Soft Acoustic Mode Research Articles

First-principles calculations of the high-temperature phase transformation in yttrium tantalate

The high-temperature phase transition between the tetragonal (scheelite) and monoclinic (fergusonite) forms of yttrium tantalite (${\mathrm{YTaO}}_{4}$ ) has been studied using a combination of first-principles calculations and a Landau free-energy expansion. Calculations of the Gibbs free energies show that the monoclinic phase is stable at room temperature and transforms to the tetragonal phase at 1430 \ifmmode^\circ\else\textdegree\fi{}C, close to the experimental value of $1426\ifmmode\pm\else\textpm\fi{}7$ \ifmmode^\circ\else\textdegree\fi{}C. Analysis of the phonon modes as a function of temperature indicate that the transformation is driven by softening of transverse acoustic modes with symmetry ${E}_{u}$ in the Brillouin zone center rather than the Raman-active ${B}_{g}$ mode. Landau free-energy expansions demonstrate that the transition is second order and, based on the fitting to experimental and calculated lattice parameters, it is found that the transition is a proper rather than a pseudoproper type. Together these findings are consistent with the transition being ferroelastic.

Unusual Pressure Effect on the Shear Modulus in MgAl2O4Spinel

Compressional (VP) and shear (VS) wave velocities of polycrystalline MgAl2O4 spinel have been measured up to 14 GPa and 900 K using ultrasonic interferometry and in situ X-ray diffraction techniques. Here, we observed a weaker pressure dependence in shear modulus (G) for MgAl2O4 spinel, as compared to a stronger ∂G/∂P for magnesium silicate/germanate counterpart. Our first-principles calculations show that the tetragonal shear modulus CS = (C11–C12)/2 decrease with pressures, indicating acoustic mode softening, which further supports our observed experimental results. Using a finite strain equation of state approach the elastic bulk and shear moduli, as well as their pressure and temperature derivatives, are derived from the directly measured velocities and densities, yielding KS0 =196.0(9) GPa, G0 = 109.0(4) GPa, ∂KS/∂P = 4.60(9), and ∂G/∂P = 0.58(3) independent of pressure calibration. The temperature derivatives for the bulk and shear moduli were tightly constrained from acoustic velocity measurements ...

Comment on “First-principles study of the influence of (110)-oriented strain on the ferroelectric properties of rutile TiO2”

In a recent article, Gr\"{u}nebohm et al. [Phys. Rev. B 84 132105 (2011), arXiv:1106.2820] report that they fail to reproduce the A2u ferroelectric instability of TiO2 in the rutile structure calculated with density functional theory within the PBE-GGA approximation by Montanari et al. [Chem. Phys. Lett 364, 528 (2002)]. We demonstrate that this disagreement arises from an erroneous treatment of Ti 3s and 3p semi-core electrons as core in their calculations. Fortuitously the effect of the frozen semi-core pseudopotential cancels the phonon instability of the PBE exchange-correlation, and the combination yields phonon frequencies similar to the LDA harmonic values. Gr\"{u}nebohm et al. also attempted and failed to reproduce the soft acoustic phonon mode instability under (110) strain reported by Mitev et al. [Phys. Rev. B 81 134303 (2010)]. For this mode the combination of PBE-GGA and frozen semi-core yields a small imaginary frequency of 9.8i. The failure of Gr\"{u}nebohm et al. to find this mode probably arose from numerical limitations of the geometry optimization approach in the presence of a shallow double well potential; the optimization method is not suitable for locating such instabilities.

The effect of torsional deformation on thermal conductivity of mono-, bi- and trilayer graphene nanoribbon

Physical deformation and geometrical change of a low dimensional nanostructure influence the phonon transport leading to appreciable changes in the thermal characteristics. In this paper, we report the calculation of the thermal conductivity of twisted graphene nanoribbon (GNR) using nonequilibrium molecular dynamics (NEMD). A reduction in the value of thermal conductivity of GNR is observed with an increase in the angle of twist. It is observed that the value of thermal conductivity of twisted GNR is dependent on the length of GNR and the temperature at which physical deformation is taking place. Comparing with monolayer GNR, the reduction in the thermal conductivity of bilayer and trilayer GNR is less due to the interactions between the adjacent layers. Analysis of the phonon transport in twisted graphene implies that the reduced thermal conductivity of twisted graphene nanoribbon is due to the phonon softening of acoustic phonon modes.

