The total scattering method is the simultaneous study of both the real- and reciprocal-space representations of diffraction data. While conventional Bragg-scattering analysis (employing methods such as Rietveld refinement) provides insight into the average structure of the material, pair distribution function (PDF) analysis allows for a more focused study of the local atomic arrangement of a material. Generically speaking, a PDF is generated by Fourier transforming the total measured reciprocal-space diffraction data (Bragg and diffuse) into a real-space representation. However, the details of the transformation employed and, by consequence, the resultant appearance and weighting of the real-space representation of the system can vary between different research communities. As the worldwide total scattering community continues to grow, these subtle differences in nomenclature and data representation have led to conflicting and confusing descriptions of how the PDF is defined and calculated. This paper provides a consistent derivation of many of these different forms of the PDF and the transformations required to bridge between them. Some general considerations and advice for total scattering practitioners in selecting and defining the appropriate choice of PDF in their own research are presented. This contribution aims to benefit people starting in the field or trying to compare their results with those of other researchers.

A vast source of methane is found in gas hydrate deposits, which form naturally dispersed throughout ocean sediments and arctic permafrost. Methane may be obtained from hydrates by exchange with hydrocarbon byproduct carbon dioxide. It is imperative for the development of safe methane extraction and carbon dioxide sequestration to understand how methane and carbon dioxide co-occupy the same hydrate structure. Pair distribution functions (PDFs) provide atomic-scale structural insight into intermolecular interactions in methane and carbon dioxide hydrates. We present experimental neutron PDFs of methane, carbon dioxide and mixed methane-carbon dioxide hydrates at 10 K analyzed with complementing classical molecular dynamics simulations and Reverse Monte Carlo fitting. Mixed hydrate, which forms during the exchange process, is more locally disordered than methane or carbon dioxide hydrates. The behavior of mixed gas species cannot be interpolated from properties of pure compounds, and PDF measurements provide important understanding of how the guest composition impacts overall order in the hydrate structure.

Identification of radioactive materials is a critical goal of resource exploration, basic actinide science, and nuclear forensics, and we provide here new insights toward rapid, nondestructive analysis of uranium-containing minerals and technogenic phases. Raman and infrared spectroscopic data are powerful indicators of solid-phase U(VI) coordination chemistry. In addition, U(VI) minerals exhibit high chemical and structural diversity as artifacts of geochemical processes leading to ore formation. Spectral signals of axial UO22+ (U-Oyl) bond lengths and the influences of additional oxyanions on these values are well documented for uranium oxide and oxysalt minerals and technogenic phases. Additional insight regarding the underlying crystallographic structure and chemical composition of uranium materials can be extracted through a survey of all available Raman spectroscopic data for these phases. To this end, we have developed the Compendium of Uranium Raman and Infrared Experimental Spectra (CURIES). CURIES was compiled via a thorough review of literature and databases, and for mineral species that lack measured and recorded spectra, data were obtained either from museum and academic collections or by direct syntheses. Characteristic Raman spectroscopic features for subgroups of uranyl minerals within CURIES were elucidated using multivariate statistical analyses. In addition, average spectra for groups of uranyl minerals were determined, providing insight into common spectroscopic characteristics that are indicative of the structural origins from which they arise. As of publication, 275 mineral species and technogenic phases have been entered in CURIES, and of these, 83 phases have published spectra that have been included in the CURIES database. Data collection is ongoing, and we have triaged missing data sets to assess CURIES for completion and to identify mineral groups that lack representation and should therefore be prioritized for data acquisition and inclusion in the database.

We prove that, within the class of pair potential Hamiltonians, the excess entropy is a universal, temperature-independent functional of the density and pair correlation function. This result extends Henderson’s theorem, which states that the free energy is a temperature dependent functional of the density and pair correlation. The stationarity and concavity of the excess entropy functional are discussed and related to the Gibbs–Bugoliubov inequality and to the free energy. We apply the Kirkwood approximation, which is commonly used for fluids, to both fluids and solids. Approximate excess entropy functionals are developed and compared to results from thermodynamic integration. The pair functional approach gives the absolute entropy and free energy based on simulation output at a single temperature without thermodynamic integration. We argue that a functional of the type, which is strictly applicable to pair potentials, is also suitable for first principles calculation of free energies from Born–Oppenheimer molecular dynamics performed at a single temperature. This advancement has the potential to reduce the evaluation the free energy to a simple modification to any procedure that evaluates the energy and the pair correlation function.