Celebrating 100 years of the Debye scattering equation

One hundred years of the Debye scattering equation are celebrated with a series of articles arising from the DSE 2015 conference.

Peter J. W. Debye – a whole life devoted to science

Debye's works on the origin and evolution of the scattering equation and its first uses are briefly re-examined. The career of the great scientist and some of his other numerous and diverse contributions to science are also reviewed.

100 years of Debye's scattering equation

Debye's scattering equation constitutes the most accurate description of the intensity scattered by an ideal powder. Milestone applications and theoretical developments are reviewed and discussed.

Observing structural reorientations at solvent–nanoparticle interfaces by X-ray diffraction – putting water in the spotlight

Nanoparticles and solvents interact and interdependently change their structural arrangement, as probed by the X-ray pair distribution function.

A total scattering Debye function analysis study of faulted Pt nanocrystals embedded in a porous matrix

An algorithm enabling the active use of deformation fault probabilities in face-centred cubic metals within the Debye scattering equation approach implemented in the DEBUSSY suite and the subsequent characterization of Pt nanocrystals grown in a nanoporous silica matrix are presented.

Towards atomistic understanding of polymorphism in the solvothermal synthesis of ZrO₂ nanoparticles

The chemical path towards different polymorphs in the solvothermal synthesis of zirconia nanoparticles is decided by a complex interplay among reactants and applied conditions: at low temperature the structural similarity between the amorphous intermediate phase and monoclinic ZrO₂ results in almost phase-pure ∼5 nm monoclinic ZrO₂. Atomic scale pair distribution function analysis over the entire course of the reaction provides an understanding, and thereby control, of nanoparticle polymorphism.

Thermal evolution of Mg–Al and Ni–Al layered double hydroxides: the structure of the dehydrated phase

A loss of water molecules leads to the topotactic transformation of the initial structure of Mg–Al and Ni–Al layered double hydroxides having a hydrotalcite-like structure and consisting of 3R₁ and 2H₁ layered fragments with trigonal prismatic interlayers. The structure of the dehydrated phase comprises turbostratically disordered 3R₂ and 1H layered fragments with octahedral interlayers that can be related to the change in orientation of interlayer anions and the appearance of tetrahedrally coordinated cations in the interlayers.

Direct observation of incommensurate structure in Mo₃Si

Mo₃Si with a small off-stoichiometry in composition has an incommensurate crystal structure with a non-cubic unit cell. Atom-probe tomography and atomic resolution Z-contrast imaging suggest that site substitution causes the development of split atomic positions, disorder and vacancies.

Residue-based scattering factors

Amino-acid residues are chosen to form globs and empirical formulas for residue-based scattering factors have been developed.

The complete classification of five-dimensional Dirichlet–Voronoi polyhedra of translational lattices

The five-dimensional Dirichlet–Voronoi polyhedra of lattices and their contraction types are classified. Computational enumeration yields 110 244 affine types and 181 394 contraction types.

Qu­antitative theory of diffraction by ordered coaxial nanotubes: reciprocal-lattice and diffraction pattern indexing

The reciprocal lattice of an ordered coaxial nanotube, its relation to nanotube lattice parameters and the diffraction pattern indexing approach are developed on the basis of a quantitative theory of diffraction.

An alternative to the goodness of fit

A robust alternative to the goodness of fit is derived, aGoFs, and a systematic error in the experimental s.u.'s is found with the help of the aGoFs, which effectively veils the presence of other systematic errors.

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