Incoherent scattering function

Figure 10 Intermediate incoherent scattering function for the bead-spring model at T = 0.48 for different values of momentum transfer given in the legend.

Dynamics Simulation of a Glassy Polymer Melt Incoherent Scattering Function. 

Fig. 4.1 a Typical time evolution of a given correlation function in a glass-forming system for different temperatures (T >T2>...>T ), b Molecular dynamics simulation results [105] for the time decay of different correlation functions in polyisoprene at 363 K normalized dynamic structure factor at the first static structure factor maximum solid thick line)y intermediate incoherent scattering function of the hydrogens solid thin line), dipole-dipole correlation function dashed line) and second order orientational correlation function of three different C-H bonds measurable by NMR dashed-dotted lines)... 

Fig. 4.25 Elastic and inelastic contribution to the incoherent scattering function for jump motion between two sites separated by 1.5 A...

The first factor in square brackets represents the Thomson cross-section for scattering from a free electron. The second square bracket describes the atomic arrangement of electrons through the atomic form factor, F, and incoherent scatter function, S. Finally, the last square bracket contains the factor s(x), the molecular interference function that describes the modification to the atomic scattering cross-section induced by the spatial arrangement of atoms in their molecules. 

J H Hubbell, W J Veigele, E A Briggs, R T Brown, D T Cromer and R J Howerton (1975) Atomic form factors, incoherent scattering functions and photon scattering cross-sections. J. Phys. Chem. Ref. Data 4, 471 Errata in 1977, 6, 615. 

The more useful form of this expression is found by considering the incoherent scattering function obtained by taking the Fourier transform to get... 

The elastic incoherent scattering functions defined in expression (100) yields [119]... 

Fig. 9 Partly reprinted from [104]. (a) Trajectory of a single particle over 800 s in the velocity-V( I It I city plane in the co-moving frame as defined in Equation 5 for a sheared glass at a local shear rate /= 9.3 10 s . (b) Selected incoherent scattering functions Fs Qm,t, with /increasing from rz gfe to left. The dashed line schematises initial relaxation. Insef. data collapse using fs Qmf with the line showing that /j = aepl —t/ta - (c-f) Snapshots of the stmcture for / = 0.0015 s , (c) at to = 80 s after start of imaging. The grey-scale measures the change in local environment of each particle (-Q (to, di)) over the past dt = 40 s. (d) at to = 120 s and dt = 80 s.

IQNS is another local probe, but in the reciprocal space.117 In general, the incoherent cross-section of hydrogens dominates all the others, and the incoherent scattering function Sinc(2, ) carries information on the hydrogen space and time trajectory... 

For H in metals the measured QENS intensity, after the necessary ra v data corrections (background subtraction, detector efficiency, etc.) is proportional to the incoherent scattering function S , (Q, co) which can be written as the two-fold Fourier transform (in space and time) of the single-particle, space-time van Hove correlation function, Gg(r,t),... 

Here P(r,t) and U(i,t) denote the probabilities of finding a hydrogen in the occupied and unoccupied layers, respectively r and are the jump rates within the occupied and unoccupied layers, respectively (both along the jump vectors Sj to S4), and Tq and are the change-over rates from the occupied to the empty layer and vice versa, respectively (both along the jump vectors S to S ). This jump model yields a 2x2 jump matrix and subsequently an incoherent scattering function consisting of two Lorentzians. 

The experimental and calculated incoherent scattering functions S(Q,co), against the energy transfer (points represent the data, lines represent the theory). For clarity, the spectra for the [110] and the [111] directions have been shifted vertically. The calculated spectra have been convolute with the experimental resolution function [24]. 

O. Goscinski and P. Lindner Asymptotic Properties of Atomic Form Factors and Incoherent Scattering Functions J. Chem. Phys. 52, 2539 (1970) Erratum 54, 826 (1971). 

The incoherent scattering function S(Q,(i>) exhibits a Lorentzian shape with a parabolic increase of its full-width at half-maximum (fwhm), F, as a function of Q ... 

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