Encyclopedia of Color Science and Technology

2016 Edition
| Editors: Ming Ronnier Luo

Transition-Metal Ion Colors

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-8071-7_256

Synonyms

Definition

Transition metals are d-block elements with partially filled 3d, 4d, and 5d orbitals.

Color Production

The transition metals are (somewhat imprecisely) described as being colored because when cations of these elements are incorporated into colorless solids or liquids, the material frequently takes on a characteristic hue (Fig. 1, Table 1). The color arises from electronic transitions between the ionic ground state and energy levels lying between 1.77 and 3.10 eV above it, giving absorption maxima in the visible wavelength range (400–700 nm). The low-lying energy levels that give rise to color arise from interactions of the d orbitals on the cation with neighboring atoms in a material and are a function of the symmetry of the surroundings [1, 2, 3]. (These ions in the gaseous state are not colored). The energy levels that occur with the 4d and 5d transition metals are higher in energy than those of the 3d series and are of lesser importance in color terms. In this entry only the 3d transition-metal ions are covered and, in addition, only single dopants are considered. (When two or more transition-metal ion impurities are present, an alternative mechanism, charge transfer, can also lead to coloration).
Transition-Metal Ion Colors, Fig. 1

Synthetic ruby spheres consisting of normally colorless Al2O3 doped with trace amounts of Cr3+

Transition-Metal Ion Colors, Table 1

Typical 3d transition-metal ion colors

Ion

Color

Symmetry

Host matrix

Ti3+ d1

Purple

Tetrahedral

Silicate glass

V4+ d1

Red

Tetrahedral

Silicate glass

V3+ d2

Green

Tetrahedral

Silicate glass

Blue

Octahedral

Al2O3

Cr3+ d3

Green

Tetrahedral

Silicate glass

Green

Octahedral

Be3Al2Si6O18 (emerald)

Red

Octahedral

Al2O3 (ruby), TiO2, MgAl2O4

Violet

Octahedral

KCr(SO4)312H2O (chrome alum)

Mn3+ d4

Purple

Tetrahedral

Silicate glass

Mn2+ d5

Yellow

Tetrahedral

Silicate glass

Red

Octahedral

MnCO3

Green

Octahedral

MnO

Pink

Octahedral

MnSiO3

Fe3+ d5

Green

Tetrahedral

Silicate glass

Yellow

Octahedral

Al2SiO4(OH) (topaz)

Fe2+ d6

Green

Octahedral

Fe(H2O)62+ in solution and hydrates

Red

Cubic

Ca3Al2Si3O12 (garnet)

Co2+ d7

Blue

Tetrahedral

CoAl2O4, silicate glass

Pink

Octahedral

Co(H2O)62+ in solution and hydrates

Ni2+ d8

Green

Octahedral

Ni(H2O)62+ in solution and hydrates

Yellow

Octahedral

Al2O3, NiCl2

Cu2+ d9

Green

Octahedral

Cu2(OH)2(CO3) (malachite)

Blue

Octahedral

Cu(H2O)62+ in solution and hydrates

Electronic Energy Levels

Energy Levels and Terms

The energy levels of a free transition-metal cation are dominated by electron–electron repulsion and are described by term symbols. A term is a set of states which are very similar in energy. Transitions between terms, or, more precisely, the energy levels specified by the term, give rise to the observed line spectrum of the free ion. The terms of an ion can be derived by Russell–Saunders (LS) coupling [2, 4]. In this designation, each term is written as 2S+1L where L is a many-electron quantum number describing the total orbital angular momentum of the electrons surrounding the atomic nucleus and S is a many-electron quantum number representing the total electron spin. The superscript (2S+1) is called the multiplicity of the term. The total angular momentum quantum number L is given a letter symbol: S (L = 0), P (L = 1), D (L = 2), F (L = 3), and thereafter alphabetically, omitting J. The energies of the terms must be determined by quantum mechanical calculations, except for that of the ground state, which is given by Hund’s second rule: the ground state is the term with the highest multiplicity and, if more than one term of the same multiplicity is present, by that with the highest L value. The lower-energy terms of free 3d transition-metal cations are given in Table 2.
Transition-Metal Ion Colors, Table 2

