Einstein Model Research Articles

Nonequilibrium statistical physics beyond the ideal heat bath approximation.

Important models of nonequilibrium statistical physics (NESP) are limited by a commonly used, but often unrecognized, near-equilibrium approximation. Fokker-Planck and Langevin equations, the Einstein and random-flight diffusion models, and the Schnakenberg model of biochemical networks suppose that fluctuations are due to an ideal equilibrium bath. But far from equilibrium, this perfect bath concept does not hold. A more principled approach should derive the rate fluctuations from an underlying dynamical model, rather than assuming a particular form. Here, using maximum caliber as the underlying principle, we derive corrections for NESP processes in an imperfect-but more realistic-environment, corrections which become particularly important for a system driven strongly away from equilibrium. Beyond characterizing a heat bath by the single equilibrium property of its temperature, the bath's speed and size must also be used to characterize the bath's ability to handle fast or large fluctuations.

Electronic structure and anharmonic phonon mode in BaIr2Ge7 with two-dimensional Ba-Ge networks studied by photoemission spectroscopy

We report the electronic structure of ${\mathrm{BaIr}}_{2}{\mathrm{Ge}}_{7}$ with two types of cage structure by means of angle-resolved photoemission spectroscopy (ARPES) and hard x-ray photoemission spectroscopy. ARPES spectra reveal the three-dimensional and multiband Fermi surfaces (FSs) originating from the hybridized Ir $5d$ and Ge $4p$ orbitals. The observed FSs show ${C}_{2}$ symmetry, reflecting the orthorhombic $Ammm$ crystal structure of ${\mathrm{BaIr}}_{2}{\mathrm{Ge}}_{7}$. The temperature dependence of the ARPES spectra exhibits the thermal spectral broadening, and the width of the spectral peak shows a concave-downward behavior with temperature. Considering the effect of anharmonic phonon modes, we have reproduced the temperature dependence of the electrical resistivity as well as the thermal spectral broadening. The resultant renormalized phonon frequencies ${\ensuremath{\omega}}_{\mathrm{r}0}^{(1)}=146.9\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and ${\ensuremath{\omega}}_{\mathrm{r}0}^{(2)}=70.6\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ are comparable to the Einstein temperatures estimated from the previous specific heat measurement. Our results suggest the existence of the weak anharmonic phonon modes in ${\mathrm{BaIr}}_{2}{\mathrm{Ge}}_{7}$.

Einstein's model of "the movement of small particles in a stationary liquid" revisited: finite propagation speed

The aforementioned celebrated model, though a breakthrough in Stochastic processes and a great step toward the construction of the Brownian motion, leads to a paradox: infinite propagation speed and violation of the 2nd law of thermodynamics. We adapt the model by assuming the diffusion matrix is dependent on the concentration of particles, rather than constant it was up to Einstein, and prove a finite propagation speed under the assumption of a qualified decrease of the diffusion for small concentrations. The method involves a nonlinear degenerated parabolic PDE in divergent form, a parabolic Sobolev-type inequality, and the Ladyzhenskaya-Ural'tseva iteration lemma.

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.

Thermal Expansion and Rattling Behavior of Gd-Filled Co4Sb12 Skutterudite Determined by High-Resolution Synchrotron X-ray Diffraction.

In this work, Gd-filled skutterudite GdxCo4Sb12 was prepared using one step method under high pressure in a piston-cylinder-based press at 3.5 GPa and moderate temperature of 800 °C. A detailed structural characterization was performed using synchrotron X-ray diffraction (SXRD), revealing a filling fraction of x = 0.033(2) and an average <Gd-Sb> bond length of 3.3499(3) Å. The lattice thermal expansion accessed via temperature-dependent SXRD led to a precise determination of a Debye temperature of 322(3) K, from the fitting of the unit-cell volume expansion using the second order Grüneisen approximation. This parameter, when evaluated through the mean square displacements of Co and Sb, displayed a value of 265(2) K, meaning that the application of the harmonic Debye theory underestimates the Debye temperature in skutterudites. Regarding the Gd atom, its intrinsic disorder value was ~5× and ~25× higher than those of the Co and Sb, respectively, denoting that Gd has a strong rattling behavior with an Einstein temperature of θE = 67(2) K. As a result, an ultra-low thermal conductivity of 0.89 W/m·K at 773 K was obtained, leading to a thermoelectric efficiency zT of 0.5 at 673 K.

