Genesis of the Body Color of Brazilian Gem-Quality Yellow-Green Opal

: The chromaticity characterization and inﬂuencing factors of the body color of 28 yellow-green opals were studied through Fourier transform infrared spectrum (FTIR), energy-dispersive X-ray ﬂuorescence spectroscopy (ED-XRF), ultraviolet-visible spectroscopy (UV-vis) and X-Rite SP62 spectrophotometer. It was found that the hue h ◦ and the iron content of the yellow-green opal were highly negatively correlated, the chroma C* and the sum of nickel and iron content were signiﬁcantly positively correlated, and the lightness L* was signiﬁcantly negatively correlated with the chromium content. The body color of light green opal is mainly caused by nickel. The iron content will make the color yellow, and the chromium content will darken the green. With the increase of Fe content, the lowest absorption value of UV-vis absorption at 500–650 nm moves towards the long wave direction, and the hue h ◦ decreases. With the increase of the total content of Ni and Fe, the 650 nm absorption peak area and the chroma C* increase. Under CIE D65 standard light source and N9.5 Munsell neutral background, using K-Means clustering method, 28 yellow-green opal body colors were divided into three grades: (1) Fancy Intense, (2) Fancy Deep and (3) Fancy.


Introduction
Opal is composed of hydrated silica (SiO 2 •nH 2 O) microspheres with highly disordered structures.According to X-ray diffraction, naturally hydrated silica can be divided into three structural groups.Opal-C, a relatively regular accumulation of α-cristobalite, mixed with a small amount of α-tridymite; opal-CT, an amorphous structure mixed with tridymite; opal-A, amorphous and highly disordered [1].Opal-A can be opal-A G or opal-A N , depending on the long-range connections of the silicon tetrahedra.Opal-A G consists of a spherical structure with a gelatinous SiO 4 connective arrangement, and opal-A N has a similar structure to silica glass while containing varying amounts of water [2].The water in opal is a complex combination of molecules, surface adsorption, and capillaries, or chemically bound functional groups of silanol (Si−OH) [3,4].Silanols exist on internal surfaces such as capillary pores and pores, and are distributed in the body phase as isolated silanol functional groups [5].The stratification of siliceous crystal cavity samples was studied by infrared spectroscopy, and the infrared spectra of opal in the range of 4000-9000 cm −1 were well characterized, and the spectral fingerprints of each type were determined.The change of spectral characteristics is related to the difference of microstructure, hydroxyl content, and organic impurities, which is mainly caused by the Fourier transform infrared spectrum vibration of Si−OH group [6,7].Opals are usually produced in sedimentary or volcanic environments and are referred to as "sedimentary opals" and "volcanic opals" [8].Raman spectroscopy can also be used to distinguish opal-A from opal-CT, which is usually volcanic in origin and more crystalline than depositional opal-A [9].
Opals come in a variety of body colors and can be divided into two main categories based on the presence or absence of a color-changing effect.One is opal with its own colorchanging effect, also known as play-of-color [10].The color-changing effect of opal is caused Crystals 2023, 13, 316 2 of 13 by the diffraction of visible light silica spheres with a diameter 150-300 nm [11].Opals with variegated effects are highly prized and a great deal of research is currently devoted to these stones [12].The other is common opal, which is closely related to precious opals and has the same composition that can take on different body colors [13,14].Colorful opals have been mined around the world, such as blue opals from Australia [15], green opals from Bulgaria, Tanzania, Brazil, and Mexico [16][17][18][19], purple opals from Iran and Turkey [20,21], and pink opal veins found in Peru [22].Less research has been done on common opals than on precious opals.Although the common opal does not have a variegated effect, it can display different beautiful body colors, with intense color, strong luster, and fine texture, and still has significant commercial value.
Opal has been found in Brazil: the most important and famous deposits in Brazil are situated near Pedro II, in the state of Piaui [23].In the 1970s, a clear opal with dark green dendritic inclusions and a translucent apple green opal were found near Boa Nova in Bahia State.They stand out in different shades of green, from yellow to apple green to dark green [18,24].Orange opals from Buriti dos Montes are characterized by a rich orange color, high transparency, and contain various shapes of solid inclusions inside [25].In nature, gem-grade green cryptocrystalline silica is rare, and the chemical composition of this green gem shows high concentrations of trace elements such as nickel, iron, and chromium [26].The UV-vis spectrum of the more transparent green opal shows the following characteristics: increased absorption below about 500 nm and a wide peak near 650 nm [27].In silicate minerals, the region above 650 nm is attributed to the octahedral coordination of Ni 2+ [28].Previous studies have found that opals' body color is often related to their chromogenic inclusions.For example, the varying degrees of orange color of Mexican opal correlate with iron content due to the presence of iron-containing nano-inclusions [19].The color of chrysoprase is due to the presence of nickel-containing phyllosilicate inclusions with low crystallinity nanometers [21].
Color is a perception of light by the visual system of the human eye; therefore, many objective factors can influence the color of a gemstone, such as lighting conditions, object background environment, etc. [29].Lighting conditions are crucial to the presentation of an object's color, which is influenced mainly by the intensity of light, the angle of illumination and the type of light source.Based on the CIE 1976 L*a*b* uniform color space, many scholars have graded the color and evaluated the quality of different types of gemstones, such as jadeite, chrysoprase, serpentine jade, beryl, and garnet [30][31][32][33][34]. CIE 1976 L*a*b* Uniform Color Space is recommended by the International Commission on Illumination and is widely used for the testing and quantitative characterization of color.The system is composed of color coordinates a*, b* and lightness L*, with lightness L* as the Z axis and color coordinate a* and b* as the X and Y axes, respectively [35].L* indicates lightness, a* indicates the colorimetric index between red and green, and b* indicates the colorimetric index between blue and yellow [35].The distance from the projection point to the origin indicates the size of chroma C*, and the hue h • is indicated by the angle between the line from the projection point to the origin and the +a* axis [35].The position of color in color space is represented by points in three-dimensional space.C* and hue h • can be calculated by a* and b* [35].

