Zone-boundary Mode Research Articles

Ferroelastic phase transition in bismuth titanate

The Raman spectra of Bi2Ti4O11 at hydrostatic pressure or high temperature show that the frequency of the soft mode has a non-zero value at the phase transition point. The Raman spectra of Bi1.8La0.2Ti4O11 and Bi1.8Yb0.2Ti4O11 at high pressure reveal that there is an additional phonon mode in the low-frequency region. The finite soft mode frequency has proved to arise from the coupling between the soft mode and the additional phonon mode which may be a zone boundary mode. The phase transition can be considered as a second-order ferroelastic one driven by the soft mode.

Interrelation between the stability of extended normal modes and the existence of intrinsic localized modes in nonlinear lattices with realistic potentials.

Previous theoretical studies and molecular dynamics simulations indicate that the anharmonic version of a zone-boundary-mode phonon in a periodic one-dimensional lattice with nearest-neighbor quartic and quadratic interactions is unstable, and that this instability can lead to the production of intrinsic localized modes. We show here that such an instability occurs when nearest-neighbor cubic anharmonicity is added, but that the zone boundary mode is stabilized when the cubic anharmonicity becomes sufficiently large. A direct connection is established between the existence of this instability and the existence of intrinsic localized modes. Furthermore, our analysis reveals the existence of a second type of zone-boundary-mode instability, which is not related to intrinsic localized modes. This ``period-doubling'' instability is also found to occur in one-dimensional lattices with realistic potentials, such as Lennard-Jones, Morse, and Born-Mayer, whereas the instability related to intrinsic localized modes does not occur for these potentials, owing to their inclusion of higher-order anharmonicity. Likewise, intrinsic localized modes are not found in direct numerical searches for these cases, and we conclude that they do not exist in monatomic lattices with these potentials.

Neutron scattering and specific heat study of AlGe and AlSi alloys quenched under high pressure

Neutron scattering and specific heat measurements on pressure-quenched AlGe and AlSi alloys are reported. The neutron results corroborate earlier findings of a pronounced softening of the transverse zone boundary modes in these polycrystalline nonequilibrium alloys, reminiscent of a similar softening observed in metallic glasses. At lower frequencies, however, no pronounced glassy anomaly is found. The additional excitations seen around 9 meV in AlGe can be explained in terms of resonant modes of the heavier Ge atoms. At still lower frequencies, neutrons see only sound waves. The more sensitive specific heat technique shows the corresponding lattice T3 term and an electronic contribution which follows the classical BCS behaviour at the transition to superconductivity. Below 0.5 K, there remains a linear term about a factor of ten smaller than in typical glasses.

Molecular-dynamics simulations of the scattering of neutrons from solid argon.

Phonon line shapes corresponding to zone-boundary modes in crystalline argon at a temperature close to the melting point have been calculated with a realistic pair potential, using molecular-dynamics simulations. The longitudinal peak is considerably broadened and distorted, in agreement with both experiment and earlier calculations, but now the transverse peak is also substantially broadened, removing an earlier disagreement.

Neutron scattering studies of structural transitions and the dipole-glass phase in the mixed perovskite K(Ta, Nb)O3

In the past 20 years, neutron scattering has made the most elucidating contributions to the understanding of the role played by soft-modes in structural phase transitions. The classic example is SrTiO3 in which it has been demonstrated by neutron scattering that the entire TO phonon branch softens continuously as temperature is lowered,1 and that the zone-boundary Γ25 mode softens completely to zero at the Tc = 110K transition (Pm3m - I4/mcm).2 Another well-known example is KDP, in which the softening of the proton-lattice mode that accompanies the orderdisorder transition of the H—O… H bonds, as suggested by Cochran, has been confirmed by a determination of the mode eigenvector via the neutron inelastic structure factor3.

