On an atomic level, these macroscopic distinctions arise from a basic difference in the nature of the atomic motion. Figure 1--> contains schematic representations of atomic movements in a liquid and a solid. Atoms in a solid are not mobile. Each atom stays close to one point in space, although the atom is not stationary but instead oscillates rapidly about this fixed point (the higher the temperature, the faster it oscillates). The fixed point can be viewed as a time-averaged centre of gravity of the rapidly jiggling atom. The spatial arrangement of these fixed points constitutes the solid's durable atomic-scale structure. In contrast, a liquid possesses no enduring arrangement of atoms. Atoms in a liquid are mobile and continually wander throughout the material.

There are two main classes of solids: crystalline and amorphous. What distinguishes them from one another is the nature of their atomic-scale structure. The essential differences are displayed in Figure 2-->. The salient features of the atomic arrangements in amorphous solids (also called glasses), as opposed to crystals, are illustrated in the figure for two-dimensional structures; the key points carry over to the actual three-dimensional structures of real materials. Also included in the figure, as a reference point, is a sketch of the atomic arrangement in a gas. For the sketches representing crystal (A) and glass (B) structures, the solid dots denote the fixed points about which the atoms oscillate; for the gas (C), the dots denote a snapshot of one configuration of instantaneous atomic positions.

Atomic positions in a crystal exhibit a property called long-range order or translational periodicity; positions repeat in space in a regular array, as in Figure 2A-->. In an amorphous solid, translational periodicity is absent. As indicated in Figure 2B-->, there is no long-range order. The atoms are not randomly distributed in space, however, as they are in the gas in Figure 2C-->. In the glass example illustrated in the figure, each atom has three nearest-neighbour atoms at the same distance (called the chemical bond length) from it, just as in the corresponding crystal. All solids, both crystalline and amorphous, exhibit short-range (atomic-scale) order. (Thus, the term amorphous, literally “without form or structure,” is actually a misnomer in the context of the standard expression amorphous solid.) The well-defined short-range order is a consequence of the chemical bonding between atoms, which is responsible for holding the solid together.

In addition to the terms amorphous solid and glass, other terms in use include noncrystalline solid and vitreous solid. Amorphous solid and noncrystalline solid are more general terms, while glass and vitreous solid have historically been reserved for an amorphous solid prepared by rapid cooling (quenching) of a melt—as in scenario 2 of Figure 3-->.

Figure 3-->, which should be read from right to left, indicates the two types of scenarios that can occur when cooling causes a given number of atoms to condense from the gas phase into the liquid phase and then into the solid phase. Temperature is plotted horizontally, while the volume occupied by the material is plotted vertically. The temperature T_b is the boiling point, T_f is the freezing (freezing point) (or melting) point, and T_g is the glass transition temperature. In scenario 1 the liquid freezes at T_f into a crystalline solid, with an abrupt discontinuity in volume. When cooling occurs slowly, this is usually what happens. At sufficiently high cooling rates, however, most materials display a different behaviour and follow route 2 to the solid state. T_f is bypassed, and the liquid state persists until the lower temperature T_g is reached and the second solidification scenario is realized. In a narrow temperature range near T_g, the glass transition occurs: the liquid freezes into an amorphous solid with no abrupt discontinuity in volume.

The glass transition temperature T_g is not as sharply defined as T_f; T_g shifts downward slightly when the cooling rate is reduced. The reason for this phenomenon is the steep temperature dependence of the molecular response time, which is crudely indicated by the order-of-magnitude values shown along the top scale of Figure 3-->. When the temperature is lowered below T_g, the response time for molecular rearrangement becomes much larger than experimentally accessible times, so that liquidlike mobility (Figure 1-->, right) disappears and the atomic configuration becomes frozen into a set of fixed positions to which the atoms are tied (Figures 1-->, left, and 2B-->).

Some textbooks erroneously describe glasses as undercooled viscous liquids, but this is actually incorrect. Along the section of route 2 labeled liquid in Figure 3-->, it is the portion lying between T_f and T_g that is correctly associated with the description of the material as an undercooled liquid (undercooled meaning that its temperature is below T_f). But below T_g, in the glass phase, it is a bona fide solid (exhibiting such properties as elastic stiffness against shear). The low slopes of the crystal and glass line segments of Figure 3--> in comparison with the high slope of the liquid section reflect the fact that the coefficient of thermal expansion of a solid is small in comparison with that of the liquid.