The Point of Primitive Ontology

Bohmian mechanics grounds the predictions of quantum mechanics in precise dynamical laws for a primitive ontology of point particles. In an appraisal of the de-Broglie-Bohm theory, the paper discusses the crucial epistemological and conceptual role that a primitive ontology plays within a physical theory. It argues that quantum theories without primitive ontology fail to make contact with observable reality in a clear and consistent manner. Finally, it discusses Einstein's epistemological model and why it supports the primitive ontology approach.

Halide-sodalites: thermal behavior at low temperatures and local deviations from the average structure

Abstract Sodalites of the general type |Na8X2|[T1T2O4]6 with X = Cl−, Br−, I− have been synthesized for Al–Si, Ga–Si, Al–Ge and Ga–Ge as T1–T2 frameworks. The structures were examined using in-house and synchrotron X-ray diffraction, Raman spectroscopy, force-field structure optimizations and DFT based ab-initio molecular dynamics (MD) computations. Calculated phonon density of states (PDOS) of the 12 compounds show only minor differences within a framework composition with a lowering of certain phonon energies with increasing anion size. Earlier published Debye and Einstein temperatures obtained with a Debye-Einstein-anharmonicity (DEA) model approach are confirmed using the determined low-temperature lattice parameters (18 K–293 K) and show no correlation with the respective PDOS. Small-box refinements against radial pair distribution functions (PDF) allowed the determination of anisotropic displacement ellipsoids (ADP) for Na+ and O2−, indicating a strong dependency of the ADP of Na+ on the chemical composition. Significantly lower thermal displacements from MD calculations suggested an influence of structural displacements. For compounds with an aspherical ADP for sodium, structural models could be refined in which the sodium is located on two 8e or one 24i site (both partially occupied), and also temperature-dependent (100 K–300 K) for the compounds with Ga–Ge framework. 3D-plots of the bond-valence sums of Na+ further validate the structural differences. These results imply that the local structure of halide-sodalites in many cases is not best described by the known average structure and may even not be cubic.

Self-Organization of Fullerene Derivatives in Solutions and Biological Cells Studied by Pulsed Field Gradient NMR.

Fullerene derivatives are of great interest in various fields of science and technology. Fullerene derivatives are known to have pronounced anticancer and antiviral activity. They have antibacterial properties. Their properties are largely determined by association processes. Understanding the nature and properties of associates in solvents of various types will make it possible to make significant progress in understanding the mechanisms of aggregation of molecules of fullerene derivatives in solutions. Thus, this work, aimed at studying the size and stability of associates, is relevant and promising for further research. The NMR method in a pulsed field gradient was used, which makes it possible to directly study the translational mobility of molecules. The sizes of individual molecules and associates were calculated based on the Stokes-Einstein model. The lifetime of associates was also estimated. The interaction of water-soluble C60 fullerene derivatives with erythrocytes was also evaluated. The values of self-diffusion coefficients and the lifetime of molecules of their compounds in cell membranes are obtained. It is concluded that the molecules of fullerene derivatives are fixed on the cell surface, and their forward movement is controlled by lateral diffusion.

Terahertz tyrosine modes

We have measured the terahertz spectrum of pure l-tyrosine at nineteen temperatures in the range 6K to 300K using a synchrotron as the source of radiation. By fitting the temperature dependence of the observed modes with a Bose–Einstein model, we determine unequivocal low-frequency modes of l-tyrosine at absolute zero temperature occur at 1.02 ± 0.01, 1.61 ± 0.01, 1.97 ± 0.01, and 2.19 ± 0.01THz. This determination is consistent with the more reliable of the earlier measurements. We conclude that many of the recently reported features in the terahertz spectrum of l-tyrosine are experimental artefacts.

