Effect of Sb/Bi atom substitution site on electronic transport properties of Mg2Si0.375Sn0.625 alloy

Li Xin; Xie Hui; Zhang Ya-Long; Ma Ying; Zhang Jun-Tao; Su Heng-Jie

doi:10.7498/aps.71.20221364

Abstract

Authors and contacts

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1. 引　言
2. 计算与实验
2.1 计　算
2.2 实　验
3. 结果与讨论
3.1 电子结构计算
3.2 热电性能
4. 结　论

References

Abstract

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 Mg₂Si_1-xSn_x 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 Mg₂Si_0.375Sn_0.625 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 Mg₂Si_0.375Sn_0.625 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 ∆E_f values. Doped Bi atoms provide a higher electron concentration, and Sb atoms offer higher carrier effective mass. Thus, the maximum σ value of the Mg₂Si_0.375Sn_0.615Bi_0.01 alloy is 1620 S/cm. The maximum S value of the Mg₂Si_0.365Sn_0.625Sb_0.01 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 Mg₂Si_0.375Sn_0.615Sb_0.01 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.

Keywords:

PACS:

84.60.Rb	(Thermoelectric, electrogasdynamic and other direct energy conversion)
63.20.dk	(First-principles theory)
74.20.Pq	(Electronic structure calculations)
81.30.Fb	(Solidification)

Authors and contacts

School of Materials Engineering, Xi’an Aeronautical University, Xi’an 710077, China

Corresponding author: Li Xin, lixin005@xaau.edu.cn

Funds: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 51904219), the Natural Science Foundation of Shaanxi Province, China (Grant No. 2020JQ-906), and the Youth Innovation Team of Shaanxi Universities, China.

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1. 引　言

热电材料作为一种新型能源材料, 因其可以实现热能和电能间的相互转换而备受关注, 在半导体制冷和清洁能源领域有着不可替代的作用^[1-3]. 热电器件的制冷效率(η_max)和发电效率(Φ_max)可以分别表示为^[4]

${\eta _{\max }} = \frac{{{T_1}}}{{{T_1} - {T_2}}} \cdot \frac{{{{\left( {1 + Z\overline T } \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}} - {{{T_2}} \mathord{\left/ {\vphantom {{{T_2}} {{T_1}}}} \right. } {{T_1}}}}}{{{{\left( {1 + Z\overline T } \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}} + 1}},$

(1)

${\varPhi _{\max }} = \frac{{{T_1} - {T_2}}}{{{T_1}}} \cdot \frac{{{{\left( {1 + Z\overline T } \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}} - 1}}{{{{\left( {1 + Z\overline T } \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}} + {{{T_2}} \mathord{\left/ {\vphantom {{{T_2}} {{T_1}}}} \right. } {{T_1}}}}},$

(2)

式中, T₁和T₂分别为器件热端和冷端的温度, $\overline T$ = (T₁+ T₂)/2为平均温度. 由此可知, 在给定的温度下, 制冷效率和发电效率都与Z值有关, Z值越大, 效率越高, 称之为器件的热电优值, 量纲为K^–1. 其与温度的乘积ZT是一个无量纲值, 因此, 通常用无量纲优值ZT = S ²σT/(κ_e+κ_l)来衡量热电性能的优劣^[5-7], 其中, S是Seebeck系数, σ是电导率, T是开尔文温度, κ_e和κ_l分别是电子热导率和晶格热导率. 其中, 与载流子传输和散射相关的参数S, σ和κ_e之间有较强的耦合作用, 相反, κ_l则是由声子的传输和散射作用决定的相对独立的参数^[8]. 因此, 热电性能的提升可通过提高载流子浓度、能带工程等方式优化功率因子(PF = S ²σ)或通过提高声子散射来降低κ_l值^[9].

目前, 性能较高的中温区热电材料(如PbTe, CoSb₃等)由于所含元素的毒性和高昂的成本而使得其大规模应用受到了限制^[10,11]. 因此, 环境友好且价格低廉的Mg₂Si基合金成为高性能中温区热电材料最理想的替代品^[12,13]. 对于此合金系中性能较好的Mg₂Si_1–xSn_x合金, 虽然通过第三组元的加入增强了合金化散射, 从而降低了晶格热导率, 但其较低的功率因子是阻碍其性能进一步提升的主要因素^[14,15]. 研究者们采用了多种方式来对Mg₂Si_1–xSn_x合金进行优化, 例如: 通过能带工程来优化其Seebeck系数, 当Sn含量为x = 0.625时, 通过导带收敛可以使Seebeck系数达到最大值^[16,17]; 以及通过定向凝固方法制备单晶材料, 降低晶界对电子的散射来提高载流子迁移率^[18,19].

