The type of particles in each of the four main classes of crystalline solids are:
Ionic solids: Constituent particles are cations and anions.
Covalent network solids: Constituent particles are atoms.
Molecular solids: Constituent particles are monoatomic or polyatomic molecules.
Metallic solids: Constituent particles are metallic ions in a sea of electrons.
Exercise | Q 2.02 | Page 26
Out of the three types of packing, face-centered cubic (or ccp or hcp) lattice makes the most efficient use of space while simple cubic lattice makes the least efficient use of space.
Exercise | Q 2.03 | Page 26
The following pictures show population of bands for materials having different electrical properties. Classify them as insulator, semiconductor or metal.
The picture in the left represents a metal, the picture in the middle represents an insulator and the picture in the right represents a semiconductor.
Exercise | Q 2.04 | Page 26
The smallest repeating structural unit of a crystalline solid is called unit cell.
The electrical conductivity of a semiconductor increases with increasing temperature.
This is because the number of electrons with sufficient energy so as to get promoted to the conduction band increases as temperature rises.
Thus, at higher temperatures, there are more mobile electrons in the conduction band and more vacancies in the valence band than at lower temperatures.
The picture represents bands of MOs for Si. Label valence band, conduction band, and band gap.
Ionic solids are hard and brittle. They are nonconductors of electricity in solid-state. However, they are good conductors when melted. Hence, the given solid is an ionic solid.
Properties common to both hcp and ccp lattice are the same coordination number of the particles (i.e., 12) and the same packing efficiency (74%).
The substances containing large number of unpaired electrons are attracted strongly by magnetic field. Such substances are called as ferromagnetic substances.
Exercise | Q 3.01 | Page 26
The highest energy band formed by the interaction of the outermost energy levels of closely spaced atoms in solids is called the conduction band.
The conduction band may be partially occupied or vacant.
Electrons in the conduction band are mobile and delocalized over the entire solid. They conduct electricity when an electrical potential is applied.
The band having lower energy than conduction band is the valence band.
The electrons in valence band are not free to move because they are tightly bound to the respective nuclei.
|Ionic solids||molecular solids|
|The constituent particles are charged ions (cations and anions).||The constituent particles are monoatomic or polyatomic molecules|
|The constituent particles are held by the electrostatic force of attraction between oppositely charged ions.||The constituent particles are held by intermolecular forces of attractions such as London forces, dipole-dipole forces and/or hydrogen bonds.|
|They are hard and brittle.||They are soft.|
|They have high melting points.||They have low melting points.|
|They are nonconductors of electricity in solid-state. However, they are good conductors when melted or dissolved in water.||They are poor conductors of electricity.|
|e.g. NaCl, CaF2, etc.||Ice, benzoic acid, etc.|
Exercise | Q 3.03 | Page 26
A face-centred cubic (fcc) unit cell has particles at the eight corners plus particles at the centre of its six faces.
Each particle present at the corner of a given unit cell is shared with seven other neighbouring unit cells.
As a result, its contribution to the given unit cell is only ⅛.
Thus, the number of particles present at corners per unit cell
= 8 corner atoms × ⅛ atom per unit cell = 1
Each particle at the centre of the six faces is shared with one neighbouring cube.
Thus, 1/2 of each face particle belongs to the given unit cell.
Thus, the number of particles present at faces per unit cell
= 6 atoms at the faces × ½ atom per unit cell = 3
Therefore, fcc unit cell has one corner particle plus 3 face particles, making total of 4 particles per unit cell.
Exercise | Q 3.04 | Page 26
Simple cubic close-packed structures are obtained by stacking two-dimensional square close-packed layers.
So, the spheres in the first layer are placed adjacent to one another to form two dimensional square close packing (i.e., AAAA type arrangement).
All the spheres of the successive layers are placed exactly above the spheres of the lower layers.
This results in perfect horizontal and vertical alignment between the spheres of various layers.
Exercise | Q 3.05 | Page 27
Calculate the packing efficiency of metal crystal that has simple cubic structure.
Packing efficiency of metal crystal in the simple cubic lattice:
Exercise | Q 3.06 | Page 27
The substances with unpaired electrons are weakly attracted by the magnetic field.
Such substances are called as paramagnetic substances.
e.g. Oxygen, Cu2+, Fe3+, Cr3+, etc
Exercise | Q 3.07 | Page 27
Consequences of Schottky defect:
i. As the number of ions decreases, mass decreases. However, the volume remains unchanged. Hence, the density of a substance decreases.
ii. The number of missing cations and anions is equal. Hence, the electrical neutrality of the compound is preserved.
Exercise | Q 3.08 | Page 27
Cl– ions are present at corners of the cube. Cs+ ion is at the centre of the cube.
To find: Number of CsCl molecules in the unit cell.
i. Cl– ions are present at the 8 corners. The contribution of each corner particle to the unit cell is 1/8. Hence, the number of Cl– ions that belongs to the unit cell = 8 × (1/8) = 1
ii. Cs+ ion is at the centres of unit cell. The contribution of a particle at the centre to the unit cell is 1. Hence, the number of Cs+ ions that belongs to the unit cell = 1
There is one Cl– ion and one Cs+ ion in the unit cell.
