E1 Crystal Structure and Ionic-Covalent Bond

Topic

The mixed nature of the chemical bond in a ceramic—simultaneously ionic and covalent—serves as the starting point for this model. Its ultimate effect is the material's characteristic brittleness, which arises from the combination of two distinct aspects of the crystal structure: one stemming from the chemical bond itself, and the other from the geometric arrangement of the ions. Because this brittleness results from the combination of these two aspects, it cannot be explained by considering either one in isolation. We begin by examining the aspect derived from the bond.

This ionic-covalent bond possesses a certain degree of ionic character, as measured by Pauling's rule. A greater electronegativity difference between the bonded atoms increases the bond's ionic character, whereas a smaller difference renders the bond more covalent.

Higher ionic character in the bond leads to higher lattice energy in the crystal: the more ionic the bond between the constituent ions, the stronger the electrostatic attraction between them, and the greater the lattice energy accumulated by the crystal.

The second factor contributing to ceramic brittleness stems from the geometric arrangement of these same ions: the ratio of the cation radius to the anion radius determines the coordination number—that is, the number of neighboring ions of opposite charge surrounding each ion within the crystal structure. A higher cation-to-anion radius ratio (meaning the cation is large relative to the anion) allows more anions to fit around each cation, thereby increasing the coordination number; conversely, a lower ratio allows fewer anions to fit, resulting in a lower coordination number. The fact that lattice energy—derived from the ionic character of the bond—and coordination number—derived from the cation/anion radius ratio—act in concert (rather than in isolation) means that, together, they determine the characteristic brittleness of ceramics predicted by this model; neither factor alone suffices to explain that brittleness.

Consequently, this characteristic brittleness—stemming from the mixed nature of the chemical bond introduced at the start of this model—conceptually informs another model in this series: the one describing the fundamental mechanical properties of ceramics based on that very brittleness. Establishing this brittleness here allows that other model to take it as a starting point without needing to redefine it.

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