Recent progress in metallurgical thermochemistry

RECENT PROGRESS IN METALLURGICAL THERMOCHEMISTRY

O. Kubaschewski and W. Slough LIST OF SYMBOLS (in the order they appear in the text) H~

ST Cv ACp AG ° AH ° AS ° Po2 *e ( ) {} [] A~ ACp A/~ A~ v K~ AJ NA D

= enthalpy at temperature T, = entropy at temperature T, = heat capacity at constant pressure, = change in heat capacity, = change in standard free energy, = change in standard enthalpy, ---- change in standard entropy, = partial pressure of oxygen, ----- electronic transport number, = solid state, = liquid state, = solution in X, = change in the partial free energy, ---- change in the partial heat capacity, ---- change in the partial enthalpy, = change in the partial entropy, = nuclear magnetic resonance frequency, = equilibrium constant in terms of partial pressures of reactants and resultants, = change in general thermodynamic function J, = atomic fraction of A, = atom electronegativity. = dissociation energy. 1.

INTRODUCTION

By "metallurgical thermochemistry" the present authors understand the knowledge of the thermodynamic properties of substances involving metals and their application to the calculation of equilibria of practical significance as well as to a closer understanding of the causes of the stability of metallic phases.

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The laws and principles of chemical thermodynamics have been known for more than fifty years so that there is no recent progress to report. From its early stages onward, metallurgical thermochemistry has been largely an experimental problem--it still is. The classic thermochemist lived in a world of stoichiometry whereas every metallurgist knows that he is dealing with metallic solutions rather than compounds. It is therefore not surprising that progress in the field as a whole has mostly been pushed on by alloy thermochemists who are used to being confronted with non-stoichiometric phases, frequently of low affinity. The design and development of experimental methods specific to alloy thermodynamics was effectively begun not much more than forty years ago. The tendency has been and is to increase the temperature of measurement. The development of methods from the beginning will briefly be outlined in the experimental section, but references will mostly be to recent work. The limitations of our present store of experimental methods will be indicated. The types of system to be consideied will be restricted to alloy systems and the oxides, nitrides, carbides, silicides and borides of the transition metals. Metal halides will be largely disregarded despite the important role they play in metallurgical thermochemistry since a line must be drawn somewhere in a report such as the present one. High-temperature materials and substances of interest in reactor technology deserve special attention. The fundamental aspects of metallurgical thermochemistry are focused on the causes for the stability of metallic phases. Progress in this field is slow and, at best, semi-empirical. Even so, by systematic consideration of thermochemical data, it has been possible to verify certain simple models of bond mechanism and to arrive at empirical rules which help to estimate missing thermochemical information. A progress report on metallurgical thermochemistry would not be complete if some reference were not made to the successful application of the data to the calculation of equilibria of practical importance. This is, after all, the reason why an increasing number of investigators find satisfaction in the development of the field under review. 2.

EXPERIMENTAL METHODS

The quantities to be determined experimentally to describe the thermodynamic properties of substances fully are the heat and entropy of formation, and the heat capacity, in terms of temperature, concentration and pressure. The need for adapting the classic methods to non-stoichiometric phases over a wide range of affinity and, where necessary, for devising and developing new methods has been pointed out above.

2.1. Calorimetry The classic methods for measuring heats of formation and reaction were

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Berthelot's combustion bomb and aqueous solution calorimetry. As far as metallurgical thermochemistry is concerned, the combustion bomb is well past its prime. The results in the study of transition metal oxides are not sufficiently accurate and as a difference method it has never been a success in metallurgy. The principle of the combustion bomb is, however, being successfully applied for the determination of the heats of formation of metal halides--in particular fluorides.Ca) Gross and his colleaguesa0) have shown that direct reactions between metals and halogens can be performed at normal pressures in a calorimeter, with very good accuracy. The oxygen combustion bomb will soon be superseded by the hightemperature Calvet calorimeter employing thermopilesA 2°6) The measurements are so sensitive that quantities of heat of, say, 50 calories can be measured with an accuracy of better than 5 %, even at 800-1000°C. The advantage is that only small volumes of oxygen need be reacted with the condensed phase so that the change in its composition is very small. Thus, the results are virtually partial heats of reaction. This was demonstrated by Gerdanian and Dod~( 11, 12) on the phases FeOl+x and UOz+x which have significant ranges of non-stoichiometry. The differentiation of integral heats of oxidation does not even approach the accuracy achieved with the Calvet calorimeter. The principle of this calorimeter can, of course, also be used for other gas/metal reactions involving, for example, nitrogen or sulphur. The systems so far mentioned are high-affinity systems. Solid and liquid alloys presented a somewhat different problem. Nevertheless, direct reaction calorimetry has been developed for such phases. The early attempts were undoubtedly exciting and not quite without danger. Oelsen and his associates poured liquid metals, e.g. iron and aluminium, simultaneously into a lined container which was subsequently placed in a 'milk pail' with 7 litres of water and a Beckmann thermometer. One of the present authors poured liquid metals, such as lead, on sodium or lithium in a graphite container within a calorimeter, with occasionally explosive effects: a magnesium/ tellurium mixture, for instance, placed in a 700°C calorimeter went right through the ceiling of the laboratory. The surprising fact is that many of the values determined during those heydays of alloy thermochemistry have not been superseded, even to-date. The reason for this is that a value obtained by direct-reaction calorimetry, even crude, is likely to be more reliable than one obtained by difference methods because of the uncontrolled errors that may enter the latter which are difficult to spot. Direct-reaction calorimetry on liquid alloys, first promoted by Kawakami, has been developed to a high degree of accuracy by Kleppa(m and Wittig/14) both using isoperibol1" calorimeters. Dench (is) on the other hand applied the t "Isoperibol" derived from the Greeks ,r~p,flo,~,~(the surroundings) is being accepted by some thermochemists to replace the misnomer "isothermal" for a Newton law calorimeter.

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adiabatic principle based on a calorimeter originally devised by Moser. A powder compact (e.g. Cr + Mo) is enclosed, with a thermocouple and an electric heater, in a box of tantalum surrounded by an electric furnace. Differential thermocouples placed against the inner and outer surfaces of the box are connected in series to a galvanometer. Specimens in the form of compacted mixtures of metal powders are heated from a temperature where no reaction occurs to one at which alloying is completed rapidly. Temperature and heat supplied electrically to the specimen are recorded during the whole alloying process, from initial reactant mixture to final product. The energy supplied electrically is used partly to supply the change in heat content of the elements and empty calorimeter between the initial and final temperatures, and the remainder to supply the heat of alloying. Changes in heat contents are then determined in separate experiments. The estimated accuracy for heats of reaction in Dench's calorimeter is + 50 cal/g-atom, to which the 'chemical' errors have to be added. Dench's calorimeter is suitable for the investigation of endothermic reactions that go to completion within three hours at temperatures up to 1400°C. Exothermic reactions become spontaneous when the reaction mixture is properly ignited. When ignition with the normal method, e.g. a hot wire, does not provide sufficient heat, it may be necessary to incorporate a little furnace in the calorimeter. Such a method has been devised also by Dench316~ In principle, a mixture of the powders of two or three component metals is heated by a small furnace within a calorimeter until alloying takes place rapidly. The electrical energy supplied is measured by an accurate watt-hour meter. When the calorimeter is again at 25 °C, an amount of electrical energy is put into the furnace which raises the calorimeter block to the same maximum temperature as in the reaction run: the difference between the input electrical energy in the reaction- and calibration-runs is the energy evolved by the reaction. This method, originally<16> applied to transition metal aluminides, has now become quite popular (e.g. refs. 17, 18) for solid-solid reactions of moderate heat evolution (5-20 kcal/g-atom) but its accuracy suffers from 'chemical' errors due to (1) incompleteness of reaction and (2) impurity effects. Incompleteness of equilibration is due to the relatively rapid cooling after reaction, a shortcoming of spontaneous reaction-calorimetry generally when the thermostat is at about room temperature. One should therefore strive to raise the equilibrium temperature of calorimeters employed for the study of metallurgical substances as is done in the Calvet and Dench calorimeters mentioned above. The application of solution calorimetry also requires higher temperatures. It was W. Biltz who made the first systematic studies of the heats of formation of intermetallic compounds using acid solution calorimetry. Although this was a significant piece of pioneering work, the results were inaccurate and sometimes quite erratic. The principle to be applied to solution calorimetry is to choose the solvent so that as small as possible a heat of solution is evolved or absorbed. This makes the difference between the heats of

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solution of the compounded and uncompounded alloys relatively large compared with the actual heats of solution. Thus--one would use liquid metals as solvents for the investigation of alloys, liquid oxides for the study of oxides and silicates, etc. Here again, research workers have recently been quite active. Liquid tin and bismuth have been popular solvents. The calorimetric work of Bever may be mentioned as an example3TM Liquid copper and even nickel have been employed by Elliott320) Despite its sensitivity to oxidation when liquid and its high heat of oxidation, aluminium is being used to measure heats of solution of various metals by Mathieu3TM Liquid aluminium calorimetry is also being explored in other laboratories. Of course, the use of liquid-metal solution calorimetry does not save thermochemists the trouble of developing high-temperature methods because rates of solution as well as solubilities increase with temperature, and application of the method near the melting point of the solvent is rather restricted. For silicates and other oxides, aqueous hydrogen fluoride in various concentrations has been the standard solvent for a long time, but only laboratories with a sophisticated equipment and long experience, such as is found at the National Bureau of Standards, can hope to obtain reasonably accurate results. The obvious improvement, the use of liquid oxides as solvents, has been mentioned above. Kleppa~22, 2s) and his associates made, indeed, use of such solvents in a sensitive calorimeter to determine the relative stability of various modifications of alumina and the heat of formation of a number of silicates. For e- and 8-AlcOa, for instance, the solvent was a lead-cadmium borate melt in a gold container at 705°C.t22) As a striking example, it may be mentioned that, in the course of Kleppa's work, the heat of formation of sillimanite from the component oxides was corrected from --46,000 to 600 cal/mole.tea) As a result of all these efforts (i.e. improved solution calorimetry, high temperature Calvet calorimetry, 'little furnace' calorimeters, adiabatic reaction calorimetry at high temperatures), it may be said that the heats of quite a large proportion of metallurgical reactions are now accessible to experimental investigation. The experimental accuracies are being continuously improved. However, the chemical side of calorimetry still requires the greatest attention, especially at high temperatures, and the magnitude of the chemical errors is often difficult to estimate.t~) Undefined or incomplete chemical reactions of the mixtures investigated, impurity reactions, side reactions with the crucible materials and with other parts of the calorimeter, may all contribute to render the final uncertainty much greater than that due to the physical errors of measurement. The metallurgical thermochemist is usually more interested in differences of heat content at two temperatures, say, that of the liquid and solid substance, than in true heat capacities. Even so, the 'drop method', which measures heat contents, appears to be overemployed. The quenching involved in drop calorimetry does not permit equilibration, and stresses remaining -

-

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in the specimens and incomplete transformations render the results unreliable. Except for the rare, congruently melting compositions, freezing from the melt almost invariably leads to segregation in the solid samples. The resulting errors are aggravated when the heat content vs temperature curves are differentiated to calculate true heat capacities. The discrepancies in the C~/T curves obtained by different observers on the same phase bear witness to this short-coming. The present authors occasionally prefer estimated values for ACp to those derived from drop calorimetry. The answer to this problem is to measure heat capacities directly, for instance by adiabatic calorimetry. The calorimeter devised by Moser at the Physikalisch-Technische Reichsanstalt has been mentioned earlier: it was used for temperatures up to 670°C. Backhurst at the National Phsyical Laboratory extended the range of this method to 1600°C for solid and liquid metals325~ In order to make the thermal capacity of the container relatively small compared with that of the specimen, rather large-sized specimens (ca. 2 kg) were used. The adiabatic calorimeter of Dench t15~ mentioned earlier has been designed for smaller specimens and operated at temperatures up to 1400°C. It has been employed not only as a reaction calorimeter but also for the measurement of heat capacities--of iron for instance.t2a~ It may serve as a prototype for similar measurements. Other methods for the direct determination of true heat capacities are available127~ but will not be discussed here. 2.2.

