Mean Square Relative Displacement Research Articles

Understanding the phase-change mechanism of rewritable optical media.

Present-day multimedia strongly rely on rewritable phase-change optical memories. We demonstrate that, different from the current consensus, Ge(2)Sb(2)Te(5), the material of choice in DVD-RAM, does not possess the rocksalt structure but more likely consists of well-defined rigid building blocks that are randomly oriented in space consistent with cubic symmetry. Laser-induced amorphization results in drastic shortening of covalent bonds and a decrease in the mean-square relative displacement, demonstrating a substantial increase in the degree of short-range ordering, in sharp contrast to the amorphization of typical covalently bonded solids. This novel order-disorder transition is due to an umbrella-flip of Ge atoms from an octahedral position into a tetrahedral position without rupture of strong covalent bonds. It is this unique two-state nature of the transformation that ensures fast DVD performance and repeatable switching over ten million cycles.

Different temperature dependent local Cu–O displacements in the underdoped and overdoped regimes of cuprate superconductors

We have studied local structure of the La 2 − x Sr x CuO 4 system, in the underdoped and overdoped regimes, by polarized Cu K-edge extended X-ray absorption fine structure (EXAFS) measurements. The mean square relative displacements (MSRD), determined by the correlated Debye–Waller factors of the Cu–O bonds, have been measured as a function of temperature. We find that, while the Cu–O MSRD in the underdoped regime shows anomalous temperature dependence, the overdoped regime does not reveal such an anomaly. The results are consistent with decreasing charge heterogeneities in the overdoped regime, revealing importance of the local Cu–O displacements and the electron–lattice interaction in the heterogeneous nature of the cuprate superconductors.

Impact of long-range interactions on the disordered vortex lattice

The interaction between the vortex lines in a type-II superconductor is mediated by currents. In the absence of transverse screening this interaction is long-ranged, stiffening up the vortex lattice as expressed by the dispersive elastic moduli. The effect of disorder is strongly reduced, resulting in a mean-squared displacement correlator <u^2(R,L)> = <[u(R,L)-u(0,0)]^2> characterized by a mere logarithmic growth with distance. Finite screening cuts the interaction on the scale of the London penetration depth \lambda and limits the above behavior to distances R<\lambda. Using a functional renormalization group (RG) approach, we derive the flow equation for the disorder correlation function and calculate the disorder-averaged mean-squared relative displacement <u^2(R)> \propto ln^{2\sigma} (R/a_0). The logarithmic growth (2\sigma=1) in the perturbative regime at small distances [A.I. Larkin and Yu.N. Ovchinnikov, J. Low Temp. Phys. 34, 409 (1979)] crosses over to a sub-logarithmic growth with 2\sigma=0.348 at large distances.

Lattice dynamics and correlated atomic motion from the atomic pair distribution function

The mean-square relative displacements (MSRD) of atomic pair motions in crystals are studied as a function of pair distance and temperature using the atomic pair distribution function (PDF). The effects of the lattice vibrations on the PDF peak widths are modelled using both a multi-parameter Born von-Karman (BvK) force model and a single-parameter Debye model. These results are compared to experimentally determined PDFs. We find that the near-neighbor atomic motions are strongly correlated, and that the extent of this correlation depends both on the interatomic interactions and crystal structure. These results suggest that proper account of the lattice vibrational effects on the PDF peak width is important in extracting information on static disorder in a disordered system such as an alloy. Good agreement is obtained between the BvK model calculations of PDF peak widths and the experimentally determined peak widths. The Debye model successfully explains the average, though not detailed, natures of the MSRD of atomic pair motion with just one parameter. Also the temperature dependence of the Debye model largely agrees with the BvK model predictions. Therefore, the Debye model provides a simple description of the effects of lattice vibrations on the PDF peak widths.