Pressure-induced changes in electronic and vibrational properties of LaS

The high-pressure induced phase transition in LaS has been investigated by means of first-principles calculations, and density-functional linear-response theory. A pressure-induced soft-acoustic phonon mode is identified at 30 GPa, which is in favourable agreement with the measured pressure-induced phase transition in LaS from the rocksalt to the CsCl structure. Phonon calculations reveal that pressure-induced instabilities of the transverse acoustic modes at the [ϵ00] and [ϵϵ0] directions are responsible for the phase transition. Furthermore, it is found that a decrease of bonding for S-p bonds and an increase of anti-bonding for La-d bonds significantly weakens the stability of the rocksalt phase of LaS under pressure, and hence inducing the structural phase transformation.

Magnetic field enhanced structural instability in EuTiO3

EuTiO3 undergoes a structural phase transition from cubic to tetragonal at TS = 282 K which is not accompanied by any long range magnetic order. However, it is related to the oxygen octahedral rotation driven by a zone boundary acoustic mode softening. Here, we show that this displacive second order structural phase transition can be shifted to higher temperatures by the application of an external magnetic field (ΔTS ∼ 4 K for μ0H = 9 T). This observed field dependence is in agreement with theoretical predictions based on a coupled spin–anharmonic-phonon interaction model.

Thermoelectric properties of HfN/ScN metal/semiconductor superlattices: a first-principles study

Nitride-based metal/semiconductor superlattices are promising candidates for high-temperature thermoelectric applications. Motivated by recent experimental studies, we perform first-principles density functional theory based analysis of electronic structure, vibrational spectra and transport properties of HfN/ScN metal/semiconductor superlattices for their potential applications in thermoelectric and thermionic energy conversion devices. Our results suggest (a) an asymmetric linearly increasing density of states and (b) flattening of conduction bands along the cross-plane Γ–Z direction near the Fermi energy of these superlattices, as is desirable for a large power factor. The n-type Schottky barrier height of 0.13 eV at the metal/semiconductor interface is estimated by the microscopic averaging technique of the electrostatic potential. Vibrational spectra of these superlattices show softening of transverse acoustic phonon modes and localization of ScN phonons in the vibrational energy gap between the HfN (metal) and ScN (semiconductor) states. Our estimates of lattice thermal conductivity within the Boltzmann transport theory suggests up to two orders of magnitude reduction in the cross-plane lattice thermal conductivity of these superlattices compared to their individual bulk components.

First-principles study of phase stability of Ti2N under pressure

A first-principles study of phase stability of various phases of Ti${}_{2}$N under normal conditions and as a function of pressure was carried out. Among the \ensuremath{\epsilon} and \ensuremath{\delta}\ensuremath{'}phases of Ti${}_{2}$N that are observed experimentally, \ensuremath{\epsilon}-Ti${}_{2}$N is the most stable. The \ensuremath{\delta}\ensuremath{'} phase can only exist at high temperature due to the soft acoustic modes at the $X$ point. The origin of the tetragonal structure of both the \ensuremath{\epsilon} and \ensuremath{\delta}\ensuremath{'} phases is supposed to be caused by the tetragonal local lattice distortion around a nitrogen vacancy. Based on the results of the total-energy and phonon-spectrum calculations at zero temperature, the following sequence of phase transformation in Ti${}_{2}$N under pressure is predicted: \ensuremath{\epsilon}-Ti${}_{2}$N (space group P4/mnm), $P$ $=$ 77.5 GPa \ensuremath{\rightarrow} Au${}_{2}$Te type (space group C2/m), $P$ $=$ 86.7 GPa \ensuremath{\rightarrow} Al${}_{2}$Cu type (space group I4/mcm). The present study shows that, to correctly predict relative phase stability, the peculiarities of the phonon spectra of the materials under investigation have to be properly accounted for.

