Elastic Debye Temperature Research Articles

Acoustic wave velocities and effective Debye temperature in potassium alum KAl(SO4)2·12H2O crystal

The acoustic wave velocity along principal propagation directions and polarization orientations was computed for potassium alum KAl(SO4)2·12H2O crystals at 295 K, using elastic constants derived from ultrasonic resonance experiments. The mean elastic Debye temperature was subsequently determined. The temperature dependency of elastic Debye temperature was assessed, based on Brillouin scattering measurements of the longitudinal acoustic (LA) phonon propagating in the [100] direction. Comparison between the elastic Debye temperature extrapolated to T → 0 from the high-temperature phase and the calorimetric Debye temperature determined below the transition temperature (Tc = 59.7 K) revealed an 18 % disparity, primarily attributed to insufficient experimental data of velocity above and below Tc.

Pressure-Driven Responses in Cd2SiO4 and Hg2GeO4 Minerals: A Comparative Study

The structural, elastic, and electronic properties of orthorhombic Cd2SiO4 and Hg2GeO4 were examined under varying pressure conditions using first-principles calculations based on density functional theory employing the Projector Augmented Wave method. The obtained cell parameters at 0 GPa were found to align well with existing experimental data. We delved into the pressure dependence of normalized lattice parameters and elastic constants. In Cd2SiO4, all lattice constants decreased as pressure increased, whereas, in Hg2GeO4, parameters a and b decreased while parameter c increased under pressure. Employing the Hill average method, we calculated the elastic moduli and Poisson’s ratio up to 10 GPa, noting an increase with pressure. Evaluation of ductility/brittleness under pressure indicated both compounds remained ductile throughout. We also estimated elastic anisotropy and Debye temperature under varying pressures. Cd2SiO4 and Hg2GeO4 were identified as indirect band gap insulators, with estimated band gaps of 3.34 eV and 2.09 eV, respectively. Interestingly, Cd2SiO4 exhibited a significant increase in band gap with increasing pressure, whereas the band gap of Hg2GeO4 decreased under pressure, revealing distinct structural and electronic responses despite their similar structures.

Mechanical and thermal response of XFe2O4 (X = Zn, Ag and Co) spinel ferrites via IR-spectroscopy and first-principles calculations

The lack of comprehensive literature on the all-important aspect of the elasticity of spinel ferrites led to the hydrothermal synthesis of different (Co, Zn, Ag) spinel ferrites. IR spectroscopy revealed the characteristic absorption bands of metal-oxygen in all three compositions. The shifting of tetrahedral and octahedral bending vibrations towards higher frequencies owes to changes in inter-atomic and inter-ionic distances. Elastic parameters, wave velocities, and Debye temperature have been calculated using IR spectroscopy data. Elastic parameters have been higher for Co ferrites than Zn and Ag ferrites. The Poisson ratio seems to be consistent for different spinel ferrites. Shear wave velocity has been found to be higher than longitudinal wave velocity because perpendicular particle vibrations take higher energy than parallel vibrations. Wave velocities have been found to be higher in Ag ferrites than in the other two compositions. Debye temperature follows the same trend as elastic parameters. Additionally, we have confirmed the mechanical stability of the Co, Zn, and Ag ferrites using the first-principles calculations in the density functional theory (DFT) approach framework. Interestingly, the Co/Zn/Ag ferrites exhibit semiconducting nature with a band gap of 3.96/3.66/0.71 ev. Our study could pave the way for next-generation spintronic devices.

