrogen in V-H; Nb-H; and To-H solutions. MOST treatments of the statistical thermodynamics of interstitial solid solutions have followed the classic paper1 of Lacher in making the simplifying assumption that the configurational entropy of the solution is ideal. However, it is becoming increasingly apparent that there are many interstitial solutions with very large so lute-solute repulsions, and for these the assumption of ideal entropy is not valid or useful. It is important to realize that with substitutional solutions large repulsions between the component atoms must lead to phase separation, whereas in interstitial solutions the free energy of the solution is not drastically increased by large solute-solute repulsions until intrinsic saturation is reached at the concentration where further solute would be forced to enter a site in which it would experience the repulsive effect of one or more solute atoms already present. In the limiting case of an infinitely large repulsive interaction, the excess free energy would be attributable entirely to excess entropy, the enthalpy of mixing being zero. AS will be shown below, even if the repulsions are less than infinite, a treatment based on an assumption of infinite repulsions may be very satisfactory up to moderately high concentrations of the interstitial component. Often in solutions where large repulsive interactions exist, there are also small interactions — often attractive—between solute atoms in configurations other than that corresponding to the large repulsion. In such cases the excess free energy will consist of an excess entropy term attributable to the large repulsive interactions, and an enthalpy term corresponding to the other small interactions. Nomenclature to differentiate succinctly between important cases would be a convenience. In this paper the nomenclature shown in Table I will be used. In Table I, and in the preceeding discussion, excess quantities are defined in terms of standard states which are pure solid solvent and pure (possibly hypothetical) solid saturated phase of the structure in question. In practice, it is more convenient to choose the interstitial element as a component, and its conventional standard state. This will add a composition-independent term to the excess entropy and the enthalpy. The earliest paper known to the present author which treats the thermodynamics of athermal interstitial solutions was given by schei12 in 1951, but the statistical derivations in that paper are open to criticism. Speiser and Spretnak were the first to give a correct statistical treatment,3 limited, however, to concentrations sufficiently low that the number of empty sites excluded from occupancy by more than one filled site is negligible. The purpose of the present paper is to extend the statistical treatment to more concentrated solutions, and to examine the magnitude of the errors introduced by assuming that the repulsive interactions are infinite when in fact they must be finite. THE QUASICHEMICAL APPROXIMATION Fortunately, a standard method already exists for taking into account the effect of large interactions upon the entropy of mixing. This is the quasi-chemical method, in which the probability of existence of a given pair of solute atoms in a certain proximate configuration is assumed to be proportional to exp(-w/kT), where w is the energy increase of the solution when the two atoms are moved from isolated locations in the solution to the configuration in question. A quasichemical treatment of interstitial solutions was given in 1937 in a widely neglected paper by Lacher.4 The result comes out

Jan 1, 1963

By C. Ernest Birchenall, Gerd M. Rosenblatt

The pressure and molecular weight of the antimony vapor over solid solutions of tin in antimony, containing 97.4, 94.9, 93.0, and 90.7 at. pct Sb, have been measured from 445° to 545°C by the torsion-effision method. The vapor is all Sb, within experimental error. A solidus curve which differs somewhat from the accepted curve has been calculated using the measured antimony activities. Metallographic examination of additional annealed alloys substantiates the accepted solidus. The solid solutions, which show negative deviations from ideality, probably do not deviate greatly from regular solution behavior. HANSEN' considers the Sb-Sn phase diagram to be well established with the exception of the boundary of the (Sb) phase.* Although there have been no pre- Their data can be combined with data for the solid alloys to calculate the solidus curve of the (Sb) phase. This paper presents measurements of the pressure ant1 molecular weight of antimony over Sb-Sn solid solutions containing 97.4, 94.9, 93.0, and 90.7 at. pct sb. Measurements were made by simultaneous use of the volmer3 torsion and Knudsen, effusion methods. The results of these measurements have been combined with the vapor pressure of pure antimony5 to obtain the activity of antimony in the primary solid solutions. The solidus curve calculated from these data differs somewhat from the accepted curve and is rather uncertain. Metallographic examination of Sb-Sn alloys was carried out to clarify the position of the solidus of the (Sb) phase. EXPERIMENTAL The apparatus and technique have been described previously.5 The measurements were made with the same effusion cells and torsion wire used in the measurements on pure antimony. The torsion measurements were calibrated with mercury at 30" using a mercury vapor pressure of 2.96 x 10-3 mm Hg determined by concurrent, absolute, weight-loss experiments. As in the measurements on pure antimony, an extraneous vapor was observed to distill off during the first run after the cell had been loaded with A fresh sample of alloy and during the first minute or two of every run. The change in composition after a series of runs with one sample was of the order of 0.1 at. pct and thus completely negligible in the calculation of the thermodynamic properties. The alloys were prepared from pieces of Merck antimony and Matheson, Coleman, and Bell reagent-

