Microscopic theory of dielectric screening and lattice dynamics. II. Phonon spectra and effective charges

1974 ◽  
Vol 9 (6) ◽  
pp. 2573-2589 ◽  
Author(s):  
D. L. Price ◽  
S. K. Sinha ◽  
R. P. Gupta
Keyword(s):  
Lattice Dynamics ◽  
Microscopic Theory ◽  
Phonon Spectra ◽  
Dielectric Screening ◽  
Effective Charges

scholarly journals Microscopic theory for coupled atomistic magnetization and lattice dynamics

2017 ◽  
Vol 1 (7) ◽  
Author(s):  
J. Fransson ◽  
D. Thonig ◽  
P. F. Bessarab ◽  
S. Bhattacharjee ◽  
J. Hellsvik ◽  
...  
Keyword(s):  
Lattice Dynamics ◽  
Microscopic Theory

LATTICE DYNAMICS OF THE BINARY APERIODIC CHAINS OF ATOMS I: FRACTAL DIMENSION OF PHONON SPECTRA

1995 ◽  
Vol 09 (12) ◽  
pp. 1429-1451 ◽  
Author(s):  
WŁODZIMIERZ SALEJDA
Keyword(s):  
Fractal Dimension ◽  
Lattice Dynamics ◽  
Nearest Neighbor ◽  
Average Distance ◽  
Local Maximum ◽  
Fractal Dimensions ◽  
Dimension Formula ◽  
Phonon Spectra ◽  
Wide Range ◽  
Silver Mean

The microscopic harmonic model of lattice dynamics of the binary chains of atoms is formulated and studied numerically. The dependence of spring constants of the nearest-neighbor (NN) interactions on the average distance between atoms are taken into account. The covering fractal dimensions [Formula: see text] of the Cantor-set-like phonon spec-tra (PS) of generalized Fibonacci and non-Fibonaccian aperiodic chains containing of 16384≤N≤33461 atoms are determined numerically. The dependence of [Formula: see text] on the strength Q of NN interactions and on R=mH/mL, where mH and mL denotes the mass of heavy and light atoms, respectively, are calculated for a wide range of Q and R. In particular we found: (1) The fractal dimension [Formula: see text] of the PS for the so-called goldenmean, silver-mean, bronze-mean, dodecagonal and Severin chain shows a local maximum at increasing magnitude of Q and R>1; (2) At sufficiently large Q we observe power-like diminishing of [Formula: see text] i.e. [Formula: see text], where α=−0.14±0.02 and α=−0.10±0.02 for the above specified chains and so-called octagonal, copper-mean, nickel-mean, Thue-Morse, Rudin-Shapiro chain, respectively.

LATTICE DYNAMICS OF THE BINARY APERIODIC CHAINS OF ATOMS III: PROPERTIES OF VIBRATIONAL EIGENVECTORS

1995 ◽  
Vol 09 (12) ◽  
pp. 1475-1501 ◽  
Author(s):  
WŁODZIMIERZ SALEJDA
Keyword(s):  
Elastic Energy ◽  
Lattice Dynamics ◽  
Quantitative Agreement ◽  
Model Parameters ◽  
Harmonic Model ◽  
Energy Field ◽  
Qualitative And Quantitative ◽  
Phonon Spectra ◽  
Multifractal Spectra ◽  
Optical Region

We numerically study the localization and multifractal properties of normalized vibrational eigenvectors (NVEV), denoted by U, of the microscopic harmonic model of lattice dynamics in Thue-Morse (TM), generalized Fibonacci, octagonal, dodecagonal, Severin, circle and Rudin-Shapiro (RS) binary chain of atoms. Eigenvalues and NVEV are determined with the help of the Dean and Wu-Zheng algorithm, respectively, with free end boundary conditions for chains containing 103<N<104 atoms. The first FM(L) and second SM(L) moment, and the reduced participation ratios Λ red (L) are derived at 1≤L≤N for varying model parameters. All the chains studied show sinusoidal-like and packet-like extended NVEV with Λred(L)≃1, FM(L)≃N/2 and [Formula: see text] The new extended eigenstates called dimmerized NVEV have been found out in the case of the TM chain. The surface localized NVEV with Λred(L)≪1, FM(L)≃1 or FM(L)≃N and the strong tendency to localization of NVEV in RS chain have been observed. The critical NVEV, which dominate in the optical region of phonon spectra, are objects with a broad multifractal (αmin, αmax) spectra. If magnitudes of model parameters are increased then, first, [Formula: see text] and [Formula: see text] at L≪N and, second, [Formula: see text] and [Formula: see text] at L≃N. It is numerically shown that the multifractal spectra α′—f′ characterizing the curdling of the elastic energy field ε(L) are in excellent qualitative and quantitative agreement with the multifractal spectra of the critical NVEV.

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