Birefringence characteristics of nanoscale dielectrics with cubic and tetragonal lattices.

The birefringence in nanometer-scale dielectrics with the largest dimensions ranging from about 3 nm to 20 nm has been quantified by evaluating directly the summation of induced-dipole-electric-field contributions from all individual atoms within the entire dielectric volume. Various configurations in representative cubic and tetragonal systems are investigated by varying the ratio of lattice constants and the number of atoms in various directions to illustrate the chain-like and plane-like behavior regimes. The dielectric properties of the finite cubic crystal lattices change from isotropic to birefringent (uniaxial or biaxial) when the entire dielectric volume is changed from a cube to a rectangular parallelepiped in shape. In finite tetragonal crystals the birefringence increases with the increasing lattice constant ratios. The largest uniaxial birefringence occurs for non-cube dielectric volume with tetragonal lattices.