Samples
A total of 28 gem-quality square plain opals were selected as the study objects.The body color was uniform and gradually transitioned from yellow to green.Each sample was cut into a 5 mm × 5 mm square with a uniform thickness of 4 mm.Transparency was higher than common opals.The surfaces were well polished, flat, and smooth.No obvious inclusions were observed by the naked eye.The origin of the sample was Bahia State, Brazil, and they were put in the light source box with neutral gray background to take photos.The light source was D65.The sample is shown in Figure 1.Table 1 summarizes the gemological properties of opal.
inclusions were observed by the naked eye.The origin of the sample was Bahia State, Brazil, and they were put in the light source box with neutral gray background to take photos.The light source was D65.The sample is shown in Figure 1.Table 1 summarizes the gemological properties of opal.

Colorimetric Analysis
An X-Rite SP62 spectrophotometer (X-Rite, Grand Rapids, MI, USA) was selected to measure the color parameters of the samples.Three measurements were made for each sample to take an average value.The test conditions are described as follows: reflection method, excluding specular reflection; D65 (6504 K) standard light source illumination; N9.5 Munsell Neutral Grey background for background; measurement range: 400~700 nm; measurement time 2.5 s; measurement aperture, 4 mm.

Fourier Transform Infrared Spectroscopy
The mid-infrared spectra of 28 samples were measured using the Tensor 27 FTIR (Bruker, Ettlingen, Baden-Wurttemberg, Germany).Non-destructive testing with a wellpolished surface was conducted.Test conditions were: reflection method, scanning times of 30, instrument resolution of 4 cm −1 , scanning range of 400 cm −1 -2000 cm −1 .

X-ray Fluorescence
EDX-7000 energy dispersive X-ray fluorescence spectrometer (SHIMADZU, Kyoto, Japan) was used for qualitative and quantitative analysis of the samples.The test conditions were as follows: atmosphere, vacuum; the collimator diameter was 1 mm; detection element range: Al-U, Na-Sc, F, and Ne; In the Al-U range, the element test conditions were

Colorimetric Analysis
An X-Rite SP62 spectrophotometer (X-Rite, Grand Rapids, MI, USA) was selected to measure the color parameters of the samples.Three measurements were made for each sample to take an average value.The test conditions are described as follows: reflection method, excluding specular reflection; D65 (6504 K) standard light source illumination; N9.5 Munsell Neutral Grey background for background; measurement range: 400~700 nm; measurement time 2.5 s; measurement aperture, 4 mm.

Fourier Transform Infrared Spectroscopy
The mid-infrared spectra of 28 samples were measured using the Tensor 27 FTIR (Bruker, Ettlingen, Baden-Wurttemberg, Germany).Non-destructive testing with a wellpolished surface was conducted.Test conditions were: reflection method, scanning times of 30, instrument resolution of 4 cm −1 , scanning range of 400 cm −1 -2000 cm −1 .