Elastic wave speeds, Debye temperature and microhardness of YX3 (X = In, Sn, Tl and Pb) intermetallic compounds

In the present work, we reviewed and report on the theoretical prediction of the longitudinal, transverse and average elastic wave veloci-ties, and the Debye temperature for some nonmagnetic YX3 (X = In, Sn, Tl, and Pb) intermetallic compounds with stable cubic AuCu3-type structure. The lattice parameters and the elastic constants used here are taken from the work of Abraham et al [1] using the general-ized gradient approximation (PBE-GGA). Our results are analyzed and compared with the available theoretical and experimental data, and in general a good agreement is found. The deviation between our value (224.4 K) of the Debye temperature θD for YSn3 material and the experimental one (210 K) is around 6.62%, while the deviation between our result (1401 m/s) of the transverse elastic wave velocity for YTl3 intermetallic material and the calculated one (1470 m/s) is about 4.93%. In addition the Young’s Modulus and Poisson’s Ratio of YX3 intermetallic compounds for the crystallographic planes (100), (110) and (111) are predicted.

Correlation between structure, cation distribution, elastic, and magnetic properties for Bi3+substituted Mn–Zn ferrite nanoparticles

Chemical coprecipitation was used to synthesize Mn0.6Zn0.4BixFe2-xO4 ferrite nanoparticles with x values from 0.0 to 0.05. XRD indicated nanocrystalline spinel phase with typical crystallite size of 6 nm after Rietveld refinement. The IR spectra show two strong absorption bands. Using IR data, the force constant was estimated for the tetrahedral and octahedral locations to get the C11 and C12 stiffness constants. Elastic moduli (Young, bulk, and rigidity), Poisson ratio, and Debye temperature were calculated using stiffness constants and all decreased with Bi3+ content. All nanoparticles studied are superparamagnetic and lose magnetism with Bi3+ concentration. The behaviors of all these parameters were explained by linking them to the structural changes that are introduced due to Bi3+ ion substitution. Moreover, different models were used to check and compare between both theoretical and experimental values for many parameters. Finally, the magneto-mechanical properties of the ferrite nanoparticles open the door for several daily applications.

Thermal expansion anisotropy of Fe23Mo16 and Fe7Mo6 μ-phases predicted using first-principles calculations.

The intermetallic μ-phase, which precipitates in steels and superalloys, can noticeably soften the mechanical properties of their matrix. Despite the importance of developing superalloys and steels, the thermodynamic properties and directions of thermal expansion of the μ-phase are still poorly studied. In this work, the thermal expansion paths, elastic, thermal and thermodynamic properties of the Fe23Mo16 and Fe7Mo6 μ-phases are studied using the first-principles-based quasi-harmonic Debye-Grüneisen approach. A method that avoids differentiation in many variables is used. The free energies consisting of the electronic, vibrational and magnetic energy contributions, calculated along different paths of thermal expansions, were compared among themselves. A path with the least free energy was chosen as the trajectory of thermal expansion. Negative thermal expansion of the Fe7Mo6 compound was predicted, while Fe23Mo16 exhibits conventional thermal expansion. The thermal expansions of both these compounds are not isotropic. The elastic constants, moduli, heat capacities, Curie and Debye temperatures were predicted. The obtained results satisfactorily agree with the available experimental data. Physical factors affecting the stability of Fe23Mo16 and Fe7Mo6 have been studied. This study presents an essential feature of thermal expansion of the μ-phase of the Fe-Mo system, which can provide an insight into future developments.

Investigation of structural, optical and thermodynamic properties of FrBO3 (B = Ta, Nb) perovskites: first principles calculations

Abstract The utilization of inorganic cubic perovskite semiconductors has increased their prominence within industrial applications pertaining to optoelectronic and photovoltaic devices. Lead-free materials are currently receiving significant attention among many perovskite compounds, mostly due to their environmentally non-toxic nature. In the present work, the structural, optical, electronic, thermodynamic and mechanical properties of inorganic perovskites FrBO3 (B = Ta, Nb) are discussed via generalized gradient approximation based on density functional theory. The band structure, density of states, absorption, dielectric function and reflectivity are calculated to describe electronic and optical properties of the compounds. The ground states lattice parameters are found to be 4.292 Å and 4.194 Å with direct band gap of 1.175 eV and 0.90 eV, respectively. The elastic constants and Debye temperature of FrBO3 showed that the compounds are mechanically and thermodynamically stable. The results obtained by this study reveal that FrTaO3 has superior absorption and conductivity making it a more suitable candidate for various optoelectronic devices.

