Order in two-dimensional projections of thin amorphous three-dimensional structures

Two-dimensional (2D) projections underlie the technique of high resolution electron microscopy. Projections of amorphous structures are generally cons idered uninterpretable due to structural disorder. We have derived the rela tionships between the distribution functions of an amorphous three-dimensio nal (3D) structure and those of the corresponding 2D projection. We have co nfirmed the relationships using calculations on models of amorphous structu res with thickness in the range from 10.6 to 43.3 Angstrom. For example the pair and triplet distribution functions of the 2D projections show peaks c orresponding to nearest neighbour distances and bond angles (respectively). The degree of order in the 2D projection decreases as thickness increases. Similar results are expected for higher order correlation functions. Thus it has been demonstrated that 2D projections of amorphous 3D structures con tain a great deal of valuable structural information.