Elastic Constants C11 Research Articles

Theoretical prediction of mechanical and thermodynamic properties of TiMC2 (M = Hf, Mo, Nb and W) ceramics: Very promising excellent TiC - based solid solution materials

The mechanical and thermodynamic properties of TiMC2 (M = Hf, Mo, Nb and W) ceramics are investigated by the first-principles method based on density-functional theory (DFT). Meanwhile, the investigation of TiC ceramics is also carried out to verify the reliability of the calculation in this study. The results show that TiMC2 ceramics have good thermodynamic stability and possess the characteristics of advanced ceramic materials. Except for TiHfC2 ceramics, the elastic properties and melting temperature of TiMoC2, TiNbC2 and TiWC2 ceramics are significantly higher than those of TiC ceramics. Especially TiWC2 ceramics, its elastic constant C11 is as high as 732.3GPa, and its melting temperature is as high as 4581 K, which may be the highest melting temperature found in the world. TiMC2 ceramics belong to the brittle materials family, and the ductility of TiHfC2, TiNbC2 and TiWC2 ceramics is only weakly lower than that of TiC ceramics, while the ductility of TiMoC2 ceramics is significantly better than that of TiC ceramics. TiHfC2, TiMoC2, TiNbC2 and TiWC2 ceramics exhibit normal thermal expansion behavior at 0–1590 K, 0–1510 K, 0–1820 K and 0–1950 K, respectively, and the thermal expansion rate follows the order: TiMoC2>TiHfC2>TiWC2>TiNbC2, and TiMC2 ceramics belong to the medium expansion materials. The phonon thermal conductivity of TiC ceramics is always lower than that of TiNbC2 ceramics, but higher than that of TiWC2, TiMoC2 and TiHfC2 ceramics, indicating that the doping of Nb element can increases the phonon thermal conductivity of TiC ceramics, while the doping of Hf, Mo and W elements reduces the phonon thermal conductivity of TiC ceramics. By studying the elastic and thermodynamic properties of TiMC2 (M = Hf, Mo, Nb and W) ceramics, a theoretical reference is provided for its application in many fields.

Pressure effect on the physical, mechanical, and thermal properties of ternary halide perovskite AgCaCl3: a first-principles study.

As an inorganic halide perovskite material, AgCaCl3, characterized by its high stability and environmental friendliness, is considered a potential candidate for major applications in optoelectronics and lens manufacturing. This work aimed to determine the electronic properties such as density of state (DOS) and band structure (BS) of AgCaCl3. The results showed that the material has an indirect band gap almost invariably at 1.5eV in the pressure range studied. The dielectric function [Formula: see text], absorption coefficient [Formula: see text], optical conductivity [Formula: see text], reflectivity [Formula: see text], and the refractive index [Formula: see text] showed clearly that the perovskite AgCaCl3 preserved its optical characteristics within the chosen pressure range investigated. The calculated elastic constants C11, C12, and C14 as dynamic stability criteria for the elastic moduli such as bulk modulus (B), shear modulus (G), Young's modulus (Y), Poisson's ratio ([Formula: see text]), and anisotropy factor (A) showed that the material is a ductile plastic. Debye temperature ([Formula: see text]), isobaric and isochoric heat capacities (CP, CV), coefficient of the thermal expansion (α), Gibbs free energy (G), and entropy (S) were also studied. The results obtained provide a theoretical basis for experimental work and offer the possibility of future industrial applications of AgCaCl3. Density functional theory (DFT) calculations as implemented in the Wien2K code were used to study the mechanical and thermal properties of AgCaCl3 perovskite over a pressure range. Lattice parameters, electronic, and optical properties are optimized with the approximation of the generalized gradient of the Perdew-Burke-Ernzerhof function (PBE-GGA) function. The mechanical and thermodynamic properties were calculated using ElaStic and Gibbs2 codes, and the properties of AgCaCl3 over the pressure range investigated were predicted.

