Translatory Modes Research Articles

Effect of Molecular Size and Particle Shape on the Terahertz Absorption of a Homologous Series of Tetraalkylammonium Salts

The absorption coefficient and refractive index have been measured for a homologous series of tetraalkylammonium bromides over the frequency range 0.3-5.5 THz. Spectral features are found to shift to lower frequencies as the molecular mass is increased, as expected. However, to understand the detailed structure of the observed spectral features, density functional perturbation theory calculations have been performed on the first four crystalline compounds in the series. From these calculations, we find that each spectrum is dominated by three translatory modes involving asymmetric motion of the ammonium cation and bromine counterion, although the overall number of active modes increases with increasing molecular size. The experimentally observed absorption is not completely described by the infrared active phonon modes alone. We show that it is also necessary to include the coupling of the phonon modes with the macroscopic field generated by the collective displacement of the vibrating ions, and we have applied an effective medium theory, which accounts for particle shape to allow for this effect in the calculation of the terahertz spectra.

Crystal and molecular structure of ammonium beryllium sulfate dihydrate, (NH4)2Be(SO4)2·2H2O

In this paper we report the crystal and molecular structure of the title compound, (NH4)2Be(SO4)2·2H2O, as determined by single-crystal X-ray diffraction and vibrational spectroscopy data.(NH4)2Be(SO4)2·2H2O crystallizes in the monoclinic space group P21/c (a=11.448(2), b=11.876(2), c=7.439(1)Å, β=96.64(1)°, V=1004.6Å3, Z=4, R1=0.036 for 3753 Fo>4σ(Fo) and 185 variables), and is isotypic with the respective potassium and rubidium sulfates and the potassium selenate. The crystal structure is built from three-membered tetrahedral chain fragments, consisting of a central BeO2(H2O)2 group and two adjacent SO4 tetrahedra. These building blocks are linked by rather strong hydrogen bonds of the water molecules (O⋯O=2.66–2.77Å) and by moderate to weak hydrogen bonds of the NH4 groups (N⋯O≥2.78Å) to a three-dimensional framework structure.The infrared bands corresponding to the stretching modes ν3 and ν1 as well as the Raman band corresponding to ν1 of the SO42- ions are observed in the spectra as doublets, thus reflecting the existence of two crystallographically different sulfate ions. The spectroscopic experiments reveal that the sulfate tetrahedra exhibit a remarkably large extent of energetic distortion as deduced from the values of Δν3 (site group splitting) and Δνmax (the difference between the highest and the lowest wavenumbered component of the stretching modes) (111 and 183.5cm−1, respectively), which could not be predicted from the structural data. The comparison of the spectral region widths of the stretching and bending modes of the SO42- ions allows us to assume that these ions undergo a stronger energetic distortion with respect to the SO bond lengths than that with respect to the OSO bond angles. The water librations couple intensively with both the translatory modes of the Be2+ cations (BeO4 skeleton vibrations) and the normal modes of the sulfate ions, thus producing small isotopic shifts (for example, the ratio νr(H2O)/νr(D2O) has value of 1.12). The strength of the hydrogen bonds formed by the water molecules in the title compound is also commented in comparison with that of the hydrogen bonds in the respective isomorphous potassium and rubidium compounds.

Potassium beryllium sulfate dihydrate, K 2Be(SO 4) 2·2H 2O: Crystal structure and infrared spectroscopy