Bonding types and glass transition temperatures of representative amorphous solidsIt was once thought that relatively few materials could be prepared as amorphous solids, and such materials (notably, oxide glasses and organic polymers) were called glass-forming solids. It is now known that the amorphous solid state is almost a universal property of condensable matter. The Table (Bonding types and glass transition temperatures of representative amorphous solids) presents a list of amorphous solids in which every class of chemical bonding type is represented. The glass transition temperatures span a wide range.

Bonding types and glass transition temperatures of representative amorphous solidsIn the gold-silicon system of Figure 5, at compositions far from the cusp, glasses cannot be formed by melt quenching—even by the rapid splat-quench technique of Figure 4. (This is the reason that the T_g curve of Figure 5 spans only compositions near the cusp.) Amorphous solids can still be prepared by dispensing with the liquid phase completely and constructing a thin solid film in atom-by-atom fashion from the gas phase. Figure 4D shows the simplest of these vapour-condensation techniques. A vapour stream, formed within a vacuum chamber by thermal evaporation (vaporization) of a sample of the material to be deposited, impinges on the surface of a cold substrate. The atoms condense on the cold surface and, under a range of conditions (usually a high rate of deposition and a low substrate temperature), an amorphous solid is formed as a thin film. Pure silicon can be prepared as an amorphous solid in this manner. Variations of the method include using an electron beam to vapourize the source or using the plasma-induced decomposition of a molecular species. The latter technique is used to deposit amorphous silicon from gaseous silane (SiH₄). Among the amorphous solids listed in the Table (Bonding types and glass transition temperatures of representative amorphous solids), those that normally require vapour-condensation methods for their preparation are silicon (Si), germanium (Ge), water (H₂O), and the elemental metallic glasses iron (Fe), cobalt (Co), and bismuth (Bi).

Amorphous solids, like crystalline solids, exhibit a wide variety of atomic-scale structures. Most of these can be recognized as falling within one or another of three broad classes of structure associated with the following models: (1) the continuous random-network model, applicable to covalently bonded glasses, such as amorphous silicon and the oxide glasses, (2) the random-coil model, applicable to the many polymer-chain organic glasses, such as polystyrene, and (3) the random close-packing model, applicable to metallic glasses, such as Au_0.8Si_0.2 gold-silicon. These are the names in conventional use for the models. Although each of them contains the word random, the well-defined short-range order means that they are not random in the sense that the gas structure of Figure 2C--> is random.

An illustration of the continuous random-network model is shown in Figure 7A--> and of the random-coil model in Figure 7B-->. Figure 7A--> reproduces a famous diagram published by W.H. Zachariasen in 1932. It is for a hypothetical two-dimensional A₂B₃ glass in which every A atom is bonded to three B atoms and every B atom to two A atoms. This picture bears a reasonable resemblance to current models for the arsenic chalcogenide glasses As₂S₃ and As₂Se₃. (Sulfur, S, and selenium, Se, belong to the group of elements called chalcogens.) The model was introduced as a schematic analogue for the network structure of the oxide glasses. The prototypical oxide glass is amorphous SiO₂, or silica glass. (Quartz, which is present in sand, is a crystalline form of SiO₂.) In amorphous SiO₂ each silicon atom is bonded to four oxygen atoms, and each oxygen atom is bonded to two silicon atoms. This structure is difficult to represent in a two-dimensional picture, but Figure 7A--> is a useful analogue with the hollow circles representing oxygen atoms and the small solid dots representing silicon atoms. The fourth bond originating at each silicon can be imagined to be out of the plane of the diagram.

The network structure shown in Figure 7A--> clearly demonstrates how short-range order (note the triangle of neighbours surrounding each solid dot) is compatible with the absence of long-range order. At the bridging oxygen atoms, the bond angles have some flexibility, so it is easy to continue the network. Common oxide glasses are chemically more complex than SiO₂, as discussed in the next section. Chemical species such as phosphorus and germanium, which (like silicon) enter into the structure of the network by forming strong chemical bonds with oxygen atoms, are called network formers. Chemical species such as sodium and calcium, which do not bond directly to the network but which simply sit (in ionic form) within its interstitial holes, are called network modifiers.

