Valence Force Field Research Articles

Precipitation in AlxGa1-xNyAs1-y Alloys

We predict the decomposition peculiarities of the heavy isoelectronic impurities doped Al x Ga 1-x N y As 1-y alloys. The AlN and GaAs precipitates in the high GaAs and AlN content Al x Ga 1-x N y As 1-y epitaxial layers, respectively, should be formed. The free energy of the alloys is expressed as a sum of the free energies of the constituent compounds, strain and elastic energies, and configurational entropy term. The regular solution model is used for describing the free energies of the compounds and strain energy. The interaction parameters between the compounds are estimated by the valence force field model. The stiffness coefficients of the wurtzite AlAs and GaAs as well as the interaction parameter between AlN and AlAs are calculated.

Vibrational study of the Fe(phen) 2(NCS) 2 spin-crossover complex by density-functional calculations

The geometries and vibrational frequencies of an iron(II) spin-crossover complex Fe(phen) 2(NCS) 2 in the low- and high-spin states have been calculated using DFT (BP86 functional with 6-311 G ∗+ Wachters+f , 6-31G ∗ and LANL2DZ basis sets). A redundancy-free set of internal coordinates has been defined and used to obtain a valence force field. The use of the symmetry coordinates of a perfect octahedron as internal coordinates for the FeN 6 framework of the complex has enabled the description of the stretching–bending couplings. A comparison of the force constants of free ligands with the corresponding constants of the two spin states has provided a basis for the discussion of the changes in electronic charge distribution in the complex. By use of the generalized harmonic mode scrambling, it is shown that in the low-lying normal vibrations of the complex, the ligands participate as almost rigid units. Energies of these modes are close to the oscillators describing the interaction of the complex with the surrounding molecules in the solid phase.

Theoretical analysis of microscopic strain distribution and phase stability of Zn chalcogenide alloys using valence force field model

Microscopic strain distribution in II–VI–O alloy systems is theoretically analyzed using the valence force field model. ZnSeO and ZnSO alloys have a maximum strain energy at O composition of 50% due to a large lattice mismatch between constituting materials. Zn–Se bond length decreases with increasing O composition and Zn–O bond increases with decreasing O composition. Se atoms rather than O are easier to move in order to reduce strain energy because of the small elastic constant of ZnSe compared with ZnO. The lattice deformation occurs mainly at tetrahedra containing O–Zn–Se bonds with Zn atom in the center.

Vibrational analysis of mononitro substituted benzamides, benzaldehydes and toluenes: Part I. Vibrational spectra, normal coordinate analysis and transferability of force constants of nitrobenzamides, nitrobenzaldehydes and nitrotoluenes

The Raman and Fourier transform infrared (FTIR) spectra of p-, m- and o-nitrobenzamides, p-, m- and o-nitrobenzaldehydes and p-, m- and o-nitrotoluenes were recorded. Raman polarisation measurements were made for the liquid samples. A normal coordinate analysis was carried out for both in-plane and out-of-plane vibrations of these molecules using 111-parameter modified valence force field. The force constants were refined using 316 frequencies of nine molecules in an overlay least-square technique. The reliability of the force constants was tested by making a zero-order calculation for nine related molecules. Unambiguous vibrational assignments of all the fundamentals were made by using the potential energy distributions and eigen vectors.

A simple model of structural disorder in III–V quaternary alloys

A model is proposed describing the bond length and bond-bending angle distributions in quaternary A 3B 5 alloys with ZB structure in quasi-continuum approximation. The model allows to consider reasonably large crystal lattice clusters employing minimum computing resources. Analytical expressions are derived for the radial distribution functions. The developed approach is applied to the analysis of available experimental data on structural disorder in III–V alloys. Employing the valence force field Keating model the deformation energy for several alloys is evaluated.

Vibrational spectra and normal coordinate analysis of carbamoylazide

The Fourier transform Raman and infrared spectra of carbamoylazide and its deuterated derivative were recorded and the observed frequencies were assigned to various modes of vibration in terms of fundamentals and combinations by assuming Cs point group symmetry. A normal coordinate analysis was also carried out using Simple valence force field. A complete vibrational analysis is presented here for these molecule and results are briefly discussed.

