Aperiodic Mineral Structures: From Modulated To Quasicrystals.pdf

The discovery of aperiodic crystals began in the 1970s, challenging the long-held belief in the three-dimensional periodic nature of crystalline structures. This shift was prompted by observations of incommensurately modulated structures and satellite reflections surrounding main reflections in diffraction patterns.

Key Developments:

1. Superspace Theory: It was theoretically shown that crystal structures requiring more than three integers to index their diffraction patterns could be described as periodic in a higher-dimensional space, or superspace. The physical structure observed is then a three-dimensional intersection of this superspatial structure.

2. Discovery of Aperiodic Structures: Following the initial discovery of modulated structures, composite and quasicrystal structures were also identified.

3. Advancements in Data Collection: The use of CCD and imaging plate systems significantly improved the sensitivity for collecting data on aperiodic structures, leading to the development of computer programs capable of refining incommensurately modulated structures using the superspace approach.

4. Natural Occurrence: Several natural minerals with aperiodic structures have been identified, including natrite, calaverite, melilite, fresnoite, pearceite-polybasite, and cylindrite. Notably, icosahedrite and decagonite are the first naturally occurring stable quasicrystalline structures, confirming their long-term stability.

Historical Context:

The law of rational indices, once considered universally valid for indexing crystalline faces, faced challenges early on, as exemplified by calaverite (Au1-xAgxTe2) observations. Mineralogists like Penfield, Ford, Smith, Goldschmidt, Palache, and Peacock questioned its general applicability due to the presence of faces with irrational indices. Their conclusions were not fully accepted until half a century later when more sophisticated indexing methods emerged.

Today, superspace theory provides a framework for understanding and describing aperiodic crystal structures, bridging the gap between their complex atomic arrangements and their observable properties in physical space.