Temperature Dependence Of Phonon Frequencies Research Articles

Anharmonic lattice dynamics from vibrational dynamical mean-field theory

We present a vibrational dynamical mean-field theory (VDMFT) of the dynamics of atoms in solids with anharmonic interactions. Like other flavors of DMFT, VDMFT maps the dynamics of a periodic anharmonic lattice of atoms onto those of a self-consistently defined impurity problem with local anharmonicity and coupling to a bath of harmonic oscillators. VDMFT is exact in the harmonic and molecular limits, nonperturbative systematically improvable through its cluster extensions, usable with classical or quantum impurity solvers (depending on the importance of nuclear quantum effects) and can be combined with existing low-level diagrammatic theories of anharmonicity. When tested on models of anharmonic optical and acoustic phonons; we find that classical VDMFT gives good agreement with classical molecular dynamics, including the temperature dependence of phonon frequencies and lifetimes. Using a quantum impurity solver, signatures of nuclear quantum effects are observed at low temperatures. We test the description of nonlocal anharmonicity via cellular VDMFT and the combination with self-consistent phonon (SCPH) theory, yielding the powerful SCPH $+$ VDMFT approach.

Ab initio anharmonic thermodynamic properties of cubic CaSiO3 perovskite

We present an $\textit{ab initio}$ study of the thermodynamic properties of cubic CaSiO$_3$ perovskite (CaPv) over the pressure and temperature range of the Earth's lower mantle. We compute the anharmonic phonon dispersions throughout the Brillouin zone by utilizing the phonon quasiparticle approach, which characterizes the intrinsic temperature dependence of phonon frequencies and, in principle, captures full anharmonicity. Such temperature-dependent phonon dispersions are used to calculate $\textit{ab initio}$ free energy in the thermodynamic limit ($N \rightarrow \infty$) within the framework of the phonon gas model. Accurate free energy calculations enable us to investigate cubic CaPv's thermodynamic properties and thermal equation of state, where anharmonic effects are demonstrated. The present methodology provides an important theoretical approach for exploring phase boundaries, thermodynamic, and thermoelastic properties of strongly anharmonic materials at high pressures and temperatures.

Dynasor—A Tool for Extracting Dynamical Structure Factors and Current Correlation Functions from Molecular Dynamics Simulations

AbstractPerturbative treatments of the lattice dynamics are widely successful for many crystalline materials; however, their applicability is limited for strongly anharmonic systems, metastable crystal structures and liquids. The full dynamics of these systems can, however, be accessed via molecular dynamics (MD) simulations using correlation functions, which includes dynamical structure factors providing a direct bridge to experiment. To simplify the analysis of correlation functions, here the dynasor package is presented as a flexible and efficient tool that enables the calculation of static and dynamical structure factors, current correlation functions as well as their partial counterparts from MD trajectories. The dynasor code can handle input from several major open source MD packages and thanks to its C/Python structure can be readily extended to support additional codes. The utility of dynasor is demonstrated via examples for both solid and liquid single and multi‐component systems. In particular, the possibility to extract the full temperature dependence of phonon frequencies and lifetimes is emphasized.

Anharmonic Origin of the Giant Thermal Expansion of NaBr.

All phonons in a single crystal of NaBr are measured by inelastic neutron scattering at temperatures of 10, 300, and 700K. Even at 300K, the phonons, especially the longitudinal-optical phonons, show large shifts in frequencies and show large broadenings in energy owing to anharmonicity. Abinitio computations are first performed with the quasiharmonic approximation (QHA) in which the phonon frequencies depend only on V and on T only insofar as it alters V by thermal expansion. This QHA is an unqualified failure for predicting the temperature dependence of phonon frequencies, even 300K, and the thermal expansion is in error by a factor of 4. Abinitio computations that include both anharmonicity and quasiharmonicity successfully predict both the temperature dependence of phonons and the large thermal expansion of NaBr. The frequencies of longitudinal-optical phonon modes decrease significantly with temperature owing to the real part of the phonon self-energy from explicit anharmonicity originating from the cubic anharmonicity of nearest-neighbor NaBr bonds. Anharmonicity is not a correction to the QHA predictions of thermal expansion and thermal phonon shifts but dominates the behavior.

