Using first-principles calculations, this work investigated the structural, electronic, thermal and optical properties of ScAl3C3 and UAl3C3 under high pressure. Through the calculation of elastic constant, the mechanical stability of these two ceramics at high pressures were discussed. Then, by comparing the density of states of ScAl3C3 and UAl3C3 under different pressures, the pressure effect on electronic properties were discussed. What’s more, by calculating longitudinal, transverse sound, mean sound velocities, and the Debye temperatures at different pressures, the effect of high pressure on thermal properties of ScAl3C3 and UAl3C3 were explored. At the end of this work, the dielectric function ε(ω) and reflectivity R(ω) of ScAl3C3 and UAl3C3 were calculated to discuss change of their optical properties under high pressure.

In the past few decades, Mn+1AXn (MAX) compounds, as a new type of ceramic materials stacked by M–X octahedron slabs and weakly bonded A slabs, have attracted tremendous attention for excellent thermal and optical properties. This type of compounds have a layered-hexagonal structure alternately, where M is an early transition metal, A is a group 13–16 element, and X is mainly C or N. Many studies [1,2] indicate that this type of layered ternary carbides own more superior oxidation resistance and fracture toughness than their corresponding dicarbides. Based on this case, more than one hundred MAX phases [3–6] have been successful discovered at experiment or predicted in theory in the last few decades since Ti3SiC2 was first discovered by Nowotny et al. [7].

Large number of layered ternary carbides (MC)mAl3C2 (where M is metal atom, m = 1, 2, 3…), as one of the most typical classes of Mn+1AXn (MAX) compounds, have been synthesized recently years [8–10]. Studies [11–13] show that (ZrC)mAl3C2 and (HfC)mAl3C2 also have superior oxidation resistance and fracture toughness compared to ZrC and HfC. It makes them potential refractories for the high stiffness and strength of Zr-Al-C and Hf-Al-C carbides. He et al. [14] investigated the mechanical and thermal properties of 37.5 wt% Hf3Al3C5, 30.5 wt% Hf3Al4C6, and 32.0 wt% Hf2Al4C5 and found that these composites exhibit much higher strength and fracture toughness than HfC, with high stiffffness remaining up to 1600 °C. The unique properties of MAX phase materials in physical, chemical, electrical and mechanical fields make them potential applications in high temperature electrodes, friction and wear, nuclear energy structural materials and other fields. Li et al. [15] investigated optical properties of V4AlC3 using the first-principles method, and results showed that V4AlC3 has the potential to be used as a promising dielectric material and coating to avoid solar heating.

With the advantages of high melting point, high oxidation resistance and fracture toughness, (MC)mAl3C2 (M = Hf, Zr) have important potential applications in the industry field. While ScAl3C3 and UAl3C3 have similar structures with them [8]. There are few studies [16] on the related properties of these two compounds, especially for ScAl3C3. But there is no report on their properties under high pressure. In this work, first principle calculations are carried out to study the structure, electronic, thermal properties and optical properties of ScAl3C3 and UAl3C3 under high pressure to discuss their potential application fields.

2Computational methods and detailsIn present work, first-principles calculations were performed to study the structural, electronic, elastic, thermophysical and optical properties of ternary ceramic ScAl3C3 and UAl3C3 under high pressure. The crystal structures of these two ceramic were optimized by the conjugate gradient (CG) algorithm at different hydrostatic pressures. And the generalized gradient approximation designed by Perdew, Burke, and Ernzerhof (PBE) [17,18] was considered as the exchange-correlation energy in these calculations. The cut-off energy and the k points grid were set as 550 eV and 7 × 7 × 2, respectively. The Brillouin zone sampling was performed using Monkhorst-pack grid [19].

The tolerances in these calculations were 5 × 10−7 eV/atoms for the total energy variation and 0.005 eV/Å for the force per atom. The maximum ionic displacement and maximum stress were set to less than 5 × 10−4 Å and 0.02 GPa, respectively.

3Results and discussion3.1Structural stability and elastic properties at high pressureIn present work, theoretical crystal structure of ScAl3C3 and UAl3C3 are established based on experimental data from Ref [8], (Fig. 1). The structures at normal pressure were optimized by Density Functional Theory (DFT) calculations to compare with the experimental values. For the ScAl3C3 phase, the calculated lattice parameters a and c at normal pressure are 3.357 Å and 16.784 Å. While for the UAl3C3 phase, theoretical a = 3.376 Å and c = 17.441 Å. Compared with the experimental value, our computed lattice constants for both ScAl3C3 and UAl3C3 are well agreement with experimental results in Ref [8].

