Order Anharmonicity Research Articles

Particlelike Phonon Propagation Dominates Ultralow Lattice Thermal Conductivity in Crystalline Tl3VSe4

We investigate the microscopic mechanisms of ultralow lattice thermal conductivity (κ_{l}) in Tl_{3}VSe_{4} by combining a first principles density functional theory based framework of anharmonic lattice dynamics with the Peierls-Boltzmann transport equation for phonons. We include contributions of the three- and four-phonon scattering processes to the phonon lifetimes as well as the temperature dependent anharmonic renormalization of phonon energies arising from an unusually strong quartic anharmonicity in Tl_{3}VSe_{4}. In contrast to a recent report by Mukhopadhyay etal. [Science 360, 1455 (2018)SCIEAS0036-807510.1126/science.aar8072] which suggested that a significant contribution to κ_{l} arises from random walks among uncorrelated oscillators, we show that particlelike propagation of phonon excitations can successfully explain the experimentally observed ultralow κ_{l}. Our findings are further supported by explicit calculations of the off-diagonal terms of the heat current operator, which are found to be small and indicate that wavelike tunneling of heat carrying vibrations is of minor importance. Our results (i)resolve the discrepancy between the theoretical and experimental κ_{l}, (ii) offer new insights into the minimum κ_{l} achievable in Tl_{3}VSe_{4}, and (iii)highlight the importance of high order anharmonicity in low-κ_{l} systems. The methodology demonstrated here may be used to resolve the discrepancies between the experimentally measured and the theoretically calculated κ_{l} in skutterides and perovskites, as well as to understand the glasslike κ_{l} in complex crystals with strong anharmonicity, leading towards the goal of rational design of new materials.

First-principles study of thermal expansion and thermomechanics of group-V monolayers: blue phosphorene, arsenene, and antimonene

Using first-principles calculations based on quasiharmonic approximation (QHA), we systematically investigate the vibrational properties, thermal expansion and thermomechanics properties of three monoatomic group-V monolayers with honeycomb structure: blue phosphorene, arsenene and antimonene. It is found antimonene shows negative thermal expansion in the temperature range studied, while blue phosphorene and arsenene display small positive thermal expansion at high temperature. The physical mechanisms of their different thermal properties are explored. The results of Grüneisen theory are also exhibited for comparison, and the similarities and differences are studied. It is concluded the discrepancies arise from the high order anharmonicity of phonons.

Molecules and the Eigenstate Thermalization Hypothesis.

We review a theory that predicts the onset of thermalization in a quantum mechanical coupled non-linear oscillator system, which models the vibrational degrees of freedom of a molecule. A system of N non-linear oscillators perturbed by cubic anharmonic interactions exhibits a many-body localization (MBL) transition in the vibrational state space (VSS) of the molecule. This transition can occur at rather high energy in a sizable molecule because the density of states coupled by cubic anharmonic terms scales as N3, in marked contrast to the total density of states, which scales as exp(aN), where a is a constant. The emergence of a MBL transition in the VSS is seen by analysis of a random matrix ensemble that captures the locality of coupling in the VSS, referred to as local random matrix theory (LRMT). Upon introducing higher order anharmonicity, the location of the MBL transition of even a sizable molecule, such as an organic molecule with tens of atoms, still lies at an energy that may exceed the energy to surmount a barrier to reaction, such as a barrier to conformational change. Illustrative calculations are provided, and some recent work on the influence of thermalization on thermal conduction in molecular junctions is also discussed.

High-temperature thermodynamics of silver: Semi-empirical approach* *Project supported by the Major Research Project, UGC, New Delhi, India (Grant No. 42-771/2013 (SR)).

We report high-temperature thermodynamics for fcc silver by combining ab initio phonon dynamics to empirical quadratic temperature-dependent term for anharmonic part of Helmholtz free energy. The electronic free energy is added through an interpolation scheme, which connects ambient condition free electron gas model to Thomas–Fermi results. The present study shows good agreement with experimental and reported findings for several thermal properties, and the discrepancy observed in some caloric properties is addressed. The decreases in the product of volume thermal expansion coefficient and isothermal bulk modulus and in the constant volume anharmonic lattice specific heat at high temperature are the clear evidences of proper account of anharmonicity. The present study also reveals that T 2–dependent anharmonic free energy is sufficient for correct evaluation of thermal pressure and conventional Grüneisen parameter. We observe that the intrinsic phonon anharmonicity starts dominating above characteristic temperature, which is attributed to higher order anharmonicity and can be related to higher order potential derivatives. We conclude that the uncorrelated and largeamplitude lattice vibrations at high temperature raise dominating intrinsic thermal stress mechanism, which surpasses the phonon-anharmonism and requires future consideration.

