Diffracted intensities: polycrystalline fibres

Chandrasekaran, R.; Stubbs, G.

doi:10.1107/97809553602060000702

International
Tables for
Crystallography
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

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International Tables for Crystallography (2006). Vol. F. ch. 19.5, pp. 445-446 | 1 | 2 |

Section 19.5.3.6. Diffracted intensities: polycrystalline fibres

R. Chandrasekaran^a ^* and G. Stubbs^b

^aWhistler Center for Carbohydrate Research, Purdue University, West Lafayette, IN 47907, USA, and ^bDepartment of Molecular Biology, Vanderbilt University, Nashville, TN 37235, USA
Correspondence e-mail: chandra@purdue.edu

19.5.3.6. Diffracted intensities: polycrystalline fibres

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The intensity in the diffraction pattern of a polycrystalline fibre consists of Bragg reflections on layer lines (Fig. 19.5.2.1b). On each layer line, owing to the lattice sampling that arises from the lateral organization of the polymers, intensities are observed at discrete R values defined by the reciprocal-lattice points. In the case of monoclinic (with c as the unique axis), orthorhombic and hexagonal systems, the reflection positions are determined by equations (19.5.3.8), (19.5.3.9) and (19.5.3.10), respectively. $[\eqalignno{ R^{2}_{hk} &= h^{2}a^{*2} + k^{2}b^{*2} + 2hka^{*}b^{*} \cos \gamma^{*}, &(19.5.3.8)\cr R^{2}_{hk} &= h^{2}a^{*2} + k^{2}b^{*2}, &(19.5.3.9)\cr R^{2}_{hk} &= (h^{2} + k^{2} + hk) a^{*2}. &(19.5.3.10)} %fd(19.5.3.10)]$ Consequently, on each layer line, superposition occurs between reciprocal-lattice points (hkl) and ( $[\bar{h}\bar{k}l]$ ) for monoclinic; (hkl), ( $[\bar{h}kl]$ ), ( $[h\bar{k}l]$ ) and ( $[\bar{h}\bar{k}l]$ ) for orthorhombic; and (hkl), ( $[\bar{h}\bar{k}l]$ ), (khl), ( $[\bar{k}\bar{h}l]$ ), (kil), ( $[\overline{ki}l]$ ), (ikl), ( $[\overline{ik}l]$ ), (ihl), ( $[\overline{ih}l]$ ), (hil) and ( $[\overline{hi}l]$ ), where [i = -(h + k)] , for hexagonal systems. Depending upon the unit-cell dimensions, other reflections having the same R value may also be superposed to give a single intensity, and those having R values close to each other may be difficult to resolve. All superposed reflections must be considered individually when calculating such composite intensities.

References

International Tables for Crystallography (2006). Vol. F. ch. 19.5, pp. 445-446