The seven phases of sodium niobate

Sodium niobate, NaNbO3, has seven structures belonging to the perovskite family, comprising the aristotype 1 (with the ideal perovskite structure) and six hettotypes 1 (structures with lower symmetry). The differences between them can be systematized in terms of two factors, displacement of Nb from the octahedron centres, and tilting (rotation) of octahedra about the lines joining their centres. These each can be resolved into components, displacement com-potents along the three tetrad axes, and tilt components giving angles of tilt about the same three axes. Displacement components and tilt components are independent in origin but may interact. The phase changes at successive transitions involve the disappearance one by one of tilt or displacement components, until the cubic aristotype is finally reached. At the lower transitions, change of sense of tilt components occurs, leading to large energy barriers. Loss of tilts at the higher transitions is correlated with the occurrence of soft modes. Decrease of symmetry with increase of temperature at the lower transitions is noted, and the role of Na in relation to the tilt system is briefly considered.