Modeling of Physical-Chemical and Electronic Properties of Lithium-Containing 4H—SiC and Binary Phases of the Si—C–Li System

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Abstract

In the equilibrium model of the solid surface–adatom system, including a three-dimensional interfacial surface, changes in surface properties are considered, taking into account the chemical potential due to the action of surface tension. The relationship between chemical potential and electrochemical potential of the ith component in an electrochemical cell is analyzed. Using the density functional theory (DFT), the adsorption, electronic, and thermodynamic properties of 2 × 2 × 1 and 3 × 3 × 1 supercells of crystalline compounds AmBn, (, where n and m are stoichiometric coefficients) of the boundary binary systems of the ternary phase diagram of Si–C–Li are studied. The stability of phases AmBn and property calculations are carried out with the exchange-correlation functional within the framework of the generalized gradient approximation (GGA PBE). The parameters of the crystal structures of the compounds AmBn, the adsorption energy of the lithium adatom  on a 4H–SiC substrate, the electronic structure, and the thermodynamic properties of supercells are calculated. The thermodynamically stable configurations of the 4H–SiC–Liads supercells having different locations Liads are determined. The DFT GGA PBE calculations of the enthalpy of formation of compounds AmBn are carried out in the ternary Si–C–Li system. Taking into account the changes in the Gibbs free energy in the solid-phase exchange reactions between binary compounds, equilibrium sections (connodes) in the concentration triangle of the Si–C–Li phase diagram are established. An isothermal section of the Si–C–Li phase diagram at 298 K is constructed. The patterns of diffusion processes that are related to the movement of particles on the surface layer of the 6H–SiC sample are analyzed. The activation energy of lithium diffusion in 6H–SiC is calculated from the Arrhenius type relation in two temperature ranges (769–973 K) and (1873–2673 K).

About the authors

M. M. Asadov

Nagiyev Institute of Catalysis and Inorganic Chemistry, Ministry of Science and Education of Azerbaijan; Scientific Research Institute of Geotechnological Problems of Oil, Gas and Chemistry

Author for correspondence.
Email: mirasadov@gmail.com
Azerbaijan, Baku; Baku

S. S. Huseynova

Institute of Physics, Ministry of Science and Education of Azerbaijan

Email: mirasadov@gmail.com
Azerbaijan, Baku

S. N. Mustafaeva

Institute of Physics, Ministry of Science and Education of Azerbaijan

Email: mirasadov@gmail.com
Azerbaijan, Baku

S. O. Mammadova

Institute of Physics, Ministry of Science and Education of Azerbaijan

Email: mirasadov@gmail.com
Azerbaijan, Baku

V. F. Lukichev

Valiev Physics and Technology Institute, Russian Academy of Sciences

Email: lukichev@ftian.ru
Russian Federation, Moscow

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Supplementary files

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2. Fig. 1. Schematic of the Brillouin zone (ZB) of the hexagonal polytype 4H-SiC (a) and ZB of the unit cell 4H-SiC (b)

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3. Fig. 2. Spherical core-shell model of solid nanoparticles

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4. Fig. 3. Optimized atomic structures of 2 × 2 × 1 4H-SiC supercells (a) and 4H-SiC-Liads (b)

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5. Fig. 4. DFT GGA PBE calculated electronic zone structure (a), total DOS (b) and partial density of states PDOS (c) of 3 × 3 × 1 supercells based on 4H-SiC and SW-SiC-Liads (d). The PDOS shows the individual contributions of each atomic orbital without considering the spin-orbit coupling effect. In Fig. c, d: 1 - full DOS; 2 - PDOS for Si; 3 - PDOS for C; 4 - PDOS for Li. The Fermi level is set at 0 eV

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6. Fig. 5. The total (DOS) and partial electron density of states (PDOS) of α-Li2C2 with orthorhombic syngony. In Fig. a: 1, DOS; 2, PDOS C2s-2p-state; 3, PDOS Li1s-state. In Fig. b: DOS [15]. The Fermi level is set at 0 eV

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7. Fig. 6. Electron density of the DOS states of the LiSi compound: 1 - Si3s-state; 2 - Si3p-state. The Fermi level is set at 0 eV

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8. Fig. 7. Temperature dependence of heat capacity Cp of compound Li2C2 [6]

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9. Fig. 8. Our approximated experimental dependences [6] of compounds: 1 - α-SiC; 2 - α-Li2C2

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10. Fig. 9. Isothermal section of the Si-C-Li system at 298 K, plotted with DFT GGA PBE calculations taken into account

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11. Fig. 10. Depth distribution of diffusing impurity in a solid layer: a - at a constant source; b - at a limited source

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12. Fig. 11. Schemes of foreign atom location along the vacancy during diffusion

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13. Fig. 12. Schemes of foreign atom by inter-nodal arrangement during diffusion

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14. Fig. 13. Dependence of the effective lithium diffusion coefficient on the reverse annealing temperature in the 6H-SiC-Lidif p-type sample. The slope values of the above dependence calculated by us correspond to activation energies of 2.1 eV in the interval (769-973 K) [53] and 1.57 eV in the interval (1873-2673 K) [54], respectively

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15. Fig. 14. Arrangement of atoms in polytypes 3C-, 4H-, Eg according to schemes AB, ABCB and ABCACB

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16. Fig. 15. T - x phase diagram of the Si-C system [56]

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17. Fig. 16. DFT calculated concentration dependence of enthalpy of formation of binary phases of Si-C system: 1 - our DFT calculation; 2 - [58]; 3 - [57]

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