New High-Performance Piezoelectric: Ferroelectric Carbon-Boron Clathrate

High-performance piezoelectrics have been extensively reported with a typical perovskite structure, in which a huge breakthrough in piezoelectric constants is found to be more and more difficult. Hence, the development of materials beyond perovskite is a potential means of achieving lead-free and high piezoelectricity in next-generation piezoelectrics. Here, we demonstrate the possibility of developing high piezoelectricity in the nonperovskite carbon-boron clathrate with the composition of ${\mathrm{ScB}}_3{\mathrm{C}}_3$ using first-principles calculations. The robust and highly symmetric B-C cage with mobilizable Sc atom constructs a flat potential valley to connect the ferroelectric orthorhombic and rhombohedral structures, which allows an easy, continuous, and strong polarization rotation. By manipulating the cell parameter $b$, the potential energy surface can be further flattened to produce an extra-high shear piezoelectric constant $d_{15}$ of $9424\mathrm{pC}/\mathrm{N}$. Our calculations also confirm the effectiveness of the partial chemical replacement of Sc by Y to form a morphotropic phase boundary in the clathrate. The significance of large polarization and high symmetric polyhedron structure is demonstrated for realizing strong polarization rotation, offering the universal physical principles to aid the search for new high-performance piezoelectrics. This work takes ${\mathrm{ScB}}_3{\mathrm{C}}_3$ as an example to exhibit the great potential for realizing high piezoelectricity in clathrate structure, which opens the door to developing next-generation lead-free piezoelectric applications.

Figure 1

(a) Typical perovskite-type structure. (b) Oxygen octahedron with high symmetry, the polarization rotation can be realized depending on the displacements of the $B$-site atom in the oxygen cage. (c) A schematic of polarization rotation on the (010) plane, where $P_1$ is the projection of rotated $P$ in the $x$ direction.

Figure 2

(a) Structure of cubic ${\mathrm{ScB}}_3{\mathrm{C}}_3$. (b) High symmetry of carbon-boron clathrate. (c) Total energies vs full-mode distortion of orthorhombic ferroelectric phase. (d) Polarization vs the distortion. Note that only one branch of polarization quantum is chosen.

Figure 3

(a) Potential energy as a function of the amplitude of distortion mode. (b) PES as a function of ${\mathrm{\Gamma }}_4^{-}+{\mathrm{\Gamma }}_5^{+}$ (a, a, 0) and ${\mathrm{\Gamma }}_4^{-}+{\mathrm{\Gamma }}_5^{+}$ (a, a, a), as well as ${\mathrm{\Gamma }}_4^{-}+{\mathrm{\Gamma }}_5^{+}$ (a, a, 0) and ${\mathrm{\Gamma }}_4^{-}$ (a, 0, 0). (c) $c_{55}$ and $d_{33}$ as a function of longitudinal strain ${\eta }_2$. The negative $c_{55}$ indicates the phase transition. (d) PES as a function of ${\eta }_2$ and ${\eta }_5$. (e) $d_{15}$ of ${\mathrm{ScB}}_3{\mathrm{C}}_3$ compared with other inorganic perovskite ferroelectrics [35, 36, 37, 38, 39]. (e) Difference of total energy between orthorhombic and rhombohedral phases as a function of Y content.

Figure 4

(a) Temperature-dependent polarization in ${\mathrm{ScB}}_3{\mathrm{C}}_3$. (b) ${[011]}_{\mathrm{pc}}$ stereographs of the direction of polar displacement of Sc in carbon-boron clathrate. The colors exhibit the density distribution around each point on the graph.