Debye Method Research Articles

Thermodynamic properties of titanium-manganite LaСаTiMnO6

By the method of dynamic calorimetry in the range of 298.15-673 K, the heat capacity of titanium-manganite LaСаTiMnO6, obtained by solid-phase interaction at 800-1200oC from lanthanum, titanium (II), manganese (III) and calcium carbonate oxides was studied. On the dependence curve Ср°~¦(T) in the specified temperature range, a λ-shaped effect was detected at 598 K, probably related to the phase transition of the second kind. A fundamental constant is determined — the standard heat capacity of LaСаTiMnO6, equal to 221±14 J /(mol×K). Its standard entropy, equal to 206±6 J/(mol×K), was estimated by the approximate method of ion increments. Based on experimental data, taking into account the temperature of the phase transition, the equations describing the temperature dependences of Ср°~¦(T) and the thermodynamic functions So (T), Ho (T) — Ho (298.15) and Фхх(Т) of the investigated titanium-manganite lanthanum and calcium are calculated. The standard heat capacity of LaСаTiMnO6 is also calculated using the Debye method, the value of which is in good agreement with experimental data. According to the developed methodology, the standard enthalpy of titanium-manganite formation was calculated, equal to — 3867.5 kJ/mol.

Heat Capacity and Thermodynamic Functions of Titanium-Manganites of Lanthanum, Lithium and Sodium of LaLi2TiMnO6 and LaNa2TiMnO6.

Titanium-manganites of LaLi2TiMnO6 and LaNa2TiMnO6 were synthesized by the methods of ceramic technology from the oxides of lanthanum, titanium (IV), manganese (III), and the carbonates of lithium and sodium. The types of their syngony and the parameters of their gratings were determined radiographically. The isobaric heat capacities of titanium-manganites were measured with experimental calorimetry in the range of 298.15-673 K. It was found that on the dependence curve of heat capacity versus temperature of C°p~f(T), for LaLi2TiMnO6 at 348 K and 598 K, and LaNa2TiMnO6 at 348 K, there are abnormal jumps in heat capacity, probably related to phase transitions of the second kind. Taking into account the temperatures of the phase transitions, the equations of the temperature dependence of the heat capacity of titanium-manganites were derived. Their standard entropies were calculated by the ion increments method. Temperature dependences of the thermodynamic functions of S°(T), H°(T)-H°(298.15), and Φxx(T) were calculated using the experimental data on heat capacities and the calculated values of the standard entropies. The standard heat capacities of the studied compounds were calculated by the independent methods of ion increments and Debye, the values of which were in satisfactory agreement with the experimental data. The standard enthalpy of the formation of LaLi2TiMnO6 and LaNa2TiMnO6 was calculated according to the methodology developed by the authors. The conducted electrophysical studies determined the nature of the second-order phase transition and the semiconductor features of their conductivity. Thus, all the above-mentioned data on the experimental and calculated studies of the temperature dependence of heat capacity, the thermodynamic functions to determine a standard enthalpy of formation of LaLi2TiMnO6 and LaNa2TiMnO6, and the investigation of their electrical properties are absolutely new, and they have no analogues.

Electronic structure, elastic and thermodynamic properties of SnS from theoretical study

In this work, first-principles methods based on density functional theory are used to study the structural, electronic and elastic properties of rock-salt SnS in detail. Thermodynamic properties of SnS under high temperature and high pressure were studied by using the quasi-harmonic Debye model. The results show that the optimized structural parameters are in good agreement with the experimental and other theoretical values. The band structure and density of states of SnS are obtained by calculation and analysis. Based on the quasi-harmonic Debye method, the pressure and temperature dependencies of the equilibrium volume, the bulk modulus, the Debye temperature and so on are obtained.

Theoretical study on the tendency of heat capacity of nanostructures using modified Debye's method

ABSTRACT As one of the most important basic properties of thermal physics, the theoretical study of specific heat capacities impacts numerous fields. With the recent rapid discovery of nanomaterials, the specific heat capacity of nanostructures has attracted more and more attention. In recent years, relevant theoretical explanations continue to grow, but it is undeniable that theoretical models have to keep up with the new discoveries. This paper provides new theoretical approaches to properly scrutinise some of these phenomena. Two modified Debye's models are constructed and investigated, based on the assumptions of simple cubic lattice structures and the lattice vibration of structures under low temperatures (1.5–15 K). While the first model focuses on the limited degree of freedom for nanostructures, the second model retains the trend of Debye's model taking into account the sound velocity under the influence of boundary conditions. We further notify that the first model fits well with the experimental data qualitatively and the second one successfully explains the proportional relationship between the heat capacity of nanostructures of various shapes and sizes, respectively. Hence, these two models can form a basis to stimulate further theoretical developments to come.

