Computational simulation of atomic strain in body-centered cubic multi-principal element alloys

SONG Qianqian; ZHANG Bozhao; DING Jun

doi:10.7498/aps.74.20250128

Abstract

Multi-principal element alloys (MPEAs), also known as high-entropy alloys (HEAs), are novel materials that have received significant attention due to their exceptional mechanical properties, thermal stability, and resistance to wear and corrosion. These alloys are typically composed of multiple principal elements in near-equal atomic proportions, forming solid solution phases such as face-centered cubic (FCC) or body-centered cubic (BCC) structures. Despite the promising applications, a more in-depth understanding of the atomic-level behavior, particularly, lattice distortion and atomic strain, is essential to better design and optimize these materials in extreme environments. This study focuses on systematically investigating the atomic-scale lattice distortion characteristics and their influence on atomic strain in three representative BCC-based MPEAs: TaWNbMo, TiZrNb, and CoFeNiTi. We utilize molecular dynamics (MD) simulations to explore the local atomic strain distributions in these alloys at various temperatures. Von Mises strain and volumetric strain are employed as key descriptors to quantify the atomic strain, providing a clear representation of how lattice distortion on an atomic scale influences the overall strain behavior. The study specifically addresses the effects of atomic radius differences, chemical short-range ordering, and temperature on the strain characteristics of the alloys. The results obtained indicate that an increase in lattice distortion corresponds to a broader distribution of von Mises strain and volumetric strain, with strain values significantly amplified. More precisely, alloys with larger atomic radius differences exhibit greater volumetric strain, reflecting the influence of atomic size disparity on strain distribution. Furthermore, the formation of chemical short-range order (CSRO) significantly mitigates lattice distortion and atomic strain. This finding highlights the importance of short-range atomic ordering in enhancing the stability of the alloy structures, thus potentially improving their mechanical properties. Temperature effects are also investigated, revealing that elevated temperature induces more intense atomic vibration, which in turn increases the atomic strain. The findings underscore the complex interplay between atomic-scale phenomena and macroscopic mechanical properties, offering new insights into the microscopic mechanical behavior of high-entropy alloys. This study contributes to a better understanding of the underlying mechanisms driving atomic strain and lattice distortion in MPEAs. The results provide valuable theoretical insights that can guide the design of high-performance alloys tailored for high-temperature and extreme environments. By addressing the key factors influencing atomic strain, such as atomic radius, chemical ordering, and temperature, this work lays the foundation for future research aimed at enhancing the mechanical performance of MPEAs in various industrial applications.

Keywords:

Authors and contacts

1.
State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, China
2.
Advanced Interdisciplinary Science Research (AiR) Center, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China

Corresponding author: DING Jun, dingsn@xjtu.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2023YFB3712002).

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References

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Cited By

图 1 多主元合金中的晶格畸变及局域原子应变　(a)晶格畸变示意图, 局部仿射变换矩阵$ {J}_{i} $ 描述了初始与当前原子构型之间的转变; (b) 0 K下TiZrNb合金中的原子应变示例, 左图为每个原子的冯·米塞斯应变, 右图为每个原子的体积应变

Figure 1. Lattice distortion and local atomic strain in multi-principal element alloys: (a) Schematic of lattice distortion, where the local affine transformation matrix $ {J}_{i} $ describes the transition from the initial to the current atomic configuration; (b) atomic strain distribution in the TiZrNb alloy at 0 K, the left panel displays the Von Mises strain for each atom, while the right panel shows the volumetric strain.

DownLoad: Full-Size Img PowerPoint

图 2 不同合金体系的三维原子分布模型及其原子应变的分布　(a) TaWNbMo, TiZrNb和CoFeNiTi的三维原子分布模型; (b) 3种合金体系的冯·米塞斯应变和体积应变的分布

Figure 2. Three-dimensional atomic distribution models and atomic strain distributions in different alloy systems: (a) Three-dimensional atomic distribution models of TaWNbMo, TiZrNb, and CoFeNiTi; (b) distribution of Von Mises strain and volumetric strain for the three alloy systems.

DownLoad: Full-Size Img PowerPoint

图 3 三种合金体系中不同组元的冯·米塞斯应变和体积应变的分布, 展示了TaWNbMo, TiZrNb和CoFeNiTi三种合金体系中不同组元的冯·米塞斯应变和体积应变的分布, 每种合金中的不同组元(Ta, W, Nb, Mo, Ti, Zr, Nb, 和Co, Fe, Ni, Ti)分别绘制了应变分布图, 上半部分为冯·米塞斯应变的分布, 下半部分为体积应变的分布, 不同颜色的曲线对应于不同的元素, 反映了各组元在合金中的应变特性差异

Figure 3. Distribution of von Mises strain and volumetric strain for different elements in the TaWNbMo, TiZrNb, and CoFeNiTi alloy systems. The strain distributions for different elements (Ta, W, Nb, Mo, Ti, Zr, Nb, Co, Fe, Ni, Ti) in each alloy are shown. The upper part of the figure shows the distribution of von Mises strain, while the lower part shows the distribution of volumetric strain. The different colored curves represent different elements, reflecting the strain characteristics of each element in the alloy.

