Theoretical calculations of stabilities and properties of transition metal borocarbides <i>TM</i><sub>3</sub>B<sub>3</sub>C and <i>TM</i><sub>4</sub>B<sub>3</sub>C<sub>2</sub> compound
Authors: Hu Qian-Ku , Hou Yi-Ming , Wu Qing-Hua , Qin Shuang-Hong , Wang Li-Bo , Zhou Ai-Guo ,   School of Materials Science and Engineering, Henan Key Laboratory of Materials on Deep-Earth Science and Technology, Henan Polytechnic University, Jiaozuo 454000, China,   State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China
Published: December 2020

To search new hard or superhard materials in transition-metal light-element compounds is a current research focus. Most of the past researches focused on binary phases such as transition metal borides, carbides and nitrides, while the researches on ternary phases were relatively rare. The single crystals Nb<sub>3</sub>B<sub>3</sub>C and Nb<sub>4</sub>B<sub>3</sub>C<sub>2</sub> were synthesized recently by using Al-Cu alloys as auxiliary metals and their structures were determined by Hillebrechtand Gebhardt. In the present paper, 29 <i>TM</i><sub>3</sub>B<sub>3</sub>C and 29 <i>TM</i><sub>4</sub>B<sub>3</sub>C<sub>2</sub> configurations are constructed by <i>TM</i> atoms (<i>TM</i> = Sc to Zn, Y to Cd, Hf to Hg) replacing Nb atoms in the known Nb<sub>3</sub>B<sub>3</sub>C and Nb<sub>4</sub>B<sub>3</sub>C<sub>2</sub> configuration. By calculating the formation energy from first-principles density functional theories, only 13 <i>TM</i><sub>3</sub>B<sub>3</sub>C and 11 <i>TM</i><sub>4</sub>B<sub>3</sub>C<sub>2</sub> phases are stable compared with the three elemental substances of <i>TM</i>, boron and carbon. However compared with the most competing phases, only Ta<sub>3</sub>B<sub>3</sub>C, Nb<sub>3</sub>B<sub>3</sub>C and Nb<sub>4</sub>B<sub>3</sub>C<sub>2</sub> phases are stable thermodynamically. The metastable Ta<sub>4</sub>B<sub>3</sub>C<sub>2</sub> phase at 0 K becomes stable when temperature is higher than 250 K. Thus two new phases of Ta<sub>3</sub>B<sub>3</sub>C and Ta<sub>4</sub>B<sub>3</sub>C<sub>2</sub> are uncovered to be stable thermodynamically. Global structure searches conducted by the popular USPEX and CALYPSO softwares prove the Ta<sub>3</sub>B<sub>3</sub>C and Ta<sub>4</sub>B<sub>3</sub>C<sub>2</sub> phases to be the most favorable energetically. By calculating the phonon dispersion curves of the Ta<sub>3</sub>B<sub>3</sub>C and Ta<sub>4</sub>B<sub>3</sub>C<sub>2</sub> phase, no imaginary phonon frequencies are observed in the whole Brillouin zone, which demonstrates the dynamical stability of the Ta<sub>3</sub>B<sub>3</sub>C and Ta<sub>4</sub>B<sub>3</sub>C<sub>2</sub> phase. The calculated elastic constant of the Ta<sub>3</sub>B<sub>3</sub>C and Ta<sub>4</sub>B<sub>3</sub>C<sub>2</sub> phases satisfy the criteria of mechanical stability, showing that the Ta<sub>3</sub>B<sub>3</sub>C and Ta<sub>4</sub>B<sub>3</sub>C<sub>2</sub> phase are stable mechanically. The calculations of band structure and density of state show that the Ta<sub>3</sub>B<sub>3</sub>C and Ta<sub>4</sub>B<sub>3</sub>C<sub>2</sub> phases are both conducting, which mainly arises from the d electrons of Ta atoms. The calculated bulk modulus and shear modulus of the Ta<sub>3</sub>B<sub>3</sub>C and Ta<sub>4</sub>B<sub>3</sub>C<sub>2</sub> phases show their brittle nature. The hardness of Ta<sub>3</sub>B<sub>3</sub>C and Ta<sub>4</sub>B<sub>3</sub>C<sub>2</sub> phase are nearly the same and calculated to be about 26 GPa by Chen’s and Tian’s models, which illuminates that the two phases are hard but not superhard.