Bending Force Constants Research Articles

Effect of M site cation ordering on the lattice dynamical properties of the tetragonal Sr2MO4 (M=Cr, Fe, Co, Mo, and Sn) crystals

ABSTRACT Using normal coordinate analysis, the Raman and Infrared phonons are investigated for the tetragonal Ruddlesden-Popper series in phase I4/mmm and symmetry D4h 17. Three stretching and six bending force constants have been included for the calculations of the zone centre vibrational modes. Theoretical assignments for the Raman and infrared wavenumbers for Sr2CrO4, Sr2MoO4, and Sr2SnO4 compounds have been reported for the first time. As per our knowledge, no theoretical assignment has been done for the infrared frequencies for Sr2FeO4 and Sr2CoO4 compounds in I4/mmm phase so far. A strong correlation of the M site has been observed for the various frequencies giving insight into the structure of the studied compounds. The force constants involving the M-site atom show an expected set trend and also indicate the changes in values whenever the atomic orbit changes. Also, the frequencies which are completely dominated by the M atoms show a specific nature as the atomic number changes indicating the strong effect of the size of the M atom in the vibrational properties. In the tetragonal structure of the Ruddlesden-Popper phase of Sr2MO4 (M=Cr, Fe, Co, Mo, and Sn) crystals for each normal mode, the potential energy distributions have been analysed and the contributions of bending and stretching force constants towards different frequencies have been determined.

Lattice vibrations of the Ruddlesden-Popper compounds barium orthorhodate, barium orthoiridate, barium orthoplumbate, and barium orthostannate in tetragonal phase

The investigation of the Raman and Infrared phonons has been done for the tetragonal Ruddlesden-Popper compounds Barium Orthorhodate, Barium Orthoiridate, Barium Orthoplumbate, and Barium Orthostannate having phase I4/mmm and symmetry D4h 17 using normal coordinate analysis. With three stretching and six bending force constants, the zone center vibrational modes have been calculated. For the first time, the assignments for the Raman and infrared wavenumbers for the tetragonal compounds Barium Orthorhodate and Barium Orthoplumbate have been reported using Wilson’s GF-Matrix Method. The infrared wavenumbers for the compounds Barium Orthostannate and Barium Orthoiridate have been assigned theoretically in I4/mmm phase. A significant correlation of the cation Rhodium, Iridium, Tin, and Lead has been studied for the various vibrational modes providing insight into the structure of the investigated Barium Orthorhodate, Barium Orthoiridate, Barium Orthoplumbate, and Barium Orthostannate compounds. The force constants containing the cation Rhodium, Iridium, Tin, and Lead follow a predictable pattern and also exhibit changes in values as the atomic orbit varies. Further, as the atomic number varies, the vibrational modes that are governed by the cation Rhodium, Iridium, Tin, and Lead take on a distinct nature demonstrating that the size of the cation has a significant impact on the vibrational properties. The potential energy distribution for each normal mode in the tetragonal structure of the Ruddlesden-Popper phase of Barium Orthorhodate, Barium Orthoiridate, Barium Orthoplumbate, and Barium Orthostannate crystals have been analyzed and the contributions of stretching and bending force constants toward different vibrational modes have been calculated.

Unusual Force Constants Guided Distortion-Triggered Loss of Long-Range Order in Phase Change Materials.

Unusual force constants originating from the local charge distribution in crystalline GeTe and Sb2Te3 are observed by using the first-principles calculations. The calculated stretching force constants of the second nearest-neighbor Sb-Te and Ge-Te bonds are 0.372 and −0.085 eV/Å2, respectively, which are much lower than 1.933 eV/Å2 of the first nearest-neighbor bonds although their lengths are only 0.17 Å and 0.33 Å longer as compared to the corresponding first nearest-neighbor bonds. Moreover, the bending force constants of the first and second nearest-neighbor Ge-Ge and Sb-Sb bonds exhibit large negative values. Our first-principles molecular dynamic simulations also reveal the possible amorphization of Sb2Te3 through local distortions of the bonds with weak and strong force constants, while the crystalline structure remains by the X-ray diffraction simulation. By identifying the low or negative force constants, these weak atomic interactions are found to be responsible for triggering the collapse of the long-range order. This finding can be utilized to guide the design of functional components and devices based on phase change materials with lower energy consumption.