X-ray Fluorescence
EDX-7000 energy dispersive X-ray fluorescence spectrometer (SHIMADZU, Kyoto, Japan) was used for qualitative and quantitative analysis of the samples.The test conditions were as follows: atmosphere, vacuum; the collimator diameter was 1 mm; detection element range: Al-U, Na-Sc, F, and Ne; In the Al-U range, the element test conditions were 50 kV and 1000 µA, the analysis was set to '0.00-40.00', the time was set to 'live-30', and DT% was set to '15'.In the Na-Sc range, the element test conditions were 15 kV and 1000 µA, the analysis was set to '0.00-4.40', the time was set to 'live-100', and the DT% was set to '2'; the test conditions of F element were 15 kV and 1000 µA, the analysis was set to '0.48-0.88', the time was set to 'live-100', and DT% was set to '2'.The test conditions of Ne elements were 15 kV and 1000 µA, the analysis was set to '0.65-1.05', the time was set to 'live-100', and the DT% was set to '2'.

Correlation Analysis
IBM SPSS Statistics software version 26 was used to classify.The strength of the linear relationship between the parameters can be judged by the size of the Pearson correlation coefficient r.When 0 < |r| ≤ 0.3, there is weak or no correlation.When 0.3 < |r| ≤ 0.5, there is low correlation.When 0.5 < |r| ≤ 0.8, there is moderate correlation.When 0.8 < |r| < 1, there is high correlation.

UV-Vis Spectroscopy
UV-3600 UV-vis spectrophotometer (SHIMADZU, Kyoto, Japan) was used to measure the UV-visible spectrum of the samples.The experimental wavelength ranged from 300 nm to 900 nm, high-speed scanning mode, single scanning mode, sampling interval of 1.0 s, using reflection method measurement.

K-Mean Clustering Analysis and Fisher Discriminant Analysis
K-mean clustering is a kind of iterative solving clustering analysis algorithm.The number of clusters can be artificially set.Its step is to pre-divide the data into k groups, randomly select k objects as the initial clustering center, then calculate the distance between each object and each seed clustering center, and assign each object to the nearest clustering center.Fisher discriminant analysis is one of discriminant analysis methods, which is a linear discriminant method based on variance analysis.

Color Quantification
The color of 28 yellow-green opals was quantitatively characterized by X-Rite SP62 spectrophotometer under standard D65 light source with Munsell N9.    -O)) [36].The widening band of opal at 1100 can be explained by its low crystallinity.The inflection point near 1245 cm −1 in the infrared spectrum can be used as a mark to determine whether the gem is crystal or amorphous [37].Opal-C usually has an obvious band at 620 cm −1 , which is a specific strong cristobalite absorption zone, and is characterized by a wide absorption peak of 800-1250 cm −1 [7].It can be seen that the infrared spectrum of the sample is significantly different from opal-C.Opal-A and opal-CT opals have relatively standard infrared spectra.The infrared spectrum of opal-A contains 1108 cm −1 and 478 cm −1 absorption bands.Peaks around 550 cm −1 are specific to opal-A.Opal-CT has a weak absorption peak at 780 cm −1 [38][39][40].Opal-CT and opal-A can be distinguished by the location of Si−O symmetric tensile vibration near 780 cm −1 [10].The symmetric stretching vibration range of Si−O absorption band in opal-A is 796-800 cm −1 , while that of Si−O absorption band in opal-CT is 788-792 cm −1 , which is closer to the absorption position of tridymite [36].In this study, the band of the sample was near 780 cm −1 , lacking the absorption bands of 550 cm −1 and 620 cm −1 , which was closest to the infrared spectrum of opal-CT.

Relationship between Ni, Fe, Cr and Color
The relationship between color elements and color parameters in yellow and green opal samples was preliminarily investigated by measuring the composition of elements.The analysis shows that the main components of the opal samples are: SiO2 (97.961-99.329wt.%), other oxides include NiO (0.087-1.079 wt.%), FeOtot (0.093-1.295 wt.%), Cr2O3 (0.042-0.193 wt.%), CuO (0.020-0.142 wt.%), and ZnO (0-0.030wt.%).Nickel, iron, chromium, and copper are transition metal elements, often associated with the color of the gem.Bivariate correlation analysis was performed, and the results were shown in Table 2.
The results show that w(FeOtot) has a highly negative correlation with the hue h° (r = −0.811**).As shown in Figure 4a, with the increase in Fe content, the hue h° of opal samples almost linearly decreases, and the hue changes from green to yellow.Yellow opal has the highest Fe content, while light green opal has the lowest Fe content.In order to explore whether Ni contributes to the body color of opal samples, bivariate correlation analysis is conducted between Fe + Ni content and color parameters.In Figure 4b, there is a significant positive correlation between w(FeOtot + NiO) and the chroma C* (r = 0.667**), and a low negative correlation between w(FeOtot + NiO) and the lightness L* (r = −0.399),indicating that Ni also has a great influence on opal body color.Light green opal has the highest Ni content.In addition, as shown in Figure 4c, there is a significant negative correlation between w(Cr2O3) and the lightness L* (r = −0.666**).With the increase of Cr content, the lightness L* decreases.Deep green opal has the highest Cr content.According to the above Opal-C usually has an obvious band at 620 cm −1 , which is a specific strong cristobalite absorption zone, and is characterized by a wide absorption peak of 800-1250 cm −1 [7].It can be seen that the infrared spectrum of the sample is significantly different from opal-C.Opal-A and opal-CT opals have relatively standard infrared spectra.The infrared spectrum of opal-A contains 1108 cm −1 and 478 cm −1 absorption bands.Peaks around 550 cm −1 are specific to opal-A.Opal-CT has a weak absorption peak at 780 cm −1 [38][39][40].Opal-CT and opal-A can be distinguished by the location of Si−O symmetric tensile vibration near 780 cm −1 [10].The symmetric stretching vibration range of Si−O absorption band in opal-A is 796-800 cm −1 , while that of Si−O absorption band in opal-CT is 788-792 cm −1 , which is closer to the absorption position of tridymite [36].In this study, the band of the sample was near 780 cm −1 , lacking the absorption bands of 550 cm −1 and 620 cm −1 , which was closest to the infrared spectrum of opal-CT.

