The fifteen causes of color: The physics and chemistry of color · 2014-03-11 · The Fifteen Causes of Color: The Physics and Chemistry of Color The fifteen causes of color derived

Kurt Nassau AT&T Bell Laboratories 600 Mountain Avenue Murray Hill, New Jersey 07974

The Fifteen Causes of Color: The Physics and Chemistry of Color

The fifteen causes of color derived from a variety of physical and chemical mechanisms are summarized in five groups in this article. Vibrations and simple excitations explain the colors of incandescence (e.g. ,flames), gas excitations (neon tube, aurora), and vibrations and rotations (blue ice and water). Ligand-field-effect colors are seen in transition-metal compounds (turquoise, chrome-oxide green) and impurities (ruby, emerald). Molecular orbitals explain the colors of organic compounds (indigo, chlorophyll) and charge-transfer compounds (blue sapphire, lapis lazuli). Energy bands are involved in the colors of metals and alloys (gold, brass), of semiconductors (cadmium yellow, vermillion), doped semiconductors (blue and yellow diamond), and color centers (amethyst, topaz). Geometrical and physical optics are involved in the colors derived from dispersive refraction (rainbow, green flash), scattering (blue sky, blue eyes, red sunset), interjerence (soap bubbles, iridescent beetles), and diflraction (the corona aureole, opul).

Introduction

We perceive color when the different wavelengths com- posing white light are selectively interfered with by matter (absorbed, reflected, refracted, scattered, or diffracted) on their way to our eyes, or when a non-white distribution of light has been emitted by some system. Fifteen specific physical or chemical mechanisms are outlined, based on the book The Physics and Chemistry of Color. ’ More-detailed descriptions and applications can be found there, together with an extended listing for further reading. In addition to being organized by mechanisms, the book also includes extended discussions of the range of causes involved in a variety of fields including pigments, dyes, and their com- patability and deterioration; the preservation of color in our artistic heritage; color in glass, glazes, enamels, minerals, gemstones, and the atmosphere; biological colorations and color changes in foods; and color vision, light sources,

0 1987 by John Wiley & Sons, Inc.

luminescence, color television, lasers, and holography. These topics are not discussed here, neither are particle-wave dual- ism, quantum theory, and other theoretical matters.

The organization used for the fifteen causes of color is summarized in Table I. As in any attempt at detailed clas- sification, there is an element of choice, with some overlaps and some near-arbitrary assignments. The scheme uses five

TABLE I . Examples of the fifteen causes of color.

1. 2.

3.

4.

5.

6.

7.

12.

13.

14.

15.

Vibrations and simple excitations Incandescence: flames, lamps, carbon arc, limelight Gas excitations: vapor lamps, lightning, auroras, some lasers Vibrations and rotations: water, ice, iodine, blue gas flame

Transitions involving lipand-field effects Transition-metal compounds: turquoise, malachite, chrome green, copper patina, Thenard’s blue, some fluorescence, lasers, and phosphors Transition-metal impurities: ruby, emerald, aquamarine, red iron ore, some fluorescence and lasers

Transitions between molecular orbitals Organic compounds: most dyes, most biological’ colorations, some fluorescence and lasers Charge transfer: blue sapphire, magnetite, lapis lazuli, ultramarine, Prussian blue

Transitions involving energy bands Metals: copper, silver, gold, iron, brass, “ruby” glass Pure semiconductors: silicon, galena, cinnabar,^ vermillion, cadmium orange, diamond Doped semiconductors: blue and yellow diamond, light- emitting diodes, some lasers and phosphors Color centers; amethyst, smoky quartz, desert “amethyst” glass, some fluorescence and lasers

Geometrical and physical optics Dispersive refraction: rainbows, halos, sun dogs, green flash of sun, “fire” in gemstones, prism spectrum Scattering: blue sky, red sunset, blue moon, moonstone, blue eyes, skin, butterflies, bird feathers and some other biological colors, Raman scattering Interference: oil slick on water, soap bubbles, coating on camera lenses, some biological colors Diffraction: aureole, glory, diffraction gratings, opal, some biological colors, most IiQuid crvstals

4 CCC 0361 -231 7/07/01 0004-23$04.00 COLOR research and application

PLATE I. Six blue gemstones with different causes of color. Above: Maxix-type beryl (radiation-induced color center), blue spinel (ligand-field color from a cobalt impurity), spinel “doublet” (colorless spinel containing a layer of organic dye). Be-

major groupings based on the fundamental mechanisms involved: Three of these, vibrations and simple excitations, energy bands, and geometrical and physical optics, are usually considered to be part of the physics curriculum; molecular orbitals are usually a part of chemistry; and ligand fields may be covered in either discipline. It is rare, however, for even an extended academic treatment of such topics to concern itself with the colors as such.

There are some conventional color attributions such as that green is caused by copper, dark blue originates from cobalt, and so on. Yet even in a highly restricted field such as the six dark-blue gemstones of Plate I, only one is due to cobalt and five of the groups of Table I are represented;

PLATE II. Some colors produced by chromium. Above: Al- exandrite, emerald, and ruby (CP+ -impurity ligand-field colors). Center: chromium carbonate, chromium chloride, and chromium oxide (Cr3+ compound ligand-field colors). Below: am- monium dichromate and potassium chromate (02 + CP+ charge-transfer colors).

low: shattuckite (cobalt compound), blue sapphire (Fe-Ti intervalence charge transfer), lapis lazuli (S3- anion-anion charge transfer); the largest stone is 2 cm across.

a sixth could have been added if the deep-blue Hope diamond would have been available! Chromium, on the other hand, can produce almost any color as can be seen in Plate 11. It is clear that generalizations are meaningless and detailed study is needed to establish the specific cause of the color of any unknown material.

The detailed understanding of the science of color began in 1666, when Newton first used the word “spectrum” for the array of colors produced by a glass prism. He recognized that the colors comprising white light are “refracted” (bent) by different amounts and he also understood that there is no “colored” 1ight;the color being in the eye of the beholder. There is merely a range of energies-r the proportional frequencies and the inverse wavelengths-as illustrated in Fig. 1; the specific system employed depends on whether the user is a chemist, physicist, spectroscopist, and so on. For convenience, energy in electron volts (eV) and wavelength in nanometers (nm) are used here as the variables. Note that (wavelength in nm) x (energy in eV) = 1239.9.

Newton assigned seven colors to the spectrum by analogy with the musical scale. Visible light is merely a small part of the full electromagnetic spectrum, which extends from cosmic rays at the highest energies down through gamma rays, x-rays, the ultraviolet, the visible, the infrared, and radio waves to induction-heating and electric-power-trans- mission frequencies at the lowest energies. Note that this is the energy per quantum (photon if in the visible range) but not the total energy; the latter is a function of the intensity in a beam.

It might seem remarkable that so many distinct causes of color should apply to that small band of electromagnetic radiation to which the eye is sensitive, a band less than one “octave” wide in an electromagnetic spectrum of more than 80 “octaves.” So much happens in this narrow band because

Volume 12, Number 1, February 1987 5

WAVELENGTH (nm) ENERGY COLOR WAVELENGTH FREQUENCY

(NANOMETERS) ~ 1 0 ~ ~ (HERTZ) I I (ELECTRON VOLTS)

sw

ULTRA- VIOLEl

4

b

3-

2 -

V I S I

- vioL E r

L 600

700

1000

8 L UE

GREEN

ORANGE YELLOW B

-RED

INFRA-

0

FIG. 1. The spectrum, with three ways of specifying the spectral colors numerically.

this is the region in which the interaction of radiation with electrons first becomes important. Radiation at lower energies induces a relatively small motion of atoms and molecules, which we sense as heat, if at all. Radiation at higher energies has a destructive effect since it can ionize atoms, that is, completely remove one or more electrons, and can permanently damage molecules. Only in the narrow optical region, just that region to which the human eye is sensitive, is the energy of light well attuned to the electronic structure of matter with its wide diversity of colorful interactions.

Electrons are involved in essentially all of our 15 mechanisms and we “see” electrons in a real sense whenever we perceive color.

We now know that the normal dispersion curve leading to Newton’s spectrum, with the refractive index increasing with increasing energy (decreasing wavelength), is only the small central region of the full dispersion curve as shown for a colorless glass in Fig. 2 . At the left end, at low energies, there are features derived from the absorption of infrared energy, which produces excited-lattice vibrations, originating in the molecular framework derived from the bonding between atoms. At the right end in Fig. 2 , at high energies, there are features derived from the unpairing and excitation of previously paired electrons on individual atoms, leading to absorptions in the ultraviolet.

The infrared absorptions of Fig. 2 can shift to occur in the visible region with light, strongly bonded atoms, as in Mechanism 3 of Table I , discussed below. Similarly, the ultraviolet absorptions of Fig. 2 can also occur in the visible region in a wide variety of situations, leading to color from Mechanisms 1, 2 and 4-1 1 of Table I.

0.51 I I I 0.01 0.1 1 .o I0 i

ENERGY ( e v ) 0

FIG. 2. The full dispersion curve of a colorless crown glass.

