Yaoping Lua,
Titao Li*a,
Kangjie Lib,
Derek Haoc,
Zuxin Chen*b and
Haizhong Zhang*a
aJinjiang Joint Institute of Microelectronics, College of Physics and Information Engineering, Fuzhou University, Fuzhou 350108, China. E-mail: litt69@fzu.edu.cn; haizhong_zhang@fzu.edu.cn
bSchool of Semiconductor Science and Technology, South China Normal University, Foshan 528225, China. E-mail: chenzuxin@m.scnu.edu.cn
cSchool of Science, RMIT University, Melbourne, VIC 3000, Australia
First published on 2nd January 2024
This research employs first-principles calculations to address the challenges presented by processing complexity and low damage tolerance in transition metal borides. The study focuses on designing and investigating MAB phase compounds of M4AlB4 (M = Cr, Mo, W). We conduct a comprehensive assessment of the stability, phononic, electronic, elastic, and optical properties of Cr4AlB4, Mo4AlB4, and W4AlB4. The calculated results reveal formation enthalpies of −0.516, −0.490, and −0.336 eV per atom for Cr4AlB4, Mo4AlB4, and W4AlB4, respectively. Notably, W4AlB4 emerges as a promising precursor material for MABene synthesis, demonstrating exceptional thermal shock resistance. The dielectric constants ε1(0) were determined as 126.466, 80.277, and 136.267 for Cr4AlB4, Mo4AlB4, and W4AlB4, respectively. Significantly, W4AlB4 exhibits remarkably high reflectivity (>80%) within the wavelength range of 19.84–23.6 nm, making it an ideal candidate for extreme ultraviolet (EUV) reflective coatings. The insights gleaned from this study provide a strong research framework and theoretical guidance for advancing the synthesis of innovative MAB-phase compounds.
Structurally, MAB phase compounds arise from the alternate layering of Al atomic layers and TMB layers:9–12 within the TMB layers, robust B–B bonds (typically <2 Å) and TM–B bonds (typically ∼2 Å) coexist, whereas the bonds linking the TMB layers and Al layers, such as TM–Al and Al–B bonds (typically >2 Å), exhibit comparatively lower strength.16,17 The judicious selection of Poisson's ratio and modulus of elasticity from these crystal structures enables MAB phase compounds to amalgamate the favorable traits of metals-low brittleness and high ductility-with the robust attributes of ceramics, including high hardness and exceptional wear resistance. This amalgamation renders them more amenable to processing and more pragmatic in contrast to conventional TMB phases.12 Additionally, this unique structure facilitates the facile creation of MBene materials through the corrosion of Al atoms.3,18 Recently, Zhang et al. introduced a novel MAB phase, Cr4AlB4 (achieved by incorporating an Al layer into CrB material), enhancing the damage tolerance and thermal shock resistance of CrB.19
Considering the formation enthalpy and cohesive energy, Adam Carlsson et al. have conducted theoretical calculations on 420 types of MAB phase structures, efficiently screening out more than 40 potentially synthesizable materials.20 Among these, Mo4AlB4, sharing an identical structure with Cr4AlB4, also emerges as a viable synthesis candidate. Zhou et al. have demonstrated the feasibility of procuring two-dimensional MoB through chemical exfoliation.21 However, in our assessment, scope remains for refining the existing research, potentially enhance the stability of the MAB phase and minimizing possible deviations from real-world outcomes. Furthermore, the current uncertainties surrounding the mechanical and dynamic stability cast doubts about the pragmatic applicability of these materials. Thus, a sole concentration on energy-related aspects is insufficient in appraising the stability of MAB phase compounds.
In this work, we undertook a comprehensive re-evaluation of the stability of Cr4AlB4, Mo4AlB4, and W4AlB4 crystals through first-principles calculations, further exploring their potential applications. Based on the experimental results of Zhang et al.22 and the structural models of Adam Carlsson et al.,20 we performed a rigorous re-optimization of the crystal models for Cr4AlB4, Mo4AlB4, and W4AlB4. This optimization process, incorporating heightened convergence accuracy, was undertaken from multiple vantage points, encompassing formation enthalpy, cohesive energy, mechanical stability, and dynamic stability. Consequently, our investigations substantiate the stable existence of Mo4AlB4 and W4AlB4 across diverse perspectives. Further investigations have also unveiled that W4AlB4 exhibits a reflectance exceeding 80% within the 19.3–23.4 nm range, making as a potential extreme ultraviolet (EUV) reflective coatings. The suitable Poisson's ratio of Mo4AlB4 hints at its potential as a material endowed with high damage tolerance. The strategic inclusion of an Al layer within Mo4AlB4 and W4AlB4 amplifies their potential not only as materials resistant to thermal shocks but also as auspicious precursors for the development of MBene materials.
