Mean Square Relative Displacement Research Articles

Investigating zero-point vibrations of solid hydrogen via statistical moment method

Zero-point vibrations of solid hydrogen are investigated by analyzing the molecular mean-squared displacement (MSD) and mean-squared relative displacement functions within the statistical moment method approach in statistical mechanics. Numerical computations of these thermodynamic properties were conducted for solid hydrogen from 0 K to its phase transition temperature using the Wigner-Kirkwood mean-field potential derived from the Buckingham exp-6 potential. We have shown that the quantum-mechanical zero-point vibrations play an important role at low temperature. And these thermodynamic quantities increase with temperature, suggesting that both thermal and quantum effects play a significant role near the liquid-solid phase transition. The favorable consistency between our findings and the recent experimental inelastic neutron scattering measurements of MSD attests to the potential of SMM as a novel approach for determining the atomic vibrations of solid hydrogen. This approach allows us to study these effects including the anharmonicity of lattice vibrations.

Investigation of Debye temperature and temperature-dependent EXAFS cumulants of Zn, Zr, α-Ti, Ru and Hf metals

In this work, the anharmonic Einstein model is developed to determine the Debye temperature and investigate the temperature effects on the extended x-ray absorption fine structure (EXAFS) cumulants of hexagonal close-packed (hcp) metals. We have derived the analytical expressions of the anharmonic effective potential, the effective force constant, the Debye temperature and the first four EXAFS cumulants as a function of axial ratio e = c/a. Numerical calculations have been conducted for hcp Zn, Zr, α-Ti, Ru and Hf metals up to temperature 800 K. Our findings indicate that the anharmonicity of thermal lattice vibrations significantly influences the EXAFS cumulants, particularly at high temperatures. Ru atoms have the strongest coupling force causing a phenomenon that Ru lattice shows a smaller thermal disorder, and Zn has a greater thermal disorder. Additionally, we highlight the significant contributions of thermal disorder to the mean-square relative displacement at high temperatures due to thermal lattice vibrations. Moreover, our Debye temperatures derived from the developed model align reasonably well with those reported in previous studies.

Rigid covalent bond of α-sulfur investigated via temperature-dependent EXAFS

This study performs extended x-ray absorption fine structure (EXAFS) measurements for the S-K edge in the temperature range of 10 and 300 K in the transmission mode using a photodiode to detect the transmitted x-rays. It provides the first report of temperature variations in the structural parameters of α-S. As the temperature increases from 10 to 300 K in the Fourier transform of kχ(k) the first peak corresponding to the covalent bond of the eight-membered ring becomes slightly low anomalously despite thermal disturbances. However, as in normal materials, the second peak at 300 K decreases to approximately half of that at 10 K, which contains several intra- and inter-ring correlations. All structural parameters of the covalent bond obtained by nonlinear least squares fitting exhibit missing temperature variations. A value of zero for the asymmetric parameter in the EXAFS (C 3) implies that the potential of the covalent bond is symmetric, and the constant value of the mean square relative displacement (MSRD) with temperature implies that the potential is extremely high. The Einstein model fitting for the temperature variation in the MSRD yields an Einstein temperature of 942 K and force constant (K) of 405 N m−1. The value of K is the largest among those of chalcogen elements.

Temperature-dependent local structure and lattice dynamics of 1T-TiSe[formula omitted] and 1T-VSe[formula omitted] probed by X-ray absorption spectroscopy

The local atomic structure and lattice dynamics of two isostructural layered transition metal dichalcogenides (TMDs), 1T-TiSe2 and 1T-VSe2, were studied using temperature-dependent X-ray absorption spectroscopy at the Ti, V, and Se K-edges. Analysis of the extended X-ray absorption fine structure (EXAFS) spectra, employing reverse Monte Carlo (RMC) simulations, enabled tracking of the temperature evolution of the local environment in the range of 10–300 K. The atomic coordinates derived from the final atomic configurations obtained using the RMC method were used to calculate the partial radial distribution functions (RDFs) and the mean-square relative displacement (MSRD) factors for the first ten coordination shells around the absorbing atoms. Characteristic Einstein frequencies and effective force constants were determined for TiSe, TiTi, VSe, VV, and SeSe atom pairs from the temperature dependencies of MSRDs. The obtained results reveal differences in the temperature evolution of lattice dynamics and the strengths of intralayer and interlayer interactions in TiSe2 and VSe2.