Distance dependence of mean-square relative displacements in EXAFS

We have investigated the sensitivity of extended x-ray-absorption fine structure (EXAFS) to the local atomic dynamics beyond the first shell in several elements (Ge, Cu, Ni) and binary compounds (ZnS and GaSb) at low temperature (12 K and 80 K). Debye-Waller factors were extracted up to the tenth shell in some cases allowing for a comprehensive experimental investigation of the distance dependence of the mean-square relative displacement. We demonstrate that the observed distance dependencies cannot be satisfactorily described by commonly used theoretical models. The origins of these discrepancies and the importance of long-range EXAFS information are discussed.

Study of latticedynamics via extended x-ray absorption fine structure

EXAFS (extended x-ray absorption fine structure), besides being apowerful structural probe, can also give original information onlocal dynamics in solids. EXAFS is peculiarly sensitive to thecorrelation of vibrational motion, both parallel and perpendicularto the bond direction, and to anharmonicity. This paper contains anintroduction to the effects of thermal disorder on EXAFS of crystalsand to the data analysis based on the cumulant expansion. Cumulantsare easily connected to average local vibrational properties.Recently obtained experimental results concerning the mean squarerelative displacement and the thermal expansion in crystals confirmthe potentialities of EXAFS as a dynamical probe.

Ti off-center displacements inBa1−xSrxTiO3studied by EXAFS

Local structure of ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{TiO}}_{3}$ with $x=0--0.75$ has been studied using x-ray-absorption fine-structure spectra, measured at the Ba K edge at room temperature. The dependence of the mean-square relative displacements and the third cumulant of Ba-O and Ba-Ti distribution functions on the Sr concentration have been analyzed. The results show that Ba off-center displacement vanishes abruptly at $x=0.3,$ which is the boundary point between tetragonal and cubic phases, whereas Ti off-center displacement decreases gradually with Sr concentration and approaches zero at about $x=0.7.$ The change of macroscopic symmetry does not cause any significant change of Ti displacement. The results indicate that Ti atoms are disordered in a wide range of Sr concentration.

Local structure and mean-square relative displacement in SiO2and GeO2polymorphs

Extended X-ray absorption fine structure (EXAFS) spectra near the Si and Ge K-edge for SiO_2 and GeO_2 polymorphs were measured in transmission mode with synchrotron radiation at the Photon Factory, Tsukuba. The local structures and mean-square relative displacements were determined in \alpha-tridymite, \alpha-quartz and stishovite. In stishovite, Si is octahedrally coordinated and the four coplanar Si—O bonds [1.755 (8) A] are shorter than the other two axial bonds [1.813 (15) A]. The high-temperature phase tridymite [1.597 (3) A] has a smaller local bond distance than \alpha-quartz [1.618 (5) A]. The temperature variation of the local structural parameters for quartz-type GeO_2 (q-GeO_2) and rutile-type GeO_2 (r-GeO_2) have been determined in the temperature range 7–1000 K. The harmonic effective interatomic potential V(u)=\alpha{u}^2/2 was evaluated from the contribution to the thermal vibration, where u is the deviation of the bond distance from the location of the potential minimum. The potential coefficient \alpha for the Ge—O bond of the tetrahedron in q-GeO_2 is 24.6 eV A−2. The potential coefficients \alpha for the four coplanar Ge—O bonds and the two axial bonds of the octahedron in r-GeO_2 are 12.9 and 14.9 eV A−2, respectively. The potential coefficient \alpha for the second-nearest Ge—Ge distance in q-GeO_2 is 9.57 eV A−2. The potential coefficients \alpha for the second- and third-nearest Ge—Ge distances in r-GeO_2 are 11.6 and 7.18 eV A−2, respectively. The effective interatomic potential is largely influenced by the local structure, particularly by the coordination numbers. The phonon dispersion relations for q-GeO_2 and r-GeO_2 were estimated along [100] by calculating the dynamical matrix using the potential coefficients \alpha for the Ge—O and Ge—Ge motions. The quartz-type structure has a more complex structure with a wide gap between 103 and 141 meV and a highest energy of 149 meV, whereas the rutile-type structure has a continuous distribution and a highest energy of 126 meV.

