Structure of Metals and Alloys — AP Chemistry
1. Metallic Bonding and the Electron Sea Model ★★☆☆☆ ⏱ 4 min
Metallic bonding is defined as the electrostatic attraction between positively charged metal cations (nuclei plus core electrons) and a delocalized "sea" of mobile valence electrons that extends uniformly throughout the entire crystalline solid. Unlike covalent bonding (electrons localized between two atoms) or ionic bonding (electrons fully transferred to fixed charged ions), delocalization of valence electrons in metals directly explains all their signature properties.
Key properties of metals are directly explained by the electron sea model:
- **Electrical/thermal conductivity**: Mobile delocalized electrons flow under an applied voltage to carry current, and rapidly transfer kinetic energy through heated regions of the solid.
- **Malleability and ductility**: When external force is applied, layers of cations slide past each other, and the electron sea rearranges to maintain electrostatic attraction, so the solid does not fracture.
- **Melting point correlation**: Stronger electrostatic attraction (higher cation charge, more delocalized electrons) leads to higher melting points.
Exam tip: On AP exam FRQs, always explicitly connect the property of the metal to the delocalization of electrons. Examiners award points for this specific link, not just a generic reference to "metallic bonding".
2. Crystalline Unit Cell Geometry for Pure Metals ★★★☆☆ ⏱ 5 min
Nearly all pure metals form crystalline solids with close-packed atomic arrangements, because close packing maximizes attractive forces between cations and the electron sea, lowering the overall energy of the solid. The three most common cubic unit cell structures for metals are primitive cubic (52% packing efficiency, rare), body-centered cubic (BCC, 68% packing efficiency, found in iron and sodium), and face-centered cubic (FCC/CCP, 74% packing efficiency, found in copper and aluminum).
A common AP exam question asks you to relate the edge length of the unit cell ($a$) to the atomic radius ($r$) of the metal atom, based on the assumption that atoms are hard spheres that touch along the direction of packing. These relationships can always be derived from the Pythagorean theorem, so you do not need to rely solely on memorization:
- Primitive cubic (atoms touch along edge): $a = 2r$
- BCC (atoms touch along body diagonal): $\sqrt{3}a = 4r \implies r = \frac{a\sqrt{3}}{4}$
- FCC (atoms touch along face diagonal): $\sqrt{2}a = 4r \implies r = \frac{a\sqrt{2}}{4}$
Exam tip: Always show your derivation of the $a$-$r$ relationship on FRQs, even if you have memorized the formula. AP graders award points for reasoning, not just the final numerical answer.
3. Structure and Classification of Alloys ★★☆☆☆ ⏱ 3 min
Alloys are homogeneous mixtures of two or more elements, at least one of which is a metal, that retain bulk metallic properties. They are classified into two main types based on the relative atomic size of the added component, which determines its position in the original metal’s crystalline lattice:
- **Substitutional alloys**: Form when the added element has an atomic radius within ~15% of the original metal’s atomic radius. The added atom replaces the original metal atom in the crystalline lattice. Common examples: brass (copper + zinc) and 14-karat gold (gold + copper).
- **Interstitial alloys**: Form when the added element has an atomic radius more than ~30% smaller than the original metal’s atomic radius. The small added atom fits into the empty interstitial gaps between the original metal atoms in the lattice. The most common example: carbon steel (iron + carbon).
All alloys almost always have higher hardness and strength, and lower electrical conductivity, than pure metals. The added atoms disrupt the regular crystalline lattice of the pure metal: this makes it harder for layers of atoms to slide past one another (increasing hardness) and disrupts the delocalized electron sea (reducing conductivity).
Exam tip: Do not assume all alloys with a nonmetal are interstitial. Always base classification on relative atomic size, not whether the added element is metal or nonmetal.
4. AP-Style Concept Check ★★★☆☆ ⏱ 2 min
Common Pitfalls
Why: Students confuse the ability of layers to slide with bond weakness. Weak bonds lead to low melting points, not malleability.
Why: Students mix up atom positions in BCC vs FCC. BCC has an atom at the cube center, not face centers, so atoms touch along the body diagonal.
Why: Students associate nonmetals with small size, but some nonmetals (e.g., silicon, 111 pm) are similar in size to many metals.
Why: Students confuse lattice disruption with bond strength. Increased hardness does not come from stronger bonds.
Why: Students forget that two radii come from each end of the face diagonal, leading to 4r total, not 2r.