DownLoad: Full-Size Img PowerPoint

图 4 TiZrNb合金在800 K下的化学短程有序信息及其原子应变分布特征　(a)化学短程有序构型的三维原子分布模型; (b)不同原子对的Warren-Cowley参数, 展示了合金中各原子对之间的短程有序程度; (c)冯·米塞斯应变的频率分布, 分别为CSRO和RSS两种不同的化学短程有序状态下的应变分布; (d)体积应变的频率分布, 展示了不同原子对间的体积应变分布特征

Figure 4. Chemical short-range order information and atomic strain distribution characteristics of TiZrNb alloy at 800 K: (a) Three-dimensional atomic distribution model of the chemical short-range ordered configuration; (b) Warren-Cowley parameters for different atomic pairs, showing the degree of short-range order between atomic pairs in the alloy; (c) distribution of von Mises strain, showing the strain distributions under CS0 and RSS short-range order configurations; (d) frequency distribution of volumetric strain, illustrating the volumetric strain characteristics between different atomic pairs.

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图 5 不同温度下TiZrNb合金的冯·米塞斯应变和体积应变频率分布图, 图中展示的温度范围从0—1200 K, 分别以不同颜色表示不同的温度状态　(a)冯·米塞斯应变的分布; (b)体积应变的分布

Figure 5. Frequency distribution of von Mises strain and volumetric strain of TiZrNb alloy at various temperatures, ranging from 0 K to 1200 K: (a) Distribution of von Mises strain; (b) distribution of volumetric strain.

DownLoad: Full-Size Img PowerPoint

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[2]	George E P, Curtin W A, Tasan C C 2020 Acta Mater. 188 435 Google Scholar
[3]	Miracle D B 2017 J. Met. 69 2130 Google Scholar
[4]	Pickering E J, Jones N G 2016 Int. Mater. Rev. 61 183 Google Scholar
[5]	Ma E, Ding J 2025 J. Mater. Sci. Technol. 220 233 Google Scholar
[6]	Yeh J W, Chen S K, Lin S J, Gan J Y, Chin T S, Shun T T, Tsau C H, Chang S Y 2004 Adv. Eng. Mater. 6 299 Google Scholar
[7]	Li Z M, Pradeep K G, Deng F, Paabe D, Tasan C C 2016 Nature 534 227 Google Scholar
[8]	Maresca F, Curtin W A 2020 Acta Mater. 182 235 Google Scholar
[9]	Gludovatz B, Hohenwarter A, Catoor D, Chang E H, George E P, Ritchie P O 2014 Science 345 1153 Google Scholar
[10]	Shi Y Z, Yang B, Liaw P K 2017 Metals 7 18 Google Scholar
[11]	Chen P Y, Lee C, Wang S Y, Seifi M, Lewandowski J J, Dahmen K A, Jia H L, Xie X, Chen B L, Yeh J W, Tsai C W, Yuan T, Liaw P K 2018 Sci. China-Technol. Sci. 61 168 Google Scholar
[12]	Kozelj P, Vrtnik S, Jelen A, Jazbec S, Jaglicic Z, Maiti S, Feuerbacher M, Steurer W, Dolinsek J 2014 Phys. Rev. Lett. 113 107001 Google Scholar
[13]	Su Z X, Ding J, Song M, Jiang L, Shi Tan, Li Z M, Wang S, Gao F, Ma E Lu C Y 2023 Acta Mater. 245 118662 Google Scholar
[14]	Zhang Z, Su Z, Zhang B, Yu Q, Ding J, Shi T, Lu C, Ritchie R O, Ma E 2023 Proc. Natl. Acad. Sci. 120 e2218673120 Google Scholar
[15]	Zhang Y, Zuo T, Tang T, Gao M, Dahmen K, Liaw K, Lu Z 2014 Prog. Mater. Sci. 61 1 Google Scholar
[16]	Kozak P, Sologubenko A, Steurer W 2015 Z Kristallogr Cryst Mater 230 55 Google Scholar
[17]	Zhang B, Zhang Z, Xun K, Asta M, Ding J, Ma E 2024 Proc. Natl. Acad. Sci. 121 e2314248121 Google Scholar
[18]	Miracle D B, Senkov O N 2017 Acta Mater. 122 448 Google Scholar
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[24]	杨勇, 赫全锋 2021 金属学报 57 385 Google Scholar Yang Y, He Q F 2021 Acta Metall. Sin. 57 385 Google Scholar
[25]	Zou Y, Maiti S, Steurer W, Spolenak R 2014 Acta Mater. 65 85 Google Scholar
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[28]	Tian L Y, Hu Q M, Yang R, Zhao J, Johansson B, Vitos L 2015 J. Phys. Condens. Mat. 27 315702 Google Scholar
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[33]	Chen B, Li S Z, Ding J, Ding X D, Sun J, Ma E 2020 Proc. Natl. Acad. Sci. 117 16199 Google Scholar
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