Young's Modulus Versus Planar Density of Unit Cells, Super Cells, Symmetry Cells of CaTiO ₃

Calcium titanate-CaTiO ₃(Perovskite) has been used in various industrial applications due to dopant/doping mechanisms. Manipulation of defective grain boundaries in structure of perovskite is essential to maximize mechanical properties and stability, therefore attention to the structure of perovskite is done, because without mastering on the perovskite structure and diffracted planes, dopant/doping mechanisms are not understandable. In this study, area and locations of atoms and diffracted planes were designed and investigated. In this research, relationship between Young's modulus and planar density of unit cell, super cells (۲×۲×۲) and symmetry cells of nano CaTiO ₃is investigated. In this case, elastic constant, elastic compliance and Young's modulus value were recorded through the ultrasonic pulse-echo technique. As the result, C۱۱=۳۳۰.۸۹ GPa, C۱۲=۹۳.۰۳ GPa, C۴۴=۹۴.۹۱ GPa and E=۱۵۳.۸۷ GPa tandemly. Young's modulus values of CaTiO ₃extracted by planar density were calculated ۱۶۲.۶۲ GPa, ۱۵۱.۷۱ GPa and ۱۵۲.۲۱ GPa for unit cell, super cells (۲×۲×۲), and symmetry cells respectively. Young's modulus value extracted by planar density of symmetry cells was in the well agreement with Young's modulus value measured via ultrasonic pulse-echo.