ORIGINAL PAPER

Emilie Gaudry Æ Philippe Sainctavit Æ Farid Juillot

Federica Bondioli Æ Philippe Ohresser Æ Isabelle Letard

From the green color of eskolaite to the red color of ruby: an X-rayabsorption spectroscopy study

Received: 27 January 2005 / Accepted: 16 October 2005 / Published online: 10 December 2005� Springer-Verlag 2005

Abstract The best known cause for colors in insulatingminerals is due to transition metal ions as impurities. Asan example, Cr3+ is responsible for the red color of ruby(a-Al2O3:Cr

3+) and the green color of eskolaite (a-Cr2O3). Using X-ray absorption measurements, weconnect the colors of the CrxAl2�xO3 series with thestructural and electronic local environment around Cr.UV–VIS electronic parameters, such as the crystal fieldand the Racah parameter B, are related to those deducedfrom the analysis of the isotropic and XMCD spectra atthe Cr L2,3-edges in Cr0.07Al1.93O3 and eskolaite. TheCr–O bond lengths are extracted by EXAFS at the CrK-edge in the whole CrxAl2�xO3 (0.07 £ x< 2) solidsolution series. The variation of the mean Cr–O distancebetween Cr0.07Al1.93O3 and a-Cr2O3 is evaluated to be0.015 A (�1%). The variation of the crystal field in theCrxAl2�xO3 series is discussed in relation with the vari-ation of the averaged Cr–O distances.

Keywords XAFS Æ Ruby Æ Color of minerals

Introduction

The color of minerals is due to the interaction of lightwith matter. When light goes through ruby (a-Al2O3:Cr

3+), the whole yellow-green and violet radia-tions are absorbed, while red and few blue radiations are

transmitted. Therefore, ruby is red with a slight purpleovertone. On the contrary, red light is absorbed in esk-olaite (a-Cr2O3), so that this mineral looks green. Al-though it is now well known that color in ruby andeskolaite is due to the chromium ions (Nassau 1983;Burns 1993), a question remains unexplained. Why doesthe same chromium chromophore ion, with the samevalence state and the same kind of distorted octahedralsite, yield a red color in ruby and a green one in esk-olaite?

In such oxide minerals, color is generally interpretedwithin the ligand field theory. This model is based on anelectrostatic interaction between the central cation andthe ligands of its coordination sphere. It is based mainlyon the geometry and the symmetry around the centralcation. This theory has been applied successfully topredict the number of 3d–3d transitions in opticalabsorption spectra and to identify the correspondingabsorption bands (Lever 1984). Moreover, this theoryenables an empirical calculation of the transition ener-gies (Liehr 1963). The UV–VIS absorption spectra ofCr3+-containing materials present two main absorptionbands, which are already well explained by the ligandfield theory applied to the system Al2O3:Cr

3+ (Poole1964; Poole and Itzel 1963; McClure 1962, 1963; Reinen1969; Sugano and Peter 1961; Liehr 1963; MacFarlane1963; Graham 1960). The spectroscopic term of thefundamental state for the free Cr3+ coloring ion inspherical symmetry is 4F. In the octahedral symmetry,4F is split into three states of increasing energies that are4A2g,

4T2g and4T1g. The symmetry of the ground state is

4A2g. The absorption band at lower energy, labeled e1,arises from 4A2g toward 4T2g transitions. The broadband at higher energy, labeled e2, arises from 4A2g to-ward 4T1g transitions. The crystal field parameter D andthe Racah parameter B are extracted from the values ofe1 and e2 within the framework of the crystal field model.The D parameter is given by the energy e1. TheB parameter is given by B ¼ ½ð�2 � �1Þ=3�½ð2�1��2Þ=ð9�1 � 5�2Þ� (Marfunin 1979; Reinen 1969). Theoptical data given by Reinen (1969) lead to D=2.24 eV

E. Gaudry Æ P. Sainctavit (&) Æ F. Juillot Æ I. LetardLaboratoire de Minenalogie-Cristallographie,Universite Pierre et Marie Curie, UMR 7590,4 place Jussieu, 75252 Paris Cedex 05, FranceE-mail: philippe.sainctavit@lmcp.jussieu.fr

P. Sainctavit Æ P. OhresserLURE, Bat 209D Centre Universitaire,B.P. 34, 91898 Orsay Cedex, France

F. BondioliDipartimento di Ingegneria dei Materiali e dell’Ambiente,Universita di Modena e Reggio Emilia,Via Vignolese 905, 41100 Modena, Italy

Phys Chem Minerals (2006) 32: 710–720DOI 10.1007/s00269-005-0046-x

(18,070 cm�1) for ruby and D=2.07 eV (16,700 cm�1)for a-Cr2O3, while the Racah parameter B isB=0.080 eV (645 cm�1) for ruby and B=0.058 eV(468 cm�1) for a-Cr2O3. The ratio D=B increases whenthe concentration x of chromium in CrxAl2�xO3 in-creases.

Despite the success of the ligand field theory, somepoints remained misunderstood. Liehr (1963) tried tosort the minerals by increasing values of the crystal fieldD and the Racah parameter B given by optical spec-troscopy. He wanted to make an analogy with thespectroscopic and the nephelauxetic series in solutionsbut found irregular changes for the crystal field D andfor the Racah parameter B in his crystalline series. Thevariations of these parameters were also studied as afunction of the temperature T, the pressure P and theamount x of chromium in CrxAl2�xO3 (Poole 1964;Poole and Itzel 1963). Starting from the idea that thecrystal field D and the Racah parameter B depend onlyon the Cr–O distance, three different laws for theirvariations were found, depending on which parameter,T, P or x, was at the origin of the variation of the Cr–Odistance. These results tend to prove that the value of thecrystal field as measured by the 4A2g fi 4T2g transitionenergy is not simply a function of the Cr–O distance.McClure (1962) studied the optical absorption spectra ofruby (Al2O3:Cr

