Lecture Problem 3'79

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Lecture Problem 3.79

• Maddalena Jackson
• 1.26.07

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Problem Statement!

• The corundum crystal structure, found for Al2O3,
  consists of an HCP arrangement of O2- ions the
  Al3 ions occupy octahedral positions.

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Problem Statement Continued!

• (a) What fraction of the available octahedral
  positions are filled with Al3 ions?
• (b) Sketch two close-packed O2- planes stacked in
  an AB sequence, and note octahedral positions
  that will be filled with the Al3 ions.

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The Plan!

• 1. (Part a) How many octahedral positions are in
  one unit cell?
• 2. (Part a) How many of them are full of Al3
  ions?
• 3. (Part b) What does this look like?

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Octahedral Positions in HCP

• Top View 3D Side View

There are SIX octahedral positions in this unit
cell!
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How Many Al3 Ions?

• Chemical Formula
• Al2O3 contains two Al3 ions for every three O2-
  ions
• There are six O2- ions in the unit cell

Six O2- ions require FOUR Al3 ions according to
the chemical formula.
Six octahedral positions available
2/3 filled!
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How are the positions filled?
A Layer
B Layer