Temperature-dependent Phonon Research Articles

Phonon wave-packet simulations using the quantized definition of energy and a temperature-dependent phonon dispersion relation and phonon density of states.

Wave-packet simulations, regarded as phonon dynamics in the literature, have been used to explore interface conductance problems and to study the frequency-based dynamics of systems of particles. In this work we introduce an extension of the method to improve the postsimulation analysis and to add an energy aspect to the definition of a wave packet. In a wave-packet simulation the most populated frequency activated with the wave packet is known through knowledge of the wave number implemented in the atom displacement equation. The one-to-one correspondence of wave number and frequency is known through the phonon dispersion relation (PDR). We add the temperature dependence of this one-to-one correspondence to the analysis of wave packets through consideration of a temperature-dependent PDR and showed the importance of the temperature-dependent PDR in the wave-packet definition by presenting results considering and neglecting the phenomenon. In addition, the temperature-dependent PDR and the density of states provide us the chance to change the nature of the atomic displacement amplitude as an arbitrary parameter to a tuning knob for the amount of energy it carries and utilize the chance to provide a quantitative measure for the validity of molecular-dynamics simulations considering their classical nature in comparison with the quantum particle picture of phonons.

Davydov Splitting, Resonance Effect and Phonon Dynamics in Chemical Vapor Deposition Grown Layered MoS2

We present comprehensive temperature dependent Raman measurements for chemical vapor deposition grown horizontally aligned layered MoS2 in a temperature range of 4–330 K under a resonance condition. Our analysis of temperature dependent phonon frequency shift and linewidth suggests a finite role of three and four phonon anharmonic effect. We observe Davydov splitting of the out-of-plane (A 1g ) and in-plane () modes for both three layer (3L) and few layer (FL) systems. The number of Davydov splitting components are found more in FL compared to 3L MoS2, which suggests that it increases with an increasing number of layers. Further, Davydov splitting is analyzed as a function of temperature. Temperature evaluation of the Raman spectra shows that the Davydov splitting, especially for A 1g mode, is very strong and well resolved at low temperature. We observe that A 1g mode shows the splitting at low temperature, while mode is split even at room temperature, which suggests a prominent role of A 1g mode in the interlayer interaction at low temperature. Further, an almost 60-fold increase in the intensity of the phonon modes at low temperature clearly shows the temperature dependent tuning of the resonance effect.

Thermodynamic properties ofε-Fe with thermal electronic excitation effects on vibrational spectra

The thermodynamic properties of hcp-iron ({\epsilon}-Fe) are essential for investigating planetary cores' internal structure and dynamic properties. Despite their importance to planetary sciences, experimental investigations of {\epsilon}-Fe at relevant conditions are still challenging. Therefore, ab initio calculations are crucial to elucidating the thermodynamic properties of this system. Here we use a free energy calculation scheme based on the phonon gas model compatible with temperature-dependent phonon frequencies. We investigate the effects of electronic thermal excitations, which introduces a temperature dependence on phonon frequencies, and the implication for the thermodynamic properties of {\epsilon}-Fe at extreme pressure (P) and temperature (T) conditions. We disregard phonon-phonon interactions, i.e., anharmonicity and their effect on phonon frequencies. Nevertheless, the current scheme is also applicable to T-dependent anharmonic frequencies. We conclude that the impact of thermal electronic excitations on vibrational properties is not significant up to ~ 4,000 K at 200 GPa but should not be ignored at higher temperatures or pressures. However, the static free energy, Fst, must always include the effect of thermal excitation fully in a continuum of Ts. Our results for isentropic equations of state show good agreement with data from recent ramp compression experiments up to 1,400 GPa conducted at the National Ignition Facility (NIF).

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.