A normal coordinate analysis of Sr2BO4 crystals (B = Ti, V, and Mn)

Theoretical calculations on the Raman and infrared (IR) vibrational modes in the tetragonal structure of the Ruddlesden-Popper (RP) phase Sr2BO4 (B = Ti, V, and Mn) have been done in this paper. The Raman and IR vibrational modes have been investigated using Wilson’s GF matrix method for the Sr2BO4 (B = Ti, V, and Mn) compounds having space group I4/mmm and symmetry D4h17 by analyzing the normal coordinates. The measurements of the zone centre vibrational modes have been calculated including three stretching and six bending force constants. In this work, the infrared frequencies for the Sr2MnO4 compound in phase I4/mmm have been assigned first and foremost. There is an extremely strong concurrence between the observed Raman and IR vibrational modes and our calculated results. To determine the role of interatomic forces in the calculated Raman and IR vibrational modes, the potential energy distributions for the Sr2BO4 (B = Ti, V, and Mn) compounds have also been investigated.

Theoretical and experimental revision of the water bending excitation in the OH/OD + GeH4 reactions

The bending force constant associated with formation water that is selected for the potential energy surface describing the OH/OD + GeH4 reaction is shown to be important for the degree of bending excitation of H2O and HOD.

A VSEPR-inspired force field for determining molecular properties of PF5

ABSTRACTValence Shell Electron Pair Repulsion (VSEPR) theory, commonly taught in introductory chemistry courses, provides a basis for understanding the molecular structures of molecules of the type XY, where X is a central atom surrounded by m Y ligands. While VSEPR is generally thought of only as a qualitative theory, Bartell and coworkers constructed a semi-quantitative model potential to address the physical underpinnings of VSEPR by introducing a points-on-a-sphere (POS) potential such that all X-Y bonds are of fixed length and all atoms Y repel each other. More than forty years ago, this simple model was shown to be effective in reproducing relative quadratic and cubic bending force constants for a variety of binary XY compounds when compared to values computed with semi-empirical and fairly primitive methods. The work presented here endeavours to go beyond the model used in the early investigations by Bartell and coworkers. Specifically, stretching force constants are clearly omitted from any POS model with a fixed radius, and are (primitively) included here by treating all X-Y bonds as simple (and equivalent) Morse oscillators. With the additional degrees of freedom in the parametrization that come from the Morse potential, the resulting model was investigated. The degree to which this simple mechanical model can reproduce quadratic and cubic force fields for PF is studied here, as well as how it works for a more difficult problem – the energetics and transition state properties for the intermediate in the (Berry) pseudorotation process that interchanges axial and equatorial fluorines in this prototype molecule. The five parameter Morse-POS model is shown to be do quite well in describing the quadratic and cubic force fields, as well as the pseudorotation process, a fairly impressive feat given the naivete of the model.

Synthesis, structure, UV–Vis–NIR, infrared and Raman spectroscopy, and force-field investigation for A2GaSbO7 (A3+ = Y, Dy, Gd) pyrochlores

Three mixed pyrochlores, A2GaSbO7 (A3+ = Y, Dy, Gd) were synthesized using the solid-state reaction technique and characterized systematically through powder X-ray diffraction and its Rietveld analysis, SEM-EDAX, UV–Visible absorption spectra, Fourier-transform infrared and Raman spectroscopy. Scherrer analysis of the XRD pattern and SEM-image were used to estimate size of the nano-structured particles of the polycrystalline samples to be ∼40–50 nm. From the UV–Vis absorbance data, absorption band edge and optical band gap were determined, and found to be ∼350 ± 8 nm and 2–2.5 eV, respectively, for these compounds. Four F1u bands were only observed in the infrared spectra within the phonon wave numbers range of 400–800 cm−1 for these samples. The highest wave number infrared mode arises due to the interaction between bending and stretching of A−O and B−O bonds. A mode-splitting caused by the mass-difference of B-site ions was found in the other three infrared modes. The Raman spectra of these compounds exhibit six Raman modes, e.g., A1g, Eg, and 4F2g, within the experimental range of 50–1000 cm−1, with few extra bands in the higher (>700 cm−1) and lower (<200 cm−1) wave numbers range. A normal coordinate analysis using a generalized valence force-field model has been performed to assign and evaluate the vibration modes in these compounds. Five stretching and four bending force constants were considered to construct the force-field matrix. Comparison of the calculated phonon wave numbers with experimental values obtained in infrared and Raman excitation zones describes excellent agreement for all these isomorphous compounds.