Relationship between Ni, Fe, Cr and Color
The relationship between color elements and color parameters in yellow and green opal samples was preliminarily investigated by measuring the composition of elements.The analysis shows that the main components of the opal samples are: SiO 2 (97.961-99.329wt.%), other oxides include NiO (0.087-1.079 wt.%), FeO tot (0.093-1.295 wt.%), Cr 2 O 3 (0.042-0.193 wt.%), CuO (0.020-0.142 wt.%), and ZnO (0-0.030wt.%).Nickel, iron, chromium, and copper are transition metal elements, often associated with the color of the gem.Bivariate correlation analysis was performed, and the results were shown in Table 2.The results show that w(FeO tot ) has a highly negative correlation with the hue h • (r = −0.811**).As shown in Figure 4a, with the increase in Fe content, the hue h • of opal Crystals 2023, 13, 316 7 of 13 samples almost linearly decreases, and the hue changes from green to yellow.Yellow opal has the highest Fe content, while light green opal has the lowest Fe content.In order to explore whether Ni contributes to the body color of opal samples, bivariate correlation analysis is conducted between Fe + Ni content and color parameters.In Figure 4b, there is a significant positive correlation between w(FeO tot + NiO) and the chroma C* (r = 0.667 **), and a low negative correlation between w(FeO tot + NiO) and the lightness L* (r = −0.399),indicating that Ni also has a great influence on opal body color.Light green opal has the highest Ni content.In addition, as shown in Figure 4c, there is a significant negative correlation between w(Cr 2 O 3 ) and the lightness L* (r = −0.666**).With the increase of Cr content, the lightness L* decreases.Deep green opal has the highest Cr content.According to the above analysis, the color of opal samples changes from green to yellow with the increase of Fe content.With the increase of Cr content, the green tone gradually deepened.

UV-Vis Spectroscopy Characteristics
The UV-visible absorption spectra of the three groups of opal samples are shown in Figure 5, all of which show relatively similar absorption spectra.From the blue-violet zone to the green zone near 500 nm, the absorption value decreases rapidly, and the orange-red zone has a wide absorption band centered at 650 nm.Below 380 nm, iron absorbs more energy when coordinating octahedrons at this band due to the charge transfer of O 2− →Fe 3+ .The charge transfer between Fe 3+ and the surrounding oxygen results in the yellow color.The absorption peak at 450 nm is caused by the electron transition, and the absorption position is relatively fixed, which is not affected by the crystal field effect [41].As a result, a narrow transmission window appears in the green region of the ultraviolet-visible spectrum, which explains the opal's color.