X-ray Study and Computer Simulation of the Structure of Amorphous-Crystalline Titanite

The structure of amorphous-crystalline titanite obtained by mechanical activation was studied by X-ray diffraction and simulation methods. The short-range order characteristics were calculated using Finbak-Warren's method. It was found that the coordination numbers of metal atoms decreased as the result of titanite grinding. The atomic configurations of short-range order of ground titanite were constructed by translation of titanite unit cell. The theoretical X-ray patterns were calculated using Debye's method and were compared with the experimental curves. The structure of ground titanite in the mill with centrifugal factor 40 g was described satisfactorily by the model of mechanical mixture of clusters containing 2016 atoms, disordered during the molecular dynamics with clusters containing 12096 atoms. The increase of grinding intensity led to the sharp decrease of sizes of small cluster. Keywords: amorphous-crystalline titanite, X-ray diffraction, computer simulation, mechanical activation, Debye's method.

Х-ray Study and Computer Simulation of the Structure of Amorphous-Crystalline Titanite

The structure of amorphous-crystalline titanite obtained by mechanical activation was studied by X-ray diffraction and simulation methods. The short-range order characteristics were calculated using Finbak-Warren's method. It was found that the coordination numbers of metal atoms decreased as the result of titanite grinding. The atomic configurations of short-range order of ground titanite were constructed by translation of titanite unit cell. The theoretical X-ray patterns were calculated using Debye's method and were compared with the experimental curves. The structure of ground titanite in the mill with centrifugal factor 40 g was described satisfactorily by the model of mechanical mixture of clusters containing 2016 atoms, disordered during the molecular dynamics with clusters containing 12096 atoms. The increase of grinding intensity led to the sharp decrease of sizes of small cluster.

The Debye Method is Used to Create 3D Structure Models of Electroactively Transformed Microcrystalline Cellulose

In this paper, we carried out the XRD results and 3D structural models of short-range order of amorphous cellulose obtained by ball milling of microcrystalline cellulose. The amorphous cellulose has the well-reproducible effect of influence of ozone treatment on its proton conductivity, which allows to use this material as a gas sensor. Calculation of the quantitative characteristics of the short-range order (radii of coordination spheres and their dispersions, coordination numbers) of amorphous cellulose was carried out from distribution pair functions curve by using the Finback-Warren method. The space atoms configurations was carried out by Debye method. After that, the models were distorted by converting into packages disoriented relative to each other layers. The X-Ray diffraction patterns were calculated for 3D models and compared with experimental curves.

Physico-Chemical and Molecular Interactions in Sodium Dodecyl Sulfate+Acetamide, Formamide Aqueous Mixtures According to Dielectric Relaxation Spectroscopy Data at 303 K

Investigation of sodium dodecyl sulfate+acetamide, formamide aqueous mixtures of various concentrations has been performed by dielectric relaxation spectroscopy (TDR-time domain reflectometry) technique 303 K. The relaxation times were determined through the Debye method and relative viscosities of solution. The linear increase of relative viscosity has the same increasing trend as dodecyl sulfate concentrations up to 80 mM. The superposition of relaxation time between water and micelle through the rotation phenomena, whereas inside the micelle by hydrophobic phenomena, is found and discussed in light of obtained results and justified.

THE MODIFICATION AND DEVELOPMENT OF THE SPECTROSCOPIC PROPERTIES OF Cs/PVA BLEND INCORPORATED GOLD NANOPARTICLES (AuNPs) PREPARED BY PULSED LASER ABLATION IN LIQUIDS (PLAL)

In the present work, pure gold nanoparticles (AuNPs) were synthesis by pulsed laser ablation technique using Nd:YAG as a source of laser. Then, the prepared AuNPs was used with low concentrations to synthesis nanocomposite films by adding it to chitosan/polyvinyl alcohol (Cs/PVA) blend using the casting method. All peaks of pure AuNPs were recorded by X-ray diffraction with face center cubic (FCC) structure. No peaks of AuNPs were found at low concentrations in the doped nanocomposites because of the complete degradation of AuNPs within Cs/PVA matrix. The intensity of some IR bands was changed due to the chemical interaction between the components. The broad band at 3350 cm−1 was decreased due to the intermolecular interaction. Dielectric constant and dielectric loss were decreased as an increase in the frequency and temperature. The increases of direct conductivity (σdc) imply that the free charge density or of the charge mobility that results. The AuNPs addition assists the charge transfer complex (CTCs) formation in which charge transportation occurs by coulomb forces and electric field. The Cole-Cole plot shows semicircles that supports the relaxation processes were a non‐ Debye method.