Jan 1, 1962

By Michael Hoch

The phase diagrams of binary systems of some of the transition elements of Groups IV, V, and VI were used to compute the partial free energies of these elements and the free energy of formation of their Laves-type compounds. From these data, isothermal sections of ternary phase diagrams were calculated and compared with experimental results. DURING the investigation of ternary and quaternary high temperature systems formed by the transition elements of Groups IV, V and VI, the binary phase diagrams for these elements available in the literature were studied. In this study, the free energies of formation of the compounds formed in these binary systems were calculated; these values were then used to determine the general shape of the ternary and quaternary phase diagrams. Above 900°C, the transition elements of Groups IV, V, and VI are all bcc and form only Laves-type compounds in binary systems. The investigation was based on the binary phase diagrams published by Hansen.1 The Cr-Nb system was constructed from the data of Elyutin and Funke.' Several unpublished phase diagrams were taken from Schmidt'sLo and English'sl1 compilations. THE BINARY SYSTEMS valuations of the Thermodynamic Functions. Rostokers evaluated the boundaries of the (a + b) field in Ti-base alloys with a two-constant equation. The authors' interest is mainly in the center of the diagrams; therefore the miscibility gaps in the Zr-Nb, W-Cr, Ta-Zr, Ta-Hf, and Ti-W systems were used to evaluate the thermodynamic behavior of the binary systems. Lumsden's4 Equations 29.2, 32.1, and 33.1, page 287, were used for the excess integral free energy FeX, and for the excess partial free energies Fx and replaces b and b replacesP in Lumsden's notation):

Jan 1, 1962

By T. B. Massalski, Horace Pops

The occurrence and the temperature dependence of the athermal martensitic transformation in bcc Cu-Zn ß-phase alloys have been studied by cold-state microscopy, differential thermal analysis, and electrical -resistivity measurements. CinenzatograpJzic studies have shown that in the majority of alloys the transformation occurs in two stages. A thermoelastic phase, having a 'needlelike" uppearance, forms initially at the MS temperature and grows relatively slowly, chiefly in the edge (lengthwise) direction. With further cooling, an additional martensitic phase forms in rapid bursts at a lower temperature, MB, Both martensitic phases appear to have the same cry stallographic habit hut their modes of formation and growth are different. For the composition range studied, between 38.55 and 41.49 wt pct Zn, the habit planes determined are close to the (2.17 ,12) plane of the matrix, in general agreement with the prediction of the phenomenological theory of martensite formation. Thermal cycling through the MB temperature produces permanent plastic deformation in the 0 matrix and gradutally eliminates the typical burst phenomena. Thermal cycling only through the MS temperature produces no noticeable deformation effects. THE bcc Cu-Zn ß-phase alloys tend to become unstable at low temperatures and undergo a martensitic transformation,'-3 but the details of the transformation have not been completely determined. Following earlier metal log raphic and X-ray work1 Tichener and ever' determined by means of electrical-resistivity measurements the temperature range of the martensite transformation during continuous cooling. The transformation temperature was found to decrease with increasing zinc content, becoming about -130°C for an alloy containing 40.04 wt pct Zn. Hull and Garwood3 made a metallo-graphic study of Cu-Zn 0 brasses at temperatures down to -160°C, and determined the habit plane of the transformation product for an alloy containing 38.88 wt pct Zn. No metallographic studies below liquid-nitrogen temperatures have been reported. The martensitic transformation in ß-brass alloys can also be induced by deformation.1,4 The MD temperature corresponding to the appearance of the strain-induced martensite is some 300°C higher than that observed without strain, and hence the transformation can be strain-induced in alloys containing a higher percentage of zinc. Massalski and Barrett4 found that alloys containing as much as 51.89 wt pct Zn could be transformed into a faulted hcp structure by cold working at liquid-helium temperature. Because the details of the MS temperature and morphology reported in the literature are somewhat incomplete, a further study has been made of some of the above features. A design of a cryogenic stage for optical metallography5 has permitted the examination of specimens at temperatures down to 4.2oK, and the use of a cinecamera has permitted a study of the morphology on cooling and heating. The particular aim of the present work was to examine the transformation temperatures, the habit planes, and the growth morphology over a wide composition range in the ß-phase field. The effect of thermal cycling upon the subsequent transformation was also examined.

