Final Report on DOE Grant No . DE - FG 02 - 03 ER 46059 Titled : “ Structural Transformations in Ceramics : Perovskite - like Oxides and Group III , IV , and

Ceramic perovskite-like oxides with the general formula (A ′ A ′′ . . .)(B ′ B ′′ . . .)O3and titanium-based oxides are of great technological interest because of their large piezoelectric and dielectric response characteristics.[1] In doped and nanoengineered forms, titantium dioxide finds increasing application as an organic and hydrolytic photocatalyst. The binary main-group-metal nitride compounds have undergone recent advancements of in-situ heating technology in diamond anvil cells leading to a burst of experimental and theoretical interest. In our DOE proposal, we discussed our unique theoretical approach which applies ab initio electronic calculations in conjunction with systematic group-theoretical analysis of lattice distortions to study two representative phase transitions in ceramic materials: (1) displacive phase transitions in primarily titanium-based perovskite-like oxide ceramics, and (2) reconstructive phase transitions in main-group nitride ceramics. A sub area which we have explored in depth is doped titanium dioxide electrical/optical properties. Work in displacive phase transitions in ceramic-like perovskite alloys has produced six papers in print (or press)[2, 3, 4, 5, 6, 7], one submitted paper[8], and two in preparation[9, 10], which can be grouped into seven main areas: (1) We have used domain average engineering symmetry methods to study heterogeneous domain structures in perovskite ferroelectrics. The domain average symmetry that we consider is applicable to crystals having a large number of domains. For such a case, the domains form a kind of nano-composite. The result[2] was a systematic derivation of all allowed “domain sets”, their mesoscopic symmetry, information about the role of domain fractions in determining that symmetry, and the corresponding physical tensor properties for that domain set. The three cases we considered in depth corresponded to polarization (px, py, pz) oriented along [100], [110], and [111], resulting in the single domain state symmetries P4mm, Amm2, and R3m, respectively. For the [111] polarization direction the PZM-PT and PMN-PT crystals are examples of interest. The well known BaTiO3 is an example of a structural change with polarization along the [100] direction. KNbO3 is an example of a material which undergoes a transition due to the spontaneous polarization toward the edge diagonals 〈110〉. As an example of the results we obtained, the dipole ordering along [100], corresponding to BaTiO3, is shown in Table 1. ISOTROPY contains the computer implementation of our algorithm for any space group to sub-group phase transition and is freely available[11]. (2) To validate these theoretical multidomain structures we have developed a fast thermodynamic approach to recreate mesoscopic multidomain ferroelectrics.[3] Using a phase field theory free energy functional we have developed a novel multi-order parameter evolution strategy for ferroelectrics is much faster than previous simulations employing instantaneous mechanical equilibrium[12, 13, 14, 15, 16, 17, 18, 19]. We determined potential coefficients were determined via the techniques of global phase diagrams (GPDs) and have been discussed in detail for molecular crystals[20, 21, 22]. As an example of this work we briefly discuss a [100]-ordering P4mm nanocomposite. As shown in Fig. 1, the symmetry is broken by a Γ4 space group irreducible representation with six possible energetically equivalent domains (each a different color). These domains correspond to the multidomain structures given in Table 1. Figure 1 shows that without any reference to the theoretical derivations of Ref. [23], mesoscopic simulations using combinations of external fields have reproduced predicted symmetries. The group theoretical enumeration of all possible multidomain structures and its numerical validation are needed for high precision domain engineering and are vital to a “bottom-up” microand nanotechnology materials design approach to achieve macroscopic materials with precise properties. (3) We are extending this mesoscopic approach to ferroelastics and multiscale first-principles-based simulation of domain structures. Currently the mesocopic structure code (called DOMAINS) determining the dynamics of the free energy uses finite differences and fixed geometries. A better option is to use adaptive finite elements (AFE) and moving geometries. AFE allows the material to change atomic spacings during and after field changes which (a) gives better hysteresis effects, (b) is physically realistic, and (c) is computationally efficient because it uses fewer nodes in the middle of domains. Another improvement is to base our calculations on first principles simulations rather than empirical coefficients. As the QC multiscale method[24] already has many of these features built-in, we are working with its authors to apply it to multidomain structures and extend its ab initio capabilities to other materials besides metals.[25] A simple test case for this without the complexity of electric fields would be to model ferroelastic transitions[9]. This was an intended extension of DOMAINS. Other possible extensions in the future include modeling ferroelectric nanodomains useful in quantum dot FeRAMs or phase change memory.