High pressure behavior of complex phosphate K2Ce[PO4]2: Grüneisen parameter and anharmonicity properties

Herein we reported structural stability, vibrational and thermal properties of K2Ce[PO4]2, a relatively underexplored complex phosphate of tetravalent Ce4+ from in situ high-pressure Raman spectroscopic investigations up to ~ 28GPa using a diamond anvil cell. The studies identified the soft phonons that lead to a reversible phase transformation above 8GPa, and a phase coexistence of ambient (PI) and high pressure (PII) phases in a wider pressure region 6–11GPa. From a visual representation of the computed eigen vector displacements, the Ag soft mode at 82cm−1 is assigned as a lattice mode of K+ cation. Pressure-induced positional disorder is apparent from the substantial broadening of internal modes and the disappearance of low frequency lattice and external modes in phase PII above 18GPa. Isothermal mode Grüneisen parameters γi of the various phonon modes are calculated and compared for several modes. Using these values, thermal properties such as average Grüneisen parameter, and thermal expansion coefficient are estimated as 0.47, and 2.5 × 10−6K−1, respectively. The specific heat value was estimated from all optical modes obtained from DFT calculations as 314J-mol−1K−1. Our earlier reported temperature dependence of phonon frequencies is used to decouple the “true anharmonic” (explicit contribution at constant volume) and “quasi harmonic” (implicit contribution brought out by volume change) contributions from the total anharmonicity. In addition to the 81cm−1 Ag lattice mode, several other lattice and external modes of PO43- ions are found to be strongly anharmonic.

Uniaxial Negative Thermal Expansion, Negative Linear Compressibility, and Negative Poisson's Ratio Induced by Specific Topology in Zn[Au(CN)2]2.

The well-known idea of "structure determines properties" can be understood profoundly in the case of hexagonal zinc dicyanometalate. Using density functional theory (DFT) calculations, we show the uniaxial negative thermal expansion (NTE) and negative linear compressibility (NLC) properties of Zn[Au(CN)2]2. The temperature dependence of phonon frequencies within the quasi-harmonic approximation (QHA) is investigated. The abnormal phonon hardening (frequency increase on heating) is detected in the ranges of 0-225, 320-345, and 410-430 cm-1, which can be indicative of the unusual physical properties of Zn[Au(CN)2]2. Due to the significance of low-energy phonon frequencies in Zn[Au(CN)2]2, in this work, the corresponding vibrational mode of the lowest-frequency optical phonon at the zone center is analyzed. The specific topology of a springlike framework that will produce the effects of a compressed spring on heating and an extended spring under hydrostatic pressure is identified and leads to the coexistence of uniaxial-NTE and NLC behaviors in Zn[Au(CN)2]2. The distinguishing phonon group velocity along the a axis and c axis facilitates different responses for both the axes under temperature and hydrostatic pressure field. Through an analysis and visualization of the spatial dependence of elastic tensors, it is found that a negative Poisson's ratio (NPR) is presented in all projection planes due to the specific topology.

Coherent optical phonons in pure and Pr3+ doped YAG crystal studied by Optical Kerr Effect spectroscopy: Temperature and concentration dependence

Herewith we present the results of the investigation of coherent phonons in pure and Pr3+ doped YAG crystals, by means of the femtosecond Optical Kerr Effect spectroscopy. In the experiment we have followed the dynamics of the Raman-active phonon modes at different temperatures in range between 263K and 373K and for different dopant concentrations. We found that the temperature dependence of phonon frequencies and lifetimes is linear, which is characteristic for 3-phonon relaxation process. We have used our fit results to calculate the widths of homogeneously broadened Raman lines and to find the anharmonic coupling constants. The observed dependence of phonon frequency and lifetime on dopant concentration is interpreted in terms of small, dopant induced alterations in the crystal structure, where the most influenced modes involve motion of the substituted ion. High precision of the OKE experiment is of great value, as such changes are small and thus hard to measure, when only low doping is possible, which is the case for Pr:YAG.

Doping-induced ferroelectric phase transition in strontium titanate: Observation of birefringence and coherent phonons under ultraviolet illumination

The doping-induced ferroelectric phase transition in Ca-doped ${\text{SrTiO}}_{3}$ is investigated by observing the birefringence and coherent phonons. The structural phase-transition temperature is determined by the birefringence measurement. Coherent phonons of the soft modes are studied by using ultrafast polarization spectroscopy. Two phonon modes are observed to be softened toward the ferroelectric phase-transition point at 28 K and other two phonon modes are observed to be softened toward the structural phase-transition point at 180 K. Another structural deformation at 25 K is found below the ferroelectric phase-transition temperature. From the temperature dependence of phonon frequencies under an ultraviolet (UV) illumination, a shift of the ferroelectric phase-transition point toward the lower temperature side is found. A decrease in phonon frequencies after the UV illumination is also found.

