The combination of methods for two-phase systems

Assuming additivity of birefringences, it follows that for a two-phase system. 

A particular sample of a semicrystalline pol5mer with the simplest form of uniaxial orientation is found to have a birefringence of 0.042. Density measurements show that it has a volume crystallinity of 0.45 and X-ray measurements show that P2icosff)) for the crystalline phase is 0.91. Assuming that An ax is 0.050 for the crystalline phase and 0.045 for the amorphous phase, estimate (P2(cos 0)) for the amorphous phase. 

When the two phases are sufficiently different, methods such as measurement of infrared dichroism or Raman scattering can sometimes be used to characterise the orientation of the two phases independently, which will usually give more accurate results. Nevertheless, birefringence measurements are often used as a cross-check on the results, because all methods of characterising orientation are subject to errors that are sometimes difficult to quantify and it is usually desirable to obtain as much data as possible by various methods. In practice, the maximum birefringences of the various phases are not always well known, so large uncertainties can arise from using equation (10.31). 

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