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Coordination Number

The shape of solid is composed ofatoms, molecules or ions which are placed at a particular point orplace. The basic structure of solid can explain by a crystallattice where each point or atom or ion is called a lattice point. Asmallest part of lattice point which can form the entire lattice byrepeating itself is called as unit cell. The arrangement of latticepoint in unit cell determines the structure of crystal lattice.

In crystal structure; the latticepoints are represented in hard sphere model which states that atomsare like solid spheres.

There are three possible arrangements in crystal lattice; FaceCentred Cubic (FCC), Body Centred Cubic (BCC) and Hexagonal ClosePacked (HCP). Body Centred Cubic is not a close packing like rest oftwo arrangements; FCC and HCP. In this arrangement; one central atomis surrounded by eight symmetrically placed atoms.

The Coordination Number of Bcc iseight. The Coordination Number 8indicates that each point/ atom/ ion is surrounded by other eightatoms/ions. Just like coordinationnumber 4 stands that each lattice point is surrounded by otherfour units. This type of packing is much more common in metals andferric materials such as in steel, chromium, Vanadium, Tungsten andtungsten.


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In a close packed structure; thecentral atom is known as coordinator and the distance between atomsshows the distance between the central atom and the neighbouringatoms.

Let’s calculate this distance andcoordination number BCC. Abody centred cubic structure can be shown as below;


  Coordination Number


Form the triangle ABC;

(AC)2 = (AB)2 +(BC)2

Assume; AB = AD="BC=CD=a

Therefore; (AC)2 = a2+a2

AC=a√2

Since AM="AC/2

Therefore; AM="a√2/2

From triangle AMP; (AP)2 =(AM)2 + (MP)2

Since MP="a/2" , hence (AP)2=(a√2/2)2 + (a/2)2

AP= a√3/2 = 0.866a

Hence AP = BP="CP=DP=EP=FP=GP=HP=" 0.866a


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With this small distance; there are twopossible packing structures in which one contains a central atom atthe centre of the unit cell, and second contains the central atom atone of the vertices. The central atom at the center can coordinateswith the eight atoms which are located at the vertices of the unitcell.

The central atom at the vertex canshare by eight unit cells which coordinate with twelve atoms. In Bodycentered cubic structure; the first layer of square array expandedand second layer is fitted in the empty part of this layer. Thereforethis arrangement is also called as ABA....type of arrangement. It isless close packed arrangement as the packing efficiency is only 68%.


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