Temperature dependence of atomic relaxation and vibrations for the vicinal Ni(9 7 7) surface: a molecular dynamics study

Using molecular dynamics simulations and a modified analytic embedded-atom method (MAEAM), the relaxations and vibrations of Ni(9 7 7) surface are studied in the temperature range of 100–1500 K, The calculated results for the temperature dependence of phonon frequencies, line-width and the mean square amplitude show that the anharmonic effects are small for temperatures up to 900 K. The calculated interlayer separation for the first and second surface decreases, and the distance along the x direction increases between the topmost and second surface, with increasing temperature. In addition, the calculated layer structure factor indicates that the Ni(9 7 7) surface is well ordered and does not premelt up to a temperature of 1700 K.

Intrinsic lifetimes and anharmonic frequency shifts of long-wavelength optical phonons in polar crystals

Quantitative calculations of phonon lifetimes due to anharmonic three-phonon processes require knowledge of cubic anharmonic coupling coefficients. In order to determine the temperature dependence of phonon frequencies, anharmonic force constants of up to fourth order are needed. In polar crystals, the macroscopic electric field gives rise to nonanalytic terms in these coefficients. It is shown how these non-analytic terms can be determined from other physical quantities including higher-order dipole moments, Raman coefficients, and nonlinear susceptibilities. The contribution of these terms to the intrinsic damping of the long-wavelength optical phonon modes in GaAs has been determined by an ab initio calculation.

Anharmonicity and negative thermal expansion in zirconium tungstate

In order to investigate the anharmonicity of different phonons in the negative thermal expansion material zirconium tungstate, Raman spectroscopic measurements are carried out as a function of temperature over the complete range of stability of $\ensuremath{\alpha}$ phase. The temperature dependence of phonon frequencies and their line widths are analyzed based on known anharmonicity models. The reported pressure dependence of phonon frequencies is used to separate the ``true anharmonic'' (the explicit temperature effect at constant volume) and ``quasiharmonic'' (the implicit effect caused by volume change) contributions to the total anharmonicities. In addition to the $41\ensuremath{-}{\mathrm{cm}}^{\ensuremath{-}1}$ librational mode, several other lattice and bending modes of tungstate ion are found to be strongly anharmonic.

Origin of the phonon anomalies in the C-axis optical spectrum of YBa 2Cu 3O 7−δ

The c-axis optical spectra of YBa 2Cu 3O 7−δ crystals were investigated, mainly focusing on phonon behaviors. Using the crystals with three different oxygen contents, we observed typical phonon spectra for tetragonal (P4/mmm), orthorhombic I (Pmmm), and possibly orthorhombic II structure. In addition to the anomalous temperature dependences of phonon frequencies reported so far, another type of anomaly was found around 400 cm −1 in the oxygen reduced crystal with T c=50K, which might indicate an appearance of an electronic excitation.

Energy Spectrum and Phonon Excitation Damping in Many‐Component Amorphous Solids

AbstractPhonon excitations in many‐component amorphous solids are treated using the Green's function method. The equation for the energy spectrum of phonon excitations is obtained. This equation takes into account the hard core in the interatomic interaction potential, the temperature dependence of phonon frequencies, and their damping, caused by phonon scattering on structure fluctuations. Zeroth approximation is considered in a space with arbitrary dimensionality. In this case it coincides with the quasi‐crystalline one. The explicit expressions for the optic and acoustic modes as well as for the longitudinal and transverse velocity of sound are obtained as example in the two‐component case. In the space of arbitrary dimension the asymptotic of damping is studied for the one‐component system in the long‐wave region. Numerical calculations of the “frequency‐wave vector” dependence are performed for some amorphous metals in the quasi‐crystalline approximation.

