Elastic and thermal parameters of lanthanide-orthophosphate (LnPO4) ceramics from atomistic simulations

We performed extensive and accurate atomistic simulations of elastic and heat transport properties of series of rare-earth orthophosphate ceramics LnPO₄ (Ln = La, …, Lu and Y) in monazite and xenotime structures. The results show clear trends in the elastic moduli along the lanthanide-series, which complement the existing experimental data on these materials. We found that the thermal conductivities of xenotimes are about two times larger than those of monazite, which is in agreement with the experimental measurements and explained by sizes of the primitive cells. Large sets of data allowed assessment of the validity of Slack's model as well as accuracy of molecular dynamics simulations of heat flow for prediction of thermal conductivity. Last, but not least, the separation of the intrinsic and extrinsic contribution to the measured thermal diffusivities allowed for a detailed analysis of the phonon mean free paths in the considered materials.     

First‐principles investigations on elevated temperature elastic and thermodynamic properties of ZrB2 and HfB2

As promising candidates for ultrahigh temperature applications, high‐temperature properties, which are quite rare and fragmentary, have great significance to ZrB₂ and HfB₂. In this work, thermodynamic and mechanical properties of ZrB₂ and HfB₂ from 0 K to 2000 K were investigated by a combination of first principles calculations and quasi‐harmonic approximations. The ground‐state properties, including lattice parameters, elastic constants, phonon dispersion, and mode‐Grüneisen parameters are calculated. The theoretical thermal expansion, elastic and thermodynamic properties at elevated temperatures show good agreement with experiments. By discussing Grüneisen parameters anisotropy, the mechanism for the thermal expansion anisotropy of ZrB₂ and HfB₂ is uncovered. The influence of direction‐dependent sound velocities on the anisotropy of thermal conductivity is also discussed.     

Structure,mechanical, electronic and thermodynamic properties of Mo5Si3 from first-principles calculations

Transition metal silicides are promising advanced functional materials. However, the structure and relevant properties of Mo₅Si₃ are not well understood. In this work, we investigate the crystal structure, elastic properties, Vickers hardness, elastic anisotropy, electronic and thermodynamic properties of Mo₅Si₃ by using the first-principles calculations. Three structures: tetragonal, hexagonal and orthorhombic structures are considered. The calculated results show that those structures are thermodynamically stable. In particular, we firstly predict that Mo₅Si₃ with hexagonal (P63/mcm) structure is a stable phase. The calculated electronic structure shows that Mo₅Si₃ exhibits better electronic properties because of the charge overlap between Mo-4d state and Si-3p state near the Fermi level. Importantly, Mo₅Si₃ shows the strong deformation resistance and high elastic stiffness in comparison to other TM₅Si₃. Mo₅Si₃ with tetragonal structure has the smaller percentage anisotropy in compressibility and high percentage anisotropy in shear. We further find that the Debye temperature and heat capacity of tetragonal structure are larger than that of hexagonal structure. The high-temperature thermodynamic properties of Mo₅Si₃ are attributed to the vibration of Si atom.     

First principles calculations and synthesis of multi-phase (HfTiWZr)B2 high entropy diboride ceramics: Microstructural,mechanical and thermal characterization

First principles calculations were conducted on (HfTiWZr)B₂ high entropy diboride (HEB) composition, which indicated a low formation energy and promising mechanical properties. The (HfTiWZr)B₂ HEBs were synthesized from the constituent borides and elemental boron powders via high energy ball milling and spark plasma sintering. X-ray diffraction analyses revealed two main phases for the sintered samples: AlB₂ structured HEB phase and W-rich secondary phase. To investigate the performance of multi-phase microstructures containing a significant percentage of the HEB phase was focused in this study. The highest microhardness, nanohardness, and lowest wear volume loss were obtained for the 10 h milled and 2050 °C sintered sample as 24.34 ± 1.99 GPa, 32.8 ± 1.9 GPa and 1.41 ± 0.07 × 10^?4 mm³, respectively. Thermal conductivity measurements revealed that these multi-phase HEBs have low values varied between 15 and 23 W/mK. Thermal gravimetry measurements showed their mass gains below 2% at 1200 °C.     

