Anharmonic Parameters Research Articles

Hyperfine interactions of 57Fe impurity nuclei in multiferroic CuCrO2

Hyperfine interactions of 57Fe nuclei in multiferroic CuCrO2 are studied by means of Mossbauer probe spectroscopy in a wide range of temperatures, including that of the magnetic phase transition. The temperature dependences of the parameters of electric and magnetic hyperfine interactions and the anharmonicity parameter of the spin wave are obtained as part of the spatial anharmonic spin-modulated structure.

Temperature investigations of the spatial spin-modulated structure of multiferroic BiFeO3 by means of Mössbauer spectroscopy

The results from 57Fe Mossbauer spectroscopic studies of multiferroic BiFeO3 in a range of tem-peratures including that of the magnetic phase transition are presented. The Mossbauer spectra are processed and analyzed by reconstructing the hyperfine magnetic field distributions and interpreting the spectra with a cycloid-type spatial spin-modulated structure model. The temperature dependences of the hyperfine spectrum parameters (the Mossbauer line shift, the quadrupole shift, and the isotropic and anisotropic contributions to the hyperfine magnetic field) are obtained, along with the anharmonicity parameter of an incommensurate spin wave.

A higher-order finite-difference approximation with Richardson’s extrapolation to the energy eigenvalues of the quartic, sextic and octic anharmonic oscillators

In this paper, we present highly accurate numerical results for the lowest four energy eigenvalues of the quartic, sextic and octic anharmonic oscillators over a wide range of the anharmonicity parameter Also, we provide illustrative graphs describing the dependence of the eigenvalues on Our computation is carried out by using higher-order finite-difference approximation, involving the nine-and-ten-point differentiation formulas. In addition, we apply Richardson’s extrapolation method in our calculation for the purpose of achieving a maximum numerical precision. The main advantage of utilizing the finite-difference approach lies in its simplicity and capability to transform the time-independent Schrödinger equation into an eigenvalue matrix equation. This allows the use of numerical matrix algebra for obtaining several eigenvalues and eigenvectors simultaneously without consuming much of the computer time. The method is illustrated in a simple pedagogical way through which the close relation between differential and algebraic eigenvalue problems are clearly seen. The findings of our computations via MATLAB are tested on a number of accurate results derived by different methods.

In situ Raman spectroscopic studies of FeS2 pyrite up to 675 K and 2100 MPa using a hydrothermal diamond anvil cell

AbstractRaman scattering experiments of natural FeS2 pyrite were performed at simultaneous high-pressure and high-temperature conditions up to 675 K and 2100 MPa using a hydrothermal diamond anvil cell combined with micro-Raman spectroscopy. Four out of five Raman active modes [Eg, Ag, Tg(1) and Tg(3)] were resolved at ambient conditions, the remaining Tg(2) [∼377 cm–1] mode was weak and unresolved occurring ∼2 cm–1 from the intense Ag [379 cm–1] mode. The frequency shifts of the Eg [343 cm–1] and Ag [379 cm–1] modes were determined to be quadratic functions of pressure and temperature: ν343 = 343.35 – 0.0178 × ΔT – 8.4E – 6 × (ΔT)2 + 0.00367 × Δp 3.7E–7 × (Δp)2 + 1.0E–6 × ΔT × Δp and ν379 = 379.35 – 0.0295 × ΔT – 9.0E–6 × (ΔT)2 + 0.00460 × Δp – 5.3E–7 × (Δp)2 + 7.0E–7 × ΔT × Δp. The positive pressure dependence of both modes indicates stress-induced contraction of S–S and Fe–S bonds, whereas the negative temperature dependence shows temperature-induced expansion of them. The Raman spectra of pyrite were used to derive its bulk modulus at high temperatures, thermal expansion coefficient at high pressures and anharmonic parameters at high-pressure and high-temperature conditions.

