Transverse Acoustic Branch Research Articles

Electrons, phonons and superconductivity in rocksalt and tungsten–carbide phases of CrC

We present results of ab initio theoretical investigations of the electronic structure, phonon dispersion relations, electron–phonon interaction and superconductivity in the rocksalt and tungsten–carbide phases of CrC. It is found that, compared to the stable tungsten–carbide phase, the metastable rocksalt phase is characterized by a much larger electronic density of states at the Fermi level. The phonon spectra of the rocksalt phase exhibit anomalies in the dispersion curves of both the transverse and longitudinal acoustic branches along the main symmetry directions. A combination of these characteristic electronic and phonon properties leads to an order of magnitude larger value of the electron–phonon coupling constant (λ = 2.66) for the rocksalt phase compared to that for the tungsten–carbide phase (λ = 0.24). Our calculations suggest that superconducting transition temperature values of 0.01 K and 25–35 K may be expected for the tungsten–carbide and rocksalt phases, respectively.

Structural, dynamical and thermodynamics properties of YBi

We have performed first-principles calculations using the full-potential linear augmented plane-wave, plane wave pseudopotential methods and density linear-response theory to study the structural, electronic, dynamical and thermodynamic properties of the yttrium bismuth YBi. Total energy calculations of the zinc-blende, rocksalt, and cesium chloride phases are investigated. The NaCl structure is found to be the ground state phase of YBi. Bismuth atom induces strong relativistic effects, creating a large spin–orbit splitting of ∼2000meV. Moreover, the phonon band structure is characterized by an appreciable overlap between longitudinal and transverse optical modes. Furthermore we found that the transverse and longitudinal acoustic phonon branches show respectively small variation along the X→W and W→L directions, while the longitudinal optical modes show flatness along a large part of the Brillouin zone. Bismuth atoms show low vibrational amplitudes as compared with yttrium atoms. Moreover we found a strong contribution to heat capacity and entropy from optical (acoustic)-modes of Y (Bi) atoms, with relatively small contribution of Y-acoustic modes and a vanishing contribution of optical modes of Bi.

Order-disorder transition in ZnGeP2 and ZnSnP2

Lattice dynamical calculations of ZnGeP2 and ZnSnP2 have been performed to investigate the possibility of the existence of the ordered chalcopyrite-to-disordered zincblende phase transition exhibited by some similar compounds and to understand the role played by phonons. The calculated values of the lattice parameters, bulk modulii and vibrational frequencies are in good agreement with the available experimental data. We observe that with increase in pressure the transverse acoustic branches and the lowest lying optic mode show a softening, which is eventually followed by elastic instability (at 3 GPa and 6.5 GPa respectively for ZnGeP2 and ZnSnP2) of the chalcopyrite phase. However, the disordered cubic phase is found to be dynamically and mechanically stable at these pressures.

Lattice dynamics of PbTiO3

Inelastic neutron scattering experiments were performed to investigate the phonon dispersion relations along the [1,0,0], [1,1,0] and [1,1,1] directions in cubic PbTiO3. All of the transverse optic (TO) branches soften significantly toward the zone center around Tc. The zone-center TO mode stiffens considerably at 1173 K. The energies of the [ξ, 0, 0] TO branch for PbTiO3 measured at 793 K are considerably higher than those for Pb(Zn1/3Nb2/3)O3 at 423 K in the entire zone. The [ξ, 0, 0] transverse acoustic (TA) branch is found to soften slightly at 793 K. The [ξ, ξ, ξ] TA branch exhibits two minima at the middle point (1/4,1/4,1/4) and the zone boundary (1/2,1/2,1/2). These two modes are weakly temperature dependent up to 1173 K.

Giant magnetoelastic interaction in UFe2

Using the unique coverage of (Q, ω) space available on the BRISP spectrometer, we have investigated the low Q dynamical response of a single crystal of UFe2. A strong inelastic signal was found with a dispersion corresponding to the transverse acoustic phonon branch, forbidden in the first Brillouin zone. A detailed analysis of the neutron intensities as a function of temperature reveals a possible magnetic contribution superposed to this signal, which could originate from the magnon-phonon interaction, explaining the anomalous magnetoelastic behavior in this compound.

Response of Acoustic Phonons to Charge and Orbital Order in the 50% Doped Bilayer ManganiteLaSr2Mn2O7

We report an inelastic neutron scattering study of acoustic phonons in the charge and orbitally ordered bilayer manganite LaSr(2)Mn(2)O(7). For excitation energies less than 15 meV, we observe an abrupt increase (decrease) of the phonon energies (linewidths) of a transverse acoustic phonon branch at q = (h, h, 0), h ≤ 0.3, upon entering the low temperature charge and orbital ordered state (T(COO) = 225 K). This indicates a reduced electron-phonon coupling due to a decrease of electronic states at the Fermi level leading to a partial removal of the Fermi surface below T(COO) and provides direct experimental evidence for a link between electron-phonon coupling and charge order in manganites.

