Matteo Leoni

Whole powder pattern modelling

A new approach for the modelling of diffraction patterns without using analytical profile functions is described and tested on ball milled f.c.c. Ni powder samples. The proposed whole powder pattern modelling (WPPM) procedure allows a one-step refinement of microstructure parameters by a direct modelling of the experimental pattern. Lattice parameter and defect content, expressed as dislocation density, outer cut-off radius, contrast factor, twin and deformation fault probabilities), can be refined together with the parameters (mean and variance) of a grain-size distribution. Different models for lattice distortions and domain size and shape can be tested to simulate or model diffraction data for systems as different as plastically deformed metals or finely dispersed crystalline powders. TEM pictures support the conclusions obtained by WPPM and confirm the validity of the proposed procedure.

Line broadening analysis using integral breadth methods: a critical review

Integral breadth methods for line profile analysis are reviewed, including modifications of the Williamson–Hall method recently proposed for the specific case of dislocation strain broadening. Two cases of study, supported by the results of a TEM investigation, are considered in detail: nanocrystalline ceria crystallized from amorphous precursors and highly deformed nickel powder produced by extensive ball milling. A further application concerns a series of Fe–Mo powder specimens that were ball milled for increasing time. Traditional and modified Williamson–Hall methods confirm their merits for a rapid overview of the line broadening effects and possible understanding of the main causes. However, quantitative results are generally not reliable. Limits in the applicability of integral breadth methods and reliability of the results are discussed in detail.

Diffraction line profiles from polydisperse crystalline systems

Diffraction patterns for polydisperse systems of crystalline grains of cubic materials were calculated considering some common grain shapes: sphere, cube, tetrahedron and octahedron. Analytical expressions for the Fourier transforms and corresponding column-length distributions were calculated for the various crystal shapes considering two representative examples of size-distribution functions: lognormal and Poisson. Results are illustrated by means of pattern simulations for a f.c.c. material. Line-broadening anisotropy owing to the different crystal shapes is discussed. The proposed approach is quite general and can be used for any given crystallite shape and different distribution functions; moreover, the Fourier transform formalism allows the introduction in the line-profile expression of other contributions to line broadening in a relatively easy and straightforward way.

Line profile analysis: pattern modelling versus profile fitting

Powder diffraction data collected on a nanocrystalline ceria sample within a round robin conducted by the IUCr Commission on Powder Diffraction were analysed by two alternative approaches: (i) whole-powder-pattern modelling based upon a fundamental microstructural parameters approach, and (ii) a traditional whole-powder-pattern fitting followed by Williamson-Hall and Warren-Averbach analysis. While the former gives results in close agreement with those of transmission electron microscopy, the latter tends to overestimate the domain size effect, providing size values about 20% smaller. The origin of the discrepancy can be traced back to a substantial inadequacy of profile fitting with Voigt profiles, which leads to systematic errors in the following line profile analysis by traditional methods. However, independently of the model, those systematic errors seem to have little effect on the volume-weighted mean size.

Thermal diffusivity/microstructure relationship in Y-PSZ thermal barrier coatings

A set of yttria partially stabilized zirconia coatings with different thickness was deposited on flat nickel-base alloy coupons by air plasma spray (APS) under uncontrolled temperature conditions. In this way, the length of the spraying process (and consequently the coating thickness) had a direct effect on phase composition as well as on the thermal properties of the material. In particular, both the monoclinic phase percentage and thermal diffusivity increased considerably with the thickness. Because this trend was observed together with a slight but clearly visible increase in the total porosity, the interpretation of the results was not straightforward, but required a detailed discussion of the thermal transport mechanism. Considering the complex microstructure typical of APS coatings and the relevant role of porosity, it was shown how a modest reduction in the fraction of closed pores can account for the observed increase in diffusivity. It was then proposed that the volume change associated with the progressive tetragonal to monoclinic phase transformation can be responsible for the reduction of the closed porosity of lenticular shape oriented parallel to the surface, in spite of the observed increase in the total porosity.