相比而言, 元素掺杂仍然是优化电子传输性能最有效的方式. 对于Mg₂Si_1–xSn_x合金, 采用第五主族的Bi和Sb元素进行n型掺杂可以有效提高其电子浓度^[20]. 此外, 掺杂原子形成的点缺陷也有利于增强声子的散射, 从而进一步降低晶格热导率^[21]. 不同成分的Mg₂Si_1–xSn_x合金通过Sb和Bi掺杂后最高ZT值分别可以达到1.3和1.55^[22,23]. 掺杂元素的含量越高, 载流子浓度越大, 虽然可以提升电导率, 但Seebeck系数随之降低, 因此需要改变掺杂浓度获得最优的掺杂含量来获得最高的功率因子值. 基于此, 目前关于掺杂研究仍更多的关注于元素种类和含量对载流子浓度的影响, 从而调控合金的电子传输性能参数^[24,25]. 而对于掺杂原子在合金中的掺杂位置, 以及不同的掺杂位置对电子结构和传输性能的影响方面的研究还有所欠缺. 不同的掺杂元素在Mg₂Si_1–xSn_x合金中不同的掺杂位置均会对电子结构产生较大的影响, 从而影响合金中载流子的有效质量(m^*)和迁移率(μ)等参数^[26]. 同载流子浓度(n)一样, m^*和μ也是影响Seebeck系数和电导率的重要参数, 对合金性能的提升起到关键作用^[27,28].

在本文中, 通过第一性原理计算对Mg₂Si_0.375Sn_0.625合金中Bi, Sb原子分别取代Si, Sn位的缺陷形成能进行了计算, 并对不同掺杂条件下合金的电子结构、能带和态密度等进行了分析, 确定了其对电子传输性能参数的影响关系. 通过甩带快速凝固方法制备了相应掺杂条件下的Mg₂Si_0.375Sn_0.625合金, 对其热电性能参数进行了测试, 并与求解Boltzmann方程所得的计算结果进行对比, 系统分析了不同掺杂元素和原子置换位置对电子传输和散射的影响规律, 为进一步通过掺杂优化Mg₂Si_1–xSn_x合金热电性能提供了理论基础.

2. 计算与实验

2.1 计　算

Mg₂Si_1–xSn_x合金属于反萤石结构的面心立方晶体, Fm $\overline 3$ m(No. 225)空间群^[29]. 本研究基于Mg₂(Si, Sn)晶体的原胞结构, 按照Mg₂Si_0.375Sn_0.625合金的成分比构建了Mg₁₉₂Si₃₆Sn₆₀超晶胞, 并对超晶胞内的Si, Sn原子位分别进行一个Sb, Bi原子取代(图1). 对构建的晶胞采用基于密度泛函理论的CASTEP软件包进行结构优化, 以及能带和态密度计算. 采用平面波展开方式并采用广义梯度的GGA-PBE函数计算电子交换能, 原子间电子-离子间交互作用采用超软赝势^[30,31]. 计算所用原子波函数截断能设为380 eV, 对简约Brillouin区采用8×8×8 k点进行划分. CASTEP模块优化后的晶体结构可以导入WIEN2k软件进行计算, 并通过求解Boltzmann方程来对电子传输性能进行预测, 计算中同样采用平面波展开方式并采用广义梯度的GGA-PBE函数计算电子交换能, 原子核与价态分离能为–6.0 Ry, 不可约Brillouin区中k点数量为16×16×16, 设定计算能量收敛于0.0001 Ry^[32,33]. 求解Boltzmann方程可以得出的Seebeck系数(S)、电导率(σ)和电子热导率(κ_e)等热电性能参数如下方程所示^[32]:

$图 1 Mg2(Si, Sn)晶体的晶胞、原胞和超晶胞结构示意图\r\nFig. 1. Conventional cell, primitive cell and supercell of Mg2(Si, Sn) crystal.$

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.

