Analogies and differences between the crystalline and the disordered state

Abstract

We report on a general feature of liquid and amorphous systems (metals, ionic systems, semiconductors), namely the spherical periodicity of nearest-neighbour shell distances and its influence on several properties. The electronic states as well as the dynamic excitations are influenced by two effects: spherical periodicity creates pseudogaps in their density of states at high energies, and its limited total mass causes low-energy effects. The former are mainly responsible for the stability of the phase and for absolute values of electronic transport properties, the latter for their temperature dependencies. Under particular conditions there is a spherical-periodic resonance between the electronic states, the static structure, as well as its dynamic excitations, which may be described as a new quasiparticle, the so called spheron. Besides its influence on electronic transport properties spherons may also affect dielectric glasses. Whenever there is periodicity in an arrangement of atoms, strong influences arise on electronic states (band-structure effects) as well as on dynamic excitations due to coherent scattering effects. In crystals there are mirror planes and, accordingly, planar electron interferences and planar dynamic excitations (phonons) get formed, both with the same periodicity as the periodic arrangement of the atoms. In liquid and amorphous systems, more in the latter than in the former, over the years it became obvious that there is spatial limited, spherical-periodic order (SPO) around any atom [5]. During phase formation the SPO is caused by a selforganized optimization process of spherical resonances between two subsystems, namely the valence electrons (s+p) in total as the one and the forming static structure as the other one. It is based on characteristic momenta of both subsystems and hence is a global effect. It was recognized that, irrespective of the presence of itinerant electrons, the resonance occurs not only in metallic systems [6], but also in glassy semiconductors and insulators [7], in ionic glasses [8], as well as glassy quasicrystals [5]. Spherical periodicity is the characteristic structural feature of condensed matter at early stages. Correlated with the resonance a gap opens at the Fermi energy E F (Peierls-like) [9]. Due to this gap, electronic transport, up to localization, will strongly depend on the strength of the resonance [5,6]. Differences to the crystalline case arise from the facts that in spatially limited, spherical periodic systems there is only a broad pseudo Bragg peak instead of a sharp one in a crystal, and in addition, there is a limited total mass of the ordered region.

Second-Nearest-Neighbor Correlations from Connection of Atomic Packing Motifs in Metallic Glasses and Liquids

“…At length scales longer than that typically described by this SRO, i.e., beyond the first NNs corresponding to the first peak in the radial distribution function (RDF), characterizing the atomic structure of these materials becomes even more complicated and challenging [9,10,[20][21][22][23][24][25][26][27][28][29][30]. For example, efficient packing of quasi-equivalent "clusters" [9,10] (the motifs) has been proposed, where the packing of the polyhedra in three-dimensional space is pictured to follow an icosahedral or face-centered cubic (F.C.C) pattern.…”

“…There is also the notion of possible self-similar packing of atomic clusters with the characteristics of a fractal network of dimension 2.31 or 2.50 20 21 . Additionally, the concept of spherical-periodic order, derived from the resonance between static order and the electronic system, was modified to involve additional local crystal-like translational symmetry to describe atomic order up to the long-range scale 22 23 24 27 . However, before one can establish the nature of extended order (such as those postulated in these models, which most likely vary from one alloy system to another), a useful step is to first understand the atomic correlations with atoms in the second nearest neighbor shell.…”

On modifications of the well-known Hume-Rothery rules: Amorphous alloys as model systems

“…The r-space structure is dominated by a so-called spherical periodic order (SPO) with equidistant shells around any ad-atom, which can be considered as an analog to the mirror planes in a crystal [10]. Resonance in r-space is given by the ions located in the minima of the so-called Friedel oscillations with a wavelength k Fr = 2p/2k F .…”

On the impact of global interactions on the structure of metallic glasses

“…This leads to the occurrence of gaps (c-systems) or pseudogaps, i.e. local minima, (a-systems) bordered by maxima in the electronic density of states (DOS) [25,26]. If optimally F lies close to the centre of the (pseudo)gap, only the states shifted to lower energies are occupied and the energy of the whole system is decreased, i.e.…”

“…In that situation an a-system is especially stable since the atoms are located in the minima of the effective pair potential [3,[38][39][40]. Alternatively, the SPO can be understood as the result of a selforganisation between the atoms and the valence electrons during structure formation to adjust the interatomic distances for an optimised pseudo-Bragg scattering in order to enhance the pseudogap [25,26]. It has to be noted that the SPO, in its current form, does not distinguish between the different species in an alloy and hence cannot explain the occurrence of the individual partial pair correlation functions.…”