Mean Square Displacements Of Atoms Research Articles

Theory of the special displacement method for electronic structure calculations at finite temperature

Calculations of electronic and optical properties of solids at finite temperature including electron-phonon interactions and quantum zero-point renormalization have enjoyed considerable progress during the past few years. Among the emerging methodologies in this area, we recently proposed a new approach to compute optical spectra at finite temperature including phonon-assisted quantum processes via a single supercell calculation [Zacharias and Giustino, Phys. Rev. B 94, 075125 (2016)]. In the present work we considerably expand the scope of our previous theory starting from a compact reciprocal space formulation, and we demonstrate that this improved approach provides accurate temperature-dependent band structures in three-dimensional and two-dimensional materials, using a special set of atomic displacements in a single supercell calculation. We also demonstrate that our special displacement reproduces the thermal ellipsoids obtained from X-ray crystallography, and yields accurate thermal averages of the mean-square atomic displacements. At a more fundamental level, we show that the special displacement represents an exact single-point approximant of an imaginary-time Feynman's path integral for the lattice dynamics. This enhanced version of the special displacement method enables non-perturbative, robust, and straightforward ab initio calculations of the electronic and optical properties of solids at finite temperature, and can easily be used as a post-processing step to any electronic structure code. Given its simplicity and numerical stability, the present development is suited for high-throughput calculations of band structures, quasiparticle corrections, optical spectra, and transport coefficients at finite temperature.

Investigation of tetracosane thermal transport in presence of graphene and carbon nanotube fillers––A molecular dynamics study

Abstract This paper examines the thermal properties of pure tetracosane paraffin, tetracosane-graphene, and tetracosane-carbon nanotube mixed phase change materials (PCM). The most important properties studied were thermal capacity in constant volume (Cv), mean square displacement of atoms (MSD), radial distribution function (RDF), density, phonon density of states (PDOS) and thermal conductivity (k) under different temperatures. The results show that graphene and carbon nanotube increase the thermal conductivity of the tetracosane at different temperatures, but decrease the molecular movement and its thermal capacity (except after about 360 K), and it can be said that this slightly decreases the paraffin melting temperature. It was demonstrated that carbon nanotube is more efficient than graphene to increase the thermal conductivity of the proposed PCM.

Effect of Substrate Cooling on the Microstructure and Phase Composition of Ti–6Al–4V Titanium-Based Alloy Products Obtained Using Additive Technologies

The microstructure, phase composition, and parameters of α-Ti-based solid solutions in a Ti–6Al–4V alloy obtained by the 3D printing method without cooling and with water cooling of the titanium substrate are investigated using X-ray diffraction analysis, transmission diffraction and scanning electron microscopy, and optical metallography. It is found that water cooling of the substrate reduces the sizes of prior β-grains, increases the volume fraction of the β-phase, and decreases the volume fraction of the α"-phase and the total mean square displacement of atoms in the α-Ti crystal lattice, and also increases the elastic macrostrain of the samples.

Change in the Phase Composition and Lattice Parameters of the Solid Solution Based on α-Ti in the Surface Layers of the Ti–6Al–4V Alloy Subjected to Electron-Beam Treatment

The microstructure, phase composition, and lattice parameters of the α-Ti- based solid solution in the Ti–6Al–4V alloy treated by pulsed and continuous electron beams with the energy density of 18–24 and 450 J/cm2, respectively, have been investigated using the methods of X-ray diffraction analysis and transmission and scanning electron microscopy. In the initial state, the two-phase (α + β) alloy had a polycrystalline structure with the equiaxed α-phase grains and β-phase grains located at the junctions or along the boundaries of the α-phase grains. After the electron-beam treatment, α' martensite with a lamellar structure is formed in the molten surface layer, which then experiences an α' → α + α'' + β phase transformation. In the α phase, the lamellar structure inherited from the α' martensite is retained; the β phase is located along the boundaries of lamellar grains of the α phase; the α'' phase is located both in the β phase and inside the lamellar grains of the α phase. It has been revealed that the greater the total volume fraction of the β and α'' phases, the greater the lattice parameters of α-Ti and their axial ratio c/a, and the less the total mean-square displacements of atoms in the 101 direction in the α-Ti phase. The decrease in the total mean-square displacements in the α-Ti phase is due to the diffusion of the vanadium atoms into the β phase. With an increase in the energy density of the electron beam and with a decrease in the rate of cooling of the molten layer, the total volume fraction of the β and α'' phases increases and reaches 6%.

