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Co-ordination Number
It is defined as the number of atoms surrounding a particular atom and is known as co-ordination number.
- In simple cubic close packing co-ordination number is 6
- In hexagonal close packing number of co-ordination is 12
- In cubic close packing co-ordination number is 12
Voids
Vacant space remains unoccupied during close packing is termed as voids.
There are two types of voids:
- Tetrahedral void
- Octahedral void
1. Tetrahedral void: A void which is surrounded by four spheres; the shape of the void is not tetrahedral but the arrangement of atoms is tetrahedral. For each atom there are two tetrahedral voids.
r(void)/r(sphere)= 0.225
2. Octahedral void: A void which is surrounded by 6 spheres. The shape of void is not octahedral but arrangement of atoms around the void is octahedral. Number of voids for each atom is 1.
r(void)/r(sphere)= 0.414
Ques: Derive relation between r(void) & R(sphere) in tetrahedral void.
Ques: Derive relation between r(void) & R(sphere) in octahedral void.
Packing in Ionic solids
In ionic solids anions occupy lattice points and cations occupy voids.
Ques: What is radius ratio? Give its significance
Radius ratio: Ratio of size of cation to the size of anion i.e., r+/r-. These ratios determine the arrangement of ions in ionic solids.
Significance: Size of cation & anions can be known by radius ratio.
|
Radius Ratio |
Co-ordination no. |
Geometry |
|
0.155-0.225 0.224-0.414 0.414-0.732 0.732-1 |
3 4 6 8 |
Trigonal Tetrahedral Octahedral Cubic |
Ques: Two ions a+ and b- have radii 88 and 200 picometres respectively. In the closed pack crystal of compound AB predict co-ordination number of a+?
Ans: r+/r- = 88/200 = 0.44
Radius ratio is present in between 0.414-0.732; therefore, co-ordination number is 6.
Ques: A compound is formed by two elements X and Y, atoms of elements by making ccp and those of elements X occupy all octahedral void. What is the formula of compound?
Ans: Suppose number of octahedral voids= N
Suppose number of 4 atoms at ccp= N
Number of X atoms = N
Therefore, formula of the compound is XnYn= XY
Ques: A solid AB has NaCl structure. If radius of cation A is 100 Pico metre. What is the radius of anion B?
Solve: Since NaCl has octahedral geometry
r+/r-= 0.414-0.732
100/r-= 0.414 equ-(i)
100/r-= 0.732 equ-(ii)
From equ-(i)
r- = 100/0.414 = 241
From equ-(ii)
r- = 100/0.732 = 136
therefore, radius of anion B must be present in between 241-136 picometres.
Density of Unit cell derivation and numerical pdf
Defects/Imperfection in solids
Definition: When definite crystalline arrangement is followed throughout the solid it is known as Ideal solid (only in 0K), any deviation from ideal arrangement in solids is termed as imperfection
Types of imperfection
There are two types of imperfection or defects in solids and they are:
- Point/Atomic defect
- Line defect
|
Point/Atomic defect |
Line defect |
||
|
1. |
When atoms/molecules or
constituent particles are missing from lattice points the defect arise is known
as point defect. |
1. |
When the atoms in a line
are missing the defect arise is known as line defect. |
Point/Atomic defect in covalent solids:
We have two types of point defect in covalent solids:
1. Vacancy
2. Interstitial defect
1.Vacancy defect: When atoms are missing at lattice points.
2.Interstitial defect: When atoms are missing from lattice point and occupy interstitial site.
Point defect in Ionic solids:
We have 3 types of defects and they are:
1. Stoichiometric defects
2. Non-stoichiometric defects
3. Impurity defect
1.Stoichiometric defect: These are the defects when number of anion and cation is same as indicated by their general formula e.g.: NaCl
They are further classified;
(a) Schottky defect: When equal number of anions and cations are missing from their lattice points. Electrically neutrality is maintained after this defect.
- It can arise in solids having high co-ordination number.
- It can arise in solids where size of cation and anion don’t differ.
Changes after this defect
- Conductivity of solids increases i.e., solids become conductor.
- Density of solid decreases.
- Stability will decrease (since solid will collapse)
For example: alkali metal halides, KBr, AgBr, NaBr etc.
(b) Frankel defect: It is a type of interstitial defect when ions are missing from their lattice point and occupy interstitial sites such defect is termed as Frankel defect.
- It occurs when co-ordination number is low.
- It can occur when the size of cation is very small as compared to anions i.e., when there is very large difference between size of r+ and r-.
Changes after this defect:
- Conductivity of solids increases.
- There is no change/impact on density.
- Stability remains constant (no effect)
- Solids having Frankel defect increases their dielectric constant.
Ques: Differentiate between Schottky and Frankel defect.
2. Non-stoichiometric defect: When number of cations and anions are not same as indicated by their general formula for example Fe¹O¹, but in reality Fe0.98O1
Metal excess defects: When metals are in excess. It can arise due to
Anion vacancies: in these types of defects generally the anions are missing from their lattice points in order to maintain electrical neutrality of the solid electrons are trapped in these anion vacancies such centres are known as f-centres.
Ques: Define f-centre.
Ans: In metal excess defect when electrons are trapped in anion vacancies such centres are known as f-centres. These centres are responsible for colours when solids are heated.
Ques: NaCl, ZnO becomes yellow in colour when heated? Explain.
Ans: NaCl, ZnO when heated due to f-centres becomes yellow in colour.
Ques: What is fool’s gold? Or ZnO becomes yellow when heated?
Ans: ZnO is known as fool’s gold. Due to f-centres ZnO becomes yellow.
ZnO→ O2 + Zn2+ 2e-
In this effect cation occupy interstitial sites and electrical neutrality of solids is retained by the electrons also trapped in interstitial sites.
Metal deficiency defect
Cation vacancies: This type of defect is shown by the solids where metal show variable oxidation state. For example, fool’s gold, FeS
In FeS the cation is missing from its lattice point and the electrical neutrality of solid is maintained by the other cations having higher oxidation state.
e’ transition occur in FeS. So, it is lustres in nature
Anions occupy interstitial sites: This type of defect is not common because anions are larger in size and fail to occupy interstitial sites.
3. Impurity defect: When impurity is added to pure crystalline solid the defect arise is known as impurity defect.
(a) In ionic solids: In ionic solids if we add impurity for example, we add SrCl2 to NaCl, then impurity defect is produced as a result NaCl becomes conductor due to holes/extra positive charge
(b) In covalent solids:
Doping: When small amount of foreign impurity is added in pure crystalline solid the phenomena is known as doping.
p-type semiconductor: - When we put lower group element into higher group.
Or
Whenever higher group elements are doped with lower group elements p-type semiconductor are produced. Here the conduction is due to holes.
n-type semiconductor: When lower group elements are doped with higher elements n-type semiconductors are produced. Here conduction is due to excess of electrons.
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