Baker, J; (2020) Long Range Order in Ferroelectric and Antiferroelectric Perovskites Meets Large Scale Density Functional Theory. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The technological applications of the ferroelectric and antiferroelectric perovskite oxides are extensive. With use cases ranging from ultrafast read/write memories to high energy density storage devices, they are the subject of a vast body of research. In particular, these materials have a rich history of discovery using ab initio techniques based on density functional theory (DFT). While conventional implementations of DFT can be used to great avail, unfortunately, calculations become prohibitively computationally expensive for simulations involving more than a few hundred atoms; a situation often encountered. Many then migrate to lower levels of theory embracing the mantra of ‘multiscale modelling’. While this in principle can be a good idea, many move away from DFT too soon; neglectful of the latest advancements in large scale DFT promising to restore quantum mechanical accuracy over larger length scales. The scope of this thesis is tripartite. Firstly, we re-examine the Pb(Ti, Zr, Hf)O3 isoelectronic series and the archetypal piezoelectric solid solution PbZr1-xTixO3 (PZT) by means of a comparative lattice dynamical study. Dynamical instabilities at q away from high symmetry points indicate competitive distortions over longer length scales than previously expected. Studying their condensation with conventional DFT can then become of a prohibitive expense. Further, a popular method designed to sidestep large scale simulations in some systems - the virtual crystal approximation - is found to be insufficient to describe the character of these distortions. Remarkably, when examining the phonon dispersions of antiferroelectric PbZrO3 and PbHfO3, they are found to be dynamically unstable and suggest that a Pnma structure is more stable than the established Pbam. This stability is corroborated at the LDA, GGA and meta-GGA levels suggesting a small modification to the known ground state. Our second goal is to demonstrate the readiness of large scale DFT to accurately simulate the perovskite oxides. Reformulating DFT in terms of the Kohn-Sham density matrix, we use the CONQUEST code to study the structural and electronic accuracy resulting from the use of basis sets of pseudoatomic orbitals (PAOs) compared to plane wave pseudopotential calculations. Using PbTiO3, PbZrO3, PZT and other technologically important materials as test cases, we find that a carefully designed basis of PAOs can rival the accuracy of plane wave calculations for lattice constants, bulk moduli, charge densities and Bader-assigned ionic charges. Equipped now with a method of proven robustness, we advance to our final goal: to target otherwise intractable problems for standard DFT. Simulating thousands of atoms, we investigate ferroelectric domain morphologies in low-dimensional PbTiO3 films finding properties ripe for exploitation in new functional devices. When mounted on a SrTiO3 substrate, we see the emergence of exotic chiral textures as a result of an internal bias field born of the compositionally broken inversion symmetry present in any film/substrate system. Strong coupling of local polar modes to surface antiferrodistortions drives a previously unknown p(2 $\times \Lambda$) surface reconstruction; demonstrating unequivocally the local compliance of the two order parameters. Finally, we investigate the interaction of engineered surface trenches with the domain structure and alignment of domain walls informing advances in domain wall nanoelectronics.

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