Large harmonic softening of the phonon density of states of uranium

Phonon density-of-states curves were obtained from inelastic neutron scattering spectra from the three crystalline phases of uranium at temperatures from 50 to 1213 K. The alpha-phase showed an unusually large thermal softening of phonon frequencies. Analysis of the vibrational power spectrum showed that this phonon softening originates with the softening of a harmonic solid, as opposed to vibrations in anharmonic potentials. It follows that thermal excitations of electronic states are more significant thermodynamically than are the classical volume effects. For the alpha-beta and beta-gamma phase transitions, vibrational and electronic entropies were comparable.     

Theory of surface force-constant changes in body-centered cubic lattices

A calculation has been made of force-constant changes at the (100) and (110) surfaces of body-centered cubic crystals. A model consisting of first, second and third-neighbor Lennard-Jones interactions together with harmonic angle-bending interactions is employed. The parameters characterizing the interactions are chosen to fit the equilibrium lattice spacing, the elastic constants, and certain phonon frequencies at high symmetry points in the Brillouin zone. The procedure consists of first calculating the static displacements produced by the creation of the surface and then calculating the change in force constants produced by the cubic and quartic anharmonic terms in the potential energy. Specific results have been obtained for chromium, iron, tungsten, and molybdenum.     

Molecular dynamics calculations of anharmonic properties of the vibrational spectrum of BCC zirconium under pressure

The structural stability and lattice dynamics of the high-pressure bcc phase of Zr at a constant temperature T = 500 K are studied for various volumes using molecular dynamics simulation with the Animalu pair pseudopotential. Dispersion curves of the vibrational spectrum calculated by the molecular dynamics method for various volumes are compared to the phonon spectrum obtained in the harmonic approximation. It is demonstrated that, as the volume decreases, all frequencies of the vibrational spectrum increase gradually and bcc zirconium remains strongly anharmonic along all high-symmetry directions of the Brillouin zone over the entire range of volumes studied. The strongly anharmonic N _T1 phonon is significantly softened near the point of structural instability of bcc-Zr at T = 500 K and V = 0.87V ₀. As the volume decreases to V = 0.73V ₀ under pressure, the anharmonic corrections for this phonon decrease by almost an order of magnitude and the phonons near the H point of the Brillouin zone become anharmonic. The damping of the T ₁ phonon mode along the [110] direction is calculated as a function of pressure.     

Entropy driven stabilization of energetically unstable crystal structures explained from first principles theory

Conventional methods to calculate the thermodynamics of crystals evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the harmonic approximation, such as the body-centered cubic (bcc) crystal structure when it appears as a high-temperature phase of many metals. A method for calculating temperature dependent phonon spectra self-consistently from first principles has been developed to address this issue. The method combines concepts from Born's interatomic self-consistent phonon approach with first principles calculations of accurate interatomic forces in a supercell. The method has been tested on the high-temperature bcc phase of Ti, Zr, and Hf, as representative examples, and is found to reproduce the observed high-temperature phonon frequencies with good accuracy.     

一维分子链中激子与声子的相互作用和呼吸子解

运用连续极限近似，求解声子与激子相互作用的运动方程，得到了简谐分子链和 非简谐分子链中晶格振动的孤子解，在考虑三次非简谐势的情况下，一维分子链晶格振动具 有扭结孤子解，在考虑具有四次非简谐势的情况下，得到一维分子链晶格振动具有呼吸子解 . 关键词： 一维分子链 激子 声子 孤子 呼吸子 非线性效应     

Approaching the strongly anharmonic limit with ab initio calculations of materials’ vibrational properties – a colloquium*

Despite ab initio computational techniques have opened new possibilities to interpret experimental results and predict the properties of new materials, their applications are limited by the adopted approximative schemes. Consequently, the first-principles calculation of many physical properties and phenomena is hindered and ab initio methods need to be further developed to overcome such limits. For example, the standard harmonic approximation used to assess the vibrational properties of materials often completely breaks down, so that the vibrational properties need to be calculated including strong anharmonic effects. The harmonic approximation has also intrinsic failures as it cannot estimate the lattice thermal conductivity of materials nor the temperature dependence of the phonon frequencies, crucial to account for temperature driven second-order phase transitions. Several methods developed in the last years to account for anharmonicity in the non-perturbative regime and overcome such difficulties are briefly reviewed in this colloquium paper. In particular, the stochastic self-consistent harmonic approximation, a variational method that allows calculating vibrational properties in strongly anharmonic systems, is described in further detail. Applications of the latter method to superconducting palladium, platinum, and sulfur hydrides are discussed, where anharmonicity has a huge impact on their vibrational and superconducting properties.     