Fig. 1 Crystal structure of M4AlB4 (M = Cr, Mo, W), the projection of atoms on (001) (a) planes, (100) (b) planes and (010) (c) planes. |
According to the crystal structure, M4AlB4 can be seen as M4B4 with Al atoms stacked in an ABABAB pattern. Normally, the interaction between M and B atoms is strong, while the interaction between M and Al atoms is weak. This crystal structure could therefore be favorable for the preparation of MABene 2D materials. Optimized structural parameters of these M4AlB4 tetraboride compounds are listed in Table 1, which are the same as Cr4AlB4 tetraboride compound experimental data and previous theoretical results.22 Within our study, we found discrepancies between computed and empirical lattice parameters a, b, and c to be just 0.613%, 0.238%, and 1.244%, respectively. This shows a strong correlation between optimized Cr4AlB4 structural parameters and experimental data,3 confirming the effectiveness of our computational approach in investigating M4AlB4 tetraboride compounds.
As a ceramic material, it is crucial for the MAB phase to present thermodynamic stability. Cohesion energy and formation enthalpy are used here to represent the thermodynamic stability of the MAB phase material. The cohesion energy and formation enthalpy of Cr4AlB4, Mo4AlB4 and W4AlB4 can be calculated by the following equations:10,31,32
(1) |
(2) |
In eqn (1) and (2), E(M4AlB4) (M = Cr, Mo, W) and ΔH(M4AlB4) are cohesive energy and formation enthalpy, respectively. Eiso represents the energy of an atom in an isolated state, which is usually obtained by placing the atom in a 15 × 15 × 15 (Å) lattice. Ec(M4AlB4) represents the cohesion energy. The energy of each atom in the bulk state is represented by Ebulk, often expressed as the energy of each atom in a simple substance, where E(B2) is the energy of a single crystal of boron. Regularly, the more negative of the cohesion energy and formation enthalpy, the more stable the material is. With a focus on energy, both Ec and ΔH are negative, indicating that these substances can be stabilized. Meanwhile, ΔH(Cr4AlB4) < ΔH(Mo4AlB4) < ΔH(W4AlB4), indicating that Cr4AlB4 is thermodynamically more stable compared to Mo4AlB4 and W4AlB4, therefore Cr4AlB4 can be more easily synthesized.
The stability of three-dimensional bulk materials is governed by a combination of thermodynamics and dynamics. Furthermore, the stability of these materials can also be assessed through the examination of phonon dispersion curves. If no imaginary frequencies appear in the phonon dispersion curve, then the material is dynamically stable, otherwise it is unstable. During the research, the thermodynamic stability of these three tetraboride compounds were performed by using the PHONOPY code. Fig. 2 contains the phonon dispersion curves and phonon density of states images for M4AlB4 (M = Cr, Mo, W). The phonon dispersion curves of a crystal with n atoms consist of 3n branches, 3 of which are acoustic branches, while the remaining 3n − 3 are optical branches. Furthermore, the phonon dispersion curves of Cr4AlB4, Mo4AlB4 and W4AlB4, all have non-zero values throughout the Brillouin zone, an indication of their stability in molecular dynamics.33 The phonon density of states corresponds to the phonon dispersion curves, which indicates the high accuracy of the calculated results. Besides, from Fig. 2, the contribution of B atoms in Cr4AlB4 to the phonon density of states is concentrated in the high frequency region. The contribution of Cr and Al atoms to the phonon density of states is concentrated in the low-frequency region. It is probably related to the mass of the atoms, where the lighter masses are more likely to vibrating at high frequencies, while the larger masses tend to vibrate at low frequencies.17,34 The similar situation is also seen in the phonon dispersion curves of two tetraborides, Mo4AlB4 and W4AlB4. Furthermore, the phonon density of states reflects an increasing contribution of Mo and W atoms with increasing atomic mass in the lower frequency region. More interestingly, Al atoms behave more like separate atoms in these tetraborides. The optical branch of Al atoms appears mainly at 10 THz in phonon density of states, while the acoustic expenditure appears at 7–7.5 THz, which is perhaps related to the weaker bonding between Al atoms and other atoms. The results mean that Mo4AlB4 and W4AlB4 may be able to prepare the corresponding MABene materials easier.
