Phonon Eigenfrequencies Research Articles

Vibrational dynamics of Zr 67Ni 33 amorphous alloy

Vibrational dynamics of Zr 67Ni 33 amorphous alloy has been studied at room temperature in the framework of pseudopotential formalism. The effective pair potential is computed using partial pair potential approach in Wills and Harrison form. This effective pair potential in turn is used to study the eigenfrequencies of longitudinal and transverse phonon modes. The results of phonon eigenfrequencies of this amorphous alloy have been compared with the available Molecular Dynamics results at different temperatures. Further, thermal and elastic properties viz. longitudinal and transverse velocities of sound, Debye temperature, Isothermal Bulk Modulus of the amorphous alloy have also been calculated from the zero-frequency limit of the phonon dispersion curves. Computed results are found in good agreement with available experimental data.

Vibrational dynamics of Pd80Si20 glass

AbstractThe vibrational dynamics of Pd80Si20 glass has been studied at room temperature in terms of the phonon eigenfrequencies of longitudinal and transverse modes employing the theoretical formulations of Hubbard and Beeby as well as of Takeno and Goda. The effective interatomic pair potential in this glass is obtained using the experimental partial pair correlation functions and the hypernetted chain (HNC) equation. Long wavelength limits of the phonon modes are then used to get information on the elastic and thermal properties of the system. It has been found that the theoretical results of these properties as computed through Hubbard and Beeby's method are in good agreement with the available experimental results.

Study of phonon eigenfrequencies in ternary transition metal‐metalloid Fe40Ni40B20 glass

AbstractThe study of the ternary Fe40Ni40B20 metal‐metalloid glass has been made through a partial pair‐potential approach. Six partial pair potentials of this ternary glass have been computed using pseudopotential‐based interatomic forces. In particular, the model employed here for the calculation of the potential is in analogy with the three‐partial‐structure‐factor approach of Sietsma and Thijsse with the assumptions that Fe and Ni atoms have identical distributions with respect to like neighbours and hence the partial pair potentials of Fe‐B and Ni‐B are identical. The calculated effective pair potential using the partial pair potentials is then employed to investigate the longitudinal and transverse phonon eigenfrequencies. Further, from the elastic part of the frequency spectrum, elastic and thermal properties have been computed. The computed results for these properties are found to be in good agreement with the available experimental results.

Structure and thermal properties of metallic glasses: Theoretical and experimental aspects

The structure and dynamics of two component metallic glasses (Fe-B, Pd-Si) have been studied through the calculation of eigenfrequencies of phonons using different theoretical approaches in the framework of a pseudopotential. It has been concluded through these studies that short wavelength collective modes arise from the longitudinal phonon excitations and not from the diffused Umklapp scattering from long wavelength transverse acoustic modes, as pointed out earlier. Additionally, the long wavelength limit of phonon dispersion curves has been employed to compute the thermal and elastic properties in these systems. An effort has also been made to study experimentally the crystallization kinetics and specific heat of Cu 60Zr 40, Cu 50Zr 50 and Cu 50Ti 50 binary glasses using differential scanning calorimetry. The relation between glass transition temperatures, crystallization peak temperatures and energy released during crystallization with heating rates are also discussed. These studies indicate that a microstructure examination of these glasses is necessary.

Dynamics of substitutional impurities in C 60

A detailed simulation is presented of the vibrational properties of a single C 60 molecule substitutionally doped with heterovalent or isotopical impurities. The calculations have been performed by means of a transferable version of the bond charge model which allows a consistent calculation of the phonon eigenfrequencies and their relative intensities in Raman and IR optical spectra. Silent modes activation and dopant localized phonon optical lines are present in both Raman and IR spectra and may allow for the experimental identification of these doped molecules.

Elastic Constants and Phonon Dispersion of Amorphous Copper with Embedded‐Atom Force

AbstractElastic constants and phonon dispersion of amorphous copper are studied by assuming that the interatomic potential is transferable from the crystalline state and can be represented by the analytical model of the embedded‐atom method given by Johnson. To test its effectiveness, the force model used to calculate the phonon eigenfrequencies in the copper crystal and the result is in perfect agreement with experimental values measured at 80 K. Based on the embedded‐atom method and in connection with the radial distribution function, the formulae for calculating the elastic constants of the amorphous phase and the modified Takeno‐Goda formula for studying phonon dispersion in amorphous materials are presented. For an easy implementation, the formulae are simplified by using the Bhatia‐Singh approximation, in which only the nearest‐neighbour contribution is considered.

