New high-performance ferroelectric materials based on Pb(Zr{sub 1-x}Ti{sub x})O{sub 3} (PZT) that are doped with cryolite-type strontium niobate (SNO, Sr{sub 4}(Sr{sub 2-2y/3}Nb{sub 2+2y/3})O{sub 11+y}V{sub 0,1-y} with 0 {le} y {le} 1), hence denoted PZT:SNO, and their microscopic structure are described. The combination of exceptional piezoelectric properties, i.e. a piezoelectric strain constant of d{sub 33} {approx} 760 pm/V, with excellent stability and degradation resistance makes ferroelectric PZT:SNO solid solutions very attractive for use in novel and innovative piezoelectric actuator and transducer applications. Extended X-ray absorption fine-structure (EXAFS) analyses of PZT:SNO samples revealed that {approx}10 % of the Sr cations occupy the nominal B-sites of the perovskite-type PZT host lattice. This result was supported by EXAFS analyses of both a canonical SrTiO{sub 3} perovskite and two SNO model and reference compounds. Fit models that do not account for Sr cations on B-sites were ruled out. A clear Sr-Pb peak in Fourier transformed EXAFS data visually confirmed this structural model. The generation of temporary oxygen vacancies and the intricate defect chemistry induced by SNO-doping of PZT are crucial for the exceptional materials properties exhibited by PZT:SNO materials.

The aim of this paper is the development of equilibrium and non-equilibrium extensions of the quasicontinuum (QC) method. We first use variational mean-field theory and the maximum-entropy formalism for deriving approximate probability distribution and partition functions for the system. The resulting probability distribution depends locally on atomic temperatures defined for every atom and the corresponding thermodynamic potentials are explicit and local in nature. The method requires an interatomic potential as the sole empirical input. Numerical validation is performed by simulating thermal equilibrium properties of selected materials using the Lennard-Jones pair potential and the EAM potential and comparing with molecular dynamics results as well as experimental data. The max-ent variational approach is then taken as a basis for developing a three-dimensional non-equilibrium finite temperature extension of the quasicontinuum method. This extension is accomplished by coupling the local temperature-dependent free energy furnished by the max-ent approximation scheme to the heat equation in a joint thermo-mechanical variational setting. Results for finite-temperature nanoindentation tests demonstrate the ability of the method to capture non-equilibrium transport properties and differentiate between slow and fast indentation.