Diagnostics of a spatial spin-modulated structure using nuclear magnetic resonance and Mössbauer spectroscopy

Methods of the diagnostics of the spatial spin-modulated structure of the cycloidal type in multiferroics based on nuclear magnetic resonance and Mossbauer spectroscopy have been considered. It has been established that Mossbauer spectroscopy makes it possible to determine the anharmonicity parameter of the spatial spin-modulated structure of the cycloidal type with no worse accuracy than nuclear magnetic resonance with higher resolution. Mossbauer spectroscopy, being sensitive to the hyperfine quadrupole interaction of the nucleus in the excited state, makes it possible to obtain additional information on the features of the spatial spin-modulated structure.

A universal modified van der Waals equation of state. Part I: Polymer and mineral glass formers.

PVT data of glass formers (minerals and polymers) published in the literature are re-analyzed. All the polymer glass formers (PS, PVAc, PVME, PMMA, POMS, PBMA, PVC, PE, PP, PMPS, PMTS, PPG) present two main properties which have never been noted: a) the isobars P(V) have a fan structure characterized by the two parameters T* and V*; b) the isotherms verify the principle of temperature-pressure superposition for P < P*. From these properties we show that the Equation Of State (EOS) can be put on a modified van der Waals form (VW-EOS), (V - V*) = (V0 - V*)P*/(P + P*). The characteristic pressure P* and the covolume V* are T and P independent. In polymer glass formers P* and V* have same values in the α (melt) and β (glass) domains. The characteristic temperatures T* deduced from the Fan Structure of the Isobar (FSIb) above and below T(g) are different. The characteristic temperature T*(α) of the melt state is found near the Vogel temperature T0 for linear polymers and more than 100 K below T0 for atactic polymers (with pendent groups). This difference in atactic polymers (and in some low molecular weight compounds) is explained by the importance of the β motions due to the pendent groups. The independence of T0 on P is discussed. A modified VFT equation (analogous to the compensation law and Meyer-Neldel rule) giving the relaxation time τ of the α motions as a function of P and T is proposed. The fan structure of the isotherm logτ versus P is explained. It is shown that organic non-polymeric liquids (C6H12, C6H14, DHIQ, OTP, Glycerol, Salol, PDE, DGEBA), mineral glass (SiO2, Se, GeSe4, GeSe2, GeO2, As2O3 and two metallic glasses (LaCe and CaAl alloys) verify this VW-EOS with similar accuracy. The relation P* = B 0/γ B among the characteristic pressure P*, the zero-pressure modulus B0 and the Slatter-Grüneisen anharmonicity parameter γ(B0 deduced from the VW-EOS, is observed in all the glass formers.

Calcite V: a hundred-year-old mystery has been solved

Since Boeke's finding of a reversible phase transition of calcite (calcium carbonate, CaCO3) at elevated temperatures [Boeke, H. E. (1912). Neues Jahrb. Mineral. 1, 91–121], and following W. L. Bragg's determination of the structure of the room-temperature Phase I [Bragg, W. L. (1914). Proc. R. Soc. Lond. A 89, 468–489.], the high-temperature Phase V of calcite has been an enduring mystery. Here, we summarize a paper on the structure of Phase V [Ishizawa, N., Setoguchi, H. and Yanagisawa, K. (2013). Sci. Rep. 3, 2832], as well as the intermediate Phase IV which exists between Phases I and V, and add new aspects. An in situ single-crystal X-ray diffraction study revealed that the I–IV and IV–V transitions occurred reversibly at approximately 985 and 1240 K, respectively, in a carbon dioxide atmosphere. Phase V was stable only over a narrow temperature range between 1240 and 1275 K. The crystal decomposed immediately at temperatures above 1275 K, leaving a nanoporous calcium oxide reaction product which retained the shape of the parent calcite crystal. The I–IV transition can be described as an orientational order/disorder transition of the carbonate group, occurring within the same space group $R\bar 3c$. In Phase V, the oxygen sublattice is melted. The joint-probability density function obtained from the anharmonic atomic displacement parameters of the oxygen atoms revealed that the oxygen triangles of the carbonate group in Phase V do not sit still at specified Wyckoff positions in the space group $R\bar 3m$, but are instead distributed with equal probability along the undulated circular orbital about the central carbon. The carbonate group in Phase V is no longer flat on the basal plane when the oxygen triangle comes to troughs or peaks in the undulated orbital, but is instead deformed like an umbrella. Assuming that the oxygen triangle migrates about carbon, the carbonate group should repeat the umbrella inversion in Phase V as a function of time. Finally, possible thermal decomposition mechanisms of calcite are briefly discussed.