THERMODYNAMIC, THERMAL AND ELASTIC PROPERTIES OF TITANIUM NITRIDE TiN: COMPARISON OF VARIOUS DATA AND DETERMINATION OF THE MOST RELIABLE VALUES

The analysis of literary data on thermodynamic, thermal and elastic properties of titanium nitride TiN which included values Debye temperature θD, volume coefficient of thermal expansion αV and bulk modulus B under standard conditions is carried out. It has been shown that the known data have a significant spread of values from 20 to 43 %. The 8 most rational variants of optimizing calculations are proposed, which make it possible to reveal the most reliable values of some TiN parameters. At the same time, the minimum and maximum values of θD and αV were used from literary sources, as well as the least contradictory data on isobaric heat capacity Cp, melting temperature Tm.p and density d of TiN. To improve the calculated results, the values of θD(TiN) determined using the methods of Magnus ‒ Lindeman and Debye were also used. The Mayer’s relation was the basic test expression. The obtained values of the bulk modulus were compared with the literature data. This made it possible to distinguish the least and most reliable values of αV and θD, as well as make a refinement correction for the last value. As a result, it was found that under standard conditions, the value of θD(TiN) close to the optimal should be within 746‒769 K, and for its isochoric heat capacity CV ‒ in the range 36.55‒37.19 J/(mol×K). The range of values, after optimization, does not exceed 3 %, unlike the 20 % available in the literature. A more accurate definition of Debye temperature for TiN needs to radically refine the values of its αV and B

Comparación entre la función de cole-cole y la función de Debye para modelar el tejido biológico

The study of the biological tissue varies its behavior, in function of the frequency to which it is subjected. The functions of Cole-Cole, Debye and Lorentz are considered the most used to study the parameters of conductivity and permittivity of biological tissue such as: liver, stomach, gray matter, pancreas, blood, breast tissue to name a few. Depending on the frequency, there may be three different relaxation times. These depend on the nature and physical characteristics of the tissue and its effect in the presence of an electromagnetic signal. The Cole-Cole function is most appropriate when considering a study in the frequency domain, and the Debye function is established to perform the study in the time domain. It is of particular interest to make a comparison between the methods of Cole-Cole and Debye, to define the advantages and disadvantages of each of them. The Lorentz function is used for frequencies of the Tera-Hertz order. Comparative graphs are obtained between both for the biological tissues mentioned above. For each of them the electrical parameters are calculated in a frequency range between 100 Hz and 10 GHz.

Polarity of selected derivatives of diselenophosphinic acid

Polarity of diselenophosphinates in benzene solution has been determined by second Debye method. We suggest that these compounds exist as a mixture of several conformers with cis and gauche arrangement of substituents at the phosphorus atom with respect to the P=Se bond.

An approach to improve energy performance of electric vehicle: Theoretical evaluation of electric motor winding heat capacity and electrical resistivity using Debye and Bloch-Gruneisen approximations

New analytical accurate approximations to the evaluation temperature dependence of heat capacity and electrical resistivity of motor winding are presented. The approach is based on the Debye method and Bloch-Gruneisen theory for controlling the heat capacity and electrical resistivity of motor winding with variation of temperature. This analytical evaluation is general and it shows that the results of motor winding heat capacity and resistivity are satisfactory for the wide range temperature variations. Comparison of the calculation results with the other literature data show that our approach is accurate and efficient.

Stability-limit ⿿Ouzo region⿿ boundaries for poly(lactide-co-glycolide) nanoparticles prepared by nanoprecipitation

The introduction of ⿿Ouzo diagrams⿿ has enhanced the applicability of the basic nanoprecipitation process for drug delivery research. The current study investigated the interaction of two relevant polymer/solvent systems, which is thought to impact the location of the stability⿿limit ⿿Ouzo boundary⿿.Viscosity measurements (Kurata⿿Stockmayer⿿Fixman approach) and static light scattering (Debye method) underlined a distinct interplay of the employed polymer (poly(lactide-co-glycolide)) with the utilized organic solvents (acetone and tetrahydrofuran). Both methods indicated that tetrahydrofuran was the ⿿better⿿ solvent for poly(lactide-co-glycolide). Thus, nanoprecipitation of this polymer/solvent composition resulted in larger nanoparticles. This observation can be attributed to the chain configuration of poly(lactide-co-glycolide) in the organic solvent, which influenced the extent of the break-up of the injected solvent layer. Accordingly, the stability⿿limit curve of the ⿿Ouzo region⿿ was shifted to lower poly(lactide-co-glycolide) fractions for tetrahydrofuran.Overall, the location of the ⿿Ouzo region⿿, which is an essential tool for drug delivery research, is influenced by the employed organic solvent. The current study described two distinct methods suitable to identify relevant polymer⿿solvent interactions, which dictate the stability⿿limit ⿿Ouzo boundary⿿ for relevant poly(lactide-co-glycolide).

