G. Cacciamani

Thermodynamic measurements and assessment of the Al–Sc system

Abstract A study of the binary Al-Sc phase diagram has been performed by means of thermodynamic calculations and experimental measurements. The enthalpy of formation of all intermetallic compounds has been determined and a cursory examination of the phase equilibria carried out, for compositions greater than 40 at% Sc. Two new invariant reactions have been identified in the Sc-rich part of the diagram: L ↔ (βSc)+Sc2Al at 1185°C and (βSc) ↔ Sc2Al+(αSc) at 970°C. A coherent set of Gibbs energy expressions for all the phases in the system has been generated by a least square optimisation procedure using all the experimental data available. The overall agreement is satisfactory but some uncertainties still persist, especially concerning the ScAl phase, owing to experimental difficulties.

The Al–R–Mg (R=Gd, Dy, Ho) systems. Part II: Thermodynamic modelling of the binary and ternary systems

Abstract The thermodynamic modelling and optimisation of the Al–R, R–Mg and Al–R–Mg (R=Gd, Dy, Ho) systems has been carried out, the Al–Mg system being already optimised in literature. The Compound Energy Formalism (CEF) has been used to describe the thermodynamic functions of either solutions and stoichiometric phases present in the systems. In particular, the order/disorder relation between cI2-W (A2) and cP2-CsCl (B2) phases present in the systems has been taken into account and thermodynamically modelled. Moreover γ-(Mg,Al) and R5(Mg1-xAlx)24 (R=Dy, Ho) phases, related to the cI58-αMn (A12) type structure, have been modelled as different sublattice occupations of the same A12 phase. The thermodynamic modelling of the ternary systems is mainly based on the experimental investigation carried out in our laboratory and reported in a separate paper in this issue [1]. As a result, a complete description of the solid-solid and solid-liquid phase equilibria in the six binary and three ternary systems has been obtained.

Thermodynamic analysis of glass formation in Fe-B system

Abstract A thermodynamic optimisation of the Fe-B system has been carried out in order to model metastable phases. Amorphous and Fe 3 B metastable phases have been considered in the assessment in order to describe, from a thermodynamic point of view, the well known glass forming ability of this system. An excess specific heat has been considered for the liquid alloys in order to take into account ordering processes on undercooling. The glass transition has been considered as a second order transition between undercooled liquid and amorphous phases. The effect of lattice stabilities on assessment has been discussed considering different descriptions for the free energy of undercooled pure liquid Fe. The calculated stable and metastable phase diagrams are in good agreement with experimental data, as well as invariant equilibria and thermodynamic properties. The results evidence the existence of an excess specific heat for glass forming Fe-B liquid alloys, which allows a reasonable description of thermodynamic functions for all phases in a wide temperature range.

The Al-Er-Mg ternary system Part II: Thermodynamic modeling

A thermodynamic modeling and optimization of the Al-Er, Er-Mg, and Al-Er-Mg systems has been carried out, the Al-Mg system having already been optimized in the literature. The sublattice model has been used to describe the thermodynamic functions of both the solution phases and the stoichiometric phases present in the systems. In particular, the order/disorder relationship between the couples of phases A2/B2 and A1/L12 present in the system as bcc-(Er,Mg)/Er(Mg1−x Al x ) and fcc-(Al)/(Al1−x Mg x )3Er, respectively, has been taken into account and thermodynamically modeled. Moreover γ-(Al,Mg) and Er5(Mg1−x Al x )24 phases, both related to the cI58-αMn (A12) type structure, have been modeled as different sublattice occupations of the same A12 phase. The thermodynamic modeling and the experimental investigation of the phase equilibria (reported in part I of this work) have been carried out by a recursive procedure. As a result, complete descriptions of the solid-solid and solid-liquid phase equilibria have been obtained.

Contribution to the evaluation of rare earth alloy systems

It is well known that within the family of the rare earth elements (especially the “trivalent” ones) several properties change according to well-recognized and systematic patterns. A general consideration of the constitutional properties (thermodynamic properties, crystal structures, and phase diagrams) of alloys formed by the various rare earths enables a number of empirical regularities to be deduced. This behavior can constitute a prediction scheme and a reliability criterion in the evaluation of the data concerning series of various rare earth alloys with the same element. Examples of the application of this behavior to phase diagram assessment and prediction are mentioned. Special attention is given to the binary rare earth alloys formed with magnesium and aluminum. The predicted versions of the Tb-Mg and Tb-Al phase diagrams are presented at the end.

