U. Bismayer

Analysis of Short and Long Range Atomic Order in Nanocrystalline Diamonds with Application of Powder Diffractometry

Abstract Fundamental limitations, with respect to nanocrystalline materials, of the traditional elaboration of powder diffraction data like the Rietveld method are discussed. A tentative method of the analysis of powder diffraction patterns of nanocrystals based on the examination of the variation of lattice parameters calculated from individual Bragg lines (named the “apparent lattice parameter”, alp) is introduced. We examine the application of our methodology using theoretical diffraction patterns computed for models of nanocrystals with a perfect crystal lattice and for grains with a two-phase, core-shell structure. We use the method for the analysis of X-ray and neutron experimental diffraction data of nanocrystalline diamond powders of 4, 6 and 12 nm in diameter. The effects of an internal pressure and strain at the grain surface are discussed. The results are based on the dependence of the alp values on the diffraction vector Q and on the PDF analysis. It is shown, that the experimental results lend a strong support to the concept of a two-phase structure of nanocrystalline diamond.

Phase transition(s) in titanite CaTiSiO5: An infrared spectroscopic, dielectric response and heat capacity study

The structural phase transition in titanite near 500 K (averaged symmetries A2/a→P21/a) and a second anomaly around 900 K have been studied using infrared spectroscopy on single crystals aqnd powder samples, measurements of the dielectric properties and the specific heat. The same synthetic single crystal was used in all experiments.The phase transition near 500 K is associated with a break in the temperature evolution of phonon frequencies and absorption intensities. Some phonon signals decrease rapidly under further heating and their extrapolated intensities disappear at ca. 850 K. The most dominant temperature effect relates to Ti-O phonons with amplitudes along the crystallographic a axis. These phonons show large LO-To splitting and continue to soften under heating even at temperatures above the transitions point (ca. 500 K).The softening of these modes correlates directly with the increase of the real part of the dielectric constant with a well-pronounced anomaly at 500 K. The dielectric losses also increse with increasing temperature. Measurements under strong field do not show antiferroelectricity. The transition at 500 K generates a small but sharp λ-anomaly in the excess specific heat. A second, weaker anomaly was found near 850 K. The results are discussed in terms of thermodynamic models.

On the thickness of ferroelastic twin walls in lead phosphate Pb3(PO4)2 an X-ray diffraction study

Abstract The effective thickness of ferroelastic twin-walls (W-walls) in Pb3(PO4)2 at room temperature ( 0.7 T c ) was determined by X-ray diffraction. The diffraction profiles were analysed using a wall profile e=eotanh x/w where W is the effective wall thickness including the effects of wall bending and surface relaxations. The experimental value W is around 10 unit cells which is larger than expected from standard renormalization arguments. The limitations of such experimental studies are discussed.

Ferroelastic phases in Pb3(PO4)2–Pb3(AsO4)2; X‐ray and optical experiments

Mixed crystals Pb3(PO4)2--Pb3(AsO4)2 are ferroelastic at low temperatures. The phase diagram contains three different phases a (paraelastic), \tt b and \tt c (both ferroelastic). The transformation \tt a-\tt b is first order for Pb3(PO4)2 and approaches second-order behaviour with increasing As content. The spontaneous strains and the birefringence follow approximately a Curie-Weiss law, with a corresponding order-parameter exponent β = ¼. The mutual high-temperature phases give diffuse X-ray reflections due to inelastic scattering. The soft-mode model is discussed for these results.

The crystal structure of NdGaO3 at 100 K and 293 K based on synchrotron data

Abstract The crystal structure of NdGaO 3 is studied at 100 K and 293 K using synchrotron single crystal data. The NdGaO 3 structure belongs at low and at room-temperatures to the orthorhombically distorted perovskite-type (space group Pbnm , Z =4). The analysis reveals that both structures differ considerably in the character of the thermal motions of the cations. The Nd and Ga thermal ellipsoids at 100 K are reorientated compared with those at 293 K. The anharmonic thermal motions of Nd and Ga, determined for 100 K and 293 K, are displayed by 4-rank polar tensors. The thermal anomaly of the physical properties of NdGaO 3 seems therefore, to be well reflected by the thermal behaviour of the cations.

Intrinsic activation energy for twin-wall motion in the ferroelastic perovskite CaTiO3

Even in a topologically perfect crystal, a moving twin wall will experience forces due to the discrete nature of the lattice. The potential energy landscape can be described in terms of one of two parameters: the Peierls energy, which is the activation energy for domain wall motion in a perfect crystal; and the Peierls stress, the maximum pinning stress that the potential can exert. We investigate these parameters in a one order parameter discrete Landau-Ginzburg model and a classical potential model of the ferroelastic perovskite

Lattice parameters, spontaneous strain and phase transitions in Pb3(PO4)2

{\mathrm{CaTiO}}_{3}

High Pressure X-Ray Diffraction Studies on Nanocrystalline Materials

. Using the one order parameter model we show that the Peierls energy scales with the barrier height of the Landau double well potential and calculate its dependence on the width of the wall numerically. In

Renormalization phenomena in Ba-diluted ferroelastic lead phosphate, (Pb1-xBax)3(PO4)2

{\mathrm{CaTiO}}_{3}

Chapter 242 Perovskite-Type Aluminates and Gallates

we calculate the Peierls energy and stress indirectly from the one order parameter model and directly from the interatomic force field. Despite the simplicity of the one order parameter model, its predictions of the activation energy are in good agreement with calculated values.