Evaluation of Temperature Variation in the Debye-Waller Factor for Single Crystalline Bulk Silicon Germanium by XAFS

1. Background and purpose Silicon germanium (SiGe) is expected as a next-generation electronic and thermoelectric device materials because of its higher carrier mobility than Si and lower thermal conductivity than Si and Ge. Therefore, it is important to understand the carrier scattering and phonon transport properties in order to apply SiGe as a device. We have reported that the atomic vibration in Si-rich SiGe thin films on Si substrates may be suppressed by the lattice strain, based on X-ray absorption fine structure (XAFS) measurements [1]. In this study, we demonstrated XAFS spectra of strain-free single crystalline bulk SiGe and estimated the Einstein temperature (T E) which characterizes phonons, to investigate the influence of Ge fraction and lattice strain in SiGe at nanoscale. 2. Experimental method Strain-free single crystalline bulk SiGe were grown by the traveling liquidus zone method with Ge fractions of 32 and 45 % [2]. We measured the XAFS spectra of the Ge-K absorption edge for the bulk SiGe in the transmission mode at BL14B2 in the SPring-8 synchrotron facility. We also measured a single crystalline bulk Ge as a reference sample. The sample temperature was controlled between 10 - 600 K using a refrigerator or a heating cell during measurements. Then, we extracted the EXAFS oscillations from the obtained XAFS spectra in order to investigate the temperature variation of the Debye-Waller factor. 3. Results and discussion Figure 1 shows the temperature dependence of the change in the Debye-Waller factor with reference to 10 K (Δσ 2) for Ge, SiGe thin films, and bulk SiGe. From Fig. 1, the change in Δσ 2 with temperature is slower for SiGe than for Ge. The effect of Ge fraction on the change in Δσ 2 is negligible. Further, the changes in Δσ 2 with temperature for SiGe were similar regardless of the lattice strain. Therefore, it is confirmed that the Ge fraction and the lattice strain in SiGe have little effect on the atomic vibration.Here, since σ 2 is expressed by Eq. (1) [3], Δσ 2 can be expressed as Eq. (2), where T is the absolute temperature, σ s 2 is the static Debye-Waller factor, A is a constant, and T E is the Einstein temperature. σ 2(T) = σ s 2 + Acoth(T E / 2T), (1)Δσ 2(T) = A[coth(T E / 2T) – coth{T E / (2 × 10)}], (2)The relationship between T E and the Ge fraction obtained from Eq. (2) is shown in Fig. 2. Figure. 2 indicates that T E decreases with increasing Ge fraction in Si-rich SiGe, suggesting that phonons are easily excited in SiGe with a high Ge fraction. Thus, it is considered that the effect of Ge fraction on atomic vibration in SiGe is much larger than their inner strains. 4. Acknowledgment The XAFS measurements were performed at BL14B2 in SPring-8, approved by JASRI, under proposal numbers 2019A1773, 2019B1802, and 2021A1661.

A description of the thermodynamic properties of pure indium in the solid and liquid states from 0 K

Thermodynamic data for the crystalline phase of indium were critically assessed using an extended Einstein model from 0 K. The heat capacity between 6 K and 354 K was measured using an automated vacuum adiabatic calorimeter to compensate for a lack of published data between 21 K and 273 K. Data for the liquid phase were described using a two state model. During the assessment, careful analysis of the experimental data was carried out. In order to derive a precise value for So298 an additional technique using multiple Einstein functions was used, which allows the experimental heat capacity and enthalpy data for the solid phase to be approximated accurately from 0 K up to the melting point.

Comprehensive experimental investigations and theoretical predictions on the physical properties of natural rubber composites

AbstractConducting elastomers are highly desirable in the present world because of their major applications in the electronic industry. Conductive carbon black (CCB) is a conventional reinforcing filler commonly used in elastomers to modify the mechanical as well as electrical properties. The present study focuses on the experimental and theoretical computation of filler reinforcement, dielectric, mechanical, dynamic mechanical, and surface morphology of natural rubber (NR)/CCB composites. Two step processing method is adopted to attain homogeneous dispersion of filler in the matrix: preparation of NR/CCB masterbatch through melt mixing using internal mixer followed by compounding in a two‐ roll mill. Improved DC conductivity in the order of 10−6was obtained at higher filler loading indicating the formation of a continuous conductive network in the matrix. Percolation threshold was computed using Power law equation and obtained a value of 0.154 vol%. Theoretical predictions of mechanical modulus and tensile strength were done using rule of mixtures, Einstein, Guth and Kerner models and Nicolais‐Narkis and Kuneri‐Geil models respectively. A remarkable change in tensile strength is observed for NR as a function of the weight percentage of CCB; it is increased to 26.3 ± 0.9 MPa at 20 phr CCB from 17.1 ± 0.9 MPa for NR.