Anisotropy in elasticity,sound velocities and minimum thermal conductivity of zirconia from first-principles calculations

The anisotropies of mechanics and thermodynamics properties of zirconia with three zero-pressure polymorphs were studied by using first-principles calculations. It has been shown that Young’s moduli of three phases strongly depend on directions. The sound velocities of faster mixed mode (v₊) is much larger than that of slower mixed mode (v₋) and pure transverse mode (v_t) in monoclinic phase. For both tetragonal phase and the cubic phase, most pure longitudinal mode (v_l) have the greatest sound velocity among the three acoustic modes. According to the Clarke's model, three zero-pressure polymorphs zirconia also have pronounced anisotropic minimum thermal conductivity.     

Elastic and electronic properties of XB2 (X=V,Nb, Ta,Cr, Mo,and W) with AlB2 structure from first principles calculations

The crystal structure, electronic properties, mechanical properties, and anisotropy of XB₂ (X=V, Nb, Ta, Cr, Mo, and W) were calculated by first principles calculations based on density functional theory (DFT) with the generalized gradient approximation (GGA). The results are in good agreement with available theoretical and experimental values. The calculated cohesive energy and formation enthalpy indicate that they are thermodynamically stable structures. The elastic constants satisfy all of the mechanical stability criteria. The mechanical moduli were predicted by the Voigt–Reuss–Hill approximation. The mechanical anisotropy was indicated by the surface constructions of Young's moduli, and the results show that anisotropy of WB₂ is stronger than others. The electronic structure indicates that the bonding behaviors of XB₂ (X=V, Nb, Ta, Cr, Mo, and W) are the combinations of covalent and metallic bonds. The hardness of the borides was also evaluated, and the result reveals that TaB₂ is the hardest compound among them.     

Mechanical properties of tape casted Lanthanum Tungstate for membrane substrate application

Advances in the development of asymmetric membrane concepts require the development of porosity optimized, mechanically reliable substrate materials. The current study focuses on the characterization of the room temperature mechanical properties of tape casted Lanthanum Tungstate of different porosities for membrane substrate applications. Elastic modulus and hardness are assessed using indentation testing. Characteristic strength and Weibull modulus are determined from data obtained using a ball-on-3-balls test that is particularly advantageous for the rather thin tape casted material. Particular emphasis is placed on the effect of the surface composition onto the fracture strength.     

Elastic,mechanical, electronic,and defective properties of Zr–Al–C nanolaminates from first principles

By means of first principles calculations, Zr–Al–C nanolaminates have been studied in the aspects of chemical bonding, elastic properties, mechanical properties, electronic structures, and vacancy stabilities. Although the investigated Zr–Al–C nanolaminates show crystallographic similarities, their predicated properties are very different. For (ZrC)_nAl₃C₂ (n = 2, 3, 4), the Zr–C bond adjacent to the Al–C slab with the C atom intercalated in the Zr layers is the strongest, but the one with the C atom intercalated between the Zr layer and Al layer is the weakest. In contrast, the situation for (ZrC)_nAl₄C₃ (n = 2, 3) is just the opposite. For Zr–Al–C nanolaminates, the calculated bulk, shear and Young's modulus increase in the sequence of Zr₂AlC < Zr₃AlC₂ < Zr₂Al₄C₅ < Zr₃Al₄C₆ < Zr₂Al₃C₄ < Zr₃Al₃C₅ < Zr₄Al₃C₆. The (ZrC)_nAl₃C₂ (n = 2, 3, 4) series exhibit the most outstanding elastic properties. In the presence of the external pressure, the bulk and shear moduli exhibit a linear response to the pressure, except for Zr₂AlC and Zr₃AlC₂, both of which belong to the so‐called MAX phases. The two materials also exhibit very distinct properties in the strain‐stress relationship, electronic structures and vacancy stabilities. As the intercalated Al layers increase, the formation energy of V_Zr and V_Al increases, while the formation energy of V_C decreases.     