Analyzing chaos in higher order disordered quartic-sextic Klein-Gordon lattices using q-statistics

In the study of subdiffusive wave-packet spreading in disordered Klein–Gordon (KG) nonlinear lattices, a central open question is whether the motion continues to be chaotic despite decreasing densities, or tends to become quasi-periodic as nonlinear terms become negligible. In a recent study of such KG particle chains with quartic (4th order) anharmonicity in the on-site potential it was shown that q−Gaussian probability distribution functions of sums of position observables with q > 1 always approach pure Gaussians (q=1) in the long time limit and hence the motion of the full system is ultimately “strongly chaotic”. In the present paper, we show that these results continue to hold even when a sextic (6th order) term is gradually added to the potential and ultimately prevails over the 4th order anharmonicity, despite expectations that the dynamics is more “regular”, at least in the regime of small oscillations. Analyzing this system in the subdiffusive energy domain using q-statistics, we demonstrate that groups of oscillators centered around the initially excited one (as well as the full chain) possess strongly chaotic dynamics and are thus far from any quasi-periodic torus, for times as long as t=109.

Transient Raman spectra, structure, and thermochemistry of the thiocyanate dimer radical anion in water.

Time-resolved resonance-enhanced Stokes and anti-Stokes Raman spectra of the thiocyanate dimer radical anion, (SCN)2•-, prepared by pulse radiolysis in water, have been obtained and interpreted in conjunction with theoretical calculations to provide detailed information on the molecular geometry and bond properties of the species. The structural properties of the radical are used to develop a molecular perspective on its thermochemistry in an aqueous solution. Twenty-nine Stokes Raman bands of the radical observed in the 120-4200 cm-1 region are assigned in terms of the strongly enhanced 220 cm-1 fundamental, weakly enhanced 721 cm-1, and moderately enhanced 2073 cm-1 fundamentals, their overtones, and combinations. Calculations by range-separated hybrid density functionals (ωB97x and LC-ωPBE) support the spectroscopic assignments of the 220 cm-1 vibration to a predominantly SS stretching mode and the features at 721 cm-1 and 2073 cm-1 to CS and CN symmetric stretching modes, respectively. The corresponding bond lengths are 2.705 (±0.036) Å, 1.663 (±0.001) Å, and 1.158 (±0.002) Å. A first order anharmonicity of 1 cm-1 determined for the SS stretching mode suggests a convergence of vibrational states at an energy of ∼1.5 eV, using the Birge-Sponer extrapolation. This value, estimated for the radical confined in solvent cage, compares well with the calculated gas-phase energy of 1.26 ± 0.04 eV required for the radical to dissociate into SCN• and SCN- fragments. The enthalpy of dissociation drops to 0.60 ± 0.03 eV in water when solvent dielectric effects on the radical and its dissociation products upon S-S bond scission are incorporated in the calculations. No frequency shift or spectral broadening was observed between light and heavy water solvents, indicating that the motion of solvent molecules in the hydration shell has no perceptible effect on the intramolecular dynamics of the radical. The Stokes and anti-Stokes Raman frequencies were found to be identical within the experimental uncertainty, suggesting that the frequency difference between the thermally relaxed and spontaneously created vibrational states of (SCN)2•- in water is too small to be observable.