An extended Stokes–Einstein model for condensed ionic water structures with topological complexity

‘What is the structure of water?’ This has been a perplexing question for a long time and water structure with various phases is a great topic of research interest. Topological complexity generally occurs because hydrophilic ions strongly influence the size and shape of condensed water structures owing to their kosmotropic and chaotropic transitions. In this study, an extended Stokes–Einstein model incorporating Flory–Huggins free energy equation is proposed to describe the constitutive relationship between dynamic diffusion and condensed water structure with a topological complexity. The newly developed model provides a geometrical strategy of end-to-end distance and explores the constitutive relationship between condensed ionic water structures and their dynamic diffusion behaviors. A free-energy function is then formulated to study thermodynamics in electrolyte aqueous solution, in which the condensed ionic water structures undergo topologically complex changes. Finally, effectiveness of the proposed model is verified using both molecular dynamics simulations and experimental results reported in literature.

Computational study of the effect of different doping elements on the thermal conduction properties of graphene nanoribbons

The dopant's atoms of various elements can be incorporated into the crystal lattice of graphene for the purpose of modulating its structural, optical and electrical properties. While the dopant's presence negatively affects the thermal conductivity, the exact effect of doping is still poorly understood and the mechanisms involved remain obscure. The effect of different doping elements on the thermal conductivity of graphene ribbons was investigated by performing molecular dynamics simulations to understand how impurities affect the thermal conduction properties of the nanostructured material. Graphene ribbons were doped with silicon, boron, or nitrogen elements to modify their nanostructure and thermal properties. The importance of edge structure was evaluated in comparison with that of doping. The Callaway model and the Einstein's model were used to provide the theoretical upper and lower bounds on the thermal conductivity. The contribution of optical phonons at different temperatures was evaluated in order to further understand the microscopic mechanisms of thermal conduction in the two-dimensional doped crystal. A computational analysis of thermal behavior was carried out in terms of the maximum density of states. The results indicated that a small number of dopant atoms can greatly change the ability to conduct heat. The thermal conductivity of the doped nanomaterial decreases successively in the order of nitrogen, boron, and silicon. Acoustical phonons still dominate the thermal conduction in the doped crystal, but the contribution of optical phonons become larger, especially at higher temperatures. The contribution of phonons in the optical branches increases with the doping concentration and can be as large as 6.0 %. In the presence of doping, the edge structure does not significantly affect the thermal conductivity and the maximum density of states. When graphene is heavily doped, the effect of ribbon length is insignificant while doping becomes dominant. The results have significant implications for the understanding of the relations between doping elements and thermal conduction properties.

Extending quantum anharmonic correlated Einstein model in studies of anharmonic EXAFS Debye–Waller factor of BCC structure metals

Extending quantum anharmonic correlated Einstein model in studies of anharmonic EXAFS Debye–Waller factor of BCC structure metals

Thermodynamic Properties and Equation of State for Solid and Liquid Aluminum

High-temperature equations of state for solid and liquid aluminum were constructed herein using experimental data on thermodynamic properties, thermal expansion, compressibility, bulk modulus and sound velocity measurements, supplemented with phase diagram data (melting curve). The entire set of experimental data was optimized using the temperature-dependent Tait equation over a pressure range of up to 800 kbar and over a temperature range from 20 K to the melting point for solid aluminum and to 3800 K for liquid aluminum. The temperature dependence of thermodynamic and thermophysical parameters was described by an expanded Einstein model. The resultant equations of state describe well the totality of experimental data within measurement errors of individual variables.

