Diffracting “stacks of cards” - some thoughts about small-angle scattering from bone

Abstract

Small-angle x-ray scattering (SAXS) has been used extensively in recent years to characterize the thickness and orientation of mineral particles in bone. While the determination of these parameters is straight forward, the detailed shape of the SAXS curve turned out to be much more difficult to analyze quantitatively, because it is influenced by the shape as well as by the arrangement of the particles. The spherically averaged SAXS curve I(q) has been found to vary with bone type and species. For bone from mice and rats, I(q) is proportional to q ^-1 at small q, which is compatible with needle-like particles, and it is proportional to q^-2 for human bone, which is compatible with plate-like particles. On the other hand, such differences may also be due to varying spatial arrangements of plate-like particles. Results from electron microscopy and atomic force microscopy reveal parallel arrangements of platelets similar to stacks of cards in all types of mature bone tissue. In the present paper, we consider arrangements of this type and derive simple analytical expressions for small-angle scattering from short-range ordered stacks of plate-like particles. Qualitatively, these expressions can describe all types of SAXS curves published for different types of bone.

Dedicated to Prof. W. Ruland at the occasion of his 80th birthday