Glasses are known to possess low-frequency excess modes beyond the Debye prediction.For decades,it has been assumed that evolution of low-frequency density of excess modes D(ω) with frequency ω follows a power-law s...Glasses are known to possess low-frequency excess modes beyond the Debye prediction.For decades,it has been assumed that evolution of low-frequency density of excess modes D(ω) with frequency ω follows a power-law scaling:D(ω)~ω~γ.However,it remains debated on the value of γ at low frequencies below the first phonon-like mode in finitesize glasses.Early simulation studies reported γ=4 at low frequencies in two-(2D),three-(3D),and four-dimensional(4D)glasses,whereas recent observations in 2D and 3D glasses suggested γ=3.5 in a lower-frequency regime.It is uncertain whether the low-frequency scaling of D(ω)~ω^(3.5) could be generalized to 4D glasses.Here,we conduct numerical simulation studies of excess modes at frequencies below the first phonon-like mode in 4D model glasses.It is found that the system size dependence of D(ω) below the first phonon-like mode varies with spatial dimensions:D(ω) increases in2D glasses but decreases in 3D and 4D glasses as the system size increases.Furthermore,we demonstrate that the ω^(3.5)scaling,rather than the ω~4 scaling,works in the lowest-frequency regime accessed in 4D glasses,regardless of interaction potentials and system sizes examined.Therefore,our findings in 4D glasses,combined with previous results in 2D and 3D glasses,suggest a common low-frequency scaling of D(ω)~ ω^3.5) below the first phonon-like mode across different spatial dimensions,which would inspire further theoretical studies.展开更多
One hallmark of glasses is the existence of excess vibrational modes at low frequenciesωbeyond Debye’s prediction.Numerous studies suggest that understanding low-frequency excess vibrations could help gain insight i...One hallmark of glasses is the existence of excess vibrational modes at low frequenciesωbeyond Debye’s prediction.Numerous studies suggest that understanding low-frequency excess vibrations could help gain insight into the anomalous mechanical and thermodynamic properties of glasses.However,there is still intensive debate as to the frequency dependence of the population of low-frequency excess vibrations.In particular,excess modes could hybridize with phonon-like modes and the density of hybridized excess modes has been reported to follow D_(exc)(ω)~ω^(2)in 2D glasses with an inverse power law potential.Yet,the universality of the quadratic scaling remains unknown,since recent work suggested that interaction potentials could influence the scaling of the vibrational spectrum.Here,we extend the universality of the quadratic scaling for hybridized excess modes in 2D to glasses with potentials ranging from the purely repulsive soft-core interaction to the hard-core one with both repulsion and attraction as well as to glasses with significant differences in density or interparticle repulsion.Moreover,we observe that the number of hybridized excess modes exhibits a decrease in glasses with higher density or steeper interparticle repulsion,which is accompanied by a suppression of the strength of the sound attenuation.Our results indicate that the density bears some resemblance to the repulsive steepness of the interaction in influencing low-frequency properties.展开更多
It is shown that the traditional explanation of the free electron properties, such as mean free electron path, drift mobility, and the relaxation time, by lattice vibrations, is not valid for real free randomly moving...It is shown that the traditional explanation of the free electron properties, such as mean free electron path, drift mobility, and the relaxation time, by lattice vibrations, is not valid for real free randomly moving (RM) electrons in materials with degenerate electron gas. It is shown that the effective density of the free RM electrons in elemental metals is completely determined by density-of-states at the Fermi surface and by absolute temperature. The study has shown that the lattice vibrations excite not only the free RM electrons but also produce the same number of weakly screened ions (so-named electronic defects), which cause the scattering of the free RM electrons and related electron kinetic characteristics.展开更多
选用密度泛函理论中的B3LYP杂化泛函,在B3LYP/6-31++g(d,p)(C,H,N,S)水平下,优化了2-巯基-5-硝基苯并咪唑分子(MNBMZ)的结构,优化结果表明,2-巯基-5-硝基苯并咪唑分子是一个近平面结构。通过频率计算,获得了2-巯基-5-硝基苯并咪唑分子(M...选用密度泛函理论中的B3LYP杂化泛函,在B3LYP/6-31++g(d,p)(C,H,N,S)水平下,优化了2-巯基-5-硝基苯并咪唑分子(MNBMZ)的结构,优化结果表明,2-巯基-5-硝基苯并咪唑分子是一个近平面结构。通过频率计算,获得了2-巯基-5-硝基苯并咪唑分子(MNBMZ)的拉曼光谱,并和实验获得的拉曼光谱图进行了对比,200~800cm^-1波数段实验获得的拉曼谱带波数和理论计算波数相比,有一定程度的蓝移,800~1800cm^-1波数段实验获得的拉曼谱带波数和理论计算波数相比,发生了一定的红移。对实验和理论计算光谱主要振动峰进行线性回归拟合,相关系数r=0.998,标准偏差14.98。实验和理论计算获得的拉曼光谱图基本上是一致的,表明本文选取的DFT理论计算方法是可靠的。结合VEDA4软件对2-巯基-5-硝基苯并咪唑分子的拉曼谱带简正振动模式进行了指认。此外,分析并讨论了2-巯基-5-硝基苯并咪唑分子(MNBMZ)前线轨道及HOMO,LUMO轨道的组成,HOMO和LUMO轨道能级差为3.31eV,电子有从HOMO跃迁到LUMO的趋势。HOMO轨道中S原子的贡献是52.53%,LUMO轨道中硝基N和O原子的贡献分别为23.03%,19.97%和19.36%。采用含时密度泛函理论(time dependent density functional theory,TDDFT)对2-巯基-5-硝基苯并咪唑分子(MNBMZ)的激发态进行了计算分析,计算结果表明甲醇溶剂中2-巯基-5-硝基苯并咪唑分子(MNBMZ)理论计算的吸收波长为213,281和437nm;实验获得的吸收波长223,272和353nm。对研究2-巯基-5-硝基苯并咪唑分子的性质,提供了理论基础。展开更多
