Physical Chemistry – The Solid State – Cubic Crystals – Face Corners, Edge ,Diagonal, center- part-5.

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Contents

0.1 Physical Chemistry – The Solid State (Cubic Crystals) – Part 5
0.2 1. Types of Cubic Crystals
0.3 2. Face, Corners, Edge, Diagonal, and Center in Cubic Crystals
0.4 (A) Corners
0.5 (B) Faces
0.6 (C) Edges
0.7 (D) Diagonal
0.8 (E) Center
0.9 3. Summary Table of Atoms in a Unit Cell
0.10 Key Takeaways
0.11 Physical Chemistry – The Solid State – Cubic Crystals – Face Corners, Edge ,Diagonal, center- part-5.
0.12 Solid State Chemistry
0.13 UNIT 5 SOLID STATE
0.14 Solid state physics Unit 1 Crystal Structure
0.15 SOLID STATE

1 Solid State – Cubic Crystals (Part 5): Face, Corners, Edges, Diagonals, Center

Physical Chemistry – The Solid State (Cubic Crystals) – Part 5

In solid-state chemistry, cubic crystals are a key concept in understanding crystal structures. Let’s break down the important elements: Face, Corners, Edges, Diagonal, and Center in cubic crystals.

1. Types of Cubic Crystals

Cubic crystals exist in three main forms:
1⃣ Simple Cubic (SC) – Atoms at corners only
2⃣ Body-Centered Cubic (BCC) – Atoms at corners + one atom at the center
3⃣ Face-Centered Cubic (FCC) – Atoms at corners + one atom at the center of each face

Important: The number of atoms per unit cell differs for each type:
SC: 1 atom
BCC: 2 atoms
FCC: 4 atoms

2. Face, Corners, Edge, Diagonal, and Center in Cubic Crystals

(A) Corners

In a cubic unit cell, there are 8 corners, each occupied by an atom.
But each corner atom is shared among 8 unit cells → Contribution per unit cell = 1/8

Total corner atoms in a unit cell =

$\times \frac{1}{8} = 1$

(B) Faces

A cube has 6 faces, and in FCC, each face contains 1 atom at its center.
Each face-centered atom is shared between 2 unit cells → Contribution per unit cell = 1/2

Total face atoms in FCC unit cell =

$\times \frac{1}{2} = 3$

(C) Edges

A cube has 12 edges, and sometimes atoms are located at edge centers.
Each edge-centered atom is shared between 4 unit cells → Contribution per unit cell = 1/4

Total edge atoms =

$12 \times \frac{1}{4} = 3$

(D) Diagonal

Face Diagonal (dₑ): Connects opposite corners of a face. $\sqrt{2}a$
Body Diagonal (d_b): Connects opposite corners of the entire cube. $db=3ad_b = \sqrt{3}a$

Where a = edge length of the cube

Used in calculating atomic radius (r)
SC: $\frac{a}{2}$
BCC: $\frac{\sqrt{3}a}{4}$
FCC: $\frac{\sqrt{2}a}{4}$

(E) Center

In BCC, there is one atom exactly at the center of the cube.
This atom is completely inside the unit cell → Full contribution

Total atoms in BCC unit cell =

$(\text{corner atoms}) + 1 (\text{body-centered atom}) = 2$

3. Summary Table of Atoms in a Unit Cell

Structure	Corner Atoms	Face Atoms	Center Atom	Total Atoms
SC	8 × (1/8) = 1	0	0	1
BCC	8 × (1/8) = 1	0	1	2
FCC	8 × (1/8) = 1	6 × (1/2) = 3	0	4

Key Takeaways

Corner atoms contribute 1 per unit cell (shared among 8).
Face atoms contribute 3 in FCC (shared among 2 per face).
Edge atoms contribute 3 in edge-centered structures (shared among 4).
Center atom is fully inside the unit cell in BCC.
Diagonals help in finding atomic radius and packing efficiency.

Want practice questions or more explanations? Let me know!