Sampling spatial averaging

The last term in (1.34) follows by approximating S evaluated at the bin center by its value at a sample point contained in the bin. In the limit where the fine grid becomes infinitely fine, the last term is just the spatial-average chemical source term ... 

This is the PM state of a material having non-interacting PM moments. An instantaneous snap shot of the PM state (in zero applied field) would have each cationic moment frozen in some random direction, such that the spatial average over all instantaneous moment vectors in the large sample is also zero (

s = (1/N) Z [O = 0 ). 

Experimentally, the EISF is the fraction of the total quasielastic intensity contained in the purely elastic peak. For an exact experimental determination of the EISF the neutron spectra have to be fitted with the correct scattering function which consists of the elastic and a series of quasielastic terms (see [14, 28, 29]). Approximately, however, the EISF can be determined in a kind of model-indepen-dent data evaluation by fitting the neutron spectrum with a single Lorentzian plus an elastic term. Although in this way the line shape is not correct (except for N = 2 and 3), the EISF thus obtained allows statements to be made about the geometry for the localized motion. For the present chapter two EISFs, both spatially averaged (for powder samples), are of particular relevance ... 

In the following the spin polarization of the Gd(OOOl) surface state is quantified as observed by SPSTS and compared to data obtained by spatially averaging surface sensitive techniques. The spin polarization P as a function of the applied sample bias U can be estimated by... 

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