Page 112 - Materials Chemistry, Second Edition

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2.3. The Crystalline State

metal and ligands. For instance, the blue color of the gemstone lapis lazuli (i.e.,
(Na, Ca) 8 (Al, Si) 12 O 24 (S, SO 4 )), is due to ligand-metal charge transfer (LMCT)
initiating from the sulfur atoms in the ligand. [55]

Properties resulting from crystal anisotropy
Crystals are classified as being either isotropic or anisotropic depending on the
equivalency of their crystallographic axes. All crystals that do not belong to
the cubic crystal system possess anisotropic symmetry. Since electromagnetic
radiation partially comprises an electrical component, the velocity of light passing
through a material is partially dependent upon the electrical conductivity of the
material. The relative speed at which electrical signals travel through a material
varies with the type of signal and its interaction with the electronic structure of the
solid, referred to as its dielectric constant (e or k).
Anisotropic crystals are composed of a complex crystal lattice orientation that has
varying electrical properties depending upon the direction of the impinging light ray.
As a result, the refractive index will vary with direction when light passes through an
anisotropic crystal, giving rise to direction-specific trajectories and velocities. This
effect is most easily observed in crystals when there are large differences in the
refractive indices of the crystallographic axes. This phenomenon is referred to as
birefringence and is illustrated by the double refraction exhibited by optical calcite
shown in Figure 2.65. Examples of the two distinct refractive indices for represen-
tative crystals are calcite (1.6584 and 1.4864), tourmaline (1.669 and 1.638), and
rutile (2.616 and 2.903). The birefringence exhibited by a crystal is dependant on the
difference in the refractive indices experienced by the extraordinary and ordinary
rays as they propagate through a crystal.
If birefringence occurs in a colored crystal, the observed color is often dependent
on the viewing angle, as already discussed above for alexandrite. This phenomenon
is known as pleochroism, and is caused by the incident light beam following
different paths within the crystal, with each path absorbing different colors of
light. Whereas tetragonal, trigonal, and hexagonal crystals often show two colors
(dichroic, Figure 2.66a), orthorhombic, monoclinic, and triclinic crystals may

"Ordinary Ray"

"Extraordinary Ray"

Calcite crystal
"Fast medium"
(relatively small index
of refraction)

Figure 2.65. Illustration of the double refraction phenomenon exhibited by calcite crystals.