Mechanism 1: Color Produced by Incandescence

Our colloquial usage of “red hot,” “white hot,” and so on, is part of the color sequence black, red, orange, yellow, white, and bluish white, seen as an object is heated to successively higher temperatures. The light produced consists of photons emitted when atoms and molecules release part of their thermal vibration energy. Max Planck found in 1900 that the quantization of energy was necessary to explain the idealized “black-body” radiation, thus leading to the modem quantum theory. At any given temperature there is a peak in the emission of radiation, as can be seen in the curves of Fig. 3, with a shift of the peak of the emission curve toward shorter wavelength (higher energy) with increasing temperature (Wien’s law). The emission from the 5700°C temperature of the surface of the sun gives us our definition of white; its peak near 550 nm (2.25 eV) is mirrored in the maximum sensitivity of our eyes in the same region, reflecting our evolution in the vicinity of the sun.

The color of incandescence is used in radiation pyro- meters to measure temperature. Illumination sources from the primitive candle through limelight, arc lamps, and the modem incandescent-filament lamps and flash bulbs all uti- lize incandescence; usually the aim is to avoid color. Part of the light from pyrotechnic devices is also derived from chemical-reaction-produced incandescence.

Mechanism 2: Color Produced by Gas Excitation

The incandescence discussed above applies to the color of any substance when heated. However, in gas excitations it is specific atoms, present as a vapor or a gas, which have their electrons raised into higher energy levels by a variety of excitations; light is then emitted when the excess energy is released as photons. Examples include electrical excitations as in arcs, sparks, lightning, neon tubes, and sodium- and mercury-vapor lamps; chemical excitation as in the chemists’s flame test for sodium and a few other elements (also utilized in pyrotechnic devices); and high-energy particles as in the northern and southern auroral displays. An unusual Occurrence is found in triboluminescence, as when

6 COLOR research and application

10

8 -

6 -

F

z W I-

5 4 -

z

2 -

WIEN’S

-

L

‘ 900 \

I I I

I I I

. AW

- 0 1000 2000 3000 4000 5000

WAVELENGTH (nm)

FIG. 3. Blackbody curves for different temperatures, also showing the displacement of the maximum according to Wien’s law.

we crunch a wintergreen “lifesaver” in front of a mirror in the dark. The high-voltage field produced during the formation of new electrically-charged sugar crystal surfaces accelerates electrons which excite nitrogen-gas molecules to produce the ion N2+ which has a blue luminescence; some ultraviolet is also produced and causes the oil of wintergreen (methyl salicilate) to fluoresce with a particularly intense blue-light production.

Some of the possible energy levels for a gaseous sodium atom are shown in Fig. 4. A high voltage, as in a sodium- vapor lamp, produces ionization from the initial “ground state” into Na+ plus one electron at the top line of this figure. As the electron recombines the system passes along transitions, only a few of which are shown as arrows in Fig. 4, with the emission of radiation. The position of the various levels shown, as well as the specific transitions which the system can follow, are explained by quantum theory; all paths are constrained by the “selection rules” to terminate in the lowest two arrows, which correspond to the emission of the bright-yellow sodium “doublet” lines at 589.7 and 589.0 nm.

IONIZED No’ at 5.12 eV

- 1-/- -\-\-

FIG. 4. Energy-level scheme of an atom of sodium, showing some of the allowed transitions in returning back to the ground state after ionization.

Sodium- and mercury-vapor lamps efficiently emit yellow and bright blue, respectively, and are often used in parking lots, where they distort the color of our autos. The mercury also produces much ultraviolet light; in fluorescent-tube lamps this is converted by a phosphor coating into lower-energy yellow, orange, and red light to produce a better color balance for indoor lighting. Gas lasers, as in the helium-neon laser, use gas excitations with optical feedback from mirrors at each end of the tube to produce coherent light, in which all the light waves have almost the same frequency and are coherent, that is, in step, both in space and in time.

Mechanism 3: Color Produced by Vibrations and Rotations

As discussed in connection with Fig. 2 above, most vibrations between atoms absorb only at very low energies in the infrared. Just as the pitch of a vibrating string is raised if the mass of the string is reduced and the tension applied to the string is increased, so the highest-frequency vibrations occur with the lightest atoms, as with hydrogen, when most strongly bonded, as in the hydrogen bonding in water. The bent water molecule in the free state has three fundamental vibrations, as shown in Fig. 5. It is helpful to think of metal spheres fixed on strong springs in visualizing these vibrations. When water molecules are trapped in the channels of


0.

f

b.

c. LATTICE VIBRATIONS C H R O M O P H O R E S

B V M O L E C U L E V I B R I \ T I O N ; o y

C.

/ FIG. 5. The three normal modes of the bent water molecule H20: (a) the symmetrical stretch, (b) the symmetrical bend, and (c) the antisymmetrical bend.

the gemstone emerald, the absorption spectrum of Fig. 6 clearly shows features that can be identified with these vI , v2 , and v3 vibrations in the ultraviolet region at the left, as well as overtones and combination tones at somewhat higher frequencies (higher energies, shorter wavelengths).

In liquid water or solid ice, the hydrogen bonding between adjacent molecules raises the energies yet a little further and

0 I .o 2 0 3 0

ENERGY [ aV f

FIG. 6. The absorption spectrum of colorless beryl (b) and emerald (e), including vibrational absorptions derived from water molecules and carbon dioxide. [After D. L. Wood and K. Nassau, Am. Mineral. 53, 777 (1968).]

PLATE Ill. Iodine vapor produced by heating iodine crystals (combined electronic-vibration-rotation color).

leads to a very small combination absorption at the low- energy red end of the visible spectrum. As a result, pure water and ice have a pale blue color, best seen at tropical white-sand beaches and in ice caves in glaciers (green colors are usually derived from algae).

One might assume that some other hydrogen-containing liquids and solids beside water, such as liquid ammonia, could possess traces of bluish color because of similar effects. However, water and ice are the only two chemical substances we normally have the opportunity to observe in pure form in sufficiently large bulk so that a weak coloration becomes detectable.

Vibrational states as well as the related rotational states also can modify the energy of the electronic excitations of the previous section, and are involved in the violet color of the iodine vapor of Plate 111, the reddish-brown of bromine, and the green of chlorine. The blue-green light emitted by an oxygen-rich gas flame as seen on a kitchen range also involves such combination vibrational, rotational, and electronic excitations in the unstable molecules CH and Cz.

Mechanisms 4 and 5: Color Produced by Ligand-Field Effects

An extremely high energy is required to excite paired electrons in most inorganic substances, resulting in electronic absorptions in the ultraviolet as in the transparent glass of Fig. 2. However, when unpaired electrons are present in transition-metal compounds, usually in d orf orbitals, then the absorptions can occur at lower energies. This leads to the ligand-field colors of Mechanism 4 and provides the colors of many minerals and paint pigments. This same scheme applies to Mechanism 5 , in which the transition metal may be only an impurity, typically present at the one- percent level, thus providing the color in many of our gemstones and in some glass.

Consider a crystal of pure A1203, also known as corundum and as colorless sapphire when in gem-quality form. In this material each aluminum is surrounded by six oxygens in the form of a slightly distorted octahedron, as shown in Fig.


I I I Al surrounded by Irregular Regular six 0 i v AI,03 octahedron octahedron

FIG. 7. The distorted-octahedral oxygen-ligand environ- ment around an Al ion in corundum AI,O3 shown in two different ways, (A) and (B), and a regular octahedron (C).

7. All electrons are paired and there is no absorption of light. Now replace one out of every hundred aluminums by a chromium. Chromium in the trivalent state has 18 paired electrons in the 1s through 3p orbitals, but only three unpaired electrons in the 3d orbitals, which have the capacity to hold ten electrons. In an isolated triply charged chromium ion all the 3d electrons would occupy levels having the same energy, as shown in the central part of Fig. 8 , so that, again, light-absorbing transitions could not occur.

Such energy levels, however, are perturbed by the existence of the six neighboring oxygens-the “1igands”- -as in Fig. 7; both the geometrical distribution (here distorted octahedral) and the strength of the bonding (or the equivalent size of the electric field produced by the oxygen ions-the “crystal field” or “ligand field”) affect the dis-

A. B:

e- da2-y2,dz2

TETRAHEDRAL FREE OCTAHEDRAL FIELD ION FIELD

FIG. 8. The splitting of the five 3d orbitals in a tetrahedral and an octahedral ligand field.

tribution and spacing of the levels, as indicated in Fig. 8. The study of the energy-level spacing and the transition rules is called ligand-field theory, which can also be viewed as a special case of the molecular-orbital theory discussed below; an earlier, less-sophisticated version was crystal-field theory.

The specific way in which 1% or so C?’ in A1203, usually called ruby, leads to color and fluorescence is shown in parts A through C of Fig. 9. The symmetry of the ligand field and its strength combine to give the energy-level scheme,

c

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3.0 ‘TI

2.5 -

4 2.0 Ti?

