Encyclopedia of Color Science and Technology

2016 Edition
| Editors: Ming Ronnier Luo

Lanthanoid Ion Color

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-8071-7_257



The lanthanoids (often designated Ln) are the 15 elements with atomic numbers 57 (lanthanum) to 71 (lutetium).

Colors, Electron Configurations, and Energy Levels


Most of the lanthanoid ions exhibit rather pale characteristic colors when introduced into transparent solids or in water solutions, the most important being the Ln3+ state (Table 1). These colors arise from electronic transitions between the ionic ground state and energy levels derived from 4f electron configurations lying between 1.77 and 3.10 eV above it, giving absorption maxima in the visible wavelength range (700–400 nm). Of more practical importance is color produced when ions excited to higher energy levels fall back to these 4f-derived levels and thence to the ground state, giving rise to characteristic visible emission spectra, which are used in many applications including fluorescent printing inks used as security markers on banknotes.
Lanthanoid Ion Color, Table 1

Characteristic color of lanthanoid ions



4f occupancyb












Pale yellow



















Pale yellow










Red brown











Pale pink




Pale yellow






























aLn3+ is the principal ionic state encountered

bThere is uncertainty about the exact f-orbital occupation in many compounds

The 4f electrons in the lanthanoids are well shielded beneath an outer electron configuration, (5s2 5p6 6s2), and so are little influenced by the surrounding solid matrix, and although crystal-field effects (see Transition-Metal Ion Colours) contribute to the fine structure of the electronic spectra of the lanthanoid ions, these do not have a gross effect upon the color. This implies that the most important optical properties attributed to the 4f electrons on any particular lanthanoid ion do not (usually) depend significantly upon the host structure, so that lanthanoid elements find use in phosphors, lasers, and other light-emitting devices, where a host lattice can be chosen with respect to processing conditions without significantly changing the desirable color properties of the ion.

Lanthanoid Free-Ion Energy Levels

The energy levels of a free lanthanoid ion are usually labeled with atomic term symbols derived by Russell-Saunders (LS) coupling (although other coupling schemes are also used in this respect). A term is a set of states which are very similar in energy, and the appropriate term symbol is written as2S+1L where L is a many-electron quantum number describing the total orbital angular momentum of all 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 and is given a name: 1, singlet; 2, doublet; 3, triplet; 4, quartet; and so on. The total angular momentum quantum number L is given a letter symbol: L = 0, S; L = 1, P; L = 2, D; L = 3, F; 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 term symbol does not account for the true complexity of the energy levels of the lanthanoid ions. This arises from the interaction between the spin, S, and the orbital momentum, L, called spin-orbit coupling. For this the quantum number, J, is needed. It is given by:
$$ J = \left(L + S\right), \left(L + S\hbox{--} 1\right) \dots \left|L-S\right| $$
where |LS| is the modulus (absolute value) of the quantity LS. Each value of J represents a different energy level. The new quantum number is incorporated as a subscript to the term, now written 2S+1L J and called a level. It is found that a singlet term always gives rise to 1 level, a doublet 2, a triplet 3, and so on (Table 2). The energies of these levels can be sorted in terms of energy by Hund’s third rule: the level with the lowest energy is that with the lowest J value if the valence shell is up to half full and that with the highest J value if more than half full. The separation between the components of the spin-orbit energy levels is of the order of 0.1–0.25 eV. (For comparison, crystal-field splitting of these energy levels, which is due to the interaction of the f orbitals with the surrounding atoms in a solid or liquid, is about 0.01 eV.)
Lanthanoid Ion Color, Table 2

