Non-Debye Relaxations: The Ups and Downs of the Stretched Exponential vs. Mittag–Leffler’s Matchings

Experimental data collected to provide us with information on the course of dielectric relaxation phenomena are obtained according to two distinct schemes: one can measure either the time decay of depolarization current or use methods of the broadband dielectric spectroscopy. Both sets of data are usually fitted by time or frequency dependent functions which, in turn, may be analytically transformed among themselves using the Laplace transform. This leads to the question on comparability of results obtained using just mentioned experimental procedures. If we would like to do that in the time domain we have to go beyond widely accepted Kohlrausch–Williams–Watts approximation and become acquainted with description using the Mittag–Leffler functions. To convince the reader that the latter is not difficult to understand we propose to look at the problem from the point of view of objects which appear in the stochastic processes approach to relaxation. These are the characteristic exponents which are read out from the standard non-Debye frequency dependent patterns. Characteristic functions appear to be expressed in terms of elementary functions whose asymptotics is simple. This opens new possibility to compare behavior of functions used to describe non-Debye relaxations. It turnes out that the use of Mittag-Leffler function proves very convenient for such a comparison.

EXAFS Debye-Waller Factors of B2-FeAl Alloys

This work develops the anharmonic correlated Debye model to study the temperature-dependent extended X-ray absorption fine structure (EXAFS) Debye-Waller factors (DWFs) of B2-FeAl alloys. We derived the analytical expressions of the EXAFS DWF and Debye frequency as functions of temperature. Numerical calculations were performed for Fe1-yAly alloys with various Al concentration (y = 0.35, 0.40, 0.45 and 0.50) in which Fe-Al alloys still maintained B2 structure. The good agreement between our theoretical results with previous data verifies our developed theory. Our calculations show that DWFs of Fe1-yAly alloys increase robustly when temperature and/or Al concentration in Fe1-yAly alloys increase. The increasing of DWF will cause the reduction of the amplitude of EXAFS.

Nonadiabatic superconductivity in a Li-intercalated hexagonal boron nitride bilayer

When considering a Li-intercalated hexagonal boron nitride bilayer (Li-hBN), the vertex corrections of electron–phonon interaction cannot be omitted. This is evidenced by the very high value of the ratio λωD/εF ≈ 0.46, where λ is the electron–phonon coupling constant, ωD is the Debye frequency, and εF represents the Fermi energy. Due to nonadiabatic effects, the phonon–induced superconducting state in Li-hBN is characterized by much lower values of the critical temperature (T LOVC C ∈ {19.1, 15.5, 11.8} K, for μ* ∈ {0.1, 0.14, 0.2}, respectively) than would result from calculations not taking this effect into account (T ME C∈ {31.9, 26.9, 21} K). From the technological point of view, the low value of T C limits the possible applications of Li-hBN. The calculations were carried out under the classic Migdal–Eliashberg formalism (ME) and the Eliashberg theory with lowest-order vertex corrections (LOVC). We show that the vertex corrections of higher order (λ3) lower the value of T LOVC C by a few percent.

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.

A Lattice Dynamical Approach for Finding the Lithium Superionic Conductor Li3ErI6

<p>Driven by the increasing attention that the superionic conductors Li₃MX₆ (M = Y, Er, In, La; X = Cl, Br, I) have gained recently for the use of solid-state batteries, and the idea that a softer, more polarizable anion sublattice is beneficial for ionic transport, here we report Li₃ErI₆, the first experimentally-obtained iodine-based compound within this material system of ionic conductors. Using a combination of synchrotron and neutron diffraction, we elucidate the structure, the lithium positions and possible diffusion pathways of Li₃ErI₆. Temperature-dependent impedance spectroscopy shows low activation energies of 0.37 and 0.38 eV alongside promising ionic conductivities of 0.65 mS·cm^-1 and 0.39 mS·cm^-1directly after ball milling and the subsequently annealed Li₃ErI₆, respectively. Speed of sound measurements are used to determine the Debye frequency of the lattice as a descriptor of the lattice dynamics and overall lattice softness, and Li₃ErI₆ is compared to the known material Li₃ErCl₆. The softer, more polarizable framework from the iodide anion leads to improved ionic transport, showing that the idea of softer lattices holds up in this class of materials. This work provides Li₃ErI₆ as an interesting novel framework for optimization in the class of halide-based ionic conductors.</p>

