稀土（La，Pr，Nd）镓酸盐的晶格振动谱的计算
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摘要
稀土镓酸盐由于其特有的性质而受到广泛的关注。例如:LaGaO_3,NdGaO_3和PrGaO_3可用做高温超导(HTSC)外延生长的基底材料。在870~1070 K,掺杂锶和镁后,这几种物质表现出高氧离子导电性,是一种很有潜力的中温固体氧化物燃料电池(SOFC)固体电解质。
在高温超导体中,内部声子的重要性吸引了许多人进行大量了晶格动力学理论研究和对这些化合物在半导体(非超导)与声子相关的性质研究。在某些程度上,这项工作的进展受到势能模型的影响,表现在对这些固体的凝聚、弹性及晶格动力学特性的理解方面。原子间相互作用势能也是决定计算机模拟研究可靠性的关键因素,计算机模拟研究已经广泛的应用在完美晶体和有缺陷的离子材料。目前,人们应用短距离力常数模型计算出LaGaO_3和NdGaO_3的声子谱,但还没有对PrGaO_3进行相关研究。
本文将对正交相PrGaO_3的晶体结构进行分析,计算出其声子谱。针对稀土镓酸盐的空间结构特点,选择了位置群分析方法对PrGaO_3的振动模式分类,并指认出LaGaO_3声子谱中的一些拉曼光谱线并计算出其偏振方向。其次,使用了壳模型,应用GULP程序计算了PrGaO_3的正交相晶格振动频率,及其声子色散关系和态密度。也对LaGaO_3 , NdGaO_3和PrGa_(0.95)Mg_(0.05)O_3进行了晶格动力学计算。
合成了LaGaO_3、PrGaO_3、NdGaO_3和PrGa_(0.95)Mg_(0.05)O_3,其红外和拉曼光谱数据与计算结果符合的很好,说明了所选择模型和计算方法的合理性与正确性。
Rare earth gallates, due to their particular properties, have attracted wide attention. For instance, NdGaO_3, LaGaO_3, PrGaO_3 as well as solid solutions are used as substrate materials for epitaxial growth of high temperature superconductors (HTSC). It was reported that lanthanum, neodymium and praseodymium gallates, doped with strontium and magnesium show high oxygen ion conductivity at temperatures of about 870–1070 K, and are considered as prospective solid electrolytes for the application of solid oxide fuel cells (SOFCs).
The general interest and importance of phonons in HTSC have provided the motivation for our theoretical studies of the lattice dynamics and the phonon- related properties of these compounds. This work is stimulated in part by the importance of potential models in understanding cohesive, elastic and lattice dynamical properties of these solids. Interatomic potentials are also key factor in determining the reliability of computer modeling studies which have been widely applied to perfect lattice and defect properties of ionic materials. So far a short range force model has been applied to investigate the phonons in LaGaO_3 and NdGaO_3 perovskite in the orthorhombic phase. However, there is little research about phonon-related properties of PrGaO_3.
In this paper, we analyzed the crystal structure of PrGaO_3 and calculated its lattice vibration spectrum. Several methods calculating lattice vibration modes were compared and site symmetry analysis was used to classify the lattice vibration modes of PrGaO_3 and give the polarization and symmetry assignment of LaGaO_3 Raman modes. Then a shell model has been applied for the first time to investigate the phonon spectrum of PrGaO_3 perovskite with orthorhombic phase by using GULP software, and the frequencies of phonons, phonon dispersion curves and density of states were obtained. The phonon spectra of LaGaO_3, NdGaO_3 and PrGa_(0.95)Mg_(0.05)O_3 are also calculated.
LaGaO_3, PrGaO_3, PrGa_(0.95)Mg_(0.05)O_3和NdGaO_3 were synthesized, whose infrared and Raman spectra showed good agreement with calculated results, indicating that correct and reasonable model was selected.
