Zone-center Phonon Frequencies Research Articles

Zone center phonon frequencies in tetragonal zirconia: lattice dynamical study and new assignment proposition

A normal mode calculation of the zone center phonons in the tetragonal structure of ZrO2 compound has been performed with particular emphasis on the low frequency modes. A restricted set of stretching and bending force constants have been introduced and lead to a good agreement between theoretical and experimental Raman and IR phonon frequencies. The Eg symmetry of the two low frequency Raman modes which are involved in the softening process observed with increasing pressure were confirmed and none were left for a low frequency A1g totally symmetric mode as proposed in the literature.

Influence of Spontaneous and Piezoelectric Polarizations on the Lattice Dynamics of III-Nitride Structures

ABSTRACTThe influence of pyroelectric and piezoelectric polarizations on the lattice dynamics of strained III-nitride based structures is investigated within a macroscopic framework. New relationships between stress and strain are derived, which take into account the piezoelectric fields, which appear in the strained III-nitride layers. Consequently, the strained phonon frequencies in such systems differ from those calculated within the elasticity theory framework. In the case of strained, free-standing GaN/AlN superlattices grown along the [0001] axis, the difference of the spontaneous polarizations of GaN and AlN also contributes to the change in the effective strain along the growth direction. The corresponding shift of the zone center phonon frequencies of GaN and AlN might be negligible or significant, depending on the value of the ratio of the GaN and AlN layer thickness.

The Raman spectra of the hexagonal and cubic (spinel) forms of Ge3N4: an experimental and theoretical study

The Raman spectra of the hexagonal (β) and cubic spinel (γ) forms of Ge3N4, newly obtained by high-pressure synthesis, have been measured and are compared with zone-center phonon frequencies calculated using first principles methods in a plane wave pseudopotential local density approximation. The observed and calculated phonon frequencies are in excellent agreement and we use the calculated values to perform mode assignment for both the phases. Both phases show all the expected Raman active modes.

Linear augmented-plane-wave frozen-phonon calculation, shell-model lattice dynamics, and specific-heat measurement of SnO

An ab initio linear augmented-plane-wave (LAPW) calculation of the zone-center phonon frequencies of SnO has been performed. ${E}_{g}$ symmetry has been ascribed to the mode observed at $113 {\mathrm{cm}}^{\ensuremath{-}1}$ in Raman measurements, discarding a previous ${B}_{1g}$ assignment. The other phonon modes measured by Raman spectroscopy are also well reproduced. A shell model has also been developed that gives good agreement of the zone-center frequencies compared to the measured data and the LAPW results. Specific-heat measurements have been performed between 5 and 110 K. Computation of the specific heat and the M\"ossbauer recoilless fraction with the improved shell model shows a good agreement with the experimental data as a function of temperature.

Noncubic Behavior of Antiferromagnetic Transition-Metal Monoxides with the Rocksalt Structure

We give evidence that some nonmagnetic (i.e., spin-integrated) properties of the antiferromagnetic late transition-metal monoxides (MnO, FeO, CoO, NiO) are substantially noncubic below the N\'eel temperature even when assuming the ideal rocksalt structure for the ions. Our findings, which are at variance with the currently accepted picture, are based on ab initio and model calculations for the case study of MnO. The calculated zone-center optic phonon frequencies and Born effective charge tensor of this material show a significant magnetic-induced anisotropy.

Electronic Raman and infrared spectra of acceptors in isotopically controlled diamonds

The Lyman spectrum of substitutional boron acceptors in diamonds with natural composition and that in a ${}^{13}\mathrm{C}$ diamond exhibit remarkably similar features, but shifted to higher energies in the latter by 0.4--1.5 meV. Additional lines appear when the spectra are recorded as a function of temperature, indicating the thermal population of a level ${\ensuremath{\Delta}}^{\ensuremath{'}}\ensuremath{\sim}2\mathrm{meV}$ above the ground state; this can be interpreted as the spin-orbit splitting of the $1s$ acceptor ground state into ${1s(p}_{3/2})$ and ${1s(p}_{1/2}),$ the latter located ${\ensuremath{\Delta}}^{\ensuremath{'}}$ above the former. The Raman-allowed ${1s(p}_{3/2})\ensuremath{\rightarrow}{1s(p}_{1/2})$ electronic transition is directly observed at 2.07(1) and 2.01(1) meV in the Raman spectrum of natural and ${}^{13}\mathrm{C}$ diamond, respectively. Polarization features of the ${\ensuremath{\Delta}}^{\ensuremath{'}}$ Raman line reveal that it is predominantly ${\ensuremath{\Gamma}}_{5}$ in character, as predicted by a theoretical calculation formulated in terms of the known values of Luttinger parameters. The theoretical expression for the Raman cross section for ${\ensuremath{\Delta}}^{\ensuremath{'}}$ enables the acceptor concentration to be deduced from an intercomparison of the intensity of the ${\ensuremath{\Delta}}^{\ensuremath{'}}$ line and that of the zone-center optical phonon. The presence of boron acceptors produces a quasicontinuous absorption spectrum in the range of the optical phonon branch, flanked by a sharp feature at the zone-center optical phonon frequency; their appearance can be attributed to the partial breakdown of the translational symmetry and the activation of otherwise inactive vibrations.

