Phonon Contribution Research Articles

Disordered layers and dimerization in the crystal structure of TaOCl2

Understanding the properties of transition metal materials requires consideration of the competition between the various types of electrons that comprise the system, whether they be delocalized and metallic, localized and magnetic, or localized and bonded. Here we report the refined crystal structure determination and physical properties of the two-dimensional layered compound TaOCl2. Within each layer we find a strong in-plane dimerization of Ta atoms perpendicular to the Ta-O-Ta chains, with significant disorder in the positioning of dimers in adjacent layers, suggesting that the free electron of each Ta localizes in Ta-Ta bonds. This is supported by resistivity measurements (ρ300K = 4.4*108 Ω-cm) as well as featureless, temperature-independent magnetic susceptibility up to T = 750 K. Analysis of the phonon contribution to specific heat shows the presence of a localized Einstein mode with TE = 175 K, attributed to the localized vibrations of the Ta-Ta dimers. Density functional theory calculations show that the magnitude of the Ta displacements (0.24 Å) has a dramatic effect on the electronic structure, changing from a metal with a bandwidth of 3.2 eV to an insulator with a flat band just below EF. Our results show how direct exchange interactions between Ta atoms that are relatively far from each other can still play a central role in the behavior of 5d transition metal compounds, taking advantage of the extended 5d atomic orbitals, and produce localized dimers with a bond distance of approximately 2.84 Å.

Thermal conductivity reduction due to phonon geometrical scattering in nano-engineered epitaxial germanium

Nano-engineering crystalline materials can be used to tailor their thermal properties. By adding new nanoscale phonon scattering centers and controlling their size, one can effectively decrease the phonon mean free path, hence the thermal conductivity of a fully crystalline material. In this Letter, we use the 3ω method in the temperature range of 100–300 K to experimentally report on the more than threefold reduction of the thermal conductivity of an epitaxially grown crystalline germanium thin film with embedded polydispersed crystalline Ge3Mn5 nano-inclusions with diameters ranging from 5 to 25 nm. A detailed analysis of the structure of the thin film coupled with Monte Carlo simulations of phonon transport highlights the role of the nano-inclusions volume fraction in the reduction of the phononic contribution to the thermal conductivity, in particular its temperature dependence, leading to a phonon mean free path that is set by geometrical constraints.

Elastic and inelastic phonon scattering effects on thermal conductance across Au/graphene/Au interface

Heat dissipation from graphene devices is predominantly limited by heat conduction across the metal contacts with complex phonon scattering. In this work, the effects of elastic and inelastic phonon scattering on the interfacial thermal conductance (ITC) across the Au/graphene/Au interface are studied using both atomistic Green's function (AGF) and reverse non-equilibrium molecular dynamics methods. The results show that the contribution of inelastic phonon scattering to the ITC increases with the enhancement of interfacial bonding strength. Moreover, the overlap of the vibrational density of states across the interface shows that the coupling between the Au layer (adjacent to the Au/graphene interface) and graphene's out-of-plane modes plays the dominant role in ITC across the Au/graphene interface. By comparing the transmission functions calculated with AGF and spectral heat current decomposition methods, the inelastic phonon scattering process facilitates phonon transmission in the lower and higher frequency range but hinders phonon transmission in the intermediate frequency range. It is expected that this study can contribute to a better understanding of the thermal conduction mechanism across the metal/graphene interface, providing guidance for thermal management and heat conduction optimization of graphene in microelectronic devices.

Materials properties of defect-stabilized off-stoichiometric τ-phase Al2Ge2Mg

We have performed a quantum-mechanical study of off-stoichiometric Al2Ge2Mg τ-phase intermetallic compounds. Our calculations focused on evaluating the formation energy of static lattices, their elastic properties as well as free energy of formation including phonon contributions. While the stoichiometric Al2Ge2Mg τ phase was found thermodynamically, mechanically and dynamically stable, we have identified an off-stoichiometric composition Al7Ge8Mg5 which exhibits the free energy of formation lower than the stoichiometric compound. The Al7Ge8Mg5 was found both mechanically and dynamically stable as well. This off-stoichiometric compound has Mg atoms located also at the Al sublattice, i.e. these defects exhibit a stabilizing effect. Phonon contributions into the free energy of formation have turned out to be crucial for a proper description of the thermodynamic stability. In contrast, several other off-stoichiometric states are significantly thermodynamically destabilized by anti-site atoms at the Ge sublattice. The formation energy and the homogenized polycrystal Young's modulus are found anti-correlated indicating a connection between the thermodynamic and mechanical stability. Regarding the theoretical values of homogenized polycrystal Young's moduli, our measurements resulted in values quite close to the predicted ones.

