Unit Cell Chemistry Simple Cubic, Body Centered Cubic, Face Centered Cubic Crystal Lattice Structu

The Organic Chemistry Tutor
14 Jan 202117:22

Summary

TLDRThis video provides an introduction to three key crystal structures: Simple Cubic (SC), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC). It explains their atomic arrangements, coordination numbers, and space efficiency. The SC structure has one atom per unit cell with 52% space utilization, while the BCC structure has two atoms per unit cell and occupies 68% of space. The FCC structure is the most efficient, with four atoms per unit cell and 74% space utilization. The video also includes key formulas relating atomic radius, edge length, and volume in each structure.

Takeaways

  • 😀 Simple Cubic (SC) structure has one atom per unit cell, with a coordination number of 6.
  • 😀 Body-Centered Cubic (BCC) structure contains two atoms per unit cell and has a coordination number of 8.
  • 😀 Face-Centered Cubic (FCC) structure contains four atoms per unit cell and has a coordination number of 12.
  • 😀 The Simple Cubic (SC) structure uses 52% of the volume for atoms, with 48% empty space.
  • 😀 The Body-Centered Cubic (BCC) structure is 68% efficient, meaning 32% of the volume is empty space.
  • 😀 The Face-Centered Cubic (FCC) structure is the most efficient, with 74% of its volume occupied by atoms.
  • 😀 In the Simple Cubic (SC) structure, the edge length (x) is twice the atomic radius (2r).
  • 😀 In the Body-Centered Cubic (BCC) structure, the edge length (x) is 4/√3 times the atomic radius (r).
  • 😀 In the Face-Centered Cubic (FCC) structure, the edge length (x) is √8 times the atomic radius (r).
  • 😀 The volume of atoms in a unit cell can be calculated by dividing the volume of the atoms by the volume of the cube, resulting in a percentage efficiency.

Q & A

  • What are the three cubic structures discussed in the video?

    -The three cubic structures discussed are the simple cubic structure, the body-centered cubic structure, and the face-centered cubic structure.

  • How many atoms are present in one unit cell of the simple cubic structure?

    -In the simple cubic structure, there is only one atom per unit cell.

  • What is the coordination number for the simple cubic structure?

    -The coordination number for the simple cubic structure is 6, meaning each atom is adjacent to 6 other atoms.

  • What is the efficiency of space usage in the body-centered cubic structure?

    -The body-centered cubic structure is 68% efficient, meaning that 68% of the volume of the cube is occupied by atoms, while the remaining 32% is empty space.

  • What is the coordination number for the face-centered cubic structure?

    -The coordination number for the face-centered cubic structure is 12, meaning each atom is adjacent to 12 other atoms.

  • Why is the face-centered cubic structure known as cubic closest packing?

    -The face-centered cubic structure is known as cubic closest packing because it is the most efficient use of space, with atoms arranged in such a way that they occupy 74% of the cube's volume.

  • What is the relationship between the edge length (x) and atomic radius (r) in the simple cubic structure?

    -In the simple cubic structure, the edge length (x) is equal to twice the atomic radius (x = 2r).

  • How do you calculate the edge length of the body-centered cubic structure in terms of atomic radius?

    -The edge length (x) for the body-centered cubic structure is given by the formula x = (4/√3) * r, where r is the atomic radius.

  • What is the formula for the volume of the cube in the simple cubic structure?

    -The volume of the cube in the simple cubic structure is given by the formula V = x³, where x is the edge length, and x = 2r (twice the atomic radius).

  • How is the volume occupied by atoms in the simple cubic structure calculated?

    -To calculate the volume occupied by atoms in the simple cubic structure, divide the volume of the atoms in the unit cell by the volume of the cube. This results in a volume occupancy of approximately 52.36%.

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Related Tags
Unit CellsCrystallographyAtomic StructureBCC StructureFCC StructureSimple CubicCoordination NumberMaterial ScienceCrystalline SolidsEdge LengthEfficiency