Thermal Displacements Of Atoms Research Articles

Ab Initio Calculation of the Gilbert Damping Parameter via Linear Response Formalism

A Kubo-Greenwood-like equation for the Gilbert damping parameter α is presented that is based on the linear response formalism. Its implementation on the basis of the fully relativistic Korringa-Kohn-Rostoker (KKR) band structure method together with the Coherent Potential Approximation (CPA) alloy theory allows application to a wide range of situations. This is demonstrated by results obtained for the alloy system bcc Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> as well as for a series of alloys of permalloy with 5 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> transition metals. To account for the thermal displacements of atoms as a scattering mechanism, an alloy-analogy model is introduced. In line with experiment, calculations for Ni correctly describe the rapid change of α when small amounts of Cu are introduced substitutionally.

First-principles calculation of the Gilbert damping parameter via the linear response formalism with application to magnetic transition metals and alloys

A method for the calculations of the Gilbert damping parameter $\ensuremath{\alpha}$ is presented, which, based on the linear response formalism, has been implemented within the fully relativistic Korringa-Kohn-Rostoker band structure method in combination with the coherent potential approximation alloy theory. To account for thermal displacements of atoms as a scattering mechanism, an alloy-analogy model is introduced. This allows the determination of $\ensuremath{\alpha}$ for various types of materials, such as elemental magnetic systems and ordered magnetic compounds at finite temperature, as well as for disordered magnetic alloys at $T=0$ K and above. The effects of spin-orbit coupling, chemical- and temperature-induced structural disorder, are analyzed. Calculations have been performed for the 3$d$ transition metals bcc Fe, hcp Co, and fcc Ni; their binary alloys bcc Fe${}_{1\ensuremath{-}x}$Co${}_{x}$, fcc Ni${}_{1\ensuremath{-}x}$Fe${}_{x}$, fcc Ni${}_{1\ensuremath{-}x}$Co${}_{x}$ and bcc Fe${}_{1\ensuremath{-}x}$V${}_{x}$; and for $5d$ impurities in transition-metal alloys. All results are in satisfying agreement with experiment.

Inter-atomic force constants from correlation effects among thermal displacement of atoms in PbTe

Diffuse neutron scattering measurements have been performed on powder PbTe at 10 and 294 K using high resolution powder diffractometer installed at JRR-3 in Japan Atomic Energy Agency. Oscillatory diffuse scattering intensity is clearly observed at 294 K. The observed diffuse scattering intensities are analysed by including correlation effects among thermal displacements of atoms in the function describing background in refinement analysis. The force constants between the first and second nearest neighbouring atoms in PbTe are obtained from the values of correlation effects and Debye–Waller temperature parameters.

Inter-atomic force constants of Ag2O from diffuse neutron scattering measurement

Diffuse neutron scattering measurements have been performed on powder Ag2O at 8 and 295K with the use of High Resolution Powder Diffractometer installed at JRR-3 in Japan Atomic Energy Agency. Oscillatory diffuse scattering intensities are clearly observed at 8 and 295K. The observed diffuse scattering intensities are explained by including the correlation effects among thermal displacements of atoms. The force constants among neighboring atoms in Ag2O are obtained from the values of correlation effects and Debye–Waller temperature parameters at 295K.

Force Constants of Cu Crystals from Diffuse Neutron Scattering Measurement

Diffuse neutron scattering measurement on Cu crystals was performed at 10 K and 300 K. Oscillatory forms were observed in the diffuse scattering intensities. The observed diffuse scattering intensities are analyzed by including the correlation effects among thermal displacements of atoms in the theory. Using the values of correlation effects among neighboring atoms and the values of Debye-Waller temperature parameter, force constants among first, second and third nearest neighboring atoms have been evaluated. The result of correlation effects in Cu crystals are compared to that of ionic crystal and semiconductor. The relation between correlation effects and the inter-atomic distance is not depending much on the crystal binding types. Received: 12 October 2010; Revised: 22 October 2010; Accepted: 16 December 2010