Layered Hydride LiH4 with a Pressure-Insensitive Superconductivity.

For hydride superconductors, each significant advance is built upon the discovery of novel H-based structural units, which in turn push the understanding of the superconducting mechanism to new heights. Based on first-principles calculations, we propose a metastable LiH4 with a wavy H layer composed of the edge-sharing pea-like H18 rings at high pressures. Unexpectedly, it exhibits pressure-insensitive superconductivity manifested by an extremely small pressure coefficient (dTc/dP) of 0.04 K/GPa. This feature is attributed to the slightly weakened electron-phonon coupling with pressure, caused by the reduced charge transfer from Li atoms to wavy H layers, significantly suppressing the substantial increase in the contribution of phonons to Tc. Its superconductivity originates from the strong coupling between the H 1s electrons and the high-frequency phonons associated with the H layer. Our study extends the list of H-based structural units and enhances the in-depth understanding of pressure-related superconductivity.

Glass-Like Phonon Dynamics and Thermal Transport in a GeTe Nano-Composite at Low Temperature.

In this work, the experimental evidence of glass-like phonon dynamics and thermal conductivity in a nanocomposite made of GeTe and amorphous carbon is reported, which is of interest for microelectronics, and specifically phase change memories. It is shown that, the total thermal conductivity is reduced by a factor of three at room temperature with respect to pure GeTe, due to the reduction of both electronic and phononic contributions. This latter, similarly to glasses, is small and weakly increasing with temperature between 100 and 300 K, indicating a mostly diffusive thermal transport and reaching a value of 0.86(7)Wm-1K-1 at room temperature. A thorough investigation of the nanocomposite's phonon dynamics reveals the appearance of an excess intensity in the low energy vibrational density of states, reminiscent of the Boson peak in glasses. These features can be understood in terms of an enhanced phonon scattering at the interfaces, due to the presence of elastic heterogeneities, at wavelengths in the 2-20 nm range. The findings confirm recent simulation results on crystalline/amorphous nanocomposites and open new perspectives in phonon and thermal engineering through the direct manipulation of elastic heterogeneities.

Thermal, optoelectronic and thermoelectric properties of inorganic double perovskites semiconductors Cs2(Sn, Pt, Te)I6 for application as intermediate-band solar cells

First-principle calculations using the Wien2k code and the GGA-mBJ exchange potential were used in the study of the thermodynamic, dynamic, chemical and elastic stability, as well as the electronic, optical and thermoelectric properties of Cs2(Sn, Pt, Te)I6. The presence of an intermediate band in Cs2(Sn, Pt, Te)I6 semiconductors confirmed by absorption peaks appeared at photon energy corresponding to the band gap enhances the efficiency of solar cells. The ideal band gap, high dielectric constants and optimal absorption make the double perovskites under study perform well in solar cells. The calculated minimum formation energy, Helmholtz free energy and phonon modes through the first Brillouin zone for the investigated Cs2(Sn, Pt, Te)I6 family confirm their thermal, thermodynamic and dynamic stability. The acoustic phonon contribution modes come from the Cs-6s and I-5p electrons, while the Pt-6s, Sn-5p, Te-5p and I-5p electrons participate in the optical phonon modes. The narrowness of the upper valence band and the band gap in the visible region for Cs2PtI6 advantage this double perovskite in energy harvesting. The geometric Goldschmidt tolerance factor value between 0.8 and 1.0 and octahedral factor 0.41 indicate that Cs2SnI6 double perovskite is more stable.

Ultralow Glassy Thermal Conductivity and Controllable, Promising Thermoelectric Properties in Crystalline o-CsCu5S3.

