Table 1 - uploaded by Victor Milman
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Equilibrium structure of ZrB 2 . Deviations from the experimental results are given in brackets. a (Å) c (Å) c/a Comment
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The stiffness and thermal expansion coefficient of ZrB2 are calculated within the density functional theory formalism. The stiffness tensor obtained here using the static finite strain technique is in good agreement with the results of
resonant ultrasonic measurements and points to a possible misinterpretation of the experimentally obtained compres...
Context in source publication
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... used five different temperatures from 300 to 1100 K for linear fitting of the a(T ) dependence; see figure 2. We obtained the CTE of 7.4(5) × 10 −6 K −1 , in satisfactory agreement with the experimental result [1]. The extrapolation to T = 0 K produces a = 3.169 Å, in good agreement with the result of direct geometry optimization (see table 1). ...
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Citations
... The theoretical studies reported K′ for HfB 2 as, 3.85-3.87 [30], and 4.16 [31], the average being close to 4. For many elements and compounds, K′ was reported to be quite close to 4 as that for TiB 2 (3.7) and ZrB 2 (3.9) [32,33]. The Birch-Murnaghan equation of state reduces to the Birch equation of state for K′=4. ...
Hafnium diboride (HfB2) is an ultra-high temperature ceramic that has attracted increased attention for its fascinating properties. In this study, temperature derivatives of the bulk modulus of HfB2 were calculated from room temperature up to 2273 K by using the relevant theoretical thermodynamic equations for the bulk modulus. The equations used involve the parameters as the enthalpy, thermal expansion and heat capacity in addition to the Anderson Grüneisen parameter. The calculations were performed using the pressure derivative of the bulk modulus for the Anderson Grüneisen parameter and the experimental temperature dependent values for the other parameters of the used equations. Temperature derivatives of the bulk modulus of HfB2 were found to be, −0.012 / −0.013 GPa/K at 293 K and −0.015 / −0.016 GPa/K at 2273 K. These values are in good agreement with the corresponding experimental data, and quite close to the corresponding values reported for ZrB2 and TiB2. However, the experimental temperature derivatives of the bulk moduli for the three diborides, TiB2, ZrB2, and HfB2 are quite smaller in magnitude than the corresponding theoretical values. The Grüneisen parameter of HfB2 decreases from 1.2 to about 1.0 with increasing temperature up to about 500 K, and then it has a small variation at higher temperatures. HfB2, with its high strength, high density and small temperature derivatives of the bulk modulus, may be useful for the aerodynamic and nuclear applications. The method presented in our studies is a practical way to predict temperature dependencies of the bulk moduli. This method may be more useful at ultra-high temperatures where the experimental bulk moduli measurements are quite difficult.
... The initial five constants are known as independent elastic constants while the final one takes into consideration; 66 = ( 11 − 12 )/2 [29]. A mechanically stable Fe 2 P-type compounds need to obey the following criteria for mechanical stability of hexagonal symmetry [30,31,32]. 11 > 0 , 33 > 0 , 44 > 0, 11 > | 12 |, ( 11 2 > 12 2 ) and ( 11 + 2 12 ) 33 > 2 13 2 . ...
... In our approach of calculations of stiffness constants, we used the equilibrium structure to deform symmetry-dependent strain configurations with different magnitudes and optimized the internal structure with varying parameters. By linear fitting of energy-strain data, we get three stiffness constants for cubic crystal structure (C 11 , C 12 , C 44 ) [56,57]. C 11 , C 12 and C 44 describe the modulus for axial compression, modulus for transverse expansion and resistance against shear deformation respectively. ...
The objective of this work is to explore structural, mechanical and thermal stability including electronic, optical and thermoelectric properties of state-of-the-art AlNiX (X = P, As and Sb) half-Heusler compounds having 18 valence electron count (VEC). Calculations have been carried out in the framework of density functional theory (DFT) implemented in WIEN2k code followed by the solution of the Boltzmann transport equation with constant relaxation time approximation. In the most energetically favorable structure, their lattice constants lie in the range of 5.501 Å – 5.983 Å and band gaps have been found to be 0 eV, which confirm the metallic behavior of these compounds. The different elastic and thermodynamic parameters confirm their mechanical and thermal stability with a mechanically anisotropic and ductile nature. Specific heat and entropy of these materials increase as the atomic number of X atom increases. The calculated optical parameters prove their candidature for promising photovoltaic devices and shields for UV radiation. The thermal conductivity has been computed using Slack's model. This detailed study shows that these compounds are promising for materials scientists due to their very high lattice thermal conductivity and low figure of merit. We deny recommending them as good thermoelectric applications.
... ) with a hexa gonal crystal structure (space group symmetry P6/mmm) [1][2][3] has been the object of considerable study as one of the most widely used ultra-high temperature ceramics (UHTC) due to its high melting point (3519K) [2,4], chemical stability and properties of resistance to erosion/corrosion, and relatively low density of about 6.08 [5]. In addition, it also possesses good thermal-shock resistance as a result of its high hardness, excellent thermal conductivity [6][7][8][9][10][11], and high tensile strength ( ) in both normal and elevated temperature [12][13][14]. ...
First principles calculation has been used to investigate the effects of Y on structural stability, mechanical property, and cohesion strength of ZrB2. It is revealed that the substitution of Zr by Y in ZrB2 is energetically favorable, while decreases the structural stability and mechanical property of ZrB2. Calculation also shows that chemical potential of B (μB) has an important effect on interface stability, i.e., the Zr- and B-terminated Y(0001)/ZrB2(0001) interfaces are thermodynamically more stable when −8.25eV≤μB≤-7.87eV and −7.87 eV≤μB≤ -6.75 eV, respectively. Moreover, the addition of Y could considerably decrease the cohesion strength of ZrB2, and the Y particle and Zr-terminated Y/ZrB2 interface would be the fracture positions due to their low cohesion strength. The calculated results are in good agreement with experimental/calculated observations in the literature.
