A Quantitative Description of the Causes of Color in Corundum
The color of a gemstone is inextricably linked to its chemical composition, yet the quantitative relationship between color and chemistry is poorly understood in most cases. Here we use corundum to present a comprehensive quantitative description of the causes of color in a gem material and illustrate its predictive power. Natural corundum has six major chromophores that cause color: Cr3+, h•-Cr3+, Fe3+, h•-Fe3+, Fe2+-Ti4+, and V3+. We use synthetic samples doped with a single chromophore to study their light absorption behavior in isolation. Natural samples are used as well to study single chromophores, and we can subtract out the absorption of additional chromophores that might be present. Combining quantitative visible absorption spectroscopy with chemical analysis by SIMS, we are able to calculate the absorption cross section of each chromophore. The absorption cross section information is used to determine the depth of color that would occur in corundum of a given size (optical path length) containing a specific chromophore of a given concentration.
Gemstones are valued for their beauty, rarity, and durability, and what typically captures our attention is their magnificent array of colors. Corundum exhibits an extremely wide range of colors in nature (figure 1). From pigeon’s blood red ruby to cornflower blue and lemon yellow sapphire, nearly every color is represented. The only corundum color not represented in nature is a saturated intense emerald green. However, less intense olive green to teal green stones are often found in basalt-hosted corundum deposits.
Corundum’s broad range of colors is related to its detailed chemistry. Some minerals possess inherent color because the chromophore is one of the basic chemical components of its makeup. Such stones are termed idiochromatic, meaning self-colored. For example, turquoise, whose chemical formula is CuAl6(PO4)4(OH)8•4H2O, is colored by copper, a primary component of its structure.
Other minerals such as corundum are, when very pure, completely colorless. In fact, pure corundum, with the chemical formula Al2O3, is absolutely transparent from the deep ultraviolet region into the infrared. Such minerals are termed allochromatic. Their colors in nature are caused by minor impurities, referred to as trace elements, or other point defects in the crystal lattice that have been incorporated during growth or later equilibration in nature. The causes of color in corundum are many and have been primarily addressed in a non-quantitative way for many years (see, for example, Fritsch and Rossman, 1987, 1988; Häger, 2001; Emmett et al., 2003). Trace elements themselves can be the direct cause of color. Cr3+, for example, creates pink and red coloration in corundum. Trace elements can also interact with each other, creating a new chromophore. The Fe2+-Ti4+ pair is such an example, strongly absorbing in the yellow and red regions of the spectrum and thus creating magnificent blue sapphires.
When beryllium-diffused corundum entered the marketplace, we were surprised by the wide range of colors that were produced, seemingly by a single element (Emmett et al., 2003). Measurements of the beryllium levels showed that the concentrations were generally from a few to a few tens of parts per million atomic (ppma), yet the colors produced were often intense. For comparison, red coloration in corundum requires several hundred to a few thousand ppma of Cr3+, a concentration at least two orders of magnitude greater than Be2+, to produce strong color.
Our studies of the beryllium-diffused stones (Emmett et al., 2003) demonstrated that the Be2+ ion itself was not the cause of color. However, replacing a trivalent aluminum ion with a divalent beryllium ion required the creation of a trapped hole (h•) for charge compensation. A trapped hole is an oxygen ion with a valence of –1 rather than –2. It is this O–1 ion that is the strong absorber of light (Kvapil et al., 1973). In natural stones, this trapped hole associating with either iron or chromium creates intense golden yellow or intense orange colors, respectively.
In natural corundum, beryllium only rarely, if ever, exists in solution in the corundum lattice and thus does not produce these colors. Instead, natural corundum usually contains some amount of magnesium. Magnesium, like beryllium, is divalent (Mg2+, Be2+) when it replaces Al3+ in corundum and thus requires charge compensation. If the stone is acceptor-dominated1 with [Mg + Ni] > [Si + Ti + H] (square brackets denote concentrations in ions/cm3), and formed in conditions of relatively high oxygen fugacity, the charge compensation is by a trapped hole (h•). Since it is the trapped hole in association with iron or chromium and not the beryllium or magnesium that produces color, the colors produced naturally by magnesium or by diffusion of beryllium are very similar (Emmett et al., 2003, 2017b; Kröger, 1984).
