Lotgering factor

The evaluation of texture is an important issue for the engineering of ferroelectric ceramics. Both, domain and crystallographic texture can be evaluated qualitatively or quantitatively using either microscopy or neutron and X-ray diffraction (XRD). The Lotgering factor, f, a commonly used assessment of texture using XRD analysis, relates the relative intensities of (001) reflections to all observed reflections in a coupled 0-20 powder XRD spectrum [102] ... 

Although the Lotgering factor is often used for texture estimation due to its simplicity, it can be very impredse as a qualitative assessment of texture since, in some cases, it depends heavily on the reflections induded in the calculations [104]. A more careful analysis of texture can be provided using an orientation distribution... 

On the other hand, po is calculated similarly to Phkl but using peak intensities from a texture-free sample of the same material (the intensities from the corresponding PDF card for this material are typically used for po). The Lotgering factor varies between 0 and 1, being 0 for the case of completely random orientation (Phkl = Po)> and 1 for a highly-oriented material. 

Figure 1.11a, b show 2Q/(o scans from Au samples with <100> and <111> texture, respectively. Figure 1.11c shows the relative intensity from a texture-free Au powder sample (as reported in the ICDD PDF 00-004-0784 [8]). Notice that the pattern in Fig. 1.11a is dominated by the strong peaks from (100) and (200), while in Fig. 1.1 lb peaks from (111) and (222) are considerably stronger relative to the other orientations compared to the relative intensity depicted in Fig. 1.11c. By using Eqs. 1.5 and 1.6, Lotgering factors/loo (for the case of Fig. 1.11a) and/i 11 (for the case of Fig. 1.11b) were determined to be 0.75 and 0.92, respectively. Those values not only confirm the strong texture in each case, but also suggest that the texture for the Au sample in Fig. 1.1 lb (larger Lotgering factor) is actually stronger than the one in Fig. 1.11a.

Lotgering, 1956) but their magnetic ordering, which is the important factor for applications, is observed only at low temperatures and therefore they are unsuitable for applications at room temperature. A particular case is maghemite, y-Fe203, which possesses a defect spinel structure. The Fe cations are in the trivalent state, and a fraction of the cation sites is vacant (Verwey, 1935). 

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