过渡金属及其合金团簇的稳定性、电子结构和磁性研究
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摘要
纳米团簇一直是材料科学研究领域的热门课题,特别是过渡金属团簇。因它们关联于与磁相关的特征物理长度恰好处于纳米量级,从而将呈现出与块体完全不一样的反常磁学性质。虽然过渡周期中只有3d周期内Fe、Co、Ni的块体材料表现铁磁性,但已有的研究表明大部分过渡周期元素团簇都表现出较强的磁性特征。对它们的深入研究有助于人们理解团簇的各种奇异性质,是开发高密度存储,微电子,光电子通讯,和高效催化等高新技术材料的基础。本文研究了过渡金属团簇的结构演化、电子结构和磁学性质,主要集中在:
1.第III主族Sc,Y元素团簇的结构演化和磁性
人们利用Stern-Gerlach实验测量了5-20原子的Sc,Y,La团簇的磁性演化行为,而此前还没有相关的系统理论研究。本文中,我们采用密度泛函理论下(DFT)的广义梯度近似(GGA)方法,非限制对称性的优化了Sc_n(n≤16)和Sc_n(n≤17)团簇的可能结构构型,得到了Sc,Y团簇的结构演化规律、电子结构、和磁性特征。研究结果表明,Sc,Y团簇与La团簇一样倾向于二十面体结构的密堆积生长模式,Sc13和Y13团簇都为Ih高对称性的二十面体结构,其中n = 7, 13的团簇尺寸相比其近邻更加稳定,可以认为是该主族元素团簇的幻数尺寸。计算结果很好的重现了Sc、Y团簇在n = 6, 8, 13处的高磁矩和其余尺寸的弱磁性的实验测量,结果显示这些团簇的总磁矩随尺寸增大近似而呈现出震荡行为,其中Sc13和Y13团簇都具有19μB的高磁矩。虽然我们的计算高估了部分尺寸的实验测定值,但定性的演化趋势与实验吻合的较好。研究还发现n = 7的尺寸是Sc、Y团簇从铁磁性序到反铁磁序的转变尺寸,但n = 8, 13, 14团簇的基态还是表现出铁磁序排布。分析表明,Sc和Y团簇具有的相似结构构型是造成它们相似磁性演化的主要原因。此外,计算得到的电离势与已有的实验符合的较好,这说明我们所确定的团簇基态结构是正确的,并由此得到的相关团簇性质也是可靠合理的。
2.中性和获电Bin(n = 2 -24)团簇的研究
采用DFT下的标量相对论有效核势(RECP)和GGA近似,研究了中性和获电Bi_n(n = 2 -24)团簇的结构演化、电子结构、和磁性。结果显示,中性和获电Bi团簇的结构演化与同族其它元素团簇相似,其中Bi_4和Bi_8团簇分别具有四面体和楔状构型,大尺寸Bi团簇的结构则是由Bi_4,Bi_6,和Bi_8这些稳定单元组装而成,但随着尺寸的增大团簇趋向于形成不定型结构。团簇的二阶差分能量曲线呈现出明显的奇偶震荡行为,说明偶数(奇数)原子尺寸的中性(阳离子)Bi团簇要相对稳定。计算得到奇数原子的中性Bi团簇具有1μB的磁矩,而偶数原子团簇不显磁性,理论与实验之间的磁性差异可能是由于计算中忽略轨道磁矩的原因。研究表明,n < 7的阳离子Bi_n~+团簇将碎裂为一个中性Bi原子和一个Bi_(n-1)~+子团簇,而n > 7时团簇则碎裂到Bi_4和Bi_7~+的道,得到的这些的碎裂行为与实验吻合的很好,这些现象再次证实了Bi_4和Bi_7~+团簇特别稳定。团簇原子的键级分析和HOMO-LUMO能隙大小暗示我们所研究尺寸范围内的小Bi团簇将呈现出半导体性质而不为金属性。
3. V_(12)TM团簇的磁性第一性原理研究
采用DFT下的GGA方法,对V_(13)团簇及V_(12)TM掺杂团簇(TM: Sc, Ti, Cr, Mn,Fe, Co, Ni, Y, Zr, Nb, Mo, Tc, Ru)的电子结构和磁性进行研究。通过对团簇的基态几何构型优化计算得到了团簇束缚能,电子结构,以及磁矩的大小,系统的分析了V_(13)及V_(12)TM团簇磁矩的形成机理以及电子结构与磁性的变化关系。发现掺杂团簇V_(12)Fe、V_(12)Ru为具有大束缚能和大能隙间隔的闭壳电子结构,V_(12)Y团簇具有11μB的大磁矩,而其它的掺杂团簇则表现弱磁性。
4. Bi-Mn二元合金团簇的结构与磁性
利用DFT下的GGA方法,研究了Bi_nMn_m(n≤13,m≤6)团簇的结构演化,电子结构,和磁性。结果表明,Mn掺杂原子保持近似不变的4μB/atom的局域磁矩,其中团簇结构、组份浓度、和局域环境等因素对它的影响非常小,但Mn_m成份之间的磁序耦合却与这些因素有敏感的依赖关系。当团簇中Bi与Mn的组份比例接近2(n : m = 2 : 1)时掺杂Mn_m之间主要为铁磁序耦合,而Bin成份主要对团簇磁性提供了很微弱的反铁磁性微扰贡献。Mn-3d和4p与Bi-6p之间的杂化作用降低了1μ_B的Mn原子磁矩而在Bi原子上诱导出-0.1μ_B的磁矩值,计算得到的不同组份系列的磁性演化规律整体上与近期的实验测量符合较好。结构分析表明,Bi_nMn m团簇结构呈现出分块效应,其中Mn_m掺杂成份聚集形成内部的五角双锥核心构型,而Bin成份则围绕在核心成份的周围。低浓度掺杂的团簇结构为不定型构型,而高浓度掺杂的大尺寸团簇则趋向于形成有部分缺陷的多二十面体结构交错的结构构型。束缚能和二阶能量差分的计算表明,单元子Mn掺杂的Bi_nMn团簇中n = 4, 6, 10, 12的尺寸要比其紧邻更加稳定。随着掺杂Mn浓度的增加,Bi_nMn_m团簇的HOMO-LUMO能隙逐渐降低,这说明团簇的金属性在增强。