High-pressure high-temperature EXAFS and Debye–Waller factor of platinum

The temperature and pressure effects on the mean-square relative displacement (MSRD) corresponding to the extended X-ray absorption fine structure (EXAFS) Debye–Waller factor of platinum have been studied based on the statistical moment method in quantum statistical mechanics. We implement numerical calculations for platinum up to pressure of 400 GPa. Examining the temperature effects on the EXAFS Debye–Waller factor at ambient pressure we show that theoretical MSRD curve is in good agreement with the previous measurement and calculations up to nearly 800 K. When pressure increases, our pressure-dependent MSRD curve follows very well with the prediction based on the numerical integration along the Hugoniot. Using the theoretical EXAFS Debye–Waller factor, we obtain the Hugoniot temperatures which are highly consistent with recent experimental results. This research advances the correlated Einstein model on the calculation of MSRDs of materials at high temperature and high pressure, specifically, it includes the zero-point vibrations at low temperature and contains the anharmonicity contributions caused by thermal lattice vibrations at high temperature.

Anisotropic Local Structure of SrFe2-xNixAs2 (x = 0.00, 0.16, and 0.23) Superconductor Probed by Polarized X-ray Absorption Fine Structure Measurements.

We have investigated the effect of the Ni substitution on the local structure and the valence electronic states of the SrFe2-xNixAs2 (x = 0.00, 0.16, and 0.23) superconductor with a multi-edge extended X-ray absorption fine structure (EXAFS) and X-ray absorption near edge structure (XANES) spectroscopy. The As K-edge and Fe K-edge EXAFS measurements in the two polarizations (E‖ab and E‖c) show a clear change in the local structure with Ni concentration. The near-neighbor bondlengths and the related mean-square relative displacements (MSRDs) decrease as the Ni content increases. The polarized XANES spectra at the As, Fe and Ni K edges reveal a systematic change in the anisotropy of the valence electronic structure. The results suggest that the quasi 2D electronic structure of this system tends to become more isotropic as the Ni content increases. The local structure and the valence electronic states are discussed in the frame of the evolving electronic transport of the SrFe2-xNixAs2 system.

High-accuracy transmission and fluorescence XAFS of zinc at 10 K, 50 K, 100 K and 150 K using the hybrid technique.

The most accurate measurements of the mass attenuation coefficient for metals at low temperature for the zinc K-edge from 9.5 keV to 11.5 keV at temperatures of 10 K, 50 K, 100 K and 150 K using the hybrid technique are reported. This is the first time transition metal X-ray absorption fine structure (XAFS) has been studied using the hybrid technique and at low temperatures. This is also the first hybrid-like experiment at the Australian Synchrotron. The measured transmission and fluorescence XAFS spectra are compared and benchmarked against each other with detailed systematic analyses. A recent method for modelling self-absorption in fluorescence has been adapted and applied to a solid sample. The XAFS spectra are analysed using eFEFFIT to provide a robust measurement of the evolution of nanostructure, including such properties as net thermal expansion and mean-square relative displacement. This work investigates crystal dynamics, nanostructural evolution and the results of using the Debye and Einstein models to determine atomic positions. Accuracies achieved, when compared with the literature, exceed those achieved by both relative and differential XAFS, and represent a state-of-the-art for future structural investigations. Bond length uncertainties are of the order of 20-40 fm.