1We use the terms “acceptor-dominated” and “donor-dominated” and also refer to chemical reactions among trace elements here without detailed explanations. These matters are discussed in detail in Emmett et al. (2003), with corrections and extensions in Emmett et al. (2017a,b). Rather than repeat these discussions, we refer the reader to these references and the extensive references therein. Furthermore, we will not repeatedly restate these references throughout this text.
Having identified the h•-Fe3+ and the h•-Cr3+ as two additional chromophores in natural corundum, we have six major chromophores that are responsible for the multitude of colors in natural corundum: Fe3+, Cr3+, V3+, Fe2+-Ti4+, h•-Fe3+, and h•-Cr3+. Individually, their colors in corundum are as follows:
Pink, Red: Cr3+
Yellow: Fe3+, h•-Fe3+
Blue: Fe2+-Ti4+, V3+
Green, Purple: V3+
These chromophores can occur singly in a corundum sample (again, see figure 1), though it is common for natural corundum to contain more than one color-causing agent, as all natural corundum generally contains measureable levels of trace elements Mg, Si, Ti, V, Cr, Fe, and Ga that have been incorporated into the lattice. When multiple chromophores are present, the apparent color of the corundum sample results from the sum of the light absorption by each of the chromophores present (Emmett et al., 2017a).
To determine the visual color of a corundum sample from the chemical analyses, we need to know four additional factors: the absorption spectrum of each of the chromophores, the absorption “strengths” of the chromophores, the thickness and crystallographic orientation of the sample, and the color temperature of the illumination.
All of these factors are well known in gemology with the exception of the absorption “strength.” The term for the absorption “strength” in physics is the absorption cross section (see box A on pp. 6–9; we strongly advise reading box A before proceeding). The absorption cross section quantitatively determines the effectiveness of a single ion or ion pair in a particular host material (such as corundum) in absorbing light of a given wavelength. The larger the absorption cross section, the stronger the chromophore. The unit of the absorption cross section is centimeters squared (cm2), which represents an area. One can conceptually visualize this as the size of the absorbing area that a single chromophore particle presents to the light beam. However, note that it is not the actual physical size of an ion or an ion pair.
Knowing the absorption cross sections is absolutely critical to determining the origin of color of a given sample. Before detailed chemical analyses were available, it was often assumed that iron was primarily responsible for yellow color in sapphire. However, we now know that there are yellow sapphires with 3000 ppma Fe and yellow sapphires with 200 ppma Fe with similar depth or intensity of color, so clearly these are not colored by the same chromophore.
The objective of this paper is to present the results of our efforts over more than a decade to determine both the E⊥c (O-ray) and E||c (E-ray) (see box B) absorption cross sections for all six chromophores in corundum and to describe how they were determined. We also illustrate the range of colors these chromophores produce. Finally, the digital files at 1.5 nm resolution and 1 nm wavelength intervals from 200 to 1100 nm for each of these chromophores are available to the reader to download for their own use (see https://www.gia.edu/doc/sp20-corundum-chromophores-absorption-cross-section-data.xlsx).
Determining the absorption cross sections relies upon accurate determination of the chromophore concentrations in the samples. These determinations were made possible by secondary ion mass spectrometry (SIMS) analysis at the California Institute of Technology (Caltech). SIMS was calibrated with single-element ion implants in sapphire standards, eliminating any matrix effects. The calibration of SIMS, a major effort in itself, is described in detail in Stone-Sundberg et al. (2017).
The chromophore concentrations in this paper have largely been determined by SIMS analyses from synthetic corundum crystals grown doped only with a single chromophore. This is true of Cr3+, V3+, h•-Fe3+, and h•-Cr3+. The Fe3+ chromophore and Fe2+-Ti4+ chromophore data were determined using both natural and single-doped synthetic crystals grown by the Czochralski method (figure 2). Unlike many other minerals, corundum contains only a single small cation site. Additionally, the energy required to force a cation into an interstitial site is very high (Matsunaga et al., 2004). These facts, together with the fact that the crystal must be rigorously electrically neutral, very strongly constrain what trace elements and what valence states of these trace elements can exist in corundum. For example, iron in corundum by itself will be Fe3+ because the crystal must be electrically neutral. That is, the valence of Fe must equal the valence of Al3+. Unless there is a tetravalent donor such as Si4+ or Ti4+ or an H+ interstitial (El-Aiat and Kröger, 1982; Norby, 1989; Beran and Rossman, 2006; Li and Robertson, 2014) to charge compensate it, Fe2+ will not exist. If there is such a donor, the Fe2+-Si4+ and Fe2+-Ti4+ pairs will form. Thus the concentration of Fe2+ is limited by the concentrations of H+, Si4+, and Ti4+. This is why we thoroughly analyze even the singly doped synthetic crystals.