Atomic, electronic, and superconducting properties of Zr[formula omitted]Ir compound

We have investigated the structural, electronic, mechanical, phononic, and superconducting properties of the Zr2Ir compound with a body-centered tetragonal crystal structure using first-principles calculations. Our analysis reveals that the Zr2Ir compound shows mechanical and dynamically stable by using with and without spin–orbit coupling (SOC) effect. After calculating some properties such as elastic constants, Bulk modulus, Young’s modulus, Poisson ratio, Debye temperature, and sound velocity, we found that Zr2Ir is ductile. When the elastic constants C11 and C33 are compared, it is determined that the situation changes in the opposite direction under the effect of SOC, that is, more compressibility along the x-axis turns into the z-axis. Here, the electronic band structure and intensity of the states calculated for the compound show a metallic character. The superconducting critical temperature (Tc) and electron–phonon coupling constant (λ) were found to be 7.50 K and 0.93 without SOC and 7.62 K and 0.96 with SOC, respectively. We determined that although the Zr2Ir compound has a strong electron–phonon coupling regime, the inclusion of SOC slightly reduces its critical temperature and electron–phonon coupling constant.

Micro Hardness Study of Macro Wire of Bismuth Samples Using Contact Model

Abstract: The micro-hardness test is often used to pre-determine the mechanical properties of a material. The Vickers method can be used for testing metals, particularly those with extremely hard surfaces. The study of the correlation between applied load and the measured value of the microhardness was carried out for Bismuth wire samples. Bismuth is a semimetal in bulk, it is not a good thermal electrical material. Bismuth nanowires (10nm) have a thermal electric figure while exhibiting semiconductor behaviour. Mechanical characterization is critical for the formation of nanowires made of various materials. The microhardness testing of bismuth wire plate samples was performed on a microscopic scale in this communication. Vicker's number variation is reported. At low indentation test loads, an indentation size effect was observed for Bismuth wire plate samples. For all samples, the variation of microhardness number (Hv) with variable loads is non-systematic. PSR ( Proportional specimen Resistance )Model, MPSR ( Proportional specimen Resistance )Model for the calculation of elastic stiffness constant C11, Wooster’s empirical relations used with obtain hardness data.

Effect of nonstoichiometry on anisotropy of elastic properties of disordered cubic zirconium carbide ZrCy

The elastic constants c11, c12, c44 are determined for the first time as functions of the carbon content y in the homogeneity region ZrC0.60 - ZrC1.00 of nonstoichiometric disordered cubic ZrCy zirconium carbide. It is established that the elastic stiffness constants cij of disordered ZrCy carbide decrease with an increase in the defectiveness of the carbon sublattice of zirconium carbide. An increase in the deviation of the ZrCy composition from stoichiometry leads to a slight decrease in the anisotropy of the elastic properties. The elastic properties of zirconium carbide are anisotropic, since they change depending on the crystallographic direction [hkl] due to differences in the arrangement of atoms and interatomic bonds in various directions. It is found that the values of elastic moduli depend on the crystallographic direction [hkl], and the maximum and minimum the Young's moduli are observed in the [001], [010], [100] or [±1 ± 1 ± 1] directions of cubic ZrCy carbide, respectively. Small changes in the elastic characteristics of ZrCy depending on the [hkl] direction indicate a weak elastic anisotropy of cubic zirconium carbide. It is shown that the calculated Vickers hardness and Debye temperature of polycrystalline disordered cubic ZrCy carbide increase non-linearly with increasing relative carbon content y.

Doping Engineering for Optimizing Piezoelectric and Elastic Performance of AlN

The piezoelectric and elastic properties are critical for the performance of AlN-based 5G RF filters. The improvement of the piezoelectric response in AlN is often accompanied by lattice softening, which compromises the elastic modulus and sound velocities. Optimizing both the piezoelectric and elastic properties simultaneously is both challenging and practically desirable. In this work, 117 X0.125Y0.125Al0.75N compounds were studied with the high-throughput first-principles calculation. B0.125Er0.125Al0.75N, Mg0.125Ti0.125Al0.75N, and Be0.125Ce0.125Al0.75N were found to have both high C33 (>249.592 GPa) and high e33 (>1.869 C/m2). The COMSOL Multiphysics simulation showed that most of the quality factor (Qr) values and the effective coupling coefficient (Keff2) of the resonators made with these three materials were higher than those with Sc0.25AlN with the exception of the Keff2 of Be0.125Ce0.125AlN, which was lower due to the higher permittivity. This result demonstrates that double-element doping of AlN is an effective strategy to enhance the piezoelectric strain constant without softening the lattice. A large e33 can be achieved with doping elements having d-/f- electrons and large internal atomic coordinate changes of du/dε. The doping elements-nitrogen bond with a smaller electronegativity difference (ΔEd) leads to a larger elastic constant C33.

