The alpha (low) Cristobalite (SiO_2) Structure

The alpha (low) Cristobalite (SiO₂) Structure

Last modified 5 April 2001

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Also note that this structure differs from the ST12 structure of Si only by the handedness of the screw axis.

Prototype: alpha Cristobalite SiO₂
Pearson Symbol: tP12
Space Group: P4₁2₁2 (Cartesian and lattice coordinate listings available)
Number: 92
Primitive Vectors:
- A₁ = a X
- A₂ = a Y
- A₃ = c Z
Basis Vectors:
The Si atoms are on the (4a) sites, and the O atoms are on the (8b) sites
- B₁ = x₁ A₁ + x₁ A₂ = x₁ a X + x₁ a Y (Si)
- B₂ = - x₁ A₁ - x₁ A₂ + ½ A₃ = - x₁ a X - x₁ a Y + ½ c Z (Si)
- B₃ = (½ - x₁) A₁ + (½ + x₁) A₂ + ¼ A₃ = (½ - x₁) a X + (½ + x₁) a Y + ¼ c Z (Si)
- B₄ = (½ + x₁) A₁ + (½ - x₁) A₂ + ¾ A₃ = (½ + x₁) a X + (½ - x₁) a Y + ¾ c Z (Si)
- B₅ = x₂ A₁ + y₂ A₂ + z₂ A₃ = x₂ a X + y₂ a Y + z₂ c Z (O)
- B₆ = - x₂ A₁ - y₂ A₂ + (½ + z₂) A₃ = - x₂ a X - y₂ a Y + (½ + z₂) c Z (O)
- B₇ = (½ - y₂) A₁ + (½ + x₂) A₂ + (¼ + z₂) A₃ = (½ - y₂) a X + (½ + x₂) a Y + (¼ + z₂) c Z (O)
- B₈ = (½ + y₂) A₁ + (½ - x₂) A₂ + (¾ + z₂) A₃ = (½ + y₂) a X + (½ - x₂) a Y + (¾ + z₂) c Z (O)
- B₉ = y₂ A₁ + x₂ A₂ - z₂ A₃ = y₂ a X + x₂ a Y - z₂ c Z (O)
- B₁₀ = - y₂ A₁ - x₂ A₂ + (½ - z₂) A₃ = - y₂ a X - x₂ a Y + (½ - z₂) c Z (O)
- B₁₁ = (½ - x₂) A₁ + (½ + y₂) A₂ + (¼ - z₂) A₃ = (½ - x₂) a X + (½ + y₂) a Y + (¼ - z₂) c Z (O)
- B₁₂ = (½ + x₂) A₁ + (½ - y₂) A₂ + (¾ - z₂) A₃ = (½ + x₂) a X + (½ - y₂) a Y + (¾ - z₂) c Z (O)

See these vectors in a better notation.

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