在高温超导体中,内部声子的重要性吸引了许多人进行大量了晶格动力学理论研究和对这些化合物在半导体(非超导)与声子相关的性质研究。在某些程度上,这项工作的进展受到势能模型的影响,表现在对这些固体的凝聚、弹性及晶格动力学特性的理解方面。原子间相互作用势能也是决定计算机模拟研究可靠性的关键因素,计算机模拟研究已经广泛的应用在完美晶体和有缺陷的离子材料。目前,人们应用短距离力常数模型计算出LaGaO_3和NdGaO_3的声子谱,但还没有对PrGaO_3进行相关研究。
本文将对正交相PrGaO_3的晶体结构进行分析,计算出其声子谱。针对稀土镓酸盐的空间结构特点,选择了位置群分析方法对PrGaO_3的振动模式分类,并指认出LaGaO_3声子谱中的一些拉曼光谱线并计算出其偏振方向。其次,使用了壳模型,应用GULP程序计算了PrGaO_3的正交相晶格振动频率,及其声子色散关系和态密度。也对LaGaO_3 , NdGaO_3和PrGa_(0.95)Mg_(0.05)O_3进行了晶格动力学计算。
合成了LaGaO_3、PrGaO_3、NdGaO_3和PrGa_(0.95)Mg_(0.05)O_3,其红外和拉曼光谱数据与计算结果符合的很好,说明了所选择模型和计算方法的合理性与正确性。
Rare earth gallates, due to their particular properties, have attracted wide attention. For instance, NdGaO_3, LaGaO_3, PrGaO_3 as well as solid solutions are used as substrate materials for epitaxial growth of high temperature superconductors (HTSC). It was reported that lanthanum, neodymium and praseodymium gallates, doped with strontium and magnesium show high oxygen ion conductivity at temperatures of about 870–1070 K, and are considered as prospective solid electrolytes for the application of solid oxide fuel cells (SOFCs).
The general interest and importance of phonons in HTSC have provided the motivation for our theoretical studies of the lattice dynamics and the phonon- related properties of these compounds. This work is stimulated in part by the importance of potential models in understanding cohesive, elastic and lattice dynamical properties of these solids. Interatomic potentials are also key factor in determining the reliability of computer modeling studies which have been widely applied to perfect lattice and defect properties of ionic materials. So far a short range force model has been applied to investigate the phonons in LaGaO_3 and NdGaO_3 perovskite in the orthorhombic phase. However, there is little research about phonon-related properties of PrGaO_3.
In this paper, we analyzed the crystal structure of PrGaO_3 and calculated its lattice vibration spectrum. Several methods calculating lattice vibration modes were compared and site symmetry analysis was used to classify the lattice vibration modes of PrGaO_3 and give the polarization and symmetry assignment of LaGaO_3 Raman modes. Then a shell model has been applied for the first time to investigate the phonon spectrum of PrGaO_3 perovskite with orthorhombic phase by using GULP software, and the frequencies of phonons, phonon dispersion curves and density of states were obtained. The phonon spectra of LaGaO_3, NdGaO_3 and PrGa_(0.95)Mg_(0.05)O_3 are also calculated.
LaGaO_3, PrGaO_3, PrGa_(0.95)Mg_(0.05)O_3和NdGaO_3 were synthesized, whose infrared and Raman spectra showed good agreement with calculated results, indicating that correct and reasonable model was selected.
