Debye-Waller Factor Research Articles

Correlated and Uncorrelated Debye-Waller Factors and Correlation Function in Atomic Vibrations Including Many-Body Effects

Correlated and Uncorrelated Debye-Waller Factors and Correlation Function in Atomic Vibrations Including Many-Body Effects

The low-temperature thermal conduction and millimeter-wave dielectric properties of β-Si3N4 as a heat-dissipation substrate

Increasing operating frequency is required in wireless communication systems. In use, this generates heat, which results in serious problems for semiconductor devices. Silicon nitride (Si3N4) has high thermal conductivity and fracture strength. Therefore, it is expected to be suitable for heat dissipation in active circuit substrates for wireless communication. In this study, Si3N4 with varying thermal conductivities were prepared by controlling starting material and sintering conditions and their low-temperature thermal conductivities were measured. The mean free path of phonons in β-Si3N4 influences its thermal conductivity. The temperature dependence of the Debye–Waller factor obtained by synchrotron radiation scattering supported the high thermal conductivity of the β-Si3N4. The degradation of thermal conductivity was interpreted in terms of the full width at half maximum of Raman spectra. Further, infrared reflectivity and first-principles calculation for β-Si3N4 confirmed their superior dielectric properties compared with other high thermal conductive materials.

Investigating Anharmonic XAFS Debye-Waller Factor of Crystalline Tungsten Based on Einstein Model

The anharmonic X-ray absorption fine structure (XAFS) Debye-Waller (DW) factor of the crystalline tungsten (W) has been investigated in the temperature-dependent. This DW factor is calculated in explicit forms using the quantum anharmonic correlated Einstein model developed from the correlated Einstein model based on the anharmonic effective potential and the quantum statistical theory. The numerical results of W in the temperature range from 0 to 900 K are in good agreement with those obtained by the other theoretical models and experiments at several temperatures. The analytical results show that the anharmonic correlated Einstein model is suitable for analyzing the experimental XAFS data of metals.

Selection rules in the excitation of the divacancy and the nitrogen-vacancy pair in 4 H - and 6 H -SiC

In this study, we address selection rules with respect to the polarization of the optical excitation of two color centers in 4H−SiC and 6H−SiC with potential for applications in quantum technology, the divacancy and the nitrogen-vacancy pair. We show that the photoluminescence of the axial configurations of higher symmetry (C3v) than the basal ones (C1h) can be canceled using any excitation (resonant or nonresonant) with polarization parallel to the crystal axis (EL||c). The polarization selection rules are determined using group-theoretical analysis and simple physical arguments showing that phonon-assisted absorption with EL||c is prohibited despite being formally allowed by group theory. A comparison with the selection rules for the silicon vacancy, another defect with C3v symmetry, is also carried out. Using the selection rules, we demonstrate selective excitation of only one basal divacancy configuration in 4H−SiC, the PL3 line, and discuss the higher contrast and increased Debye-Waller factor in the selectively excited spectrum. Published by the American Physical Society 2024

Impact of random nanoscale roughness on gas-scattering dynamics.

The impact of nanoscale wall roughness on rarefied gas transport is widely acknowledged, yet the associated scattering dynamics largely remain elusive. In this paper, we develop a scattering kernel for surfaces having nanoscale roughness that distinctly characterizes the two major types of interactions between gas molecules and rough surfaces. Namely these are (a) the weak perturbations arising from the thermal motion of wall atoms, essentially gas-phonon collisions, which are captured by the well-established Cercignani-Lampis model, and (b) the hard collisions owing to the irregularities of the rough, static potential energy surface, which are generally described by the fully diffuse model. Drawing an analogy between wave-surface and gas-surface scattering, a pseudo Debye-Waller factor is incorporated into the modeling as a weighting coefficient to allow the transition between smooth and rough surface conditions. The proposed scattering kernel is validated through high-fidelity molecular dynamics simulations that are performed for systems with varying roughness, temperature, and gas-surface combinations. The results indicate that the model well captures the scattering dynamics of gas molecular beams impinging on surfaces at different velocities, specifically for the accommodation coefficients and reflection patterns. Additionally, in flow and heat transport cases, it accurately predicts macroscopic quantities such as velocity slip and temperature jumps across the range of tested conditions.