Valence force field theory, elastic, acoustic and thermodynamic properties and a potential function of TeO 2 glass

A short survey has been made on the extensive work that is being done on the pressure derivatives of the second order elastic constants (SOEC) to ascertain various properties of substances. Hence an attempt has been made to correlate the pressure derivatives to some properties of the substances. Thus some equations have been derived to correlate the Grüneisen parameter which is evaluated from Schofield's equations and Bhatia-Singh's (BS) parameters. They have been used to compute the longitudinal ( γ g L) and transverse ( γ g T) Grüneisen constants. γ g L calculated by different methods agree well with experiment. γ g T obtained from BS parameters gives rather higher value while Schofield's equations give results in agreement with experiment. The DeLaunay–Nath–Smith (DNS) equation has been used to derive a relation to compute γ g el (elastic). A method has been extended to calculate the third order elastic constants (TOEC) and it is found to give excellent values of TOECs in agreement with experiment. The absorption band position of TeO 2 has been predicted to occur at 276 cm −1. The phonon dispersion curves have been calculated through BS equations for TeO 2. Several other properties of TeO 2 have been computed such as thermal Grüneisen parameter γ g th, its pressure derivatives ( γ g th)′≡(d γ g th/d P), the pressure variation of bulk modulus C 1≡(d K T /d P) T and its pressure derivatives that is (d C 1/d P) T which is in turn related to ( γ g th)′, the heat capacity at constant volume C V, and the second Grüneisen constant Q. In some cases we calculated these quantities by different methods and the agreement between them is good. Besides we evaluated δ T AG the Anderson Grüneisen parameter. Another important aspect of the present investigations is the formulation of the potential function (PF) of TeO 2 from which we calculated SOECs and these are found to be in excellent agreement with experiment. All other properties mentioned already have also been calculated through the use of the newly formulated PF and the calculated values obtained through various other equations are in good agreement with those obtained from PF. According to valence force field (VFF) all atomic forces can be resolved into bond bending β and bond stretching α forces. It is shown that TeO 2 does not satisfy Martins unity rule. Hence it is concluded that there is an effective dynamic charge on Te in TeO 2. Using the experimental elastic constants the bond bending force β and bond stretching force α and also their pressure derivatives have been evaluated. In addition the reststrauhlen optic frequency ω has been calculated. A self consistent check has been made by evaluating C 44 through the calculated values of α and β.

Valence force field theory, elastic, acoustic and thermodynamic properties and a potential function of TeO2 glass

A short survey has been made on the extensive work that is being done on the pressure derivatives of the second order elastic constants (SOEC) to ascertain various properties of substances. Hence an attempt has been made to correlate the pressure derivatives to some properties of the substances. Thus some equations have been derived to correlate the Grüneisen parameter which is evaluated from Schofield's equations and Bhatia-Singh's (BS) parameters. They have been used to compute the longitudinal (γgL) and transverse (γgT) Grüneisen constants. γgL calculated by different methods agree well with experiment. γgT obtained from BS parameters gives rather higher value while Schofield's equations give results in agreement with experiment. The DeLaunay–Nath–Smith (DNS) equation has been used to derive a relation to compute γgel (elastic). A method has been extended to calculate the third order elastic constants (TOEC) and it is found to give excellent values of TOECs in agreement with experiment. The absorption band position of TeO2 has been predicted to occur at 276 cm−1. The phonon dispersion curves have been calculated through BS equations for TeO2. Several other properties of TeO2 have been computed such as thermal Grüneisen parameter γgth, its pressure derivatives (γgth)′≡(dγgth/dP), the pressure variation of bulk modulus C1≡(dKT/dP)T and its pressure derivatives that is (dC1/dP)T which is in turn related to (γgth)′, the heat capacity at constant volume CV, and the second Grüneisen constant Q. In some cases we calculated these quantities by different methods and the agreement between them is good. Besides we evaluated δTAG the Anderson Grüneisen parameter. Another important aspect of the present investigations is the formulation of the potential function (PF) of TeO2 from which we calculated SOECs and these are found to be in excellent agreement with experiment. All other properties mentioned already have also been calculated through the use of the newly formulated PF and the calculated values obtained through various other equations are in good agreement with those obtained from PF. According to valence force field (VFF) all atomic forces can be resolved into bond bending β and bond stretching α forces. It is shown that TeO2 does not satisfy Martins unity rule. Hence it is concluded that there is an effective dynamic charge on Te in TeO2. Using the experimental elastic constants the bond bending force β and bond stretching force α and also their pressure derivatives have been evaluated. In addition the reststrauhlen optic frequency ω has been calculated. A self consistent check has been made by evaluating C44 through the calculated values of α and β.

