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, Chapter 1
Crystal Structure of Solids
1.1. Introduction
Matter exists in three states: solid, liquid and gas. The
structure of solids form the backbone of the study of the
various properties of solids.
Classifications of solids:
1. Crystalline solids
2. Amorphous solids
Crystal is a Greek word meaning clear ice and this word
was originally used for quartz. Johannes Kepler wrote a
book ‘Hexagonal Snow’ in which it is described that
snow is built of closely packed spheres with hexagonal
,symmetry-first thought of symmetry in nature.
1.2. Close Packing of Atoms:
The packing of atoms in a
minimum total volume is
called close packing. Fig.
1.1 shows the close packing
of atoms in a plane.
Packing fraction is defined as
f p = Va / V0 (1.1)
1.3. Crystal lattice and basis:
Lattice consists of an infinite periodic array of points
in three dimensions. It is a mathematical abstraction.
, The translation vector can be written as
3
Rn = na
i =1
i i (1.2)
The choice of the lattice points is not unique. Fig. 1.2
shows some choices of the lattice points. Crystal is
formed by associating a basis of atoms with each lattice
point. The position of the
mth atom in the nth cell is
given as
R nm = R n + R m (1.3)
3
R m = mi ai (1.4)
i=1
, Chapter 1
Crystal Structure of Solids
1.1. Introduction
Matter exists in three states: solid, liquid and gas. The
structure of solids form the backbone of the study of the
various properties of solids.
Classifications of solids:
1. Crystalline solids
2. Amorphous solids
Crystal is a Greek word meaning clear ice and this word
was originally used for quartz. Johannes Kepler wrote a
book ‘Hexagonal Snow’ in which it is described that
snow is built of closely packed spheres with hexagonal
,symmetry-first thought of symmetry in nature.
1.2. Close Packing of Atoms:
The packing of atoms in a
minimum total volume is
called close packing. Fig.
1.1 shows the close packing
of atoms in a plane.
Packing fraction is defined as
f p = Va / V0 (1.1)
1.3. Crystal lattice and basis:
Lattice consists of an infinite periodic array of points
in three dimensions. It is a mathematical abstraction.
, The translation vector can be written as
3
Rn = na
i =1
i i (1.2)
The choice of the lattice points is not unique. Fig. 1.2
shows some choices of the lattice points. Crystal is
formed by associating a basis of atoms with each lattice
point. The position of the
mth atom in the nth cell is
given as
R nm = R n + R m (1.3)
3
R m = mi ai (1.4)
i=1
