All of this information can be found elsewhere on the site, but here is a quick reference sheet if you want to study the basic crystals quickly before an exam. Here are the links for the thorough comparisons of: FCC vs BCC, and FCC vs HCP.
| Simple Cubic (SC) |  |
| Body-Centered Cubic (BCC) |  |
| Face-Centered Cubic (FCC) |  |
| Hexagonal Close-Packed (HCP) |  |
Outline
Geometric Ratios of the Basic Crystal Structures
Here are the crystal geometric ratios for simple cubic, body-centered cubic, face-centered cubic, and hexagonal close-packed. This table shows the edge length (lattice parameter), face diagonal length ([110] length), body diagonal length ([111] length), c/a lattice parameter ratio, atomic packing factor (APF) and coordination number (CN).
| Crystal Structure | SC | BCC | FCC | HCP |
| Edge Length | a = 2R | a = 4R/√3 | a = 2R√2 | a = 2R, c = 1.633a |
| Face Diagonal Length | 2R√2 | (4R√2)/√3 | 4R | 6R |
| Body Diagonal Length | 2R√3 | 4R | 2R√6 | (2R√11)/√3 |
| c/a Ratio | 1 | 1 | 1 | 1.633 |
| Atomic Packing Factor (APF) | 52% | 68% | 74% | 74% |
| Coordination Number (CN) | 6 | 8 | 12 | 12 |
If you want to prove any of these numbers, check out my article about Atomic Packing Factor.
Interstitial Sites in the Basic Crystal Structures
This table summarizes the number and type of interstitial sites for simple cubic, body-centered cubic, face-centered cubic, and hexagonal close-packed crystals.
| Crystal Structure | SC | BCC | FCC | HCP (primitive) | HCP (conventional) |
| Number of Tetrahedral Sites | — | 12 | 8 | 4 | 12 |
| Radius of Tetrahedral Sites | — | r = 0.291R | r = 0.225R | r = 0.225R | r = 0.225R |
| Number of Octahedral Sites | — | 6 | 4 | 2 | 6 |
| Radius of Octahedral Sites | — | r = 0.155R | r = 0.414R | r = 0.414R | r = 0.414R |
| Number of Cubic Sites | 1 | — | — | — | — |
| Radius of Cubic Sites | r = 0.732R | — | — | — | — |
Check out my in-depth article about interstitial sites if you would like more diagrams, or proof of these values.
Slip Systems for the Basic Crystal Structures
Quick reminder: a slip system is a combination of a slip plane and a slip direction!
| Crystal Structure | Slip Plane | Slip Direction | Number of Slip Systems |
| SC |  |  | 6 |
| FCC |  |  | 12 |
| BCC |  |  | 12 |
| BCC |  | | 12 |
| BCC |  | | 24 |
| HCP |  |  | 3 |
| HCP |  | | 3 |
| HCP |  | | 6 |
Elements in Each of the Basic Crystal Structures
Here is a list of all elements that have a simple cubic, body-centered cubic, face-centered cubic, or hexagonal close-packed crystal structure at standard temperature and pressure.
| Crystal Structure | Simple Cubic (SC) | Body-Centered Cubic (BCC) | Face-Centered Cubic (FCC) | Hexagonal Close-Packed (HCP) |
| Examples of Elements | Po | Li, Na, K, V, Cr, Fe, Rb, Nb, Mo, Cs, Ba, Ta, W, Fr, Ra, Db, Sg, Ds, Rg, Eu | Al, Ca, Ni, Cu, Sr, Rh, Pd, Ag, Ir, Pt, Au, Pb, At, Mt, Fl, Yb, Ac, Th, Es, Fm, Md, No | Be, Mg, Sc, Ti, Co, Zn, Y, Zr, Tc, Ru, Cd, Hf, Re, Os, Tl, Rf, Bh, Hs, Cn, Nh, Gd, Tb, Dy, Ho, Er, Tm, Lu, Lr |
Summary of Properties of the Basic Crystal Structures
| Crystal Structure | SC | BCC | FCC | HCP |
| Unit Cell Type | Cubic | Cubic | Cubic | Hexagonal |
| Edge length | a = 2R | a = 4R/√3 | a = 2R√2 | a = 2R, c = 1.633a |
| Close-Packed Structure | No | No | Yes | Yes |
| Atomic Packing Factor (APF) | 52% | 68% | 74% | 74% |
| Coordination Number (CN) | 6 | 8 | 12 | 12 |
| Number of Atoms per Unit Cell | 1 | 2 | 4 | 6 |
| c/a Ratio | 1 | 1 | 1 | 1.633 |
| Face Diagonal Length | 2R√2 | (4R√2)/√3 | 4R | 6R |
| Body Diagonal Length | 2R√3 | 4R | 2R√6 | (2R√11)/√3 |
| Number of Slip Systems | 6 (3 independent) | 48 (5 independent) | 12 (12 independent) | 12 (3 independent) |
| Stacking Sequence | — (Not Close-Packed) | — (Not Close-Packed) | ABC-ABC… | AB-AB-AB… |
| Number and Size of Cubic Interstitial Sites | 1 void, r = 0.732R | — | — | — |
| Number and Size of Octahedral Interstitial Sites | — | 6 voids, r = 0.155R | 4 voids, r = 0.414R | 6 voids, r = 0. 414R |
| Number and Size of Tetrahedral Interstitial Sites | — | 12 voids, r = 0.291R | 8 voids, r = 0.225R | 12 voids, r = 0.225R |
| Examples of Elements (at STP) | Po | Li, Na, Fe, Nb, W | Al, Ca, Ni, Cu, Sr | Be, Mg, Sc, Ti, Co |
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