UV-Vis Spectroscopy Characteristics
The UV-visible absorption spectra of the three groups of opal samples are shown in Figure 5, all of which show relatively similar absorption spectra.From the blue-violet zone to the green zone near 500 nm, the absorption value decreases rapidly, and the orange-red zone has a wide absorption band centered at 650 nm.Below 380 nm, iron absorbs more energy when coordinating octahedrons at this band due to the charge transfer of O 2− →Fe 3+ .The charge transfer between Fe 3+ and the surrounding oxygen results in the yellow color.The absorption peak at 450 nm is caused by the electron transition, and the absorption position is relatively fixed, which is not affected by the crystal field effect [41].As a result, a narrow transmission window appears in the green region of the ultravioletvisible spectrum, which explains the opal's color.The light green opal shows a wide absorption band centered at 650 nm, which is caused by the 3 A2g(F)→ 3 T1g(F) electron transition of Ni 2+ .This absorption band is typical of Ni 2+ in the octahedral coordination [26,27].The results of the green opal test are basically consistent with the previous results of the chrysoprase test [42,43].A wide transmission window formed between 500-600 nm explains the typical color of the nickel-bearing mineral (apple green).The yellow-green opal has a wide absorption band at 654 nm and moves towards the long wave direction due to the charge transfer of Fe 2+ →Fe 3+ .Yellowgreen opal has a lower nickel content than light green opal, and its high iron content is responsible for strong absorption in the near-UV range, giving the opal a greenish-yellow color [44].With the deepening of green tone, part of the deep green opal UV-vis spectrum shows a wide absorption peak centered at 618 nm, which is caused by the 4 A2g→ 4 T2g(4F) d-d electron transition of Cr 3+ [45].Due to Fe 2+ →Fe 3+ charge transfer, a transmission window appears in the green area, which explains the color of the opal.The presence of chromium will darken the color of green opal.
The different content and proportion of the three chromic elements, nickel, iron, and chromium, make opal show different shades of green.Based on the analysis results of XRF and UV-vis absorption spectra, it can be seen that Brazilian yellow-green opal can be subdivided into three main types: (1) Nickel type, represented by light green opal, high nickel content, low chromium and iron content; (2) Iron type, represented by yellow-green opal, high in nickel and iron and almost free of chromium; (3) The chrome type, represented by dark green opal, contains a large amount of nickel, with an equal amount of chromium and iron.The light green opal shows a wide absorption band centered at 650 nm, which is caused by the 3 A 2g (F)→ 3 T 1g (F) electron transition of Ni 2+ .This absorption band is typical of Ni 2+ in the octahedral coordination [26,27].The results of the green opal test are basically consistent with the previous results of the chrysoprase test [42,43].A wide transmission window formed between 500-600 nm explains the typical color of the nickel-bearing mineral (apple green).The yellow-green opal has a wide absorption band at 654 nm and moves towards the long wave direction due to the charge transfer of Fe 2+ →Fe 3+ .Yellow- green opal has a lower nickel content than light green opal, and its high iron content is responsible for strong absorption in the near-UV range, giving the opal a greenish-yellow color [44].With the deepening of green tone, part of the deep green opal UV-vis spectrum shows a wide absorption peak centered at 618 nm, which is caused by the 4 A 2g → 4 T 2g (4F) d-d electron transition of Cr 3+ [45].Due to Fe 2+ →Fe 3+ charge transfer, a transmission window appears in the green area, which explains the color of the opal.The presence of chromium will darken the color of green opal.
The different content and proportion of the three chromic elements, nickel, iron, and chromium, make opal show different shades of green.Based on the analysis results of XRF and UV-vis absorption spectra, it can be seen that Brazilian yellow-green opal can be subdivided into three main types: (1) Nickel type, represented by light green opal, high nickel content, low chromium and iron content; (2) Iron type, represented by yellow-green opal, high in nickel and iron and almost free of chromium; (3) The chrome type, represented by dark green opal, contains a large amount of nickel, with an equal amount of chromium and iron.

