Geometry and Topology of Structure in Amorphous Solids
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I.
INTRODUCTION
MECHANICAL, optical, magnetic and electronic properties of amorphous materials hold great promise towards current and emergent technologies. Gallium arsenide is used for infrared transmitting glasses and night vision (FLIR) systems. IR transmitting fibers and bundles are used as sensor lenses and temperature sensors (Amorphous Materials Inc., Garland, TX). Current research on amorphous silicon includes memory devices, field effect transistors, and image sensors. The ferromagnetic properties of metallic glasses have also received a great deal of attention because of the possibility that these materials can be used as transformer cores. Amorphous materials are used as pharmaceuticals. Obsidian is used in cardiac surgery because the cutting edge is many times sharper than high-quality steel surgical scalpels. There are numerous research groups around the world working on amorphous materials.[1] The knowledge of the atomic-scale structure of crystalline and pseudo-crystalline solids has been gained over the past century because of the developments in mathematical crystallography and X-ray diffraction. A most important element in this success is the fact that the methods of crystallography are based on the concept of an ideal (perfect) crystal in which unit cells or building blocks of the material are stacked in perfectly repeating rows and columns to form a periodic array of atoms or molecules (of infinite extent). Although real crystals only ever approximate this ideal (some not very closely), it is this ideal structure that is always used as a permanent base-line relative to which real crystalline materials are compared, and can be understood. For amorphous or glassy materials, this method is largely unavailable because of the lack of definition of ZBIGNIEW H. STACHURSKI, A/Professor, is with the College of Engineering and Computer Science, Australian National University, Canberra, Australia. Contact e-mail: [email protected] T. RICHARD WELBERRY, Professor, is with the Research School of Chemistry, Australian National University, Canberra, Australia. Manuscript submitted February 15, 2010. Article published online July 23, 2010 14—VOLUME 42A, JANUARY 2011
the ideal amorphous structure. A search of recently published literature on atomic structure of metallic glassy alloys will reveal that the main effort towards solving this problem is directed to atomistic molecular dynamics simulations. As glassy materials are nonequilibrium structures, one should anticipate that the results of each simulation, carried out in different laboratories, will be different; no asymptotically unique structure can be achieved by this method. In light of the preceding discussion, we conjecture that this is not the right approach to define the base-line model for the structure of amorphous materials. Instead, a geometrical model should be sought. Such a geometrical ideal amorphous solid (IAS) based on monosized spheres has been described in detail previously.[2]
II.
TOPOLOGY AND ATOMIC CLUSTERS
The construction of an
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