Page 109 - Materials Chemistry, Second Edition

96 2 Solid-State Chemistry

the metal and ligand electrons for an octahedral Cr 3þ complex. Since the d z2 and
d x2 y2 orbitals are located directly along the internuclear bond axes, a greater
electrostatic repulsion will occur resulting in an increase in energy. The energy
gap between the two sets of d-orbitals is designated as 10 Dq or D o (o ¼ octahedral
complex; D t refers to a tetrahedral complex, etc.). Visible light is capable of being
absorbed by the complex, causing the excitation of electrons into empty d z2 or
d x2 y2 orbitals. As you are well aware, the color we observe will be the reflected,
or complementary, color of that being absorbed. For instance, absorbed wavelengths
in the 490–560 nm regime (green) will appear red, whereas absorption of
560–580 nm (yellow) radiation will appear blue/violet, and so on.
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Figure 2.62 also illustrates the Tanabe-Saguno diagram for the d Cr 3þ ion of
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ruby, showing the ground state molecular term symbol as A 2g (g ¼ gerade, since an
octahedral ligand field has a center of symmetry), with two spin-allowed transitions
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2
4
to T 2g (green, 550 nm) and T 1g (blue, 420 nm); the transition from A 2g ! E g is
spin-forbidden. [52] It should be noted that the Laporte selection rule disfavors
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electronic transitions between the ground A 2g and excited T states since they
both exhibit even parity. However, the absorption of energy and electronic excita-
tion occurs because Cr 3þ doping distorts the perfect octahedral environment of the
corundum host, mixing in states of odd parity. Rather than simple relaxation back to
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the ground state and accompanying fluorescent emission, there is a fast (10 s )
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intersystem crossing (ISC) into the metastable doublet state, E g . Even though this
[53]
non-radiative decay process is spin-forbidden, it is driven by spin-orbit coupling,
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which becomes more pronounced with increasing nuclear charge (i.e.,Z ). Since the
2
transition from the E g intermediate state to the ground state is also spin-forbidden, the
electrons experience a finite lifetime in the doublet intermediate state before relax-
ing to the ground state, with emission of red light (l ¼ 694 nm). The relatively long
lifetime of an excited state (ca. 3 ms for ruby) is characteristic of phosphorescence,
relative to fluorescence in which electrons exhibit fast relaxation (ca. 5 ps–20 ns)
from excited to ground states.
Interestingly, if Cr 3þ is substituted for Al 3þ in the beryl (Be 2 Al 2 Si 6 O 18 ,
Figure 2.63) base lattice of emerald gemstones, the crystal appears green rather
than red. Since the coordination spheres about the Cr 3þ centers for both ruby and
emerald are distorted octahedra, the shift in the absorption wavelength must
result from the lattice structure. In the beryl lattice, the Be 2þ ions pull electron
density away from the oxygen ions, which will cause less electron–electron repul-
sions between the Cr 3þ d-orbitals and lone pairs of the oxygen ligands. This will
correspond to a decrease in the D o value, the absorption of lower-energy wave-
lengths, and a shift of the reflected color from red to green. It should be noted that
red phosphorescence is also present in emerald; however, this is outweighed by the
strong yellow/red absorption that yields the familiar green color.
Not only does the observed color depend on the nature of the transition metal
impurity, but on the oxidation state of the dopant. For instance, the color of a
beryl-based crystal changes from blue to yellow, upon doping with Fe 2þ and
Fe 3þ (Aquamarine and Heliodor), respectively. For Mn 2þ and Mn 3þ impurities