Debye Characteristic Temperature Research Articles

Effect of Phosphorus Substitution in the Cyclopentadienyl Ring of Ferrocene: Combined Mössbauer Spectroscopy and DFT Studies

A series of phosphaferrocenes with different numbers of phosphorus atoms and phenyl groups in the cyclopentadienyl ring were successfully synthesized and studied by Mössbauer spectroscopy. Revealed Mössbauer hyperfine parameters are in line with density functional theory (DFT) calculations. It was found that substitution of CH-units by phosphorus atoms in the cyclopentadienyl ring affects the population of the molecular orbitals related to iron. These changes influence on Mössbauer hyperfine parameters, especially on the quadrupole splitting values. Intermolecular vibrations were analyzed in terms of the Debye model of solids based on the temperature dependence of Mössbauer absorption. The characteristic lattice Debye temperatures and the intermolecular force constants were calculated for each studied sample.

Magnetic and electric hyperfine parameters of antiferromagnet FеBO3 intended for monochromatization of synchrotron radiation

In this work, Mössbauer spectroscopy and X-ray diffraction were used to determine the precision values of the hyperfine interaction parameters and the crystal structure of FeBO3 single crystals in a wide temperature range, including the region of magnetic phase transitions (TN). A theoretical model has been developed to describe nuclear resonance transitions in iron atoms in the approximation of a combined magnetic dipole and electric quadrupole hyperfine interaction. A technique for correcting the Mössbauer spectra, considering the effective thickness of the absorber, has also been elaborated.It is shown that the appearance of two additional resonance lines in the hyperfine structure significantly affects the shape of the FeBO3 spectra near the N é el temperature (ТN). The characteristic Debye temperatures for Fe and B cations in the iron borate structure have been determined. The developed technique and the results obtained are extremely important for the use of FeBO3 crystals in new high-tech branches of science and technology, including optoelectronics and synchrotron technologies.

Crystal structure of bismuth-containing NdFe3(BO3)4 in the temperature range 20-500 K.

Neodymium iron borate NdFe3(BO3)4 is an intensively studied multiferroic with high electric polarization values controlled by a magnetic field. It is characterized by a large quadratic magnetoelectric effect, rigidity in the base plane and a rather strong piezoelectric effect. In this work, the atomic structure of (Nd0.91Bi0.09)Fe3(BO3)4 was studied by single-crystal X-ray diffraction in the temperature range 20-500 K (space group R32, Z= 3). The Bi atoms found in the composition partially substitute the Nd atoms in the 3a position; they entered the structure due to the growth conditions in the presence of Bi2Mo3O12. It was shown that in the temperature range 20-500 K there is no structural phase transition R32→P3121, which occurs in rare-earth iron borates (RE= Eu-Er, Y) with an effective rare-earth cation radius smaller than that of Nd. The temperature dependence of the unit-cell c parameter reveals a slight increase on cooling below 90 K, which is similar to the results obtained previously for iron borates of Gd, Y and Ho. The atomic distances (Nd,Bi)-O, (Nd,Bi)-B, (Nd,Bi)-Fe, Fe-O, Fe-B and Fe-Fe in the iron chains and between chains decrease steadily with decreasing temperature from 500 to 90 K, whereas the B1(3b)-O distance does not change and the average B2(9e)-O distance increases slightly. There is a uniform decrease in the atomic displacement parameters with decreasing temperature, with a more pronounced decrease for the Nd(3a) and O2(9e) atoms. The O2(9e) atoms are characterized by the maximum atomic displacement parameters and the most elongated atomic displacement ellipsoids. The characteristic Debye and Einstein temperatures, and the static component in the atomic displacements were determined for cations using multi-temperature diffraction data. It was shown that the Nd cations have the weakest bonds with the surrounding atoms and the B cations have the strongest.