Ground state terms and levels of principal lanthanoid ions




La3+ f0


1 S 0

Ce3+ f1


2 F 5/2 2F7/2

Pr3+ f2


3 H 4 3H53H6

Nd3+ f3


4 I 9/2 4I11/24I13/24I15/2

Pm3+ f4


5 I 4 5I55I65I75I8

Sm3+ f5


6 H 5/2 6H7/26H9/26H11/26H13/26H15/2

Eu3+ f6


7 F 0 7F17F27F37F47F57F6

Eu 2+ f7


8 S 7/2

Gd3+ f7


8 S 7/2

Tb3+ f8


7 F 6 7F57F47F37F27F17F0

Dy3+ f9


6 H 15/2 6H13/26H11/26H9/26H7/26H5/2

Ho3+ f10


5 I 8 5I75I65I55I4

Er3+ f11


4 I 15/2 4I13/24I11/24I9/2

Tm3+ f12


3 H 6 3H53H4

Yb3+ f13


2 F 7/2 2F5/2

Lu3+ f14


1 S 0

aIn ascending energy order, ground state level bold

In the presence of a magnetic field, the spin-orbit levels are split further due to the Zeeman effect. The same is true of static electric fields, where it is called the Stark effect. In both cases, atoms or ions in a gas or free space will show an average effect because of the motion of the particles. However, in a crystal the atom and ion positions are more or less fixed, and the application of either magnetic or electric fields along certain symmetry directions will, in general, cause different degrees of splitting of the levels than the same fields applied along other symmetry directions. Zeeman splitting has been used to change the optical properties of lanthanoid ions in optical-magnetic materials.

Selection Rules

Electron transitions are governed by selection rules that give the probability that the transition will occur. Transitions between energy levels derived purely from f orbitals are forbidden by the Laporte selection rule. However, this rule may break down for ions in compounds. The main reason for this is that a degree of mixing between s, p, d, and f orbitals can occur when an ion is not located at a center of symmetry. As s, p, or d to f transitions are allowed, transitions giving rise to color are also allowed, to that a degree corresponding to the amount of orbital mixing achieved. 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 and in some circumstances can also contribute to observed lanthanoid color. The weak colors exhibited by Ln3+ ions are primarily due to these restrictions, especially when compared to typical crystal-field colors of the 3d transition-metal ions (see Transition-Metal Ion Colours).

Some Lanthanoid Absorption Colors

The 4f0 ions La3+ and Ce4+ and f14 ions Yb4+ and Lu3+ have no f – f energy levels and are colorless. The colorless ions Gd3+ and Tb4+ have a stable 4f7 configuration, and there are no energy levels in the appropriate energy range to give rise to color. The same is true for the 4f13 ion Yb3+.

Ce3+ and Eu2+

The lowest energy levels of Ce3+, arising from the single f electron, are2F7/2 and2F5/2. The next higher energy state for Ce3+ is the 5d level. Due to interaction of the more exposed 5d electrons with the surrounding crystal structure, this is broadened into a band of energies, which may also overlap with another broadened band of energies derived from the 6s energy level (Fig. 1a). Transitions between the 5d band and 4f levels are allowed, and the colors produced by transitions of this type are intense. This transition absorbs at violet end of the spectrum, and the absorption band often encroaches into the visible with a consequence that to the eye compounds are perceived as pale yellow.
Lanthanoid Ion Color, Fig. 1

Energy level diagrams (schematic) for Ce3+ and Eu2+ ions

Eu2+, with a configuration 4f7, also has a simple energy level diagram because the energy of the state obtained by transferring an f electron to the outer 5d orbitals is lower than the other 4f energy levels (Fig. 1b). As in the case of Ce3+, transitions from the ground state to the upper energy band are allowed. The energy gap is slightly smaller than in the case of Ce3+, and so the absorption moves slightly deeper into the visible spectrum. Because of this, the color of compounds is described as red brown.

Note that as the d orbitals interact strongly with the surrounding anions, the exact position of the band depends upon the host crystal. Thus, the colors of Ce3+ and Eu2+ compounds, unusually for lanthanoid ions, vary with host structure.

