Phonon Contribution Research Articles

Electronic thermal transport measurement in low-dimensional materials with graphene non-local noise thermometry.

In low-dimensional systems, the combination of reduced dimensionality, strong interactions and topology has led to a growing number of many-body quantum phenomena. Thermal transport, which is sensitive to all energy-carrying degrees of freedom, provides a discriminating probe of emergent excitations in quantum materials and devices. However, thermal transport measurements in low dimensions are dominated by the phonon contribution of the lattice, requiring an experimental approach to isolate the electronic thermal conductance. Here we measured non-local voltage fluctuations in a multi-terminal device to reveal the electronic heat transported across a mesoscopic bridge made of low-dimensional materials. Using two-dimensional graphene as a noise thermometer, we measured the quantitative electronic thermal conductance of graphene and carbon nanotubes up to 70 K, achieving a precision of ~1% of the thermal conductance quantum at 5 K. Employing linear and nonlinear thermal transport, we observed signatures of energy transport mediated by long-range interactions in one-dimensional electron systems, in agreement with a theoretical model.

Quantitatively predicting modal thermal conductivity of nanocrystalline Si by full-band Monte Carlo simulations

Thermal transport of nanocrystalline Si is of great importance for the application of thermoelectrics. A better understanding of the modal thermal conductivity of nanocrystalline Si will be expected to benefit the efficiency of thermoelectrics. In this work, the variance reduced Monte Carlo simulation with full band of phonon dispersion is applied to study the modal thermal conductivity of nanocrystalline Si. Importantly, the phonon modal transmissions across the grain boundaries which are modeled by the amorphous Si interface are calculated by the mode-resolved atomistic Greens function method. The predicted ratios of thermal conductivity of nanocrystalline Si to that of bulk Si agree well with that of the experimental measurements in a wide range of grain size. The thermal conductivity of nanocrystalline Si is decreased from 54 percent to 3 percent and the contribution of phonons with mean free path larger than the grain size increases from 30 percent to 96 percnet as the grain size decreases from 550 nm to 10 nm. This work demonstrates that the full band Monte Carlo simulation using phonon modal transmission by the mode-resolved atomistic Greens function method can capture the phonon transport picture in complex nanostructures, and therefore can provide guidance for designing high performance Si based thermoelectrics.

Mechanism of low thermal conductivity for Fe76Si13B8Nb2Cu1 amorphous and nanocrystalline alloys at room temperature

Fe-based amorphous and nanocrystalline alloys offer application prospects in the field of coating materials, and their thermal transport property is crucial for their application in thermal insulation coating. However, the mechanism of thermal conductivity in the process of isothermal annealing preparation of Fe-based nanocrystalline alloys are still unclear. In this work, the thermal conductivity of Fe76Si13B8Nb2Cu1 amorphous alloy isochronal annealed at different temperature was examined. It was found that the thermal conductivity of the amorphous alloy is as low as 7.06 W/mK, whereas significantly increases to 10.38 W/mK after annealing at 693 K for 1800s. The result of the limited increase in thermal conductivity at annealing temperatures below the 693 K can be ascribed to the conflicting variations of electronic and phonon contributions with increasing temperature. At annealing temperature above 693 K, the two contributors start to cooperate, leading to abrupt enhancement of thermal conductivity. This work provides an insight into the thermal transport mechanisms for amorphous alloys.

Thermal conductivity of α-U with point defects

We develop a theoretical model for thermal conductivity of α-U that combines density functional theory calculations and the coupled electron–phonon Boltzmann transport equation. The model incorporates both electron and phonon contributions to thermal conductivity and achieves good agreement with experimental data over a wide temperature range. The dominant scattering mechanism governing thermal transport in α-U at different temperatures is examined. By including phonon–defect and electron–defect scatterings in the model, we study the effect of point defects including U-vacancy, U-interstitial, and Zr-substitution on the thermal conductivity of α-U. The degradation of anisotropic thermal conductivity due to point defects as a function of defect concentration, defect type, and temperature is reported. This model provides insights into the impact of defects on both phonon and electron thermal transport. It will promote the fundamental understanding of thermal transport in α-U and provide a ground for investigation of coupled electron–phonon transport in metallic materials.

