Modes of vibrations due to (U-center + additive anion impurities) in KC1—II

Defect modes due to U-centers in potassium chloride containing additive anion impurities have been computed by Green's functions techniques. Local vibrations due to U-centers in alkali halides have cubic symmetry, but when one of the twelve nearest neighbour anions is replaced by an additive impurity, the site symmetry of the system reduces from O_h to C_2v and gives rise to new vibrational modes. The phonon Green's functions have been analysed according to the irreducible representation of the point group symmetry, pertaining to the substitutional impurity. We have considered the vibrations of the U-center, additive anion impurity and their nearest neighbours i.e. 36-dimensional defect space. Using group theory, symmetry coordinates were constructed and the 36 x 36 dimensional matrix was block diagonalised into various irreducible representations. The computed local mode frequencies have been conpared with the experimental measurements. Reasonably good agreement is found between them. The computed results for resonant mode frequencies are also displayed.     

Defect modes due to substitutional impurities in FCC lattice: Green's function approach

Lattice dynamical study of monoatomic fcc crystals containing substitutional impurities has been made by the Green's function technique, using group theory. The impurity and its 12 nearest neighbors constitute an XY₁₂ impurity space having O_h symmetry. The phonon Green function matrix is analyzed according to the irreducible representations of the point group pertaining to the substitutional impurity in the fcc lattice. The effects due to change in mass at the impurity site and the change in nearest neighbor force constants for the impurity-host atom interactions are taken into account. Analytical expressions for the various modes of vibrations pertaining to the defect space have been obtained. Local mode frequencies due to various substitutional impurities, corresponding to F_1u mode (defect atom moving) have been computed. A special model is chosen for the defecthost force and it is assumed that there are no distortions of the lattice structure due to the defect. A Kihara hardcore potential with parameters fitted to neutron data has been used to compute lattice dynamics and Green functions of the host lattices. Our theoretical results have been compared with available experimental and theoretical results. Our results show reasonably good agreement with experimental results.     

Off-center substitutional ions in alkali-halide crystals

The potential wells of alkali and halogen ions as impurities in alkali halides are investigated by means of a deformation-dipole model with single-ion parameters. The calculations indicate that Li⁺ is off center in seven and F^? in six of the sixteen rocksalt-type crystals considered. In about half of the off-center systems the configuration has D_4h symmetry if the impurity is kept at its lattice position. The minimum-energy configuration of the off-center system KCl:Li⁺ is calculated in detail, and the influence of hydrostatic pressure is investigated. Our results are in qualitative agreement with experiment.     

The symmetry properties of the normal vibrations of C-15 type superconductor HfV2

The symmetry species of the normal vibrations of HfV₂ are analysed. The symmetry vectors at Г, δ and X, and phonon dispersion ω(δ) are given. The irreducible representation Г'₂ is responsible for the structural transition O_h⁷ → C_2v²⁰.     

U-center modes in potassium bromide containing additive cation impurity

The localized modes due to hydride ion in potassium bromide containing rubidium as additive impurity have been computed by Green function method and compared with the experimental measurements.     

Local modes due to U-centers in RbCl containing potassium additive impurity

The frequencies of the localised modes of vibrations of hydride ions in rubidium chloride containing cation impurity have been computed by Green function technique and compared with the experimental measurements. There is found to be a satisfactory agreement between the theoretical and the experimental values.     

Peculiarities of the SEHRS spectrum of 4,4′-bipyridine molecule

The SEHRS spectrum of 4,4′-bipyridine is analyzed on the base of the Dipole-Quadrupole theory. It is demonstrated that there appear strong lines caused by vibrations transforming after the unit irreducible representation of the D₂ symmetry group, which is most probably describes the symmetry properties of the molecule. These lines are nearly forbidden for the molecule, adsorbed on rough metal surfaces. Appearance of these lines is associated with a strong quadrupole light–molecule interaction, which exists in this system. In addition, there are lines caused by contributions from both the vibrations transforming after the unit irreducible representation A and the representation B₁, which describes transformational properties of the d_z component of the dipole moment, which is perpendicular to the surface. This result is associated with the specific geometry of the molecule, when the indicated vibrations can be nearly degenerate and cannot be resolved by the SEHRS spectra analysis. Analysis of the SEHRS spectra for the possible geometry of the molecule with the D_2h symmetry group leads to similar results. This issue is in a full coincidence with the results of the SEHRS Dipole-Quadrupole theory.     