Applications of X-ray Wavefunction Refinement

X-ray wavefunction refinement (XWR) is a way of modeling the total aspherical electron density from an X-ray diffraction experiment on a single crystal of a molecular compound. It is a combination of existing quantum-crystallographical techniques: In the first step, geometry is determined using Hirshfeld atom refinement,[1] which is based on a stockholder partitioning of quantum-mechanical aspherical electron densities. In the second step, the same wavefunction is fitted to the experimental data to reproduce the diffraction pattern and simultaneously minimize the molecular energy.[2] The XWR protocol involves embedding the molecule into a field of point charges and dipoles as well as termination strategies to avoid overfitting.[3] Results from an X-ray wavefunction refinement are not restricted to the analysis of electron density: the full reconstructed density matrix is available. Therefore, chemical problems can be tackled with suitable tools for any given question including, e.g., experimentally derived bond orders, electron-pair localisation information, or energetics. We will present first applications of this protocol for a selection of organic (hydrogen maleate salts, sulfur-containing protease inhibitors) and inorganic (siloxanes, sulfur dioxide) compounds, for which we measured high-resolution low-temperature X-ray diffraction data at various synchrotron facilities. We will show geometry improvements, anisotropic displacement parameters for hydrogens, anharmonic motion parameters for sulfur and chlorine atoms, and improved total electron-density distributions in comparison to results from multipole modeling. Moreover, we will discuss the contribution of the experimental data to the final constrained wavefunction (defect density) and demonstrate how the experimentally derived orbital-based descriptors assist in solving fundamental chemical problems.

Formation of cyanoallene (buta-2, 3-dienenitrile) in the interstellar medium: a quantum chemical and spectroscopic study

The interstellar medium, filling the vast space between stars, is a rich reservoir of molecular material ranging from simple diatomic molecules to more complex, astrobiologically important molecules such as vinylcyanide, methylcyanodiaccetylene, cyanoallene, etc. Interstellar molecular cyanoallene is one of the most stable isomers of methylcynoacetylene. An attempt has been made to explore the possibility of forming cyanoallene in interstellar space by radical-radical and radical-molecule interaction schemes in the gaseous phase. The formation of cyanoallene starting from some simple, neutral interstellar molecules and radicals has been studied using density functional theory. The reaction energies and structures of the reactants and products show that the formation of cyanoallene is possible in the gaseous phase. Both of the considered reaction paths are totally exothermic and barrierless, thus giving rise to a high probability of occurrence. Rate constants for each step in the formation process of cyanoallene in both the reaction paths are estimated. A full vibrational analysis has been attempted for cyanoallene in the harmonic and anharmonic approximations. Anharmonic spectroscopic parameters such as rotational constants, rotation-vibration coupling constants and centrifugal distortion constants have been calculated.

Phonon Scatterings in the Lattice Thermal Conductivity of Si_(1-x) Ge_x Alloy Nanowires: Theoretical Study

Theoretical investigation of the alloy concentration and temperature dependences of the lattice thermal conductivity of silicon-germanium nanowires is performed using the Steigmeier and Abeles model. Phonon scattering processes are represented by frequency-dependent relaxation time approximation. In addition to the commonly considered acoustic three-phonon umklapp processes, phonon-boundary and point-defect scattering mechanisms are assumed. No distinction is made between longitudinal and transverse phonons. The importance of all the mechanisms involved in the model is clearly demonstrated. Analysis of the results shows that: (1) alloy scattering is the dominant scattering mechanism at intermediate and high temperatures; (2) thermal conductivity is mainly depends on the alloy concentration across the full range of temperatures; (3) weak diameter dependence of thermal conductivity is observed in Si_(1-x) Ge_x alloy nanowires; (4) the roughness of nanowires depends on the alloy concentration and has a major role in decreasing thermal conductivity at low temperatures; (5) the anharmonicity parameter is not size-dependent, as compared to Si and Ge nanowires. These findings provide new insights into the fundamental understanding of high-performance nanostructural semiconductors of relevance to optoelectronic and thermoelectric devices.