Fourier modelling of the anisotropic line broadening of X-ray diffraction profiles due to line and plane lattice defects

A new model of line-profile broadening due to the effect of linear and planar lattice defects has been incorporated into the conventional Rietveld algorithm for the structural refinement and whole-pattern fitting of powder data. The proposed procedure, applied to face-centred cubic (f.c.c.) structure materials, permits better modelling, even in the case of anisotropic line broadening and other hkl-dependent effects that can be related to the presence of dislocations and planar defects (stacking faults and twinning). Besides better quality of the profile fitting, detailed information on the defect structure can be produced: dislocation density and cut-off radius, stacking- and twin-fault probabilities can be refined together with the structural parameters. For each phase (in different samples or in multi-phase samples) the appropriate size–strain model can be selected. The Fourier formalism, which is the basis of the line-profile modelling, also permits an easy adaptation to different lattice-defect models. New approaches can be easily introduced and tested against or together with the existing ones. Finally, the devised program can also be used for the simulation of powder patterns for materials with different types and amounts of line and plane lattice defects.

Simultaneous refinement of structure and microstructure of layered materials

The recursive description of stacking in layered crystals, originally developed by Treacy et al. [Proc. R. Soc. London Ser. A (1991), 433, 499–520] and implemented in the DIFFaX code, is enclosed in a non-linear least-squares minimization routine and combined with additional models (of specimen-related broadening and instrumental broadening) to allow the simultaneous refinement of both structural and microstructural parameters of a layered crystal. This implementation is named DIFFaX+. As examples, the refinements both of a simulated pattern of diamond, showing fault clustering, and of the observed powder pattern of a synthetic stoichiometric nanocrystalline chrysotile are reported.

Nanocrystalline domain size distributions from powder diffraction data

The need for an a priori domain size distribution is one of the main limitations of existing line profile analysis methodologies. A numerical modification of the whole-powder-pattern modelling algorithm is proposed, to allow the refinement of a general domain size distribution from powder diffraction data. The shape of domains has to be inferred for the specimen under study. The algorithm is robust enough to unveil fine details in the refined distribution, as witnessed by the results of tests performed both on simulated and on real patterns of nanocrystalline ceria.

Dislocation effects in powder diffraction

Owing to the lack of proper models, mainly for the strain broadening component due to dislocations, full exploitation of whole powder pattern modelling for the microstructural analysis of materials has been limited so far to high-symmetry lattices. An extension of the dislocation-induced broadening model, valid for any lattice symmetry, is proposed here. Dislocation effects are modelled through the description of the dislocation contrast factor in terms of a crystallographic invariant whose terms can be either calculated when the material constants and slip systems are known (allowing a dislocation density to be refined) or refined on the experimental data for an effective estimation of dislocation effects.

Phase stability of scandia-yttria-stabilized zirconia TBCs

Abstract The evolution in phase composition resulting from 1400°C ageing of ZrO 2 samples stabilized by ∼4–7 mol.% each of Y 2 O 3 (YSZ), Sc 2 O 3 (ScSZ), or a mixture of Sc 2 O 3 –Y 2 O 3 (SYSZ) was studied by synchrotron radiation X-ray diffraction (SR XRD) using whole powder pattern fitting (WPPF), a recently proposed Rietveld-based method for the simultaneous refinement of phase composition and crystal microstructure. The results suggest that SYSZ has better high temperature tetragonal phase stability than the current state-of-art YSZ. For example, a plasma-sprayed coating of SYSZ (6.57 mol.%Sc 2 O 3 –1.00 mol.%Y 2 O 3 ) remained 96.7% in its original tetragonal phase (presumably t′, c / a of 1.0058) after being aged 100 h at 1400°C and then 24 h at 1480°C, whereas a 4.5 mol.% YSZ coating was transformed into two new tetragonal phases, one a low-stabilizer phase with c / a of 1.0154 (44.8%) and the other a high-stabilizer zirconia phase with c / a of 1.003 (46.5%), with some monoclinic (8.7%) formed. The phase compositions found for the various powder and coating specimens, together with information regarding lattice parameters, crystalline domain size and microstrain, also obtained by WPPF, are discussed in terms of the high-temperature phase stability of the YSZ vs SYSZ systems.