Explaining Colour Change in Pyrope-Spessartine Garnets

Article Explaining Colour Change in Pyrope-Spessartine Garnets

Yan Qiu and Ying Guo *

School of Gemmology, China University of Geosciences (Beijing), Beijing 100083, China; [email protected] * Correspondence: [email protected]

Abstract: A colour-changing garnet exhibits the “alexandrite effect”, whereby its colour changes from green in the presence of daylight to purplish red under incandescent light. This study examines this species of garnets as well as the causes of the colour change by using infrared and ultraviolet visible (UV-Vis) spectroscopy. The infrared spectra show that the colour-changing garnets in this paper belong to the solid solution of pyrope-spessartine type. CIE1931 XYZ colour matching functions are used to calculate the colour parameters inﬂuencing garnet colour-changing under different light sources. The UV-Vis spectra show two zones of transmittance, in the red region at 650–700 nm and the blue-green region at 460–510 nm. As they exhibit the same capacity to transmit light, the colour of the gem is determined by the external light source. The absorption bands of Cr3+ and V3+ at 574 nm in the UV-Vis spectra are the main cause of the change in colour. With the increase in the area of peak absorption, the differences in the chroma and colour of the garnet gradually increase in daylight and incandescent light, and it exhibits a more prominent colour-changing effect.

Keywords: colour-changing garnet; FTIR; UV-Vis spectra; CIE1931 XYZ colour matching functions

Citation: Qiu, Y.; Guo, Y. Explaining 1. Introduction Colour Change in Pyrope-Spessartine Garnets are a common group of minerals that undergo complex changes in their Garnets. Minerals 2021, 11, 865. composition. The island silicate garnet belongs to the cubic space group, Ia3d, Z = 8 [1], https://doi.org/10.3390/ and has the general chemical formula A3B2[SiO4]3. Position A is occupied by divalent min11080865 cations, such as Mg2+, Fe2+, Mn2+, and Ca2+, with eight-fold coordination in a dodecahedral site. Position B is occupied by trivalent cations, such as Al3+, Fe3+, and Cr3+, with six-fold Academic Editors: Lluís Casas and coordination occupying the octahedral site. Si4+ is a tetravalent cation that can be partially Roberta Di Febo replaced by a small amount of Ti4+, and occupies the tetrahedral position with four-fold coordination [2]. The divalent cations Mg2+, Fe2+, and Mn2+ have smaller ionic radii Received: 18 June 2021 than Ca2+, and thus struggle to replace one another. Garnets can hence be divided into Accepted: 6 August 2021 two isomeric series: pyralspite and ugrandite. Published: 11 August 2021 In gemology, a change in colour that occurs when the source of illumination switches from daylight to incandescent light is called “alexandrite effect”. Many gemstones naturally Publisher’s Note: MDPI stays neutral change colour, such as alexandrite [3], diaspore [4,5], Tavernier diamond [6], corundum [7], with regard to jurisdictional claims in and garnet [8–11]. published maps and institutional afﬁl- A special kind of pyralspite garnet exhibits the alexandrite change in colour. Such iations. garnets appear yellow-green in daylight and purple-red under incandescent light. Colour- changing garnets can be divided into two categories based on their chemical composition: Cr-rich spessartine, and Cr, V-rich pyrope-spessartine solid solutions [12]. Generally the perceived colour of the surface of an object remains constant when the Copyright: © 2021 by the authors. intensity of light and the spectral components of illumination change. The alexandrite Licensee MDPI, Basel, Switzerland. effect is a phenomenon of distinctive changes in the colour of a gem when observed under This article is an open access article daylight and incandescent light [13]. A change of 20◦ in the absolute hue angle is used to distributed under the terms and identify the alexandrite effect [14]. conditions of the Creative Commons Attribution (CC BY) license (https:// Tang [15], Cheng [16], and Wang [17] used an X-Rite SP62 portable spectrophotometer creativecommons.org/licenses/by/ to visually measure the colours of gems. Guo et al. [18,19] used Spectrophotometer Colour 4.0/). i5 and the GemDialogue colour chip to quantitatively characterize the colour of jadeite, and

Minerals 2021, 11, 865. https://doi.org/10.3390/min11080865 https://www.mdpi.com/journal/minerals Minerals 2021, 11, x 2 of 15

Tang [15], Cheng [16], and Wang [17] used an X-Rite SP62 portable spectrophotome- Minerals 2021, 11, 865 ter to visually measure the colours of gems. Guo et al. [18,19] used Spectrophotometer2 of 15 Colour i5 and the GemDialogue colour chip to quantitatively characterize the colour of jadeite, and Tooms et al. [20] used colour matching functions to calculate colour. Kasajima et al. [21,22] used the CIE1931RGB colour matching functions to calculate the colours of Tooms et al. [20] used colour matching functions to calculate colour. Kasajima et al. [21,22] the leaves and flowers of the genera Torenia and Cyclamen. Sun et al. [23] used the used the CIE1931RGB colour matching functions to calculate the colours of the leaves CIEXYZ colour matching functions to calculate the colour of synthetic Cr-bearing chryso- and ﬂowers of the genera Torenia and Cyclamen. Sun et al. [23] used the CIEXYZ colour beryl. matching functions to calculate the colour of synthetic Cr-bearing chrysoberyl. The human retina has three kinds of colour photoreceptors, or cones, that are sensi- The human retina has three kinds of colour photoreceptors, or cones, that are sensitive tive to red, green, and blue light. The S cones detect the short wavelength (blue), the M to red, green, and blue light. The S cones detect the short wavelength (blue), the M cones detect the medium wavelength (green), and the L cones detect the long wavelength cones detect the medium wavelength (green), and the L cones detect the long wavelength (red). Xie et al. [24] used the responses of the L, M, and S spectra to calculate the colour of (red). Xie et al. [24] used the responses of the L, M, and S spectra to calculate the colour alexandrite. of alexandrite. When irradiated, the spectral stimulation energy is absorbed by photoreceptors of When irradiated, the spectral stimulation energy is absorbed by photoreceptors of the thethree three cones cones in in our our eyes. eyes. The The cone cone cells cells produce produce different different degreesdegrees ofof responses followed followed byby neurophysiological neurophysiological reactions. reactions. The The Intern Internationalational Commission Commission on Illumination on Illumination (CIE) (CIE) es- tablishesestablishes a series a series of colour-matching of colour-matching functions functions through through visual visual experiments. experiments. As a As proxy a proxy for functionsfor functions of the of responsivity the responsivity of the of cones, the cones, CIE colour-matching CIE colour-matching functions functions are used are usedto rep- to resentrepresent linear linear combinations combinations of the of average the average visual visual response response [25]. [ 25]. MatchingMatching functions functions can can be be used used to to calculate calculate the the energy energy of of light light that that enters enters the the human human eyeeye and and produces produces the the sensation sensation of of colour. colour. Due Due to to the the particularity particularity of of colour-changing colour-changing gar- gar- nets,nets, this this study study uses CIE1931XYZ colour-matchingcolour-matching functionsfunctions to to quantitatively quantitatively characterize character- izecolour, colour, and and investigates investigates the the colour colour of garnets of garnets between between daylight daylight and and incandescent incandescent light. light. The Theauthors authors also also analyze analyze the the relationship relationship between between the the ultraviolet–visible ultraviolet–visible (UV-Vis) (UV-Vis) spectra spectra and andthe parametersthe parameters inﬂuencing influencing the perceptionthe perception of colour. of colour.

