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对于重要热电材料之一的填充方钴矿材料，其低热导率的成因存在两种观点：1）填充原子的局域振动引起共振散射降低热导率；2）填充原子的引入加强了三声子倒逆过程来降低热导率.本文采用含有限温度效应的第一性原理分子动力学方法模拟了YbFe4Sb12的动力学过程，并通过温度相关有效势场方法得到了充分包含非线性作用的等效非谐力常数，研究了微扰近似下的声子输运性质.结果显示，在填充原子振动全部参与三声子倒逆散射过程的近似下，相比于纯方钴矿体系，声子寿命大幅地降低，填充原子的振动是热阻的重要来源.但即便如此，理论计算结果与实验的晶格热导率之间仍存在明显偏离.不同填充原子振动之间的较弱关联性质也揭示其明显偏离经典的声子图像，表现为一种强烈的局域特征振动模式，并以此散射其他晶格声子，因而对热阻的贡献也超出了传统三声子的理论框架.通过将填充原子Yb振动模式的寿命进行共振散射形式的修正，可以使晶格热导率与实验结果符合较好.以上结果表明，YbFe4Sb12的低晶格热导率是由声子间相互作用以及具有局域振动特征的共振散射两方面因素导致.Filled skutterudite is a typical thermoelectric material with high thermoelectric figure of merit at intermediate temperatures. One of the important features is the low lattice thermal conductivity (L) caused by the low frequency vibrations of filler atoms in the oversized void cages. In the past decades, it has been still under debate whether the underlying phonon scattering mechanism should be considered to be resonant scattering or enhanced three-phonon process. To clarify the role played by the filler atoms in reducing the lattice thermal conductivity, we study the microscopic dynamical process of filler and related interactions by means of ab initio molecular dynamics (AIMD) and temperature dependent effective potential (TDEP) technique. Firstly, we simulate the dynamical trajectories of fully filled skutterudite YbFe4Sb12 at different temperatures through AIMD. In this approach, the nonlinear guest-host interactions at finite temperatures are taken into consideration naturally from dynamical trajectories. Then, we extract the effective temperature-dependent harmonic and anharmonic interatomic force constants (IFCs) by TDEP method through the statistical analyses of both trajectories and forces. The atomic participation ratios and lifetimes of phonon modes are calculated based on the effective IFCs. The results demonstrate that the local vibration modes of Yb couple with acoustic branches and reduce the lifetimes of the lattice phonons significantly. However, the calculated L, which is on the assumption that the filler interacts with lattice phonons through three-phonon collision, still deviates from the experimental result. In order to rationalize the discrepancy, we analyze the correlation properties between different Yb atoms by velocity coherence in atomic dynamical motions. The localized and independent vibration characteristic of Yb is found in this analysis. This implies that the motions of Yb atoms deviate from the periodic and collective vibration excitation paradigm of phonon. Therefore, the mechanism for how filler atoms scatter lattice phonon and enhance thermal resistance is beyond three-phonon scattering process. We thus introduce resonant scattering into the lifetimes of Yb-dominant localized vibration modes, and so-calculated L is in a good agreement with the experimental data. Overall, we come to a conclusion that both the phonon-phonon interaction and the resonant scattering due to the localized oscillators cause the low lattice thermal conductivity of YbFe4Sb12.
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Keywords:
- filled skutterudite /
- finite temperature /
- correlation of atoms /
- beyond three-phonon scattering
[1] Shi X, Xi L L, Yang J, Zhang W Q, Chen L D 2011 Physics. 40 710(in Chinese) [史迅, 席丽丽, 杨炯, 张文清, 陈立东 2011 物理 40 710]
[2] Nolas G S, Morelli D T, Tritt T M 1999 Annu. Rev. Mater. Sci. 29 89
[3] Shi X, Bai S, Xi L, Yang J, Zhang W, Chen L, Yang J 2011 J. Mater. Res. 26 1745