引文
1 T. Ishihara, H. Matsuda, Y. Takita. Doped LaGaO3 Perovskite-type Oxide as a New Oxide Ionic Conductor. J. Am. Chem. Soc. 1994, 116: 3801~3803
2 Man Feng, J. B. Goodenough. A Superior Oxide-ion Electrolyte. Eur. J. Solid State Inorg. Chem. 1994, 31: 663~672
3 T. Ishihara, H. Matsuda, Y. Takita. Oxide Ion Conductivity in Doped Ga Based Perovskite Type Oxide. Solid State Ion. Diffus. React. 1996: 86~88, 197~201
4 T. Ishihara, H. Furutani, H. Arikawa, M. Honda, T. Akbay, Y. Takita. Oxide Ion Conductivity in Doubly Doped PrGaO3 Perovskite-type Oxide. J. Electrochem. Soc. 1999, 146: 1643~1649
5 E. P. Murray, T. Tsal, S. A. Bamett. A Direct-methane Fuel Cell with a Ceria-Based Anode. Nature. 1999, 400: 649~651
6 W. Marti, P. Fischer, F. Altorfer, H. Scheel and M. Tadin. Crystal-structures and Phase-transitions of Orthorhombic and Rhombohedra RGaO3 (R = La, Pr, Nd) Investigated by Neutron Powder Diffraction. J. Phys. Condens. Matter. 1994, 6: 127~135
7 M. Lerch, H. Boysen, and T. Hansen. High-temperature Neutron Scattering Investigation of Pure and Doped Lanthanum Gallate. J. Phys. Chem. Solids. 2001, 62: 445~455
8 C. Howard and B. Kennedy. The Orthorhombic and Rhombohedral Phases of LaGaO3– a Neutron Powder Diffraction Study. J. Phys. Condens. Matter. 1999, 11: 3229~3236
9 P. R. Slater, J. T. S. Irvine, T. Ishibara and Y. Rakita. High-temperature Powder Neutron Diffraction Study of the Oxide Ion Conductor La0.9Sr0.1Ga0.8Mg0.2O2.85. J. Solid State Chem. 1998, 139: 135~143
10 J. Suda, T. Mori, H. Saito, O. Kamishima, T. Hattori and T. Sato. First-order Raman Spectra and Lattice Dynamics of NdGaO3 Crystal. Phys. Rev. B. 2002, 66: 174302-1~9
11 L. Vasylechko, L. Akselrud, W. Morgenroth, U. Bismayer, A. Matkovskii, and D. Savytskii. The Crystal Structure of NdGaO3 at 100 K and 293 KBased on Synchrotron Data. J. Alloys Compd. 2000, 297: 46~52
12 D. I. Savytskii, D. Yu. Sugak, A. O. Matkovskii, A.Suchocki, I.V. Savyskii, V. I. Dzhala, and P. Kaczor. Optical Spectroscopy and Symmetry of NdGaO3. Proc. Soc. Photo-opt. Ins. 1997, 3178: 283~286
13 S. Ubizskii, L. Vasylechko, D. Savytskii, A. Matkovskii, and I. Syvorotka. The Crystal Structure and Twinning of Neodymium Gallium Perovskite Single Crystals. Supercond. Sci. Technol. 1994, 7: 766~772
14 D. Savytskii, L. Vasylechko, A. Senyshyn, A. Matkovskii, C. B?htz, M. L. Sanjuán, U. Bismayer and M. Berkowski. Low-temperature Structural and Raman Studies on Rare-earth Gallates. Phys. Rev. B. 2003, 68: 24101-1~8
15 L. Vasylechko, Ye. Pivak, A. Senyshyn, D. Savytskii, M. Berkowski, H. Borrmann, M. Knapp and C. Paulmann. Crystal Structure and Thermal Expansion of PrGaO3 in the Temperature Range 12-1253 K. J. Solid State Chem. 2005, 178: 270~278
16 L. Vasylechko, A. Matkovskii, D. Savytskii, A. Suchocki, and F. Wallrafen. Crystal Structure of GdFeO3-type Rare Earth Gallates and Aluminates. J. Alloy. Compd. 1999, 291(1-2): 57~65
17小威尔逊.分子振动.北京:科学出版社, 1985
18 T. Shimanouchi, M. Tsuboi and T. Miyazawa. Optically Active Lattice Vibrations as Treated by the GF-Matrix Method. J. Chem. Phys. 1961, 35: 1597~1612
