Thermodynamic modeling of the Sr–X (X=H, Li, Na, Sc) systems
Highlights
► The Sr−X (X=H, Li, Na, Sc) systems have been critically reviewed and modeled by means of the CALPHAD technique. ► The enthalpies of formation at 0 K for the Sr6Li23 and Sr3Li2 have been computed by means of first-principles calculations. ► A set of self-consistent thermodynamic parameters was obtained for each of these binary systems.
Introduction
Al alloys are widely used for commercial applications mainly due to the low density as well as good mechanical properties. H, Li, Na, Sc and Sr are important elements that affect the mechanical properties of Al alloys. Hydrogen embrittlement is considered as an embrittlement mechanism in Al alloys, which appears during the corrosion process [1]. The addition of Li to Al offers the promise of substantially reducing the weight of Al alloys and increasing the performance [2]. Modification of Al alloys with addition of Na or Sr is being applied to further improve the mechanical properties of Al alloys. Na has historically been the predominant modifying agent for Al–Si alloys. However, Sr has substituted for Na in recent years owing to three disadvantages of Na modified Al alloys: difficulty in controlling the concentration, fuming during addition and difficulty in keeping modification effect [3], [4], [5]. Sc, which is an alloying element in Al alloys, has extensively received an interest due to the grain refinement during casting or welding, precipitation hardening resulting from Al3Sc particles and grain structure control from Al3Sc dispersoids [6]. In the production of Al alloys, knowledge of phase diagrams and thermodynamic properties is essential.
The thermodynamic descriptions for the Sr–X (X=H, Li, Na, Sc) binary systems are a continuing effort of our previous attempts [7], [8], [9], [10], [11] to establish a thermodynamic database for multicomponent Al alloys. However, to the best of our knowledge, so far there are no thermodynamic assessments for these binary systems. A thorough thermodynamic assessment of the Sr–X (X=H, Li, Na, Sc) systems is needed in order to provide a reliable basis for thermodynamic extrapolations and calculations in related ternary and higher-order systems. The purpose of the present work is devoted to providing a self-consistent set of thermodynamic parameters for each of these binary systems by means of a hybrid approach of CALPHAD method and first-principles calculations.
Section snippets
The Sr–H system
The only experimental phase diagram of pseudobinary Sr–SrH2 system was determined by Peterson and Colburn [12] by means of differential thermal analysis (DTA), chemical analysis of isothermal equilibration and X-ray diffraction (XRD). The maximum solubility of H in (βSr) was determined to be 43.2 at% H at the peritectic reaction of 880 °C. The αSrH2, which was stable at low temperature, transformed into βSrH2 at 855 °C. An intermediate solution phase γ with Hcp_A3 structure was observed to be
Unary phase
The descriptions of the Gibbs energy of the pure element i (i=Sr, H, Li, Na, Sc) in the phase φ are taken from the SGTE database [20], and the functions are expressed by the following equation:where is the molar enthalpy of the element i at 298.15 K and 1 bar in its standard element reference (SER) state, and T is the absolute temperature.
The Sr–X (X=Li, Na, Sc) system
The liquid, (αSr), (Li), (Na), (βSc), (βSr) and (αSc) phases are modeled as completely disordered
First-principles calculation
In the present work, first-principles calculations based on density functional theory (DFT) [34] are carried out to evaluate the enthalpies of formation of Sr6Li23 and Sr3Li2 in the Sr–Li system, which employ the plane-wave pseudopotential total energy method and are implemented in Vienna ab initio simulation package (VASP) [35], [36]. Herein, the calculations adopt projector augmented wave potentials [37] and the generalized gradient approximation of Perdew–Burke–Ernzerhof [38] to depict
Results and discussion
The optimization of the thermodynamic parameters in the Sr–X (X=H, Li, Na, Sc) systems was performed with the PARROT module of the Thermo-calc software [42]. The step-by-step optimization procedure described by Du et al. [43] was adopted in the present assessment.
Taking the Sr–H system as an example, the optimization began with the βSrH2 phase, and was fixed according to the experimental enthalpy of formation [16]. In view of the experimental data associated with the liquid phase and the
Conclusion
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A critical literature review of the Sr–X (X=H, Li, Na, Sc) systems has been made to the experimental phase diagram and thermodynamic data. The enthalpies of formation for the two compounds Sr6Li23 and Sr3Li2 computed via first-principles calculations are used in the present thermodynamic modeling.
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A set of self-consistent thermodynamic parameters is obtained by the CALPHAD approach for the Sr–X (X=H, Li, Na, Sc) systems. The comprehensive comparisons show that the calculated phase diagram and
Acknowledgments
The financial support from the National Basic Research Program of China (Grant no. 2011CB610401) and the National Natural Science Foundation of China (Grant nos. 50831007, 51021063 and 50971135) are greatly acknowledged.
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