3+) in detail. To interpret some features,he needed to consider complex models. He calculated thepotential for a chromium impurity displaced by 0.1 Atoward or away from the nearest cation in the structureand proposed a tetragonal distortion of the excited state.These high-quality and detailed studies of Al2O3–Cr2O3

solid solution series were made within the virtual crystalapproximation, in which the chromium atom is sup-posed to substitute exactly for the aluminum atom in thestructure, so that the Cr–O distances in ruby are thesame as the Al–O distances in a-Al2O3. This leads tomistakes and to misunderstandings. Actually, whenchromium substitutes for aluminum, the chromium siteis expected to be different from the aluminum site in a-Al2O3, due to the larger ionic radius of chromium(rCr3+=0.615 A) compared to that of aluminum

(rAl3+=0.535 A) in an octahedral site (Shannon 1976). As

a consequence, the understanding of the local environ-ment around the chromium atom is absolutely needed toexplain the evolution of physical properties with respectto the chromium content x in CrxAl2�xO3.

Subsequently, many studies have been undertaken todetermine the chromium site in ruby (a-Al2O3:Cr

3+).Single crystal X-ray diffraction (McCauley and Gibbs1972; Moss and Newnham 1964), UV–VIS spectroscopy(McClure 1962; Langer 2001; Andrut et al. 2004) andEPR spectroscopy (Buscher et al. 1987) have shown theexistence of relaxations around the chromium atom in a-Al2O3. Extended X-ray absorption fine structure (EX-AFS) has been performed at the Cr K-edge on powders(Kizler et al. 1996) or single crystals (Emura et al. 1993)of ruby. In a previous piece of work, we determined Cr–O bond lengths in the coordination shell by linear di-

chroic EXAFS at the chromium K-edge in a-Al2O3:Cr

3+ (Gaudry et al. 2003). However, to ourknowledge, no EXAFS experiment has been undertakenon the whole Al2O3–Cr2O3 solid solution.

In a first step, we evaluate the influence of the crystalfield D and the Racah parameter B on the colors of thegreen eskolaite and the red ruby. These two parametersare usually deduced from the positions of large featuresin the UV–VIS spectra, using a semi-quantitative theory.Our approach is to analyze the isotropic X-ray absorp-tion spectra and the X-ray magnetic circular dichroic(XMCD) spectra at the Cr L2,3-edges with the quanti-tative ligand field multiplet (LFM) theory followingTheo Thole’s developments (Cowan 1981; Butler 1981;Thole et al. 1985), in order to address the values of Dand B from a different point of view. In addition, thisanalysis gives access to the nature of the Cr–O bondingin a-Cr2O3 and Cr0.07Al1.93O3. To our knowledge, no X-ray absorption spectroscopy (XAS) at the Cr L2,3-edgesin CrxAl2�xO4 has yet been made. The structural envi-ronment around chromium in the whole solid solutionAl2O3–Cr2O3 is also specified by XAS at the chromiumK-edge. We especially focused on the determination ofthe mean Cr–O distances for several values of x inCrxAl2�xO3, in order to make a link between the colorchange and the local environment around chromium inthe Al2O3–Cr2O3 series. Given that the same technique isused for the whole solid solution series, the results fordifferent chromium concentrations are directly compa-rable.

Materials and methods

Synthesis of the samples

Corundum, a-Al2O3, and eskolaite, a-Cr2O3, belong tothe R�32=c space group (Wyckoff 1964). They are astacking of distorted octahedra made of six oxygenatoms, at the center of which lies an aluminum atom (ina-Al2O3) or a chromium atom (in a-Cr2O3). The sixoxygen atoms are gathered into two groups of threeatoms to comply with the C3 local symmetry. These twogroups lie at two different distances from the centralatom. The nearest three oxygen atoms, labeled O1, arebetween edge-shared octahedra and lie at 1.96 A in a-Cr2O3 and 1.86 A in a-Al2O3. The farther three oxygenatoms, labeled O2, are between face-shared octahedraand lie at 2.01 A in a-Cr2O3 and 1.97 A in a-Al2O3. Thecloser Cr–Cr pairs in a-Cr2O3 lie at 2.65 A (one pair)and 2.88 A (three pairs), while the closer Al–Al pairs ina-Al2O3 lie at 2.65 A (one pair) and 2.79 A (three pairs)(Pearson 1962; Finger and Hazen 1980).

The Al2�xCrxO3 powders were prepared by co-pre-cipitation and subsequent calcination (Bondioli et al.2000). The amorphous gels of Al3+ and Cr3+ hydrox-ides were co-precipitated with ammonia (NH4OH, RPE,Carlo Erba, Milan, Italy) from aluminum nitrate[Al(NO3)3, RPE, Carlo Erba] and chromium nitrate

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[Cr(NO3)3, RPE, Carlo Erba] solutions at pH 9. Theamorphous co-precipitated hydroxides, carefully washedwith distilled water, were dried in a conventional furnaceat 120�C and then ground in an agate mortar. Thepowders obtained were calcined in air, in an electricfurnace, for 3 h at 1,300�C. All the heat-treated samplesform a highly pure and crystalline solid solution, what-ever the level of chromium content. The samples havebeen characterized by many techniques presented else-where (Bondioli et al. 2000).

X-ray absorption spectroscopy

Cr K-edge EXAFS

Fine powders of the Al2�xCrxO3 samples (x=2.00, 1.00,0.45, 0.29, 0.07) were mixed with cellulose and mountedon a sample holder for EXAFS data collection atbeamline D44 of DCI storage ring at LURE (France).Spectra were collected at the Cr K-edge (5,989 eV) intransmission mode using a pair of Si(111) monochro-mator crystals. The beamline is equipped with a pair ofborosilicate parallel mirrors working in specular reflec-tion to reject harmonic reflections. The monochromatorwas calibrated by assigning an energy value of 5,989 eVto the first inflection point in the absorption edge of a Crmetal reference foil. Samples were mounted in a liquidnitrogen cryostat (.77 K) to decrease thermal disorder.Three spectra were collected for all samples exceptAl1.93Cr0.07O3, for which ten spectra were registered. Astandard procedure is used to extract the normalizedEXAFS signal from the absorption spectra (Winterer1997). The EXAFS spectra at the Cr K-edge of the fivesamples are shown in Fig. 1.