Na in diamond: high spin defects revealed by the ADAQ high-throughput computational database

Color centers in diamond are at the forefront of the second quantum revolution. A handful of defects are in use, and finding ones with all the desired properties for quantum applications is arduous. By using high-throughput calculations, we screen 21,607 defects in diamond and collect the results in the ADAQ database. Upon exploring this database, we find not only the known defects but also several unexplored defects. Specifically, defects containing sodium stand out as particularly relevant because of their high spins and predicted improved optical properties compared to the NV center. Hence, we studied these in detail, employing high-accuracy theoretical calculations. The single sodium substitutional (NaC) has various charge states with spin ranging from 0.5 to 1.5, ZPL in the near-infrared, and a high Debye-Waller factor, making it ideal for biological quantum applications. The sodium vacancy (NaV) has a ZPL in the visible region and a potential rare spin-2 ground state. Our results show sodium implantation yields many interesting spin defects that are valuable additions to the arsenal of point defects in diamond studied for quantum applications.

Effect of calcination temperature on structure evolution of hematite nanoparticles

The objective of this study is to investigate the transition structure of iron oxide, specifically the change from magnetite to hematite, as well as the influence of calcination temperature on the structural growth of hematite nanoparticles. The magnetite was extracted from the native iron sand in Indonesia using the coprecipitation procedure. To generate hematite, magnetite was calcined at various temperatures (350, 500, 650, and 800 °C). The structural changes resulting from the effect of calcination temperature were investigated by combining a number of characterisation methods. The crystal structure was examined using synchrotron x-ray diffraction (SRD) and the local structure was examined using x-ray absorption spectroscopy (XAS). Crystallite size was calculated using the Debye-Schrerrer equation at the most dominant SRD peak. Surface morphology was investigated using scanning electron microscopy (SEM). SRD data revealed that the sample calcined at 350 °C displayed both the Fe3O4 and α-Fe2O3 phases, while higher temperatures revealed the single-phase α-Fe2O3. Furthermore, an increase in calcination temperature was shown to be associated with an increase in crystallinity and crystallite size. For the samples H350 and H800, the crystallinity increased from 95.56 to 98.17%. In the magnetite, H350, H500, H650, and H800 samples, the crystallite size increased from 9.57 to 29.55, 16.40, 28,48, 29.26, and 29.55 nm. Higher calcination temperatures, on the other hand, increase the interatomic distance while decreasing the Debye–Waller factor, according to XAS fitting data. It can be inferred that around 500 °C, the transition from Fe3O4 to single-phase α-Fe2O3 was observed. While a greater calcination temperature of at least 800 °C would alter the structural parameters, it would not affect the phase.

Pressure and non-ideal axial ratio effects on thermodynamic properties of hexagonal close-packed Mg and Zn metals

ABSTRACT The Debye model has been developed to study the pressure dependence of the extended X-ray absorption fine structure Debye–Waller factor, the Debye frequency and temperature of hexagonal close-packed (hP2) metals. The effects of the non-ideal axial ratio c/a of hP2 structure on these thermodynamic quantities at high pressures have also been considered. Additionally, based on the combination of the Debye model and the Lindemann melting law, we derive the analytic expression of melting temperature of hP2 metals as a function of pressure. Numerical calculations have been implemented for Mg and Zn metals up to 20 and 50 GPa, respectively. We have shown that Debye frequency and temperature, as well as melting temperature of these two metals increase robustly with pressure and non-ideal axial ratio plays important role in these thermodynamic quantities. The remarkable consistency observed between our calculations and various experimental results validates the reliability of the currently presented melting curve. Meanwhile, at high pressure non-ideal axial ratio gives a small contribution to pressure-dependent Debye–Waller factor of Mg (up to 20 GPa) and Zn (beyond 20 GPa), and can be safely neglected in the suggested pressure range.

Synthesis of nanocrystalline zinc powder: Investigating the influence of crystallite size and lattice strain on Debye-Waller factors

In this investigation, nano-sized zinc particles were synthesized through a ball milling process. The Zn metal powder, milled for durations ranging from 0 to 150 h, underwent analysis using X-ray diffraction (XRD). The study focused on determining PS (particle size) and assessing the influence of LS (lattice strain) on the DWFs (Debye–Waller factors), employing XRD principles. LSs were induced in zinc through varying milling durations, and X-ray diffractograms were captured at different stages of the milling process. The results revealed a reduction in PS and an increase in LS with prolonged milling, reaching a predominantly amorphous state at 150 h. By establishing the correlation between strain and effective DWF, the study estimated DWFs for zero strain in zinc.

The far-field diffraction of a plane wave on a system of randomly and in average periodically located point scatterers: the Debye-Waller factor

The description of the superposition field of a system of point sources with a random and, on average, periodic structure is considered. The description is given in the far field and the point sources are considered as centers of secondary sphere waves generated by an external plane wave. In contrast to the traditional approach, where description of the diffraction pattern is given on the base of wave field averaging, here the intensity is averaged.In the framework of the suggested approach the analytic formula of dependence of the average intensity on the direction observation is found. The influence of disorder on the values of intensity of main maximums of a periodic structure is investigated. It is shown that this influence depends on the ordinal numbers of the maximum and in the case of central main maximum this influence vanishes. The question of applicability of the Debye-Weller factor for describing of the statistic of diffracted field is discussed.