Fig. 2 Phonon dispersion curves and phono density of state for (a) Cr4AlB4, (b) Mo4AlB4 and (c) W4AlB4. |
Fig. 3 Band-structures of (a) Cr4AlB4, (b) Mo4AlB4 and (c) W4AlB4 and projected band-structure of (d) Cr atoms in Cr4AlB4, (e) Mo atoms in Mo4AlB4 and (f) W atoms in W4AlB4. |
Fig. 4 exhibits the total and partial density of states (DOS) for Cr4AlB4, Mo4AlB4, and W4AlB4, where the dashed lines denote the Fermi energy level. The DOS plots reveal non-zero values at the Fermi energy level, indicating the conductivity and metallic nature of these tetraborides. The partial DOS (PDOS) profiles demonstrate that the DOS of these compounds primarily originates from the M-d orbitals and the B-p orbitals, while the contribution from Al orbitals is relatively lower. This characteristic is consistent with other MAX- and MAB-phase compounds. In the energy range from −15 to −10 eV, strong hybridization is observed between the B-2s and the ds orbitals of the M atoms, whereas the hybridization between the Al-3s and the B-2p orbitals is less marked.
This facilitates bonding between the transition metals and B atoms, resulting in a high elastic modulus of the MAB-phase compound. In the −10 to −2 eV range, the 3d orbitals of the transition elements significantly hybridize with the B-2p orbitals. The density of states near the Fermi energy level is primarily composed of the 3d orbitals of the M elements, indicating that the conductivity of these tetraborides is mainly governed by the transition metal elements rather than Al. This conclusion aligns with the findings from the projected density of states analysis. In addition, the B-2p orbitals make a substantial contribution to the density of states near the Fermi energy level. The Al-3s and Al-3p orbitals make a relatively small contribution, mainly in the energy range of 5–25 eV. Meanwhile, COHP and IpCOHP calculations by using a Lobster code.35,36 The calculated −pCOHP curves of Cr4AlB4, Mo4AlB4 and W4AlB4 are presented in Fig. 5. The COHP images of these three compounds display comparable features and all exhibit substantial bonding states. TM–Al possesses mainly bonding states, with TM–B and Al–B occupied by slightly antibonding states in proximity to the Fermi energy level. Conversely, the bonding states of the B–B bond lie above the Fermi energy level, demonstrating a noticeable degree of covalency in the B–B bond.
IpCOHP is a common method to illustrate the distinction between bonding and antibonding. It is obtained by integrating −pCOHP. Table 2 displays the results obtained from calculating IpCOHP using PBE and LDA, which reveal a similar trend across both artefacts. According to Table 2, the total IpCOHP of these compounds progressively becomes more negative as the mass of the TM atoms increases, indicating greater bonding. Consequently, both Mo4AlB4 and W4AlB4 are considered stable. The B–B bond exhibits high covalent bond strength among the compounds and has the greatest contribution to their overall bonding. On the other hand, the TM–Al bond has the least contribution to their overall bonding. Notably, the strength of the Al–B bond in Mo4AlB4 remains stable, but the image shows more antibonding states close to the Fermi energy level, decreasing the structural strength of Mo4AlB4.
Cr4AlB4 | Mo4AlB4 | W4AlB4 | ||||
---|---|---|---|---|---|---|
Type | ICOHP | Type | ICOHP | Type | ICOHP | |
Total | −2.107 | Total | −2.440 | Total | −2.518 | LDA |
Cr–Al | −1.151 | Mo–Al | −1.545 | W–Al | −1.667 | |
Cr–B | −1.947 | Mo–B | −2.268 | W–B | −2.380 | |
Al–B | −2.500 | Al–B | −2.703 | Al–B | −2.739 | |
B–B | −4.865 | B–B | −5.216 | B–B | −5.004 | |
Total | −1.749 | Total | −1.948 | Total | −2.891 | PBE |
Cr–Al | −1.011 | Mo–Al | −1.348 | W–Al | −1.423 | |
Cr–B | −1.766 | Mo–B | −1.863 | W–B | −2.177 | |
Al–B | −2.492 | Al–B | −3.976 | Al–B | −5.207 | |
B–B | −4.936 | B–B | −4.617 | B–B | −7.731 |
Overall, the findings of COHP and IpCOHP indicate that the stability of TM4AlB4 grows as the mass of TM atoms increases.
