Phonon Frequency Distribution Function Research Articles

Neutron Scattering in Nanotubes

Abstract: Neutron scattering has got numerous applications in various fields of research like material research, crystallography etc. Thermal neutron scattering in randomly un-aligned multi walled carbon nanotubes is based on its anisotropic frequency distribution function. This frequency distribution function is obtained using a dynamical model which includes the presence of both the surface modes and intertube coupling. Experimentally measured values of specific heat for randomly un-aligned multi walled carbon nanotubes has been studied to detect the phonon frequency distribution function. Elastic scattering is used for analyzing structures. Inelastic scattering is applied for the study of atomic vibrations. The dynamical model has been used to find the scattering values. Both scattering values are calculated and compared. It was concluded that the difference in their values is large. This difference would affect the transport processes in randomly un-aligned multi walled carbon nanotubes Keywords: Specific heat, Elastic scattering, Inelastic scattering, Neutron Diffraction, Frequency Distribution Function

Phonon frequency distribution function and temperature variation of Rayleigh Mössbauer scattering fraction from aligned multiwalled carbon nanotubes

The phonon frequency distribution function (FDF) of aligned multiwalled carbon nanotubes (MWNTs) was obtained by unfolding its observed temperature variation of specific heat in the temperature range 1.8 to 250 K. An anisotropic dynamical model which incorporates the presence of two-dimensional modes on the surface of the tube and the intertube coupling was used as a trial function to carry out the unfolding process numerically. Temperature variation of Rayleigh Mössbauer scattering fraction of Sn-119 gamma-photons was computed using the trial and final FDF of MWNT. The temperature variation of Rayleigh Mössbauer scattering fraction in each case is quite marked and can be observed experimentally.

On the excess specific-heat of single-walled carbon-nanotube ropes due to the adsorption of helium atoms in the temperature range 2-20 K

Experimental specific-heat measurements in single-walled carbon-nanotube (SWNT) ropes show marked increase when He-4 is allowed to be adsorbed, the increase in the values varying from 2 to 2.5 times in the temperature range 2-20 K. Beyond 20 K, the effect of adsorption on the specific heat of SWNT ropes is negligible. The phonon frequency distribution function (FDF) of the dynamical modes was extracted by employing the unfolding technique from the observed experimental temperature variation of the specific heat and a trial phonon FDF. The agreement between the observed experimental values of specific heat and the values obtained using the above method is quite good, the error being less than 10% in the temperature range 2-20 K and within 6% for 20 T 300 K at most of the temperature values. The change in the values of the specific heat can be attributed to the fact that the phonon FDF of He-4 adsorbed SWNT ropes shows marked difference from that when there is no adsorption for energies less than 200 K. The sensitivity of specific heat to adsorption at low temperatures by SWNT ropes is highlighted, particularly, by the appearance of large number of dynamical modes at 15 K. This can be experimentally checked using Rayleigh recoilless fraction of Mossbauer -ray photons from the carbon nanotube ropes sample.

Dynamical modes of a graphite surface, on top and in the middle- by unfolding the observed temperature dependent displacement–displacement auto-correlation function

Making use of the unfolding technique to determine the phonon frequency distribution function (FDF) from the temperature dependent displacement–displacement auto-correlation function suggested by the authors, the experimentally observed displacement–displacement auto-correlation functions of a graphite surface located either at the top or in the middle of the crystal have been unfolded. The final unfolded FDF shows marked differences for the two cases, exhibiting the potentiality of the unfolding technique to accurately determine the dynamics and hence the difference in the FDF of the two layers, located at different sites in a crystal.

DIFFERENTIAL AND TOTAL PHONON FREQUENCY DISTRIBUTION FUNCTIONS FROM THE CORRESPONDING MEASURED TEMPERATURE DEPENDENT MEAN SQUARE DISPLACEMENTS IN AN ANISOTROPIC CRYSTAL USING UNFOLDING TECHNIQUE

It is shown, for the first time, that phonon frequency distribution function (FDF) can be successfully extracted from the measured temperature dependent mean square displacement (MSD) of a particle in a condensed system using unfolding technique. In particular, the observed MSD of a Zinc atom in the basal plane, along the z direction and the total have been unfolded to obtain corresponding phonon FDF which yield much better values of the temperature dependent MSD than the trial FDF. The method can be fruitfully utilized to obtain FDF of elastic vibrations both for ordered and disordered solids from the readily available experimental MSD.

Effect of anisotropic phonons on superconductivity

Effect of crystal anisotropy which results in the anisotropic phonon frequency distribution function has been studied on superconductivity in a strongly coupled superconductor. The dependence of the superconducting critical temperature, T c, on the degree of anisotropy is quite involved. In highly anisotropic systems superconductivity is suppressed. The expression for T c is related to the total mean square displacement of the vibrating ion, yielding the result that, for superconductivity, the phonon frequency distribution function from mean square displacement is preferred to that obtained from other studies for consistent physical parameters. Explicit calculations for 67Zn are reported.

