Crystal binding
Crystalline material can be classified in many ways. For example,
crystals can be classified according to their mechanical properties. etc. The
most convenient basis for the classification of crystal is the character of the
inter-atomic binding force in various types of crystalline materials.
The atoms of a solid are bound together. This is called
crystal binding we consider all types of matter in the solid form. For example, we consider even gases in the solid form and treat them as crystals. The binding
of the atoms is due to the mutual attraction between the atoms.
However a solid
has very low compressibility which means it is very difficult to compress a
solid and decrease its volume. We conclude that the atoms after crossing an
equilibrium configuration, if brought still closer will try to repel each
other. Therefore in the atomic scale, the attraction exists only at a distance greater
than the critical distance. When we bring the atoms closer the critical distance
is only repulsion.
When two atoms
are brought closer there is a repulsive interaction coming into play in
addition to the attractive interaction. This repulsive interaction is due to the electronic charge overlapping of the atoms and Pauli’s exclusion principle
when the two charge distributions are just separated and repulsion.
Pauli’s principle states that the two electrons in an atom cannot
have all the quantum numbers alike. At least one quantum number should be
different. When the charge distributions overlap, the outermost orbits of the
two atoms also overlap. Thus there is a tendency for the two electrons having
like spins to occupy the same orbit.
This is impossible. Therefore the
electrons in the first orbit are excited to the higher state and the overlapping
electron occupies its position therefore the total energy of the system
increases. We know that the attraction decreases the energy and therefore the
tendency for an increase of energy will produce repulsion.
Periodic arrays of atoms
A crystal is identified by two properties namely periodicity
and symmetry. These two properties give the crystal a regular shape. Periodicity
means the repetition of atoms at regular intervals. Symmetry means that the
configuration remains indistinguishable after an operation like translation rotation or reflection is performed.
In actual
crystals, either an atom or a group of atoms is repeated in space. The group of
atoms is called the basic in the theoretical study of crystal structure; the basis
is replaced by points. Which means the entire crystal is replaced by an
imaginary array of points. Such a theoretical arrangement is called a space
lattice.
The actual
crystal structure is obtained by replacing the lattice points with the basis. In the lattice,
the points are shown separately. But in the actual crystal structure, the atoms are
jam-packed.
The space lattice is a regular periodic array of points in space.
The crystal structure is formed when a basis of atoms is attached identically
to every lattice point.
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