Heat capacity, entropy, formation energy and spin-fluctuation behavior of U3Si5 from 2.4 to 397.4 K

• Heat capacity data of U3Si5 were obtained using a Quantum Design Physical Properties Measurement System (PPMS) from 2.4 to 397.4 K. • An upturn characteristic of spin-fluctuations in Cp/T (T) was observed below 10 K. • The Gibbs free energy of formation of U3Si5 from the elements was determined to be –45.2 ± 9.0 kJ•mol−1•atom−1. U-Si intermetallic compounds are of considerable interest for their applications as accident-tolerant nuclear fuels. Here we present low-temperature heat capacity (LTHC) measurements of one of the U-Si phases, U 3 Si 5 , using a Quantum Design Physical Properties Measurement System (PPMS) from 2.4 to 397.4 K. We observed an upturn in C p /T (T) below 10 K and have attributed this behavior to potential spin-fluctuations (SF) with an SF temperature (T sf ) of 27 K. An enhancement of LTHC was also observed, as manifested by a large electronic heat capacity coefficient (γ el ) of 342.9 mJ/mol•K 2 . From the heat capacity data, the following thermodynamic parameters were determined: the characteristic Debye temperature ( θ D ) over the temperature range 30 – 397 K is 177 ± 2 K, and the standard entropy ( Δ 0 298 . 15 S ∘ ) is 283.3 ± 5.7 J•mol −1 •K −1 (equivalent to 35.4 ± 0.7 J•mol −1 •atom −1 •K −1 ). Combined with our previously measured formation enthalpy ( Δ f H e l ∘ ) of U 3 Si 5 , the Gibbs free energy of formation of U 3 Si 5 from the elements ( Δ f G e l ∘ ) was determined to be –45.2 ± 9.0 kJ•mol −1 •atom −1 .

Low-temperature heat capacity and thermodynamic functions of thulium and lutetium titanates and Schottky anomaly in Tm2Ti2O7

The temperature dependence of the heat capacity of Tm2Ti2O7 and Lu2Ti2O7 compounds over the range of 4.5–320 K has been researched by adiabatic calorimetry. Based on the experimental data, the basic thermodynamic functions of the compounds over the range of 5–320 K have been determined. Tm2Ti2O7 sample has revealed an additional component in the heat capacity associated with the presence of the Schottky anomaly. The temperature dependence behavior of the Debye characteristic temperature of Lu2Ti2O7 sample indicates the absence of anomalies in the heat capacity. Standard thermodynamic functions at 298.15 K are: for Tm2Ti2O7 – Cp,298.15 = 221.0 ± 1.2 J·mol−1·K−1, S298.15 = 261.3 ± 2.4 J·mol−1·K−1, ΔH0298.15 = 39.45 ± 0.29 kJ·mol−1; for Lu2Ti2O7 – Cp,298.15 = 206.9 ± 1.1 J·mol−1·K−1, S298.15 = 229.8 ± 2.2 J·mol−1·K−1, ΔH0298.15 = 35.70 ± 0.26 kJ·mol−1.

Thermal properties of monolayer MoS2 and WS2/MoS2 heterojunction under three strain states

In this paper, the thermal properties of single-layer MoS2 and WS2/MoS2 heterostructure under three strain states are systematically studied. The first-principles calculation method based on density functional theory is used to obtain the phonon dispersion curves and related thermal parameters of crystals. The results show that Van der Waals cleaves phonons only in the vertical direction. The thermal properties of the two crystals are changed by the application of biaxial compressive strain. Taking the monolayer MoS2 as an example, the curves of the heat capacity and the Debye characteristic temperature of the monolayer MoS2 under the three strain states of biaxial tension, biaxial compression and biaxial tension and compression are comprehensively analyzed. It is found that the thermal properties of the crystal will change differently in different strain states. And at high temperatures, the heat capacity is more sensitive to the effect of strain.

Modulation of the Physical Properties of Lead Zirconate by the Stress‐Induced Structural Defects

The influence of the stress‐induced structural defects in PbZrO3 on its structural, optical, and dielectric properties is studied systematically for the first time. The PbZrO3 ceramics is prepared by a conventional solid state synthesis. The structural defects in PbZrO3 are generated by the combined action of mechanical compression due to applied pressure in the 40–320 MPa range and the shear strain appearing in the rotating Bridgman anvils. The pressure dependencies of the cell parameters, the mean size of coherent scattering regions and the microstrain, the Debye characteristic temperature, and the isotropic Debye–Waller factor are calculated from processing the X‐ray diffraction (XRD) data and commented on. The local structure around Pb and Zr atoms is probed with the X‐ray absorption near edge structure (XANES). This approach demonstrates the possibility of controlling the dielectric, electronic, and structural parameters of PbZrO3 by changing the concentration of the stress‐induced structural defects.