These normalized EXAFS signals at the Cr K-edgewere further analyzed by two complementary methods.The contributions from oxygen shells in the coordina-tion sphere were isolated and analyzed by a Fourierseries of plane wavelets. The typical k range used to

obtain the radial structure function in real space was3.90–15.60 A�1. The EXAFS function was k2-weighted.An appropriate r range was selected to separate thecontributions of the nearer shells from the total experi-mental signal using back Fourier transform. Typically,the r range was 0.90–1.96 A. EXAFS fitting was per-formed using the program EXAFS (Bonnin et al. 1985)with theoretical phases, amplitudes and mean free pathscalculated with the FEFF8 code (Ankudinov et al.1998). Starting models for these calculations included a-Cr2O3 and a structural model resulting from an ab initioenergy minimization (see below). Four adjustableparameters (rj, rj, Nj, DE0

j ) were fitted for one shell. Theisotropic signal was analyzed with only one mean metal–oxygen distance for the fit, although the difference be-tween the shorter Cr–O1 and the longer Cr–O2 distancesshould lead to two separate Cr–O distances. Indeed, thisdifference was expected to be less than 0.09 A for both a-Cr2O3 and Cr0.07Al1.93O3 (Pearson 1962; Gaudry et al.2003), which would induce a beating effect on thespectra, with a first node for 2kDr=p, where k=18 A�1

for Dr=0.09 A. Since our spectra were recorded on ashorter k range, this beating effect cannot be seen andthe terms corresponding to the Cr–O1 and Cr–O2 shellscan then be mixed together to give a single term corre-sponding to a mean Cr–O distance, with an additionalcontribution to rstatic (Teo 1985). This point has beenextensively discussed in Fig. 5 of Gaudry et al. (2003).The rstatic values can be found in Table 1. As a secondmethod, we applied a global simulation of v(k) usingstructural models and calculation of the Cr K-edge (seebelow).

Cr L2,3-edges

The experiments were carried out both at beamline ID8of the European Synchrotron Radiation Facility(ESRF) in Grenoble (France) and at beamline SU23 ofthe Super-ACO storage ring at LURE in Orsay(France). On ID8 the photon source was an Apple IIundulator that delivers a high flux of circularly polarizedlight with a polarization rate of about 100%. Themonochromator was a Dragon type one with sphericalgrating. Isotropic and XMCD signals of sampleCr0.07Al1.93O3 have been measured at �6 K in a mag-netic induction of 7 T. On SU23 the photon source wasan asymmetric wiggler that delivers a moderate flux ofelliptically polarized light above and below the orbitplane of the storage ring. The polarization rate wasestimated to be around 45%. The photons were mono-chromatized by a plane grating with fixed exit slit (Arrioet al. 1999). The isotropic cross-section has been mea-sured at 4.2 K for Cr2O3 and for Cr0.14Al1.86O3. XMCDon Cr0.14Al1.86O3 has also been measured. The resultsconcerning Cr0.14Al1.86O3 are in line with those mea-sured at ESRF on Cr0.07Al1.93O3 and are not presentedhere. Since a-Cr2O3 is antiferromagnetic (Brown et al.

0 5 10 15k (Å

-1)

-10

20

50

k3 χ(k)

1 2 3 4r (Å)

Cr2O

3

x=1.00

x=0.45

x=0.29

x=0.07

Cr2O

3

x=1.00

x=0.45

x=0.29

x=0.07

Fig. 1 EXAFS k3v(k) functions (left) and Fourier transforms(right) for the CrxAl2�xO3 powders (x =0.07, 0.29, 0.45, 1.00, 2.00)

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2002), its XMCD signal is zero. The spectra at the CrL2,3-edges are reported in Fig. 2.

Theoretical calculations

Cr K-edge

X-ray absorption spectra are calculated within a realspace multiple scattering approach (FEFF8) for a muf-fin-tin potential with a screened core hole (Ankudinovet al. 1998). Structural models are validated by a directcomparison between the experimental and the calculatedk3v(k). The structural model for a-Cr2O3 is a rhombo-hedral unit cell defined by a=5.35 A and a=55.12�(Finger and Hazen 1980). The EXAFS signal for thisstructural model is computed for a cluster size of 6.3 Aaround the absorbing atom. The total number of pathswhose intensities are larger than 4% of the EXAFScontribution from the first three oxygen neighborswas found to be equal to 150. For all these paths, thenumber of legs was strictly less than six. The FEFF8EXAFS curve was then multiplied by a broadeningGaussian function to take into account the Debye

Waller broadening (r=0.06 A). The structural modelfor Cr0.07Al1.93O3 is given by an ab initio energyminimization using the density functional theory and thespin polarized local density approximation (Car andParrinello 1985). The cell used in the density functionalcalculations is a super-cell built on the vectors2~aR; 2~bR; 2~cR ( ~aR;~bR;~cR are the base vectors of therhombohedral unit cell) and contained 80 atoms asfollows: 1 chromium atom, 31 aluminum atoms and 48oxygen atoms. The lattice constants are those resultingfrom the calculation of reference (Duan et al. 1998):aR=5.11 A and h=55.41�. The super-cell is largeenough to minimize interaction between two paramag-netic ions: the minimum distance between two of these is10.22 A. The spin multiplet degeneracy imposed on thetrivalent paramagnetic ions is four for Cr3+. Thecalculations are performed with the cpmd program(Hutter et al. 1996). From this structural model, atheoretical EXAFS was calculated by the FEFF8 code.For this calculation, we used the same set of parame-ters as those detailed for Cr2O3 except for the DebyeWaller factor that we choose equal to r=0.04 A.