Mechanical and elastic properties of vitrified radioactive wastes using ultrasonic technique

It is important that radioactive and nuclear wastes are immobilized in a glass composition with lower melting temperatures due to their economy. In this study, the elastic and mechanical properties of sodium borate-based vitrified radioactive waste were measured using ultrasonic techniques. Many ultrasonic parameters, such as elastic moduli, Poisson's ratio, and microhardness, were calculated by measuring the ultrasonic velocities of the glasses. The ultrasonic velocity data, the density, the calculated elastic moduli, micro-hardness, softening temperature, and Debye temperature depending on the glass composition were evaluated, and the relation with the structure was clarified. It was observed that the elastic modulus and Poisson ratio increased as the Cs2O content increased in glasses containing Cs waste. This result shows that the rigidity of the network structure of these glasses increases in contrast to the glass containing Sr.

Impact of nonstoichiometry on the mechanical properties and thermal conductivity of gadolinium zirconate ceramics

Low elastic properties, high hardness, and low thermal conductivity are desirable for a rare-earth zirconate thermal barrier coating material. Realizing nonstoichiometry is a significant way to improve the elastic properties, hardness and thermal conductivity of rare-earth zirconate to further meet the requirements of thermal barrier coating materials, nonstoichiometric Gd2-xZr2+xO7+0.5x (x = 0, ±0.125, and ±0.25) was studied by first-principles calculations first and then verified by the solid-state reaction methods. Calculations revealed that excess Gd3+ and Zr4+ decrease the elastic modulus, sound velocity, and Debye temperature of Gd2Zr2O7, and increase its ductility. The elastic properties of the material exhibit significant anisotropy, which further increases with increasing Gd3+ and Zr4+ contents, resulting from lattice distortion caused by excess Gd3+ and Zr4+ entering the lattice. The hardness of Gd2Zr2O7 increases with a moderate excess of Zr4+, while it decreases with an excess of Zr4+ and Gd3+. In addition, with the disordered occupation of lattice atoms, the anharmonicity of lattice waves is increased, and phonon scattering is enhanced as the concentrations of Gd3+ and Zr4+ increase, resulting in the reduction of the phonon thermal conductivity. Moreover, Zr4+ is more conducive to the decrease in the thermal conductivity. The experimental consequences match well with the calculation consequences. This work is expected to provide support for improving mechanical properties and thermal conductivity of rare-earth zirconate materials.

XRD, FTIR and ultrasonic investigations of cadmium lead bismuthate glasses

Cadmium lead bismuthate glasses in the system xCdO–(1−x)[0.5PbO + 0.5Bi2O3](40 mol% ≤ x ≤ 90 mol%) were successfully prepared by melt-quenching method. The structural and elastic properties have been investigated using XRD, FTIR and ultrasonic pulse–echo techniques. The XRD patterns confirmed the amorphous nature of the samples prepared. Density and ultrasonic velocity data were used to evaluate various elastic properties. Addition of CdO gave rise to decreased density and molar volume and increased elastic moduli, micro-hardness, and Debye temperature. The FTIR analysis revealed that increasing CdO content enhances the BiO6 octahedral sites at the expense of the BiO3 and PbO4 units. This results in the formation of Pb–O–Bi(6) and Bi(3)–O–Bi(6) linkages in the glass network, which stiffen the structure and improve the elastic properties. A correlation between elastic and compositional parameters was achieved on the basis of theories and approaches in the field.