Computer coupling of thermodynamics and phase diagrams: the gadolinium-magnesium system as an example

Abstract A thermodynamic analysis of the binary Gd-Mg system is presented, and its description is optimized using the experimental phase diagram and thermodynamic values. The excess Gibbs energies of the liquid and solid (α-Gd, β-Gd and Mg) solutions were described according to the Redlich-Kister polynomial expansion. The intermediate compounds (GdMg, GdMg2, GdMg3 and GdMg5) were assumed to be stoichiometric phases. A good agreement between the experimental and the computed phase diagram is shown. The results are briefly discussed and compared with those for other binary rare earth-Mg alloys.

Driving forces for crystal nucleation in Fe–B liquid and amorphous alloys

Abstract The Fe–B system has been reassessed in order to model metastable and amorphous phases. An excess specific heat term has been added to describe Gibbs free energy of the liquid phase on undercooling and glass transition has been considered as a second-order transition. In addition, a recently proposed description of pure Fe lattice stabilities has been used for this optimisation. Stable and metastable phase diagrams have been calculated, as well as thermodynamic properties, which turn out in agreement with experimental data. Thermodynamic driving forces for crystal nucleation have also been evaluated for liquid and amorphous phases. According to experimental findings, it was found that the first nucleating phase is b.c.c. Fe for B-poor amorphous alloys. However, for B-rich compositions, a competition between Fe2B and Fe3B nucleation has been evidenced. A full explanation of the crystallisation process requires the evaluation of interfacial energies.

ON THE THERMOCHEMISTRY OF THE RARE EARTH ANTIMONIDES. THE Dy-Sb SYSTEM

Abstract The data in the literature relevant to the rare earth antimonide phase diagrams and the crystallochemical and thermodynamic properties of the rare earth antimonides are summarized. The data obtained in an investigation of Dy-Sb compounds are reported. This investigation was performed using X-ray and metallographic analyses and calorimetric measurements of the heats of formation. The values of Δ H form (kJ (g atom) −1 ±2.0) for the following compounds were obtained for the reaction in the solid state at 300 K (the crystal structure data have also been confirmed): Dy 5 Sb 3 (hP16-Mn 5 Si 3 -type),−105.5; Dy 4 Sb 3 (cI28-anti-Th 3 P 4 -type), −111.5; DySb (cF8-NaCl-type), −114. These data, together with those relevant to the other rare earth antimonides, are discussed and their trends are in good agreement with the relationships proposed by Gschneidner. The experimental data are in agreement with those computed according to Miedemas model and, in the case of the rare-earth-rich alloys, also agree with those calculated according to Kubaschewskis suggestion based on the effective coordination numbers.

Thermodynamic modelling of the Co–Ti system

Abstract In the Co–Ti system many solid solutions are present: A1, L12, A2, B2, A3, and Laves C15 and C36 phases. Two of them exhibit order/disorder transitions: A1 and L12, A2 and B2. In this optimisation the sublattice model has been used to describe the thermodynamic functions of the above-mentioned phases. The order/disorder transformation A1↔L12 has been described by modelling the L12 phase with either two or four sublattices both descriptions being mathematically equivalent. The A2↔B2 relation was also modelled in a similar way. The cited solid solutions, together with the liquid (Redlich–Kister excess model) and the CoTi2, considered as stoichiometric, phases have been optimised by means of the Thermo-Calc software, on the basis of the literature data concerning both phase equilibria and thermodynamics.

On the thermochemistry of the rare earth compounds with thep-block elements

A summary is given of the experimental work carried out to determine the heats of formation of the rare earth compounds with a number of elements of thep-block of the periodic table (in particular Al, In, Sn, Pb, As, Sb, and Bi). The experimental methods and the devices constructed to this end are briefly described and commented on. Some results recently obtained in the thermochemical investigation of binary (Pr-Al and Gd-Pb) and ternary (Ce-Ni-Al and La-Sb-Bi) alloys are presented.