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Acta Metall Sin  2017, Vol. 53 Issue (9): 1133-1139    DOI: 10.11900/0412.1961.2016.00583
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First Principles Study on Elastic and Thermodynamic Properties of Mg1-xZnx Alloys
Ronghua CUI, Xinyu WANG, Zhengchao DONG, Chonggui ZHONG()
School of Sciences, Nantong University, Nantong 226019, China
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Abstract  

As one of the lightest metal materials in current industrial applications, Mg alloys are being widely used in automotive, aircraft, aerospace and biomedical industries because of their super high strength-to-weight ratio and biodegradability. However, their limited ductility and workability at room temperature have become a bottleneck for many applications. Therefore, it has become critically important to obtain the Mg alloys with improved strength and ductility. On the other hand, Zn is a transition metal element, often applied to improve the mechanical properties. Also it has basic safety for biomedical applications. So the Mg-Zn alloys have attracted considerable attentions in recent years. Extensively investigated experiments indicated that the hardness of Mg-Zn alloys increases with increasing Zn content. However, there are only a few reported works about their mechanical properties and theoretically thermodynamic properties of Mg-Zn alloys. In this work, first-principles investigations have been performed on lattice parameters, elastic properties and thermodynamic properties of hcp Mg and eight kinds of Mg1-xZnx alloys with different contents of Zn less than 2% (atomic fraction), using the virtual crystal approximation in the frame of the density functional theory and the density functional perturbation theory. The elastic constants of Mg and Mg1-xZnx alloys with different Zn contents have been investigated by using optimized lattice, and their Young's moduli, Poisson ratios and elastic anisotropies have been analyzed in detail. Also, the thermodynamic properties, including Helmholtz free energies, internal energies, entropy and constant volume heat capacities of these alloys as a function of temperature were discussed. The results show that with increasing Zn content in Mg1-xZnx alloys, the lattice constants a and c, the entropy and constant volume heat capacity of Mg1-xZnx alloy decrease, while the elastic constants, Helmholtz free energy and internal energy of Mg1-xZnx alloy increase correspondingly. On the other hand, further discussions find that the effects of Zn content on free energy and entropy of Mg1-xZnx alloy are enhanced and the effect on heat capacity of each alloy at constant volume first increases, then decreases as the temperature rises. In summary, it can be given the conclusions that the high content of Zn in Mg1-xZnx alloy is beneficial to increasing the hardness and ductility of such Mg1-xZnx alloy, but decreasing its isotropy.

Key words:  Mg1-xZnx alloy      elastic property      thermodynamic property      first principle     
Received:  30 December 2016     
ZTFLH:  TG146.2  
Fund: Supported by National Natural Science Foundation of China (No.11447229) and Natural Science Foundation of Jiangsu Province (No.BK2012655)

Cite this article: 

Ronghua CUI, Xinyu WANG, Zhengchao DONG, Chonggui ZHONG. First Principles Study on Elastic and Thermodynamic Properties of Mg1-xZnx Alloys. Acta Metall Sin, 2017, 53(9): 1133-1139.

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https://www.ams.org.cn/EN/10.11900/0412.1961.2016.00583     OR     https://www.ams.org.cn/EN/Y2017/V53/I9/1133

Alloy a / nm c / nm c/a Method Reference
Mg 0.321 0.524 1.632 This work
0.319 0.523 1.639 GGA-PBE Calc.[7]
0.318 0.522 1.642 GGA-PW91 Calc.[6]
0.321 0.521 1.623 Exp.[18]
0.320 0.520 1.625 Exp.[19]
Mg0.9975Zn0.0025 0.321 0.521 1.623 This work
Mg0.9950Zn0.0050 0.320 0.520 1.625 This work
Mg0.9925Zn0.0075 0.319 0.519 1.627 This work
Mg0.9900Zn0.0100 0.319 0.519 1.629 This work
Mg0.9875Zn0.0125 0.318 0.518 1.629 This work
Mg0.9850Zn0.0150 0.317 0.517 1.632 This work
Mg0.9825Zn0.0175 0.316 0.517 1.636 This work
Mg0.9800Zn0.0200 0.315 0.516 1.636 This work
Table 1  Lattice parameters a, c and c/a of Mg and eight Mg1-xZnx alloys
Alloy C11 C12 C13 C33 C44 Method Reference
Mg 61.80 24.58 17.86 63.52 15.98 This work
59.30 25.80 21.00 61.60 14.20 GGA-PW91 Calc.[23]
64.82 25.76 19.57 65.55 17.86 GGA-PW91 Calc.[6]
61.00 24.00 21.00 69.00 21.00 GGA-PW91 Calc.[11]
61.40 26.80 21.80 65.10 17.70 GGA-PBE Calc.[22]
59.43 25.60 21.40 61.64 16.42 Exp.[25]
63.48 25.94 21.70 66.45 18.42 Exp.[24]
Mg0.9975Zn0.0025 61.72 24.68 18.60 65.41 16.44 This work
Mg0.9950Zn0.0050 63.17 25.20 19.18 66.79 16.60 This work
Mg0.9925Zn0.0075 64.70 25.76 19.76 68.12 16.73 This work
Mg0.9900Zn0.0100 66.21 26.35 20.32 69.34 16.81 This work
Mg0.9875Zn0.0125 67.73 26.99 20.93 70.69 16.92 This work
Mg0.9850Zn0.0150 69.13 27.62 21.53 71.90 17.00 This work
Mg0.9825Zn0.0175 70.63 28.31 22.13 73.07 17.05 This work
Mg0.9800Zn0.0200 72.13 29.04 22.75 74.26 17.12 This work
Table 2  Elastic constants of Mg and eight Mg1-xZnx alloys
Alloy B / GPa G / GPa Y / GPa ν B/G AU
Mg 34.17 18.38 46.75 0.272 1.859 0.106
Mg0.9975Zn0.0025 34.73 18.57 47.29 0.273 1.870 0.093
Mg0.9950Zn0.0050 35.58 18.90 48.16 0.274 1.883 0.096
Mg0.9925Zn0.0075 36.45 19.21 49.02 0.276 1.897 0.101
Mg0.9900Zn0.0100 37.30 19.49 49.79 0.278 1.914 0.108
Mg0.9875Zn0.0125 38.20 19.77 50.59 0.279 1.932 0.115
Mg0.9850Zn0.0150 39.05 20.01 51.27 0.281 1.951 0.121
Mg0.9825Zn0.0175 39.93 20.24 51.95 0.283 1.972 0.130
Mg0.9800Zn0.0200 40.83 20.48 52.64 0.285 1.994 0.137
Table 3  Bulk moduli B, shear moduli G, Young's moduli Y, Poisson ratios ν, B/G and anisotropy indexes AU of Mg and eight Mg1-xZnx alloys
Fig.1  Helmholtz free energy (F) curves of Mg and Mg1-xZnx alloys in the range of temperature 0~600 K (Inset shows the Helmholtz free energy curves of Mg and Mg1-xZnx alloys near 400 K)
Fig.2  Internal energy (U) curves of Mg and Mg1-xZnx alloys in the range of temperature 0~600 K (Inset shows the internal energy curves of Mg and Mg1-xZnx alloys near 400 K)
Fig.3  Entropy (S) curves of Mg and Mg1-xZnx alloys in the range of temperature 0~600 K (Inset shows the entropy curves of Mg and Mg1-xZnx alloys near 400 K)
Fig.4  Heat capacity (CV) curves of Mg and Mg1-xZnx alloys in the range of temperature 0~600 K (Inset shows heat capacity curves of Mg and Mg1-xZnx alloys near 400 K)
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