Ab InitioCalculation of the Gilbert Damping Parameter via the Linear Response Formalism

A Kubo-Greenwood-like equation for the Gilbert damping parameter α is presented that is based on the linear response formalism. Its implementation using the fully relativistic Korringa-Kohn-Rostoker band structure method in combination with coherent potential approximation alloy theory allows it to be applied to a wide range of situations. This is demonstrated with results obtained for the bcc alloy system Fe(1-x)Co(x) as well as for a series of alloys of Permalloy with 5d transition metals. To account for the thermal displacements of atoms as a scattering mechanism, an alloy-analogy model is introduced. The corresponding calculations for Ni correctly describe the rapid change of α when small amounts of substitutional Cu are introduced.

Separate determination of the amplitude of thermal vibrations and static atomic displacements in titanium carbide by neutron diffraction

The amplitude of thermal (dynamic) atomic vibrations and meansquare static atomic displacements in titanium carbide TiCx (x = 0.97, 0.88, 0.70) have been separately determined by measuring neutron diffraction patterns at two temperatures (T1 = 300 K and T2 = 80 K). The static lattice distortions in stoichiometric titanium carbide are experimentally found to be negligible. In the TiCx homogeneity range, the amplitude \(\sqrt {\overline {u_{dyn}^2 } } \) of thermal atomic vibrations significantly increases with a decrease in the carbon concentration. The Debye temperature has been determined for the first time in the TiCx homogeneity range at both room and liquid-nitrogen temperatures.

Ab initio simulation of resonant forbidden reflections in Ge crystals

Forbidden reflections are observed in the case of diffraction of synchrotron radiation with wave-lengths close to the absorption edges in crystals. A new method for calculating the intensity of thermal-motion-induced (TMI) forbidden reflections is proposed in this paper. It includes two stages: simulation of instantaneous thermal atomic displacements using ab initio molecular dynamics and subsequent quantum-mechanical calculations of the resonance scattering amplitude for various configurations. This procedure is used to calculate the temperature dependence of the 600 reflection intensity for Ge. The proposed method for simulating forbidden TMI reflections is suitable for any crystal structures and can explain many results so far obtained using synchrotron.

Thermal and elastic properties of Ge-Sb-Te based phase-change materials

ABSTRACTPhase-change materials undergo a change in bonding mechanism upon crystallization, which leads to pronounced modifications of the optical properties and is accompanied by an increase in average bond lengths as seen by extended x-ray absorption fine structure (EXAFS), neutron and x-ray diffraction. The reversible transition between a crystalline and an amorphous phase and its related property contrast are already employed in non-volatile data storage devices, such as rewritable optical discs and electronic memories. The crystalline phase of the prototypical material GeSb2Te4 is characterized by resonant bonding and pronounced disorder, which help to understand their optical and electrical properties, respectively. A change in bonding, however, should also affect the thermal properties, which will be addressed in this study. Based on EXAFS data analyses it will be shown that the thermal and static atomic displacements are larger in the meta-stable crystalline state. This indicates that the bonds become softer in the crystalline phase. At the same time, the bulk modulus increases upon crystallization. These observations are confirmed by the measured densities of phonon states (DPS), which reveal a vibrational softening of the optical modes upon crystallization. This demonstrates that the change of bonding upon crystallization in phase-change materials also has a profound impact on the lattice dynamics and the resulting thermal properties.

