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中温区Mg2(Si, Sn)基热电材料因其廉价、无毒无害等优点极具发展潜力. 其中, 三元Mg2Si1–xSnx合金的电子传输性能须通过元素掺杂来进行优化, 最常见的掺杂元素Bi和Sb均可以对载流子浓度、迁移率和有效质量等传输性能参数进行调节, 而不同的原子置换位置会对合金的电子传输特性产生较大的影响. 因此, 本文采用第一性原理计算的方法, 对Sb, Bi元素分别置换Si, Sn位置的缺陷形成能进行了分析, 结合能带结构和态密度的变化分析其对载流子传输性能参数的影响. 通过甩带快速凝固方法制备了Bi, Sb掺杂Mg2Si1–xSnx晶体, 结合求解Boltzmann方程对电子传输性能的预测结果进行对比分析. 结果表明, Bi, Sb原子均更加倾向于取代Si位, Sb原子的取代具有更低的形成能. 与Bi元素相比, 相同成分的Sb掺杂下载流子浓度较低, 但可以提供更大的载流子有效质量, 因此可以获得更高的Seebeck系数和功率因子, 最高值可达–228 μV/K和4.49 mW/(m·K2), 而Bi掺杂可以提供更高的电导率. 本研究结果可以为掺杂优化Mg2(Si, Sn)基合金的热电性能提供理论参考.Mg2(Si,Sn)-based thermoelectric materials, which are environmentally friendly and low-cost, have great development potential in a moderate temperature range. Electronic transport properties of Mg2Si1-xSnx alloys can be optimized by doping elements. Doping is still one of the most effective methods of optimizing electronic transport performance, such as carrier concentration, mobility, and effective mass. The most effective doping elements are Sb and Bi. Much attention has been paid to the influence of element type and doping content. Different substitution sites will also greatly affect the electronic transport parameters. In this work, the defect formation energy value of Mg2Si0.375Sn0.625 alloy for substituting Sb atoms and Bi atoms for Sn sties and Si sites, respectively, are calculated by first-principles calculations. The influence on electronic transport parameters is systematically analyzed by combining the calculated results of band structures and density of states. Corresponding component Sb and Bi atoms doped Mg2Si0.375Sn0.625 alloys are prepared by rapid solidification method, and microstructures, Seebeck coefficients, and electrical conductivities of the alloys are measured. Combined with the predicted results by solving the Boltzmann transport equation, electronic transport performances are compared and analyzed. The results indicate that both Sn and Si sites are equally susceptible to Sb and Bi doping, but the Si sites are preferentially substituted due to their lower ∆Ef values. Doped Bi atoms provide a higher electron concentration, and Sb atoms offer higher carrier effective mass. Thus, the maximum σ value of the Mg2Si0.375Sn0.615Bi0.01 alloy is 1620 S/cm. The maximum S value of the Mg2Si0.365Sn0.625Sb0.01 alloy is –228 μV/K. Correspondingly, the highest PF value for this alloy is 4.49 mW/(m·K) at T = 800 K because of the dominant role of S values. Although its power factor is slightly lower, the Mg2Si0.375Sn0.615Sb0.01 alloy is expected to exhibit lower lattice thermal conductivity due to the lattice shrinkage caused by substituting Sb sites for Sn sites. The optimal doping concentration of the Bi-doped alloy is lower than that of the Sb-doped alloy. These results are expected to provide a significant reference for optimizing the experimental performance of Mg2(Si, Sn)-based alloys.
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Keywords:
- first-principles calculation /
- atomic substituted sites /
- electronic transport performance /
- rapid solidification
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图 1 Mg2(Si, Sn)晶体的晶胞、原胞和超晶胞结构示意图
Fig. 1. Conventional cell, primitive cell and supercell of Mg2(Si, Sn) crystal.
图 2 Bi/Sb掺杂的Mg192Si36Sn60晶体的电荷密度分布图
Fig. 2. Electron density of Bi/Sb doped Mg192Si36Sn60 alloys.
图 3 未掺杂 Mg2Si0.375Sn0.625合金单胞(a)和Sb/Bi原子分别取代Si/Sn位(b)—(e)的Mg2Si0.375Sn0.625合金超晶胞的能带结构图
Fig. 3. Band structures of undoped Mg2Si0.375Sn0.625 conventional cell (a) and the supercells with Sb/Bi doped at different Si/Sn sites (b)–(e).
图 4 不同掺杂条件下Mg2Si0.375Sn0.625合金的DOS计算结果(a)和各成分合金中不同元素对DOS的贡献(b)—(f)
Fig. 4. Calculated results of total DOS (a) and the weighting of elements in total DOS (b)–(f) for the Mg2Si0.375Sn0.625 alloys under different doping conditions.
图 5 快速凝固Mg2Si0.375Sn0.625合金微观组织图(a)以及Mg, Si和Sn元素分布的面扫描结果(b)—(d)
Fig. 5. Microstructure of rapid solidified Mg2Si0.375Sn0.625 crystal (a) and the elements mapping images of Mg, Si, and Sn (b)–(d).
图 6 不同掺杂条件下快速凝固Mg2Si0.375Sn0.625合金的粉末XRD图(a)和(111), (220)衍射峰的局部放大图(b)
Fig. 6. Power XRD patterns of the rapid solidified Mg2Si0.375Sn0.625 crystals under different doping conditions (a) and partial enlarged peaks of (111) and (220) (b).
