Constants C11 Research Articles

Engineering Ferroelectricity and Large Piezoelectricity in h-BN.

Hexagonal boron nitride (h-BN) is a well-known layered van der Waals (vdW) material that exhibits no spontaneous electric polarization due to its centrosymmetric structure. Extensive density functional theory (DFT) calculations are used to demonstrate that doping through the substitution of B by isovalent Al and Ga breaks the inversion symmetry and induces local dipole moments along the c-axis, which promotes a ferroelectric (FE) alignment over antiferroelectric. For doping concentrations below 25%, a "protruded layered" structure in which the dopant atoms protrude out of the planar h-BN layers is energetically more stable than the flat layered structure of pristine h-BN or a wurtzite structure similar to w-AlN. The computed polarization, between 7.227 and 21.117 μC/cm2, depending on dopant concentration and the switching barrier (16.684 and 45.838 meV/atom) for the FE polarization reversal are comparable to that of other well-known FEs. Interestingly, doping of h-BN also induces a large negative piezoelectric response in otherwise nonpiezoelectric h-BN. For example, we compute d33 of -24.214 pC/N for Ga0.125B0.875N, which is about 5 times larger than that of pure w-AlN (5 pC/N), although the computed e33 (-1.164 C/m2) is about 1.6 times lower than that of pure w-AlN (1.462 C/m2). Because of the layered structure, the rather small elastic constant C33 provides the origin of the large d33. Moreover, doping makes h-BN an electric auxetic piezoelectric. We also show that ferroelectricity in doped h-BN may persist down to its trilayer, which indicates high potential for applications in FE nonvolatile memories.

The influence of site preference on the elastic properties of FCC_CoCrFeNi multi-principal element alloy

The influence of the existing site preference of the constituent elements on the sublattice on elastic properties is rarely explored in multi-principal element alloys (MPEAs). In this work, in order to explore the influence of the site preference of constituent atoms on the thermodynamic properties and elastic properties, the ordered configurations based on the previously predicted site occupying fractions (SOFs) and the disordered configuration based on a special quasi-random structure (SQS) were established, and the thermodynamic properties and elastic properties were predicted using the quasi-harmonic approximation (QHA) method first. It was found that the site preferring behaviors of atoms on the sublattices will not only improve the stability of the structure but will also lead to bigger elastic properties than its ideal disordered structure. Although the prediction of the temperature-dependent elastic properties using the QHA method shortens the time costs by only considering the effects of thermal expansion, it ignores the significant effect of lattice vibration on elastic properties at high temperatures. In order to explore the influence of lattice vibration on the temperature-dependent elastic properties further, the elastic properties of the ordered FCC_CoCrFeNi MPEA were predicted using the ab initio molecular dynamics (AIMD) method at several selective temperatures. The results show that except for the elastic constant C12 and bulk modulus, the lattice vibration reduces other elastic properties on the basis of thermal expansion. The predicted temperature-dependent shear and Young's moduli agree well with the limited experimental literature data. Thus, the temperature-dependent elastic properties can be reasonably predicted using the AIMD method based on site preference. The predicted polycrystalline elastic moduli B, G, and E of FCC_CoCrFeNi MPEA at 973 K are 146.68, 53.79, and 143.78 GPa, respectively.

Experimental-computational approach to investigate elastic properties of struvite.

The research presented in the paper concerns the elastic properties of struvite. The article combines theoretical and experimental research. Experimental studies were carried out on struvite single crystals grown in sodium metasilicate gel by single diffusion. This unique method leads to obtaining crystals of sufficiently large size to conduct, for the first time, experimental measurement of elastic properties of monocrystalline struvite. Using the nanoindentation method, the Ez = 29.1 ± 0.7GPa value of the component of Young's modulus was determined for a struvite single crystal. In addition, the elastic constants C11, C22, and C33 were determined using micro-Brillouin spectroscopy. Theoretical calculations of the abovementioned properties have been carried out by employing density functional theory methods. Scaling of the theoretical elastic constants leads to obtaining good agreement with the experimental values. Values of the Ex and Ey components of the Young's modulus, not available from the experimental nanoindentation technique, have been determined theoretically as 23GPa and 27GPa, respectively. Differences in the values of elastic components and Young's modulus components are related to the layered crystal structure of struvite and directional character of the hydrogen-bonding pattern.