Cr L2,3-edges: ligand field multiplet calculations

The L2,3-edges are analyzed with the LFM calculations.These calculations describe the transition for a singlechromium ion in a given symmetry, from a 2p63d3

ground state to a 2p53d4 excited state (Cowan 1981;Butler 1981; Thole et al. 1985). The calculation isparameterized. The parameters are adjusted to minimizethe differences between the calculated and the experi-mental spectra. Coulomb interactions, exchange inter-actions and 2p and 3d spin–orbit interactions in theinitial (Fdd

2 , Fdd4 , f3d) and final states (Fdd

2 , Fdd4 , Fpd

2 , Gpd1 ,

Gpd3 , f2p, f3d) are calculated in the spherical symmetry.

The electron–electron interactions are reduced by afactor labeled jX that takes into account effects such ascovalency and charge transfer. All electron–electronintegrals are reduced by the same factor. Although thelocal Cr3+ site symmetry in a-Cr2O3 is a slightly dis-torted octahedron (C3 symmetry), with three Cr–O dis-tances of 1.96 A and three Cr–O distances of 2.01 A(Finger and Hazen 1980), we described the local sym-metry of the chromium site in CrxAl2�xO3 by Oh. In fact,the isotropic absorption spectrum does not depend onsuch small distortions (Theil et al. 1999). In Oh sym-metry, the monoelectronic 3d level is split into eg and t2g.The energy separation between these two states is thecrystal field parameter, labeled DX ¼ �eg � �t2g ; for the X-ray energy range. For LFM calculation applied to L2,3-edges, one is dealing with transitions between 2p63d3

toward 2p53d4. One then needs two sets of parametersfor the initial and the final states. The initial statesparameters are set to the values obtained by UV–VISspectroscopy, i.e., D=2.24 eV (18,070 cm�1) andB ¼ ð9F 2 � 5F 4Þ=441 ¼ 0:080 eV (645 cm�1) forCr0.07Al1.93O3 and D=2.07 eV (16,700 cm�1) and

Table 1 Mean Cr–O distances in the coordination shell of chro-mium in the whole solid solution series Al2O3–Cr2O3

Sample r (A) r (A) N DE0 (eV) GOF

Cr2O3 1.980 0.062 6.0 �3.0 0.006CrAlO3 1.970 0.059 5.6 �3.7 0.008Cr0.45Al1.55O3 1.965 0.052 6.4 �5.3 0.013Cr0.29Al1.71O3 1.965 0.057 5.7 �5.3 0.008Cr0.07Al1.93O3 1.965 0.051 6.4 �2.3 0.009

0

0.5

1

Abs

orpt

ion

(ar

b. u

nits

)

Cr0.07

Al1.93

O3

Cr2O

3

575 580 585 590

Energy (eV)

-0.15

0

0.15

a

b

cd

ef

gh

Fig. 2 Isotropic (top) and XMCD (bottom) spectra at the Cr L2,3-edge in a-Cr2O3 (dashed line) and Cr0.07Al1.93O3 (solid lines). Thespectra are normalized to 1.0 at the maximum of the isotropic L3-edge

713

B=0.058 eV (468 cm�1) for a-Cr2O3. In fact we checkedthat the LFM calculations do not depend much on theparameters for the initial state (2p63d3). On the contrarythe set of parameters DX and BX for the final state(2p53d4) strongly modifies the intensities and energies ofthe transitions. One then proceeds to a fit betweenexperiment and calculations to determine the set ofparameters for the final state. They are not expected tobe exactly identical to those found from UV–VIS spec-troscopy, due to the 2p core hole. The broadening of theline spectrum is determined by the lifetime of the finalstates and is mainly determined by Auger decay fromthis final state (2p53d4). The relaxation rate of eachindividual final state is unknown. Individual spectralfeatures and shoulders can have different broadeningfactors. The calculated spectra are broadened using aLorentzian with a 2C full width at half maximum(FWHM), with 2C=0.2 eV (L3) and 2C=0.6 eV (L2)and convoluted with a Gaussian with 0.5 eV FWHM, todescribe the total lifetime and instrumental broadeningprocesses.

In the UV–VIS range, the LFM calculations are alsoused to evaluate the dependence of various band ener-gies of chromium in the 2p63d3 initial state (4T1g,

2T2g,4T2g,

2T1g,2E1g) as a function of D=B:

Results and discussion

Our ultimate purpose is to connect the green color ofeskolaite (a-Cr2O3) and the red color of ruby (a-Al2O3:Cr

3+) to the local organization around chro-mium. To do so, it is worth knowing the effects of thestructural and electronic parameters around chromiumon the positions of the transmission and absorptionbands.

Color and band energies in CrxAl2�xO3

In this part, LFM calculations are performed to (1)evaluate the contributions of the electronic parameters Dand B on the positions of the UV–VIS transmissionbands of a-Cr2O3 and Cr0.07Al1.93O3 and (2) interpretthe X-ray absorption spectra at the L2,3-edges in a-Cr2O3 and Cr0.07Al1.93O3.

Band energies

The colors of eskolaite and ruby are mainly due to thepositions of the transmission bands. One of them liesapproximately at the middle of the two absorptionbands of energies e1 and e2. When one affirms that theposition of the transmission band is given by�m ¼ ð�1 þ �2Þ=2; one makes the assumption that thetransitions 4A2g(Oh) towards

4T2g(Oh) and4A2g(Oh) to-

wards 4T1g(Oh) have similar intensities and similarwidths for powders. The difference of the exact position

of the transmission maximum with our estimation em ofthe transmission maximum is evaluated to be around0.025 eV (200 cm�1).