基金the support from the National Natural Science Foundation of China(Grant Nos.12374202 and 12004001)Anhui Projects(Grant Nos.2022AH020009,S020218016,and Z010118169)Hefei City(Grant No.Z020132009)。
文摘Glasses are known to possess low-frequency excess modes beyond the Debye prediction.For decades,it has been assumed that evolution of low-frequency density of excess modes D(ω) with frequency ω follows a power-law scaling:D(ω)~ω~γ.However,it remains debated on the value of γ at low frequencies below the first phonon-like mode in finitesize glasses.Early simulation studies reported γ=4 at low frequencies in two-(2D),three-(3D),and four-dimensional(4D)glasses,whereas recent observations in 2D and 3D glasses suggested γ=3.5 in a lower-frequency regime.It is uncertain whether the low-frequency scaling of D(ω)~ω^(3.5) could be generalized to 4D glasses.Here,we conduct numerical simulation studies of excess modes at frequencies below the first phonon-like mode in 4D model glasses.It is found that the system size dependence of D(ω) below the first phonon-like mode varies with spatial dimensions:D(ω) increases in2D glasses but decreases in 3D and 4D glasses as the system size increases.Furthermore,we demonstrate that the ω^(3.5)scaling,rather than the ω~4 scaling,works in the lowest-frequency regime accessed in 4D glasses,regardless of interaction potentials and system sizes examined.Therefore,our findings in 4D glasses,combined with previous results in 2D and 3D glasses,suggest a common low-frequency scaling of D(ω)~ ω^3.5) below the first phonon-like mode across different spatial dimensions,which would inspire further theoretical studies.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12374202 and 12004001)Anhui Projects(Grant Nos.2022AH020009,S020218016,and Z010118169)+1 种基金Hefei City(Grant No.Z020132009)Anhui University(start-up fund)。
文摘One hallmark of glasses is the existence of excess vibrational modes at low frequenciesωbeyond Debye’s prediction.Numerous studies suggest that understanding low-frequency excess vibrations could help gain insight into the anomalous mechanical and thermodynamic properties of glasses.However,there is still intensive debate as to the frequency dependence of the population of low-frequency excess vibrations.In particular,excess modes could hybridize with phonon-like modes and the density of hybridized excess modes has been reported to follow D_(exc)(ω)~ω^(2)in 2D glasses with an inverse power law potential.Yet,the universality of the quadratic scaling remains unknown,since recent work suggested that interaction potentials could influence the scaling of the vibrational spectrum.Here,we extend the universality of the quadratic scaling for hybridized excess modes in 2D to glasses with potentials ranging from the purely repulsive soft-core interaction to the hard-core one with both repulsion and attraction as well as to glasses with significant differences in density or interparticle repulsion.Moreover,we observe that the number of hybridized excess modes exhibits a decrease in glasses with higher density or steeper interparticle repulsion,which is accompanied by a suppression of the strength of the sound attenuation.Our results indicate that the density bears some resemblance to the repulsive steepness of the interaction in influencing low-frequency properties.
文摘It is shown that the traditional explanation of the free electron properties, such as mean free electron path, drift mobility, and the relaxation time, by lattice vibrations, is not valid for real free randomly moving (RM) electrons in materials with degenerate electron gas. It is shown that the effective density of the free RM electrons in elemental metals is completely determined by density-of-states at the Fermi surface and by absolute temperature. The study has shown that the lattice vibrations excite not only the free RM electrons but also produce the same number of weakly screened ions (so-named electronic defects), which cause the scattering of the free RM electrons and related electron kinetic characteristics.
文摘选用密度泛函理论中的B3LYP杂化泛函,在B3LYP/6-31++g(d,p)(C,H,N,S)水平下,优化了2-巯基-5-硝基苯并咪唑分子(MNBMZ)的结构,优化结果表明,2-巯基-5-硝基苯并咪唑分子是一个近平面结构。通过频率计算,获得了2-巯基-5-硝基苯并咪唑分子(MNBMZ)的拉曼光谱,并和实验获得的拉曼光谱图进行了对比,200~800cm^-1波数段实验获得的拉曼谱带波数和理论计算波数相比,有一定程度的蓝移,800~1800cm^-1波数段实验获得的拉曼谱带波数和理论计算波数相比,发生了一定的红移。对实验和理论计算光谱主要振动峰进行线性回归拟合,相关系数r=0.998,标准偏差14.98。实验和理论计算获得的拉曼光谱图基本上是一致的,表明本文选取的DFT理论计算方法是可靠的。结合VEDA4软件对2-巯基-5-硝基苯并咪唑分子的拉曼谱带简正振动模式进行了指认。此外,分析并讨论了2-巯基-5-硝基苯并咪唑分子(MNBMZ)前线轨道及HOMO,LUMO轨道的组成,HOMO和LUMO轨道能级差为3.31eV,电子有从HOMO跃迁到LUMO的趋势。HOMO轨道中S原子的贡献是52.53%,LUMO轨道中硝基N和O原子的贡献分别为23.03%,19.97%和19.36%。采用含时密度泛函理论(time dependent density functional theory,TDDFT)对2-巯基-5-硝基苯并咪唑分子(MNBMZ)的激发态进行了计算分析,计算结果表明甲醇溶剂中2-巯基-5-硝基苯并咪唑分子(MNBMZ)理论计算的吸收波长为213,281和437nm;实验获得的吸收波长223,272和353nm。对研究2-巯基-5-硝基苯并咪唑分子的性质,提供了理论基础。