Влияние охлаждения подложки на микроструктуру и фазовый состав изделий из титанового сплава Ti-6Al-4V, полученных методами аддитивных технологий

The microstructure, phase composition, and parameters of the -Ti based solid solution in the Ti-6Al-4V alloy obtained by 3D printing without cooling and with water cooling of the titanium substrate were studied by the methods of X-ray diffraction analysis, transmission diffraction and scanning electron microscopy, and optical metallography. It was found that the use of water cooling of the substrate leads to a decrease of the hereditary  grains sizes, an increase in the volume fraction of the  phase, a decrease in the volume fraction of the  phase and the total mean square displacement of atoms in the -Ti crystal lattice, as well as an increase in the elastic macrostrain of the samples.

Influence of a thin amorphous surface layer on de-channeling during aluminum implantation at different temperatures into 4H-SiC

Ion implantation is an important technique in semiconductor processing and has become a key technology for 4H-SiC devices. Today, aluminum (Al) implantations are routinely used for p-type contacts, p+-emitters, terminations and many other applications. However, in all crystalline materials, quite a few ions find a path along a crystal channel, so-called channeling, and these ions travel deep into the crystal. This paper reports on the channeling phenomenon during Al implantation into 4H-SiC, and in particular, the influence of a thin native oxide will be discussed in detail. The effects of thermal lattice vibrations for implantations performed at elevated temperatures will also be elucidated. 100 keV Al ions have been implanted along the [000-1] direction employing samples with 4° miscut. Before implantation, the samples have been aligned using the blocking pattern of backscattered protons. Secondary ion mass spectrometry has been used to record the Al depth distribution. To predict implantation profiles and improve understanding of the role of crystal structure, simulations were performed using the Monte-Carlo binary collision approximation code SIIMPL. Our results show that a thin surface layer of native oxide, less than 1 nm, has a decisive role for de-channeling of aligned implantations. Further, as expected, for implantations at elevated temperatures, a larger degree of de-channeling from major axes is present due to increased thermal vibrations and the penetration depth of channeled aluminum ions is reduced. The values for the mean-square atomic displacements at elevated temperatures have been extracted from experimental depth profiles in combination with simulations.

Weighted-Persistent-Homology-based Machine Learning for RNA Flexibility Analysis

With the great significance of biomolecular flexibility in biomolecular dynamics and function analysis, various experimental methods and theoretical models are developed. Experimentally, Debye-Waller factor, also known as B-factor, measures atomic mean-square displacement and is usually considered as an important measurement for flexibilities. Theoretically, elastic network models, Gaussian network model, flexibility-rigidity model, and other computational models, have been proposed for flexility analysis by shedding light on the biomolecular inner topological structures. Recently, a topology-based machine learning model is proposed. By using the features from persistent homology, this model achieves remarkable high accuracy in protein B-factor prediction. Motivated by its success, we propose weighted-persistent-homology (WPH)-based machine learning (WPHML) models for RNA flexibility analysis. Our WPH is a newly-proposed model, which incorporate physical, chemical and biological information into topological measurements using a weight function. In particular, we use local persistent homology (LPH), which is not to consider the topology of a whole RNA structure, but to focus on the topological information of local regions. Our WPHML model is validated on a well-established RNA dataset, and numerical experiments show that our model can achieve a Pearson correlation coefficient up to 0.5822. The comparison with the previous sequence-information-based learning models shows that a consistent increase of accuracy by at least 10% is achieved in our current model.