The field of transition metal (TM) nanostructures has become one of the most impor-tant issues in nanotechnology due to possible important applications in electronic devices,magnetic recording, effective catalysis, optical communication and so on. Due to the largesurface to volume ratio, small TM clusters show a different magnetic behavior from that ofthe corresponding bulk. Although the ferromagnetism bulk is only find in Fe, Co, Ni ele-mental material, previous studies indicate that most TM clusters do exhibit high magneticmoments, especially for 4d and 5d elemental clusters. The geometrical evolution, electronicstructure, and magnetism of small TM clusters are investigated in this thesis, and we mainlyconcern the following contents:
1. Theoretical study of geometrical evolution and magnetism of group-III clusters.
More recently, Knickelbein has measured the magnetic moments of Sc_n, Y_n, and La_n(n = 5 - 20) clusters in the Stern- Gerlach molecular-beam deffection experiment, whereasfor scandium and yttrium clusters, until now, there are no systematical theoretical calcula-tions on their structures, stabilities, and magnetic properties. With this in mind, we performan extensive study on the evolution of the structural and electronic properties as well asmagnetism for Scn and Yn clusters up to n = 17 by using a fully self-consistent density-functional-theory (DFT) based method. The calculated results show that the structural evo-lution of yttrium and scandium clusters favors a compact and icosahedral structural growthpattern, and Sc_(13) and Y_(13) clusters adopt the Ih icosahedron structure. The group-III elemen-tal clusters with n = 7, 13 atoms have higher stability than their neighboring sizes and canbe regarded as magic number. The theoretical magnetic behavior follows the experimentaltrend qualitatively well as a function of the cluster size, including the experimentally ob-served minima and maxima (n = 6, 8, 13), and we find that Sc13 and Y13 clusters have agiant moment of 19μ_B. Although our calculations overestimate these some values, the size-dependent trend is generally consistent with the experimental trend. Additionally, it is ob-served that the clusters undergo a change from ferromagnetic(FM) ordering for the smallestsizes n < 7 to antiferromagnetic(AF) ordering for the intermediate sizes n = 7-12, 15-16.The comparison between the Y_n clusters and Sc_n clusters indicates that the displayed samemagnetic features are the consequence of a similar structural motif for these two series. Ourcalculated ionization potentials (IPs) trend is qualitatively in agreement with the experimen-tal one, indicating that the structures would be close with reality and our obtained physical properties are appropriate.