Significant phonon anharmonicity drives phase transitions in CsPbI3

Due to its high chemical stability and high power conversion efficiency as a solar cell absorber, the inorganic halide perovskite, CsPbI3, is considered one of the most promising competitors to its hybrid organic-inorganic counterpart, CH3NH3PbI3. However, the phase transition from the photoactive black phase to the inactive yellow phase is a remarkable limitation that harms long-term phase stability. In particular, the phase transitions follow different pathways as the temperature increases and/or decreases, a phenomenon that is anomalous and remains poorly understood. In this study, we systematically calculated the temperature-dependent free energy of CsPbI3 in different crystal phases (α, β, γ, δ) by considering the phonon contribution to the Gibbs free energy. It is found that the free energy results from calculations that include harmonic phonons cannot reproduce experimental observations. Alternatively, we utilized the renormalized phonon quasiparticle approach to derive the free energies of different CsPbI3 phases at finite temperatures. Based on these calculated free energies, whose derivations included the anharmonic effect, we observed phase-transition processes consistent with experimental results. The analysis of the temperature effect on the phonon frequencies further demonstrated that anharmonic effects in the CsPbI3 had a significant influence on its phase transitions.

Lattice thermodynamic behavior in CeO2 from first principles

By combining the first principles with Boltzmann's transport equation, we have carried out a detailed calculation and analysis of the lattice thermal transport properties of CeO2. We found that as the pressure increases, the acoustic mode and optical mode of CeO2 gradually separate and an obvious bandgap appears. In addition, the lattice thermal conductivity increases significantly with increasing pressure, and can be increased from 16.99 W/mK (0 GPa) to 237.73 W/mK (160 GPa) at 300 K. By studying the contribution of phonons to the lattice thermal conductivity at different frequencies, we found that the lattice thermal conductivity of CeO2 is mainly provided by low-frequency phonons (<400 cm−1). Based on this we calculated and studied the phonon group velocity of low-frequency phonons, scattering rate, three-phonon scattering phase space and Grüneisen parameters. The results show that an increase in pressure significantly reduces the three-phonon scattering rate of CeO2 and the anharmonicity of the system, which in turn affect the lattice thermal conductivity seriously. Our work provides a theoretical basis for the subsequent study of CeO2 under high pressure.

Photoluminescence study of solution-deposited Cu2BaSnS4 thin films

To experimentally identify the character of radiative transitions in trigonal Cu2BaSnS4, we conduct temperature and excitation intensity dependent photoluminescence (PL) measurements in the temperature range of 15–300 K. The low-temperature near band edge PL spectrum is interpreted as the free exciton at 2.11 eV and the bound exciton at 2.08 eV, coupled with associated phonon-assisted transitions. In the low energy region, we assign the dominant defect emission at 1.96 eV to donor–acceptor-pair recombination and the weak broad emission at 1.6 eV to the free-to-bound transition. The activation energies and temperature shift for the radiative transitions are determined and discussed. Above 90 K, the free exciton recombination becomes the dominant radiative transition, with its energy shift mainly governed by the contribution of optical phonons.

Impurity Substitution Enhances Thermoelectric Figure of Merit in Zigzag Graphene Nanoribbons

The thermoelectric properties of zigzag graphene nanoribbons (ZGNRs) are sensitive to chemical modification. In this study, we employed density functional theory (DFT) combined with the nonequilibrium green’s function (NEGF) formalism to investigate the thermoelectric properties of a ZGNR system by impurity substitution of single and double nitrogen (N) atoms into the edge of the nanoribbon. N-doping changes the electronic transmission probability near the Fermi energy and suppresses the phononic transmission. This results in a modified electrical conductance, thermal conductance, and thermopower. Ultimately, simultaneous increase of the thermopower and suppression of the electron and phonon contributions to the thermal conductance leads to the significant enhancement of the figure of merit in the perturbed (i.e., doped) system compared to the unperturbed (i.e., nondoped) system. Increasing the number of dopants not only changes the nature of transport and the sign of thermopower but also further suppresses the electron and phonon contributions to the thermal conductance, resulting in an enhanced thermoelectric figure of merit. Our results may be relevant for the development of ZGNR devices with enhanced thermoelectric efficiency.