We thoroughly investigated the anharmonic lattice dynamics and microscopic mechanisms of the thermal and electronic transport characteristics in orthorhombic o-CsCu5S3 at the atomic level. Taking into account the phonon energy shifts and the wave-like tunneling phonon channel, we predict an ultralow κL of 0.42 w/mK at 300 K with an extremely weak temperature dependence following ∼T-0.33. These findings agree well with experimental values along with the parallel to the Bridgman growth direction. The κL in o-CsCu5S3 is suppressed down to the amorphous limit, primarily due to the unconventional Cu-S bonding induced by the p-d hybridization antibonding state coupled with the stochastic oscillation of Cs atoms. The nonstandard temperature dependence of κL can be traced back to the critical or dominant role of wave-like tunneling of phonon contributions in thermal transport. Moreover, the p-d hybridization of Cu(3)-S bonding results in the formation of a valence band with "pudding-mold" and high-degeneracy valleys, ensuring highly efficient electron transport characteristics. By properly adjusting the carrier concentration, excellent thermoelectric performance is achieved with a maximum thermoelectric conversion efficiency of 18.4% observed at 800 K in p-type o-CsCu5S3. Our work not only elucidates the anomalous electronic and thermal transport behavior in the copper-based chalcogenide o-CsCu5S3 but also provides insights for manipulating its thermal and electronic properties for potential thermoelectric applications.

Heat Capacity and Features of the Phonon Spectrum of Single Crystals of Solid Solutions of Yttrium–Lutetium Aluminum Garnets

The temperature dependences of the heat capacity were measured and the general patterns of the formation of the phonon spectrum of single crystals of solid solutions of yttrium-lutetium aluminum garnets Y3 – xLuxAl5O12 at 0 ≤ x ≤ 3 were investigated in the temperature range from 1.9 to 220 K. According to the data obtained at temperatures below 10 K, the Debye temperatures were calculated. The features of the phonon spectrum in the intermediate temperature range are interpreted as a superposition of optical modes for yttrium and lutetium garnets. It is shown that the low heat capacity values due to the contribution of acoustic phonons for Y2.25Lu0.75Al5O12 correlate with anomalies in the concentration dependences of the phonon transport, the absorption of acoustic waves, and the shape of the aluminum NMR line.

First-principles calculations of electronic, vibrational, and thermodynamic properties of nitrogen-rich salt of 3,6-dinitramino-1,2,4,5-tetrazine [(DAG)2(DNAT)·H2O

In recent years, nitrogen-rich salts as green and efficient energetic materials have garnered widespread attention. This study focuses on a novel green synthesized salt, (DAG)2(DNAT)·H2O, which obtained through DNAT synthesis. Employing first-principles calculations, we conducted theoretical investigations to elucidate the electronic structure, vibrational, and thermodynamic properties of (DAG)2(DNAT)·H2O. Our computed lattice parameters align with experimental values from literature data. Analysis of the band structure and electronic states of atoms within the compound was performed. Vibrational modes for each peak in the infrared and Raman spectra were meticulously described, accompanied by phonon dispersion curves and phonon density of states plots for phonon contribution analysis. Thermochemical functions including enthalpy (H), heat capacity at constant volume (CV), Helmholtz free energy (F), Debye temperature (θ), and entropy (S) were computed based on vibrational characteristics, providing essential references for future research endeavors.

Tailoring-compensated ferrimagnetic state and anomalous Hall effect in quaternary Mn–Ru–V–Ga Heusler compounds

Abstract Cubic Mn2Ru x Ga Heusler compound is a typical example of compensated ferrimagnet with attractive potential for high-density, ultrafast, and low-power spintronic applications. In the form of epitaxial thin films, Mn2Ru x Ga was shown to exhibit high spin polarization and high tunability of compensation temperature by freely varying the Ru content x over a broad range (0.3 < x < 1.0). Here, we systematically studied Mn-Ru-Ga-based polycrystalline bulk buttons prepared by arc melting and found that, in equilibrium bulk form, the cubic structure is unstable when x < 0.75. To overcome this limitation, we alloyed Mn-Ru-Ga with a fourth element V. By adjusting the content of V in the Mn2Ru0.75V y Ga and Mn2.25-y Ru0.75V y Ga quaternary systems, the magnetic compensation temperature was regulated. Compensation was achieved near 300 K which was confirmed by both the magnetic and anomalous Hall effect measurements. Analyses of the anomalous Hall effect scaling in quaternary Mn-Ru-V-Ga alloys revealed the dominant role of skew scattering, notably that contributed by the thermally excited phonons, in contrast to many other 3d ferromagnets and Heusler compounds. We further showed that the Ga antisites and V content can simultaneously control the residual resistivity ratio (RRR) as well as the relative phonon and defect contribution to the anomalous Hall effect a’’/a’ in Mn-Ru-V-Ga, leading to a scaling relation a’’/a’ ∝ RRR1.8.