2. Density-functional study of small neutral and cationic bismuth clusters Bin andBi_n~+ (n = 2 - 24).
DFT with scalar-relativistic pseudopotential(RECP) and a generalized gradient correc-tion(GGA) is used to calculate the neutral and cationic Bin clusters (n = 2-24), with the aimto elucidate their structural evolution, relative stability, and magnetic property. The structuresof neutral Bi clusters are found to be similar to that of other group-V elemental clusters, withthe extensively studied sizes of n = 4 and 8 having a tetrahedron and wedgelike structure,respectively. Generally, larger Bi clusters consist of a combination of several stable units ofBi4, Bi6, and Bi8, and they have a tendency to form an amorphous structure with the increaseof cluster sizes. The curves of second order energy difference exhibit strong odd-even alter-nations for both neutral and cationic Bi clusters, indicating that even-atom (odd-atom) sizesare relatively stable in neutral clusters (cationic clusters). The calculated magnetic momentsare 1μ_B for odd-atom clusters and zero for even-atom clusters. We propose that the differ-ence in magnetism between experiment and theory can be greatly improved by consideringthe orbital contribution. The calculated fragmentation behavior agrees well with the experi-ment, and for each cationic cluster the dissociation into Bi4 or Bi_7~+ subclusters confirms thespecial stability of Bi_4 and Bi_7~+ . Moreover, the bond orders and the gaps between the high-est occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO-LUMOgap) show that small Bi clusters would prefer semiconductor characters to metallicity.
3. First-principle investigation of the electronic structure and magnetism in V_(12)TMclusters.
The DFT with the GGA method is adopted to study the electronic structures and mag-netic properties of V_(13) cluster and doped V_(12)TM clusters (TM: Sc, Ti, Cr, Mn, Fe, Co, Ni,Y, Zr, Nb, Mo, Tc, Ru, Rh). The binding energy, electronic structure and magnetism of theclusters have been obtained. Further more, the information of cluster magnetism and therelationship between magnetic moments and electronic structures of clusters were analyzed.The results show that V_(12)Fe and V_(12)Ru clusters are the most stable structures which havethe closed-shell system with larger binding energies and larger HOMO-LUMO gaps. V_(12)Ycluster has a giant moment of 11μ_B. The ground states of most clusters are shown to bemagnetic, but their magnetic moments are not striking.
4. Geometrical evolution, electronic structures, and magnetic properties of Bi-Mn bi- nary clusters.
The geometrical evolution, electronic structures, and magnetic properties of small bi-nary clusters Bi_nMn_m (n≤13, m≤6) are investigated using DFT with the view ofexplaining the experimentally observed magnetic moments in these systems. The resultsdemonstrate that the magnetic moments of the dopant Mn atoms exhibit a weak dependenceon the structure, composition, and environment, holding a general constant of 4μB/atomapproximately, whereas the magnetic couplings among these Mn atoms are strongly depen-dent. We propose that the preferred ferromagnetic couplings in the dopant Mn_m componentsresult in pronounced magnetic moments represented by certain combinations in which theBi to Mn ratio is close to 2. Moreover, a faint antiferromagnetic perturbation is providedby the Bin units. The hybridization among Mn 3d, 4s, and Bi 6p induces -0.1μB on Biatoms and reduces the Mn atomic moments by 1μ_B. On the whole, the calculated magnetictrends of the different composition series qualitatively fit well with experimental measure-ments. The lowest-energy structures of the clusters are segregated cases in which the dopantMn_m components assemble together, forming a pentagonal bipyramid shape and surroundedby irregular Bin components. Generally, an amorphous configuration is observed for low-Mn-concentration clusters, but the evolution of a defective polyicosahedron pattern with aMn core shell is favored for high-Mn-concentration clusters and this tendency will keep themost stable geometrical structure for larger sizes. By analyzing the binding energies andthe second-order energy differences, we find that the monatomic doping BinMn series con-taining n = 4, 6, 10, and 12 is more stable than its neighboring sizes. Furthermore, theHOMO-LUMO gaps decrease as a function of Mn concentration in the clusters, indicatingan enhancement of metallicity.