Influence of octahedral site chemistry on the elastic properties of biotite

Brillouin light scattering spectroscopy was used along with detailed composition information obtained from electron probe microanalysis to study the influence of octahedral site chemistry on the elastic properties of biotite crystals. Elastic wave velocities for a range of directions in the AC and BC crystallographic planes were obtained for each crystal by application of the Brillouin equation with refractive indices and phonon frequencies obtained from the Becke line test and spectral peak positions, respectively. In general, velocities increase with decreasing Fe content, approach those of muscovite at low Fe concentrations. 12 of the 13 elastic constants for the full monoclinic symmetry were obtained for each crystal by fitting analytic expressions for the velocities as functions of propagation direction and elastic constants to corresponding experimental data, with the remaining constant estimated using hexagonal symmetry. Elastic constants C11, C22, and C66 are comparable to those of muscovite and show little change with Fe concentration due to strong bonding within layers. In contrast, nearly all remaining constants show a pronounced dependence on Fe content, likely due to the weak interlayer bonding. Similar behaviour is shown by elastic stability, which falls greatly as Fe concentration increases, and elastic anisotropy within the basal cleavage plane, which decreases with Fe content. This consistent dependency of all measured elastic constants on Fe content suggests that biotite elasticity is a function of octahedral site chemistry and gives a method to determine the elastic constants and elastic stability of most biotite compositions provided, Fe or Mg concentrations are known. Moreover, the good agreement between elastic constants of Fe-poor biotite and those of phlogopite obtained from DFT simulations indicate a method to predict elastic properties of biotites.

The structural, mechanical, thermal, electronic and optical properties of halide perovskites [formula omitted]: First-principles investigations

The structural, mechanical, thermal, electronic and optical properties of inorganic Pb-free double perovskites Cs2TiX6(X=Cl,Br,I) compounds are investigated. Using the first-principles with full-potential linearized augmented plane wave (FP-LAPW) method, supported the density functional theory, and therefore the generalized gradient approximation (GGA-PBE) and Hybrid exchange-correlation functionals with and without spin-orbit coupling. The computation of the lattice constants showed an honest agreement between our results and the experimental results and the theoretical data available. Using the three independent elastic constants C11, C12 and C44, various mechanical and thermal properties are obtained such as: bulk modules B, shear modules G, Young's modules Y, Pough's ratio B/G, Frantesvich ratio G/B, Poisson's ratio υ, Shear anisotropy character A and Debye temperature ΘD for Cs2TiI6, Cs2TiBr6 and Cs2TiCl6 respectively. Our calculated elastic constant results show that Cs2TiI6, Cs2TiBr6 and Cs2TiCl6 are mechanically stable, anisotropic and ductile in nature. Furthermore, the Cs2TiCl6 compound has the highest Debye temperature, which indicates the highest melting temperature. The electronic band structures reveal the semiconductor conductivity of the three compounds, with a band gap suitable for photovoltaic applications, within the range of 1.5–2.96 eV. Finally, Cs2TiCl6(X=Cl,Br,I) HPs compounds exhibit excellent optical properties like optical absorption, conductivity and refraction index.

The rendering from the periodic system of elements on the stability, elastic, and electronic properties of M2AC phases

MAX phases are nanolaminated ternary materials that combine metallic and ceramic properties. Currently, the A-site elements replacement in traditional ones by later transition-metals opens a door to explore new types of MAX phases. In this work, we performed a systematic first-principle study to explore trends in stability, electronic structure and elastic properties of 288 compositions of M2AX phases (M=Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, W; A=Al, Si, P, S, Ga, Ge, As, Se, In, Sn, Sb, Te, Tl, Pb, Bi, Mn, Fe, Co, Ni, Cu, Zn, Tc, Ru, Rh, Pd, Ag, Cd, Os, Ir, Pt, Au, Hg; X=C). Such a dataset, combined with the rigid-band model been applied to most transition metal carbides, shows us the fundamental trends in bonding mechanisms and elastic properties of MAX phases endowed with the periodic arrangements of M/A-site elements. In particular, the M-A d-d interactions of MAX phases uniquely contribute to the elastic constant C33.