19 N. Velentin. Popov. Shell model parameters for layered copper oxides. J. Phys. Condens. Matter. 1995, 7: 1625~1638
20 T. Kalisik, P. Majumdar, et al. Comparison of Scattering Rates and Thermal Conductivity in Diamond Using Dispersion Curve Data. Ht2005: Proceedings of the Asme Summer Heat Transfer Conference. 2005, 1: 433~447
21 Tokuhisa, Atsushi, Joti, Yasumasa, Nakagawa, Hiroshi, et al. Non-Gaussian Behavior of Elastic Incoherent Neutron Scattering Profiles of Proteins Studied by Molecular Dynamics Simulation. Phys. Rev. E. Stat. Nonlin. Soft Matter Phys. 2007, 75: 41912-1~8
22 M. L. Sanjuán, V. M. Orera, R. I. Merina and J. Blasco. Raman and X-Ray Study of La1-xGaxO3 (0≤x≤1) Perovskite Solid Solutions. J. Phys. Condens.Matter. 1998, 10: 11687~11702
23 G. A. Tompsett, N. M. Sammes, R. J. Philips. Raman spectroscopy of the LaGaO3 phase transition. J. Raman Spectrosc. 1999, 30: 497~500
24 Z. M. Zhang, B. I. Choi, M. I. Flik and A. C. Anderson. Infrared Refractive-Indexes of LaAlO3, LaGaO3, and NdGaO3. J. Opt. Soc. Am. B. 1994, 11: 2252~2257
25 N. Rani, V. B. Gohel and H. C. Gupta. Zone Center Wave numbers of the Orthorhombic LaGaO3 Perovskite. J. Raman Spectrosc. 2000, 31: 877~880
26 N. Rani, V. B. Gohel, H. C. Gupta, M. K. Singh and L. M. Tiwari. A Lattice Dynamical Investigation of the Zone Center Frequencies of the Orthorhombic NdGaO3 Perovskite. J. Phys. Chem. Solids. 2001, 62: 1003~1006
27赵朋,李晓和张仲.光谱实验室.硅酸镓镧晶体的Raman光谱分析. 2005, 22: 1161~1163
28 J. D. Gale and A. L. Rohl. The General Utility Lattice Program (GULP). Mol. Simulat. 2003, 29(5): 291~341
29 J. D. Gale, Z. Kristallogr. GULP: Capabilities and Prospects. 2005, 220(5-6): 552~554
30冯端,师昌绪,刘治国.材料科学导论-融贯的论述.第1版.北京:化学工业出版社, 2002: 463~464
31李树棠.晶体X射线衍射学基础.冶金工业出版社, 2002: 1~100
32方容川.固体光谱学.中国科学技术大学出版社, 2003: 346
33张光寅.晶格振动光谱学.高等教育出版社, 2003: 93~94
34 B. G. Dick, A. W. Overhauser. Theory of the Dielectric Constants of Alkali Halide Crystals. Phys. Rev. 1958, 112: 90~103
35 C. Y. Wang, C. Q. Ru and A. Mioduchowski. Orthotropic Elastic Shell Model for Buckling of Microtubules. Phys. Rev. E. 2006, 74: 52901-1~4
36 M. Horoi, S. Stoica, et al. Shell-model Calculations of Two-Neutrino Double-Beta Decay Rates of Ca-48 with the GXPF1A Interaction. Phys. Rev. C. 2007, 75: 34303-1~4
37 Y. Utsuno, T. Otsuka, et al. Structure of Exotic Nuclei by Large-scale Shell Model Calculations. Aip. Conf. Proc. 2006, 865: 101~106
38 K. J. Ahn, F. Milde, A. Knorr. Phonon-wave-induced ResonanceFluorescence in Semiconductor Nanostructures: Acoustoluminescence in the Terahertz Range. Phys. Rev. Lett. 2007, 98: 27401-1~6
39 A. M. Vora. Computation of Phonon Dynamics of Mg70Zn30 Metallic Glass. J. Mater. Sci. 2007, 42: 935~940
40 A. Koreeda, S. Saikan, et al. Quasielastic Light Scattering by Phonon-Density Fluctuations in Dielectric Crystals and a Novel Macroscopic Analysis for the Scattered Spectra. Ferroelectrics. 2007, 347: 12~16
41 H. J. Monkhorst and J. D. Pack. Special Points for Brillouin-zone Integrations. Phys. Rev. B. 1976, 13: 5188~5192
42 Li Ying, Wu Di, Li Zhi-Ru, et al. Structural and Electronic Properties of Boron-Doped Lithium Clusters: Ab Initio and DFT Studies. J. Comput. Chem. 2007, 28(10): 1677~1684