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.

Exploring the Underlying Correlation between the Structure and Ionic Conductivity in Halide Spinel Solid-State Electrolytes with Neutron Diffraction.

The development of cutting-edge solid-state electrolytes (SSEs) entails a deep understanding of the underlying correlation between the structure and ionic conductivity. Generally, the structure of SSEs encompasses several interconnected crystal parameters, and their collective influence on Li+ transport can be challenging to discern. Here, we systematically investigate the structure-function relationship of halide spinel LixMgCl2+x (2 ≥ x ≥ 1) SSEs. A nonmonotonic trend in the ionic conductivity of LixMgCl2+x SSEs has been observed, with the maximum value of 8.69 × 10-6 S cm-1 achieved at x = 1.4. The Rietveld refinement analysis, based on neutron diffraction data, has revealed that the crystal parameters including cell parameters, Li+ vacancies, Debye-Waller factor, and Li-Cl bond length assume diverse roles in influencing ionic conductivity of LixMgCl2+x at different stages within the range of x values. Besides, mechanistic analysis demonstrates Li+ transport along three-dimensional pathways, which primarily governs the contribution to ionic conductivity of LixMgCl2+x SSEs. This study has shed light on the collective influence of crystal parameters on Li+ transport behaviors, providing valuable insights into the intricate relationship between the structure and ionic conductivity of SSEs.

Correlating Structural Disorder in Metal (Oxy)hydroxides and Catalytic Activity in Electrocatalytic Oxygen Evolution.

Understanding the correlation between the structural evolution of electrocatalysts and their catalytic activity is both essential and challenging. In this study, we investigate this correlation in the context of the oxygen evolution reaction (OER) by examining the influence of structural disorder during and after dynamic structural evolution on the OER activity of Fe-Ni (oxy)hydroxide catalysts using operando X-ray absorption spectroscopy, alongside other experiments and theoretical calculations. The Debye-Waller factors obtained from extended X-ray absorption fine structure analyses reflect the degree of structural disorder and exhibit a robust correlation with the intrinsic OER activities of the electrocatalysts. The enhanced OER activity of in situ-generated metal (oxy)hydroxides derived from different pre-catalysts is linked to increased structural disorder, offering a promising approach for designing efficient OER electrocatalysts. This strategy may inspire similar investigations in related electrocatalytic energy-conversion systems.

A METHOD FOR CALCULATION OF MORSE POTENTIAL FOR FCC, BCC, HCP CRYSTALS APPLIED TO DEBYE-WALLER FACTOR AND EQUATION OF STATE

Analytical expressions for the Morse potential parameters for fcc, bcc and hcp
 crystals have been developed. They contain the energy of sublimation, the compressibility
 and the lattice constant. Numerical results for Cu (fcc), W (bcc) and Zn (hcp) agree well
 with the measured values. Debye-Waller factors in X-ray absorption fine structure (XAFS)
 and equation of state computed using the obtained Morse potential parameters agree well
 with the experimental results.

Role of additive size in the segmental dynamics and mechanical properties of cross-linked polymers.

Thermoset materials often involve the addition of molecular and nanoparticle additives to alter various chemo-physical properties of importance in their ultimate applications. The resulting compositional heterogeneities can lead to either enhancement or degradation of thermoset properties, depending on the additive chemical structure and concentration. We tentatively explore this complex physical phenomenon through the consideration of a model polymeric additive to our coarse-grained (CG) thermoset investigated in previous works by simply varying the size of additive segments compared to those of polymer melt. We find that the additive modified thermoset material becomes chemically heterogeneous from additive aggregation when the additive segments become much smaller than those of the thermoset molecules, and a clear evidence is observed in the spatial distribution of local molecular stiffness estimated from Debye-Waller factor 〈u2〉. Despite the non-monotonic variation trends observed in dynamical and mechanical properties with decreasing additive segmental size, both the structural relaxation time and moduli (i.e., shear modulus and bulk modulus) exhibit scaling laws with 〈u2〉. The present work highlights the complex role of additive size played in the dynamical and mechanical properties of thermoset polymers, which should provide a better understanding for the glass formation process of cross-linked polymer composites.

Direct measurement of the structural change associated with amorphous solidification using static scattering of coherent radiation.