The boson peak in silicate glasses: insight from molecular dynamics.

In the low-frequency regime, ≈1 THz, glasses show an anomalous excess in their vibrational density of states called the boson peak (BP). The origin of BP has been a subject of debate since its first discovery a few decades ago. Although BP has been the focus of numerous studies, no conclusive answers have been found about its origins, which remained elusive to date. Here, we present results based on molecular dynamics of several binary and ternary silicate glasses with different network intermediates and modifier oxides. The vibrational density of states and the BP are reported for all the studied glasses. Their correlation with the elastic constant C44, structural, and dynamical properties are extensively discussed in terms of Voronoi atomic volume and the vibrational mean square displacement of Q4 species specifically. We also question the classical classification of alkali oxides as modifiers, and we suggest that Li2O plays the role of pseudo-intermediate oxide in lithium silicate glasses. This claim is supported by the effect of Li on various vibrational modes, and this effect differs from the other alkali metals. Furthermore, we demonstrate a correlation between the BP intensities and both the Voronoi volume of the Q4 and Q3 units and vibrational mean square displacements.

Elastic Properties of B2-NiAl with W addition: A first-principles study

The effect of tungsten alloying on the elastic properties of B2-NiAl at low-temperature and high-temperature distribution of W atoms on sublattices. By means of the exact muffin-tin orbitals method in conjunction with the coherent potential approximation, the constants C11,C12,C44, Young's modulus E, shear modulus G, Cauchy pressure values, G/B ratios are calculated. Using phenomenological criteria of the correlation between ductility and elastic properties of solution phases, it has been shown that the addition of tungsten could yield improved ductility for B2-NiAl in both types of alloys. It is established that with the high-temperature distribution of W atoms on the Al sublattice, there is a loss of mechanical stability and a decrease in mechanical properties with increasing W concentration. In alloys with a low-temperature distribution of tungsten atoms between Al and Ni sites a unique combination of properties occurs: in addition to the ductility enhancement, a simultaneous increase of the elastic constants C44 and C11 and C11, shear modulus G, Young's modulus E with increasing W content is observed. The differences in the behavior of elastic constants in alloys with different types of tungsten distribution on NiAl sublattices are analyzed by calculating the density of electronic states. Keywords: NiAl, alloying elements, tungsten, elastic properties, ductility, first-principles calculations.

Упругие свойства B2-NiAl с добавлением W: исследование из первых принципов

The effect of tungsten alloying on the elastic properties of B2 NiAl at low-temperature and high-temperature distribution of W atoms on sublattices. By means of the exact muffin-tin orbitals method in conjunction with the coherent potential approximation, the constants C11, C12, C44, Young's modulus E, shear modulus G, Cauchy pressure values, G/B ratios are calculated. Using phenomenological criteria of the correlation between ductility and elastic properties of solution phases, it has been shown that the addition of tungsten could yield improved ductility for B2 NiAl in both types of alloys. It is established that with the high-temperature distribution of W atoms on the Al sublattice, there is a loss of mechanical stability and a decrease in mechanical properties with increasing W concentration. In alloys with a low–temperature distribution of tungsten atoms between Al and Ni sites a unique combination of properties occurs: in addition to the ductility enhancement, a simultaneous increase of the elastic constants C44 and C11, shear modulus G, Young modulus E with increasing W content is observed. The differences in the behavior of elastic constants in alloys with different types of tungsten distribution on NiAl sublattices are analyzed by calculating the density of electronic states.

First-principle insight into the structural, electronic, elastic and optical properties of Cs-based double perovskites Cs2XCrCl6 (X = K, Na).

This study communicates the theoretical investigations on the cubic double perovskite compounds Cs2XCrCl6 (X = K or Na). Density functional theory (DFT) calculations were carried out using the TB-mBJ approximation. These compounds were found to be stable in the cubic perovskite structure having lattice constants in the range of 10.58-10.20. The stability of the investigated materials was assessed by the Gold-Schmidt tolerance method, which resulted in the tolerance factor values of 0.891 and 0.951 for Cs2KCrCl6 and Cs2NaCrCl6, respectively. The calculated values of the elastic constants C11, C12, and C44 of the cubic compounds studied by our research team confirm the elastic stability. The values of the formation energies were also calculated for both the compounds and were found in the range from -2.1 to -2.3. The electronic behavior of the presently investigated materials was examined by inspecting their band structures and the density of states. It was observed that both the materials have half-metallic nature. To check the suitability of the studied compounds in optical applications, we determined the real and imaginary parts of their respective dielectric functions, absorption coefficients, optical conductivities, refractive index, and reflectivity as a function of a wide range of incident photon energies up to 40 eV.

