Wavelength dynamic scattering

Static and dynamic scattering techniques are spectroscopic characterisation methods in the sense of Sect. 2.2. These techniques evaluate the functional dependency of measurement signals on a spectral parameter, i.e. on time, space, or classically on wavelength or frequency. The major advantage of spectroscopic methods is the reduced sample preparation (no fractionation), but they involve the inversion problem. That is, the spectrum is a—most frequently incomplete and discrete— nonlinear projection of the size distribution. Beside the scattering techniques, there are further spectroscopic methods which are based on the extinction of radiation or on any other response of the particle system to an external field. This section describes optical, acoustic, and electroacoustic methods that have gained relevance for the characterisation of colloidal suspensions. 

Fig. 12— Voltage dependence of diffraction by domains. The intensity distribution of the diffraction rings (for a single wavelength) with increasing dc voltage demonstrates a constant intensity profile even at 60 volts where the diffraction angle is nearly 50 . No dynamic scattering occurs. ...

The normalized dynamic structure factor thus gives the probability that a scattering event occurs at a certain wavelength change 8X = (m/2n) 3co at a given momentum transfer Q. The Fourier time t in the argument of the cosine is determined by the transformation from the phase angle Acp = [Pg.9]

The exponent Mk depends on the mean square displacement of the atom from its equilibrium position and hence upon temperature. It is linear with (kT/m Xsin / where k is the Boltzmann constant, T the absolute temperature, the scattering angle, the wavelength and m the atomic mass (for a monatomic material). In addition there are complicated expressions dependent upon the crystal symmetry. As an example, for silicon at room temperature the /, are reduced by approximately 6%. With this correction all the equations of dynamical theory still apply. 

One of the most serious difficulties for experimentally accessing the dynamics in the low Q plateau is the presence of multiple scattering [210]. In order to assess this effect, NSE spectra were taken above and below the multiple scattering threshold. For neutron wavelengths A 14 A the first structure factor peak cannot be seen with neutrons and therefore multiple scattering contributions... 

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