Rocking curve profile

The simplest expression for the rocking curve profile is in terms of a deviation parameter, which varies from -1 to +1 in the range of total reflection. The reflectivity as a function of angle is then... 

The rocking curve profile in the asyrmnetric Lane case withont absorption is... 

A third problem with simulation of high resolution diffraction data is that there is no unique instrament function. In the analysis of powder diffraction data, the instalment function can be defined, giving a characteristic shape to all diffraction peaks. Deconvolution of these peaks is therefore possible and fitting techniques such as that of Rietveld can be used to fit overlapping diffraction peaks. No such procedure is possible in high resolution diffraction as the shape of the rocking curve profile depends dramatically on specimen thickness and perfection. Unless you know the answer first, you cannot know the peak shape. 

Fig. 6.4. Typical rocking curve profile containing multiple peaks...

Accurate measurements of low order structure factors are based on the refinement technique described in section 4. Using the small electron probe, a region of perfect crystal is selected for study. The measurements are made by comparing experimental intensity profiles across CBED disks (rocking curves) with calculations, as illustrated in fig. 5. The intensity was calculated using the Bloch wave method, with structure factors, absorption coefficients, the beam direction and thickness treated as refinement parameters. 

In addition, the measurements are rapid and simple, and are now even used in 100% inspection for quality control of multiple-layer semiconductors. An example is shown in Figure 1.6. This is a GaAs substrate with a ternary layer and a thin cap. The mismatch between the layer and the substrate is obtained immediately from the separation between the peaks, and more subtle details may be interpreted with the aid of computer simulation of the rocking curve. This curve can be obtained in a matter of minutes. Routine analysis of such curves gives the composition of ternary epilayers, periods of superlattices and thicknesses of layers, whilst more advanced analysis can give a complete strain and composition profile as a lunction of depth. 

It is possible to compensate for curvature in theoretical simulation of the rocking curve. If the beam profile is square, then the rocking curve is simply correlated with... 

Formulae for rocking curve widths, profiles and intensities... 

Figure 6.15 Experimental and simulated rocking curves with differing lattice parameter profiles through the well-barrier wall. (Courtesy R.Mtlller, University of Munich)...

The line shapes are described by Voigt functions, which reflect the Lorentzian line profiles due to natural line width and Gaussian profiles due to Doppler broadening. The instrumental broadening by the rocking curve of the crystal, de-focusing and the finite resolution of the detector is described well by a Voigt profile shape too [3[. 

Figure 14.4 Example of a rocking curve scan along the specular crystal truncation rod of a Ag 111 surface at -0.23 V versus Ag/AgCI (a) and -+0.52 V (b), with the best fits shown as the solid lines. The differences in the profiles observed have been attributed to differences in the distribution of water molecules at the interface as a function of the applied potential. Reprinted from Ref [11]. Copyright (1995) with permission from Elsevier.

Fig. 31. X-ray rocking curves (005 reflection) of a Y123 crystal, produced by the SRL-CP method, demonstrating improvement of crystallinity in the necking process the thin line profile corresponds to a bottom facet of an initially grown seed crystal the profile with an intermediate line thickness is given for the as-cut (necked) single crystal used to grow the final crystal the thickest profile characterizes the final crystal with the smallest FWHM (Namikawa et al. 1996c, Kusao et al. 1997).

Both current electrodes, A and B, are placed in the host rocks on ground surface (Ryss, 1973, 1983). Current, as a linear function of time, is introduced into the ground by means of these electrodes (Fig. 2-45). If there is an electron-conducting ore body at depth this current flows into the ore body at one end (the zone of cathodic polarisation) and flows out of the ore body at the other end (the zone of anodic polarisation). This results in a potential difference with different signs and values in different parts of the ore body. This double electrical layer creates a secondary electrical field in the host rocks that can be measured by means of the measuring electrodes, M and N. For this measurement electrode M is moved along a profile to successive positions M), M2,. .M whilst electrode N is placed at infinity (Fig. 2-45). For each position of electrode M the CLPC polarisation curve is recorded. This curve is dependent on current I in the... 

In the following section we will apply the fluid-rock ratio Equations (56) and (57) to these infiltration-reaction curves by inserting values from the calculated continuum mechanics profiles into these equations. The idea is, that each calculated value represents a sample collected from a one-dimensional hydrothermal alteration profile. 

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