Differentiating contributions of electrons and phonons to the thermoreflectance spectra of gold

To better understand the many effects of temperature on the optical properties of metals, we experimentally and theoretically quantify the electron vs. phonon contributions to the thermoreflectance spectra of gold. We perform a series of pump/probe measurements on nanoscale Pt/Au bilayers at wavelengths between 400 and 1000 nm. At all wavelengths, we find that changes in phonon temperature, not electron temperature, are the primary contributor to the thermoreflectance of Au. The thermoreflectance is most sensitive to the electron temperature at wavelength of ~480 nm due to interband transitions between d-states and the Fermi-level. In the near infrared, the electron temperature is responsible for only ~2% of the total thermoreflectance. We also compute the thermoreflectance spectra of Au from first principles. Our calculations further confirm that phonon temperature dominates thermoreflectance of Au. Most of Au's thermoreflectance is due to the effect of the phonon population on electron lifetime.

Pressure Tunable Electronic Bistability in Fe(II) Hofmann-like Two-Dimensional Coordination Polymer [Fe(Fpz)2Pt(CN)4]: A Comprehensive Experimental and Theoretical Study.

A comprehensive experimental and theoretical study of both thermal-induced spin transition (TIST) as a function of pressure and pressure-induced spin transition (PIST) at room temperature for the two-dimensional Hofmann-like SCO polymer [Fe(Fpz)2Pt(CN)4] is reported. The TIST studies at different fixed pressures have been carried out by magnetic susceptibility measurements, while PIST studies have been performed by means of powder X-ray diffraction, Raman, and visible spectroscopies. A combination of the theory of elastic interactions and numerical Monte Carlo simulations has been used for the analysis of the cooperative interactions in TIST and PIST studies. A complete (T, P) phase diagram for the compound [Fe(Fpz)2Pt(CN)4] has been constructed. The critical temperature of the spin transition follows a lineal dependence with pressure, meanwhile the hysteresis width shows a nonmonotonic behavior contrary to theoretical predictions. The analysis shows the exceptional role of the total entropy and phonon contribution in setting the temperature of the spin transition and the width of the hysteresis. The anomalous behavior of the thermal hysteresis width under pressure in [Fe(Fpz)2Pt(CN)4] is a direct consequence of a local distortion of the octahedral geometry of the Fe(II) centers for pressures higher than 0.4 GPa. Interestingly, there is not a coexistence of the high- and low-spin (HS and LS, respectively) phases in TIST experiments, while in PIST experiments, the coexistence of the HS and LS phases in the metastable region of the phase transition induced by pressure is observed for a first time in a first-order gradual spin transition with hysteresis.

Polarization, specific heat, band gap and phonon energy of multiferroic GaV[formula omitted]S[formula omitted

The recently experimentally observed multiferroic properties of GaV4S8 are studied using a microscopic model and a Green’s function technique. The polarization P in 〈111〉 direction is saturated at low temperatures. For higher temperatures P increases and goes through a maximum at TN∼ 13 K, then decreases strongly approaching the phase transition temperature Tfe. The polarization decreases by increasing an external magnetic field h and at higher h values the maximum vanishes. The specific heat Cp shows two maxima, at TN and TJT. Cp(h) is also observed. We have discussed the electronic and phonon contributions to Cp in dependence on the temperature region. The phonon energy ω for the phonon mode at 440 cm−1 and their damping γ are also calculated in dependence on temperature T and magnetic field h. P(h) and ω(h) is an evidence for the multiferroic behavior. The temperature dependence of the band gap energy for GaV4S8 and GaNb4S8 is obtained.

Tuning the phonon transport in bilayer graphene to an anomalous regime dominated by electron-phonon scattering

Recent studies have revealed the significance of electron-phonon interaction (EPI) in phonon transport at intermediate temperatures. In some metals, the EPI can even dominate over the anharmonic phonon-phonon (ph-ph) scattering, leading to an anomalous phonon transport regime in which the lattice thermal conductivity ${\ensuremath{\kappa}}_{L}$ becomes nearly temperature ($T$) independent in contrast to the usual $1/T$ dependence. However, the experimental verification of this anomalous transport regime is very challenging due to the difficulty in separating the phonon contributions from the dominating electron ones to the measured total thermal conductivity in metals. In this work, using first-principles calculations, we predict that in bilayer graphene, the phonon transport can be driven to the anomalous regime by tuning the doping level. At high doping levels close to the Van Hove singularity, the EPI can result in a fivefold reduction of ${\ensuremath{\kappa}}_{L}$ at room temperature, and ${\ensuremath{\kappa}}_{L}$ becomes $T$ independent. This anomalous behavior is found to have its origin in three aspects: (i) mirror symmetry breaking enables direct coupling between flexural phonons, the dominant carriers of ${\ensuremath{\kappa}}_{L}$, and electrons; (ii) dominance of normal processes in the anharmonic ph-ph scattering facilitates the EPI to be more prominent; (iii) dominance of these normal ph-ph processes induces the indirect effect of EPI on ${\ensuremath{\kappa}}_{L}$. This is distinct from monolayer graphene, where the mirror symmetry prohibits the direct scattering of the flexural phonons by electrons and only the indirect EPI affects ${\ensuremath{\kappa}}_{L}$. This work gives insight into the manipulation of heat conduction via externally induced EPI in two-dimensional materials in which mirror symmetry breaks and normal processes dominate the ph-ph scattering.

