金团簇的结构、电子特性及其X光吸收谱近边结构的理论研究
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摘要
本文基于密度泛函理论,应用VASP软件对Au_n (n≤28)团簇最稳定构型和电子特性进行了详细计算。计算结果表明Au_n (n≤28)团簇的平均键长、平均配位数和结合能随尺寸的增大呈递增趋势,并且结合能出现奇偶振荡情况。二阶差分能、电子亲和势出现了明显的奇偶交替现象。这些振荡表明了偶数个原子团簇比邻近奇数个原子团簇具有更高的稳定性。从结构上看Au_n团簇从n=14开始由平面结构向立体结构过渡。我们计算得到的结果与已发表文章的理论结果、实验数据符合很好。
在已优化好的结构基础上,基于多重散射、自洽场、实空间格林函数理论,运用FEFF8软件计算了Au_n团簇X光吸收谱的近边结构。研究发现,随着团簇尺寸的改变,吸收谱中吸收边的强度及相邻峰值均发生变化;对于同一团簇,不同位置的原子谱线也不相同,这一差别与吸收原子周围近邻原子的个数有关。可见,X光吸收谱的近边结构为研究团簇的几何结构和原子的配位信息提供了理论依据。本文的研究结果更进一步的丰富了目前对于金团簇理论和实验的研究。
During the past few years, gold clusters have attracted the attention of a wide range of researchers .Apart from the understanding of the finite size effect on the physicochemical properties, the interest on gold clusters is primarily due to various applications, ranging from molecular electronic devices, catalysis, etc.
As is well known, the catalysis of nanoclusters is dependent on environment, cluster size, and the geometrical and electronic structure. But the present experiment condition was not able to determining the microcluster structure, now the information of clusters’structures can only be derived from theoretical calculations.
In this paper, we study the geometry structure and x-ray absorption near edge structure of Aun (n?28) clusters. First, we have carried out the geometry structure optimization for Aun(n?28) clusters. Calculation was performed using the ab initio molecular dynamics simulation method as implemented in VASP. The total energy calculation used projected augmented wave (PAW) method under the spin–polarized generalized gradient wave (GGA). We have chosen the Perdew-Wang(PW91) exchange–correlation functional. The atomic pseudopotentials include the mass-velocity term and Darwin term to account for the scalar-relativistic effects. A simple cubic supercell with theгpoint for the Brillouin zone integration was considered for these calculations. The geometries are considered to be converged when the forces on each ion become 0.05eV/ A? . The cutoff energy for the plane–wave basis set was 280ev.The total-energy convergence was test with respect to the plane-wave basis size and simulation cell size and the total energy was found to be accurate within 0.0001ev. The calculation results are in good agreement with experiment and other theoretical calculations. It shows that the parameters are the best choice for the study of the gold clusters.
The ground states geometries of Aun(n?28)clusters are found to favor planar configurations to 13,which is much larger than in copper and silver clusters, owing to the strong relativistic effects and the strong hybridization of the gold atomic 5d and 6s orbital. From n=14 onwards, Aun clusters show significant change in the geometry arrangement, which favor three-dimensional configurations. Aun(n?28)clusters’average bond and average coordination number increase with the atomic number increasing. The stability analysis has been carried out by calculating the average binding energy, the second order difference in energy and energy gap. The binding energy increases with the increase in size for Aun (n>5) and exhibits an odd-even effect,which has a relatively higher binding energy with clusters having even numbers of atoms than neighboring clusters having odd numbers of atoms . The second difference energy exhibits obvious even-odd oscillation on increasing cluster size. There are no obvious odd-even oscillating behaviors in the energy gap. For the calculated electron affinities of gold clusters also show a remarkable characteristic oscillation effect, which implies that the clusters with odd numbers of atoms have higher EA values than the neighboring clusters with even numbers of atoms. Based on the results obtained for Aun , it is found that Aun having even numbers of atoms are more stable than those with odd numbers of atoms.
