There are at least 17 known crystalline forms of water (Brini et al. 2017). Thus, the phase diagram of water has several triple points, as well as one critical point and possibly more (Mochizuki and Koga 2015). A simplified phase diagram is presented in Figure 2.12. It can be seen that one of the most familiar phases of ice, given pressure and temperature conditions on Earth's surface, is hexagonal ice, I h.
The hexagonal structure of ice, I h, cannot be easily seen in bulk ice, but can be readily seen sometimes, under drier conditions/low humidity, in a single freshly fallen flake of snow (Figure 2.13). The structure is noticeable because a snowflake forms by the accumulation of water molecules (H2O) directly from the vapor phase to solid state. Solidification from the vapor phase is relatively slower in the upper atmosphere (due to low pressures and temperatures) than that from liquid water, and this slow growth allows for the demonstration of the hexagonal crystal structure of ice, I h. In ice, the basic hexagonal structure is driven by the hydrogen‐bonding interactions between six molecules, but all six oxygen (O) atoms are not in one plane. Figure 2.13b illustrates the arrangement of water molecules forming I h. Out of the six O‐atoms, three are in one plane and the other three are on a different plane. Figure 2.13c illustrates a schematic diagram of the basal plane of I h, showing the locations of the oxygen atoms (open and closed circles in two slightly different planes, 9.23 nm apart), c‐axis, or optic‐axis (perpendicular to the page), and one of the three a‐axes; broken line joining two oxygen atoms in the same plane provides a measure of the distance (45.23 nm) between molecules. A standard snowflake can be made up of over a quintillion (1018) molecules. While the I h structure forms the basis, temperature and humidity also play a role in the growth of plates, prisms, dendrites, columns, and even needles. This variety combined with natural defects that occur during crystal growth gives rise to the beautiful variation of snowflakes (Brini et al. 2017).
Figure 2.12 Simplified phase diagram of water showing stable ice polymorphs.
Source: Adapted from Chaplin (n.d.) and Brini et al. (2017).
Figure 2.13 Snowflake and hexagonal ice. (a) Natural snowflake photographed near the North Pole by N. K. Sinha in 1989.
Source: International Glaciological Society (2009).
(b) Arrangement of water molecules forming a hexagonal structure with surrounding water molecules in gray. (c) Positions of oxygen atoms in (0001) or basal plane. (d) Hexagonal prism with three equatorial axes: a1, a2, and a3, and one c‐axis or optic‐axis, ˂0001˃.
2.7 Ceramics
As defined in Section 2.1, ceramics are inorganic materials primarily held by covalent or ionic bonds. The ceramic class of materials thus encompasses a broad range of materials, including the network glasses explored in Section 2.4. In this section, we focus on crystalline ceramics and ceramic composites.
Ceramics include some of the earliest man‐made materials, such as brick and pottery produced from clay. Modern ceramics include the widely used asphalt concrete in roads and pavements, high dielectric materials used in electronics, and strong, lightweight, high‐temperature materials for engines and turbines.
The crystalline structures of ceramic materials are generally more complex than those of metals due to their composition of atoms of widely different sizes and bonding capability. In ionic bonding, the development of negatively charged ions or anions and positively charged ions or cations strongly impacts the structural characteristics of the ceramic. Although ionic bonds are nondirectional, spatial considerations lead to positive ions being surrounded by negative ions in definite ordered structures that depend on the nature of the cation. The coordination number (CN), which is the number of atoms/ions bonded to a central atom, also depends on the relative sizes of the atoms involved. The structure of many ceramics, particularly those with large oxygen anions, often includes smaller ions occupying interstitial sites.
Figure 2.14 Schematic of (a) NaCl structure with sixfold polyhedral coordination and (b) zincblende structure with tetrahedral coordination.
Common ceramics structure includes the rock salt/sodium chloride (NaCl) structure and the zinc blende (ZnS) structure. The NaCl structure can be best thought of as two interpenetrating FCC latices, as shown in Figure 2.14a. If we start with chlorine anions at FCC points, the sodium cations occupy spaces in the middle of each choline to form a second FCC structure. In this 1:1 compound, all ions have a CN = 6 forming a polyhedral coordination structure with six neighbors. The ZnS structure is also based on the FCC structure. It can be thought of as two interpenetrating FCC lattices with one displaced by 1/4 of the diagonal along a cubic cell such that each site is tetrahedrally coordinated (CN = 4), as shown in Figure 2.14b. If all the atoms in the ZnS structure are carbon atoms, this would form diamond.
Ceramic materials are generally particularly strong in compression and shear. Dislocation movement is much harder in ceramics than metals due to the dissimilar nature of the atoms in the crystal structure – especially when opposite charges exist as the strong repulsive forces of nearby ions act as strong barriers to motion. The number of possible slip directions is generally lower in ceramics and the force required to cause movement is greater. Ceramics also tend to have higher melting points and are, generally, more resistant to chemical attack than metals and alloys. On the other hand, because ceramics do not flow under stress, they tend to be very brittle and will likely fail by cracking mechanisms. Acoustic emissions have been used to study the development and propagation of cracks; this is discussed in more detail in Chapter 4.
As