The Solid State - Unit Cells Video Lecture | Additional Study Material for Class 12

in this module you will learn about the
number of atoms in a unit cell
you already know that every crystal
lattice is made of an infinite number of
unit cells and every lattice site is
occupied by a constituent particle
that may be an atom an ion or a molecule
now let's examine what portion of each
particle belongs to a particular unit
cell
consider three types of cubic unit cells
for the sake of simplicity assume that
the constituent particle is an atom
let's start with a simple or primitive
cubic lattice
a simple cubic lattice consists of 8
atoms at the eight corners of a cube
in the open structure shown here the
distances between the atoms are greatly
exaggerated
in reality the atoms are packed much
more closely together as shown in the
space filling model here
the space-filling model shows that the
atoms touch along the edges of the cell
by considering the potion of atoms
inside the cell boundary we can generate
a unit cell of a simple cubic lattice
from this it is evident that each atom
at the corners contributes 1/8 of its
original volume to each unit cell
there are eight atoms at the eight
corners
does the number of atoms in each unit
cell is equal to 8 corner atoms into 1
by 8 of an atom per unit cell which is
equal to 1
a body-centered unit cell contains 8
corner atoms just like in a simple cubic
unit cell
however there is one more atom at its
body center
as a result the atoms at the corners no
longer touch along the edges of the cell
in the space filling model
you
the unit seller for body centered cubic
cell is shown here
you
it is clear that the eight atoms at the
Conner's contribute 1/8 of their actual
volume each
in addition one atom lies completely
inside the cell
therefore the number of atoms at the
corners per unit cell is equal to 8
corner atoms into 1 by 8 of an atom per
unit cell which is equal to 1
there is one atom at the center of the
cube
does the total number of atoms in a
body-centered cubic unit cell is too
the face centered cubic lattice consists
of 8 corner atoms just like in the
simple and body centered cubic lattice
however it also contains six more atoms
at the six faces of the cube cell
the atoms touch along the diagonals and
each touches four corner atoms
you
a unit cell of a face-centered cubic
cell is shown here
you
it is clear that the atoms at the
corners contribute 1/8 of their original
volume each
in addition there are six atoms at the
six phases which contribute half of
their original volume each
the number of atoms at the corners full
unit cell is equal to 8 corner atoms
into 1 by 8 of an atom per unit cell
which is equal to 1
number of atoms present at the faces per
unit cell is equal to six atoms at the
faces into half an a temper unit cell
which is equal to three
does the total number of atoms per
face-centered cubic unit cell is 4
you have now reached the end of this
module in this module you learned that
every crystal lattice is made of an
infinite number of unit cells and every
lattice site is occupied by a
constituent particle there is one atom
in a simple cubic unit cell there are
two atoms in a body-centered unit cell
there are four atoms in a face-centered
unit cell