To study the mechanical stability of ScAl3C3 and UAl3C3 under high pressures, elastic constants of them at different pressures were calculated and shown in Table 1. For a hexagonal crystals, if it satisfy the mechanical stability criterion as following,

it can be said that this material is stable in mechanics.Calculated elastic constants of ScAl3C3 and UAl3C3 at different pressures.

Compound | Pressure (GPa) | C11 | C12 | C13 | C33 | C44 | C66 | B | G | E | Ref |
---|---|---|---|---|---|---|---|---|---|---|---|

HfC | 0 | 525 | 108 | 160 | 247 | 180 | 489 | [20] | |||

Hf3Al3C5 | 0 | 425 | 120 | 99 | 362 | 175 | 152 | 205 | 160 | 381 | [20] |

Zr3Al3C5 | 0 | 429 | 110 | 93 | 378 | 179 | 160 | 202 | 166 | 391 | [21,22] |

UC | 0 | 169 | 146 | 47 | 154 | 61 | 162 | [23] | |||

UAl3C3 | 0 | 304 | 115 | 97 | 326 | 154 | 95 | 172 | [16] | ||

0 | 302 | 110 | 100 | 282 | 147 | 96 | 167 | 114 | 279 | This work | |

10 | 369 | 150 | 122 | 397 | 165 | 109 | 213 | 135 | This work | ||

20 | 416 | 190 | 142 | 447 | 179 | 113 | 247 | 145 | This work | ||

30 | 452 | 218 | 172 | 514 | 189 | 117 | 282 | 152 | This work | ||

40 | 482 | 244 | 195 | 572 | 198 | 119 | 311 | 159 | This work | ||

ScAl3C3 | 0 | 368 | 94 | 68 | 293 | 147 | 137 | 164 | 139 | 325 | This work |

10 | 422 | 131 | 91 | 363 | 167 | 145 | 202 | 155 | This work | ||

20 | 473 | 163 | 116 | 417 | 186 | 155 | 238 | 169 | This work | ||

30 | 517 | 198 | 142 | 467 | 202 | 159 | 273 | 179 | This work | ||

40 | 561 | 229 | 169 | 508 | 218 | 166 | 306 | 190 | This work |

From elastic constants listed in Table 1, it can be judged that both ScAl3C3 and UAl3C3 satisfy the mechanical stability criterion in the pressure range of this study. That is to say, they are mechanically stable in the pressure range we studied.

To further investigate the mechanical properties of them, the bulk and shear modulus are calculated. According to Voigt approximation, the bulk and shear modulus can be expressed by the second-order elastic constants as follow,

where Bv and Gv are the bulk and shear modulus in the Voigt scheme.According to Reuss approximation, the bulk and shear modulus can be expressed by the second-order elastic constants as follow,

where BR and GR are the bulk and shear modulus in the Reuss scheme [24].Using the Voigt, Reuss and Hill approximation, the polycrystalline bulk modulus B and shear modulus G can be obtained as follow,

The bulk and shear modulus of ScAl3C3 and UAl3C3 at different pressures are computed by above method. The calculated results are presented in above Table 1. And there also presents the elastic constants of some Hf- and Zr-containing (MC)nAl3C2 at 0 GPa obtained from references. The bulk and shear modulus of ScAl3C3 and UAl3C3 are much lower that their counterpart of Hf- and Zr-containing (MC)nAl3C2. It means that the compressive and shear deformation resistance of ScAl3C3 and UAl3C3 are inferior to that their counterpart of Hf- and Zr-containing (MC)nAl3C2 at normal pressure. But with the increasing of pressure, the bulk and shear modulus of ScAl3C3 and UAl3C3 increase quickly. At 40 GPa, these two moduli for two compounds exceed the value of (HfC)nAl3C2 and (ZrC)nAl3C2 at 0 GPa.

In a word, mechanical properties of both ScAl3C3 and UAl3C3 have improved under high pressure.

3.2Electronic structure under high pressureTo study the pressure effect on electronic properties, the density of states of ScAl3C3 and UAl3C3 were calculated at different pressures. Fig. 2(a) and (b) presents the partial electronic density of states (PDOS) of ScAl3C3 and UAl3C3 at normal pressure, respectively. The existence of electronic density of states at the Fermi levels for both ScAl3C3 and UAl3C3 indicates their metallic-like nature. So they are good electrical conductors. By further investigate the PDOS, it can be seen that Sc d states, Al p states and C p states mainly contribute to the metallic-like behavior of ScAl3C3; while the f orbitals of U atoms are mainly contributions for the electronic conduction behavior of UAl3C3.