If a very high-purity synthetic crystal doped only with Fe3+ is processed at high temperature in a highly reducing atmosphere, oxygen vacancies with a charge of +2 with regard to the lattice may form and thus charge compensate two Fe2+ ions. It is for this reason that we process at high temperature in a pure oxygen atmosphere many of the synthetic crystals we have grown. This eliminates any oxygen vacancies, assuring a valence of +3. Additional possibilities for alternate valences of other ions, or interferences from different pair absorption spectra, have been addressed using the variety of synthetic crystals indicated in Appendix 1 at https://www.gia.edu/doc/sp20-corundum-chromophores-appendix1.xlsx.
Such considerations, plus the processing of synthetic crystals in a high-temperature oxygen atmosphere and thorough analyses for other trace elements, assure that the chromophore concentrations equal the SIMS-determined concentrations.
In the following sections, we will first describe the Cr3+ chromophore and how its cross section was determined. Much of this same detail will apply for the other five chromophores and thus will not be repeated. We present the origin of the samples (again, see figure 2), their crystallographic orientation, the absorption cross sections determined for both E⊥c and E||c, color circle arrays for different areal densities of the chromophore, viewing directions, and illumination sources. Detailed information on these samples can be found in Appendix 1.
THE Cr3+ CHROMOPHORE
Cr3+ is the trace element primarily responsible for coloring ruby red and sapphire pink (McClure, 1962) and in doing so creates some of the most beautiful gems in the world. This coloration results from Cr3+ ions replacing some of the Al3+ ions in the corundum lattice.
High-purity synthetic sapphire doped with Cr3+ has been available since the invention of the laser in 1960. The very first laser employed synthetic ruby as the active element (Maiman et al., 1961). Interest in ruby lasers for many applications drove the development of large, exceedingly high-optical-quality and high-purity synthetic ruby crystals. Our samples were from excess material salvaged from several different laser-quality single-crystal ingots (boules) grown by St. Gobain Crystals and Detectors in Washougal, Washington.
Wafer samples cut from these boules were crystallographically oriented to an accuracy of approximately 1.5° using an optical instrument (Thomas et al., 2014) with the c-axis in the plane of the wafer. The absorption spectra were measured with a resolution of 1.5 nm using a Hitachi Model 2910 spectrophotometer modified by Tim Thomas at GIA to enable rotation of the polarization plane of the probe beam, thus allowing the separate recording of both E⊥c and E||c spectra. The spectra were corrected for the multiple reflections between the two polished surfaces of the wafer by summing all the reflections (see box A). Wafers from four different boules were fabricated and measured, and the one with the lowest absorption at approximately 226 nm was chosen as the most pure. 226 nm is between the two highest-energy absorption bands of Cr3+ yet below the first Cr3+ charge transfer band. However, at this wavelength the charge transfer bands of Fe, Ti, and other metals are very strong (Tippins, 1970), and thus minimal absorption at this wavelength is a good relative indicator of crystal purity.
Quantitative data on this sample with the minimum 226 nm absorption (and all of the other samples characterized in this study) were obtained using a Cameca IMS 7f-GEO SIMS instrument. SIMS is a highly precise analytical technique that can detect all elemental masses to the sub-ppma level. To achieve accuracy, however, relative sensitivity factors (RSF) need to be developed to correctly convert the secondary ion signal for each trace element in the matrix of interest into concentration. This is best done by creating ion implant standards. For each trace element we wish to quantify, a chosen isotope of this trace element is implanted in a high-purity wafer of the intended matrix. Our developed RSF values were based upon multiple measurements validating the “dose” of each of these ion implants, and upon multiple SIMS depth profiles of these same implants (Stone-Sundberg et al., 2017). The calculated RSF values account for all of the identified and quantifiable sources of uncertainty; for the final SIMS-generated concentration values for all of the subsequently measured samples, we report a total uncertainty that is equal to the square root of the sum of the squares of the error associated with each source. In total, there are four separately quantified sources of error: the ion implant standard dose measurement, determination of the peak depths for the ion implants, differences between the multiple depth profiles for each ion implant, and the set of measurements of the trace element of interest in the sample. For the Cr3+ chromophore, the concentration and total combined error is 134 ppma ± 7.6%. The determined detection limit for Cr3+ in corundum to the 95% confidence level using our conditions was 0.002 ppma (2 parts per billion atomic, ppba).
