A Quantitative Description of the Causes of Color in Corundum

Figure 6 (left) shows the three sets of color circles for E⊥c, E||c, and E⊥c + E||c under D65 illumination for V³⁺. There is a significant hue difference between the E⊥c color, which is a grayish blue, and the E||c color, which is distinctly green at the lower concentrations. Nearly the same amount of color difference also exists between the E⊥c color and the E⊥c + E||c color. The color of a faceted stone can therefore be quite different depending on the orientation of the cut. While the hue differences between the E⊥c color and E||c color for Cr³⁺ illustrated in the previous section are certainly noticeable, the hue difference for V³⁺ illustrated in this section is very substantial.

Figure 6 (right) presents the E⊥c, E||c, and E⊥c + E||c data for illuminants A and D65. While all three orientations show a noticeable hue difference for the two illuminants, the E||c color and E⊥c + E||c color show a very strong hue difference, which would certainly qualify as a color-change gem when properly cut. The hue difference in these orientations is produced because the D65 light source is richer in blue to green wavelengths than the A light source. Consequently, the stone transmits more green light under D65 illumination, giving the stone a greener hue. The A light source is richer in orange to red wavelengths, so the stone transmits proportionally more of these wavelengths, giving the stone a purplish color. Given the hue differences, it would be interesting to cut some faceted stones from this synthetic crystal, and to search for unusually colored natural high-V pieces from Myanmar.

Fe³⁺: MULTIPLE CHROMOPHORES

Iron is nearly ubiquitous in gem corundum, present over a very wide range of concentrations from less than a few ppma to nearly 5000 ppma. While this makes it difficult to characterize, the fact that Fe³⁺ can exist as single ions replacing aluminum, Fe³⁺ ion pairs, and perhaps larger Fe³⁺ clusters pose yet greater problems. Because the Fe³⁺ spectrum is composed of all of these species whose individual concentrations depend in a nonlinear way upon the total iron concentration in the sample, the spectrum’s dependence on concentration can be quite complex (Ferguson and Fielding, 1971 and 1972; Krebs and Maisch, 1971). In addition to these problems, the Fe³⁺ chromophore is the weakest chromophore in natural corundum. Its peak absorption cross section at 450 nm in the visible region does not exceed 2.5 × 10^–20 cm² ± 8.0%, and it is quite narrow. Thus a variety of samples with a wide range of total Fe³⁺ concentrations is required to characterize the spectra.

Directly growing synthetic sapphire at its melt temperature (~2050°C) doped with iron is limited by the fact that iron and its oxides all have very high vapor pressures at this temperature and thus vaporize from the melt. This imposes a practical limit of a few hundred ppma of iron for crystals grown this way. Flux growth at temperatures of 900–1300°C would seem to be an attractive alternative, and it has been tried (Ferguson and Fielding, 1972), yet the spectroscopy applied still employed only natural crystals. Another problem is that the fraction of pairs and larger clusters would certainly be dependent on the thermal history of the crystal, which would not necessarily mimic nature. For these reasons we too are constrained to using natural crystals for part of our characterization.

Figure 7 shows the absorption cross section spectra of a natural corundum sample with a very high iron concentration determined with SIMS of 4730 ppma, with a total combined uncertainty of 8.0%, the highest concentration among our samples. The detection limit to the 95% confidence level for Fe was 0.003 ppma. The highest concentration was chosen as the cross sections will most easily be measured. At such a high iron concentration, one can easily observe and compare the weak broad features of both the E⊥c and E||c absorptions. This sample is from the Subera deposit in Queensland, Australia. Yellow sapphires of similar iron concentrations are found in the Garba Tula deposit in Kenya, the Chanthaburi area of Thailand, and other alkali basalt-hosted deposits, but they are not common. Usually such sapphires also include a few ppma of Fe²⁺-Ti⁴⁺ pairs, which shifts the yellow to a greenish yellow, or they contain a few tenths of a ppma of h^•-Fe³⁺ pairs, which adds some golden yellow coloration.