DIELECTRIC, PIEZOELECTRIC, AND ELASTIC PROPERTIES OF BaTiO3/SrTiO3 FERROELECTRIC SUPERLATTICES FROM FIRST PRINCIPLES

The effect of epitaxial strain on the phonon spectra, crystal structure, spontaneous polarization, dielectric, piezoelectric, and elastic properties of (001)-oriented ferroelectric ( BaTiO 3)m/( SrTiO 3)n superlattices (m = n = 1-4) was studied using the first-principles density functional theory. The ground state of free-standing superlattices is the monoclinic Cm polar phase. Under the in-plane biaxial compressive strain, it transforms to tetragonal P4mm polar phase, and under the in-plane biaxial tensile strain, it transforms to orthorhombic Amm2 polar phase. When changing the in-plane lattice parameter, a softening of several optical and acoustic modes appears at the boundaries between the polar phases, and corresponding components of dielectric, piezoelectric, and elastic tensors diverge critically. The comparison of the mixing enthalpy of disordered Ba0.5Sr0.5TiO3 solid solution modeled using two special quasirandom structures SQS-4 with the mixing enthalpy of the superlattices reveals a tendency of the BaTiO3–SrTiO3 system to short-range ordering and shows that these superlattices are thermodynamically quite stable.

First-principles analysis of ZrN/ScN metal/semiconductor superlattices for thermoelectric energy conversion

We present a first-principles density functional theory-based analysis of the electronic structure, vibrational spectra, and transport properties of ZrN/ScN metal/semiconductor superlattices aiming to understand its potential and suitability for thermoelectric applications. We demonstrate (a) the presence of Schottky barriers of 0.34 eV at the metal/semiconductor interface and (b) a large asymmetry in the electronic densities of states and flattening of electronic bands along the cross-plane directions near the Fermi energy of these superlattices, desirable for high Seebeck coefficient. The vibrational spectra of these superlattices show softening of transverse acoustic phonon modes along the growth direction and localization of ScN phonons in the vibrational energy gap between metal and semiconductor layers. Boltzmann transport theory-based analysis suggests a reduction of lattice thermal conductivity by an order of magnitude compared to its individual bulk components, which makes these materials suitable for thermoelectric applications.

First principle calculation of elastic and thermodynamic properties of stishovite

Using ab initio plane-wave pseudo-potential density functional theory method, the elastic constants and band structures of stishovite were calculated. The calculated elastic constants under ambient conditions agree well with previous experimental and theoretical data. C13, C33, C44, and C66 increase nearly linearly with pressure while C11 and C12 show irregularly changes with pressure over 20 GPa. The shear modulus (C11-C12)/2 was observed to decrease drastically between 40 GPa and 50 GPa, indicating acoustic mode softening in consistency with the phase transition to CaCl2-type structure around 50 GPa. The calculated band structures show no obvious difference at 0 and 80 GPa, being consistent with the high incompressibility of stishovite. With a quasi-harmonic Debye model, thermodynamic properties of stishovite were also calculated and the results are in good agreement with available experimental data.

Pressure effects on relaxor ferroelectricity in disordered Pb(Sc1/2Nb1/2)O3

High-pressure Brillouin and Raman scattering spectroscopy and x-ray diffraction measurements were carried out on disordered Pb(Sc1/2Nb1/2)O3, considered to be a model system for phase transitions in relaxor ferroelectrics and related materials. The observed pressure-dependent Raman spectra are unusual, with the relaxor state distinguished by broad Raman bands. Raman spectra as a function of pressure reveal a new peak at 370 cm−1, with two peaks near 550 cm−1 merge above 2–3 GPa, indicating a structural phase transition in this pressure range consistent with earlier dielectric measurements. A significant softening in the longitudinal acoustic mode is observed by Brillouin scattering. Both the temperature and pressure dependencies of the linewidth reveal that the longitudinal acoustic mode softening arises from electrostrictive coupling between polar nanoregions and acoustic modes. X-ray diffraction indicates that the pressure-volume compression curve changes near 2 GPa.