Realization of diversity in physical properties of Zr2Se(B1‐xSex) MAX phases through DFT approach

AbstractThe discovery of a series of MAX phases, Zr2Se(B1‐xSex), with Se at both A‐ and X‐sites, drives a new chemical diversity to the MAX family. Here, we employed the density functional theory (DFT) approach to realize the diversity in physical properties of Zr2Se(B1‐xSex). All compositions of Zr2Se(B1‐xSex) are mechanically stable and the dynamical stability of the end member Zr2SeSe is confirmed. The elastic constant C33 and bulk moduli B show a decrease almost monotonically with Se‐content x while other constants and moduli change irregularly. All elastic constants and moduli except C12 and C13 are highest for the end member Zr2SeB. Additionally, the Vickers hardness, Debye temperature, minimum thermal conductivity, and lattice thermal conductivity are highest for Zr2SeB. The increase of Se‐content x at X‐site reduces most of the properties of Zr2Se(B1‐xSex). The electronic band structures change drastically with increasing Se‐content x. This diversity in electronic band structures is mainly the reason for the diversity in physical properties of Zr2Se(B1‐xSex). All compositions of Zr2Se(B1‐xSex) have the potential to be thermal barrier coating materials, and Zr2SeB has the potential to be etched into 2D MXene, Zr2B.

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.

Semi-analytical solution for the elastic wave propagation due to a dislocation source in a transversely isotropic half-space

SUMMARY In this paper, the 3-D theoretical seismogram at the free surface of an elastic half-space with ‘vertical transverse isotropy (VTI)’ and an ‘elliptic anisotropy‘ is synthesized via semi-analytical formulation. To this end, the time-domain solution is obtained via the Hankel and Laplace integral transforms and the Cagniard contour integration scheme. The formulations include complete Green's functions expressed in compact and elegant formulations in terms of some elementary line integrals over the finite interval (0, π/2), due to the general point force and point double-couple source of arbitrary orientation, varying with time as Heaviside step function. This solution is further implemented to model seismic waves generated from moment tensor source with a ramp-type slip function. The solution clearly delineates compressional P waves, shear SV waves and SH waves, diffracted SPwaves and surface Rayleigh waves, with two critical distances in which the mode conversion happens. The first marks the conversion of the total reflection of SV wave into the diffracted SPwave travelling on the free surface with the velocity of compressional wave. The second, however, marks a location where the order of arrival times of SP and SH waves is reversed. The interesting phenomenon of shear wave splitting by the apparent time lag between the arrivals of SV and SHwaves is further demonstrated. Studied also is the effect of non-double-couple (non-DC) components of the moment tensor of the shear fault. Particularly, it is shown that non-DC components may lead to large amplitude of the P wave in the presence of anisotropy, resulting in the changed polarity of P wave at the onset of the motion. It is found that for the elliptic anisotropy, and for oblique-thrust faults, the isotropic moment (ISO) is always negative if the elastic constants satisfy C11 > C33 and C44 > C66, whereas it is always positive if C11 < C33 and C44 < C66 (for oblique-reverse faults, the situation is reversed). It is shown that for some sedimentary rocks, the decomposition of moment tensor in the general VTI and in its elliptic approximation are close to each other, and that the moment tensor decomposition in VTI media is very sensitive to the elastic coefficients, such that a small change in the elastic constants may lead to a remarkable change in the moment tensor decomposition. Particularly, the effect of elastic constant C13 is shown to be significant. While the time-domain solution obtained in this paper can be also degenerated to the solution in the corresponding isotropic half-space, the Mathematica code of the solution provided can be served as benchmark to other numerical solutions, applicable for the computation of the theoretical seismogram in the involved media.

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.

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.

