A new approach for the modelling of diffraction patterns without using analytical pro®le 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 re®nement 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 re®ned 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 ®nely dispersed crystalline powders. TEM pictures support the conclusions obtained by WPPM and con®rm the validity of the proposed procedure.

Integral breadth methods for line pro®le analysis are reviewed, including modi®cations of the Williamson±Hall method recently proposed for the speci®c 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 modi®ed Williamson±Hall methods con®rm 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.

The vibronic bands in the dipole-allowed absorption spectrum of N2 associated with the lowest three electronic 1Σ+u and the lowest three electronic 1Πu states are represented in a basis of electronically coupled diabatic states as well as in the basis of nuclear-momentum coupled adiabatic states. Parameters defining the diabatic states and their electronic coupling energies are first evaluated by fitting the eigenvalues of a vibronic interaction matrix to the observations. The coupled-oscillator equations are then solved directly by Johnson’s numerical integration method and the diabatic representation is redetermined via the matrix method and coupled equations iteratively. The fit of the experimental vibronic terms, B values, and absorption intensities achieved with R-independent electronic coupling energies in a diabatic basis of valence and Rydberg-type states (b′+c′+e′)1Σ+u and (b+c+o)1Πu is satisfactory. Comparison with the corresponding adiabatic representation shows that the nonadiabatic perturbations are larger in that basis than in the diabatic one. The vibronic intensity distributions observed in the absorption spectrum show numerous interesting examples of intensity envelopes over discrete vibronic progressions with Fano-type resonance profiles as well as with distinctly non-Fano-type profiles which can be attributed to variations of the relevant coupling terms over the widths of the vibronic resonances.

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.

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