A possible scenario for two soft branches in PMN

The acoustic–optic mode coupling model proposed earlier as a framework for interpretation of the apparent vertical soft optic mode branch dispersion in lead-based perovskite relaxors has been tentatively extended by taking into account the two-component nature of the lowest frequency optic phonon mode. Inelastic scattering spectral function and the course of the apparent phonon dispersion branches were calculated for parameters relevant to Pb(Mg1/3Nb2/3)O3 (PMN) relaxor. Dynamical parameters of the zone-centre soft mode components in the problematic region around the Burns temperature have been described with the help of the recent hyper-Raman scattering study [A. Al-Zein, J. Hlinka, J. Rouquette, and B. Hehlen, Soft mode doublet in PbMg1/3Nb2/3O3 relaxor investigated with hyper-Raman scattering, Phys. Rev. Lett. 105 (2010), p. 017601] on PMN. We show that the vertical dispersion (waterfall anomaly) is primarily due to the coupling of the transverse acoustic branch to the lower frequency component of the TO1 phonon branch. As in the inelastic neutron scattering experiments, in this model the temperature interval in which the vertical dispersion (waterfall anomaly) appears is roughly restricted by the freezing and Burns temperatures.

Neutron scattering study of acoustic phonon softening in BiVO4

Inelastic neutron scattering has been used to study the transverse acoustic (TA) phonon propagating on the (0,0,1) plane polarized on this plane in BiVO${}_{4}$ above the ferroelastic phase transition at $T$${}_{c}$$=528$ K. The energies of the TA phonon dispersion curve along $[0.7\ensuremath{\xi},\ensuremath{\xi},0]$ are slightly lower than those along $[\ensuremath{\xi},\ensuremath{\xi},0]$, indicating that the acoustic symmetry direction deviates from the high-symmetry $[\ensuremath{\xi},\ensuremath{\xi},0]$ direction. The $[0.7\ensuremath{\xi},\ensuremath{\xi},0]$ TA branch softens in a limited range $\ensuremath{\xi}\ensuremath{\lesssim}0.2$ as the temperature approaches $T$${}_{c}$ from above. The gradual decrease in the initial slope of the $[0.7\ensuremath{\xi},\ensuremath{\xi},0]$ TA branch is quite different from the complete softening of the TA mode reported from Brillouin scattering measurements. A temperature-dependent central peak is associated with the $[0.7\ensuremath{\xi},\ensuremath{\xi},0]$ TA mode. Furthermore, an elastic diffuse streak along $[1,\overline{1},0]$ exists up to 878 K. These precursor effects are discussed in connection with the TA phonon softening.

Ab initio Lattice Dynamics and Grüneisen Parameters of TlGaSe2

The first-principles calculations of the lattice dynamics of the TlGaSe2 ternary semiconductor compound are presented in this paper. Calculations were performed using open-source code ABINIT on the basis of the density functional perturbation theory within the plane-wave pseudopotential approach. Results on the frequencies of phonon modes in the centre of Brillouin zone and the dispersion of transverse shear acoustic branch of the phonon spectra agree well with experimental data on Raman scattering, infrared reflectivity and ultrasound wave propagation in TlGaSe2. The calculated and experimental temperature dependencies of heat capacity are in a good agreement up to the room temperature. Along the layer, the low-frequency acoustic branch displays the bending wave behavior which is characteristic of the layer crystal structures. We have calculated also the elastic compliances tensor, the directional Grüneisen functions and the coefficients of the linear thermal expansion for TlGaSe2. We obtained that both principal components of the coefficients of linear expansion are positive in the range of temperature above 5 K.

Density functional theory investigation of the phonon instability, thermal equation of state and melting curve of Mo

The phonon instability and thermal equation of state of Mo are extensively investigated using density functional theory. The calculated phonon dispersion curves agree well with experiments. Under compression, we captured a large softening in the transverse acoustic (TA) branches of body-centred cubic Mo. When the pressure is raised to 716 GPa, the frequencies along Γ-N in the TA branches soften to imaginary frequencies, indicating structural instability. For face-centred cubic Mo, the phonon calculations predicted the stability by promoting the frequencies from imaginary to real. Within quasi-harmonic approximation, we predicted the thermal equation of state and some other properties including the thermal expansion coefficient α, product αK(T), heat capacity C(V), entropy S, Grüneisen parameter γ and Debye temperature Θ(D). The melting curves of Mo were also obtained successfully.