n-SiC拉曼散射光谱的温度特性

测量了采用离子注入法得到掺N的n-SiC晶体从100—450 K的拉曼光谱. 研究了SiC一级拉曼谱、电子拉曼散射谱及二级拉曼谱的温度效应. 实验结果表明,大部分SiC一级拉曼峰会随温度升高向低波数方向移动,但声学模红移(峰值位置向低频方向移动)的幅度较光学模小. 重掺杂4H-SiC的纵光学声子等离子体激元耦合(LOPC)模频率随温度升高表现出先蓝移(峰值位置向高频方向移动)后红移的变化趋势,表明LOPC模的温度特性不仅会受到非简谐效应的影响,还与实际已离化杂质浓度有关. 电子拉曼散射峰线宽随温度升高而增 关键词： 碳化硅 温度 纵光学声子等离子体激元耦合模 电子拉曼散射     

一种基于荧光材料的聚合物白光发光二极管

制备了一种基于荧光聚合物共混的单发光层聚合物白光发光二极管.器件结构为铟锡氧化物/苯磺酸掺杂聚乙烯基二氧噻吩/发光层/ 1,3,5-三(N-苯基-2-苯并咪唑-2)苯41/Ba/Al,蓝光材料芴-氟化喹喔啉共聚物(PF-BPFQ5)、绿光材料苯基取代的聚对苯乙炔(P-PPV)和红光材料聚(2-甲氧基-5-(2′-乙基己氧基)-1,4-对苯乙炔)(MEH-PPV)共混为发光层.当PF-BPFQ5,P-PPV,MEH-PPV的质量比例为100∶06∶06时,获得标准的白光,色坐标为（033 关键词： 聚合物发光二极管 白光 共混     

Portable Implementation of a Quantum Thermal Bath for Molecular Dynamics Simulations

Recently, Dammak and coworkers (Phys. Rev. Lett. 103:190601, 2009) proposed that the quantum statistics of vibrations in condensed systems at low temperature could be simulated by running molecular dynamics simulations in the presence of a colored noise with an appropriate power spectral density. In the present contribution, we show how this method can be implemented in a flexible manner and at a low computational cost by synthesizing the corresponding noise ‘on the fly’. The proposed algorithm is tested for a simple harmonic chain as well as for a more realistic model of aluminium crystal. The energy and Debye-Waller factor are shown to be in good agreement with those obtained from harmonic approximations based on the phonon spectrum of the systems. The limitations of the method associated with anharmonic effects are also briefly discussed. Some perspectives for disordered materials and heat transfer are considered.     

Phase transition and thermodynamic properties of ThO2：Quasi-harmonic approximation calculations and anharmonic effects

The thermodynamic properties and the phase transition of ThO2 from the cubic structure to the orthorhombic structure are investigated using the first-principles projector-augmented wave method. The vibrational contribution to Helmholtz free energy is evaluated from the first-principles phonon calculations. The anharmonic contribution to quasi-harmonic free energy is accounted for by using an effective method(2010 Phys. Rev. B 81 172301). The results reveal that at ambient temperature, the phase transition from the cubic phase to the orthorhombic phase occurs at 26.45 GPa, which is consistent with the experimental and theoretical data. With increasing temperature, the transition pressure decreases almost linearly. By comparing the experimental results with the calculation results, it is shown that the thermodynamic properties of ThO2 at high temperature improve substantially after including the anharmonic correction to quasi-harmonic free energy.     

Anomalous heat capacity of nanoparticles

It was shown experimentally that the specific heat of nanosized particles was higher than that of macroscopic particles of the same nature. It was also found that the heat capacity increased as the size of nanoparticles decreased. We analyzed the reasons for the anomalous behavior of the heat capacity of nanoparticles. For this purpose, we considered nanoparticles with a simple cubic lattice and an arbitrary external geometric shape. The simplest harmonic interaction potential between the nearest neighbor particles was used. Qualitative agreement with experimental data was obtained. The main factor responsible for the anomalous behavior of small particles was phonon spectrum softening compared with bulk material when free boundary conditions were used. The lower frequencies make a larger contribution to heat capacity. It was found that, apart from particle size, the geometric shape and defect structure of nanoparticles influenced their heat capacity: given the same number of particles, an increase in asymmetry and disorder caused an increase in heat capacity.     

