Chapter 2
B.sc 1st year Book
(Page 4)
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1 Periodic variation of Atomic and Ionic Radii

Periodic variation of Atomic and Ionic Radii

In a group: in a group moving from top to bottom atomic and ionic radii increases regularly with an increase in atomic number. This is due to an increase in the number of orbital cells. The increase in the number of shells tends to increase the covalent radii while the increase in effective nuclear.
charge Z∗ tend to decrease the covalent rad in a group which is not compensated by the nuclear charge as shown in table 2.6. Also, the size of a cation decreases with an increase in oxidation states e.g.
increase in oxidation states
Comparative values of covalent, atamic and ionic radiiIn a period: On moving from left to right in a period of the periodic table the value of covalent. ionic and atomic rad decreases with the increase of atomic number. In the case of normal elements, the values of atomic radii for the elements of the second period are given in table 2.7 in A.
Atomic radii in A of second-period elements
Thus, in a period alkali metals show the largest values of atomic radii whereas halogens (excluding the zero groups) show the smallest values.

Structure of ionic solids :
The ionic crystals include salts, oxides, hydroxides, sulfides, and other inorganic compounds. An Ionic crystal contains a large number of cations and anions These ions are arranged in space in such a way to produce maximum stability. An ionic crystal contains a large number of cations and anions. Evidently, cations are smaller in size than anions. These Ions are arranged in such a way that there is more electrostatic attraction between the oppositely charged ions than the electrostatic repulsive forces between the same charged ions. The total number of nearest oppositely charged ions by which a given ion is surrounded is called the ‘coordination number‘. Thus, the coordination number of a cation is the number of nearest anions by which the cation is surrounded and vice-versa. In the case of Ionic crystal of AX-type e.g. NaCl, ZnS, CsCl, etc. In which both the cation and anion Cl Ions are six each. But it differs in the case of ionic crystals of the type AX2 orA2X. For example in CaF2 and Na2S, the number of each kind of ion is not the same i.e. the coordination number of the positive ion is different from that of the negative ion. In the case of CaF2, the coordination number of Ca2+ ions is just double that of F−ion i.e. the coordination number of Ca2+ and F−ions are 8 and 4 respectively.

Radius ratios (Rr) in ionic Crystals:

The structure of ionic solids depends upon the relative ratio of cations and anions. The ratio of ionic radius of cation and anion in AX crystal.
Lap. radius ratio is called ‘radius ratio’. With the help of radius radio (Rf), it is possible to predict the coordination number of ions and their arrangement in a different ionic crystal.
Let us consider radius ratio values for the trigonal sites. If a cation is surrounded by three negative ions (X-) Fig. 2.05 (a). It was found by simple geometry that the radius ratio of cation and anion is equal to0.155 which is a lower limit for the coordination number 3, thus the structure of solid is trigonal planar. If the value is less than 0.155 then the positive Ion is still shorter and has no contact with anions. It rattles in the hole and the structure of the solid is unstable fig. 2.05 (c) then in between these two, a limiting case arises when the X-ions are also in contact with one another as shown in fig2.05 (b).
Sizes of Ions for coordination number 3
Now it the radius ratio is greater than 0.155 then it is possible to fit three Xions around each
cation. With the increase in the size of cations, the radius ratio also increases, and at the point, radius ratiois equal to 0.255, there is a possibility to fit four anions around one cation, then the structure of the solid is tetrahedral. Similarly, there is the possibility to fit 6 or 8 anions around one cation.
Value of radius ratio and structure
Value of radius ratio and structure

Where ‘ccp’ is cubic close packing and ‘hcp’ is hexagonal close packing Thus, the radius ratio plays a very important role in deciding the stable structure of the ionic crystal.

Larger cations prefer to occupy larger holes (cubic) and smaller cations prefer to occupy smaller holes (tetrahedral) The preferred direction of the structure with an increase in the radius ratio is as follows:
Planar triangular(0.225) < Tetrahedral (0.414)< Octahedral(0.732)< Cubic (>0.732)

Classification and structure of ionic solids :
There are different groups of ionic compounds of the type AX, AX2, A2X1, and AX3 depending on the relative number of positive and negative ions e.g. NaCl, ZnS1, CaF2, Na2S, CrCl2, and Cl l2, etc.

Structure of Sodium Chloride :
In NaCl, the radius ratio is 0.524 which lies between 0.414 to 0.732 (Table 2.8), which suggests that the crystal has either a square planar or octahedral structure, an X-ray study of NaCl crystal has shown that the crystal has octahedral structure li. e, each. Cl−ion is surrounded by six Na+ions (placed at the comers of a regular octahedron) and each Na+ ion is surrounded by six Cr – ions. In other words, the stoichiometry of Na+Cl is 1=1 and the coordination number is 6:6.figuro (2.06 ).

A face centre structure of Rock saft (NaCl)

Structure of Zinc Chloride :
The value of radius ratio in ZnS is 0.40 which lies between 0.255 to 0.414and suggests a tetrahedral arrangement of ions i.e each Zn2+ ion is surrounded by four S2- ions and each S2- ion is surrounded by four Zn2+ions tetrahedrally. The coordination number of both ions is 4 and the stoichiometry is 4:4. There are two different forms of Zinc sulfide ore, one is Zinc blende and the other is wurtzite. Both have a 4:4 structure. The structure of the Zinc blende is a cubic close pack (ccp) Whereas the wurtzite structure is a hexagonal close pack (hcp). In both, structures Zn2+ ions occupy tetrahedral holes in the lattice.

Structure of Cesium Chloride :
This ionic crystal has a radius ratio value of 0.93 which lies between 0.732 to 0.999. Thus, this crystal has a body-centered cubic (bcc) arrangement. lie, each Cs+ ion is surrounded by eight Cl−ions and vice-versa. In other words, the coordination number is 8:8 and the stoichiometry of Cs+C- is 1:1.

Body centred structure of CsCl

Structure of Calcium Fluoride :
The value of the radius ratio in CaF2 is 0.73. In this case, each Ca2+ ion is surrounded by eight F−ions, giving a body-centered cubic arrangement of F−ions around each Ca2+ion and four Ca2+ ions are tetrahedrally arranged around each F – ion. Thus, the coordination number of Ca2+ and F−ions are 8 and 4 respectively and the stoichiometry of CaF2 is 8:4.

Limitations of radius ratio concept: The radius ratio concept of ionic crystals is valid when:
1- the accurate ionic radii are known.
2- ions are spherical in shape and behave as hard inelastic spheres.
3- the arrangement of ions is stable and they will touch each other.
4- the bonding between the ions is 100% logical in character.
5- Ions may adopt the highest possible coordination number.

Importance of radius ratio in atoms: Although radius ratio predicts the correct structures we can figure out that in many cases the values of ionic radii can not be measured absolutely. However, they are estimated. The radius of ions is not constant, it varies with change in their arrangements in ionic solid. In other words, the ionic radius changes with a change in coordination number. As discussed earlier smaller ions do not fit the site, it must either rattle or be compressed. In the case of transitional elements, ions are not hard inelastic spheres and do not have a center of symmetry. The transition metal ions of some specific groups viz. in IVB and IB, the arrangement of electrons in d-electrons produces ‘Jathn- Teller distortion‘ which is due to unequal distribution of electrons in t2g and eg orbitals. Such partially-filled orbitals give rise to a structure with some long and some short bonds resulting in a distorted structure. It is also not possible that bonding is absolutely 100% ionic. There must be a small contribution of covalency.
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