1.第III主族Sc,Y元素团簇的结构演化和磁性
人们利用Stern-Gerlach实验测量了5-20原子的Sc,Y,La团簇的磁性演化行为,而此前还没有相关的系统理论研究。本文中,我们采用密度泛函理论下(DFT)的广义梯度近似(GGA)方法,非限制对称性的优化了Sc_n(n≤16)和Sc_n(n≤17)团簇的可能结构构型,得到了Sc,Y团簇的结构演化规律、电子结构、和磁性特征。研究结果表明,Sc,Y团簇与La团簇一样倾向于二十面体结构的密堆积生长模式,Sc13和Y13团簇都为Ih高对称性的二十面体结构,其中n = 7, 13的团簇尺寸相比其近邻更加稳定,可以认为是该主族元素团簇的幻数尺寸。计算结果很好的重现了Sc、Y团簇在n = 6, 8, 13处的高磁矩和其余尺寸的弱磁性的实验测量,结果显示这些团簇的总磁矩随尺寸增大近似而呈现出震荡行为,其中Sc13和Y13团簇都具有19μB的高磁矩。虽然我们的计算高估了部分尺寸的实验测定值,但定性的演化趋势与实验吻合的较好。研究还发现n = 7的尺寸是Sc、Y团簇从铁磁性序到反铁磁序的转变尺寸,但n = 8, 13, 14团簇的基态还是表现出铁磁序排布。分析表明,Sc和Y团簇具有的相似结构构型是造成它们相似磁性演化的主要原因。此外,计算得到的电离势与已有的实验符合的较好,这说明我们所确定的团簇基态结构是正确的,并由此得到的相关团簇性质也是可靠合理的。
2.中性和获电Bin(n = 2 -24)团簇的研究
采用DFT下的标量相对论有效核势(RECP)和GGA近似,研究了中性和获电Bi_n(n = 2 -24)团簇的结构演化、电子结构、和磁性。结果显示,中性和获电Bi团簇的结构演化与同族其它元素团簇相似,其中Bi_4和Bi_8团簇分别具有四面体和楔状构型,大尺寸Bi团簇的结构则是由Bi_4,Bi_6,和Bi_8这些稳定单元组装而成,但随着尺寸的增大团簇趋向于形成不定型结构。团簇的二阶差分能量曲线呈现出明显的奇偶震荡行为,说明偶数(奇数)原子尺寸的中性(阳离子)Bi团簇要相对稳定。计算得到奇数原子的中性Bi团簇具有1μB的磁矩,而偶数原子团簇不显磁性,理论与实验之间的磁性差异可能是由于计算中忽略轨道磁矩的原因。研究表明,n < 7的阳离子Bi_n~+团簇将碎裂为一个中性Bi原子和一个Bi_(n-1)~+子团簇,而n > 7时团簇则碎裂到Bi_4和Bi_7~+的道,得到的这些的碎裂行为与实验吻合的很好,这些现象再次证实了Bi_4和Bi_7~+团簇特别稳定。团簇原子的键级分析和HOMO-LUMO能隙大小暗示我们所研究尺寸范围内的小Bi团簇将呈现出半导体性质而不为金属性。
3. V_(12)TM团簇的磁性第一性原理研究
采用DFT下的GGA方法,对V_(13)团簇及V_(12)TM掺杂团簇(TM: Sc, Ti, Cr, Mn,Fe, Co, Ni, Y, Zr, Nb, Mo, Tc, Ru)的电子结构和磁性进行研究。通过对团簇的基态几何构型优化计算得到了团簇束缚能,电子结构,以及磁矩的大小,系统的分析了V_(13)及V_(12)TM团簇磁矩的形成机理以及电子结构与磁性的变化关系。发现掺杂团簇V_(12)Fe、V_(12)Ru为具有大束缚能和大能隙间隔的闭壳电子结构,V_(12)Y团簇具有11μB的大磁矩,而其它的掺杂团簇则表现弱磁性。
4. Bi-Mn二元合金团簇的结构与磁性
利用DFT下的GGA方法,研究了Bi_nMn_m(n≤13,m≤6)团簇的结构演化,电子结构,和磁性。结果表明,Mn掺杂原子保持近似不变的4μB/atom的局域磁矩,其中团簇结构、组份浓度、和局域环境等因素对它的影响非常小,但Mn_m成份之间的磁序耦合却与这些因素有敏感的依赖关系。当团簇中Bi与Mn的组份比例接近2(n : m = 2 : 1)时掺杂Mn_m之间主要为铁磁序耦合,而Bin成份主要对团簇磁性提供了很微弱的反铁磁性微扰贡献。Mn-3d和4p与Bi-6p之间的杂化作用降低了1μ_B的Mn原子磁矩而在Bi原子上诱导出-0.1μ_B的磁矩值,计算得到的不同组份系列的磁性演化规律整体上与近期的实验测量符合较好。结构分析表明,Bi_nMn m团簇结构呈现出分块效应,其中Mn_m掺杂成份聚集形成内部的五角双锥核心构型,而Bin成份则围绕在核心成份的周围。低浓度掺杂的团簇结构为不定型构型,而高浓度掺杂的大尺寸团簇则趋向于形成有部分缺陷的多二十面体结构交错的结构构型。束缚能和二阶能量差分的计算表明,单元子Mn掺杂的Bi_nMn团簇中n = 4, 6, 10, 12的尺寸要比其紧邻更加稳定。随着掺杂Mn浓度的增加,Bi_nMn_m团簇的HOMO-LUMO能隙逐渐降低,这说明团簇的金属性在增强。
The field of transition metal (TM) nanostructures has become one of the most impor-tant issues in nanotechnology due to possible important applications in electronic devices,magnetic recording, effective catalysis, optical communication and so on. Due to the largesurface to volume ratio, small TM clusters show a different magnetic behavior from that ofthe corresponding bulk. Although