无序β-Ti1-xNbx合金自由能及弹性性质的第一性原理计算:特殊准无序结构和相干势近似的比较

doi:10.11900/0412.1961.2020.00015

金属学报

2020, Vol. 56

Issue (9): 1304-1312 DOI: 10.11900/0412.1961.2020.00015

本期目录 | 过刊浏览

无序β-Ti₁_-_xNb_x合金自由能及弹性性质的第一性原理计算:特殊准无序结构和相干势近似的比较

张海军¹^,², 邱实³, 孙志梅³, 胡青苗¹(

), 杨锐¹

1 中国科学院金属研究所沈阳 110016
2 中国科学技术大学材料科学与工程学院沈阳 110016
3 北京航空航天大学材料科学与工程学院北京 100191

First-Principles Study on Free Energy and Elastic Properties of Disordered β-Ti₁_-_xNb_x Alloy: Comparison Between SQS and CPA

ZHANG Haijun¹^,², QIU Shi³, SUN Zhimei³, HU Qingmiao¹(

), YANG Rui¹

1 Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
2 School of Materials Science and Engineering, University of Science and Technology of China, Shenyang 110016, China
3 School of Materials Science and Engineering, Beihang University, Beijing 100191, China

引用本文:

张海军, 邱实, 孙志梅, 胡青苗, 杨锐. 无序β-Ti₁_-_xNb_x合金自由能及弹性性质的第一性原理计算:特殊准无序结构和相干势近似的比较[J]. 金属学报, 2020, 56(9): 1304-1312.
Haijun ZHANG, Shi QIU, Zhimei SUN, Qingmiao HU, Rui YANG. First-Principles Study on Free Energy and Elastic Properties of Disordered β-Ti₁_-_xNb_x Alloy: Comparison Between SQS and CPA[J]. Acta Metall Sin, 2020, 56(9): 1304-1312.

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摘要:

采用第一性原理方法(VASP及EMTO)结合特殊准无序结构(SQS)和相干势近似(CPA)的方法，对比研究了bcc结构β-Ti_1-_xNb_x无序合金的晶格参数、自由能及弹性常数随成分x的变化。结果表明，VASP-SQS及EMTO-CPA计算得到的晶格参数符合良好，均随Nb含量增加而增加，局域晶格弛豫对晶格参数的影响可以忽略；EMTO-CPA自由能计算预测β-Ti_1-_xNb_x中存在相分解，但VASP-SQS计算因依赖于具体SQS结构，难以合理地描述合金的相分解。EMTO-CPA及无弛豫VASP-SQS计算得到的弹性常数C₁₁和C₁₂随Nb含量增加而增大，C₄₄减小，但EMTO-CPA高估了合金的弹性稳定性；低Nb含量时，由于β-Ti_1-_xNb_x的bcc结构不稳定，导致VASP-SQS计算得到的局域晶格畸变显著增加，使得考虑原子弛豫的VASP-SQS计算得到的自由能及弹性常数随Nb含量的变化偏离正常趋势。

关键词 ：钛合金, 无序合金, 特殊准无序结构, 相干势近似, 弹性常数, 第一性原理计算

Abstract：

Elastic modulus is one of the key properties for the application of biomedical β titanium alloy as human bone replacement because the elastic modulus of the alloy has to match that of the bone so as to avoid the stress shielding effect. Alloying of Nb is commonly used in biomedical β titanium alloys. In the present work, the lattice parameter, free energy and elastic modulus of β-Ti_1-_xNb_x alloy were investigated by using first-principles method based on density functional theory. The random distribution of Nb atoms in the alloy were described by using both special quasirandom structure (SQS) and the coherent potential approximation (CPA) techniques, in combination with first principles plane-wave pseudopotential (VASP) and exact muffin-tin orbital (EMTO) methods, respectively. The results showed that the lattice constants from both VASP-SQS and EMTO-CPA calculations increase linearly with Nb content x, while the influence of the local lattice distortion is negligible. The calculations of the free energies demonstrated that EMTO-CPA predicts reasonably the phase decomposition of β-Ti_1-_xNb_x at relatively low temperature whereas VASP-SQS does not, which might be ascribed to the fact that the free energy depends strongly on the detailed SQS structures. The elastic constants C₁₁ and C₁₂ calculated by using EMTO-CPA and VASP-SQS without atomic relaxation increase with Nb content whereas C₄₄ decreases. EMTO-CPA overestimates the elastic stability of β-Ti_1-_xNb_x. At low Nb content, the local lattice distortion is abnormally large due to the lattice instability of the β-Ti_1-_xNb_x, making the free energy and elastic constant against x from VASP-SQS calculations with atomic relaxation deviate significantly from the general trend.

Key words： titanium alloy random solid solution special quasirandom structure coherent potential approximation elastic constant first-principles calculation

收稿日期: 2020-01-10

ZTFLH:

TG146.2

基金资助:国家重点研发计划项目(2016YFB0701301);国家自然科学基金项目(91860107);国家重点基础研究发展计划项目(2014CB644001)

作者简介: 张海军，男，1991年生，博士

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图1 β-Ti1-xNbx合金的晶格常数随Nb含量的变化

图2 β-Ti1-xNbx合金的形成焓随Nb含量的变化

图3 不同温度下β-Ti1-xNbx合金的Gibbs自由能(ΔG)随Nb含量的变化及相图

图4 β-Ti1-xNbx合金的弹性常数随Nb含量的变化Color online

图5 Ti30Nb24、Ti24Nb30和Ti18Nb36剪切模量和Young's模量随晶体取向的变化Color online

图6 β-Ti1-xNbx合金的机械稳定性随Nb含量的变化

图7 β-Ti1-xNbx合金的局域晶格畸变(Δd)和畸变能(ΔE)随Nb含量的变化

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