A large fraction of the everyday materials called plastics (plastic) are amorphous solids composed of long-chain molecules known as polymers (polymer). Each polymer chain has a backbone consisting of a string of many (up to roughly 100,000) carbon atoms bonded to each other. These organic polymeric glasses are present in innumerable familiar molded products (e.g., pens, tires, toys, appliance bodies, building materials, and automobile and airplane parts). The random-coil model of Figure 7B-->, first proposed in 1949 by P.J. Flory (Flory, Paul J.) (who later received a Nobel Prize in Chemistry for his pioneering work on polymers), is the established structural model for this important class of amorphous solids. As schematically sketched in the figure, the structure consists of intermeshed, entangled polymer chains. The chain configurations are well-defined, statistically, by a mathematical trajectory called a three-dimensional random walk.

Characteristics of oxide glassesThe above glasses all have silica as the glass former. With other glass formers, glasses have special properties. For example, if boric oxide is present, X rays are transmitted and rare-earth glasses will exhibit low dispersion and a high refractive index. Phosphate glasses (used as optical glasses) based on phosphorus pentoxide (P₂O₅) are highly resistant to hydrofluoric acid and act as efficient heat absorbers when iron oxide is added. The Table (Characteristics of oxide glasses) gives the compositions and physical properties of some typical commercial oxide glasses of the types described.

Some of the general differences between the properties of crystals and glasses, in addition to the fundamental one of the glass transition (as discussed above in connection with Figure 3--> and also below with regard to its value in technological settings), are noted here. The atomic-scale disorder present in a metallic glass causes its electrical conductivity to be lower than the conductivity of the corresponding crystalline metal, because the structural disorder impedes the motion of the mobile electrons that make up the electrical current. (This lower electrical conductivity for the amorphous metal can be an advantage in some situations, as discussed below in the section Magnetic glasses (amorphous solid).) For a similar reason, the thermal conductivity of an insulating glass is lower than that of the corresponding crystalline insulator; glasses thus make good thermal insulators. Crystals and glasses also differ systematically in their optical spectra, which are the curves that describe the wavelength dependence of the degree to which the solid absorbs infrared, visible, or ultraviolet light. Although the overall spectra are often similar, crystal spectra typically exhibit sharp peaks and other features that specifically arise as a consequence of the long-range order of the crystal's atomic-scale structure. These sharp features are absent in the optical spectra of amorphous solids.

Characteristics of oxide glassesThe continuous liquid-to-solid transition near T_g, the glass transition, has a profound significance in connection with classical applications of glasses. While crystallization abruptly transforms a mobile, low- viscosity liquid to a crystalline solid at T_f, near T_g the liquid viscosity increases continuously through a large range in the transformation to an amorphous solid. Viscosity, expressed in units of poise, is used in the Table (Characteristics of oxide glasses) to specify characteristic working temperatures in the processing of the liquid precursors of various oxide glasses. A poise is the centimetre-gram-second (cgs) unit of viscosity. It expresses the force needed to maintain a unit velocity difference between parallel plates separated by one centimetre of fluid: one poise equals one dyne-second per square centimetre. Molten glass may have a viscosity of 10¹³ poise (similar to honey on a cold day), and it quickly gets stiffer when cooled since the viscosity steeply increases with decreasing temperature. The ability to “tune” the viscosity of the melt (by changing temperature) allows glass to be conveniently processed and worked into desired shapes; glassblowing is a classic example of the usefulness of this widely exploited property.

The Table--> lists some important technological uses of amorphous solids. In addition to the application, the general type of amorphous solid used, and the material properties that make the application possible, the table also includes information about the chemical compositions of typical materials employed in these techniques. While the first entry—namely, window glass—represents the present status of a centuries-old technology, the other entries correspond to technologies that have blossomed during the second half of the 20th century. A significant theme of the Table--> is the role of amorphous solids in applications calling for large-area sheets or films. Amorphous solids often have great advantages over crystalline solids in such applications, since their use avoids the functional problems associated with polycrystallinity or the expense of preparing large single crystals. Thus, while it would be prohibitively expensive to fabricate large windows out of crystalline SiO₂ (quartz), it is practical to do so using SiO₂-based silicate glasses.

Characteristics of oxide glassesThe terms glass and window glass are often used interchangeably in everyday language, so familiar is this ancient architectural application of amorphous solids. Not only are oxide glasses, such as those characterized in the Table (Characteristics of oxide glasses), excellent for letting light in, they are also good for keeping cold out, because (as mentioned above) they are efficient thermal insulators.