Pr3+, Tm3+, and Nd3+

The presence of Pr3+ ions generally colors the host matrix green. The principal transitions that contribute to the absorption spectrum are from the ground state3H4 to3P0, at approximately 485 nm (blue green), to3P1 at approximately 470 nm (blue), and to3P2 at approximately 450 nm (blue). A weak spin-forbidden transition to1D2 at approximately 590 nm (orange) is also present. Between these absorption peaks is a window of low absorption in the green region of the spectrum (Fig. 2a). The other “green” ion is Tm3+. Here the main transitions are from the ground state3H6 to3F3 at approximately 690 nm (red) and to3F2 at approximately 665 nm (red) and a weak spin-forbidden transition to1G4 at approximately 465 nm (blue). Between these absorption bands is a similar green transmission window to Pr3+ (Fig. 2b). The Nd3+ ion tends to impart a lilac hue to materials. The main transition here is from the ground state4I9/2 to4G5/2, which absorbs strongly at approximately 585 nm (yellow), together with a transition to4G7/2 at approximately 525 nm (green) and2G9/2 at 510 nm (blue green). These absorption peaks remove the middle part of the optical spectrum, leaving both the violet and red extremes, so imparting a lilac hue to compounds.
Lanthanoid Ion Color, Fig. 2

Energy level diagrams (schematic) for (a) Pr3+, (b) Tm3+, and (c) Nd3+

Some Applications of Lanthanoid Fluorescence Colors

Trichromatic Fluorescent Lamps

Trichromatic (color 80) fluorescent lamps use phosphors with active lanthanoid ions. Generally the lanthanoid ions can absorb a wide range of ultraviolet radiation efficiently, exciting the ions from the 4f-derived ground state to a broad band of energies formed from interaction of 5d and 6s band. Energy is then lost internally, in effect causing the phosphor matrix to warm slightly, until the sharp 4f-derived energy levels are reached. Photon emission between these energy levels then occurs, giving color output. The favored red emitter is Eu3+ doped into Y2O3, (Y2O3:Eu), with the Eu3+ ions occupying the Y3+ sites. The ground state of Eu3+ is7F0. A transition from this state to the higher energy band 5d band absorbs the ultraviolet radiation given off by excited mercury atoms at 254 nm. Subsequent internal energy loss leaves the ion in the5D0 level. The main optical transition is between this level and7F2, producing emission at 611 nm (Fig. 3a). The green emission is from Tb3+ in host matrices La(Ce)PO4, LaMg(Ce)Al11O19, or La(Ce)MgB5O10, in which the Tb3+ ions replace La3+. Tb3+ absorbs the mercury emission poorly so is coupled with a sensitizer, usually Ce3+, which is able to absorb the 254 nm wavelength mercury radiation efficiently by way of the 5d band. This absorbed energy is then transferred to the Tb3+ ions. The green emission, at wavelength close to 540 nm, is mainly from a5D47F5 transition (Fig. 3b). Three other peaks of lesser intensity occur:5D47F6, 489 nm;5D47F4, 589 nm; and5D47F3, 623 nm. The blue emission is produced by Eu2+ ions. The excitation and emission is directly to and from the 5d-derived band. The position of this band is strongly influenced by the host structure (see above) and the usual tricolor lamp phosphor, BaMgAl10O17: Eu is chosen so as to have a suitable blue emission, with a maximum at 450 nm (Fig. 3c).
Lanthanoid Ion Color, Fig. 3

Energy level diagrams (schematic) for (a) Eu3+, (b) Ce3+/Tb3+, and (c) Eu2+ in trichromatic lamp phosphors. ET energy transfer

Plasma Displays

Plasma display panels are made up of a pair of glass plates containing a series of cells each of which acts as a miniature fluorescent lamp as described above. Each lamp is several hundred microns in size, and there are several million such lamps in a display. Each pixel consists of three lamps, giving off red, blue, and green light. The working gas in the cells is a mixture of helium and xenon. When a high voltage is applied across two electrodes above and below a well, the gas is excited into a state that emits ultraviolet radiation, with principal wavelengths of 147 nm and 172 nm. Each well is coated internally with a red, green, or blue phosphor. The main lanthanoid phosphors used at present are a yttrium gadolinium borate doped with europium, (Y, Gd)BO3:Eu3+, which gives a red emission, barium magnesium aluminate doped with europium, BaMgAl14O23:Eu2+, for blue emission (see Fig. 3). The green emission utilizes Mn2+ rather than a lanthanoid ion.