Proposal for ultrafast switching of ferroelectrics using midinfrared pulses

I propose a method for ultrafast switching of ferroelectric polarization using mid-infrared pulses. This involves selectively exciting the highest frequency $A_1$ phonon mode of a ferroelectric material with an intense mid-infrared pulse. Large amplitude oscillations of this mode provides a unidirectional force to the lattice such that it displaces along the lowest frequency $A_1$ phonon mode coordinate because of a nonlinear coupling of the type $g Q_{\textrm{P}} Q_{\textrm{IR}}^2$ between the two modes. First principles calculations show that this coupling is large in transition-metal oxide ferroelectrics, and the sign of the coupling is such that the lattice displaces in the switching direction. Furthermore, I find that the lowest frequency $A_1$ mode has a large $Q_{\textrm{P}}^3$ order anharmonicity, which causes a discontinuous switch of electric polarization as the pump amplitude is continuously increased.

Design of a dynamically orthogonalized Penning trap with higher order anharmonicity compensation

We present an analysis of a doubly compensated, open ended, cylindrical Penning ion trap including the effect of realistic gaps between adjacent electrodes. This work is a generalization of the work of X. Fei, W.M. Snow, Nuclear Instruments and Methods A 425(1999) 431. By varying the lengths of the electrodes, we have been able to make the trap dynamically orthogonalized and tune out higher order anharmonicities up to C8 term over a wide range of inner radii of the cylindrical trap and gap lengths between adjacent electrodes. This work should help to generate a higher quality quadrupolar potential near the center of the cylindrical trap and be useful for studies involving high precision measurements of the trapped particles.

Lattice dynamics above structural phase transitions

Continuous structural phase transitions driven by a soft R-corner mode are considered. The well-known role of fourth order anharmonicities for the occurrence of a soft mode is discussed in different approximations. For SrTiO3 a particular mechanism discussed in an earlier paper is reconsidered and its effect on the zero-frequency peak in neutron scattering is estimated to be too small.

Fluctuations, higher order anharmonicities, and Landau expansion for barium titanate

The correct description of the ferroelectric phase transition in barium titanate requires that, in the expansion of the free energy, not only the sixth-order terms but also the eighth-order terms should be retained. One more unusual feature of the BaTiO3 compound is that the coefficients B 1 and B 2 of the terms P 4 x and P 2 x P 2 y in the Landau expansion depend on the temperature. It is demonstrated that the temperature dependence of the coefficients B 1 and B 2 can be associated with the thermal fluctuations of polarization under conditions where the fourth-order anharmonic constants are anomalously small; i.e., a nonlinearity of the type P 4 and higher order anharmonicities make comparable contributions. Regular (noncritical) fluctuation contributions to the coefficients B 1 and B 2 are calculated to the first order in the sixth- and eighth-order anharmonic constants. Both contributions increase monotonically with increasing temperature, which is in agreement with the experimental dependences of these coefficients. The proposed theory without additional assumptions makes it possible to determine the ratio of the fluctuation components of the coefficients B 1 and B 2. This ratio also appears to be very close to that observed in the experiment.

Empirical relationships for ion conduction based on vibration amplitude in perovskite-type proton and superionic conductors

For superionic and deformed perovskite-type H+-ion conductors, empirical relationships among atomic mass of host or substituted ion, H+-ion conductivity, σPR, activation energy, transition temperature Tc, etc. are proposed. We elucidate the roles of heavy host ion and specific crystal structures below and above the Tc on the H+-ion conduction by noticing a large amplitude of O-ion vibration mode arising from a large fourth order anharmonicity. We clarify the important role of strengthened ionic force for the host cation lattice at and above Tc on the H+-ion jumping, and interpret reasonably the σPR value depending on the concentration of doping ion, a large broadening of vibration band and an enhanced amplitude of OH-vibration mode, etc. We suggest the extension of this consideration to stabilized zirconium and superproton conductors, etc.

Temperature dependences of phonon and mobile-ion spectra in superionic conductor CuBr

The temperature dependence of far-infrared reflectivity spectra in sintered CuBr has been measured from 18 to 570 K. Phonon and mobile-ion parameters are evaluated by the fitting procedure with the factored form of the dispersion relation. A strong fourth order anharmonicity is assigned. Estimated values of optical dielectric constant and optical ionic mobility μ op decrease with increasing temperature within a limited temperature region. For μ op value, the effects of mobile ion scattering by optical phonons and of the expansion of interionic distance are discussed with respect to the phonon damping constant and the ionic character of the interionic force.