The spectra of Fe³⁺ containing corundum is quite complex. In figure 7, the narrow peaks at 377 and 450 nm are attributed to Fe³⁺-Fe³⁺ pairs, as is the weak but broad band at 540 nm. The narrow peak at 388 nm is attributed to single Fe³⁺ ions. The weak but broad bands at 700, 1050, and 1085 nm are only really quantifiable at high Fe³⁺ concentrations. The lack of temperature dependence in the absorption coefficient of these bands implies that they arise from single Fe³⁺ ions (Ferguson and Fielding, 1972). There is also a broad band at 330 nm that is identified as an Fe³⁺-Fe³⁺ pair band, but it is not visible in this spectrum. It can be seen in two of the spectra presented in figure 8. The relatively narrow spectral features at 377, 388, and 450 nm are observable in the spectra of most corundum samples with a Fe concentration of 150 ppma or higher. This is because the absorbance, absorption coefficient, and absorption cross section of different species are additive, and thus a weak narrow feature can be easily seen on top of a much stronger wide band.

The ratio of the peaks of the 388 nm band to the 377 nm band changes dramatically with concentration. This is because the 388 peak is primarily a single Fe³⁺ ion, while the 377 nm peak is a pair of Fe³⁺ ions. Our earlier studies of about 40 different natural samples with widely varying Fe³⁺ concentrations indicate that the peak absorption coefficient at 450 nm, which is a pair of ions, increases very approximately with C^1.5, where C is the total Fe³⁺ concentration. This implies that the absorption cross section of the 450 nm band increases approximately with the square root of C. If there was not a concentration dependence of this cross section, there would be a single curve for E⊥c in figure 8, just as we see for Cr³⁺ and V³⁺. This dependence of the cross section on concentration is currently under study by the authors with over 100 natural samples analyzed by laser ablation–inductively coupled plasma–mass spectrometry (LA-ICP-MS).

Because the absorption cross section is not independent of the iron concentration, our usual presentation of color circles as a function of the areal density, ppma-cm, is not a valid characterization. Thus we present some E⊥c color circles at a few fixed concentrations and as a function of the path length through the sample. Figure 9 (left) compares the E⊥c color circles for D65 illumination. Figure 9 (right) also shows the same color circles but under illuminant A. Fe³⁺ exists in natural gem corundum over a much wider concentration range than any other chromophore. At a few thousand ppma, Fe does indeed cause strongly colored yellow sapphire. However, it is such a weak chromophore that only at these higher concentrations does it contribute much color to a gem. Presenting a more detailed discussion of the color contributed by iron will require a much better physical model of iron in the corundum crystal, as the pair or larger cluster concentrations will also be dependent on the thermal histories of the samples. We encourage our colleagues to study this matter.

THE Fe²⁺-Ti⁴⁺ CHROMOPHORE

Fe²⁺-Ti⁴⁺ pairs are the primary chromophore of blue sapphire (Townsend, 1968; Mattson and Rossman, 1988; Moon and Phillips, 1994). The defect chemistry that creates this pair is interesting. Titanium in corundum is a donor, and iron in corundum can be an acceptor. They electrostatically attract each other and locate on adjacent Al³⁺ sites in the crystal, creating a donor-acceptor pair. Neither Fe²⁺ nor Ti⁴⁺ alone has absorption features in the visible region. Ti⁴⁺ is a closed-shell electron configuration, and Fe²⁺ is expected to absorb only in the near infrared, but that absorption has not yet been observed. Yet when these two ions are located on neighboring aluminum sites, strong absorption bands arise across the visible and near infrared region of the spectrum. For E⊥c the band peaks at 580 nm, while for E||c the peak is at 700 nm. While the theory of the energy levels of a single transition metal ion in a crystal is quite well developed, the theory for ion pairs or clusters in a crystal is not.

The most commonly proposed explanation for the absorption spectra of blue sapphires is that of intervalence charge transfer (IVCT) between the two cations as follows:

where hν is Planck’s constant, h, times the optical frequency, ν. This a common way to indicate that a photon has been absorbed to enable the chemical reaction.

