Guinier formula

This very general expression is known as the Guinier formula... 

Figure 28a shows the result of SAXS on sample BrlOOO. We used Guinier s formula (see eq. 6) for the small angle scattering intensity, I(k), from randomly located voids with radius of gyration, Rg. Although Guinier s equation assumes a random distribution of pores with a homogeneous pore size, it fits our experimental data well. The slope of the solid line in Fig. 28b gives R - 5.5 A and this value has been used for the calculated curve in Fig. 28a. This suggests a relatively narrow pore-size distribution with an equivalent spherical pore diameter of about 14A. Similar results were found for the other heated resin samples, except that the mean pore diameter changed from about 12 A for samples made at 700°C to about 15 A for samples made at 1100°C.

At small values of Q, the Debye formula reduces to the Guinier approximation,... 

Recently formula for P ( for structures of various shapes have been tabulated by Fournet and Guinier (1950). 

The average crystal size (D) has been calculated using Scherrer s formula (Guinier, 1963) based on the full width at halh maximum (FWHM) of the prominent peaks due to (111) plane. 

In Guinier s approach, the key term is the scattering factor, which can be analyzed in terms of Debye s formula (the sine function in a power series). The same set of experimental data I h) can also be analyzed by a different approach. Here, we discuss the correlation function (see the Appendix to Chapter 5). Since the evaluation of (ry) is related to statistics, we can define a correlation function y(r) as the average of the product of two fluctuations at a distance r ... 

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