Characterization of anharmonicities on complex potential energy surfaces: Perturbation theory and simulation

We have systematically investigated the effect of anharmonicity on the equilibrium properties of systems with a complex potential energy surface. Anharmonicities are modeled by the temperature dependence of the harmonic frequencies {νi} near a stationary point of the PES. The low-temperature behavior is described by a simple thermal expansion ν(i)(β)=ν0(i)[1−α1(i)/β+α2(i)/2β2+⋯], where the coefficients {αj(i)} are obtained from perturbation theory. Using a simple diagrammatic representation, we give the complete expressions for the first two coefficients α1 and α2 in terms of derivatives of the potential. This approach is illustrated for the example of a bulk Lennard-Jones system of 32 particles, in both the solid and the liquid states. We also determine the anharmonic frequencies from reversible-scaling Monte Carlo simulations, which appear particularly well suited to this problem. As an example, we have studied a model biopolymer that exhibits significant first and second order anharmonicities. To show the importance of treating anharmonicities properly, we have calculated the caloric curve (heat capacity) of the quantum Ne13 cluster in both the classical and quantum regimes. For this calculation we have used a superposition approximation and exact anharmonic classical corrections to second order in perturbation theory. When every vibrational mode of each inherent structure is treated separately, we find good agreement between our results and previous quantum Monte Carlo calculations.

Enhanced interionic forces above Tc in ABX 3-type superionic conductors

In order to investigate interionic forces in ABX 3-type superionic conductors, we measure far-infrared reflectivity spectra of CsPbCl 3 in the temperature range from 40 to 381 K. Four phonon bands are observed in the low temperature region, and a contribution of the fourth order anharmonicity to the phonon damping constant is suggested. A rapid increase and decrease in bindings between the frame ions, and between the mobile and frame ions at T c, respectively, are suggested from the long-range force f L, and short-range force f S, that are estimated from the two high frequency bands in CsPbCl 3 and in Ag 3SX (X=Br, I), using the point charge model. These forces are related to several relationships for the ion conduction.

Initial Condition Sensitivity in Photoinduced Structural Phase Transitions – An Iterative Equation for Exciton Proliferation during Lattice Relaxation –

We theoretically study lattice relaxation dynamics of photogenerated excitons, which proliferate during this relaxation, and finally result in a macroscopic excited domain in insulating solids. This macroscopic domain formation phenomenon is usually called “photoinduced structural phase transition (PSPT)”. According to recent experiments, occurrence or nonoccurrence of this PSPT is found to depend very sensitively on the way of the photoexcitation, even if the total absorbed photonic energy is same. It is nothing else but “initial condition sensitivity” peculiar to nonlinear systems. We concentrate our attention on this sensitivity, and investigate criticality of this proliferation, using an iterative equation for its time evolution. As one of the models describing such a sensitivity, we consider a 1-dimensional strongly coupled many exciton-Einstein phonon system interacting with a reservoir. In our system, excitons can proliferate through their third order anharmonicity. This anharmonicity originates from the long range Coulomb interaction among electrons and holes constituting excitons. Within the Markov approximation for the reservoir, the time evolution of the density matrix of this exciton-phonon system is investigated full-quantummechanically. In order to overcome numerical complexities, we solve our iterative equation for the proliferation by the following principle. We always focus only on the most front of the expanding photoinduced domain, and the contributions from the other excitons, not in this front, are approximated by a mean field. As the proliferation proceeds, this front moves. Accordingly, we, step by step, iterate this procedure till the excess phonon energy, initially given by the photoexcitation, is exhausted. Thus, we can investigate the whole process of the time evolution of the domain formation, until this domain contains a large number of excitons. As for the aforementioned initial condition sensitivity, we cast the difference of the initial conditions into the difference of the initial distance between adjacent photogenerated excitons. Net proliferation is concluded to occur only when this initial distance is moderate, being not too small nor too large. This sensitivity to the initial distance results from the aforementioned third order anharmonicity.