Jan 1, 1964

By Charles F. Hickey, Eric B. Kula

Thermomechanical treatments applied to the maraging steels include a) cold working in the austenitic condition at 650°F, followed by transformation to martensite and aging, b) cold working in the murtensitic condition and aging, and c) cold working in the aged condition with and without subsequent reaging. The strength increases in these steels are very small compared to the increases observed in conventional carbon and alloy steels. The changes that are observed are compatible with the strengthening mechanisms operative during thermomechanical treatment of conventional steels, however. Differences are caused by the absence of a carbide precipitate and the low work-hardening rate in both the solution-treated and the aged conditions. ThE 18 pct Ni maraging steels represent a class of steels which are finding great interest for high-strength applications.1~2 They are essentially carbon-free, and contain 7 to 9 pct Co, 3 to 5 pct Mo, and 0.2 to 0.8 pct Ti. Although austenitic at elevated temperatures, they can be air-cooled to room temperature to form a martensite, which because of the absence of carbon is relatively soft. On subsequent reheating age hardening occurs and strength levels of 250 to 300 ksi yield strength can be attained. These steels appear to be particularly suitable for studying the response to various thermome-chanical treatments for additional reasons other than the obvious one of attempting to improve their already attractive properties. Thermomechanical treatments can be defined as treatments whereby plastic deformation, generally below the recrystal-lization temperature, is introduced into the heat-treatment cycle of a steel in order to improve the properties. With an absence of intermediate transformation products on air cooling the maraging steels have good hardenability and hence can readily be cold-worked in the austenitic condition prior to transformation to martensite. Further, they can be worked in the martensitic condition prior to aging, and even can be deformed in the fully aged condition. Finally, it is of interest to compare their re- sponse to that of the more conventional alloy and carbon steels, where the role of carbides is important in the strength increase by thermomechani-cal treatments. The thermomechanical treatment of conventional steels has been the subject of a recent review.' I) MATERIALS AND PROCEDURE The steel used in this investigation was a commercially produced vacuum-melt heat, which had been rolled to 0.090 in. and mill-annealed. The composition of the alloy was as follows: 0.02 C, 0.08 Mn, 0.10 Si, 0.009 P, 0.009 S, 18.96 Ni, 7.34 Co, 5.04 Mo, 0.29 Ti, 0.05 Al, 0.004 B, 0.01 Zr, and 0.05 Ca. Unless otherwise stated the heat treatments used were the standai-d solution treatment at 1500°F for 1 hr, air cool, followed by a 900°F, 3 hr age. In this condition, the material exhibited 232 ksi yield strength and 239 ksi tensile strength. Mechanical properties were determined by Vicker's hardness measurement (20 kg) and by tensile tests on standard 1/2-in.-wide, 2-in.-gage-length sheet tensile specimens. Notch tensile tests were run using the 1-in.-wide NASA type, edge-notched specimen.4 Fracture-toughness determinations were made on 3-in.-wide, center-notched, fatigue-cracked specimens, following the recommendations of the ASTM Committee on Fracture-Toughness Testing.4 An electric-potential technique was used for measuring the crack size at the onset of rapid crack propagation5 which is necessary for calculations of Kc, the critical stress-intensity factor under plane-stress conditions. The critical stress-intensity factor under plane-strain conditions KI, was also calculated, using the stress at which the first observable crack growth occurred. 11) RESULTS A) Cold-Worked in the Austenitic Condition. The reported M, temperature for the 18 pct Ni maraging steel is about 310°F.1 Therefore, a temperature of 650°F was selected as suitable for rolling in the austenitic condition. Specimens were solution-treated at 1500°F for 1 hr, air-cooled to 650°F, and rolled varying percentages from 0 to 60 pct, at 20 pct reduction per pass. Tensile and hardness properties after aging at 900°F for 3 hr are shown in Fig. 1. The tensile strength increases from 253 to 271 ksi and the yield strength from 247 to 265 ksi as a result of a reduc-