Phosphor Electroluminescent Displays

Electroluminescent displays containing a thin film of a phosphor, called thin film electroluminescent (TFEL) displays, find use as flat panel color displays and backlighting in products such as instrument panels. The most promising devices use ac supplies in a thin film electroluminescent (ACTFEL) display. Under the influence of an applied electric field, electrons enter the phosphor at the junction with a surface insulating coating. These are accelerated under the influence of the field until they collide with the luminescent centers in the phosphor, transferring energy in the process. The excited luminescent centers then fall back to the ground state and release energy by light emission.

Red emission is from calcium sulfide doped with europium (CaS:Eu2+), the color being generated by the transition from the 5d band to the ground state8S7/2 (Fig. 4a). At first sight this is surprising as the Eu2+ derived tricolor lamp phosphor has a blue output. However the position of the upper energy band depends upon the interaction of the d orbitals with the surrounding crystal, and in ZnS the softer bonding gives a broad emission centered close to 640 nm. Green emission is produced by zinc sulfide doped with terbium (ZnS:Tb2+), with an output at a wavelength close to 545 nm, mainly from a5D47F5 transition (Fig. 4b). Three other peaks of lesser intensity occur:5D47F6, 489 nm;5D47F4, 589 nm; and5D47F3, 623 nm. Blue emission still poses a problem for these displays, but the thiogallates CaSr2S4, SrGa2S4, and BaGa2S4 doped with the 4f1 ion Ce3+ are currently favored. The transitions between the 5d band and the 4f1 ground state doublet2F5/2 and2F7/2 are both in the blue region of the spectrum centered at 459 nm for the Ca compound and 445 nm for the Sr and Ba phases (Fig. 4c).
Lanthanoid Ion Color, Fig. 4

Energy level diagrams (schematic) for (a) Eu2+, (b) Tb3+, and (c) Ce3+ in ac powered Thin Film Electroluminescent Display (ACTFEL) displays


The conversion of infrared radiation to visible is variously known as upconversion, frequency upconversion, anti-Stokes fluorescence, or cooperative luminescence. The majority of studies of upconversion have involved the lanthanoid ions Er3+, Tm3+, Ho3+, and Yb3+. At present the most efficient upconversion materials for infrared to visible conversion are lanthanoid fluorides such as NaLnF4 doped with Yb3+/Er3+ or Yb3+/Tm3+ couples. The energy for upconversion can be gained by the active ion via several competing energy transfer processes. In principle, the simplest is for the active ion to pick up photons in two distinct steps. The first photon excites the ion from the ground state to an excited energy level, a process referred to as ground state absorption (GSA). A subsequent photon is then absorbed to further promote the excited ion to a higher energy level again – excited state absorption (ESA). The oxide CeO2 doped with approximately 1 % Er3+ exhibits upconversion in this way. Irradiation with near-infrared photons with a wavelength close to 785 nm excites the Er3+ ions from the4I15/2 ground state to the4I9/2 level:
$$ {}^4{\mathrm{I}}_{15/2}+h\nu {\left(785\ \mathrm{nm}\right)}^4\to {\mathrm{I}}_{9/2} $$
Subsequent internal energy loss drops the energy to the4I11/2 and4I13/2 levels (Fig. 5a). The ions are then excited by ESA. Those in the4I11/2 energy level are excited to the4F3/2, 5/2 doublet:
$$ {}^4{\mathrm{I}}_{11/2}+h\nu {\left(785\;\mathrm{nm}\right)}^4\to {\mathrm{F}}_{3/2,5/2} $$
Lanthanoid Ion Color, Fig. 5

Upconversion using Er3+ doped into CeO2, schematic: (a) GSA + relaxation; (b) ESA + relaxation; (c) ESA + relaxation; (d) light emission