Hence, the number of CsCl molecules in the unit cell = 1.
Number of CsCl molecules in the unit cell = 1.
Exercise | Q 3.09 | Page 27
Given: Type of unit cell is fcc.
Edge length of unit cell (a) = 495 pm
To find: Radius of Cu atom (r)
Formula: For fcc unit cell, r = 0.3535 a
Calculation: Using formula,
r = 0.3535 a
= 0.3535 × 495 pm = 175 pm
Radius of Cu atom (r) is 175 pm.
Exercise | Q 3.1 | Page 27
Obtain the relationship between the density of a substance and the edge length of the unit cell.
Exercise | Q 4 | Page 27
The density of iridium is 22.4 g/cm3. The unit cell of iridium is fcc. Calculate the radius of iridium atom. Molar mass of iridium is 192.2 g/mol.
Exercise | Q 5 | Page 27
Exercise | Q 6 | Page 27
Exercise | Q 7 | Page 27
Two dimensional hexagonal close-packed layer has triangular voids which is formed by three spheres.
When the triangular voids of the first layer are covered by spheres of the next layer, tetrahedral voids are formed.
A tetrahedral void is surrounded by four spheres.
The overlapping triangular voids from the two layers together form an octahedral void.
An octahedral void is surrounded by six spheres.
Thus, the depressions in which spheres of second layer rest are tetrahedral voids while the depressions in which no sphere rests are octahedral voids.
Exercise | Q 8 | Page 27
In ccp structure, the spheres of the third layer are not aligned with those of the first layer or second layer.
Hence, the third layer is called ‘C’ layer.
The spheres of the fourth layer get aligned with the spheres of the first layer.
Hence, the fourth layer is called ‘A’ layer. The resulting pattern of layers is called ‘ABCABC….’.
Exercise | Q 9 | Page 27
Exercise | Q 10 | Page 27
Exercise | Q 11 | Page 27
|Metals are good conductors of electricity.||Insulators are nonconductors of electricity.||Semiconductors have conductivity that is intermediate between conductors and insulators.|
|In metal conductors, the conduction band is partially filled and there is no band gap or there is overlapping between the valence band and conduction band.||In insulators, the valence band and conduction band in insulators are separated by a large energy gap called the forbidden zone.|
In semiconductors, the valence band is completely filled with electrons, and the conduction band is empty. However, the energy gap between the two bands is smaller than that in an insulator.
An extrinsic semiconductor, which is obtained by adding group 15 element to an intrinsic semiconductor which belongs to group 14, is called an n-type semiconductor.
e.g. Silicon doped with phosphorus
n-type semiconductor contains an increased number of electrons in the conduction band.
Consider the doping of Si with phosphorus.
Si has a crystal structure in which each Si atom is linked tetrahedrally to four other Si atoms.
When a small quantity of phosphorous is added to pure Si, the P atoms occupy some vacant sites in the lattice in place of Si atoms.
The overall crystal structure of Si remains unchanged.
Four of the five valence electrons of P are utilized in bonding the closest to four Si atoms.
Thus, P has one extra electron than needed for bonding.
Therefore, Si doped with P has more number of electrons in the conduction band than those in the conduction band in pure Si.
Thus, the conductivity of Si-doped with P is higher than that of pure Si.
The electrons in the conduction band move under the influence of an applied potential and conduct electricity.
P atom occupying regular site of Si atom
a. Frenkel defect arises when an ion of an ionic compound is missing from its regular lattice site and occupies an interstitial position between lattice points. The cations are usually smaller than anions. Therefore, the cations occupy interstitial sites.
b. The smaller cation is displaced from its normal site to interstitial space. It, therefore, creates a vacancy defect at its original position and an interstitial defect at its new location in the same crystal. Frenkel defect can be regarded as the combination of vacancy defect and interstitial defect.
c. This defect is found in ionic crystals like ZnS, AgCl, AgBr, AgI and CaF2.
a. Frenkel defect occurs in ionic compounds with large difference between sizes of cation and anion.
b. The ions of ionic compounds must have low coordination number.
a. As no ions are missing from the crystal lattice as a whole, the density of solid and its chemical properties remain unchanged.
b. The crystal as a whole remains electrically neutral because the equal numbers of cations and anions are present.
Exercise | Q 14 | Page 27
i. Impurity defect arises when foreign atoms, that is, atoms different from the host atoms, are present in the crystal lattice.
ii. There are two kinds of impurity defects: Substitutional and interstitial impurity defects.
iii. Formation of vacancy through aliovalent impurity:
Vacancies are created by the addition of impurities of aliovalent ions (that is, ions with oxidation state different from that of host ions) to an ionic solid.
e.g. Consider a small amount of SrCl2 impurity added to NaCl during its crystallization.
The added Sr2+ ions (O.S. = +2) occupy some of the regular sites of Na+ host ions (O.S. = +1). In order to maintain electrical neutrality, every Sr2+ ion removes two Na+ ions. One of the vacant lattice sites created by the removal of two Na+ ions is occupied by one Sr2+ ion. The other site of Na+ ion remains vacant as shown in the figure.