A prediction of the thermodynamic,thermophysical, and mechanical properties of CrTaO4 from first principles

It is reported that the self-forming CrTaO₄ oxide scale can protect refractory high-entropy alloys from oxidation, superior to Cr₂O₃. In this paper, the phase stability, mechanical, and thermal properties of three polymorphous phases of CrTaO₄ are systematically investigated from first-principles density functional theory calculations. The mechanical properties predicted using the strain–energy methods indicated that all three phases are mechanically stable. The temperature dependence of elastic constants and polycrystalline moduli of three phases demonstrated the thermal softening as temperature increase. The Helmholtz-free energies as a function of volume and temperature are derived from phonon dispersions within the quasi-harmonic approximation at six strained volumes. The calculated apparent bulk coefficients of thermal expansion of these three phases are evaluated, the highest value approximately 13.4× 10⁻⁶ K⁻¹ within a temperature range of 500–2000 K for the rutile I4₁md phase. The lattice thermal conductivity calculated by the Debye–Callaway model suggested that the rutile type I4₁md phase has the lowest value of approximately 2.1 W/m/K at 1800 K. The other two phases, C2/m and P2/c, exhibit higher values due to relatively lower Grüneisen parameters and larger phonon velocities. The melting point of CrTaO₄ is predicted to be between 1975 and 2449 K using ab initio molecular dynamics simulations. This work provides a comprehensive theoretical understanding of the thermodynamic, mechanical, and thermal properties for the new material CrTaO₄ and serves as an example of a viable computational design strategy for improved oxidation resistance of refractory alloys at high temperatures.     

Electronic structure,anisotropic elastic and thermal properties of monoclinic Ca2Nb2O7

The electronic structure, anisotropic elastic and thermal properties of monoclinic Ca₂Nb₂O₇ have been investigated by density functional theory (DFT) calculations and further are verified by experimental results. It has been shown that the monoclinic Ca₂Nb₂O₇ is a direct band gap insulator with the calculated band gap of 3.07 eV which is comparable with the experimental value of 3.33 eV. The bottom of the conduction band (CB) is dominated by the 4d orbitals of the Nb atoms and the 2p orbitals of O atoms, while the top of valence band (VB) mainly consists of the 2p orbitals of O atoms. Calculated sound velocities of different directions show that the faster mixed mode (v₊) is much larger than that of slower mixed mode (v_- ) and pure transverse mode (v_t ) in both [100] and [001] directions. The pure longitudinal mode v_l has the greatest sound velocity among the three acoustic modes in the [010] direction. According to Clarke's model, monoclinic Ca₂Nb₂O₇ has low limit thermal conductivity with 1.43 Wm⁻¹K⁻¹ at high temperature, and minimum thermal conductivity in (100), (110), (010) and (001) planes sensitively depends on the directions.     

Effect of Ba concentration on phase stability and mechanical and thermal properties of La2Mo2O9

Ba-substituted La₂Mo₂O₉ ((La_1−xBa_x)₂Mo₂O_9−δ, x = 0–0.12) was prepared and the thermal and mechanical properties were evaluated. The thermal expansion coefficients (TECs) were determined from high-temperature X-ray diffraction (XRD) analysis. Phase transition in La₂Mo₂O₉ was suppressed via substitution of Ba for La, as demonstrated by differential scanning calorimetry (DSC) analysis. The mechanical properties, such as the bulk modulus, shear modulus, Young’s modulus, compressibility, and Debye temperature were evaluated from the measured sound velocities. The thermal conductivity was evaluated from the thermal diffusivity, heat capacity, and density in the temperature range from room temperature to 1073 K. The thermal conductivity decreased with increasing Ba content. Theoretical calculations based on the Klemens–Callaway model were performed to analyze the thermal conductivity, and the results suggest that the reduction of the thermal conductivity was mainly attributed to oxygen defects in the anion sublattice of La₂Mo₂O₉.     

