Quadrupolar ordering in LaMnO3 revealed from scattering data and geometric modeling

Quantitative three-dimensional local order analysis of nanomaterials through electron diffraction

Structure-property relationships in ordered materials have long been a core principle in materials design. However, the introduction of disorder into materials provides structural flexibility and thus access to material properties that are not attainable in conventional, ordered materials. To understand disorder-property relationships, the disorder - i.e., the local ordering principles - must be quantified. Local order can be probed experimentally by diffuse scattering. The analysis is notoriously difficult, especially if only powder samples are available. Here, we combine the advantages of three-dimensional electron diffraction - a method that allows single crystal diffraction measurements on sub-micron sized crystals - and three-dimensional difference pair distribution function analysis (3D-ΔPDF) to address this problem. In this work, we compare the 3D-ΔPDF from electron diffraction data with those obtained from neutron and x-ray experiments of yttria-stabilized zirconia (Zr0.82Y0.18O1.91) and demonstrate the reliability of the proposed approach.

Refining perovskite structures to pair distribution function data using collective Glazer modes as a basis

Structural modelling of octahedral tilts in perovskites is typically carried out using the symmetry constraints of the resulting space group. In most cases, this introduces more degrees of freedom than those strictly necessary to describe only the octahedral tilts. It can therefore be a challenge to disentangle the octahedral tilts from other structural distortions such as cation displacements and octahedral distortions. This paper reports the development of constraints for modelling pure octahedral tilts and implementation of the constraints in diffpy-CMI, a powerful package to analyse pair distribution function (PDF) data. The model in the program allows features in the PDF that come from rigid tilts to be separated from non-rigid relaxations, providing an intuitive picture of the tilting. The model has many fewer refinable variables than the unconstrained space group fits and provides robust and stable refinements of the tilt components. It further demonstrates the use of the model on the canonical tilted perovskite CaTiO₃ which has the known Glazer tilt system α⁺β^-β^-. The Glazer model fits comparably to the corresponding space-group model Pnma below r = 14 Å and becomes progressively worse than the space-group model at higher r due to non-rigid distortions in the real material.

Designing disorder into crystalline materials

Crystals are a state of matter characterized by periodic order. Yet, crystalline materials can harbour disorder in many guises, such as non-repeating variations in composition, atom displacements, bonding arrangements, molecular orientations, conformations, charge states, orbital occupancies or magnetic structure. Disorder can sometimes be random but, more usually, it is correlated. Frontier research into disordered crystals now seeks to control and exploit the unusual patterns that persist within these correlated disordered states in order to access functional responses inaccessible to conventional crystals. In this Review, we survey the core design principles that guide targeted control over correlated disorder. We show how these principles - often informed by long-studied statistical mechanical models - can be applied across an unexpectedly broad range of materials, including organics, supramolecular assemblies, oxide ceramics and metal-organic frameworks. We conclude with a forward-looking discussion of the exciting link between disorder and function in responsive media, thermoelectrics and topological phases.

Defining the flexibility window in ordered aluminosilicate zeolites

The flexibility window in zeolites was originally identified using geometric simulation as a hypothetical property of SiO₂ systems. The existence of the flexibility window in hypothetical structures may help us to identify those we might be able to synthesize in the future. We have previously found that the flexibility window in silicates is connected to phase transitions under pressure, structure amorphization and other physical behaviours and phenomena. We here extend the concept to ordered aluminosilicate systems using softer 'bar' constraints that permit additional flexibility around aluminium centres. Our experimental investigation of pressure-induced amorphization in sodalites is consistent with the results of our modelling. The softer constraints allow us to identify a flexibility window in the anomalous case of goosecreekite.

Reverse Monte Carlo study of spherical sample under non-periodic boundary conditions: the structure of Ru nanoparticles based on x-ray diffraction data

A new method to fit experimental diffraction data with non-periodic structure models for spherical particles was implemented in the reverse Monte Carlo simulation code. The method was tested on x-ray diffraction data for ruthenium (Ru) nanoparticles approximately 5.6 nm in diameter. It was found that the atomic ordering in the ruthenium nanoparticles is quite distorted, barely resembling the hexagonal structure of bulk Ru. The average coordination number for the bulk decreased from 12 to 11.25. A similar lack of structural order has been observed with other nanoparticles (e.g. Petkov et al 2008 J. Phys. Chem. C 112 8907-11) indicating that atomic disorder is a widespread feature of nanoparticles less than 10 nm in diameter.