A Lattice Dynamical Approach for Finding the Lithium Superionic Conductor Li3ErI6

<p>Driven by the increasing attention that the superionic conductors Li₃MX₆ (M = Y, Er, In, La; X = Cl, Br, I) have gained recently for the use of solid-state batteries, and the idea that a softer, more polarizable anion sublattice is beneficial for ionic transport, here we report Li₃ErI₆, the first experimentally-obtained iodine-based compound within this material system of ionic conductors. Using a combination of synchrotron and neutron diffraction, we elucidate the structure, the lithium positions and possible diffusion pathways of Li₃ErI₆. Temperature-dependent impedance spectroscopy shows low activation energies of 0.37 and 0.38 eV alongside promising ionic conductivities of 0.65 mS·cm^-1 and 0.39 mS·cm^-1directly after ball milling and the subsequently annealed Li₃ErI₆, respectively. Speed of sound measurements are used to determine the Debye frequency of the lattice as a descriptor of the lattice dynamics and overall lattice softness, and Li₃ErI₆ is compared to the known material Li₃ErCl₆. The softer, more polarizable framework from the iodide anion leads to improved ionic transport, showing that the idea of softer lattices holds up in this class of materials. This work provides Li₃ErI₆ as an interesting novel framework for optimization in the class of halide-based ionic conductors.</p>

Conclusive Research Design and Development of the Effect of Linear Deformation on Some Debye Properties of Metals

This Work, Debye Temperature And Debye Frequency Of Metals Were Computed And Studied Using Quantum Einstein Theory. The Electron Density Parameters Of Strained Metals Is Obtained And Used In The Computation.. The Results Obtained Revealed That There Is Agreement Between The Computed And Experimental Values Of Debye Temperature And Debye Frequency. This Shows That The Model Can Be Used To Study Debye Properties Of Metals. The Debye Temperature And Debye Frequency Obtained Are More Concentrated In The High Density Limit. This Revealed That Debye Temperature And Debye Frequency Of Metals Depend On The Electronic Concentration. Also, The Experimental Value Of Debye Temperature And Debye Frequency Is Higher Than The Computed Value, This Is Because Of Some Factor Which Debye Temperature And Debye Frequency Relied On That The Theory Failed To Account For. Debye Temperature And Debye Frequency Of Metals Reduces As Strain Increase. This Shows That As Strain Increase, Space Between Lattice Atom Increase Which Reduces Strength Of Electron Interaction And There-By Forces Debye Temperature, Debye Frequency To Decrease As Deformation Increase. This Behavior Of Metals Reveal That Debye Temperature And Debye Frequency Is Greatly Affected By Deformation.

Melting temperature depression due to the electronic spin transition of iron

The electronic spin transition of iron has been shown to strongly affect many thermoelastic properties of the host mineral. However, the response of melting temperatures to the spin transition remains largely unexplored. Here, we study the melting of lower mantle minerals, ferropericlase and bridgmanite, using Lindemann's Law. This empirical law predicts a negligible melting temperature depression for Earth-relevant bridgmanite but a substantial depression for Earth-relevant ferropericlase across the spin transition of iron, consistent with extant experimental results. This melting depression can be explained within the framework of Lindemann's Law for a Debye-like solid. The transition of iron from high- to low-spin configuration reduces the molar volume and the bulk modulus of the crystal, leading to a decrease in Debye frequency and consequently lowering the melting temperature. Thermodynamically, the melting depression likely derives from a more negative Margules parameter for a liquid mixture of high- and low-spin end-members as compared to that of a solid mixture. This melting depression across the spin transition of iron may be the process responsible for the formation of a deep molten layer during the crystallization of a magma ocean in the past, and a reduced viscosity layer at present.