Uncovering the influence mechanism of nonmetallic atoms on the mechanical properties of Ni3Co alloy

The introduction of solute atoms has a critical effect on the mechanical properties of nickel-cobalt alloys. In the present study, we first prepare the Ni3Co alloy coating by electrodeposition and perform structural characterization. The results show that the alloy has a single-phase FCC structure with no other distinct characteristic peaks. On this basis, we established the L12-Ni3Co crystal model, and detailed analysis of the mechanism of varying nonmetallic atoms (C, B, N, P) on the elastic properties of the alloy by first-principle calculation. The results of mechanical and thermal performance parameters such as elastic modulus, hardness and Debye temperature show that compared with the other three elements, the strengthening effect of N atom is the best, especially when in the interstitial site, the strengthening effect of smaller non-metallic atoms is more significant. Moreover, the doped systems are both elastic and sound velocity anisotropic, and the strength of the alloy is approximately positively correlated with the degree of anisotropy. The analysis of the electronic structure shows that the introduction of interstitial atoms leads to a transformation of the local bonding properties, and the strengthening effect can be attributed to the strong covalent interaction between them and the Ni or Co atoms.

Mechanical properties, thermophysical properties and electronic structure of Yb3+ or Ce4+-doped La2Zr2O7-based TBCs

First-principles calculations based on density functional theory were performed to investigate the cohesive energies, elastic modulus, Debye temperatures, thermal conductivities and density of states of La2−xYbxZr2O7, La2Zr2−xCexO7 and La2−xYbxZr2−xCexO7 (x = 0.00, 0.25, 0.50, 0.75, 1.00) ceramics. The results show that doping Yb3+ or Ce4+ into La2Zr2O7 reduces its elastic modulus, thermal conductivity and Debye temperature. Compared with La2−xYbxZr2O7 (x ≠ 0.00), La2Zr2−xCexO7 compounds have better ductility and lower Debye temperature. The Debye temperature values of La2Zr2−xCexO7 (x ≠ 0.00) compounds are in the range of 485.0–511.5 K. Among all components, the fluorite-type La2−xYbxZr2−xCexO7 (x = 0.75, 1.00) compounds exhibit better mechanical and thermophysical properties, and their thermal conductivity values are only 1.213–1.246 W/(m∙K) (1073 K), which are 14.5%–16.7% lower than that of the pure La2Zr2O7. Thus, our findings open an entirely new avenue for TBCs.

High-Temperature Mechanical and Dynamical Properties of γ-(U,Zr) Alloys

High-temperature body-centered cubic (BCC) γ-U is effectively stablized by γ-(U,Zr) alloys that also make it feasible to use it as a nuclear fuel. However, relatively little research has focused on γ-(U,Zr) alloys due to their instability at room temperature. The effect of Zr composition on its mechanical properties is not clear yet. Herein, we perform molecular dynamics simulations to investigate the mechanical and dynamical stabilities of γ-(U,Zr) alloys under high temperatures, and we calculate the corresponding lattice constants, various elastic moduli, Vickers hardness, Debye temperature, and dynamical structure factor. The results showed that γ-U, β-Zr, and γ-(U,Zr) are all mechanically and dynamically stable at 1200 K, which is in good agreement with the previously reported high-temperature phase diagram of U-Zr alloys. We found that the alloying treatment on γ-U with Zr can effectively improve its mechanical strength and melting points, such as Vickers hardness and Debye temperature, making it more suitable for nuclear reactors. Furthermore, the Zr concentrations in γ-(U,Zr) alloys have an excellent effect on these properties. In addition, the dynamical structure factor reveals that γ-U shows different structural features after alloying with Zr. The present simulation data and insights could be significant for understanding the structures and properties of UZr alloy under high temperatures.

Debye temperature of CaO under high pressure up to 65.2 GPa

In the present work we used the experimental relative volume unit cell and the elastic stiffness constants measured by Speziale et al. (Journal of Geophysical Research, Vol. 111, (2006), pp. B02203 (12 pages)) using the Radial X-Ray Diffraction at high pressure from 5.6 up to 65.2 GPa to investigate the effect of high pressure on the bulk modulus, aggregate shear modulus, elastic wave velocities and Debye temperature of calcium oxide (CaO) ceramic material in cubic rock-salt (B1) phase. Our obtained values show that the bulk modulus increases monotonously with increasing pressure, while the aggregate shear modulus, the mean elastic wave velocity and the Debye temperature of CaO material varied non-linearly and non-monotonously with increasing pressure from 5.6 up to 65.2 GPa.