Low-energy terms of free 3d transition-metal cations

Ion

Free-ion termsa

Ti3+V4+ d1

2 D

V3+ d2

3 F3P 1D 1G

Cr3+ d3

4 F4P 2G 2P

Mn3+ Cr2+ d4

5 D

Mn2+ Fe3+ d5

6 S4G 4P 4D 4F

Fe2+ d6

5 D

Co2+ d7

4 F4P 2G 2P

Ni2+ d8

3 F3P 1D 1G

Cu2+ d9

2 D

aGround state term bold

Crystal Field Splitting

When a cation is placed into a crystal, the d electrons interact with the surrounding anions and give rise to new energy states. The simplest conceptual model that describes the formation of the color-producing energy levels is called crystal field theory [5, 6]. In this approach the electrostatic effect of neighboring anions upon the energies of the cationic d orbitals is considered in terms of surrounding point charges. More comprehensive treatments, which include the effects of covalent bonding, fall into the domain of ligand field theory [7, 8], although the two expressions are often used interchangeably.

The d orbitals on a 3d transition-metal cation can be described as pointing along or between a set of x-, y-, and z-axes (Fig. 2). The orbitals directed between the axes are the dxy, dyz, and dxz set and those pointing along the axes are the \( {\mathrm{d}}_{{\mathrm{x}}^2-{\mathrm{y}}^2} \) and \( {\mathrm{d}}_{{\mathrm{z}}^2} \) pair. If electronelectron interactions are ignored, all of these orbitals are degenerate (have the same energy). However, this is not true when the ion is placed into a crystal because of the interaction (most easily imagined as repulsion) between the electrons on the surrounding ions and the electrons occupying d orbitals. If these surrounding charges were distributed evenly over the surface of a sphere, the five d orbitals would still be energetically degenerate, although at a higher energy by an amount E0. In a crystal the charges are not smeared out but arranged in a pattern. This removes the degeneracy and gives rise to a new set of energy levels (Fig. 3). The pattern of this crystal field splitting depends upon the symmetry of the surrounding anions.
Transition-Metal Ion Colors, Fig. 2

Electron density lobes of d orbitals

Transition-Metal Ion Colors, Fig. 3

Change of d-orbital energies when a free ion is introduced into a crystal (schematic)

The two most important geometries to consider, especially for oxide pigments and ceramics, are octahedral and tetrahedral coordination (Fig. 4a, b). When a cation is surrounded by six anions arranged at the vertices of a regular octahedron, the \( {\mathrm{d}}_{{\mathrm{x}}^2-{\mathrm{y}}^2} \) and \( {\mathrm{d}}_{{\mathrm{z}}^2} \) orbitals point directly toward the surrounding anions and are raised in energy more than the dxy, dxz, and dyz trio, which point between the anions. This splits the originally degenerate energy levels into two groups. The higher-energy state, labeled eg, consists of two equal-energy levels, derived from the \( {\mathrm{d}}_{{\mathrm{x}}^2-{\mathrm{y}}^2} \) and \( {\mathrm{d}}_{{\mathrm{z}}^2} \) orbitals. The lower-energy state, labeled t2g, consists of three equal-energy levels, derived from the dxy, dxz, and dyz orbitals (Fig. 5). The energy gap between the t2g orbitals and the eg orbitals is written Δ or 10Δq, with the t2g set at −4Δq and the eg set at +6Δq with respect to the spherically symmetrical situation. When Δ is small, the crystal field is said to be weak, and when large it is referred to as strong. Strong crystal fields arise from ions with multiple charges and relatively short cation–anion spacing, together with contributions due to covalent bonding.
Transition-Metal Ion Colors, Fig. 4

(a) Octahedral and (b) tetrahedral coordination geometry. A cation is at the cube center. In (a), anions are at the center of each face. In (b), four anions occupy half the cube corners

Transition-Metal Ion Colors, Fig. 5

Splitting of d-orbital energy levels in a crystal field: octahedral and tetrahedral symmetries