Secondly, we calculated the X-ray absorption near edge structure of Aun clusters. Calculations, based on a self full multiple scattering, self-consistent field ,real-space Green’s function approach implemented in the ab initio FEFF8 code .The resulting calculated XANES should be average over all atoms absorption coefficient, because Au atom in each shell has a different absorption coefficient. Our results using FEFF8 for the different Aun clusters show that XANES provide a characteristic signature of clusters shape. The calculated L1、L 2edge spectra of the different size Aun clusters are compared .The peak in the edge was found to increase as function of cluster size .And it exits a more clear peak in the edge and the peak move ahead in the post edge when it presents for 3D structures. We also compared with the L1 edge spectra of atom in the different sites of Aun clusters. The atom spectra of the different sites are difference. The atom spectra exits obvious peak in the edge, when the number its surrounding atom is increased. The results show the Aun XANES provide information on clusters geometry and shape. Finally, we compared the experimental date with of Au metal with the calculated L 3 XANES edge of the Au cluster .The results show that as the cluster size increases, there is an increase in the white line, and closer to the Au metal.
So, through the theory research of the Aun cluster XANES, we could afford some important information for the research of the cluster structure in the experiment.
在已优化好的结构基础上,基于多重散射、自洽场、实空间格林函数理论,运用FEFF8软件计算了Au_n团簇X光吸收谱的近边结构。研究发现,随着团簇尺寸的改变,吸收谱中吸收边的强度及相邻峰值均发生变化;对于同一团簇,不同位置的原子谱线也不相同,这一差别与吸收原子周围近邻原子的个数有关。可见,X光吸收谱的近边结构为研究团簇的几何结构和原子的配位信息提供了理论依据。本文的研究结果更进一步的丰富了目前对于金团簇理论和实验的研究。
During the past few years, gold clusters have attracted the attention of a wide range of researchers .Apart from the understanding of the finite size effect on the physicochemical properties, the interest on gold clusters is primarily due to various applications, ranging from molecular electronic devices, catalysis, etc.
As is well known, the catalysis of nanoclusters is dependent on environment, cluster size, and the geometrical and electronic structure. But the present experiment condition was not able to determining the microcluster structure, now the information of clusters’structures can only be derived from theoretical calculations.
In this paper, we study the geometry structure and x-ray absorption near edge structure of Aun (n?28) clusters. First, we have carried out the geometry structure optimization for Aun(n?28) clusters. Calculation was performed using the ab initio molecular dynamics simulation method as implemented in VASP. The total energy calculation used projected augmented wave (PAW) method under the spin–polarized generalized gradient wave (GGA). We have chosen the Perdew-Wang(PW91) exchange–correlation functional. The atomic pseudopotentials include the mass-velocity term and Darwin term to account for the scalar-relativistic effects. A simple cubic supercell with theгpoint for the Brillouin zone integration was considered for these calculations. The geometries are considered to be converged when the forces on each ion become 0.05eV/ A? . The cutoff energy for the plane–wave basis set was 280ev.The total-energy convergence was test with respect to the plane-wave basis size and simulation cell size and the total energy was found to be accurate within 0.0001ev. The calculation results are in good agreement with experiment and other theoretical calculations. It shows that the parameters are the best choice for the study of the gold clusters.
The ground states geometries of Aun(n?28)clusters are found to favor planar configurations to 13,which is much larger than in copper and silver clusters, owing to the strong relativistic effects and the strong hybridization of the gold atomic 5d and 6s orbital. From n=14 onwards, Aun clusters show significant change in the geometry arrangement, which favor three-dimensional configurations. Aun(n?28)clusters’average bond and average coordination number increase with the atomic number increasing. The stability analysis has been carried out by calculating the average binding energy, the second order difference in energy and energy gap. The binding energy increases with the increase in size for Aun (n>5) and exhibits an odd-even effect,which has a relatively higher binding energy with clusters having even numbers of atoms than neighboring clusters having odd numbers of atoms . The second difference energy exhibits obvious even-odd oscillation on increasing cluster size. There are no obvious odd-even oscillating behaviors in the energy gap. For the calculated electron affinities of gold clusters also show a remarkable characteristic oscillation effect, which implies that the clusters with odd numbers of atoms have higher EA values than the neighboring clusters with even numbers of atoms. Based on the results obtained for Aun , it is found that Aun having even numbers of atoms are more stable than those with odd numbers of atoms.