2 Man Feng, J. B. Goodenough. A Superior Oxide-ion Electrolyte. Eur. J. Solid State Inorg. Chem. 1994, 31: 663~672
3 T. Ishihara, H. Matsuda, Y. Takita. Oxide Ion Conductivity in Doped Ga Based Perovskite Type Oxide. Solid State Ion. Diffus. React. 1996: 86~88, 197~201
4 T. Ishihara, H. Furutani, H. Arikawa, M. Honda, T. Akbay, Y. Takita. Oxide Ion Conductivity in Doubly Doped PrGaO3 Perovskite-type Oxide. J. Electrochem. Soc. 1999, 146: 1643~1649
5 E. P. Murray, T. Tsal, S. A. Bamett. A Direct-methane Fuel Cell with a Ceria-Based Anode. Nature. 1999, 400: 649~651
6 W. Marti, P. Fischer, F. Altorfer, H. Scheel and M. Tadin. Crystal-structures and Phase-transitions of Orthorhombic and Rhombohedra RGaO3 (R = La, Pr, Nd) Investigated by Neutron Powder Diffraction. J. Phys. Condens. Matter. 1994, 6: 127~135
7 M. Lerch, H. Boysen, and T. Hansen. High-temperature Neutron Scattering Investigation of Pure and Doped Lanthanum Gallate. J. Phys. Chem. Solids. 2001, 62: 445~455
8 C. Howard and B. Kennedy. The Orthorhombic and Rhombohedral Phases of LaGaO3– a Neutron Powder Diffraction Study. J. Phys. Condens. Matter. 1999, 11: 3229~3236
9 P. R. Slater, J. T. S. Irvine, T. Ishibara and Y. Rakita. High-temperature Powder Neutron Diffraction Study of the Oxide Ion Conductor La0.9Sr0.1Ga0.8Mg0.2O2.85. J. Solid State Chem. 1998, 139: 135~143
10 J. Suda, T. Mori, H. Saito, O. Kamishima, T. Hattori and T. Sato. First-order Raman Spectra and Lattice Dynamics of NdGaO3 Crystal. Phys. Rev. B. 2002, 66: 174302-1~9
11 L. Vasylechko, L. Akselrud, W. Morgenroth, U. Bismayer, A. Matkovskii, and D. Savytskii. The Crystal Structure of NdGaO3 at 100 K and 293 KBased on Synchrotron Data. J. Alloys Compd. 2000, 297: 46~52
12 D. I. Savytskii, D. Yu. Sugak, A. O. Matkovskii, A.Suchocki, I.V. Savyskii, V. I. Dzhala, and P. Kaczor. Optical Spectroscopy and Symmetry of NdGaO3. Proc. Soc. Photo-opt. Ins. 1997, 3178: 283~286
13 S. Ubizskii, L. Vasylechko, D. Savytskii, A. Matkovskii, and I. Syvorotka. The Crystal Structure and Twinning of Neodymium Gallium Perovskite Single Crystals. Supercond. Sci. Technol. 1994, 7: 766~772
14 D. Savytskii, L. Vasylechko, A. Senyshyn, A. Matkovskii, C. B?htz, M. L. Sanjuán, U. Bismayer and M. Berkowski. Low-temperature Structural and Raman Studies on Rare-earth Gallates. Phys. Rev. B. 2003, 68: 24101-1~8
15 L. Vasylechko, Ye. Pivak, A. Senyshyn, D. Savytskii, M. Berkowski, H. Borrmann, M. Knapp and C. Paulmann. Crystal Structure and Thermal Expansion of PrGaO3 in the Temperature Range 12-1253 K. J. Solid State Chem. 2005, 178: 270~278
16 L. Vasylechko, A. Matkovskii, D. Savytskii, A. Suchocki, and F. Wallrafen. Crystal Structure of GdFeO3-type Rare Earth Gallates and Aluminates. J. Alloy. Compd. 1999, 291(1-2): 57~65
17小威尔逊.分子振动.北京:科学出版社, 1985
18 T. Shimanouchi, M. Tsuboi and T. Miyazawa. Optically Active Lattice Vibrations as Treated by the GF-Matrix Method. J. Chem. Phys. 1961, 35: 1597~1612
19 N. Velentin. Popov. Shell model parameters for layered copper oxides. J. Phys. Condens. Matter. 1995, 7: 1625~1638