Calculation of the optical phonons in ordered Ba2MgWO6 perovskite using short‐range force field model

AbstractBa2MgWO6 is a double perovskite tungstate presenting a cubic structure with cubic space group . This B‐site ordered system has potential applications as microwave ceramics in communication systems. Here, we present our results on the lattice dynamics calculations using short‐range force field model to describe both Raman (A1g ⊕ Eg ⊕ 2F2g) and infrared (4F1u) optical phonons at Γ‐point of the Brillouin zone in Ba2MgWO6 perovskite. Short‐range interactions were parameterized through four stretching and three bending force constants in light of the Wilson's GF‐matrix method. Satisfactory agreement between experimental and calculated vibrational data was found. We have used the potential energy distribution (PED) coefficients to determine the contribution of each force constant to the optical modes. The PED analysis elucidates that the W atom has a nonnegligible contribution in describing both A1g breathing and Last‐type (F1u) modes. Such a modeling provided insights into vibrational modes, enabling correlation between optical phonons, disorder effects, and physical properties for applications.

Mechanical properties of AlPxSb1-x semiconductor alloys under the effect of temperature and pressure

Using the empirical pseudo-potential method (EPM) combined with the virtual crystal approximation (VCA) included the compositional disorder effect, some of optoelectronic and mechanical properties of AlPxSb1-x ternary alloys under the effect of pressure and temperature have been studied. Our results for the energy band gaps, refractive index, dielectric constants, elastic constants and some related parameters like elastic moduli, Poisson's ratio, bond stretching and bond bending force constants, internal strain parameter, linear compressibility, Cauchy ratio and anisotropy factor are successfully calculated for different values of temperature and pressure. A good agreement is noticed between our results and the available experimental and theoretical published data.

Influence of composition, temperature and pressure on the optoelectronic and mechanical properties of InPxSb1-x alloys

A detailed study of the effect of composition, temperature and pressure on the mechanical and optoelectronic properties of InPxSb1-x alloys has been reported. The calculations have been done using pseudo-potential method (EPM) within the improved virtual crystal approximation (VCA), where the compositional disorder effect is taken into account. Our results for the elastic constants, elastic moduli, Poisson's ratio, bond stretching force constant, bond bending force constant, internal strain parameter, linear compressibility, Cauchy ratio, and anisotropy factor are successfully calculated and compared with the available published data.

Lattice dynamical investigation of the Raman and infrared wave numbers and heat capacity properties of the pyrochlores R2Zr2O7 (R = La, Nd, Sm, Eu)

A short-range electrostatic forcefield model has been applied for the first time to investigate the Raman and infrared wave numbers in pyrochlore zirconates R2Zr2O7 (R3+ = La, Nd, Sm, Eu). The calculations of phonons involve five stretching and four bending force constants in the Wilson GF matrix method. The calculated phonon wave numbers are in reasonable agreement with the observed spectra in infrared and Raman excitation zones for all of these isomorphous compounds. The contributions of force constants to each mode show a similar trend of variation for all of these compounds. Furthermore, to validate the established forcefield model, we calculated the standard thermodynamic functions, e.g., molar heat capacity, entropy and enthalpy, and compared the results with the previous experimental data for each compound. Using the derived wave numbers for the acoustic and optical modes, the total phonon contribution to the heat capacity was calculated for all these zirconate compounds. The Schottky heat capacity contributions were also calculated for the magnetic compounds, Nd2Zr2O7, Sm2Zr2O7 and Eu2Zr2O7, taking account of crystal-field level schemes of the lanthanide ions. The derived total heat capacity and the integrated values of molar entropy and molar enthalpy showed satisfactory correlations at low temperatures with the experimental results available in the literature for these compounds. At higher temperatures, the discrepancies may be caused by the anharmonic effects of vibrations, phonon dispersion, distribution of phonon density of states, etc.

Vibrational Analysis of Semicrystalline Polyethylene Using Molecular Dynamics Simulation

The vibrational spectra of semicrystalline polyethylene and its distinct domains were investigated using molecular dynamics (MD) simulations. A method for the vibrational analysis of the domains within the lamellar stack model of semicrystalline polymers has been developed and demonstrated on semicrystalline polyethylene using force fields having either united atom (UA) or explicit atom (EA) detail. In the UA description, the calculated vibrational spectra were found to differ from the observed skeletal vibrations of polyethylene with the force field used in this work. Therefore, a modified UA force field with different stretching and bending force constants is proposed, which was found to reproduce the observed frequencies of the skeletal vibrations. In the EA description, the vibrational spectra of semicrystalline polyethylene were in satisfactory agreement with typical infrared and Raman signatures of polyethylene melts and crystals. Experimental interpretations regarding the assignment of peaks in the Raman spectra to components of semicrystalline polyethylene were examined. The spectrum of the interphase domain obtained using the EA model was found to be adequately reproduced by a superposition of the spectra of the crystalline and amorphous domains, at variance with experimental observation. The lack of a distinct interphase spectrum in the EA model was attributed to the absence of the CH2 bending peak associated with the orthorhombic phase, despite confirming an orthorhombic crystal structure in the crystalline domain.

