computer programs J. Appl. Cryst. (2010). 43, 1543–1547 doi:10.1107/S0021889810041889 1543 Journal of Applied Crystallography ISSN 0021-8898 Received 4 August 2010 Accepted 16 October 2010 # 2010 International Union of Crystallography Printed in Singapore – all rights reserved DEBUSSY: a Debye user system for nanocrystalline materials Antonio Cervellino, a Cinzia Giannini b and Antonietta Guagliardi b,c * a Swiss Light Source, Paul Scherrer Institute, CH-5232 Villigen, Switzerland, b Istituto di Cristallografia, CNR, Via G. Amendola 122/O, I-70126 Bari, Italy, and c Universita ` dell’Insubria, Dipartimento di Scienze Chimiche e Ambientali, Via Valleggio 11, I-22100 Como, Italy. Correspondence e-mail: antonella.guagliardi@ic.cnr.it DEBUSSY is a new free open-source package, written in Fortran95 and devoted to the application of the Debye function analysis (DFA) of powder diffraction data from nanocrystalline, defective and/or non-periodic materials through the use of sampled interatomic distance databases. The suite includes a main program, taking the name of the package, DEBUSSY, and dealing with the DFA of X-ray, neutron and electron experimental data, and a suite of 11 programs, named CLAUDE, enabling users to create their own databases for nanosized crystalline materials, starting from the list of space-group generators and the asymmetric unit content. A new implementation of the Debye formula is adopted in DEBUSSY, which makes the approach fast enough to deal with the pattern calculation of hundreds of nanocrystals, to sum up their contributions to the total pattern and to perform iterative algorithms for optimizing the parameters of the pattern model. The package strategy uses the sampled- distance database(s) created previously by CLAUDE and combines, for any phase, a log-normal or a bivariate log-normal function to deal with the sample- size distribution; four different functions are implemented to manage possible lattice expansions/contractions as a function of crystal size. A number of output ASCII files are produced to supply some statistics and data suitable for graphical use. The databases of sampled interatomic non-dimensional distances for cuboctahedral, decahedral and icosahedral structure types, suitable for dealing with noble metal nanoparticles, are also available. 1. Introduction The Debye function (DF) (Debye, 1915; Cervellino et al. , 2003), like the more popular pair distribution function (PDF) (Debye & Menke, 1930; Egami & Billinge, 2003; Juha ´s et al. , 2006), is a total scattering approach which is nowadays acknowledged to be more effective than standard Rietveld-like methods (Rietveld, 1969; Cheary & Coelho, 1992) for extracting relevant (micro)structural details of nano- crystalline systems from their powder diffraction data (Hall, 2000; Hall et al., 2000; Kaszkur, 2000; Palosz et al., 2000; Cervellino et al. , 2004; Cozzoli et al., 2006; Guagliardi et al., 2010). The short length scale of the domains, sometimes coupled with structural defects and/ or distortions caused by surface effects, results in some peculiar features in the diffraction pattern (Warren, 1990; Neder & Proffen, 2008; Neder, 2010). Conventional powder diffraction approaches, mainly developed for microcrystalline specimens and relying strongly on instrumental broadening as the dominant contribution to the experimental pattern, can fail in modelling such sample effects or at best reach this goal through a phenomenological model which allows the indirect estimation of physical parameters. For both isotropically and anisotropically shaped nanoparticles with very small coherent domains and/or a high defect concentration, the instrumental broadening usually becomes negligible with respect to the finite size, shape and structure-based sample contributions. Furthermore, domains in real samples are likely distributed in size or shape along one (the isotropic shape case), two or even three growth directions. These sample features can be described through a physically based model within the Debye function approach as it works in direct space. In addition, unlike the PDF, the DF does not transform the experi- mental data, thus keeping the advantage of simultaneously dealing with both reciprocal and direct spaces. In reciprocal space, the experimental data can (in principle) be almost exactly reproduced by the formula, provided that extra-sample contributions to the back- ground, such as air and sample-holder scattering, are properly accounted for and as long as a number of requirements are achieved in direct space. These are (within the averaged-volume approxima- tion of the powder diffraction technique) as follows: (a) a reliable structural model (ordered, disordered or defective); (b) a suitable model for the shape and size of nanocrystals (NCs) and their possible distributions, according to a physically and chemically sound description. The main advantage of using the Debye formula when investi- gating short-range ordered materials such as nanocrystalline compounds is the ability to model simultaneously both Bragg (if any) and diffuse sample scattering, all arising from the distribution of the interatomic distances within the sample and not requiring periodicity and order. Considering the general case of a particle containing N a atomic species and N s atoms of the sth species (s =1 ... N a ), each atom of the same species is identified by a mean position vector r sj ( j = 1 ... N s ), a mean occupancy o s , a scattering length b s and an isotropic Debye–Waller thermal factor T s . The diffracted intensity is obtained