Free Energy Measurements

Two major methods are available for the determination of free energies of reaction: the electromotive force (EMF) method and measurements of dissociation or reaction pressures. In the EMF method, the chemical reaction to be investigated must be harnessed in such a way that its energy produces electromotive force: two electrodes are separated by a predominantly ionic conductor. For instance, the free energy of formation of hydrogen chloride can be measured by separating a hydrogen and a chlorine electrode by an aqueous solution of hydrogen chloride in water and measuring the EMF by a compensation method, usually employing a potentiometer: (Pt) (H2)/[HCI]aq/(CI2) (Pt~ (H2, 02, 1 atm) AG°Hcl = --zFE where F, the Faraday, is 23,066 cal/volt and z, the valency, is one. To measure the free energy of solution of, say, zinc in a brass, a solution of zinc chloride in a eutectic mixture of sodium and potassium chlorides may be employed, {Zn}/[Zn ++] {KC1-NaCI }/(Cu-Zn)a. In order to investigate solid electrodes by this method, the temperature

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must be high enough to ensure suitably rapid diffusion at the electrodes. The higher the melting points of the electrode materials, the higher must be the temperature of measurement. Quite a number of metal chlorides have been investigated with cells of the type, ( C ) {Me}/{MeClx}/(C12) (C), by Lorenz and others. In alloy thermodynamics, numerous cells of the type shown for a brass have been studied. The early work of J. H. Hildebrand at the University of California may be mentioned in this connection. The use of molten alkali chlorides as electrolyte solvents is still quite popular. However, there are substantial experimental difficulties,~27~ and the measurements are limited to temperatures below, say, 700°C. The search for other suitable electrolytes has therefore continued. Hauffe suggested glass, which is a sodium ion conductor, for the investigation of sodium alloys, and one of the present authors demonstrated that silver dissolves in solid glass in the form of ions and used this solution for the determination of the free energy of solution of silver in silver-gold alloys. The recent development in the use of solid electrolytes began with the work reported by Wagner and Kiukkola~ zsl on simple cells of the type: (Ni, NiO)/(CaO-ZrOz)/(Cu20,Cu). The electrolyte is a solid solution of lime in zirconia (ca. 18 mole 70 CaO). The transport number of the oxygen ion in the solid solution is virtually unity but subsequent work by Schmalzriedt 29~ has shown that significant electron conduction occurs below Po2 ~ 10-19 atm 02 at 1000°C. This excludes metals that are baser than, say, iron and their oxides and alloys from the study by means of the electrolyte mentioned. Other fluorite-type solid solutions based on thoria, with lime, yttria or lanthana additions, have been found to have an oxygen-ion transport number of virtually unity in the po 2 range, 10 -~ to 10 -28 atm, where the lower limit does not necessarily represent the pressure below which significant electron conduction will occur (i.e. re > 0"05). The investigation of the limitations of solid oxide electrolytes continues. Recent applications of solid oxide electrolytes have been to the determination of the chemical potentials of oxygen in metal/oxide systems, such as Nb-Nb2Os,t a°~ of oxygen dissolved in metals, such as ironl311 or copper,( a21 and the chemical potentials in alloy systems, such as coppernicke133a~ Undoubtedly, the recent developments of solid electrolytes have considerably extended the range of application of the E M F method for the determination of thermochemical data. It would be most valuable to have similar electrolytes for nitrides, carbides and borides but the prospects are not promising. One way out of this dilemma might be the determination of the chemical potentials of the metallic constituents but a Duhem-Margules

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evaluation must then be invoked, with the resulting loss in accuracy, in order to obtain the chemical potentials of the non-metallic constituent. Many of the free energies of substances of interest in metallurgy have been and are still being obtained from measurements of dissociation and reaction pressures. Most methods date back longer than the others so far mentioned in this article. It will therefore suffice to enumerate here the methods of long standing and report only some recent developments. Vapour pressures and dissociation pressures may be determined by dynamic, static or effusion methods. A typical dynamic method is the transpiration or transportation method in which an inert carrier gas is passed, at different flow rates, over the heated substance, the vapour being condensed in some cooler part of the apparatus. Recent improvements mainly concern the evaluation of the flow-rate vs. apparent-pressure curve (e.g. ref. 34). A number of static vapour pressure methods are available, for instance the dew-point method which dates back to 1889 (Lescoeur), the isoteniscope (Smith and Menzies, 1910), and the sulphur valve (Bodenstein, 1908). The light-absorption cell for metal vapours is a relative newcomer (1929) but complications involved in this method have not been wholly overcome. (For details of these methods, see ref. 27, for instance.) At present most widely used are the so-called effusion methods in the forms devised by Knudsen, Langmuir and Volmer, respectively. Again. no details of the methods will be presented here because they are well known among physico-chemists. Recent achievements mostly concern an increase of the operating temperature. Measurements on chromium alloys using a Knudsen technique combined with a tracer method have been made at temperatures up to 1500°C. (35) A torsion-effusion cell has even been operated at temperatures above 2000°C for the determination of vapour pressures of refractory oxides by Alcock and Peleg.~ a6) An effusion method employing a capillary for the determination of vapour or reaction pressures by comparing them with a known equilibrium pressure was devised by Gross.(aT) For instance, values for the free energy of formation of aluminium monofluoride were obtained by comparing the known pressure of lead as standard with that of the reaction 2 {A1} -k (A1Fa) -3(A1F), both the lead and the reaction mixture being enclosed in the reaction vessel bearing the tube. Although this method was described 20 years ago, it has received less attention than it deserves. Ten to fifteen years ago, the mass spectrometer had not been applied to systematic measurements of vapour pressures. Nowadays it is hardly possible to visit a meeting on high-temperature chemistry without seeing at least one slide on which the familiar mass spectrometer is sketched. This apparatus offers, of course, a valuable method for the identification of the species in a complex vapour. The molecules or atoms are ionized with a well defined electron beam and the resulting ions are analysed for charge to mass ratio by electric and magnetic field deflection or by electric field acceleration and time of flight measurements over a fixed trajectory. The power of

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the method lies in its ability to make the measurement of several vapour species possible in the same experiment. Accurate vapour pressures can only be obtained from the measured ion currents when ionization cross section and detection efficiency are available, otherwise the apparatus is best used for obtaining relative vapour pressures. (For pertinent literature, see refs. 38 and 39.) The conventional methods for the determination of the chemical potential of oxygen in metal/oxide systems involve the equilibrium with HzO/H2 or CO2/CO mixtures. Much important work of this kind was done by investigators such as J. Chipman, who mostly dealt with ferrous metals and iron alloys. However, the method is restricted to metals of moderately low affinity for oxygen, mainly because it is very difficult to have experimental systems reasonably free of water vapour. The EMF method employing solid oxide electrolytes at its present stage of development somewhat extends the range of application of the gaseous equilibration methods. Komarek,t4°) stimulated by work of one of the present authors, equilibrated solutions of oxygen in metals for which it has a high affinity with magnesium oxide and magnesium vapour, according to the chemical equation, e.g., (MgO) = (Mg) + [O]Tl. Using tubes made of titanium and varying the pressure of magnesium, he was able to determine the free energy of solution of oxygen in titanium, zirconium and hafnium. Summarizing, we have the following major methods for the determination of the dissociation pressures in oxide systems in terms of calories per mole O2 at, say, 1000°C: Method

Direct dissociation H~O/H~and COs/CO equilibria EMF (solid oxideelectrolytes) Equilibration with Mg/MgO

A(~o,, kcal 0--40 20-I 30 25-150 200--240

There is an obvious gap between 150 and 200 kcal/mole 02. It is possible that the EMF method may carry us somewhat beyond the 150 kcal limit. There is also a small advantage to be gained by choosing different temperatures. Probably the gap will be closed by working on ternary systems and extrapolating into the binaries. Work that is being undertaken by E. Fromm at the Max Planck Institut at Stuttgart on the system tantalum-oxygen-carbon appears to be such an example. The dependence of the CO equilibrium pressure over tantalum on the content of dissolved oxygen and carbon is being determined at 1700-2000°C. The dependence of the oxygen activity on carbon concentration can thus be calculated and may be extrapolated to zero carbon concentration.

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There is much scope for the improvement of experimental methods for the determination of oxygen potentials. However, the position with the nitrides, carbides and borides is even less satisfactory. The conventional methods for the nitrides and carbides are the equilibration with NH3/H2 and CH4/H2 mixtures, respectively. Owing to the relatively low stability of ammonia and methane, only low-affinity systems can be studied, but not systems such as titanium-nitrogen, thorium-nitrogen and zirconium-carbon. In the case of nitrides and nitrogen solutions, ultra-high vacuum techniques, that are now feasible, considerably assist with the experimental development. Griffiths and Pryde,t41) for instance, have recently measured the dissociation pressures of tantalum-nitrogen solid solutions in the temperature-pressure-concentration ranges 10-s to 10-3 torr, 1600-2300°K 0.0044 to 1 at. Yo N, respectively. There are a number of other equilibrium methods of less wide application which will, however, not be enumerated here. There is one method, however, of which the present authors make frequent use and which may be mentioned: phase boundaries in metallurgical equilibrium diagrams actually represent thermochemical information. Where these are really reliable and accurate, they may be incorporated in thermochemical evaluations, for instance, for the calculation of a solidus-liquidus gap, by adjusting the thermochemical data of the liquid and/or solid solutions so that the experimental liquidus curve is exactly reproduced, and subsequently calculating the solidus curve with the adjusted values. The present authors would almost invariably prefer such a calculated solidus curve to an experimental one. 2.3.

M a g n e t i c R e s o n a n c e Spectroscopy

Although of not such wide application as thermochemical experimental methods already described, much information about the nature of the bonding in intermetallic alloy systems has come from magnetic resonance spectroscopy, particularly nuclear magnetic resonance, despite earlier fears of restricted usefulness owing to quadrupole broadening (although the clearest information is still obtained in systems with nuclei of spin ½, i.e. absence of quadrupole moment). This topic has recently been reviewed.~42) The most common experimental parameter measured is the Knight shift which is defined, K = (v,n -- Vr)/vr,

where Vm and vr are the resonant frequencies of the nucleus in question in a metallic system and non-metallic standard reference compound respectively. With this experimental approach, for example, electron transfer on the addition of Au to Pt, filling the d band, has been studied.Ca3) Useful information on diffusion processes has also been obtained using n.m.r, spectroscopy--for instance study of the proton resonance in TiH~-x shows the dependence of hydrogen diffusion rate on vacancy concentration

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directly344~ It has also been suggested that the use of pulsed field gradients with spin echo techniques would allow n.m.r, measurement of diffusion to be made at higher temperatures and on larger samples, which would greatly enhance the value of the method. The utility of spectroscopic techniques such as those mentioned is in the direct study of bonding interactions of nuclei in the solid or liquid state. 3.

FUNDAMENTALEQUATIONS

It will hardly be necessary to describe the fundamental laws of thermodynamics in a progress report, but the more important equations that are in constant use may be set down for further reference. The Gibbs-Helmholtz equation may be written for chemical reactions as AG °

=

(1)

AH ° -- TAS °

where the superscript indicates standard thermodynamic functions relating their changes to the elements in their natural state of aggregation at 25°C gases at 1 atm pressure. The standard free energy at temperature T is related to the mass action constant, K~, by AG~

=

-- RT

In Kp = -- 4.574 T log K~

(2)

It follows from equation (1) that heats and entropies of reaction may be obtained from free energy measurements at two temperatures or more. However, in the experience of the authors, the temperature coefficients in free energy measurements on reactions involving solid phases are rather unreliable, and in the preceding chapter as much emphasis was therefore placed on calorimetric methods as on free energy methods. The independent determination of entropies will be discussed below. Disregarding for the moment the temperature dependence of AH and AS, the connections between partial and integral thermodynamic functions may first be written down, the former being denoted by a bar, AJ = N A ~

+ NBAJ~ + . . .

(3)

where J = H, S, G and NA, N B . . . denote the atomic fractions of the constituents A, B . . . Free energy measurements are by nature determinations of partial functions whereas calorimetric measurements mostly produce integral values. In multi-component systems, the partial free energy of only one component can, as a rule, be determined accurately. In this case a Duhem-Margules integration must be invoked for a full evaluation. For a binary system, this may be written as follows: NA =

I A/A

dNx

(f =

H,

S, G;

NA

+ NB = 1)

(4)

o

The partial quantities for component B can then be obtained by means of equation (3).

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It may be seen from equation (4) that, for the integration to be reliable, measurements of A?/A must be made down to low concentrations of A. This is a constant source of worry because such measurements are difficult. The change in heat content with temperature is given by Kirchhoff's equation, T: t~

Hrl -- H r 2 -= I CvdT

(5)

T~

where Cv is the heat capacity; and for the entropy, correspondingly, T2

Srl -- ST 2 =

-~ dT

(6)

TI

Where phase transitions occur, the heats and entropies of transformation, fusion and/or vaporization must be introduced. Heat capacities of substances of metallurgical interest may be represented by empirical equations of the type,

Cv = a + f l T - 4 - ~ T

2 + 8T -2

(7)

where a, fl, y and a are constants, but often two or three of these suffice to describe the measured results within the experimental accuracy. For condensed reactions, Neumann-Kopp's rule which states that heat capacities are additive is usually assumed to apply. As more good C~ measurements, on alloy systems for instance, become available, the more the validity of Neumann-Kopp's rule is being challenged, but a systematic survey would be premature. In particular, the accuracies achieved by differentiating heat content curves (drop calorimetry, p. 7) are not high enough for the assessment of partial heat capacities, AC~, which are required for refining the equations involving partial heats and entropies. Where such data are required, as in the evaluation of the thermochemical properties of the UO2+x phase,~ 45) A~ v is still taken to be independent of composition. According to equations (5) and (6), the total energies and entropies of a substance are as follows: T s,,

l i t = I CvdT + Ho

(8)

d

0 T

(9) 0

Although theoretical physicists are devoting much thought to a derivation of the internal energy at absolute zero from first principles (e.g. ref. 8), the

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day when it will be feasible to estimate energies accurately from first principles alone is still a long way off. On the other hand, owing to the efforts of Nernst and his school, more can be said about the entropy. In the formulation of Planck, the entropy of a crystalline, ordered substance in equilibrium at zero degrees is zero, so that, T

ST = I C~TdT

(10)

0

A special chapter may be devoted to the entropy in metallurgical systems. 4.