Performance of Supplemental Inertial Devices for Base-Isolated Structures

The seismic response of base-isolated structures with supplemental inertial devices subjected to stationary and real earthquake excitation is presented. Three types of devices, namely inertial mass damper (IMD), tuned mass damper-inerter (TMDI), and clutching inerter damper (CID), are considered. The seismic response of the base-isolated structure with and without inertial devices is compared to assess their effectiveness. Under stationary white-noise excitation, the optimum parameters of these devices were obtained. The criterion selected for optimality is the minimization of the mean-square relative displacement and absolute acceleration of the isolated structure. An equivalent linearization method was used for base-isolated structures with CID under stochastic excitation. It was observed that the IMD is not very effective in controlling the response of base-isolated structures. Optimally designed TMDI, on the other hand, was found to be effective in controlling the displacement and acceleration response of the isolated structure, with the effectiveness increasing as the inertance mass ratio increased. The CID involved in the base-isolated structure reduces the structural natural frequency and increases structural damping, thereby reducing isolator displacement and structural acceleration. The high-frequency components were present in the absolute acceleration of base-isolated structure with inertial devices (more pre-dominating for IMD and CID), which may have detrimental effects on installed high-frequency sensitive equipment.

Effects of Sn-ion irradiation on local structure and flux pinning properties of MgB2 thin films

We studied the effects of tin (Sn) ion irradiation on the local structure and flux pinning properties of 412-nm-thick MgB2 thin films. Ions with 2 MeV incident energy were irradiated onto MgB2 thin films at room temperature and various dose levels from 2 × 1012 to 7 × 1013 atoms/cm2. X-ray diffraction and extended X-ray absorption fine-structure results confirmed extended average bond lengths and increased mean-square relative displacement that correlated with crystalline disorder serving as artificial pinning centers induced by ion irradiation. While the superconducting transition temperature (Tc) exhibited a decreasing trend, the magnetization Jc (H) of the irradiated films measured at both 5 K and 20 K were remarkably enhanced compared to that of pristine films at high applied magnetic fields. The decreases in exponent β from 1.1 and 1.13 to 0.69 and 0.62 after irradiation at 5 K and 20 K, respectively, as the dose increased to 5 × 1013 atoms/cm2 indicates a shift in the pinning mechanism from weak collective pinning to strong plastic pinning according to collective pinning theory. In addition, the scaling behavior of the flux pinning force density (Fp) in the irradiated MgB2 films showed a crossover from surface pinning to normal point pinning. These results suggest that intermediate-energy irradiation by heavy ions such as Sn generates effective pinning sources for improving Jc(H) in MgB2 superconductors.

Coupling between γ-irradiation and synchrotron-radiation-based XAFS techniques for studying Mn-doped ZnO nanoparticles.

γ-Irradiation and synchrotron-radiation-based X-ray absorption fine-structure (XAFS) spectroscopy have been used to induce structure disorder through the interaction of γ-rays (200 kGy) with fabricated Mn-doped ZnO nanoparticles (NPs) and then to examine thoroughly the resultant structural change. The extracted electronic/fine XAFS structural parameters reflect a compositional and γ-irradiation co-dependence. The average crystal structure of samples prepared by the sol-gel method was investigated by X-ray diffraction (XRD). A detailed structural XRD data analysis was carried out by applying a Rietveld refinement using the MAUD program. XAFS spectra were collected at the Zn K-edge (9659 eV) in transmission mode and at the Mn K-edge (6539 eV) in fluorescence mode. Direct evidence of the solubility of Mn ions in the ZnO structure was demonstrated by fitting the extended-XAFS (EXAFS) signal. Near-edge XAFS (XANES) analysis provided the oxidation states of Zn and Mn ions through fingerprint XANES spectra of the sample along with those of standard compounds. Linear combination fitting showed that the most fit chemical forms of Zn and Mn in the samples are ZnO and MnO, respectively. The oxidation states of both Zn and Mn XAFS absorbers were confirmed from pre-edge fitting. The results of the magnetic measurements were explained in light of the average and electronic/local structural information obtained from XRD, XANES and EXAFS techniques. The magnetic properties of the samples translate into an induced change in the average crystal and electronic/local structures upon Mn concentration change and γ-irradiation. XRD confirmed the successful preparation of hexagonal Mn-doped ZnO NPs with a crystallite size in the range 33-41 nm. Both XRD and EXAFS analysis detected a minor amount of Mn3O4 as a secondary phase. XANES and EXAFS provided information exploring the outstanding potential of the utilized protocol for detecting precisely the presence of the secondary phase of Mn3O4, which changes with Mn content (x). Mean-square relative displacement (σ2) values extracted from the EXAFS fitting were found to grow for Zn-Zn/Mn paths demonstrating the substitution of Mn/Zn into Zn crystal sites. The EXAFS analysis explains the reasons behind the enhancement in the magnetic properties and shows that the Mn doping content at x = 0.05 produces the most local atomic disorder in ZnO NPs. There is a strong harmony among the XRD, XANES, EXAFS and magnetization behavior of the Mn-doped ZnO NPs. Maximum magnetization was acquired at an Mn content of 0.05. γ-Ray-irradiated Zn1-xMnxO NPs are recommended as optimized candidates for showing the diversity of the applications.