Yb0.5Ca0.75Si7.5Al4.5O1.5N14.5 α-SiAlON ceramics: A hard material with low thermal conductivity

High hardness is desirable for thermal insulation materials in various applications to improve wear resistance. However, hard materials like diamond, Si3N4, and SiC are often accompanied by high thermal conductivity, due to their strong covalent bonds and high Young’s modulus, which increase sound velocity and benefit heat transportation. How to achieve concurrent high hardness and low thermal conductivity remains a challenge in thermal insulation materials. In this work, we report (Yb+Ca) co-doped α-SiAlON (Yb0.5Ca0.75Si7.5Al4.5O1.5N14.5, a solid solution of α-Si3N4) with a low thermal conductivity of 3.4 W/(m·K) and a hardness of 18.1 GPa at 25℃. The thermal conductivity of α-SiAlONs co-doped by (Yb+Nd/Lu) were also studied, and we found that phonon scattering could be significantly increased only when there was a remarkable difference in cation mass and radius between the co-doping cations, like that between Yb3+ and Ca2+. Additionally, high-entropy α-SiAlONs co-doped by five kinds of cations were studied (e.g., Nd0.1Gd0.1Dy0.1Er0.1Yb0.1Si9.5Al2.5ON15), and we found that the high-entropy strategy is not so effective in pursuing low thermal conductivity in α-SiAlONs. The contribution of different phonon scattering mechanisms in the α-SiAlONs was discussed based on inverse thermal diffusivity. Compared with most other ceramics (e.g., 8YSZ and rare-metal zirconates) with low thermal conductivity, (Yb+Ca) co-doped α-SiAlON has a lower bulk density, higher hardness, and higher toughness, which makes it a potential candidate material for applications requiring both thermal insulation and good mechanical properties.

Linear electro-optic effect in strontium barium niobate: A first principles study

We report a first-principles study of the linear electro-optic or Pockels effect in SrxBa1-xNb2O6 (SBN). SBN is an attractive material for building electro-optic modulators in silicon photonics as it has one of the highest known Pockels coefficients and can be integrated on Si. We investigate the microscopic mechanism behind the giant Pockels effect and find that the optical phonon contribution dominates the electro-optic response. We identify the phonon modes that have a significant contribution to the Pockels response and discuss the microscopic origin of the response. In addition, we analyze the contribution of the converse piezoelectric effect to the Pockels response. We find good agreement when comparing our results to available experiment.

Phonon-assisted carrier transport and indirect optical absorption of cubic boron nitride from first-principles

Inquiring the isotopically engineered carrier transport in polar materials remains an open question. Herein, the phonon-limited drift carrier mobility of single-crystal cubic boron nitride is presented using first-principles calculations. Natural c-BN has the predicted electron mobility of 1230 and 760 cm2/V s by solving the iterative Boltzmann transport equation and self-energy relaxation time approximation, respectively. The hole mobility under the Boltzmann transport equation and self-energy relaxation time approximation is 193 and 105 cm2/Vs, respectively. Subsequently, the electron and hole mobilities at the stable isotope levels of boron and nitride are predicted, and nitride isotopes are found to be more effective than boron for carrier mobility. Those carrier mobilities further decrease with increasing temperature due to the strengthened electron–phonon interactions. Moreover, the phonon-assisted indirect optical absorption of c-BN is investigated by considering the contribution of phonons to the indirect electronic inter-band transitions. The predicted imaginary part of the dielectric function is in better agreement with previous experiments. This work aims to understand the role of phonons in determining the carrier mobility and indirect optical absorption of c-BN.