Jan 1, 1964

By O. N. Carlson, H. A. Wilhelm, H. E. Lunt, J. M. Dickinson

On the basis of data obtained from microscopic examination, melting observations, cooling curves, X-ray analyses, and resistance measurements, phase diagrams have been proposed for the Th-Cb and Th-Ti alloy systems. Both are simple eutectic systems and have no terminal solid solubility or intermediate phases. The eutectic between thorium and columbium occurs at a composition of about 8 wt pct Cb and a temperature of 1435°C. The Th-Ti eutectic occurs at 1190°C at the composition 12 wt pct Ti. No change was observed in the transformation temperature of thorium in either system or in the titanium transformation. RECENT study of thorium and its alloys has been promoted because of the possibility of employing this metal in nuclear reactors. Their corrosion resistant properties, nuclear characteristics, and high melting points put columbium and titanium among the many metals being employed in the study of thorium alloys. Since a knowledge of the phase relationships would be important in the application of such an alloy, investigations were undertaken to propose phase diagrams for the Th-Cb and Th-Ti systems. Experimental Procedures Thorium metal sponge was specially prepared for use in this investigation. Carbon in a quantity less than 0.04 wt pct was the principal impurity. There was also less than 0.01 pct each of iron, calcium, zinc, aluminum, and nitrogen in the thorium. Columbium, both as a powder and sheet metal, was obtained from the Fansteel Metallurgical Corp. The manufacturer's specifications indicated that the metal contains less than 1 wt pct total impurities. An analysis of the metal showed approximately 0.18 pct C in the powder and less than 0.05 pct C in the sheet. The titanium used was commercial sponge, reported to be 99.5 pct Ti. An analysis showed that this metal contained 0.2 pct Fe. Preparation of Alloys—Since the metals used in this investigation are reactive and might become contaminated on melting in a refractory crucible, the alloys were prepared by arc melting. The titanium sponge was employed in the form of small lumps while the columbium additions were made either as pressed pellets of powder or as clippings from sheet. The alloying material and the thorium sponge were melted together under argon in conventional arc melting equipment employing a tungsten electrode and a water cooled copper crucible.

Jan 1, 1957

By G. S. Tint, M. Herman, V. V. Damiano

Dislocation arrays and substructures were studied in cadmium doped zinc crystals using a newly devised etching technique. Cadmium precipitates delineating the dislocations were revealed by etching a surface closely parallel to the (0001) slip plane. Cinephotomicrography of the continuous etching process revealed the three-dimensional aspects of dislocations in the bulk crystal. Dislocation etch patterns were studied in both deformed and annealed crystals after suitable aging at room temperature. The effect of annealing was evidenced by a rearrangement of the dislocations into low-angle boundaries and hexagonal networks. ETCH pit techniques have been used extensively to study dislocations in both deformed and annealed bulk metal crystals. Ideally one hopes to obtain a one-to-one correspondence between the etch pits and the points of emergence of the dislocations at the surface. One then attempts to deduce the way in which dislocations are arranged in the bulk crystal from the arrangement of etch pits on the surface. It is clear that one can obtain only limited information of the dislocation configurations inside the crystal from etch pit studies of single surfaces. Considerably more information is obtained if one is able to follow the course of the dislocations through the crystal using progressive etching technique. Techniques of this sort were used by Gilmanl to study dislocations on the slip planes of NaCl crystals and by Damiano and Tint2 to study dislocation arrangement in zinc crystals grown from the melt. The present paper makes use of a technique first described by Tint and Damiano3 to observe and continuously record the dislocation structures which appear while a crystal surface was being progressively etched. Studies were made on cleaved (0001) surfaces to reveal the dislocations along their length on the surface closely parallel to the slip plane. The technique for revealing segments of dislocations along their length by etching is well known. Wilsdorf and Kuhlmann-wilsdorf4 revealed disloca- tions along their length in aluminum containing a few percent copper, when precipitates segregated along the dislocations. The technique was used by Low and Guard5 to study dislocation configurations on the slip plane in Fe-Si alloys containing carbon. In the present work the technique was applied to zinc containing cadmium since it was shown by Gil-man6 that a cadmium-rich phase could be made to precipitate from supersaturated solutions along dislocations in zinc. Segments of dislocations delineated by the precipitates were revealed by etching a surface prepared by cleaving the crystal. The three-dimensional nature of dislocations and substructures was thus studied from the cinephotomicro-graphic record of the continuous etching process. EXPERIMENTAL Single crystals of zinc containing the order of 0.1 pct Cd were prepared by slowly lowering a graphite crucible containing the melt through a temperature gradient of 15°C per cm at a rate of 1.5 X 10-3 cm per sec. "As grown" crystals were aged for periods of 1 month at room temperature, then cleaved in liquid nitrogen, and etched according to the procedure used by Gilman.' The etchant containing 32 g of CrO3, 6 g of hydrated Na2SO3 in 100 ml of water behaved as a chemical polish for zinc and etch pits were produced at the site of precipitates or inclusions. After the precipitates or inclusions were removed from the surface, the etch pits left behind were eventually polished smooth. This behavior enabled one to continuously observe the surface while the specimen was immersed in the etchant. Best results were obtained when the specimen surface was vertical and the reaction products of polishing were continuously removed by gravitational convection. Some crystals were heavily deformed in excess of 25 pct strain, others were lightly deformed the order of a few pct by compression such that the deformation occurred essentially by basal glide. Some crystals were etched immediately after deformation, others were allowed to age at room temperature for several weeks prior to etching. Heavily deformed crystals were annealed at various temperatures and etched on the cleavage plane immediately after annealing, others were allowed to age at room temperature for several weeks prior to etching. The etched structures of deformed and annealed structures were studied. Similar experiments were conducted on 99.9999 pct pure zone refined Tadanac zinc crystals which

