The optimized structures of the Ti 3 (Si x Al 1−x )C 2 are shown in Fig. 3, as are visualized by the VESTA, in the form of hexagonal, nano-layered structures. The resultant lattice parameters of the Ti 3 (Si x Al 1−x )C 2 are shown in Fig. 4, and compared to experimental results. As it can be in Fig. 4, both of the calculated and experimented results show that the c lattice parameter decreases more than the a lattice parameter with increasing amount of Si.
Fig. 5 is a 2-dimensional representation of the ELF for Ti 3 (Si x Al 1−x )C 2 on the (100) plane [32]. The
ELF represents the sum of squares of the wave function, which corresponds to the number of electrons. ELF is suitable for the observation of electrons in real space, which corresponds to chemical bonding of each …show more content…
In particular, B, G, and
E of hexagonal structure are expressed as follows [34]: where B, G, and E are bulk, shear, and Young’s modulus, respectively. The resultant elastic constants, bulk, shear, and Young’s modulus are summarized in Table 2. Here, it can be seen that the B, G, and E are increasing with increasing amount of Si on the A site. This could be attributed to the charge density shown in Table 1. In particular, the substitution of Al with Si increases the total charge density of the A element atoms from 33.248 to 43.024. However, the total charge density of M and X element atoms does not change significantly, i.e. only from 45.72 to 45.192, and 105.024 to 103.776, respectively. The increased charge density makes the M-A bonds stronger, and thus harder to stretch. The Young’s modulus, shown in
Fig. 7, agrees well with the available experimental data, which also linear increase with increasing amount of Si on the A site. Moreover, in the Ti 3 (Si x Al 1−x )C 2 , C 11 changes from 355.45 GPa to 370.47 GPa,
Fig. 5 is a 2-dimensional representation of the ELF for Ti 3 (Si x Al 1−x )C 2 on the (100) plane [32]. The
ELF represents the sum of squares of the wave function, which corresponds to the number of electrons. ELF is suitable for the observation of electrons in real space, which corresponds to chemical bonding of each …show more content…
In particular, B, G, and
E of hexagonal structure are expressed as follows [34]: where B, G, and E are bulk, shear, and Young’s modulus, respectively. The resultant elastic constants, bulk, shear, and Young’s modulus are summarized in Table 2. Here, it can be seen that the B, G, and E are increasing with increasing amount of Si on the A site. This could be attributed to the charge density shown in Table 1. In particular, the substitution of Al with Si increases the total charge density of the A element atoms from 33.248 to 43.024. However, the total charge density of M and X element atoms does not change significantly, i.e. only from 45.72 to 45.192, and 105.024 to 103.776, respectively. The increased charge density makes the M-A bonds stronger, and thus harder to stretch. The Young’s modulus, shown in
Fig. 7, agrees well with the available experimental data, which also linear increase with increasing amount of Si on the A site. Moreover, in the Ti 3 (Si x Al 1−x )C 2 , C 11 changes from 355.45 GPa to 370.47 GPa,