Normal vibration modes and the structural phase transitions in caesium trichloroplumbate CsPbCl3

The perovskite crystal CsPbCl3 is built up by a three-dimensional chain of PbCl6 octahedra. The symmetry, the compatibility relation and the normal vibration modes of this crystal are studied by using the multiplier representation of group theory along the Gamma - Delta -X-Z-M-T-R direction in phase I and along the Gamma - Lambda -Z direction in phase II. The successive structural phase transitions (SPT) in CsPbCl3 at Tc1=47 degrees C, Tc2=42 degrees C and Tc3=37 degrees C are induced by the condensation of the cubic zone boundary mode tau 3 at the M point and the tetragonal zone boundary modes x9 chi and y9 gamma at the Z point separately. The interpretation of these successive displacive phase transitions with the normal vibration modes from the author's study is in good agreement with experimental investigation. A similar result from a previous investigation of layered perovskite RbAlF4, which has a two-dimensional octahedral network, is also compared and discussed.

Tight-binding molecular-dynamics study of phonon anharmonic effects in silicon and diamond.

The anharmonic effects on phonons in silicon and diamond have been studied by molecular-dynamics simulations using an empirical tight-binding Hamiltonian. One-phonon spectral intensities of the zone-center and zone-boundary ({ital X}) modes have been calculated through the Fourier transform of the velocity-velocity correlation functions. This scheme allows a quantitative and nonperturbative study of phonon frequency shift and phonon linewidth as a function of temperature. The results obtained are in good agreement with experimental data.

HighTcsuperconductors as ionic metals and the role of phonons in highTcsuperconductivity

Abstract We have investigated a number of zone center and zone boundary (X-point) modes in La2CuO4 using the full potential Linearized Augmented Plane Wave (LAPW) method and find excellent agreement with experiment for phonon frequencies, showing that the local density approximation (LDA) is an excellent approximation for the total energies, charge density, and static density response in high T c superconductors. Results are compared with those of a non-empirical ionic model for La2CuO4 and YBa2Cu3O7. Self-consistent calculations show that the ionic nature of these materials leads to large changes in the potential with atomic displacements. The ionic contributions to the electron-phonon matrix elements, which were neglected in previous studies, are large and possibly sufficient to explain high T c .

Theoretical calculations and Raman spectrum of intercalation modes in LixInSe

By using an extended linear-chain model which includes the interlayer forces, we have calculated the new vibrational modes, of Li intercalated InSe. The dispersion curves along thekz wavevector perpendicular to the layers for the γ-polytype are determined in the first Brillouin zone. Assuming that the interlayer interaction is not modified upon intercalation and the interaction between lithium atom and adjacent layers in the van der Waals plane has the same value than the interlayer one, the new modes are determined with the force constant given by the rigid layer mode of the, e-polytype at 18 cm−1. This model gives the variation of the acoustic branches and the appearance of two optical intercalation modes at higher frequencies. The Brillouin zone boundary modes of the acoustic branches at 18 and 41 cm−1 in the pure material are calculated to be 22 and 50 cm−1 respectively forx=1/2. The dispersion of the new optical branches is flat along thez-direction and frequencies are obtained at 96 cm−1 for the Li mode perpendicular tokz and at 218 cm−1 for the Li mode parallel tokz. We compare also our results with the Li mode frequencies obtained in a total energy calculation. Raman scattering experiments have been performed in intercalated sample in order to verify the proposed model.

Electronically driven instabilities of La2-xMxCuO4.

We have studied the electronic structure and magnetic and structural instabilities of La/sub 2-//sub x/M/sub x/CuO/sub 4-//sub y/ (M = Sr, Ba) using a tight-binding model and the electron-phonon interaction derived from it. We include both the e/sub g/ orbitals of Cu atoms and the p orbitals of both inequivalent O atoms. For hopping parameters derived from band-structure calculations and a Cu intra-atomic Coulomb repulsion U of 2.5 eV, antiferromagnetic instabilities are favored when the number of electrons in the system is in excess with respect to the stoichiometric compound, while structural instabilities, such as a dimerization of Cu atoms, are more likely to occur for electronic deficient compounds, for which the interaction of the electrons with high-frequency zone-boundary phonon modes has a maximum as a function of the composition parameter. For U>3 eV, the system is unstable against antiferromagnetism for all compositions of interest.