Generalization on Entropy-Ruled Charge and Energy Transport for Organic Solids and Biomolecular Aggregates.

Herein, a generalized version of the entropy-ruled charge and energy transport mechanism for organic solids and biomolecular aggregates is presented. The effects of thermal disorder and electric field on electronic transport in molecular solids have been quantified by entropy, which eventually varies with respect to the typical disorder (static or dynamic). Based on our previous differential entropy (hs)-driven charge transport method, we explore the nonsteady carrier energy flux principle for soft matter systems from small organic solids to macrobiomolecular aggregates. Through this principle, the synergic nature of charge and energy transport in different organic systems is addressed. In this work, entropy is the key parameter to classify whether the carrier dynamics is in a nonsteady or steady state. Besides that, we also propose the formulation for unifying the hopping and band transport, which provides the relaxation time–hopping rate relation and the relaxation time–effective mass ratio. The calculated disorder drift time (or entropy-weighted carrier drift time) for hole transport in an alkyl-substituted triphenylamine (TPA) molecular device is 9.3 × 10–7 s, which illustrates nuclear dynamics-coupled charge transfer kinetics. The existence of nonequilibrium transport is anticipated while the carrier dynamics is in the nonsteady state, which is further examined from the rate of traversing potential in octupolar molecules. Our entropy-ruled Einstein model connects the adiabatic band and nonadiabatic hopping transport mechanisms. The logarithmic current density at different electric field-assisted site energy differences provides information about the typical transport (whether trap-free diffusion or trap-assisted recombination) in molecular devices, which reflects in the Navamani–Shockley diode equation.

Anharmonic extended X-ray absorption fine structure Debye-Waller factor of diatomic bromine

In this work, the anharmonic extended X-ray absorption fine structure Debye-Waller factor of diatomic bromine has been analyzed in the temperature-dependent. The amplitude reduction and phase shift of the extended x-ray absorption fine structure oscillation are presented in terms of the Debye-Waller factor using the cumulant expansion approach. The temperature-dependent extended X-ray absorption fine structure cumulants are calculated based on the quantum anharmonic correlated Einstein model. The obtained numerical results are in good agreement with those obtained from the experimental extended X-ray absorption fine structure data and other theoretical approaches at various temperatures. These results show that the present theoretical model is useful for analyzing the experimental extended X-ray absorption fine structure signals of diatomic bromine and other molecules.

Heat Capacity of Layered Perovskite Compounds: EsBaCuFeO 5 (Es = Ho, Gd, and Yb)

The layered perovskite compounds, which show multiferroic properties, have attracted interest due to their interesting magnetic and electronic properties. In this study, we have investigated the heat capacity of EsBaCuFeO5 (Es = Ho, Gd and Yb) as a function of the temperature by using the overall equation of fitting. The Debye temperature, Einstein temperature, the coefficients m and γ have been derived by fitting experimental heat capacity data with the overall equation of fitting that consist of the contribution from electronic, Debye and Einstein terms. The values of the fitting parameters obtained are in good agreement with the results in the literature. The results display that the method can be used for calculation of the heat capacity of the layered perovskite compounds over the entire range of temperature. This article is protected by copyright. All rights reserved.

Photoconductivity study of Ca2Si epitaxial film on Si(111) substrate

Semiconductor calcium semi-silicide (Ca2Si) with a complex crystal and energy band structure is theoretically characterized by a direct fundamental transition, which is difficult to identify experimentally in Ca2Si films due to high absorption at defect levels. The study of the temperature dependences of photoconductivity in Ca2Si epitaxial films is one of the methods for assessing both the nature of the fundamental transition and a number of thermodynamic parameters. In this work, photoconductivity was firstly observed in an epitaxial Ca2Si film grown on a Si(111) substrate in the temperature range from 10 K to 300 K. Based on an analysis of the parameters of three thermodynamic models, the existence of a direct fundamental transition Eg = 1.195 eV at 0 K was proved, and the effective phonon energy (<Eph>), the Einstein (Ξ) and Debye (ΘD) temperatures, as well as the electron-phonon coupling constant, and the hole mobility were determined.