(3) |
M4AlB4 | C11 | C12 | C13 | C22 | C23 | C33 | C44 | C55 | C66 |
---|---|---|---|---|---|---|---|---|---|
Cr4AlB4 | 567 | 116 | 133 | 492 | 132 | 481 | 183 | 241 | 192 |
Cr4AlB4 (ref. 19) | 538 | 116 | 122 | 490 | 124 | 477 | 173 | 219 | 176 |
Mo4AlB4 | 529 | 148 | 162 | 428 | 158 | 477 | 152 | 194 | 136 |
W4AlB4 | 536 | 176 | 199 | 451 | 182 | 504 | 159 | 212 | 158 |
As can be determined from the elastic constants in Table 3, these tetraborides meet the mechanical stability requirements. Elastic constants C11, C22, and C33 correspond to the resistance to linear compression of these compounds along the [100], [010], and [001] directions, respectively. Typically, larger elastic constants correspond to larger resistance to linear compression. Moreover, these three compounds have the largest resistance to linear compression in the [100] direction, C22 > C33 in Cr4AlB4 single crystals and C33 > C22 in Mo4AlB4 and W4AlB4 single crystals. It indicates that the resistance to linear compression of Cr4AlB4 is greater in the [010] direction than in the [001] direction. And the resistance to linear compression in the [001] direction is greater than that in the [010] direction in the Mo4AlB4 and W4AlB4 single crystals in the table. The C44 and C66 in the table indicate the shear stress resistance of these compounds in the (100) plane along the [001] and [110] directions. The larger values of C44 and C66 indicate the higher shear modulus of the material,39,40 while the hardness of the material is proportional to the value of C44.39,41 According to the data in Table 3, the order of C44 is Cr4AlB4 > W4AlB4 > Mo4AlB4, which indicates that the highest shear modulus and hardness of Cr4AlB4 are the largest, and the shear modulus and hardness of Mo4AlB4 are the smallest, similar findings are also evident in the analysis of results from COHP and IpCHOP.
Moreover, the elastic characteristics of these tetraborides, such as the modulus as well as the Poisson's ratio ν, were obtained using the Voigt–Reuss–Hill approximation. These data were mainly calculated by the following equations:38,42
ν = (3BH − E)/6BH | (4) |
BH = (BV + BR)/2 | (5) |
GH = (GV + GR) | (6) |
E = 9BHGH/(3BH + GH) | (7) |
Table 4 presents the crucial elastic properties of the investigated tetraborides. The bulk modulus B reflects the compressibility of materials under hydrostatic pressure (HP), while the shear modulus G and Youngs modulus E indicate their resistance to deformation. Generally, a high bulk modulus B signifies low compressibility, whereas a large shear modulus G indicates excellent shear resistance. Based on the data in Table 4, Cr4AlB4 exhibits outstanding shear resistance, whereas W4AlB4 demonstrates relatively good compression resistance. However, the deformation resistance of Mo4AlB4 is comparatively weaker.
M4AlB4 | BV | BR | BH | GV | GR | GH | E |
---|---|---|---|---|---|---|---|
Cr4AlB4 | 255.7 | 254.7 | 255.2 | 200.6 | 198.0 | 199.3 | 474.4 |
Mo4AlB4 | 263.5 | 261.4 | 262.5 | 161.0 | 158.2 | 159.6 | 398.1 |
W4AlB4 | 289.7 | 287.6 | 288.7 | 168.0 | 165.1 | 166.6 | 419.1 |
Furthermore, the E values of these compounds are remarkably significant. Previous studies have indicated that MAX-phase materials with high E values hold great promise for thermal shock resistance.31,43 These compounds possess structures that are similar to conventional MAX-phase materials and exhibit notable E values, making them potential candidates for thermal shock resistance.