ENTROPY

Undoubtedly, the Third Law of Thermodynamics, represented by equation (10), applies to a large number of inorganic substances, such as pure metals and strongly ionic or covalent compounds, within the limits of experimental accuracy. However, metallurgists predominantly deal with solid solutions or phases of wide homogeneity ranges (e.g. Fig. 6, p. 31). It is true, disordered compositions are not expected to persist in equilibrium near absolute zero. In practice, however, equilibria are 'frozen in' at much higher temperatures, and it is doubtful whether perfect atomic order is often attained in such phases. There is a growing suspicion among metallurgical thermochemists that the usefulness of the Third Law is restricted. A case in point is the titanium monoxide phase. Gillest 4e) has scrutinized the experimental evidence supplied mostly by Kelley, Komarek and Kubaschewski, and found discrepancies which could only be resolved if changes were made in the heat of formation of TiO (of the order of 10 kcal/mole) or 6 to 8 e.u. were added to the standard entropy. The present authors believe that the discrepancies are predominantly due to a significant zero-point entropy owing to frozen-in equilibrium. It would appear that a systematic investigation of the limitations of the applicability of the Third Law to metallurgical phases would be an important subject of thermochemical research. Co-operation of several laboratories, each specialized in a certain type of thermochemical measurement, may be envisaged, typical phases and compositions being agreed upon. The uncertainties in the applicability of equation (10) are the reason for the fact that methods for only the heats and free energies of reaction were discussed in the experimental chapter of the present article, whereas measurements of heat capacities at low temperatures were disregarded. Also, the thermochemical methods in the present authors' laboratory are confined to measurements of heat and free energy, and heat capacity at relatively high temperatures. 'Compounds' derive their stability mainly from their heat of formation. In contrast, ideal solutions derive it from the positional entropy. An 'ideal

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solution' is, by definition, one with a zero heat of mixing and solely positional entropy of mixing: A H °, A/-I°A, A H ° B = 0

A~A = -- R In NA; A~B = -- R In NB

(11)

and hence, according to equation (3), ASmtxing = -- R(NA In NA ÷ NB In NB).

(12)

Few metallic systems, however, are ideal. Only where the atomic sizes are very similar and the chemical nature of the component metals closely related would one expect near ideal behaviour. Mixtures of rare earth metals fall into this category. This has been confirmed within the experimental errors for the Pr-Nd system by measurements of heat, free energy and density by Lundin et al.(aT) Calculations of the solidus-liquidus gaps in the systems Mo-WI 4s) and Hf-Zrt 49) based on the assumption that both the liquid and the solid solutions are ideal showed reasonably good agreement with the results of thermal determinations of the solidus and liquidus curves. Niobium and tantalum presumably also form nearly ideal solutions in the solid and liquid states. HayestS0) measured the heat of mixing of solid nickel and cobalt and found it to be very small. These binary systems, with the possible addition of Ir-Pt and Rh-Pd, are almost all in the field of metallurgy that may be expected to be ideal within the experimental errors. Hypothetical systems, the entropy of mixing of which derives entirely from the positional entropy (equations 11 and 12) but which have a finite heat of mixing expressed by a parabola, AH = const.NxNs, are denoted 'regular systems'. When Weibke and Kubaschewski in the early forties compiled the then known thermodynamic data of alloy systems and presented them in a book entitled Thermochemie der Legierungen, they identified the excess free energies, AGA xs ~--- AGAxptl - -

RTIn N A ; A~Bxs : A~Bxptl - - RTIn NB

AGxs : AGxptl -- RT(Na In NA + NB In NB),

(13)

with the heats of mixing. As more accurate values for the entropies of mixing became available, it was recognized that appreciable deviations from the regular solution model are the rule rather than the exception. These deviations may be expressed by the so-called excess entropy: A~A xa = A~A xptl + R In NA; ASB~ = ASh xptx q- R In NB

AS xs = AS xpu + R(NA In NA + NB In NB).

(14)

In Fig. 1 are shown the integral excess entropies vs. concentrations in a few liquid metal systems. A more extensive survey of the maximum integral excess entropies and maximum heats of mixing of binary solid and liquid solutions in systems of complete mutual solubility is presented in Table 1. The data have been

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taken from the most reliable in the two available compilations of the thermodynamic properties of alloyst51,52) supplemented by new assessments of published results from the current literature. The same data are plotted in Fig. 2.(TM In this diagram the regular solutions would be represented by the line at ASX~x = zero. Instead, one finds an inclined straight line passing through the value for ideal solutions. This is represented by:

(15)

ASXa~x = 0"64 AHraax/½(Tel -t- Tee)

where Tel and Te2 are the absolute boiling points of the component metals. It may be seen from Table 1 that the systems considered are of apparently quite different bond mechanisms. Nevertheless, they all seem to fall into a single pattern, indicating that the fundamental causes for the values of the excess functions are similar, and that interpretations of one must also account for the other. That a system exhibiting a finite heat of mixing must also have a finite excess entropy has been pointed out before [e.g. Rushbrooke (54)] but equation (15) is purely empirical. A similar relationship seems to exist between the excess volumes and the heats of alloying. However, the known values for the volume changes on mixing are rather inaccurate, for experimental reasons.

0-5 A B o

tr -o.5

-I.0

m =Sn,Bi,Pb, Tn or M g -~.5

I

i

I

I

o.L

0.2

o.s

0.4

I

I

I

I

I

0.5 "

0-6

07

o.e

0-9

i.o

Nm FIG. ]. Excess entropies of mixing in various liquid systems. A, Au-Pb; B, Ag-Bi; C, Cd-ln; D, Pb-Sn; E, Na-Pb: F, Cu-Mg; (3, Na-Sn.

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TABLE 1 Maximum Excess Entropies and Maximum Heats of Mixing of Binary Solutions per g-atom (Tel, Tee = normal boiling points of component metals) System

ASXSmax/R

N2

AHmax/

N2

½R(Tel + Te2) Liquid Solutions Na-Hg K-Hg Na-Sn Mg-Bi Fe-Si Na-Pb Na-TI Mg-Sn Mg-Pb Mg-Cd Mg-Cu Mg-Zn Mg-AI Cu-Zn Ag-Au Cd-Hg TI-Pb Zn-Hg Cd-Sb Sn-Sb TI-Sn Hg-Pb Hg-TI Hg-In Zn-Sb TI-Bi Sn-Bi Hg-Sn Pb-Sn Zn-Cd Cd-Ga Pb-Bi K-Na Pb-Sb In-Sb In-Pb Cd-In Cd-Pb Cd-TI In-Sn TI-Sb Zn--Ga Cd-Sn Ag-Cu Zn-Al Zn-In Cd-Bi Ag-Bi AI-Sn Au-TI Zn-Bi

--2"63 --

1"96

--1-17 (--1"12) --1-11 --0-92 --0'41 --0"41 --0"38 --0"38 --0"35 --0"30 (--0"25) (--0"19) -0-17 --0"135 --0"105 --0.09 --0'09 --0'085 --0'085 --0"08 --0'07 - - 0"06 --

0"05

--0-045 --0"04 --0'04 0"0 +0"02 +0-01 +0-025 +0-03 +0"05 +0-07 + 0"07 +0"07 +0"11 +0"12 +0"125 (+0.125) +0-125 +0.14 +0.14 +0"15 +0"15 +0-19 +0-195 +0-23 +0"26 +0"26

0'6 0"47 0-44 0"3 0.33 0-35 0-55 0"38 0-48 0"48 0"55 0"5 0"5 0-5 0"46 0'5 0'5 0'38 0'41 0-4 0"35 0.38 0'48 0'48 0'4 0'4 0'2

0'5 0-6 0"33 0.48 0'58 0'46 0'35 0.4 0.40 0'61 0'45 +0"11 0'33 0"51 0"48 0"35 0"55 0"48 0'55 0-5

--3"75 3.19 - - 1 "25 (-- 1"45) --1"36 --1'31 --0"935 --0"81 --0-68 --0"725 --0"57 --0"555 --0"22) (--0"45) --0"20 --0'39 --0"10 +0'055 --0"26 --0"105 +0"035 +0"055 --0"105 --0-185 --0-265 --0"295 +0'005 +0"06 +0'07 +0"22 +0'18 - - 0"065 +0"085 --0"02 --0'16 +0"05

+0.10 +0.22 +0"20 --0"01 (-0'12) +0"105 +fill +0.19 +0"16 +0'22 +0-075 +0"115 +0"175

0"59 0'56 0"44 0"4 0"39 0"5 0"4 0"38 0"48 0"51 0"66 0"5 0"5 0"47 0"47 0"43 0-65 0'47 0.44 0.57 0"29 0.42 0,48 0'48 0'47 0"5 0'38 0"47 0'48 0'48 0-5 0.57 0.67 0'45 0"5 0'46 O'47 0.44 0'33 0'39 0"45 0"45 0"44 0"48 0"45 0-3 0"65 0"45

(0.0) +0.365

0"42

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TABLE 1 .--continued

System

ASXSmsx/R

N2

AHmax/

N2

½R(Tel + Te2) Zn-Zn

Au-Pb Ag-Pb Zn-Pb

+0'28 +0-31 +0"215 +0"36

0-45 0-33 0"53 0'35

+0'20 (0"0) +0"19 +0"58

0"43 0-75 0"52 0"43

+0'32 +0'23 +0.09 --0.02 --0"125 --0.14 --0"17 --0.18

0.47 0"46 0-42 0"6 0-76 0"4 0"5 0-43

+0"25 +0"22 +0'22 --0'22 --0'15 +0"07 -0-20 -0.55

0"50 0"48 0"5 0'57 0"75 0"67 0'47 0'48

Solid Solutions

Cr-Fe Cr-Mo Au-Ni Au-Cu Fe-Ni Cu-Ni Ag-Au Mg-Cd

The excess entropies of mixing of the solutions listed in Table 1 are known with an estimated accuracy of 4- 0.2 e.u./g-atom, and it is therefore difficult to locate the position of the m a x i m u m or minimum in terms of concentration. One can say, however, that the experimental data are consistent with the assumption that the maxima or minima in the A H and AS xs curves occur at the same composition in a particular system. If this is correct, then it is possible to estimate maximum excess entropies from free-energy measurements alone. It follows from equation (15) that the excess free energies are related to the excess entropies in the following manner : - -

6Gm~_~x ASx]x =

0"78(Tel + Tee) -- Tobs

(16)

where Tobs is the absolute temperature at which the free energy has been measured. The present authors use equations (15) and (16) rather than the regular solution model for the estimation of the heats of mixing from experimental free energies in systems formed by metals with metals or meta-metals. The regular solution model retains its usefulness, within the present experimental accuracy, for the description of dilute solutions. Henry's Law may be represented by an equation of the form, AGA = AR~, + R T I n NA - - A~AsT,

(17)

when a metal A is dissolved in another metal. In such cases the excess entropy term is usually small. When diatomic gases, X2, are dissolved in metals, Henry's Law assumes the form of Sieverts' Law: Adx2 = A//x, + 2 R T l n N x - - AS~:S,T.

(18)

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This equation implies that the gas, Xz, dissociates on solution and that its atoms or ions are randomly distributed in the lattice.t Generally, equations (17) and (18) represent the experimental data well up to a few atomic percent, but clustering in the form of pairs, triplets, etc., of gases in metals cannot be ruled out [e.g. Wert( ss)]. More accurate measurements of the thermodynamic properties as well as the structure of interstitial solutions are obviously called for.

o.5

x ~x~

×,x)?(" ~-

x/X/

-

-0-5 ~_~ "" - i.o

X ('IX X

-Iq

- 2.(

-2.5 I -3-5

I -3"0

I -2"5

I -2"0

I -I-5

I -I'0

I 0"5

] 0

I 0-5

AHmo, '/zR (TE +TEz)

FIG. 2. Plot of maximum or minimum heats vs. excess entropies of mixing of solid and liquid solutions. The advantage of equations (17) and (18) is that the constants can be determined by means of a few experimental measurements and the equations then used at any composition in the range of higher dilution. When only the solubility is known for a gas or a metal in a metal in equilibrium with a compound, the free energy of which is also known, the constants in equations (17) or (18) can be obtained since the partial free energies in the heterogeneous range between the saturated solution and the compound are independent of composition. The thermochemical data for quite a number of solutions in metals can be obtained in this manner.(56) Similarly, when a higher compound, a higher oxide for instance, is in equilibrium with a lower oxide or a saturated solution in the metal, the concentration dependence of the free energy in the higher compound can be estimated in certain cases. This is important in oxidation theory. When

t For interstitial solutions, the positional term assumes the form 2RT ln[Nx/(1 -- zNx)] where z is a number between 1 and 6 depending on the atomic model but it may be seen that, with increasing dilution, this term approaches the one in equation (18).

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C. Wagner developed a mechanism of diffusion-controlled oxidation across uniform and coherent oxide layers, he assumed validity of the ideal mass action law with respect to the point defects in the oxide lattice. Recent work, employing C0/C02 equilibria, by Kofstad, confirmed this to some extent for oxides such as Nb2Os-x,(57) TiO2-x,(5s) etc. In these oxides, the defects probably consist of oxygen ion vacancies, and the reaction may be described by the following chemical equation: (02) + 2 0 0 = + 4 e- -----zero

(19)

where []O= denotes oxygen ion vacancies and e- excess electrons. Applying the ideal mass action law (e = concentration), Po2 x e9'oo = × ~ - =

constant,

and, since Ce- ---- 2 Crao=, PO2 -1/6 ~--- C X c o o =

(20)

where C ( = constant1/6 x 2-2/3) is a constant. Kofstad has indeed shown that the vacancy concentration in Nb2Os-x and TiO2-x is essentially proportional to Po2-1/6 where Po2 is the oxygen dissociation pressure. The corresponding free-energy equation at a given temperature, T, is: AGo2 = A + 6 x 4.574Tlog Coo= Introducing an excess entropy term to account for the temperature dependence, we may write corresponding to equation (18), AGo2 = ~X/~o2 + 27"45Tlog N n o = -- AS xs T.