TEMPERATURE DEPENDENCE OF THE DAMPING CONSTANT CLOSE TO THE I–II PHASE TRANSITION IN s-TRIAZINE

The damping constant is calculated here at various temperatures for the Raman mode II in s-triazine using the soft mode–hard mode coupling model. The temperature dependence of the order parameter is used as the input data to calculate the damping constant of the Raman mode studied in this coupling model for s-triazine close to the I–II transition (Tc = 198 K ). The soft mode–hard mode coupling model which considers the coupling of the soft acoustic mode with the optic modes in s-triazine, is fitted to the observed halfwidths of the Raman mode II close to the I–II phase transition in this crystal.

Landau model for the elastic properties of the ferroelastic crystalRb4LiH3(SO4)4

Using sound velocity measurements, we report a detailed investigation of the elastic properties ofRb4LiH3(SO4)4 realized as a function of temperature and pressure. Results are compared to predictions of aphenomenological Landau model. Supported by recent Raman scattering measurements, weassume that the structural transformation observed atTc = 134 K corresponds to a pseudo-proper ferroelastic transition. For the numerical analysis, all couplingparameters are determined using the temperature dependence of the frequency of the soft opticalB mode, the temperature dependence of spontaneous strains, and the pressure dependencedTc/dP = 191 ± 2 K GPa−1 also determined in this work. Our comparison indicates that the structural transition in Rb4LiH3(SO4)4 is fully consistent with predictions derived using our pseudo-proper ferroelastic model. Thus, alldata presented in this paper corroborate that the mechanism leading to the structural transitionat Tc = 134 K results from the softening of the B optical mode observed at31 cm−1. This detailed analysis also refutes the idea thatRb4LiH3(SO4)4 shows incomplete softening of the soft acoustic mode also associated with that structuraltransition.

Lattice dynamics of cubicNaNbO3: An inelastic neutron scattering study

The phonon-dispersion relations for cubic ${\text{NaNbO}}_{3}$ have been determined along the [100], [110], and [111] directions using inelastic neutron scattering. A simultaneous softening of transverse acoustic (TA) phonon modes occurs at the zone-boundary $M(0.5,0.5,0)$ and $R(0.5,0.5,0.5)$ points, indicating the instabilities of in-phase and out-of-phase rotations of the oxygen octahedra about the [001] direction. These zone-boundary modes exhibit an extremely gradual softening as the temperature is lowered toward ${T}_{c1}=913\text{ }\text{K}$. The inelastic diffuse scattering at the $M(0.5,0.5,0)$ point polarized along the $[1\overline{1}0]$ direction remains up to 9 meV, whereas the inelastic diffuse scattering at the $M$ point polarized along the [001] direction is suppressed. Polarization dependence shows that the inelastic diffuse scattering at the $M$ and $R$ points originates from the dynamical motion of oxygen octahedra. The transverse optic (TO) phonon modes along the [110] direction polarized with the [001] direction also soften around $\mathbf{q}=[0.15,0.15,0]$ and merge into the lower-energy TA phonon modes. This is basically similar to the waterfall phenomenon observed for Pb-based perovskite relaxor ferroelectrics. The extreme broad longitudinal acoustic (LA) and TA modes in ${\text{NaNbO}}_{3}$ contribute significantly to the inelastic diffuse scattering around Bragg points. The broadening of TA and TO modes are attributed to the anharmoic lattice potential in ${\text{NaNbO}}_{3}$. The coexistence of long-wavelength and zone-boundary phonon instabilities above ${T}_{c1}=913\text{ }\text{K}$ is closely related to the complex sequence of phase transitions in ${\text{NaNbO}}_{3}$.

Molecular dynamics simulations of laser-induced damage of nanostructures and solids

A theoretical approach to treat laser induced femtosecond structural changes in covalently bonded nanostructures and solids is described. Our approach consists in molecular dynamic simulations performed on the basis of time-dependent, many-body potential energy surfaces derived from tight-binding Hamiltonians. The shape and spectral composition of the laser pulse is explicitly taking into account in a non-perturbative way. We show a few examples of the application of this approach to describe the laser damage and healing of defects in carbon nanotubes with different chiralities and the ultrafast nonequilibrium melting of bulk germanium, initiated by the laser-induced softening and destabilization of transversal acoustic phonon modes.

