How many atoms are present in fcc unit cell?

An fcc unit cell contains 4 atoms: 8 corner atoms contribute 1 atom in total and 6 face-centred atoms contribute 3 atoms.

What is Schottky defect?

Schottky defect is a vacancy defect in ionic crystals where equal numbers of cations and anions are missing from their lattice sites, so electrical neutrality is maintained.

Tamil Nadu Class 12 Chemistry Solid State — Samacheer Kalvi

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Quick Summary

Solid state explains how particles are arranged in crystals and how that arrangement controls density, conductivity, defects, and magnetic properties. Board questions often centre on unit cells, packing, density formula, and point defects.

Crystalline and Amorphous Solids

Feature	Crystalline solid	Amorphous solid
Arrangement	long-range order	short-range order
Melting	sharp melting point	softens over a range
Shape	regular geometry	irregular
Example	NaCl, quartz	glass, rubber

Unit Cells

Unit cell	Particles per unit cell	Coordination number	Packing efficiency
Simple cubic	1	6	52.4%
Body-centred cubic	2	8	68%
Face-centred cubic	4	12	74%

Useful Relations

Simple cubic: a = 2r
BCC: sqrt(3)a = 4r
FCC: sqrt(2)a = 4r

Density of a Unit Cell

rho = ZM / (a^3 N_A)

where:

Z = number of particles per unit cell
M = molar mass
a = edge length
N_A = Avogadro constant

Be careful to convert a into centimetres when density is required in g cm^-3.

Voids and Packing

Tetrahedral voids: twice the number of close-packed particles
Octahedral voids: equal to the number of close-packed particles
In close packing, particles occupy 74% of space and voids occupy 26%.

Point Defects

Defect	What happens	Effect
Schottky	equal cations and anions missing	density decreases
Frenkel	ion leaves lattice site and occupies interstitial site	density unchanged
F-centre	electron trapped in anion vacancy	colour appears
Metal excess defect	extra cation or anion vacancy with electrons	non-stoichiometry

Electrical and Magnetic Properties

Conductors: partially filled bands allow electron flow
Insulators: large energy gap between valence and conduction bands
Semiconductors: small gap; conductivity increases with temperature
Diamagnetic: all electrons paired
Paramagnetic: one or more unpaired electrons
Ferromagnetic: magnetic domains align in the same direction

Important Questions

One Mark

1. Define unit cell. 2. How many atoms are present in a bcc unit cell? 3. State the packing efficiency of fcc. 4. What is an F-centre? 5. Which defect lowers density: Schottky or Frenkel?

Short Answer

1. Distinguish crystalline and amorphous solids. 2. Derive the number of particles in fcc unit cell. 3. Compare Schottky and Frenkel defects. 4. Explain why semiconductors conduct better at higher temperature.

Long Answer / Problems

1. Derive the density equation for a unit cell and solve a numerical. 2. Explain simple cubic, bcc, and fcc unit cells with coordination number and packing efficiency. 3. Discuss point defects in ionic crystals with examples.

Common Mistakes

Forgetting fractional contributions: corner = 1/8, face = 1/2, body centre = 1
Using edge length in picometres directly inside the density equation
Saying Frenkel defect changes density
Confusing tetrahedral and octahedral void counts
Mixing bcc and fcc radius-edge relations

Revision Checklist

[ ] Crystal vs amorphous comparison
[ ] Z, coordination number, and packing efficiency table
[ ] Radius-edge relations
[ ] Density formula numericals
[ ] Schottky, Frenkel, and F-centre defects
[ ] Conductors, semiconductors, and magnetic types

Frequently Asked Questions

A unit cell is the smallest repeating portion of a crystal lattice that reproduces the whole crystal when repeated in three dimensions.