20 T. Kalisik, P. Majumdar, et al. Comparison of Scattering Rates and Thermal Conductivity in Diamond Using Dispersion Curve Data. Ht2005: Proceedings of the Asme Summer Heat Transfer Conference. 2005, 1: 433~447
21 Tokuhisa, Atsushi, Joti, Yasumasa, Nakagawa, Hiroshi, et al. Non-Gaussian Behavior of Elastic Incoherent Neutron Scattering Profiles of Proteins Studied by Molecular Dynamics Simulation. Phys. Rev. E. Stat. Nonlin. Soft Matter Phys. 2007, 75: 41912-1~8
22 M. L. Sanjuán, V. M. Orera, R. I. Merina and J. Blasco. Raman and X-Ray Study of La1-xGaxO3 (0≤x≤1) Perovskite Solid Solutions. J. Phys. Condens.Matter. 1998, 10: 11687~11702
23 G. A. Tompsett, N. M. Sammes, R. J. Philips. Raman spectroscopy of the LaGaO3 phase transition. J. Raman Spectrosc. 1999, 30: 497~500
24 Z. M. Zhang, B. I. Choi, M. I. Flik and A. C. Anderson. Infrared Refractive-Indexes of LaAlO3, LaGaO3, and NdGaO3. J. Opt. Soc. Am. B. 1994, 11: 2252~2257
25 N. Rani, V. B. Gohel and H. C. Gupta. Zone Center Wave numbers of the Orthorhombic LaGaO3 Perovskite. J. Raman Spectrosc. 2000, 31: 877~880
26 N. Rani, V. B. Gohel, H. C. Gupta, M. K. Singh and L. M. Tiwari. A Lattice Dynamical Investigation of the Zone Center Frequencies of the Orthorhombic NdGaO3 Perovskite. J. Phys. Chem. Solids. 2001, 62: 1003~1006
27赵朋,李晓和张仲.光谱实验室.硅酸镓镧晶体的Raman光谱分析. 2005, 22: 1161~1163
28 J. D. Gale and A. L. Rohl. The General Utility Lattice Program (GULP). Mol. Simulat. 2003, 29(5): 291~341
29 J. D. Gale, Z. Kristallogr. GULP: Capabilities and Prospects. 2005, 220(5-6): 552~554
30冯端,师昌绪,刘治国.材料科学导论-融贯的论述.第1版.北京:化学工业出版社, 2002: 463~464
31李树棠.晶体X射线衍射学基础.冶金工业出版社, 2002: 1~100
32方容川.固体光谱学.中国科学技术大学出版社, 2003: 346
33张光寅.晶格振动光谱学.高等教育出版社, 2003: 93~94
34 B. G. Dick, A. W. Overhauser. Theory of the Dielectric Constants of Alkali Halide Crystals. Phys. Rev. 1958, 112: 90~103
35 C. Y. Wang, C. Q. Ru and A. Mioduchowski. Orthotropic Elastic Shell Model for Buckling of Microtubules. Phys. Rev. E. 2006, 74: 52901-1~4
36 M. Horoi, S. Stoica, et al. Shell-model Calculations of Two-Neutrino Double-Beta Decay Rates of Ca-48 with the GXPF1A Interaction. Phys. Rev. C. 2007, 75: 34303-1~4
37 Y. Utsuno, T. Otsuka, et al. Structure of Exotic Nuclei by Large-scale Shell Model Calculations. Aip. Conf. Proc. 2006, 865: 101~106
38 K. J. Ahn, F. Milde, A. Knorr. Phonon-wave-induced ResonanceFluorescence in Semiconductor Nanostructures: Acoustoluminescence in the Terahertz Range. Phys. Rev. Lett. 2007, 98: 27401-1~6
39 A. M. Vora. Computation of Phonon Dynamics of Mg70Zn30 Metallic Glass. J. Mater. Sci. 2007, 42: 935~940
40 A. Koreeda, S. Saikan, et al. Quasielastic Light Scattering by Phonon-Density Fluctuations in Dielectric Crystals and a Novel Macroscopic Analysis for the Scattered Spectra. Ferroelectrics. 2007, 347: 12~16
41 H. J. Monkhorst and J. D. Pack. Special Points for Brillouin-zone Integrations. Phys. Rev. B. 1976, 13: 5188~5192
42 Li Ying, Wu Di, Li Zhi-Ru, et al. Structural and Electronic Properties of Boron-Doped Lithium Clusters: Ab Initio and DFT Studies. J. Comput. Chem. 2007, 28(10): 1677~1684