Lattice dynamics of layered ferroelectric semiconductor compound TlGaSe2

Abstract We present the first-principles calculation of the lattice dynamics of the TlGaSe 2 ternary semiconductor having highly anisotropic crystal structure. Calculations have been performed using open-source code ABINIT on the basis of the density functional perturbation theory within the plane-wave pseudopotential approach. Results on the frequencies of phonon modes in the centre of Brilloin zone and the dispersion of transverse shear acoustic branch of the phonon spectra agree well with the experimental data on Raman scattering, infrared reflectivity and ultrasound wave propagation in TlGaSe 2 . The calculated and experimental temperature dependencies of heat capacity are in a good agreement up to the room temperature. Along the layer, the low-frequency acoustic branch displays the bending wave behavior which is characteristic of the layer crystal structures.

Phonons and superconductivity in fcc and dhcp lanthanum

We have investigated the structural and electronic properties of lanthanum in the face-centered-cubic (fcc) and double hexagonal-close-packed (dhcp) phases using a generalized gradient approximation of the density functional theory and the ab initio pseudopotential method. It is found that double hexagonal-close-packed is the more stable phase for lanthanum. Differences in the density of states at the Fermi level between these two phases are pointed out and discussed in detail. Using the calculated lattice constant and electronic band structure for both phases, a linear response approach based on the density functional theory has been applied to study phonon modes, polarization characteristics of phonon modes, and electron-phonon interaction. Our phonon results show a softening behavior of the transverse acoustic branch along the $\ensuremath{\Gamma}\text{\ensuremath{-}}L$ direction and the $\ensuremath{\Gamma}\text{\ensuremath{-}}M$ direction for face-centered-cubic and double hexagonal-close-packed phases, respectively. Thus, the transverse-phonon linewidth shows a maximum at the zone boundary $M(L)$ for the double hexagonal-close-packed phase (face-centered-cubic phase), where the transverse-phonon branch exhibits a dip. The electron-phonon coupling parameter $\ensuremath{\lambda}$ is found to be 0.97 (1.06) for the double hexagonal-close-packed phase (face-centered-cubic phase), and the superconducting critical temperature is estimated to be 4.87 (dhcp) and 5.88 K (fcc), in good agreement with experimental values of around 5.0 (dhcp) and 6.0 K (fcc). A few superconducting parameters for the double hexagonal-close-packed phase have been calculated and compared with available theoretical and experimental results. Furthermore, the calculated superconducting parameters for both phases are compared between each other in detail.

Giant Kohn Anomaly and the Phase Transition in Charge Density WaveZrTe3

A strong Kohn anomaly in ZrTe3 is identified in the mostly transverse acoustic phonon branch along the modulation vector q_{P} with polarization along the a;{*} direction. This soft mode freezes to zero frequency at the transition temperature T_{P}, and the temperature dependence of the frequency is strongly affected by fluctuation effects. Diffuse x-ray scattering of the incommensurate superstructure shows a power-law scaling of the intensity and the correlation length that is compatible with an order parameter of dimension n=2.

Phonon density of states of SmS under high pressure determined byS149mnuclear inelastic scattering

The impact of the pressure-induced valence transition on the phonon density of states (DOS) in SmS was studied by $^{149}\text{S}\text{m}$ nuclear inelastic scattering of synchrotron radiation. The derived phonon DOS shows drastic differences between the divalent phase at ambient pressure and the intermediate valent phase at 1.5, 2.9, and 4.6 GPa. The phonon DOS at ambient pressure shows two peaks which can be assigned to the transverse-acoustic (TA) and longitudinal-acoustic (LA) phonon branches, while at high pressures only one broad peak is observed. The data were analyzed with a simple model for the TA and LA phonon branches, which could well describe the measured spectra. In the intermediate valent phase the pressure dependence of the cutoff energies of the TA and LA phonon branches is very different and reflects the strong modifications of the LA branches in the intermediate valent phase. This behavior is also responsible for a characteristic variation in the derived Lamb-M\ossbauer factors and Debye temperatures.

Synthesis and Raman spectroscopic characterisation of carbon nanoscrolls

Raman characteristics of nanoscrolls including the G-peak, the D-peak and new bands in the low-wavenumber region are discussed. Distinct peaks at ∼450 cm −1, ∼600 cm −1, ∼690 cm −1 and ∼870 cm −1 are identified to originate from transverse optic and transverse acoustic phonon branches at the K-point, the M-point and the Γ-point. The Raman spectrum of nanoscrolls is compared with that of highly oriented pyrolytic graphite (HOPG) and the elastic strain in the scrolls due to curvature is estimated analytically to account for the broadening of the G-peak. Synthesis of carbon nanoscrolls by splitting and rupturing graphene planes is also described in detail. The structure and composition of graphene were verified using X-ray diffraction and X-ray photoelectron spectroscopy. The structure of the nanoscrolls was confirmed by electron microscopy.