Fig. 2(c) and (c) presents the total density of states (TDOS) of ScAl3C3 and UAl3C3 at different pressures, respectively. For these two compounds, the peak of the densities of states on both sides of the Fermi level exhibit a trend of outward migration under high pressure. Actually, there is a very small band gap of 0.063 eV for ScAl3C3 at 0 GPa. But under high pressure, even such a small gap disappeared, and it is fully conductive. So the electronic conduction behavior of ScAl3C3 has been improved obviously at high pressures.

3.3Thermophysical propertiesTo study thermophysical properties of ScAl3C3 and UAl3C3 under high pressure, Debye temperatures were calculated at different pressures for both these two compounds. Debye temperature, as an important thermal quantity, can be obtained from Debye model. According to this model, the longitudinal sound vl, transverse sound vt, mean sound velocities va and Debye temperature of ScAl3C3 and UAl3C3 at different pressures are calculated and given in Table 2. In addition, the Debye temperatures for YAl3C3, Zr2Al3C4 and Zr3Al3C5 at normal pressure obtained from previous studies are also listed in Table 2. Debye temperature is an important parameter to measure the melting point of materials. The larger the value of Debye temperature, the higher the melting point. From Table 2, it can be seen that the Debye temperature of ScAl3C3 is even higher than YAl3C3, Zr2Al3C4 and Zr3Al3C5, which means it has a higher melting point. Studies show [10,25] that YAl3C3, Zr2Al3C4 and Zr3Al3C5 have relatively good high temperature resistance. So it can be said that ScAl3C3 also possess this merit. What’s more, its Debye temperature increases as the pressure is increased. It means its melting point become ever higher at a high pressure.

Calculated density; longitudinal, transverse sound, mean sound velocities, and the Debye temperatures obtained from the mean sound velocities of ScAl3C3 and UAl3C3 at different pressures; and corresponding data for YAl3C3, Zr2Al3C4 and Zr3Al3C5 obtained from previous studies.

Compounds | Pressure (GPa) | ρ (g/cm3) | vl (m/s) | vt (m/s) | va (m/s) | ΘD (K) | Ref |
---|---|---|---|---|---|---|---|

YAl3C3 | 0 | 3.90 | 9382 | 5970 | 6563 | 837 | [10] |

Zr2Al3C4 | 0 | 4.80 | 9249 | 5792 | 6379 | 830 | [25] |

Zr3Al3C5 | 0 | 5.28 | 8954 | 5607 | 6175 | 806 | [25] |

ScAl3C3 | 0 | 3.29 | 10311 | 6505 | 7158 | 938.8 | This work |

10 | 3.47 | 10849 | 6682 | 7372 | 984.8 | This work | |

20 | 3.63 | 11291 | 6819 | 7539 | 1022.6 | This work | |

30 | 3.78 | 11634 | 6881 | 7623 | 1047.6 | This work | |

40 | 3.91 | 11955 | 6968 | 7729 | 1074.6 | This work | |

UAl3C3 | 0 | 6.62 | 6943 | 4151 | 4593 | 592.5 | This work |

10 | 6.98 | 7505 | 4398 | 4877 | 640.2 | This work | |

20 | 7.29 | 7771 | 4459 | 4953 | 659.9 | This work | |

30 | 7.57 | 8000 | 4480 | 4986 | 672.8 | This work | |

40 | 7.83 | 8171 | 4505 | 5020 | 685.1 | This work |

For UAl3C3, its temperature resistance is much poorer than YAl3C3, Zr2Al3C4 and Zr3Al3C5, but this performance has been greatly improved due to the Debye temperature increases from 592.5 K at 0 GPa to 685.1 K at 40 GPa. The Debye temperature of UAl3C3 at 40 GPa could compare with its counterpart of YAl3C3, Zr2Al3C4 and Zr3Al3C5 at 0 GPa. So it can be said that it still exhibits a relatively good high temperature resistance at high pressures.

In a word, thermophysical properties of both ScAl3C3 and UAl3C3 have greatly improved under high pressure.

