Precision Measurement of Lattice Parameters

2a being the full angular aperture of the incident beam in the diffractometer plane. The first term in (3.6) arises from the flat sample effect and the second and third terms from the beam penetration effect. The first effect is minimized by using an incident beam with a small divergent angle a. For small t it is easily seen that the second and third terms are about equal in magnitude and cancel each other out, and therefore a thin sample should be used to minimize the error due to the second effect. 

A practical way of obtaining good accuracy in the lattice parameters, without requiring accurate calibration of all the elements in a diffractometer, is to make use of a calibration standard, that is, to have a material of known lattice parameters mixed in the polymer sample being investigated. Best results are obtained when such a standard material is not simply spread thinly over the surface but is blended with the polymer so that the standard is dispersed throughout the sample. Powders of inorganic materials such as quartz and silicon, for example, are used for this purpose. 

3 Examples of Lattice Parameter Measurements with Polymers 

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The most precise measurement of lattice parameter is made in the back-reflection region, as discussed in greater detail in Chap. 11. The most suitable camera for such measurements is the symmetrical back-reflection focusing camera illustrated in Fig. 6-8. 

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