The arrangements of domains that arise in single crystals of barium titanate in the ferroelectric tetragonal phase have been studied in detail. The domains are the results of tetragonal (101) twinning, and appear by the formation of wedge-shaped laminar domains between two converging (101) twin planes. The distance of penetration of thin wedge-shaped laminae into the crystal follows changes in an applied electric field reversibly. Often thin laminae extend through the thickness of a crystal plate at an angle of 45° to the surface. These laminae frequently advance in groups in the two perpendicular directions parallel to the edges of the rectangular plate. As a result of the intersections of these groups, the domain pattern becomes an array of laminated and unlaminated pyramids and tetrahedra, the birefringence properties of which give rise to net-like patterns of multicolored squares in polarized light. The evidence indicates that the squarenet pattern is an arrangement of twinning reducing as much as possible the total energy of lattice strains. These strains are probably due to an inhomogeneous distribution of impurities causing a bending effect, as in a bimetallic disk.

A preliminary investigation of the phase transitions near 5°C and -70°C has been completed. Using clearly defined optical observations, we conclude that the crystal is orthorhombic $\mathrm{Cmm}$ between 5°C and -70°C, and trigonal $R3m$ below -70°C, with the lattice stretched along the polar axis. The twinning is identified in terms of these lattices. It is maintained that the transitions near 5°C and -70°C can only be of the first order, in contrast with the $\lambda$-transition at 120°C. While a statistical mechanical treatment of the properties of barium titanate would be exceedingly difficult, a definite qualitative thermodynamic correlation of its properties has been made. Due to the piezoelectric "inter-action," the free energy can be visualized in the ferroelectric states in terms of a simultaneous polarization and lattice deformation. The overall situation may be regarded as one in which a ferroelectric $\lambda$-transition from the (ordered) cubic phase can, in principle, take place along any direction of the highly symmetric cubic lattice, but subject to anisotropy effects which favor the [100] directions down to 5°C, the [110] directions between 5°C and -70°C, and the [111] directions below -70°C.

• Received 5 May 1949

DOI:https://doi.org/10.1103/PhysRev.76.1187