In-plane coherence length

For H" the upper critical field Is always by he smallest coherence length (0 K) - jk. For H the upper critical field becomes the larger Setween H 2 And H 2 as given above. This may explain the discrepancy In the reported K values of the In-plane coherence length ( in(0) 34A, (0) -22A), as well as the kink In the H 2 data. ... 

The capillary wave broadening is therefore dependent on the in-plane coherence length of the neutron, 20pm, the dispersive capillary length, A, ... 

In contrast to that, the in-plane coherence length 1,, which is directed along the incident beam projection onto the surface, is always significantly greater than two other coherence lengths and ly (Section 2.15.3). This is due to the fact that the uncertainty Aicf ktXiAai< pi and, consequently, lx 2./(a,Ao,)> 4, ly. The ctoss section of the 3D coherence volume with the surface plain results in the two-dimensional (2D) ellipsoid with dramatically extended x-axis at the above conditions 0.1 mm, if the angle of incidence a, 10 mrad. 

The more recent neutron reflectivity studies have established that flattened surface micelle or fragmented bilayer structure in more detail and with more certainty, using contrast variation in the surfactant and the solvent [24, 31]. However, the extent of the lateral dimension (in the plane of the surface) and the detailed structure in that direction is less certain. From those neutron reflectivity measurements [24, 31] and related SANS data on the adsorption of surfactants onto colloidal particles [5], it is known that the lateral dimension is small compared with the neutron coherence length, such that averaging in the plane is adequate to describe the data. The advent of the AFM technique and its application to surfactant adsorption [15] has provided data that suggest that there is more structure and ordering in the lateral direction than implied from other measurements. This will be discussed in more detail in a later section of the chapter. At the hydrophobic interface, although the thickness of the adsorbed layer is now consistent with a monolayer, the same uncertainties about lateral structure exist. 

The previous treatment deals with a one-component order parameter (such as for a commensurate Peierls distortion) but does not apply to situations where the order parameter is complex with an amplitude and a phase (superconductivity, incommensurate Peierls, or spin density wave transitions). The latter situation is analogous to classical moments which can rotate freely in an XY plane. The coherence length of the XY model is less strongly divergent at low temperature than for the Ising model,... 

The end points define the lateral distance in the sample plane across which a given spherical wave front becomes out of phase by n degrees. For a spherical wavelength of 5 A emanating from a source 5 m away, the length I is of the order of 100 pm. In practice, the lateral coherence length depends on the energy spread and the wave vector spread of the incident neutron wave front If the instrumental... 

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