Noncrystalline solids – three-dimensional imperfections

Some engineering materials lack the repetitive, crystalline structure. These noncrystalline, or amorphous, solids are imperfect in 3 dimensions. The 2-dimentional schematic of Fig. 4.22a shows the repetitive structure of a hypothetical crystalline oxide. Fig. 4.22b shows a noncrystalline version of this material. The latter structure is referred to as the Zachariasen model and, in a simple way, it illustrates the important features of oxide glass structures.

Fig.4.22. Two-dimensional schematics give a comparison of (a) a crystalline oxide and (b) a noncrystalline oxide. The noncrystalline material retains short-range order (the triangularly coordinated building block) but loses long-range order Noncrystalline solids – three-dimensional imperfections (crystallinity).


1) The building block of the crystal (the AO3-3 “triangle”) is retained in the glass; that is, short-range order (SRO) is retained.

2) Long-range order (LRO) – that is, crystallinity – is lost in the glass.

3) The Zachariasen model is the visual definition of the random network theory of glass structure. This is the analog of the point lattice associated with crystal structure.

Our first example of a noncrystalline solid was the traditional oxide glass because many oxides (especially the silicates) are easy to form in a noncrystalline state. This is the direct result of the complexity of the oxide crystal Noncrystalline solids – three-dimensional imperfections structures. Rapidly cooling a liquid silicate or allowing a silicate vapor to condense on a cool substrate effectively “freezes in” the random stacking of silicate building blocks (SiO4-4 tetrahedra). Since many silicate glasses are made by rapidly cooling liquids, the term-supercooled liquid is often used synonymously with glass.


In fact, there is a distinction.

1) The supercooled liquid is the material cooled just below the melting point, where it still behaves like a liquid (e.g., deforming by a viscous flow mechanism).

2) The glass is the same material cooled to a sufficiently low temperature that it has become Noncrystalline solids – three-dimensional imperfections a truly rigid solid (deforming by an elastic mechanism).

The atomic mobility of the material at these low temperatures is insufficient for the theoretically more stable crystalline structures to form. Those semiconductors with structures similar to some ceramics can be made in amorphous forms also.


1) There is an economic advantage to amorphous semiconductors compared to preparing high-quality single crystals.

2) A disadvantage is the greater complexity of the electronic properties.

3) The complex polymericstructure of plastics causes a substantial fraction of their volume to be noncrystalline.

4) Very popular the newest member of the class amorphous metals, also known as Noncrystalline solids – three-dimensional imperfections metallic glasses.

Because metallic crystal structures are typically simple in nature, they can be formed quite easily. It is necessary for liquid metals to be cooled very rapidly to prevent crystallization. Cooling rates of

10C per microsecond are required in typical cases. This is an expensive process but potentially worthwhile due to the unique properties of these materials.


The uniformity of the noncrystalline structure eliminates the grain boundary structures associated with typical polycrystalline metals. This results in unusually high strengths and excellent corrosion resistance. Fig. 4.23 illustrates a useful method for visualizing an amorphous metal structure:

Bernal model Noncrystalline solids – three-dimensional imperfections, which is produced by drawing lines between the centers of adjacent atoms. The resulting polyhedra are comparable to those illustrating grain boundary structure in Fig. 4-20. In the totally noncrystalline solid, the polyhedra are again irregular in shape but, of course, lack any repetitive stacking arrangement.

Fig.4.23. Bernal model of an amorphous metal structure. The irregular stacking of atoms is represented as a connected set of polyhedra. Each polyhedron is produced by drawing lines between the centers of adjacent atoms

At this point it may be unfair to continue to use the term imperfect as a general description of noncrystalline solids. The Zachariasen Noncrystalline solids – three-dimensional imperfections structure (Fig. 4.22b) is uniformly and “perfectly” random. Imperfections such as chemical impurities, however, can be defined relative to the uniformly noncrystalline structure as shown in Fig. 4.24.

Addition of Na+ ions to silicate glass substantially increases formability of the material in the supercooled liquid state (i.e., viscosity is reduced).

Finally, the state-of-the-art in our understanding of the structure of noncrystalline solids is represented by Fig. 4.25, which shows the nonrandom arrangementof Ca2+ modifier ions in a CaO-SiO2 glass.

Fig.4-24. A chemical impurity such as Na+is a glass modifier, breaking up the random network and Noncrystalline solids – three-dimensional imperfections leaving non-bridging oxygen ions.

What we see in Fig. 4.25 is, in fact, adjacent octahedral rather than Ca2+ ions. Each Ca2+ ion is coordinated by 6 O2- ions in a perfect octahedral pattern. In turn, the octahedral tend to be arranged in a regular, edge-sharing fashion. This is in sharp contrast to the random distribution of Na+ ions implied in Fig. 4.24. The evidence for medium-range order in the study represented by Fig. 4.25 confirms long-standing theories of a tendency for some structural order to occur in the medium range of a few nanometers,

Fig.4.25. Schematic illustration of medium Noncrystalline solids – three-dimensional imperfections-range ordering in a CaO-SiO2 glass. Edge sharing CaO6 octahedra have been identified by neutron diffraction experiments.

between the well-known short-range order of the silica tetrahedral and the long-range randomness of the irregular linkage of those tetrahedral. As a practical matter, the random network model of Fig.4.22b is an adequate description of vitreous SiO2

Medium-range order such as that in Fig. 4.25 is, however, likely to be present in common glasses containing significant amounts of modifiers, such as Na2O and CaO.

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