When a cation is surrounded by a tetrahedron of anions, the crystal field splitting found for octahedral coordination is reversed. In this case the higher-energy group, now labeled t2, is derived from the dxy, dxz, and dyz orbitals, and the lower-energy group, now labeled e, is derived from the \( {\mathrm{d}}_{{\mathrm{x}}^2-{\mathrm{y}}^2} \) and \( {\mathrm{d}}_{{\mathrm{z}}^2} \) orbitals. The t2 set is at +4Δq and the e set is at −6Δq with respect to the spherically symmetrical situation (Fig. 5). The magnitude of Δ for tetrahedrally coordinated cations is 4/9 of that for the same cation when octahedrally coordinated.

Term Splitting

The electronic energy levels of a free transition-metal ion arise from electron–electron interactions, and the simple model just outlined must be adapted so as to apply to the free-ion terms. It is found that a term may split into several energy states. The number of states that arise is a function of the value of L and the symmetry of the surrounding neighboring anions (Table 3). The magnitude of the splitting is a function of the anion–cation separation and the charges on the ions involved. The multiplicity of the term is carried over onto the new states. The energy states in the crystal are given labels that describe the degeneracy of the orbitals: A is a singly degenerate state, E represents a doubly degenerate state, and T represents a triply degenerate state. Different configurations of sets of orbitals with the same degeneracy are labeled with a subscript 1, 2, and so on. Thus a P term gives rise to a T1 term, while a D term gives rise to a T2 term. The subscript “g” means a center of orbital symmetry exists. The energy of the new states needs to be calculated using quantum mechanical methods or determined experimentally from spectra.
Transition-Metal Ion Colors, Table 3

Splitting of terms in fields of cubic symmetry

Free-ion term

Terms in tetrahedral crystal field

Terms in octahedral crystal field

S

A1

A1g

P

T1

T1g

D

E, T2

Eg, T2g

F

A2, T1, T2

A2g, T1g, T2g

G

A1, E, T1, T2

A1g, Eg, T1g, T2g

Selection Rules

Electron transitions are governed by selection rules that give the probability that a transition will occur. Transitions between d orbitals are forbidden by the Laporte selection rule. However, this rule may break down for ions in compounds. The main reason for this is a degree of mixing between s, p, and d orbitals can occur when an ion is not located at a center of symmetry. As s or p to d transitions are allowed, transitions giving rise to color are also allowed, to a degree corresponding to the amount of orbital mixing achieved. Thus ions situated in tetrahedral coordination, which are not at a center of symmetry, show quite strong colors. Ions at the center of a perfect octahedron are at a center of symmetry and color-producing transitions are forbidden, but in most solids and liquids, thermal agitation of the surroundings and crystal distortions remove the precise symmetry, making such transitions weakly allowed. As a consequence, they are often less intense than those from similar ions in tetrahedral sites.

In addition, transitions are only allowed between states of the same multiplicity, called spin-allowed transitions. Transitions between states of differing spin can be weakly allowed in some circumstances, but in general these do not give rise to strong colors.

The Color of 3d Transition-Metal Ions

Color and Term Splitting

Using Tables 2 and 3, a qualitative energy level diagram can be readily constructed for the splitting of the ground state terms (Fig. 6). It is seen that the arrangement of the energy levels is symmetrical about the d5(6S) term and the arrangement for tetrahedral coordination the inverse of that for octahedral coordination. The colors exhibited by many transition-metal ions can now be understood.
Transition-Metal Ion Colors, Fig. 6

Splitting of ground state free-ion terms in crystal fields of octahedral and tetrahedral symmetry. Transitions that give rise to color shown as arrows (subscripts g should be omitted for tetrahedral coordination)

Figure 6 indicates that octahedrally coordinated d5 ions (Fe3+, Mn2+) exhibit no ground state crystal field splitting and are not expected to show any colors. This is so, and compounds of these ions are at best weakly colored due to other factors. The free-ion ground state of octahedrally coordinated d1 ions (Ti3+, V4+), d4 ions (Cr2+, Mn3+), d6 ions (Fe2+), and d9 ions (Cu2+) splits into two, and these ions will show one absorption band, corresponding to a transition between these two energy levels. If all or part of this band is in the visible, compounds containing these cations will show color (Table 4).
Transition-Metal Ion Colors, Table 4