The crystal and molecular structure of the title compound, K 2Be(SO 4) 2·2H 2O, as determined by single crystal X-ray diffraction and infrared spectroscopy is reported and discussed. K 2Be(SO 4) 2·2H 2O crystallizes in the monoclinic space group P2 1/ c ( a=11.143(2), b=11.515(2), c=7.314(1) Å, β=95.08(1)°, V=934.8 Å 3, Z=4, R1=0.034 for 3524 F o>4 σ( F o) and 153 variables). The structure is characterized by tetrahedral chain fragments consisting of a BeO 2(H 2O) 2 group sharing corners with two SO 4 tetrahedra. These [Be(SO 4) 2(H 2O) 2] 2− units are interlinked by irregular KO 7 polyhedra and hydrogen bonds. Generally, the observed bond lengths and angles comply well with crystal chemical experience. Most of the infrared and Raman bands corresponding to the internal vibrations of the SO 4 2 − ions appear as doublets, thus reflecting the existence of two crystallographically different [SO 4]-tetrahedra in agreement with the structural data. The strengths of the hydrogen bonds as deduced from the infrared wavenumbers of the uncoupled OD modes of matrix-isolated HDO molecules (bands at 2278, 2352 and 2388 cm −1, liquid nitrogen temperature) are discussed in terms of the the O w⋯O bond distances, the different hydrogen bond acceptor capabilities of the oxygen atoms and the Be–OH 2 interactions. The intramolecular OH bond lengths are derived from the ν OD vs. r OH correlation curve [J. Mol Struct. 404 (1997) 63]. The water librations couple intensively with the translatory modes of the Be 2+ ions (BeO 4 skeleton vibrations) and the normal modes of SO 4 2 − ions, thus producing small isotopic shifts. The SO 4 2 − guest ions matrix-isolated in the isostructural host lattice K 2Be(SeO 4) 2·2H 2O exhibit doublet bands in the region of the stretching modes (the bands corresponding to the bending modes could not be recognized well), thus indicating a statistical distribution of the guest ions over the two available crystallographic positions. The distortion of the SO 4 2 − guest ions in the host selenate lattice is weaker than that of the same ions in the neat sulfate owing to the larger unit-cell volume of the host compound, i.e. to the smaller repulsion potential of the host lattice.

Beryllium selenate tetrahydrate, BeSeO 4·4H 2O: crystal structure and infrared spectroscopy

The crystal and molecular structure of the title compound, BeSeO 4·4H 2O, as determined by single crystal X-ray diffraction and infrared spectroscopy is discussed. BeSeO 4·4H 2O crystallizes in the orthorhombic space group Cmca (at 295 K: a=11.920(1), b=11.449(1), c=10.764(1) Å, V=1468.8 Å 3, Z=2, wR2=0.057 for 2035 reflections and 68 variables, R1=0.022). The crystal structure is composed of isolated Be(H 2O) 4 and SeO 4 tetrahedra which are interconnected by strong hydrogen bonds with O w⋯O lengths between 2.619 and 2.661 Å. Contrary to expectation, the cell volume and the mean Be–O and Se–O distances increase with decreasing temperature. The structure is closely related with that of acentric tetragonal BeSO 4·4H 2O, but differs in pronounced polyhedral rotations and a partial rearrangement of the hydrogen bonding scheme. The infrared spectrum of BeSeO 4·4H 2O in the region of the uncoupled OD modes (matrix-isolated HDO molecules) reveals that very strong hydrogen bonds are formed in the title compound, analogical to other hydrated beryllium salts due to the strong synergetic effect of the Be 2+ ions. The appearance of two bands only (2327 and 2239 cm −1) corresponding to OD stretches instead of four expected is owing to both the similar O w⋯O hydrogen bond distances and the strong Be–OH 2 and O w⋯OSeO 3 interactions. The water librations which couple intensively with the translatory modes of the Be 2+ ions (BeO 4 skeleton vibrations) are also discussed. Matrix-isolated SO 4 2 − guest ions in BeSeO 4·4H 2O display a higher local symmetry (close to T d ) than the crystallographic one ( C 2( x), in correlation with the host ion distortion and the large unit-cell volume of the host (repulsion potential of the lattice) if the S–O stretching modes are considered.

Adaptive synchronization control of the magnetically suspended rotor system

An adaptive controlapproach to the implementation of synchronization control forthe magnetically suspended rotor system is presented. The controlsystem enables a translatory mode for the whirling rotor alongthe bearing axes, thereby eliminating the gyroscopic effectsthat can vastly degrade the rotor stability at high speeds. Thecontrol method features the integration of adaptive control andcross feedback control for the electromagnetic circuit, in whichan adjustment system is trained to tune the adaptation parametersto minimize the differential errors of state variables throughouta cross coupling controller. Under this control process, thecontrol variables are updated in a way to suppress the conicalmodes against the gyroscopic forces. This paper develops twokinds of synchronization control algorithms in conjunction withan optimization design, and the simulation of synchronizationcontrol for a magnetically suspended rotor system is presented.