Drastic enhancement of mechanical properties of Ca3Co4O9 by B4C addition

Ca₃Co₄O₉ with B₄C additions in different proportions (0, 0.10, 0.25, 0.5, and 0.75 wt.%) have been fabricated using the classical solid-state method. Powder XRD patterns have displayed that Ca₃Co₄O₉ phase is the major one in all samples. Microstructural observations showed that B₄C has been superficially oxidized, producing liquid B₂O₃ during sintering, and reacting with the Ca₃Co₄O₉ grains to produce bridges between them. In spite of the increase of porosity, these bridges led to an important raise (more than two times) of mechanical properties when compared to the pristine materials. On the other hand, while B₄C addition has not influenced S values, it has decreased electrical resistivity, thermal conductivity, and thermal expansion. Consequently, ZT values have been also increased, reaching 0.24 at 800 °C in 0.25 wt.% B₄C containing samples, which is very close to the best values reported in the literature, and two times higher than the obtained in pure materials in this work.     

Elastic modulus prediction based on thermal conductivity for silica aerogels and fiber reinforced composites

The speed of sound is a critical parameter in the test of mechanical and thermal properties. In this work, we proposed a testing method to obtain the elastic modulus of silica aerogel from the sound speed formulas. The solid thermal conductivity of the silica aerogel is experimentally measured for predicting the sound speeds, and then the elastic modulus is calculated based on the elasticity sound speed model. The experimental data of the solid thermal conductivity of silica aerogels with different densities are employed and the obtained elastic modulus is fitted as a power-law exponential function of the density. Two existing sound speed models and three groups of available experimental data are also employed to validate the present fitting relation, and good agreement is obtained for the silica aerogel in the density range of 150–350 kg/m³. The fitting formula can also be extended to estimate the elastic modulus of the glass fiber-reinforced silica aerogel composite. The results show that the elastic modulus of the aerogel composite is sensitive to the glass fiber volume fraction, while the thermal conductivity is weakly dependent on the glass fiber volume fraction at room temperature in the studied range of fiber volume fraction.     

Magnetic properties of double-side partially fluorinated graphene from first principles calculations

Density functional theory calculations were used to study the structural, electronic, and magnetic properties of double-side partially fluorinated graphene. Both even and uneven fluorinated structures examined. It is found that midgap states and magnetic moments only appear in the uneven double-side fluorinated graphene. The magnetic moments mainly come from the carbon atoms at the edge of the fluorinated region in unevenly double-side fluorinated graphene. The dependence of magnetic moments on external tensile strain was also examined, which shows that the induced magnetic moments can be significantly increased by increasing the tensile strain.     

Investigating the elastic,mechanical, and thermal properties of polycrystalline Mo2C under high pressure and high temperature

Understanding pressure-induced acoustic velocity-elasticity behavior has extraordinary significance in the fields of materials science and earth science. Herein, we used an advanced high-pressure high-temperature (HPHT) method to synthesize pure-phase β-Mo₂C bulk ceramics. The sound velocity-elasticity behavior, thermodynamic properties, and mechanical behavior of the synthesized β-Mo₂C ceramics were systematically investigated by in-situ high-pressure ultrasonic interferometry and theoretical calculations. The compressive and shear wave velocities, isothermal bulk modulus, shear modulus, Vickers hardness, fracture toughness, Debye temperature, and melting temperature of polycrystalline β-Mo₂C exhibited a monotonic increase with increasing pressure. The experimental and calculation results showed that β-Mo₂C had strong ductile behavior and was a ductile ceramic. Additionally, the temperature-hardness relationship of the as-synthesized polycrystalline β-Mo₂C was investigated by in-situ high-temperature Vickers indentation measurements. The hardness of β-Mo₂C gradually decreased with increasing temperature, and this ceramic still maintained a hardness as high as 12.3 GPa at 500 °C. These results suggest that the intrinsic mechanical and thermodynamic properties of β-Mo₂C are dominated by its unique electronic structure and bonding mode.     