Secondly, we calculated the X-ray absorption near edge structure of Aun clusters. Calculations, based on a self full multiple scattering, self-consistent field ,real-space Green’s function approach implemented in the ab initio FEFF8 code .The resulting calculated XANES should be average over all atoms absorption coefficient, because Au atom in each shell has a different absorption coefficient. Our results using FEFF8 for the different Aun clusters show that XANES provide a characteristic signature of clusters shape. The calculated L1、L 2edge spectra of the different size Aun clusters are compared .The peak in the edge was found to increase as function of cluster size .And it exits a more clear peak in the edge and the peak move ahead in the post edge when it presents for 3D structures. We also compared with the L1 edge spectra of atom in the different sites of Aun clusters. The atom spectra of the different sites are difference. The atom spectra exits obvious peak in the edge, when the number its surrounding atom is increased. The results show the Aun XANES provide information on clusters geometry and shape. Finally, we compared the experimental date with of Au metal with the calculated L 3 XANES edge of the Au cluster .The results show that as the cluster size increases, there is an increase in the white line, and closer to the Au metal.
So, through the theory research of the Aun cluster XANES, we could afford some important information for the research of the cluster structure in the experiment.
引文
[1]王广厚.簇物理的进展[M].物理学进展.沈阳:辽宁科技出版社1994,14(2):121
[2] BJORNHOLM S. Clusters, Condensed Matter in Embryonic Form [J], Contemporary Physics. 1990, 31,5: 309-324.
[3]冯端,金国钧.聚态物理学新论[M].上海:上海科学技术出版社, 1992, 286.
[4] CASTLEMAN A W, BOWEN KH, Jr. Clusters: Structure, Energetics, and Dynamics of Intermediate States of Matter [J]. Phys. Chem. B. 1996, 100,31:12911-12944.
[5] OCHS S A, COTE R E, KUSCH P. On the Radiofrequency Spectrum of the Components of a Sodium Chloride Beam. The Dimerization of the Alkali Halides [J]. J. Chem. Phys.B.1953, 21: 459.
[6] BECKER E W and BIER K. Strahlen aus kondensierten Atomen und Molekln im Hochvakuum[J].Z.Phys.1956,146:333-336
[7] BENTLEY P G .Chemical Engineering Polymers of Carbon Dioxide[J].Nature,1961,190:432
[8] HAYAT M A ,Collodial Gold :Principle Methods and Applications, Academic press, an Diego[M].1991
[9] LI SHUN ANFANG, LI HAISHENG, LIU JING [J]. Phys. Rev.B2007, 76, 045410
[10] MICHAELIAN K ,RENDON AND GARZON I L .Structure and energetics of Ni, Ag, and Au nanoclusters [J]. Phys. Rev.B. 1999, 60:2000-2010
[11]廖沐真,吴国是,《量子化学从头计算方法[M].京:清华大学出版社1984
[12] HARTREE D. calculations of Structure[M].New York, Wiley 1957
[13]【美】J.A.波普尔,D.L.贝弗里奇,江元生译《分子轨道近似方法理论》[M].科学出版社,1978
[14] KOCH WOLFRAM, HOLTHAUSE MAX C.A Chemist’s Guide to Density Functional Theory[M].Second Edition,2001,Wiley-Vch Verlag Gmbh
[15] D JACK, GRAYBEAL. Molecular Spectroscopy [M]. New York: McGraw-Hill Book Company, 1988.
[16] HOHENBERY P,KOHN W. Inhomogeneous Electron Gas ? [J] .Phys. Rev B ,1964,136:864
[17] KOHN W, SHAM L J, Self–Consistent Equations Including Exchange and Correlation Effects ? [J] .Phys. Rev. A, 1965, 140:11335
[18] GUNNARSON O, LUNDQVIST B I, Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism ?[J]. Phys. Rev. B. 1976, 13:4274
[19] MUSKAT J, WANDER A, HARRISON N M. On the prediction of band gaps from hybrid functional theory [J] .Chem. Phys. Lett. 2001, 342:397
[20] KOHN W,BECKE A D,PARR Q G. Density Functional Theory Electronic Structure [J] .J. Phys. Chem. 1996,100:12974-12980
[21] BECKE A D, A new mixing of Hartree-Fock and local density–functional theories [J] .J. Chem. Phys. 1993, 98: 1372-1377
[22] BECKE A D. Density-functional thermochemistry.Ⅲ.The role of exact exchange [J]. J. Chem. Phys. 1993, 98: 5648-5652
[23] RAJAGOPAL.A.K and CALLAWAY.J .Inhomogeneous Electron Gas [J]. Phys. Rev. B. 1973 ,7, 5:1912-1919