Observation of a superparamagnetic breakdown in gadolinium chloride filled double-walled carbon nanotubes

In this article, the magnetic properties of gadolinium chloride-filled double-walled carbon nanotubes (GdCl3@DWNTs) in the temperature range 2-300 K are explored. The temperature-dependent phonon frequencies of the G-band were studied from 80-300 K to investigate the effect of temperature on the magnetic ordering. Temperature-dependent susceptibility measurements show that the GdCl3@DWNTs sample has a pronounced superparamagnetic phase from 83 K. The temperature dependence of the G-band frequency for filled tubes exhibited a distinct difference compared to pristine nanotubes, where a sharp phonon hardening at low temperatures was observed. A correlation between the onset temperature of superparamagnetism and the abrupt G-band phonon hardening in the filled tubes was verified. GdCl3@DWNTs were characterized by a finite remnant magnetization at 300 K which decreased as the temperature was lowered because of the presence of the discontinuous magnetic nanoparticles, providing a superparamagnetic contribution characterized by an S-shaped non-saturating hysteresis loop at 2 K. Remarkably, the onset of superparamagnetism, marked by the bifurcation point, occurred at roughly the same temperature where the G-band phonon frequency showed a pronounced hardening at approximately 80 K, indicating a close correlation between phonon modes and spin clusters.

Lattice thermal conductivity of zigzag and armchair black phosphorus: Role of normal phonons

Theoretical investigations of size and temperature dependent normal phonon effects on lattice thermal conductivity of zigzag and armchair black phosphorus are carried out employing Boltzmann transport formalism. The phonons – heat carriers, are assumed to be scattered by resistive processes and conservative normal processes. The effects of normal phonons on scattering rates due to longitudinal and transverse phonons show significant contributions along zigzag and armchair black phosphorus. The transition of resistive scattering regime to combined resistive-normal scattering regime and its demarcation for zigzag and armchair black phosphorus is investigated at practically relevant temperatures. This transition in zigzag and armchair direction shifts towards higher phonon mean free path with decrease in temperature. The size dependent thermal conductivity investigations show considerable contributions of normal phonons in higher dimension samples. Significant reduction in thermal conductivity due to normal phonons is reported and results are compared with recent available experimental data.

Phase Transition-Induced Temperature-Dependent Phonon Shifts in Molybdenum Disulfide Monolayers Interfaced with a Vanadium Dioxide Film.

We report the optical phonon shifts induced by phase transition effects of vanadium dioxide (VO2) in monolayer molybdenum disulfide (MoS2) when interfacing with a VO2 film showing a metal-insulator transition coupled with structural phase transition (SPT). To this end, the monolayer MoS2 directly synthesized on a SiO2/Si substrate by chemical vapor deposition was first transferred onto a VO2/c-Al2O3 substrate in which the VO2 film was prepared by a sputtering method. We compared the MoS2 interfaced with the VO2 film with the as-synthesized MoS2 by using Raman spectroscopy. The temperature-dependent Raman scattering characteristics exhibited the distinct phonon behaviors of the E2g1 and A1g modes in the monolayer MoS2. Specifically, for the as-synthesized MoS2, there were no Raman shifts for each mode, but the enhancement in the Raman intensities of E2g1 and A1g modes was clearly observed with increasing temperature, which could be interpreted by the significant contribution of the interface optical interference effect. In contrast, the red-shifts of both the E2g1 and A1g modes for the MoS2 transferred onto VO2 were clearly observed across the phase transition of VO2, which could be explained in terms of the in-plane tensile strain effect induced by the SPT and the enhancement of electron-phonon interactions due to an increased electron density at the MoS2/VO2 interface through the electronic phase transition. This study provides further insights into the influence of interfacial hybridization for the heterogeneous integration of 2D transition-metal dichalcogenides and strongly correlated materials.

Pressure- and temperature-dependent inelastic neutron scattering study of the phase transition and phonon lattice dynamics in para-terphenyl.

Inelastic neutron scattering has been performed on para-terphenyl at temperatures from 10 to 200 K and under pressures from the ambient pressure to 1.51 kbar. The temperature dependence of phonons, especially low-frequency librational bands, indicates strong anharmonic phonon dynamics. The pressure- and temperature-dependence of the phonon modes suggest a lack of phase transition in the region of 0-1.51 kbar and 10-30 K. Additionally, the overall lattice dynamics remains similar up to 200 K under the ambient pressure. The results suggest that the boundary between the ordered triclinic phase and the third solid phase, reported at lower temperatures and higher pressures, is out of the pressure and temperature range of this study.

Constructing highly sensitive ratiometric nanothermometers based on indirectly thermally coupled levels.