The effect of crystal anisotropy on the temperature-dependent mean square displacement, its temperature derivatives and second-order Doppler shift in zinc up to 600 K

Anisotropic mean square displacements, their temperature derivatives and second-order Doppler shift in the temperature range 0-600 K have been calculated in zinc by making use of the recently suggested anisotropic phonon frequency distribution function (1989) which takes into account the presence of planar modes. The calculated values of both the anisotropic mean square displacements and their temperature derivatives at various temperatures are in reasonable agreement with the corresponding experimental results. The effect of planar modes is found to be significant in the entire temperature range for all the three parameters studied.

Effect of anisotropic phonons and planar acoustic plasmons on superconductivity in lanthanum cuprates

Abstract A realistic anisitropic phonon frequency distribution function for superconducting lanthanum cuprates, which takes account of (i) the presence of planar modes, (ii) is quite close to the experimental phonon frequency distribution function and (iii) yields the specific heat values in the temperature range 5 to 50 K in reasonable agreement with the various measured values, has been used to calculate the superconducting critical temperature, T c , making use of the expression based on the strongly coupled theory of superconductivity and other realistic parameters. The calculated value of T c ≅34.8 K is in reasonable agreement with the observed results. The effect of thermal phonons and two-dimensional acoustic plasmons has been studied (when both electron-phonon and electron-plasmon mechanisms are present) which results in an increase of ~3 K and ~9 K, respectively. Finally the variation of T c with the change of phonon anisotropy has been reported and it is found that the T c is noticeably dependent on the degree of phonon anisotropy. A significant result is that for superconductivity to occur in these compounds, coupling between the Cu-O planes is essential.

Thermal Neutron Scattering Kernel for Polyethylene of Various Degrees of Crystallinity

AbstractA thermal neutron inelastic scattering kernel for polyethylene (PE) of any degree of crystallinity based on a recently proposed dynamic model is suggested. The dynamic model takes proper account of the anisotropic linear chain structure of PE that gives rise to an acoustic phonon frequency distribution function, which is quite different from the usual Debye type, and that has been successful in explaining the observed temperature variation of the specific heat of PE of different degrees of crystallinity. The expressions for zero-phonon and one-phonon neutron scattering cross sections are derived by making use of the frequency distribution function. The kernel incorporates the contribution of two-phonon acoustic modes and also that of optical modes. The kernel has been used to calculate the total scattering cross sections of thermal neutrons from crystalline and noncrystalline PE, including amorphous PE. The calculated values of total scattering cross sections are in reasonable agreement with the e...

Lattice dynamics of black phosphorus

A force-constant model calculation of the phonon dispersion and frequency distribution function of black phosphorus, which is a narrow-gap and layer-like semiconductor, is presented. In calculation, we assume the valence force model for intralayer atomic interactions and the axially symmetric force model for interlayer ones. The calculated results explain experiments on optical phonons, specific heat and second-order Raman spectrum satisfactorily and sound velocities semi-quantitatively. Large discrepancy between theory and experiment on the linear compressibilities exists.

Lattice dynamical study of face centred tetragonal indium

The phonon dispersion relations and the phonon frequency distribution function of fct indium have been deduced, for the first time, using a lattice dynamical model which expresses the atomic interactions in terms of central, angular, and volume forces. Six elastic constants, four zone boundary frequencies, and an equilibrium condition were used in the evaluation of the force constants. It is shown that this model is elastically consistent and conforms with the translational symmetry of the lattice; the phonon frequencies of indium deduced from it are in very good agreement with the experimental values of Reichardt and Smith and the theoretical values of Garrett and Swihart, but disagree with the theoretical values of Chulkov et al. as well as those of Gunton and Saunders at several wave vectors and polarizations. In addition the phonon frequency distribution curve obtained from this model is in overall agreement with those obtained from the electron tunnelling data, the inelastic scattering of neutrons as well as a pseudopotential model. The apparent characteristic features of these curves, the implications of the crystallographic equivalence between fct and bet lattices, and their relevance in the lattice dynamical study of indium are discussed.

Lattice dynamical study of body-centred tetragonal indium

The phonon dispersion curves, phonon frequency distribution function as well as the lattice specific heat of body-centred tetragonal indium have been deduced using a lattice dynamical model which includes central, angular and volume forces. Six elastic constants, four zone boundary frequencies and an equilibrium condition were used in the evaluation of the force constants. It is shown that this model is elastically consistent and satisfies the symmetry requirements of the lattice, the phonon frequencies of indium deduced from it are in very good agreement with the experimental values of Reichardt and Smith and the theoretical values of Garrett and Swihart, and theθ D values compare well with the experimental values over a wide temperature range. The apparent discrepancies in the phonon dispersion curves and theθ D-T curves obtained from deficient models, importance of umklapp processes and the significance of angular forces in the lattice dynamical models are discussed.