The absorption cross sections thus determined over the 200–1100 nm range are shown in figure 3. The data range includes the visible region of the electromagnetic spectrum, which extends from 400 nm (violet) to 700 nm (red). The vertical axis is labeled “absorption cross section × 1019 cm2.” This means that the actual values plotted are from 0 to 4 × 10–19 cm2; we will use the same labeling convention for subsequent cross section spectra presented in this article. Figure 3 shows the absolute absorption cross section spectra for both the E⊥c (ordinary) and E||c (extraordinary) rays for Cr3+ in the high-purity synthetic ruby. These two spectra fully characterize, at 1.5 nm resolution, the absorption characteristics of Cr3+ in corundum over the range from 200 to 1100 nm. Whether in a high-purity synthetic crystal containing only Cr3+, a natural ruby containing Cr3+ and iron, or a purple sapphire containing Fe2+-Ti4+ pairs and Cr3+, the absorption cross section of Cr3+ is the same. The broad bands near 560 nm are termed the U bands, while the two near 400 nm are designated the Y bands. At a wavelength of 694 nm, there is a weak, narrow absorption feature. This is known as the R-line. In actuality, the R-line is two weak lines, R1 and R2, which are separated by 1.4 nm. Since our instrumental resolution is 1.5 nm, these two lines appear as a single weak feature. The weak lines near 660 nm most clearly observable in the E⊥c spectrum are called the S-lines, while the weak lines in both spectra near 470 nm are referred to as the B-lines (Powell, 1998). Shown along with the spectra is an image of a faceted sapphire we selected as representative of a stone that is very close to being colored by only the Cr3+ chromophore. In the following sections, we show a representative faceted stone alongside the spectra for each chromophore, selected as representative of the color that would be produced by that chromophore in isolation.
Note that the E⊥c peak cross section of 1.62 × 10–19 cm2 ± 7.6% we determined for the 560 nm U band represents a moderately strong absorber, and thus Cr3+ is a moderately strong chromophore. It is the magnitude of this cross section in the visible region of the spectrum, and to a lesser extent the width and position of the bands, that determines the “strength” of the chromophore (see box A). The position and width of the absorption bands determine the color. Approximately speaking, the larger the cross section and the wider the bands in the visible region, the more color produced.
It is interesting to note that apparently the first determination of Cr3+ cross section was published in 1961 in the seminal paper reporting the achievement of the first laser—the ruby laser (Maiman et al., 1961). His value of the peak cross section for the E⊥c U band was approximately 1.8 × 10–19 cm2. The small difference between his value and ours probably reflects the improved analytical instrumentation for determining Cr3+ concentration available to us today. Subsequently, the absorption and emission spectrum of ruby has been extensively studied by many researchers; see, for example, Powell (1966, 1998) and Henderson and Bartram (2000).
While the absorption cross section provides the definitive characterization of a chromophore, it is not easy to guess the color from simply examining the spectra. It is, however, straightforward to calculate the color from these spectra. The color coordinates (Berns, 2000) are usually calculated from the sample’s transmission spectrum and the characteristics of the light source. Calculation of the color coordinates for a given color temperature was performed via Thermo Scientific’s GRAMS/AI spectroscopy software, a general-purpose spectra manipulation code that includes color coordinate calculations. There are many color coordinate systems, and we chose the CIE 1976 L*a*b* system for its approximately uniform color space. We used color temperatures of 6500 K (D65 illuminant) and 2856 K (A illuminant) in order to maximize the color temperature difference and the color difference, thereby maximizing the visual effects of different light sources for the reader. Having determined the color coordinates for a particular sample thickness and chromophore concentration, a color circle is then created by specifying the color coordinates to the drawing program. We have used Photoshop, EasyDraw, and other graphics programs to produce the color circles. Visualizing the color from the absorption spectrum of the sample has broad application in gemology. We first used this technique to determine the amount of diffused beryllium that would cause a visible reduction in the depth of color of a dark blue sapphire.
