Crystal Structure Types

Why This Matters

Crystal structures aren't just abstract geometry—they're the foundation for understanding why materials behave the way they do. When you're tested on crystallography, you're really being asked to connect atomic arrangement to macroscopic properties like hardness, conductivity, melting point, and density. The way atoms pack together determines coordination numbers, packing efficiency, and bonding characteristics, which in turn explain why diamond cuts glass while table salt dissolves in water.

Don't just memorize the names of these structures. For each one, know what type of bonding holds it together, how efficiently atoms pack, and what properties result. Exam questions love to ask you to predict material behavior from structure, or to compare why two structures with similar packing efficiencies (like FCC and HCP) appear in different materials. Master the why behind each arrangement, and you'll handle anything from multiple choice to free-response problems.

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Close-Packed Metallic Structures

These structures achieve maximum packing efficiency by arranging atoms in layers where each atom nestles into the gaps of the layer below. The difference between them lies in how the third layer stacks—directly over the first (HCP) or offset (FCC).

Cubic Close-Packed (Face-Centered Cubic)

• Packing efficiency of ~74%—one of the densest possible arrangements, with atoms at each cube corner and face center
• Coordination number of 12 means each atom touches 12 neighbors, maximizing metallic bonding strength
• Common in ductile metals like aluminum, copper, and gold—the multiple slip planes allow easy deformation

Hexagonal Close-Packed

• ABAB stacking sequence—two alternating layers create a hexagonal unit cell with the same 74% packing efficiency as FCC
• Coordination number of 12, identical to FCC, but with fewer slip planes making these metals less ductile
• Found in magnesium, titanium, and zinc—metals that tend to be more brittle than their FCC counterparts

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Lower-Efficiency Metallic Structures

Not all metals prioritize maximum packing. Some structures sacrifice density for other advantages, like accommodating larger atoms or enabling specific electronic configurations.

Body-Centered Cubic

• 68% packing efficiency with atoms at cube corners plus one atom in the cube's center
• Coordination number of 8—fewer contacts than close-packed structures, but still strong metallic bonding
• Characteristic of iron, chromium, and tungsten—metals that often exhibit high strength and higher melting points

Simple Cubic

• Only 52% packing efficiency—the least dense crystal structure with atoms only at cube corners
• Coordination number of 6, the lowest among common structures, resulting in weaker overall bonding
• Extremely rare in nature—polonium is the only element that adopts this structure at standard conditions

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Covalent Network Structures

These structures feature atoms locked into rigid positions by strong directional covalent bonds. The tetrahedral geometry of $sp^3$ hybridization dominates, creating exceptional hardness but limited conductivity.

Diamond Cubic

• Tetrahedral coordination with each carbon bonded to exactly four neighbors via strong $sp^3$ covalent bonds
• Based on FCC lattice but with only half the tetrahedral holes filled, creating a more open structure
• Extreme hardness and electrical insulation—found in diamond and silicon, the backbone of semiconductor technology

Wurtzite (Hexagonal Zinc Sulfide)

• Hexagonal structure with tetrahedral coordination—each zinc bonds to four sulfurs and vice versa
• Anisotropic properties mean physical characteristics like conductivity and thermal expansion vary with crystal direction
• Important semiconductor structure—found in ZnS, GaN, and AlN used in LEDs and high-power electronics

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Ionic Crystal Structures

Ionic structures balance the electrostatic attraction between cations and anions while accommodating their different sizes. The radius ratio ($r_{cation}/r_{anion}$) determines which structure is most stable.

Rock Salt (Sodium Chloride)

• FCC arrangement of anions with cations filling all octahedral holes, creating a 1:1 stoichiometry
• Coordination number of 6 for both ions—each $Na^+$ surrounded by 6 $Cl^-$ and vice versa
• High melting point (~801°C) due to strong ionic bonding throughout the three-dimensional lattice

Cesium Chloride

• Simple cubic anion arrangement with cations in the cube center, not BCC despite appearances
• Coordination number of 8—larger cesium ions can accommodate more chloride neighbors than sodium can
• Favored when radius ratio exceeds ~0.73—the larger cation needs more space than octahedral holes provide

Fluorite

• FCC arrangement of cations with anions filling all tetrahedral holes, giving $CaF_2$ stoichiometry
• Coordination numbers of 8 (Ca) and 4 (F)—calcium sits in a cube of fluorides while each fluoride has tetrahedral calcium neighbors
• Anti-fluorite structure occurs when cation/anion positions reverse, as in $Li_2O$

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Complex Ionic Structures

These structures accommodate multiple cation types or unusual stoichiometries, creating versatile frameworks with tunable properties. Their flexibility makes them essential in modern materials science.

Perovskite

• General formula $ABX_3$ with large A cations at cube corners, small B cations at the center, and X anions on face centers
• Tolerance factor determines stability—calculated as $t = \frac{r_A + r_X}{\sqrt{2}(r_B + r_X)}$, with $t \approx 1$ being ideal
• Extraordinary property tunability—used in solar cells, superconductors, and ferroelectrics by swapping A and B cations

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Quick Reference Table

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Self-Check Questions

1. Both FCC and HCP have 74% packing efficiency and coordination number 12. What structural difference explains why FCC metals are typically more ductile than HCP metals?

2. Given that $Na^+$ adopts rock salt structure with $Cl^-$ but $Cs^+$ adopts cesium chloride structure, what does this tell you about the relationship between ionic radius and coordination number?

3. Compare diamond cubic and wurtzite: what bonding feature do they share, and how does their underlying lattice geometry differ?

4. If an FRQ asks you to predict which crystal structure an ionic compound will adopt, what single ratio would you calculate first, and what coordination numbers correspond to different ranges of this ratio?

5. Why is perovskite ($ABX_3$) considered more versatile than simpler ionic structures like rock salt or fluorite for designing new materials with specific electronic properties?