... In the calculations of stiffness constants, we have used the equilibrium structure to deform symmetry-dependent strain configurations with different magnitudes and optimized the internal structure with varying parameters. By linear fitting of energy-strain data we get three stiffness constants for cubic crystal structure (C 11 , C 12 , C 44 ) [30,31]. Computed values of these stiffness constants are listed in Table 3. Cubic crystal is found to be mechanically stable against elastic deformations if C 11 -C 12 > 0; C 11 þ 2C 12 > 0C 44 > 0; and C 11 > 0 [32]. ...
We have investigated the structural, electronic, optical, thermoelectric, elastic, and thermodynamic characteristics of antiperovskites ANX3 (A= P, As, Sb, Bi; X= Sr, Ca, Mg) by the first-principles calculation based on the density functional theory (DFT) accompanied via semi-classical Boltzmann theory employing linearized augmented plane wave (LAPW) method with PBE+TB-mBJ potentials. All are direct band gap semiconductor and the outcomes are in strong agreement with existing experimental data. We have also computed various optical parameters, which are followed by the investigation of thermoelectric parameters at 300 K, 500 K, 700 K, and 900 K. Furthermore, to examine the mechanical behaviour of antiperovskites materials, we have investigated the elastic properties. The thermodynamic measurements have been carried out within the quasi-harmonic approximations at the considered temperature range. Most of the computed parameters have been mentioned for the very first time. The proposed work authenticates that these materials may turn out to be rebellious substances because of their narrow band gap, low cost, high absorption, and excellent elastic, thermoelectric, and thermal properties.
... The use of ZrB 2 as a high-temperature material requires knowledge of its thermal properties, the temperature dependence of its thermal expansion coefficient (TEC), and its anisotropy. The thermal expansion of ZrB 2 has been studied for more than 60 years now, which has made it possible to accumulate a large amount of experimental data [6][7][8][9][10][11][12][13][14][15]. ...
... Применение ZrB 2 в качестве высокотемпературного материала требует информации о его термических свойствах, анизотропии и температурной зависимости КТР. Исследования КТР ZrB 2 ведутся уже более 60 лет и позволили накопить большой экспериментальный материал [6][7][8][9][10][11][12][13][14][15]. ...
... A relatively small increase in K R value as a function of the crack extension was reported for pure ZrB 2 , where the intrinsic toughness K 0 ≈3 MPa m 1/2 had been reported at ≈35 μm crack extension and the fracture toughness K R rises to the maximum value of ≈3.35 MPa m 1/2 reaching a plateau at 525 μm crack extension, which is indicative of the presence of crack bridging toughening mechanisms acting in pure ZrB 2 ceramics. While no detailed structural analysis was performed to determine the mechanisms responsible for rising Rcurve behaviour of pure polycrystalline ZrB 2 in [27], if one recollects R-curve behaviour in polycrystalline Al 2 O 3 with hexagonal anisotropic grains, the same considerations might be used for explanations of Rcurve behaviour of ZrB 2 that also crystallise in the hexagonal structure [41]. The crystallographic anisotropy of ZrB 2 grains would play a role on the formation of thermal residual microstresses that would affect and deviate the crack path resulting in the observed Rcurve behaviour. ...
R-curve and controlled stable crack growth behaviour of ZrB2–17vol.-%SiC and ZrB2–45vol.-%SiC ceramic composites was studied on V-notched samples using four-point bending at room temperature. The rising K1R behaviour was determined as a function of the crack extension Δa with a crack bridging mechanism being dominant in such behaviour. Significant differences in crack growth rates were found within the same composition of ceramics simply as the crack length varied during crack growth processes. These differences are indicative of the significant influence of microstructural parameters of the ceramics on crack propagation. The peculiarities of stress intensity factor K1 and the crack growth-specific behaviour in ZrB2–SiC particulate ceramic composites are discussed.
... The tolerance for geometry optimization was set as the difference of total energy within 5. 10-6eV/atom, maximum ionic Hellmann-Feynman force within 0.001 eV/˚ A and maximum stress within 0.02 eV/˚A3. Several methods are available for computation of stiffness coefficients, but currently the tress-strain method seems to be most commonly used and this method used in present work [13]. In this approach, the ground state structure is strained according to symmetry-dependent strain patterns with varying amplitudes and a subsequent computing of the stress tensor after a re-optimization of the internal structure parameters, i.e. after a geometry optimization with fixed cell parameters. ...
In this paper we reported calculation of the mechanical properties of the two phases of aluminiumthiophosphate ht-AlPS 4 and lt-AlPS 4 at high and low temperature as well as for the indiumthiophosphate InPS 4. We used density functional theory (DFT) to show that the low phase AlPS 4 has a two-dimensional distribution with a large degree of anisotropy between the different axes x, y and z for the mechanical properties such as the Young modulus and the compressibility (in the xy, xz and yz planes). Both phases of AlPS 4 show a the spatial distribution of the atoms and the bonds in the different axes. The indiumthiophosphate is showing a three-dimensional (3D) distribution, leading to a different types of bonds that will affect the mechanical properties and stability and anisotropy of each structure.
... Milman et al. had investigated the average TEC of ZrB 2 through an ab initio molecular dynamics approach at temperatures up to 1200°C. 8 Gonzales et al. used ab initio molecular dynamics (AIMD) to study the TECs and elastic constants of ZrB 2 and HfB 2 . 9 However, the fitness between the theoretical TEC and experimental results was not quite satisfactory. ...
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.