Phononic properties of a periodic nanostructure including vacuum gap in the presence of effective interatomic interactions.

Using the harmonic approximation and Green's function technique, we investigate the contribution of phonons to heat transport across a narrow vacuum gap by an extended mass-spring chain model. We base the investigation on the van Beest-Kramer-van Santen potential that applies to two cases of simple and alternating mass systems at a finite temperature. Employing this model, we show that in specific values of interaction strengths, incoming phonon frequency, and gap distance, the phonon transmission across the vacuum gap can be improved. Finally, the thermal conductance of the system is computed as a function of interaction strength, gap distance, and temperature. These calculations reveal a suitable fitting function that can provide valuable insight into determining the internal interaction strengths from this quantity or controlling it by variation of the gap distance.

Extreme near-field heat transfer between gold surfaces

Extreme near-field heat transfer between metallic surfaces is a subject of debate as the state-of-the-art theory and experiments are in disagreement on the energy carriers driving heat transport. In an effort to elucidate the physics of extreme near-field heat transfer between metallic surfaces, this paper presents a comprehensive model combining radiation, acoustic phonon, and electron transport across sub-10-nm vacuum gaps. The results obtained for gold surfaces show that in the absence of bias voltage, acoustic phonon transport is dominant for vacuum gaps smaller than $\ensuremath{\sim}2$ nm. The application of a bias voltage significantly affects the dominant energy carriers as it increases the phonon contribution mediated by the long-range Coulomb force and the electron contribution due to a reduced potential barrier. For a bias voltage of 0.6 V, acoustic phonon transport becomes dominant at a vacuum gap of 5 nm, whereas electron tunneling dominates at sub-nm vacuum gaps. The comparison of the theory against experimental data from the literature suggests that well-controlled measurements between metallic surfaces are needed to quantify the contributions of acoustic phonon and electron as a function of the bias voltage.

Thermal conductivity assessment in a low dimension structure

The thermal conductivity of low dimensional structures remains critical for various applications. These structures can be formed from various thin films. and proper assessment of effective thermal conductivity becomes vital for the stable operation of such structures. Effective thermal conductivity of low dimension structure composing of silicon‑aluminum films is examined incorporating the thermal resistances generated in the structure. Frequency-depended phonon transfer in the structure is considered, and equivalent equilibrium temperature is adopted representing the phonon intensity. Thermal boundary resistance, resistance due to phonon scattering, and interfacial resistance are incorporated to evaluate the overall thermal resistance in the structure. The effective thermal conductivity predicted for the silicon film is compared to that of the results of the early formulation. The findings show that thermal conductivity predictions for the silicon film are in agreement with that presented in the early formulation. The slight differences in both results are because of the contribution of the ballistic phonons to thermal resistance. In addition, enlarging the silicon film thickness in the structure increases the thermal conductivity.

Revisiting the Electronic Structures and Phonon Properties of Thermoelectric Antimonide-Tellurides: Spin–Orbit Coupling Induced Gap Opening in ZrSbTe and HfSbTe

We report theoretical studies based on density functional theory within spin-orbit coupling to explore electronic structures, lattice dynamical properties of ZrSbTe and HfSbTe. With spin−orbit coupling included, our findings reveal that ZrSbTe and HfSbTe exhibit a semiconducting behavior with narrow indirect band gaps of 0.10 eV, and 0.15 eV, respectively. Besides, the lattice dynamical properties revealed that the explored materials based on antimonide−tellurides are dynamically stable. On the basis of electronic structures, the thermoelectric properties were computed using the Landauer-Buttiker formula by considering both electron and phonon contributions in the transport properties calculation. We employed Green’s-function method based on the Green-Kubo-Mori formula, where the thermoelectric properties such as the electrical conductivity σ and thermopower α were estimated in terms of the correlation functions. The present work could be viewed as a significant amendment of the electronic nature of ZrSbTe and HfSbTe that were reported to be metallic in literature.