the ferromagnetism bulk is only find in Fe, Co, Ni ele-mental material, previous studies indicate that most TM clusters do exhibit high magneticmoments, especially for 4d and 5d elemental clusters. The geometrical evolution, electronicstructure, and magnetism of small TM clusters are investigated in this thesis, and we mainlyconcern the following contents:
1. Theoretical study of geometrical evolution and magnetism of group-III clusters.
More recently, Knickelbein has measured the magnetic moments of Sc_n, Y_n, and La_n(n = 5 - 20) clusters in the Stern- Gerlach molecular-beam deffection experiment, whereasfor scandium and yttrium clusters, until now, there are no systematical theoretical calcula-tions on their structures, stabilities, and magnetic properties. With this in mind, we performan extensive study on the evolution of the structural and electronic properties as well asmagnetism for Scn and Yn clusters up to n = 17 by using a fully self-consistent density-functional-theory (DFT) based method. The calculated results show that the structural evo-lution of yttrium and scandium clusters favors a compact and icosahedral structural growthpattern, and Sc_(13) and Y_(13) clusters adopt the Ih icosahedron structure. The group-III elemen-tal clusters with n = 7, 13 atoms have higher stability than their neighboring sizes and canbe regarded as magic number. The theoretical magnetic behavior follows the experimentaltrend qualitatively well as a function of the cluster size, including the experimentally ob-served minima and maxima (n = 6, 8, 13), and we find that Sc13 and Y13 clusters have agiant moment of 19μ_B. Although our calculations overestimate these some values, the size-dependent trend is generally consistent with the experimental trend. Additionally, it is ob-served that the clusters undergo a change from ferromagnetic(FM) ordering for the smallestsizes n < 7 to antiferromagnetic(AF) ordering for the intermediate sizes n = 7-12, 15-16.The comparison between the Y_n clusters and Sc_n clusters indicates that the displayed samemagnetic features are the consequence of a similar structural motif for these two series. Ourcalculated ionization potentials (IPs) trend is qualitatively in agreement with the experimen-tal one, indicating that the structures would be close with reality and our obtained physical properties are appropriate.
