Elsevier

Thermochimica Acta

Volume 529, 10 February 2012, Pages 74-79
Thermochimica Acta

Thermodynamic assessment of the Sn–Sr system supported by first-principles calculations

https://doi.org/10.1016/j.tca.2011.11.026Get rights and content

Abstract

A hybrid approach of CALPHAD and first-principles calculations was employed to perform a thermodynamic modeling of the Sn–Sr system. The experimental phase diagram and thermodynamic data available in the literature were critically reviewed. The enthalpies of formation for the 6 stoichiometric compounds (i.e. Sr2Sn, Sr5Sn3, SrSn, Sr3Sn5, SrSn3 and SrSn4) at 0 K were computed by means of first-principles calculations. These data were used as the experimental values in the optimization module PARROT in the subsequent CALPHAD assessment to provide thermodynamic parameters with sound physical meaning. A set of self-consistent thermodynamic parameters was finally obtained by considering reliable literature data and the first-principles computed results. Comprehensive comparisons between the calculated and measured quantities indicate that all the reliable experimental information can be satisfactorily accounted for by the present thermodynamic description.

Highlights

► All the literature data of Sn–Sr system is critically reviewed. ► First-principles calculation of enthalpy of formation is carried out for each compound. ► Thermodynamic parameters for Sn–Sr system are obtained by CALPHAD method. ► A hybrid approach of CALPHAD and first-principles calculations is recommended.

Introduction

Sn is one of the most prominent candidates to study the relationship between atomic structure and physical properties because a metallic and nonmetallic allotrope almost equal in stability exits for Sn [1]. This fact manifests also in binary phases of tin and electropositive metals, such as SrSn3 and SrSn4 stoichiometric compounds, which can be both superconducting under certain conditions [1], [2], [3]. In addition, Sn and Sr are important additive elements in several multi-component commercial Al alloys. The thermodynamic description for the Sn–Sr system is within our project to establish a precise thermodynamic database for multi-component Al alloys. Furthermore, a thorough thermodynamic assessment of the Sn–Sr system is needed to provide a reliable basis for thermodynamic extrapolations and calculations in related ternary and higher-order systems. This binary phase diagram has been constructed by several groups of researchers [3], [4], [5], [6], [7], [8]. The crystal structures of all the intermetallic compounds in the Sn–Sr system have been investigated [1], [2], [3], [5], [8], [9], [10], [11], [12], [13], [14]. Limited thermodynamic data are also available in the literature [15], [16], [17]. However, no thermodynamic modeling has been carried out up to now, and thus a thermodynamic modeling of the Sn–Sr system is the major target in the present work.

Recent studies have indicated that the incorporation of first-principles calculations based on density functional theory (DFT) [18] into the CALPHAD framework can be quite fruitful [19], [20], [21]. Using the atomic numbers and crystal structure information as input, first-principles calculations can compute thermodynamic and structural properties for both stable and metastable phases, which can be used as the experimental values in the optimization module PARROT for the modeling of the system. The enthalpy of formation, as the leading term in the Gibbs energy, is the predominant quantity among various thermodynamic properties. Calculation of this thermodynamic quantity for all the Sn–Sr intermetallic compounds is one of the main focuses targeted by first-principles calculations.

This paper will critically review the experimental phase diagram, crystallographic and thermodynamic data available in the literature first, as presented in Section 2. The theoretical background of the first-principles calculations and the corresponding results will be given in Section 3. Subsequently, the theoretical parts CALPHAD modeling and the optimization strategy will be concisely introduced in Sections 4 Thermodynamic models, 5 Optimization strategy, respectively. In Section 6, the results from thermodynamic modeling will be addressed in detail. Finally, the conclusions of the present work will be drawn in Section 7.

Section snippets

Phase diagram and crystallographic data

As early as in 1930, Ray [4] measured the phase equilibria of the Sn–Sr system within the concentration range of 63–100 at.% Sn using thermal analysis (TA) and microscopy. Two compounds, SrSn5 and SrSn3, were observed by Ray [4]. Later, Marshall and Chang [6] investigated the phase equilibria from 65 to 100 at.% Sn using a combination of differential thermal analysis (DTA), microprobe analysis, metallography and X-ray diffractography (XRD). However, Marshall and Chang [6] found that the phase in

Theoretical background

According to the review in Section 2.2, there is only one piece of information about the enthalpy of formation for Sr2Sn [15], while no any thermochemical information exists for the other 5 intermetallic compounds (i.e. Sr5Sn3, SrSn, Sr3Sn5, SrSn3 and SrSn4). As described in Section 2.1 and shown in Table 1, the crystal structures of all the 6 intermetallic compounds are well established, which is the only input required for the first-principles calculations of their enthalpies of formation.

The

Thermodynamic models

According to Palenzona and Pani [8], there are 11 stable phases in the binary Sn–Sr system, i.e. liquid, β-Sr, α-Sr, β-Sn, α-Sn, Sr2Sn, Sr5Sn3, SrSn, Sr3Sn5, SrSn3 and SrSn4. The liquid phase is treated as a substitutional solution phase and its Gibbs energy can be described by the Redlich–Kister polynomials [26]:GmLHSER=xSnGSnL0+xSrGSrL0+RT(xSnlnxSn+xSrlnxSr)+xSnxSr[a0+b0T+(xSnxSr)(a1+b1T)+(xSnxSr)2(a2+b2T)+]in which HSER is the abbreviation of xSnHSnSER+xSrHSrSER, R is the ideal gas

Optimization strategy

The thermodynamic optimization of the parameters was performed using the PARROT module of Thermo-Calc [28]. This module works by minimizing the sum of the squares of the difference between experimental values and the computed ones. The step-by-step optimization procedure described by Du et al. [29] was utilized in the present assessment. Firstly, the presently first-principles calculated enthalpy of formation for each compound was fixed as the values of coefficient A in Eq. (3) for each

Results and discussion

Fig. 1 shows the calculated Sn–Sr phase diagram according to the thermodynamic parameters obtained in the present work. The detailed comparison between the calculated Sn–Sr phase diagram and the experimental data from different sources [3], [4], [5], [6], [8], [13] are presented in Fig. 2. As can be seen in Fig. 2, the presently calculated phase diagram can describe most of the reliable experimental data. The calculated invariant equilibria of the Sn–Sr system according to the presently

Conclusion

  • All the experimental phase diagram and thermodynamic data available in the literature have been critically reviewed. The enthalpies of formation for the 6 stoichiometric compounds (i.e. Sr2Sn, Sr5Sn3, SrSn, Sr3Sn5, SrSn3 and SrSn4) in the Sn–Sr system were computed by means of first-principles calculations. Such calculated enthalpies of formation can provide reasonable energy levels for the thermodynamic properties of binary compounds.

  • A set of self-consistent thermodynamic parameters was

Acknowledgements

The financial support from the Creative Research Group of National Natural Science Foundation of China (Grant No. 51021063) and the key program of the National Natural Science Foundation of China (Grant No. 50831007) is acknowledged. Jingrui Zhao thanks the Ministry of Education of China for over-sea student fellowship (Grant No. 2010637064). One of the authors (Lijun Zhang) would like to thank the Alexander von Humboldt Foundation of Germany for supporting and sponsoring the research work at

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