The Local Structure and Metal-Insulator Transition in a Ba3Nb5-xTixO15 System.

The local structure of the filled tetragonal tungsten bronze (TTB) niobate BaNbTiO (x = 0, 0.1, 0.7, 1.0), showing a metal-insulator transition with Ti substitution, has been studied by Nb K-edge extended X-ray absorption fine structure (EXAFS) measurements as a function of temperature. The Ti substitution has been found to have a substantial effect on the local structure, that remains largely temperature independent in the studied temperature range of 80–400 K. The Nb-O bonds distribution shows an increased octahedral distortion induced by Ti substitution, while Nb-Ba distances are marginally affected. The Nb-O bonds are stiffer in the Ti substituted samples, which is revealed by the temperature dependent mean square relative displacements (MSRDs). Furthermore, there is an overall increase in the configurational disorder while the system with Nb 4d electrons turns insulating. The results underline a clear relationship between the local structure and the electronic transport properties suggesting that the metal-insulator transition and possible thermoelectric properties of TTB structured niobates can be tuned by disorder.

Study of High-Temperature Behaviour of ZnO by Ab Initio Molecular Dynamics Simulations and X-ray Absorption Spectroscopy.

Wurtzite-type zinc oxide (w-ZnO) is a widely used material with a pronounced structural anisotropy along the c axis, which affects its lattice dynamics and represents a difficulty for its accurate description using classical models of interatomic interactions. In this study, ab initio molecular dynamics (AIMD) was employed to simulate a bulk w-ZnO phase in the NpT ensemble in the high-temperature range from 300 K to 1200 K. The results of the simulations were validated by comparison with the experimental Zn K-edge extended X-ray absorption fine structure (EXAFS) spectra and known diffraction data. AIMD NpT simulations reproduced well the thermal expansion of the lattice, and the pronounced anharmonicity of Zn–O bonding was observed above 600 K. The values of mean-square relative displacements and mean-square displacements for Zn–O and Zn–Zn atom pairs were obtained as a function of interatomic distance and temperature. They were used to calculate the characteristic Einstein temperatures. The temperature dependences of the O–Zn–O and Zn–O–Zn bond angle distributions were also determined.

Determination of linear bond Grüneisen parameter of GaAs using Extended X-ray Absorption Fine Structure (EXAFS)

The bond Grüneisen parameter of gallium arsenide’s first shell was directly evaluated using temperature-dependent Extended X-ray Absorption Fine Structure (EXAFS) data. A quasi-harmonic approach based on the anharmonic contribution to parallel Mean Square Relative Displacement (MSRD) has led to a positive and weakly temperature-dependent linear bond Grüneisen parameter (GP) of GaAs in the entire region (14–300 K). For all temperatures, we report linear bond GPs greater than those retrieved with EXAFS using an anharmonic Einstein model. The comparison with volumic Grüneisen parameters given by diffraction or dilatometric techniques shows a significant difference which could be attributed to the different definitions used to connect frequency and bond length (or lattice parameter). These results are an evidence of the inadequacy of the quasi-harmonic model to deal with local properties using EXAFS.