XANES and EXAFS at Mo K-edge in (AgI)1−x(Ag2MoO4)x glasses and crystals

(AgI)1−x(Ag2MoO4)x glasses and crystals have been studied by X-ray absorption spectroscopy at the Mo K-edge. All the measured samples contain isolated [MoO4] tetrahedra with R(Mo–O)=1.785±0.008 Å and mean square relative displacement (MSRD) σ2=0.0043±0.0013 Å2, which are unchanged upon insertion of AgI. The glasses have a quite similar environment around molybdenum, which resembles that of the crystal (AgI)x(Ag2MoO4)x with x=0.33. The presence of AgI modifies the local environment around molybdenum already in the second coordination shell.

XAFS study on RbC60.

The Rb K-edge XAFS spectra for the stable phase of RbC60 which is a quasi one-dimensional polymer were measured in the temperature range from 14.6 to 210 K in order to clarify the origin of the metal-insulator transition around 50 K. The distances and mean-square relative displacements between the Rb atom and the neighboring C atoms determined by XAFS exhibited no change around 50 K, implying that the metalinsulator transition originates from the SDW instability.

On the Dynamical Propeties of a Strongly Anharmonic Face-Centered Cubic Crystal

We study the interatomic correlations and mean square relative displacements (MSRD) in anharmonic crystals on the basis of the correlative method of unsymmetrized self-consistent field (CUSF). Here we present general formulae for crystals with the anharmonicity, including the strong one, up to the fourth anharmonic terms and perform calculations of the quadratic correlation moments (QCM) in a crystal with face centered cubic lattice, namely in solid Ar. The second order of CUSF allows one to investigate correlations in this lattice between the nearest, second, third and fourth neighbors. The anharmonicity was demonstrated to have strong effect on the interatomic correlations at temperatures above 0.4 of the melting temperature causing a drastic rise near the spinodal point. The dependence of QCM on the distance between atoms and on the crystallographic direction is discussed.

Electron-beam induced amorphization of stishovite: Silicon-coordination change observed using Si K -edge extended electron energy-loss fine structure

The analysis of the extended energy-loss fine structure (EXELFS) of the Si K-edge for sixfold-coordinated Si in synthetic stishovite and fourfold-coordinated Si in natural α-quartz is reported by using electron energy-loss spectroscopy (EELS) in combination with transmission electron microscopy (TEM). The stishovite Si K-edge EXELFS spectra were measured as a time-dependent series to document irradiation-induced amorphization. The amorphization was also investigated through the change in Si K- and O K-edge energy-loss near edge structure (ELNES). For α-quartz, in contrast to stishovite, electron irradiation-induced vitrification, verified by selected area electron diffraction (SAED), produced no detectable changes of the EXELFS. The Si K-edge EXELFS were analysed with the classical extended X-ray absorption fine structure (EXAFS) treatment and compared to ab initio curve-waved multiple-scattering (MS) calculations of EXAFS spectra for stishovite and α-quartz. Highly accurate information on the local atomic environment of the silicon atoms during the irradiation-induced amorphization of stishovite is obtained from the EXELFS structure parameters (Si−O bond distances, coordination numbers and Debye-Waller factors). The mean Si−O bond distance R and mean Si coordination number N changes from R=0.1775 nm and N=6 for stishovite through a disordered intermediate state (R≈0.172 nm and N≈5) to R≈0.167 nm and N≈4.5 for a nearly amorphous state similar to α-quartz (R=0.1609 nm and N=4). During the amorphization process, the Debye-Waller factor (DWF) passes through a maximum value of \(\) as it changes from \(\) for sixfold to \(\) for fourfold coordination of Si. This increase in Debye-Waller factor indicates an increase in mean-square relative displacement (MSRD) between the central silicon atom and its oxygen neighbours that is consistent with the presence of an intermediate structural state with fivefold coordination of Si. The distribution of coordination states can be estimated by modelling the amorphization as a decay process. Using the EXELFS data for amorphization, a new method is developed to derive the relative amounts of Si coordinations in high-pressure minerals with mixed coordination. For the radiation-induced amorphization process of stishovite the formation of a transitory structure with Si largely in fivefold coordination is deduced.