Macroscopic quantum many-body tunneling of attractive Bose-Einstein condensate in anharmonic trap

We study the stability of attractive atomic Bose-Einstein condensate and the macroscopic quantum many-body tunneling (MQT) in the anharmonic trap. We utilize correlated two-body basis function which keeps all possible two-body correlations. The anharmonic parameter (λ) is slowly tuned from harmonic to anharmonic. For each choice of λ the many-body equation is solved adiabatically. The use of the van der Waals interaction gives realistic picture which substantially differs from the mean-field results. For weak anharmonicity, we observe that the attractive condensate gains stability with larger number of bosons compared to that in the pure harmonic trap. The transition from resonances to bound states with weak anharmonicity also differs significantly from the earlier study of [N. Moiseyev, L.D. Carr, B.A. Malomed, Y.B. Band, J. Phys. B 37, L193 (2004)]. We also study the tunneling of the metastable condensate very close to the critical number N cr of collapse and observe that near collapse the MQT is the dominant decay mechanism compared to the two-body and three-body loss rate. We also observe the power law behavior in MQT near the critical point. The results for pure harmonic trap are in agreement with mean-field results. However, we fail to retrieve the power law behavior in anharmonic trap although MQT is still the dominant decay mechanism.

Spectroscopic Study of the I2 Formation from the Photolysis of Iodomethanes (CHI3, CH2I2, CH3I, and CH2ICl) at Different Wavelengths

Emission spectra following the photolysis of iodomethanes (CHI3, CH2I2, CH3I, and CH2ICl) at 266 nm were recorded in a slow flow cell. In addition to emission from the electronically excited species including CH (A(2)Δ, B(2)Σ(-), and C(2)Σ(+)), C2 (d(3)Πg), and atomic iodine ((4)P(o)), a series of emission bands was observed in the 12,000-19,000 cm(-1) region. The dominant structure of these emission bands was verified as the I2 B(3)Π(+)(0,u)-X(1)Σ(+)g emission at the 532 nm excitation, and the observed I2 was formed from collisions between iodine atoms generated from the C-I bond dissociation in these iodomethanes. The I2 emission spectra following the photolysis of CH2I2 at different wavelengths were acquired, and the threshold energy for the first C-I bond cleavage was determined to be 208 ± 1 kJ mol(-1). We also obtained the emission spectra of pure I2 at several visible excitation wavelengths for comparison with those from the photolysis of iodomethanes, and a least-squares global fit of the observed I2 emission bands yields more accurate anharmonicity parameters for the vibrational structure in the I2 B-X transition.

Studies on thermodynamic properties of pure poly(ethylene glycol)-400 in the temperature range 299–363 K using volume expansivities

Dilatometric studies have been performed on the pure poly(ethylene glycol) of average molecular mass 400 g.mol−1(PEG-400). From these studies, molar volumes and volume expansion coefficients (α) of this sample have been estimated at different temperatures. Using the data, a number of thermodynamic, thermo-acoustic and anharmonic parameters of the sample have been evaluated. All these parameters have been discussed to throw light on the internal structure, molecular order, anharmonicity and intermolecular interactions.

Crystal structure, Raman and FTIR spectroscopy, and equations of state of OH-bearing MgSiO3 akimotoite