图 7 不同掺杂条件下Mg2Si0.375Sn0.625合金Seebeck系数(a)和电导率(b)随温度的变化曲线; T = 800 K时Seebeck系数随载流子浓度的变化曲线(c)和框选部分的局部放大图(d)
Fig. 7. Temperature dependence of Seebeck coefficient (a) and electrical conductivity (b) of Mg2Si0.375Sn0.625 crystals under different doping conditions. Calculated Seebeck coefficient as a function of carrier concentration (c) and magnified view (d) of the outlined area at T = 800 K.
图 8 不同s掺杂条件下Mg2Si0.375Sn0.625合金功率因子(a)、热导率(b)和ZT值(c)随温度的变化曲线
Fig. 8. Temperature dependence of power factor (a), thermal conductivity (b), and ZT (c) of Mg2Si0.375Sn0.625 crystals under different doping conditions.
表 1 Bi/Sb掺杂Mg192Si36Sn60晶体晶格常数、键长度和Mulliken布居数的计算结果
Table 1. Calculated results of lattice constant, bond length and Mulliken population for Bi/Sb doped Mg192Si36Sn60 crystals.
超晶胞结构 晶格常数/Å 键类型 Mulliken
布居数键长
度/Å形成
能/eVMg192Si36Sn60 18.436 Mg—Sn 0.26 2.846 — Mg—Si 0.19 2.748 Mg192Si36Sn59Sb 18.422 Mg—Sb 0.10 2.896 –1.102 Mg—Sn 0.33 2.814 Mg—Si 0.22 2.708 Mg192Si36Sn59Bi 18.442 Mg—Bi 0.22 2.963 –0.674 Mg—Sn 0.27 2.849 Mg—Si 0.20 2.763 Mg192Si35Sn60Sb 18.438 Mg—Sb 0.14 2.935 –1.337 Mg—Sn 0.30 2.831 Mg—Si 0.21 2.727 Mg19Si35Sn60Bi 18.440 Mg—Bi 0.17 2.989 –0.945 Mg—Sn 0.20 2.855 Mg—Si 0.20 2.766 
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表 2 不同掺杂条件下Mg2Si0.375Sn0.625合金的理论成分和实验所得样品的EDS成分测试结果
Table 2. Nominal and measured results of elementary composition of Mg2Si0.375Sn0.625 alloys under different doping conditions
理论成分 元素含量/% 实际成分 Mg Si Sn Sb/Bi Mg2Si0.375Sn0.625 66.91 12.51 20.58 — Mg2.007Si0.375Sn0.618 Mg2Si0.375Sn0.615Sb0.01 66.82 12.43 20.36 0.39 Mg2.004Si0.373Sn0.611Sb0.012 Mg2Si0.375Sn0.615Bi0.01 66.88 12.41 20.30 0.41 Mg2.006Si0.372Sn0.609Bi0.013 Mg2Si0.365Sn0.625Sb0.01 66.93 12.01 20.74 0.32 Mg2.008Si0.360Sn0.623Sb0.009 Mg2Si0.365Sn0.625Bi0.01 66.77 12.07 20.71 0.45 Mg2.003Si0.362Sn0.621Bi0.014
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[1] Bahrami A, Schierning G, Nielsch K 2020 Adv. Energy Mater. 10 1904159
Google Scholar
[2] Mao J, Chen G, Ren Z F 2021 Nat. Mater. 20 454
Google Scholar
[3] 赵英浩, 张瑞, 张波萍, 尹阳, 王明军, 梁豆豆 2021 物理学报 70 128401
Google Scholar
Zhao Y H, Zhang R, Zhang B P, Yin Y, Wang M J, Liang D D 2021 Acta Phys. Sin. 70 128401
Google Scholar
[4] 程立东, 刘瑞恒, 史迅 2018 热电材料与器件 (北京: 科学出版社) 第8—13页
Cheng L D, Liu R H, Shi X 2018 Thermoelectric Materials and Devices (Beijing: Science Press) pp8–13 (in Chinese)
[5] 范人杰, 江先燕, 陶奇睿, 梅期才, 唐颖菲, 陈志权, 苏贤礼, 唐新峰 2021 物理学报 70 137102
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Fan R J, Jiang X Y, Tao Q R, Mei Q C, Tang Y F, Chen Z Q, Su X L, Tang X F 2021 Acta Phys. Sin. 70 137102
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[6] Chen L C, Chen P Q, Li W J, Zhang Q, Struzhkin V V, Goncharov A F, Ren Z F, Chen X J 2019 Nat. Mater. 18 1321
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[7] 李彩云, 何文科, 王东洋, 张潇, 赵立东 2021 物理学报 70 208401
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Li C Y, He W K, Wang D Y, Zhang X, Zhao L D 2021 Acta Phys. Sin. 70 208401
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Huang Q S, Duan B, Chen G, Ye Z C, Li J, Li G D, Zhai P C 2021 Acta Phys. Sin. 70 157401
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Google Scholar
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[14] Gao P, Lu X, Berkun I, Schmidt R D, Case E D, Hogan T P 2014 Appl. Phys. Lett. 105 202104
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