Molecular dynamics simulation of helium ion implantation into silicon and its migration

In this paper, a model of helium ion implanted monocrystalline Si was constructed by using molecular dynamics (MD) simulation method to study the interaction mechanism of helium ion with monocrystalline Si and helium ion migration. In order to study the damage effect of helium ion implantation on monocrystalline Si, identify diamond structure (IDS), radial distribution function, temperature analysis were calculated and analyzed. The effects of ion doses, beam currents and energies on the damage were studied. Helium ion implanted Si with ion doses of 1 × 1014/cm2 was subsequently heated to 300 K. MD simulation results indicated that IDS damage induced by ion implantation was positively correlated with ion doses as the ion implantation increased to 1 × 1014/cm2. The mean-square displacement of helium atoms was calculated during the temperature rising to 300 K. It was found that the high permeability of helium atoms in Si and the acceleration of atomic thermal motion owing to elevated temperature as well as the existence of larger stress would be helpful to the migration of implant helium atoms.

Temperature-dependent atomic B factor: an ab initio calculation.

The Debye-Waller factor explains the temperature dependence of the intensities of X-ray or neutron diffraction peaks. It is defined in terms of the B matrix whose elements Bαβ are mean-square atomic displacements in different directions. These quantities, introduced in several contexts, account for the effects of temperature and quantum fluctuations on the lattice dynamics. This paper presents an implementation of the B factor (8π2Bαβ) in the thermo_pw software, a driver of Quantum ESPRESSO routines that provides several thermodynamic properties of materials. The B factor can be calculated from the ab initio phonon frequencies and displacements or can be estimated, although less accurately, from the elastic constants, using the Debye model. The B factors are computed for a few elemental crystals: silicon, ruthenium, magnesium and cadmium; the harmonic approximation at fixed geometry is compared with the quasi-harmonic approximation where the B factors are calculated accounting for thermal expansion. The results are compared with the available experimental data.

Structural and Thermomechanical Properties of Zincblende-Type ZnX (X = S, Se, Te)

The structural and thermomechanical properties of zincblende ZnX (X = S, Se, Te) compounds have been investigated based on the moment method in statistical mechanics. Expressions for the lattice constant, atomic mean-square displacement (MSD), and elastic moduli (Young’s modulus, bulk modulus, and shear modulus) of the zincblende compounds were derived. The results show that the quantum-mechanical zero-point vibrations make the main contribution to the atomic MSDs at low temperature. At high temperature, due to the predominance of anharmonicity, the atomic MSDs increase rapidly with increasing temperature. The Young’s modulus and shear modulus of the zinc chalcogenides ZnX (X = S, Se, Te) were calculated. The data derived from this research can be seen as useful references for future experiments.

Effect of Aluminum Concentration on the Lattice Parameters and Mean-Square Displacements of Atoms in Cu–Al and Ti–6Al–4V Alloys

It is shown that the fcc lattice parameter and the total mean-square displacements of atoms increase when copper is doped with aluminum. Parameters а and с of the hcp α-Ti lattice decrease when titanium is doped with aluminum and vanadium. This effect is attributed to the size factor of radii of alloy elements. The lattice parameter of Ti–6Al–4V alloy samples subjected to electron-beam processing may vary either way compared to α-Ti prior to processing. It is demonstrated that the observed variation of the lattice parameter is induced by the redistribution of aluminum and silicon in surface layers. The mean-square displacement of atoms and the lattice parameters in α-Ti and the Ti–6Al–4V alloy are directly proportional.

Fluctuations as a source of new physical properties of ultra-small CdSe nanoparticles