2.2. Materials Materials and and Methods Methods 2.1.2.1. Samples Samples WeWe collected collected 10 10 samples samples of of colour-changing colour-changing garnets, garnets, four four oval oval faceted faceted gems gems (dimen- (dimen- sionssions from from 3 3 mm mm ×× 55 mm mm to to 4 4 mm mm ×× 5.75.7 mm) mm) an andd six six double-sided double-sided polished polished flats ﬂats with with a a thicknessthickness of of 3 3 mm. mm. They They appeared appeared gray-green gray-green under under daylight daylight (Figure (Figure 11a)a) and purplish red underunder incandescent incandescent light light (Figure (Figure 11b),b), showing a distinct colour-changing effect.effect.

(a)

(b)

FigureFigure 1. 1. PhotographPhotograph of of 10 10 samples samples of of colour-changing colour-changing garnets. garnets. ( (aa)) Gray-green Gray-green under standard D65 D65light. light. (b) Purplish(b) Purplish red red under under standard standard A light. A light.

2.2. Fourier Transform Infrared (FTIR) Spectroscopy The infrared spectra of the samples were measured by a Tensor 27 FTIR spectrometer (Bruker, Germany). The settings of the instrument were: resolution 4 cm−1; scanning range 400–2000 cm−1; run time 30 s per scan.

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2.3. UV-Vis Spectroscopy The UV-Vis were carried out using a UV-3600 UV-VIS spectrophotometer (Shimadzu, Tokyo, Japan). The test conditions were: wavelength range 200–900 nm; slit width 2 nm; scanning speed high; sampling interval 0.5 s; and the single scanning mode was used.

2.4. Correcting the UV-Vis Spectra Energy is used in three ways when light passes through a sample. A is the total absorbance of the sample measured directly from the spectrophotometer, and includes Ac (loss of chromophore light), Arl (loss due to reﬂection of light on the surface of the gem), and Aisl (loss due to inclusion scattering of light) [12]:

A = Ac + Arl + Aisl (1)

The absorption (Arl) of the incident light reflects along the boundary is related to the refractive index (n) of the sample. The Sellmeier equation is an empirical formula describing the refractive index and wavelength in a specific transparent medium, and is used to determine the dispersion of light in a medium. Different materials have different Sellmeier coefficients. According to research by Wemple and Di Domenico [26,27], and Wemple et al. [28], we obtained the following Sellmeier equation:

1 A = − + B (2) n2 − 1 λ2

λ2 n2 = 1 + (3) Bλ2 − A Medenbach et al. [29] measured the relevant empirical formulae for silicate minerals, and obtained the Sellmeier coefﬁcients of garnets as A = 54 × 10−16 m2 = 5400 nm2, and B = 0.4599. The relationship between the refractive index of garnet and the wavelength is as follows: λ2 n2 = 1 + (4) 0.4599λ2 − 5400 According to the Lambert–Beer law:

1 A = lg = kbc (5) T where A is absorbance, T is transmissivity, k is the molar absorbance coefﬁcient, c is the concentration of the absorbent substance, and b is the optical path of light. In the ideal state, when unpolarized light is perpendicular to the incident on the surface of the sample, it has not produced a certain length of the optical path inside the gem. In this case, optical absorption inside the gem can be ignored and the transmittance through the surface of the gem can be expressed as:

T = 1 − R (6)

Transmissivity can be converted into absorbance according to the Lambert–Beer law:

T = 10−A = 1 − R (7)

A = −lgT = −lg(1 − R) (8) n − n 2 R = 0 1 (9) n0 + n1 " 2# n0 − n1 Arl = 2A = −2lg 1 − (10) n0 + n1 Minerals 2021, 11, 865 4 of 15

where R is reflectivity, n0 =1 is the refractive index of light in air, n1 is the refractive index of light in the garnet, T is transmissivity, A is the absorbance generated by reflection at a single boundary, and Arl is the absorbance generated by reflection at two boundaries [30,31].

2.5. CIE1931 XYZ Colour Matching Functions In 1931, the CIEXYZ colour system was proposed by the International Commission on Illumination. A colour-matching function, the CIE 1931 standard colorimetric observer spectrum tristimulus value, was obtained by matching the isoenergetic spectrum. The tristimulus values X, Y, and Z can be calculated by the colour-matching functions as follows:

Z 780 X = kϕ(λ)x(λ)dλ ≈ ∑ kϕ(λ)x(λ)∆λ (11) λ 380

Z 780 Y = kϕ(λ)y(λ)dλ ≈ ∑ kϕ(λ)y(λ)∆λ (12) λ 380 Z 780 Z = kϕ(λ)z(λ)dλ ≈ ∑ kϕ(λ)z(λ)∆λ (13) λ 380 100 k = R (14) λ S(λ)y(λ)∆λ In the formula, S(λ) is the relative spectral power distribution of the light source. For non-luminous objects, ϕ(λ) is the product of the spectral transmittance T(λ) and the relative spectral power of the light source S(λ), expressed as T(λ) S(λ), or the product of its spectral reﬂectance R(λ) and the relative spectral power S(λ), expressed as R(λ)S(λ). K is the naturalization coefﬁcient. For non-luminous objects, the value of Y of the selected standard illuminant was adjusted to 100 [32,33].