(21)

In the case of Nb~O5_x,(57) for instance, AGo2 = 213,800 + 27.45Tlog Coo= -- 30.5T These equations are undoubtedly oversimplifications, in particular when stoichiometry is approached, as has been pointed out by Kofstad. Equation (21) implies that stoichiometry can only be reached at infinitely high oxygen pressure [so as a pure metal can only be obtained at infinitely low gas pressure, according to equation (18)]. The problem in obtaining really accurate experimental results lies in the excessive demands that are made on chemical analysis, in these eases. This problem is also paramount when one deals experimentally with the thermochemical properties of intermediate phases with both appreciable deviations from stoichiometry and tendency to order at one composition. Schottky and Wagner have discussed the concentration dependence of the partial entropy of solution in such phases and ~)lander(59) has applied the concept to some experimentally relatively simple eases, such as 'AuCd', 'AgCd' and 'CuZn' which phases exhibit rather wide homogeneity ranges. Using only positional entropy terms, Olander derived the ASI vs. Ni curves for a component i in a homogenous phase with tendency to order at Nl = 0"5

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for various degrees of disorder,'~ shown in Fig. 3. The line denoted ov would apply if the atomic distribution remained completely disordered throughout the homogeneity range. If, at a critical composition, complete ordering were to occur, Ag should show a "jump" from -- oo to + oo. With partial ordering, S-shaped curves result, as shown in the diagram, the height depending on the degree of order. Olander obtained partial entropies in the phases mentioned from the temperature coefficients of EMF measurements, and by comparing the results with the theoretical curves in Fig. 3 was able to estimate the degree of order at composition 1 : 1.

10-5~ -

O ~ 10-5 . I 0"42

I

I 0'46

I

~1 0'50

I

.

. I

0-54

. .1

I 0"58

Ni FIG. 3. Effect of atomic order on the partial entropy in homogeneous alloy phases after Olander. Figures in the diagram indicate the degree of order.

For a long time, these considerations have been disregarded because direct measurements of partial entropies and heats are very difficult to carry out whereas their evaluation from the temperature coefficients of free energy data is unreliable (see p. 15). However, when free energy measurements on the UO2+x phase were discussed more recently at a panel meeting of the I.A.E.A. in Vienna,(4) it became evident that some such phenomenon applies near the composition UO2.000. Gerdanian and Dod6(m have now succeeded in applying their sensitive Calvet calorimeter to the measurement of partial heats of solution of oxygen in UO~+x at 800 and 1100°C. With reference to Fig. 3, the ARo2 vs. No curves should show similar shapes to the Ago2 curves, otherwise instability would result. The rather important findings of t Degree of disorder = ratio of the number of all the misplaced number of lattice sites.

atoms

to the total

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Gerdanian and Dod6 are reproduced in Fig. 4. Since UOz.00 is the lowest limit of stability at 1000°C, the A/7o2 curve represents only half of the Sshaped curve expected. Nevertheless, it is obvious that the shape of the curve in Fig. 4 is due to partial ordering around the composition UO2.00 and considerable disorder at higher values of x, borne out by X-ray studies.t4) In order to deal with this type of phase, far more accurate measurements of heats and entropies must be demanded, as was pointed out in the experimental section of the present article. 200

I00

In: <~ ~

,,, ~

._._..___ ~ , ~ , m

-- - - - - ' - ' ~

"----

~Q

"....." I 000

2.005

I

I

2.010

2-Olfi

I 7'.020

O/U

FIG. 4. Partial molar heat of solution of oxygen in the UO~+x phase after Gerdanian and Dod6.

This is further illustrated by Fig. 5 in which the partial entropies of solution of oxygen in the UO2+x phase are plotted against composition. On the one hand the heats of solution of Gerdanian and Dod6t 12) have been combined with the free energies obtained by Markin and Boneste°) (EMF measurements, 650-1000°C) and Hagemark ~61) (CO/CO2 equilibria, 1100-1400°C), respectively. On the other hand, the A$o2-No curves calculated from the temperature coefficients of the AGo2 data are also drawn. It seems unlikely that the evaluation of the temperature coefficients could ever achieve the required accuracy, in view of the small differences in concentration involved. There are various empirical methods for the estimation of the standard entropies of phases of narrow homogeneity ranges. For predominantly ionic compounds, Latimer's tables (see ref. 27), based on ionic mass, size

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and charge, are still the best method for reasonably good estimates. Similar, later, attempts have not improved on them. For the entropy of formation of transition metal carbides, Worrell(62) suggested the following relationship: ASz9s = -- 6"0 + 6"0(~M/Oc) [e.u. per g-atom C] where ~ and Oc are the melting points of the metal and the carbide, respectively, in °C. The standard entropies of ordered intermetallic compounds may be taken additively from those of their solid components. When more such data become available for comparisons, one may improve on this cursory method of estimation. Johnson/63> for instance, has reviewed the thermochemical data of the alloy phases of Pu, Th and U with other metals and has suggested an empirical relation for predicting the entropy of formation of these compounds. 60

5C

•-----o-,-- Gerdanian ( A ~ ) and Markin ( ' ~ ) ---x--...... ....

Gerdanion (Z~H) ond Hogemork (Z~i~) Hogernork (d /XG/d T) Morkinond and Bones (d A G / d T )

40

3O

m

20

I0

2.000

z.oo~

2.oto

2-015

2-o2o

Flo. 5. Partial m o l a r entropy o f solution of oxygen in the UO2+x phase.

Those who require standard entropies for special phases should not servilely rely on tabulated, estimated, data but try to improve on them by comparisons with recently measured values on similar substances. 5.

EXPERIMENTALDATA

The annual output of thermochemical data pertaining to metals has appreciably increased during recent years and their accuracy, in general, improved.

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In the field of alloys, earlier systematic work was mostly confined to metals with relatively low melting points ( < 1100°C) with a natural preference for the more noble metals. Iron alloys have also received considerable attention from the thermochemists, mainly perhaps because the iron and steel industry has for some time shown a remarkable interest in fundamental research. More recently, the demands made by reactor technology as well as the development of high temperature materials have stimulated much thermochemical work on metals and alloys employed in these fields. Experimental data on alloys of the metals Th, U, Pu, Ti, Zr, Hf, Nb, Ta, Mo, and W have just been reviewed and tabulated by one of the authors. (64) Alloy systems that have been investigated thermochemically to-date will be summarized later (Table 2) whilst a number of recent investigations in addition to those mentioned in report(64) may be indicated as follows. The heats of formation of liquid alkali metal alloys have been determined in a new low-temperature calorimeter,(65) those of liquid antimony with In, T1, Sn and Pb by Wittig's well tried method.(66) Liquid-tin solution calorimetry has been employed for the study of the phases Mg2Ge, MgzSn, Mg~Pb(67) and MgAg,(6s) the solid solutions Pd-Au,(69) Pt-Co, Pt-Cu, Pd-Cu and Pd-Ag(7°) and the liquid solutions Au-Sn; (71) liquid-copper calorimetry for solid and/or liquid Cu-Ni, Cu-Co, Cu-Ag and Cu-Sn. (2°,7z) The 'little furnace calorimeter' (p. 6) was used to measure the heats of formation in the Pd-A1 and Au-AI systems, (78) and the Calvet-Tian calorimeter those of the gallium-indium alloys.(74) EMF measurements employing solid electrolysis for the study of alloy systems have been quite popular. The following systems are examples: Au-Ni, (75) Fe-Pt, (76) Ni-Pd, (77,7a) Co-Pt, (79) Co-Pd, Ni-Pt, (Ts) Mo-Co, CoNb,( s°l Ni-Pb,(sl) Pd-Pb and Pt-Pb.(s2) Liquid halide electrolytes have been employed for several systems, such as Na-Ga, (8z) Na-TI(8a) Mg-In~s5) and Mg-Zn, (s6) Ce and Er in various low-melting-point metals,(sT) Mn-Cu,(s8) Ag-In, Ag-Sn and Ag- Sb,(89) In-Sb, In-Bi(9°) and A1-Ge.(91) Both the dew-point and Knudsen methods were used to study liquid and solid Ca-Zn alloys,(92) the Knudsen technique alone for solid systems, such as Th-Pb(98) and Cr-Ti,(9a) and the torsion-effusion method for V-Cr and Fe-V.(95) The transpiration method was applied to the liquid systems Na-Bi, (96)Li-Mg and Mg-Ca,~97) the dew-point method to Y-Zn, Sm-Zn~9s) and Ni-Cd,(99) an improved isopiestic method to Mg-Ge, Mg-Si, Mg-Sn, MgPb (1°°) and Fe-AI,(101) and finally, the mass spectrometer to liquid alloys in the systems Ni-Fe and Co-Fe.(102) In view of the potential application of thermodynamic principles to ternary and multicomponent systems, any systematic study of such systems is of interest. Recent investigations include free-energy measurements in the systems Mn-Fe-Ni,(~03) Ni-Cr-Al,(xoa) Mn-Pb-Bi(105) and some low-meltingpoint alloys [Sn-Zn-Bi, Zn-In-Bi, Sn-Zn-In, Zn-In-Ga], (1°6,1°7) and measurements of heats of formation in Ti-V-A1 and Ti-Ni-A1. (1°8) Numerical information on the thermochemical properties of gases in

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metals has just been summarized by Kubaschewski.<56) This tabulation mostly pertains to solutions of hydrogen in metals. Some additional information on the systems Ce-H2,t 1°9) V-H2,(tl°, t~t) Ta_H2(n2)and Ag-Pd-H2<~za) is available. The known thermochemical data for oxygen and nitrogen have also been summarized<56~including the results of Komarek on high-affinity solutions,(40) mentioned earlier, and those of Pemsler<114) obtained near the melting points of niobium and tantalum. For the determination of nitrogen in such solutions (e.g. Nb-1% Zr + [N]) at somewhat lower temperatures, ultrahigh vacuum techniques must be employed.
o

z5

50 at.% O

75

0

z5

Uncertain Liquid syslem

50 75 at.%N

0

25

5o at.%C

75

ioo

FIG. 6. E x t e n t o f the h o m o g e n e o u s phase fields in systems of t r a n s i t i o n metals w i t h oxygen, n i t r o g e n a n d carbon, respectively, at a t e m p e r a t u r e of a b o u t 10001200°C a n d a pressure 1 a t m.

ranges at 1000-1200°C is indicated for oxides, nitrides and carbides.(117) We know very little of the concentration dependence of the oxygen potentials within these ranges. The UOa+x phase is one that has been more thoroughly investigated (see Figs. 4 and 5). Repeated attempts have been made to assess the thermodynamic properties of the titanium-oxygen system (e.g. ref. 117). Even so, as has been pointed out by Gilles and mentioned earlier, substantial uncertainties remain.t4e) The work of Kofstad<5s) on the properties of the

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TiOz-x phase has been mentioned and reference to similar work by others may be added.OlS) Equilibrium measurements on the ZrOz-x phase by Aronsontng~ require confirmation. Kofstad has also studied the NbzOs-x phase tS~ but results by Sch~ifertl~O~indicate that the phase relationships in the range Nb204-NbzO5 are more complicated than hitherto assumed. Morozova and EgertX~l~have determined the heats of combustion across the vanadiumoxygen system in rather small steps of composition, but even so a more sensitive method yielding near-partial heats of dissociation would be preferable. Quite a large number of individual, scattered, thermodynamic measurements on transition metal oxides have been made during the past ten years or so, but a unifying assessment is still absent. Even then, it will be found that far more work is to be done. The metal sulphides correspond in their thermochemical properties to the oxides although the heats of formation are proportionally lower. Published experimental measurements are fewer, and the early systematic work of W. Biltz still retains some of its significance. Detailed investigations of the ferrous chalcogenides are under way at Oslo University under the direction of F. GrSnvold in collaboration with E. Westrum of the University of Michigan. The activities of sulphur in liquid iron, cobalt and nickel and their alloys have been studied by Alcock and Cheng.tlz2~ Individual investigations of heterogeneous equilibria using H2S/H2 mixtures are being made, such as those in the ranges 'Cr'-'CrS', 'Mo'-'Mo2Sa' and 'W'-'WS~'312a) Hager and Elliottt12a) have estimated the standard entropies of a number of transition metal sulphides at various compositions. Good recent work on metal nitrides is also scarce, particularly in the nonstoichiometric regions. Some thermochemical work on solutions of nitrogen in metals has already been mentioned. Two references on heterogenous equilibria in the Th-ThN (124)and VNo.52 -- VNo.7(125)ranges may be added.The main reason for the scarcity of reliable results is the lack of adequate experimental methods for high-affinity nitrides, other than ultrahigh vacuum methods. With regard to metal phosphides, again the early systematic work of Biltz pertaining to the higher transition metal phosphides may be mentioned. Present systematic investigations, including non-stoichiometrie, high-affinity, phases, are being carried out by Gingerich [e.g. ThPl_x(126)] whose massspectrometric and other work also reveals the considerable experimental difficulties. Thermochemical data for transition metal carbides have been measured and summarized by Worrell and Chipman.tl2V~ Gurevichtl~S) made a special survey of vanadium carbides and Alekseyev and Shvartsmant129) studied the tungsten-carbon system. Only results for the heterogenous regions are given in these papers. Few reliable data are available for the important nonstoichiometric regions. Heats of combustion have been carefully measured in the niobium-carbontla0,1al) and tantalum-carbont132) systems, while a comprehensive evaluation of the solid Nb-C system is now possible.tXaa~ Some work on metal silicides,"mostly heat contents and heats of combustion

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determined by Russian authors [e.g. Mn silicidestla4)], has recently been published. Except for the Fe-Si and U-Si systems, however, considerably more thermochemical work need s to be done before full evaluations can be made. The thermochemistry of silicates and glasses is still in a backward state, mainly because of the scarcity of reliable methods (p. 7). Systematic work by Kleppa with a liquid-oxide solution calorimetert23) has been mentioned. This work continues but the field is so wide that more laboratories should join the effort. Existing data for these systems have recently been gathered together in an internally published report.t 135) By reacting alkali and alkaline earth metal carbonates with TiOa and ZrO2, respectively, in a bomb calorimeter, Feodos'ev, L'vova and Panfilov~lae,laT) obtained the heats of formation of the titanates and zirconates from the respective oxides. Very little is known about the thermochemistry of metal borides. Some recent thermochemical work may be quoted.tlaa) Metal halides are now well covered but will not be included in this survey, More investigations of fluorides and iodides still have to be done, and the thermochemistry of gaseous sub-halides also requires further work. In view of the purification of reactor fuels by molten salts, attention has recently been focused on the thermochemical properties of fused salts and salt mixtures. A review paper by Kleppaaag) may be perused for reference, and Lumsdena40) has devoted a recent monograph to the discussion of the thermodynamic background. Sufficient numerical material on salt mixtures has now accumulated for a critical compilation in the form available for alloystS~,52) to be justifiable and highly desirable, 5.1.