Molecular and Dissociative Adsorption of Water on (TiO2)n Clusters, n = 1-4.

The low energy structures of the (TiO2)n(H2O)m (n ≤ 4, m ≤ 2n) and (TiO2)8(H2O)m (m = 3, 7, 8) clusters were predicted using a global geometry optimization approach, with a number of new lowest energy isomers being found. Water can molecularly or dissociatively adsorb on pure and hydrated TiO2 clusters. Dissociative adsorption is the dominant reaction for the first two H2O adsorption reactions for n = 1, 2, and 4, for the first three H2O adsorption reactions for n = 3, and for the first four H2O adsorption reactions for n = 8. As more H2O's are added to the hydrated (TiO2)n cluster, dissociative adsorption becomes less exothermic as all the Ti centers become 4-coordinate. Two types of bonds can be formed between the molecularly adsorbed water and TiO2 clusters: a Lewis acid-base Ti-O(H2) bond or an O···H hydrogen bond. The coupled cluster CCSD(T) results show that at 0 K the H2O adsorption energy at a 4-coordinate Ti center is ∼15 kcal/mol for the Lewis acid-base molecular adsorption and ∼7 kcal/mol for the H-bond molecular adsorption, in comparison to that of 8-10 kcal/mol for the dissociative adsorption. The cluster size and geometry independent dehydration reaction energy, ED, for the general reaction 2(-TiOH) → -TiOTi- + H2O at 4-coordinate Ti centers was estimated from the aggregation reaction of nTi(OH)4 to form the monocyclic ring cluster (TiO3H2)n + nH2O. ED is estimated to be -8 kcal/mol, showing that intramolecular and intermolecular dehydration reactions are intrinsically thermodynamically allowed for the hydrated (TiO2)n clusters with all of the Ti centers 4-coordinate, which can be hindered by cluster geometry changes caused by such processes. Bending force constants for the TiOTi and OTiO bonds are determined to be 7.4 and 56.0 kcal/(mol·rad(2)). Infrared vibrational spectra were calculated using density functional theory, and the new bands appearing upon water adsorption were assigned.

Lattice dynamical investigations of Raman and infrared wavenumbers of scheelite structured silicates

Lattice dynamical investigations have been made for MSiO4 (M=Zr, Hf, U) silicates having space group I41/a and symmetry C64h by calculating Raman and infrared wavenumbers. Wilson's GF matrix method has been used with normal coordinate analysis to compute the zone center phonons. The model involves four stretching and six bending force constants for the calculation of wavenumbers. The calculated zone center frequencies show satisfactory agreement with the available experimental results. All the infrared wavenumbers have been computed for HfSiO4 and USiO4 in the present study. A complete assignment of modes for the calculated Raman and infrared frequencies has also been made. An appropriate assignment of infrared modes of HfSiO4 and USiO4 has been made by using theoretical calculations. Evaluation for potential energy distribution for each mode has been made to determine the role of force constants for Raman and infrared wavenumbers.

Angular dependence of hydrogen bond energy in neutral and charged systems containing CH and NH proton donors

The effects of angular distortions on the H-bond energy are computed in both neutral and ionic complexes. F3CH, NCH, and HNCH+ are taken as CH donors and HCNH, HCNH+, and NH4+ are NH donors. Ionic complexes are more strongly bound and suffer a greater loss of H-bond energy upon angular distortion. However, when bending force constants k are normalized against intrinsic H-bond strength Eb, the k/Eb ratios are similar, only slightly larger for NH than for CH donors, and with only small perturbations caused by overall charge. The source of destabilization arising from angular deformation is traced to exchange repulsion.

Strength of the pnicogen bond in complexes involving group Va elements N, P, and As.