Temperature dependence of the correlation function in EXAFS spectra: Application to Cu-Ag alloys

Correlation ratios between the mean square displacement (MSD), mean square relative displacement (MSRD), and correlated displacement function were studied in extended X-ray absorption fine structure spectra (EXAFS). The expressions of MSD, MSRD, and correlation function were determined using Debye models. Hardy problems due to many-particles effects were considered and replaced by a calculation based on the effective anharmonic potential, including the interaction of absorbing and scattering atoms with their nearest neighbours atoms. Based on the Debye-Waller factor, the difference between MSRD and MRD was analyzed, and their ratios have calculated. The methods were applied to fcc crystals and their alloys. Numerical results for Cu, Ag crystals and CuAg50 alloys agreed with experimental values and other studies.

The role of Ga and Bi doping on the local structure of transparent zinc oxide thin films

Transparent undoped ZnO and additionally doped with Ga and Bi thin films were produced by magnetron sputtering. The thin films were comprehensively characterized by X-ray absorption, X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), transmission and scanning transmission electron (TEM, STEM) microscopy and Raman spectroscopy. All undoped and doped films crystallise in a ZnO phase with the hexagonal wurtzite crystal structure. The local structure of the thin films was investigated by temperature-dependent X-ray absorption spectroscopy at the Zn and Ga K-edges, as well as at the Bi L3-edge. It was found that the doping of Ga3+ and Bi3+ ions in the ZnO wurtzite structure produces distinct effects on the thin film microstructure. The substitution of Zn2+ ions by smaller Ga3+ ions introduces a static disorder to the thin film structure, which is evidenced by an increase in the mean-square relative displacements σ2(Zn‒O) and σ2(Zn‒Zn). At the same time, large Bi3+ ions do not substitute zinc ions, but are likely located in the disordered environment at the ZnO grain boundaries. This conclusion was directly supported by energy-dispersive X-ray spectroscopy combined with TEM and STEM observations as well as by resonant and non-resonant μ-Raman experiments at room temperature, where the ZnO and ZnO:Bi spectra are similar, suggesting a lack of structural disorder in the wurtzite cell. On the other hand, the Raman disorder-activated phonon is pronounced for Ga-doping of the ZnO lattice, confirming the compositional disorder. Both XRD and XPS ruled out Ga2O3 phase in Ga-doped ZnO; conversely, Bi2O3 and a small amount of Bi‒metal phases are clearly discerned by XPS experiments, further suggesting that Bi is not incorporated in the ZnO wurtzite cell, but segregated to grain boundaries.

Theoretical investigation of thermal disorder in CuCo alloys

In this work, we investigate thermal disorder in intermetallic CuCo alloys by extending the anharmonic correlated Einstein model in extended X-ray absorption fine structure (EXAFS) theory. The expressions of bond-stretching force constants, Einstein frequency and temperature, the atomic mean-square relative displacement characterizing the EXAFS Debye–Waller factor have been derived in terms of Morse potential parameters. We perform numerical calculations for CuCo alloys up to temperature 800 K to study the temperature effects on these thermodynamic quantities. Our research shows that Co–Co bonds are stiffer than Cu–Cu bonds. This leads to the atomic mean-square relative displacement curve of CuCo alloys is lower than the one of Cu metal, but higher than the one of bulk Co. The increasing of Co concentration in CuCo alloys will make the increasing of thermal disorder in the alloy system. Moreover, the dynamic disorder caused by thermal lattice vibrations gives significant contribution to the EXAFS Debye–Waller factor at high temperature.