The study of phase transition of KHF 2 doped with sodium ions with Raman intensities of the lattice modes as the order parameter

The phase transition of doped K 1- x Na x HF 2 is studied with the K + translatory mode and the HF − 2 librational mode, which are Raman active in the low temperature phase while inactive in the high temperature phase, as the order parameter. Particular attention is paid to the elucidation of the critical exponent β which is defined as the parameter relating the lattice Raman intensity to the temperature near T c through ( T c - T) β. β values for various dopings are interpreted to understand the dynamics of the phase transition in the critical region. The analysis shows that a very small amount of doping results in a drastically large effect in the critical region. Further doping does not induce further a critical effect in a proportional way. This enables one to define the undoped and doped systems with a very small amount of dopant as two distinct states.

Intrazeolite semiconductors: sodium-23 MAS NMR, thallium(1+) luminescence quenching and far-IR studies of acid-base precursor chemistry in zeolite Y

Proton-loaded zeolites, prepared from fully dehydrated zeolites and gaseous, anhydrous Bransted acids, represent an important step in the synthesis of intrazeolite semiconductor quantum supralattices. Adsorption-induced 23Na MAS NMR chemical shifts, far-1R Na+ and TI+ translatory mode frequency shifts, and TI+ luminescence quenching effects were chosen as probes of cation-anion interaction in these materials. Samples of zeolite Y with various loadings of TI+ were prepared via aqueous ion-exchange techniques. The samples were characterized by powder X-ray diffraction and far-IR spectroscopy. Luminescence measurements revealed TI+ excitation and emission bands in the UV spectral region. Exposure of thallium TI(1) zeolite Y to anhydrous HBr quenched the luminescence intensity. The intensity quenching followed Stern-Volmer quenching kinetics. Preliminary luminescence lifetime studies of this system supported a static ion pair quenching model. Compelling additional evidence in favor of cation-anion pair formation comes from the observation of a-cage site-specific *)Na MAS NMR chemical shifts in HBr/Na%Y compared to virgin NaFY. The relevance of these observations for proton-loaded zeolite Y to the acid-base precursor chemistry involved in the synthesis of semiconductor nanostructures encapsulated in zeolite Y is critically discussed.

Lattice dynamics and structural phase transitions in the chain compounds TMMC and TMCC. III. Landau theory

For pt.II see ibid., vol.2, p.8229 (1990). A phenomenological model is developed in the framework of Landau theory, in order to account for the structural phase transitions occurring in TMMC and TMCC. This model includes pseudo-spin coordinates attached to the orientation of tetramethylammonium groups that describe order-disorder processes, coupling terms with rotatory and translatory modes of the octahedra chains leading to displacive contributions and coupling terms with the strain components that account for the ferroelastic behaviour. Thus, the phase transitions between phases I', I, II and III are described in a satisfactory way, when compared with the experimental data. It is shown that the complex structure of phase IV must be seen as the result of a lock-in transition from a hypothetical incommensurate phase.

Polarized infrared reflection studies on MClO 4 (M = NH 4, K, Rb, and Cs)

Polarized infrared reflection spectra of single crystals of baryte type perchlorates MClO 4 (M = NH 4, K, Rb, and Cs) are recorded and analysed for the frequencies of the transversal and longitudinal optical zone centre phonon modes by means of oscillator-fit method and Kramers-Kronig analyses. Complete assignment of the internal and partially of the external modes is given. The TO/LO splittings of the reststrahlen bands, which are greatest for three of the five asymmetric ClO stretching vibrations ν 3 (50–70 cm −1) and for the highest-energy translatory modes at 100–180 cm −1 (10–70 cm −1), are used for assigning and interpreting the vibrational modes with respect to site group and correlation splittings, librational and translatory motions, and repulsive effects of the lattice potential.