Longitudinal phonons in gallium phosphide at high pressures

Frequencies of the zone-centre and zone-boundary phonon modes in GaP are evaluated ab initio using the density-functional theory within the local-density approximation, with atomic numbers as the only experimental input. The norm-conserving pseudo-potentials are applied with Ceperley-Alder exchange and the plane-wave expansion formulation is used for calculation of total energy. Variation in the LO(X) and LA(X) frequencies at high and very high compressions is predicted. Eigendisplacements determined for the TO(X) and TA(X) modes are compared with the predictions provided by different phenomenological models which were developed for the lattice dynamics in the past.

The optical properties of (TMTSF) 2ReO 4 and (TMTSF) 2BF 4 through the metal-insulator transition, for [formula omitted

The E | a properties of (TMTSF) 2ReO 4 and (TMTSF) 2BF 4 from 30 to 2500 cm −1, above and below their metal-insulator transitions, are presented and compared. Also reported are some details of the experiment, in which all of the measurements were made in a single automatic rapid-scan Fourier spectrometer and with a single small crystal. The new BF 4 results show more clearly the one-dimensional nature of the semiconducting conductivity. Along with the activated totally-symmetric a g modes, a strong triplet thought to be caused by zone-folding of the zone-boundary longitudinal acoustic mode, involving only the TMTSF molecule, is observed near 50 cm −1 in both materials.

Infrared activity of alpha -AlPO4.

Performing polarized reflectivity and absorption measurements in the experimental range 15--1500 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, we have investigated the infrared activity of phonons in aluminum phosphate. We report both ${\ensuremath{\Gamma}}_{2}$ (E\ensuremath{\parallel}c) and ${\ensuremath{\Gamma}}_{3}$ (E\ensuremath{\perp}c) polarized components and, in order to identify all modes predicted by group theory arguments, we compare with similar measurements performed on \ensuremath{\alpha}-quartz. We have found the following. In polarization E\ensuremath{\parallel}c, we resolve from reflectivity spectra all but one infrared-active ${\ensuremath{\Gamma}}_{2}$ components. Since they are exclusively infrared active, they could not be found from any other technique. To investigate the missing mode, which corresponds to the folded acoustic branch, we performed a series of transmission measurements. In this way we could find a weak absorption structure, which appears at room temperature at 48 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. In polarization E\ensuremath{\perp}c, we find 15 infrared-active ${\ensuremath{\Gamma}}_{3}$ components which compare satisfactorily with previously published Raman data. Two modes, at 112 and 126 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, form a close doublet which resolves only when running absorption measurements at liquid-helium temperature. The high-energy component (126 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) comes from the folded acoustic branch and the second is the infrared counterpart in aluminum phosphate of the 128-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonon of \ensuremath{\alpha}-quartz. This is clearly established from a comparison of both reflection and transmission experiments performed on the same sample. Finally, performing a series of oscillator fits, we get quantitative values for (i) the LO-TO splitting of the phonon modes under consideration and (ii) the corresponding oscillator strengths. The series of parameters obtained in this way compare satisfactorily with a simple model of infrared exclusive modes in \ensuremath{\beta}-quartz admixed twice: first, with silent or Raman exclusive components (this is the case in the \ensuremath{\alpha} variety) and, second, with zone-boundary modes (this appears in berlinite when doubling the length of the unit cell).

Lattice dynamics of cristobalite

Abstract Dispersion relations are calculated in a number of symmetry directions for α-cristobalite, using three force constants describing bond stretching, and bond bending at both silicon and oxygen atoms. A Keating representation is used for the first two, but for stability a Born potential was used to describe bending at the oxygen atom. The calculation shows that very-low-frequency zone-boundary transverse acoustic modes arise naturally in the perfect crystal, giving a density of states at low frequencies that explains the low-temperature heat capacity.

