Find the following parameters for HCP structure (i) co-ordination No. (ii) Atomic Radius (iii) No of atoms per unit cell (iv) APF (v) c/a ratio.

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teamques10 ★ 68k

Cell of an HCP lattice is visualized as a top and bottom plane of 7 atoms, forming a regular hexagon around a central atom. In between these planes is a half-hexagon of 3 atoms.
There are two lattice parameters in HCP,a andc, representing the basal and height parameters respectively.

The number of atoms that surround a central atom in a solid is calledcoordination number.
Each atom in structure is positioned in the empty space formed by 3 adjacent atoms of the top layer and by 3 adjacent atoms in bottom layer and is surrounded by 6 neighbour atoms in the middle layer
All these 12 atoms are in contact with atom under consideration, hence the coordination number of the atoms in this structure is 12.
The packing factor is 0.74.
The HCP structure is very common for elemental metals and some examples include beryllium, cadmium, magnesium, titanium, zinc and zirconium.
There are 6 number of atoms per unit cell.
The APF(atomic packing factor) is the ratio of the total sphere volume, to the unit cell volume, .
For HCP, there are the equivalent of six spheres per unit cell, and thus

Now, the unit cell volume is the product of the base area times the cell height, c.
The base area can be calculated as follows. The following figure shows an HCP unit cell and the basal plane. The base area is equal to six times the area of the equilateral triangle.

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