April 23, 2021

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Partial Radial Distribution Functions

        Lars Borjesson and Aleksandar Matic specialize in the diffraction study of amorphous materials. Their research group has pioneered the combined use of ND and RMC simulation techniques to examine the details of the structure of binary glasses. The Chalmers students will combine the ND and XRD data to generate more accurate partial radial distribution functions for the MGF glasses and this will provide input data for refined modeling of the structures of the MGF glasses.

      As in the case of XRD, in ND structural information is obtained from the static structure factor S(Q), directly measured in the experiment, and the real space Fourier transform G(r), the pair distribution function. Whereas G(r) can provide information on the short range order (r < 10Ã…), nearest neighbor distances and coordination numbers, S(Q) can provide information on the intermediate range order, r ≈ 10-30 Ã… from the position of the first diffraction peak. The latter is particularly important in the studies of ion conducting glasses as it can be related to the size and dimensionality of the conduction pathways in the structure and thus to the macroscopic conductivity. We have previously shown the direct relation between the structural expansion, related to the intermediate range order, and the conductivity of oxide-based ion conducting glasses.

      ND and XRD are complementary due to the fact that the contrasts in the two experiments are quite different. The atomic form factor in XRD directly depends on the number of electrons of the atomic species in the glass whereas the ND cross-section varies non-regularly throughout the periodic table. Indeed, even different isotopes of the same element might have drastically different scattering lengths. Thus, XRD weights more on the heavy elements and in case of the materials in the present project it will therefore highlight the glass network. In ND one can also resolve light elements in a surrounding of a heavy matrix, e.g. the Li-ions in a sulfide glass network.

      In this project we will use ND to reveal the structure of the ternary MGF glasses proposed above. We will take particular advantage of the fact that 6Li and 7Li have different scattering lengths and in this way by isotopic substitution highlight the contrast for Li and thus better reveal the local environment of these ions. We have previously successfully investigated several binary alkali borate- and phosphate-based ion conducting glasses using the combination of ND and XRD with RMC simulations. In the present project we will build on this experience when investigating the more complicated ternary MGFE systems.

     Even though several features of the glass structure can be extracted directly from the static structure factor, S(Q), or the pair distribution function, G(r), structural modeling in conjunction with experiments is usually necessary to fully reveal the structure of complicated systems such as MGF ternary glasses. The RMC method has proven to be particularly useful for these kinds of investigations. In the RMC method, 3-D structural models are produced in agreement with experimental data, such as ND or XRD. The RMC technique is based on a metropolis MC algorithm with the difference being that the deviation between calculated and experimental data are minimized, where E and C denote the experimental and calculated structure factors, S(Q), respectively. Actually, several data sets, from different experimental techniques, can be fitted simultaneously to one configuration.

     Using experiments where different structural features are differently weighted, as from XRD and ND and/or using isotope substitution in ND, reliable structural models can be obtained. From the obtained models, the different pair correlations can be extracted and the structure can be analyzed in detail and ion sites and conduction pathways can be identified. S(Q)s will be calculated from computer configurations of 5,000 to 15,000 atoms confined in a cubic box with dimensions adjusted to the experimental macroscopic density. To reproduce physically relevant models, closest approach constraints are applied for the different pair correlations. An important feature of the RMC method is that the experimental data, SE(Q), is directly fitted rather than the Fourier transform G(r), since the limited Q-range in the experiments introduce errors in the real space function. Furthermore, low-Q features in the structure factor usually do not correspond to well defined structures in G(r), and will not be accurately reproduced if the fitting is done in real space.  

      The results from ND (Chalmers) and XRD (CMU) will be combined as inputs to the RMC simulations. Chemical knowledge about MGF glasses will be obtained from IR and Raman (ISU), NMR (Munster), and XRD (CMU) and these chemistry and coordination constraints will be used in the simulations. An obvious disadvantage with RMC, compared to other simulation techniques (Ilmenau), is that it is a static simulation technique. Since there is no potential used, no dynamical information can be obtained. However, the RMC models can be used as a starting point for dynamical simulations (Ilmenau) as described below. Chalmers will support one graduate and one undergraduate student to carry out their research