We evaluate the dependence of �m ¼ ð�1 þ �2Þ=2 anded=e1�e2 by multiplet calculations, taking into accountthe spin–orbit coupling and the trigonal distortion of thechromium site. We performed the calculation with spin–orbit coupling and trigonal distortion to see how thesplittings due to these effects would spread the varioustransitions. The trigonal distortion arises from the factthat in M2O3 compounds, the metallic atom (M) lies in aC3 symmetry site (Hahn 1995). However, it is allowed totreat it as if it were C3v in the absence of external mag-netic field (Sugano and Tanabe 1958). In C3v symmetry,the 4A2g(Oh) spectroscopic term becomes 4A2(C3v), whilethe 4T2g(Oh) spectroscopic term is split into 4E(C3v) and4A1(C3v) and the 4T1g(Oh) spectroscopic term is split into4E(C3v) and

4A2(C3v). So, for the trigonal splitting, weintroduced a C3v distortion yielding the experimentallyobserved splittings on the 4T2g(Oh) and

4T1g(Oh) levels.Spin–orbit coupling on the 3d level was extracted fromatomic calculations (f3d=35 meV). The various levelsabove the ground state are reported in Fig. 3. We do notconsider the negligible 4A2g(Oh) ground-state splitting(<0.08 meV). From Fig. 3, one notices that the energyspread for 4T2g(Oh) levels is quite large. For the partic-ular set of parameters of a-Cr2O3, the 4T2g(Oh) and2T2g(Oh) states can hybridize efficiently. This means thatthe e1 transition cannot be assigned to the single tran-sition 4A2g(Oh) toward

4T2g(Oh) any more, but rather toa set of nine different transitions spread around125 meV (�1,000 cm�1, 6% of D).

From LFM calculation, the variations dem of em andded of ed as functions of the variations dD of D and dB ofB are

d�m ’ 4:2 dBþ 1:02dD ð1Þ

and

d�d ’ 8:5 dBþ 0:057B

0:068 ðeVÞdD: ð2Þ

Since the parameter D ranges from 2.24 eV(18,070 cm�1) in ruby to 2.07 eV (16,700 cm�1) in esk-olaite and the Racah parameter B from 0.080 eV(645 cm�1) in ruby to 0.058 eV (468 cm�1) in eskolaite(Reinen 1969), 35% of the variation of em is due to thevariation of B and the remaining 65% to the variation ofD, while the variation of ed is mainly due to the variationof B (95%). The spin–orbit coupling and the trigonaldistortion lead to a broadening of the states. Forexample, due to spin–orbit coupling, the 4T2g(Oh) ismixed with the 2T2g(Oh). The broadness of these bandscan be greater than the range of variation of one state asa function of x in the whole CrxAl2�xO3 composition.

The covalence of the Cr–O bonding (Racah param-eter B) efficiently conditions the color (35%). Theanalysis of the X-ray absorption spectra at the L2,3-edgesis then meaningful because this technique is a probe for

714

the 3d orbitals that are effective in the appearance ofcoloration.

XAS at the Cr L2,3-edges

The isotropic signal of the a-Cr2O3 and theCr0.07Al1.93O3 samples are quite identical because theyare the signature of a Cr3+ ion with the 3d3 ionic con-figuration in an octahedral environment (Fig. 2). Eightsimilar features appear on the spectra of both samples.However, the positions and intensities of some of themare different. The difference Eg�Ec between the c (L3-edge) and g (L2-edge) features is 8.2 eV for a-Cr2O3

while it is 7.9 eV for Cr0.07Al1.93O3. The differenceEb�Ec between the b and c features of the L3-edge islarger (1.20 eV) for Cr0.07Al1.93O3 than it is for a-Cr2O3

(1.05 eV). The position and the shape of peak a is dif-ferent for the two samples. These isotropic L2,3-edgescan be analyzed with LFM calculations.

We are interested in the determination of twoparameters, namely DX and BX. The last parameter isclosely linked to the jX parameter by jX ¼ BX=B0

X whereBX0 is the calculated Racah parameter for the free ion

(BX0=0.154 eV). From the optical spectra of free ions

and extrapolation, Sugano and Tanabe (1958) giveB0=0.114 eV. The theoretical BX

0 and experimental B0

values differ, due to the presence of the 2p core hole inthe X-ray range. For the isotropic signals, it is worthnoticing that when the parameter DX increases, the peaka appears progressively. When the parameter jX in-creases, the peak a disappears steadily, the peak b isdisplaced toward lower energies and increases in inten-sity. To have a precise idea of the influence of the DX andjX parameters on the position of the b feature, we haveplotted the difference Ec�Eb between the calculated band c features for different values of DX and jX (seeFig. 4). The difference Ec�Eb is almost independent ofthe DX parameter for a given value of jX in the energy

range 1.6–2.2 eV, but it increases steadily with the jXparameter, for a given value of DX. It is then possible todetermine the jX value from the experimental value ofEc�Eb, which is about 1.05 eV for a-Cr2O3 and 1.20 eVfor Cr0.07Al1.93O3. It implies a jX value of 0.55 for a-Cr2O3 and 0.65 for Cr0.07Al1.93O3. The DX value isdetermined by the shape of the spectra, in particular bythe relative intensity of the a feature. Therefore, we havecompared the calculated and experimental Cr L2,3-edges.The calculations were made for 14 different values of DX,in the range 1.5–2.8 eV, with either jX=0.65 orjX=0.55. From all these calculations, we deduce DX(a-Cr2O3)=1.8 eV and DX(Cr0.07Al1.93O3)=2.1 eV. Thedichroic signal provides useful information on theseparameters too. It is worth noticing that when the DX

parameter increases, the Ia=Ib ratio increases, where Iaand Ib are the intensities of peak a and b, respectively(the labeling of the spectral features is defined in Fig. 2),while when the jX parameter increases, the Ia=Ib ratiodecreases. In addition, the difference Ec�Eb is almostindependent of the variation of the DX parameter, whileit increases with the jX parameter. Similar to theisotropic signals analysis, we can deduce values of jXand DX that agree with the previous values. This cor-roborates the previous DX and jX parameters forCr0.07Al1.93O3.