Theoretical interpretation of the vibrational spectrum of bicyclo[1.1.0]butane in terms of an ab initio anharmonic model

The anharmonic vibrational IR and Raman spectra of the bicyclo[1.1.0]butane molecule have been calculated in the range of up to 4000 cm^?1 using a numerical and analytical realization of the van Vleck second-order operator perturbation theory. Cubic and quartic force constants in normal coordinates, as well as cubic surfaces of the dipole moment and polarizability, have been found by numerical differentiation of the corresponding first and second derivatives calculated by the MP2/cc-pVTZ quantum-mechanical method. In order to increase the prediction accuracy of vibrational transitions, corresponding harmonic frequencies have been obtained by the CCSD(T)/cc-pVTZ high-precision quantum mechanical method. The anharmonic intensities of the IR and Raman spectra have been calculated using canonical transformations of the operators of the dipole moment and polarizability expanded into a Taylor series around the equilibrium configuration. The assignment of experimental vibrational bands in the IR and Raman spectra has been analyzed. It has been shown that the anharmonic calculation based on the above-described procedure of combining more exact harmonic frequencies with the anharmonic force field obtained with a more economical method makes possible the reliable interpretation of the majority of spectral bands, including Fermi and Darling-Dennison resonances.     

On the spin-phonon interaction in anharmonic crystals

In this paper, a theory is developed for examining the influence of the spin-phonon interaction on the phonon dynamics in anharmonic crystals. In contrast to a harmonic approximation such an approach allows for comparing the role of the direct interaction between lattice vibrations with that of the indirect interaction via spins in the propagation and attenuation of sound as well as in the behaviour of thermodynamic quantities. Explicit expressions are derived for the phonon self-energy using successively higher approximations obtained from a cumulant expansion of the density of interparticle distances. It is shown that even in the harmonic approximation the two-spin correlation function and the four-spin correlation function enter into the expression of the generalized dynamical matrix in deviation from previous results. The modification of this harmonic dynamical matrix due to the renormalization of the harmonic phonons and due to phonon-phonon scattering processes is given employing a “weak coupling” approximation between the localized spins and the interparticle-distance density of the crystal. The resemblance of the present approach to an earlier microscopic treatment of electronic contributions to phonon dynamics in anharmonic crystals is pointed out.     

Isotopic phonon effects in β-rhombohedral boron--non-statistical isotope distribution

On the basis of the spectra of IR- and Raman-active phonons, the isotopic phonon effects in β-rhombohedral boron are analysed for polycrystalline (10)B- and (11)B-enriched samples of different origin and high-purity (nat)B single crystals. Intra- and inter-icosahedral B-B vibrations are harmonic, hence meeting the virtual crystal approximation (VCA) requirements. Deviations from the phonon shift expected according to the VCA are attributed to the anharmonic share of the lattice vibrations. In the case of icosahedral vibrations, the agreement with calculations on α-rhombohedral boron by Shirai and Katayama-Yoshida is quite satisfactory. Phonon shifts due to isotopic disorder in (nat)B are separated and determined. Some phonon frequencies are sensitive to impurities. The isotopic phonon effects yield valuable specific information on the nature of the different phonon modes. The occupation of regular boron sites by isotopes deviates significantly from the random distribution.     

石墨烯低温热膨胀和声子弛豫时间随温度的变化规律

考虑到原子非简谐振动和电子-声子相互作用,用固体物理理论和方法研究了石墨烯格林艾森参量和低温热膨胀系数以及声子弛豫时间随温度的变化规律,探讨了原子非简谐振动项对它们的影响.结果表明:1)在低于室温的温度范围内,石墨烯的热膨胀系数为负值,随着温度的升高,其热膨胀系数的绝对值单调增加,室温热膨胀系数为-3.64×10~(-6)K~(-1);2)简谐近似下的格林艾森参量为零.考虑到非简谐项后,格林艾森参量在1.40-1.42之间并随温度升高而缓慢增大,几乎成线性关系,第二非简谐项对格林艾森参量的影响小于第一非简谐项;3)石墨烯声子弛豫时间随着温度的升高而减小,其中,温度很低(T10 K)时变化很快,此后变化很慢,当温度不太低(T300 K)时,声子弛豫时间与温度几乎成反比关系.     

Dynamics of the crystallized one-component plasma

The dynamics and energy of the crystallized one-component plasma (OCP) is evaluated using the self-consistent-phonon (SCP) theory of lattice dynamics. Melting of the crystal is also examined. The OCP crystal is harmonic for particle rms vibrational amplitudes as large as 25% of the interparticle spacing. This is due to the soft (r^?1) core of the Coulomb potential. Anharmonic effects are, however, entirely responsible for the eventual mechanical instability, identified here with melting, of the crystal at large enough rms amplitudes. This takes place at r_s = 180 at T = 0 K for the most sophisticated SCP theory. In the classical limit, this SCP theory predicts the crystal to be more stable than does the “exact” Monte Carlo study of melting by Pollock and Hansen. This suggests that including further anharmonic terms in the SCP theory leads to melting at even larger r_s at T = 0 K. However, comparison of crystal and fluid energies by Ceperley, Hansen, and Mazighi suggest melting in the range r_s = 65 to 135. Near melting the anharmonic contributions shift the phonon frequencies by a factor of 2 and the phonon lifetimes become very short.     

