The paracrystalline model of as-deposited tetrahedral amorphous semiconductor thin films was developed in response to fluctuation microscopy measurements showing that as-deposited amorphous germanium (a-Ge) thin films exhibit significant medium-range order which is reduced by thermal annealing (Treacy et al 1998,Treacy and Gibson 1997). A paracrystalline film consists of small grains (< 3 nm) which have topologically crystalline bonding but within which the atoms are significantly displaced from their crystalline lattice positions by strain caused by the grain boundaries. Because the grains are dilute and strongly deformed, they appear amorphous to diffraction experiments. They do however contribute significant medium-range order to the material which is detectable by fluctuation microscopy.
Simulations of the electron microscopy imaging process from paracrystalline models yield structure in V(k) similar to that observed in fluctuation microscopy experiments. Simulations from a variety of continuous random network (CRN) structures created by different authors using different methods and potentials show no such structure (Treacy et al 1998).
The first paracrystalline models were constructed by Keblinski using molecular dynamics quenching from the melt with the Stillinger-Weber potential (Treacy et al 1998). These models provide better agreement with experimental V(k) than any CRN and approximate matches to the experimental vibrational density of states and Raman spectra. However, they contain too many coordination defects to match the experimental electron density of states (Voyles et al 2001a). Better models have been constructed also by Keblinski by melt-quench using the Bazant-Kaxiras environment-dependent interatomic potential (Voyles et al 2001a). The best models so far were constructed by Nakhmanson with a variation of the Wooten, Wiener, and Weaire (WWW) bond-switching algorithm (Nakhmanson et al 2001). In these models, the topological crystallinity is preserved by construction by forbidding bond switches in small crystalline volumes of the model. The WWW models have a small bond angle standard deviation, a vibrational density of states in good agreement with experiment, a clean electronic band gap, and the best agreement so far of any model with the fluctuation microscopy experiments (Nakhmanson et al 2001). Some of the valence band tail states are found to be localized on the grain boundaries, suggesting that grain boundaries in paracrystalline silicon may be electrically active (Nakhmanson et al 2001).
The idea of “topological crystallinity” is put on a firmer footing using analysis of Schlafli clusters (Treacy et al. 2000a, Treacy et al 2000b). An atom’s Schlafli cluster consists of those atoms and bonds that close all the rings emanating from the central atom. All small-unit-cell (i.e. not zeolites) four-connected crystals have topologically distinct Schlafli clusters, so we refer to an atom that has a Schlafli cluster found in a crystal as “topologically crystalline”. The Schlafli cluster idea was previously developed in another context by L. H. Hobbs et al.
Nucleation and Recrystallization in Amorphous Al-alloys
Our FEM results on amorphous Al92Sm8 show that rapid quenching of this alloy from the liquid leads to the formation of small ordered clusters similar in structure to crystalline Al (Stratton 2005). Figure 1 shows FEM data V(k) for Al92Sm8 amorphized by rapid quenching and by intense mechanical deformation. For the as-quenched glass, the peaks in V(k) correspond to the Al (200) and (220) reflections. Simulations confirm that these peaks arise from Al-like clusters. These measurements were performed at 1.5 nm spatial resolution, which limits the cluster size to a range of approximately 1-3 nm.
The mechanically amorphized sample, on the other hand, shows no peaks in any Al reflection position, indicating a completely different form of nanoscale order. Mechanically amorphized Al92Sm8 also does not crystallize to Al nanocrystals, strongly suggesting that the Al-like clusters in the as-quenched samples drive that crystallization reaction.
Figure 1: V(k) measured at 1.5 nm spatial resolution for amorphous Al92Sm8, as-quenched, quenched then annealed at 140 deg C, and mechanically amorphized. The as-quenched V(k) has peaks at the Al (200) and (220) reflections at 0.49 A-1 and 0.69 A-1 respectively. The mechanically amorphized V(k) shows no crystalline Al-like peaks.
Annealing the quenched samples causes a reduction in V(k) at both peak positions, indicating a reduction in nanoscale order. The reduced order could come from a reduction in the size of the clusters, their density, or both. (It is not possible to separate the effects of size and density from this data.) This suggests that at least some of the clusters we are measuring are subcritical in size and therefore unstable at this annealing temperature. Future experiments will further probe the relaxation of these subcritical clusters.
All of these structural results are consistent with the quenched-in nuclei hypothesis: we see small clusters with the same internal structure as the eventual crystallization products. Some of the clusters are subcritical, and the clusters are not present in a sample with different crystallization. Similar FEM results indicating nanoscale Al-like clusters have also been observed in rapidly quenched Al88Y7Fe5.
This work is supported by the US National Science Foundation under contract DMR-0347746.