Fluorescence intensity ratio-based temperature sensing with a self-referencing characteristic is highly demanded for reliable and accurate sensing. Lanthanide ions with thermally coupled levels have been widely used for ratiometric temperature sensing. However, these systems suffer from low relative temperature sensitivity and poor luminescence signal discriminability. Herein, the concept of indirectly thermally coupled levels is introduced and employed to actualize high performance temperature sensing. By means of the temperature-dependent phonon-assisted non-radiative relaxation, the 4I13/2 excited state (with infrared emission) of Er3+ can be indirectly thermally coupled with the 4S3/2 excited state (with visible emission) under 808 nm or 980 nm excitation. This is experimentally realized in specially designed NaErF4:10Yb@NaYF4 nanocrystals, and the corresponding ratiometric nanothermometer shows excellent luminescence thermal sensing performance with a maximum relative sensitivity value up to 3.76% K-1 at 295 K.

Temperature-dependent phonon dynamics of Ag3PO4 microcrystals

In this work, we present the study of the temperature-dependent behavior of silver orthophosphate (Ag3PO4) microcrystals using in situ Raman scattering. The Ag3PO4 as-synthesized microcrystals were prepared by the precipitation method and characterized by powder X-ray diffraction (XRD), scanning electron microscopy (SEM), Raman and infrared spectroscopy, and differential scanning calorimetry (DSC). Temperature-dependent phonon dynamics were performed on Ag3PO4 microcrystals and pointed to a first-order phase transition in the temperature range 500–515 °C: Phase I (25–500 °C) → Phase II (515–590 °C). The phase transition is reversible and a temperature hysteresis was observed during the heating – cooling process: Phase II (590–470 °C) → Phase I (455–25 °C). The reversible phase transition is related to the distortion of the tetrahedral symmetry of PO4 caused by the decrease in the crystalline order. DSC analysis confirmed the results of temperature-dependent Raman spectroscopy.

Temperature-dependent phonon lifetimes and thermal conductivity of silicon by inelastic neutron scattering and ab initio calculations

Inelastic neutron scattering on a single crystal of silicon was performed at temperatures from 100 to 1500 K. These experimental data were reduced to obtain phonon spectral intensity at all wave vectors $\stackrel{P\vec}{Q}$ and frequencies $\ensuremath{\omega}$ in the first Brillouin zone. Thermal broadenings of the phonon peaks were obtained by fitting and by calculating with an iterative ab initio method that uses thermal atom displacements on an ensemble of superlattices. Agreement between the calculated and experimental broadenings was good, with possible discrepancies at the highest temperatures. Distributions of phonon widths versus phonon energy had similar shapes for computation and experiment. These distributions grew with temperature but maintained similar shapes. Parameters from the ab initio calculations were used to obtain the thermal conductivity from the Boltzmann transport equation, which was in good agreement with experimental data. Despite the high group velocities of longitudinal acoustic phonons, their shorter lifetimes reduced their contribution to the thermal conductivity, which was dominated by transverse acoustic modes.

Temperature-dependent phonon dynamics and anharmonicity of suspended and supported few-layer gallium sulfide

Phonons play a fundamental role in the electronic and thermal transport of 2D materials which is crucial for device applications. In this work, we investigate the temperature-dependence of A and A Raman modes of suspended and supported mechanically exfoliated few-layer gallium sulfide (GaS), accessing their relevant thermodynamic Grüneisen parameters and anharmonicity. The Raman frequencies of these two phonons soften with increasing temperature with different temperature coefficients. The first-order temperature coefficients θ of A mode is ∼ −0.016 cm−1/K, independent of the number of layers and the support. In contrast, the θ of A mode is smaller for two-layer GaS and constant for thicker samples (∼ −0.006 2 cm−1 K−1). Furthermore, for two-layer GaS, the θ value is ∼ −0.004 4 cm−1 K−1 for the supported sample, while it is even smaller for the suspended one (∼ −0.002 9 cm−1 K−1). The higher θ value for supported and thicker samples was attributed to the increase in phonon anharmonicity induced by the substrate surface roughness and Umklapp phonon scattering. Our results shed new light on the influence of the substrate and number of layers on the thermal properties of few-layer GaS, which are fundamental for developing atomically-thin GaS electronic devices.