Structural, electronic, mechanical and phonon properties of half-Heusler GaNiSb, InNiSb and InPdSb alloys via first-principles calculations

In this report, the ground state properties of the half-Heusler GaNiSb, InNiSb and InPdSb alloys in the cubic LiAlSi-type structure, are investigated using the Full Potential Linearized Augmented Plane Wave (FP-LAPW) method as implemented in WIEN2k code, based on Density Functional Theory (DFT). The Perdew–Berke–Ernzerhof (PBE) Generalized Gradient Approximation (GGA) is used for exchange–correlation functional. The calculated formation energies and volume-optimization curves of three different structural configurations (Type 1, Type 2 and Type 3) of these alloys reveal that Type 3 configuration is the most favorable (lowest energy structure) structure. According to the Slater–Pauling rule, the studied alloys are non-magnetic in nature in the stable Type 3 configuration. Therefore, the calculation of ground state properties of these alloys are examined in the Type 3 structural configuration and non-magnetic state. The results of electronic structure and density of states reveal that these alloys are metallic in nature. These alloys are dynamically stable as demonstrated by their calculated phonon dispersion spectra. As the three independent elastic constants C11, C12 and C44 satisfy Born–Huang stability condition, these alloys are stable elastically. The studied alloys are ductile in nature, elastically anisotropic and GaNiSb is found to be stiffer than InNiSb and InPdSb by the calculation of mechanical properties. The present work is in good agreement with the previously reported results.

Volume-matched piezoelectric LaN/REN superlattices from first-principles

LaN/rare earth nitride (REN) superlattices, having magnetic REN as one of the parent components, are constructed and studied by first-principles calculations. In particular, they are found to be mechanically and dynamically stable with (anti-)ferromagnetic and ferroelectric orderings. We reveal that the volume matching condition is applicable to these superlattices, which results in the elastic constant C33 softening and, when combined with a small c/a value, induces a huge piezoelectric response near the unstrained state. We also show that in-plane biaxial strain can precisely control the nature (indirect or direct) and value of the electronic bandgap. Moreover, the unpaired magnetically active 4f-electrons reduce the c-direction off-centric distortion of the wurtzite structure, making possible the switching of the ferroelectric polarization. This work, therefore, reveals that the volume matching condition also applies to magnetic materials and provides guidance for the design of multiferroic rare-earth nitride superlattices in piezoelectric devices.

Quantum effects on the elastic properties of cubic boron nitride by path-integral Monte Carlo simulation

Using path-integral Monte Carlo simulation, we study the quantum effects on the elastic properties of cubic boron nitride (c-BN) crystal in a wide temperature range from 40 to 2000 K and a pressure range varying from 1 atm to 160 GPa. The Tersoff–Albe potential is employed to describe the interatomic interactions, and the elastic constants are determined by a direct method derived from the stress–strain curves. The calculations show that elastic constants C11, C12, and C44 are temperature and pressure dependent, and their values are in satisfactory agreement with available experimental results at room temperature. Furthermore, we estimate the Poisson ratio, anisotropic factor, longitudinal-wave elastic constant, Cauchy pressure, and Pugh’s ratio and their temperature and pressure dependence. In general, the quantum effect contributions to the elastic properties of the c-BN are extracted quantitatively from the differences between the path-integral and classical Monte Carlo simulation results. The quantum contribution is negligible at high temperatures but can be significant at low temperatures. It is responsible for variations of about 5∼7% of the elastic constants C11 and C44, and C12. The impacts of quantum contribution on the elastic properties of the c-BN crystal are similar to those found in the diamond.