We have plotted in Fig. 5 the final fit of our data. Theparameters used for the Cr3+ (2p53d4) final configura-tion are DX=2.1 eV (16,940 cm�1), jX=0.65,f2p=5.902 eV and f3d=0.047 eV for Cr0.07Al1.93O3, andDX=1.8 eV (14,520 cm�1), jX=0.55, f2p=6.034 eV andf3d=0.047 eV for a-Cr2O3. The Racah parameter BX

deduced from jX is greater in Cr0.07Al1.93O3 (0.100 eV)than in eskolaite (0.085 eV). The crystal field DX isgreater in Cr0.07Al1.93O3 (2.1 eV) than in eskolaite(1.8 eV). These results are in line with the ones given byUV–VIS spectroscopy, which are D=2.24 eV(18,070 cm�1) for ruby and D=2.07 eV (16,700 cm�1)for eskolaite and B=0.080 eV (645 cm�1) for ruby andB=0.058 eV (468 cm�1) for eskolaite. From the fittingprocedure, one sees that DX varies by +15% between a-Cr2O3 and Cr0.07Al1.93O3 and BX by +17%. This is thesame general trend as the one observed in UV–VISspectroscopy. Indeed, the crystal field D increases byabout +8% when the concentration x decreases from 2to 0, while variation of the Racah parameter B is +32%(Reinen 1969). However, the values of the variations ofthe amplitudes given by UV–VIS spectroscopy or XASare different. This difference is related to the fact that theparameters DX and BX are by definition different from Dand B, due to the 2p core hole.

Color and structural environment around Crin CrxAl2�xO3

Since the variation of em, causing the green color of a-Cr2O3 and the red color of ruby, is mainly due to thevariation of the crystal field D (65%), we examine in the

Fig. 3 Variations of the ratio E=B; where E is the energy of variousbands (4T1g,

2T2g,4T2g,

2T1g,2Eg in Oh symmetry), as a function of

D=10B: From UV–VIS spectroscopy, D=10B ¼ 3:475 for Cr2O3,and D=10B ¼ 2:784 for ruby

715

following whether the only variation of the Cr–O dis-tance in the solid solution series can explain the varia-tion of D.

XAS at the Cr K-edge

The EXAFS functions of the five samples are shownin Fig. 1 (left panel). The spectra of a-Cr2O3 andCr0.07Al1.93O3, the two poles of the solid Al2O3–Cr2O3

solid solution, are very different from each other,suggesting a different local environment for chromiumatoms in both structures. The spectra of a-Cr2O3 con-tains more features. In the k range 5-13 A�1, charac-teristic features disappear steadily from a-Cr2O3 toCr0.07Al1.93O3. For instance, the three sharp features atabout 8–9 A�1, which are present in the spectra ofa-Cr2O3, become two features in the spectra ofCr0.07Al1.93O3. It is the same for the three features at

about 6–7 A�1 on the spectra of a-Cr2O3. The FEFF8calculations show that these EXAFS features are mainlydue to single Cr–Cr scattering paths (up to 6 A) in a-Cr2O3. The substitution of chromium atoms by Alatoms from a-Cr2O3 to Cr0.07Al1.93O3 could explain thedisappearance of these features, because aluminumatoms have lower back-scattering amplitude than chro-mium atoms. However, structural changes between a-Cr2O3 and Cr0.07Al1.93O3 could also explain the changesobserved in EXAFS spectra. On Fig. 1 (left panel), onenotices that there is a continuous change of the Cr K-edge X-ray absorption signals from a-Cr2O3 toCr0.07Al1.93O3. An attempt to fit EXAFS spectra forintermediate composition with a linear combination ofthe EXAFS spectra of the two poles (a-Cr2O3 andCr0.07Al1.93O3) by a least square fitting procedure failed.This result indicates that the local environment aroundchromium in CrxAl2�xO3 is not a ponderated average ofchromium environment in Cr0.07Al1.93O3 and Cr2O3.This result can be interpreted as continuous modifica-tion of chromium environment within the series. It alsoshows that there is no chromium clustering in the sam-ples, in agreement with previous work (Bondioli et al.2000). The first peak of the Fourier transform thatcontains the contributions of two Cr–O pairs, with quitesimilar Cr–O distances, is comparable from a-Cr2O3 toCr0.07Al1.93O3, suggesting that there is no significantstructural change in the chromium coordination spherein the whole range Cr2O3–Al2O3. From a-Cr2O3 toCrAlO3, the other peaks are very similar (Fig. 1, rightpanel), but their intensity decreases considerably. Thisdecrease would be due to the increase of aluminumconcentration from a-Cr2O3 to CrAlO3. This hypothesisis supported by the canceling of the Cr–Cr and Cr–Alpairs contributions, shown in Fig. 6. In Cr0.45Al1.55O3

and Cr0.29Al1.71O3, the intensities of the second andthird peaks in the Fourier transform are almost null. Thecanceling of the Cr–Cr and Cr–Al pairs contributions isadded to a probably large spreading of bonds lengths inthe structure. In Cr0.07Al1.93O3, the second peak in theFourier transform increases. The structure aroundchromium becomes again enough organized, but in adifferent way as that occurred in the a-Cr2O3 structure.

