Step-(2) Another 2D hexagonal
close sheet (B-layer)
is taken and it is just over the depression (Pit) of the first layer (A) .When
the second layer is placed in such a way that its spheres find place in the ‘b’ voids
of the first layer, the ‘c’ voids will be left unoccupied. Since under
this arrangement no sphere can be placed in them, (c voids), i.e. only half (50%)
the triangular voids in the first layer are occupied by spheres of the second
layer (i.e. either b or c)
Step-(3) There are two
alternative ways in which spheres in the third layer can be arranged over the
second layer
(1) When
a third layer is placed over the second layer in such a way that the spheres
cover the tetrahedral
or ‘a’ voids; a three dimensional closest packing is obtained where
the spheres in every third or alternate layers are vertically aligned (i.e. the
third layer is directly above the first, the fourth above the second layer and
so on) calling the first layer A and second layer as layer B, the arrangement is
called ABAB …………. pattern
or hexagonal
close packing (HCP) as it has hexagonal symmetry.
ANALYSIS OF HCP UNIT CELL:
(1) Number of effective atoms in HCP unit cell (Z):
Lattice point: corner- total
12 carbon contribute 1/6 to the unit cell
Lattice point: face- total face 2
contribute ½
Lattice point: body centre- total atom 3
(100% contribution)
(2) Radius of atom in HCP unit cell:
Let the edge of
hexagonal base =( a) And the height
of hexagon =( h) And radius of
sphere =( r)
(3) Area of hexagon:
Area
of hexagonal can be divided into six
equilateral triangles with side 2r
(4) Height of HCP unit cell:
(5) Volume of hexagon = area of base x height
(6) Volume of spheres:
(7) Packing efficiency:
Percentage of space occupied by sphere.
(8)
Voids %: 100 - PE= 26 %
(9) Coordination
Numbers: 12 (each spheres touches 6
spheres in its layer,3 above and 3 below).
Most recommended books of Physical Chemistry Books
Book
by O.P Tandon
(2) Physical chemistry
Book by KS Verma (Cengage
Publications)
(3) Physical Chemistry
Book by P.W. Atkins (Oxford publication)
(4) Physical Chemistry
Book by P. Bahadur
(5) Physical Chemistry
Book by Ranjeet
Shahi (Arihant publication)
(6) Balaji Advanced problems
in Physical chemistry
Book by Narendra
Awasthi
(7) Modern
Approach to Chemical Calculations
Book by R.C. Mukherjee
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