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$\sigma {\text{ = }}{e^{\text{2}}}{F^{(2)}},$

(3)

$S{\text{ = }}\frac{{e{k_{\text{B}}}}}{\sigma }{F^{(1)}},$

(4)

${\kappa _{\text{e}}}{\text{ = }}k_{_{\text{B}}}^{\text{2}}T{F^{(2)}},$

(5)

${F^{(n)}}{\text{ = }}\int {{\text{d}}{{\varepsilon}} \left( { - \frac{{\partial {f_0}}}{{\partial {{\varepsilon}} }}} \right)\varXi \left( {{\varepsilon}} \right){{\left( {\frac{{{{\varepsilon}} - \mu }}{{{k_{\text{B}}}T}}} \right)}^n}} ,$

(6)

$\varXi = \sum\nolimits_{\boldsymbol{k}} {{{\boldsymbol{\nu }}_{\boldsymbol{k}}}{{\boldsymbol{\nu }}_{\boldsymbol{k}}}{{\boldsymbol{\tau }}_{\boldsymbol{k}}}} .$

(7)

式中, e为电子电量, k_B为Boltzmann常数, ε为能带能量, f₀为无电场条件下Fermi分布方程f(ε)的定解, μ为元素化学势, ${\boldsymbol{\nu }}$ 和τ_k分别为晶体动量k分量下的群速度和弛豫时间.

2.2 实　验

采用甩带快速凝固结合放电等离子烧结(spark plasma sintering, SPS)的方式对Mg₂Si_0.375Sn_0.625,Mg₂Si_0.375Sn_0.615Sb_0.01, Mg₂Si_0.375Sn_0.615Bi_0.01, Mg₂Si_0.365Sn_0.625Sb_0.01和Mg₂Si_0.365Sn_0.625Bi_0.01五个成分的合金进行制备. 快速凝固过程中真空度达到–5×10^–3 Pa以下, 凝固速率选择3200 r/min, 即50 m/s, 所得的带材经研磨后进行烧结, 采用升温速度为50 ℃/min, 烧结温度为600 ℃、保压时间为5 min. 采用电子扫描显微镜(scanning electron microscope, SEM)对所得晶体的微观组织进行分析, 通过能谱仪(energy dispersive spectrometer, EDS)和X射线衍射仪(X-ray diffraction, XRD)分析元素成分和相组成. 采用LinseisLSR-3热电分析系统对Seebeck系数和电导率进行测试, 试样尺寸为4 mm×4 mm×10 mm.

3. 结果与讨论

3.1 电子结构计算

首先对Sb/Bi分别取代Si/Sn位的Mg₂Si_0.375Sn_0.625合金进行了几何优化, 以及化学键和缺陷形成能的计算, 计算结果如表1所列. 从晶格常数计算结果中可知, Sb取代Sn位后晶格常数减小, 而Sb取代Si位和Bi取代Sn或Si位时, 晶格常数均增大, 这一结果与所熟知的Sb原子半径略大于Sn不符. 通过化学键计算对这一现象进行了解释. 从Mulliken布居数计算结果可知, Mg—Si和Mg—Sn键均为极性共价键, 由于Si比Sn具有更强的非金属性, Mg—Si键的布居数(0.19)小于Mg—Sn键(0.26), 具有更强的极性. Sb取代Sn位后Mg—Sb键的布居数为0.1, 表明Mg—Sb共价键具有更强的极性. 从图2的电荷密度分布图中也可以得出类似的结论, 未掺杂条件下, Si, Sn原子附近比Mg原子有更高的电荷密度, 因此表现出极性, Mg—Si键极性明显强于Mg—Sn键. 而Sb原子掺入后, 其周围电荷密度略高于Si原子, 因此Mg—Sb为强极性共价键. 这一结果导致了掺杂Sb原子周围的Mg—Si和Mg—Sn键极性降低(共用电子对向Mg靠近), 键长变短, 从而产生了晶格收缩的现象, 这一现象有助于晶格热导率的降低^[34]. 而Sb和Si原子的电负性相差不大, 因此Sb取代Si位晶格常数变化不明显. 由于Bi与Sb相比具有更强的金属性, 因此Bi原子掺入后周围电荷密度略低于Si原子(图2(b)), 而原子半径更大的Bi取代Sn/Si位后均使晶格常数增大, 这种掺杂形式可能更有利于电导率的提升. 后续将通过能带和态密度计算结果对此进行进一步分析.

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/eV
Mg₁₉₂Si₃₆Sn₆₀	18.436	Mg—Sn	0.26	2.846	—
Mg₁₉₂Si₃₆Sn₆₀	18.436	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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$图 2 Bi/Sb掺杂的Mg192Si36Sn60晶体的电荷密度分布图\r\nFig. 2. Electron density of Bi/Sb doped Mg192Si36Sn60 alloys.$

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.