The second application in the Table--> represents a modern development that carries the property of optical transparency to a phenomenal level. The transparency of the extraordinarily pure glasses that have been developed for fibre-optic telecommunications is so great that, at certain wavelengths, light can pass through 1 kilometre (0.6 mile) of glass and still retain 95 percent of its original intensity.

polystyrene, the organic polymer listed in the Table-->, is a prototypical example of a polymeric glass. These glasses, whose atomic-scale structure has been discussed in connection with Figure 7B-->, make up a broad class of lightweight structural materials important in the automotive, aerospace, and construction industries. These materials are also ubiquitous in everyday experience as plastic molded objects. The quantity of polymer materials produced each year, measured in terms of volume, exceeds the quantity of steel produced.

Amorphous silicon thin films are used in solar cells (solar cell) that power handheld calculators. This important amorphous semiconductor is also used as the image sensor in facsimile (fax) (“fax”) machines, and it serves as the photoreceptor in some xerographic copiers. All these applications exploit the ability of amorphous silicon to be vapour-deposited in the form of large-area thin films. As shown in the Table-->, the practical form of this amorphous semiconductor is not pure silicon but a silicon-hydrogen alloy containing 10 percent hydrogen. The key role played by hydrogen, in what is now called hydrogenated amorphous silicon, emerged in a scientific puzzle that took years to solve. Stated briefly, hydrogen eliminates the electronic defects that are intrinsic to pure amorphous silicon.

The last entry in the Table--> is an application of metallic glasses having magnetic properties. These are typically iron-rich (iron) amorphous solids with compositions such as Fe_0.8B_0.2 iron-boron and Fe_0.8B_0.1Si_0.1 iron-boron-silicon. They are readily formed as long metallic glass ribbons by melt spinning or as wide sheets by planar flow casting. Ferromagnetic glasses are mechanically hard materials, but they are magnetically soft, meaning that they are easily magnetized by small magnetic fields. Also, because of their disordered atomic-scale structure, they have higher electrical resistance than conventional (crystalline) magnetic materials. The three attributes of ease of manufacture, magnetic softness, and high electrical resistance make magnetic glasses extremely suitable for use in the magnetic cores of electrical power transformers. High electrical resistance (which arises here as a direct consequence of amorphicity) is a crucial property in this application, because it minimizes unwanted electrical eddy currents and cuts down on power losses. For these reasons, sheets of iron-based magnetic glasses (glass) are used as transformer-core (transformer) laminations in electrical power applications.

Works on solids in general include Lawrence H. Van Vlack, Elements of Materials Science and Engineering, 6th ed. (1989), an elementary textbook; Charles A. Wert and Robb M. Thomson, Physics of Solids, 2nd ed. (1970), an intermediate-level text; Charles Kittel, Introduction to Solid State Physics, 6th ed. (1986), the standard college textbook; Neil W. Ashcroft and N. David Mermin, Solid State Physics (1976), an advanced textbook; George E. Bacon, The Architecture of Solids (1981), an introduction to bonding and structure; and Linus Pauling, The Nature of the Chemical Bond and the Structure of Molecules and Crystals, 3rd ed. (1960, reissued 1989), the classic reference work on chemical bonding.Gerald D. Mahan On amorphous solids in particular, a lucid introductory text accessible to a nontechnical reader is Richard Zallen, The Physics of Amorphous Solids (1983), with coverage of structural models for the various classes of amorphous solids as well as percolation theory, a modern paradigm for disordered systems. A classic advanced work is N.F. Mott and E.A. Davis, Electronic Processes in Non-crystalline Materials, 2nd ed. (1979), which features many of the theoretical contributions of Nobel Laureate coauthor Mott. A text providing a thorough treatment of oxide glasses is J. Zarzycki, Glasses and the Vitreous State (1991; originally published in French, 1982). A reference work with wide coverage of recent research topics, including detailed treatment of chalcogenide glasses, is S.R. Elliott, Physics of Amorphous Materials, 2nd ed. (1990). A comprehensive collection of detailed reviews is contained in R.W. Cahn, P. Haassen, and E.J. Kramer (eds.), Materials Science and Technology, vol. 6, Glasses and Amorphous Materials, ed. by J. Zarzycki (1991), including coverage of glass technology, formation, and structure, oxide glasses, chalcogenide glasses, metallic glasses, polymeric glasses, and the optical, electric, and mechanical properties of glasses. Amorphous silicon is treated in detail in another work, R.A. Street, Hydrogenated Amorphous Silicon (1991).Richard Zallen