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Neutron Diffraction Studies of Water and Aqueous Solutions
Published in Fausto Martelli, Properties of Water from Numerical and Experimental Perspectives, 2022
where δαβ is the Kroneker delta, k and Q are the incident and exchanged neutron wave vector, in the elastic approximation, 2θ is the scattering angle, and ca, ba the atomic fraction and neutron scattering length (Sears 1992) of the species a. Saself the integral of the self contribution to the van Hove dynamic structure factor and does not bring information on the structure of the material, being a flat (in the ideal case) or smoothly decreasing profile. The structural information is embedded in the second addendum of Eq. (1), where Hαβ(Q) is the integral of the distinct dynamical structure factor (Lovesey 1986, Fernandez-Alonso and Price 2017). Indeed, the Hαβ(Q) are related by Fourier transform to the site-site pair distribution functions (PDF), which are the basis of the statistical mechanical theory of liquids (Hansen and McDonald 2013): Hαβ(Q)=4πρ∫r2[gαβ(r)−1]sinQrQr
Characterization of Biological and Environmental Particles Using Static and Dynamic Light Scattering
Published in Jacques Buffle, Herman P. van Leeuwen, Environmental Particles, 2018
Peter Schurtenberger, Meredith E. Newman
where the dynamic structure factor F(Q,τ) is given by () F(Q,τ)=(N<A2>)−1<∑j∑j′AjAj′eiQ→(r→j(0)−r→j′(τ))>
Dynamics of water in real space and time
Published in Molecular Physics, 2019
Atomic dynamics can be studied by measuring the dynamic structure factor, S(Q, E), by inelastic neutron or X-ray scattering. Phonons are readily identified by the dispersion in S(Q, E), and diffusivity can be evaluated through the quasielastic scattering at low Q. In liquids, however, phonons are overdamped, and dynamic properties depend on correlated local atomic dynamics which are hidden in S(Q, E). In order to bring the hidden information to light, we can make use of the Van Hove function, G(r, t), which is obtained by the double-Fourier-transformation of S(Q, E). The self-part of the VHF describes the diffusive motion, whereas the distinct-part provides the information pertinent to viscosity. Even though the VHF has been known for a long time, only recently it became practical to determine it experimentally by scattering measurements. Our first attempt to determine both diffusivity and viscosity at the same time from the same set of data on water at room temperature, however, exposed a puzzling inconsistency between our results on oxygen diffusivity and the published values of hydrogen diffusivity, even though it is generally assumed that they are equal. Further research is due to unravel this mystery.
Thermal Transport in Disordered Materials
Published in Nanoscale and Microscale Thermophysical Engineering, 2019
Freddy DeAngelis, Murali Gopal Muraleedharan, Jaeyun Moon, Hamid Reza Seyf, Austin J. Minnich, Alan J. H. McGaughey, Asegun Henry
For propagons, Moon et al. [12, 42] have calculated the dynamic structure factors to identify propagons, finding for a-Si that an isotropic linear dispersion exists for longitudinal and transverse acoustic branches with finite linewidths that are inversely proportional to the lifetime. The dynamic structure factor is the space and time Fourier transform of the particle density correlation function and therefore contains important information on the collective vibrational dynamics [12]. This information enables a Debye model to be used to calculate the propagon contribution to the thermal conductivity of amorphous materials [41].