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为了进一步确定Sb/Bi掺杂原子的取代位置和掺杂的难易程度, 对Sb/Bi原子分别取代Sn/Si位的缺陷形成能( $\Delta {E_{\text{f}}}$ )进行了计算, 其表达式为^[35]

$\Delta {E_{\text{f}}} = \left( {{E_{\text{D}}} - {E_{\text{H}}}} \right) + q{E_{\text{F}}} + \sum {{n_\alpha }{\mu _\alpha }} ,$

(8)

其中, E_D和E_H分别为元素掺杂产生点缺陷和未掺杂的原始超晶胞结构的总能量, q为掺杂后超晶胞中电子(q < 0)或空穴(q > 0)的增加量, E_F为Fermi能级, n_α为掺杂原子(n < 0)和被置换原子(n > 0)数, μ_α为相应元素的化学势. 计算结果如表1所列, 可以看出, Sb/Bi原子分别取代Sn/Si位的 $\Delta {E_{\text{f}}}$ 均为负值, 表明Si和Sn两个位置对掺杂元素Sb和Bi均比较敏感. Sb元素取代Si位时, 具有最小 $\Delta {E_{\text{f}}}$ 值为–1.337 eV, 表明其为最稳定的掺杂形式. 而Bi元素取代Sn位由于较高的 $\Delta {E_{\text{f}}}$ 值(–0.674), 相对来说掺杂比较困难. Sb元素不管是取代Si位还是Sn位均比Sb元素掺杂的 $\Delta {E_{\text{f}}}$ 值更低, 因此有望获得更高的掺杂效率和掺杂量.

结合能带结构和态密度计算结果对不同掺杂条件引起的电子结构变化进行分析. 图3(a)所示为未掺杂Mg₂Si_0.375Sn_0.625晶胞的能带结构图, 从图3(a)可以看出此合金为直接能隙半导体, 带隙为0.16 eV, 价带顶和导带底均位于G点, 本征条件下Fermi能级位于禁带中且偏向于导带, 因此其电子和空穴载流子浓度均不高, 且表现为n型半导体, 与之前的实验结果一致^[17,35]. Sb/Bi原子分别取代Sn/Si位后, 如图3(b)—(e)所示, E_F向导带移动, 粉色和橙色两条导带移动到E_F以下, 表明Sb/Bi均为n型掺杂元素, 提供了更多的电子载流子, 表现出金属特性. 其中, Bi分别取代Sn/Si位(图3(c)和图3(e))后, 导带降低到E_F以下0.74 eV和0.77 eV, 高于图3(b)和图3(d)中Sb取代Sn/Si位时的情况, 表明同等掺杂量下, Bi元素下可以提供更高的电子载流子浓度. 但Sb掺杂后的导带底(橙色能带)变化更加平缓, 表明Sb掺杂条件下具有更高的载流子有效质量(m*), 从而获得更高的Seebeck系数值(S ∝ m*).

$图 3 未掺杂 Mg2Si0.375Sn0.625合金单胞(a)和Sb/Bi原子分别取代Si/Sn位(b)—(e)的Mg2Si0.375Sn0.625合金超晶胞的能带结构图\r\nFig. 3. Band structures of undoped Mg2Si0.375Sn0.625 conventional cell (a) and the supercells with Sb/Bi doped at different Si/Sn sites (b)–(e).$

图 3 未掺杂 Mg₂Si_0.375Sn_0.625合金单胞(a)和Sb/Bi原子分别取代Si/Sn位(b)—(e)的Mg₂Si_0.375Sn_0.625合金超晶胞的能带结构图

Fig. 3. Band structures of undoped Mg₂Si_0.375Sn_0.625 conventional cell (a) and the supercells with Sb/Bi doped at different Si/Sn sites (b)–(e).

