中子散射技术在Zintl相化合物热导率研究中的应用

张翠萍; 朱金峰; 沈晓玲; 舒明方; 任清勇; 马杰

doi:10.7498/aps.74.20241163

摘要

Zintl相化合物因为其独特的晶体结构和优异的输运性能, 在能源存储及转换领域尤其是热电材料应用中受到广泛关注. 为了理解Zintl相化合物优异热电性能起源, 科研工作者们利用中子散射技术结合分子动力学模拟, 对晶格热导和电声耦合效应展开研究, 取得了一系列成果. 本文系统总结了中子散射对一些Zintl相化合物的结构及其晶格动力学的相关研究工作, 按照零维A₁₄MPn₁₁型化合物、一维链状化合物、二维层状AB₂X₂型化合物和其结构变体AB₄X₃型化合物, 层状ZrBeSi结构Zintl相化合物的顺序依次梳理了其低晶格热导率的物理起源. 通过中子衍射技术探讨了晶体结构、原子位移参数等信息; 围绕中子非弹性散射实验, 探讨了声子态密度的测量方法及其对Zintl相化合物动力学性质的研究. 在深入认识Zintl相化合物的同时, 揭示了其微观结构和优化材料性能, 以期对设计新型热电功能材料具有一些启发.

关键词:

Abstract

Due to the unique crystal structures and excellent transport properties, the Zintl phase thermoelectric materials have aroused extensive interest in energy storage and conversion. To explore the origins of those excellent performances, a series of experimental and theoretical techniques have been applied, such as neutron scattering, thermal conductivity, and molecular dynamics simulations with machine learning. In this paper, the progress of neutron scattering research on the structure and dynamics of Zintl phase is summarized, for example A₁₄MPn₁₁ compounds with zero-dimensional (0D) substructures, 1D chains-based compounds, 2D layered A₂BX₂ compounds (including the binary Mg₃Sb₂) and their structural variants, as well as AB₄X₃, and ZrBeSi-type compounds. The underlying mechanisms of intrinsically low lattice thermal conductivity in those Zintl phase are discussed in detail. These compounds generally exhibit the following characteristics: 1) strong anharmonicity, which is characterized by strong atomic vibrations and anharmonic phonon-phonon scattering; 2) weak chemical bonding, which usually leads to low sound velocity and interatomic force constants, and corresponding to low-energy phonon branches; 3) intrinsic vacancy defect, which weakens the bond strengths, softens the lattice, and enhances anharmonic phonon-phonon scattering. Neutron diffraction is applied to studying crystal structures, lattice parameters, atomic occupancies, and atomic displacement parameters. Inelastic neutron scattering measures the lattice dynamics, and density of states, which are related to lattice thermal conductivity. Hence, the physical mechanisms of Zintl compounds are analyzed for optimizing material properties and designing new functional materials.

Keywords:

作者及机构信息

1.
上海交通大学物理与天文学院, 上海　200240

2.
散裂中子源科学中心, 东莞　523803

3.
中国科学院高能物理研究所, 北京　100049

4.
广东省极端条件重点实验室, 东莞　523803

通信作者: 马杰, jma3@sjtu.edu.cn

基金项目: 国家重点研发基金(批准号: 2022YFA1402702)、国家自然科学基金(批准号: U2032213, 12474024)、广东省极端条件重点实验室(批准号: 2023B1212010002)和广东省自然科学基金(批准号: 2021B1515140014)资助的课题.

Authors and contacts

1.
School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China

2.
Spallation Neutron Source Science Center, Dongguan 523803, China

3.
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

4.
Guangdong Provincial Key Laboratory of Extreme Conditions, Dongguan 523803, China

Corresponding author: MA Jie, jma3@sjtu.edu.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2022YFA1402702), the National Natural Science Foundation of China (Grant Nos. U2032213, 12474024), the Guangdong Provincial Key Laboratory of Extreme Conditions (Grant No. 2023B1212010002), and the Natural Science Foundation of Guangdong Province, China (Grant No. 2021B1515140014).

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施引文献

图 1 中子散射的三维示意图

Fig. 1. Three-dimensional schematic of neutron scattering.

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图 2 (a), (b) Yb₁₄MnSb₁₁的晶体结构和粉末X射线衍射谱^[44]; (c) Yb₁₄MnSb₁₁的X射线吸收光谱^[46]; (d) C_p/T随T ²的变化^[46]

Fig. 2. (a), (b) Crystal structure and rietveld refinement of powder X-ray diffraction of Yb₁₄MnSb₁₁^[44]; (c) X-ray absorption near edge structure spectra of Yb₁₄MnSb₁₁^[46]; (d) C_p/T vs. T ² ^[46].

