Phonon dispersion of bcc iron to 10 GPa

The phonon dispersion of bcc iron under high pressure to 10 GPa was measured at 300 K by inelastic neutron scattering. Its pressure dependence is surprisingly uniform. Contrary to the behavior found in other bcc elements, there is a lack of any significant pretransitional behavior close to the martensitic bcc-hcp transition which could be related to the Burgers mechanism. This finding confirms predictions by spin-polarized total energy calculations that explain the transition by the effect of pressure on the magnetism of iron. The high pressure frequencies were used to develop a lattice dynamical model from which thermodynamic quantities can be determined at any pressure to 10 GPa.     

Phonon dispersion relation of liquid metals

The phonon dispersion curves of some liquid metals, viz. Na (Z = 1), Mg (Z = 2), Al (Z = 3) and Pb (Z = 4), have been computed using our model potential. The charged hard sphere (CHS) reference system is applied to describe the structural information. Our model potential along with CHS reference system is capable of explaining the phonon dispersion relation for monovalent, divalent, trivalent and tetravalent liquid metals.     

Phonon dispersion curves of VI B group metals

The phonon dispersion curves of chromium, molybdenum and tungsten have been computed along the principal symmetry directions using an angular force model with volume forces. The results obtained are in very good agreement with the experimental observations.The author is grateful to Dr. V. Ramamurthy of I.I.T. Delhi for many valuable and stimulating discussions.     

Phonon dispersion curves of V B group of metals

The phonon frequencies of vanadium, niobium and tantalum along the principal symmetry directions are computed using an angular force model. The calculated dispersion curves are in very good agreement with the experimental results.The author is grateful to Dr. V. Ramamurthy and Dr. S. B. Rajendraprasad of IIT Delhi for many valuable and stimulating discussions.     

A simple analytical EAM model for bcc metals including Cr and its application

An analytical embedded atom method (EAM) model, which can treat bcc transition metal Chromium, has been developed. In this model, a new potential was presented, and a modified term has been introduced to fit the negative Cauchy pressure P _c=(C₁₂-C₄₄)/2 for element Cr. The new model was applied to calculating the thermodynamic properties of binary alloys of all bcc transition metals V, Nb, Ta, Cr, Mo, W and Fe. The calculated dilute-solution enthalpies and formation enthalpies of random alloys are in good agreement with the experimental data available, the results from the first-principles calculations, and the results of thermodynamic calculations.     

Phonon dispersion curves for niobium

Conclusion The experimentally measured phonon dispersion relation for niobium is very complex. This complexity may be due to the incomplete electronicd shells which make an important contribution to very large cohesive energy, and its likely effect on the phonon frequencies. Also the anomalies in the dispersion curves may be due to the departure of the Fermi surface from sphericity. In the present study none of the above effects is included explicitly and so theory fails to achieve exact agreement with the experimental data. Finally, we would like to put a concluding remark that an appropriate microscopic treatment given tod electron could explain the phonon dispersion curves of transition metal like niobium.One of the authors (ARJ) would like to express his appreciation to Professor M. K. Agarwal (Head of the Department) for his support and encouragement to carry out this work. Thanks are also due to Sardar Patel University for providing computer facilities.     

Phonon dispersion of d and f shell metals: A dynamical treatment

The effective pair potential is written as the sum of s-s, d-d, s-d, f-f and s-f contributions. The free electron part of the pair potential is obtained in second-order perturbation theory using rational dielectric function (RDF) in conjunction with Heine-Abarenkov model pseudopotential (HAMP). The exchange-correlation corrections due to Taylor are inherent to RDF. The overlap between d states and f states on different ions and the effect of sd and hybridization are included in an approximate manner, as has been suggested by Wills and Harrison [Phys. Rev. B 28 (1983) 4363], and Harrison [ibid., 550]. An approximate temperature dependence has been included in the effective potential through an asymptotic factor. The ion-ion interaction so defined is used to calculate the phonon dispersion curves for hcp metals Tb and Ho. The calculated phonon frequencies are found to be real and in reasonably good agreement with the neutron inelastic scattering measurements which establishes the validity of the effective pair potential for rare earths.     

Effects of lattice dispersion and elastic anisotropy on the thermal properties of bcc metals

Two new parameters which take into account the effects of elastic anisotropy and phonon dispersion on lattice specific heat in the case of sodium and potassium have been evaluated. A new graded mesh method which uses a 162-direction approximation in (1/16) part of the Brillouin Zone (BZ) has been considered to evaluate the two parameters.     

Phonon anomalies and martensitic transitions in bcc materials

The general systematics of phonon spectral anomalies are considered for materials with bcc and B2 structures. In a model of central pair-wise interactions, it is shown that anomalies on the TA₂ branch at =1/3 (211), the LA phonon branch at =2/3 (111), and on the TA branch at =1/2 (111) arise simultaneously with the softening of the shear elastic moduli C' and C₄₄. The TA phonon anomaly at =1/3 (110) is not due to softening of the elastic moduli, but rather is due to the long range nature of the pair-wise or multiparticle interaction. A model is proposed for the nucleation of the martensitic phase for B2 compounds, the distinctive feature of which is a consideration of the softening of the shear moduli, which is modulated by lattice relaxation around ordering defects, along with the possibility of additional defect ordering near the transition.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 10, pp. 31–39, October, 1993.     

Phonon dispersion curves of transition metals using modified general tensor force model

The general tensor force model has been modified by incorporating separately the electron-ion interactions. The model satisfies the translational symmetry requirements of the lattice and is used to obtain the phonon dispersion curves of chromium, molybdenum and tungsten. The agreement between the theoretical and experimental frequencies is very good.     

Phonon dispersion relations for potassium thiocyanate

Measurements of some low frequency phonon dispersion curves in potassium thiocyanate have been made using inelastic neutron scattering techniques. The measured phonon frequencies are presented along with ones calculated from a simple model comprising axially-symmetric force constants between nearest neighbour atoms. The applicability of such a model in describing the lattice dynamics of this crystal structure is discussed.     

Phonon dispersion in graphite

We measured the dispersion of the graphite optical phonons in the in-plane Brillouin zone by inelastic x-ray scattering. The longitudinal and transverse optical branches cross along the Gamma-K as well as the Gamma-M direction. The dispersion of the optical phonons was, in general, stronger than expected from the literature. At the K point the transverse optical mode has a minimum and is only approximately 70 cm(-1) higher in frequency than the longitudinal mode. We show that first-principles calculations describe very well the vibrational properties of graphene once the long-range character of the dynamical matrix is taken into account.     

Phonon dispersion in Xe

The predictions of the Mie-Lennard-Jones potentials for phonon dispersion in solid Xe at 10°K and at 77°K are compared with the results of recent measurements. The dynamics of the crystal are described by the first order self-consistent phonon theory for the imaginary part of the one phonon Green's function. The fit obtained is quite poor though we point out that no conclusion can be drawn about the size of three-body forces. We conclude that improved potentials are needed to account for the experimental data.