Total Anharmonicity Research Articles

Zero thermal expansion in Cs2W3O10

Zero thermal expansion materials are important for the practical applications due to their shape stability as changing temperature. The reported concept of average atomic volume is an available method to hunt new zero thermal expansion materials. Here, according to this concept, a tetragonal tungstate Cs2W3O10 with zero expansion has been found. There is no structure phase transition as increasing temperature from 150 K to 573 K. The coefficient of thermal expansion of axes and volume are αa = 0.0074 × 10−6 K−1, αc = 1.63 × 10−6 K−1, and αV = 1.60 × 10−6 K−1, respectively, in the temperature range of 150 ∼ 573 K. The temperature- and pressure-dependent Raman spectra reveal that the vibrations of WO6 octahedra libration modes with positive total anharmonicity and W-O-W bending mode with negative Grüneisen parameter are possibly the origin of zero thermal expansion in Cs2W3O10.

Estimation of anharmonic parameters of nano-crystalline Sc2O3 and Nd2O3

We report anharmonic characteristics of cubic Scandium Oxide (Sc2O3) and hexagonal Neodymium Oxide (Nd2O3) through temperature dependent phonon mode variation in the temperature range 80–440 K. The samples were characterized as nanocrystalline and stoichiometric with crystallite sizes of 31 nm for Sc2O3 and 59 nm for Nd2O3. Under ambient conditions, Sc2O3 was found to have 10 phonon modes out of expected 22 Raman modes while Nd2O3 showed all 4 predicted phonon modes. The temperature dependent shift in wavenumber of Raman modes and broadening of the phonon modes has been analysed in light of thermal and anharmonic effects. The lattice expansion and strong anharmonic interactions were observed with an increase in temperature that resulted in measurable phonon softening. However, both samples were found to have stable phases within the studied temperature range. The total anharmonicity and anharmonic parameters along with phonon lifetimes are estimated. For the most intense phonon modes of Sc2O3 and Nd2O3, the total anharmonicity is calculated as − 3.44 × 10−5 K−1 and − 5+.47 × 10−5 K−1 respectively. The estimated anharmonic constants revealed the predominance of the three phonon process for decay as a function of temperature.

Structure and Negative Thermal Expansion in Zr0.3Sc1.7Mo2.7V0.3O12.

A2M3O12-based materials have received considerable attention owing to their wide range of negative thermal expansion (NTE) and chemical flexibility toward novel materials design. However, the structure and NTE mechanism remain challenging. Here, Zr4+ and V5+ are used as a unit to compensatorily replace Sc3+ and Mo6+ in Sc2Mo3O12 to tune its thermal expansion. Its crystal structure, phase transition, NTE property, and corresponding mechanisms are studied by high-resolution synchrotron X-ray diffraction, powder X-ray diffraction, ultralow-frequency Raman spectroscopy, and density functional theory calculations. The results show that Zr0.3Sc1.7Mo2.7V0.3O12 adopts an orthorhombic (Pbcn) structure at room temperature, with V atoms occupying the position of Mo1 atoms and Zr atoms occupying the position of Sc atoms, and transforms to monoclinic (P21/a) structure at ∼133 K (45 K lower than that of Sc2Mo3O12). It exhibits excellent NTE in a broader range. Most of the phonon modes below 350 cm-1 have negative Grüneisen parameters, of which the lowest and next-lowest frequency (38.5 and 45.8 cm-1) optical phonon modes arising from the translational vibrations of the Sc/Zr and Mo/V atoms in the plane of the nonlinear linkage Sc/Zr-O-Mo/V have the largest and next-largest negative Grüneisen parameters and positive total anharmonicity, and contribute most to the NTE.

