Thermodynamic Properties of Elements and Compounds in Al-Sc Binary System from Ab Initio Calculations Based on Density F

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I.

INTRODUCTION

SC is known as an outstanding alloying element to enhance the strength of Al-based alloy.[1] Fine dispersed intermetallics in Al-Sc system is an important strengthening precipitate for Al-based alloys which have been used extensively for structural material in aircraft, vessel, and weapon due to their low specific weight, high strength, and good chemical stability. The crystal structure information of element FCC Al, HCP Sc, and binary intermetallic compounds are shown in Table I. To design such kind of enhanced Al-based alloy, it is essential to know the thermodynamic properties of FCC Al, HCP Sc, B2 AlSc, C15 Al2Sc, B82 AlSc2, and L12 Al3Sc. In the specific field of phase diagram and thermodynamic properties of alloys, one currently needs to calculate three additive contributions to the free energy, depending on the required accuracy and the complexity of studied system. With the advanced computational methods and computer infrastructure, the ab initio calculation based on density functional theory is becoming a powerful tool in understanding and predicting the structural and physical properties of materials.[2–8] The first contribution to the free energy to be considered is the cold energy or the 0 K (273 °C) total energy, which is considerably easy to calculate for solid materials. ZEYOU ZHOU, SHUSHI DOU, CHUNFENG ZHAO, YUANPENG XIONG, YUFENG WU, and SHANGJIN YANG, Master Degree Candidates, BO WU, Ph.D., Professor, and ZHENYI WEI, Doctoral Candidate, are with the Multiscale Computational Materials Facility, School of Materials Science and Engineering, Fuzhou University, University Town, Fuzhou 350100, P.R. China. Contact e-mail: [email protected], [email protected] Manuscript submitted June 17, 2013. METALLURGICAL AND MATERIALS TRANSACTIONS A

To calculate the structural, mechanical, acoustic, spectroscopic, and thermodynamic properties at finite temperatures, the contribution of lattice thermal vibration to the total free energy needs to be taken into account.[9–12] Theoretically, the commonly accepted method is the lattice dynamics or phonon approach. In the latter approach, within the harmonic or quasi-harmonic approximation, all thermodynamic formulas are strictly derived from the basis of statistical physics. One of the main advantages is that all the quantities needed for inputting to the phonon theory can be calculated by the ab initio methods.[13–17] The ab initio calculation of phonon characteristics falls into two classes: the linear response method[18] and the direct method.[9,19] The phonon dispersions of FCC Al were calculated by de Gironcoli[20] and Debernardi et al.[21] using local density approximation (LDA), respectively. However, their results show slightly higher frequencies than the experimental result.[22] While the computed results of Wang et al.[23] using the linear response theory agree well with the experimental data.[22] Bose et al.[24] and Singh and Prakash[25] calculated the phonon dispersion of HCP Sc. Although the overall agreement is considerably well, they underestimat

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