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 ofSlip 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 ofCubic Interstitial Sites | 1 void, r = 0.732R | — | — | — |

Number and Size ofOctahedral Interstitial Sites | — | 6 voids, r = 0.155R | 4 voids, r = 0.414R | 6 voids, r = 0. 414R |

Number and Size ofTetrahedral 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 |

### References and Further Reading

This page is a “cheat-sheet” for quickly looking information about the common crystal structures.

If you want more information, you may be interested in my other crystallography articles. Here is that list, in recommended reading order:

Introduction to Bravais Lattices

What is the Difference Between “Crystal Structure” and “Bravais Lattice”

Atomic Packing Factor

How to Read Miller Indices

How to Read Hexagonal Miller-Bravais Indices

Close-Packed Crystals and Stacking Order

Interstitial Sites

Primitive Cells

How to Read Crystallography Notation

What are Point Groups

List of Point Groups

If you are interested in more details about any specific crystal structure, I have written individual articles about simple crystal structures which correspond to each of the 14 Bravais lattices:

1. Simple Cubic

2. Face-Centered Cubic

2a. Diamond Cubic

3. Body-Centered Cubic

4. Simple Hexagonal

4a. Hexagonal Close-Packed

4b. Double Hexagonal Close-Packed (La-type)

5. Rhombohedral

5a. Rhombohedral Close-Packed (Sm-type)

6. Simple Tetragonal

7. Body-Centered Tetragonal

7a. Diamond Tetragonal (White Tin)

8. Simple Orthorhombic

9. Base-Centered Orthorhombic

10. Face-Centered Orthorhombic

11. Body-Centered Orthorhombic

12. Simple Monoclinic

13. Base-Centered Monoclinic

14. Triclinic