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不同掺杂条件下相应的态密度(density of states, DOS)计算结果如图4(a)所示, 为了便于观察, 将Bi掺杂的两条曲线放至Y负半轴. 可以看出, Mg₂Si_0.375Sn_0.625合金中掺入Sb/Bi原子后, DOS曲线整体向左分别平移0.06 eV和0.077 eV, 此外, 带隙有一定程度降低. 与此同时, 掺杂原子的加入使得合金的导带能级由于杂质诱导而扩大, 与能带结构图中所得结果一致. 图4(b)—(f)为不同掺杂条件下各元素对DOS的贡献, 可以看出, 价带主要由Si和Sn原子贡献, 而导带则主要来源于Mg原子. Sb/Bi原子取代Sn/Si位后, 仍主要贡献于价带, 而其对导带的贡献率也高于Sn/Si原子, 因此掺杂后导带的态密度曲线均明显高于未掺杂态. 图4(c)和图4(d)可以看出, Sb/Bi原子取代Sn位时DOS曲线趋势与未掺杂情况几乎一致, 表明此掺杂条件下电子传输性质与母合金基本一致. 而Sb/Bi原子取代Si位时, DOS曲线有较大的变化, 特别是E－E_F > 0.5 eV部分. 这种掺杂形式更容易提高电子的散射程度, 从而对电子传输性质产生影响.

$图 4 不同掺杂条件下Mg2Si0.375Sn0.625合金的DOS计算结果(a)和各成分合金中不同元素对DOS的贡献(b)—(f)\r\nFig. 4. Calculated results of total DOS (a) and the weighting of elements in total DOS (b)–(f) for the Mg2Si0.375Sn0.625 alloys under different doping conditions.$

图 4 不同掺杂条件下Mg₂Si_0.375Sn_0.625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 Mg₂Si_0.375Sn_0.625 alloys under different doping conditions.

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3.2 热电性能

根据电子结构分析结果, 通过甩带快速凝固+SPS的方式分别制备了相应成分的Sb/Bi原子取代Sn/Si位的合金, 结合第一性原理计算的晶胞结构求解Boltzmann方程, 对不同成分合金的电子传输性能参数进行分析. 快速凝固所得样品的SEM和不同元素的面扫描结果如图5(a)—(d)所示, 从图5可以看出, Mg, Si和Sn元素在合金中的分布基本均匀, 通过EDS测试不同掺杂条件下合金的理论成分和实际成分如表2所列. 结合图6(a)所示实验所得样品的粉末XRD测试结果可知, 不同成分合金所得的衍射峰均位于Mg₂Sn和Mg₂Si标准峰之间, 表明所得的合金中仅包含Mg₂Si_1–xSn_x相. 同时从图6(b)中(111)和(220)衍射峰的局部放大图可以看出, 随着掺杂元素的加入, 衍射峰相对于未掺杂的Mg₂Si_0.375Sn_0.625合金会发生一定的偏移, Mg₂Si_0.375Sn_0.615Bi_0.01, Mg₂Si_0.365Sn_0.615Sb_0.01和Mg₂Si_0.365Sn_0.615Bi_0.01三个成分均向左偏移, 而Mg₂Si_0.375Sn_0.615Bi_0.01则向右偏移. 由Bragg衍射方程可知, 衍射峰向左偏移表明晶格常数增大, 而向右偏移则晶格常数减小, 这一结果与表1中的计算结果相符.

$图 5 快速凝固Mg2Si0.375Sn0.625合金微观组织图(a)以及Mg, Si和Sn元素分布的面扫描结果(b)—(d)\r\nFig. 5. Microstructure of rapid solidified Mg2Si0.375Sn0.625 crystal (a) and the elements mapping images of Mg, Si, and Sn (b)–(d).$

图 5 快速凝固Mg₂Si_0.375Sn_0.625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 Mg₂Si_0.375Sn_0.625 crystal (a) and the elements mapping images of Mg, Si, and Sn (b)–(d).

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表 2 不同掺杂条件下Mg₂Si_0.375Sn_0.625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 Mg₂Si_0.375Sn_0.625 alloys under different doping conditions

理论成分	元素含量/%				实际成分
理论成分	Mg	Si	Sn	Sb/Bi	实际成分
Mg₂Si_0.375Sn_0.625	66.91	12.51	20.58	—	Mg_2.007Si_0.375Sn_0.618
Mg₂Si_0.375Sn_0.615Sb_0.01	66.82	12.43	20.36	0.39	Mg_2.004Si_0.373Sn_0.611Sb_0.012
Mg₂Si_0.375Sn_0.615Bi_0.01	66.88	12.41	20.30	0.41	Mg_2.006Si_0.372Sn_0.609Bi_0.013
Mg₂Si_0.365Sn_0.625Sb_0.01	66.93	12.01	20.74	0.32	Mg_2.008Si_0.360Sn_0.623Sb_0.009
Mg₂Si_0.365Sn_0.625Bi_0.01	66.77	12.07	20.71	0.45	Mg_2.003Si_0.362Sn_0.621Bi_0.014

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| 显示表格

$图 6 不同掺杂条件下快速凝固Mg2Si0.375Sn0.625合金的粉末XRD图(a)和(111), (220)衍射峰的局部放大图(b)\r\nFig. 6. Power XRD patterns of the rapid solidified Mg2Si0.375Sn0.625 crystals under different doping conditions (a) and partial enlarged peaks of (111) and (220) (b).$

图 6 不同掺杂条件下快速凝固Mg₂Si_0.375Sn_0.625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 Mg₂Si_0.375Sn_0.625 crystals under different doping conditions (a) and partial enlarged peaks of (111) and (220) (b).

