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金属学报  2017, Vol. 53 Issue (9): 1133-1139    DOI: 10.11900/0412.1961.2016.00583
  本期目录 | 过刊浏览 |
Mg1-xZnx合金的弹性和热力学性质的第一性原理研究
崔荣华, 王歆钰, 董正超, 仲崇贵()
南通大学理学院 南通 226019
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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摘要: 

基于密度泛函理论及密度泛函微扰理论为基础的第一性原理计算,采用虚晶近似的方法,研究了具有hcp结构且Zn含量在2% (原子分数)范围内的8种Mg1-xZnx合金的晶格常数、弹性性质和热力学性质。通过优化结构计算Mg和Zn含量不同的Mg1-xZnx合金弹性常数,对Young's模量、Poisson比、弹性各向异性等进行了详细分析,给出了Mg及Mg1-xZnx合金的晶格振动Helmholtz自由能、内能、熵和定容热容等随温度变化情况。结果表明,随着Zn含量增加晶格常数ac均相应减小,弹性常数、自由能和内能增大,熵及定容热容减小;另一方面,随温度升高,Zn含量对自由能和熵的影响程度增大,而对定容热容的影响程度先增大后减小。Mg1-xZnx合金中Zn含量的增加有利于提高材料硬度和韧性,但也增大了材料的各向异性。

关键词 Mg1-xZnx合金弹性性质热力学性质第一性原理    
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 wordsMg1-xZnx alloy    elastic property    thermodynamic property    first principle
收稿日期: 2016-12-30      出版日期: 2017-05-26
ZTFLH:  TG146.2  
基金资助:国家自然科学基金项目No.11447229和江苏省自然科学基金项目No.BK2012655
作者简介:

作者简介 崔荣华,男,1978年生,硕士

引用本文:

崔荣华, 王歆钰, 董正超, 仲崇贵. Mg1-xZnx合金的弹性和热力学性质的第一性原理研究[J]. 金属学报, 2017, 53(9): 1133-1139.
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.

链接本文:

http://www.ams.org.cn/CN/10.11900/0412.1961.2016.00583      或      http://www.ams.org.cn/CN/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
表1  Mg和8种Mg1-xZnx合金的晶格常数a、c以及c/a
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
表2  Mg和8种Mg1-xZnx合金弹性常数
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
表3  Mg和8种Mg1-xZnx合金的体积模量B、剪切模量G、Young's模量Y、Poisson比ν、B/G、弹性各向异性指数AU
图1  0~600 K内Mg和Mg1-xZnx合金的Helmholtz自由能曲线
图2  0~600 K内Mg和Mg1-xZnx合金的内能曲线
图3  0~600 K内Mg和Mg1-xZnx合金的振动熵曲线
图4  0~600 K内Mg和Mg1-xZnx合金的定容热容曲线
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