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1“ FLUORESCENCE

{ 0.5

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FIG. 9. The term diagram of CP+ in a distorted octahedral field (A), the energy levels and transitions in ruby (B), and

the resulting absorption spectrum and fluorescence of ruby (C) and emerald (D).


PLATE IV. (a) White-light and (b) ultraviolet views of a min- era1 specimen from Franklin, New Jersey, containing calcite CaC03 (tan color with red fluorescence) and willemite ZnSi04 (brown with green fluorescence), both containing Mn2+, as

well as green synthetic emerald BesSisOje:Cr and red synthetic ruby AI2O3:Cr, both showing the red CP’ fluorescence; the ruby is 2 cm across.

the “term diagram,” at A and the transition scheme at B in Fig. 9. Here the violet and yellow-green regions of light passing through ruby are absorbed, as in the two upward arrows leading to the 4TI and 4T2 levels, thus producing the absorption spectrum shown at C in Fig. 9 and giving ruby its deep red color with purple (bluish) overtones.

In losing its energy again, the C$+ must pass through the state labeled 2E with the emission of some heat. In returning from ’E back down to the ground state, a quantum of red light, the red fluorescence of ruby, is emitted. This is best seen under ultraviolet illumination as in Plate IV; here the Cr’ + is excited into higher energy levels, not shown in Fig. 9, but nevertheless returns back down through the 2E level as required by the selection rules mentioned previously.

Consider now the circumstances when chromium is present in beryllium aluminum silicate Be2AI2Si6Ol8, known as beryl in the absence of chromium but as emerald in its presence. Here too the symmetry is distorted octahedral, but the ligand field is a little weaker, 2.05 eV instead of the 2.23 eV of ruby at A in Fig. 9. This relatively small change produces a significant shift in the absorption bands, as shown at D in Fig. 9, thus resulting in a change from the red color of ruby to the green color of emerald.

Interestingly enough, the position of the ’E level involved in the fluorescence does not change significantly with the ligand field, as can be seen at A in Fig. 9, so that the same red fluorescence is present in both red ruby and green emerald, as illustrated in Plate 1V. The absorption and fluorescence of emerald can also be seen in Fig. 6. The red fluorescence in ruby is employed in the ruby laser.

With such a drastic change in color in going from ruby to emerald resulting from a relatively small change in the ligand field, one might wonder what would be the result of a ligand field intermediate between those of emerald and ruby. Nature has provided for us an answer to this question in the form of the extremely m e and precious gemstone alexandrite, an answer that demonstrates how she can con- found our expectations and yet turn out to be perfectly

reasonable in retrospect. The absorption bands are so del- icately balanced in alexandrite that in blue-rich daylight or the similar-quality light from a fluorescent-tube lamp we see an intense blue-green color, somewhat resembling that of an emerald, while in red-rich candle light or the light from an incandescent lamp we perceive a deep-red color, somewhat resembling that of a ruby, as shown in Plate V. Nature has found a way of avoiding the almost-impossible task of providing a color truly intermediate between the green of emerald and the red of ruby!

One result of the symmetry of the ligand field is “pleo- chroism,” the existence of up to three colors in different directions in a crystal. The two “dichroic” colors, orange. and purple, are seen with polarized light in a ruby, as shown in Plate VI.

As the chromium concentration of ruby is increased, there is a change from red through gray to green as the ligand field becomes weaker, as shown in Fig. 10; pure chromium oxide Cr203 is the dark-green pigment chrome green. A specimen on the red side of gray can be turned green by heating it to cause a reduction of the ligand field as the atoms move apart from thermal expansion in “thermochro-

PLATE V. A synthetic alexandrite gemstone, 5 mm across, changing from a reddish color in the light from an incandescent lamp to a greenish color in the light from a fluorescent- tube lamp.


PLATE VI. The purple-orange dichroism (CF+ ligand-field colors) in a 3-cm-diameter synthetic ruby; the arrows indicate the electric vectors of the polarizers.

mism”; in the reverse “piezochromism,” green can be turned red by the application of pressure.

Under Mechanism 4 are included “idiochromatic” (self- colored) transition-metal substances, including pigments such as the green viridian Cr,O(OH), and the chrome-oxide green mentioned above; the blue smalt glass K2CoSi308 and Then- ard’s blue, Al,CoO,; gems such as pink rhodochrosite MnCo3 and green malachite Cu2(C03)(OH),; and minerals and ores such as brown manganite MnO(OH), red iron ore Fe2O3, yellow geothite FeO(OH), and green bunsenite NiO.

Small amounts of these same transition metals provide color in otherwise colorless substances in Mechanism 5; these are sometimes called “allochromatic” (other-colored). Examples include many gemstones such as the chromium- based ruby, emerald, and alexandrite discussed above; the manganese-containing pink-colored morganite form of beryl; and the iron-colored blue and green aquamarines, yellow citrine, and green jade (in part). Some colors in glass, glazes, and enamels are also based on transition-metal compounds or impurities.

Mechanism 6: Color Produced by Molecular Orbitals

Under this heading is covered color in organic compounds involving electrons belonging to several atoms; the related

2,25~,COLORLESS SAPPHIRE

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2.151 I \ -I

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10. The variation of the liaand field and the color in the mixed system of colorless sapphire Al2O3 and chrome green Cr203 [After D. Reinen, Struct Bonding (Berlin) 6, 39 (1 969) .]

FIG. 11. Two resonance structures of crystal violet (left), and a nitrophenylenediamine dye (right).

charge-transfer colors are discussed separately as the next mechanism.

A “conjugated” system in an organic compound consists of alternating single and double bonds in a chain of atoms, usually carbons; a result of such an arrangement is that the “wbonding” electrons involved in the second bond of the double bonds are no longer localized but can be considered to belong to the whole conjugatd chain. The excited states of such electrons occur at much lower energies than those of the usual paired electrons, resulting in energy-level schemes that can absorb and emit light. The absorptions of the conjugated cyclic benzene C6H6 or the linear 2,4 hexadiene CH3--CH=CH-CH=CH--CH3 are still in the ultraviolet, much as in Fig. 2; with the conjugated linear ten- carbon chain 2,4,6,8 decatetraene C10H14, however, the absorption has just moved into the blue end of the spectrum and a pale yellow color results.

In addition to extending the length of the conjugated chain, there are a variety of other means of obtaining the desired “bathochromic” shift of the absorptions to lower energies. Such shifts are produced by the presence of electron-donor groups that pump electrons into the conjugated system, such as the -NH2 group in the dye methyl violet C+(C6H4NH2)3 shown at the left in Fig. 11, or electron- acceptor groups that pump electrons out of the conjugated system, such as the -NO, group. An example of a molecule containing both is shown at the right in Fig. 11; this absorbs at 470 nm in the blue part of the spectrum and is one of the nitrophenylenediamines used in hair dyes, able to penetrate into the hair because of the small size. In general, systems that have many resonance structures tend to provide large bathochromic shifts; two of the resonance forms of crystal violet produced by electron shifts are shown at the left in Fig. 11.

A large multi-ring quinone compound is the red-violet

Indigo Violanthrone

FIG. 12. Violanthrone (left) and indigo (right).


1.5 2.0 2.5 ENERGY teV)

FIG. 13. Absorption and fluorescence spectrum of cresyl violet, also known as the laser dye oxazine 9, dissolved in ethanol. [After K. H. Drexhage, in F. P. Schafer, Ed., Dye Lasers, Springer Verlag, New York, 1973, p. 173.1

vat dye violanthrone shown at the left in Fig. 12, which is attractive to look at even in the formula!

A useful conjugated “chromophore” (color-bearing) group is that of the blue dye indigo, shown at the right in Fig. 13. This has been used since antiquity, e.g., in the form of woad by the “Picts” (painted people) whom Julius Caesar fought in Britain in 58 BC, up to today’s all-pervading blue jeans. With two bromine atoms present, the result is Tyrian purple, laboriously extracted from certain sea shells and worn by the Roman emperors as a symbol of their status.

Molecular-orbital dyes occur widely in the plant and animal kingdoms as well as in the triumphs of the modem synthetic dye and pigment industry. Just as with ligand-field energy levels, some of the absorbed energy may be re- emitted in the form of fluorescence. This is used in dye lasers, where tuning of the wavelength of the fluorescence laser light may be possible because the fluorescence peaks tend to be rather broad, as shown in Fig. 13. Chemical energy can also excite such a system and lead to fluorescence (or the much-slower phosphorescence), as in the biolumi- nescence of fireflies and angler fishes and in the chemoluminescent “lightsticks” of Plate VII, in which a slow chemical reaction can liberate light over a period of several hours.

PLATE VII. Four chemoluminescent “Cyalume” light sticks, 15 cm long, made by the American Cyanamid Company.

Mechanism 7: Color Produced by Charge Transfer

A crystal of corundum containing a few hundredths of one percent of titanium is colorless. If, instead, it contains a similar amount of iron, a very pale yellow color may be seen. If both impurities are present together, however, the result is a magnificent deep-blue color, that of blue sapphire, as seen in Plate I . The process at work is “intervalence charge transfer,” the motion of an electron from one transition-metal ion to another produced by the absorption of light energy; this results in a temporary change in the valence state of both ions. Such a mechanism is the cause of the blue of sapphire and the dark colors of many transition- metal oxides such as the black iron oxide magnetite Fe304. This mechanism is sometimes also called cooperative charge transfer.