Two-strain mechanism of pressure-induced body-centered-tetragonal to hexagonal-close-packed transition in Hg and HgxCd

The body-centered-tetragonal (bct) phase of ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Hg}}_{x}$ ($x>0.25$) alloys is correlated by atomic displacements of the $\mathrm{T}{\mathrm{A}}_{1}[110]〈1\overline{1}0〉$ zone-boundary mode to the high-pressure hexagonal-close-packed (hcp) phase. We have evaluated the degree of softening of this mode by a frozen-phonon calculation. The electronic force was calculated using the linear muffin-tin-orbital scheme. It is found that the uniform strain required to make $\ensuremath{\theta}=120\ifmmode^\circ\else\textdegree\fi{}$ is strongly coupled to the shuffling strain, supporting the recent theory of martensitic transformation by Lindgard and Mouritsen.

Lattice instability and high-Tc superconductivity in La2-xBaxCuO4.

${\mathrm{La}}_{1.85}$${\mathrm{Ba}}_{0.15}$${\mathrm{CuO}}_{4}$ exhibits high-${\mathrm{T}}_{\mathrm{c}}$ superconductivity with an onset temperature near 33 K as measured by resistivity and magnetic susceptibility. The nonsuperconducting end-member compound, ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$, which has an orthorhombic, Cmca structure, exhibits semiconducting behavior. The orthorhombic distortion is proposed to result from a Peierls 2${\mathrm{k}}_{\mathrm{F}}$ instability or a soft zone-boundary phonon mode. The role of Ba is to suppress the instability and stabilize a higher-symmetry tetragonal, I4/mmm structure which is metallic and superconducting.

Magneto-optical activity at the structural phase transition in paramagnetic KMnF 3

The magneto-optical Verdet constant ø has been measured in the paramagnetic phase of KMnF 3 and particularly in the neighbourhood of the cubic-tetragonal phase transition driven by the softening of zone boundary modes. ø is positive and displays a sizeable decrease on cooling, thus indicating the presence of a temperature dependent paramagnetic contribution that, in view of the 6 S ground state of the Mn 2+ ion, is attributed to the role of spin-orbit interaction. In a temperature range of about 20K around T c = 186K, a cusp-shaped anomaly of ø is observed. From the dependence on the wavelength, and by taking into account also EPR linewidth and g measurements and optical absorption spectra, an analysis of the possible mechanisms for the cusp-shaped anomaly is given. It is argued that the enhancement of the critical rotational fluctuations of the MnF 6 octahedra can be responsible for this effect.

Lattice dynamical analysis of β ↔ γ phase transformation in silicon under high pressure

β-tin and the one-atom primitive hexagonal structure (γ phase), the two high-pressure polymorphs of Si, are related to each other by correlated displacement of atoms. This is interpreted in terms of a zone boundary mode softening 1 2 (101) γ . It is confirmed by detailed lattice dynamical calculations.

Structure of the distorted fcc high-pressure phase of the trivalent rare-earth metals

The crystal structure of the high-pressure distorted fcc phase, which is so far the last in the sequence of crystal structures for the trivalent rare-earth metals, is assigned the trigonal space group $P{3}_{1}21({D}_{3}^{4})$ or $P{3}_{2}21({D}_{3}^{6})$ with $Z=6$. In this space group the distortion of the fcc lattice occurs continuously and is consistent with the second-order nature of this phase transition. The observed intensity ratios of reflections for the distorted fcc phase of Y, La, and Pr are satisfactorily explained. This structure can be described by the softening of a zone-boundary longitudinal phonon mode accompanied by the shearing of the hexagonal layers in the basal plane.

Temperature and Uniaxial Stress Dependence of Rigid Layer Mode in Squaric Acid (H2C4O4)

The rigid layer mode of a shear type in squaric acid has been studied at several temperatures by Brillouin and Raman scatterings under a uniaxial stress applied perpendicularly to layer planes. The temperature and uniaxial stress dependences of a transverse acoustic mode ( c 44 ) in the low temperature phase are essentially the same as those of the low frequency A g -optic mode below T c , which corresponds to the zone-boundary acoustic mode in the high temperature phase. This rigid layer mode is analyzed by a one dimensional model with a single force constant f 1 between the nearest neighbor layers and the value of f 1 is calculated to be 1.18 ×10 4 dyn/cm at room temperature. The variation of f 1 with interlayer distance is also estimated.