Structure and thermodynamics of the key precipitated phases in the Al–Mg–Si alloys from first-principles calculations Dongdong Zhao • Liangcai Zhou • Yi Kong • Aijun Wang • Jiong Wang • Yingbiao Peng • Yong Du • Yifang Ouyang • Wenqing Zhang Received: 1 May 2011 / Accepted: 1 July 2011 / Published online: 13 July 2011 Ó Springer Science+Business Media, LLC 2011 Abstract First-principles calculations have been carried out to investigate the structure, stability, and finite-tem- perature thermodynamic properties of the key precipitates in the Al–Mg–Si alloys including b 00 -Mg 5 Si 6 , U1- Al 2 MgSi 2 , U2-Al 4 Mg 4 Si 4 , b 0 -Mg 9 Si 5 , and b-Mg 2 Si. The calculated phonon densities of states indicate that these precipitated phases are vibrationally stable. Within the framework of the quasiharmonic approach, the finite-tem- perature thermodynamic properties of these precipitated phases including entropy, enthalpy, and Gibbs free energy have been calculated. The heat capacities at constant pressure for these precipitates are predicted. The finite- temperature entropies of formation, enthalpies of formation, and Gibbs free energy of formation for these precipitates are also computed. The acquired thermodynamic properties are expected to be utilized for the prediction of the meta- stable equilibria in the Al–Mg–Si alloys. Introduction The Al–Mg–Si alloys have received considerable attention due to the wide applications of 6xxx alloys in automotive industries [1–7]. These alloys have good extrudability and age hardening characteristics as well as excellent corrosion, surface, and welding properties [5, 8–10], which make them find applications in a wide range of areas, such as in the construction, automobile, and aerospace industries. An increasing demand for the improved control of the prop- erties of the Al–Mg–Si alloys requires knowledge of the finest details of the precipitation sequence, which includes diffusion, solute clustering, nucleation, growth, and trans- formation of the precipitates. The precipitation sequence of the Al–Mg–Si alloys during age hardening is complex and involves a wide variety of metastable phases (e.g., Guinier– Preston zones (GP-zones), b 00 , U1, U2, B 0 , b 0 , b)[5, 9]. The generic precipitation sequence generally accepted for the Al–Mg–Si alloys is as follows [5, 9]: SSSS ! GP  zones ! b 00 ðMg 5 Si 6 Þ!ðU1; U2; B 0 ; b 0 Þ ! bðMg 2 SiÞ; Si where SSSS stands for the supersaturated solid solution, GP- zones are aggregates of solute atoms in the aluminum matrix. Among these metastable precipitate phases, the b 00 phase with a monoclinic structure of a composition Mg 5 Si 6 [2] is believed to be the most effective strengthening pre- cipitate. Here, the phases U1, U2, and B 0 are also referred to ‘‘type A’’, ‘‘type B’’, and ‘‘type C’’ precipitates, respectively [4]. The b 0 precipitate is in rod shape, and is reported to be present in over-aged specimens [4]. Vissers et al. [11] have determined the detailed structure of b 0 phase using electron diffraction (ED), and reported that b 0 has a composition of Mg 9 Si 5 [11]. It is worth noting that except for the equilib- rium phases b-Mg 2 Si and Si, all phases are metastable. D. Zhao  L. Zhou  Y. Kong  A. Wang  J. Wang  Y. Peng  Y. Du (&) State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083, People’s Republic of China e-mail: yongducalphad@gmail.com Y. Ouyang Department of Physics, Guangxi University, Nanning 530004, People’s Republic of China W. Zhang State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, People’s Republic of China 123 J Mater Sci (2011) 46:7839–7849 DOI 10.1007/s10853-011-5765-4