Связь макроскопических характеристик твердого тела с энергией связи иона в решетке металлов

Abstract: The paper examines the relationship between the macroscopic parameters, such as the Young's modulus in the Hooke's law, the sound speed and the Debye characteristic temperature, with the binding energy of an individual atom. A formula for calculating the elastic deformation modulus is proposed. A simple formula is obtained to calculate the sound speed in a metal rod. It is suggested that the Debay characteristic temperature is connected with the binding energy of the ion in the solid lattice.

X-ray diffraction study of phonon and magnon properties of Eu2Cu6P5 ferromagnet

Ternary europium copper phosphide Eu₂Cu₆P₅ was synthesized from the elements by the standard ampule method as a phase-pure product and studied by means of X-ray powder diffraction. Temperature dependencies of the tetragonal unit cell parameters and volume revealed pronounced anisotropy. The observed anomalies on the a(T) and c(T) curves at about TC ≈ 36 K were related to magnetic phase transition in the phosphide under study. The linear spontaneous magnetostrictions in the basal plane and in the direction of the c axis have different signs that indicates a pronounced anisotropy of the thermal expansion at the temperatures of magnetic ordering. Temperature changes of the unit cell volume Vu(T) were analyzed within the Debye-Einstein approximation. The parameters of the model applied (Debye and Einstein characteristic temperatures, shares of the correspondence contributions) were determined. It was shown that the ratio of the shares of the Debye and Einstein contributions to the thermal characteristics are 0.85/0.15; consequently, in the region of moderately low temperatures, the thermal properties of Eu2Cu6P5 are determined mainly by the Debye vibrations of the Cu/P framework. Experimental data on thermal expansion and calculated heat capacity were used to calculate the temperature-dependent Grüneisen parameter, γ(T), for the further analysis of the lattice dynamics of Eu2Cu6P5. The revealed monotonic growth of γ(T), which is a measure of the anharmonicity of lattice vibrations, indicates an increasing influence of anharmonicity on the thermal properties of Eu₂Cu₆P₅. The anisotropy of the vibrations of europium atoms, as well as local regions of structural heterogeneity of the sample that leads to the appearance of local stresses in the crystal structure can be the reasons for the increasing influence of anharmonicity.

THE DEPENDENCE OF THE COMPRESSION MODULUS OF ICE-SIX AND THE COEFFICIENT OF VOLUME EXPANSION ON PRESSURE AND TEMPERATURE

This pioneering study investigated the partial derivatives of the dependence of the compression modulus of ice-six on pressure and temperature, and the coefficient of volume expansion on the temperature at high pressure and low temperature. Ice six is documented on the phase diagram between the pressures 600 and 2000 MPa and between the temperatures 110 and 330 K. The pressure and temperature dependence of the all-round compression module was practically implemented in a multilayer cylinder-piston vessel. The change in the relative volume of the sample was measured using a transducer which converts linear translational motion into electrical pulses. The pressure of the sample was measured by measuring the electrical resistance of tin and gallium conductors and phase transition points of polymorphic ice modifications. The temperature of this ice-six modification was determined by a graduated copperconstantan thermocouple. Moreover, in this paper, the Debye characteristic temperatures of ice-six and the Gruneisen constant are estimated.

Crystal Growth and Temperature Evolution of the Atomic Structure of Pr3Ga5SiO14 from the Langasite Family

Pr3Ga5SiO14 crystals from the langasite family have been grown by the floating zone melting technique. Their X-ray diffraction analysis is performed at 16 different temperatures in range of 94–293 K. An experiment with ultrahigh resolution at 94 K has yielded the most exact structural model: sp. gr. P321, Z = 1, a = 8.07636(4) A, c = 5.06586(2) A, R1/wR2 = 1.192/1.185%, and Δρmin/Δρmax = –0.93/+0.79 e/A3 for 3852 unique reflections and 123 refined parameters. The temperature evolution of atomic displacement parameters is estimated based on multitemperature data using the extended Einstein and Debye models. Static components of atomic displacements are selected and the characteristic Einstein and Debye temperatures for structure atoms are determined. No structural anomalies have been found.

