Perovskite structure Rocksalt structure and Fluorite Structure Rocksalt Structure Fluorite Structure erovskite structure coordinationofTi The Perovskite(CaTiO.Unit Cell Perovskite R: ionic radius: R(O*)=1.40A tructure:ABO aa and ag natural size of each layer If a polyhedron is used to represent the Ti centered coordination environments, then anO atom lies at each vertex. the Ca= is shown in black. R(A)+R(O=aa R(B)+R(O)=a,/2 tolerance factor: O. 90- An 0 atom lies at a s shown in blac B10 Tolerance Factor 1 R(A)+R(O)a Structure of Cuprate Superconductors √2RB)+RO 1Oxygen' s from a CuO, layer are"shared by the perovskite unit cell. The actual cell size a is determined from aa and a t a I is needed. Layered perovskites are more Hn the perovskite cell, the Ba *(Black) and Ya+ bstitute for Ca2+. The Cu(blue) tolerant centers substitute for Ti(v) a=3.8~4.0A R(A)=1.3~1.4A,R(B)=0.5~06A Three factors to consider 1. valence 2. oxygen coordination number 3. ionic radius6 Perovskite Structure Octahedronal coordination of Ti Perovskite Structure Rocksalt Structure and Fluorite Structure Rocksalt Structure Fluorite Structure The Perovskite (CaTiO3 ) Unit Cell If a polyhedron is used to represent the Ti centered coordination environments, then an O atom lies at each vertex, the Ca 2+ is shown in black. An O atom lies at each vertex, the Ca 2+ is shown in black. Perovskite structure: ABO3 B A a a R(B) R(O) R(A) R(O) 2 1 t = + + = × tolerance factor: R: ionic radius: R(O 2- ) ≡ 1.40 Å aA and aB: natural size of each layer AO layer: R( A) + R(O) = a A / 2 R(B) + R(O) = aB / 2 BO2 layer: B O O A The actual cell size a is determined from aA and aB . t ≈ 1 is needed. Layered perovskites are more tolerant. a = 3.8 ~ 4.0 Å R(A) = 1.3 ~ 1.4 Å, R(B) = 0.5 ~ 0.6 Å Three factors to consider: 1. valence 2. oxygen coordination number 3. ionic radius Tolerance Factor: B A a a R(B) R(O) R(A) R(O) 2 1 t = + + = × Structure of Cuprate Superconductors Oxygen's from a CuO2 layer are “shared”by the perovskite unit cell. In the perovskite cell, the Ba2+ (Black) and Y3+ (Gray) ions substitute for Ca2+. The Cu (blue) centers substitute for Ti(IV)