Critical Compilations ~141~

Since the experimental results are scattered throughout the scientific literature, it is very difficult for the individual user to obtain even a moderate supply of consistent and reliable information pertaining to his own range of interest. It is thus that the critical compilation and evaluation of physicochemical data has developed into a new field of scientific research. The thermodynamic properties lend themselves to a critical examination because of the variety of independent methods available for the assessment of the values of the three main functions and therefore the possibility of checking and counterchecking. An example will be described later. Such monumental works as the Landolt-Brrnstein and the International Critical Tables in their sections on chemical thermodynamics were not really critical as we understand it now. The first truly critical and consistent assessments of thermochemical data on a large scale were those by K. K. Kelley, entitled Contributions to the Data on Theoretical Metallurgy and Bichowsky and Rossini's Thermochemistry of the Chemical Substances. Both these works, published over thirty years ago, were pioneering landmarks in critical thermochemical data assessment and have pointed the way for successors. In the late forties, Brewer t2°7) compiled a comprehensive set of thermochemical data for the elements, their halides and chalcogenides, ingeniously

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making use even of scraps of information on chemical reactions to provide estimates for the thermochemical values of less well studied compounds. Bichowsky and Rossini's b o o k was the predecessor of the more comprehensive Circular 500 of the National Bureau of Standards (1952). (142) It is the most reliable source for the thermochemical properties o f inorganic compounds at r o o m temperature including their aqueous solutions and every attempt has been made to make the tabulated values consistent. A new edition is in preparation, parts of which appear at present in the f o r m of NBS Technical Notes (270-1,270-2 and 270-3). The special demand for comprehensive tabulations of the thermochemical properties of high-temperature materials is being met by the J A N A F tables edited and published by the D o w Chemical C o m p a n y in the U.S.A. (D. R. Stull et al.) and two volumes entitled Termodinamiyeskie Svoistva Individunikh Veshchestv published by the A c a d e m y o f Sciences in the U.S.S.R. (L. V. Gurvich et al.). A special feature is the production o f extensive tables giving, for example, h e a t entropy and free energy functions at m a n y temperatures. In the early stages, J A N A F was not as critical as might have been desired (as was freely admitted) but they are improving rapidly in this respect as the original 'grey' sheets are being replaced by revised tables on white sheets. Nesmeyanov~ 148) has assessed the v a p o u r pressures of the elements and Hultgren and his colleagues< 52) all the t h e r m o d y n a m i c properties of metals. The last mentioned critical tables are being revised continuously. Hultgren et al. have also compiled and critically assessed the thermochemical properties of alloys, thus superseding an earlier assessment by Kubaschewski and Catterall, ~51) but have not yet included the oxides, sulphides and nitrides of the transition metals as did the last-named authors. An alloy system may be selected as an example for the evaluation of its thermochemical properties which m a y be quite involved and requires a good knowledge of the t h e r m o d y n a m i c principles as well as the reliability and applicability o f the experimental methods. Nickel and the f.c.c, modification of iron form a complete series of solid solutions. Various sets of free energy measurements on these solutions have produced such divergent results <144)that a reliable evaluation cannot be based on them. On the other hand, Dench <15) and Steiner and Krisement (x45) have measured the heats of formation of ~, Fe-Ni alloys, the former alloying the metals directly in an adiabatic calorimeter at 1050°C (p. 6), the latter using liquid-tin solution calorimetry (p. 7). The proclaimed and acceptable accuracy of both methods is of the order of -4- 100 cal/g-atom. Within these limits the agreement is good. The weighted and smoothed curve is accepted for the integral heats of formation of the ~, alloys. Oelsen and Lichtenberg~x48)have measured the heat contents across the whole range of composition between 1600 and 20°C, and 1000 and 20°C, respectively, by drop calorimetry. It is assumed that any difference between the two sets of measurements is sufficiently small for a conversion of the heats of formation at 1000°C into heats of mixing of the liquid alloys at 1600°C. The results may be represented by the following series expansion: AHIIQ = -- NNI NFe [2840 + 1840 (NNI -- NFe) q- 294 (Nr~l -- NFe) 2 -- 655(NNI--NFe)3] Partial heats for the solution o f liquid iron or nickel in the alloys are calculated using the constants of this equation.

Dissociation pressures of liquid Fe-Ni alloys have been measured by Zellars et aLOa7) (1830-1891°K, Nr~l = 0.1--0.9), Speiser et al. <~48)(1783-1873°K, N~l = 0"1 -- 0.9) and

30

P R O G R E S S IN M A T E R I A L S SCIENCE

Grieveson and Mills (x49) (1600 and 2200°K). When all these results are combined with the derived heats, it is found that the excess entropies are close to zero. The average excess entropies of mixing do not exceed -- 0"075 and + 0'035 e.u./g-atom. The experimental variation of free energies with temperature, from which entropies could also be derived, are disregarded although Grieveson and Mills indicate slightly negative excess entropies deviating but little from the accepted regular behaviour of the solutions. The next step is to calculate partial free energies, A~Fe , for the liquidus curve and to combine these values with the partial heats of solution in the solid alloys at the corresponding compositions of the solidus curve. The partial heats of the solid solutions are obtained by differentiating the assessed integral curve after Dench and Steiner and Krisement and the solidus-liquidus gap adopted from Hansen (~5°) and Hellawell and Hume-Rothery.(TM) The resulting excess entropies, A~Fe xB, are plotted against concentration as the full line in Fig. 7.

0

0

A

~

-I

-2

-3/[-

x yon Gotdbeck, I 0 0 0 OK +von Goldbeck, 1200 OK ~. Oriani, 1113OK o Fleischer, E l l i o t t 13730K ~Colculoted f r o m liquid

I

0"1

I

0"2

I

0'3

I

0'4

I

0"5

I

0"6

I

0"7

I

0"8

I

0-9

NFe

FI~. 7. Assessed and experimental partial entropies of solution of iron in solid iron-nickel alloys. Von Goldbeck (152) and Oriani (ls3) both studied equilibria of the form (H20) + [Fe]ve_~i = (Ha) + 'FeO' at 930-1200°K and calculated the activities of iron in the alloys. Fleischer

and Elliott(TM) estimated the activities of iron and nickel from solubility measurements of the alloys in liquid lead. The results are converted into excess entropies, using the accepted heats of solution. The A~Fe xs values are also shown in Fig. 7. Agreement with the accepted entropy curve is good only above 60 at. % Fe. Below this composition the discrepancies become pronounced but neither of the free-energy methods used for the solid alloys is sufficiently reliable to challenge the calculated results. Integral excess free energies estimated for the binary system from vapour pressure measurements of M n in the ternary system Fe-Ni-Mn by Smith, Paxton and McCabe(155) are considerably more negative than the values accepted here. Mass spectrometric vapour pressure measurements of Lyubimov et al. (x56) on Fe-Ni scatter too widely to permit quantitative evaluation. Having assessed the thermochemical properties of the disordered solid solutions, those of the ordered phase FeNia can be calculated from heat capacity measurements as described

RECENT

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31

by Catterall,(5~)relyingmostlyon the recent results of Stuart.txsv)The followingvalues are obtained: AH°formatlon= - 1760 cal/g-atom and AS°lormatlon= - 0"26 e.u./g-atom. Apart from the two compilations of the thermochemical properties of alloys mentioned,(51,5z) there is also a contribution on alloy thermochemistry to one of the latest volumes (vol. II. 4, p. 807) of Landolt-Biirnstein by one of the present authors. In the same volume, W. Auer tabulated the thermochemical properties of inorganic compounds. It is, however, evident that this type of compilation demands too much from the authors in that too few contributors are involved in too much tabular matter. In future, critical assessments of thermochemical data will have to be split up into many individual volumes. The prototype may be the attempt by the International Atomic Energy Agency to publish a series of monographs on the physicochemical properties of metals of interest in reactor technology, their compounds and alloys, a number of authors contributing to each volume under one editor. One monograph, on plutonium, has already appeared,t 158) another, on niobium, is in press.t la3) Further volumes on beryllium, titanium, zirconium, hafnium, tantalum, molybdenum and thorium are in preparation. A similar assessment of the thermochemistry of phases involving uranium was published by Rand and Kubaschewskit45) but now requires revision. Computers are playing an increasingly important role in thermochemical data compilation. The JANAF Tables, for instance, are evaluated by computer and stored on magnetic tape. Other tabulations make similar use of computers. A great and commendable effort to store all the available thermochemical data for inorganic and metallurgical substances and to apply these to the evaluation of phase diagrams and other problems of practical interest is being made by a French group at Grenoble under the direction of E. Bonnier.(l~9) A number of important issues, such as the representation of the thermodynamics of concentrated metallic solutions is being explored (e.g., ref. 160). A group at the N.P.L. is working out a similar programme, in co-operation with the French group.

5.2. Available Thermochemical Information It appears to be desirable to indicate in this article how much reasonably reliable information on systems of interest in metallurgical thermochemistry is available. However, a full tabulation of the data would far exceed the ambition of this article and the stamina of the authors. In Table 2 are therefore listed merely the solid (s) and liquid (/) binary systems for which good free energies (G), heats (H) and, occasionally, entropies (S) have been determined experimentally. Where the information is incomplete, of low accuracy or uncertain, small letters (g, h, s) are used. It may be repeated that heats and entropies obtained from the temperature coefficients of free energies alone are often unreliable and are therefore

32

-~

0

PROGRESS

IN MATERIALS SCIENCE

~

~

-~

~

_

~

-~o

E

E

-~E

E

o

¢.)

K Rb Be Mg

Li Na

Sn

Cd

Ca Pr Zn

Li Na K Cs Be Mg

sh

sg sh

Ce

Pr

Y

sG

lhG sHG lhg shg lh sh

sh

La

sG

sH

Ba

IHG sHG

IH sGH

sH

Sr

sG

mn

mn

mn

mn

mn

sh sHG lhg

Ca

mrl

mn

mn mn

Mn

Fe

mn

sG

Co

mn

lhg sHG lg

Ni

mn

Cu

mn

Ag

lhg shg lhg shG IgH sg

L

sh IHg shG lhg shG 1H sHG

sh

Au

TABLE 2--continued

o

/1

mn

0

IH

o

IHG IH IH

mn mn

IH

IH

mn

lg

mR

ITI

shg

Zr

Na

,

V

K Rb

sG

sh

mn mn

Nn

mn

i

I

I I

I

Cs

Ta

Mg

m

Mo

E:

o

rr~

t"

70

> [.t-

7~

o

t~

34

PROGRESS

IN

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SCIENCE

O

O

t".,I

Z

0~

O~

O

O

~

~

R E C E N T P R O G R E S S IN M E T A L L U R G I C A L

I

¢q

,<

b-

THERMOCHEMISTRY

35

36

P R O G R E S S IN MATERIALS SCIENCE TABLE 2--contintted

H O S Se N P Be Mg Ca AI Ga In TI

Th

U

Pu

sg

sGs sHG shg

sg sH

shg

La

Ce Fe Zn Cd Hg Bi

SS

sg sg

shG sgS sH mn mn sH shg shg shg

sG sg

Pd Ti Zr V Nb Ta Cr Mo

Re Fe Co Ni

= = = = = = =

shg sg lg

Ni

sH sg

Co

sh

sg

sHG

Fe

sh shg shG sg sHG

sg lh sg mn

lg sg sg sgh

IHG sHG sHg

sG shg lg

Pb Sn Ge Si C U

sH

sH

Mn

H G S h g s m n

Th

IG sHG

shG sG sG sg mn

Mn

Mo

U

Pu

m

lG lg sh l/sg l/sg

shg sHG sHG sg lg sHG sHG sHG sG sHG sHG o

Cr -

shg lg

Hf

sG sHG sg

sG sHG

~l-lG

0

IHG sh mn O

O

reliable and complete heat determinations. reliable and complete free energy determinations. reliable and complete entropy determinations. less reliable or incomplete heat determinations. less reliable or incomplete AG determinations. less reliable or incomplete entropy determinations. miscibility gap, liquid "~ solid solubility very small J (both implicating positive heat of formation).

RECENT PROGRESS IN M E T A L L U R G I C A L T H E R M O C H E M I S T R Y

37

rarely recorded. Wide miscibility gaps in the solid and liquid states and immeasurably small solubilities indicate appreciable positive heats of mixing and are therefore reported as m and 11 respectively. Binary systems considered are all the alloy systems and those formed by transition metals with hydrogen, the chalcogenides, nitrogen, phosphorus, carbon, silicon, and boron. The halides are disregarded but knowledge of their thermochemical properties may be taken as fairly complete The literature consulted in constructing Table 2 includes most of the references mentioned above, in particular Hultgren's t52) and Catterall's t51) compilations, Metallurgical Thermochemistry, ~27) a review on gas-metal solutionst 56) and individual monographs.t 45,183,15a) Quite a number of individual references have been mentioned in the first section of the present chapter, and this and other information have also been considered in Table 2. 6. APPLIED CHEMICAL THERMODYNAMICS It has been pointed out in the introduction that much of the development in metallurgical thermochemistry is due to the interest in applying its principles and data to chemical equilibria of industrial and other practical significance. This aspect can be subdivided into (1) the application of existing thermochemical data to practical problems with the aid, where necessary, of estimated data and (2) specific experimental investigations of existing or potential processes where chemical equilibrium is important.

