Structure with Variable Lamella Thickness

2 Structure with Variable Lamella Thickness The sharp peaks predicted by Equation (5.135) are broadened and reduced in height if various types of imperfections degrade the structure from the ideal two-phase model envisioned above. Most of such imperfections find their counterparts in three-dimensional crystals, and the methods of analysis to account for such imperfections, developed in Section 3.4, can be applied to the small-angle scattering equally well and need not be elaborated here again. There is, however, one type of imperfection 

The amplitude A(q) of scattering from such a parallel stack of lamellae is given by 

Note that the upper limit of the summation with respect to m is written as N instead of A — j in view of the aforementioned approximation of regarding N as practically equal to infinity. 

In the above, in replacing the exponential factors with their expectation values, we recognize the fact that the thicknesses of the neighboring lamellae are uncorrelated. Making use of (5.142) we then find 

This is the expression giving the scattering intensity I q) in terms of the lamellae thickness distributions. The above derivation is based on the one given by Hosemann and Bagchi.35 

---

The form in which elastin is laid down varies considerably in the different types of elastic tissue. Membranes with a very high elastin content are found in the walls of the larger arteries, in some parts of the heart, and in the trachea and bronchi. In the larger arteries the structural units of the elastic tissue formation are concentric lamellae which are often of rather variable thickness and always contain many irregular openings. In the ligamentum nuchae of some animals, particularly the ox, the structure is quite different and thick longitudinal elastic fibers, of almost circular cross section, form most of the tissue. 

---