It would seem straightforward to determine the absorption cross sections of this transition by just analyzing a fairly uniform piece of natural blue sapphire and measuring the Fe and Ti concentrations to determine the concentration of Fe²⁺-Ti⁴⁺ pairs. However, as discussed elsewhere (Emmett et al., 2017b), it is difficult to accurately determine the amount of titanium available, [Ti]_available, to pair with Fe²⁺ creating the blue color. Since the Si donor state lies above the Ti donor state in the corundum band gap, it will preferentially pair with acceptors such as Mg and Ni. Thus the Ti available to pair with Fe can be expressed as:

[Ti]_available = [Ti] + [Si – Mg – Ni] for [Si – Mg –  Ni] < 0

[Ti]_available = [Ti] for [Si – Mg – Ni] ≥ 0

Note that the square brackets around ions denote atomic concentrations. The standard deviation (SD) of [Ti]_available is the square root of the sum of the squares of SDs of Ti, Mg, Ni, and Si. Thus the standard deviation of [Ti]_available can be very large, often exceeding the value itself, making accurate estimates of [Ti]_available difficult.

It would also seem straightforward to just grow a synthetic crystal doped only with Fe and Ti, measure the concentrations, and calculate the Fe²⁺-Ti⁴⁺ pair concentration. Such crystals were grown by Milan Kokta at the Union Carbide Corporation crystal growth factory in the 1980s for synthetic gem material. However, two problems arose with the use of synthetic crystals. First, at the Czochralski growth temperature of sapphire (~2050°C), the Fe²⁺-Ti⁴⁺ pairs are largely dissociated. They only partially re-form as the stone cools over a day or two from growth temperature. Thus there are fewer pairs than the concentrations of [Fe] and [Ti] would imply, and we could not determine what fraction of the possible pairs were indeed present.

In nature the growth temperature is much lower, so there is less dissociation, and the cooldown is presumably extremely slow, so the pairs should more fully form. If so, the concentration of pairs should be determined by the ion concentrations.

To re-form the pairs, we heated the synthetic crystals in air for a few thousand hours. The temperature of 750°C was chosen to be low enough that many of the pairs would re-form, yet high enough that the diffusion coefficients of the ions were still large enough that clustering would take place at some finite rate. The absorption coefficients were remeasured at intervals of 50 and 100 hours to track the increase. This process was carried on until no further increase with time was noted, and thus equilibrium was reached. For our samples with the highest Ti concentration, equilibrium was reached in 1500 hours, with the absorption coefficient at 580 nm being 2–2.5 times higher than before heat treatment. It is likely that some additional pairs would form if the temperature were lowered further and the time greatly increased. Just what percentage we have achieved of the low-temperature equilibrium pair concentration is difficult to estimate.

Another problem with the growth of synthetic crystals doped with Fe²⁺-Ti⁴⁺ is determining what fraction of iron in the crystal is actually in solution rather than present as microscopic iron particles. Under the oxygen partial pressure of Czochralski growth from an iridium crucible, all the iron present may not be trivalent and thus soluble in the melt. We have observed microscopic iron crystals in some synthetic Fe-Ti doped crystals. Presently we have no reliable way to determine what portion of the iron in the crystal is actually in solution as Fe³⁺. The synthetic crystals did, however, give us very high-quality E⊥c and E||c spectra without the interference from high concentrations of iron and other trace elements (Si, Cr, V, and Ni).

To achieve reasonably good approximation of the cross sections of the Fe²⁺-Ti⁴⁺ pair, we have chosen a combination of both synthetic crystals and natural crystals. After examining a wide variety of natural crystals, we have chosen Yogo sapphires for their rather extreme optical and chemical uniformity, which far exceeds all other natural crystals we have studied, and for the fact that there is no 880 nm absorption band in this material. Since the synthetic crystals have no interference to the shape of the spectrum from other chromophores, they have been used to accurately determine the shape of the Fe²⁺-Ti⁴⁺ pair absorption spectra.