2.6. CIE1976 La*b* Colour System The CIE1976 La*b* colour space is the most widely used in the ﬁeld of colourimetry. The system consists of the axes of plane chromaticity a* and b*, and the vertical axis L*. +a* represents red, −a* represents green; +b* represents yellow, and −b* represents blue. The chroma C* and hue angle h(◦) can be calculated from the chromaticities a* and b* [32,34]: q C∗ = a∗2 + b∗2 (15)

b∗ h = arctan (16) a∗ To calculate the colour difference of garnets under different sources of illumination, we chose the CIE Lab(∆E*ab) colour difference formula: q ∗ ∗ 2 ∗ 2 ∗ 2 ∆Eab = (∆L ) + (∆a ) + (∆b ) (17)

∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ◦ where ∆a = aD65 − aA, ∆b = bD65 − bA, and ∆L = LD65 − LA, and ∆h( ) is the hue angle difference under different sources of illumination:

∆h = hD65 − hA (18)

where ∆C∗ is the chroma difference under different sources of illumination:

∗ ∗ ∗ ∆C = CD65 − CA (19) Minerals 2021, 11, 865 5 of 15

2.7. Colour Space Conversion To easily observe the colour distribution, the colour tristimulus values in CIEXYZ were non-linearly converted to obtain the colour parameters L*, a* and b* in the CIE1976 L*a*b* colour space system [32,34]. The formula for conversion is as follows:

1 X 3 L∗ = 116 − 16 (20) Xn

" 1 1 # X 3 Y 3 a∗ = 500 − (21) Xn Yn

" 1 1 # Y 3 Z 3 b∗ = 200 − (22) Yn Zn

For the D65 light source, Xn = 95.04, Yn = 100, and Zn = 108.88. For light source A, Xn = 109.85, Yn = 100, and Zn = 35.58. Xn, Yn, and Zn are colorimetric data obtained from the CIE 1931 standard colorimetric observer (2◦)[35].

3. Results 3.1. Infrared Spectral Characteristics of Colour-Changing Garnet The infrared spectra of the garnets are shown in Figure2. Vibrations inside the 4− −1 [SiO4] group produced the A–G absorption bands above 500 cm . The A–D absorption zone (bands in the range 800–1100 cm−1) is due to the antisymmetric stretching vibration of the [SiO4] tetrahedron, and is caused by the splitting of the υ3 triplet degenerate inside [SiO4]. The E–G absorption zone relates to the antisymmetric bending vibration of [SiO4], −1 and shows a peak at 500–700 cm due to double-degeneracy splitting of υ2 or triple- degeneracy splitting of υ4. External vibrations, namely lattice vibrations, produce the H–K absorption band, below 500 cm−1. The H–I absorption bands within this are related to vibrations of the trivalent cation (B3+), and the J–K absorption band to vibrations of the divalent cation (A2+)[36,37]. In the lattice of the garnets, the volume of the octahedral [BO6] group is higher than that of [SiO4], and the B-O bond is weaker than the Si-O bond. This is reﬂected in the decrease in the bond force constant K in the infrared spectra, and leads to the absorption band appearing in the low-frequency region [36]. Most garnets have E bands in the 600–650 cm−1 range. The intensity of band E is related to the ratio Pyr/Alm, and it decreases with the increase of the composition content of pyrope. Band E is stronger in spessartine, but the band G is weak or even missing [36]. When irradiated by infrared light, the sample selectively absorbs wavelengths that match its vibrational frequency and produce energy-level transitions. The energy required for vibration-induced transition depends on the reduced mass of atoms at both ends of the q 1 K bond and its force constant. According to the vibration equation ν = 2Π m , when the group is ﬁxed, its vibrational frequency is proportional to the chemical bond force constant K. That is, with the increase in the radius of the cation, electronegativity decreases, as does the bond energy between the metal cation and the oxygen ion. This reduces the vibrational frequency of the chemical bond, and the band frequency shifts to the region of low frequency [38]. In the garnets considered, the radius of Mn2+ is larger than those of Fe2+ and Mg2+ (Mn2+ > Fe2+ > Mg2+). As the radius increases, the bond force constant decreases and the band frequency shifts to the red region. The infrared spectrum of the colour-changing garnet is located between spessartine and pyrope, and belongs to the solid solution of pyrope-spessartine garnets. Minerals 2021, 11, x 6 of 15

creases and the band frequency shifts to the red region. The infrared spectrum of the colour-changing garnet is located between spessartine and pyrope, and belongs to the solid Minerals 2021, 11, x 6 of 15 solution of pyrope–spessartine garnets.

creases and the band frequency shifts to the red region. The infrared spectrum of the col- Minerals 2021, 11, 865 our-changing garnet is located between spessartine and pyrope, and belongs6 ofto 15 the solid solution of pyrope–spessartine garnets.

Figure 2. FTIR spectra of the colour-changing garnet (the spectral line data of pyrope and spessartine in the figure derived from subspecies of garnets identified by EPMA).

FigureFigure3.2. UV-Vis 2.2. FTIRFTIR spectra spectraSpectral of of the Characterithe colour-changing colour-changingstics garnet of Colour-Changing garnet (the spectral (the spectral line data Garnet line ofpyrope data of and pyrope spessartine and spessar- tinein the in ﬁgure the figure derived derived from subspecies from subspecies of garnets of identiﬁed garnets identified by EPMA). by EPMA). The crystal structure of garnet (Figure 3) is composed of an isolated [SiO4] tetrahe- 3.2. UV-Vis Spectral Characteristics of Colour-Changing Garnet 3+ 3+ 3+ 3.2.dron UV-Vis bound Spectral to an Characteri [AlO6] octahedronstics of Colour-Changing in which some Garnet Al ions are replaced by Fe and Cr . SomeThe large crystal dodecahedral structure of garnet voids (Figure are3) formed is composed between of an isolated the tetrahedron [SiO 4] tetrahedron and the octahedron, The crystal structure of garnet (Figure 3) 3+is composed of an isolated3+ [SiO3+4] tetrahe- boundthe top to anof [AlOeach6] corner octahedron is occupied in which some by O Al2- ions,ions areand replaced the center by Fe containedand Cr . divalent metal dronSome bound large dodecahedral to an [AlO6] voidsoctahedron are formed in which between some the Al tetrahedron3+ ions are and replaced the octahedron, by Fe3+ and Cr3+. Sometheions. top large Each of each dodecahedral divalent corner is occupiedion voids is surrounded by are O2- formedions, and by between theeight center oxygen,the contained tetrahedron and divalent have and metaleight-fold the octahedron, ions. coordination. theEachThe top divalentoptical of each ionabsorption corner is surrounded is occupiedspectra by eight and by oxygen, Ocolour2- ions, andof and th havee thegarnet eight-fold center are contained coordination.determined divalent Theby transition metal metal ions.opticalions Each that absorption divalentoccupied spectra ion site is and surroundedA colourof the of dodecahedron the by garnet eight are oxygen, determined ([AO and8]) andhave by transition site eight-fold B of metal the coordination. octahedron ions ([BO6]). ThethatOn optical occupied site A, absorption Mn site2+ A and of the spectraFe dodecahedron2+ induce and colour optical ([AO of8 ]) absorptionth ande garnet site B ofare bands the determined octahedron in the visible by ([BO transition6]). spectrum, On metal while on site A, Mn2+ and Fe2+ induce optical absorption bands in the visible spectrum, while on ions that occupied3+ 3+ site3+ A of the dodecahedron3+ ([AO8]) and site B of the octahedron ([BO6]). sitesite B, B, Fe Fe3+, Mn, Mn3+,V3+, V, and, and Cr3+ Crareresponsible are responsible for optical for transitions optical transitions [39]. [39]. On site A, Mn2+ and Fe2+ induce optical absorption bands in the visible spectrum, while on site B, Fe3+, Mn3+, V3+, and Cr3+ are responsible for optical transitions [39].