A set of 36 pnicogen homo- and heterodimers, R3E···ER3 and R3E···E′R′3, involving differently substituted group Va elements E = N, P, and As has been investigated at the ωB97X-D/aug-cc-pVTZ level of theory to determine the strength of the pnicogen bond with the help of the local E···E′ stretching force constants k(a). The latter are directly related to the amount of charge transferred from an E donor lone pair orbital to an E′ acceptor σ* orbital, in the sense of a through-space anomeric effect. This leads to a buildup of electron density in the intermonomer region and a distinct pnicogen bond strength order quantitatively assessed via k(a). However, the complex binding energy ΔE depends only partly on the pnicogen bond strength as H,E-attractions, H-bonding, dipole-dipole, or multipole-multipole attractions also contribute to the stability of pnicogen bonded dimers. A variation from through-space anomeric to second order hyperonjugative, and skewed π,π interactions is observed. Charge transfer into a π* substituent orbital of the acceptor increases the absolute value of ΔE by electrostatic effects but has a smaller impact on the pnicogen bond strength. A set of 10 dimers obtains its stability from covalent pnicogen bonding whereas all other dimers are stabilized by electrostatic interactions. The latter are quantified by the magnitude of the local intermonomer bending force constants XE···E′. Analysis of the frontier orbitals of monomer and dimer in connection with the investigation of electron difference densities, and atomic charges lead to a simple rationalization of the various facets of pnicogen bonding. The temperature at which a given dimer is observable under experimental conditions is provided.

Lattice dynamical investigations for Raman and infrared frequencies of Te doped Bi1−xTa1−xTe2xO4; 0 ⩽ x ⩽ 0.2

We have applied short range force constant model and used normal coordinate analysis based on G–F matrix method in investigating for Raman and infrared modes in Te doped Bi1−xTa1−xTe2xO4; 0⩽x⩽0.2 in its orthorhombic phase. The zone centre phonons calculations is made by using six stretching and seven bending force constants in its orthorhombic phase having space group Pnna with four formula units. All zone centre modes have been assigned in this calculation for the first time. The calculated Raman and infrared wave numbers agree satisfactorily with the available experimental results. The significant contribution of each force constant towards calculated Raman and infrared wave numbers has also been made through investigating the potential energy distribution. The Te-atom is present in equal amount at Bi and Ta site in this compound. The role of tellurium atom is exhibiting one mode behaviour in the ternary compound Bi1−xTa1−xTe2xO4 (0⩽x⩽0.2).

A normal coordinate analysis of AMoO4 crystals (A = Sr, Ba and Pb)

In this paper, we report on the lattice dynamical investigation of the Raman and the infrared frequencies of the tetragonal AMoO4 (A = Sr, Ba and Pb) crystals obtained by normal coordinate analysis. The calculation of zone centre phonons has been made by using four stretching and five bending force constants. The calculated Raman and infrared wavenumbers are in very good agreement with the observed ones. The comparison of experimental and theoretical values for BaMoO4 has resulted in creating a benchmark for both Raman and infrared modes in case of AMoO4 (A = Sr, Ba and Pb) crystals. The potential energy distribution has also been investigated for determining the significance of contribution from each force constant towards the Raman and the infrared frequencies.

Investigation of Raman and infrared modes for Sr doped double perovskite oxides Ba2−xSrxMWO6 (M=Ni, Co); for 0≤x≤1.2

A short-range force constant model has been applied to investigate the Raman and infrared modes in Sr doped ordered double perovskite oxides Ba2−xSrxMWO6 (M=Co, Ni); 0≤x≤1.2 (cubic phase) using normal coordinate analysis based on the G–F matrix method. In the present work, calculations on zone centre phonons have been made with three stretching and two bending force constants in its cubic phase (space group: Fm-3m) only. The calculated Raman wave numbers are in well agreement with the available experimental results. The infrared modes are calculated and proposed for the first time. The significant contribution of each force constant towards every Raman and the infrared wave numbers has also been determined by investigating the potential energy distribution.

Investigation of Raman and infrared phonon modes in case of barium bismuth tantalate (BaBi2Ta2O9)

The Raman and the infrared wavenumbers in the Aurivillius structure BaBi2Ta2O9 (BBT) having space group I4/mmm (no. 139-D4h17) are investigated using normal coordinate analysis. The calculation of zone center phonons incorporates seven stretching and seven bending force constants. The Raman and the infrared frequencies for BBT have been assigned for the first time in I4/mmm phase. The calculated Raman and infrared wavenumbers are in very good agreement with the observed ones. The potential energy distributions (PED) are also investigated for each normal mode in BBT and the contributions of different force constants to various frequencies are determined.