[24] YANAI T et al. A highly efficient algorithm for electron repulsion integrals over relativistic four–component Gaussian-type spinors [J]. J. Chem. Phys. 2002, 116: 10122
[25] BATHE.H.A and SALPETER. E .E .Quantum Mechanics of one-and two-Electron Atoms[M].Springer,Berlin,1957
[26] BAERAENDS .E.J. Relativistic calculation of nuclear magnetic shielding tensor using the regular approximation to the normalized elimination of the small component.Ⅱ.Consideration of perturbations in the metric operator[J].J.Chem.Phys. 1993,99: 4597-4610
[27] NAKAJIMA T, HIRAO K. A new relativistic theory: a relativisticscheme by eliminating small components (RESC) [J] .Chem. Phys. Lett. 1999, 302: 383
[28] NAKAJIMA T, HIRAO K. The higher-order Douglas-kroll transformation [J] J. Chem. Phys. 2000, 113:7786
[29]徐光宪,黎乐民《量子化学基本原理和从头算计算法》[M]中册科学出版社,北京,1981
[30] BONIFACIC, HUZINAGA.Model potential xαmethod for the electronic structure calculations [J].International Journal of Quantum Chemistry. 1980, 18 ,1:25-29
[31] H?kkinen .H and Landman .Gold clusters(AuN ,2 ? N ?10)and their anions.[J].Phys.Rev.B.2000,62:2287-2290
[32] Sankaran M and Viswanathan.A DFT study of the electronic property of gold nanoclusters (Aux, x=1-12atoms)[J].Bulletin of the Catalysis Society of India 2006 5:26-32
[33] Wang jinlan and Wang Guanghou. Density–functional study of Aun, n=2-20) clusters: Lowest-energy structures and electronic prope -rties [J] Phys.Rev.B. 2002,66:035418-1-135418-6
[34] MAYAR .R.J AND MUJICA .V. Density-functional study of magnetism in bare Au nanoclusters: Evidence of permanent size–dependent spin polarization without geometry relaxiation[J]. 2007, Phys.Rev.B. 75:144421-1-144421-7
[35] FA WEI and LUO CHUANFU.Bulk fragment and tubelike of Aun,(n=2-26) [J].2005,Phys.Rev.B. 72:205428 -1-205428-4
[36] MUSTAFA B?YUKATA. Molecular-dynamics study of possible packing sequence of medium size gold clusters : Au2-Au43 [J]. 2006, Physica E.33:182-190
[37] Bulusu Satya and Zeng X.C. Structures and relatives stability of neutral gold clusters: Aun,(n=15-19)[J].J.Chems.Phys. 2006, 125: 154303 -1-154303-5
[38] PERDEW.J.P. Atoms,molecular, solids,and surfaces : Applications of the generalized gradient approximation for exchange and correlati- on[J]. Phys.Rev .B. 1992, 46, 11: 6671 -6687
[39] KRESSE G and HAFNER J .Ab initio molecular dynamics for liquid metals [J]. Phys .Rev. B 1993,47,1: 558 -561
[40] WEAST R C. CRC Handbook of Chemistry and Physics [M]. 49th ,1969
[41] Kulshreshtha S.K structure and electronic properties of Aun (n=2-10) clusters and their interactions with single S atoms :Ab initio molecular dynamic simulationsPRB,73,155427-1-155427-9
[42] H?kkinen .H and Moseler. M.Bonding in Cu, Ag and Au clusters: Relativistic Effects, Trends, and surprises [J] .Phys.Rev.Lett. 2002,89, 033401-1-033401-4
[43] Li J, Li X, Zhai H J and Wang L S. Aun : A Tetrahedral cluster [J] .Science, 2003, 299:864.
[44] TALOR K.J and PTTTIE-HALL.Ultravlolet photoelectron spectra of coinage metal clusters [J].J.Chem.Phys.1992,96,3319-3329
[45]寇元,殷元骐.近边X光吸收谱(XANES)的发展[M] .化学通报,1989,6:23-27
[46] ST?HR JOACHIM.NEXAFS Spectroscopy [M] springer-verlog 1991
[47] A VICTOREEN. The Absorption of Incident Quanta by the Atoms as Defined by the Mass Photoelectric Absorption Coefficient and the Mass Scattering Coefficient [J]. Journal of Applied Physics. 1948, 19:855-860
[48] YUAN FENG PING .The strain effect on CMR thin films[M].民国九十六年
[49]寇元殷元骐.近边X光吸收谱(XANES)的发展[j].化学通报,1989,6:24-28
[50] QI BOYUN ,PEREZ I, L2 and L3 measurement of transition -metal 5d orbital occupancy spin-orbit effects and chemical bonding [J] .PRB, 1987,36:2972-2975
[51] LEEYOUN-SEOUNG,JEOE YONGSEOG. Charge Redistribution and Electronic Behavior in Pd-Au Alloys [J]. Journal of Korean Physical Society 2000, 37:451-455
[2] BJORNHOLM S. Clusters, Condensed Matter in Embryonic Form [J], Contemporary Physics. 1990, 31,5: 309-324.