Temperature-dependent phonon mode and interband electronic transition evolutions of ε-InSe films derived by pulsed laser deposition

We report the temperature-dependent phonon modes and interband electronic transitions of InSe films on SiO2/Si substrates prepared by pulsed laser deposition. The microstructure results proved the ε phase structure and monochalcogenide phase composition with well-defined hexagonal InSe sheets. The temperature effects on lattice vibrations were discovered by Raman spectra from 123 K to 423 K. The frequency and full width at half maximum of the A2g1(LO) mode show a strong nonlinearity with the temperature. The energy band structure and electron–phonon interaction were studied by temperature-dependent spectroscopic ellipsometry with the aid of the Tauc–Lorentz model. It was found that five electronic transitions around 1.33, 1.61, 2.53, 3.73, and 4.64 eV generally show a redshift trend with the temperature. The present results can provide a valuable reference for future optoelectronic applications of InSe films.

Anharmonicity and Ultralow Thermal Conductivity in Lead-Free Halide Double Perovskites.

The lead-free halide double perovskite class of materials offers a promising venue for resolving issues related to toxicity of Pb and long-term stability of the lead-containing halide perovskites. We present a first-principles study of the lattice vibrations in Cs_{2}AgBiBr_{6}, the prototypical compound in this class and show that the lattice dynamics of Cs_{2}AgBiBr_{6} is highly anharmonic, largely in regards to tilting of AgBr_{6} and BiBr_{6} octahedra. Using an energy- and temperature-dependent phonon spectral function, we then show how the experimentally observed cubic-to-tetragonal phase transformation is caused by the collapse of a soft phonon branch. We finally reveal that the softness and anharmonicity of Cs_{2}AgBiBr_{6} yield an ultralow thermal conductivity, unexpected of high-symmetry cubic structures.

High-temperature structural phase transition and infrared dielectric features of La2CoMnO6

In this paper, we present the temperature-dependent far-infrared reflectivity spectra of partially ordered magnetodielectric La2CoMnO6 from room temperature to 673 K. We demonstrate a clear first-order structural phase transition (SPT) from a monoclinic structure with P21/n symmetry to a rhombohedral phase with R3¯ symmetry from the behavior of the polar phonon modes at TC ∼ 590 K. The temperature-dependent transversal and longitudinal phonon branches, dielectric strengths, and damping of the strongest dielectric modes support the significant contribution of the phonon modes to the SPT and reveal an important lattice anharmonicity, especially for the low-frequency modes. Also, these investigations showed that structural ordering does not inhibit the SPT and provided valuable information regarding the polar phonons and their effects on the intrinsic dielectric constant in double perovskites and related compounds.

Phonon-assisted diffusion in bcc phase of titanium and zirconium from first principles

Diffusion is the underlying mechanism for many complicated materials phenomena, and understanding it is basic to the discovery of novel materials with desired physical and mechanical properties. Certain groups of solid phases, such as the bcc phase of IIIB and IVB metals and their alloys, which are only stable when they reach high enough temperatures and experience anharmonic vibration entropic effects, exhibit "anomalously fast diffusion". However, the underlying reason for the observed extraordinary fast diffusion is poorly understood and due to the existence of harmonic vibration instabilities in these phases the standard models fail to predict their diffusivity. Here, we indicate that the anharmonic phonon-phonon coupling effects can accurately describe the anomalously large macroscopic diffusion coefficients in the bcc phase of IVB metals, and therefore yield a new understanding of the underlying mechanism for diffusion in these phases. We utilize temperature-dependent phonon analysis by combining ab initio molecular dynamics with lattice dynamics calculations to provide a new approach to use the transition state theory beyond the harmonic approximation. We validate the diffusivity predictions for the bcc phase of titanium and zirconium with available experimental measurements, while we show that predictions based on harmonic transition state theory severely underestimates diffusivity in these phases.

First-principles predictions of temperature-dependent infrared dielectric function of polar materials by including four-phonon scattering and phonon frequency shift

Recently, first-principles calculations based on density functional theory have been widely used to predict the temperature-dependent infrared spectrum of polar materials, but the calculations are usually limited to the harmonic frequency (0 K) and three-phonon scattering damping for the zone-center infrared-active optical phonon modes, and fail to predict the high-temperature infrared optical properties of materials such as sapphire ($\ensuremath{\alpha}\ensuremath{-}{\text{Al}}_{2}{\text{O}}_{3}$), GaAs, $\text{Ti}{\text{O}}_{2}$, etc., due to the neglect of high-order phonon scattering damping and phonon frequency shift. In this work, we implemented first-principles calculations to predict the temperature-dependent infrared dielectric function of polar materials by including four-phonon scattering and phonon frequency shift. The temperature-dependent phonon damping by including three- and four-phonon scattering as well as the phonon frequency shift by including cubic and quartic anharmonicity and the thermal expansion effect are calculated based on anharmonic lattice dynamics method. The infrared dielectric function of $\ensuremath{\alpha}\ensuremath{-}{\text{Al}}_{2}{\text{O}}_{3}$ is parameterized, and then the temperature-dependent infrared optical reflectance is determined. We find that our predictions agree better with the experimental data than the previous density functional theory-based methods. This work will help to effectively predict the thermal radiative properties of polar materials at elevated temperature, which is generally difficult to measure, and will enable predictive design of new materials for radiative applications.

