## Doctoral Dissertations

5-3-2017

4-26-2017

#### Keywords

Materials Science, Landau Theory, Classical Molecular Dynamics, First-principles Calculations, Ferroelectrics

S. Pamir Alpay

Gayanath W. Fernando

Niloy Dutta

Physics

#### Degree

Doctor of Philosophy

Open Access

#### Abstract

Computational materials science has become an important branch of research with the advent of high performance computers and efficient algorithms. The viability of solving fundamental theories allows not only to understand experimental results, but predict properties of exotic materials or materials at extreme conditions. There exists fundamental theories that has been applied in different domains of length and time scales, where certain approximations are employed which enable improved performance with minimum compromise of accuracy.

In this Thesis, various computational approaches at different length scales are considered to investigate different classes of organic and inorganic ferroelectric materials to describe structural-property relations. The in-plane and out-of-plane piezoelectric properties of (001) strontium titanate (SrTiO$_3$, STO) epitaxial thin films on pseudo-cubic (001) substrates are computed as a function of in-plane misfit strain. A nonlinear thermodynamic model is employed, which takes into account the appropriate mechanical boundary conditions, the electromechanical coupling between the polarization and the in-plane lattice mismatch, and the self-strains of the ferroelastic and ferroelectric phase transformations. The piezoelectric behavior of epitaxial STO films is described in various strain-induced ferroelectric phase fields in a temperature range from $-$50 to 50 $\degree$C. These results indicate that strain engineered STO films may be employed in a variety of sensor and actuator applications as well as surface acoustic wave devices and thin-film bulk acoustic resonators.

Implementing the same technique, piezoelectric properties of epitaxial (001) barium strontium titanate (BST) films are computed as functions of composition, misfit strain, and temperature using a non-linear thermodynamic model. Results show that through adjusting in-plane strains, a highly adaptive rhombohedral ferroelectric phase can be stabilized at room temperature with outstanding piezoelectric response exceeding those of lead based piezoceramics. Furthermore, by adjusting the composition and the in-plane misfit, an electrically tunable piezoelectric response can be obtained in the paraelectric state. These findings indicate that strain engineered BST films can be utilized in the development of electrically tunable and switchable surface and bulk acoustic wave resonators.

The theoretical model of ferroelectric bilayers using basic thermodynamics taking into account the appropriate electrical boundary conditions and electrostatic fields is present. We show that ferroelectric multilayers are not simple capacitors in series (CIS) and treating these as CIS may lead to misinterpretation of experimental results and to erroneous conclusions. The spontaneous polarization mismatch in ferroelectric/ferroelectric (FE/FE), FE/paraelectric (FE/PE), and FE/dielectric (FE/DE) bilayers results in a non-linear electrostatic coupling which produces significant deviations in the overall dielectric response if it is computed using the simple capacitor-in-series (CIS) model. Our results show that the CIS approach is a good approximation only for DE/DE multilayers and for FE heterostructures if the individual layers are electrostatically screened from each other.

As a second method for this Thesis, classical molecular dynamics computations are considered to calculate the structural, elastic, and polar properties of crystalline ferroelectric $\beta$ phase poly(vinylidene fluoride), PVDF, with randomized trifluoroethylene TrFE as a function of TrFE content. The results show that molecular dynamics can be used to predict the mechanical and polarization-related behavior of ferroelectric poly(VDF\textit{-co-}TrFE). The same computational approach might be also utilized for other polymeric materials in the desired temperature and/or composition range. Furthermore, temperature-induced and deformation-induced phase transitions are reported, which are consistent with the experimental observation.

Finally, the fundamental theory of electron physics, also called the first-principles formalism, is applied to study the polarization of the layered ferroelectric bismuth titanate (BiT). The electronic structure studies of pure BiT and technologically significant lanthanum-doped bismuth titanate (La-doped BiT) are performed. The results and the extension of current progress of A-site substitutional BiT using first-principle calculations could provide the theoretical evidence of the formation of oxygen vacancies, which is recognized to be associated with the leakage current and polarization properties. Studies on the optical properties of BiT are performed using a beyond-density functional theory (beyond-DFT) method. This is done because the regular approximation for electron-electron coupling in the DFT specific generalized gradient approximation (GGA) has limitations in predicting the band gap of semiconductors/insulators. The Heyd-Scuseria-Ernzerhof (HSE) screened hybrid-functional method is adopted.

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