X-ray absorption spectroscopy and molecular dynamics studies of hydration in aqueous solutions

The hydration of ions in aqueous solutions was studied at room temperature by x-ray absorption spectroscopy and molecular dynamics (MD) simulation. The extended x-ray absorption fine structure (EXAFS) above the Zn K-edge was interpreted using the multiple-scattering approach by taking into account only one coordination shell composed of water molecules at R(Zn - O) = with a mean square relative displacement (MSRD) . No evidence of significant contributions from the second hydration shell to the EXAFS signal was found in the solutions. This is explained by the cancellation interference effect between double-scattering and single-scattering EXAFS signals in the second shell due to large thermal/static disorder as predicted by our MD simulation and by known results of diffraction techniques.

Temperature-dependent vibrational properties of NiAl, CoAl, and FeAl β-phase alloys

Temperature-dependent vibrational properties of \ensuremath{\beta}-phase NiAl, CoAl, and FeAl alloys have been studied by the extended x-ray-absorption-edge fine-structure (EXAFS) technique. From the $K$-edge EXAFS of the transition-metal element, the temperature dependence of the mean-squared relative displacements has been obtained, where these relative displacements are between the absorbing atom and the first, second, or third coordination shell. For NiAl, excellent agreement is obtained with calculations we have carried out, which are based on input from neutron-scattering data obtained by others. We find that the changes with temperature of the mean-squared relative displacements of corresponding atomic pairs are similar for NiAl and FeAl, but CoAl is significantly different from the other two alloys in this regard. In particular, the temperature dependence of the second- and third-neighbor Co-Co mean-squared relative displacement in CoAl is significantly less than the temperature dependence of the corresponding Ni-Ni and Fe-Fe mean-squared relative displacements in NiAl and FeAl, respectively.

Size dependence of structural and dynamic properties of CdS‐nanoparticles

AbstractTemperature‐dependent EXAFS (Extended X‐ray Absorption Fine Structure) measurements between 5 and 290 K show that structural and dynamic properties of CdS nanoparticles with 13‐120 Å diameter depend on their particle size and the way of surface stabilization. The mean Cd‐S distance of thiolcapped CdS nanoparticles (13‐40 Å) increases with decreasing particle size with respect to CdS bulk. In contrast, mean interatomic distances in polyphosphate‐stabilized particles (30‐120 Å) are slightly contracted. This demonstrates that the covalently bound thiol ligands induce the nanocluster lattice expansion. From the temperature dependence of the mean‐square relative displacement (MSRD), a slight stiffening of the Cd‐S bond can be observed with decreasing particle size. The static part of the MSRD, reflecting static disorder of the Cd‐S bond, exhibits a maximum at cluster sizes of about 30 Å. For particles larger than 30 Å diameter, the increase of the static disorder follows the change of the surface to volume ratio. This ratio also determines the size dependence of the asymmetry of the interatomic Cd‐S pair potential. Furthermore, in CdS bulk and CdS nanoparticles with the thermodynamically favored wurtzite structure this asymmetry is significantly enlarged in comparison to nanoparticles with zincblende structure.

EXAFS Debye–Waller Factor and Thermal Vibrations of Crystals

The EXAFS Debye-Waller factor depends on the correlation of atomic motion and can yield original information on the vibrational dynamics of crystalline solids. In this paper an introductory treatment of thermal disorder in EXAFS, based on thc cumulant approach, is given. Thc general relation between mean-square relative displacement (MSRD) measured by EXAFS and atomic thermal vibrations in harmonic approximation is explored. Strengths and limitations of the phenomenological Einstein- and Debye-correlated models are discussed. Some of the most significant results so far obtained are reviewed. A relatively simple method for estimating anharmonic corrections to the MSRD is proposed.