Structural phase transition and manifestation of eddy currents in IR reflection spectra of PbSnTe semiconductor films

Infrared reflection spectra of thin (∼60 nm) Pb1−x SnxTe (x = 0.25, 0.53, 0.59) films grown by molecular beam epitaxy on GaAs/CdTe hybrid substrates have been measured at frequencies from 20 to 5500 cm−1 and temperatures from 5 to 300 K. The spectra have been used to determine temperature-dependent transverse phonon and plasmon frequencies in the films, which has made it possible to identify a structural phase transition at TC ≈ 50 K. The plasma frequency of the films has been shown to increase with decreasing band gap on cooling from 300 to 77 K. The increase in plasma frequency is mainly attributable to the increase in carrier concentration and a transition of the carriers from vortex states on the film surface to the valence band.

Microstructure and temperature-dependence of Raman scattering properties of β-(AlxGa1-x)2O3 crystals

Abstract Bulk crystals of β-Ga2O3, (Al0.1Ga0.9)2O3 and (Al0.2Ga0.8)2O3 were grown by the optical floating zone and edge-defined film-fed methods. Their microstructure and temperature-dependent phonon characteristics were investigated systematically by using high resolution X-ray diffraction (HR-XRD) and Raman scattering spectroscopy. HR-XRD results revealed a very good crystalline phase for all the samples. As compared to the pure β-Ga2O3, the interplanar spacings in (Al0.1Ga0.9)2O3 and (Al0.2Ga0.8)2O3 samples are found decreasing with the increase of Al contents – exhibiting distorted lattice structures. Due to the deformations in (AlxGa1-x)2O3, the Raman peaks revealed redshifts and linewidth broadening as the Al composition (x) is increased. The lattice distortion mainly affected the Raman modes in the range of less than 600 cm−1 and had a relatively trivial effect on the modes higher than 600 cm−1. With the increase of temperature, the Raman peaks are also redshifted and linewidth broadened. Similar to a pure β-Ga2O3, our Raman shifts in the two (AlxGa1-x)2O3 crystals revealed quadratic dependence on temperature – showing specific relationships. However, the temperature dependent widening of the Raman active phonons in (AlxGa1-x)2O3 exhibited a convoluted behavior different from β-Ga2O3. The results are significant for further understanding of (AlxGa1-x)2O3 crystals and evaluating its use in device applications.

Magnetodielectricity induced by coexisting incommensurate conical magnetic structure and cluster glass-like states in polycrystalline BaFe10In2O19

Indium doped barium hexaferrite BaFe10In2O19 is shown to exhibit complex magnetic behaviour below 110 K wherein there is a coexistence of a long-range conical magnetic order along with a cluster spin-glass-like state. Temperature dependent dc magnetization measurements reveal that the system exhibits an anomaly around 110 K. Temperature dependent neutron diffraction (ND) measurements measured in the Q-range 0.28–7.35 Å−1 characterize this anomaly as a transition to a longitudinal conical magnetic state from the ferrimagnetic state at room temperature. Ac susceptibility and thermoremanent magnetization relaxation measurements also reveal the existence of cluster spin-glass like behavior below 110 K, indicating coexistence with conical magnetic order. The lattice parameters determined from the analysis of ND data show a sharp change at ∼110 K which is also reflected in the anomalous changes seen in the temperature dependent Raman phonon modes around this temperature. This gives a clear indication of spin lattice coupling in the system. Finally, temperature and magnetic field dependent dielectric constant measurements reveal the occurrence of large magnetodielectric effect (MDE) near 110 K. This intriguing intrinsic magnetodielectric feature can be explained in terms of spin lattice coupling.