These states subsequently relax to the2H11/12,4S3/2 and4F9/2 levels:
$$ {}^4{\mathrm{F}}_{3/2,5/2}{\to}^2{\mathrm{H}}_{11/2} {+}^4 {\mathrm{S}}_{3/2} {+}^4{\mathrm{F}}_{9/2}+\mathrm{phonons} $$
The ions in the4I13/2 energy level follow a similar path, being excited to the2H11/2 energy level:
$$ {}^4{\mathrm{I}}_{13/2}+h\nu {\left(785\ \mathrm{nm}\right)}^2\to {\mathrm{H}}_{11/2} $$
then subsequently relax to the4S3/2 and4F9/2 levels:
$$ {}^2{\mathrm{H}}_{11/2}{\to}^4{\mathrm{S}}_{3/2} +^4{\mathrm{F}}_{9/2} + \mathrm{phonons} $$
The result of this is that the levels2H11/2,4S3/2 and4F9/2 are populated to varying degrees, depending upon the precise details of the excitation and relaxation steps. Subsequent loss of energy from these levels gives rise to green and red emission:
$$ {}^2{\mathrm{H}}_{11/2}{\to}^4{\mathrm{I}}_{15/2}+h\nu \left(\sim 525\ \mathrm{nm},\ \mathrm{green}\right) $$
$$ {}^4{\mathrm{S}}_{3/2}{\to}^4{\mathrm{I}}_{15/2}+h\nu \left(\sim 550\ \mathrm{nm},\ \mathrm{green}\right) $$
$$ {}^4{\mathrm{F}}_{9/2}{\to}^4{\mathrm{I}}_{15/2}+h\nu \left(\sim 655\ \mathrm{nm},\ \mathrm{red}\right) $$
All upconversion spectra from Er3+, including those using different mechanisms, are similar, but the relative intensities of the three peaks vary with concentration of the ions and the nature of the host matrix.

Energy transfer, in which input radiation is picked up by a sensitizer and is then passed to the emitter, is the mechanism of operation of host structures containing the co-dopants Yb3+/Er3+ which gives a strong green emission and Yb3+/Tm3+ that gives a blue emission. The ion that absorbs the incoming infrared radiation is the Yb3+ ion, which then transfers energy to Er3+ or Tm3+ centers. Other upconversion mechanisms are also known.

Quantum Cutting

Quantum cutting is the reverse of upconversion, as one high-energy photon is processed (i.e., cut) to give out several lower energy photons, typically transforming ultraviolet to visible. There are several mechanisms for quantum cutting; here photon cascade emission, exhibited by Pr3+ ions, is described. Initial absorption of high-energy 185 nm ultraviolet photons results in excitation to the 5d-6s energy band (Fig. 6). Subsequent relaxation takes the ion to the1S0 level. Thereafter, the transitions giving rise to visible output are the following:
$$ {}^1{\mathrm{S}}_0{\to}^3{\mathrm{P}}_3 \mathrm{at} \sim 400\ \mathrm{nm},{\mathrm{then}}^3{\mathrm{P}}_0{\to}^3{\mathrm{H}}_4 \mathrm{ground}\ \mathrm{state}\ \mathrm{at}\sim 480\ \mathrm{nm} $$
$$ {}^1{\mathrm{S}}_0{\to}^1{\mathrm{D}}_2 \mathrm{at} \sim 330\ \mathrm{nm},\ \mathrm{the}{\mathrm{n}}^1{\mathrm{D}}_2{\to}^3{\mathrm{H}}_4 \mathrm{ground}\ \mathrm{state}\ \mathrm{at} \sim 605\ \mathrm{nm} $$
Other ions such as Tb3+ are also candidates for quantum cutting devices, but the mechanisms involved are more complex than that with Pr3+.
Lanthanoid Ion Color, Fig, 6

Visible light emission (quantum cutting) via photon cascade emission from Pr3+ ions irradiated by ultraviolet light



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Authors and Affiliations

  1. 1.Queen’s BuildingsCardiff UniversityCardiffUK