Poisson's ratio ν and Pugh's ratio provide insights into the brittleness or ductility of solid materials. Table 5 presents the calculated Poisson's ratio ν, Pugh's ratio, and Vickers hardness of the examined tetraborides. For MAB phase compounds, a Poisson's ratio ν < 0.33 and a ratio of bulk modulus to shear modulus (B/G) < 1.75 indicate brittleness, whereas values exceeding these thresholds suggest ductility.31,44 Analysis of Table 5 reveals that these tetraborides exhibit brittleness while demonstrating excellent hardness.
M4AlB4 | ν | B/G | HV |
---|---|---|---|
Cr4AlB4 | 0.19 | 1.28 | 30.15 |
Mo4AlB4 | 0.169 | 1.64 | 18.78 |
W4AlB4 | 0.26 | 1.73 | 18.02 |
Herein, it has been determined that all of these tetraborides exhibit mechanical stability. These tetraborides are potential thermal shock resistant materials. In particular, Cr4AlB4 has a high shear modulus and high hardness, Mo4AlB4 and W4AlB4 also have well hardness, while Mo4AlB4 has a more prominent damage tolerance.
ε(ω) = ε1(ω) + iε2(ω) | (8) |
(9) |
The following equation is then used to calculate the imaginary part of the dielectric function:17,31,44
(10) |
The symbol fkn in this equation denotes the Fermi–Dirac distribution function, m and e denote the mass of the electron and charge of an electron, respectively, Ekn(k) represents the energy that each individual electron has, while is the projection of the elements of the momentum dipole matrix in the direction of the field v for the initial and final states.49,50 Optical anisotropy of these tetraborides can also be calculated from the data in Table 5 by calculating the dielectric constants of the materials and also by obtaining the single-crystal and polycrystal optical properties of these materials. The optical anisotropy of a solid material can be calculated by the following equation:44,51
(11) |
Compounds | ε1(0) | n(0) | k(0) | Rmax | AOPT | |
---|---|---|---|---|---|---|
Cr4AlB4 | Polycrystal | 126.466 | 11.310 | 1.207 | 0.704 | |
x | 107.547 | 10.422 | 1.030 | 0.683 | [0.850, 0.921] | |
y | 178.270 | 13.458 | 1.691 | 0.746 | [1.410, 1.120] | |
z | 93.581 | 9.704 | 0.768 | 0.663 | [0.740, 0.858] | |
Mo4AlB4 | Polycrystal | 80.277 | 8.988 | 0.711 | 0.641 | |
x | 49.513 | 7.041 | 0.245 | 0.566 | [0.617, 0.783] | |
y | 128.740 | 11.411 | 1.216 | 0.707 | [1.604, 1.300] | |
z | 62.578 | 7.923 | 0.451 | 0.603 | [0.780, 0.882] | |
W4AlB4 | Polycrystal | 136.267 | 11.756 | 1.386 | 0.999 | |
x | 55.710 | 7.476 | 0.431 | 0.998 | [0.409, 0.636] | |
y | 115.367 | 10.790 | 1.028 | 0.997 | [0.847, 0.918] | |
z | 237.724 | 15.577 | 2.219 | 1.000 | [1.745, 1.325] |
In addition, it is worth noting that the Rmax value of W4AlB4 is very high, which indicates that W4AlB4 is extremely reflective of light at certain wavelengths. Fig. 6 plots the reflectance spectra of Cr4AlB4, Mo4AlB4 and W4AlB4. When the incident photon energy has multiple peaks in the 0–100 eV range, the peaks for Cr4AlB4, Mo4AlB4 and W4AlB4 are 0.704, 0.640, and 0.999 respectively. For the polycrystalline Cr4AlB4 and Mo4AlB4, the highest reflectivity was observed at 0 eV with Rmax values of 0.704 and 0.641 respectively. The results indicate that for the polycrystalline Cr4AlB4 and Mo4AlB4, they have relatively high reflectance in the far-infrared spectral region. This is similar to most of the MAB or MAX phase materials which appear to be relatively common. In contrast, W4AlB4 also performs relatively normally for light in the 0–20 eV range. However, it is surprising that W4AlB4 has a significantly higher reflectance (above 80%) for light from 19.84–23.6 nm, which is even more surprising than the previously reported MAX phase compound. The higher reflectance indicates that W4AlB4 is a promising new material with a strong reflection effect on EUV region. Potential applications include reflective coatings for EUV lithography equipment and EUV imaging telescopes.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ra06267h |
This journal is © The Royal Society of Chemistry 2024 |