We have carefully measured the trace element composition of 14 Yogo sapphires by SIMS at Caltech. The SIMS technique gives the smallest SDs of our current measurement techniques, and only SIMS can quantify Si. These analyses provided accurate determinations of Fe, Ti, Mg, Si, Ni, Cr, and V. The detection limits for Cr, V, and Fe were previously given, and the determined detection limits for Ti, Mg, Si, and Ni were 0.039, 0.001, 0.552, and 0.030 ppma, respectively. The higher detection limit for Si is partially due to its larger RSF value, but mainly due to the difficulty of removing all traces of Si from the chamber and mass spectrometer. Because [Si – Mg – Ni] is always negative for Yogo sapphires due to their high Mg concentrations (~100 ppma), the [Ti]_available as noted above was calculated as

[Ti]_available = [Ti] + [Si] – [Mg] – [Ni]

The absorption spectra of the 14 Yogo samples were measured and the contributions from Cr³⁺ and V³⁺ subtracted from each using the absorption cross sections of Cr³⁺ and V³⁺ previously determined. The shape of the remaining Fe²⁺-Ti⁴⁺ absorption band closely matched the shape determined from the synthetic crystals. The resulting absorption cross sections are shown in figure 10. The band shapes are from the synthetic crystals, and the band peak values are determined from the averages of the 14 Yogo crystals studied. The peak E⊥c absorption cross section at 580 nm thus determined is 1.94 × 10^–18 cm² ± 25%.

These spectra have been terminated at 330 nm in the UV. This was necessary because the first O → Fe³⁺ charge transfer band (Tippins, 1970) peaks at 259 nm. We have determined the peak cross section for this transition as 1.66 × 10^–17 cm², which is extremely large. The sloping band edge on the long-wavelength side of this band mixes with the short-wavelength side of the Fe²⁺-Ti⁴⁺ pair and rapidly exceeds the dynamic range of the spectrophotometer. Thus we terminated the Fe²⁺-Ti⁴⁺ spectra before the charge transfer absorption became significant.

In the course of our study of the Fe²⁺-Ti⁴⁺ band in many natural sapphires from many locations, we have found some whose Fe²⁺-Ti⁴⁺ cross sections appear much larger (by factors of two or three) than those determined here using synthetic and Yogo sapphires. Nearly all of these non-Yogo samples contain very high iron content and substantial OH, as revealed by FTIR measurements. We do not know if this is a correct determination and thus represents an enhanced Fe²⁺-Ti⁴⁺ cross section due to the presence of iron pairs or clusters with the Ti⁴⁺, or whether it results from the fact that our chemical analyses only measure a very thin layer on the stone’s surface rather than the bulk composition. Many of these samples demonstrating anomalous Fe²⁺-Ti⁴⁺ cross sections are strongly color zoned, meaning that the concentration of Fe²⁺-Ti⁴⁺ pairs along the optical path can vary substantially, something our surface-level measurements would not be able to capture. Additional research on this topic is definitely needed.

It is interesting to note that in the synthetic and Yogo crystals, the peak of the E⊥c cross section at 580 nm of 1.94 × 10^–18 cm² ± 25% is about 12 times larger than that of Cr³⁺ at 560 nm. The large cross section and the width of the band in the visible region make the Fe²⁺-Ti⁴⁺ pair a strong chromophore. Less than one-tenth the amount of it relative to Cr³⁺ is needed to produce strong coloration.

Figure 11 presents the color circles calculated from the cross section determinations. As in the discussion of the Cr³⁺ chromophore, we have used the areal density in ppma-cm to present the data. Figure 11 (left) shows the three sets of color circles for E⊥c, E||c, and E⊥c + E||c under illuminant D65. As we saw with the Cr³⁺ chromophore, the E⊥c and E||c colors are quite distinct. This is because the E⊥c absorption spectrum is more effective at blocking the blue-green and green portions of the spectrum than the E||c spectrum, thus transmitting a purer blue color.

Figure 11 (right) compares the color observed under illuminants A and D65. While the color differences shown between illuminants D65 (daylight) and A (tungsten lamp) are not dramatic, the color circles for the D65 illuminant exhibit a brighter blue resulting from the greater portion of blue light in the D65 spectrum.