First principle calculation of thermoelectric transport performances of new dual transition metal MXene

The quantum restriction effect of charge carriers in two-dimensional materials can significantly improve their power factors. MXene, as a new type of two-dimensional double transition metal material, has attracted extensive attention due to thermoelectric properties, and higher controllability than single transition metal MXene, which has potential applications in thermoelectric devices. In this work, new two-dimensional monolayer double transition metal MXene, i.e. TiZrCO<sub>2</sub> and VYCO<sub>2</sub>, are designed and their stabilities, electronic and thermoelectric properties are studied by the first principles and Boltzmann transport theory. It has been shown that both are indirect bandgap semiconductors with mechanical, thermodynamic and kinetic stability, and their thermoelectric properties (Seebeck coefficients, electrical and electronic thermal conductivities and lattice thermal conductivities) in a temperature range from 300 K to 900 K are studied. For the optimal carrier concentration at 300 K, the p-type TiZrCO<sub>2</sub> power factor is 11.40 mW/(m·K<sup>2</sup>), much higher than that of n-type one, and the VYCO<sub>2</sub> power factor of p-type (2.80 mW/(m·K<sup>2</sup>)) and n-type (2.20 mW/(m·K<sup>2</sup>)) are similar to each other. At 300 K, TiZrCO<sub>2</sub> and VYCO<sub>2</sub> have low lattice thermal conductivities of 5.08 W/(m·K) and 3.22 W/(m·K), respectively, and the contributions of optical phonon to the lattice thermal conductivity are both about 30%, i.e. 2.14 W/(m·K) and 1.09 W/(m·K) at 900 K, respectively. At the same time, it is found that at 300 K, when the material sizes of TiZrCO<sub>2</sub> and VYCO<sub>2</sub> are within 12.84 nm and 5.47 nm respectively, their lattice thermal conductivities are almost unchanged, and can be adjusted by adjusting the compositions. At 900 K, the thermoelectric value of p-type TiZrCO<sub>2</sub> and VYCO<sub>2</sub> reach 1.83 and 0.93, respectively, which are better than those of n-type, 0.23 and 0.84. The double transition metals MXene TiZrCO<sub>2</sub> and VYCO<sub>2</sub> have better thermoelectric properties than the single transition metal MXene (such as Sc<sub>2</sub>C(OH)<sub>2</sub>, <i>ZT</i> = 0.5), and have the potential applications in new thermoelectric materials with excellent comprehensive properties. A set of calculation methods used in this paper can also provide some reference for exploring the thermoelectric properties of a new double transition metal element MXene.

Recent progress and frontier issues in thermal transport theory of metals

Metal is one of the most widely used engineering materials. In contrast to the extensive research dedicated to their mechanical properties, studies on the thermal conductivity of metals remain relatively rare. The understanding of thermal transport mechanisms in metals is mainly through the Wiedemann-Franz Law established more than a century ago. The thermal conductivity of metal is related to both the electron transport and the lattice vibration. An in-depth understanding of the thermal transport mechanism in metal is imperative for optimizing their practical applications. This review first discusses the history of the thermal transport theory in metals, including the Wiedemann-Franz law and models for calculating phonon thermal conductivity in metal. The recently developed first-principles based mode-level electron-phonon interaction method for determining the thermal transport properties of metals is briefly introduced. Then we summarize recent theoretical studies on the thermal conductivities of elemental metals, intermetallics, and metallic ceramics. The value of thermal conductivity, phonon contribution to total thermal conductivity, the influence of electron-phonon interaction on thermal transport, and the derivation of the Lorenz number are comprehensively discussed. Moreover, the thermal transport properties of metallic nanostructures are summarized. The size effect of thermal transport and the Lorenz number obtained from experiments and calculations are compared. Thermal transport properties including the phonon contribution to total thermal conductivity and the Lorenz number in two-dimensional metals are also mentioned. Finally, the influence of temperature, pressure, and magnetic field on thermal transport in metal are also discussed. The deviation of the Lorenz number at low temperatures is due to the different electron-phonon scattering mechanisms for thermal and electrical transport. The difference in thermal conductivity among metals is induced by the difference in pressure among different metals and is related to the electron state at the Fermi level as well. The effect of magnetic field on thermal transport is related to the coupling between the electron and the magnetic field, therefore the electron distribution in the Brillouin zone is an important factor. In addition, this review also looks forward to the future research directions of metal thermal transport theory.

Strain effects on Auger–Meitner recombination in silicon

We study the effects of compressive and tensile biaxial strain on direct and phonon-assisted Auger–Meitner recombination (AMR) in silicon using first-principles calculations. We find that the application of strain has a non-trivial effect on the AMR rate. For most AMR processes, the application of strain increases the AMR rate. However, the recombination rate for the AMR process involving two holes and one electron is suppressed by 38% under tensile strain. We further analyze the specific phonon contributions that mediate the phonon-assisted AMR mechanism, demonstrating the increased anisotropy under strain. Our results indicate that the application of tensile strain increases the lifetime of minority electron carriers in p-type silicon and can be leveraged to improve the efficiency of silicon devices.