6.1. Calculation of Equilibria from Existing Data It is not possible to gather from the published literature the extent to which chemical thermodynamics are used to deal efficiently with problems arising in practice. There is now a growing number of young thermochemists in industry and other research laboratories quite capable of doing just that whereas publicizing these efforts may not be in the interest of their sponsors. Personal enquiries addressed to the authors of this article and their colleagues in the field as well as contacts during meetings and similar functions indicate that considerable and fruitful use is being made of chemical thermodynamics for practical applications on a large scale. This article can only refer to the published literature. There are a number of monographs on thermochemistry which provide the reader with numerous examples of practical application, often taken from the authors' personal experiences. Some of these books may be mentioned. They are: Metallurgical Thermochemistry [1967],~27) Problems in Applied Thermodynamics [1966]~1~1) and Physical Chemistry of Metallurgical Processes [196213162) There are at least three recent books devoted to the physical chemistry of iron and steel making [1962, 1963, 1967]~163-165) of which the latest places the emphasis on the important kinetic rather than the thermodynamic aspects. A monograph entitled Extractive Metallurgy of Tin [1966] ~166)deals with the thermochemical as well as the empirical approach.

38

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There have been meetings on the physical chemistry of process metallurgy, in particular those arranged by the Deutsche Bunsengesellschaft in 1937/208) the Faraday Society in 1948(2o9) and the A.I.M.E.(21o) ten years later. The first attempt to devote an entire meeting to the application of thermodynamics to practical problems was made by Fitterer(7) at Pittsburgh University in 1964. The meeting being the first of its kind and contributors being individualists, there were deviations from the main theme but, on the whole, the meeting was very successful. A comparison of the proceedings of these meetings demonstrates the remarkable advances that have been made during the last 30 years, in the field under review. In recognition of the importance of thermodynamics for the development of materials in reactor technology, the International Atomic Energy Agency in Vienna has devoted three international symposia to this subject in 1962, 1965 and 1967(3) and intends to continue this activity. Rand and Roberts(1~7) summarized the application of thermochemical data and concepts to the various practical problems that arise in the development of nuclear power for civilian uses. From the earlier stages onward up to-date, particular attention has been paid to the application of chemical thermodynamics to the requirements of the iron and steel industry. This is firstly due to the interest this industry has always shown to developments in the field and secondly to the ability of its representatives, such as Rudolf and Hermann Schenck, F. K6rber and W. Oelsen, in Germany, J. Chipman and his colleagues in the U.S.A., and F. D. Richardson in Great Britain. Numerous types of practical problems can profitably be handled by the thermochemical approach. Important ones are: production and refining of metals at elevated and high temperatures, reactions of metals and alloys with refractories as well as with gases, or impurities in general, high-temperature analysis, such as vacuum fusion, purification of gases, and certain aspects in the oxidation of metals, such as exploring the efficiency of protection of metals in high-temperature corrosion (e.g. coating). Individual recent examples of the application of data described in the published literature are as follows: Production of metals. Aluminothermic-type reactions for the production of uranium(45) and plutonium(168) by reduction of their halides with calcium, magnesium, etc. Reduction of calcined dolomite or magnesia by silicon(27,161) and of magnesium chloride by hydrogen.(27) Production of aluminium. (169) The zinc-lead blast furnace.(17°) The thermodynamics of the iron blast furnace have frequently been discussed. Gas-metal equilibria have quite recently been described, the thermodynamic aspects of the vacuum fusion method in particular by Sloman and Harveyt1~1) and the thermodynamic and kinetic aspects of vacuum degassing by Bradshaw and Richardson.aTe) For the purification of hydrogen by metals, see Bodsworth.a61) Several new monographs on the fundamentals, including the thermo-

R E C E N T P R O G R E S S IN M E T A L L U R G I C A L

THERMOCHEMISTRY

39

dynamic aspects, of metal oxidation are available (e.g. ref. 173). Refining of metals. Quite a number of examples have recently been calculated and discussed, such as the refining of iron, ~27,161~purification of lead from copper, ~161) silver and zinc, t27) refining by chemical transport reactions TM) and partition of fused salts and metallic solutions in uranium and plutonium.(17s,16s) The killing of steel by aluminium described by the equations, (AltOs> = 2[A1]Fe -k 3[O]Fe; Kv = c21 cao,

(22)

has almost become a standard example for many reactions of a similar type" Thermochemical calculations by Chipman and the present authors all give an equilibrium constant of about 10 -lz at 1600°C in terms of weight percent whereas most experimental measurements gave values of the order of 10-9. (176) [5 × 10 -11 and 5 × 10-7, respectively, in atomic percent]. P15ckinger et a/.(177) have shown by electron probe microanalysis that the oxide in final equilibrium with the melt is in fact pure alumina. The discrepancy between calculated and experimental values was difficult to explain, in particular as similar calculations for the deoxidation of iron by silicon and manganese showed good agreement with the experiments. Careful new experiments by Repetylo, Olette and Kozakevitch (17s) under purified argon at 1600°C have now demonstrated that the deoxidation constant varies with time approaching a 'final' figure of 5 x 10-13. The phenomenon shown to be responsible for this behaviour is the elimination of the alumina suspension, the coarser particles being eliminated in 7-10 min, whilst a finer suspension ( < 20/~) remains in the melt even 20 min after addition. The free energy pertaining to the chemical equation (22) can also be used to calculate the solubility of alumina in liquid iron when one assumes the melt is contained in a closed A12Oa vessel so that the aluminium/oxygen ratio is about 2/3 atoms. The result (ca. 0.0025 wt. ~o of each A1 and O at 1600°C) agrees with analytical results obtained at the N.P.L. on 25 lb ingots of pure iron melted in alumina pots.t ~7) The underlying arguments can be applied to any metal/refractory interaction. This has been and is being done frequently, and some examples have been published, such as the solubility of alumina in solid nickelt27) and of beryllia in liquid uranium,¢ 45) the interaction of chromium carbide precipitates in steel ~179)and of chromiumcobalt alloys with various refractories.Cla0) 6.2.

Calculation of Equilibrium Diagrams

Evidently, all this work in applied chemical thermodynamics involves phase diagrams. The next step was obviously to establish whole equilibrium diagrams by measuring their thermochemical properties and calculate the phase boundaries. Work to study temperature/concentration, pressure/ concentration and temperature/pressure diagrams is indeed being carried out systematically. One of the present authors is responsible for the systematic work on

40

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temperature/concentration diagrams.(49,181) The principle is to measure experimentally the heats and free energies of formation of all the phases present in a system (which must be known), then to calculate the free energy vs. concentration curves of the phases at various temperatures and to draw the tangents which touch these curves at the phase boundaries at the given temperatures. It is always the phase or mixture of phases with the lowest free energy of formation that is stable. First, the method was applied to systems for which the experimental equilibrium diagram and the thermochemical data are well established, such as Mg-Cd, Cd-Sb and Zn-Sn. It was soon discovered that, in certain cases, the phase boundaries obtained by conventional methods are rather inaccurate or uncertain, mostly owing to kinetic checks. In particular, solidus curves and solid solubilities are prone to such errors because the investigators of phase diagrams are not always aware of the length of time needed for equilibration. In the case of Ga-Zn, the difficulties are due to the tendency of gallium to supercool and, after the calculation of the liquidus curve, it was found that equilibration near the eutectic had to be awaited for days, even in the liquid state.(181)

I00

-JO0;

-20C

a

6oo%/

<] -50c

815°C -70(

L o

r 2o

FIG. 8. F r e e e n e r g i e s o f f o r m a t i o n

I 40

I I ] 60 80 too at. % , Cr o f t h e a a n d o p h a s e s in t h e s y s t e m i r o n -

chromium at three temperatures.

RECENT PROGRESS IN M E T A L L U R G I C A L T H E R M O C H E M I S T R Y

41

Systems with complete mutual solubility at some higher temperature and a positive heat of formation must show, at lower temperatures, a solid miscibility gap which can be calculated. The miscibility gap in the system Cr-Mo, for instance, was calculated from measured heats and free energies, and the phase boundary then confirmed by conventional methods, but annealing had to be continued for over a year. (4a,lsx~ As an example, the free energy vs. concentration curves at 460, 600 and 815°C of ~- and ~-Cr-Fe alloys obtained from measurements of heats and free energies of formation between 800 and 1370°C are shown in Fig. 8. Phase boundaries are obtained by the 'common-tangent method' as indicated. Since the disorderedalloys have a higher entropy than the ordered ones, the ~ phase becomes metastable at some higher temperature (815°C). Because of the different shapes of the enthalpy and entropy ctrrves, the characteristic free-energy curves, as shown, result at lower temperatures. While the inverted humps in the AG/N curve for ~ must persist at negative values with decreasing temperature to near absolute zero, the AG/N curve for o must eventually disappear in the inverted trough (460°C) owing to its positive heat term. The resulting equilibrium diagram is shown in Fig. 9. 900

--~ .....

Cook and ,Jones -Calculated Calculated Metastable

/I\

o /,',

,oo

o

1/

/i !

400

u + u'

\ l

300

:e

I

20

I

I

40 60 Atomic % C r

I

80

Or I

I00

FIc. 9. Part of the equilibrium diagram of the system iron-chromium.

Recent results of magnetic and electrochemical measurements around 475°C by Imai, Izumiyama and MasutnokoOa2) confirm that the a alloys separate into chromium-rich and iron-rich a solid solutions. The advantages of the thermochemical method in this case are obvious. The temperatures at which chromium steels are used in practice are rather lower than those at which the equilibration rate is sufficiently fast to make the measurements within a reasonable experimental time. The application of the thermochemical method should be extended to D

42

P R O G R E S S IN MATERIALS SCIENCE

ternary diagrams, and such investigations are under way. A preliminary attempt to construct the phase boundaries in the Fe-Cr-Ni system at 650°C from thermochemical data estimated from those of the binary systems(ls3) showed that the method is at least promising. KaufmanOa4) has tried to estimate phase boundaries of binary transitionmetal systems on the basis of the ideal solution model, confining himself to the b.c.c., f.c.c, and h.c.p, structures. He first established the enthalpy and entropy differences between the various modifications of the transition metals from (1) direct measurements, (2) extrapolations from binary systems and (3) estimates. He then assumed that the same structural modification of two metals forms ideal solutions and constructed the idealized equilibrium diagrams by the common-tangent method from the resulting free-energy curves for the various modifications, including, of course, the metastable ones, in a system. The resulting phase diagrams are quite inaccurate and give only an impression of the actual phase relationships, the deviations arising from the interference of stable structures other than the three mentioned and, of course, from the non-ideal nature of the metallic solutions (p. 17). Even so, Kaufman's approach may be used as a starting point for more elaborate equilibrium diagram considerations, as the actual thermodynamic properties become better known.

I 3

.TizO TizO +

o-Ti "~"~a+fl

TiO + Tiz03

TiO

TiO

!!ll

Tiz03 + Ti305 Ti305

Ti407 Ti30~

\_

Vopor

O

01.2

I 0.4

I 0.6

I 0.8

[ I.O O/Ti

I 1.2

I 1.4

I 1.6

I ].8

2.0

FIG. 10. Pressure--concentration diagram of the system titanium-titanium dioxide.

Oxide/oxide phase diagrams, such as MgO-NiO,(Iss) AlsOs-U02, M g O U O % UOs-SiOs, UOs-ThOs and BcO-ZrOs,(Ise) have also bccn calculated from estimated data alone, based on thermochcmical principles.It may be seen from the originalpapers that the agreement with the experimental diagrams is quite good--and in some cases very good.

RECENT

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43

Gilles has investigated systematically for some time vapour pressure vs. concentration diagrams of oxide, nitride and sulphide systems. As an example, the diagram for the Ti-TiO2 system is shown in Fig. 10.tls71 Naturally, such equilibrium diagrams can be calculated from the free energies, where these are known, in a similar manner as indicated above for temperature/ concentration diagrams. Gilles has described the underlying principle in some detail.tlss) Whereas Gilles' work refers to pressures less than 1 atm, KaufmantlSgl has discussed the thermodynamic factors controlling the stability of solid phases at high pressures up to 100 kbar. He comes to the conclusion that rarely can quantitative thermodynamic predictions be carried out at a level of accuracy and reliability comparable to current highpressure observation. However, useful qualitative predictions of high-pressure effects can be made by properly applying thermochemical data at one atmosphere. Knacke has pointed out that pressure vs. temperature diagrams are often the form of representation of thermochemical data most useful in practice. With this in mind, he and his colleagues(19o) have worked out and discussed such phase fields in the system Fe-FeO-Fe304-FezOa-FeS-FeS~-Fez(SO4)a in dependence on temperature and the composition of the gas phase with the components 02, $2, H2, CO, COz, SO2, SOs, H20 and HzS. In the nickelsulphur-oxygen system the phase relations are somewhat simpler. The 8

jo NiO

Ni -t ~'20

I

I

I

-16

-12

.-8

I, - 4

0

FIG. 11. Predominance area diagram for the nickel-sulphur-oxygensystem at IO00°K. diagram in Fig. 11, in which Pso2 is plotted against Po2 at 1000°K and predominance areas shown, has been constructed by Ingraham.(191) From such diagrams for various metals conclusions can be drawn concerning, for

44

P R O G R E S S IN MATERIALS SCIENCE

instance, the selective sulphation of metallic sulphides and oxides. Such diagrams can also be very useful to the engineer who is dealing with corrosion problems. 6.3.

