MAS.020UF Introduction to Solid State Physics

CaTiO₃

CaTiO₃ has what is known as the ideal perovskite structure. Calcium atoms are at the corners of cube, a titanium atom is at cube body center, and oxygen atoms are at cube face centers. Take the cube edge length to be $a$.

a) What is the Bravais lattice type?

b) Write down a set of primitive lattice vectors.

c) Verify that there are 3 oxygen atoms, 1 titanium atom and 1 calcium atom the basis of this crystal structure.

d) Give the positions of the atoms in the basis in fractional coordinates of the primitive lattice vectors.

Solution