Temperature dependent Raman investigation of multiwall carbon nanotubes

We report anomalous observations in our investigations of the temperature dependent Raman spectroscopic measurement of multiwall carbon nanotubes. The Micro-Raman spectra were recorded with the laser source having 514.5 nm wavelength and within the temperature range of 80–440 K. The major Raman bands, the G and D band, are observed at 1584 and 1348 cm−1, respectively, at ambient. The absence of the radial breathing mode confirms the multiwall nature of carbon nanotubes. It has been observed that with an increase in the temperature above 120 K, there is a shift in Raman bands towards the higher wave-number region. However, a drop in the G and D bands is observed from 80 to 120 K which was not observed for the second order band. Thereafter, all Raman modes exhibited mode hardening up to about 320 K followed by mild softening of the phonon modes. Linear temperature coefficients were found to have higher contribution to mode hardening as compared to higher order terms. Total anharmonicity estimation shows a predominant effect of the quasi-harmonic term as compared to the true anharmonic term.

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.

Phonon anharmonicity in zirconium tungstate single crystal investigated by broadband light scattering

We measured light scattering in a single crystal of ZrW2O8 (ZWO) in the frequency range between 0.1 and 1100 cm−1 and in the temperature range between 3.5 and 300 K. From the temperature dependence of the optical and acoustic phonon frequencies, we found that low-frequency phonon modes below 100 cm−1 have large relative temperature coefficients (total anharmonicity values). The longitudinal acoustic mode, whose Brillouin light scattering has not been reported thus far, was found to have the largest negative total anharmonicity in a wide temperature range, indicating the possibility that the acoustic modes, as well as the low-frequency optical modes that are associated with the motions of WO4 and ZrO6 polyhedra, should contribute to the negative thermal expansion of ZWO.

Structural and Thermal Properties of BaTe2O6: Combined Variable-Temperature Synchrotron X-ray Diffraction, Raman Spectroscopy, and ab Initio Calculations.

Variable-temperature Raman spectroscopic and synchrotron X-ray diffraction studies were performed on BaTe2O6 (orthorhombic, space group: Cmcm), a mixed-valence tellurium compound with a layered structure, to understand structural stability and anharmonicity of phonons. The structural and vibrational studies indicate no phase transition in it over a wider range of temperature (20 to 853 K). The structure shows anisotropic expansion with coefficients of thermal expansion in the order αb ≫ αa > αc, which was attributed to the anisotropy in bonding and structure of BaTe2O6. Temperature evolution of Raman modes of BaTe2O6 indicated a smooth decreasing trend in mode frequencies with increasing temperature, while the full width at half-maximum (fwhm) of all modes systematically increases due to a rise in phonon scattering processes. With the use of our earlier reported isothermal mode Grüneisen parameters, thermal properties such as thermal expansion coefficient and molar specific heat are calculated. The pure anharmonic (explicit) and quasiharmonic (implicit) contribution to the total anharmonicity is delineated and compared. The temperature dependence of phonon mode frequencies and their fwhm values are analyzed by anharmonicity models, and the dominating anharmonic phonon scattering mechanism is concluded in BaTe2O6. In addition to the lattice modes, several external modes of TeOn (n = 5, 6) are found to be strongly anharmonic. The ab initio electronic structure calculations indicated BaTe2O6 is a direct band gap semiconductor with gap energy of ∼2.1 eV. Oxygen orbitals, namely, O-2p states in the valence band maximum and the sp-hybridized states in the conduction band minimum, are mainly involved in the electronic transitions. In addition a number of electronic transitions are predicted by the electronic structure calculations. Experimental photoluminescence results are adequately explained by the ab initio calculations. Further details of the structural and vibrational properties are explained in the manuscript.

Temperature Dependent Variations of Phonon Interactions in Nanocrystalline Cerium Oxide

The temperature dependent anharmonic behavior of the phonon modes of nanocrystalline CeO2 was investigated in the temperature range of 80–440 K. The anharmonic constants have been derived from the shift in phonon modes fitted to account for the anharmonic contributions as well as the thermal expansion contribution using the high pressure parameters derived from our own high pressure experimental data reported previously. The total anharmonicity has also been estimated from the true anharmonicity as well as quasiharmonic component. In the line‐width variation analysis, the cubic anharmonic term was found to dominate the quartic term. Finally, the phonon lifetime also reflected the trend so observed.