3.4Optical properties at high pressureTo study the optical properties under high pressure, dielectric function ε(ω) and reflectivity R(ω) of ScAl3C3 and UAl3C3 are calculated (Figs. 3 and 4). As an optical property reflects the respond of a material to the application of an electric field, dielectric function ε(ω) can be expressed by the density of states between the valence bands and conduction bands. Its imaginary part can be deduced from the matrix element between the occupied and unoccupied states by following formula,

While the real part, which is associated with polarization and anomalous dispersion, can be expressed from Kramers-Kronig relations as following [26,27].

The real part ε1(ω) and imaginary part ε2(ω) of dielectric function ε(ω) for ScAl3C3 and UAl3C3 are presented in following Figs. 3(a) and (b), respectively. The curves of the imaginary part ε2(ω) show the same trend as ε1(ω). For ε1(ω), the values of ε1(0) are found to be 11.3 and 265.0 for ScAl3C3 and UAl3C3, respectively. In Section 3.2, the calculations of electronic properties imply that both ScAl3C3 and UAl3C3 own metallic-like nature. What’s more, Sc d states, Al p states and C p states mainly contribute to the metallic-like behavior of ScAl3C3; while the f orbitals of U atoms and the p orbitals of Al atoms are mainly contributions for the electronic conduction behavior of UAl3C3. Therefore, for ScAl3C3, the ε2(ω) peaks are dominated by the electronic transitions between Sc and Al atoms, or between Al and C atoms. As a result, the prominent ε2(ω) peak is contributed by the electrons transferring from Sc-3d to Al-3p states, or from Al-3p states to C-2p states. While for UAl3C3, the ε2(ω) peaks are dominated by the electronic transitions between U-d states to Al-3p states.

Reflectivity R(ω) can be computed by the dielectric function with the formulas as following,

For ScAl3C3, reflectivity R(ω) at normal pressure reaches its maximum value at the energy around 11.6 eV which corresponding to a light with the wavelength about 107 nm. With the pressure increases, the peak of reflectivity R(ω) has blue-shifted, but the value of the peak does not change much. The wavelength corresponding to the peak of reflectivity changes from 107 nm at 0 GPa to 97 nm at 40 GPa. These wavelength are located in the far ultraviolet ray range, so it can be applied as optical shielding devices for far ultraviolet radiation.

For UAl3C3, in the ultraviolet range from 130 to 147 nm, its reflectivity R(ω) is greater than 0.9, and the maximum value is near to the energy around 9.2 eV which corresponding to a light with the wavelength about 134 nm. So it can be applied as optical shielding devices for ultraviolet radiation. Similar investigations on tungsten borides and LdCd3P3 by Liu et al. [28,29] and Feng et al. [30], respectively. But as the pressure is increased to 40 GPa, the maximum value of reflectivity R(ω) has also blue-shifted, and decreased to 0.83. So the pressure effect have significant impact on the optical property of UAl3C3.

4ConclusionIn this paper, the mechanical, electronic, thermophysical and optical properties of ScAl3C3 and UAl3C3 under high pressure were investigated by performing the first-principles calculations to explore their potential applications. Main results of the present work are as follows,

- 1)
Both of these two compounds are mechanical stable from 0 to 40 GPa. So they are stable at atmospheric temperature and pressure. The bulk and shear modulus of them has been greatly improved under high pressure.

- 2)
Both ScAl3C3 and UAl3C3 present metallic-like nature at 0 GPa. And the electronic conduction behavior of ScAl3C3 has been improved obviously at high pressures.

- 3)
The calculations of thermophysical properties under high pressure show that the temperature resistance of both ScAl3C3 and UAl3C3 have greatly improved, and they exhibit relatively good high temperature resistance under high pressure.

- 4)
The investigation of optical properties under high pressure show the peak of reflectivity R(ω) has blue-shifted for both ScAl3C3 and UAl3C3.

Through the results of this work, a theoretical guidance for the potential industrial applications of ternary ceramic ScAl3C3 and UAl3C3 can be obtained. Good electronic conduction behavior makes them to be potential conductive materials in the industrial field. High temperature resistance under high pressure render them good structural materials for application in high temperature and pressure environments. High reflectivity of light with different wavelengths make them optical shielding devices for different light radiations. Results show ScAl3C3 and UcAl3C3 can be applied as optical shielding devices for far ultraviolet radiation and ultraviolet radiation, respectively.

Conflicts of interestThe authors declare no conflicts of interest.

Supported by the Key Scientific Research Projects of Henan Province (Nos. 18A140036 and 17A140030) and the Fund of Laboratory of Computational Physics, Beijing, China (Grant No. 6142A05180101).

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