The far-infrared response of the ceramic high temperature superconductor YBa 2Cu 4O 8

Far-infrared reflectivity measurements on ceramic samples of YBa 2Cu 4O 8, a high- T c superconductor with T c = 80 K, were made over the temperature range of 20–300 K and frequency range of 20–1000 cm −1. Six phonons were observed at 130 cm −1, 192 cm −1, 300 cm −1 (doublet), 500 cm −1, and 603 cm −1 and their temperature dependences were studied. Through comparisons with 1–2–3 compounds, these phonons were identified and assigned to the respective lattice vibrations of B 1u symmetry (i.e. along the c-axis). The observed temperature dependences of phonon frequencies, lineshapes and reflectivity ratios all point to the existence of two superconducting energy gaps, one in the c direction at about 150 cm −1 and another (somewhat more speculatively) in the ab plane at about 450 cm −1. While the c-axis gap occurs at a nearly BCS-like value of ∼ 2.7 kT c, the a−b plane gap corresponds to ∼ 8 kT c, in agreement with the work of others on single crystals of YBa 2Cu 3O 7.

A study of the isochoric frequency shift of the phonons in Al and Cu

The temperature dependences of phonon frequencies for Al and Cu have been measured under constant volume as a function of the wave vector k by means of inelastic neutron scattering. The isochoric condition was achieved by using high pressure. The common feature of the present results for Al and Cu as well as the previous results for solid Ne by Skalyo et al., is that the frequency shift for k less than 0.5 ( 2π a ) can be expressed as -∝k (1 + 3k 2) , where ∝ is inversely proportional to the melting temperature. This result can be understood by means of a nonlinear wave theory which is based on the modified Korteweg-de Vries equation.

Temperature dependence of phonon-frequencies and — Linewidths for weakly anharmonic molecular crystals

Results of model calculations of the shift of phonon frequencies and of phonon widths with temperature and pressure are compared with experimental results for α-N2 , NH3 , benzene, naphthalene and anthracene. The molecular crystals are assumed to be perfect, neglecting the influence of electronic excitations, impurities and lattice defects. A short description of harmonic models, often used for the lattice dynamics of molecular crystals preceeds the treatment of the models of anharmonic crystal vibrations. Within the framework of the theory shifts and widths are in qualitative, often in quantitative agreement with experiment. At low temperatures the width of external and low energy internal phonons can be nearly always explained by a population relaxation effect.

Raman scattering study of LiNH4C4H4O6·H2O and LiKC4H4O6·H2O crystals

LiNH4C4H4O6·H2O (LAT) and LiKC4H4O6·H2O (LPT) crystals were studied in low temperature region. Anomalous low-lying mode has been observed in LAT and LPT. The results of Raman spectra indicate a phase transition of LPT at ∼50K, where the intensity of the anomalous low-lying mode vanishes and anomalous kinks are observed in temperature dependence of phonon frequencies. The phase transition of LPT has been confirmed by observation of a specific heat anomaly. Possible transition mechanism of LPT and the nature of the low-lying mode are discussed on the basis of comparison between LAT and LPT. It can be concluded that H2O motion plays an important role in the phase transition of LPT.

On the temperature dependence of phonon frequencies in TTF-TCNQ at constant volume

Comparison between napthalene (or anthracene) and TTF-TCNQ indicates that in the latter, the constant volume variation in the frequency of some intermolecular modes agrees with previous estimates required to account for the temperature dependence of the electrical resistivity at constant volume in TTF-TCNQ.

Dephasing times and linewidths of optical transitions in molecular crystals. Temperature dependence of line shapes, linewidths, and frequencies of Raman active phonons in naphthalene

The temperature dependence of linewidths, line shapes, and frequencies is investigated for Raman active librational phonons of naphthalene in order to derive the mechanism of optical dephasing for phonon excitations and to measure their dephasing times. Theoretical background is presented on various manifestations of anharmonic interactions particularly in relation to dephasing and relaxation. For the case of the naphthalene crystal, it is shown that the temperature dependences of the phonon frequencies and of their respective linewidths do not manifest by the same mechanism. The dominant contribution to the temperature dependence of phonon frequencies is from the thermal expansion of the lattice. On the other hand, the line shapes are asymmetric Lorentzian and the temperature dependence of the linewidth is consistent with the dephasing process due to T1 relaxations in which a phonon exchanges energy with two other phonons through cubic anharmonic interaction.

Anharmonicity as an explanation for anomalous resistance of high- Tc superconductors

Experimental evidence about the temperature dependence of phonon frequencies in V 3Si is used to demonstrate that anharmonicity is a major factor in causing the resistance anomalies recently observed in many high- T c superconductors.