FigureFigure 3. Crystal3. Crystal structure structure of the garnetof the (Novakgarnet and (Novak Gibbs (1971)and Gibbs [2]). (1971) [2]). Figure 3. Crystal structure of the garnet (Novak and Gibbs (1971) [2]). The UV-visible spectrum of the colour-changing garnet is shown in Figure4. Four weak absorptionThe UV-visible peaks are spectrum present in of the the blue-green colour-changing region. The garnet absorption is shown at 525 nm in Figure 4. Four The UV-visible spectrum2+ of the colour-changing garnet is shown2+ 5 in3 Figure 4. Four andweak 460 absorption nm correspond peaks to Mn are andpresent the spin-forbidden in the blue-green transitions region. of Fe The( E absorptiong- T1g and at 525 nm and weak5 3 absorption peaks are present2+ in the blue-green region. The absorption at 5252+2+5 nm3 and 5 460Eg- Enm1g). Thecorrespond absorption to at Mn 506 nm and corresponds the spin-forbidden to spin-forbidden transitions transitions of ofFe Fe (,Eg- T1g and Eg- 2+ 2+ 5 g 3 1g 5 g 460 nm correspond to Mn2+ and the spin-forbidden transitions2+ of Fe ( E - T and E - 4843E1g nm). The corresponds absorption to Mn at, and506 424nm nm corresponds corresponds to to Mn spin-forbiddenand six-fold spin-forbidden transitions of Fe2+, 484 nm 3E1g). The absorption at 506 nm corresponds to spin-forbidden transitions of Fe2+, 484 nm

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Minerals 2021, 11, 865 7 of 15 corresponds to Mn2+, and 424 nm corresponds to Mn2+ and six-fold spin-forbidden transitions of Fe3+ (6A1g-4A1g and 6A1g-4Eg). The three absorption bands of Fe3+ in the yellow-green 3+ 6 4 6 4 3+ areatransitions showed of Fe the( typicalA1g- A1g absorptionand A1g- E patterng). The three of the absorption “iron–aluminum bands of Fe window”in the in the spec- yellow-green area showed the typical absorption pattern of the “iron–aluminum window” troscopein the spectroscope [40–44]. [ 40–44].

Figure 4. 4.UV-Vis UV-Vis specturm specturm of the of colour-changing the colour-changing garnet sample garnet B3 sample (Two transmission B3 (Two windowstransmission windows appear at at 460–510 460–510 and and 650–700 650–700 nm). nm). Two strong absorption bands are centered at 410 nm and 574 nm in the blue–purple and orange–yellowTwo strong region,absorption respectively. bands The are absorption centered at at these 410 twonm positions and 574 are nm related in the blue–purple andto the orange–yellow d–d electron transition region, of respectively. V3+, and are assigned The absorption to the spin-allowed at these two transitions positions are related 3 3 3 3 3+ toT1g the(3F) d–d→ T 2gelectron(3F) and transitionT1g(3F) → T of1g(3P) V3+ [,45 and], respectively. are assigned Cr mainly to the occupies spin-allowed site B transitions in the garnet crystal. With the action of the octahedral field, the d orbital undergo energy- 3T1g(3F) → 3T2g(3F) and3T1g(3F) → 3T1g(3P) [45], respectively. Cr3+ mainly occupies site B in level splitting, and electrons in the low-energy d orbital absorb energy and transmit to the garnet crystal. With the4 action4 of the octahedral field, the d orbital undergo energy- the high-energy d orbital. The A2g → T2g transition leads to absorption in the blue 4 4 leveland purple splitting, region, and and electrons the A2g → in Tthe1g transition low-energy leads d to orbital absorption absorb in the energy orange and and transmit to the yellowhigh-energy region ofd orbital. visible light The [ 464A].2g Two → 4T transmission2g transition windows leads to appear absorption at 460–510 in the and blue and purple region,650–700 nmand that the transmit 4A2g → blue-green 4T1g transition and red leads light, respectively.to absorption When in thetransmittance orange and yellow region of thevisible two regions light [46]. is almost Two the transmission same, the colour windows of the gem appear is determined at 460–510 by the externaland 650–700 nm that light source. transmit blue-green and red light, respectively. When the transmittance of the two regions is3.3. almost Correcting the the same, Absorbance the colour of UV-Vis of Spectrathe gem is determined by the external light source. Accurate visible spectroscopic measurements rely on correctly identifying the spectral 3.3.baseline. Correcting A relatively the Absorbance clean place in of the UV-Vis interior Spectra was selected for the UV-Vis spectrum test to eliminate loss due to the scattering of light caused by inclusion. Sample B3 is used as an example.Accurate The spectrumvisible spectroscopic after baseline correction measurements by the Sellmeier rely on equation correctly is shown identifying in the spec- tralFigure baseline.5. The green A relatively line represents clean the place original in spectrum,the interior the was yellow selected line the absorptionfor the UV-Vis spectrum testspectrum to eliminate after baseline loss correction, due to the and scattering the gray line, of which light is caused approximately by inclusion. a straight line,Sample B3 is used asrepresents an example. absorption The caused spectrum by boundary after baseline reﬂection. correction by the Sellmeier equation is shown in Figure 5. The green line represents the original spectrum, the yellow line the absorption spectrum after baseline correction, and the gray line, which is approximately a straight line, represents absorption caused by boundary reflection.

