ChemistrySolid stateClass 12

Solid state crystal lattices & voids: interactive simulation

Crystalline solids feature repeating three-dimensional unit cells. The geometrical arrangement of constituent spheres dictates packing efficiency, density, coordination numbers and the spaces (voids) in between.

Useful for: JEE Main, JEE Advanced, NEET, CBSE Boards · 3 modes in one lab

What you can explore

  1. 1

    Unit Cells: SC, BCC & FCC

    3D rotatable unit cells with atom count Z and packing fraction readouts.
  2. 2

    Tetrahedral & Octahedral Voids

    Positions and counts of tetrahedral (2Z) and octahedral (Z) voids in FCC.
  3. 3

    Schottky vs Frenkel Defects

    Vacancy defect with density decrease vs dislocation defect with constant density.

Try this

Rotate unit cells in 3D to see atomic contributions at corners, faces and body centres, locate all 4 octahedral and 8 tetrahedral voids in FCC, and see why Schottky defects lower crystal density while Frenkel defects leave it unchanged.

  1. 1

    Rotate the FCC unit cell in 3D.

    What you should see

    8 corners contribute 8 × ⅛ = 1 atom, and 6 faces contribute 6 × ½ = 3 atoms, giving total rank Z = 4 atoms per unit cell.

  2. 2

    Inspect Voids in FCC.

    What you should see

    Octahedral voids equal Z = 4 (1 at body centre + 12 at edge centres × ¼). Tetrahedral voids equal 2Z = 8 (2 per body diagonal).

  3. 3

    In Defects, switch from Schottky to Frenkel.

    What you should see

    Schottky defect has missing cation-anion pairs (density decreases). Frenkel defect has a cation dislocated into an interstitial site (density remains constant).

Formulas behind it

Density of unit cell formula

d=Z⋅Ma3⋅NAd = \frac{Z \cdot M}{a^3 \cdot N_A}

Packing efficiencies (SC, BCC, FCC)

SC: 52.4%,BCC: 68.0%,FCC: 74.0%\text{SC: } 52.4\%, \quad \text{BCC: } 68.0\%, \quad \text{FCC: } 74.0\%

Atomic radius relation (FCC)

r=24a=a22(4r=2a)r = \frac{\sqrt{2}}{4} a = \frac{a}{2\sqrt{2}} \quad (4r = \sqrt{2}a)

Atomic radius relation (BCC)

r=34a(4r=3a)r = \frac{\sqrt{3}}{4} a \quad (4r = \sqrt{3}a)

Common mistakes

  • Forgetting that AgBr shows BOTH Schottky and Frenkel defects — an iconic NCERT/JEE question!
  • Using Z = 1 for FCC — simple cubic has Z = 1, BCC has Z = 2, and FCC has Z = 4.
  • Confusing radius ratio for tetrahedral void (0.225) with octahedral void (0.414).
Stuck on a solid state crystal lattices & voids question?Snap it and get a whiteboard video solution.

FAQ

What is the coordination number of an atom in an FCC crystal?

12: each sphere touches 4 neighbors in its own plane, 4 in the plane above and 4 in the plane below.

Why does Frenkel defect not occur in alkali metal halides?

Because alkali metal ions (Na⁺, K⁺) are too large to fit into interstitial sites.

What is an F-centre?

An anionic site occupied by an unpaired electron, responsible for imparting color (e.g. yellow color in NaCl, pink in LiCl).

Related simulations

All 65 simulations
Hydrogen spectrum (Bohr model)Chemistry, Class 11 & Class 12Galvanic cell, Nernst & electrolysisChemistry, Class 12Reaction kinetics & Arrhenius activationChemistry, Class 12Coordination chemistry & crystal fieldChemistry, Class 12Organic reaction mechanisms (SN1 & SN2)Chemistry, Class 12Carbonyl, Aldol & Cannizzaro reactionsChemistry, Class 12

Want a specific topic or simulation added?

Tell us in our feedback box which chapter or concept you want visualised next.

Send feedback