[4] Rull-Bravo M, Moure A, Fernndez J F, Martn-Gonzlez M 2015 RSC Adv. 5 41653
[5] Shi X, Yang J, Salvador J R, Chi M, Cho J Y, Wang H, Bai S, Yang J, Zhang W, Chen L 2011 J. Am. Chem. Soc. 133 7837
[6] Rogl G, Aabdin Z, Schafler E, Horky J, Setman D, Zehetbauer M, Kriegisch M, Eibl O, Grytsiv A, Bauer E 2012 J. Alloys Compd. 537 183
[7] Xi L L, Yang J, Shi X, Zhang W Q, Chen L D, Yang J H 2011 Sci. China: Phys. Mech. Astron.. 41 706(in Chinese) [席丽丽, 杨炯, 史迅, 张文清, 陈立东, 杨继辉 2011 中国科学: 物理学 力学 天文学 41 706]
[8] Slack G A, Tsoukala V G 1994 J. Appl. Phys. 76 1665
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[10] Huang L F, Li Y L, Ni M Y, Wang X L, Zhang G R, Zeng Z 2009 Acta Phys. Sin.. 58 306(in Chinese) [黄良锋, 李延龄, 倪美燕, 王贤龙, 张国仁, 曾雉 2009 物理学报 58 306]
[11] Keppens V, Mandrus D, Sales B C, Chakoumakos B C, Dai P, Coldea R, Maple M B, Gajewski D A, Freeman E J, Bennington S 1998 Nature 395 876
[12] Hermann R P, Jin R, Schweika W, Grandjean F, Mandrus D, Sales B C, Long G J 2003 Phys. Rev. Lett. 90 135505
[13] Dimitrov I K, Manley M E, Shapiro S M, Yang J, Zhang W, Chen L D, Jie Q, Ehlers G, Podlesnyak A, Camacho J, Li Q 2010 Phys. Rev.. 82 174301
[14] Feldman J L, Singh D J, Mazin I I, Mandrus D, Sales B C 2000 Phys. Rev.. 61 R9209
[15] Koza M M, Johnson M R, Viennois R, Mutka H, Girard L, Ravot D 2008 Nat. Mater. 7 805
[16] Li W, Mingo N 2015 Phys. Rev.. 91 144304
[17] Qiu W, Xi L, Wei P, Ke X, Yang J, Zhang W 2014 Proc. Natl. Acad. Sci. USA 111 15031
[18] Qiu W, Ke X, Xi L, Wu L, Yang J, Zhang W 2016 Sci. China: Phys. Mech. Astron. 59 627001
[19] Broido D A, Malorny M, Birner G, Mingo N, Stewart D A 2007 Appl. Phys. Lett. 91 231922
[20] Togo A, Oba F, Tanaka I 2008 Phys. Rev.. 78 134106
[21] Li W, Carrete J, A. Katcho N, Mingo N 2014 Comput. Phys. Commun. 185 1747
[22] Hellman O, Steneteg P, Abrikosov I A, Simak S I 2013 Phys. Rev.. 87 104111
[23] Hellman O, Abrikosov I A 2013 Phys. Rev.. 88 144301
[24] Srivastava G P 1990 The Physics of Phonons (Boca Raton: CRC press) p88
[25] Hellman O, Broido D A 2014 Phys. Rev.. 90 134309
[26] Li C W, Hellman O, Ma J, May A F, Cao H B, Chen X, Christianson A D, Ehlers G, Singh D J, Sales B C, Delaire O 2014 Phys. Rev. Lett. 112 175501
[27] Slack G A, Galginaitis S 1964 Phys. Rev. 133 A253
[28] Chen L D, Kawahara T, Tang X F, Goto T, Hirai T, Dyck J S, Chen W, Uher C 2001 J. Appl. Phys. 90 1864
[29] Nolas G S, Fowler G, Yang J 2006 J. Appl. Phys. 100 043705
[30] Guo R, Wang X, Huang B 2015 Sci. Rep. 5 7806
[31] Hafner J, Krajci M 1993 J. Phys.: Condens. Matter 5 2489
[32] Pailhes S, Euchner H, Giordano V M, Debord R, Assy A, Gomes S, Bosak A, Machon D, Paschen S, de Boissieu M 2014 Phys. Rev. Lett. 113 025506
[33] Euchner H, Pailhs S, Nguyen L T K, Assmus W, Ritter F, Haghighirad A, Grin Y, Paschen S, de Boissieu M 2012 Phys. Rev.. 86 224303
[34] Zhao X Y, Shi X, Chen L D, Zhang W Q, Bai S Q, Pei Y Z, Li X Y, Goto T 2006 Appl. Phys. Lett. 89 092121
[35] Cowley R A 1968 Rep. Prog. Phys. 31 123
[36] Christensen M, Abrahamsen A B, Christensen N B, Juranyi F, Andersen N H, Lefmann K, Andreasson J, Bahl C R, Iversen B B 2008 Nat. Mater. 7 811
[37] Pohl R 1962 Phys. Rev. Lett. 8 481
[38] Qiu P F, Yang J, Liu R H, Shi X, Huang X Y, Snyder G J, Zhang W, Chen L D 2011 J. Appl. Phys. 109 063713
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[1] Shi X, Xi L L, Yang J, Zhang W Q, Chen L D 2011 Physics. 40 710(in Chinese) [史迅, 席丽丽, 杨炯, 张文清, 陈立东 2011 物理 40 710]