In this paper, we demonstrate that the weak temperature dependence of the structure factor of supercooled liquids, a defining feature of the glass transition, is a consequence of the averaging of the scattering intensity due to angular averaging. We show that the speckle at individual wavevectors, calculated from a simulated glass former, exhibits a Debye-Waller factor with a sufficiently large temperature dependence to represent a structural order parameter capable of distinguishing liquid from glass. We also extract from the speckle intensities a quantity proportional to the variance of the local restraint, i.e., a direct experimental measure of the amplitude of structural heterogeneity.

Cavity-Enhanced Emission from a Silicon T Center.

Silicon T centers present the promising possibility of generating optically active spin qubits in an all-silicon device. However, these color centers exhibit long excited state lifetimes and a low Debye-Waller factor, making them dim emitters with low efficiency into the zero-phonon line. Nanophotonic cavities can solve this problem by enhancing radiative emission into the zero-phonon line through the Purcell effect. In this work, we demonstrate cavity-enhanced emission from a single T center in a nanophotonic cavity. We achieve a 2 order of magnitude increase in the brightness of the zero-phonon line relative to waveguide-coupled emitters, a 23% collection efficiency from emitter to fiber, and an overall emission efficiency into the zero-phonon line of 63.4%. We also observe a lifetime enhancement of 5, corresponding to a Purcell factor exceeding 18 when correcting for the emission to the phonon sideband. These results pave the way toward efficient spin-photon interfaces in silicon photonics.

Experimental study and modeling of extreme ultraviolet 4000 lines/mm diffraction gratings coated with periodic and aperiodic Al/Mo/SiC multilayers.

Multilayer coated diffraction gratings are crucial components for extreme ultraviolet (EUV) applications such as spectroscopy or spectro-imaging. However, for high groove density, the smoothening of the grating surface profile with multilayer deposition remains a limitation that requires further investigation. In this paper, we report on the design, characterization, and modeling of 4000 lines/mm diffraction gratings coated with periodic and aperiodic Al/Mo/SiC multilayers for EUV radiation. Two types of gratings with different groove depths are compared. Multilayer coatings were designed using a genetic algorithm to maximize the first-order diffraction efficiency in the 17-21 and 19-23nm wavelength ranges at normal incidence. Periodic and aperiodic multilayers with different numbers of layers were deposited by magnetron sputtering on the two types of fused silica gratings, and the grating groove profile evolution was measured by atomic force microscopy and cross-section transmission electron microscopy. The first-order diffraction efficiency was measured in the EUV at 5° incidence using monochromatic synchrotron radiation and modeled using the rigorous coupled-wave analysis method. The simulation models refined by using the Debye-Waller factor to account for the multilayer interfacial roughness show good agreement with experimental data. The results reported in this study will allow for designing efficient EUV multilayer gratings for high-resolution spectro-imaging instruments.

First-Principles Investigation of Near-Surface Divacancies in Silicon Carbide.

The realization of quantum sensors using spin defects in semiconductors requires a thorough understanding of the physical properties of the defects in the proximity of surfaces. We report a study of the divacancy (VSiVC) in 3C-SiC, a promising material for quantum applications, as a function of surface reconstruction and termination with -H, -OH, -F and oxygen groups. We show that a VSiVC close to hydrogen-terminated (2 × 1) surfaces is a robust spin-defect with a triplet ground state and no surface states in the band gap and with small variations of many of its physical properties relative to the bulk, including the zero-phonon line and zero-field splitting. However, the Debye-Waller factor decreases in the vicinity of the surface and our calculations indicate it may be improved by strain-engineering. Overall our results show that the VSiVC close to SiC surfaces is a promising spin defect for quantum applications, similar to its bulk counterpart.

Investigation of ferroelectric Ba1−xCaxZryTi1−yO3 single crystal by in situ temperature-dependent x-ray diffraction and first-principles calculations

In situ temperature-dependent crystal structure of lead-free ferroelectric perovskite Ba0.798Ca0.202Zr0.006Ti0.994O3 single crystal was characterized using x-ray diffraction from 170 to 380 K. Three phases were identified at different temperatures of 170, 220, and 298 K, revealing rhombohedral (R3m), orthorhombic (Pmm2), and tetragonal (P4mm) crystal structures, respectively. The change in the bond length and its distortion are reported for both AO12 and BO6 polyhedrons, allowing for the estimation of the spontaneous polarization. The Debye–Waller factor is reported as a function of temperature for A and B-sites. Density-functional theory calculations on the tetragonal phase were performed to obtain information on the distribution of the Ca ions, the local atomic displacements, and the ideal value of the spontaneous polarization of a defect-free crystal at 0 K. We find that Ca prefers to arrange in columnar 2D plates oriented along the tetragonal axis. The Ca ions avoid being next neighbors of Zr; however, the specific arrangement of Ca has only a minor impact on the spontaneous polarization.