A lattice dynamical investigation for the zone-centre phonon frequencies of the NaMnF 3 perovskite

A short range force constant model has been applied to investigate the lattice dynamics of NaMnF 3 in its orthorhombic phase. The calculated zone-centre Raman frequencies agree fairly well with the measured values. The infra red measurements have been assigned the proper species for the first time on the basis of the present calculations.

Phonons in La2CuO4: Local density calculations

A full set of zone center phonon frequencies and polarization vectors of tetragonal I4 mmm La 2 CuO 4 are determined using local density approximation calculations. Reasonable agreement with experimental frequencies is obtained for modes that do not involve c-axis motions of the plane O atoms or motions of the apical O atoms parallel to the CuO 2 planes. The modes that do involve such displacements have frequencies that are lower than experiment. This is understood in terms of stiffening of these modes due to tilts of the octahedra in the actual structure. Two soft Γ point modes involving the apical O are found. However, the Γ point instability is much weaker than the X point tilt mode.

Pressure-dependent dynamical and dielectric properties of cubic SiC

The plane-wave pseudopotential approach to the density-functional theory (DFT) in the local-density approximation (LDA) is used for an ab initio calculation of pressure-dependent structural, lattice-dynamical, and dielectric properties of cubic silicon carbide (3C SiC). Whereas the influence of hydrostatic pressure on the structural and the underlying bonding properties is treated within the DFT-LDA, the linear-response theory is applied to describe the pressure dependence of the zone-centre phonon frequencies, the dielectric constant, and the Born effective charge of 3C SiC. Furthermore, the results for 3C SiC are compared with the corresponding ones for silicon and diamond.

Optical phonons in GaN

We report on all optically active phonon frequencies of wurtzite GaN determined using Raman, infrared reflection, and attenuated total reflection spectra of a high quality GaN film of 2 μm thickness. We also show results of lattice dynamical calculations using a rigid ion model. Force constants and charge as fitting parameters were determined so as to reproduce all zone-center phonon frequencies and sound velocities for the high symmetry lines. We present phonon dispersion curves and phonon density of states of wurtzite GaN.

Lattice dynamics of CuAlS 2 and CuAlSe 2

We have measured the first-order Raman spectra of CuAlSe 2 and the second-order Raman spectra of CuAlS 2 and CuAlSe 2, and reexamined two-phonon absorption spectra of CuAlS 2. Lattice dynamical calculations have been performed using a rigid ion model. Force constants and charges as fitting parameters have been determined so as to reproduce zone-center phonon frequencies and the two-phonon spectra observed. Calculated two-phonon density of states shows reasonable agreements with those spectra.

Generalized-gradient approximations to density-functional theory: A comparative study for atoms and solids.

Pseudopotential calculations within density-functional theory for a few selected solids (Si, GaAs, and Al) are used to assess the validity of two generalized-gradient approximations (GGA's), the one proposed by Becke and Perdew (BP) and the more recent one proposed by Perdew and Wang (PW) in comparison with the currently used local-density approximation (LDA). The GGA's give total energies of atoms and cohesive energies of solids that are closer to experiment than the LDA results. Lattice constants are reproduced with the same accuracy as in LDA, while bulk moduli and zone-center phonon frequencies are underestimated with respect to both the LDA and the experimental values. Comparison to all-electron results shows that in both GGA schemes the validity of the pseudopotential approach is as good as in LDA. The predictions of the two GGA's are similar, the PW functional yielding results marginally, but systematically, closer to experiment. The calculated values of the transition pressure in Si between the diamond and the beta-tin structure are 72 kbar (LDA), 164 kbar (BP), and 135 kbar (PW), to be compared with the two available experimental values of 103 and 125 kbar.

Optical Absorption Spectra in One-Dimensional Mixed-Valence Complexes Pt-X (X=Cl, Br, I)

Optical absorption spectra associated with non-linear excitations in halogen-bridged mixed-valence Pt complexes Pt-X (X=Cl, Br, I) are investigated theoretically on the basis of the one-dimensional single-band Peierls-Hubbard model. The expressions for the zone-center phonon frequencies in the CDW state are derived by calculating the second order expansion coefficients of the adiabatic potential. Then, the parameters in the model Hamiltonian are determined by utilizing the observed values of the energy gap, the halogen displacement and the frequencies of the zone-center phonons. The optical absorption spectra associated with the non-linear excitations such as solitons and polarons are calculated, and the origins for the three lines of photo-induced mid-gap absorption observed in each Pt-X are assigned as follows. In Pt-Cl all the three lines are due to polarons. In Pt-Br and Pt-I, on the other hand, two of the three lines are due to polarons, but the remaining one is due to charged-solitons.