[2] Nolas G S, Morelli D T, Tritt T M 1999 Annu. Rev. Mater. Sci. 29 89
[3] Shi X, Bai S, Xi L, Yang J, Zhang W, Chen L, Yang J 2011 J. Mater. Res. 26 1745
[4] Rull-Bravo M, Moure A, Fernndez J F, Martn-Gonzlez M 2015 RSC Adv. 5 41653
[5] Shi X, Yang J, Salvador J R, Chi M, Cho J Y, Wang H, Bai S, Yang J, Zhang W, Chen L 2011 J. Am. Chem. Soc. 133 7837
[6] Rogl G, Aabdin Z, Schafler E, Horky J, Setman D, Zehetbauer M, Kriegisch M, Eibl O, Grytsiv A, Bauer E 2012 J. Alloys Compd. 537 183
[7] Xi L L, Yang J, Shi X, Zhang W Q, Chen L D, Yang J H 2011 Sci. China: Phys. Mech. Astron.. 41 706(in Chinese) [席丽丽, 杨炯, 史迅, 张文清, 陈立东, 杨继辉 2011 中国科学: 物理学 力学 天文学 41 706]
[8] Slack G A, Tsoukala V G 1994 J. Appl. Phys. 76 1665
[9] Nolas G, Cohn J, Slack G 1998 Phys. Rev.. 58 164
[10] Huang L F, Li Y L, Ni M Y, Wang X L, Zhang G R, Zeng Z 2009 Acta Phys. Sin.. 58 306(in Chinese) [黄良锋, 李延龄, 倪美燕, 王贤龙, 张国仁, 曾雉 2009 物理学报 58 306]
[11] Keppens V, Mandrus D, Sales B C, Chakoumakos B C, Dai P, Coldea R, Maple M B, Gajewski D A, Freeman E J, Bennington S 1998 Nature 395 876
[12] Hermann R P, Jin R, Schweika W, Grandjean F, Mandrus D, Sales B C, Long G J 2003 Phys. Rev. Lett. 90 135505
[13] Dimitrov I K, Manley M E, Shapiro S M, Yang J, Zhang W, Chen L D, Jie Q, Ehlers G, Podlesnyak A, Camacho J, Li Q 2010 Phys. Rev.. 82 174301
[14] Feldman J L, Singh D J, Mazin I I, Mandrus D, Sales B C 2000 Phys. Rev.. 61 R9209
[15] Koza M M, Johnson M R, Viennois R, Mutka H, Girard L, Ravot D 2008 Nat. Mater. 7 805
[16] Li W, Mingo N 2015 Phys. Rev.. 91 144304
[17] Qiu W, Xi L, Wei P, Ke X, Yang J, Zhang W 2014 Proc. Natl. Acad. Sci. USA 111 15031
[18] Qiu W, Ke X, Xi L, Wu L, Yang J, Zhang W 2016 Sci. China: Phys. Mech. Astron. 59 627001
[19] Broido D A, Malorny M, Birner G, Mingo N, Stewart D A 2007 Appl. Phys. Lett. 91 231922
[20] Togo A, Oba F, Tanaka I 2008 Phys. Rev.. 78 134106
[21] Li W, Carrete J, A. Katcho N, Mingo N 2014 Comput. Phys. Commun. 185 1747
[22] Hellman O, Steneteg P, Abrikosov I A, Simak S I 2013 Phys. Rev.. 87 104111
[23] Hellman O, Abrikosov I A 2013 Phys. Rev.. 88 144301
[24] Srivastava G P 1990 The Physics of Phonons (Boca Raton: CRC press) p88
[25] Hellman O, Broido D A 2014 Phys. Rev.. 90 134309
[26] Li C W, Hellman O, Ma J, May A F, Cao H B, Chen X, Christianson A D, Ehlers G, Singh D J, Sales B C, Delaire O 2014 Phys. Rev. Lett. 112 175501
[27] Slack G A, Galginaitis S 1964 Phys. Rev. 133 A253
[28] Chen L D, Kawahara T, Tang X F, Goto T, Hirai T, Dyck J S, Chen W, Uher C 2001 J. Appl. Phys. 90 1864
[29] Nolas G S, Fowler G, Yang J 2006 J. Appl. Phys. 100 043705
[30] Guo R, Wang X, Huang B 2015 Sci. Rep. 5 7806
[31] Hafner J, Krajci M 1993 J. Phys.: Condens. Matter 5 2489
[32] Pailhes S, Euchner H, Giordano V M, Debord R, Assy A, Gomes S, Bosak A, Machon D, Paschen S, de Boissieu M 2014 Phys. Rev. Lett. 113 025506
[33] Euchner H, Pailhs S, Nguyen L T K, Assmus W, Ritter F, Haghighirad A, Grin Y, Paschen S, de Boissieu M 2012 Phys. Rev.. 86 224303
[34] Zhao X Y, Shi X, Chen L D, Zhang W Q, Bai S Q, Pei Y Z, Li X Y, Goto T 2006 Appl. Phys. Lett. 89 092121
[35] Cowley R A 1968 Rep. Prog. Phys. 31 123
[36] Christensen M, Abrahamsen A B, Christensen N B, Juranyi F, Andersen N H, Lefmann K, Andreasson J, Bahl C R, Iversen B B 2008 Nat. Mater. 7 811
[37] Pohl R 1962 Phys. Rev. Lett. 8 481
[38] Qiu P F, Yang J, Liu R H, Shi X, Huang X Y, Snyder G J, Zhang W, Chen L D 2011 J. Appl. Phys. 109 063713
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