Close Packed Structures — Revision Notes

⚡ 30-Second Revision

1D Packing: — CN=2
2D SCP: — CN=4, Square voids
2D HCP: — CN=6, Triangular voids
3D HCP: — A-B-A-B stacking, Hexagonal unit cell, CN=12, PE=74%, Examples: Mg, Zn
3D CCP (FCC): — A-B-C-A-B-C stacking, FCC unit cell, CN=12, PE=74%, Examples: Cu, Ag, Au
Voids: — For N atoms:

- Octahedral voids = N - Tetrahedral voids = 2N

Radius Ratios:

- Tetrahedral void: $r_{void}/r_{host} = 0.225$ - Octahedral void: $r_{void}/r_{host} = 0.414$

2-Minute Revision

Close packed structures are the most efficient ways to arrange identical spheres in a crystal, maximizing density. This starts with 1D (CN=2), then 2D. In 2D, hexagonal close packing (HCP, CN=6) is more efficient than square close packing (SCP, CN=4). Building 3D structures from 2D HCP layers leads to two main types: Hexagonal Close Packing (HCP) and Cubic Close Packing (CCP), which is equivalent to Face-Centered Cubic (FCC).

HCP has an A-B-A-B stacking sequence, while CCP has an A-B-C-A-B-C sequence. Both HCP and CCP are highly efficient, boasting a coordination number of 12 and a packing efficiency of 74%. Key examples include Mg, Zn for HCP, and Cu, Ag, Au for CCP/FCC.

When spheres pack, they create interstitial spaces called voids. For 'N' atoms in a close-packed structure, there are 'N' octahedral voids and '2N' tetrahedral voids. Understanding these void numbers is crucial for determining the stoichiometry of ionic compounds where smaller ions occupy these sites.

Remember the radius ratios for these voids: $0.225r$ for tetrahedral and $0.414r$ for octahedral, where 'r' is the radius of the host atom.

5-Minute Revision

Close packed structures are about arranging atoms, visualized as spheres, in the most compact way possible. This concept is fundamental to solid-state chemistry. We build up from 1D linear packing (CN=2) to 2D. In 2D, hexagonal close packing (HCP) with a coordination number of 6 is more efficient than square close packing (SCP) with a coordination number of 4. The real complexity and relevance come in 3D.

Three-dimensional close packing is achieved by stacking 2D hexagonal close-packed layers. When a second layer is placed on the first, it creates two types of interstitial voids: tetrahedral voids (smaller, surrounded by 4 spheres) and octahedral voids (larger, surrounded by 6 spheres). A critical relationship to remember is that for 'N' atoms in a close-packed structure, there are 'N' octahedral voids and '2N' tetrahedral voids.

When adding a third layer, two distinct close-packed structures emerge:

1
Hexagonal Close Packing (HCP): — Characterized by an A-B-A-B-A-B... stacking sequence, where the third layer aligns with the first. It has a hexagonal unit cell. Examples: Mg, Zn, Ti.
2
Cubic Close Packing (CCP): — Characterized by an A-B-C-A-B-C... stacking sequence, where the third layer is in a new position. This structure is identical to a Face-Centered Cubic (FCC) unit cell. Examples: Cu, Ag, Au, Al.

Both HCP and CCP share crucial properties: a coordination number of 12 (each atom touches 12 neighbors) and a maximum packing efficiency of 74%. This means 74% of the volume is occupied by atoms, and 26% is empty space. For comparison, simple cubic has 52.4% and body-centered cubic (not truly close-packed) has 68% packing efficiency.

Worked Example: An ionic solid has anions $A^-$ forming a CCP lattice, and cations $B^+$ occupying 1/4th of the tetrahedral voids. What is the formula of the compound?

Step 1: — Anions $A^-$ form CCP. In a CCP (FCC) unit cell, the number of effective atoms (N) is 4. So, we have 4 $A^-$ ions.
Step 2: — Number of tetrahedral voids = $2N = 2 \times 4 = 8$.
Step 3: — Cations $B^+$ occupy 1/4th of tetrahedral voids. Number of $B^+$ ions = $\frac{1}{4} \times 8 = 2$.
Step 4: — Ratio of $B^+ : A^-$ is $2 : 4$, which simplifies to $1 : 2$. The formula is $BA_2$ or $A_2B$.

Prelims Revision Notes

Close Packed Structures: NEET Revision Notes

1. Basic Concepts:

Close Packing: — Arrangement of identical spheres to maximize occupied space and minimize voids.
Coordination Number (CN): — Number of nearest neighbors an atom touches.
Packing Efficiency (PE): — Percentage of total volume occupied by spheres.

2. Dimensional Packing:

1D Packing: — Linear arrangement. CN = 2.
2D Packing:

* Square Close Packing (SCP): AAAA... stacking. CN = 4. Square voids. * Hexagonal Close Packing (HCP): ABAB... stacking. CN = 6. Triangular voids. More efficient than SCP.

3. Three-Dimensional (3D) Close Packing (from 2D HCP layers):

Types of Voids:

* Tetrahedral Voids (T-voids): Surrounded by 4 spheres. Smaller. For N atoms, $2N$ T-voids. * Octahedral Voids (O-voids): Surrounded by 6 spheres. Larger. For N atoms, $N$ O-voids.

Two Main Structures:

* Hexagonal Close Packing (HCP): * Stacking: A-B-A-B-A-B... * Unit Cell: Hexagonal * Coordination Number: 12 * Packing Efficiency: 74% * Examples: Mg, Zn, Ti, Cd * Cubic Close Packing (CCP) / Face-Centered Cubic (FCC): * Stacking: A-B-C-A-B-C... * Unit Cell: Face-Centered Cubic (FCC) * Coordination Number: 12 * Packing Efficiency: 74% * Examples: Cu, Ag, Au, Al, Ni

4. Other Important Structures (for comparison):

Simple Cubic (SC): — PE = 52.4%, CN = 6.
Body-Centered Cubic (BCC): — PE = 68%, CN = 8. *Not truly close-packed*.

5. Radius Ratio Rules (for ionic compounds):

For tetrahedral void: $r_{void}/r_{host} = 0.225$
For octahedral void: $r_{void}/r_{host} = 0.414$

6. Key for Void-based Problems:

If N is the number of atoms forming the close-packed lattice (e.g., anions in an ionic solid):

* Number of Octahedral Voids = N * Number of Tetrahedral Voids = 2N

Use this to determine the ratio of ions and the compound's formula.

Vyyuha Quick Recall

HCP is ABAB, CCP is ABCABC. Both are 12 and 74.

Hexagonal Close Packing: Alternating Basic Arrangement By Aligning Back.
Cubic Close Packing: All Balls Change Alignment Between Centers.
Voids: — 'O' for Octahedral is like 'One' (N voids). 'T' for Tetrahedral is like 'Two' (2N voids). Octahedral is 'O' (big letter), so it's the larger void. Tetrahedral is 'T' (small letter), so it's the smaller void.