Maximally localized Wannier functions in LaMnO3 within PBE + U, hybrid functionals and partially self-consistent GW: an efficient route to construct ab initio tight-binding parameters for eg perovskites

Using the newly developed VASP2WANNIER90 interface we have constructed maximally localized Wannier functions (MLWFs) for the e(g) states of the prototypical Jahn-Teller magnetic perovskite LaMnO(3) at different levels of approximation for the exchange-correlation kernel. These include conventional density functional theory (DFT) with and without the additional on-site Hubbard U term, hybrid DFT and partially self-consistent GW. By suitably mapping the MLWFs onto an effective e(g) tight-binding (TB) Hamiltonian we have computed a complete set of TB parameters which should serve as guidance for more elaborate treatments of correlation effects in effective Hamiltonian-based approaches. The method-dependent changes of the calculated TB parameters and their interplay with the electron-electron (el-el) interaction term are discussed and interpreted. We discuss two alternative model parameterizations: one in which the effects of the el-el interaction are implicitly incorporated in the otherwise 'noninteracting' TB parameters and a second where we include an explicit mean-field el-el interaction term in the TB Hamiltonian. Both models yield a set of tabulated TB parameters which provide the band dispersion in excellent agreement with the underlying ab initio and MLWF bands.

Template-Based Geometric Simulation of Flexible Frameworks

Specialised modelling and simulation methods implementing simplified physical models are valuable generators of insight. Template-based geometric simulation is a specialised method for modelling flexible framework structures made up of rigid units. We review the background, development and implementation of the method, and its applications to the study of framework materials such as zeolites and perovskites. The "flexibility window" property of zeolite frameworks is a particularly significant discovery made using geometric simulation. Software implementing geometric simulation of framework materials, "GASP", is freely available to researchers.

Structural and thermal properties of LaMnO3 from neutron diffraction and first principles studies

Neutron diffraction experiments have been performed on powder samples of LaMnO(3) below and above the Jahn-Teller transition temperature of 750 K. Experimental investigations are assisted by density functional theory calculations. Theoretical studies are carried out for the orbitally ordered state of LaMnO(3) which allows one to compare the behavior of the orbitally ordered and disordered structures as a function of temperature. The temperature dependences of the structural parameters characterizing the Jahn-Teller distortions are reported and discussed. A gradual departure of the experimental data from theoretical predictions is observed above 650 K. In this range of temperatures, anions surrounding the Jahn-Teller active cations perform more isotropic thermal motion. The onset of structural phase transition induces a reduction of the crystal volume by about 0.4% which follows from the structural transformations yielding more regular oxygen octahedra formed above the phase transformation. It is found that above the Jahn-Teller transition the distortions of the MnO(6) octahedra are not completely removed. The non-vanishing distortions are accompanied by the lifted degeneracy of the Mn e(g) states. Weak residual distortions can be assigned to the short-range orbital order that persists within a local scale but it seems quenched on average giving rise to a disappearance of the long-range order coherency of the Jahn-Teller effect.

Origin of Jahn-Teller distortion and orbital order in LaMnO3

The origin of the cooperative Jahn-Teller distortion and orbital order in LaMnO3 is central to the physics of the manganites. The question is complicated by the simultaneous presence of tetragonal and GdFeO3-type distortions and the strong Hund's rule coupling between e{g} and t{2g} electrons. To clarify the situation we calculate the transition temperature for the Kugel-Khomskii superexchange mechanism by using the local density approximation+dynamical mean-field method, and disentangle the effects of superexchange from those of lattice distortions. We find that superexchange alone would yield T{KK} approximately 650 K. The tetragonal and GdFeO3-type distortions, however, reduce T{KK} to approximately 550 K. Thus electron-phonon coupling is essential to explain the persistence of local Jahn-Teller distortions to greater than or approximately 1150 K and to reproduce the occupied orbital deduced from neutron scattering.