Data Processing Steps in Neutron Diffraction: From the Raw Data to the Differential Cross Section

Abstract

Neutron diffraction is a well established tool to investigate the structure of matter in a wide range of disciplines including Physics, Chemistry, Materials Sciences, Life Sciences, Earth Sciences and Engineering. One of its most required applications is the refinement of structures for which a considerable instrumental development has been devoted. In particular, the improvement of the instrumental resolution has been hitherto one of the main concerns in the development of the technique. In other words, most of the efforts in the instrumental development and methods has been devoted to improve the abscissas of the experimental scale (angle or momentum transfer), while on the other hand, the final results in ordinates are normally left in arbitrary units, since most of the applications do not require an absolute normalization.Nevertheless, there is a growth in the requirements of updated neutron cross section data driven by the need of improved nuclear data libraries by Nuclear Engineers, that currently employ cross sections that sometimes are guessed or extrapolated from very old experiments. Such need could be satisfied by the highly-developed experimental neutronfacilities to provide excellent quality data in absolute scales. However, this capacity remains under-exploited, as well as the procedures that are necessary to perform an absolute calibration (in the scale of ordinates), in the sense of transforming the measured number of counts into a physically meaningful scale, and expressing the final result as a crosssection. This lack is closely related with the underdevelopment of data processing procedures and methods specific to each experimental configuration in neutron scattering techniques.As an example, neutron diffraction users at big facilities still employ the simple data processing correction procedures developed for X-rays techniques (Blech & Averbach, 1965; Paalman & Pings, 1962) in times when computer resources were limited. However, as shown by many reference works in the literature (Copley et al., 1986; Sears, 1975), the situation in the field of neutron scattering is far more complex, and involves the evaluation of multiple scattering effects that can be tackled efficiently only by numerical simulations, that nowadays can be carried out with the currently available computer power.To illustrate the consequences of this lack of a developed standard procedure to achieve an absolute normalization, let us consider the long-lasting controversy about the Hydrogen cross section for epithermal neutrons in electron-Volt spectroscopy (eVS), that began when a cross section significantly lower than commonly accepted values was reported in the literature (Chatzidimitriou-Dreismann et al., 1997), and supported by further experimental results [see e.g. (Abdul-Redah et al., 2005)]. The results stirred many criticisms, both on the theoretical likelihood of such phenomenon [see e.g. (Colognesi, 2007)], and also on the general methodology employed in the measurements and data analysis (Blostein et al.,2001) (Blostein et al., 2005). Different experiments contradicting the appearance of anomalies, employing electron-Volt spectroscopy and other techniques were also reported (Blostein et al.,2003; 2009), thus increasing the uncertainty on the matter. As an outcome of the discussion, the idea arose that the data processing methodology employed was not ready to produce a cross section in absolute units in eVs experiments. This thought led to the recent formulation of a whole body of experimental and data processing procedures (Rodríguez Palomino et al.,2011), and its application resulted in Hydrogen cross sections that are in conformity with tabulated values (Blostein et al., 2009).In the specific case of diffraction, the problem of absolute normalization was also addressed (Rodríguez Palomino et al., 2007) following a similar approach, and the procedures were applied to a set of standard samples, measured at diffractometer D4 (ILL, Grenoble, France)(Fischer et al., 2002), and also recently to a set of light and heavy water with the aimto study the structural characteristics (Dawidowski & Cuello, 2011). The goal of the process (that will be the subject of the present work) is to provide a modus operandi that starts from the experimental raw data and ends in the differential scattering cross section. The startingpoint of the task consists in the description of the measured magnitudes through analytic expressions.Elementary textbooks state the expressions of the measured magnitude in a diffraction experiment for point-like samples, thus finding a direct relation with the differential cross section. However, in a real experiment where extended samples are used, the formalism that describes the intensity of the scattered beam includes the sample geometry (Sears, 1975), and will be the first point to be treated. The expressions that we will show describe the measured macroscopic magnitude and its relationship with the sought microscopic differential cross section, that is not directly accessible to the experiment due to the multiple scattering, beam attenuation and detector efficiency effects. The evaluation of such effects is made through numerical simulations that follow the general guidelines stated by Copley (Copley et al.,1986). In this work we will make a detailed account of the computer code, as well as the different strategies employed to make use of the experimental data and models of interaction between the neutrons and the systems to feed the simulation program.