*Article* **Relationship between Young's Modulus and Planar Density of Unit Cell, Super Cells (2** *×* **2** *×* **2), Symmetry Cells of Perovskite (CaTiO3) Lattice**

**Marzieh Rabiei 1, Arvydas Palevicius 1,\*, Sohrab Nasiri 1,\*, Amir Dashti 2, Andrius Vilkauskas <sup>1</sup> and Giedrius Janusas 1,\***


**Abstract:** Calcium titanate-CaTiO3 (perovskite) has been used in various industrial applications due to its dopant/doping mechanisms. Manipulation of defective grain boundaries in the structure of perovskite is essential to maximize mechanical properties and stability; therefore, the structure of perovskite has attracted attention, because without fully understanding the perovskite structure and diffracted planes, dopant/doping mechanisms cannot be understood. In this study, the areas and locations of atoms and diffracted planes were designed and investigated. In this research, the relationship between Young's modulus and planar density of unit cell, super cells (2 × 2 × 2) and symmetry cells of nano CaTiO3 is investigated. Elastic constant, elastic compliance and Young's modulus value were recorded with the ultrasonic pulse-echo technique. The results were C11 = 330.89 GPa, C12 = 93.03 GPa, C44 = 94.91 GPa and E = 153.87 GPa respectively. Young's modulus values of CaTiO3 extracted by planar density were calculated 162.62 GPa, 151.71 GPa and 152.21 GPa for unit cell, super cells (2 × 2 × 2) and symmetry cells, respectively. Young's modulus value extracted by planar density of symmetry cells was in good agreement with Young's modulus value measured via ultrasonic pulse-echo.

**Keywords:** nano-perovskite (CaTiO3); X-ray diffraction; Young's modulus; ultrasonic-pulse echo; planar density