Elasticity of stishovite and acoustic mode softening under high pressure by Brillouin scattering

Brillouin scattering measurements on single-crystal stishovite, a high-pressure polymorph of SiO 2, were carried out to 22 GPa. Acoustic velocities in three 30-μm thick crystal platelets of synthetic stishovite were measured in a forward symmetric scattering geometry, and the full set of elastic constants were retrieved to 12 GPa. The measured velocity data were fit to Christoffel’s equation, yielding ambient-pressure elastic constants of C 11 = 455(1) GPa, C 33 = 762(2) GPa, C 12 = 199(2) GPa, C 13 = 192(2) GPa, C 44 = 258(1) GPa, and C 66 = 321(1) GPa. The elastic modulus ( C 11 − C 12)/2 was observed to decrease with pressure, indicating acoustic mode softening, consistent with theoretical predications for the behavior of stishovite as it approaches the transition to the CaCl 2-type phase. The bounds on the aggregate adiabatic bulk and shear moduli are K S0 = 315(1) GPa, G 0 = 240(1) GPa for the Voigt bound, K S0 = 301(1) GPa, G 0 = 216(1) GPa for the Reuss bound. Pressure derivatives of aggregate bulk and shear moduli were constrained to be ( ∂K S/ ∂P) T0 = 4.34(16) and ( ∂G/ ∂P) 0 = 0.7(1) for the Reuss bound, and ( ∂K S/ ∂P) T0 = 4.0(1) and ( ∂G/ ∂P) 0 = 1.1(1) for the Voigt–Reuss–Hill (VRH) average, respectively, by fitting the data to Eulerian finite strain equations. The volume compression curve obtained from our Brillouin measurement is in very good agreement with previous compression studies up to 50 GPa.

Diffuse X-ray scattering and nanoclusters in the Hg2Br2 model ferroelastics

Diffuse maxima are revealed and studied for the first time in the x-ray scattering patterns of Hg2Br2 single crystals. These maxima originate from clusters of the orthorhombic phase due to the phase transition in the paraphase tetragonal matrix. The nucleation and growth of clusters are initiated by spatiotemporal fluctuations of the order parameter corresponding to the soft transverse acoustic mode at X points of the Brillouin zone boundary. Information on the behavior of the susceptibility and correlation length with variations in temperature and on the shape and anisotropy of the clusters is obtained, and the critical exponents are determined.

Study on Ferroelastic Phase Transition of Hexagonal System by Slowness-Curved-Surface and Polarization

The relationship between the slowness curved surface and the softening of the acoustic mode is discussed. The acoustic mode softening of hexagonal system corresponds to the maximum slowness. The eigenvector of soft mode corresponds to the polarization of acoustic mode. By solving the Christoffel equation, the maximum slowness and the polarization of the acoustic mode can be obtained. The symmetry change of proper ferroelastic phase transition can be determined by analyzing the solutions of the Christoffel equation and by using Curie principle.

Lattice instability at phase transitions near the Lifshitz point in proper monoclinicferroelectrics

The temperature dependence of acoustic properties of theSn2P2(SexS1−x)6 uniaxial ferroelectric in the vicinity of the Lifshitz point (LP) was investigated byBrillouin spectroscopy and analysed in the Landau–Khalatnikov approximation. Ananomalous decrease of the longitudinal hypersound velocity in the paraelectricphase caused by fluctuation effects and crystal structure defects has been foundnear the LP. Besides this, a small softening of the transverse acoustic phonons isobserved, which is due to their linear interaction with the soft optic mode found forincommensurate phase transitions in proper ferroelectrics. The lattice instability analysis ofSn2P2S6 and Sn2P2Se6 crystals and their solid solutions in a polarizable ion model shows that a possible reason forthe absence of a soft acoustic mode is nonorthogonality of the spontaneous polarizationvector and modulation wavevector which both lie in the monoclinic symmetry plane.