ChemInform Abstract: Far‐IR Spectroscopy of Alkali‐Metal and Alkaline‐Earth Cations in Faujasite Zeolites

Abstractis used to study the factors influencing the frequencies of far‐IR cation translatory modes in faujasites, namely, the mass, charge, and size of the cation as well as its local environment.

Ferroelectric Phase Transition in (NH4)2BeF4. Possibility of Molecular Distortion Type of Transition

AbstractThe possibility of molecular distortion type (MD‐type) microscopic mechanism (recently proposed for (NH4)2SO4) and the role of BeF ion in the phase transition of amonium fluoberryllate are examined by analysing crystal structural data in both, the paraelectric and ferroelectric phases. The results show that BeF ion attains a dipole moment in the FE phase and contribute significantly to the spontaneous polarisation (Ps). The computed value of Ps due to NH and BeF ions (0.21 μC/cm2) matches satisfactorily with the experimental results. The nature of the phase transition is found to be mainly of MD‐Type. The soft mode of the transition is proposed as a mixed mode having the internal mode of BeF ion and translatory modes of NH ions.

Far-IR spectroscopy of alkali-metal and alkaline-earth cations in faujasite zeolites

is used to study the factors influencing the frequencies of far-IR cation translatory modes in faujasites, namely, the mass, charge, and size of the cation as well as its local environment.

Coupling interaction between the sulfate ion ν2 modes and the lithium modes in LiKSO4

Resonant couplings between the sulfate ion ν2 mode and the lithium ion translatory mode in E2 and E1 symmetries have been studied in single crystal 7 LiKSO4 and 6 LiKSO4 from polarized Raman spectra between 298 and 519 K and from infrared reflectivity spectra at room temperature. Coupling effects are negligible in 7 LiKSO4 whereas in 6 LiKSO4 the lithium isotope effect shifts the lithium translatory mode into resonant coupling with the sulfate ion ν2 mode. The resonant coupling mechanism between the two fundamental E2 modes is elucidated by a comparative analysis of the temperature dependence of the frequency shifts and the relative intensities. The coupling interaction in E1 symmetry can be only qualitatively described due to poor resolution of the Raman bands. It is possible to distinguish anharmonic processes which couple two modes from anharmonic processes which perturb each state individually. It was found that coupling anharmonicity decreased while perturbative anharmonicity increased with increasing temperature. Detailed consideration of various intensity ratios in E2 symmetry allows the separation of the isotope effect from the coupling contribution to the polarizability derivative tensor. In E1 symmetry TO–TO and LO–LO coupling interactions between the ν2 mode of the sulfate ion and the lithium translatory mode were deduced from the frequency and intensity data.

Lithium isotope effects in the vibrational spectra of Li 2SeO 4

Polarized Raman scattering spectra have been measured in single crystal 7Li 2SeO 4 and 6Li 2SeO 4. Based on these data, symmetry-based band assignments are proposed for the ν 2, ν 4 and lithium mode regions. Vibrational coupling interactions are noted between the ν 2, ν 4 and the lithium translatory modes.

Spectroscopic Studies of a Superionic Plastic Phase Crystal: Lithium Sulfate

AbstractTemperature dependent Raman spectroscopic studies of single crystal lithium sulfate are summarized. Coupling between sulfate ion bending modes and the lithium ion translatory modes becomes weaker with increasing temperature until the lithium modes can no longer be observed above 250° C. The temperature interval above 450° in the monoclinic phase is marked by the onset of significant sulfate ion reorientational motion, as evidenced by the bandshape studies of the sulfate ion v1, mode and the librational modes. Bandshape analysis of the v3mode in the plastic phase strongly suggests that the symmetry of the sulfate ion potential energy environment has planar anisotropy.The lithium ion-sulfate ion interactions are modeled for correlated sulfate ion configurations as a function of lithium ion position. The results support the role of the octahedral site in lithium ion transitions contributing to the ionic conductivity.