Other Applications

In this chapter, applications of thermochemical data have so far been reported which were not necessarily designed for the express purpose to which they were applied. Experimental equilibrium studies of direct application to practical problems have also been carried out in the recent past. Investigations of the use of solid electrolytes for the determination of oxygen in liquid copper~ 32) and iron~al) in practice have been mentioned earlier (p. 9). Much work has been devoted to problems in iron and steel making, for instance the behaviour of sulphur(~9z-~95) and phosphorus( x95, ~96) in slag/ metal equilibria. In particular F. D. Richardson, H. Schenck and E. T. Turkdogan and their colleagues are very active in this field. However, a detailed report of such work would go beyond the scope of the present article. 7.

PHASE STABILITY AND BOND MECHANISM

As indicated by Zener, the stability of a phase is determined by two factors: the binding energy at absolute zero and the entropy of the system which may be identified with uncertainties in the specification of the parameters of the system.t10~) Ultimately, the heat and entropy of chemical phases are to be derived from first principles, but progress in this field is involved and consequently slow. The thermochemist's method therefore is to measure experimentally the thermodynamic properties of a large number of substances and to compare these with other properties that appear to contribute to the thermodynamic stabilities. This approach is by nature empirical. The wide gap betweeen what one may call the chemist's and the physicist's approaches was clearly demonstrated at the recent Battelle Colloquium on phase stability in metals and alloys.tS) It was as if the two groups spoke two different languages. For instance, no connection between the binding energy at absolute zero and the entropy of the system can as yet be recognized from first principles. However, as stated earlier, it can be shown empiricallyt53) that an approximate straight line relationship exists between the maximum excess entropy and the maximum heat of mixing of solid and liquid metallic systems of complete mutual solubility. Another concept that was discussed at some length at the Battelle Colloquium was 'electronegativity' which is of relevance to phase stability through the polar bonding contribution. It was agreed that for the interpretation of the stability of the phases under review, Pauling's electronegativities are 'quite useful quantities but rather indefinite'. Hume-Rothery pointed out that high values of the electronegativity difference between two metals correlate with low electron concentrations at the a solubility limit in copper, silver and gold and also indicated qualitatively the connection

RECENT PROGRESS IN METALLURGICAL THERMOCHEMISTRY

45

between electronegativity difference and thermal stability, i.e. melting point. Relative values for the electronegativities have been derived by various authors (e.g., ref. 198) from the heats of formation of the metal halides. In turn, these values may be used to estimate the heats of formation of ionic compounds using the following equation: AH29s = 23"07Z (EA - - ~A)2

(23)

where ~ is the electronegativity and z the number of valency links. According to the Born cycle, the heat of formation of a metal-non-metal compound is composed of the heat of sublimation and the ionization energy of the metal, the heat of dissociation and the electron affinity of a gaseous non-metal, and the lattice energy, where the four first-named factors are characteristics of the metal or non-metal alone. Only the lattice energy involves both compoments. Since the ionic radii of the elements are nearly constants, the use of equation (23) for the calculation of the heats of formation of ionic compounds is a sensible empirism. TABLE 3 Heat of Formation of Some Compounds of Magnesium at 25°C in kcal/mole as observed experimentally and estimated from AHert = -- 23,066 z (~Mg -- EB)z. [cMg = 1'2]

Compound

cB

--AHxpu

MgFe MgCI2 MgI2 MgO MgS MgTe MgaSb2

3"5 3'0 2"55 2"9 2-5 2"1

MgaBi2

1'8 1-7 1"6 1"5/1"9 1"8 1"8

266"0 153"4 86-0 143"7 83'0 50"0 79-0 40.5 18'3 12'5 12"0 9'2 13-5

Mg2Sn Mg~Pb MgTI MgAg MgNi2

1"85

--AHest 244 150 84 133 78 51 59 50 23 14-5 4'1/22"5 16.5 16.5

In Table 3, the experimental heats of formation of magnesium compounds, reaching from the ionic to the metallic types, are compared with those calculated by means of equation (23).o991 The table conveys a representative impression of the accuracy that can be expected when estimating heats of formation of predominantly ionic compounds from electronegativities. It also indicates that the percentage deviations of calculated and experimental heats become larger the more covalent bonding prevails. It should also be remembered that in compounds, such as Mg3Bi2 and Mg2Pb, the element B is obviously the anionic component whereas the electronegativity values were obtained for it being the cationic one. A much more direct derivation of electronegativity difference between two metals, A and B, is now available from the dissociation energy of the gaseous diatomic metal species, AB,

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[cf. Drowartlas)]. Electronegativities derived in this manner would not be open to this objection, but could only be obtained where gaseous species are observed. The electronegativity difference is related to the dissociation energies by D(AB) = ½[D(A2) q- D(B2)] = 23(EA -- ~B)2. As one passes into the more metallic range, the significance of z loses its meaning, and the electronegativities become indefinite as was pointed out by Hume-Rothery and mentioned above. In Table 3, a value of z = 2 has arbitrarily been taken for the metallic compounds but, it must be added, one cannot assume that the electronegativity is always the same for a given element since different electronic states have different electronegativities (e.g. TI). Also the electronegativity of a metal atom (or ion) in a mixed crystal lattice, or influenced by other metal atoms in a disordered a~ray (solid or liquid), will be modified from the value derived from metal halide decomposition, or any method using gaseous molecular species. More sophisticated descriptions of the polar interaction could be formulated, e.g. by consideration of states involving partial back electron transfer between two metal ions, the canonical structures representing the extremes of no back electron transfer and complete transfer being A+N - and AB respectively (i.e. description of the wave function in terms derived from electron donoracceptor theory, cf. Mulliken(200)). However, it is not apparent at this stage how more sophisticated models of this type could lead through to ab initio calculation of thermodynamic values for these systems. Therefore, lacking anything more fundamental, the concept of electronegativity and its empirical values may be retained but must be used with caution. The covalent bond in metallic systems is even less tangible than the polar bond. It appears that changes in covalent bond energy can make a positive or negative contribution to the heat of formation, and examples have been presentedt53) but quantitative conclusions, even empirical ones, cannot yet be drawn. The so-called Brewer-Engel correlation is still a controversial subject.lsl Its fundamental assumption is that numbers of electrons can be associated with crystal structures 1 e/a with b.c.c., 2 e/a with h.c.p, and 3 e/a with f.c.c. In describing bonding interactions, due cognition is made of electron spin whereas in band theory the energy of an atom is built up without this consideration. In the present article, we are only concerned with quantitative conclusions concerning stability of phases whether drawn from empirical findings or first principles and shall not be drawn into the controversy around the Brewer-Engel correlation to which relevant objections have been raised. However, it is fair to point out that this correlation is able to predict the approximate nature of quite a large number of phase diagrams involving the crystal structures mentioned. Brewert201) also predicted particularly high energies of formation of phases such as ZrPts, Zrlr3 and HfPts which have been confirmed. Too few reliable thermochemical data for systems

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formed between transition metals are at present available to convert Brewer's contention into some quantitative empirical relationship pertaining to heat of formation but it is suggested that they should be borne in mind and may act as a guide. The three bond types mentioned, the polar or ionic, the covalent, and the metallic bonds are too vague to be more than useful guides for further thought in metallurgical thermochemistry. For long, Hume-Rothery has operated with three factors responsible for the types of equilibrium diagram formed by two metals---equally vague but qualitatively important concepts. These are: the size factor, the electron concentration and the electrochemical factor. The latter corresponds to the polar bond. The size factor seems to be even more important for the stability of metallic phases than has hitherto been realized. One of the present authors demonstratedt202~ this point by estimating the heats of formation of binary intermetallic compounds from the heats of sublimation of the component metals A and B with the assumption that the A-B bond energies are the mean of the A-A and B-B bond energies and that the stability of the compounds derive from the increase in co-ordination. For this purpose, a redefinition of the co-ordination number and a simplified assumption for the dependence of bond energy on interatomic distance was made. The calculated heats of formationt202~ agree reasonably well with the experimental ones for compounds formed by metals of groups In through IIB, and the concept is therefore used by the present authors as a mode of estimating unknown heats of formation, preferably in conjunction with other methods. Alcockt 2°3~has shown that the model applies relatively even to compounds involving meta-metals such as the UMea compounds where Me = Si, Ge, A1, Sn, Pb, Ga, In and TI: the negative heat of formation increases with the heat of sublimation of the meta-metal. As a consequence of this concept, stable intermetallic compounds are expected to form when the larger atom is the 'stronger binder', i.e. has the higher heat of sublimation, because it is the larger atom that will gain in co-ordination while the smaller atom will lose. If the larger atom has the lower heat of sublimation, positive heats of formation are expected and, above a certain size difference, liquid miscibility gaps should appear. The type of phase diagram formed by any two metals is entered into a diagram, Fig. 12, of (rA - - rB/)½(r.~ -b rB) VS. (LA - - LB)/½(LA -k LB) where rA and rB are the atomic radii, and LA and LB the heats of sublimation, at 25°C, of the component metals. A mostly small correction term, (~A -- ~B)~ has been added empirically to the heat-of-sublimation term in order to account for the electrochemical factor. From the simplified diagram in Fig. 12 it may be seen that the type of equilibrium diagram formed occurs predominantly in certain areas with regions of transition between. Of the original 350 binary metal systems examined (only the simpler ones of which are entered in Fig. 12) less than

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48 0"5

¢k

0"4

0"5 v x7

,+

$.

,~ •

x7

~7

Or2

vv

0"1

.,

(/ooo

•

'J, / ~ •.

'4

-1"2

-t-0

-0"8

-0-6

-0"4

~

-0-2

oO

oo

0

oo o :,\

0-2

,~

0"4

\

0"6

•

0'8

FO

1"2

}'4

LA-L B

2(LA+ LB) "l'- ((A-(B)2

FIG. 12. Diagram indicating in terms of atomic radius, heat of sublimation and electronegativity of the component metals, A and B, regions of preference for the formation of certain types of binary equilibrium diagrams. O complete solid solubility; O pronounced mutual solubility; ~ as O with miscibility gap; ~ as O with positive AH; (~ as O with negative AH; • eutectic system; • miscibility gap in the liquid; * compound forming systems; V Laves phases. 2000

xcu 1500

it._ E o ~

1000

jxCd

E o 500

J 0

Xl n I 5

I

tO

I

15

I

20

25

Relative differences of atomic volumes of component metals

Fzo. 13. Maximum heats of mixing of liquid lead alloys plotted against the relative differences of atomic volumes of the component metals after Predcl.

1"6

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20 do not fit the present pattern. Among the exceptions are systems involving Mn and U, the atomic diameters of which are difficult to assess, and also the so-called Hume-Rothery systems, possibly because of the low co-ordination of Zn and Cd despite their hexagonal structure. For systems of complete mutual solid solubility, the so-called Hume-Rothery 15 ~-rule is recognizable with the additional restriction imposed by the heat of sublimation factor. The present model does not consistently explain the positive heats of mixing in systems involving meta-metals but even here the size factor seems to be important. In Fig. 13 are plotted the maximum heats of mixing vs. the relative differences in atomic volume of various binary lead alloys after Predel and Sandig (see ref. 204). These authors ascribe the increase in heat of mixing with difference in atomic volume to a misfit energy, and it is difficult to find another sensible explanation. Predelt2OS) has presented a systematic survey of the maximum temperatures of liquid miscibility gaps as a function of excess volumes which indicate a similar relationship. Attempts to estimate misfit energy in metallic melts have not been entirely successful, probably because the interaction between misfit and chemical bonding is difficult to assess.lZ04) 8.

CONCLUSIONS

The subject of metallurgical thermochemistry has attracted considerable interest during the last ten years or so, and continues to do so, due to the potentialities of applying thermodynamic data and principles to various types of practical problems involving chemical equilibrium. Some examples of practical significance have been discussed above. The development of new, and improvement of existing, methods for the measurement of heats and free energies of reaction is still a matter of primary importance. Although much development work has been done during the last forty years to adapt experimental chemical thermodynamics to the special requirements of metallurgical systems, the accuracy and versatility of the methods is still lagging behind the demands. In particular, high-temperature methods must be further developed for the study of the important hightemperature materials: alloys, oxides, carbides, silicides, etc. More attention must be paid to the non-stoichiometric nature of many metal-non-metal phases at high temperatures. Present accomplishments and promising lines for further progress have been indicated in the experimental section. A good store of reasonably reliable data for substances of interest in metallurgy is now available and additional data are continuously being measured. The systems in question have been surveyed in Table 2. There are, however, important gaps, in particular with the thermochemical properties of high-melting-point alloys, the carbides, silicides, borides, phosphides and even nitrides of transition metals, of silicates and other double oxides, and of fused salt mixtures. Much more experimental effort is to be devoted to such systems.