MineralsMinerals 20212021, 11, 11, x, 865 8 of 15 8 of 15

FigureFigure 5. CorrectedCorrected UV-Vis spectraspectra of of the the colour-changing colour-changing garnet garnet sample sample B3, B3, and and relationship relationship betweenbetween refractiverefractive index index and and wavelength. wavelength. 3.4. Colour Calculation by CIE1931 XYZ Colour Matching Functions 3.4. Colour Calculation by CIE1931 XYZ Colour Matching Functions The “alexandrite effect” originally referred to an observed change in colour in the varietyThe of “alexandrite the mineral chrysoberyl effect” originally (from green referred under to daylight an observed to reddish-purple change in undercolour in the varietyincandescent of the light) mineral [47]. chrysoberyl Typically, the (from light sourcesgreen under are represented daylight into colourimetryreddish-purple by under incandescentstandardized illuminants.light) [47]. Typically, The CIE Illuminant the lightD65 sources represents are represented average daylight in colourimetry with a by standardizedcorrelated colour illuminants. temperature The of approximately CIE Illuminant 6504 D65 K, and represents the CIE Illuminant average daylight A represents with a cor- relatedincandescent colour light temperature with a correlated of approximately colour temperature 6504 K, ofand approximately the CIE Illuminant 2856 K. TheirA represents spectral power distributions are shown in Figure6a,b. incandescent light with a correlated colour temperature of approximately 2856 K. Their The colour of transparent gems can be calculated according to the spectra of the light spectralsource and power the transmissiondistributions spectra are shown of the in gems. Figure The 6a,b. integral of the curve of spectral responseThe colour corresponds of transparent to the signal gems emitted can be by calculated cones of the according human eye. to the The spectra spectra of of the light sourceresponses and of the the transmission cones, the illuminants, spectra andof the the gems transmittance. The integral of the of stones the arecurve combined of spectral re- sponseto determine corresponds the perception. to the signal Figure 6emitted shows spectralby cones responses of the human of the CIEXYZeye. The colour- spectra of re- sponsesmatching of functions. the cones, In the Figure illuminants,6c,d, the products and the of transmittance the illuminant spectraof the stones and the are spectra combined to determineof the colour the matching perception. functions Figure are 6 plotted.shows spec The integralstral responses of these of curves the CIEXYZ correspond colour-match- to ingsignals functions. sent by theIn Figure cones, and6c,d, their thevalues products are markedof the illuminant (D65: X = 95.04, spectra Y = and 100, Zthe = 108.87;spectra of the A: X = 109.85, Y = 100, Z = 35.58). These are approximately the colours of white objects colour matching functions are plotted. The integrals of these curves correspond to signals perceived under the two light sources. The spectral response curve obtained in Figure6c,d sentis multiplied by the cones, by the and transmission their values spectra are (T( markedλ)) of garnet (D65: to X obtain= 95.04, the Y colour = 100, of Z the = 108.87; gems A: X = 109.85,under the Y = D65 100, and Z = A 35.58). light sources These by are integrating approximately the response the colours curve (Figure of white6e,f) objects (data on perceived underthe CIEXYZ the two colour-matching light sources. functions The spectral were obtainedresponse from curve the obtained ofﬁcial CIE in websiteFigure [6c,d48]). is multi- pliedIn by light the of transmission the UV-Vis spectrum spectra of(T( theλ)) colour-changing of garnet to obtain garnet, the it iscolour clear thatof the the gems gem under theabsorbs D65 theand blue-violet A light sources light and by orange-yellow integrating the light, response and allows curve equal (Figure transmittance 6e,f) (data of on the CIEXYZred and green colour-matching light. The colour functions of the gem were is thusobtain determineded from the by theofficial external CIE light website source. [48]). DaylightIn light has aof higher the UV-Vis spectral spectrum energy distribution of the colour-changing in the blue-green garnet, region. it Whenis clear light that is the gem incident on the gem, Figure6e shows that the spectral curve has the strongest response absorbs the blue-violet light and orange-yellow light, and allows equal transmittance of in the blue-green region. The sample appears green under daylight (X = 34.58, Y = 36.69, redZ = and 32.19). green light. The colour of the gem is thus determined by the external light source. Daylight has a higher spectral energy distribution in the blue-green region. When light is incident on the gem, Figure 6e shows that the spectral curve has the strongest response in the blue-green region. The sample appears green under daylight (X = 34.58, Y = 36.69, Z = 32.19).

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FigureFigure 6. Analysis 6. Analysis and explanation and explanation of the alexandrite of the alexandrite effect (with effect sample (with B3 as samp an example).le B3 as Thean example). spectral response The curvesspectral of the CIE1931response XYZ curves colour of matching the CIE1931 functions XYZ are colour shown. matching (a) The spectral functions power are distribution shown. (a of) The the CIE spec- D65 representingtral power daylight distribution (colour temperature, of the CIE 6504D65 K).repres (b) Theenting spectral daylight power (colou distributionr temperature, of the incandescent 6504 K). light (b) The CIE A (colourspectral temperature, power distribution 2856 K). (c) Responseof the incandesce curves ofnt spectra light of CIE D65 A obtained (colour fromtemperature, the colour-matching 2856 K). functions.(c) Re- (d) Responsesponse curves curves of spectraspectra of of A D65 obtained obtained from thefrom colour-matching the colour-matching functions. functions. (e) Response (d curves) Response of the curves colour matchingof spectra functions of A of obtained the colour-changing from the garnet colour-matching under D65. (f) Responsefunctions. curves (e) Response of the colour curves matching of the functions colour of the colour-changingmatching functions garnet under of A.the The colour-changing tristimulus values garnet and the simulatedunder D65. colour (f) obtainedResponse by thecurves integration of the of colour the curve are shownmatching in the functions ﬁgure. of the colour-changing garnet under A. The tristimulus values and the simulated colour obtained byIncandescent the integration light of has the a curve higher are spectral shown energy in the distribution figure. in the red zone, causing the sample to transmit more components of red that obscured the green light. Figure6f Incandescentshows light thathas thea higher spectral spectral curve has en theergy strongest distribution response in in the the red red zone, zone; redcausing light was dominant, and is superimposed with a small amount of the transmitted purple light. The the sample to transmitgarnet thusmore appears components purplish-red of red (X = that 44.72, obscured Y = 37.24, Zthe = 11.50). green light. Figure 6f shows that the spectralThe curve values has of the the colour strongest tristimulus response XYZ were in non-linearly the red zone; converted red intolight the was param- dominant, and is superimposedeters of colour in thewith CIE1976 a small L*a*b* amount colour of space, the andtransmitted the chroma purple value C* light. and hue The angle garnet thus appears purplish-red (X = 44.72, Y = 37.24, Z = 11.50). The values of the colour tristimulus XYZ were non-linearly converted into the parameters of colour in the CIE1976 L*a*b* colour space, and the chroma value C* and hue angle h(°) of the colour under the D65 and A light sources were calculated. The results are shown in Table 1. Under D65 light, the average colour lightness (𝐿∗) is 63.07, the chroma average (𝐶∗) is 12.37, and the average hue angle (ℎ) is 97.92°, representing green. Under light source A, the average colour lightness (𝐿∗) is 63.53, the chroma average (𝐶∗) is 13.72, and the average hue angle (ℎ) is 42.56°, representing red. In the CIE1976 L*a*b* colour space, the difference in hue angle is often used to quantitatively evaluate the intensity of colour-changing effect. When the difference in the hue