MgSiO3 akimotoite is stable relative to majorite-garnet under low-temperature geotherms within steeply or rapidly subducting slabs. Two compositions of Mg–akimotoite were synthesized under similar conditions: Z674 (containing about 550 ppm wt H2O) was synthesized at 22 GPa and 1,500 °C and SH1101 (nominally anhydrous) was synthesized at 22 GPa and 1,250 °C. Crystal structures of both samples differ significantly from previous studies to give slightly smaller Si sites and larger Mg sites. The bulk thermal expansion coefficients of Z674 are (153–839 K) of a 1 = 20(3) × 10−9 K−2 and a 0 = 17(2) × 10−6 K−1, with an average of α 0 = 27.1(6) × 10−6 K−1. Compressibility at ambient temperature of Z674 was measured up to 34.6 GPa at Sector 13 (GSECARS) at Advanced Photon Source Argonne National Laboratory. The second-order Birch–Murnaghan equation of state (BM2 EoS) fitting yields: V 0 = 263.7(2) A3, K T0 = 217(3) GPa (K′ fixed at 4). The anisotropies of axial thermal expansivities and compressibilities are similar: α a = 8.2(3) and α c = 10.68(9) (10−6 K−1); β a = 11.4(3) and β c = 15.9(3) (10−4 GPa). Hydration increases both the bulk thermal expansivity and compressibility, but decreases the anisotropy of structural expansion and compression. Complementary Raman and Fourier transform infrared (FTIR) spectroscopy shows multiple structural hydration sites. Low-temperature and high-pressure FTIR spectroscopy (15–300 K and 0–28 GPa) confirms that the multiple sites are structurally unique, with zero-pressure intrinsic anharmonic mode parameters between −1.02 × 10−5 and +1.7 × 10−5 K−1, indicating both weak hydrogen bonds (O–H···O) and strong OH bonding due to long O···O distances.

Positive or Negative Thermal Expansion in Anharmonic Vibrational Systems in EXAFS study

An EXAFS expression was introduced for analysis of positive or negative thermal expansion. The EXAFS parameters were directly related to the interatomic potential. Also, it was shown that the sign of anharmonic potential parameter k3 depends on the sign of thermal expansion coefficient. Simulation works showed that the positive or negative thermal expansion can be sensitively measured by EXAFS study.

Raman spectroscopic study of phase stability and anharmonicity in Bi12TiO20

Raman spectroscopic studies on lead-free piezo-electric compound Bi12TiO20 is reported as a function of pressure upto 25 GPa at room temperature. Results indicate that the compound remains in stable crystalline phase upto 25 GPa. Temperature dependent Raman spectroscopic investigations on Bi12TiO20 indicate that the compound is also stable at high temperatures upto 850 K. From measurements of temperature and pressure dependence of Raman mode frequencies, intrinsic anharmonic parameters are calculated for each of the Raman active modes which are useful in modeling of thermodynamic entities. The results are compared with that of analogous compound Bi12SiO20.

Thermal equation of state and thermodynamic properties of molybdenum at high pressures

A comprehensive P-V-T dataset for bcc-Mo was obtained at pressures up to 31 GPa and temperatures from 300 to 1673 K using MgO and Au pressure calibrants. The thermodynamic analysis of these data was performed using high-temperature Birch-Murnaghan (HTBM) equations of state (EOS), Mie-Grüneisen-Debye (MGD) relation combined with the room-temperature Vinet EOS, and newly proposed Kunc-Einstein (KE) approach. The analysis of room-temperature compression data with the Vinet EOS yields V0 = 31.14 ± 0.02 Å3, KT = 260 ± 1 GPa, and KT′ = 4.21 ± 0.05. The derived thermoelastic parameters for the HTBM include (∂KT/∂T)P = −0.019 ± 0.001 GPa/K and thermal expansion α = a0 + a1T with a0 = 1.55 ( ± 0.05) × 10−5 K−1 and a1 = 0.68 ( ± 0.07) × 10−8 K−2. Fitting to the MGD relation yields γ0 = 2.03 ± 0.02 and q = 0.24 ± 0.02 with the Debye temperature (θ0) fixed at 455-470 K. Two models are proposed for the KE EOS. The model 1 (Mo-1) is the best fit to our P-V-T data, whereas the second model (Mo-2) is derived by including the shock compression and other experimental measurements. Nevertheless, both models provide similar thermoelastic parameters. Parameters used on Mo-1 include two Einstein temperatures ΘE10 = 366 K and ΘE20 = 208 K; Grüneisen parameter at ambient condition γ0 = 1.64 and infinite compression γ∞ = 0.358 with β = 0.323; and additional fitting parameters m = 0.195, e0 = 0.9 × 10−6 K−1, and g = 5.6. Fixed parameters include k = 2 in Kunc EOS, mE1 = mE2 = 1.5 in expression for Einstein temperature, and a0 = 0 (an intrinsic anharmonicity parameter). These parameters are the best representation of the experimental data for Mo and can be used for variety of thermodynamic calculations for Mo and Mo-containing systems including phase diagrams, chemical reactions, and electronic structure.