Williamson-Hall and Size-strain plot based micro-structural analysis and evaluation of elastic properties of Dy3+ substituted Co-Zn nano-spinels

Polycrystalline Co-Zn nanoferrites doped with rare earth Dy3+ ions having general chemical formula Co0.9Zn0.2DyxFe1.9-xO4 (x = 0.0, 0.015, 0.03, 0.045 and 0.06) were synthesized via sol-gel auto-combustion route. Powder X-ray diffraction (XRD), scanning electron microscopy (SEM) and Fourier transform Infrared Spectra (FTIR) were performed to investigate the structural, microstructral, surface morphology and elastic properties. Well indexed XRD patterns confirm the phase purity and cubic spinel structure of the samples. Fractional doping of Dy3+ ions shifts the Bragg’s lines slightly towards the lower angles which in turn increases the lattice lengths from 8.3795 Å to 8.3834 Å. The strain induced in the crystal lattice was estimated by using Williamson-Hall and Size – Strain Plot methods. Both methods confirm that the tensile type strain was induced in the crystal lattice and increases with the substitution of Dy3+ ions. Surface morphology of the samples was studied by using SEM images which reveals that the grains are almost spherical in nature and the size obtained is analogues with XRD results. FTIR spectra shows the existence of two main absorption bands within the wave number range 388 – 586 cm−1 which confirm the characteristics of spinel ferrites. Elastic properties were estimated by using FTIR data. Elastic moduli and Debye temperature increases with the substitution of Dy3+ ions which are interpreted on the basis of interatomic bondings.

Pressure Dependent Elastic and Thermo-Physical Properties of U Ternaries with ZrNiAl Structure Compounds

bstract: The Thermophysical and ultrasonic aspects of U- ternaries are examined theoretically under high pressure. In order to determine the second- and third-order elastic constants of U- ternaries (URhAl and ThRhAl) compounds under pressure conditions (0-45GPa), the potential model technique has been used. The assessed second-order elastic constants are used along with the pressure-dependent ultrasonic velocities, thermal relaxation time, and other significant and important thermophysical data to determine the orientation. It is observed that thermal relaxation time and mechanical & thermal properties exhibit an increasing trend with increasing pressure for U-ternaries URhAl and ThRhAl compounds. The effect of increasing pressure on the URhAl and ThRhAl compounds shows up as an increase in elastic constants, ultrasonic velocities, ultrasonic attenuation, and Debye temperature. The ratio B/G increases with pressure which indicates that the materials are ductile in nature. We have used the approximate values of SOECs, density, and lattice properties in calculating the melting point, ultrasonic velocity, and thermal conductivity.

Multifunctionality of AlBaFe12O19 /CoZnFe2O4 hybrid nanocomposite: Promising structural, elastic, morphological, compositional, optical, and magnetic properties

A detailed report on the influence of Aluminum doped Barium Hexaferrite (ABH) on structure, elasticity, morphology, composition, and optical and magnetic behavior of hybrid ABH-CZF (AlBaFe12O19)1-x/(CoZnFe2O4) x with X = 0.1, 0.2, 0.3, 0.4 nanocomposites is presented. A new study on the role of ABH in the composite made by the physical mixing method. The composites were characterized by XRD, SEM, EDAX, FTIR, UV, PL, and VSM analysis. XRD confirms the formation of hexagonal and spinel structures in the composite along with their cell volume, lattice parameters, stress, strain, and other structural parameters. Elastic parameters and Debye temperature were measured using FTIR. The composite AC 60–40 is found best suited for high-density optical storage devices and as lead-free radiation shielding materials. From the UV analysis, Both the direct and indirect band gap energies are found to be increasing with increasing ABH concentration. The overall structural and optical properties also prove that the material can be used in tunable photonic applications. The refractive index of the composite is between 3.0 and 3.2, which can be used for photo-electrochemical cells, optical detectors, or reflectors. Magnetic properties examined using VSM showed a decrease in Ms, Mr, and Hc values along with ABH concentration which may be suitable for data storage applications such as rewritable storage hard drives. The maximum values for Ms (7.85 emu/g), Mr (20.44 emu/g), and Hc (2.01 kOe) are found for AC90-10 nanocomposite material. By plotting loop width (ΔH) versus magnetization (M), the magnetic interaction between the composite is studied.

