Analytic-quadratic method of calculating the density of states

Methfessel, Michael; Boon, M. H.; Mueller, F. M.

doi:10.1088/0022-3719/16/27/002

Cited by 31 publications

(13 citation statements)

References 5 publications

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“…The resulting piecewise quadratic representation of the band structure is directly converted into a DOS using the analytic quadratic approach of Methfessel. 27 The representation of the wavefunctions in terms of plane waves allows the direct quantitative evaluation of the matrix element, in contrast to the more frequent approaches which are simply symmetry projected local DOS. In our evaluation of the matrix elements, the initial core states are taken from all electron calculations for the isolated atoms.…”

Section: Calculationmentioning

confidence: 99%

Cubic boron nitride: Experimental and theoretical energy-loss near-edge structure

et al. 2001

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A comparison between experimental and theoretical electron Energy Loss Near Edge Structure (ELNES) of B and N K-edges in cubic boron nitride is presented. The electron energy loss spectra of cubic boron nitride particles were measured using a scanning transmission electron microscope. The theoretical calculation of the ELNES was performed within the framework of density functional theory including single particle core-hole effects. It is found that experimental and calculated ELNES of both the B and N K-edges in cubic boron nitride show excellent agreement.

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Section: Calculationmentioning

confidence: 99%

Cubic boron nitride: Experimental and theoretical energy-loss near-edge structure

et al. 2001

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“…This function can be regarded as the imaginary part of a diagonal matrix element of the resolvent operator: (15) where u~"') is the 3 N components vector with components N-112 e p exp(ik. d) for the atom at .p position d, and H(k) is the dynamical matrix at wave vector k. The function I e p (k, w) can be calculated using a recursion method [9].…”

Section: N"6mentioning

confidence: 99%

“…T m is a tridiagonal matrix of order m and V m is the m x n transformation matrix whose first column is the vector ut) Substitution in (15) (17) where the m components vector v I is a unit vector whose first component is equal to 1, whereas all other components are equal to O. Using a matrix inversion formula we obtain:…”

Section: N"6mentioning

confidence: 99%

“…Methfessel [15] showed that with the quadratic fit the integration (8) can be performed analyticaUy. However, we did not adopt this approach, but used, instead, the so-called hybrid method of MacDonald et al [14].…”

Section: Appendix Bmentioning

confidence: 99%

“…Due to the 8-function this integral can be replaced by a surface integral : where f means integration over the surface of constant frequency and n denotes a unit vector Sw orthogonal to the branch surface at wave vector k. For the numerical evaluation of the DOS from (8) we used either a local linear or a local quadratic interpolation of the branch surface. Local quadratic interpolation was also used by MacDonald et al [14] and by Methfessel [15]. The interpolated branch surfaces were fitted on a cubic grid of k-points inside the Brillouin zone.…”

Section: Introduction_mentioning

confidence: 99%

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Phonons in models for icosahedral quasicrystals : low frequency behaviour and inelastic scattering properties

1993

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Abstract. -A detailed study of the low frequency behaviour of the phonon spectrum for 3-dimensional tiling models of icosahedral quasicrystals is presented, in commensurate approximations with up to 10 336 atoms per unit cell. The scaling behaviour of the lowest phonon branches shows that the widths of the gaps relative to the bandwidths vanish in the low frequency limit. The density of states at low frequencies is calculated by Brillouin zone integration, using either local linear or local quadratic interpolation of the branch surface. For perfect approximants it appears that there is a deviation from the normal w 2-behaviour already at relatively low frequencies, in the form of pseudogaps. Also randomized approximants are considered, and it turns out that the pseudogaps in the density of states are flattened by randomization. When approaching the quasiperiodic limit, the dispersion of the acoustic branches becomes more and more isotropic. and the two transversal sound velocities tend to the same value. The dynamical structure factor isdetermined for several approximants, and it is shown that the linearity and the isotropy of the dispersion are extended far beyond the range of the acoustic branches inside the Brillouin zone. A sharply peaked response is observed at low frequencies, and broadening at higher frequencies. To obtain these results, an efficient algorithm based on Lanczos tridiagonalisation is used.

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Correctly Weighting Tetrahedron Method for k‐Space Integration of F.C.C. Structures

Hanke

Kühn²,

Strehlow³

1984

Physica Status Solidi (b)

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Analytic-quadratic method of calculating the density of states

Cited by 31 publications

References 5 publications

Cubic boron nitride: Experimental and theoretical energy-loss near-edge structure

Cubic boron nitride: Experimental and theoretical energy-loss near-edge structure

Phonons in models for icosahedral quasicrystals : low frequency behaviour and inelastic scattering properties

Correctly Weighting Tetrahedron Method for k‐Space Integration of F.C.C. Structures

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