The local environment of chromium in the Al2O3–Cr2O3 solid solution series is specified by the EXAFSanalysis. The results for the first shell are presented inTable 1. The parameter DE0 can be different for eachsample and for each shell, because it depends on elec-tronic effects of the chemical bond taken into account(Teo 1985). The influence of this parameter on the finalCr–O distance was checked by fitting the Cr2O3 firstshell with a mean Cr–O distance set at 1.980 A and withvarious fixed values for DE0. Results indicate that thevariation of the goodness of fit for each fit, defined as

n2 ¼X k3vexpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

k6v2expq � k3vfitffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

k6v2expq

0B@

1CA

2

;

1.5 1.75 2 2.25

∆X

(eV)

1

1.1

1.2

1.3

1.4E

c-Eb (

eV)

0.5 0.6 0.7 0.8

κX

(eV)

1.8 eV2.0 eV2.2 eV

κX

=0.60

κX

=0.70

Fig. 4 Influence of the DX and jX parameters on the differenceEc�Eb between the features b and c of the calculated isotropicabsorption spectra at the Cr L2,3-edges

0

0.5

1

1.5

Abs

orpt

ion

(arb

. uni

ts)

575 580 585 590Energy (eV)

-0.2

-0.1

0

0.1

0.2

exp.fit

Cr0.07

Al1.93

O3

Cr2O

3

Cr0.07

Al1.93

O3

Fig. 5 Fitted isotropic and dichroic spectra of Cr2O3 andCr0.07Al1.93O3. The straight line is the fit and the dashed line isthe experimental spectra (see text for calculation parameters)

716

is lower than 0.01 for �5 £ DE0 £ 0 (Fig. 7, right).The influence of DE0 on the final Cr–O distance is thennegligible. In the same way, the error on the mean Cr–Odistance was evaluated by fitting the Cr2O3 first shellwith DE0 set at �1 eV and with various fixed values forthe mean Cr–O distance. Results indicate that a maj-oration of 0.005 A for the mean Cr–O distance yields adegradation of �100% for the goodness of fit (Fig. 7,left). Considering these results, the relative precision onthe mean Cr–O distances can be estimated to be 0.005 Afor the whole series.

Concerning the a-Cr2O3 pole, the mean Cr–O dis-tance (1.980 A) is in good agreement with the one(1.985 A) given by Finger and Hazen (1980). Concerningthe Cr0.07Al1.93O3 pole, our mean Cr–O distance(1.965 A) is similar to EXAFS results on powders(1.96 A) given by Kizler et al. (1996) and from opticalspectra (1.96 A) given by Langer (2001). It is larger thanthe one (1.95 A) given by Andrut (2004) from theapplication of the superposition model to opticalabsorption data. Our mean Cr–O distance is also similarto the one (1.97 A) determined from a previous work onsingle crystals (Gaudry et al. 2003). The EXAFS anal-ysis shows that the average Cr–O bond length inCrxAl2�xO3 (0.07 £ x< 2) increases by �1% in thewhole Al2O3–Cr2O3 series (Fig. 8). This average Cr–Odistance in CrxAl2�xO3 is close to the mean Cr–O dis-tance in a-Cr2O3: 1.980 A from this EXAFS study or1.985 A from Finger and Hazen (1980). It is longer thanthe averaged Al–O bond (1.915 A) in a-Al2O3 in thewhole range Al2O3–Cr2O3. Such a behavior matches thePauling (1967) model. The relaxation parameter

f ¼ RCr�OðCr0:07Al1:93O3Þ � RAl�OðAl2O3ÞRCr�OðCr2O3Þ � RAl�OðAl2O3Þ

defined by Martins and Zunger (1984) is equal to �0.76.This is less than the value found for Co(II), Zn(II),

Pb(II) or Mn(II) in calcite (0.8–0.9) (Reeder et al. 1999;Lee et al. 2002). It is also less than the ones found for Sor Se in CdSxSe1�x (0.87–0.88) (Levelut et al. 1991). Thef value for Cr0.07Al1.93O3 is, however, larger than f=0.5in FeO–MgO solid solutions (Waychunas et al. 1994)and values found by studies on alkali halide solid solu-tions lying between 0.4 and 0.6 (Martins and Zunger1984; Boyce and Mikkelsen 1985; Frenkel et al. 1996).Actually, the corundum structure is made of edge andface-sharing octahedra that allow less flexibility than thecorner-sharing octahedra structure of calcite, but moreflexibility than the compact rock salt structure of MgO,FeO and alkali halide solid solutions.

For a-Cr2O3, the structure from Finger and Hazen(1980) allowed the calculation of the v(k) signal for achromium atom in such a crystal. This is compared inthe upper part of Fig. 9 with the raw (non-Fourier fil-tered) experimental v(k) signal. For the Cr0.07Al1.93O3

sample, the structural model is built as follows: a 6.3 Adiameter cluster around chromium is determined fromthe ab initio energy minimization calculation, except forthe average Cr–O distance of the chromium coordina-tion shell, which is reduced by 0.5% to rescale it to theone found from isotropic EXAFS analysis (1.965 A).The lower part of Fig. 9 shows that this model forCr0.07Al1.93O3 is consistent with the experimental v(k)signal. It can be noticed that the FEFF8 EXAFS cal-culation without this Cr–O rescaling yields the samefeatures as those in Fig. 9 (lower panel).

Influence of the Cr–O bonding on the crystal field

Since we determined how the variation of D induces thecolor change, we now turn to the question of the rela-tionship between the variation of the Cr–O distance withthe variation of D. In the point charge model, thedependence of the crystal field D on the mean metal–ligand distance is given by

D ¼ 5

3ZLe2hr4iR�5Cr�O; ð3Þ

where RCr–O is the mean Cr–O distance, ZL e2 theeffective charge of the ligands and hr4i ¼

Rr2 dr R2ðrÞ2r4;

where R2(r) is the radial part of the d orbitals (Dunnet al. 1965). According to Langer (2001), the quantitiesZL e2 and Ær4æ would be constant along the Al2O3–Cr2O3

solid solution series, because chromium lies in the samekind of site, with the same oxygen ligands in the wholerange. Equation 3 is then rewritten as

D ¼ aR�5Cr�O; ð4Þ

where a is a constant. As shown from the EXAFSanalysis at the Cr K-edge, the variation of the Cr–Odistance in the whole composition range is �1%, while itis 8% for the D crystal field. According to Eq. 4, avariation of the Cr–O distance by 1.6% (more than0.03 A) would be necessary to explain the variation of D

0 5 10 15 20

k (Å-1

)