Ab initio investigations of the phonon anomaly and superconductivity in fcc La

We have employed the ab initio plane wave pseudopotential method within a generalized gradient approximation of the density functional theory and a linear response approach to investigate the phonon anomaly and superconductivity in fcc La. Our results confirm the presence of the experimentally observed softening behavior of the transverse acoustic branch along the [111] direction for both zero pressure. This behavior is found to be present even at a pressure of 50 kbar. With a reasonable choice of 0.1 for the Coulomb pseudopotential μ∗, our estimate of the superconducting critical temperature of 6.44 K at zero pressure is in good agreement with the experimental value of 6.0 K. Our work further suggests that at 50 kbar the critical temperature will increase to 9.26 K.

Lattice dynamics investigations of SiGe core-shell nanowires

We present results from lattice dynamics calculations on the phonon modes and specific heat of SiGe core-shell nanowires. The results show that phonon dispersion relation of SiGe nanowires consists of four acoustic branches. The frequency of the first optical mode at Γ point shifts to low frequency as the Ge concentration is increasing. There are three strong peaks in the spectra of density of states. The peaks at 9.0 THz and 15.0 THz can be attributed to the high frequency Ge-Ge and Si-Si bond vibration. The broad peak around 3.0 THz of pure silicon nanowire corresponds to the transverse acoustic branch of bulk silicon. Moreover, specific heat of SiGe nanowires increases (decreases) with the increase of the concentration x at low (high) temperature. The specific heat at 300 K can be fitted by C V = x 2 C Ge + (1 − x)C Si, where C Ge and C Si are specific heat of pure germanium and silicon nanowires respectively.

Structural, elastic, and electronic properties of Fe3C from first principles

Using first-principles calculations within the generalized gradient approximation, we predicted the lattice parameters, elastic constants, vibrational properties, and electronic structure of cementite (Fe3C). Its nine single-crystal elastic constants were obtained by computing total energies or stresses as a function of applied strain. Furthermore, six of them were determined from the initial slopes of the calculated longitudinal and transverse acoustic phonon branches along the [100], [010], and [001] directions. The three methods agree well with each other; the calculated polycrystalline elastic moduli are also in good overall agreement with experiments. Our calculations indicate that Fe3C is mechanically stable. The experimentally observed high elastic anisotropy of Fe3C is also confirmed by our study. Based on electronic density of states and charge density distribution, the chemical bonding in Fe3C was analyzed and was found to exhibit a complex mixture of metallic, covalent, and ionic characters.

Measurement of phonon dispersion relation in negative thermal expansion compound ZrW2O8

Isotropic negative thermal expansion (NTE) is found in cubic AX2O8(A = Zr, Hf: X=W, Mo) up to high temperatures (1050 K). Anharmonicity of low energy phonon modes plays an important role in leading to the NTE behaviour. Earlier we verified our predictions of large phonon softening for low energy phonons (below 8 meV) through high-pressure inelastic neutron scattering measurements on powder samples at ILL, France. Now we have measured the phonon dispersion relation from a single crystal of ZrW2O8. The measurements are useful to verify our prediction of highly anharmonic nature of specific phonon branches, in particular the transverse acoustic branch, and other branches up to 10 meV. These modes below 10 meV mainly contribute to the NTE in ZrW2O8.

Pressure-induced amorphization ofCuFeS2studied byFe57nuclear resonant inelastic scattering

Static and dynamic structural properties of $\mathrm{Cu}\mathrm{Fe}{\mathrm{S}}_{2}$ under high pressure were investigated by x-ray diffraction and $^{57}\mathrm{Fe}$ nuclear resonant inelastic scattering. Using x-ray diffraction, we obtained evidence that a pressure-induced amorphization occurs at about $6.3\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, which represents a metal-insulator transition. Although partial phonon densities of states extracted from $^{57}\mathrm{Fe}$ nuclear resonant inelastic scattering spectra are similar in the two phases, the derived thermodynamical parameters show anomaly at the transition. The results of extracted partial phonon densities of states and ab initio phonon calculations indicate that this pressure-induced amorphization is caused by anomalous pressure dependences of the lower optical phonon branches and the initial slopes of the transverse acoustic phonon branches.