Laue zero order

By definition, a zone axis is normal to both g and h and other reciprocal lattice vectors in the plane defined by these two vectors. The reciprocal lattice plane passing through the reciprocal lattice origin is called the zero-order zone axis. A G-vector with z - G=n with n O is said to belong to a high order Laue zones, which separate to upper Laue zones (n>0) and lower Laue zones (n<0). 

A diffraction pattern with diffraction spots belonging to both zero-order Laue zone and higher order Laue zones can be used to determine the three-dimensional unit-cell of the crystal. 

The dynamic calculations include all beams with interplanar distances dhki larger than 0.75 A at 120 kV acceleration voltage and thickness between 100 A and 300 A for the different zones. The structure factors have been calculated on the basis of the relativistic Hartree - Fock electron scattering factors [14]. The thermal difiuse scattering is calculated with the Debye temperature of a-PbO 481 K [15] at 293 K with mean-square vibrational amplitude

= 0.0013 A following the techniques of Radi [16]. The inelastic scattering due to single-electron excitation (SEE) is introduced on the base of real space SEE atomic absorption potentials [17]. All calculations are carried out in zero order Laue zone approximation (ZOLZ). 

The primitive cell volumes can be deduced easily from CBED unindexed patterns, as was shown by Carpenter and Page in [7]. By combining the measurements from the ZOLZ, (zero order Laue zones, which appear in the center of the CBED pattern) and the HOLZ (higher order Laue zone, which appears as rings around the ZOLZ pattern) it is possible to calculate the primitive cell... 

A disk in the CBED pattern usually consists of broad fringes due to the dynamic interaction between beams belonging to the zero-order Laue zone (ZOLZ). Finer lines are formed by the interaction of high-order Laue zone reflections (HOLZ) with the zero-order beams (Fig. 39). The geometry of the HOLZ lines is determined by the accelerating potential and the lattice parameters comparison of computer-simulated and observed patterns allows determination of one parameter if the other is known [171], [172]. 

Inside the BF pattern as shown in Fig. 5.10a there are thick fringes from zero-order Laue zone and thin dark lines from high-order Laue zone (HOLZ). These HOLZ lines are very sensitive to lattice parameter changes, therefore they can be used to measure strain fields [13]. In the two-beam or systematic diffraction conditions, CBED can be used to measure the specimen thickness and the stmctiue factor [14]. 



Figure 3.12. Facing page, (a) Diagram showing the Ewald sphere cutting the reciprocal lattice rods of zero and higher order Laue zones and (b) a schematic diagram of the corresponding diffraction pattern.

Fig. 3 Ewald construction. The white half-circle indicates the Ewald sphere in two dimensions. The points of intersection between the reciprocal lattice rods and the Ewald sphere form the set of reciprocal lattice points (bright) which obey Bragg s law and appear as diffraction spots in the diffraction pattern. Zero-, first- and second-order Laue zone are indicated. Eor electron diffraction in TEM, the ratio between the radius of the Ewald sphere and the reciprocal lattice unit is larger than visualized in the figure. (View this art in color at www.dekker. com.)...

The. hkl file consists of one line per reflection in FORMAT (3I4,2F8.2,I4) for h, k, 1, Fl, a (Fq), and (optionally) a batch number. This file should be terminated by a record with all items zero individual data sets within the file should not be separated from one another—the batch numbers serve to distinguish among groups of reflections for which separate scale factors are to be refined. The reflection order and the batch number order are unimportant. The. hkl file is read when the hklf instruction (which terminates the. ins file) is encountered. The HKLF instruction specifies the format of the. hkl file, and allows scale factors and a reorientation matrix to be applied. Lorentz, polarization and absorption corrections are assumed to have been applied to the data in the. hkl file. Note that there are special extensions to the. hkl format for Laue and powder data, as well as for twinned crystals that cannot be handled by a TWIN instruction alone. 



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