Worksheet: Centering in Ionic Lattices

In this worksheet, we will practice predicting Bravais lattice types of cubic ionic lattices from the charges and relative sizes of cations and anions.

Q1:

N a C l and CsCl both have cubic structures. Why do the chloride ions in CsCl have a higher coordination number than the chloride ions in NaCl?

  • AChloride ions are much smaller than cesium ions but similar in size to sodium ions and so occupy octahedral holes in CsCl and tetrahedral holes in NaCl.
  • BChloride ions are much smaller than cesium ions but similar in size to sodium ions, so CsCl is body-centered cubic while NaCl is face-centered cubic.
  • CChloride ions are much smaller than cesium ions but similar in size sodium ions and so occupy tetrahedral holes in CsCl and octahedral holes in NaCl.
  • DChloride ions are similar in size to cesium ions but much larger than sodium ions and so occupy octahedral holes in CsCl and tetrahedral holes in NaCl.
  • EChloride ions are similar in size to cesium ions but much smaller than sodium ions, so CsCl is body-centered cubic while NaCl is face-centered cubic.

Q2:

The radius of a cation in a cubic ionic lattice is 10% smaller than the radius of the anion. The charges of the cation and anion are equal in magnitude. How many anions are likely in contact with each cation?

Q3:

The radius of a cation in a cubic ionic lattice is 40% smaller than the radius of the anion. The charges of the cation and anion are equal in magnitude. How many anions are likely in contact with each cation?

Q4:

How many complete fluorine atoms are present in a single unit cell of fluorite (CaF)2?

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