Ground-state properties of CoSi2 determined by a total-energy pseudopotential method.

We calculate the lattice properties and electronic structure of cobalt disilicide using an ab initio total-energy method with optimized pseudopotentials. Special attention is paid to the development of a soft robust pseudopotential for the 3d element Co. The calculated band structure of ${\mathrm{CoSi}}_{2}$ agrees well with the results of all-electron studies and the equilibrium lattice constant, bulk modulus, and zone-center phonon frequencies obtained are in good agreement with experimental data.

First-principles investigation of ferroelectricity in perovskite compounds.

We have used a first-principles ultra-soft-pseudopotential method in conjunction with an efficient preconditioned conjugate-gradient scheme to investigate the properties of a series of eight cubic perovskite compounds. The materials considered in this study are ${\mathrm{BaTiO}}_{3}$, ${\mathrm{SrTiO}}_{3}$, ${\mathrm{CaTiO}}_{3}$, ${\mathrm{KNbO}}_{3}$, ${\mathrm{NaNbO}}_{3}$ ${\mathrm{PbTiO}}_{3}$ , ${\mathrm{PbZrO}}_{3}$, and ${\mathrm{BaZrO}}_{3}$. We computed the total-energy surface for zone-center distortions correct to fourth order in the soft-mode displacement, including renormalizations due to strain coupling. Quantities calculated for each material include lattice constants, elastic constants, zone-center phonon frequencies, Gr\"uneisen parameters, and band structures. Our calculations correctly predict the symmetry of the ground-state structures of all compounds whose observed low-temperature structure retains a primitive five-atom unit cell. The database of results we have generated shows a number of trends which can be understood using simple chemical ideas based on the sizes of ions, and the frustration inherent in the cubic perovskite structure.

A study of the interatomic interaction in oxide spinel MnCr 2O 4

The strengths of interatomic interaction in oxide spinel have been investigated by using a short-range force constant model. The interatomic ionic interaction between Cr-O in MnCr 2O 4 dominates the other interatomic interactions. The zone-centre phonon frequencies thus calculated are found to be in agreement with the observed results.

Lattice Dynamics of Oxide-Spinel ZnCr2O4

The short-range force model has been applied to study the zone-center phonon frequencies of oxidespinel ZnCr2O4. A comparative study of interatomic forces is also made between oxide spinel ZnCr2O4 and chromium sulfide/selenide spinels. Our short-range model provides fair agreement with the available experimental results.

Lattice vibrations in Bi 2CaSr 2Cu 2O 2

The lattice dynamics of Bi 2CaSr 2Cu 2O 8 is worked out employing the conventional central force model. The nearest neighbour interactions within a radius of 4 Å are taken into account. The force constants for these interactions are calculated from the already available crystal data and from the vibrational frequencies of diatomic molecules. The calculated values of zone centre phonon frequencies compare reasonably with the available Raman scattering data.

Zone-center phonon frequencies for graphite and graphite intercalation compounds: Charge-transfer and intercalate-coupling effects.

The frequencies of several zone-center vibrational modes in graphite have been calculated from first principles, with results in very good agreement with experiment. By studying the effect of charge transfer and lattice-constant change on ${E}_{2g}$-mode frequencies, we find that the systematic stage dependences of both Raman- and infrared-active modes in graphite intercalation compounds can be understood by introducing a coupling to the intercalate of unconventional form.

Local-field effects and phonon screening in polar semiconductors

We study here the redistribution of the electronic charge associated to zone-center phonon modes in polar semiconductors, within the linear-response microscopic theory of lattice dynamics. In a polar material zone-center phonons are only well defined in the longwavelength limit. Both transverse and longitudinal phonons correspond, in the ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{0}\ensuremath{\rightarrow}0$ limit, to the same ionic displacements in the unit cell; owing to the presence of long-range forces, they induce a different microscopic polarization. For a TO phonon the electronic response is exactly the same as induced by a frozen-in distortion having the lattice periodicity (${\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{0}=0$). We develop in detail the formalism needed to describe the screening difference between LO and TO phonons, which is basically due to nonanalytic terms in the dielectric matrix. We show that this longitudinal-transverse difference is closely related to other basic local-field effects, which have recently been studied. Detailed calculations are presented for ZnSe; in order to illustrate the trends with increasing ionicity the results for Ge, which is nonpolar and isoelectronic to ZnSe, are also shown. Both calculations are based on first-principles dielectric matrices recently published. We show that the effects of the local fields are very important and essential to account for the basic trends with increasing ionicity. The same feature has recently been proved for the calculated zone-center phonon frequencies.