The influence of hetero-substitution in the aromatic ring of amino pyrimidine on amino group characteristics in free and H-bonded molecules

The spectra of free and H-bonded (1:1 and 1:2) molecules of aminopyrimidines with CH 3CN, THF, dioxane, DMF, DMSO, and HMPA were studied in the area of stretching and bending vibrations of amino group. The spectral moments of absorption bands M (0), M (1), M (2) and ‘effective’ half-width (Δ ν 1/2) eff=2( M (2)) 1/2 were determined. The temperature dependence of spectral moments was studied in the range of 290–330 K. Equilibrium constants K 298 and enthalpy–Δ H 1 of 1:1 complexes of 2- and 4-aminopyrimidines with DMF, DMSO and HMPA were determined. Valence angles γ(HNH), force constants K(NH), electro optical parameters ∂ μ/∂ q NH and ∂ μ/∂ q′ NH were calculated within R-NH 2 model of valence force field for free and H-bonded molecules of aminopyrimidines. The distribution of electron density on C–NH 2 moiety and dipole moments μ e of aminopyridines were estimated using semi-empirical AM1, PM3 and DFT-B3LYP/6-31G**, ab initio MP2/6-31G** quantum mechanical methods. The comparative analysis stated the influence of heteroatom position and number in the aromatic ring on spectral, geometric, force and energetic characteristics of free and H-bonded molecules in the row of compounds: Aniline, aminopyridines, aminopyrimidines. Correlations between spectral and structural, electrooptic and force characteristics of amino group in aminopyrimidines were established. It was stated that position and number of hetero atoms in the aromatic ring profoundly influence parameters and proton donor ability of amino group in intermolecular H-bonded complexes. However, the parameters of the correlation function change slightly upon the second nitrogen introduction into aromatic ring. Temperature sensitivity of spectral moments M (0) (integrated intensity) and M (1) (center gravity position) of aminopyrimidines compared to aminopyridines shows a great increase.

Calculations of surface effects on phonon modes and Raman intensities of Ge quantum dots

Phonon modes and Raman intensities of Ge quantum dots (QDs) with two different types of surfaces, a free standing surface or a fixed surface, in a size range from five atoms to 7 nm in diameter, are calculated by using a microscopic valence force field model. The results are compared, and the effects of surfaces on phonon properties of QDs are investigated. It is found that phonon modes and Raman intensities of QDs with these two different types of surfaces have obvious differences which clearly reveal the effects of the surfaces of QDs. The calculated results agree with existing experimental observations. We expect that our calculations will stimulate more experimental measurements on phonon properties and Raman intensities of QDs.