Thermodynamic Properties of Nanosized Cobaltite (Nickelite) Cuprate Manganites LaMgCoCuMnO6 and LaMgNiCuMnO6

The temperature dependences of the specific heat capacities of nanosized samples of lanthanum magnesium cobaltite cuprate manganite LaMgCoCuMnO6 and lanthanum magnesium nickelite cuprate manganite LaMgNiCuMnO6 are studied via calorimetry in the temperature range of 298.15–673 K. Curve $$C_{p}^{ \circ }$$(T) shows that LaMgCoCuMnO6 and LaMgNiCuMnO6 undergo second-order phase transitions at 398 and 523 K, respectively. The standard specific heat capacities of the above compounds are calculated with independent means based on characteristic Debye temperatures determined via the Koref and Nernst–Lindemann equations. Their values agree satisfactorily with experimental data. The temperature dependences of functions S°(T), H°(T) – H°(298.15), and Фхх(T) are calculated.

Jahn–Teller Lattice Distortions and Asymmetric Electron Density Distribution in the Structure of TmB12 Dodecaboride in the Temperature Range of 85–293 K

The structure of single-crystal dodecaboride TmB12, which possess metallic properties, has been studied by X-ray diffraction at nine temperatures in the range of 85–293 K. Jahn–Teller distortions of the cubic lattice are revealed. They are found to cause an asymmetric electron density distribution in crystal. Static components of atomic displacements are selected, and characteristic Einstein and Debye temperatures are determined for thulium and boron atoms, respectively. Temperature dependences of interatomic distances are obtained. The problem of localizing conduction electrons by means of X-ray diffraction analysis is stated.

A Study of Thermal Properties of Au25Pd75 Alloy Using X-Ray Diffraction

Abstract—The structure and thermal properties of Au25Pd75 alloy were studied using X-ray diffraction (XRD) technique. The change in lattice parameter a(T) was measured as a function of temperature using the Bragg line displacement method. The diffraction data obtained in the temperature range of 308–1158 K was utilized to determine the thermal parameters like the characteristic Debye temperature ΘD, mean square amplitude of vibration $$\overline {{{u}^{2}}(T)} $$ , and the coefficient of thermal expansion α(T). The results show that the alloy forms a single phase solid solution having a face centered cubic structure (A1-type) in said temperature range. Further, it is found that the addition of gold to palladium leads to an increase in the value of lattice parameter and reduction in the value of Debye temperature, mean square amplitude of vibration, and the coefficient of thermal expansion. The mean square amplitude of vibration was found to obey the classical Gruneisen relationship, as is seen in the case of most of cubic alloys.

DebyeFit: a simple tool to obtain an appropriate model of atomic vibrations in solids from atomic displacement parameters obtained at different temperatures

DebyeFit is a simple tool to calculate the Debye or Einstein characteristic temperature of thermal vibrations in crystals from the equivalent atomic displacement parameters (ADPs) of any atom obtained at several temperatures. The ADP values are separated into static and dynamic components to get a best fit to the Debye, Einstein or mixed model. The static term is added to account for possible static disorder. A nonlinear least-squares technique is used to refine the parameters of the model for sets of ADPs observed in multi-temperature structural studies. The program provides a good fit between theoretical and observed ADP values.

Magnetic, Transport, and Phonon Properties of the Trivalent Eu Metallic Compound EuBe13