Elastic anisotropy and thermal properties of M-B-N (M = Al, Ga) systems using first-principles calculations

In this paper, the elastic properties, Debye temperatures, thermal conductivities, and sound velocities of M-B-N nitrides are explained systematically by considering the first-principles calculations based on density functional theory. The three-dimensional (3D) surface construction and planar projection of elastic anisotropy indicated that the elastic modulus is in the sequence of M3BN4 > MBN2 > MB3N4 and Al–B–N nitrides > Ga-B-N nitrides. The thermal properties were analyzed according to elastic modulus, and the obtained Debye temperatures, sound velocities and minimum thermal conductivities of these M-B-N nitride are anisotropic. AlB3N4 has the highest Debye temperature, indicating that AlB3N4 has the highest hardness and the largest minimum thermal conductivity among these nitrides.

Comparative first-principles study of the (TiZrHfNbTa)B2 high entropy solid solution and its constituent binary diborides

The stability, electronic and phonon structures, optical, mechanical and thermodynamic properties of the random high entropy (TiZrHfNbTa)B2 solid solution (alloy) were studied in comparison with those of TiB2, ZrB2, HfB2, NbB2 and TaB2 using first-principles calculations. The mixing enthalpy of −0.842 kJ/mol of atoms for the high entropy diboride points to that it is stable against decomposition into the constituting binary diborides. All the diborides studied are thermodynamically, mechanically and dynamically stable. The dielectric function, reflectivity and extinction coefficient of the diboride compounds were comprehensively studied. Both (TiZrHfNbTa)B2 and binary diborides are found to be good reflective materials in infrared, visible and ultraviolet regions. The calculated elastic moduli, B/G ratio, Vickers hardness, fracture toughness and Debye temperature of (TiZrHfNbTa)B2 are medium between largest and lowest ones of the constituents, approximately obey the rule of mixture. Calculations of the stress-shear strain relations for (TiZrHfNbTa)B2 point to the possibility of the activation of both basal and prismatic slip systems. The elastic moduli and linear compressibility exhibit the spatial anisotropy inherent to hexagonal structures. The thermodynamic characteristics of the diborides studied are well reproduced in a temperature range up to 800–1000 K.

First‐Principles Calculations of Physical Properties and Stability of Orthorhombic FeN2 under High Pressure

The physical properties and stability of orthorhombic FeN2 under high pressure remain an open question. The spin‐polarized first‐principles calculations within the generalized gradient approximation GGA + U functional are used to study the structural, elastic, electronic, magnetic properties and the stability of orthorhombic FeN2 under high pressure. The variations of the lattice constants and bond lengths as a function of pressure in the range 0–100 GPa are presented. The elastic constants, moduli, Poisson's ratio, elastic wave velocities, Debye temperature, and thermal expansion coefficient as a function of pressure in the range 0–100 GPa are also given. The high bulk modulus and low compression make it a promising high‐energy‐density material. FeN2 is both mechanically and dynamically stable in the studied pressure range. FeN2 is elastic anisotropic and its anisotropy increases with pressure. At pressure less than 45 GPa, the orthorhombic FeN2 is a magnetic metal, while at pressure increasing to 45 GPa, a nonmagnetic metal is obtained. When the pressure goes beyond 45 GPa, the outline of the density of states is similar, showing that the pressure has less effect on electronic properties. It is hoped that these results can provide reference for further researches.