What Is A Coordination Number

Coordination Number, Void, Ionic Radii and Radius Ratio Rule

Coordination Number, Void, Ionic Radii and Radius Ratio Dominion:

Coordination Number:

It is the number of spheres that are in contact with a item sphere in the closest packing. Both hexagonal shut packing (hcp) and cubic close packing (ccp) modes of stackings have a coordination number of 12 considering a sphere in these arrangements has 12 closest neighbours- six other spheres in its ain layer, 3 spheres in the layer above and 3 in the layer below.

Factors affecting coordination number:

Size of central particle- If the central particle is minor in size and then it can accommodate a lesser number of peripheral particles compare to a state of affairs where the cardinal particle is big in size.
Size of peripheral particles- If the size of peripheral particles is smaller then the coordination number of the cardinal particle volition be larger compare to a state of affairs where particles size of peripheral particles is larger.
Temperature and pressure level- Increase in pressure decreases the interparticle distance hence increases coordination number and reverse happen if the temperature is depression.

Type of Voids:

In hcp besides as in ccp, only 74% of the available space is occupied by spheres. The remaining space (26%) left unoccupied betwixt the spheres in close packing constitutes interstices, voids or holes. On arranging the 2d layer of spheres over triangular voids (B or C) of the first layer, two types of voids are obtained in three-dimensional shut packing.

Tetrahedral Voids- These are ordinary voids in the 2d layer over the spheres of the showtime layer and are shown in the effigy as 'B' voids. Thus a elementary triangular void bounded by four spheres (one of the first and three of the 2nd) is known as a Tetrahedral void because the centres of these four spheres are at the corners of a regular tetrahedron. In close packing, the number of tetrahedral voids is double the number of spheres; one above the sphere and i below the sphere. The radius of the tetrahedral void relative to the radius of the sphere is 0.225 i.e. r_void = 0.225 x r_sphere.
Octahedral Voids- These type of voids are produced past the combination of two triangular voids, one of the 2d layer and the other unoccupied void of the beginning layer and are shown in the figure every bit 'C' voids. Thus a double triangular void divisional by six spheres is known as an octahedral void because this is enclosed between six spheres, the centres of which occupy corners of a regular octahedron. The number of octahedral voids is equal to the number of spheres. The radius of the octahedral void relative to the radius of the sphere is 0.414 i.e. r_void / r_sphere = o.414. Thus, an octahedral void is larger than a tetrahedral void.

Ionic Radii:

If ions are considered to exist spheres, so the radius of the sphere is ionic radii or it may be defined equally the distance from the centre of the nucleus up to the point the electron cloud of that ion exists. It shows an increasing trend on moving downward a group from top to bottom while a decreasing trend on moving from left to right along a period.

Radius Ratio Rules:

In crystals generally, the anions (larger ions) form a close-packed arrangement and the cations (smaller ions) fit into the interstitial sites. For the stability of an ionic compound, each cation should exist surrounded past a maximum number of anions and vice-versa which depends upon the radius ratio. Radius Ratio may be defined as the ratio of the radius of cation to the radius of the anion of the ionic solid.

Radius Ratio = Radius of the Cation (r⁺)/Radius of the Anion (r^–)

A cation volition fit exactly into an octahedral void and would have a coordination number of six if r⁺/r^– = 0.414.

Similarly, if r⁺/r^– = 0.225, the cation volition fit exactly into a tetrahedral void and have a coordination number of four. The relationship between the radius ratio, coordination number and the structural arrangement is chosen radius ratio rules and are given below-

Radius Ratio (r⁺/r^–)	Coordination Number of Cation	Structural System of Anions effectually the Cation	Examples
0 to 0.155	2	Linear	—–
0.155 – 0.225	3	Plane-Triangular	B₂O₃
0.225 – 0.414	4	Tetrahedral	ZnS
0.414 – 0.732	6	Octahedral	NaCl
0.732 – i.000	8	Torso-Centred Cubic	CsCl