The infrared and laser Raman spectra of K2Zn(SO4)2 · 6H2O

The Raman spectra of the single crystal of K2Zn(SO4)2·6H2O belonging toC 2 5 space group in the 40–1200 cm−1 region in different scattering geometries and their spectra ofthe microcrystalline salt in the 1500-50 cm−1 region have been reported. The dynamics of the crystal has been described in terms of 186 phonon modes under the unit cell approximation. The weak bands in the region 400–900 cm−1 have been assigned to the libratory modes of H2O molecules in contradiction to the assignments reported by Ananthanarayanan. The ambiguities existing in the literature about the assignments ofν 2 andν 5 modes of [Zn(H2O)6]2+ have also been removed. The translatory and libratory modes of different units of the crystal have been identified and assignments are made using farir and Raman data on various isomorphous tutton salts. It has been inferred that both SO 4 2− tetrahedron and [Zn(H2O)6]2+ octahedron undergo linear as well as angular distortions from their free state symmetries in the crystal.

Raman spectra of ammonium sulphamate single crystal

AbstractRaman scattering from single crystals of ammonium sulphamate have been recorded in the region 30–3400 cm−1 with He‐Cd laser excitation. The libratory and translatory modes observed in all the six polarizations were assigned. The assignment of internal modes of ammonium ion indicates minimum distortion of the ion from the tetrahedral symmetry. The presence of medium hydrogen bonding and the range of correlation field splitting are discussed.

Solid-state metal carbonyls. Part 1.—Single-crystal infrared and Raman spectra of the group VI hexacarbonyls

Single-crystal infrared reflectance spectra in polarised light (200–2500 cm–1) at liquid-nitrogen temperature are reported for M(CO)6(M = Cr, Mo, W). The reflectance accessory used is described. All the permitted factor-group components are identified and used to construct the first complete assignment for the v(CO) region of these solids. The general features of the mull spectra are accounted for. Both site- and factor-group splittings for the v3(Eg) and v6(T1u) molecular modes are deduced: these effects are very slight for v3 but considerable for v6. The weak Raman band near 1966 cm–1 in Mo(CO)6 was shown to be of v6 origin.In the v(M—C), δ(MCO) region the reflectance spectra allowed identification of factor-group components but the splitting is small except for v7(T1u) of Cr(CO)6.Many new bands are found in the far-i.r. region, the lowest being at 31.5 cm–1. All the permitted lattice modes are located. Components of the molecular modes v9(T1u), v11(T2g) and v13(T2u) are all present in the numbers allowed by site group rules. Combining i.r. and Raman data, they are located near 90, 110 and 65 cm–1, respectively. Bands below 60 cm–1 are attributed to translatory and libratory lattice modes.

On the Motion of Rectangular Prismatic Bodies

Rectangular prismatic bodies can assume either a translatory or an auto-rotating mode of motion during free motion in the atmosphere. The translatory mode is stable only when the dimensionless moment of inertia of the bodies is large, however, large perturbations will always start auto-rotation. The characteristics of the auto-rotational mode are shown to depend primarily on the aspect ratio of the bodies which determines the dimensionless rotational speed and the lift coefficient. Both the average drag and lift-coefficients of auto-rotating bodies are estimated, but it is shown that secondary effects make it impossible to determine their exact trajectories in atmospheric flows.

Raman-, IR- und FIR-Messungen an wasserfreiem Natriumperchlorat NaClO4 im Temperaturbereich zwischen 90 und 600 K

Abstract This paper reports a detailed study of the k = 0 vibrational spectra of the anhydrous orthorhombic anhydrite type sodium perchlorate NaClO4 in the temperature range from 90 to 600 K. The i.r., FIR and Raman spectra have been recorded and discussed on the basis of both the unit cell group and the site group of the ClO4− ions. The assignment of the modes was done with help of Raman single crystal measurements. Dynamic interactions of the vibrations of adjacent ClO4− ions are very small (Davydov splitting 40 cm−1). Splitting of the vibrations due to isotopic effects of chlorine atoms has not been observed with exception of one mode of the fundamental ν4 of the perchlorate ions. The site group splittings diminish at temperatures above 480 K and disappear with the exception of a shoulder at the bending fundamental ν2 above 581.3 K, the temperature of the phase transition to the cubic high temperature form (NaCl-type). The librational fundamentals and the translatory modes of NaClO4 are very broad, even at 90 K and of unusually weak intensity in the Raman spectra.