The presence the static mean-square displacement of atoms from the equilibrium position caused by the structural defects can lead to the order-disorder transition in the ultra-small nanoparticles (USNs). It is shown that after the appropriate choose of the order parameter, the Landau mean-field theory can be used to describe this transition in USNs. In present article, the fluctuations of the order parameter are considered by statistical methods. The order-disorder transition in USNs is accompanied by large fluctuations of the order parameter. The order parameter changes continuously around its equilibrium value. This dynamic state of USNs can be considered as a new state of matter at the nanoscale, which is characterized by a continuous change of the order parameter. For the first time, the Landau theory is applied to describe the white-light emitting of USNs. It is shown that the fluctuations nearby the order-disorder transition are responsible for the white-light emission and that the emission spectrum has a crossover between the monochromatic and white-light emission at the critical nanoparticle diameter. Methods for controlling USNs properties by changing the order parameter are presented for the first time. The present theory gives a new approach to explain the white-light emission by CdSe quantum dots. It also follows from the present theory that the crossover can be suppressed (or shifted to a region of smaller nanoparticles) by an artificial change of the order parameter. The developed theory gives a new approach to predict the physical properties of USNs.

New insights into methane hydrate dissociation: Utilization of molecular dynamics strategy

Hydrate reserves play a crucial role in energy storage and resources across the world. Gas hydrate formation may lead to various forms of blockages in oil/gas production and transportation processes, resulting in high capital and operating costs. Hence, it is important to determine the methane hydrate formation conditions and to understand the vital process and thermodynamic parameters. In this study, molecular dynamic (MD) simulations are conducted to investigate the microscopic mechanisms/phenomena and intermolecular forces involved in methane hydrate decomposition, where molecular interactions, structures, and behaviours need to be appropriately determined/selected. Through a systematic parametric sensitivity analysis, the impacts of temperature, pressure, and cage occupancy on hydrate dissociation are studied. Furthermore, the diffusion coefficient, density, and heat capacity of the methane hydrates are determined by employing MD strategy. The stability of water cages is examined at various decomposition times, temperatures, and pressures. According to the radial distribution function and mean square displacement of oxygen-oxygen and carbon-carbon atoms, the stability of hydrate cages decreases with increasing temperature, while it increases with increasing the cage occupancy and pressure. The addition of inhibitors (e.g., methanol) to small cavities in the hydrate structure creates new hydrogen bonds between the water and inhibitor molecules in the cages, accelerating the decomposition of hydrates. A good agreement is noticed between the outcomes of this research work and the results obtained in experimental and theoretical studies available in the literature. Analysing the outcome of the present and previous research works, the current study provides new reliable/logical information on the molecular level of the hydrate dissociation process. It is expected that such a research investigation offers effective tips/guidelines to deal with hydrate formation and dissociation in terms of utilization, prevention, and processing.

Molecular Simulations of Sputtering Preparation and Transformation of Surface Properties of Au/Cu Alloy Coatings Under Different Incident Energies

The surface properties of coatings during deposition are strongly influenced by temperature, particle fluxes, and compositions. In addition, the precursor incident energy also affects the surface properties of coatings during sputtering. The atomistic processes associated with the microstructure of coatings and the surface morphological evolution during sputtering are difficult to observe. Thus, in the present study, molecular dynamics simulation was employed to investigate the surface properties of Au/Cu alloy coatings (Cu substrate sputtering by Au atoms) with different incident energies (0.15 eV, 0.3 eV, 0.6 eV). Subsequently, the sputtering depth of the Au atoms, the particle distribution of the Au/Cu alloy coating system, the radial distribution function of particles in the coatings, the mean square displacement of the Cu atoms in the substrate, and the roughness of the coatings were analyzed. Results showed that the crystal structure and the sputtering depth of Au atoms were hardly influenced by the incident energy, and the incident energy had little impact on the motion of deep-lying atoms in the substrate. However, higher incident energy resulted in higher surface temperature of coatings, and more Au atoms existed in the coherent interface. Moreover, it strengthened the motion of Cu atoms and reduced the surface roughness. Therefore, the crystal structure of coatings and the motions of deep-lying atoms in the substrate are not influenced by the incident energy. However, the increase in incident energy will enhance the combination of coatings and the base while optimizing the surface structure.