Octahedral crystal field absorption peaks

Ion

Crystal field termsa

Absorption

Position/nm

Comments

Peaks

Ti3+ d1

2T2g2Eg

2Eg¬2T2g

493

In [Ti(H2O)6]3+

V3+ d2

3T1g3T2g3A2g

3T2g¬3T1g

575

In Al2O3,

3T1g¬3T1g from 3P

 

397

3A2g¬3T1g

294

Cr3+ d3

4A2g4T2g4T1g

T2g¬A2g

556/575

In Al2O3/[Cr(H2O)6]3+

T1g¬A2g

400/408

Mn3+ Cr2+ d4

5Eg5T2g

5T2g¬5Eg

461/476

In MnF6/[Mn(H2O)6]3+

Mn2+ Fe3+ d5

6A1g

0

  

Fe2+ d6

5T2g5Eg

5Eg¬5T2g

1,000

In [Fe(H2O)6]2+

Co2+ d7

4T1g4T2g4A2g

4T2g¬4T1g

1,176

In [Co(H2O)6]2+

 

500

4T1g¬4T1g from 4P

4A2g¬4T1g

560

Ni2+ d8

3A2g3T2g3T1g

3T2g¬3A2g

1,176/935

In [Ni(H2O)6]2+/[Ni(NH3)6]2+

3T1g¬3A2g

741/571

429/355

3T1g¬3A2g from 3P

Cu2+ d9

2Eg2T2g

2T2g¬2Eg

780

In [Cu(H2O)6]2+

aDerived from ground state term for a free ion in an octahedral field, listed in ascending order

The situation with the ions d2 (V3+), d7 (Co2+), and d8 (Ni2+) is not so simple. Figure 6 indicates that these should show two transitions, but the experimental data (Table 4) makes it clear that three transitions are observed. As transitions giving rise to color are between states of the same multiplicity, for these ions it is necessary to take into account the existence of other terms with the same multiplicity as the ground state. The ions d2 (V3+), d3 (Cr3+), d7 (Co2+), and d8 (Ni2+) have two free-ion terms of the same multiplicity, 3F 3P for d2 and d8 and 4F 4P for d3 and d7 (Table 2). In the crystal field, the higher-energy 3P or 4P states give rise to 3T and 4T states (Fig. 7). Spin-allowed transitions to these additional energy levels give rise to three absorption bands in the case of V3+, Co2+, and Ni2+(Table 4). In Cr3+ ions the transition to the 4T state is at a high energy and is not recorded in the visible spectrum.
Transition-Metal Ion Colors, Fig. 7

Splitting of ground state and higher free-ion terms with the same multiplicity in a crystal field of octahedral symmetry, schematic. Transitions that give rise to color shown as arrows

Effect of Crystal Field Strength and Other Factors

Although crystal field splitting gives an accurate picture of the number of absorption peaks observed, the actual position of these peaks depends upon the crystal chemistry of the surroundings, which alters the effective strength of the crystal field. Moreover, the absorption peaks are frequently broad or show shoulders, indicating that the simple description given above is in need of refinement. Here just one example will be given. Octahedrally coordinated Cr3+ ions can induce a variety of colors including ruby red, emerald green, and violet. In all cases the color arises from transitions between the 4A2g ground state and the higher 4T2g and 4T1g levels. Ruby consists of colorless corundum (Al2O3) crystals with ~1 % of Cr3+ ions occupying octahedral Al3+ sites. In this material the absorption peaks are the following:
  • 4T2g¬4A2g; maximum 556 nm; green yellow

  • 4T1g¬4A2g; maximum 400 nm; violet

The absorption at 556 nm removes green yellow and the absorption at 400 nm removes violet. Between the absorption curves there is a relatively small transmission window at approximately 486 nm and a red transmission window is present at wavelengths greater than 650 nm. This means that the color transmitted by the ruby will be red with something of a blue undertone.