Order–disorder transition and Fano-interference in thermoelectric Cu3SbSe3 nanoparticles

Temperature dependent Raman scattering measurements were carried out to investigate the phonon behavior of thermoelectric Cu3SbSe3 nanoparticles. The anomalous behavior of phonon mode (Ag) frequency with temperature indicates the possibility of a lattice instability related to the order–disorder structural transition at 380 K. In the low temperature region (80–250 K) we found an asymmetric line shape of Ag mode, which is analyzed and discussed in the light of phonon–continuum Fano-interference effect. We have obtained the thermal conductivity (κ) ∼ 2.04 W/mK at room temperature. The change in thermal conductivity with temperature strongly correlates with the change in total anharmonicity of the Cu3SbSe3 lattice.

Anharmonic behavior and structural phase transition in Yb2O3

The investigation of structural phase transition and anharmonic behavior of Yb2O3 has been carried out by high-pressure and temperature dependent Raman scattering studies respectively. In situ Raman studies under high pressure were carried out in a diamond anvil cell at room temperature which indicate a structural transition from cubic to hexagonal phase at and above 20.6 GPa. In the decompression cycle, Yb2O3 retained its high pressure phase. We have observed a Stark line in the Raman spectra at 337.5 cm−1 which arises from the electronic transition between 2F5/2 and 2F7/2 multiplates of Yb3+ (4f13) levels. These were followed by temperature dependent Raman studies in the range of 80–440 K, which show an unusual mode hardening with increasing temperature. The hardening of the most dominant mode (Tg + Ag) was analyzed in light of the theory of anharmonic phonon-phonon interaction and thermal expansion of the lattice. Using the mode Grüneisen parameter obtained from high pressure Raman measurements; we have calculated total anharmonicity of the Tg + Ag mode from the temperature dependent Raman data.

Vibrational properties and phonon anharmonicity in ZnS1−xSex: Inelastic neutron scattering, Raman scattering, X-ray diffraction measurements and lattice dynamical studies

Inelastic neutron scattering, Raman and X-ray diffraction measurements coupled with lattice dynamical calculations (employing a semi-empirical transferable potential model) have been carried out to gain a detailed understanding of the peculiar vibrational spectrum exhibited by the mixed crystal ZnS1−xSex. Raman scattering measurements performed over a varying range of temperature (100–800K) and pressure (up to 13GPa) have confirmed that the additional mode observed in the spectra are visible over the entire range of temperature and pressure. Correlation of the individual motions of atoms (obtained from computed total and partial phonon density of states) with the inelastic neutron scattering measurements (carried out over the entire Brillouin zone) have then indicated that the existence of the additional mode in ZnS1−xSex is due to the vibrations of the Se atom being in resonance with that of the S atom. Further, it has been shown that the presence of this additional mode can be tuned by varying the mass of the atom at the Se site. In addition, an analysis of bond-length distribution with increasing Se concentration have elucidated that bond-length spread is not responsible for the presence of the additional mode. An analysis of the peak shifts of the Raman modes with temperature and pressure indicate that the anharmonicity of the vibrational modes increases with increasing compositional disorder. This is attributed to the fact that increasing Se concentration gives rise to a distribution of bond-lengths in ZnS1−xSex, which is responsible for this compositional disorder induced anharmonicity. Our computations have thus revealed that mass of the anion is responsible for the presence of additional mode while bond-length distribution gives rise to the existence of compositional disorder induced anharmonicity in ZnS1−xSex. Further, it is observed that the contribution of explicit anharmonicity to the total anharmonicity becomes dominant at higher temperatures. This compound also exhibits negative thermal expansion at low temperatures as obtained from our X-ray diffraction measurements as a function of temperature (10–800K).

Anharmonic Vibrational Properties from Intrinsic n-Mode State Densities

A method for calculating fully anharmonic vibrational state counts, state densities, and partition functions for molecules is presented. The method makes use of a new quantity, the intrinsic density of states, which is associated with the states that uniquely arise from a given mode, mode pairing, or higher-order mode coupling. By using only low-order intrinsic densities, the fully coupled anharmonic vibrational result can be constructed, as shown by our application of the method to methane, CH4, and cyclopropene, C3H4. Truncation of the intrinsic expansion at the coupling of pairs of modes yields greatly improved scaling over direct evaluation of the full-dimensional result and recovers a large fraction of the total anharmonicity. We also discuss the relation of the new quantities to the structure of the potential energy surface.