Color Causes of Yellow-Green Opal
As shown in Figure 6a, the troughs of the UV-vis absorption spectrum between 500 and 650 nm determine the hue h • of the sample.There is a trough in the green region of the UV-vis spectrum at 500-550 nm, and as the wavelength corresponding to this lowest absorption value changes, so does the hue h • of the opal.As the lowest wavelength increases, the hue decreases and the body color changes to yellow.As shown in Figure 6b, with the increase of Fe content, the lowest absorption value between 500-650 nm in the spectrum shifts to the long-wave direction, and the body color change is manifested as the hue decreases and the body color tends to yellow-green.
As shown in Figure 6a, the troughs of the UV-vis absorption spectrum between 500 and 650 nm determine the hue h° of the sample.There is a trough in the green region of the UV-vis spectrum at 500-550 nm, and as the wavelength corresponding to this lowest absorption value changes, so does the hue h° of the opal.As the lowest wavelength increases, the hue decreases and the body color changes to yellow.As shown in Figure 6b, with the increase of Fe content, the lowest absorption value between 500-650 nm in the spectrum shifts to the long-wave direction, and the body color change is manifested as the hue decreases and the body color tends to yellow-green.This may be due to the high iron content of the yellow opal, which absorbs more energy when coordinating the octahedron at 380 nm.When λ-dependent light scattering is applied to the tiny defects inside the opal, the spectral absorption value decreases, making the wavelength with the lowest absorption value in the green region of the spectrum This may be due to the high iron content of the yellow opal, which absorbs more energy when coordinating the octahedron at 380 nm.When λ-dependent light scattering is applied to the tiny defects inside the opal, the spectral absorption value decreases, making the wavelength with the lowest absorption value in the green region of the spectrum shift towards the long wave direction.The hue drops and the tone tends to yellow.This is consistent with the previous EDXRF conclusion that Fe content is negatively correlated with hue h • .It is proved that the body color of opal is related to the content of iron, and the content of iron mainly affects the hue of opal.The higher the content of iron, the smaller the hue h • , and the more yellow the body color of opal.
Figure 6c directly shows that the higher the FeO tot + NiO content of the sample, the higher the chroma, the larger the absorption region, and the larger the 650 nm absorption peak area.As shown in Figure 6d, when the sum of FeO tot + NiO content is higher, the chroma C* will be higher.This is consistent with EDXRF's conclusion that the sum of nickel and iron content is positively correlated with chroma C*.It is proved that the body color of opal is not only related to iron content, but also related to nickel, and the sum of nickel and iron content mainly affects the chroma of opal; the higher the sum of nickel and iron content, the higher chroma.
The color of an opal is usually associated with the presence of tiny inclusions.The more disordered the structure, the more microstructure defects there will be, which can accommodate more impurities, affecting the opal body color.In this study, we observed that the body color of opal is correlated with the content of Ni, Fe, and Cr.Therefore, it is preliminarily believed that Fe 3+ , Fe 2+ , Ni 2+ , and Cr 3+ are the main factors affecting opal color.Since Ni 2+ itself cannot displace Si 4+ , nickel is present in the silica matrix in the form of fine nickel compounds.Fe 3+ exists mainly as a substitute for Si 4+ by entering the lattice.Chromium may be present as a micro-inclusion of an unknown mineral.It is characterized by wide absorption peaks in the UV-vis absorption spectrum.The more Fe and Ni chromogenic impurities are contained, the larger the 650 nm peak area and the larger the chroma.

Color Grading of Yellow-Green Opal
Many factors can affect the value of opal, and there is currently no standardized method for grading gem-grade opal.K-mean clustering analysis and Fisher discriminant analysis were applied to evaluate the color of gemstones, such as jadeite and tourmaline [46,47].Therefore, based on CIE 1976 L*a*b* uniform color space, 28 yellowgreen opal samples were classified using the same method.With color parameters L*, a* and b* as variables, when the number of clustering is set to 3, the classification effect is the best and the classification scheme is feasible (Sig < 0.01), the number of cases in each category is 9, 9, 10.The clustering analysis results are shown in Table 3, and the color center of opals are shown in Table 4. Fisher discriminant was used to test clustering: the accuracy was 100%, which proved the effectiveness and feasibility of the classification scheme, and the corresponding discriminant function was obtained:

Conclusions
The sample was preliminarily determined to be opal-CT.In UV-vis spectrum, the absorption of Fe 3+ below 380 nm is the cause of opals' yellow color, and the transmission window between 500-650 nm determines the hue h°; the octahedral coordination of Ni 2+ shows 650 nm wide absorption band, and the charge transfer of Fe 2+ →Fe 3+ , together determines the chroma C*; the octahedral coordination of Cr 3+ shows a typical 618 nm wide absorption band.It was found by EDXRF that Fe content is negatively correlated with hue h°, the sum of Ni and Fe content is positively correlated with chroma C*, and Cr content

Conclusions
The sample was preliminarily determined to be opal-CT.In UV-vis spectrum, the absorption of Fe 3+ below 380 nm is the cause of opals' yellow color, and the transmission window between 500-650 nm determines the hue h°; the octahedral coordination of Ni 2+ shows 650 nm wide absorption band, and the charge transfer of Fe 2+ →Fe 3+ , together determines the chroma C*; the octahedral coordination of Cr 3+ shows a typical 618 nm wide absorption band.It was found by EDXRF that Fe content is negatively correlated with hue h°, the sum of Ni and Fe content is positively correlated with chroma C*, and Cr content

Conclusions
The sample was preliminarily determined to be opal-CT.In UV-vis spectrum, the absorption of Fe 3+ below 380 nm is the cause of opals' yellow color, and the transmission window between 500-650 nm determines the hue h°; the octahedral coordination of Ni 2+ shows 650 nm wide absorption band, and the charge transfer of Fe 2+ →Fe 3+ , together determines the chroma C*; the octahedral coordination of Cr 3+ shows a typical 618 nm wide absorption band.It was found by EDXRF that Fe content is negatively correlated with hue h°, the sum of Ni and Fe content is positively correlated with chroma C*, and Cr content This took place under the D65 standard light source, with Munsell N9.5 as the background.According to the color test results, referring to the Gemological Institute of America grading standards for colored diamonds [48]: the opal samples with the hue of (108