Vibrational signatures of Watson–Crick base pairing in adenine–thymine mimics

The vibrational fingerprints of hydrogen-bonding associated with the adenine-thymine (A-T) Watson-Crick (WC) base pair have been identified in an infrared study of the A-T mimics 4-aminopyrimidine-1-methylthymine (4APM-1MT) and 4-aminopyrimidine-6-methyl-4-pyrimidinone (4APM-M4PMN) in the gas-phase. The IR vibrational spectra were measured via a double resonance scheme utilizing femtosecond multiphoton ionization. The changes in the molecular structure, anharmonic vibrational parameters, and the assignment of the observed vibrational spectra in the NH/CH stretch region were investigated by carrying out high-level theoretical calculations of the anharmonic spectra. The experimental observations and theoretical calculations indicate that the hydrogen bonds associated with WC base-pairing are relatively stronger than those associated with reverse WC (rWC) base pairing. This is manifested in a more pronounced red-shift of the H-bonded vibrational modes associated with the WC as compared with the rWC base-pairing. An analysis of the factors contributing to the anharmonicity of the vibrational modes associated with H-bonding reveals that the magnitude of the off-diagonal anharmonic coupling of the H-bonded -NH2 stretch and the -NH2 bend is much smaller in WC base-pairing than in the corresponding rWC base-pairing. The chemical and biological implications of these results, especially in the context of using vibrational spectroscopy as a tool for identifying the signatures of nucleotide base vibrations is addressed.

Toward an improved understanding of the AsH2 free radical: Laser spectroscopy, ab initio calculations, and normal coordinate analysis

Spectra of the Ã(2)A(1)-X̃(2)B(1) transition of the jet-cooled AsD(2) and AsHD isotopologues of the arsino radical have been studied by laser induced fluorescence and wavelength resolved emission techniques. A high-resolution spectrum of the AsD(2) 0(0)(0) band has been recorded, and an improved r(0) structure [r(0)(') = 1.487(4) Å, θ(0)(') = 123.0(2)°] for the à state has been determined from the rotational constants. To aid in the analysis of the vibrational levels, an ab initio potential energy surface of the X̃(2)B(1) state has been constructed and the rovibronic energy levels of states on that potential have been determined using a variational method. The vibrational levels observed in wavelength resolved emission spectra have been fitted to a local mode Hamiltonian with most anharmonic parameters fixed at ab initio values, and the resulting harmonic frequencies have been used to perform a normal coordinate analysis which yielded an improved set of quadratic force constants and an estimate of the equilibrium ground state structure.

Correlated High-Frequency Molecular Motions in Neat Liquid Probed with Ultrafast Overtone Two-Dimensional Infrared Spectroscopy.

In this work, an overtone two-dimensional infrared (2D IR) method is shown to allow correlated molecular motions at the frequencies of overtone transitions to be studied. Waiting-time-dependent overtone 2D IR results of the C-O stretching in neat liquid methanol reveal that the autocorrelation of the v = 0 → 2 transition and the cross correlation of the v = 0 → 2/v = 2 → 4 transitions differ considerably (relaxation time being 700 fs and 2 ps, respectively), suggesting different spectral diffusion dynamics. Quantum-chemical computations in combination with ab initio molecular dynamics simulations show that the overtone transition frequency of the C-O stretching mode in liquid methanol is of more structural sensitivity than the fundamental frequency. This work demonstrates a new 2D IR approach to examining the structural sensitivities of the anharmonic potential parameters of higher vibrational states, which can be used to gain new insight into the ultrafast structural dynamics particularly for neat liquids.