Consider two adjacent Al sites in corundum (see Fig. 7) occupied by Fe2+ and Ti4+ ions, as in Fig. 14. The transfer of an electron from the Fe to the Ti can now change the valence state of both atoms:

Fez+ + Ti4+ Fe3+ + Ti3+.

This process requires energy, as shown in Fig. 15; since the energy corresponds to the absorption of yellow light, as shown at the center of Fig. 16, the complementary color blue results. There can be adjacent pairs in directions other than that shown in Fig. 14; since the spacing between the atoms is different, so will be the energy-level spacing of Fig. 15, leading to the blue-green dichroism, seen in Fig. 16, analogous to that of ruby in Plate VI.

Blue sapphire is an example of “heteronuclear” charge transfer with two different transition-metal ions involved. In magnetite, the black iron oxide Fe304 or Fe2+0 . Fe2”03,


WAVELENGTH (nm) 1000 700 600 500 4 00 1

Fet+

t - 0x1s

I I

7 2.65

FIG. 14. Two adjacent octahedral sites containing Fe2+ and Ti4+ in blue sapphire; compare Fig. 7.

Fe3+ + Ti3+

0 t Fe2++ Ti4+ 0- ray

FIG. 15. Transition from the ground state to the excited state in blue sapphire.

I I

t 8

8

2

8 Q P

I I 1 1 , I I I

10 1.5 20 2 5 30 35 ENERGY (eV)

FIG. 16. The dichroic o-ray and e-ray absorption spectra of blue sapphire. Band a is derived from Fe2+ += Fe3+ charge transfer, band b from Fez+= Ti4+ charge transfer, band c from a ligand-field transition in Fe3+, and band d from 02- += Fe3+ charge transfer. [After G. Lehman and H. Harder, Am. Mineral 55, 98 (1970).]

there is “homonuclear” charge transfer with two valence states of the same metal in two different sites, A and B:

Fei+ + Fe$+ + Fe:+ + Fe;’.

The right-hand side of this equation represents a higher energy than the left-hand side, leading to energy levels, light absorption, and the black color. In sapphire this mechanism is also present, but there it absorbs only in the infrared, as at a in Fig. 16. This same mechanism gives the carbon-amber (beer-bottle) color in glass made with iron sulfide and charcoal, and the brilliant blue color to the pigment potassium ferric ferrocyanide, Prussian blue Fe43+[Fe2+(CN)6]3. The brown-to-red colors of many rocks, e.g., in the Painted Desert, derive from this mechanism from traces of iron.

Charge transfer can also occur between metal and ligand atoms. One example is the oxygen-to-chromium charge transfer in the yellow chromate K,CrO, and the orange dichromate (NH4)2Cr207 of Plate 11; note that the formal valence of 6 + on the Cr leaves no unpaired electrons and therefore rules out ligand-field colors as in the other trivalent chromium colors of Plate 11. In sapphire this mechanism is also present, but there absorption occurs only in the ultraviolet as at d in Fig. 15. A final example of charge transfer is the deep-blue gemstone lapis lazuli of Plate I, which has the same composition as the pigment ultramarine, approximately CaNa7A16S&024S3S04. This color derives from charge transfer among the three sulfur atoms of the S3- ion.

Charge-transfer transitions are strong because they are “allowed” by quantum considerations, hence intense colors are produced by as little as 1/100 percent Fe and Ti in blue sapphire; by contrast, the “forbidden” transitions in the ligand-field-colored ruby are so weak that one to three percent Cr is required for an intense red color.


Mechanism 8: Band-Theory Colors in Metals

Consider the formation of molecular orbitals in the bonding between two hydrogen atoms, as shown in Fig. 17. The combination of two equal-energy atomic orbitals, one from each hydrogen atom, leads to two molecular orbitals. One of these, the bonding molecular orbital, has a lower energy, while the other, the antibonding orbital, has a higher energy. The molecular orbitals can accommodate exactly the same number of electrons as the atomic orbitals from which they were formed, namely two per orbital. For the normal bonding distance d between the two atoms, the energies shown in Fig. 17 lead from the two atomic orbitals at A in Fig. 18 to the two molecular orbitals at B.

If, instead of two atoms, we now consider four atoms, we expect to see four molecular orbitals as at C in Fig. 18. Extrapolating this approach to the bonding in a piece of metal containing some lo2? atoms per cubic centimeter, we could reasonably expect molecular orbitals in an “energy b a n d as at D. There are so many levels in this band that for all practical purposes it may be viewed as being continuous. If the band is 1 eV wide, then the spacing between adjacent levels would be eV, an immeasur- ably small quantity.

Band theory gives a full explanation of the properties of the metallic elements of the periodic table and of the alloys formed between them. The shape of the energy band depends on the atomic orbitals involved and the geometrical arrangement and spacing between the atoms. The electrons available for bonding, that is, the sum of the valence electrons for all the atoms present, now occupy the band from

ATOMIC MOLECULAR ORBITALS BAND ORBITAL

ANTIBONDING

Id Id

DISTANCE

FIG. 17. The energy of bonding and antibonding molecular orbitals of the hydrogen molecule H2.

. , . . .:

I ATOM 2 ATOMS 4 ATOMS lo*’ ATOMS

A 8. C D

FIG. 18. The conversion of atomic orbitals into molecular orbitals and bands.

the bottom upward, as in Fig. 19. This “density-of-states’’ diagram shows that the capacity to hold electrons varies with the energy within the band. The top of the electron filling is called the Fermi surface, usually designated E,, and is illustrated for metallic iron in Fig. 19; the changed position for the closely related copper, which has three more bonding electrons per atom, is also indicated. These bonding

NUMBER OF ELECTRONS - Density-of-states diagram for the metals iron Fe

and copper Cu; vertical arrows indicate transitions produced by electricity, heat, or light.


electrons no longer belong to individual atoms, but to the piece of metal as a whole; they are “delocalized.”

The good electrical and thermal properties of metals immediately follow from this description. An electric field raises an electron from below the Fermi surface to a higher energy level in the band, as indicated by the vertical arrows in Fig. 19, thus creating a movable negatively-charged electron above E, and a movable positively-charged “hole” below E,. In the applied electric field these two species move in opposite directions, representing an electric current. Heat also produces electrons and holes, both of which diffuse away from the hot region, thus producing a flow of energy and resulting in thermal conductivity without any net charge movement.

When light falls onto a piece of iron, the electrons below the Fermi surface can also become excited into higher energy levels in the band by absorbing the energy from the light, as in Fig. 19, producing electron-hole pairs. The light is so intensely absorbed that it can penetrate to a depth of only a few hundred atoms, typically less than a single wavelength. Since the metal is a conductor of electricity, this absorbed light, which is, after all, an electromagnetic wave, will induce alternating electric currents on the metal surface. These currents immediately re-emit the light out of the metal, thus providing strong reflection of a polished metal surface.

The efficiency of this process depends on the selection rules that apply to the atomic orbitals from which the energy band had formed. If the efficiency of absorption and re- emission is approximately equal at all optical energies, then the different colors in white light will be reflected equally well, thus leading to the “silvery” color of polished iron and silver surfaces. However, if the efficiency decreases with increasing energy, as is the case for gold and copper, the reduced reflectivity at the blue end of the spectrum results in yellow and reddish colors, respectively.

The colors of alloys follow a similar pattern, but are difficult to predict a priori. For example, the addition of 25 percent silver to pure gold produces a green alloy while a similar amount of copper produces a red one.

The direct light absorption of a metal in the absence of reflection is observed only in rare instances. Gold is so malleable that it can be beaten into gold leaf less than 100 nm thick, then revealing a bluish-green transmitted-light color. When gold is in metallic colloidal form, however, as in the 10-nm-diameter particles in “ruby glass,” the very complex “Mie scattering theory” has to be used to explain the unexpected red color illustrated in Plate VIII; the yellow glass in this figure is colored by Mie scattering from metallic colloidal silver particles.

Mechanism 9: The Band Theory of Semiconductors

In some materials it is possible for a gap, the “band gap,” to occur at some point within a band. This has important consequences for color where there happen to be exactly four valence electrons per atom available for entry into the

PLATE VIII. Antique engraved Czechoslovakian glass colored yellow with silver and red with gold (both Mie scattering from colloidal particles).

band. As shown at the left in Fig. 20, the result is that the lower-energy band, the “valence band,” is exactly filled to capacity, and the upper band, the “conduction band,” is exactly empty. The magnitude of the energy spacing between the two bands is the “band gap” or “energy gap,” usually designated Eg. Consider now the absorption of light as represented by the vertical arrows A, B, and C in Fig. 20. Since there are no electron energy levels in the band gap between the valence and conduction bands, the lowest- energy light that can be absorbed corresponds to arrow A, involving the excitation of an electron at the top of the valence band up to a level at the bottom of the conduction band, corresponding to the band-gap energy Eg. Light of any higher energy can also be absorbed as indicated by the arrows B and C.