Jan 1, 1963

By H. D. Kessler, Joseph B. McAndrew

WHEN there is occasion to make structural use of metals at temperatures above 900°C (1652°F), the choice of alloys is severely limited, and those materials which meet special requirements as to density, strength, toughness, and resistance to creep, oxidation, or fatigue at such temperatures are at a premium. Any new type of high temperature alloy which is found to be outstanding with respect to several of these properties is therefore likely to find special applications for which it is uniquely advantageous as compared to other alloys. Such is the case with the 7 titanium-aluminum alloys. This y phase is an intermediate phase based on the composition TiAl, and extends from about 35.5 to 44.5 wt pct Al at temperatures up to 1000°C, above which the field broadens to include 60 pct A1 at 1340°C.' The alloys of principal interest have a narrow melting range, with 7 forming by the peri-tectic reaction, melt + ß=y at about 1460°C. Unlike most intermediate phases, the binary alloys containing titanium and aluminum in approximately equiatomic proportion possess low room temperature hardness,' in addition to which they have low density, good resistance to oxidation, and relatively high modulus of elasticity.' Unpublished work done at Armour Research Foundation showed

Jan 1, 1957

By D. J. DeLazaro, W. Rostoker, R. E. Riley, M. Hansen

KNOWLEDGE of the isothermal transformation behavior and the TTT chart method of graphically summarizing such information has been of invaluable aid to the ferrous metallurgist in understanding and developing heat treatments intended to provide specific mechanical properties. It is to be expected that similar lines of study directed to titanium-base alloys will be as profitable. This paper summarizes, on conventional TTT charts, the isothermal transformation products and pertinent reaction rate data for binary alloys of titanium containing 1, 3, 5, 7, 9, and 11 pct Mo, respectively. The results so presented were derived from metal-lographic examination. Some X-ray diffraction work was done to clarify certain points of question. Ti-Mo System To the authors' k.nowledge, TTT charts have only been used to describe the reaction rates of eutectoidal decompositions. It would seem that the kinetics of decomposition of any unstable solid solution might be conveniently described in this manner. The equilibrium diagram of the Ti-Mo system' is shown in Fig. 1. The similarity with the Fe-Ni system will be recognized. Additions of molybdenum serve to stabilize the /3 phase to increasingly lower temperatures. The solubility of molybdenum in the a phase is restricted to less than 1 pct at 600°C. Under normal conditions. a homogeneous ,8 structure quenched to a, temperature in the a f & field will reject a of invariant composition. The rate at which this occurs depends on the degree of undercooling and the degree of supersaturation of /3. The structural character of the rejected phase may also be expected to be related to the undercooling. Materials and Experimental Methods A sponge titanium was used which has a nominal impurity content as reported in Table I. The nominal composition of the molybdenum used is also included. The alloys were prepared in 150 g melts by arc melting in an evacuated water-cooled copper crucible of the type reported in an earlier paper.' The pancake-type ingots were forged to 1/4x1/4 in. bars and homogenized for 24 hr at 1000°C in evacuated Vycor bulbs. Specimens Vi in. thick were cut from these bars for heat treatment. The heat treatment cycles followed an invariant procedure. The specimens were soaked at 1000°C for 20 min under a helium protective atmosphere prior to quenching into a lead bath held at a temperature corresponding to a chosen degree of undercooling. After a prescribed period of time at this temperature, the specimen was removed and water quenched. A series of specimens so treated for progressively longer periods served to establish the times for initiation and completion of the decomposition of the /3 phase at a particular temperature. Although heat treatment of unprotected specimens in a lead bath does permit surface contamination by lead diffusion, this method is necessary to insure sufficiently rapid quenching rates. As long as the bath treatments were of less than 1 hr duration. the contaminated surface was not unduly deep and could be removed without excessive grinding. Metal-lographically, the contaminated zone could be readily distinguished from the pure binary alloy. Transformation Characteristics of Ti-Mo Alloys Metallographic examination showed that a supersaturated p phase may decompose by one of two processes. Alloys containing 1 to 9 pct Mo, when quenched in water from the homogeneous /3 field,