下载: 全尺寸图片幻灯片

图7(a)和图7(b)所示为相应成分合金的Seebeck系数和电导率测试结果. 从Seebeck系数随温度变化曲线可以看出, 所有曲线的Seebeck系数绝对值均随着温度的升高呈上升趋势, 这一规律符合掺杂条件下非本征半导体的变化趋势. Seebeck系数表达式可表示为^[36]

$图 7 不同掺杂条件下Mg2Si0.375Sn0.625合金Seebeck系数(a)和电导率(b)随温度的变化曲线; T = 800 K时Seebeck系数随载流子浓度的变化曲线(c)和框选部分的局部放大图(d)\r\nFig. 7. Temperature dependence of Seebeck coefficient (a) and electrical conductivity (b) of Mg2Si0.375Sn0.625 crystals under different doping conditions. Calculated Seebeck coefficient as a function of carrier concentration (c) and magnified view (d) of the outlined area at T = 800 K.$

图 7 不同掺杂条件下Mg₂Si_0.375Sn_0.625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 Mg₂Si_0.375Sn_0.625 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.

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$S{\text{ = }}\frac{{{\text{8}}{{\text{π}}^{\text{2}}}k_{\text{B}}^2}}{{3e{h^2}}}{m^*}T{\left( {\frac{{\text{π }}}{{3n}}} \right)^{{2 \mathord{\left/ {\vphantom {23}} \right. } 3}}},$

(9)

其中, k_B为Boltzmann常数, e为电子电量, h为Planck常量. 由(9)式可知, 低温下(T < 650 K)载流子浓度和有效质量均不会随温度发生太大的变化, 使得S值随温度呈上升趋势. 当温度达到650 K以上时, 所有S值的升高趋势减缓, 这是由于热激发现象产生的空穴-电子对使得n值急剧升高, 并且空穴载流子浓度的升高使得其余电子载流子形成的Seebeck系数值符号相反, 从而相互抵消使得S值降低. 相同掺杂含量下, Sb掺杂的Mg₂Si_0.375Sn_0.625合金Seebeck系数值更高, T = 800 K时, S最大值可达–228 μV/K, 而Bi掺杂下最高S值仅为–201 μV/K, 这与前面能带结构分析结果一致, 即Sb元素掺杂下的载流子有效质量更高. 同种掺杂元素分别取代Si/Sn位时, Sb/Bi原子取代Si位时的Seebeck系数值略高于Sn位取代.

从图7(b)电导率随温度变化曲线可以看出, σ值的变化趋势与S相反, 随着温度的升高而降低, 这是由于随着温度的升高, 载流子散射程度增大导致迁移率降低, 从而使电导率(σ = nμe)降低, 这一趋势也符合掺杂条件下非本征半导体特征. Bi掺杂下的曲线在测试温度范围内均高于Sb掺杂的合金, 因而掺入Bi元素可以获得更高的电导率值, 这一结论与能带结构计算所得的同等掺杂量下Bi元素可以提供更高的载流子浓度一致. 同种元素取代不同位置时, Sn位取代的合金电导率高于Si位取代, 这是由于Sn位取代下载流子迁移率比Si位取代更高, 通过DOS计算结果已经对此进行了证实. 因此, T = 300 K时, Bi原子取代Sn位的电导率最大值可达1620 S/cm, 而Sb取代Si位的电导率最大值仅为1380 S/cm.