Emerald consists of the colorless mineral beryl with Cr3+ impurity ions occupying octahedral Al3+ sites. In beryl the octahedra surrounding the Cr3+ ions are slightly larger than in corundum, and so the crystal field experienced by the Cr3+ in emerald is weaker than in ruby, causing a shift in the 4T1g and 4T2g levels toward the ground state with the result that the transitions move slightly toward the lower-energy end of the spectrum:
  • 4T2g¬4A2g; absorption maximum 650 nm; orange red

  • 4T1g¬4A2g; absorption maximum 450 nm; blue

The band that absorbs green yellow in ruby now absorbs orange red in emerald, and the violet absorbing band in ruby now absorbs blue. Between the absorption curves, there is a blue-green transmission window at 500 nm. The result of these small shifts is to transform the ruby red into emerald green.

In crystalline chrome alum and water solution, the Cr3+ ions are at the center of an octahedron of O2- ions in the complex [Cr(H2O)6]3+. The crystal field now gives rise to the absorption bands:
  • 4T2g¬4A2g; absorption maximum 575 nm; yellow

  • 4T1g¬4A2g; absorption maximum 408 nm; violet

These bands are positioned so as to emphasize purple violet, the dominant tone of chrome alum.

Although the overall color of transition-metal ions in solids is explained by crystal field effects, the eye can detect subtle variations that require more complex explanations. Again ruby serves as an example. In this gemstone the octahedra that are occupied by the Cr3+ ions are distorted, causing the 4T2g and 4T1g levels to split due to a change of local symmetry. The separation of the new levels is small but does give a color change that adds to the value of the stones and also produces polarization effects. In addition an energy level 2Eg (derived from splitting of the free-ion 2G term) falls between the ground state and the 4T2g level. This level is also split in the distorted octahedral sites in these crystals. Although direct excitation to and from the ground state to the 2Eg levels is forbidden by the multiplicity selection rule, it is populated indirectly, and that gives rise to two closely spaced emission lines R1 at 693.5 nm and R2 at 692.3 nm in the ruby spectrum. This radiation enhances the color of the best rubies and is made to dominate light emission during ruby laser action.

Color as Structural Probe

The absorption spectrum of a transition-metal ion in a solid can give structural and chemical information that is not easily obtained via other techniques. This is because the absorption spectrum depends upon the local geometry of the site occupied and the valence state of the colored ion. Although this information is sometimes available from X-ray diffraction, in crystals where several cations with more than one valence state may statistically occupy the same site, X-ray diffraction data can be ambiguous. Moreover, the measurement of absorption spectra is diagnostic of the oxidation state of transition-metal ion and can be used to infer the local conditions prevailing during formation.

For example, the spinel structure is adopted by many compounds with a formula AB2O4, where A and B are medium-sized cations. In this structure the cations sit in both octahedral and tetrahedral sites. The absorption spectra of transition-metal ions are quite different for these geometries, and so the site occupancy can be easily and unambiguously determined. The spinel NiAl2O4 is a case in point. The absorption spectrum of this material reveals that the Ni2+ ions are found in both positions. In the related spinel NiGa2O4, the Ni2+ ions exclusively occupy octahedral sites.

The problem of site occupancy is more acute in amorphous or disordered materials such as glasses because these structures cannot be determined by X-ray crystallography. However, it is often possible to incorporate a small amount of a transition metal into the structure as a probe of local geometry. For example, silicate glasses containing a small quantity of Co2+ are colored blue, typical of tetrahedral coordination, indicating that these ions replace Si4+ in the glass network. Similarly, small amounts of Mn2+, Co2+, and Fe2+ incorporated into a ZnCl2 glass show that in each case the absorption spectrum corresponds to that expected from tetrahedrally coordinated ions and indicates that the structure is formed from a random network of linked ZnCl4 tetrahedral units.

Cross-References

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Authors and Affiliations

  1. 1.Queen’s BuildingsCardiff UniversityCardiffUK