Force Constant Change in Sn–Impurity Systems: 107Pd:119 Sn, 197Au:119Sn, and 63.5Cu:119Sn

AbstractThe recoilless fraction f and the SOD data for the Sn as impurity in 107Pd, 197Au, and 63.5Cu are analysed for any force constant change in the framework of Mannheim's model, using the experimentally determined phonon frequency distribution function for the hosts. Furthermore, correction for anharmonicity is applied, wherever necessary. On the basis of f‐values, the force constant ratio λ′/λ turns out to be 0.46 ± 0.02, 0.86 ± 0.04, and 0.58 ± 0.03, respectively, for the systems 107Pd:119Sn, 197Au:119Sn, and 63.5Cu:119Sn. All these cases are of weak binding. This conclusion is at variance with an earlier report of strong binding for the system 107Pd:119Sn. Expectedly no localized modes are found to exist for either of the systems.

A new phonon frequency distribution function for quasi-two-dimensional systems

A new phonon frequency distribution function for quasi-two-dimensional systems is proposed. Using it, the lattice specific heat of crystalline graphite is calculated and compared with experiment.

Mössbauer anisotropic elastic scattering fraction from crystalline polyethylene at various temperatures

Mössbauer elastic scattering fraction from crystalline polyethylene in the temperature range 0–425 K, calculated on the basis of its recent phonon frequency distribution function suggested by the authors, are markedly different along and perpendicular to the polyethylene chains. The difference in the anisotropic scattering increases with increasing temperature of the crystal, and is easily measurable even at room temperature.

Lattice dynamics of a mixed diatomic lattice

A pseudo-unit-cell model is utilized to calculate some lattice-dynamical properties of a mixed diatomic lattice of the form $A{B}_{1\ensuremath{-}x}{C}_{x}$, where $0\ensuremath{\le}x\ensuremath{\le}1$. The pseudo unit cell is formed by $A$, $(1\ensuremath{-}x)B$, and $\mathrm{xC}$ ions and the resulting mixed crystal lattice is a repetition of such cells. The lattice dynamics of both a linear and a three-dimensional mixed zinc-blende lattice have been studied. The lattice-dynamical model consists of central and noncentral short- and long-range interactions among ions of appropriate effective ionic charge. The model parameters are deduced from physical observables such as the elastic constants and the long-wavelength optical and impurity mode frequencies of the end systems when $x\ensuremath{\rightarrow}0$ and $x\ensuremath{\rightarrow}1$. Explicit calculations for the phonon dispersion and frequency distribution function have been performed for the linear mixed diatomic lattice and for $\mathrm{Zn}{\mathrm{S}}_{1\ensuremath{-}x}{\mathrm{Se}}_{x}$ and $\mathrm{Ga}{\mathrm{P}}_{1\ensuremath{-}x}{\mathrm{As}}_{x}$.

Gaussian Approximation for Phonon Frequency Distribution Function for PuO2and UO2

The phonon frequency distribution function for PuO2 and UO2 has been approximated by a one-parameter Gaussian distribution. By comparing the limiting forms of the specific heat and the Debye-Waller factor calculated with this approximate distribution function with the corresponding limiting values of these quantities in the Debye model, the value of the parameter is found to vary inversely as the temperature T. The constant of proportionality is found to be of the order of Debye's temperature. Values of the parameter for UO2 are calculated from its Debye's temperature and its experimental data on Debye-Waller factor, Debye's temperature and specific heat. The value of the parameter is also calculated for PuO2 from its specific heat data.

A model for the phonon frequency distribution function for crystalline polyethylene

A model for the phonon frequency distribution function of crystalline polyethylene has been developed considering the mass of the vibrating unit to be two methylene groups and distinguishing between the ‘hard’ longitudinal and transverse dispersive modes. It explains the temperature variation of specific heat of polyethylene and can be used for other studies.

Gaussian Approximation for Phonon Frequency Distribution Function for PuO2 and UO2

The phonon frequency distribution function for PuO2 and UO2 has been approximated by a one-parameter Gaussian distribution. By comparing the limiting forms of the specific heat and the Debye-Waller factor calculated with this approximate distribution function with the corresponding limiting values of these quantities in the Debye model, the value of the parameter is found to vary inversely as the temperature T. The constant of proportionality is found to be of the order of Debye's temperature. Values of the parameter for UO2 are calculated from its Debye's temperature and its experimental data on Debye-Waller factor, Debye's temperature and specific heat. The value of the parameter is also calculated for PuO2 from its specific heat data.

Anharmonic contributions to the Mössbauer fraction for 77.3 keV transition of 197Au in gold metal

Using the theoretical phonon frequency distribution function for gold of Christensen and Seraphil, the recoillness fraction has been calculated over a temperature range 4.2–100°K after incorporating the contribution due to anharmonicity. The results are in good agreement with the experimental measurements of Erickson et al. Further, basing on the recently measured equation of state, the pressure dependence of Mössbauer fraction is predicted and this gives ƒ ( P=200) ƒ(0) = 1.431 and 6.596 at 4.2 and 80°K respectively.