Strain and band edges in single and coupled cylindrical InAs/GaAs and InP/InGaP self-assembled quantum dots

A comparative study is made of the strain distribution in cylindrical InAs/GaAs and InP/InGaP self-assembled quantum dots as obtained from isotropic elasticity theory, the anisotropic continuum mechanical model, and from atomistic calculations. For the isotropic case, the recently proposed approach [J. H. Davies, J. Appl. Phys. 84, 1358 (1998)] is used, while the finite-element method, the valence force field method, and Stillinger–Weber potentials are employed to calculate the strain in anisotropic structures. We found that all four methods result in strain distributions of similar shapes, but with notable quantitative differences inside the dot and near the disk–matrix boundary. The variations of the diagonal strains with the height of the quantum dot, with fixed radius, as calculated from all models, are almost linear. Furthermore, the energies of the band edges in the two types of quantum dots are extracted from the multiband effective-mass theory by inserting the strain distributions as obtained by the four models. We demonstrated that all strain models produce effective potentials for the heavy and light holes which agree very well inside the dot. A negligible anisotropy of all normal strains in the (x,y) plane is found, which, providing the axial symmetry of the kinetic part of the multiband effective-mass Hamiltonian, justifies the use of the axial approximation. Strain propagation along the vertical direction is also considered with the aim to study the influence of strain on the electron coupling in stacks of quantum dots. We found that the interaction between the strain fields of the individual quantum dots makes the effective quantum wells for the electrons in the conduction band shallower, thereby counteracting the quantum mechanical coupling.

Spinodal decomposition range of InxGa1−xNyAs1−y alloys

Spinodal decomposition range of InxGa1−xNyAs1−y quaternary alloys as the result of the strain and coherency strain energies, transformations of the bonds, and a lattice mismatch between the GaAs substrate and an alloy is described. The alloys are considered in the strictly regular approximation. The strain energy is presented in the valence-force field model. The spinodal decomposition temperatures of InxGa1−xNyAs1−y alloys are demonstrated up to 1000 °C. It is shown that nitrogen dramatically increases the temperature of the coherent spinodal.

Unit cell group analysis of rare earth elpasolites

Vibrational frequencies of rare earth elpasolites, with general formula M 2ALnX 6 (M=Cs, Rb; A=K, Na, Li; Ln=lanthanide element or yttrium; X=I, Br, Cl, F) have been determined from Raman spectroscopy and electronic absorption and emission spectra, at temperatures down to 10 K. A compilation has been made together with available literature data. The 10 unit cell group vibrational frequencies have been satisfactorily fitted by using a modified valence force field. The trends in the derived force constants are reasonable from a physical viewpoint.

Why do (2×4) GaAs and InAs (001) surfaces exposed to phosphorus have so different behavior? Elastic strain arguments

When exposed to phosphorus, the (2×4) GaAs surface tends rapidly to roughen whereas it is not the case for the (2×4) InAs one, even after long exposure times. X-ray photoemission measurements show that the incorporated phosphorus amount is similar in both cases. The elastic energy difference between these two materials with incorporated phosphorus, calculated within the valence force field approximation, appears to be strong enough to explain this phenomenon. The role of surface reconstruction, mainly dimerization, on phosphorus incorporation is also emphasized.

Vibrational properties of a regular helical Se chain

In this paper we calculated the phonon dispersion curves and the infrared (IR)/Raman spectra of an infinite regular helical selenium (Se) chain. The ingredients needed for their calculations, i.e., the force constant matrix, dynamical-charge tensor (DCT), and polarizability-derivative tensor (PDT), were obtained from ab initio molecular orbital calculations with the second-order M\o{}ller-Plesset perturbation theory for a Se chain with finite length. Assignments for the IR and Raman spectra were performed in terms of a rotational angle \ensuremath{\tau} of the helix; i.e., the phonon modes with wave number $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{Q}=0$ or \ensuremath{\tau} are IR active, while the phonon modes with $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{Q}=0,$ \ensuremath{\tau}, or 2\ensuremath{\tau} are Raman active. Therefore, IR and Raman spectroscopy are useful, not only for identifying the static structure but also for deriving the phonon dispersions of the Se chain. From analyses based on a valence force field model, we found that the ab initio phonon dispersion curve of the stretching band strongly depends on the off-diagonal couplings in the force constant matrix and on the chain geometry, especially the bond angle. The ab initio DCT and PDT were also analyzed with the so-called bond-current and bond-polarizability models, respectively. We found that these simple models reproduce the ab initio IR/Raman intensities quite accurately.