Study of Phonon Eigenfrequencies in Metallic Glasses

AbstractThe density fluctuations in terms of phonon eigenfrequencies are studied in Ni50Zr50 and Cu66Ti34 metallic glasses using two different theoretical approaches. The calculated results of phonon eigenfrequencies show all the main characteristic features of the dispersion curves. The effective interatomic interactions are studied in terms of a pair potential using the extended theory of the Wills‐Harrison potential which includes the effect of d‐band electrons. Finally, from the low wave‐vector transfer region of the dispersion curves, some thermodynamical properties are also calculated which are in agreement with each other.

A theoretical study of the structure and dynamics of amorphous Fe

The extended theory of transition-metal potential, which includes the transition-metal d states, is used to obtain the effective interatomic interactions in terms of pair potential for amorphous Fe. Pair potential for amorphous Fe is also computed using a simple approach for liquid metals given by de-Angelis and March. We employ the so obtained pair potentials to calculate the longitudinal- and transverse-phonon eigenfrequencies using the theory of phonons in amorphous solids. The results for the phonon eigenfrequencies obtained from these potentials are in good qualitative agreement with the molecular-dynamics results as well as with the theoretical results of Bhatia and Singh. Computation of the Debye temperature and the isothermal bulk modulus also shows a close agreement with other results.

Dynamical correlations and collective excitations in liquid K0.5Cs0.5 alloy

A model developed by Glass and Rice for Brownian particles in liquids is employed for the computations of the velocity autocorrelation function and mean square displacement in liquid K0.5Cs0.5 alloy introducing the concept of the motion of 'effective atoms'. Further, collective excitations in this liquid metal alloy have been studied by computing the longitudinal and transverse phonon eigenfrequencies employing three different approaches. The computed results show good qualitative and quantitative agreement with each other. The effective interatomic pair potential used for the study of dynamics (single particle as well as collective motions) of K0.5Cs0.5 alloy is obtained using the empty-core pseudopotential given by Ashcroft. Also, some thermodynamical properties have been calculated using the longitudinal and transverse phonon velocities and are in good agreement with the available results.

The derivation of force constants from phonon frequencies

A transformation is given which relates the phonon eigenfrequencies at very few points in the Brillouin zone of a body-centred cubic lattice to force constants describing the interaction of sublattices. The use of this transformation is illustrated by determining the sublattice force constants of sodium from experimentally determined phonon eigenfrequencies. It is shown that the transformation method allows the intrinsic uncertainties in atomic force constants described by Leigh et al (1971) to be expressed in the form of indeterminate parameters.

A Theory of Phonon-Like Excitations in Non-Crystalline Solids and Liquids

Elementary excitations associated with atomic motion in non-crystalline solids and liquids are studied with particular attention paid to the dependence of their dispersion on local order. In doing this, an attempt is made to obtain an exact formal expression for an dy­ namical matrix giving the eigenfrequencies of phonons in a non-crystalline solid in terms of effective pair-correlation functions. A brief remark is also given on the moment method and sum rules for the dynamic structure factor to study high-frequency collective motion in liquids. It is suggested that under certain restrictions the phonon-rotan-like behavior of ex­ citations as observed in liquid helium is likely to exist in almost all types of structure or topological disorder systems (amorphous and glassy solids, liquids, etc.). To substantiate this, a model one-dimensional system is chosen to show how a phonon dispersion curve in a crystal lattice is modified, as the partial disorder characterizing a structure disorder system is intro­ duced. Such a local disorder is shown to give rise to a frequency gap which decreases with increasing local order and eventually vanishes in the case of complete order. This result is also in qualitative agreement with the pressure- and the temperature-dependence of the rotan minimum energy in liquid helium. Simple numerical calculations are made to compare the obtained results with experiments for collective motion in liquid argon and also in liquid helium. Fairly good agreement is obtained.

A Theory of Phonons in Amorphous Solids and Its Implications to Collective Motion in Simple Liquids

A theoretical study is made of phonons in amorphous solids using a self-consistent phonon scheme. In treating the structural disorder inherent in the problem, a theory is formulated from the viewpoint of multiple scattering theory and designed to give phonon eigen-frequencies which are expressed in terms of many-body correlation functions of atoms as well as of interatomic potentials in the solids. For this purpose, a conditional averaging procedure is applied to equations for phonon Green's functions, obtainable using the renormalized harmonic approximation. A set of hierarchy equations is thereby obtained, for which various decoupling approximations are employed. As an application of the results obtained here, numerical calculations of the eigenfrequencies of longitudinal and transverse phonons in liquid argon are using the “quasi-crystalline approximation” and the Lennard-Jones model potential. Fairly good agreement with experiment is obtained. A systematic and approximate self-consistent method for treating the hierarchy equations, which may be of some use in studying the general properties of the energy spectra of elementary excitations in disordered systems, is also obtained.