Thermal vibrations and polymorphic β → γ transition in cerium

Method of neutron diffraction was used to determine the temperature dependence of the Debye-Waller factor and the related thermal atomic displacements for two polymorphic modifications of cerium, namely, for β-Ce with a double hexagonal closed-packed (dhcp) structure and for γ-Ce with a face-centered cubic (fcc) structure. It has been shown that the phase transition does not lead to substantial changes in the root-mean-square thermal atomic displacements and that the Debye temperatures of the two modifications are close: 131 K for β-Ce and 127 K for γ-Ce. However, the relative (with respect to the lattice parameters) displacements along the axes change considerably. The transition from the anisotropic hexagonal to the isotropic cubic modification leads, because of a redistribution of thermal atomic displacements along the crystallographic axes, to a decrease in the maximum values of these quantities and to a weakening of their temperature dependence. It has also been shown that a change in the thermal atomic vibrations and in the vibrational contribution to the entropy of the polymorphic transformations is connected with the sign of the volume effect of the transformation (stronger upon a positive effect and weaker, upon a negative one). The reasons for this behavior are discussed.

Estimation of inter-atomic force constants and phonon dispersion using correlation effects among thermal displacement of atoms in Ge

Neutron diffraction measurements have been performed on powder Ge at 6, 150 and 300 K. Oscillatory diffuse scattering intensity is clearly observed at 150 and 300 K. The diffuse scattering theory including correlation effects among thermal displacements of atoms is applied to background function in the Rietveld analysis. The inter-atomic distance and temperature dependence of the values of correlation effects are discussed. The force constants among the first, second and third nearest neighboring atoms in Ge are obtained from the values of correlation effects and Debye–Waller temperature parameters. A phonon dispersion spectrum in Λ [111] direction for Ge crystal has also been calculated at 80 K using inter-atomic force constants and the crystal structure.

Correlation effects among thermal displacements of atoms in KBr

Neutron diffraction measurements have been performed on powder KBr at 7 and 298 K. An oscillatory diffuse scattering intensity is observed at 298 K. The oscillatory scheme of the diffuse scattering intensity is explained by the values of correlation effects which are almost the same as those in other ionic crystals. The value of the correlation effects as suggested by earlier studies using EXAFS measurement cannot explain the observed diffuse scattering intensity. Force constants among first, second and third nearest neighboring atoms are obtained from the correlation effects and used to estimate the phonon dispersion curves by computer simulation.

Resonant diffraction of synchrotron radiation in rubidium dihydrophosphate crystals

Purely resonant Bragg reflections 006, 5\( \bar 5 \)0, and 666 in a rubidium dihydrophosphate (RbH2PO4) crystal at the K edge of rubidium have been experimentally and theoretically investigated. These reflections remain forbidden when the resonant dipole-dipole (E1E1) contribution to the resonant atomic factor is taken into account; they may be due to the dipole-quadrupole (E1E2) transitions as well as to the anisotropy atomic factor, which is caused by thermal atomic displacements (thermally induced contribution) and/or local jumps of hydrogen atoms. A numerical simulation showed that, at room temperature (experimental conditions), the thermally induced contribution to the “forbidden” reflections is dominant.

Diffuse Scattering of γ-PbF2

γ-PbF 2 belongs to cubic structure with disordered arrangements of F atoms and shows high ionic conductivity at high temperature. Neutron diffuse scattering intensity measurement has been performed at 773 K. Strong and oscillatory diffuse scattering intensity has been observed. The diffuse scattering can be explained by the correlation effects among thermal displacements of atoms and the short-range order in disordered arrangements of F atoms.

Correlation effects among thermal displacements of atoms in VSe by diffuse neutron scattering measurement

Neutron diffraction measurements have been performed on powder VSe at 294 K. The diffuse scattering theory including correlation effects among thermal displacements of atoms is applied to background function in the Rietveld analysis. The oscillatory scheme of the diffuse scattering intensity from hexagonal VSe is explained by the correlation effects among far-neighboring Se–Se atoms. The values of the correlation effects depend on the inter-atomic distance and not on the crystal structure. The relation between correlation effects and force constants is discussed.