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h(◦) of the colour under the D65 and A light sources were calculated. The results are shown in Table1. Under D65 light, the average colour lightness L∗ is 63.07, the chroma average C∗ is 12.37, and the average hue angle h is 97.92◦, representing green. Under light source A, the average colour lightness L∗ is 63.53, the chroma average C∗ is 13.72, and the average hue angle h is 42.56◦, representing red. Minerals 2021, 11, x 10 of 15

Table 1. Colour parameters, hue angle, chroma and colour difference between the light sources in CIE 1976 La*b* colour space (the original data is presented in the supplementary materials). angle is greater than 20°, prominent changes in colour can be observed [14]. The 10 sam- D65 A ples selected in this study exhibit significant change in colour with ◦hue angle difference Sample ◦ ◦ ∆h( ) ∆C* ∆E*ab greater than L*20°. Figure C* 7 shows h( ) the simula L*ted C* colour h( block) calculated by the colour matchingB1 functions. 62.04 11.79It had a high 104.64 degree 62.34 of reduction 10.84 to 50.71the real colour 53.93 of− the0.94 sample. 10.30 B2 68.01 16.69 105.18 68.44 14.22 72.22 32.97 −2.48 9.10 Table 1. Colour parameters, hue angle,B3 chroma 67.04 and colour 10.00 differenc 95.70e between 67.46 the light 12.73 sources 31.43 in CIE 64.271976 La*b* 2.73 colour space. 12.31 B4 57.94 10.80 107.80 58.16 9.62 48.67 59.13 −1.18 10.13 D65B5 42.70 9.84 85.22A 43.30 14.14 31.26 53.96 4.30 11.60 Sample Δh(°) ΔC* ΔE*ab L* C* B6 62.11 h(°) 14.15L* 90.54C* 62.83h(°) 17.92 36.92 53.62 3.77 14.87 B7 68.87 12.46 96.37 69.38 14.54 38.06 58.31 2.08 13.29 B1 62.04 11.79B8 104.64 65.70 14.0762.34 97.0810.84 66.26 50.71 15.08 45.18 53.93 51.90−0.94 1.0110.30 12.80 B2 68.01 16.69B9 105.18 68.95 12.1968.44 97.7514.22 69.42 72.22 14.41 35.85 32.97 61.89−2.48 2.229.10 13.82 B3 67.04 10.00B10 95.70 67.29 11.7067.46 98.9112.73 67.71 31.43 13.71 35.3464.27 63.57 2.73 2.02 12.31 13.50 B4 57.94 10.80 107.80 58.16 9.62 48.67 59.13 −1.18 10.13 B5 42.70 9.84 In the85.22 CIE1976 L*a*b*43.30 colour14.14 space, the31.26 difference 53.96 in hue angle4.30 is often11.60 used to B6 62.11 14.15quantitatively 90.54 evaluate 62.83 the intensity17.92 of colour-changing36.92 53.62 effect. When 3.77 the difference 14.87 in B7 68.87 12.46the hue angle96.37 is greater69.38 than 20◦, prominent14.54 changes38.06 in colour58.31 can be 2.08 observed [ 13.2914]. The B8 65.70 14.0710 samples 97.08 selected in66.26 this study15 exhibit.08 signiﬁcant45.18 change51.90 in colour 1.01with hue 12.80 angle ◦ B9 68.95 12.19difference greater97.75 than69.42 20 . Figure147 .41shows the35.85 simulated 61.89 colour block 2.22 calculated 13.82 by the B10 67.29 11.70colour matching98.91 functions.67.71 It had a13 high.71 degree35.34 of reduction 63.57 to the real colour 2.02 of the 13.50 sample.

Figure 7. Fashioned gems and the corresponding simulated colours calculated by using the colour matching functions. Figure 7. Fashioned gems and the corresponding simulated colours calculated by using the colour matching functions.

4.4. Discussion Discussion 4.1.4.1. Effect Effect of of Standard Standard Light Light Source Source on on Appearance Appearance of of Colour-Changing Colour-Changing Garnet Garnet AnAn one-way one-way analysis analysis of of variance variance (ANOVA) (ANOVA) of the parameters influencing influencing colour is conductedconducted under under the the D65 D65 and and A A light light sources, sources, and and the the results results are are shown shown in in Table Table 22.. TheThe differentdifferent standard standard light light sources sources have have no no significant significant effect effect on the lightness L* and chroma C*C* of of the the colour-changing colour-changing garnet garnet ( (pp >> 0.05), 0.05), but but have have a a significant significant effect effect on on the the colorimetric colorimetric coordinatescoordinates a* a* and and b* b* as as well well as as the the hue hue angle angle h(°) h(◦)( (pp << 0.05). 0.05).

Table 2. ANOVA results for the colour parameters.

Colour Parameters df Mean Square F p L* 1 1.070 0.017 0.898 a* 1 688.632 116.762 0.000 b* 1 50.444 11.696 0.003 C* 1 9.146 1.888 0.186 h(°) 1 15,320.707 152.244 0.000

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Table 2. ANOVA results for the colour parameters.

Colour Parameters df Mean Square F p

Minerals 2021, 11, x L* 1 1.070 0.01711 of 0.898 15 a* 1 688.632 116.762 0.000 b* 1 50.444 11.696 0.003 C* 1 9.146 1.888 0.186 h(◦) 1 15,320.707 152.244 0.000 Figure 8 shows a comparison of the colour parameters under the D65 and A light sources. The results showFigure that8 showsthe lightness a comparison of the of garnet the colour under parameters A is slightly under the higher D65 and than A light that under D65, andsources. most of The the results samples show exhi thatbit the higher lightness chroma of the garnet values under under A is A. slightly When higher the than light source is changedthat underfrom D65,D65 andto A, most the of colorimetric the samples exhibitcoordinate higher a* chroma changes values from under nega- A. When tive to positive, thatthe is, light from source green is changed to red; fromthe colorimetric D65 to A, the colorimetriccoordinate coordinate b* decreases, a* changes and from negative to positive, that is, from green to red; the colorimetric coordinate b* decreases, the concentration ofand yellow the concentration decreases. of yellowSample decreases.s with higher Samples colorimetric with higher colorimetric coordinates coordinates a* a* and b* in the light sourceand b* inD65 the are light also source higher D65 are under also higher light undersource light A. source A.