Structural changes of the metallic glass Zr65Al7.5Cu27.5 during glass transition and in the undercooled liquid region

The metallic glass Zr65Al7.5Cu27.5 exhibits a wide temperature range in the undercooled liquid region. This offers the possibility of examining the phenomena that occur during glass transition. We investigated this glass by x-ray diffraction and x-ray absorption spectroscopy (XAS) at room temperature and at elevated temperatures below and above the glass transition temperature. The total number of nearest neighbors determined by x-ray diffraction remained unchanged. Using XAS irreversible changes in the short range order (SRO) towards the SRO of crystalline Zr2Cu is observed in the nearest neighbor shell which is consistent with the x-ray diffraction results. The long range order was not affected by these changes. From the temperature dependence of the atomic mean-square relative displacements σ2, Debye temperatures were determined and they compare well with low temperature specific heat measurements. Above Tg the slope of σ2 increases drastically and is attributed to anharmonic effects.

Anisotropic Anharmonic Vibrations of the Surface S–Ni and Cl–Ni Bonds in c(2×2)S and Cl/Ni(100) Systems Studied by Molecular Dynamics

The vibrational anisotropy and anharmonicity of the surface adsorbate-substrate bonds in c(2×2)S and Cl/Ni(100) systems were investigated by means of classical molecular dynamics calculations. The obtained results were compared to those experimentally given by surface extended X-ray absorption fine structure and high-resolution electron energy loss spectroscopies. Good agreement between calculated and experimental results indicates high reliability of the present method. The calculations allow us to distinguish the component of motions parallel to the surface from the normal one. In both systems, the mean-square displacements of the adsorbates were found to be noticeably greater in the normal direction than in the lateral one. On the other hand, it was revealed that the mean-square relative displacement concerning the S–Ni pair is enhanced in the vertical direction, while that of the Cl–Ni one shows less directional dependence. Such a difference can simply be understood from the local surface geometries.

Thermal expansion and anharmonicity of solid Kr studied by extended x-ray-absorption fine structure

Kr K-edge extended x-ray-absorption fine-structure spectra of solid Kr were measured over the temperature range of 24--43 K. The thermal expansion and Debye temperature were obtained by the analysis of the first-, third-, and fourth-nearest-neighbor (NN) Kr-Kr shells. For the third- and fourth-NN shells, the conventional Gaussian-distribution approximation was found to give the proper thermal expansion. On the other hand, for the first-NN shell, the cumulant-expansion analysis including the third-order asymmetry of the distribution function is necessary, although the higher-NN shells are more largely disordered in terms of the mean-square relative displacements. These results were confirmed by the classical Monte Carlo simulations. Effective cancellation of the asymmetric contribution was thus clarified for the higher-NN shells. The quantum-statistical calculations of the first-NN cumulants of Kr clusters were also carried out by varying the cluster size in order to examine the relationship between the pair potential and observed cumulants, and to justify the employed Kr-Kr pair potential.

EXAFS Studies on the Size Dependence of Structural and Dynamic Properties of CdS Nanoparticles

Size-dependent structural and dynamic properties of CdS nanocrystals with 13−120 Å diameter and of molecular crystals consisting of three-dimensional superlattices of these nanoparticles have been determined by extended X-ray absorption fine structure spectroscopy (EXAFS) at the Cd K edge at temperatures between 5 and 290 K. It is shown that these properties are governed by the surface-to-volume ratio and the way of surface stabilization of the nanoparticles. Thiol-capped CdS nanoparticles with diameters from 13 to 40 Å show an expansion of the mean Cd−S distance whereas mean interatomic distances in polyphosphate-stabilized particles with 30−120 Å diameter are slightly contracted with respect to CdS bulk. By measuring the EXAFS spectra between 5 and 290 K, the total mean-square relative displacement could be separated into a static part which is independent of temperature and into a dynamic temperature-dependent part. The temperature-independent mean-square relative displacement (or static disorder) of the Cd−S bonds exhibits a maximum at cluster sizes of about 30 Å separating thermodynamically and kinetically controlled growth regimes. Vibrational amplitudes of the Cd−S bonds are only very slightly damped with decreasing particle size. Careful investigations of the asymmetry of the interatomic Cd−S pair potential indicate the possibility to distinguish between CdS nanoparticles with zinc blende and wurtzite structure in cases where alternative methods such as powder X-ray diffraction or transmission electron microscopy fail.