Jan 1, 1953

By O. W. Simmons, L. W. Eastwood, C. M. Craighead

Binary alloys of titanium with silver, lead, tin, nickel, copper, beryllium, boron, silicon, chromium, molybdenum, manganese, vanadium, iron, and cobalt were studied. One-half-pound ingots of the alloys were prepared in an arc furnace, employing a water-cooled copper crucible, an argon atmosphere, and a water-cooled tungsten electrode. The half-pound ingots were fabricated by forging at 1700°F in air to 1/4-in. slab, followed by hot rolling at 1450°F to 0.060-in. sheet. Tensile properties, minimum bend radii, hardnesses, response to heat treatment and aging treatment, and phase relationships were determined for these alloys. EARLY in 1947, as one phase of the evaluation of materials for Air Force Project RAND, Battelle successfully arc melted Bureau of Mines titanium and obtained a few basic properties of unalloyed titanium and several titanium-base alloys. The low density, excellent resistance to corrosion, and high tensile properties of these materials stimulated a great deal of interest among metallurgists and designers seeking better materials of construction. As a result of this early work, Battelle, under contract with the Air Materiel Command, Wright-Patterson Air Force Base, has continued extensive studies of titanium alloys. The result of the first year's work is described in three papers. The present one deals with binary alloys, the second with ternary alloys, and the third paper with quaternary alloys. Melting Method The arc furnace for melting titanium and other refractory metals was developed at Battelle Institute under Air Force Project RAND. During the present work, considerable improvement has been made in the design and operation of this furnace for making small ingots of titanium and titanium alloys. The improved furnace design is illustrated by fig. 1, which shows a cross-sectional view with the dimensions of various parts and their relationship to one another. The essential features of the furnace are the inert argon atmosphere, the water-cooled copper crucible, and the water-cooled tungsten elec- trode. The melting crucible is formed by spinning 0.064-in. annealed copper sheet. A groove for an O-ring seal is spun into the flange of the crucible. A fiber gasket between the crucible flange and the water-cooled brass cover provides electrical insulation. The brass cover is fitted with a sight glass, an opening for the water-cooled electrode, and a tube through which the material is charged. Direct current is used for melting, with the positive electrical terminal connected to the water jacket and the negative terminal to the electrode. A typical heat is made in the new furnace as follows: Approximately, 0.20 lb of titanium under 2 mesh per in. and the alloy addition, if any is to be used, are placed in the bottom of the crucible. The cover is clamped on the crucible so that the O-rings make a tight seal. The remainder of the charge is placed in a glass bottle, and this is connected by a rubber hose to the charging tube of the furnace. The crucible and the charge are evacuated with a mechanical pump to a pressure below 50 mm of mercury, or less if desired, and held at this reduced pressure for 5 min. Hot water is circulated through the jacket during the evacuation period to assist in outgassing the crucible. Following the evacuation, tank argon of 99.92+ pct purity is flushed through the crucible for 5 min and then adjusted to give a positive pressure of 1 to 2 psi. During subsequent operation, an argon pressure regulator introduces only enough argon to compensate for the small leakage which occurs through a mercury trap. Re-evacuation and reflushing the melting chamber with argon produced a negligible reduction in contamination. Two 550-amp generators, connected in parallel, constitute the power source. Normally, about 800 amp are used for melting alloys which are not extremely refractory. The generators are set for 90 v open circuit and 200 amp. The arc is struck and the electrode is withdrawn to produce an arc of 23 to 26 v. This voltage is maintained while the electrode tip is moved slowly around a circle 1 in. smaller than the diameter of the ingot. The current