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图 3 (a) Yb₁₄MnSb₁₁的动态结构因子^[44]; (b) 将图(a)数据减去弹性峰并通过玻色-爱因斯坦因子修正后的动态结构因子^[44]; (c), (d)声子态密度和约化声子态密度的温度依赖性^[44]

Fig. 3. (a) Dynamical structure factor of Yb₁₄MnSb₁₁^[44]; (b) dynamical structure factor after subtracting the elastic line in panel (a) and correcting it by the Bose-Einstein factor^[44]; (c), (d) temperature dependence of the phonon density-of-states and reduced phonon density-of-states^[44].

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图 4 (a) Eu₁₄MnSb₁₁, Yb₁₄MnSb₁₁和Zn₄Sb₃的元素特定核非弹性散射光谱^[44]; (b) Eu₁₄MnSb₁₁中的分波和总声子态密度(上), Yb₁₄MnSb₁₁, Eu₁₄MnSb₁₁和Zn₄Sb₃中Sb的分波声子态密度(中)及约化后的分波声子态密度(下)^[44]

Fig. 4. (a) Element-specific nuclear inelastic scattering spectra measured in Eu₁₄MnSb₁₁, Yb₁₄MnSb₁₁, and Zn₄Sb₃^[44]; (b) partial and total phonon density-of-states in Eu₁₄MnSb₁₁ (top), the partial phonon density-of-states (middle) and the reduced partial phonon density-of-states (bottom) in Yb₁₄MnSb₁₁, Eu₁₄MnSb₁₁, and Zn₄Sb₃^[44].

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图 5 (a), (b) Yb₁₄MnSb₁₁的动态结构因子^[51]; (c), (d) Yb₁₄MnSb₁₁加权声子态密度和声子能带结构^[51]; (e) Yb₁₄MnSb₁₁晶格热导率$ {\kappa }_{{\mathrm{L}}} $与双通道晶格动力学模拟值的比较^[51–53], 其中$ {\kappa }_{{\mathrm{p}}{\mathrm{h}}} $和$ {\kappa }_{{\mathrm{d}}{\mathrm{i}}{\mathrm{f}}{\mathrm{f}}} $分别为声子-气体通道、扩散子通道

Fig. 5. (a), (b) Dynamical structure factor of Yb₁₄MnSb₁₁^[51]; (c), (d) phonon density-of-states and phonon band structure Yb₁₄MnSb₁₁^[51]; (e) comparison of the lattice thermal conductivity of Yb₁₄MnSb₁₁ with the simulated values of dual channel lattice dynamics^[51–53], $ {\kappa }_{{\mathrm{p}}{\mathrm{h}}} $, $ {\kappa }_{{\mathrm{d}}{\mathrm{i}}{\mathrm{f}}{\mathrm{f}}} $ represent phonon-gas and diffusion channel, respectively.

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图 6 (a)—(c) TlInTe₂的粉末X射线衍射分析和沿不同角度的晶体结构, 椭球尺寸代表所有原子的各向异性原子位移参数大小^[60]; (d) C_p/T随T ²的变化^[60]; (e) C_p/T ³随T的变化^[60]; (f)吸收系数^[60]

Fig. 6. (a)–(c) Rietveld refinement of powder X-ray diffraction and crystal structure of TlInTe₂, the anisotropic atomic displacement parameters of all the atoms plotted as ellipsoids^[60]; (d) C_p/T vs. T ^{2 [60]}; (e) C_p/T ³ vs. T^[60]; (f) absorption coefficient^[60].

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图 7 (a) Tl原子的原子位移参数^[63]; (b)—(d) TlInTe₂的加权声子态密度、声子线宽和声子寿命^[63]

Fig. 7. (a) Atomic displacement parameters of Tl^[63]; (b)–(d) neutron-weighted phonon density-of-states, phonon linewidth, and phonon lifetime of TlInTe₂^[63].

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图 8 (a), (b) CaMg₂Bi₂的晶体结构和粉末X射线衍射^[83]

Fig. 8. (a), (b) Crystal structure and rietveld refinement of powder X-ray diffraction patterns of CaMg₂Bi₂^[83].

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图 9 (a), (b) CaZn₂Sb₂和YbZn₂Sb₂的晶格常数及各向同性原子位移参数^[90]

Fig. 9. (a), (b) Lattice constants and isotropic atomic displacements of CaZn₂Sb₂ and YbZn₂Sb₂^[90].