Dual Space Analyzing Based on Symmetry Properties for Phonons fo Si Quantum Dot**The project supported by Special Funds for Major State Basic Research Project of China (G20000683) and National Natural Science Foundation of China (Nos. 69876021 and 60176007). REN Shang-Fen is supported by the National Science Foundation of USA (INT0001313)

Phonon modes in spherical Si quantum dots (QDs) with up to 7.9 nm in diameter are calculated by using the projection operators of the group theory into valence force field model. The phonons of dot modes in each of five irreducible representations (symmetries) are classified by using a dual space analysis method. It is found that the bulk-like modes with localization radius much smaller than the dot's radius have clearly pronounced bulk specific- point parentage, , from specific part of the Brillouin zone (BZ) (Γ-derived, X-derived etc.) and from definite bulk band (one in six modes). In Si dots of all sizes, each specific bulk-like dot mode has specific symmetry. The bulk TO(Γ)-like and the bulk LO(Γ)-like dot modes always have T2 and A1 symmetries, respectively. Except the bulk-A(Γ)-like dot modes of which the frequencies blue-shift as the dot size reducing, the bulk-like Γ-derived LO and TO dot modes and bulk-like X-derived TA and LA dot modes red-shift in frequency with decreasing dot size. There is almost not LO/TO mixing for bulk-like modes. As for the surface-like modes localized at the periphery of the dot, their eigenmodes have not a dominant bulk specific- point parentage or a dominant BZ parentage around some special point. They are a superposition of many bulk bands with from all over the bulk BZ. They have much significant mode mixing than the bulk-like phonons. The classification of dot modes based on the symmetry of group theory will bring advantageous to the discussion of Ramam spectrum, electron-phonon interaction and other phonon-assisted effects in QDs.

Vibrational Properties of Cubic AlxGa1?xN and InxGa1?xN Ternary Alloys

The phonon dispersion curves and phonon density of states of the cubic AlxGa1—xN and InxGa1—xN alloys were calculated within the framework of a valence force field method and an effective charge approach for the long-range Coulomb interaction. The valence-force parameters and effective charges for the cubic GaN, AlN and InN binary compounds were fitted to the phonon frequencies at high-symmetry points in the Brillouin zone measured by Raman spectroscopy and calculated by ab initio methods. The scaling factor approximation was used to obtain the valence-force parameters and effective charges for the alloys. A good agreement between our calculations and recent Raman data for the alloys is achieved.

Valence force field theory, elastic, acoustic and thermodynamic properties and a potential function of TeO2 glass

Valence force field theory, elastic, acoustic and thermodynamic properties and a potential function of TeO2 glass

Assignment of the in-plane molecular vibrations of the electron-donor molecule BDT-TTP based on polarized Raman and infrared spectra, in which BDT-TTP is 2,5-bis(1,3-dithiol-2-ylidene)-1,3,4,6-tetrathiapentalene

Infrared and Raman spectra of 2,5-bis(1,3-dithiol-2-ylidene)-1,3,4,6-tetrathiapentalene (BDT-TTP) and 1,3,4,6-tetrathiapentalene-2,5-dione (TTP-DO) are reported. The vibrational modes of TTP-DO are assigned with the aid of the depolarization ratio of solution Raman spectra, polarized reflection spectra and polarized Raman spectra. A D 2h symmetry is assumed for the BDT-TTP molecule and its in-plane fundamental vibrations are assigned with the aid of the polarization ratio and the correlation with TTP-DO, tetrathiafulvalene (TTF), tetramethyltetrathiafulvalene (TMTTF) and bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF). Normal coordinate calculation with a modified internal valence force field was carried out for the in-plane fundamental vibrations of TTP-DO and BDT-TTP. Ab initio calculations of the normal modes of BDT-TTP 0 and BDT-TTP + are compared with the empirical analysis.

An Extension of the Consistent Valence Force Field (CVFF) with the Aim to Simulate the Structures of Vanadium Phosphorus Oxides and the Adsorption of n-Butane and of 1-Butene on their Crystal Planes

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