为了进一步证实Sb/Bi原子不同置换位置下的载流子浓度关系, 通过求解Boltzmann方程得到T = 800 K下Seebeck系数随载流子浓度变化曲线, 如图7(c)所示. 从图7(c)可知, 不同掺杂条件下Seebeck系数随载流子浓度的变化趋势一致. 为了更加清晰区分不同掺杂条件下的曲线变化, 对图7(c)进行局部放大, 结果如图7(d)所示. 根据图7(a)中800 K时的S值, 确定了对应的载流子浓度, 可以看出相同掺杂元素对应的载流子浓度非常接近, 不同掺杂位置对其没有太大影响, 这与前面的实验结果一致. Bi掺杂能够为合金提供更多的电子载流子, 浓度在1.80×10²⁰—1.95×10²⁰ cm^–3之间, 而Sb掺杂下载流子浓度为1.37×10²⁰—1.45×10²⁰ cm^–3之间, 这一结果与之前报道的实验值接近^[22,37].

根据图7中Seebeck系数和电导率结果, 计算得到功率因子随温度变化曲线如图8(a)所示. 可以看出, 由于具有更高的Seebeck系数值, 同等掺杂量下Sb元素掺杂的PF值高于Bi元素. Sb取代Si位时, 在整个温度区间均获得较高的PF值, 在T = 670 K时获得最高PF值可达4.49 mW/(m·K). 而Bi掺杂条件下因提供了更高的载流子浓度使得功率因子值略低, 因此Bi的最优掺杂浓度与Sb相比更低, 这一结论也与之前的报道一致^[19,38]. 图8(b)为不同掺杂条件下合金的热导率(κ)的测试结果, 可以看出, 由于同样的掺杂浓度和晶粒尺度对声子散射效率相同, Bi掺杂Si/Sn位和Sb掺杂Si位时的合金热导率非常接近, 只是由于Sb掺杂Si位时较低的电导率使其电子热导率 (κ_e = LσT) 较低, 从而得到的总热导率略低. Sb取代Sn位时的κ值则明显低于其他三个成分的合金, 根据3.1节计算结果可知, Sb取代Sn位时, 由于Mg—Sb键具有更强的极性, 其导致的晶格收缩有利于提高声子的散射, 因此在测试温度范围内Mg₂Si_0.375Sn_0.615Sb_0.01合金具有最低的热导率值. 根据图8(a)和图8(b)的结果计算得到的热电优值(ZT)随温度的变化曲线如图8(c)所示, 所有曲线均随温度呈不断上升的趋势, Sb掺杂的Mg₂Si_0.375Sn_0.625合金因具有更高的PF值而获得更优的ZT值, Sb取代Si位的合金在T = 770 K时ZT值可达1.1. 虽然Sb取代Sn位的Mg₂Si_0.375Sn_0.615Sb_0.01合金PF值明显低于Mg₂Si_0.365Sn_0.625Sb_0.01合金, 但更低的热导率使得二者的ZT值相差无几, 因此有望通过调整掺杂浓度来提高功率因子的方式对其热电优值进行进一步优化.

$图 8 不同s掺杂条件下Mg2Si0.375Sn0.625合金功率因子(a)、热导率(b)和ZT值(c)随温度的变化曲线\r\nFig. 8. Temperature dependence of power factor (a), thermal conductivity (b), and ZT (c) of Mg2Si0.375Sn0.625 crystals under different doping conditions.$

图 8 不同s掺杂条件下Mg₂Si_0.375Sn_0.625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 Mg₂Si_0.375Sn_0.625 crystals under different doping conditions.

下载: 全尺寸图片幻灯片

综上所述, 通过第一性原理计算的缺陷形成能分析了不同掺杂元素和置换位置的难易程度, 根据其成键类型、电荷密度分布、能带和态密度计算结果, 得到了对载流子浓度、迁移率和有效质量的贡献率. 对甩带快速凝固+SPS方法制备相应成分的合金进行电子传输性能进行测试, 并结合求解Boltzmann方程对电子传输性能进行的预测结果进行对比分析. 可以得到不同的元素掺杂类型和原子置换位置对各电子传输性能参数的贡献率, 通过此本文的计算和实验分析可以优化Mg₂Si_0.375Sn_0.625合金的掺杂条件, 为其热电性能的进一步提升提供有效的理论指导.