Collective excitations in solid hydrogen as observed by incoherent neutron scattering

Incoherent neutron scattering experiments are reported at a number of scattering angles for solid H₂ using the time-of-flight technique. The samples had an ortho concentration ofX0.91 and the temperatures were 4.2, 2.2 and 1.2 K. The recorded scattering functions exhibit the elastic line, the ortho-para conversion line, the phonon spectrum on the energy-gain side of the neutrons and finally the phonon spectrum on the energy-loss side. Analysis of the data shows multiple scattering to be very important especially at small scattering angles. Accordingly, the results of an extensive calculation are reported that include up to four-fold scattering. The phonon spectrum that brings calculation and experiment in agreement at all angles is presented. It is concluded from the comparison between the spectra at various temperatures that unexpectedly the samples have always remained in the hexagonal close-packed phase even below the usual transition temperature into the cubic phase. Comparison is made with the spectrum (also in thehcp phase) obtained from coherent neutron scattering. The high-energy phonon tail, to be expected for quantum crystals, is observed and is qualitatively consistent with that in a similar spectral density derived theoretically from ortho-para conversion data under pressure. No evidence of a libron spectrum atT=2.2 K for a sample withX=0.91 could be found, which is consistent with the absence of the cubic orientationally ordered phase in these experiments.Supported in this research by a grant from the National Science Foundation     

Prediction of superconductivity of Ta2AlC: in situ Raman spectrometry and density functional investigations

In this paper, in situ Raman spectra of Ta₂AlC are measured in the temperature range of 80–500 K at ambient pressure. The frequencies of the Raman modes decrease with increasing temperature, which have been explained by the anharmonic and thermal expansion effects. The line‐width of E_2g (ω₃) mode increases at elevated temperatures, which is found to be due to the anharmonic phonon–phonon scatterings. On the other hand, the line‐widths of E_2g (ω₁) and A_1g (ω₄) modes decrease continuously with increasing temperature, which is explained by the electron–phonon couplings of these two phonon modes with the Ta 5d electrons. The electron–phonon coupling strengths are obtained both in experiments and density functional calculations. Finally, Ta₂AlC is predicted to be a new superconductive MAX phase. Copyright © 2014 John Wiley & Sons, Ltd.     

Critical evaluation of anharmonic corrections to the equilibrium isotope effect for methyl cation transfer from vacuum to dielectric continuum

Harmonic and anharmonic vibrational frequencies are computed for isotopologues of methyl cation in vacuum and in a polarised continuum model (PCM) dielectric continuum (? = 80) within Gaussian09. Comparison of results in vacuum for two methods (B3LYP and second-order Møller–Plesset perturbation theory) and three basis sets (6-31+G(d), cc-aug-PVDZ, cc-aug-PVQZ) with published anharmonic frequencies obtained from an accurate vibrational configuration interaction (VCI) method shows the smallest root mean square error in the frequencies from B3LYP/6-31+G(d) with anharmonic corrections. Using this method to calculate isotopic partition function ratios (IPFRs) for all six pairs of CH₃⁺, CH₂D⁺, CHD₂⁺ and CD₃⁺ gives better results for anharmonic frequencies than for unscaled harmonic frequencies, but scaled harmonic frequencies give even better results for less cost. The scaling factor is simply the ratio of the sum of the anharmonic VCI frequencies to the sum of the harmonic B3LYP/6-31+G(d) frequencies, which corresponds to the dominance of zero-point energy changes in determining the IPFRs. Both the scaled and unscaled harmonic frequencies provide reasonable estimates for the equilibrium isotope effects (EIEs) upon transfer of methyl cation from vacuum to PCM ‘water’, but the anharmonic PCM calculations give erratic results. The use of scaled B3LYP/6-31+G(d) harmonic frequencies is recommended for the estimations of EIEs rather than expensive anharmonic corrections.     

Activation-Like Processes at Zero Temperature

We examine the possibility that a metastable quantum state could experiment a phenomenon similar to thermal activation but at zero temperature. To do that we study the real-time dynamics of the reduced Wigner function in a simple open quantum system: an anharmonic oscillator with a cubic potential linearly interacting with an environment of harmonic oscillators. Our results suggest that this activation-like phenomenon exists indeed as a consequence of the fluctuations induced by the environment and that its associated decay rate is comparable to the tunneling rate as computed by the instanton method, at least for the particular potential of the system and the distribution of frequencies for the environment considered in this paper. However, we are not able to properly deal with the term which leads to tunneling in closed quantum systems, and a definite conclusion cannot be reached until tunneling and activation-like effects are considered simultaneously.