Pressureless sintering and properties of (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C high-entropy ceramics: The effect of pyrolytic carbon

A novel (Hf_0.2Zr_0.2Ta_0.2Nb_0.2Ti_0.2)C high-entropy ceramic was successfully prepared by pressureless sintering at 2200 °C. With increasing content of resin-derived-carbon, the density, and mechanical and thermal properties increased up to a maximum content of 2～4 wt% resin addition, after which further addition was detrimental. All specimens showed high strength (≥347±36 MPa), with the highest value achieving 450±64 MPa, and fracture toughness significantly higher (>20 %) than those of the corresponding monocarbides and Ta_0.5Hf_0.5C, (Ta_1/3Zr_1/3Nb_1/3)C. The thermal conductivity was approximately equivalent to the lowest value of the corresponding mono-carbides, which was assumed to be due to the lattice distortion effect.     

Elastic properties of porous porcelain stoneware tiles

Porcelain stoneware tiles are industrially processed by using high sintering temperatures and fast firing cycles that result in products characterized by an almost impervious surface layer surrounding a rather porous bulk material. Since mechanical properties are affected by porosity, the knowledge of the material stiffness is an important parameter to define the service behavior of tiles. In the present investigation, porcelain stoneware samples having different closed porosity were investigated in order to understand the influence of the porosity on the elastic constants of the materials.Based on the quantitative XRD phase composition, elastic constants have been calculated via Voigt-Reuss-Hill averaging, and the influence of porosity has been taken into account via power-law and exponential relations. It is shown that the effective elastic constants predicted by exponential and power-law relations are in agreement with experimental values. It may be concluded that for this class of materials, in the porosity range below 14–16%, both exponential and power-law relations are helpful tools to design tiles with controlled microstructure and tailored mechanical properties.     

Local orders,lattice distortions,and electronic structure dominated mechanical properties of (ZrHfTaM1M2)C (M = Nb,Ti, V)

High-entropy carbides (HECs) are regarded as potential candidate structural materials with attractive mechanical properties due to their ultra-high hardness. It is essential to reveal the atomic and electronic basis for strengthening mechanism in order to develop the advanced HECs. In the present work, C (M = Nb, Ti, V) are selected as case studies. The effects of transition metals (M) on the lattice parameters, bulk modulus, enthalpy of formation, electron work function (EWF), and bonding morphology/strength of HECs are comprehensively studied by first-principles calculations. It is found that the lattice parameters, equilibrium volumes, and bulk modulus of HECs are improved with the increase of M atomic volumes. The atomic-size differences among various groups of elements not only result in the lattice mismatch/distortion but also contribute to the formation of weak spots. In the view of bonding charge density, the electron redistributions caused by the coupling effect of the lattice distortion and valance electron differences can be revealed obviously, which identify the different bonding strength. Moreover, in terms of EWF, the proposed power-law-scaled hardness of HECs is validated and matches well with those reported theoretical and experimental results, providing a strategy to design advanced HECs with excellent mechanical properties.     

Elastic anisotropy and thermodynamics properties of BiCu2PO6, BiZn2PO6 and BiPb2PO6 ceramics materials from first-principles calculations

In present work, the elastic properties, anisotropy in elasticity and thermodynamics properties for BiCu₂PO₆, BiZn₂PO₆ and BiPb₂PO₆ ceramics materials were investigated using the first-principles calculation. The formation enthalpy and phonon frequencies confirm that three BiX₂PO₆ (X = Cu, Zn, and Pb) compounds exhibit the structural stability. The calculated elastic constants and elastic moduli indicate that BiZn₂PO₆ has the better mechanical properties than BiCu₂PO₆ and BiPb₂PO₆ at ground state. The values of B/G confirm that three BiX₂PO₆ compounds all exhibits the ductile behavior. The values of anisotropic parameters, three-dimensional surface constrctions and two-dimensional projection curves of the Young's modulus reveal the anisotropic degree of three BiX₂PO₆ compounds. The thermodyanmic parameters indicate that three BiMn₂XO₆ materials show the thermal stability from 0 to 1000 K. The obtained physical parameters can provide the useful data for the further experimental investigations.