Density functional study of carbon vacancies in titanium carbide

Area of Science:

• Materials Science
• Computational Materials Science
• Solid-State Chemistry

Background:

• Titanium carbide (TiC) is known to exhibit carbon vacancies under various environmental conditions.
• Understanding vacancy formation is crucial for predicting TiC's properties and performance.

Purpose of the Study:

• To investigate the thermodynamic favorability of carbon vacancy formation in TiC.
• To explore the influence of different chemical environments (C-rich vs. Ti-rich) on vacancy formation energy.
• To analyze the role of atomic relaxations and kinetics in vacancy stabilization.

Main Methods:

• Density functional theory (DFT) calculations were employed.
• Vacancy formation energies were computed under varying C-rich and Ti-rich conditions.
• Multiple exchange-correlation functional approximations were utilized.
• Thermodynamics of the carbon reference state and growth conditions were considered.

Main Results:

• Carbon vacancy formation is thermodynamically favorable under Ti-rich conditions.
• Vacancy formation is slightly energetically unfavorable under C-rich conditions.
• Long-ranged atomic relaxations near vacancy sites significantly stabilize vacancies.
• Calculated formation energies align with experimental observations of vacancies in TiC.

Conclusions:

• Thermodynamics favor carbon vacancies primarily in Ti-rich TiC.
• The experimental observation of vacancies in C-rich TiC suggests a significant role for kinetics.
• High activation energies and slow vacancy diffusion likely 'freeze-in' vacancies, explaining their presence under non-ideal conditions.