Neutron Scattering - JUWEL - Forschungszentrum Jülich

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analysis is no longer valid.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