Concept explainers
Interpretation:
The volume of a monoclinic unit cell has to be derived.
Concept Introduction:
From a vector analysis, we know that volume of a geometric system can be alternatively written as
Explanation of Solution
First we have to derive the volume of a triclinic unit cell. Then we can take it as the reference to derive the volume of a monoclinic unit cell.
Derivation of the volume of a triclinic unit cell:
The cell dimensions of a triclinic unit cell is
There are many choices for the primitive vectors in the triclinic system. So we are taking
Figure 1
Then,
Therefore,
This is the expression for the volume of a triclinic unit cell.
Derivation of the volume of a monoclinic unit cell:
The cell dimensions of a triclinic unit cell is
Now substituting these values in the expression of the volume of a triclinic unit cell, we can get the exact expression for the monoclinic unit cell.
The above expression is for the volume of a monoclinic unit cell.
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Chapter 15 Solutions
Atkins' Physical Chemistry
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