Application of the Debye model to study anharmonic correlation effects for the CuAgX (X = 72; 50) intermetallic alloy

Based on the Debye - Waller factor in extended x-ray absorption fine structure spectra, the correlated displacement function, mean square displacement (MSD) and mean square relative displacement (MSRD) were determined. Analytical expressions of MSD and MSRD were considered using Debye models. Challenging problems due to many-particles effects were replaced by a calculation based on the anharmonic effective potential, including the interaction of absorbing and scattering atoms with their nearest neighbours atoms. The difference between MSRD and MRD was analyzed. The methods were applied to face-centred-cubic crystals and their alloys, and have discovered irregularities in the structure of CuAg (at a 50:50 rate) alloy at low temperatures. Numerical results for copper (Cu) crystal and copper–silver alloys (CuAgX (X = 72; 50)) agreed with experimental values and calculations conducted in other studies.

Pressure effects on the EXAFS Debye-Waller factor of iron.

The pressure effects on atomic mean-square relative displacement characterizing the extended X-ray absorption fine structure (EXAFS) Debye-Waller factor of iron metal have been investigated based on the Debye model. The analytical expressions of the Debye frequency and EXAFS Debye-Waller factor have been derived as functions of crystal volume compressibility. Based on the well established equation-of-state including the contributions of the anharmonic and electronic thermal pressures, numerical calculations have been performed for iron up to a pressure of 220 GPa and compared with experimental data when possible. These results show that the Debye frequency increases rapidly with compression, and beyond 150 GPa it behaves as a linear function of pressure. Meanwhile the mean-square relative displacement curve drops robustly with pressure, especially at pressures smaller than 100 GPa. This phenomenon causes the enhancement of EXAFS signals at high pressure. Reversely, the increasing of temperature will reduce the amplitude of EXAFS spectra.

Temperature dependence of EXAFS spectra of BCC crystals analyzed based on classical anharmonic correlated Einstein model

In this work, the temperature dependence of extended X-ray absorption fine structure (EXAFS) of the body-centered cubic crystals was investigated based on the anharmonic correlated Einstein model using the classical statistical theory. The oscillation of the anharmonic EXAFS spectra presented in terms of the cumulant expansion up to the fourth order. Here, the thermodynamic parameters of a system are derived from an anharmonic effective potential that has taken into account the influence of all nearest neighbors of absorbing and backscattering atoms. Analytical expressions of the first four EXAFS cumulants are obtained in simple forms of temperature or parallel mean-square relative displacement. The numerical results for crystalline molybdenum in the temperature range from 0 to 900 K are found to be in good agreement with those obtained using the other theoretical methods and experiments at various temperatures. The analytical results for the contributions of the cumulants to the amplitude reduction and phase shift of the EXAFS oscillation discover the role and meaning of high-order cumulants in analyzing the temperature dependence of the EXAFS spectra.

BaZrO3 stability under pressure: The role of nonlocal exchange and correlation

The ground-stale structure of BaZrO3 is experimentally known to be cubic down to absolute zero. However, there exist several measured properties and experimental characterizations that earlier computational works have failed to accurately describe and explain within this cubic symmetry. Among these properties and observations are the dielectric constant and the parallel mean-squared relative displacement value that tracks the fluctuations in distance for Ba-O atom pairs. Previous density-functional theory (DFT) studies have resolved the issue by assuming that BaZrO(3 )undergoes a phase transition from cubic to tetragonal I4/mcm symmetry, possibly while forming a glasslike state that reflects cubic symmetry on average. In this paper, we show that the set of experimental results can indeed be satisfactorily explained by DFT entirely within the cubic symmetry. We find that past theory limitations arose from the choice of exchange-correlation-functional approximations and that the inclusion of Fock exchange in hybrids significantly improves the DFT performance. We also find that the inclusion of nonlocal correlation effects is beneficial. We conclude by making a prediction for the phase-transition pressure for the transition from cubic to tetragonal symmetry at zero kelvin.