  We investigate the electrostrictive response across a ferroelectric phase
transition from first-principles calculations and refute the prevailing view of
constant electrostriction across the ferroelectric phase boundary. We take as a
case study the epitaxial strain-induced transition from para- to
feroelectricity of \ce{KTaO3}. We show that the magnitude of the
electrostriction diverges with the permitivity at the transition, hence
exhibiting giant responses through a calculation of both the M and Q
electrostrictive tensors. We explain the origin of this giant electrostrictive
response in \ce{KTaO3} using a microscopic decomposition of the
electrostriction coefficients, and use this understanding to propose design
rules for the development of future giant electrostrictors for
electromechanical applications. Finally, we introduce a further means to
calculate electrostriction, specific to ferroelectrics, and not yet utilised in
the literature.
