scholarly journals Atomic Structure of Decagonal Al-Cu-Rh Quasicrystal–Revisited: New Correction for Phonons

Crystals ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 78 ◽  
Author(s):  
Radoslaw Strzalka ◽  
Ireneusz Buganski ◽  
Pawel Kuczera ◽  
Lucjan Pytlik ◽  
Janusz Wolny
Keyword(s):  
Distribution Function ◽  
Diffraction Data ◽  
Structure Refinement ◽  
Waller Factor ◽  
Correction Function ◽  
Phonon Modes ◽  
Atomic Displacements ◽  
Alternative Description ◽  
Debye Waller Factor ◽  
Gaussian Distribution Function

The standard approach applies the Gaussian distribution function to estimate atomic displacements due to thermal vibrations in periodic and aperiodic systems, which is used in a form of the Debye–Waller factor during the structure refinement. Acoustic phonons provide the largest contribution to the Gaussian correction although the character of other phonon modes remains relatively unclear. In this paper, we provide an alternative description of localized and dispersionless phonons based on an assumption of the harmonic displacement distribution function, which was recently proposed for model quasicrystals, and apply this approach for a decagonal Al-Cu-Rh quasicrystal that was previously studied by Kuczera et al. in 2012. We used the same X-ray diffraction data and the statistical method of structural analysis of the aperiodic systems. The correction function for phonons takes the form of a Bessel function instead of a conventional (Gaussian) Debye–Waller factor. This allowed us to achieve R-factor of 7.2% compared to 7.9% reported in the original paper. A significant improvement of the calculated atomic composition towards experimentally obtained and minor positional changes is also reported compared to the original paper. The results show the usefulness of investigating different corrective terms for diffraction data during a structure refinement.

scholarly journals Pushing the limits of crystallography

2016 ◽  
Vol 49 (6) ◽  
pp. 2106-2115 ◽  
Author(s):  
Janusz Wolny ◽  
Ireneusz Buganski ◽  
Pawel Kuczera ◽  
Radoslaw Strzalka
Keyword(s):  
Statistical Approach ◽  
Structure Refinement ◽  
Waller Factor ◽  
Theoretical Research ◽  
High Quality ◽  
Consistent Theory ◽  
Debye Waller Factor ◽  
Weak Reflection ◽  
Novel Method ◽  
Quasiperiodic Systems

A very serious concern of scientists dealing with crystal structure refinement, including theoretical research, pertains to the characteristic bias in calculatedversusmeasured diffraction intensities, observed particularly in the weak reflection regime. This bias is here attributed to corrective factors for phonons and, even more distinctly, phasons, and credible proof supporting this assumption is given. The lack of a consistent theory of phasons in quasicrystals significantly contributes to this characteristic bias. It is shown that the most commonly used exponential Debye–Waller factor for phasons fails in the case of quasicrystals, and a novel method of calculating the correction factor within a statistical approach is proposed. The results obtained for model quasiperiodic systems show that phasonic perturbations can be successfully described and refinement fits of high quality are achievable. The standard Debye–Waller factor for phonons works equally well for periodic and quasiperiodic crystals, and it is only in the last steps of a refinement that different correction functions need to be applied to improve the fit quality.

Temperature-dependent atomic B factor: an ab initio calculation

2019 ◽  
Vol 75 (4) ◽  
pp. 624-632 ◽  
Author(s):  
Cristiano Malica ◽  
Andrea Dal Corso
Keyword(s):  
Ab Initio ◽  
Harmonic Approximation ◽  
Debye Model ◽  
Waller Factor ◽  
Temperature Dependent ◽  
Atomic Displacements ◽  
Debye Waller Factor ◽  
Diffraction Peaks ◽  
Effects Of Temperature ◽  
Quantum Espresso

The Debye–Waller factor explains the temperature dependence of the intensities of X-ray or neutron diffraction peaks. It is defined in terms of the B matrix whose elements B αβ are mean-square atomic displacements in different directions. These quantities, introduced in several contexts, account for the effects of temperature and quantum fluctuations on the lattice dynamics. This paper presents an implementation of the B factor (8π2 B αβ) in the thermo_pw software, a driver of Quantum ESPRESSO routines that provides several thermodynamic properties of materials. The B factor can be calculated from the ab initio phonon frequencies and displacements or can be estimated, although less accurately, from the elastic constants, using the Debye model. The B factors are computed for a few elemental crystals: silicon, ruthenium, magnesium and cadmium; the harmonic approximation at fixed geometry is compared with the quasi-harmonic approximation where the B factors are calculated accounting for thermal expansion. The results are compared with the available experimental data.