Elemental partitioning and corrosion resistance of Ni–Cr alloys revealed by accurate ab-initio thermodynamic and electrochemical calculations

Elemental partitioning during thermal processing can significantly affect the corrosion resistance of bulk alloys operating in aggressive electrochemical environments, for which, despite decades of experimental and theoretical studies, the thermodynamic and electrochemical mechanisms still lack accurate quantitative descriptions. Here, we formulate an ab initio thermodynamic model to obtain the composition- and temperature-dependent free energies of formation (ΔfG) for Ni–Cr alloys, a prototypical group of corrosion-resistant metals, and discover two equilibrium states that produce the driving forces for the elemental partitioning in Ni–Cr. The results are in quantitative agreement with the experimental studies on the thermodynamic stability of Ni–Cr. We further construct electrochemical (potential–pH) diagrams by obtaining the required ΔfG values of native oxides and (oxy)hydroxides using high-fidelity ab-initio calculations that include exact electronic exchange and phononic contributions. We then analyze the passivation and electrochemical trends of Ni–Cr alloys, which closely explain various oxide-film growth and corrosion behaviors observed on alloy surfaces. We finally determine the optimal Cr content range of 14–34 at%, which provides the Ni–Cr alloys with both the preferred heat-treatment stability and superior corrosion resistance. We conclude by discussing the consequences of these findings on other Ni–Cr alloys with more complex additives, which can guide the further optimization of industrial Ni–Cr-based alloys.

Thermoelectric properties of La1.96Sr0.04CuO4 for energy harvesting and storage applications

AbstractThe polycrystalline pellet of La2‐xSrxCuO4 with x = 0.04, has been sintered using the solid‐state reaction process. X‐ray diffraction (XRD) and field emission scanning electron microscopy (FESEM) have been carried out for microstructural characterizations. The transport properties (electrical and thermal) of La2‐xSrxCuO4 for x = 0.04 have been investigated in the temperature range between 15 and 300 K with the aid of a closed‐cycle refrigerator (CCR). The DC four‐probe resistivity measurement confirms a decrease in resistivity with increasing temperature below 200 K. However, above 200 K, an increase in resistivity with temperature (metallic behaviour) has been noticed due to charge carrier localization. The Hall measurement conveys hole‐type conduction and phonon‐dominated mobility with carrier concentration ~1018/cm3, which lie somewhere between non‐degenerate and degenerate limit. The Seebeck coefficient also confirms hole type conduction and its temperature dependence can be explained in the light of the model applicable for mixed‐valence heavy fermions systems. The steady‐state method for thermal conductivity measurement has been employed. The plot of thermal conductivity (λ) as a function of temperature (T) shows a hump‐like structure at around 65 K, which may be attributed to an increase in the quasi‐particle mean free path. Further, the electronic and lattice (phononic) contributions to thermal conductivity have been separated using electrical conductivity data with the help of the Wiedemann‐Franz law. Our analysis confirms the phononic dominance in the thermal conductivity of the investigated sample. The figure of merit (ZT) estimated from the experimental data has a maximum value of 0.086 at 290 K and hence shows its inherent energy harvesting properties that can further be stored in a battery or capacitor.

Determination of acoustic phonon anharmonicities via second-order Raman scattering in CuI

We demonstrate the determination of anharmonic acoustic phonon properties via second-order Raman scattering exemplarily on copper iodide single crystals. The origin of multi-phonon features from the second-order Raman spectra was assigned by the support of the calculated 2-phonon density of states. In this way, the temperature dependence of acoustic phonons was determined down to 10 K. To determine independently the harmonic contributions of respective acoustic phonons, density functional theory in quasi-harmonic approximation was used. Finally, the anharmonic contributions were determined. The results are in agreement with earlier publications and extend CuI’s determined acoustic phonon properties to lower temperatures with higher accuracy. This approach demonstrates that it is possible to characterize the acoustic anharmonicities via Raman scattering down to zero-temperature renormalization constants of at least 0.1 cm−1.