Study of the properties of liquid crystals modified by nanoparticles

The dielectric anisotropy and the response time of polymer-dispersed liquid-crystal films mixed with various nanoparticles were measured. The different types of nanoparticles used included metallic, dielectric, and biphasic core-shell or Janus type nanoparticles. Two methods were used for the determination of the dielectric anisotropy: a bridge method and a current-voltage method. The dipole moments of the nanoparticles were measured by the method of diluted solutions (Debye method). It was shown that the dielectric anisotropy plays a crucial role in the electro-optical properties of modified liquid crystals which in turn depend on the dipole moment and thus on the physical nature of the introduced nanoparticles.

Extension of the Lorenz–Mie–Debye method for electromagnetic scattering to the time-domain

In this paper, we extend the frequency domain Lorenz–Mie–Debye formalism for the Maxwell equations to the time-domain. In particular, we show that the problem of scattering from a perfectly conducting sphere can be reduced to the solution of two scalar wave equations — one with Dirichlet boundary conditions and the other with Robin boundary conditions. An explicit, stable, and high-order numerical scheme is then developed, based on our earlier treatment of the scalar case. This new representation may provide some insight into transient electromagnetic phenomena, and can also serve as a reference solution for general purpose time-domain software packages.

BCL::SAXS: GPU accelerated Debye method for computation of small angle X-ray scattering profiles.

Small angle X-ray scattering (SAXS) is an experimental technique used for structural characterization of macromolecules in solution. Here, we introduce BCL::SAXS--an algorithm designed to replicate SAXS profiles from rigid protein models at different levels of detail. We first show our derivation of BCL::SAXS and compare our results with the experimental scattering profile of hen egg white lysozyme. Using this protein we show how to generate SAXS profiles representing: (1) complete models, (2) models with approximated side chain coordinates, and (3) models with approximated side chain and loop region coordinates. We evaluated the ability of SAXS profiles to identify a correct protein topology from a non-redundant benchmark set of proteins. We find that complete SAXS profiles can be used to identify the correct protein by receiver operating characteristic (ROC) analysis with an area under the curve (AUC) > 99%. We show how our approximation of loop coordinates between secondary structure elements improves protein recognition by SAχS for protein models without loop regions and side chains. Agreement with SAXS data is a necessary but not sufficient condition for structure determination. We conclude that experimental SAXS data can be used as a filter to exclude protein models with large structural differences from the native.

First-Principles Study of Structural and Thermal of <i>α</i>-Ni<sub>4</sub>N

This paper reports a study on the structure and elastic properties of cubic α-Ni4N by performing first principles calculations within Generalized gradient approximation (GGA). The calculated lattice constant and elastic constants are in good agreement with the available experimental or theoretical value. The thermal properties including the bulk modulus, thermal expansion, Grüneisen parameter and Debye temperature have also been calculated within the quasi-harmonic Debye method.

Dielectric analysis of binary systems of primary diols with 1-hexanol and 1,4-dioxane at various temperatures

Experimental relative permittivity data for polar–polar and polar–nonpolar binary systems of (1,3-propanediol+1-hexanol or 1,4-dioxane) and (1,4-butanediol+1-hexanol or 1,4-dioxane) were obtained as a function of composition at T=(298.15, 308.15, and 318.15)K and p=101.32±0.40kPa. The permittivity deviations were correlated using Redlich–Kister equation for the estimation of the binary coefficients and the standard errors. For the polar–non-polar systems, the permittivity increments become more negative in the order of the mixtures containing 1HA<1,4BD<1,3PD. The molecular dipole moments were determined using Guggenheim–Debye method. The Kirkwood–Frohlich equation was used to evaluate the effective dipole moments of the pure and their binary mixtures. In order to obtain valuable information about intermolecular interactions, the excess parameters such as the excess permittivity and the excess Helmholtz energy were estimated. The obtained data were interpreted in terms of homo- and hetero-interactions and structure of the investigated binary mixtures.

An alternative use of Kieffer’s lattice dynamics model using vibrational density of states for constructing thermodynamic databases

We use Kieffer’s model to represent the vibrational density of states (VDoS) and thermodynamic properties of pure substances in pressure–temperature space. We show that this model can be simplified to a vibrational model in which the VDoS is represented by multiple Einstein frequencies without significant loss of accuracy in thermodynamic properties relative to experimental data. The resulting analytical expressions for thermodynamic properties, including the Gibbs energy, are mathematically simple and easily accommodated in existing computational software for making thermodynamic databases. We show for aluminium, platinum, orthoenstatite and forsterite that thermodynamic properties can be represented with comparable accuracy as with Kieffer’s model with the same number of fitting parameters as in the Mie–Gruneisen–Debye model. We demonstrate that the method enables to achieve thermodynamic properties with superior accuracy relative to the Mie–Gruneisen–Debye method. The method is versatile in the sense that it allows incorporating dispersion of Gruneisen parameters. It is possible to extend the formalism to include other physical effects, such as intrinsic anharmonicity in the same way as in vibrational models based on Kieffer’s formalism.