Physical Chemistry of Foods

the water molecules present allow a closer packing and/or a greater number

of hydrogen bonds.

Crystal Systems. To understand several aspects of crystallization,

it is useful to know about a few of the rudiments ofcrystallography.

Crystallographers study the geometrical structure of crystals. They

consider an idealized picture of a crystal, ignoring the nonidealities

mentioned above. A crystal then is defined as aninfinite real homogeneous

discontinuum. The infinity is introduced to keep the mathematics simple. The

crystal is discontinuous at the scale of the building entities or smaller, but is

homogeneous in the sense that at a larger scale all regions are identical.

To characterize a crystal lattice, straight lines are drawn through fixed

points, such as the centers of the molecules or of a particular atom in each

molecule. Plane faces then are constructed through parallel lines. The

perfect order of an ideal crystal lattice guarantees that such straight lines

and plane faces can be constructed. The planes will have a variety of

directions and will thus enclose volume elements. The smallest volume

element that contains all geometrical information about the lattice is called a

unit cell. The whole crystal can be considered as a perfect three-dimensional

stacking of unit cells. Figure 15.2a gives an example where the unit cell is a

cube. There are molecules at each of the eight corners of the cube.

Nevertheless, the unit cell contains the equivalent of one molecule, since

each of the molecules is part of eight adjacent cells. This is not the only

manner in which molecules can form a cubic unit cell. The two other

possibilities are also shown. In (b) the unit cell contains two, in (c) four

molecules.

It can be shown that 14 different unit cells orBravais latticescan be

distinguished (three of which are in Figure 15.2). By convention these are

grouped into seven crystal systems (or by some authors into six). These are

FIGURE15.2 Cubic unit cells. The dots represent building entities (often single and
identical molecules). The dotted lines are drawn to clarify the position of dots not at
the corners. (a) Simple cubic. (b) Body-centered cubic. (c) Face-centered cubic.