(a) (b)

FigureFigure 8. Comparison8. Comparison of colour of colour parameters parameters under two under kinds two of standard kinds lightof standard sources. (lighta) Comparison sources. of(a) lightness Com- L*, chromaparison C*, of and lightness hue angle L*, h(◦ );chroma (b) Comparison C*, and of hue colorimetric angle h(°); coordinates (b) Comparison a* and b*. of colorimetric coordinates a* and b*. 4.2. Effect of UV-Vis Absorbance Peak Area on Colorimetric Coordinate a* and Hue Angle h(◦) 4.2. Effect of UV-Vis AbsorbanceThe strong Peak absorption Area on bandColorimetric at 574 nm Coordinate in the UV-Vis a* spectrumand Hue playsAngle a decisiveh(°) role in determining the colour of a colour-changing garnet [39]. The ﬁrst derivative of the The strong absorptionUV-Vis spectrum band at is calculated,574 nm in and the points UV-Vis with spectrum a zero derivative plays near a decisive 510 nm and role 680 nm in determining the colourare selected of a ascolour-changing starting and ending garnet points, [39]. respectively, The first for derivative calculating of the the peak UV- area of Vis spectrum is calculated,absorption and at 574points nm (Figure with 9a). zero derivative near 510 nm and 680 nm are selected as starting andThe ending results points, show that respectively, the colorimetric for coordinate calculating a* is the positively peak correlatedarea of ab- with the area of the peak at 574 nm (D65: R2 = 0.909; A: R2 = 0.821, Figure 10a). With the increase in sorption at 574 nm (Figurethe area, 9). the colorimetric coordinate a* gradually increases, that is, the concentration of The results showgreen that decreases the colorimetric under the D65 coordi lightnate source, a* and is positively the concentration correlated of red increaseswith the under area of the peak at 574the Anm light (D65: source. R2 = 0.909; A: R2 = 0.821, Figure 10a). With the increase in the area, the colorimetric coordinate a* gradually increases, that is, the concentration of green decreases under the D65 light source, and the concentration of red increases under the A light source. A negative correlation is noted between the hue angle h(°) and the peak area at 574 nm (D65: R2 = 0.771; A: R2 = 0.774, Figure 10b). With the increase in the peak area, the hue angle h(°) decreases gradually. Under the D65 light source, h(°) changes from 107.80° to 85.22°, and the colour of the garnet changes from green to yellow-green. Under light source A, h(°) changes from 72.22° to 31.26°, and the colour of the garnet changes from orange-red to red and purplish-red.

Minerals 2021, 11, 865 12 of 15 Minerals 2021, 11, x 12 of 15 Minerals 2021, 11, x 12 of 15

Figure 9. 9. TheThe area area of of the the absorption absorption peak peak at 574 at 574 nm nm affects affects the thecolour-changing colour-changing garnet. garnet. Taking Taking Figure 9. The area of the absorption peak at 574 nm affects the colour-changing garnet. Taking sample B3 as an example, the gray line is the first derivative curve of its UV-Vis spectrum, and the samplesample B3 B3 as as an an example, example, the the gray gray line line is is the the first ﬁrst derivative derivative curv curvee of of its its UV-Vis UV-Vis spectrum, spectrum, and and the the point where the first derivative is equal to zero is selected as the starting and ending points of the pointpoint where where the the first ﬁrst derivative derivative is is equal equal to to zero zero is isselected selected as as the the starting starting and and ending ending points points of ofthe the range at 574 nm absorption peak. rangerange at at 574 574 nm nm absorption absorption peak. peak.

(a) (b) (a) (b) Figure 10. The colorimetric coordinate a* and the hue angle h(°) are related to the peak area of Figure 10. The colorimetric coordinate a* and the hue angle h(°) are◦ related to the peak area of absorptionFigure 10. atThe 574 colorimetric nm. Under the coordinate D65 and a* A andlight the sour hueces, angle a* is positively h( ) are related correlated to the with peak the area area of absorption at 574 nm. Under the D65 and A light sources, a* is positively correlated with the area ofabsorption the absorption at 574 peak nm. Under(a) whereas the D65 h is and negatively A light sources, correlated a* iswith positively it at 574 correlated nm (b). with the area of ofthe the absorption absorption peak peak (a ()a whereas) whereas h h is is negatively negatively correlated correlated with with it atit at 574 574 nm nm (b ().b).

4.3. Effect of UV-Vis Absorbance Peak Area on Chroma Difference◦ ΔC* and Colour Difference 4.3. ∗EffectA negative of UV-Vis correlation Absorbance is noted Peak Area between on Chroma the hue Difference angle h( Δ) andC* and the Colour peak area Difference at 574 nm 𝛥𝐸∗ 𝛥𝐸(D65: R2 = 0.771; A: R2 = 0.774, Figure 10b). With the increase in the peak area, the hue The calculated colour of the garnet is plotted in the CIE1976 La*b* colour space (Fig- angleThe h( ◦calculated) decreases colour gradually. of the Undergarnet theis plotted D65 light in the source, CIE1976 h(◦) La*b* changes colour from space 107.80 (Fig-◦ to ure 11). In three-dimensional space, the line connecting the points under the two light ure85.22 11).◦, andIn three-dimensional the colour of the garnet space, changes the line from connecting green to yellow-green.the points under Under the light two source light sources signifies the Euclidean distance, which represents the colour difference (Δ𝐸∗ ) be- sourcesA, h(◦) changessignifies fromthe Euclidean 72.22◦ to 31.26distance,◦, and wh theich colour represents of the the garnet colour changes difference from orange-red(Δ𝐸∗) between the light sources. The colour of the garnets changes from green under D65 light tweento red the and light purplish-red. sources. The colour of the garnets changes from green under D65 light source to orange-red and purple-red under A light source, with a change in the hue angle source to orange-red and purple-red under A light source, with a change in the hue angle greater than 20°. When changing the light source from D65 to A, difference in the hue greater than 20°. When changing the light source from D65 to A, difference in the hue

