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Polymer, Vol.37, No.9, 1509-1512, 1996
On the Calculation of (P-N(COS(Chi))) Coefficients from X-Ray-Diffraction Measurements Made on Hkl Reflections
Wide-angle X-ray diffraction measurements of the orientation distribution of(hkl) crystal planes give values of some of the (P-n(cos(chi)))(c) coefficients, characterizing the orientation of the molecular chains, which disagree with those obtained from hk0 or 00l reflections. In this present article, a calculation method is proposed for obtaining reliable (P-n(cos(chi)))(c) values from any hkl reflection. This procedure involves an angular shift of the Legendre polynomial curves for the calculation of the coefficients relative to the (hkl) plane orientation, which is followed by a correction for this shift to yield the (P-n(cos(chi)))(c) coefficient. A comparison is made between results obtained by the regular and the angular shift procedures for oriented polypropylene sheets. It is shown that the calculation of the (P-n(cos(chi)))(c) coefficients from the 111,(1) over bar 31/041 and 022/(1) over bar 12 reflections, using the regular procedure, gives results which are, in some cases, outside the boundaries of the function, whereas results obtained by the angular shift procedure agree with those computed from the (110), (040) and (130) crystal planes.