Extension of MAX phases from ternary carbides and nitrides (X = C and N) to ternary borides (X = B, C, and N): A general guideline

AbstractAlthough significant progress has been made on understanding the structure–property relationship of MAX phases, a clear answer has not been given to the outstanding question whether MAX phases can be extended from carbides and nitrides (X = C and N) to borides (X = B). Herein, based on the systematically investigations on the general trend of lattice constants and elastic properties of the experimentally found MX and M2AX (X = B, C, and N) with the valence electron concentration (VEC), a guideline for the discovery of new MAX borides is given. The MX and M2AX (X = B, C, and N) compounds are situated in a small range of VEC, and their lattice constants generally decrease with VEC. Second‐order elastic constants c11, c33, and bulk modulus B of M2AX (X = B, C, and N) increase with VEC due to enhanced bonding, c44 and G, however, increase up to some critical values and then decline with the further increase of VEC. Based on the electronic structure–elastic property relationship and the presence of rock salt–structured transition metal monoborides, nine possible MAX phase borides M2AB (M = Zr, Hf, Nb, A = P, As, and Sb) are predicted. Thus, MAX phases can be extended from X = C and N to X = B, C, and N.

Lattice dynamics and elastic properties of α-U at high-temperature and high-pressure by machine learning potential simulations

Studying the physical properties of materials under high pressure and temperature through experiments is difficult. Theoretical simulations can compensate for this deficiency. Currently, large-scale simulations using machine learning force fields are gaining popularity. As an important nuclear energy material, the evolution of the physical properties of uranium under extreme conditions is still unclear. Herein, we trained an accurate machine learning force field on α-U and predicted the lattice dynamics and elastic properties at high pressures and temperatures. The force field agrees well with the ab initio molecular dynamics (AIMD) and experimental results and it exhibits higher accuracy than classical potentials. Based on the high-temperature lattice dynamics study, we first present the temperature-pressure range in which the Kohn anomalous behavior of the Σ4 optical mode exists. Phonon spectral function analysis showed that the phonon anharmonicity of α-U is very weak. We predict that the single-crystal elastic constants C44, C55, C66, polycrystalline modulus (E, G), and polycrystalline sound velocity (CL, CS) have strong heating-induced softening. All the elastic moduli exhibited compression-induced hardening behavior. The Poisson's ratio shows that it is difficult to compress α-U at high pressures and temperatures. Moreover, we observed that the material becomes substantially more anisotropic at high pressures and temperatures. The accurate predictions of α-U demonstrate the reliability of the method. This versatile method facilitates the study of other complex metallic materials.

Ultrasonic inverse identification of surface integrity of aviation functional coatings through material-oriented regularization

Accurately controlling surface integrity of aviation functional coatings including defect, geometry, structure, and property is important to balance the comprehensive performance of aviation parts. In this paper, a new ultrasonic inverse method of surface integrity of aviation functional coatings is presented through a developed material-oriented regularization scheme, which combines model regularization, data regularization, and sensitivity matrix analysis. A sensitivity-matrix-based inversion method of ultrasonic detecting multiple surface integrity parameters is developed using the optimized high-sensitivity characteristic detection signal. Taking ultrasonic inverse detection of elastic constants of plasma-sprayed Al2O3 coating and inverse prediction of porosity of ZrO2 coating as examples, the validity of proposed ultrasonic inversion method is illustrated. Results show that the inverted elastic constants C11, C13, C33, and C44 of Al2O3 coating are 123.81 GPa, 34.38 GPa, 190.20 GPa, and 24.63 GPa, respectively. The relative error between inverted and experimental C33 and C44 are all less than 4.0%. The inverted elastic constants show obvious “inverse” elastic anisotropy, which is due to the preferred orientation of micro-cracks in Al2O3 coating. Compared with actual porosity of ZrO2 coating, the predicted porosity using sensitivity matrix optimized Gaussian process regression algorithm has a relative error of less than 5.3%. The proposed ultrasonic inverse method provides a new path for solving the complex ultrasonic non-destructive detecting problems, which are difficult for traditional “trial-and-error” ultrasonic methods.

Out-of-plane longitudinal sound velocity in SnS2 determined via broadband time-domain Brillouin scattering

Here, we report time-resolved broadband transient reflectivity measurements performed in a single crystal of SnS2. We made use of time-domain Brillouin scattering and a broadband probe to measure the out-of-plane longitudinal sound velocity, υL=(2950±100)ms–1, in this semiconducting two-dimensional metal dichalcogenide. Our study illustrates the potential of this non-invasive all-optical pump–probe technique for the study of the elastic properties of transparent brittle materials and provides the value of the elastic constant c33=(39±3)GPa.