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Crystallographic Texture


Texture measurement is done in most cases by measuring pole figures. A pole figure Phkl describes the volume fraction dV/V of the crystallites whose crystallographic directions <hkl> have a certain orientation in space: 
         dV/V = Phkl(α, β)·sin α dα dβ

A pole figure is given graphically as a frequency distribution if crystal orientations on the reference sphere that is stereographically projected into the "equator" plane in sample space.  

 Schematics of a pole figure and its stereographic projection

Schematics of a pole figure and its stereographic projection

The TEM as an automated texture goniometer


Acquisition of pole figures by post-specimen beam deflection, but manual correction for the ellipticity of diffraction rings.
 F.J. Humphreys: Textures and Microstructures 6 (1983) 45-62


Analytical and experimental on-line intensity correction for SAD pole figures in pre- and post-specimen beam deflection mode.
R. Schwarzer: Beitr. Elektronenmikr. Direktabb. Oberfl. (BEDO) 16 (1983) 131-134  


Automated SAD pole-figure measurement with pre- and post-specimen beam deflection. On-line correction for background, absorption, diffracting volume and ring ellipticity by the software.
H. Weiland and R. Schwarzer: Proc. ICOTOM 7 (1984) 857-862

R. Schwarzer: BEDO 18 (1985) 61-68
R.A. Schwarzer and H. Weiland: in H.J. Bunge (ed.): Experimental techniques of texture analysis. DGM Informations-Ges. Oberursel, 1986, 287-300  


RHEED pole-figure measurement on bulk surfaces in the TEM. A digital CCD camera is used as an area detector.
B. Schäfer and R.A. Schwarzer: Materials Science Forum 273-275 (1998) 223-228


           + Measured area:  SAD           1 μm .... 500 μm                   RHEED       ~ 0.1 - 2 mm
           + High speed: ~ 5 min for the acquisition of several pole figures            
           + Extremely high sensitivity.  

The principles of SAD pole-figure measurement

The principles of SAD pole-figure measurement.