The structure of amorphous solids

Abstract

INTRODUCTION Before the discovery of x-ray diffraction it was relatively easy to make definite statements about 'crystalline' and 'amorphous': if the outer contours of a material showed crystal faces it was considered to be crystalline, a material showing irregular contours without faces was considered amorphous. In fact, such a definition makes proper use of the word 'amorphous', the etymological meaning of which is 'without form' and not 'disordered structure'. After the discovery of x-ray diffraction many of the substances considered as amorphous turned out to be micro-crystalline and, since the internal structure is by far more essential for the understanding of the solid state than the outer contours, the word 'amorphous' was more and more used in the sense 'disordered structure' or 'frozen-in liquid structure' which means that an amorphous structure is considered essentially 'non-crystalline' and with some resemblance to the structure of liquids. It was especially the latter aspect which was pursued in the earlier studies of the glass structure1' 2 and in the interpretation of rubber elasticity3—6. The most general statement one can make about the difference between 'crystalline' and 'amorphous' is that the former implies a three-dimensional long-range order whereas the latter does not. Since intermediate structures with one-dimensional or two-dimensional long-range order exist (e.g. in liquid crystals) and the term 'amorphous' is in general not used for such structures, it is more appropriate to use the term 'non-crystalline' for all structures which do not possess a three-dimensional long-range order and reserve the term 'amorphous' for those structures which do not have a long-range order in any direction. General agreement exists as far as the absence of long-range order is concerned; however, there is a definite disagreement about the basic feature of the short-range order in liquid and liquid-like structures. One school, of which the main protagonist is Bernal7, postulates that this shortrange order bears no resemblance whatsoever to the crystalline order whereas the other, of which the principal advocate is Hosemann8, considers a 'paracrystalline' structure as representative for all types of short-range order. The attraction of the 'paracrystalline' concept is its relatively concise theory which greatly facilitates the interpretation of scattering diagrams, whereas the Bernal model does not lend itself easily to a straightforward mathematical treatment so that a quantitative check of its validity by scattering experiments is extremely difficult. It is not the aim of this paper to review the earlier work done in this field, for which one finds an excellent bibliography by Kruh9, but to discuss some