If the substance represented by this figure has a large band gap, such as the 5.4 eV of diamond or the similar value of corundum, then no light in the visible spectrum can be absorbed and these substances are indeed colorless when pure. Such “large-band-gap semiconductors” are excellent insulators and are more usually treated as covalently bonded materials.

GREEN YELLOW

‘ 0

COLOR REMAININ9 BELOW BAND OAP

coLonL ESS

Y E L L O l

O n A M e E

aEo

B L A C K

NUMBER OF ELECTRONS --t

FIG. 20. The absorption of light in a band-gap material (left), and the variation of color with the size of the band gap (right); see also Plate IX.


Consider now a “medium-band-gap semiconductor,” a material with a somewhat smaller band gap, such as the compound cadmium sulfide CdS; this is also the pigment cadmium yellow and the mineral greenockite, as shown in Table 11. Here the 2.6 eV band-gap energy permits absorption of violet and some blue but none of the other colors, leading to a yellow color, as can be deduced from the color scale at the right of Fig. 20. A somewhat smaller band gap that permits absorption of violet, blue, and green produces an orange color; a yet-smaller band gap as in the pigment vermillion (the mineral cinnabar HgS) with a band gap of 2.0 eV results in all energies but the red being absorbed and thus leads to a red color. All light is absorbed when the band-gap energy is less than the 1.77 eV (700nm) limit of the visible spectrum and these “narrow-band-gap semiconductors” are black, as in the last three materials of Table 11.

An illustration of this change in the band-gap size is shown by mixed crystals of yellow cadmium sulfide CdS, (E , = 2.6 eV), and black cadmium selenide CdSe (E , = 1.6 eV), which have the same structure and form a solid-solution series. Plate 1X illustrates the yellow-orange-red-black sequence of these mixed crystals as the band-gap energy decreases, following the sequence of Fig. 20. Mixed crystals such as Cd,SSe3 form the painter’s pigment cadmium orange and are also used to color glass and plastic. Mercuric sulfide HgS exists in two different crystalline forms. Cinnabar (the pigment vermillion) with Eg = 2.0 eV is a deep red but can transform on exposure to light in an improperly for- mulated paint to the black metacinnabar with ER = 1.6 eV in as little as five years; this has happened in a number of old paintings.

Mechanism 10: Color Produced by Impurities in Semiconductors

There is another way in which light energy can be absorbed in or emitted from a band-gap semiconductor, namely, if an added substance forms an impurity level within the gap. A diamond crystal is composed only of carbon atoms, each of which has four valence electrons in its outermost shell. Now consider a diamond in which a few carbon atoms out of a million have been replaced by nitrogen atoms, each containing five valence electrons. The structure of the diamond is not significantly perturbed, but the extra electrons enter a “donor level,” so called because, with the absorption

TABLE II. Color of some band-gap semiconductors.

SubstanceMineral name Pigment name Band gap, eV Color C Diamond - ZnO Zincite Zinc white CdS Greenockite Cadmium yellow CdS,,Se, - Cadmium orange HgS Cinnabar Vermillion HgS Metacinnabar - Si PbS Galena -

- -

5.4 3.0 2.6 2.3 2.0 1.6 1.1 0.4

Colorless Colorless Yellow Orange Red Black Black Black

PLATE IX. Mixed crystals of yellow cadmium sulfide CdS and black cadmium selenide CdSe, showing the intermediate-band-gap colors as in Fig. 20.

of energy, these electrons can be donated to the empty conduction band as shown at the left in Fig. 2 I . Note that the valence band is completely filled. The donor level is broadened by a number of factors, including thermal vibrations, as at the right of this figure; the resulting absorption at the blue end of the spectrum leads to a yellow color seen in both natural and synthetic nitrogen-containing diamonds, as in Plate X.

Boron has one less electron than carbon, and the presence of a few borons per million carbons in diamond leads to a hole level in the band gap as shown in Fig. 22. This is called an “acceptor” level since it can accept an electron from the full valence band. The energy required for this change is very small and, because of broadening, absorbs at the red end of the spectrum, leading to the blue color also seen in Plate X. Since the acceptor-level energy is so small, even the thermal energy at room temperature can produce this change, and the resulting holes in the valence band can now move in the presence of an electric field; accordingly, blue boron-containing diamonds, including the famous Hope diamond, conduct electricity.

Some materials containing both donors and acceptors, as in Fig. 23, can absorb ultraviolet or electrical energy to

CONDUCTiON CONDUCTiON

NUMBER OF ELECTRONS - NUMBER OF ELECTRONS - FIG. 21. The location of the nitrogen donor in the band gap of diamond (left) forms a broadened band and results in the absorption of light (right) and a yellow color; see Plate X.


PLATE X. Synthetic diamond crystals; colorless (pure), yellow (containing nitrogen donor), and blue (containing boron acceptor), grown at the General Electric Co.; largest is 3 mm across.

produce the transition a. If the return path proceeds viaf, g, and d, then light may be emitted corresponding to the energy release from g; this is then fluorescence or electroluminescence, respectively. The former occurs in “phosphor” powders, for example zinc sulfide ZnS containing Cu and other additives. Such powders are used as a coating in fluorescent lamps to convert the plentiful ultraviolet produced by the mercury arc into visible light, particularly into red light so as to produce a “warmer” light approximating daylight. Phosphors are also used inside a television screen, activated by a stream of electrons (cathode rays) in catho- doluminescence. Electroluminescence can use a similar

CONDUCTION 1 BAND

I I --f Eg= 5.4 eV

NUMBER OF ELECTRONS A

FIG. 22. The location of the boron acceptor in the band gap of diamond produces a blue color; see Plate X.

powder deposited onto a metallic plate and covered with a transparent conducting electrode to produce lighting panels, often used for nightlights.

Some phosphors contain impurities which form “trapping” levels, as at the right in Fig. 23. When an electron falls into a trap, as by process j , in this figure, it can only be released when additional energy is added to permit process k and subsequent light emission, say, viaf, g, and d. If the trap level is close to the conduction band, then even room temperature may be able to supply the required energy slowly, thus resulting in phosphorescence. If the required energy is a little larger, then infrared light may permit the escape, so that higher-energy visible light is produced in an activated infrared-detecting screen.

Finally, there is injection luminescence in a crystal containing a junction between differently doped semiconducting regions. An electric current now produces recombination between electrons and holes in the junction region, giving light from light-emitting diodes (LEDs, usually red), widely used on display devices in electronic equipment. With a suitable geometry, the emitted light can be coherent in the similarly operated semiconductor lasers.

Mechanism 11: Color Produced by Color Centers

Take a century-old glass bottle, and expose it in the desert to the ultraviolet radiation present in the strong sunlight. Come back after ten years, and the glass will have acquired an attractive purple color. Heat the bottle in an oven, and the color disappears. Next expose the bottle to an intense source of energetic radiation, as in the cobalt-60 gamma ray cell of Fig. 24, and within a few minutes an even deeper purple color appears, as shown in Plate XI.

The color in this “desert amethyst glass” derives from a color center, as do the colors of the natural gemstones amethyst, smoky quartz, and blue and orange topaz. Many other

CONDUCTION BAND

VALENCE BAND

FIG. 23. Possible absorption and emission transitions in the band gap of a phosphor containing an acceptor, a donor, and a trapping level.


FIG. 24. A sample being placed into a gamma-ray cell for irradiation by the author.

PLATE XI. Color centers. Above: century-old glass bottle irradiated to form “desert amethyst glass,” colorless synthetic- quartz crystal as grown, and one that has been irradiated to form smoky quartz. Below: a synthetic citrine quartz colored yellow by Fe and one that has been additionally irradiated to form amethyst.

materials, both natural and man-made, can bc irradiated to produce color centers, including irradiated blue, yellow, and grccn diamonds. Some of these colors, such as all the ones mentioned so far, are perfectly stable, losing thcir color only when heated. Other color centers are unstable and fade when exposed to light, while yet others fade cvcn in thc dark.

The term “color center” is sometimes used so loosely that cven transition-metal and the band-gap colorations are included. This rare usage ignores the unique characteristics of color ccntcrs; the conventional narrow interpretation is followed here.

Consider an ionic crystal, such as the alkali halide sodium chloride NaCl (ordinary table salt), which consistsof a thrcc- dimensional array of Na’ and C1- ions. A single Cl- can be missing in two ways. If a compensating Na’ is also missing, then the crystal remains neutral and there are no consequences of interest with respect to color. If, however, a Na+ is not missing, then one way of maintaining electrical neutrality is for a free electron, designated e-, to occupy the spot vacated by the Cl-. This IS called an F-center, after the German “Farbe” (color), as shown at the top left of Fig. 25. One can view this electron as if it were part of a transition metal in the ligand field of the surrounding K’ ions or. preferably, onc can view this electron as providing a trapping energy level within the band gap of this transparent wide-band-gap semiconductor material, as shown in Fig. 26.