[3]冯端,金国钧.聚态物理学新论[M].上海:上海科学技术出版社, 1992, 286.
[4] CASTLEMAN A W, BOWEN KH, Jr. Clusters: Structure, Energetics, and Dynamics of Intermediate States of Matter [J]. Phys. Chem. B. 1996, 100,31:12911-12944.
[5] OCHS S A, COTE R E, KUSCH P. On the Radiofrequency Spectrum of the Components of a Sodium Chloride Beam. The Dimerization of the Alkali Halides [J]. J. Chem. Phys.B.1953, 21: 459.
[6] BECKER E W and BIER K. Strahlen aus kondensierten Atomen und Molekln im Hochvakuum[J].Z.Phys.1956,146:333-336
[7] BENTLEY P G .Chemical Engineering Polymers of Carbon Dioxide[J].Nature,1961,190:432
[8] HAYAT M A ,Collodial Gold :Principle Methods and Applications, Academic press, an Diego[M].1991
[9] LI SHUN ANFANG, LI HAISHENG, LIU JING [J]. Phys. Rev.B2007, 76, 045410
[10] MICHAELIAN K ,RENDON AND GARZON I L .Structure and energetics of Ni, Ag, and Au nanoclusters [J]. Phys. Rev.B. 1999, 60:2000-2010
[11]廖沐真,吴国是,《量子化学从头计算方法[M].京:清华大学出版社1984
[12] HARTREE D. calculations of Structure[M].New York, Wiley 1957
[13]【美】J.A.波普尔,D.L.贝弗里奇,江元生译《分子轨道近似方法理论》[M].科学出版社,1978
[14] KOCH WOLFRAM, HOLTHAUSE MAX C.A Chemist’s Guide to Density Functional Theory[M].Second Edition,2001,Wiley-Vch Verlag Gmbh
[15] D JACK, GRAYBEAL. Molecular Spectroscopy [M]. New York: McGraw-Hill Book Company, 1988.
[16] HOHENBERY P,KOHN W. Inhomogeneous Electron Gas ? [J] .Phys. Rev B ,1964,136:864
[17] KOHN W, SHAM L J, Self–Consistent Equations Including Exchange and Correlation Effects ? [J] .Phys. Rev. A, 1965, 140:11335
[18] GUNNARSON O, LUNDQVIST B I, Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism ?[J]. Phys. Rev. B. 1976, 13:4274
[19] MUSKAT J, WANDER A, HARRISON N M. On the prediction of band gaps from hybrid functional theory [J] .Chem. Phys. Lett. 2001, 342:397
[20] KOHN W,BECKE A D,PARR Q G. Density Functional Theory Electronic Structure [J] .J. Phys. Chem. 1996,100:12974-12980
[21] BECKE A D, A new mixing of Hartree-Fock and local density–functional theories [J] .J. Chem. Phys. 1993, 98: 1372-1377
[22] BECKE A D. Density-functional thermochemistry.Ⅲ.The role of exact exchange [J]. J. Chem. Phys. 1993, 98: 5648-5652
[23] RAJAGOPAL.A.K and CALLAWAY.J .Inhomogeneous Electron Gas [J]. Phys. Rev. B. 1973 ,7, 5:1912-1919
[24] YANAI T et al. A highly efficient algorithm for electron repulsion integrals over relativistic four–component Gaussian-type spinors [J]. J. Chem. Phys. 2002, 116: 10122
[25] BATHE.H.A and SALPETER. E .E .Quantum Mechanics of one-and two-Electron Atoms[M].Springer,Berlin,1957
[26] BAERAENDS .E.J. Relativistic calculation of nuclear magnetic shielding tensor using the regular approximation to the normalized elimination of the small component.Ⅱ.Consideration of perturbations in the metric operator[J].J.Chem.Phys. 1993,99: 4597-4610
[27] NAKAJIMA T, HIRAO K. A new relativistic theory: a relativisticscheme by eliminating small components (RESC) [J] .Chem. Phys. Lett. 1999, 302: 383
[28] NAKAJIMA T, HIRAO K. The higher-order Douglas-kroll transformation [J] J. Chem. Phys. 2000, 113:7786
