Frustration, strain and phase co-existence in the mixed valent hexagonal iridate Ba$_{3}$NaIr$_{2}$O$_{9}$

Using detailed synchrotron diffraction, magnetization, thermodynamic and transport measurements, we investigate the relationship between the mixed valence of Ir, lattice strain and the resultant structural and magnetic ground states in the geometrically frustrated triple perovskite iridate Ba$_{3}$NaIr$_{2}$O$_{9}$. We observe a complex interplay between lattice strain and structural phase co-existence, which is in sharp contrast to what is typically observed in this family of compounds. The low temperature magnetic ground state is characterized by the absence of long range order, and points towards the condensation of a cluster glass state from an extended regime of short range magnetic correlations.

Phase coexistence and negative thermal expansion in the triple perovskite iridate Ba$_{3}$CoIr$_{2}$O$_{9}$

The anomalous thermal expansion in a layered 3$d$-5$d$ based triple perovskite iridate Ba$_{3}$CoIr$_{2}$O$_{9}$ is investigated using high resolution synchrotron diffraction. Below the magneto-structural transition at 107,K, the onset of antiferromagnetic order is associated with a monoclinic distortion of the hexagonal structure. Deeper within the magnetically ordered state, a part of the monoclinic phase distorts even further, and both these structural phases co-exist down to the lowest measured temperatures. We observe negative thermal expansion in this phase co-existence regime, which appears to be intimately connected to the temperature driven relative fractions of these monoclinic phases. The significant NTE observed in this system could be driven by magnetic exchange striction, and is of relevance to a number of systems with pronounced spin orbit interactions.

Texture corrections for total scattering functions

Many functional materials are today synthesised in form of nanoparticles displaying preferred orientation effects to some small or large extent. The analysis of diffraction data of such kind of systems is best performed in the framework of the total scattering approach that prescinds from translation symmetry assumptions. We therefore derived modified expressions for the most common total scattering functions, in particular the Debye Scattering Equation (DSE) that yields the texture-averaged differential cross section as a function of atomic coordinates and texture parameters. The modified DSE encodes higher-order even spherical Bessel functions which account for the texture effect. Selection rules arising from experimental geometries and symmetries are discussed. In addition the duality of the texture effect is introduced showing the effects of texture on both the I(Q) and G(r). The paper includes several definitions and appendices which are meant to be useful for those involved in the development of crystallographic computing.

The local structure of electrically stressed liquid water and implications for modelling of dielectric relaxation

In a floating water bridge the total radiation scattering of water stressed by a moderately strong electric field (1mV/nm) was compared to water without an applied electric field using X-ray and small angle neutron scattering. Structure refinement was carried out using the EPSR method and the TIP4P/2005 water model. These results did not reveal a significant difference in the local static structure of water however analysis of the simulation indicated that the modeled local potential energy surface reveals a departure between electrically stressed and unstressed water. The observed differences show that the local environment is changed by the applied electric field although weak relative to the intermolecular coulombic field. When discussing the results we show that the current methods used to simulate the pair potentials are still insufficient to treat such non-equilibrium systems and further simulation techniques have to be developed to properly reconstruct the microscopic dielectric relaxation process.

Generalization of a theorem of Caratheodory

Caratheodory showed that $n$ complex numbers $c_1,...,c_n$ can uniquely be written in the form $c_p=sum_{j=1}^m rho_j {epsilon_j}^p$ with $p=1,...,n$, where the $epsilon_j$s are different unimodular complex numbers, the $rho_j$s are strictly positive numbers and integer $m$ never exceeds $n$. We give the conditions to be obeyed for the former property to hold true if the $rho_j$s are simply required to be real and different from zero. It turns out that the number of the possible choices of the signs of the $rho_j$s are {at most} equal to the number of the different eigenvalues of the Hermitian Toeplitz matrix whose $i,j$-th entry is $c_{j-i}$, where $c_{-p}$ is equal to the complex conjugate of $c_{p}$ and $c_{0}=0$. This generalization is relevant for neutron scattering. Its proof is made possible by a lemma - which is an interesting side result - that establishes a necessary and sufficient condition for the unimodularity of the roots of a polynomial based only on the polynomial coefficients. Keywords: Toeplitz matrix factorization, unimodular roots, neutron scattering, signal theory, inverse problems. PACS: 61.12.Bt, 02.30.Zz, 89.70.+c, 02.10.Yn, 02.50.Ga