Metals

Ab initio calculation of the band structure and properties of modifications of the Ti$_3$Sb compound doped with lithium

M. M. Asadov^ab, S. O. Mammadova^c, S. S. Guseinova^c, S. N. Mustafaeva^c, V. F. Lukichev<sup>d

a</sup> Nagiyev Institute of Catalysis and Inorganic Chemistry, Azerbaijan National Academy of Sciences, Baku, Azerbaijan
^b Nagiyev Institute of Catalysis and Inorganic Chemistry, Ministry of Science and Education Republic of Azerbaijan, Baku, Azerbaijan
^c Institute of Physics Azerbaijan Academy of Sciences, Baku, Azerbaijan
^d Valiev Institute of Physics and Technology of Russian Academy of Sciences, Moscow, Russia

Abstract: Using the density functional theory (DFT) in the local electron spin density approximation (LSDA), 2 $\times$ 2 $\times$ 2 supercells based on the Ti$_3$Sb compound have been studied. The supercells contained their own vacancies and doped lithium atoms replacing Ti and/or Sb. The DFT-LSDA method was used to calculate the structural, electronic, and magnetic properties, the enthalpy of formation, and the cohesion energy of supercells of two modifications of the Ti$_3$Sb compound. We studied supercells with cubic system (A15 type structure; $a$ = 5.217 $\mathring{\mathrm{A}}$) and tetragonal system (D8$_{\mathrm{m}}$ type structure; $a$ = 10.457 $\mathring{\mathrm{A}}$, $c$ = 5.258 $\mathring{\mathrm{A}}$). It has been established that the distribution of the density of states of the Ti$_3$Sb cubic system has a more metallic character than for the D8$_{\mathrm{m}}$ Ti$_3$Sb modification. The enhancement of “metallicity” in the cubic modification A15 Ti$_3$Sb is associated with an increase in the Ti–Sb interatomic distance in the crystal. Due to this, the degree of metallic bonding increases during the electronic interaction between Ti and Sb atoms near the Fermi level in Ti$_3$Sb.
In DFT calculations, the spin-polarized density of states was taken into account. It has been established that in both modifications (A15 and D8$_{\mathrm{m}}$) of Ti$_3$Sb near the Fermi level for $s$-, $p$-, $d$-states with spin “up” and spin “down” there is a spin imbalance in the population of energy levels.
Defect-containing supercells based on Ti$_3$Sb were studied by DFT-LSDA calculations. It is shown that Ti and/or Sb vacancies in the lattices of Ti$_3$Sb crystals of both modifications (A15 and D8m) increase the magnetic moment $(M)$ as compared to the value of $M$ ($M$ = 0.08 $\mu_{\mathrm{B}}$) of a “pure” Ti$_3$Sb crystal. Considering that Al5 Ti$_3$Sb is also interesting as a material for Li-ion batteries, we studied Ti$_3$Sb–Li supercells doped with lithium. Li-doping and the creation of own Ti and/or Sb vacancies changes the distance between atoms in Ti$_3$Sb. Correspondingly, the resulting local magnetic moments near the Ti or Sb vacancies also change. The enthalpy of formation and magnetic moment of Ti$_3$Sb and Ti$_3$Sb–Li based supercells are calculated. DFT calculations of the structural stability of binary compounds (phases) have been carried out, and the stability of conodes between phases in the Ti–Sb–Li system has been established. The isothermal section of the Ti–Sb–Li system was plotted at 298 K. It is shown that the introduction of various lithium concentrations ($\le$ 6.25 at.% Li) into the Ti$_3$Sb (Space group $Pm\bar{3}n$; N 223; $a$ = 5.217 $\mathring{\mathrm{A}}$) crystal lattice reduces the partial magnetic moment of Ti in the Ti$_3$Sb–Li supercell.

Keywords: Ti$_3$Sb intermetallic compounds, A15 cubic modification, D8$_{\mathrm{m}}$ tetragonal modification, doping with lithium, Ti$_3$Sb–Li, DFT-LSDA calculations, supercell, electronic and magnetic properties, Ti–Sb–Li phase stability.

Received: 02.07.2022
Revised: 02.07.2022
Accepted: 03.07.2022

DOI: 10.21883/FTT.2022.11.53312.395

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