Anharmonic correlated Debye model for thermal disorder in iron-rich B2-FeAl intermetallic alloy

The anharmonic correlated Debye model has been developed to investigate the thermal disorder in B2-type FeAl intermetallic alloy. We derive analytical expressions of the bond-stretching force constants, the Debye temperature and frequency, the atomic mean-square displacement and the first three extended X-ray absorption fine structure (EXAFS) cumulants. Numerical calculations of these thermodynamic quantities have been performed for B2-type Fe-40 at.%Al up to temperature 1300 K using the Morse potential whose parameters were derived within the Möbius lattice inversion scheme. Our research shows that the anharmonicity contributions of thermal lattice vibrations are important to the EXAFS cumulants at high temperature. The theoretical predictions are compared with available experimental data when possible to verify the developed anharmonic correlated Debye model.

Picosecond Dynamical Response to a Pressure-Induced Break of the Tertiary Structure Hydrogen Bonds in a Membrane Chromoprotein.

We used elastic incoherent neutron scattering (EINS) to find out if structural changes accompanying local hydrogen bond rupture are also reflected in global dynamical response of the protein complex. Chromatophore membranes from LH2-only strains of the photosynthetic bacterium Rhodobacter sphaeroides, with spheroidenone or neurosporene as the major carotenoids, were subjected to high hydrostatic pressure at ambient temperature. Optical spectroscopy conducted at high pressure confirmed rupture of tertiary structure hydrogen bonds. In parallel, we used EINS to follow average motions of the hydrogen atoms in LH2, which reflect the flexibility of this complex. A decrease of the average atomic mean square displacements of hydrogen atoms was observed up to a pressure of 5 kbar in both carotenoid samples due to general stiffening of protein structures, while at higher pressures a slight increase of the displacements was detected in the neurosporene mutant LH2 sample only. These data show a correlation between the local pressure-induced breakage of H-bonds, observed in optical spectra, with the altered protein dynamics monitored by EINS. The slightly higher compressibility of the neurosporene mutant sample shows that even subtle alterations of carotenoids are manifested on a larger scale and emphasize a close connection between the local structure and global dynamics of this membrane protein complex.

Pressure effects on EXAFS Debye-Waller factor and melting curve of solid krypton

The pressure effects on atomic mean-square displacement, extended X-ray absorption fine structure (EXAFS) Debye-Waller factor and melting temperature of solid krypton have been investigated in within the statistical moment method scheme in quantum statistical mechanics. By assuming the interaction between atoms can be described by Buckingham potential, we performed the numerical calculations for krypton up to pressure 120 GPa. Our calculations show that the atomic mean-square displacement and EXAFS Debye-Waller factor of krypton crystal depend strongly on pressure. They make the robust reduction of the EXAFS peak height. Our results are in good and reasonable agreements with available experimental data. This approach gives us a relatively simple method for qualitatively calculating high-pressure thermo-physical properties of materials. Moreover, it can be used to verify future high-pressure experimental and theoretical works.

Finite temperature properties and phase transition behavior of quasi-planar B36 nanocluster from first principles

Density-functional molecular dynamics simulations within the Car-Parrinello approach have been carried out to investigate the finite temperature properties and the thermal phase transition behavior of quasi-planar B36 nanocluster via calculating a number of representative indicators such as root-mean-square bond length fluctuations, mean square displacement, radial distribution function, and total energy at forty equilibrium temperatures ranging from zero to 3200 K. Dramatic changes in the temperature dependence of these quantities take place from 1900 to 2200 K found as the phase transition region of the cluster. A detailed analysis of the total energy curve and mean square displacements of individual atoms within this melting region yields Tm ≃ 2125 K as the melting point. Results broadly support the view that the nanocluster preserves its hexagonal structure and quasi-planarity up to the phase transition region, exhibiting a high thermal stability by taking into account its ultra-small size and the melting point, which can be more increased in the case of nanostructures made of several B36 units.

