Crystallography: An Introduction

Abstract

Renal calculi are predominantly formed from crystals of one or more substances. Crystals can be defined as groups of particles accurately and orderly arranged in 3 dimensions.

A crystal is different from glass, in that particles are not orderly arranged in the latter. It is sufficient to examine the fracture planes of both materials to have a hint of the regularity of the first and of the disorder of the second, at the level of the disposition of the respective constituent units.

The particles forming the crystal, i.e. atoms, ions or molecules, are set at a reciprocate distance of about 10^-8 cm. It is fortunate for the investigators that such a value coincides with the wavelength of x rays. Crystal-x ray interaction, called “diffraction”, allow us to “see” these distances, which are as charactersitic, as an identity card for each crystalline “phase.”

This is why crystallographic methods enable us to recognize the crystals of a given substance. The observed distances are different in the case of a salt (e.g. calcium oxalate) and its hydrate derivative (calcium oxalate bihydrate). They are different in the case of tricalcium phosphate, Ca₃ PO₄, and of acid calcium phosphate, Ca HPO₄. They are different even in the case of the two classical natural modifications (or “crystalline phases”) of Ca C03, namely calcite and aragonite.

Along with progress in knowledge, crystallography has developed new methods, always based on x ray-crystal interaction, which allows us to obtain a quantitative detection of a substance present in a renal stone, even in very small amounts.

More recently, with the aid of electron microscopy, interesting speculations have been put forward about the modalities of crystal growth, based on morphological observation of crystals. The investigations were carried on together with the mathematical analysis of energetic phenomena on the specific deposition surfaces and with the study of dimensions of elementary granules. It is assumed that elementary particles per se do not give rise to growth by regular arrangement, but only in the presence of small pre-aggregated nuclei, forming the growth units.

Together with qualitative and quantitative diagnosis, the problem of the growth of a renal calculus is one of the most fascinating aspects for a crystallographer. It is to be hoped that close cooperation with urologists will help in solving such a basic problem.