Direct Energy, 2018a

1 INTRODUCTION 13
rial may dier. Electrons can ow more easily through a pure crystalline
material while electrons are more likely to be scattered or absorbed as they
ow through an amorphous material, crystalline materials with impurities,
or a crystalline material with crystal defects.
We can further classify crystals as either isotropic or anisotropic [10,
p. 210]. A crystal is isotropic if its macroscopic structure and material
properties are the same in each direction. A crystal is anisotropic if the
macroscopic structure and material properties are dierent in dierent directions.
We can also classify materials based on how they behave when a voltage
is applied across the material [11]. In a conductor, electrons ow easily
in the presence of an applied voltage or electric eld. In an insulator,
also called a dielectric, electrons do not ow in the presence of an applied
voltage or electric eld. In the presence of a small external voltage or
electric eld, a semiconductor acts as an insulator, and in the presence of a
strong voltage or electric eld, a semiconductor acts as a conductor. Both
solids and liquids can be conductors, and both solids and liquids can be
insulators. For example, copper is a solid conductor while salt water is a
liquid conductor.
1.5.2 Microscopic Properties
The electron conguration lists the energy levels occupied by electrons
around an atom. The electron conguration can describe neutral or ionized
atoms, and it can describe atoms in the lowest energy state or excited
atoms. For example, the electron conguration of a neutral aluminum atom
in the lowest energy state is 1s 2 2s 2 2p 6 3s 2 3p 1 . The electron conguration
of an aluminum Al + ion in the lowest energy state is 1s 2 2s 2 2p 6 3s 2 , and the
electron conguration of a neutral aluminum atom with an excited electron
can be written as 1s 2 2s 2 2p 6 3s 2 4s 1 .
Electrons are labeled by four quantum numbers: the principle quantum
number, the azimuthal quantum number, the magnetic quantum number,
and the spin quantum number [6] [12]. No two electrons around an atom
can have the same set of quantum numbers. The principle quantum number
takes integer values, 1, 2, 3 and so on. All electrons with the same principle
quantum number are said to be in the same shell. The large numbers in
the electron conguration refer to principle quantum numbers. The neutral
aluminum atom in the lowest energy state has two electrons in the 1 shell,
eight electrons in the 2 shell, and three electrons in the 3 shell. For most
atoms, especially atoms with few electrons, electrons with lower principle
quantum numbers both are spatially closer to the nucleus and require the