Jan 1, 1951

By O. W. Simmons, L. W. Eastwood, C. M. Craighead

H. Schwartzbart and W. F. Brown, Jr.—The authors have divided the effects of recovery on the true stress-true strain curve into two types; metarecovery, which effects only the first part of the curve or the yield strength, and orthorecovery, which effects the flow stress at any strain. Both of these are said to be true recovery effects, involve no recrystallization, and are explained by the removal of two different types of imperfections caused by work hardening. However, there seems to be some question as to whether the data are sufficiently conclusive to exclude, as an explanation of the authors' results, a mechanism based on the relief of residual stresses between the grains or slip bands and recrystallization. It appears that metarecovery could be interpreted in the same fashion as a customary interpretation of the Bausch-inger effect. The balanced system of internal stresses which exists between grains in a strained specimen due to varying orientation and, hence, yield strengths, of the different grains is responsible for a reduced yield strength in compression following pre-tension, and, similarly, for an elevated yield strength in tension following pre-tension. If the specimen is now heated so that the internal stresses are relieved by creep, then the yield strength in tension following tension will have been reduced and in compression following tension will have been raised. There seems to be a very strong case for the lack of recrystallization in the aluminum investigated by the authors, if one defines recrystallization as the presence of visually detectable new grains or accepts the X-ray evidence as conclusive. One must remember, however, that the appearance of spots on the back-reflection X-ray patterns cannot be taken as the time when recrystallization first started. The areas of recrystallized strain-free material must first have grown to a size large enough to give distinct spots on the patterns and this may take some time. Averbachl7 in an investigation of brass has shown that recrystallization can be detected by extinction measurements at temperatures lower than those based on hardness or X-ray line width determinations. It can be seen from fig. 10 that the rate of recrystallization is extremely low over a considerable time period at the onset of the process. Observations on the rate at which small amounts of recrystallization effect the flow stress would have given further insight as to whether undetectably small amounts of recrystallization might have been responsible for orthorecovery. Also, the question arises as to whether the effects observed in fig. 6 for various times and temperatures could not have been obtained if the time at 212°F were sufficiently long. In addition, the argument that the curve in fig. 10 is not sigmoidal seems weak in view of the scattering of the points. It is conceivable that an accurate determination of the curve for the first 100 hr would exhibit a relationship other than the one drawn. There is one point we would like to raise about the condition of the starting material. The authors annealed their material at 750°F for 15 min to remove the effects of any previous work hardening or machining strains. Reference to the work by Anderson and Mehl shows that this treatment may not have completely recrystallized the aluminum, so that the starting material may have had some strained areas. Higher temperatures or longer times may have been required to remove the effects of any small strains. We would like to mention some results of tests being conducted at the Lewis laboratory of the National Advisory Committee for Aeronautics in an investigation of the Bauschinger effect in relation to fatigue. Tests were performed on annealed electrolytic copper and several annealed brasses. Specimens were pre-strained 1 pct in tension and then tested in compression or tension with and without intermediate stress-relieving annealing treatments at 500°F for various times. Specimens heated at 500°F for 10 1/2 hr showed an elevation of the flow curve in compression and an approximately equal lowering of the flow curve in tension when compared with the curves for the un-heat treated specimens. After approximately 0.8 pct strain, all flow stresses coincided and were equal to the flow stress of the virgin material at this strain. This behavior is consistent with the metarecovery observed for aluminum by the authors and for which a residual stress model can be used. On the other hand, increas-

Jan 1, 1951