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 calculations of sulfur dioxide adsorption on the Ca-montmorillonite

According to the serious problem of sulfur dioxide pollution, montmorillonite is one of the effective ways in gas pollution control because of its excellent absorption properties. One of the fundamental questions is to fully understand sulfur dioxide absorption mechanism of montmorillonite. In this study, using the first-principle methods, we studied the adsorption characteristics of Ca-montmorillonite in the presence of hbox {SO}_{{2}}. The adsorption energy and elasticity constants as a function of the adsorption capacity were also studied. The calculated results show that bridge site is the most stable adsorption site for hbox {SO}_{{2}} with the adsorption energy of − 140 meV. As adsorbent, Ca-montmorillonite is a clay with layer-structure, most of bond lengths(such as Al–O, Mg–O, Si–O, and H–O) does not obviously change. As adsorbed gas, the O–S–O bond angle of adsorbed hbox {SO}_{2} change from 119.50^circ to 115.32^circ. The volume and adsorption energies of Ca-montmorillonite almost increase linearly with increasing hbox {SO}_{{2}} adsorption. By calculating the montmorillonite elasticity constants under different adsorption capacity, we found that the elasticity constant C33 which perpendicular to the crystal face, with the maximum changes from 450 to 326 GPa. In addition, Young’s modulus,bulk modulus and shear modulus significantly decrease with the increasing adsorption. The calculated results will not only help to understand the physical and chemical of montmorillonite but may also provide theoretical guidance for dealing with the problem of gas pollution.

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.

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.

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.

A molecular dynamics study of the mechanical properties of kaolinite under uniaxial and isothermal compression at various temperatures

AbstractUniaxial and isothermal compression tests of kaolinite were carried out using molecular dynamics simulations. Five different temperatures (300, 400, 500, 600 and 700 K) and pressures ranging from 0.0001 to 50 GPa were selected to study the temperature and pressure effects on the mechanical properties of kaolinite. As kaolinite may undergo a phase transition at ~1572 K, a highest temperature of 700 K was chosen to avoid such structural change. The Young's modulus, strength and elastic constants of kaolinite under various temperatures were calculated, and the relative change of the elastic constant C33 with temperature was found to be almost 12 times greater than the relative change of the interlayer constant C11. The microstructures under various compressive strains were tracked and they exhibited various failure modes in three directions. The temperature and pressure effects on the mechanical properties of three crystal directions were analysed. The results showed that the Young's modulus of the z-direction is the most affected by temperature; however, the influence of temperature on the strengths of the three crystal directions was the same. In addition, the structure of the z-direction was the most sensitive to temperature under the same hydrostatic pressure due to the weak interactions between layers.

High-throughput prediction of intrinsic properties of L12-(Nix1,Crx2,Cox3)3(Aly1,Tiy2) precipitates

The structural and mechanical properties, e.g., lattice constants, elastic constants, elastic moduli, Poisson’s ratios, and Vickers hardness, of L12-(Nix1,Crx2,Cox3)3(Aly1,Tiy2) precipitates are predicted by high-throughput first-principles calculations combined with exact muffin-tin orbitals and coherent potential approximation methods. It turned out that the elastic constants C11 and C44, shear modulus, Young’s modulus, Vickers hardness, and yield strength raise with increasing Ni, Cr, Co, or Al content as a whole, the elastic constant C12, Poisson’s ratios, and Pugh’s ratio decrease gradually, reflecting that the content change of Ni, Cr, Co elements on the left has basically similar effects on the physical properties of L12 precipitates, while the influences of Al and Ti on the right are opposite. Moreover, increasing Ni and Al, Cr and Al, or Co and Al contents at the same time is more conducive to improve the deformation resistance of alloys, but rapidly decrease the plastic properties. Meanwhile, the crystal structures of L12 precipitates may be mechanically unstable due to negative C11−C12 values when Ni, Cr, or Co concentration is less than 30 at%, and the ductile-brittle transition will occur for the L12 particles with high Cr and Al contents or Co and Al contents due to B/G<1.75. By comparison, Co3Al and Cr3Al precipitates exhibit excellent deformation resistance, (Cr,Co)3Ti and (Ni,Co)3Ti particles demonstrate outstanding plastic properties in the [001] and [111] directions, respectively. This work provides valuable insights for the intrinsic properties of L12-(Nix1,Crx2,Cox3)3(Aly1,Tiy2) precipitates.

