Can anyone please inform what makes a displacement of an ion more favored in an axis than another? To be more specific, i found that when smaller ions substitute for Ba2+ on the A site in the perovskite BaTiO3, the surrounding oxygen ions displace towards the dopant, resulting in a more open space enabling the larger displacement of Ti. Such displacement is favored along the 〈111〉 axes rather than along the 〈100〉 axis. I want to know if there is an explanation for the fact that this displacement is favorable along that axis rather than another.