Phonons and colossal thermal expansion behavior of Ag3Co(CN)6 and Ag3Fe(CN)6

Recently colossal volume thermal expansion has been observed in the framework compounds Ag3Co(CN)6 and Ag3Fe(CN)6. We have measured phonon spectra using neutron time-of-flight spectroscopy as a function of temperature and pressure. Ab initio calculations were carried out for the sake of analysis and interpretation. Bonding is found to be very similar in the two compounds. At ambient pressure, modes in the intermediate frequency part of the vibrational spectra in the Co compound are shifted slightly to higher energies as compared to the Fe compound. The temperature dependence of the phonon spectra gives evidence for a large explicit anharmonic contribution to the total anharmonicity for low-energy modes below 5 meV. We have found that modes are mainly affected by the change in size of the unit cell, which in turn changes the bond lengths and vibrational frequencies. Thermal expansion has been calculated via the volume dependence of phonon spectra. Our analysis indicates that Ag phonon modes within the energy range 2–5 meV are strongly anharmonic and major contributors to thermal expansion in both systems. The application of pressure hardens the low-energy part of the phonon spectra involving Ag vibrations and confirms the highly anharmonic nature of these modes.

Relationship between phonons and thermal expansion in Zn(CN)2and Ni(CN)2from inelastic neutron scattering andab initiocalculations

Zn (CN)${}_{2}$ and Ni(CN)${}_{2}$ are known for exhibiting anomalous thermal expansion over a wide temperature range. The volume thermal expansion coefficient for the cubic, three-dimensionally connected material, Zn(CN)${}_{2}$, is negative (${\ensuremath{\alpha}}_{V}=\ensuremath{-}51\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6} {\mathrm{K}}^{\ensuremath{-}1}$) while for Ni(CN)${}_{2}$, a tetragonal material, the thermal expansion coefficient is negative in the two-dimensionally connected sheets (${\ensuremath{\alpha}}_{a}=\ensuremath{-}7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6} {\mathrm{K}}^{\ensuremath{-}1}$), but the overall thermal expansion coefficient is positive (${\ensuremath{\alpha}}_{V}=48\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6} {\mathrm{K}}^{\ensuremath{-}1}$). We have measured the temperature dependence of phonon spectra in these compounds and analyzed them using ab initio calculations. The spectra of the two compounds show large differences that cannot be explained by simple mass renormalization of the modes involving Zn (65.38 amu) and Ni (58.69 amu) atoms. This reflects the fact that the structure and bonding are quite different in the two compounds. The calculated pressure dependence of the phonon modes and of the thermal expansion coefficient, $\ensuremath{\alpha}$${}_{V}$, are used to understand the anomalous behavior in these compounds. Our ab initio calculations indicate that phonon modes of energy \ensuremath{\sim} meV are major contributors to negative thermal expansion (NTE) in both compounds. The low-energy modes of \ensuremath{\sim}8 and 13 meV also contribute significantly to the NTE in Zn(CN)${}_{2}$ and Ni(CN)${}_{2}$, respectively. The measured temperature dependence of the phonon spectra has been used to estimate the total anharmonicity of both compounds. For Zn(CN)${}_{2}$, the temperature-dependent measurements (total anharmonicity), along with our previously reported pressure dependence of the phonon spectra (quasiharmonic), is used to separate the explicit temperature effect at constant volume (intrinsic anharmonicity).

Study of the Born—Oppenheimer Approximation with Application to H2

A method for evaluating energy corrections dur to breakdown of the Born—Oppenheimer (BO) approximation in ordinary diatomic molecules has been developed. It is shown that the effective potential for nuclear motion depends upon both the vibrational momentum and the internuclear distance. Energy levels for H2 have been calculated by numerical solution of the Schrödinger equation for motion in this effective potential. The v=0 level is shifted ∼0.2 cm—1 by non-BO terms as compared to the total anharmonicity correction of about 30 cm—1. This shift is an order of magnitude too small to explain the difference between the best theoretical and experimental values of D00.