Figure 4 (left) shows an array of color circles corresponding to a range of Cr3+ areal densities. Presented are the E⊥c color, the E||c color, and a color representing equal proportions of E⊥c and E||c (we will call this E⊥c + E||c), as viewed with illuminant D65 (daylight equivalent). The E⊥c colors are seen looking through a stone along the c-axis. The E⊥c + E||c colors are what is seen looking through a stone perpendicular to the c-axis. With a properly aligned dichroscope viewing in this same direction, we see the pure E⊥c and E||c colors separated (see box B for a basic introduction to uniaxial crystal optics). L*a*b* color coordinates for these color circles and all subsequent color circles presented in this article are available in Appendix 2 at https://www.gia.edu/doc/sp20-corundum-chromophores-appendix2.xlsx.
Along the horizontal axis of the color circle array is the areal density of the Cr3+ in units of ppma-cm. Areal density is the product of the chromophore concentration in ions per cm3, times the path length through the stone in cm. The concentration of chromophore ions is 1.178 × 1017 ions/cm3 times the concentration in ppma (see box A). For a 1 cm thick sample, the numbers under the color circles are the Cr3+ concentration in ppma. For a 2 cm thick sample showing the same color, the concentration is one half the numerical ppma-cm value. For a 1/2 cm thick stone, the concentration is twice the ppma-cm value. Thus the numbers under the color circles can be viewed as presenting a stone of fixed concentration of increasing thickness, or of fixed thickness with increasing Cr3+ concentration, or any combination of the two.
The color we perceive also changes with the type of light source. Figure 4 (right) shows the three sets of color circles—E⊥c, E||c, and E⊥c + E||c—but also for each of two illuminants—D65 (daylight) and A (tungsten bulb). We have chosen these two light sources to maximize the observable color difference. Thus we can see a substantial change in the perceived color with a change in light source. While this color change is significant, ruby is not described as a color-change gem. A color-change gem is usually thought of as one where the hue changes significantly (more than one adjacent hue position), such as blue to red or green to red.
THE V3+ CHROMOPHORE
Vanadium (V3+) commonly occurs in trace element analyses of natural corundum, particularly ruby. Generally, the vanadium concentration is not high enough (<20 ppma) to have a significant impact on the color. However, recently published analyses of corundum from the Mogok Stone Tract in Myanmar (Harlow and Bender, 2013; Zaw et al., 2015) have shown concentrations as high as 2000 ppma and reported sapphire colors of “slate” (grayish blue to gray-blue) to purple as well as color-change in some cases. For concentrations at or considerably less than this extreme, vanadium will indeed impact the color of ruby and sapphire. V3+ spectra in corundum have been studied for decades (Pryce and Runciman, 1958; McClure, 1962; MacFarlane, 1964).
Several decades ago, the former Union Carbide Corporation crystal growth facility in Washougal, Washington, grew a large vanadium-doped sapphire crystal by the Czochralski technique for research purposes. A slice of this unique crystal was provided for our research. SIMS analysis showed a vanadium concentration of 116 ppma with a total combined uncertainty of ± 8.9%. The detection limit determined for V3+ in corundum at the 95% confidence level was 0.016 ppma. Wafers were fabricated from this boule with the c-axis in the plane of the wafer so that both E⊥c and E||c absorption spectra could be recorded. Since vanadium can exist in multiple valences, the wafers were heated at 1750°C in oxygen for 10 hours to assure that all of the vanadium was in the 3+ valence state, as previously discussed. Previous multiple heat treatment experiments on this material had shown these conditions were effective.
Figure 5 shows the absorption cross section for both the E⊥c and E||c for V3+ in sapphire. It is interesting to note that the V3+ spectra in the visible range show two absorption bands with similar positions and widths to those of Cr3+. However, their relative magnitudes are very different, leading to very different colors. Vanadium is a weak chromophore in corundum since its absorption band, centered at 580 nm, is much weaker than that of Cr3+ at 560 nm. We determined that vanadium’s E⊥c peak cross section for the 580 nm band is 1.0 × 10–19 cm2 ± 8.9%.