Neutron Scattering - JUWEL - Forschungszentrum Jülich
Neutron Scattering - JUWEL - Forschungszentrum Jülich
Neutron Scattering - JUWEL - Forschungszentrum Jülich
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KWS-1 & KWS-2 7<br />
Fig. 4: Guinier plot for cylindrical cross section. The first data points of the 8m, 7 ˚A measurement<br />
indicate no slope. The data points for larger Q values than 0.02 ˚A −1 are neglected.<br />
analysis is no longer valid. From the slope of the regression one can extract the diameter of the<br />
cylinder cross section (see Eq. 2). This is in the range of 120 ˚A. For the validity of the Guinier<br />
assumption, the product of the highest Q value taken and the obtained radius can be calculated.<br />
This yields 0.02 ˚A −1 × 120 ˚A= 2.4. This value is not much larger than √ 4. Therefore, the<br />
Guinier approximation is a good estimate for the cylinder diameter. The measurement error of<br />
the obtained radius is to be specified.<br />
Alternatively, the first minimum Qmin in Fig. 4 can be used for calculating the cylinder cross<br />
section. The radius is calculated according to R =3.832/Qmin. The two different radii are to<br />
be compared. Is the Guinier condition QR < 2 well enough fulfilled? Which result is more<br />
precise?<br />
9 Preparatory Exercises<br />
(I) Lysozyme inD2O<br />
The first sample of the <strong>Neutron</strong> Lab Course at the SANS instrument KWS-1 (KWS-2) will<br />
be Lysozyme in heavy water (D2O). This protein is rather globular (diameter ca. 5 nm). The<br />
Coulomb interactions of this charged molecule lead to liquid-like short-range-ordering. This<br />
will be observed in the SANS scattering experiment by a correlation peak. Simple estimations<br />
will be made now:<br />
1. Give the connection between the number density φ and the unit cell parameter assuming<br />
asimple cubic lattice!<br />
2. The chemical concentration c is usually given in g/L or mg/ml. The molar mass of the