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 |F_g| can be determined on the absolute scale by measuring the fringe spacing Λ_g on the diffraction topographs and the angles involved in a geometrical factor Φ_g. 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 Λ_g are less than 0.1% in favourable cases. At present, the accuracy in |F_g| is limited by the difficulty in determining Φ_g 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) |F_{hk, l}|/|F_hk,| of a α-quartz, (ii) the ratio of |F_g| of Si at low and room temperatures and (iii) |F_g|/|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 |F_g| and |F₀|, respectively. Since |F₀| is essentially the total charge Z in the unit cell, the |F_g| value determined by this method is the truly absolute value.