4. 结　论

通过第一性原理计算和甩带快速凝固+SPS制备方法对不同Sb/Bi原子置换位置下Mg₂Si_0.375Sn_0.625合金的缺陷形成能、电子结构和电子传输性能进行了分析和预测. 计算得到的所有的缺陷形成能均为负值, 表明Si和Sn位均可以被Sb和Bi原子取代, 而Sb/Bi原子置换Si原子具有更低的E_f值说明在掺杂过程中优先进行Si位取代. 能带结构计算结果表明Bi原子掺杂可以提供更高的电子浓度, n值最高可以达到1.95×10²⁰ cm^–3, 而相应DOS计算结果表明, Sn位进行取代可以得到更大的载流子迁移率, 因此, Mg₂Si_0.375Sn_0.615Bi_0.01合金的最大电导率值可达1620 S/cm. Sb原子掺杂则可以得到更高的载流子有效质量, 对应的Mg₂Si_0.365Sn_0.625Sb_0.01合金最大S值为–228 μV/K. Sb掺杂Si位的合金的功率因子略高于Sn位取代, 最大值在T = 800 K时可达4.49 mW/(m·K), 相应的ZT值在T = 770 K时最高可达1.1, 而Sb取代Sn位时产生的晶格收缩现象获得了更低的热导率. 同等掺杂量下Bi掺杂合金的功率因子值较低, 因此其最优掺杂浓度低于Sb元素. 基于本文中实验和计算结果可以为掺杂优化Mg₂(Si, Sn)基合金的电子传输性能提供理论依据和参考.

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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

Figure 1. Conventional cell, primitive cell and supercell of Mg₂(Si, Sn) crystal.

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图 2 Bi/Sb掺杂的Mg₁₉₂Si₃₆Sn₆₀晶体的电荷密度分布图

Figure 2. Electron density of Bi/Sb doped Mg₁₉₂Si₃₆Sn₆₀ alloys.

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图 3 未掺杂 Mg₂Si_0.375Sn_0.625合金单胞(a)和Sb/Bi原子分别取代Si/Sn位(b)—(e)的Mg₂Si_0.375Sn_0.625合金超晶胞的能带结构图

Figure 3. Band structures of undoped Mg₂Si_0.375Sn_0.625 conventional cell (a) and the supercells with Sb/Bi doped at different Si/Sn sites (b)–(e).

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图 4 不同掺杂条件下Mg₂Si_0.375Sn_0.625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)

Figure 4. Calculated results of total DOS (a) and the weighting of elements in total DOS (b)–(f) for the Mg₂Si_0.375Sn_0.625 alloys under different doping conditions.

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图 5 快速凝固Mg₂Si_0.375Sn_0.625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)

Figure 5. Microstructure of rapid solidified Mg₂Si_0.375Sn_0.625 crystal (a) and the elements mapping images of Mg, Si, and Sn (b)–(d).

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图 6 不同掺杂条件下快速凝固Mg₂Si_0.375Sn_0.625合金的粉末XRD图(a)和(111), (220)衍射峰的局部放大图(b)

Figure 6. Power XRD patterns of the rapid solidified Mg₂Si_0.375Sn_0.625 crystals under different doping conditions (a) and partial enlarged peaks of (111) and (220) (b).

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Figure 7. Temperature dependence of Seebeck coefficient (a) and electrical conductivity (b) of Mg₂Si_0.375Sn_0.625 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.

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图 8 不同s掺杂条件下Mg₂Si_0.375Sn_0.625合金功率因子(a)、热导率(b)和ZT值(c)随温度的变化曲线

Figure 8. Temperature dependence of power factor (a), thermal conductivity (b), and ZT (c) of Mg₂Si_0.375Sn_0.625 crystals under different doping conditions.

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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/eV
Mg₁₉₂Si₃₆Sn₆₀	18.436	Mg—Sn	0.26	2.846	—
Mg₁₉₂Si₃₆Sn₆₀	18.436	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Mg₂Si_0.375Sn_0.625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 Mg₂Si_0.375Sn_0.625 alloys under different doping conditions

理论成分	元素含量/%				实际成分
理论成分	Mg	Si	Sn	Sb/Bi	实际成分
Mg₂Si_0.375Sn_0.625	66.91	12.51	20.58	—	Mg_2.007Si_0.375Sn_0.618
Mg₂Si_0.375Sn_0.615Sb_0.01	66.82	12.43	20.36	0.39	Mg_2.004Si_0.373Sn_0.611Sb_0.012
Mg₂Si_0.375Sn_0.615Bi_0.01	66.88	12.41	20.30	0.41	Mg_2.006Si_0.372Sn_0.609Bi_0.013
Mg₂Si_0.365Sn_0.625Sb_0.01	66.93	12.01	20.74	0.32	Mg_2.008Si_0.360Sn_0.623Sb_0.009
Mg₂Si_0.365Sn_0.625Bi_0.01	66.77	12.07	20.71	0.45	Mg_2.003Si_0.362Sn_0.621Bi_0.014

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Vol. 71, Issue 24 - 2022-12-20

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