Some form of relatively high energy such as irradiation by ultraviolet or high-energy electrons, x-rays, or gamma rays can now promote an electron from the valence band into the trap. There are, however, excited energy levels within the trap, such as the level at E, (at 2.7 eV for NaCl), which can absorb blue light, leading to a yellow-brown color in irradiated defect-containing NaCI; this defect is now called a color center. Note that the electron in this excited energy level is still within the trap. Only by supplying energy cor-

/F F’

\ M =% \

F2+

FIG. 25. Different types of color-center defects in an ionic crystal (schematic).


IRRADIATION f 4

CONDUCTION BAND

1

HALIDE V A C A N C Y I T R A P

ABS

VALENCE BAND

FIG. 26. Trapping of energy from absorbed light in a halide- vacancy trap in an alkali-halide crystal.

responding to Eb can the electron leave the trap and return via the conduction band directly to the valence band. This can happen if the crystal is heated, and results in bleaching of the color center. If Eb is about the same size as E,, then bleaching can occur merely while the material is being il- luminated, leading to optical bleaching. If Eb is sufficiently small, the material may even fade in the dark at room temperature. This occurs in self-darkening sun glasses, in which the ultraviolet present in sunlight produces the darkening and room temperature leads to fading as soon as there is no ultraviolet. Other centers are possible in alkali halides, some of which are also shown in Fig. 25; these may absorb in the visible, the ultraviolet, or the infrared. Some such color centers also show fluorescence and some of these can function as laser materials. As alternatives to irradiation, growth in the presence of excess metal or solid-state electrolysis can also be used to generate color centers.

The most general description of a material capable of supporting a color center is given in Fig. 27, in which the colorless state is shown above and the colored state below. Two kinds of precursors are needed: a hole precursor A which can lose an electron, e.g., when absorbing irradiation, to form a hole center A + , and an electron precursor B which can gain the electron lost from A to form the electron center B-. Either A+ or B- can be the color center itself that absorbs light, or even both can do so. On heating, the electron is released from B- and returns to A + , thus restoring the colorless state of A plus B.

A number of gemstone materials derive their beauty from

- Hole Precursor Electron Precursor

Hole Center Electron Center

FIG. 27. The irradiation of hole and electron precursors (a) to form hole and electron centers (b).

color centers. Colorless “rock-crystal” quartz, shown center above in Plate XI, is composed of silicon oxide Si02, shown schematically at A in Fig. 27. All natural and synthetic quartz contains the aluminum impurity Al’+ , typically re- placing one out of every 10,000 Si4+; for charge neutrality a hydrogen ion H + or a Na+ is nearby. Such quartz is colorless, but irradiation, either natural in the ground over many thousands of years or man-provided in 20 minutes in a cobalt-60 gamma source such as that of Fig. 24, now produces smoky quartz, also shown in Plate XI. As illustrated at B in Fig. 28, irradiation ejects an electron from an oxygen adjacent to the A13+, the whole [A104]% grouping acting as the hole precursor and converting to the hole center [A104]“-. The electron is trapped by the H + electron precursor, converting it into the neutral H electron center. In this case it is the hole center that is the color center and provides the gray-to-brown-to-black color of smoky quartz seen in Plate XI. Also shown in this figure is yellow citrine (often erroneously called “smoky topaz”), which is quartz containing Fe3+ instead of A13+; this produces the purple amethyst, also shown in Plate XI, by an exactly analogous irradiation process leading to the hole color center [FeO4I6.

The colors of both amethyst and smoky quartz are stable to light but are lost on being heated to 300 to 500°C; if not overheated, the color center and the color can be restored by another irradiation, and so on.

A century ago glass used to be decolorized with manganese additions to remove the green color caused by iron impurities. It is the Mn2+ left from this process which loses


n2 - 1 = aX2(X2 - A2)-’ + bX2(X2 - B2)-’ + . . . where A, B , . . . are the wavelength of the individual ir and uv absorptions seen in Fig. 2 and a, b, . . . are constants representing the strengths of these absorptions. Two or three terms are usually enough for an excellent fit in the visible region.

If either the refractive-index variation or the coefficient- of-absorption variation is known for all wavelengths, then the other one can be calculated by using the “Kra- mers-JSronig dispersion relationships.” We usually tend to think of the absorption as the “cause” and the dispersion as the “effect,” but the two are inextricably connected, and one cannot exist without the other. Only a vacuum has no absorption and no dispersion.

When there is a light absorption in an otherwise transparent medium, then anomalous dispersion results. Instead of n it is necessary to use the complex refractive index N = n + ik, where i is the imaginary and k is the absorption coefficient. The variation of n and k in a glass having a violet color derived from an absorption in the green part of spectrum is shown in Fig. 29.

In the region of absorption of Fig. 29, the natural reson- ating frequency of the absorbers interacts with the vibration of the light in a complex manner involving the phase velocity and the phase angle to produce a speeding up of the light, thus giving a lower n on one side of the absorption, and a slowing down and a higher n on the other side. In the region of the absorption, the refractive index increases with the wavelength, instead of decreasing; this is difficult to observe since it occurs just where the light is most strongly absorbed.

If a beam of light is passed through a thin prism cut out of the colorless glass of Fig. 2, then the sequence of colors seen is the normal spectral sequence shown at the top of Fig. 30. For the green-absorbing violet glass of Fig. 29, however, the sequence in the lower half of Fig. 30 applies. The red to yellow-green sequence at (a) follows normal behavior as at the right in Fig. 29, as does the blue-green to violet sequence at (c), corresponding to the left region in Fig. 29. The yellow-green to blue-green sequence at (b)

A RADIATION

B

FIG. 28. Schematic representation of the structure of quartz (A) and the formation by irradiation of a smoky-quartz color center (B).

an electron to form the purple Mn3+ shown in Plate XI in the solarization process described at the beginning of this section.

Natural yellow-to-orange-to-brown precious topaz contains a color center stable to light; any colorless topaz can be irradiated to a similar color that, however, is usually unstable and fades in a few days in light. Blue topaz also contains a color center, which can be either natural or man- produced; here both are stable. The exact nature of most of these color centers is unknown. Interestingly enough, the irradiation of colorless diamonds can produce stable yellow, blue, brown, and green colors. Although the first two of these are similar in appearance to the N-caused yellow and the B-caused blue discussed above, they represent much less valued materials, which can be distinguished by spec- troscopic and other features.

Mechanism 12: Color Produced by Dispersive Refraction

The discovery by Newton of this phenomenon and its de- pendence on the ultraviolet (uv) electronic and infrared (ir) vibrational features was discussed at the beginning of this review. In the visible region of a colorless transparent substance, the refractive index n is given by the Sellmeier dispersion formula:

V B G I YO R 1 I

C

8 1.55 %

3 lu 2 1.50

c, P 5 1.45

4

0 0.04 3

WAVELENGTH (nm)

FIG. 29. Anomalous dispersion of a violet crown glass having an absorption band in the green at 550 nm.


in Fig. 30 is reversed; green itself is not included here since it is absorbed, The overall color sequence that would be observed from this prism is shown at (d) in this figure; compared to the normal spectrum this is truly “anomalous.” Also note how much wider the anomalous spectrum is than the normal one.

In addition to the spectrum produced by a prism, there are several analogous color-producing phenomena. In a well- faceted gemstone, a ray of light passing into the top of the stone is totally internally reflected and returned to the eye as the “brilliance.” Since the geometry of the path corresponds to that in a prism, the reflected rays are also refracted, leading to flashes of color, the “fire” in a stone. The amount of fire depends on the magnitude of the dispersion; diamond is paramount among gemstones.

The refracted paths through a raindrop produce the pri- mary and secondary rainbows; higher orders can be seen in the laboratory but have not been observed in nature. The refracted paths through hexagonal ice crystals produce the 22” and the 45” halos around the sun and moon, the parhelia or moondogs, as well as a variety of other effects.

Last, there is the green flash seen rarely at the setting of the sun. Here the density gradient of the atmosphere acts as a prism, separating the colors as shown in Fig. 31. Since the violet and blue rays are scattered (see below), a green image is seen under favorable circumstances for just a few seconds.

A more complicated case than dispersive refraction is “double refraction,” which provides color when optically anisotropic crystals are viewed between crossed polarizers. Here the polarized light, on entering the crystal, is separated into ordinary and extraordinary rays moving at different velocities through the crystal; these rays are then recombined in the second polarizer to produce color by interference (see below).

Mechanism 13: Color Produced by Scattering

Perfectly clean air does not appear to scatter light. Sunbeams reveal themselves in the presence of dust, most spectacularly in cathedrals. Yet even the purest substances, including gases, are found to scatter light when carefully examined.

Leonard0 da Vinci had observed that a very fine water spray produced light scattering, but for many centuries only

Y COLORLESS ROG B V CROWN GLASS

l I ” I ! ! ! I I i

-- - _ - _ - - _ _ _ 1

f l = 1.45 1.50 lL55

R-o-y>G (a)] CROWN (b) VIOLET

5 G L 5 - v (C) GLASS

blue-green blue purple yellow (d))

FIG. 30. Color sequences produced by dispersion in the colorless crown glass of FIG. 2 (above) and the violet crown glass of FIG. 29 (below).