2. Density-functional study of small neutral and cationic bismuth clusters Bin andBi_n~+ (n = 2 - 24).
DFT with scalar-relativistic pseudopotential(RECP) and a generalized gradient correc-tion(GGA) is used to calculate the neutral and cationic Bin clusters (n = 2-24), with the aimto elucidate their structural evolution, relative stability, and magnetic property. The structuresof neutral Bi clusters are found to be similar to that of other group-V elemental clusters, withthe extensively studied sizes of n = 4 and 8 having a tetrahedron and wedgelike structure,respectively. Generally, larger Bi clusters consist of a combination of several stable units ofBi4, Bi6, and Bi8, and they have a tendency to form an amorphous structure with the increaseof cluster sizes. The curves of second order energy difference exhibit strong odd-even alter-nations for both neutral and cationic Bi clusters, indicating that even-atom (odd-atom) sizesare relatively stable in neutral clusters (cationic clusters). The calculated magnetic momentsare 1μ_B for odd-atom clusters and zero for even-atom clusters. We propose that the differ-ence in magnetism between experiment and theory can be greatly improved by consideringthe orbital contribution. The calculated fragmentation behavior agrees well with the experi-ment, and for each cationic cluster the dissociation into Bi4 or Bi_7~+ subclusters confirms thespecial stability of Bi_4 and Bi_7~+ . Moreover, the bond orders and the gaps between the high-est occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO-LUMOgap) show that small Bi clusters would prefer semiconductor characters to metallicity.
3. First-principle investigation of the electronic structure and magnetism in V_(12)TMclusters.
The DFT with the GGA method is adopted to study the electronic structures and mag-netic properties of V_(13) cluster and doped V_(12)TM clusters (TM: Sc, Ti, Cr, Mn, Fe, Co, Ni,Y, Zr, Nb, Mo, Tc, Ru, Rh). The binding energy, electronic structure and magnetism of theclusters have been obtained. Further more, the information of cluster magnetism and therelationship between magnetic moments and electronic structures of clusters were analyzed.The results show that V_(12)Fe and V_(12)Ru clusters are the most stable structures which havethe closed-shell system with larger binding energies and larger HOMO-LUMO gaps. V_(12)Ycluster has a giant moment of 11μ_B. The ground states of most clusters are shown to bemagnetic, but their magnetic moments are not striking.
4. Geometrical evolution, electronic structures, and magnetic properties of Bi-Mn bi- nary clusters.
The geometrical evolution, electronic structures, and magnetic properties of small bi-nary clusters Bi_nMn_m (n≤13, m≤6) are investigated using DFT with the view ofexplaining the experimentally observed magnetic moments in these systems. The resultsdemonstrate that the magnetic moments of the dopant Mn atoms exhibit a weak dependenceon the structure, composition, and environment, holding a general constant of 4μB/atomapproximately, whereas the magnetic couplings among these Mn atoms are strongly depen-dent. We propose that the preferred ferromagnetic couplings in the dopant Mn_m componentsresult in pronounced magnetic moments represented by certain combinations in which theBi to Mn ratio is close to 2. Moreover, a faint antiferromagnetic perturbation is providedby the Bin units. The hybridization among Mn 3d, 4s, and Bi 6p induces -0.1μB on Biatoms and reduces the Mn atomic moments by 1μ_B. On the whole, the calculated magnetictrends of the different composition series qualitatively fit well with experimental measure-ments. The lowest-energy structures of the clusters are segregated cases in which the dopantMn_m components assemble together, forming a pentagonal bipyramid shape and surroundedby irregular Bin components. Generally, an amorphous configuration is observed for low-Mn-concentration clusters, but the evolution of a defective polyicosahedron pattern with aMn core shell is favored for high-Mn-concentration clusters and this tendency will keep themost stable geometrical structure for larger sizes. By analyzing the binding energies andthe second-order energy differences, we find that the monatomic doping BinMn series con-taining n = 4, 6, 10, and 12 is more stable than its neighboring sizes. Furthermore, theHOMO-LUMO gaps decrease as a function of Mn concentration in the clusters, indicatingan enhancement of metallicity.
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