Interplanar angle, calculation from

Positions of Bragg peaks are established from the Braggs law as a function of the wavelength and the interplanar distances, i.e. (/-spacing. The latter can be easily calculated from the known unit cell dimensions (section 2.8). For instance, in the case of the orthorhombic crystal system permissible Bragg angles are found from... 

Figure 9-7. Elastic electron-diffraction pattern of a highly textured hexaphenyl film. The Miller indices are assigned using the interplanar spacings calculated in Ref. [137]. Inset Intensity of the (020) peak as a function of the angle between momentum transfer and the Teflon rubbing direction (see text) - taken from Ref. [138].

Metrics were derived as follows. Macrocyclic centers (Ct) were calculated as the centers of the four nitrogen planes (4-N plane) for each macrocycle. Interplanar angles were measured as the angle between the 4-N least-squares planes. Plane separations were measured as the perpendicular distance from one macrocycle s 4-N least-square plane to the center of the other macrocycle mean-plane separations (MPS) were the average of the two plane separations. Torsional twists were measured as the angle between the two meso carbon to spacer bonds. Uie a-b and c-d distances were obtained according to the convention shown in Fig. 7. Data is reproduced from Ref. (86). 

We measure accurately the distances between the lines on the film. From these and the dimensions of the camera, the diffraction angle 29 can be calculated for each set of planes. From the Bragg angle 9 the interplanar spacings d are calculated from the Bragg equation. 

It is clear that the XRD pattern of the modified cellulose exhibited diffraction peaks at the 20 angles of 17 and 22°. The position of the peak at 17° indicated an increase in interplanar distance of the treated fibres when compared to the pristine sugar cane leaves. The results indicated the formation of order in cofibres after chemical treatment. The crystalline content of the modified cellulose was calculated from Equation (13.1) " ... 

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