Low-Temperature Dynamical Transition in Lipid Bilayers Detected by Spin-Label ESE Spectroscopy

Data on neutron scattering in biological systems show low-temperature dynamical transition between 170 and 230 K manifesting itself as a drastic increase of the atomic mean-squared displacement, 〈x2〉, detected for hydrogen atoms in the nano- to picosecond time scale. For spin-labeled systems, electron spin echo (ESE) spectroscopy—a pulsed version of electron paramagnetic resonance—is also capable of detection of dynamical transition. A two-pulse ESE decay in frozen matrixes is induced by spin relaxation arising from stochastic molecular librations, and allows to obtain the 〈α2〉τc parameter, where 〈α2〉 is a mean-squared angular amplitude of the motion and τc is the correlation time lying in the sub- and nanosecond time ranges. In this work, the ESE technique was applied to spin-labeled amphiphilic molecules of three different kinds embedded in bilayers of fully saturated 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and mono-unsaturated 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) lipids. Two-pulse ESE data revealed the appearance of stochastic librations above 130 K, with the parameter 〈α2〉τc obeying the Arrhenius type of temperature dependence and increasing remarkably above 170–180 K. A comparison with a dry sample suggests that onset of motions is not related with lipid internal motions. Three-pulse ESE experiments (resulting in stimulated echos) in DPPC bilayers showed the appearance of slow molecular rotations above 170–180 K. For D2O-hydrated bilayers, ESE envelope modulation experiments indicate that isotropic water molecular motions in the nearest hydration shell of the bilayer appear with a rate of ~ 105 s−1 in the narrow temperature range between 175 and 179 K. The similarity of the experimental data found for three different spin-labeled compounds suggests a cooperative character for the ESE-detected molecular motions. The data were interpreted within a model suggesting that dynamical transition is related with overcoming barriers, of 10–20 kJ/mol height, existing in the system for the molecular reorientations.

Phase transitions to superionic Li2Te and Li2Se – A high-temperature neutron powder diffraction study, atom displacements, probability density functions and atom potentials

Despite much research on Li ion batteries at ambient temperature, Li-ion conductors at high temperature have received less attention. In the series of ionic Li2X compounds (X = O, S, Se, Te), superionic phase transitions have been reported for Li2O and Li2S. The lower transition temperature of Li2S, supposedly caused by the larger anion size of S, inspired the investigation of the superionic behavior of Li2Se and Li2Te. Their thermal expansion and thermally excited spatial distribution of Li cations and Se/Te anions was monitored by neutron diffraction up to 800 °C for Li2Te and up to 1000 °C for Li2Se. Both compounds exhibit positive thermal expansion with changing coefficient of expansivity at the superionic transition temperatures. No deviation from cubic metrics or abrupt changes of the cell volume were observed. Rietveld refinements of the fluorite-type structures (space group Fm3¯m) employing Gaussian spatial distribution functions reveal discontinuities in the slope of the increasing mean square displacement parameters as a function of temperature. At ~600 °C (Li2Te) and ~780 °C (Li2Se), the mean square displacements of Li atoms increase abruptly, indicating a superionic transition. For the Te/Se anions, similar discontinuities occur at slightly lower temperatures. Difference Fourier syntheses reveal strongly anisotropic Li spatial distribution density around the 8c (¼ ¼ ¼) positions of cubic site symmetry m3¯m. Moving the maximum of the density distribution to adjacent 32f (xxx) (site symmetry .3 m) positions introduces four virtual split atoms. In addition to the small displacement x along 〈111〉, denoting the mean positions of the split atoms, anisotropic spatial distributions may then be refined. Whereas x deviates from ¼ as an almost linear function of temperature, the abrupt changes in the increase of mean square amplitudes of thermal displacements with temperature are retained. Significantly improved profile refinement residuals support this flexible structure model. Temperature-dependent joint probability density function maps demonstrate the increasing delocalization of Li atoms and yield potential energy distributions, i.e. the energy barriers of ionic transport. The potential barrier between adjacent Li positions at the octahedral site at (½ ½ ½) shows an abrupt drop at the superionic phase transition temperature. The derivative of the potentials, i.e. the restoring forces of Li atom motions show clear deviations from linearity. The anharmonicity of thermally excited spatial atomic distribution refined using the Gram-Charlier series expansion with third- and fourth-order tensor components confirms the enhanced thermal motion in the high-temperature regime. The overall cubic crystal symmetry is maintained.