Alternative Approaches to the Crystallographic Description of Charge Density Wave Modulated Systems

Abstract

It has become increasingly evident that many compounds do not easily conform to the standard definition of a crystalline solid, i.e. that of a lattice of atoms repeating periodically in three dimensions. As early as the beginning of this century, it was already known that in some minerals (e.g. calaverite Au_1-xAg_xTe₂) the crystal faces violate the standard rule of rational indices [1,2]. However, it was not until after the discovery of X-rays and their subsequent use in structure determination that the origin of phenomena like crystal structure modulation and its incommensurability with the undistorted lattice could be investigated [3,4,5]. However, since modulation effects as a rule represent small perturbations of the basic structure, the corresponding X-ray diffraction effects are also weak. In addition, these effects are often restricted to small domains, which are below the resolution of X-ray analysis. The development of transmission electron microscopy and diffraction, with a wide variety of diffraction and microanalytical techniques, opened up new avenues of investigation. Structures modulated commensurately or incommensurately in one, two and three dimensions were found in metals, semiconductors and insulators [1,6]. These modulations can be generally classified as displacive or compositional in origin. Whereas in cases of compositional ordering and intergrowth phases [7,8,9], the very concept of modulation can often be questioned (since it is not always clear which of the sublattices should be considered the basic one), a displacive modulation as a rule exhibits weak distortions which follow a charge density [10] or magnetic ordering [11].