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图 10 (a), (b) Mg₃Sb₂的晶体结构和粉末X射线衍射^[91]; (c) Mg₃Sb₂中3个化学键的约化密度梯度与sign(λ₂)ρ的函数关系^[100]; (d)晶格热导率^[101,102]

Fig. 10. (a), (b) Crystal structure and powder X-ray diffraction of Mg₃Sb₂^[91]; (c) the noncovalent interaction analysis with reduced density gradient as a function of sign(λ₂)ρ for the chemical bonds in Mg₃Sb₂^[100]; (d) lattice thermal conductivity^[101,102].

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图 11 (a) Mg₃Sb₂和CaMg₂Sb₂的声子态密度^[91]; (b), (c)动态结构因子^[91]; (d) Mg₃Sb₂的分波声子态密度^[91]; (e), (f)声子态密度的温度依赖性, 并与计算结果(黑色)进行比较^[91]

Fig. 11. (a) Phonon density-of-states of Mg₃Sb₂ and CaMg₂Sb₂^[91]; (b), (c) neutron dynamical structure factor^[91]; (d) calculated partial phonon density-of-states of Mg₃Sb₂^[91]; (e), (f) temperature dependence of neutron density-of-states, and compared with the calculated results (black)^[91].

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图 12 (a), (b) RbCd₂As₂与RbCd₄As₃的晶体结构关系^[111]; (c) NaCd₄As₃的粉末X射线衍射^[111]; (d), (e) RbZn₂As₂与RbZn₄As₃的晶体结构关系^[111]; (f) RbZn₄As₃的粉末X射线衍射^[112]

Fig. 12. (a), (b) Structural relationship between RbCd₂As₂ and RbCd₄As₃^[111]; (c) rietveld refinement of powder X-ray diffraction patterns of NaCd₄As₃^[111]; (d), (e) structural relationship between RbZn₂As₂ and RbZn₄As₃^[111]; (f) rietveld refinement of powder X-ray diffraction patterns of RbZn₄As₃^[112].

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图 13 (a) RbZn_4–xCu_xAs₃的总热导率和晶格热导率^[112]; (b) Rb, Zn, As(1)和As(2)各向同性原子位移^[112]

Fig. 13. (a) Total thermal conductivity and lattice thermal conductivity of RbZn_4–xCu_xAs₃^[112]; (b) the isotropic atomic displacements of Rb, Zn, As(1), and As(2)^[112].

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图 14 (a), (b) SrCuSb的晶体结构和粉末中子衍射^[123]; (c) ACuSb格林内森常数, 橙、深蓝和酒红色点分别代表CaCuSb, SrCuSb和BaCuSb^[129]; (d) ACuSb中Ca, Sr和Ba原子的各向同性原子位移参数^[129]; (e), (f) Eu₂Zn_0.98Sb₂沿[103]方向的高角环形暗场扫描透射电子显微镜图像, 紫色、蓝色和橙色球体分别代表Eu, Sb和Zn^[130]; (g) Eu₂ZnSb₂和EuAgSb的晶格热导率^[131]; (h), (i) SrCuSb和Sr₂ZnSb₂的三声子和四声子散射率^[[132]

Fig. 14. (a), (b) Crystal structure and rietveld refinement of neutron powder diffraction of SrCuSb^[123]; (c) Grüneisen parameter of ACuSb^[129], the orange, dark blue and burgundy dots represent CaCuSb, SrCuSb and BaCuSb, respectively; (d) isotropic atomic displacements of Ca, Sr, and Ba atoms in ACuSb^[129]; (e), (f) high-angle annular dark-field scanning transmission electron microscopy image along the [103] direction of Eu₂Zn_0.98Sb₂^[130], the purple, blue and orange spheres represent Eu, Sb and Zn, respectively; (g) lattice thermal conductivity of Eu₂ZnSb₂ and EuAgSb^[131]; (h), (i) calculated three- and four-phonon scattering rates of SrCuSb and Sr₂ZnSb₂^[132].

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图 15 (a)—(c) Sr(Cu, Ag, Zn)Sb的动态结构因子^[123]; (d)—(f) (110)平面的差分电荷密度^[123]; (g)各向异性原子位移参数, 插图为Sr(Cu, Ag, Zn)Sb的晶体结构示意图, 椭圆体尺寸代表所有原子的各向异性原子位移参数大小^[123]

Fig. 15. (a)–(c) Dynamical structure factor of Sr(Cu, Ag, Zn)Sb^[123]; (d)–(f) charge density differences projected in the (110) plane^[123]; (g) the anisotropic atomic displacement parameters, insets show the schematic crystal structures of Sr(Cu, Ag, Zn)Sb with anisotropic atomic displacement parameters ellipsoids^[123].

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中子散射技术在Zintl相化合物热导率研究中的应用