Magnetic susceptibility, specific heat, and electrical resistivity measurements have been performed on single-crystal EuBe13 in the temperature range between 2 and 300 K to investigate its phonon property and the valence state of the Eu ion. The obtained temperature dependence of the magnetic susceptibility curves obey a typical Van Vleck susceptibility for Eu3+ with a nonmagnetic ground state in the entire measured temperature range. In the case of the specific heat, we observed the coexistence of Debye and Einstein phonon modes with characteristic Debye and Einstein temperatures of ~ 835 K and ~167 K, respectively, which are in good agreement with those previously reported for other isostructural MBe13 compounds (M = rare earths and actinides). The temperature dependence of the resistivity for EuBe13 shows an unusual T-cubed like dependence at low temperatures, as also observed for the nonmagnetic isostructural compound LaBe13, which can be reproduced well by calculations based on electron--phonon scattering using the estimated Debye temperature and Einstein temperature. We also summarized the relationship between the Eu-valence state and the free distance between the Eu ion and the first-nearest-neighbor atoms in several Eu-based cubic compounds, and argued that EuBe13 takes the Eu3+ state despite its larger free distance than other Eu3+ compounds.

The role of defects in the physical properties of mechanically activated PbTiO3 ferroelectrics

In this work a multi-technique characterization was performed for the first time to trace the influence of structural defects on the physical properties of PbTiO3 ferroelectrics. The structural defects were generated by the mechanical activation in the pressure range of 40–320 MPa, by combining a uniaxial strain with a shear deformation in the Bridgman anvils. The induced defectivity of PbTiO3 was assessed via calculation of unit cell parameters, estimation of the regions of coherent scattering and analysis of micro-deformations. The Debye characteristic temperature, the static mean-square displacement, the Debye–Waller isotropic factor, the vibrational spectra and dielectric properties of the activated PbTiO3 ceramics are presented. The high-quality PbTiO3 ceramics was prepared without modifiers, hence, changing the concentration of structural defects via mechanical activation constitutes a chemically clean method for fine tuning of the dielectric properties of PbTiO3.

The influence of mechanical activation on the dielectric and dynamic properties and structural parameters of the solid solution of Pb(Zr0.56Ti0.44)O3

The impact of mechanical activation on the dielectric properties, structural parameters, and lattice dynamics of the Pb(Zr0.56Ti0.44)O3 solid solution was investigated. The solution features coexisting metastable tetragonal (T) and rhombohedric (R) phases, whose ratio can be altered by applying the uniaxial compression load up to 320 MPa under torsion in Bridgman anvils. The strain-induced changes of the unit cell parameters, dielectric permittivity, Debye characteristic temperatures, temperature-dependent Debye-Waller factors, and mean square displacements were critically analyzed.

Heat capacities, entropies, and Gibbs free energies of formation of low-k amorphous Si(O)CH dielectric films and implications for stability during processing

Low-temperature heat capacities of a series of low dielectric constant amorphous films with different compositions were measured from 1.8 to 300 K using a Quantum Design Physical Property Measurement System (PPMS). By using piece wise functions to fit the heat capacities, the characteristic Debye temperatures ΘD and the standard molar entropies are determined. The standard molar entropies of these materials range from 8.8 J·K−1·mol−1 to 17.5 J·K−1·mol−1. Together with the formation enthalpies obtained by high temperature oxidative solution calorimetry in molten sodium molybdate solvent, the corresponding Gibbs free energies from elements and crystalline constituents (and gaseous products as required) are obtained. The Gibbs free energy terms of these materials are dominated by the enthalpy term rather than the entropy. These samples are thermodynamically stable at room temperature with respect to elements and the samples with oxygen incorporated are generally thermodynamically more stable than the others. However, compared to crystalline binary counterparts and gases, some of these materials possess either positive or close-to-zero Gibbs free energies of formation, indicating that they are thermodynamically metastable; while, for the rest, which are stable at ambient conditions, elevation of temperature will eventually lead to decomposition.

Low-temperature heat capacity VO2±δ and solid solutions V1-XFeXO2

The article reports the study results of the heat capacity of vanadium dioxide compounds (VO2) (within the homogeneity range) and stoichiometric solid solutions V1-xFexO2 at temperature range from 5 κ to 100 κ. Separation of various constituents of heat capacity with its additivity assumption has been conducted: crystal lattice heat capacity and defects heat capacity. It is shown that a considerable contribution to the heat capacity is produced by the crystal lattice defects (till ~ 25 κ) at low temperatures, and at higher temperatures the heat capacity is determined mainly with the crystal lattice. Using the Debye function table for the heat capacity for all compounds, the characteristic Debye temperatures θD were determined.