FIG. 31. The formation of the green flash at sunrise or sunset.

confusing and misleading ideas abounded. The English ex- perimentalist John Tyndall (1 820-1 893) demonstrated that the scattering from particles small compared to the wavelength of light depends on the wavelength, with blue being much more strongly scattered than red.

It remained for Lord Rayleigh to explain that scattering particles were not necessary, since even the purest of substances have fluctuations in their refractive index, which can scatter light. He also showed that the intensity of the scattered light I , is related to that of the incident light lo by the inverse fourth power of the wavelength A:

IJI0 = const. A4 If we take the intensity of scattered violet light at the 400- nm limit of visibility to be 100, then red light at 700 nm is scattered only at an intensity of 10.7. The terms “Rayleigh scattering” and “Tyndall blue” are often applied to the scattered blue. A dark background, such as the dark of outer space, is required for an intense blue to be perceived.

In a gas, liquid, or glass the atoms and molecules are evenly distributed on a macroscopic scale, yet at the atomic level there is considerable nonrandomness. As one example, individual molecules, as well as small clusters in a gas or a liquid coming together in collision for a brief instant before dispersing again, will act as light scattering particles much as do particles of dust. In a glass there will be similar density and refractive-index variations, both from the imperfect mixing of the various ingredients as well as from the frozen-in liquid fluctuations. Even in what might be thought of as a perfectly ordered single crystal, there usually will be a variety of point defects (impurity atoms, vacancies, and clusters of these) and line and plane defects (dislocations, low-angle grain boundaries, and the like) as well as density fluctuations from the thermal vibrations of the atoms or molecules, all of which scatter light.

Rayleigh scattering involves single light-emitting regions that are very small compared to the wavelength of light; they absorb light photons and re-emit them as single wave- lets. Since light is a transverse oscillation, the scattered light is polarized as indicated in Fig. 32; exactly perpendicular to the beam the scattered light is completely polarized in a direction perpendicular to the incident beam, while in other


/4\ INCIDENT LIGHT

\

FIG. 32. Rayleigh scattered light at 90” is fully polarized: at other angles it is only partly polarized.

directions, such as at the angle 8 shown in this figure, there is an additional component of the polarization parallel to the incident-beam direction of cos2 8. The combination ( 1 + cos2 8) gives the total light-scattering intensity distribution.

We owe some of our most spectacular atmospheric phenomena to various types of scattering: the blue of the sky, the red of the sunset, the white of clouds and, that epitome of rare occurrences, the blue moon. Most blue and green bird-feather colors involve scattering, as do many animal and some vegetable blues. We even see the same scattering phenomenon in the blue color of eyes, particularly in the intense blue of most infants, in whom dark pigments such as melanin have not yet all been formed and only blue is seen against the dark interior of the eye. Combined with a little yellow melanin, a green color of iris results; if melanin dominates, brown and black colors appear. In the absence of melanin in albinos, the blue scattering adds to the red of the underlying blood vessels to produce pink; the pink skin of light-skinned individuals is similarly produced.

If the size of the scattering particles approaches the wavelength of light or exceeds it, then the complex Mie scattering theory applies and permits colors other than blue; white is scattered at the largest sizes, as in fog and clouds. This theory also applies to scattering particles that are electrically conducting, as previously mentioned. Rayleigh and Mie scattering are called elastic scattering, with no change of the wavelength. Forms of inelastic scattering, in which there is a shift in the wavelength, include Raman scattering and Brillouin scattering; both of these can be used for laser operation.

Mechanism 14: Color Produced by Interference without Diffraction

Two light waves of the same wavelength can interact under appropriate circumstances so as to reinforce if they are in phase or cancel if they are out of phase, as shown in Fig. 33. In this section are discussed only those causes of color that involve interference without diffraction; the combination is covered in the following section.

A.

m

B

I +2

FIG. 33. Light waves 1 and 2 produce constructive reinforcement if they are in phase (A) or destructive cancellation if they are out of phase (6).

The first clear demonstration of interference without the simultaneous occurrence of diffraction was performed about 1815 by the French scientist A. Fresnel. He used a monochromatic light source reflected in two mirrors; the mirrors were made of black glass to reflect light only at the front surface and were inclined at a small angle to each other to produce two overlapping beams of light on a screen. The result was a series of “interference fringes” consisting of alternate bands of light and dark. If either mirror was covered or removed, the fringes disappeared and only the uniform illumination derived from the other mirror remained.

The availability of monochromatic light from lasers has simplified the study of interference and has led to the wide use of a variety of interference-based devices. This includes TwymanGreen and multiple-reflection interferometers, such as Fabry-Perot etalons, used for precision measurements, as well as interference filters.

Consider a plane, coherent, monochromatic beam of light A-A incident at an angle onto a thin film such as a sheet of glass or plastic, as in Fig. 34. Part of wave B will enter the film as shown. Part of this beam will be reflected at the back surface at C and a part of this reflected beam will leave in direction D. Consider a second wave E in beam A-A,

FIG. 34. Interference of light beams reflected from the front and back surfaces of a thin parallel film.


part of which is reflected at the upper surface so that it too leaves in direction D. As drawn, there is an extra path length of exactly five wavelengths while beam B traverses the distance 2b within the glass, as against the one wavelength a that beam E travels in the air. The net path difference is thus four wavelengths, so that the two beams might be expected to be exactly in phase with each other. However, reflection at a medium of higher refractive index as at the top surface produces a phase change equivalent to one-half wavelength, whereas this does not happen at the lower surface, which is reflection at a medium of lower refractive index. Accordingly, the two beams appearing in direction D are out of phase as shown and will undergo destructive cancellation as at B in Fig. 33. As either the angle, the thickness, or the wavelength changes, alternate dark regions from cancellation and light regions from reinforcement will occur.

In a tapered film with monochromatic light a series of dark and light bands occurs, while with white light the sequence of overlapping light and dark bands from the spectral colors leads to “Newton’s colors .” Starting with the thinnest film this sequence is black, gray, white, yellow, orange, red (end of the first “order”), violet, blue, green, yellow, orange-red, violet (end of the second “order”), blue, green, yellow, red, and so on. Newton’s colors are seen in the tapered air gap between touching non-flat sheets of glass, in cracks in glass or in crystals, in a soap bubble, in an oil slick on a water surface, and in the petrological microscope.

Antireflection coatings, as on camera lenses, employ this effect. A coating that has the geometrical mean value of the refractive index intermediate between those of glass and air and a thickness of one quarter the wavelength of light can reduce the overall reflected light to less than one half, while multiple layers can reduce this to less than one tenth; such a layer usually appears purple to the eye.

There are a large number of structural colorations in biological systems that are derived from thin-film interference, usually in multiple-layered structures. The layers may be composed of keratin, chitin, calcium carbonate, mucus, and so on, and are frequently backed by a dark layer of melanin, which intensifies the color by absorbing the nonreflected light. Such biological interference colorations are usually “iridescent,” this designation implying that multiple colors as in the rainbow (Latin iris) are seen, and also that the colors change with the orientation. Examples include pearl and mother of pearl, the transparent wings of house and dragon flies, and iridescent scales on beetles and butterflies, as in Plate XII, and on the feathers of hummingbirds and peacocks. An example of the complexity that can be involved is given in Fig. 35, which shows the color-causing structure of the surface of scales on the brilliant blue butterfly Morpho rhetenor. The eyes of many nocturnal animals contain multilayer structures that improve night vision and produce iridescent metalliclike reflections, as in Plate XIII.

Interference of polarized white light in an optically anisotropic substance such as ice or crumpled cellophane, derived from the double refraction mentioned above, leads to color as in Plate XIV. The same effect in the form of pho-

PLATE XII. Iridescent metalliclike colors produced by multiple interference on the 4 cm long wing of the butterfly Chry- syridia madagascarensis. [Photograph courtesy of F. Mijhout.]

toelastic stress analysis is used to check glass for strains and to study the stresses in machinery and in medieval cathedrals in deformed plastic models.

Mechanism 15: Color Produced by Diffraction

Diffraction is the term used to describe the spreading of light at the edges of an obstacle. First described in detail in the 1665 posthumous book by the Italian professor of mathematics, F. Grimaldi, diffraction was ultimately to supply the incontrovertible proof for the wave nature of light. Grimaldi studied the shadow of small objects using a small opening in a window shutter (just as did Newton to obtain the spectrum a few years later). He observed that these shadows were larger than could be accounted for by geometrical considerations and noted colored fringes, not only outside but even inside the shadow under certain conditions; he coined the word “diffraction” for the effects that he was not able to explain. A series of investigations followed, but it remained for the three contemporaries Thomas Young

A.

3 FIG. 35. Left: structure of vanes on the surface of scales on the wings of the butterfly M. rhetenor [adapted from T. F. Anderson and A. G. Richards, J. Appl. Phys. 13,748 (1959) and F. Mijhout, Sci. Am,, 245, 140 (1981)l; right: multiple interference produced by the ridges on these vanes.