Harmonic and anharmonic thermal vibrations in cubic ZnSe

Abstract The parameters of the interatomic one-particle potentials of cubic ZnSe were determined experimentally unsing X-ray diffraction methods. The harmonic force constants α of zinc and selenium were obtained from the temperature dependence of mean square displacements evaluated from the intergrated intensities of selected reflections between 50 K and 300 K at a wavelength of λ = 0.806 Å. Least squares analysis of the experimental data yields the room temperature mean square displacements 〈u 2 Zn〉 = 0.0129(10)Å2 and 〈u2 Se〉 = 0.0115(10)Å2 i.e. harmonic force constants α Zn = 3.21(1) · 10-19 J Å-2 and α Se = 3.60(1) · 10-19 J Å-2, respectively. The third order anharmonicity constant β was determined exploiting the energy dependence of the Bijvoet ratio between the reflections 666 and 6̅6̅6̅ near the K-absorption edge of Se. It amounts to β Zn = 1.48(15) · 10-19 J Å-3 assuming β Zn = -β Se. The coefficients of the one-particle potentials of the series Ge, GaAs and ZnSe α and β decreases with rising ionicity.

Infrared spectra of weak H-bonds: beyond an adiabatic description of Fermi resonances

We extend a quantum non-adiabatic treatment of damped weak H-bonds [P. Blaise, O. Henri-Rousseau, Chem. Phys., Vol. 243 (1999) 229] in order to account for Fermi resonances. We write the Hamiltonian whose potential part is a straight consequence of the linear modulation of the X– H → ⋯ Y stretching frequency by the X ← –H⋯ Y → intermonomer motion. We obtain the spectral density corresponding to this Hamiltonian by Fourier transform of the autocorrelation function of the dipole moment of the fast stretching mode. The changes which are due to the adiabatic corrections are discussed by comparing with previous adiabatic studies [O. Henri-Rousseau, D. Chamma, Chem. Phys. 229 (1998) 37]. The theoretical handling of Fermi resonances is analyzed, which leads us to define an `exchange approximation' which was implicitly used in these adiabatic studies. The non-adiabatic treatment proposed here is a starting point toward the description of stronger H-bonds for which the adiabatic separation must be overcome. The account for higher order anharmonicities will then give to the details of the theoretical spectra a meaningful role in the interpretation of experimental data.

Hot luminescence of self-trapped excitons in Xe crystal under X-ray and two-photon laser excitation

A nonperturbative theory of anharmonic multiphonon decay of strong local vibration in crystal is developed, which predicts sharp acceleration of the process caused by cubic anharmonicity near characteristic amplitudes (typically A∼0.3 Å), and abrupt switching-off of the processes caused by higher order anharmonicities at larger amplitudes (typically A∼1 Å). The first experimental observation of such a process is reported: strong acceleration of two-phonon decay of Xe2∗ quasi-molecules is found in solid xenon. The experiment is based on X-ray and two-photon laser excitation (using an excimer laser emitting at 193 and 248 nm) of hot luminescence of Xe2∗.

Rippled Commensurate Phases in DIFFOUR Model: Continuum Approximation

Landau potential functional is derived for type-I commensurate- incommensurate phase transitions that appear in the phase diagram of a simple discrete model with fourth order anharmonicity (DIFFOUR model). Coefficients of the lowest order terms (including the usual Lifshitz and lock-in terms) are given explicitly for the rippled (polar) phases with the period p = 3, 5 and 7 sites.

An International Standard Equation of State for Difluoromethane (R-32) for Temperatures from the Triple Point at 136.34 K to 435 K and Pressures up to 70 MPa

A fundamental equation of state for the Helmholtz free energy of R-32 (difluoromethane) is presented which is valid from the triple point at 136.34 K to 435 K and pressures up to 70 MPa. It is based on accurate measurements of pressure-density-temperature (p,ϱ,T), speed of sound, heat capacity, and vapor pressure currently available. New values for the isobaric heat capacity cp∘ of the ideal gas calculated from spectroscopic data taking into account also first order anharmonicity corrections are presented. The Helmholtz free energy equation of state has 19 coefficients and represents all selected experimental data within their estimated accuracy with the exception for heat capacities and speed of sound in the region close to the critical point. Typical uncertainties are ±0.05% for density, ±0.02% for the vapor pressure and ±0.5%–1% for the heat capacity. This equation of state has been compared to equations developed by other research groups by Annex 18 of the International Energy Agency and has been selected as an international standard formulation for the thermodynamic properties of R-32 by this group.