Ferroelectricity and Piezoelectric Response of (Sc,Y)N/(Al,Ga,In)N Monolayer Alternating Stacked Structures by First‐Principles Calculations

Group III‐nitrides with doping recently attract great interest because of their outstanding ferroelectric and piezoelectric properties. Herein, the spontaneous polarization and piezoelectricity of the wurtzite III‐nitrides (AN, A = Al, Ga, In) with the rare earth element (R = Sc, Y) doping (w‐R0.5A0.5N) are investigated by first‐principles calculations. The polar w‐R0.5A0.5N and nonpolar h‐R0.5A0.5N are stable, which is proved by the elastic constants and phonon band structures. The w‐Sc0.5In0.5N and w‐Y0.5In0.5N can be applied to the ferroelectric field owing to their very small ferroelectric switching barriers (0.149 eV for w‐Sc0.5In0.5N and 0.042 eV for w‐Y0.5In0.5N) with large ferroelectric polarization (1.088 C m−2 for w‐Sc0.5In0.5N and 0.937 C m−2 for w‐Y0.5In0.5N). Furthermore, the w‐Y0.5In0.5N has a large piezoelectric strain constant d33 (14.018 pC N−1) based on the elastic constant C33 softening and the increase of the piezoelectric constant e33, which is three times larger than that of w‐InN (4.191 pC N−1). It is found that the biaxial tensile strain of 2% along in‐place significantly enhances the d33 and e33, which increase to 35.572 pC N−1 and 2.669 C m−2 from 14.018 pC N−1 and 1.700 C m−2 of free w‐Y0.5In0.5N, respectively.

Unusual crystal phases of noble metals Ir, Os, and hardness of Ir-Os systems from high throughput density functional calculations

The platinum-group elements (PGMs) owing their high chemical stability, and unique properties, have recently attracted great research interest in various promising applications. Herein using state-of-the-art first-principles evolutionary algorithms, we explore the thermodynamic and mechanical properties of Ir, Os, and their alloys. Hitherto unknown polytype-phases of Ir (6H, 4H, 2H) and Os (6H, 4H) have been predicted, two of these (4H-Ir, and 4H-Os) were recently observed experimentally. Os and, to more extent, Ir polytypes divulge weak thermodynamic instabilities. Phonon dispersion and elastic constants calculations were carried out to demonstrate the dynamical and mechanical stabilities of these phases. For the Ir-Os alloys, four ordered structures (Pm-3 m (IrOs3, Ir3Os), P-6 m2 (IrOs), P-3 m1 (IrOs2)) have been predicted, which are found mechanically and dynamically stables and manifest insignificantly thermodynamic instabilities. Furthermore, our obtained results show that Ir-Os systems evince outstanding mechanical properties, IrOs3 has high bulk modulus (∼421GPa), large shear modulus (∼266GPa), and Young’s modulus (659 GPa); whereas IrOs2 possesses a remarkable large elastic constants C11 (779GPa) and C33 (814GPa). The anisotropic calculations show that IrOs3 exhibits that greatest anisotropy in the universal elastic anisotropy index AU, shear modulus (AG) and Young’s modulus (AE); while IrOs2 has the smallest elastic anisotropy. Moreover, IrOs3 reveals distinguished hardness of 27.6GPa, which is 3% weaker than 2H-Os (28.6GPa), and is so far one of the hardest materials among the PGMs binary alloys.

Synthesis and thermal expansion of chalcogenide MAX phase Hf2SeC

Thermal expansion of MAX phases along different directions tends to be different because of the anisotropy of hexagonal crystals. Herein, a new Hf2SeC phase was synthesized and confirmed to be relatively isotropic, and the coefficients of thermal expansion (CTEs) along a and c directions were determined to be 9.73 μK−1 and 10.18 μK−1, respectively. The strong MS bond endowed Hf2SC and Zr2SC lower CTEs than those of Hf2SeC and Zr2SeC. The relationship between the thermal expansion anisotropy and the ratio of elastic stiffness constant c11 and c33 was established. This straightforward approximation can be used to roughly predict the thermal expansion anisotropy of MAX phases.