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Q: What are ceramic materials?
Ans: Ceramic materials are inorganic and nonmetallic materials. Most ceramics are compounds between
metallic and nonmetallic elements for which the interatomic bonds are either totally ionic, or predominantly
ionic but having some covalent character.
Q: What is the coordination number which is related to the cation-anion radius ratio?
Ans: The coordination number is number of anions nearest neighbors for a cation.
Q: How does a stable ceramic crystal structure form? Describe configurations for stable and unstable cation-
anion coordination.
Ans: A stable ceramic crystal structure form when the anions surrounding a cation are all in contact with that
cation.
Q: Show that the minimum cation–anion radius ratio for the coordination number 3 is 0.155.
Solution:
From the right triangle APO, makes it clear that the side lengths are related to the anion and cation radii rA
and rC as
̅̅̅̅ = 𝑟𝐴
𝐴𝑃
̅̅̅̅
𝐴𝑂 = 𝑟𝐴 + 𝑟𝐶
̅̅̅̅
𝐴𝑃
̅̅̅̅
= cos 𝛼
𝐴𝑂
Since line ̅̅̅̅
𝐴𝑂 bisects the
60° angle of ΔBAC, 𝛼 is 30°.
̅̅̅̅
𝐴𝑃 𝑟𝐴
̅̅̅̅
= = 𝑐𝑜𝑠 30°
𝐴𝑂 𝑟𝐴 + 𝑟𝐶
𝑟𝐴
𝑟𝐴
𝑟𝐴 𝑟 𝐶 = 𝑐𝑜𝑠 30°
+
𝑟𝐴 𝑟 𝐴
1
𝑟 = 𝑐𝑜𝑠 30°
1+ 𝐶
𝑟𝐴
𝑟𝐶 1
1+ = 𝑐𝑜𝑠 30°
𝑟𝐴
𝑟𝐶 1
= 𝑐𝑜𝑠 30° − 1 = 0.155
𝑟𝐴
2
Q: Demonstrate that the minimum cation-to-anion radius ratio for a coordination number of 8 is 0.732.
Solution:
Q: What is AX-type crystal structures? Name some crystal structures for AX compounds.
Ans: AX-Type Crystal Structures
Some of the common ceramic materials consist of equal numbers of cations and anions. These are often
referred to as AX compounds, where A denotes the cation and X the anion.
Some crystal structures for AX compounds are rock salt, cesium chloride, zinc blende, etc.
Q: Sketch a unit cell for the rock salt or sodium chloride crystal structure.
Fig(-): A unit cell for the rock salt or sodium chloride crystal structure
(i) Discuss AmXp-type crystal structures.
Ans: AmXp-type crystal structures
If the charges on the cations and anions are not the same, a compound can exist with the chemical formula
AmXp, where m and/or p ≠ 1. An example is AX2, for which a common crystal structure is found in
fluorite (CaF2). The ionic radii ratio rC/rA for CaF2 is about 0.8 which gives a coordination number of 8.
Calcium ions are positioned at the centers of cubes, with fluorine ions at the corners. The chemical
formula shows that there are only half as many Ca2+ ions as F− ions.
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Q: Which crystal structure type is similar to CaF2 structure? Give other compounds with this crystal structure.
Ans: The crystal structure type similar to CaF2 is CsCl, except that only half the center cube positions are
occupied by Ca2+ ions.
Other compounds with this crystal structure include ZrO2 (cubic), UO2, PuO2, and ThO2.
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