,,--WAVE SHADOW

/,/GEOMETRICAL SHADOW

A \-

PLATE XIII. Multiple thin-film interference produces a green metalliclike reflection of a photographic flash from the eyes of a cat.

(1773-1829), Joseph von Fraunhofer (1787-1826), and, particularly, Augustin Fresnel (1788-1 827) to provide ad- equate descriptions and explanations.

Consider sunlight passing through an aperture and falling onto a screen. As the opening is made smaller, so does the patch of light on the screen become smaller; at the same time its edges appear to become sharper. Beyond a certain point, however, the edges become indistinct and begin to show colored fringes. The mechanism involves the spreading of a wave into the geometrical shadow region of an object, as shown in Fig. 36. A single edge in monochromatic light produces a sequence of light and dark bands, while in white light a sequence of colors is produced much as in the Newton color sequence discussed above.

When light beams diffracted from opposite sides of small particles interfere, the result is a sequence of colored rings called the “corona” (not to be confused with the “solar corona” seen only during an eclipse), usually seen around a bright light source. This can frequently be seen surrounding the sun (using very dark sunglasses), derived from cloud particles. In Fig. 37 the path difference between the two diffracted rays at A is zero, thus producing reinforcement. At B the path difference is A = d sin 8; when this is a whole wavelength, the second reinforcement occurs, while in between there will be cancellation. The size of the cloud

PLATE XIV. Interference colors in a thinned ice cube, 3 cm across, between crossed polarizers. [Photograph courtesy of R. L. Barns.]

I

I

PARALLEL WAVES OR COLLIMATED PARTICLES

FIG. 36. The geometrical and wave shadows of an opaque object produced by particles and waves, respectively.

particles can be determined from observing the diameter of the corona. With a range of sizes of particles present, merely a bluish disk, the “corona aureole,” is seen surrounding the sun. The same mechanism explains Bishop’s ring, the glory, and the specter of the Brocken. Transluscent clouds passing near the sun having uniform particle size may show a range of pastel colors, then called iridescent clouds (very dark sunglasses).

A diffraction grating consists of a regular two- or three- dimensional array of scattering objects or openings. This is most familiar when used in a spectroscope as in Fig. 38, where the path difference is nh = d sin 8. Diffraction arrays are also observed in the animal kingdom, as in the beetle Serica sericae and in the indigo or gopher snake Drymar- chon corais couperii, which show spectral colors in direct sunlight. The same effect can be obtained by a glancing view across a phonograph record or on viewing a distant streetlamp or flashlight through a black-cloth umbrella, as in Plate XV.

The most outstanding diffraction grating of all is the gemstone opal, showing on a white or a black background flashes

DROP

FIG. 37. Diffraction by drops of water leading to the corona.


LENS GRATING LENS SCREEN

/ SOURCE /-

- -- *&’ -

‘-.

FIG. 38. A diffraction grating spectroscope showing constructive reinforcement for n = 0, the zero-order line, and for n = 1, part of the first-order spectrum.

of varied colors called the “play of color,” as seen in Plate XVI. This was at one time thought to involve thin-film interference, but electron-microscope photographs taken of an opal reveal its secret, demonstrating a regular three- dimensional array of equal-size spheres as shown in Fig. 39. The actual composition of the spheres is amorphous silica, SiOz, containing a small amount of water; the spheres are cemented together with more amorphous silica containing a different amount of water so that a small refractive- index difference exists between the spheres and the cement.

Finally, there are “liquid crystals,” organic compounds

PLATE XV. Diffraction of the light from a distant flashlight viewed through a black umbrella fabric.

PLATE XVI. Colors produced by diffraction in a 12-mm- diameter synthetic black opal, grown at Ets. Ceramiques Pierre Gilson.

FIG. 39. Electron-microscope view of a synthetic opal; individual spheres are about 250 nm across. [Photograph courtesy Ets. Ceramiques Pierre Gilson.]

with a structure intermediate between that of a crystal and that of a liquid. These have twisted structures, which can intereact with light in a manner similar to diffraction to produce color, as in the thermometric film of Plate XVII, and in “mood’ rings. Some beetle colors are derived from liquid crystal structures on the outer layers of their cuticles.

PLATE XVII. Skin temperature revealed by thermography of a hand pressed against a black-backed cholesteric-liquid- crystal film; the iridescent metalliclike colors are derived from multiple-layer diffraction.


Acknowledgements

I owe a debt to many colleagues at AT&T Bell Laboratories, particularly M. E. Lines, for interactions over the years that have deepened my understanding of color. I am grateful to Ets. Ceramiques Pierre Gilson for Fig. 39, to F. Mijhout for Plate XII, and to R. L. Barns for Plate XIV; the balance of the illustrations are reproduced from K . Nassau, The Physics and Chemistry ofcolor, John Wiley and Sons, New York, 1983, with permission.

Further Reading

Apart from my own extended treatment on the subject,’ there are no comprehensive discussions of the causes of color; well over one hundred recommendations for further reading were required for a reasonably full coverage of the diffuse literature in Appendix G in my textbook.’ The following selected items are accordingly representative rather than comprehensive.

An excellent general source for many specifications is the Kirk-Othmer Encyclopedia of Chemical Technology, ’ Light and optics, often including topics such as incandescence, dispersion, scattering, interference, and diffraction, are COV-

ered in textbooks on Ligand-field theory is covered in advanced inorganic-chemistry texts‘ and also in specialized treatment^.^.^ Color in organic molecules is covered to some extent in advanced organic-chemistry texts’ and also in specialized treatments. ”*” There are very few detailed discussions of color derived from charge tran~fer.‘.~~” Band theory is covered in many solid-state text^,'^''^ although color is rarely discussed. There are a number of treatment^'^.'^ of color centers; most include some discussion of color. There are specific discussions of color in minerals and gem-

in g l a s ~ , ’ ~ . ~ ~ in plastics,2’ and six early but still- definitive studies of animal coloration.*’

1. K. Nassau, The Physics and Chemistry of Color: The Fifeen Causes of Color, Wiley, New York 1983.

2. Kirk-Othmer Encyclopedia of Chemical Technology, Wiley, New York,

3. F. A. Jenkins and H. E. White, Fundamentals of Optics, McGraw

4. R. W. Ditchburn, Light, Academic Press, New York, 3rd ed., 1976. 5. M. Born and E. Wolf, Principles of Optics, Pergamon Press, New

York, 6th ed., 1980. 6. F. A. Cotton and G. Wilkinson, Advancedlnorganic Chemitry, Wiley,

New York, 4th ed., 1980. 7. R. G. Bums, Mineralogical Applications of Crystal Field Theory,

Cambridge University Press, Cambridge, U. K., 1970. 8. D. Reinen, Ligand field spectroscopy and chemical bonding in C?’

containing oxidic solids, Struct. Bonding (Berlin) 6, 30-51 (1969). 9. A. Streitweiser and C. H. Heathcock, Organic Chemistry, Macmillan,

New York, 2nd ed. , 1981. 10. J. Fabian and H. Hartmann, Light Absorption in Organic Colorants,

Springer Verlag, New York, 1980. 11. P. F. Gordon and P. Gregory, Organic Chemistry in Color, Springer

Verlag, New York, 1983. 12. G . Smith and R. G. J . Strens, “Intervalence Transfer Absorption in

Some Silicate, Oxide and Phosphate Minerals,” in R. G. J . Strens, Ed., Physics and Chemistry ofMinerals and Rocks, Wiley, New York, 1976, p. 583.

13. C. Kittel, Introduction to Solid State Physics, Wiley, New York, 5th ed., 1976.

14. R. H. Bube, Electronic Properties of Crystalline Solids, Academic Press, New York, 1974.

15. Y. Farge and M. P. Fontana, Electronic and Vibrationnl Properties of Point Defects in Ionic Crystals, North Holland, New York, 1979.

16. A. S. Marfunin, Spectroscopy, Luminescence and Radiation Centers in Minerals, Springer Verlag, New York, 1979.

17. K. Nassau, The origin of color in minerals, Am. Mineral. 63,219-229 (1978).

18. K. Nassau, Gems Made by Man, Chilton, Radnor, PA, 1980. 19. C. R. Bamford, Color Generation and Control in Glass, Elsevier,

New York, 1977. 20. K. Nassau, “The Varied Causes of Color in Glass,” in Proceedings

1985 Defects in Glass Symposium, Vol. 61, Materials Research So- ciety, Pittsburgh, PA, 1985.

21. K. Nassau, “Color in Plastics: The Varied Causes,” in Proceedings 1986 ANTEC, Society of Plastics Engineers, Stamford, CT, 1986.

22. C. W. Mason, Structural colors in feathers, J . Phys. Chem. 27,201-251, 410447 (1923); blue eyes, ibid. 28,498-501 (1924); Structural colors in insects, ibid. 30,383-395 (1926); idem, ibid, 31,321-354,18561872 (1927).

3rd ed., 1978.

Hill, New York, 3rd ed., 1957.

Received November 2, 1985; accepted January 20, 1986


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