Simple cubic

Definition

A simple cubic structure is a type of crystal lattice arrangement where atoms are positioned at the corners of a cube, with each unit cell containing one atom. This structure is characterized by its simplicity and low packing efficiency, as each corner atom is shared among eight neighboring unit cells, resulting in an effective contribution of only one atom per unit cell.

5 Must Know Facts For Your Next Test

1. The simple cubic structure has a coordination number of 6, meaning each atom is directly surrounded by six neighboring atoms.
2. Simple cubic is the least efficient packing arrangement compared to other types, like body-centered and face-centered cubic, which can pack more atoms into the same volume.
3. Materials that crystallize in a simple cubic lattice include polonium and certain allotropes of alpha-tin.
4. The atomic radius (r) in a simple cubic lattice can be related to the lattice parameter (a) using the formula $$a = 2r$$.
5. Simple cubic lattices typically exhibit lower densities compared to more complex structures due to their larger void spaces between atoms.

Review Questions

• How does the packing efficiency of a simple cubic structure compare to that of body-centered and face-centered cubic structures?
  • The packing efficiency of a simple cubic structure is about 52%, which is lower than that of body-centered cubic at approximately 68% and face-centered cubic at about 74%. This difference arises from how atoms are arranged within these lattices. Simple cubic has only corner atoms contributing to its volume, while BCC and FCC structures have additional atoms positioned centrally or on faces, respectively, leading to more efficient use of space.
• Discuss the significance of coordination number in simple cubic lattices and how it influences atomic interactions.
  • In a simple cubic lattice, the coordination number is 6, indicating that each atom interacts directly with six neighboring atoms. This coordination influences various physical properties such as strength and stability. Higher coordination numbers generally lead to stronger atomic bonding due to increased interactions, which can impact the overall mechanical properties of materials crystallizing in different lattice types.
• Evaluate the implications of low packing efficiency in simple cubic structures for material properties and applications.
  • The low packing efficiency of simple cubic structures has significant implications for their physical properties. Materials with this type of lattice tend to have lower density and may exhibit reduced strength compared to those with higher packing efficiencies like BCC or FCC. These characteristics can limit their applications in engineering and technology, making them less favorable for structural uses but possibly suitable for niche applications where lightness is an advantage, like certain types of alloys or polymers.

Related terms

body-centered cubic: A body-centered cubic (BCC) structure has atoms at each corner of the cube and a single atom positioned in the center of the cube, leading to a higher packing efficiency compared to simple cubic.

face-centered cubic: In a face-centered cubic (FCC) structure, atoms are located at each corner and the centers of each face of the cube, resulting in an even denser packing compared to both simple cubic and body-centered cubic structures.

crystal lattice: A crystal lattice is a three-dimensional arrangement of points that represent the positions of atoms or molecules in a crystalline material, forming the framework for the solid's structure.