CHROMOPHORES INVOLVING TRAPPED HOLES

When the concentration of magnesium and nickel exceeds the sum of the concentrations of silicon, titanium, and hydrogen, the corundum sample is acceptor dominated. If this occurs in a relatively oxidizing natural environment, or if the stone is heat treated in air or oxygen, the excess acceptors will be charge compensated by trapped holes.

h^• = [acceptors] – [donors] = [Mg + Ni] – [Si + Ti + H]

If the sample also contains iron but not chromium, the h^•-Fe³⁺ pair can form, producing a strong yellow coloration. If instead the sample contains only chromium, the h^•-Cr³⁺ pair can form, producing a strong orange coloration. If the sample contains both Fe³⁺ and Cr³⁺, the hole will preferentially pair with the Cr³⁺. The association of the hole with Fe³⁺ or Cr³⁺ is unusual, as both are isoelectronic with Al³⁺ in the corundum lattice. However, isoelectronic dopants that trap electrons, holes, or excitons are well known in wide gap semiconductors (Pajot and Clerjaud, 2013). Isoelectronic traps in wide-band-gap oxides have received some study as exciton traps that can greatly increase the fluo­rescence from UV excitation (Shtepliuk et al., 2011; Zorenko et al., 2011).

To study the chromophores composed of trapped holes paired with either Fe³⁺ or Cr³⁺, two crystals were grown by the Czochralski technique at St. Gobain Crystals and Detectors; one was doped only with iron and magnesium, while the other was doped only with chromium and magnesium. As grown, the crystal containing iron and magnesium had a bright orangy yellow color, and the crystal containing chromium and magnesium had a bright orange color. The concentrations with total combined uncertainty for the h^•-Fe³⁺ crystal were Fe = 180 ± 7.7% and Mg = 2.13 ± 9.2%. If quantifiable concentrations of Si and Ti were present in this crystal, the total available Mg and its associated total combined error would have to be adjusted to account for these ions. However, both Si and Ti were below the quantification limits, eliminating the need to account for these trace elements. For the h^•-Cr³⁺ crystal, the Cr concentration with total combined uncertainty was 12.6 ± 7.7%, and the Mg concentration with total combined uncertainty was 0.813 ± 9.8% Similarly, the crystal purity was high enough that we did not need to account for Ti and Si that would scavenge available Mg. Following growth, the crystals were annealed in oxygen at 1750°C for 10 hours to assure that all magnesium was charge compensated by holes. Previous experiments under a variety of conditions indicated that this annealing condition maximizes the hole concentration. The resulting crystals were a deeper yellow, almost golden color (iron and magnesium), and a deeper orange color (chromium and magnesium).

The cross sections presented for these two chromophores are determined from the absorption spectra recorded on these double-doped samples. Since the h^•-Fe³⁺ sample also contains the Fe³⁺ chromophore by itself, that spectrum was subtracted before calculating the h^•-Fe³⁺ cross section. Since the Fe³⁺ chromophore is so weak, it only modifies the color produced by the h^•-Fe³⁺ chromophore at high Fe³⁺ concentrations. Similarly, since the h^•-Cr³⁺ sample also contains the Cr³⁺ chromophore by itself, that spectrum was subtracted before calculating the h^•-Cr³⁺ cross section. However, Cr³⁺ is a moderately strong chromophore, and thus any gemstone containing the h^•-Cr³⁺ chromophore will also exhibit a pink to red component from Cr³⁺ alone. It is these two chromophores together that create the magnificent pinkish orange padparadscha sapphire.

The spectrum in figure 12 shows the absorption cross sections for E⊥c and E||c of a sample cut from the crystal containing iron and magnesium. Note the extremely large cross section of the h^•-Fe³⁺ chromophore, 1.3 × 10^–17 cm² ± 12.0%, which is about 6.8 times that measured for the Fe²⁺-Ti⁴⁺ pair or about 80 times larger than that of Cr³⁺. It is thus a very strong chromophore in corundum. The h^•-Fe³⁺ and the h^•-Cr³⁺ are the strongest chromophores in the visible region of the spectrum for corundum. As discussed in the section on the Fe²⁺-Ti⁴⁺ pair chromophore, the spectrum of the h^•-Fe³⁺ chromophore has been terminated at 330 nm to avoid interference by the O → Fe³⁺ charge transfer band. This is not necessary for the h^•-Cr³⁺ spectra, as the first O → Cr³⁺ band is well below 200 nm (Tippins, 1970).

