Physical Chemistry of Foods

(singke) #1
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.

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