Thermal properties of ZrB2-TiB2 solid solutions

Zirconium diboride ceramics were prepared with additions of up to 50 vol.% TiB2. The resulting (Zr,Ti)B2 ceramics formed complete solid solutions based on x-ray diffraction. The addition of TiB2 resulted in grain size decreasing from 22 μm for nominally pure ZrB2 to 7 μm for ZrB2–50 vol.% TiB2. The thermal conductivity at 25°C ranged from 93 W/m⋅K for nominally pure ZrB2 to 58 W/m⋅K for ZrB2–50 vol.% TiB2. Thermal conductivity was as high as 67 W/m⋅K for nominally pure ZrB2 at 2000°C, but dropped to 59 W/m K with the addition of 50 vol.% TiB2. Electrical resistivity measurements were used to calculate the electron contribution to thermal conductivity, which was 76 W/m⋅K for nominally pure ZrB2 decreasing to 57 W/m⋅K when 50 vol.% TiB2 was added. The phonon contribution to thermal conductivity did not change significantly for ≤10 vol.% TiB2. Additions of ≥25 vol.% TiB2 reduced the phonon contribution to nearly zero for all temperatures.

Contribution of optical phonons to lattice thermal conductivity in complex structural thermal insulation materials

It has generally been believed that the lattice thermal conductivity (κL) is mainly contributed by acoustic phonons and the contribution of optical phonons can be neglected in crystalline materials. However, in this work, we demonstrate that the contribution of optical phonons play an important role in the complex structural low- κL oxides. The mode-wised κL of three representative oxides, MgO, BaHfO3 and La2Zr2O7, with different structural complexity was calculated using first-principles phonon Boltzmann transport equation (BTE) method. It is found that the contribution of optical phonons become significant as the structural complexity increases. Especially, for La2Zr2O7, the κL is dominated by optical phonons due to the large density of states. Optical phonons exhibit amorphous-like phonon-phonon scattering characteristics that are different from those of acoustic phonons. Furthermore, calculations for materials other than the three representative oxides were conducted and the results confirmed the validity of our conclusions.

The Impact of Vibrational Entropy on the Segregation of Cu to Antiphase Boundaries in Fe3Al

We performed a quantum mechanical study of segregation of Cu atoms toward antiphase boundaries (APBs) in Fe3Al. The computed concentration of Cu atoms was 3.125 at %. The APBs have been characterized by a shift of the lattice along the ⟨001⟩ crystallographic direction. The APB energy turns out to be lower for Cu atoms located directly at the APB interfaces and we found that it is equal to 84 mJ/m2. Both Cu atoms (as point defects) and APBs (as extended defects) have their specific impact on local magnetic moments of Fe atoms (mostly reduction of the magnitude). Their combined impact was found to be not just a simple sum of the effects of each of the defect types. The Cu atoms are predicted to segregate toward the studied APBs, but the related energy gain is very small and amounts to only 4 meV per Cu atom. We have also performed phonon calculations and found all studied states with different atomic configurations mechanically stable without any soft phonon modes. The band gap in phonon frequencies of Fe3Al is barely affected by Cu substituents but reduced by APBs. The phonon contributions to segregation-related energy changes are significant, ranging from a decrease by 16% at T = 0 K to an increase by 17% at T = 400 K (changes with respect to the segregation-related energy difference between static lattices). Importantly, we have also examined the differences in the phonon entropy and phonon energy induced by the Cu segregation and showed their strongly nonlinear trends.

Phonon model of heat radiation into superfluid helium by a solid with a flat surface

This paper reviews the quasiparticle model of superfluid helium and its application to describe heat transfer between a heated solid and superfluid helium. In this case, a problem is considered in which the surface of the heater is flat and the helium is at practically zero temperature. Under these conditions, heat transfer between solid and superfluid helium is determined by the transformation of the phonons of the solid into helium phonons. The work considers certain types of such transformation—elastic processes of phonon transformation, in which the number of phonons is conserved, and inelastic processes, in which the number of phonons changes. The main attention in this work is paid to the development of a quantum-mechanical approach for calculating the contribution of various polarizations phonons of solid to the heat flux formation, its magnitude, and angular distribution. The results of the work are used to explain the experimentally observed features of heat transfer from a heated solid to superfluid helium.