Page 70 - Materials Chemistry, Second Edition

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2.3. The Crystalline State

Does molecule have high symmetry
(tetrahedral, octahedral, icosahedral, spherical)?
YES NO
, n > 1)?
Is the molecule linear? Is there a proper rotation axis (C n
If more than 1, choose one with largest n
YES NO
YES NO
Is there a mirror plane T , O h,
)? d Are there n 2-fold rotation Does the molecule have a plane
I , or K axes to principle axis? of symmetry?
to the molecular axis (σ h
h
YES NO YES NO YES NO
D h C v Is there a plane of symmetry Is there a plane of C Does the molecule have
)? symmetry s
to principle axis (σ h an inversion center (i)?
)?
to principle axis (σ h
NO YES YES NO
YES NO
) D C C
Are there n diagonal planes (σ d nh i 1
containing the principle rotation axis? C nh Are there n vertical mirror planes
(σ ) containing the principle axis?
v
YES NO
D nd D n YES NO
C nv Is there an improper axis
of order 2n (S )?
2n
YES NO
S 2n C n
Figure 2.33. Scheme for determining the point group symmetry of a molecule.

Figure 2.34. Examples of symmetry group elements and molecular point group assignments.