SIGNATURE OF LOCAL STRUCTURE ANOMALY AT Tc IN THE Nb3Ge SUPERCONDUCTOR

2002 ◽  
Vol 16 (11n12) ◽  
pp. 1713-1719 ◽  
Author(s):  
M. FILLIPPI ◽  
N. L. SAINI ◽  
H. OYANAGI ◽  
A. BIANCONI
Keyword(s):  
Local Structure ◽  
Cuprate Superconductors ◽  
Waller Factor ◽  
Superconducting Transition ◽  
Temperature Dependent ◽  
Local Electron ◽  
Atomic Displacements ◽  
Debye Waller Factor ◽  
The One ◽  
X Ray Absorption

We report local structure of Nb3Ge intermetallic superconductor by Ge K-edge extended X-ray absorption fine structure (EXAFS) measurements performed in the temperature range of 6–300 K, with an emphasis to determine the local and instantaneous atomic displacements across the superconducting transition temperature T c . We find that the temperature dependent correlated Debye–Waller factor of the Ge-Nb bonds shows a drop at the T c while cooling the sample, similar to the one observed in the high-T c cuprate superconductors. The results provide a clear indication of an intimacy between the local atomic displacements and the short coherence superconductivity, and suggests that local electron-lattice interaction should be considered to explain the high-T c superconductivity in these materials.

Debye–Waller factor and the Lindemann parameter of some hexagonal close-packed metals

1980 ◽  
Vol 58 (3) ◽  
pp. 384-387 ◽  
Author(s):  
A. Ramanand ◽  
R. Ramji Rao
Keyword(s):  
Distribution Function ◽  
Harmonic Approximation ◽  
Normal Modes ◽  
Waller Factor ◽  
Hexagonal Close Packed ◽  
Debye Waller Factor ◽  
Anisotropic Temperature ◽  
Modes Of Vibration ◽  
The Mean ◽  
Temperature Factors

The Debye–Waller factor has been calculated as a function of temperature for the four hexagonal close-packed (hcp) metals cobalt, ruthenium, erbium, and scandium, using a lattice-dynamical model to evaluate the normal mode frequencies and eigenvectors in the harmonic approximation. The calculation of the anisotropic temperature factors for these metals requires a knowledge of the eigenvectors for the various normal modes of vibration. The frequency distribution function is also used to calculate the mean-square amplitude of displacement of the atoms, in the cubic approximation. The first and second negative moments of the distribution function are used to calculate the low- and high-temperature limits of [Formula: see text], respectively. The value of the Lindemann parameter obtained from the present calculations is consistent with the value quoted by Gschneidner.

The effect of temperature on high-resolution TEM image contrast

1995 ◽  
Vol 53 ◽  
pp. 640-641
Author(s):  
T. Geipel ◽  
W. Mader ◽  
P. Pirouz
Keyword(s):  
Form Factor ◽  
Inelastic Scattering ◽  
Accurate Method ◽  
Waller Factor ◽  
Effect Of Temperature ◽  
Specimen Thickness ◽  
Influence Of Temperature ◽  
Debye Waller Factor ◽  
Influence Of Temperature On ◽  
Atomic Form Factor

Temperature affects both elastic and inelastic scattering of electrons in a crystal. The Debye-Waller factor, B, describes the influence of temperature on the elastic scattering of electrons, whereas the imaginary part of the (complex) atomic form factor, fc = fr + ifi, describes the influence of temperature on the inelastic scattering of electrons (i.e. absorption). In HRTEM simulations, two possible ways to include absorption are: (i) an approximate method in which absorption is described by a phenomenological constant, μ, i.e. fi; - μfr, with the real part of the atomic form factor, fr, obtained from Hartree-Fock calculations, (ii) a more accurate method in which the absorptive components, fi of the atomic form factor are explicitly calculated. In this contribution, the inclusion of both the Debye-Waller factor and absorption on HRTEM images of a (Oll)-oriented GaAs crystal are presented (using the EMS software.Fig. 1 shows the the amplitudes and phases of the dominant 111 beams as a function of the specimen thickness, t, for the cases when μ = 0 (i.e. no absorption, solid line) and μ = 0.1 (with absorption, dashed line).

Anharmonic contributions to the Debye-Waller factor of aluminium

1989 ◽  
Vol 72 (11) ◽  
pp. 1135-1140 ◽  
Author(s):  
R.C. Shukla ◽  
H. Hübschle
Keyword(s):  
Waller Factor ◽  
Debye Waller Factor
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