Conclusions
The sample was preliminarily determined to be opal-CT.In UV-vis spectrum, the absorption of Fe 3+ below 380 nm is the cause of opals' yellow color, and the transmission window between 500-650 nm determines the hue h°; the octahedral coordination of Ni

Conclusions
The sample was preliminarily determined to be opal-CT.In UV-vis spectrum, the absorption of Fe 3+ below 380 nm is the cause of opals' yellow color, and the transmission window between 500-650 nm determines the hue h • ; the octahedral coordination of Ni 2+ shows 650 nm wide absorption band, and the charge transfer of Fe 2+ →Fe 3+ , together determines the chroma C*; the octahedral coordination of Cr 3+ shows a typical 618 nm wide absorption band.It was found by EDXRF that Fe content is negatively correlated with hue h • , the sum of Ni and Fe content is positively correlated with chroma C*, and Cr content is negatively correlated with lightness L*.Opal colors were classified into three categories by K-means clustering: (1) Fancy Intense, (2) Fancy Deep, and (3) Fancy.

Figure 1 .
Figure 1.The samples used in this study under standard D65 light.

Figure 1 .
Figure 1.The samples used in this study under standard D65 light.

Figure 2 .
Figure 2. (a) The distribution of sample parameters in CIE 1976 L*a*b* uniform color space; (b) Chroma C* is highly positively correlated with color coordinate b*; (c) Hue h° is highly negatively correlated with color coordinate b*; (d) Chroma C* is highly negatively correlated with hue h°.3.2.Infrared Spectral Characteristics FTIR was used to analyze the infrared spectrum fingerprint area of the sample to determine the type of sample.All the opal samples show relatively similar infrared spectra, as shown in the Figure 3.There are three strong bands near 480, 780, and 1110 cm −1 , which are typical features of the four-coordination silica phase, showing a typical SiO4 tetrahedral network.In addition, there is an inflection point near 1245 cm −1 , and the appearance of these bands is related to the basic vibration of Si-O.The band near 480 cm −1 is related to the O-Si-O bending vibration δ (O-Si-O), and the band near 780 cm −1 is caused by the symmetric stretching vibration of Si-O (νs (Si-O)).The band near 1110 cm −1 has been attributed to the anti-symmetric tensile vibration of Si-O (νas (Si-O))[36].The widening band of opal at 1100 can be explained by its low crystallinity.The inflection point near 1245 cm −1 in the infrared spectrum can be used as a mark to determine whether the gem is crystal or amorphous[37].

Figure 2 .
Figure 2. (a) The distribution of sample parameters in CIE 1976 L*a*b* uniform color space; (b) Chroma C* is highly positively correlated with color coordinate b*; (c) Hue h • is highly negatively correlated with color coordinate b*; (d) Chroma C* is highly negatively correlated with hue h • .

FTIR
was used to analyze the infrared spectrum fingerprint area of the sample to determine the type of sample.All the opal samples show relatively similar infrared spectra, as shown in the Figure 3.There are three strong bands near 480, 780, and 1110 cm −1 , which are typical features of the four-coordination silica phase, showing a typical SiO 4 tetrahedral network.In addition, there is an inflection point near 1245 cm −1 , and the appearance of these bands is related to the basic vibration of Si-O.The band near 480 cm −1 is related to the O-Si-O bending vibration δ (O-Si-O), and the band near 780 cm −1 is caused by the symmetric stretching vibration of Si-O (ν s (Si-O)).The band near 1110 cm −1 has been attributed to the anti-symmetric tensile vibration of Si-O (ν as (Si

Crystals 2023 ,
13,  x FOR PEER REVIEW 7 of 13 analysis, the color of opal samples changes from green to yellow with the increase of Fe content.With the increase of Cr content, the green tone gradually deepened.

Figure 4 .
Figure 4. Relationship between color parameters and transition-metal elements.(a) There is a high negative correlation between w(FeOtot) and the hue h° of opal; (b) With the increase of w(FeOtot + NiO), the chroma C* increases, and w(FeOtot + NiO) has a low negative correlation with the lightness L*; (c) With the increase of Cr content, the lightness L* decreases.

Figure 4 .
Figure 4. Relationship between color parameters and transition-metal elements.(a) There is a high negative correlation between w(FeO tot ) and the hue h • of opal; (b) With the increase of w(FeO tot + NiO), the chroma C* increases, and w(FeO tot + NiO) has a low negative correlation with the lightness L*; (c) With the increase of Cr content, the lightness L* decreases.

