The determination of structure factors by means of Pendellösung fringes

The theoretical basis and the experimental procedures of the Pendellösung method are described. Structure factors |Fg| can be determined on the absolute scale by measuring the fringe spacing Λg on the diffraction topographs and the angles involved in a geometrical factor Φg. The experimental results so far obtained on Si, Ge and α-quartz are briefly reviewed in comparison with the results obtained by other methods. Effects of absorption and of lattice distortions are estimated to be of about 0.1%. The errors in measuring Λg are less than 0.1% in favourable cases. At present, the accuracy in |Fg| is limited by the difficulty in determining Φg accurately. It is about 1%. The ratio of structure factors can be determined with an accuracy of about 0.1% by taking the ratio of the fringe spacings. The following examples are described: (i) |Fhk, l|/|Fhk,_{{ l}}| of a α-quartz, (ii) the ratio of |Fg| of Si at low and room temperatures and (iii) |Fg|/|F0| of Si. Through the experiment (ii), the increase of the Debye temperature at low temperatures (≃ 40°K) was confirmed. In experiment (iii), the Pendellösung fringes and X-ray interferometry fringes are used, whose spacings are proportional to |Fg| and |F0|, respectively. Since |F0| is essentially the total charge Z in the unit cell, the |Fg| value determined by this method is the truly absolute value.