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 the same packing efficiency (like FCC and HCP) appear in different materials with very different mechanical behavior. 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 hollows of the layer below. The difference between them comes down to how the third layer stacks: directly over the first (HCP) or offset to a new position (FCC).

Cubic Close-Packed (Face-Centered Cubic)

• ABCABC stacking sequence produces a cubic unit cell with atoms at each corner and each face center
• Packing efficiency of ~74%, the theoretical maximum for identical spheres, tied with HCP
• Coordination number of 12 means each atom touches 12 neighbors, maximizing metallic bonding contact
• Common in ductile metals like aluminum, copper, gold, and nickel. The ABCABC stacking creates four independent sets of close-packed planes (the {111} family), giving many available slip systems for plastic deformation

Hexagonal Close-Packed

• ABAB stacking sequence produces a hexagonal unit cell with the same 74% packing efficiency as FCC
• Coordination number of 12, identical to FCC, but the hexagonal symmetry provides only one independent basal slip plane, making these metals less ductile
• Found in magnesium, titanium, and zinc, metals that tend to be more brittle or show strong mechanical anisotropy compared to their FCC counterparts
• The unit cell has a characteristic c/a ratio of $\sqrt{8/3} \approx 1.633$ for ideal close packing, though real metals deviate slightly (e.g., zinc has c/a ≈ 1.856)

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Lower-Efficiency Metallic Structures

Not all metals prioritize maximum packing. Some structures sacrifice density for other advantages, like accommodating particular electronic configurations or providing high-temperature stability.

Body-Centered Cubic

• 68% packing efficiency with atoms at cube corners plus one atom at the body center of the cube
• Coordination number of 8: each center atom touches 8 corner atoms. The next-nearest neighbors (6 of them) are only ~15% farther away, so BCC metals still maintain strong cohesion
• Characteristic of iron (below 912°C), chromium, tungsten, and the alkali metals. Many BCC metals exhibit high strength and high melting points (tungsten melts at 3422°C, the highest of any metal)
• Iron's BCC $\rightarrow$ FCC $\rightarrow$ BCC phase transitions with temperature (the $\alpha \rightarrow \gamma \rightarrow \delta$ sequence) are central to understanding steel heat treatment

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 metallic structures, resulting in weaker overall cohesion
• Extremely rare in nature. Polonium is the only element that adopts this structure under standard conditions, and even it transitions to a rhombohedral form at higher temperatures

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Covalent Network Structures

These structures feature atoms locked into rigid positions by strong directional covalent bonds. Tetrahedral geometry from $sp^3$ hybridization dominates, creating exceptional hardness but limited electrical conductivity (unless doped or modified).

Diamond Cubic

• Tetrahedral coordination with each carbon bonded to exactly four neighbors via strong $sp^3$ covalent bonds, bond angle ≈ 109.5°
• Based on an FCC lattice with an additional atom placed inside half of the eight tetrahedral voids (a second interpenetrating FCC lattice offset by $\frac{1}{4}$ of the body diagonal). This creates a more open structure with only ~34% packing efficiency
• Extreme hardness and electrical insulation in diamond. Silicon and germanium adopt the same structure but have smaller band gaps, making them the backbone of semiconductor technology

Wurtzite (Hexagonal Zinc Sulfide)

• Hexagonal structure with tetrahedral coordination: each zinc bonds to four sulfurs and vice versa, built on HCP-type stacking rather than FCC-type
• Anisotropic properties mean physical characteristics like piezoelectric response, thermal expansion, and optical behavior vary with crystal direction
• Important semiconductor structure found in ZnS, GaN, and AlN, widely used in LEDs, laser diodes, and high-power electronics

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Ionic Crystal Structures

Ionic structures balance electrostatic attraction between cations and anions while accommodating their different sizes. The radius ratio ($r_{cation}/r_{anion}$) is the key predictor of which structure is most stable, because it determines how many anions can geometrically fit around a cation.

Rock Salt (Sodium Chloride)

• FCC arrangement of anions with cations filling all octahedral holes, creating a 1:1 stoichiometry. You can equivalently describe it as two interpenetrating FCC lattices
• Coordination number of 6 for both ions: each $Na^+$ is surrounded by 6 $Cl^-$ and vice versa
• Favored when the radius ratio falls between ~0.414 and ~0.732, the stability range for octahedral coordination
• High melting point (~801°C for NaCl) due to strong ionic bonding throughout the three-dimensional lattice. Other examples include MgO (mp ~2852°C), which shows how charge magnitude also affects lattice energy

Cesium Chloride

• Simple cubic arrangement of anions with the cation sitting in the cubic hole at the body center. This is not BCC, because the corner and center sites are occupied by different ions
• Coordination number of 8: the larger $Cs^+$ ion can accommodate more $Cl^-$ neighbors than $Na^+$ can
• Favored when the radius ratio exceeds ~0.732, where the cation is too large for octahedral holes and cubic (8-fold) coordination becomes geometrically stable
• Other examples include CsBr and CsI, as well as some intermetallic compounds

Fluorite

• FCC arrangement of cations with anions filling all tetrahedral holes, giving an $AB_2$ stoichiometry (e.g., $CaF_2$)
• Coordination numbers of 8 (cation) and 4 (anion): each $Ca^{2+}$ sits at the center of a cube of 8 $F^-$ ions, while each $F^-$ has tetrahedral coordination by 4 $Ca^{2+}$
• Anti-fluorite structure occurs when cation and anion positions are reversed, as in $Li_2O$ and $Na_2O$. Here the anions form the FCC lattice and cations fill the tetrahedral holes

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Complex Ionic Structures

These structures accommodate multiple cation types or unusual stoichiometries, creating versatile frameworks with tunable properties.

Perovskite

• General formula $ABX_3$ where the large A cation sits at cube corners, the small B cation sits at the body center, and X anions occupy face centers (in the idealized cubic form)
• B cation is octahedrally coordinated by 6 X anions, while the A cation has 12 X neighbors (cuboctahedral coordination)
• Tolerance factor gauges structural stability: $t = \frac{r_A + r_X}{\sqrt{2}(r_B + r_X)}$. Values near $t = 1$ give ideal cubic perovskite; values between ~0.8 and ~1.0 are generally stable but may show octahedral tilting distortions
• Extraordinary property tunability: by swapping A and B cations you can produce ferroelectrics ($BaTiO_3$), superconductors ($YBa_2Cu_3O_7$-related phases), and photovoltaic absorbers (methylammonium lead iodide in perovskite solar cells)

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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 exam 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?