Figure 5 .
Figure 5. UV-vis absorption spectra of opal in light green, yellow green and deep green.

Figure 5 .
Figure 5. UV-vis absorption spectra of opal in light green, yellow green and deep green.

Figure 6 .
Figure 6.The body color of yellow-green opal is significantly related to the lowest absorption value between 500-650 nm and the area of the 650 nm absorption peak.(a) The troughs between 500 and 650 nm determine the hue h° of the opal; (b) The relationship between the wavelength corresponding to the lowest absorption value at 500-650 nm and the hue h° and w(FeOtot)/%; (c) The chroma C* and w(FeOtot + NiO)/% of opal increase with the increase of 650 nm absorption peak area; (d) The relationship between 650 nm peak area and chroma C*, + NiO)/%.

Figure 6 .
Figure 6.The body color of yellow-green opal is significantly related to the lowest absorption value between 500-650 nm and the area of the 650 nm absorption peak.(a) The troughs between 500 and 650 nm determine the hue h • of the opal; (b) The relationship between the wavelength corresponding to the lowest absorption value at 500-650 nm and the hue h • and w(FeO tot )/%; (c) The chroma C* and w(FeO tot + NiO)/% of opal increase with the increase of 650 nm absorption peak area; (d) The relationship between 650 nm peak area and chroma C*, w(FeO tot + NiO)/%.

Figure 7 .
Figure 7. Color grading of yellow-green opal under D65 light source and N9.5 background.(a) Three groups of yellow-green opals in three-dimensional projection: Fancy Intense, Fancy Deep, and Fancy; (b) Color distribution of three groups of yellow-green opal samples.

Figure 7 .
Figure 7. Color grading of yellow-green opal under D65 light source and N9.5 background.(a) Three groups of yellow-green opals in three-dimensional projection: Fancy Intense, Fancy Deep, and Fancy; (b) Color distribution of three groups of yellow-green opal samples.

Figure 7 .
Figure 7. Color grading of yellow-green opal under D65 light source and N9.5 background.(a) Three groups of yellow-green opals in three-dimensional projection: Fancy Intense, Fancy Deep, and Fancy; (b) Color distribution of three groups of yellow-green opal samples.

Figure 7 .
Figure 7. Color grading of yellow-green opal under D65 light source and N9.5 background.(a) Three groups of yellow-green opals in three-dimensional projection: Fancy Intense, Fancy Deep, and Fancy; (b) Color distribution of three groups of yellow-green opal samples.
2+  shows 650 nm wide absorption band, and the charge transfer of Fe 2+ →Fe 3+ , together determines the chroma C*; the octahedral coordination of Cr 3+ shows a typical 618 nm wide absorption band.It was found by EDXRF that Fe content is negatively correlated with hue h°, the sum of Ni and Fe content is positively correlated with chroma C*, and Cr content is negatively correlated with lightness L*.Opal colors were classified into three categories by K-means clustering: (1) Fancy Intense, (2) Fancy Deep, and (3) Fancy.Author Contributions: Conceptualization, H.L.; methodology, H.L. and Y.G.; software, H.L.; validation, H.L. and Y.G; formal analysis, H.L.; H.L.; resources, H.L.; data curation, H.L.; writing-original draft preparation, H.L.; writing-review and editing, H.L.; visualization, H.L.; supervision, Y.G.; project administration, Y.G.All authors have read and agreed to the published version of the manuscript.Funding: This research received no external funding.

Figure 7 .
Figure 7. Color grading of yellow-green opal under D65 light source and N9.5 background.(a) Three groups of yellow-green opals in three-dimensional projection: Fancy Intense, Fancy Deep, and Fancy; (b) Color distribution of three groups of yellow-green opal samples.

Table 1 .
Gemological properties of opal samples.

Table 1 .
Gemological properties of opal samples.

Table 2 .
Results of bivariate correlation analysis.** At level 0.01 (double tail), the correlation was significant.

Table 2 .
Results of bivariate correlation analysis.** At level 0.01 (double tail), the correlation was significant.

Table 3 .
Cluster analysis results of yellow-green opal color.

Table 4 .
The color center of yellow-green opal.

Table 3 .
Cluster analysis results of yellow-green opal color.

Table 4 .
The color center of yellow-green opal.

Table 3 .
Cluster analysis results of yellow-green opal color.

Table 4 .
The color center of yellow-green opal.

Table 3 .
Cluster analysis results of yellow-green opal color.

Table 4 .
The color center of yellow-green opal.

Table 3 .
Cluster analysis results of yellow-green opal color.

Table 4 .
The color center of yellow-green opal.