[29]徐光宪,黎乐民《量子化学基本原理和从头算计算法》[M]中册科学出版社,北京,1981
[30] BONIFACIC, HUZINAGA.Model potential xαmethod for the electronic structure calculations [J].International Journal of Quantum Chemistry. 1980, 18 ,1:25-29
[31] H?kkinen .H and Landman .Gold clusters(AuN ,2 ? N ?10)and their anions.[J].Phys.Rev.B.2000,62:2287-2290
[32] Sankaran M and Viswanathan.A DFT study of the electronic property of gold nanoclusters (Aux, x=1-12atoms)[J].Bulletin of the Catalysis Society of India 2006 5:26-32
[33] Wang jinlan and Wang Guanghou. Density–functional study of Aun, n=2-20) clusters: Lowest-energy structures and electronic prope -rties [J] Phys.Rev.B. 2002,66:035418-1-135418-6
[34] MAYAR .R.J AND MUJICA .V. Density-functional study of magnetism in bare Au nanoclusters: Evidence of permanent size–dependent spin polarization without geometry relaxiation[J]. 2007, Phys.Rev.B. 75:144421-1-144421-7
[35] FA WEI and LUO CHUANFU.Bulk fragment and tubelike of Aun,(n=2-26) [J].2005,Phys.Rev.B. 72:205428 -1-205428-4
[36] MUSTAFA B?YUKATA. Molecular-dynamics study of possible packing sequence of medium size gold clusters : Au2-Au43 [J]. 2006, Physica E.33:182-190
[37] Bulusu Satya and Zeng X.C. Structures and relatives stability of neutral gold clusters: Aun,(n=15-19)[J].J.Chems.Phys. 2006, 125: 154303 -1-154303-5
[38] PERDEW.J.P. Atoms,molecular, solids,and surfaces : Applications of the generalized gradient approximation for exchange and correlati- on[J]. Phys.Rev .B. 1992, 46, 11: 6671 -6687
[39] KRESSE G and HAFNER J .Ab initio molecular dynamics for liquid metals [J]. Phys .Rev. B 1993,47,1: 558 -561
[40] WEAST R C. CRC Handbook of Chemistry and Physics [M]. 49th ,1969
[41] Kulshreshtha S.K structure and electronic properties of Aun (n=2-10) clusters and their interactions with single S atoms :Ab initio molecular dynamic simulationsPRB,73,155427-1-155427-9
[42] H?kkinen .H and Moseler. M.Bonding in Cu, Ag and Au clusters: Relativistic Effects, Trends, and surprises [J] .Phys.Rev.Lett. 2002,89, 033401-1-033401-4
[43] Li J, Li X, Zhai H J and Wang L S. Aun : A Tetrahedral cluster [J] .Science, 2003, 299:864.
[44] TALOR K.J and PTTTIE-HALL.Ultravlolet photoelectron spectra of coinage metal clusters [J].J.Chem.Phys.1992,96,3319-3329
[45]寇元,殷元骐.近边X光吸收谱(XANES)的发展[M] .化学通报,1989,6:23-27
[46] ST?HR JOACHIM.NEXAFS Spectroscopy [M] springer-verlog 1991
[47] A VICTOREEN. The Absorption of Incident Quanta by the Atoms as Defined by the Mass Photoelectric Absorption Coefficient and the Mass Scattering Coefficient [J]. Journal of Applied Physics. 1948, 19:855-860
[48] YUAN FENG PING .The strain effect on CMR thin films[M].民国九十六年
[49]寇元殷元骐.近边X光吸收谱(XANES)的发展[j].化学通报,1989,6:24-28
[50] QI BOYUN ,PEREZ I, L2 and L3 measurement of transition -metal 5d orbital occupancy spin-orbit effects and chemical bonding [J] .PRB, 1987,36:2972-2975
[51] LEEYOUN-SEOUNG,JEOE YONGSEOG. Charge Redistribution and Electronic Behavior in Pd-Au Alloys [J]. Journal of Korean Physical Society 2000, 37:451-455