Figure 13 presents the color circles for the h^•-Fe³⁺ pairs. The E⊥c and E||c spectra are quite similar. Thus the E⊥c, E||c, and E⊥c + E||c color circles under D65 illumination shown in figure 13 (left) are also similar, unlike some of the other chromophores we have studied. What is interesting to note here is the extremely small amount of h^•-Fe³⁺ pairs required to create a strong color. Only a few ppma are necessary in a 1 cm thick sample to produce strong coloration, whereas nearly 3000 ppma of Fe³⁺ alone would be required to produce similar coloration (see figure 9). Examining the color circles in figure 13 (right) for the two different illuminants, D65 and A, we see that the color differences for the two illuminants are greater than the E⊥c and E||c color differences.

The h^•-Fe³⁺ chromophore is the primary cause of color for yellow sapphires from Sri Lanka and other sources where the iron content is not extremely high. It also occasionally occurs in some high-iron sapphires from Thailand, where stones with the combination of the two chromophores are referred to as “Mekong Whisky” color sapphires.

Figure 14 shows the E⊥c and E||c absorption cross sections of the h^•-Cr³⁺ pair system. Again, note the extremely large cross sections (1.3 × 10^–17 cm² ± 12.5%), which are similar in magnitude to those of the h^•-Fe³⁺ pair. These two systems are by far the strongest chromophores in corundum.

Figure 15 illustrates the color circles for h^•-Cr³⁺ pairs. At left are shown the color circles for E⊥c, E||c, and E⊥c + E||c under D65 illumination. From the color circles we can see that this chromophore exhibits little dichroism, as the E⊥c and E||c circles are very similar in appearance. This results from the fact that strong absorption is present below 560 nm for both E⊥c and E||c. Figure 15 (right) shows the color circles for both D65 and A illuminants. There is little chromatic difference resulting from the two illuminants. The color circles for illuminant A, which contains proportionally more yellow and red light, may be slightly brighter than their D65 counterparts.

The cross sections and color circles presented for the h^•-Cr³⁺ chromophore are for the chromophore itself and do not include a contribution from the Cr³⁺. Since Cr³⁺ is a moderately strong chromophore, very little is required to shift these hues toward a more pure orange. Concentrations of only 20–40 ppma Cr³⁺ are sufficient to cause a noticeable color shift.

COMPARING THE CHROMOPHORES

Looking closely at the absorption cross section spectra for the various chromophores, one can observe a wide range of values in the visible region of the spectrum of a factor of about 500. However, the variability of the “strength” of the chromophore is even greater because the width (full width half maximum, FWHM) of the cross section features in the visible range varies from ~25 nm for Fe³⁺ to ~250 nm for the Fe²⁺-Ti⁴⁺ pair (see box A). Figure 16 shows the approximate concentrations of the six chromophores required to create roughly similar levels of color saturation for E⊥c in samples 1 cm thick. Concentrations for the chromophores were selected by visually comparing color circles and forming a consensus opinion among the authors about which circles appeared to have similar saturation levels. Comparing the chromophore concentrations in ppma under each circle emphasizes the rather extreme range in “strength,” which is greater than a factor of 1000.

The belief that yellow sapphires were colored only by iron with or without some undefined “color center” (Schmetzer et al., 1983; Nassau, 1991) was engendered by the fact that the existence of, strength, and absorption spectrum of the h^•-Fe³⁺ chromophore was unknown. Additionally, the analytical techniques available before SIMS and SIMS-calibrated LA-ICP-MS with matrix-matched standards were incapable of measurements down to the ppma level. Another key to our current understanding of chromophores in corundum was the capability of growing synthetic sapphire containing only one of the chromophores we wished to study. This allowed us to confirm what we observed in natural samples.

Determining the absorption cross sections is a powerful technique in the study of color in allochromatic minerals, as their magnitudes provide information on the types of absorbing species present. Applying it to other minerals might yield some new insights. Our current trace element analytical capability, at the ppma level or below, provides the critical capability to support such research.