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I

T’S A CURIOUS THING that elementary physical chemistry can describe a

molecule-based model of the gas phase (from the various gas laws to the

kinetic theory of gases) and the solid phase, but not the liquid phase. At one

extreme, the behavior of gas particles is so independent and random that we

can model their behaviors statistically. At the other extreme, the crystalline

solid, the individual particles (whether atoms, ions, or molecules) are distrib-

uted so regularly that it takes little knowledge to be able to describe the entire

solid. The liquid phase has neither advantage, so its description is not so sim-

ple and is considered beyond the scope of this book. (In some respects, this is

unfortunate, since many processes that are most important to us—like the

biological processes of life itself—occur in the liquid phase.)

Because of the regularity in a well-ordered solid, we can describe its struc-

ture, properties, and behaviors mathematically. That connects the study of the

solid phase to physical chemistry: we can model our understanding of the solid

state. That’s what physical chemistry does: provide models for understanding

matter. Since much of matter is in (or can be in) the solid state, a model for

understanding the solid phase is useful, just as having a model for the gas phase

is useful. This chapter introduces some of the concepts used to understand the

solid phase.

21.1. Synopsis

First, we will consider the general types of solids. Many solids do not exist as

a random arrangement of atoms and molecules. Some do, but we will focus on

those solids that exist as some regular arrangement of atoms or molecules. We

will find that there are only a few possible ways for regular arrangements,

called crystals, to exist. First, we will describe those ways. It turns out that the

regularity of crystals can be described by a very small arrangement of atoms

and molecules; this very small arrangement, repeated many times in three di-

mensions, can tell us a lot about the properties of the solid.

How do we determine these regular arrangements? As with spectroscopy,

we can use electromagnetic radiation as a probe. But rather than absorbing

or emitting radiation, crystalline solids can diffract radiation under certain

21.1 Synopsis

21.2 Types of Solids

21.3 Crystals and Unit Cells

21.4 Densities

21.5 Determination of
Crystal Structures

21.6 Miller Indices

21.7 Rationalizing Unit Cells

21.8 Lattice Energies of
Ionic Crystals

21.9 Crystal Defects and
Semiconductors

21.10 Summary

The Solid State: Crystals