Properties of bcc metals by tight-binding total energy simulations

Monovacancies of six bcc d-transition metals V, Cr, Nb, Mo, Ta and W have been studied by tight-binding (TB) simulations using the NRL-TB method. This method satisfactorily reproduces the electronic properties, phonon frequencies, thermal expansion coefficients and atomic mean-squared displacements for pure bulk systems. The TB method shows that for group-V metals the atoms in the first neighbor shell of the vacancy relax inward by about 5% and lose charge from d orbitals, while second neighbor shell atoms relax outward by about 1%. For group-VI metals both first and second neighbor shells relax inward and gain d orbital charge, and for Mo and W the relaxation is in fact stronger for the second than the first neighbor shell. These results are not significantly affected by the use of charge self-consistent terms in the TB model. The structural and charge transfer changes are accompanied by new energy bands at selected k-points for group-VI while they cover the whole Brillouin zone (BZ) for the group-V metals. Comparison to first-principles calculations for one example, Nb, shows good agreement for the presence of new energy bands as well as the charge and structural relaxation of the first and second neighbor shells.

Anisotropic phonon density of states: the application of Rietveld and Mössbauer texture analysis in aligned powders

Since it is not always feasible to synthesize single crystals of novel materials, the orientation of layered polycrystals has become an attractive basis for studying the angular dependence of inelastic scattering of X-rays or neutrons. Utilizing Rietveld analysis, the anisotropic properties of layered structures in novel manganites and cuprates have been studied with oriented powders instead of single crystals. The phonon density of states (DOS) and atomic thermal displacement are anisotropic in theA-site-ordered manganites LnBaMn2Oyfor the seriesy= 5 andy= 6 (Ln = Y, La, Sm and Gd). This article establishes the angular dependence of the DOS on texture of arbitrary strength, links the textures observed by X-ray and γ-ray techniques, and solves the problem of disentanglement of the Goldanskii–Karyagin effect and texture in Mössbauer spectra.

Anisotropy of thermal vibrations and polymorphic transformations in lanthanum and uranium

AbstractAverage thermal atomic displacements along different crystallographic axes were measured for polycrystalline samples employing the method of neutron diffraction and defining the anisotropic Debye–Waller factor, obtained by processing the corresponding reflections. In the double hexagonal close‐packed lanthanum modification, the anisotropy of vibrations is insignificant at room temperature, yet it increases markedly with increasing temperature; also, the relative displacement (in relation to the corresponding lattice parameters) in the basal plane considerably exceeds that along the hexagonal axis. In orthorhombic α‐uranium, large anisotropy is observed even at room temperature, which increases with increasing temperature. It is clearly proved that in lanthanum and uranium the polymorphic transition of low‐temperature anisotropic phases into high‐temperature cubic modifications with isotropic thermal vibrations reduces the maximum relative quantity of thermal displacements at the expense of more homogeneous distribution of vibrations along the lattice axes, and thus probably ‘prevents’ the melting of low‐temperature modifications at a lower temperature due to the critical value of these displacements being reached. (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Dynamic collective displacements of atoms in metals and their role in the vacancy mechanism of diffusion

The phenomenon of dynamic collective displacements of atoms in face-centered cubic crystals has been revealed using molecular dynamics method. This phenomenon plays an important role in the vacancy mechanism of diffusion. The vacancy mechanism is provided by the collision of two regions of collective atomic displacements that move a migrating atom and a vacancy toward each other. The collective thermal atomic displacements from crystal lattice sites occur as a result of the nonuniform momentum distribution of atoms according to the Maxwellian distribution. Owing to their statistical nature, the degree of correlation of the atomic displacements depends neither on the temperature nor on the interatomic interaction potential.

Diffuse Neutron Scattering of KBr at Room Temperature and Its Application as Background Function in Rietveld Analysis

Diffuse neutron scattering from powder KBr was measured at room temperature. The oscillatory diffuse scattering is clearly observed. The diffuse scattering theory including correlation effects among thermal displacements of atoms is applied to background function in the Rietveld analysis. The observed scattering data are analyzed by including the correlation effects among thermal displacements of first, second and third nearest neighboring atoms. The inter-atomic distance and temperature dependence of the values of correlation effects is discussed.