No Of Atoms In Hcp

Devarshi Singh answered this

12 x 1/6 + 2 x 1/2 + 3 = 6 atoms per unit cell for HCP. Coordination Number Coordination number relates the number of equidistant nearest neighbors an atom has, and is different for FCC, BCC, and HCP structures. FCC The atom in the center of a close packed plane, such as fig.3a, has six nearest. ANALYSIS OF HCP UNIT CELL: 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) Posted.

coordination no. of hcp arrangement is 12 and that of ccp is 12. refer the pattern of fcc it is ABCABCABC..... type structure i n which central atom in B type is surrounded by 6 atoms from side 3 from upward and three from downward. in ccp A and C has structural difference . but both has same no. of atoms.

in hcp there is ABABAB.................. type pattern where central atom at B is surrounded by 6 atoms of B ; 3 of A from upward and 3 atoms of A From downward.

( Refer NCERT ; Class 12 ; page no 15 )

sakshi... answered this

Vinod Sharma answered this

Rohan D. Maisuria answered this

Coordination number - The coordination number of a central atom in a molecule or crystal is the number of its near neighbours.

HCP - 12

CCP - 12

D J answered this

Nikhil Soni answered this

Shweta Singh Rajput answered this

Diksha answered this

Hemant Kumar Singh Champawat answered this

so simple u dont know it very silly of u.
study a little hard

Dheeraj Thakur answered this

Somu answered this

The C.N is 12 in CCP ....6 on the same layer ......3 in the layer above it and 3 in the layer below it

Close Packing of Spheres

Two Dimensions

One can easily see that the closest packing of spheres in two dimensions is realised by a hexagonal structure: Each sphere is in contact with six neighboured spheres.

Three Dimensions

In three dimensions one can now go ahead and add another equivalent layer. However, for ideal packing it is necessary to shift this layer with respect to first one such that it just fits into the first layer's gaps.

Now the third layer can be either exactly above the first one or shifted with respect to both the first and the second one.

So there are three relative positions of these layers possible (denoted by A, B and C). These could in principle be combined arbitrarily but in nature the sequences A-B-A-B-A-B and A-B-C-A-B-C are most common. In the following we will see that the lattice that forms the latter one is just the fcc lattice which is one of the 14 Bravais lattices we encountered before. The other one is called hcp (hexagonal close packing) but not a Bravais lattice because the single lattice sites (lattice points) are not completely equivalent! There are two different types of lattice sites which have different environments. Therefore the hcp structure can only be represented as a Bravais lattice if a two-atomic basis is added to each lattice site.

The fcc Structure

Conventional Unit Cell

The conventional unit cell is a cube with edge length $a$ and 8 lattice sites at the corners and 6 additional ones at the faces of the cube.

What is the number of lattice points per unit cell>? The 8 vertices are shared by 8 cells and contribute therefore only with $frac{1}{8}$ each (think of them as extended spheres). The 6 additional points at the faces are shared by two cells and therefore contribute with $frac{1}{2}$ respectively. So this adds up to a total of begin{align} n = 8 cdot frac{1}{8} + 6 cdot frac{1}{2} = 4 end{align} points per unit cell.^[1]^[2]

Packing Density

The packing density $varrho$ is the ratio of the volume filled by the spherical atoms within a unit cell to the total volume $V_text{uc}$ of the unit cell. Overall there are $n=4$ atoms per unit cell with a volume of $V_text{sph} = frac{4}{3} pi r^3$ each. Thus for the packing density one obtains begin{align} varrho &= frac{n cdot V_text{sph}}{V_text{uc}} = frac{ 4 cdot frac{4}{3} pi cdot left( frac{sqrt{2}}{4} right)^3 a^3}{a^3} nonumber [1ex] &= frac{sqrt{2} pi}{6} approx 74% end{align} which is the highest possible for spherical objects.^[4]^[5]

Coordination Number

In the fcc structure each atom has $c_1 = 12$ nearest neighbours (coordination number) at a distance of begin{align} d_{c_1} = 2r = frac{a}{sqrt{2}} approx 0.707a end{align} and $c_2 = 6$ next-nearest neighbours at a distance of begin{align} d_{c_2} = a approx 2.83r approx 1.415 , d_{c_1} . end{align} ^[6]^[7]

The hcp Structure

No Of Atoms In Hcp Unit Cell Is

The hcp structure is characterised by two nested hexagonal lattice that are shifted by the vector $left( frac{2}{3},frac{1}{3},frac{1}{2} right)$ (in the conventional unit cell basis) against each other. The undelying lattice is not a Bravais lattice since the individual lattice points are not equivalent with respect to their environments. But it can be looked at as a hexagonal Bravais lattice with a two-atomic basis with the atoms sitting at the positions $left( 0, 0, 0, right)$ and $left( frac{2}{3},frac{1}{3},frac{1}{2} right)$.^[8]

Number Of Atoms In Hcp Unit Cell

Even though the term hcp is used for all those lattices, a close-packing of equal atoms is only obtained for a certain ratio $frac{c}{a} = sqrt{frac{8}{3}}$ of the lattice constants.^[9]