-1

-0.5

0

0.5

1

F j(k)s

in(2

kr+

φ j(k))

Cr-Al pairs in Al2O

3:Cr

3+

Cr-Cr pairs in Cr2O

3

Fig. 6 Fj(k) sin (2kr+Uj(k)) functions for Cr–Cr pairs in a-Cr2O3

and for Cr–Al pairs in the structural model of ruby for the distancer=2.85 A

717

(8% in the Al2O3–Cr2O3 series). This variation of theCr–O distance is much larger than the one found(0.015 A), which indicates that the variation of the meanCr–O distance is not the only explanation for the vari-ation of D. A different metal–ligand charge transfer be-tween a-Cr2O3 and ruby probably occurs, so that a is nolonger a constant in the whole solid solution series. Thedifferent metal–ligand charge transfer between a-Cr2O3

and ruby might be responsible for some percent in thevariation of the crystal field. This statement is inagreement with the smaller value for the Racahparameter B in eskolaite than in ruby, and with thetheory of Sugano and Peter (1961), for which the energyof the 4A2g fi 4T2g transition is D+10n B, where n is acovalency parameter that stands for the different charge

transfer between r(eg) and p(t2g) Cr–O bonds. Thegreater Cr–O bonding covalency in a-Cr2O3 than in a-Al2O3:Cr

3+ comes from a modification of the electro-static repulsions, and to configuration interaction. Thismeans that the ground state of the chromium atom isdescribed by the configuration 2p63d3 interacting with2p63d4L where L represents a hole on a ligand.

Recent publications (Andrut et al. 2004; Brik et al.2004) suggested that the variations of D was not strictlygiven by Eq. 4. Through a fitting procedure, Andrutet al. found that the exponent in Eq. 4 was in between 5and 7.1, depending on the crystal host. By adding to thepoint charge model a contribution coming from both thecovalent bond formation and the exchange interaction,Brik et al. found that the exponent was strictly largerthan 5. On the other hand, Duclos et al. found that thepressure dependence of the D parameter was well de-scribed by D / V �5=3 (Duclos et al. 1990) in the short

1.95 1.96 1.97 1.98 1.99Cr-O distance (Å)

0

0.01

0.02

0.03

0.04

0.05G

OF

Cr2O

3Cr

0.07Al

1.93O

3

-5 -4 -3 -2 -1 0 1∆E

0 (eV)

0.006

0.008

0.01

0.012

GO

F

Fig. 7 Left panel variation of the goodness of fit (GOF) as afunction of the Cr–O distance (DE0 is fixed with DE0=�1.0 eV) ina-Cr2O3 and Cr0.07Al1.93O3. Right panel variation of the goodness

of fit as a function of the DE0 parameter in a-Cr2O3 (the Cr–O bondlength is 1.98 A)

0 0.5 1 1.5 2

x (Al2-x

CrxO

3)

1.92

1.93

1.94

1.95

1.96

1.97

1.98

1.99

mea

n C

r-O

dis

tanc

e (

Å)

Al2O

3

XRDCr

2O

3

XRD

Fig. 8 Mean Cr–O distances (A) from EXAFS analysis onCrxAl2�xO3 powders. Black dots are experimental points deducedfrom this study. Triangles are XRD data from Finger and Hazen(1980) and from Pearson (1962)

0 2 4 6 8 10 12 14 16

k (Å-1

)

-20

0

20

40

60

k3 χ(k)

Cr2O

3

Al2O

3:Cr

3+

exp.calc.

Fig. 9 The k3-weighted experimental EXAFS (solid lines) andtheoretical EXAFS (dashed line) for both the a-Cr2O3 and thea-Al2O3:Cr

3+ structural models. Isotropic signals at Cr K-edge

718

range of pressure between 0 and 35 GPa. If for suchmoderate pressure, the unit cell volume is scaling as thecube of the averaged Cr–O distance, then Eq. 4 wouldbe strictly obeyed. These pressure-dependent results arein line with those already published by Poole et al.(Poole 1964; Poole and Itzel 1963). These various find-ings can be harmonized in the following unifying pic-ture. When one is comparing small variations of Dparameter without changing the crystal host or theimpurity concentration, the point charge model (i.e.,Eq. 4) might be valid. When one is comparing variationsof D due to changes of lattice host or impurity concen-tration, then the point charge model is clearly not suf-ficient and the theory needs to be modified to take intoaccount the drastic chemical modifications around theimpurity.

Conclusion

This study indicates that the color of the red ruby andthe green eskolaite is partially due to both the crystalfield and the covalence of the Cr–O bonding. In fact, theposition of the transmission band is due 65% to the Dvalue and 35% to the Racah B value. The variation inCr–O distances from a-Cr2O3 to Cr0.07Al1.93O3 esti-mated in this work is 0.015 A (�1%). It is too low toexplain the variation of D in the point charge model.Following Sugano and Peter (1961), the variation of Dcould also be ascribed to the increase of the covalence ofthe Cr–O bond. Indeed, the Cr–Cr coupling in a-Cr2O3

might play a role in the covalence of the Cr–O bond bybroadening the 3d band.

The study of the origin of the difference of colorbetween the green emerald and the red ruby would beinteresting. The Cr–O distances in ruby and emerald areprobably close, the concentration of chromium is quiteidentical and very low in both minerals, so that no Cr–Cr coupling is expected to interfere with the colorappearance. Such a study would be able to separatecovalency effects from crystal field ones.

Acknowledgements We acknowledge the critical reading of themanuscript by Christian Brouder during its preparation. We thankSandrine Brice-Profeta and Valerie Briois for fruitful discussions.We are very grateful to Mayeul d’Avezac for a careful reading ofthe manuscript. We are glad to thank the SU23 staff at LURE andthe ID8 staff at ESRF for their skillful help during experiments.Computing time was partially supplied by the ‘‘Institut du Devel-oppement et des Ressources en Informatique Scientifique’’.

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