  We have computed the local electric field in a body-centered tetragonal (BCT)
lattice of point dipoles via the Ewald-Kornfeld formulation, in an attempt to
examine the effects of a structure transformation on the local field strength.
For the ground state of an electrorheological solid of hard spheres, we
identified a novel structure transformation from the BCT to the face-centered
cubic (FCC) lattices by changing the uniaxial lattice constant c under the hard
sphere constraint. In contrast to the previous results, the local field
exhibits a non-monotonic transition from BCT to FCC. As c increases from the
BCT ground state, the local field initially decreases rapidly towards the
isotropic value at the body-centered cubic lattice, decreases further, reaching
a minimum value and increases, passing through the isotropic value again at an
intermediate lattice, reaches a maximum value and finally decreases to the FCC
value. An experimental realization of the structure transformation is
suggested. Moreover, the change in the local field can lead to a generalized
Clausius-Mossotti equation for the BCT lattices.