Electron-lattice coupling of F centers: Particular case of NaI: F

Absorption and magnetic circular dichroism studies of the F centers in NaI reveal a strong electron-lattice coupling with the vibration modes of Γ₁⁺ symmetry in comparison with those of Γ₃⁺ and Γ₅⁺ symmetry. On the other hand, the F electron exhibits in its first excited state a large spin-orbit coupling, in agreement with the value previously calculated. These results are confirmed by the Raman spectra which show a predominant intensity for the Γ₁⁺ modes, particularly for the resonant mode at 113 cm^?1.First and second-order Raman spectra have been calculated using a “quasi-resonant” theory in which the vibrations of the ions up to the fifth shell have been taken into consideration. We have been able to determine from these calculations absolute values for the contributions of the different types of vibration modes to the broadening of the F-absorption band.     

Defect modes due to H− - D− pair impurities in KCl and KBr

Localised modes due to H^? - D^? pair impurities aligned in the [110] direction in KCl and KBr have been computed using a Green's function approach. The defect space used consists of 12 particles; the two defect ions (H^? and D^?) and their ten nearest neighbours (K⁺ ions). The system has C_2ν site symmetry around the defect ions, and this property has been used to block diagonalise the relevant 36 × 36 matrix by group theoretical techniques. Various irreducible representations thus obtained have been used to compute the defect modes. Numerical values of the various Green's functions computed on the basis of neutron-fitted shell model parameters were used. Mass changes as well as changes in the short range interactions were considered while forming the perturbation matrix. The localised modes computed are seen to be in good agreement with the experimentally observed values.     

Anderson localization and the pseudogap in the energy spectrum of holes in PbTe: Tl under resonant scattering

This paper reports on a comprehensive study of the effect of additional doping with the Na acceptor impurity on the low-temperature resistivity of PbTe samples doped with Tl (2 at %), an impurity producing a band of resonant states within the valence-band spectrum. By additional doping with Na, we have shifted the Fermi level within the band of the resonant states of Tl in PbTe and varied the hole filling (k _h ) of the thallium impurity states. The larger part of the PbTe: (Tl,Na) samples transfers to the superconducting state with a critical temperature T _c = 0.4–2.3 K. The T _c (k _h ) relation obtained argues for the fact that, in the region of resonant states in PbTe: Tl, Anderson localization of holes and a pseudogap in the density of delocalized states are observed.     

Third-order elastic constants for 2:2 chalcide crystals possessing the sodium chloride structure

Third-order elastic constants of 45 chalcide crystals having the sodium chloride structure are reported using Born-Mayer potential model. We have considered repulsive interaction up to second nearest neighbours. The temperature coefficients of the third-order elastic constants have also been computed for these crystals. As is the case for NaCl-type alkali halides we find that C₁₁₁, C₁₁₂, C₁₆₆ are negative and C₁₄₄ are positive for 2:2 chalcide crystals possessing the NaCl-type structure. We have found that a₁₂₃, a₄₅₆ and a₁₄₄ are negative whereas a₁₁₂ and a₁₆₆ are positive, once again in agreement with the situation found for the alkali halides a₁₁₁ values are positive for alkali halides whereas they are both positive and negative depending upon the interionic distance for the chalcide crystals. We have found that the nature of the variation of C⁰_αβγ with interionic separation is similar for alkali halides and for the 2:2 chalcides having the NaCl-structure. We have also computed the values of the pressure derivatives of second-order elastic constants for MgO, CaO, and SrO which agree well with the experimental values indicating the satisfactory nature of our computed data for C_αβγ.     

Radiation defect formation in strontium and calcium fluoride crystals doped by divalent cadmium and zinc ions

Ionization radiation is shown to reduce impurity ions to the univalent state in strontium and calcium fluoride crystals doped by divalent cadmium and zinc ions. In this case, a univalent ion is surrounded by eight equivalent fluorine ions and exhibits cubic symmetry O _h . At room temperature, the symmetry of the center is revealed to be sequentially lowered to C _3v and then to C _2v owing to the addition to the nearest environment of the impurity univalent ion of one or two anion vacancies, respectively, which are intrinsic defects not forming in undoped strontium and calcium fluoride crystals. Stable intrinsic defects are assumed to form through the separation of anion vacancy-interstitial fluorine ion pairs in the electric field induced by the reduced impurity ions. This electric field lowers the energy barrier to thermal separation of charged intrinsic defects.     

Vibrational properties of the F A (Li+) center in alkali halides

Abstract

The on- or off-axis behavior and the vibrational properties of the F _A (Li⁺) center are investigated in several alkali halides by means of polarized resonant Raman scattering. The observed Raman modes are interpreted and classified according to their nature and frequency. A comparison between on- and off-axis systems and between the vibrational modes of the isolated Li⁺ and the F _A (Li⁺) center reveals a displacement of the Li⁺ equilibrium position parallel to the F _A (Li⁺) defect axis and, due to the small impurity size, away from the adjacent F center.     