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Critical compilations o f e x p e r i m e n t a l d a t a are being p r o d u c e d by various expert groups. This effort m u s t c o n t i n u e a n d be expanded, preferably with the increased aid o f c o m p u t e r s . M e t h o d s are available for the e s t i m a t i o n o f missing numerical information. This type o f a p p r o a c h has led to s o m e superficial u n d e r s t a n d i n g o f b o n d mechanism, but there is still a very long w a y to go. Only semi-empirical m e t h o d s are available whereas no quantitative t h e r m o c h e m i c a l i n f o r m a t i o n can as yet be obtained f r o m first p r i n c i p l e s - - b a n d structures, for instance. W o r k should not be confined to the elements a n d stoichiometric phases b u t extended to solutions, in p a r t i c u l a r c o n c e n t r a t e d solutions. The whole question o f phase stability is a very difficult b u t also a fascinating subject d e m a n d i n g a closer c o - o p e r a t i o n between physico-chemists and theoretical physicists. Only thus can we hope to achieve the final a i m : a uniform quantitative t h e o r y of phase stability. REFERENCES Symposia ~x) Proc. N.P.L. Sympos. No. 9, Phys Chem. of Metallic Solutions and Intermetallic Compounds (Teddington, 1958). H.M.S.O., 1959. <2) SKrNNER,H. A. (Ed.); Experimental Thermochemistry, vol. II. Interscience, New York,

1962.
(e) 1967. <4)I.A.E.A. Panel Meeting. Thermodynamic and Transport Props. of Uranium Dioxide and Related Phases. Tech. Rep. Ser., No. 39. Vienna, 1965. ts) A.G.A.R.D. Conf. on Refractory Metals (Oslo, 1963). Pergamon Press, Oxford, 1964. re) Met. Soc. A.LM.E., Cmpds. of lnterest Nucl. Reactor Technology, 1964. <7) Frr~RER, G. R. (Ed.); Proc. 1st. Conf. on the Thermodynamic Props. of Materials, Applications of Fundamental Thermodyn. to Metallurgical Processes, (Pittsburgh, 1964). Gordon and Breach, New York, 1967. <8) RUDMAN,P. S., STRINGER,J. and JArrEE, R. I. (Ed.); Proc. Battelle Colloquium, Phase Stability in Metals and Alloys (Geneva, 1966). McGraw-Hill, New York, 1967. Other References

(9) HUBBARD,W. N. ; Re/'. 2, p. 95. o0) GROSS,P., HAYMAN,C. and LEVI,D. L., Trans. Faraday Soc. 51, (1955) 626; 17th Congr. I.U.P.A.C., Munich, 1959. ~11)GERDANIAN,P. and DODt~, M.; Compt. Rend. 258, (1964) 1492. ~x~)GE~A~r~AN,P. and DUD[, M.; Ref. 3(c), p. 41 (is) KLEPPA,O. J.; J. Phys. Chem. 59, (1955) 175. <14)WrrntL F. E. and HUBER, F.; Z. Elektrochem. 60 (1956) 1181.
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(z7) KUBASCHEWSKI,O., EVANS,E. L. and ALCOCK, C. B. ; Metallurgical Thermochemistry, 4th ed. Pergamon, Oxford, 1967. (as) KIUKKOLA,K. and WAGNER,C.; J. Electrochem. Soc. 104 (1957) 379. (29) SCHMALZRIED,H . ; Z . Elektrochem. 66 (1962) 572. (30) WORRELL,W. L.; Ref. 3(b), p. 131. ca1) FrrrERER, G. R.; J. Metals, Aug. 1966. ca~) DtAZ, C. M. and RICHARDSON,F. D.; Trans. Inst. Min. and Me(all. (C) 76 (1967) 196. DRAIN, L. E.; Metall. Rev. 12 (1967) 195. (43) FROIDEVAUX,C., GAUTIER,F. and WEISMANI., Proc. Intern. Conf. on Magnetism, p. 390 London, 1965. (44) STALIN.SKI,B., COOGAN, C. and GUTOWSKY, H.; J. Chem. Phys. 33 (1960) 933. (45) RAND, M. H. and KUBASCHEWSKI,O. ; 7hermochem. Props. of Uranium Cmpds. Oliver and Boyd, Edinburgh, 1963. (46) GILLES, P., J. Chem. Phys. 46 (1967) 4987. t47) LUNDIN,C. E., NACHMAN,J. F. and YAMAMOTO,A. S. ; Proc. 3rd Conf. Rare Earth Res., Clearwater, Florida, 1963. t4a) KUaAS(nEWSKI, O.; Ref. 5, p. 191. (48) KUBASCnEWStO,O.; Ref. 3(a), p. 219. (60) HAY~, F.; N.P.L. Annual Report 1967. (51) KUBASCHEWSKI,O. and CATTERALL,J. A. ; Thermochemical Data of Alloys. Pergamon, London and New York, 1956. (52) HULTGREN,R., ORR, R. L., ANDERSON,P. D. and KELLEY, K. K.; Selected Values of Thermodynamic Properts. of Metals and Alloys, J. Wiley, New York, 1963. (53) KUBASCHEWSKI,O.; Ref. 8, p. 63. ~54) RUSHBROOKE,G. S.; Proc. Roy. Soc. (A) 166 (1938) 296. (55) WERT, C. A., Ref. 5, discussion. c56) KUBASCHEWSKI, O.; Autumn Course--Gases and Metals, 1967, The Metals and Metallurgy Trust, in print. ~57) KOFSTAD,P. and ANDERSON,P. B.; J. Phys. Chem. Solids, 21 (1961) 280. (sa) KOrS'rAD, P.; J. Phys. Chem. Solids, 23 (1962) 1579. (56) (}LANDER,A.; Z. Metallkde. 11 (1937) 361. ~60) MARKIN,T. L. and BONES, R. J.; U.K.A.E.A., Rep. AERE--R4178 (1962). (61) HAGEMARK,K.; Kjeller Rep. KR-67 (1964) ~62) WORRELL,W. L.; J. Phys. Chem. 68 (1964) 954. (6a) JOHNSON,I., Ref. 6, p. 171. ~a4) KtmASCVmWSKI,O. ; Ref. (3c), p. 685 (ss) YOKOKAWA,T. and KLEPPA, O. J.; J. Chem. Phys. 40 (1964) 46. (66) WrrnG, F. E. and GEnRING, E.; Ber. Bunsenges. Phys. Chem. 71 (1967) 29, 372. (67) BEARDMORE,P., HOWLETT,B. W., LICHTER, B. n . and BEVER, M. B.; Trans. Met. Soc. AIME, 236 (1966) 102. c6a) RomNSON, P. M. and BEVER, M. B.; ibid. 230 (1964) 1487. t69) DARaY, J. B.; Acta Met. 14 (1966) 265. ~70) ORIANA, R. and MURPHY, W. K.; Acta met. 10 (1962) 879. ~71) MASSE,J. D. G., ORR, R. L. and HULTGREN, R.; Trans. Met. Soc. AIME, 236 (1966) 1202. (72) DOKKEN, R. N. and ELLIOTT,J. F.; ibid. 233 (1965) 1351. ~a) FERRO, R. and CAPELLI, R.. Atti Accad. Naz. Lincei 34 (1963) 659. (~4) BROS, J. B.; C.R. (A), 263 (1966) 977.

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(7.5) SELLARS,C. M. and MAAK F.; Trans. Met. Soc. A1ME, 236 (1966) 457. (78) SUNDARESEN,M., GERAgSIMOV,I., GEIDERIKH,V. A. and VASI~'EVA,I. A.; Zhur. Fiz. Khim. 37 (1963) 2462. (77) BIDWELL,L. R. and SPEISER, R.; ,4cta Met. 13 (1965) 61. (78) SCHWERDTFEGER,K. and MUAN, A.; Acta met. 13 (1965) 509. (79) KING, R. J.; Ph.D. Thesis, Univ. of Pittsburgh, 1967. (80) DROBYSHEV,V. N., REZUKHINA,T. N. and TARASOVA,L. A.; Zhir Fiz. Khim. 39 (1965) 141, 151. (81) CAVANAOH,C. R. and ELLIOTI,J. F.; Trans. Met. Soc. A I M E , 230 (1964) 633. (82) SCHWERI)TFEGER,K.; Trans. Met. Soc. A I M E , 236 (1966) 32. csa) LAr,rrRATOV, M. F. and TARASENKO,E. V.; Zhur. Priklad. Khim. 34 (1961) 2435.
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(128) HAGER, J. P. and ELLIOT, J. F.; Trans. Met. Soc. A1ME, 239 (1967) 513. c124) OLSON, W. M. and MULFORD, R. N. R.; J. Phys. Chem. 69 (1965) 1223. (125) BRAUER,G. and SCHNELL,W. D.; J. less-common Metals. 6 (1964) 326. ~126) GINGERICH,K. A. and WILSON,D. W.; lnorg. Chem. 4 (1965) 987. (127) WORRELL,W. L. and CHn~MAN,J.; J. Phys. Chem. 68 (1964) 860. (12s) GUREVlCH, M. A.; Zhur. Neorg. Khim. 8 (1963) 2645, 2651. (129) ALEKSEYEV,V. I. and SHVARTSMAN,L. A. ; Izvest. Akad. Nauk. SSSR, Met. i Gornoe Delo, (Tekhn) (1963) 9196. (la0) GEL'D, P. V. and KUSENKO,F. G.; Izoest. Akad. Nauk. SSSR, (2) (1960) 79. (131) HUBER, E. J., HEAD, E. L. HOLLEY, C. E., STORMS, E. K. and KRIKORIAN,N. H.; J. Phys. Chem. 65 (1961) 1846. (132) HOBER, E. J., HEAD, E. L., HOLLEY, C. E. and BOWMAN, E. L.; J. Phys. Chem. 67 (1963) 793. (133) LAVRENT'EV,V. I., GERASSIMOV,I. I., et al. ; Niobium. LA.E.A., Atomic Energy Review, Vienna, in print. (134) GOLUTVIN, YU. M., KOZLOVSKAYA,T. M. and MASLENNIKOVA,E. G.; Zhur. Fiz. Khim. 37 (1963) 1362. (135) KIRKBRIDE,B. J.; The heats of formation of crystalline compounds and of glasses at 25°C. I.R. 25, Pilkington Bros. Ltd., St. Helens, Lancs. (138) L'VOVA, A. S., and FEODOS'EV,N. N.; Zhur. Neorg. Khim. 9 (1964) 2251; Zhur. Fiz. Khim. 38 (1964) 28. Cla7~ PANFILOV,B. I. and FEODOS'EVN. N.; Zhur. Neorg. Khim. 9 (1964) 2685, 2693. tlaa) MEZAKI, R., TILLEUX,E. W., BARNES,D. W. and MARGRAVE,J. L.; Ref. 3(a), p. 778. (xag) KLEPPA, O. J.; Ref. 3(b), vol. 1, p. 383. (140) LUMSDEN,J. Thermodynamics of Molten Salt Mixtures, Academic Press, London, 1966. ~141) KUBASCHEWSKI,O. ; Ref. 3(b), vol. 2, 583. 042) ROSSINI, F. D., WAGMAN, D. D., EVANS, W. H., LEVINE, S. and JAFFEE, I.; Selected values of thermodynamic properties of chemical substances, Circular 500, Nat. Bur. Stand. 1952. (143) NESMEYANOV,A. N. ; Vapour Pressure of the Chemical Elements. Elsevier; Amsterdam 1963; translation. (1~) SMITH.J. H., PAXTON,A. W. and MCCABE, C. L.; J. Phys. Chem. 68(1964) 1345. (145) STEINER,W. and KRISEMENT,O.; Arch. Eisenhuttenw. 32 (1961) 701. (146~ KSRBER, F., OELSEN, W. and LICHTENBERG,H.; Mitt. K W I Eisenforschg. Diisseldorf, 19 (1937) 131. (14"~)ZELLARS,G. R., PAYNE, S. L., MORRIS, J. P. and KIPP, R. L.; Trans. Met. Soc. A1ME, 215 (1959) 181. ~14a) SPEISER,R., JACOBS,A. J. and SPRETNAK,J. W.; ibid. 215 (1959) 181. (149) GREVESON, P. and MILLS, K. C.; Private communication, Dec. 1964. (150) HANSEN, M. and ANDERKO, K.; Constitution of Binary Alloys. McGraw-Hill, 1958. (151) HELLAWELL,A. and HUME-ROTHERY,W.; Phil. Trans. Roy. Soe. 249 (1957) 417. (152) KUBASCHEWSKI,O. and YON GOLDBECK,O. ; Trans. Faraday Soc. 45 (1949) 948. (15a) ORIANI, R. A.; Acta met. 1 (1953) 448. (154) FLEISCHER,B. and ELLIOTr, J. F.; Ref. 1, paper 2F. (155) SMITH,J. H., PAXTON,A. W. and MCCABE.; Trans. Met. Soc. A1ME, 230 (1964) 1484. (156) LYUBIMOV,A. e., ZOBENS, V. YA. and RAKHOVSKI,V. I.; Zhur. Fiz. Khim. 32 (1958) 1804. (157) KUBASCHEWSKI,O. and STUART, L. E. H.; J. chem. Engng Data, 12 (1967) 418. (15s) RAND, i . H., LIVIEY,D. T., FESCHOTrE,P., NOWOTNY, H., SEIFERT,K. and FERRO, R. ; Plutonium: Physiochem. Prpts. of its Cpds. and Alloys, Atomic Energy Reviews, LA.E.A. 4 (1966) No. 1. ¢~59~BONNIER,E. ; Private communication. Unpublished paper, presented at the EUCHEM colloquium on High. Temp. Chem., Semmering, Oct. 1967. (160) ANSARA,J. and BONNIER,E. ; Ref. 3c, paper SM98/8; HlCTER, P., MATmEU, J., DURAND F. and BONNIER,E. ; ibid., paper SM98/7. txel) BODSWORTH,C. and APPLETON,A. S. ; Problems in Applied Thermodynamics. Longmans, London, 1966. t1~2) BISWAS,A. K. and BASHFORTH,G. R. ; The Physical Chemistry of MetallurgicaIProcesses, Chapman & Hall, London, 1962. (16a) WARD, R. G. ; Physical Chemistry of Iron & Steel Making. E. ARNOLD,London, 1962.

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P R O G R E S S IN MATERIALS SCIENCE

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