Minerals 2021, 11, 865 13 of 15

4.3. Effect of UV-Vis Absorbance Peak Area on Chroma Difference ∆C* and Colour Minerals 2021, 11, x ∗ 13 of 15 Difference ∆Eab The calculated colour of the garnet is plotted in the CIE1976 La*b* colour space (Figure 11). In three-dimensional space, the line connecting the points under the two light ∗ anglesources Δh(°) signiﬁes varies from the Euclidean 32.97° to 64 distance,.27°, the whichdifference represents in chroma the Δ colourC* varies difference from −2.48 (∆E toab ) ∗ 4.30,between and the the colour light sources.difference The Δ𝐸 colour varies of the from garnets 9.10 to changes 14.87. When from greenthe colour under difference D65 light ∗ Minerals 2021, 11, x valuesource Δ𝐸 to orange-red is greater than andpurple-red 6, the difference under between A light source, colour withis unacceptable a change13 of 15 in in the visual hue angleper- ception,greater and than obvious 20◦. When color changing change the can light be observed source from visually D65 to [32]. A, difference in the hue angle ∆h(◦) varies from 32.97◦ to 64.27◦, the difference in chroma ∆C* varies from −2.48 to 4.30, angle Δh(°) varies from 32.97° to 64.27°,∗ the difference in chroma ΔC* varies from −2.48 to and the colour difference ∆E∗ ab varies from 9.10 to 14.87. When the colour difference value 4.30,∗ and the colour difference Δ𝐸 varies from 9.10 to 14.87. When the colour difference ∆E is greater∗ than 6, the difference between colour is unacceptable in visual perception, valueab Δ𝐸 is greater than 6, the difference between colour is unacceptable in visual per- andception, obvious and obvious color color change change can can be be observedobserved visually visually [32]. [ 32].

Figure 11. The differences in chroma and colour under the D65 and A light sources in CIE1976 Figure 11. 11. TheThe differences differences in chroma in chroma and colour and under colour the D65 under and theA light D65 sources and Ain lightCIE1976 sources in CIE1976 L*a*b* L*a*b*L*a*b* colour space. space. colour space. ToTo exploreexplore factors factors affecting affecting colour colourwhen the when light source the light is changed, source the is relationship changed, the relationship betweenTo the explore area of factorspeak absorption affecting UV-Vis colour and whencolour parameters the light sourceis analyzed. is changed, The dif- the relationship between the area of peak absorption UV-Vis and colour parameters is analyzed. The dif- betweenferences in the chroma area ofand peak colour absorption of the garnet UV-Visbetween the and light colour sources parameters are positively is analyzed. The ferences in the chroma and colour of the2 garnet between the light sources are positively differencescorrelated with in the the absorption chroma peak and at 574 colour nm (R of is the0.885 garnet and 0.911, between respectively; the Figure light sources are posi- correlated12), exhibiting with good the fitting. absorption The results peak show at that574 withnm the(R2 increaseis 0.885 in and the area0.911, of peakrespectively; Figure tively correlated with the absorption peak at 574 nm (R2 is 0.885 and 0.911, respectively; 12),absorption exhibiting at 574 good nm, the fitting. differences The in results chroma showand colour that under with D65 the and increase A are large. in the area of peak FigureThis leads 12 to), a exhibiting noticeable change good in ﬁtting. colour. The results show that with the increase in the area of absorptionpeak absorption at 574 atnm, 574 the nm, differences the differences in chroma in chroma and andcolour colour under under D65 D65 and and A Aare are large. large. ThisThis leads leads to to a anoticeable noticeable change change in in colour. colour.

(a) (b)

Figure 12. Chroma difference ΔC* (a) and colour difference ΔE*ab (b) are positively correlated with the area of the absorption peak at 574 nm.

5. Conclusions The infrared spectra( ashow) that the colour-changing garnets described in this(b) paper belong to the solid solution of pyrope–spessartine garnets type. There are two zones of Figure 12. Chroma difference ΔC* (a) and colour difference ΔE*ab (b) are positively correlated with Figuretransmittance 12. Chroma in the red difference region, 650–700∆C* (a )nm, and and colour the blue-green difference region,∆E*ab 460–510(b) are positivelynm, of correlated with thethe area UV-Vis area of of the spectra the absorption absorption of a colour-changing peak peak at at 574 574 nm.garnet nm. . They allow the same amount of light to

5. Conclusions The infrared spectra show that the colour-changing garnets described in this paper belong to the solid solution of pyrope–spessartine garnets type. There are two zones of transmittance in the red region, 650–700 nm, and the blue-green region, 460–510 nm, of the UV-Vis spectra of a colour-changing garnet. They allow the same amount of light to

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5. Conclusions The infrared spectra show that the colour-changing garnets described in this paper belong to the solid solution of pyrope-spessartine garnets type. There are two zones of transmittance in the red region, 650–700 nm, and the blue-green region, 460–510 nm, of the UV-Vis spectra of a colour-changing garnet. They allow the same amount of light to pass through, because of which the colour of the gem is determined by the external light source. Daylight (D65) has a higher spectral energy distribution in the blue-green zone than incandescent light, which causes the garnet to appear green (L∗ = 63.07, C∗ = 12.37, h = 97.92◦). Incandescent light (A) has higher spectral energy distribution in the red zone, which causes the colour-changing garnet to appear purple-red (L∗ = 63.53, C∗ = 13.72, h = 42.56◦). The absorption bands of Cr3+ and V3+ at 574 nm in the UV-Vis spectrum are the main cause of the change in colour. With the increase in the area of peak absorption, the colour of the garnet changes from green to yellow green under daylight (D65), and from orange red to purple-red under incandescent light (A). The colour difference and chroma difference also increases with the peak area, rendering prominent changes in the colour of the garnet more likely.

Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/min11080865/s1, Table S1: colour parameters, hue angle, chroma and colour difference between the light sources in CIE 1976 La*b* colour space. Author Contributions: Conceptualization, Y.Q. and Y.G.; Methodology, Y.Q. and Y.G.; Validation, Y.Q. and Y.G.; Formal analysis, Y.Q.; Investigation, Y.Q. and Y.G.; Resources, Y.Q. and Y.G.; Data Curation, Y.Q.; Writing—original draft preparation, Y.Q.; Writing—review and editing, Y.G.; Visual- ization, Y.Q.; Supervision, Y.G.; Project administration, Y.G. Both authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Data Availability Statement: Not applicable. Acknowledgments: Thanks to the School of Gemmology, China University of Geoscience, Beijing. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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