B2羣和基本粒子强相互作用

计算了B₂羣不可约表示的直接乘积4×4,4×5,4×10和5×5分解中的约化系数。给出了它在基本粒子强相互作用对称性方面的应用的若干例子:推导了散射截面关系和低维数表示的质量关系,讨论了共振态的填充和衰变情况以及R反演不变性等。     

Ammonium dynamics in the disorder a-phase of K1- x (NH4) x Y (Y=Cl,Br, I). a neutron scattering study

Temperature and concentration effects on the lattice parameters and the amplitude weighted phonon density of states (AWPDS) in the mixed salts of ammonium-potassium halides were investigated by neutron powder diffraction (NPD) and incoherent inelastic scattering (IINS). In the disorder α-phase (NaCl type), ammonium ions perform a fast stochastic reorientation at phonon frequencies rate, down to ca. 80 K. The IINS spectra at 10 K displayed the four distinct ammonium excitations, two (resonant) modes below and two (localised) above the cut-off frequency of the AWPDS of potassium halides. The high frequency localised modes correspond to the translational and librational vibrations of NH₄ ions. These modes are typical for ordered phases of ammonium halides. Ammonium concentration effects on the localised and resonant modes were studied for the K_{1? x} (NH₄) _x I mixed salts and the harmonic excitations of ammonium in the hypothetical low temperature α-phase of NH₄I were approximated to ca. 30, 95, 155 and 250 cm^?1. In the real low temperature ordered γ-phase of NH₄I, translational ammonium vibrations were observed at ca. 140-160 cm^?1 and librational at ca. 300 cm^?1.     

Manifestation of a strong quadrupole interaction and peculiarities in the SERS and SEHRS spectra of 4,4'-bipyridine

The paper analyzes Surface Enhanced Raman Scattering (SERS) and Surface Enhanced Hyper Raman Scattering (SEHRS) spectra of 4,4'-bypiridine molecule for two possible geometries, which are described by D ₂ and D _2h symmetry groups. It is pointed out on appearance of sufficiently strong lines, caused by vibrations with the unit irreducible representation for both possible configurations. Appearance of these lines in the SEHRS spectrum points out the existence of a strong quadrupole light-molecule interaction. In addition one observes the lines, caused by vibrations both with the unit irreducible representations A or A _g and the irreducible representation B ₁ or B _1u . The last ones describe transformational properties of the d _z component of the dipole moment, which is perpendicular to the surface. This property of the spectrum is caused by peculiarity of the geometry of the molecule, which consists of two benzene rings, which are weakly connected with each other. The linear combinations of the vibrations of the rings create two nearly degenerated symmetric and anti symmetrical states, which cannot be identified in the experimental spectra. The result is in a full agreement with the dipole-quadrupole theory of SERS and SEHRS.     

Jahn–Teller distortions considered as steady state bifurcations

The steady state bifurcation model can be used to determine the Jahn–Teller distortion modes of a molecule having symmetry point group G to lower symmetry structures having symmetry point groups H _j ???G. In order to find such distortion modes, the trace formula arising from bifurcation theory is applied to all subgroups H _j of G to give a sum of irreducible representations Γ(G?→?H _j ) corresponding to the possible distortion modes of G to H _j . These subgroups H _j correspond to epikernel subgroups of G for any irreducible representation of G found in Γ(G?→?H _j ). This method has been applied to Jahn–Teller distortions of square (D _{4 h} ), octahedral (O _h ), and icosahedral (I _h ) molecules leading to lower symmetry structures.     

Vibrational Spectra of Some Substituted Benzene Derivatives

Abstract

The infrared spectra of 1,2,3-; 1,2,4- and 1,3,5-trimethylbenzenes have been recorded in the liquid phase in the region 250–4000 cm^?1 on a Perkin Elmer Grating Spectrophotometer model 521. Under the general symmetry considerations, the molecule 1,2,4-belongs to C_2v point group, the 1,2,3-isomer belongs to Cs and the 1,3,5-isomer to D_3h point group. The observed bands have been assigned to different modes of vibrations.     

I.R. absorption due to H− and D− Ions in BaClF and SrClF

The i.r. absorption spectra sssociated with the vibrations of H^? and D^? ions in SrClF and BaClF have been studied in the range 600–2000cm^?1.The U centers are in fluorine sites. Because of the D_2d symmetry of the fluorine site, the triple degeneracy of the U center local mode in crystals of cubic symmetry, is split in BaClF and SrClF. In these crystals (space group D⁷_4h) unlike what happens with the cubic crystals, the symmetry types of the lattice band modes which give rise to the local mode sidebands, can be known experimentally. These band modes are almost only of E symmetry type. The E symmetry modes involve a vibration of the U center.A calculation of the local mode frequencies in BaClF:H^? from the experimental one in BaF₂:H^?, has been performed. An H^? ion shell model is more adequate than a rigid ion model to account for the frequencies and the relative intensities of the localized vibrational lines. The best agreement is obtained when the shell charge and the crystal polarizability of the H^? ion in BaF₂ are respectively ?1.3 e and 2.6 ų.