Hyperfine Interactions 131: 91–102, 2000. © 2001 Kluwer Academic Publishers. Printed in the Netherlands.

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Quadrupole Splitting Distributions in Grandidierite and Kornerupine from Antarctica LI ZHE1 , TONG LAIXI1 , LIU XIAOHAN1, REN LIUDONG2, JIN MINGZHI3 and LIU MILAN3 1 Institute of Geology and Geophysics, Chinese Academy of Science, Beijing 100029, China 2 Institute of Geology, Chinese Academy of Geological Survey, Beijing 100037, China 3 Instrumental Analysis Center, Jilin University, Changchun, Jilin Province 130023, China

Received 12 October 2000; accepted 29 January 2001 Abstract. The Mössbauer spectra of grandidierite and kornerupine at 298 and 90 K were measured. The quadrupole splitting distributions from the Mössbauer spectra were obtained by using the Voigt-based method, and the assignments for QSDs in the Mössbauer spectra of both minerals are presented. Site occupancies of iron in the crystal structures of two minerals were determined, and the chemical formulas of grandidierite and kornerupine were rewritten based on the relative absorption areas and Mössbauer fraction f for Fe3+ and Fe2+ .

1. Introduction Grandidierite, (Mg,Fe)Al3 BSiO9 , is a rare aluminous borosilicate and has been reported from around 20 localities world-wide [1]. Its structure is related to andalusite and it is the only silicate in which ferrous ions are in fivefold coordination. The crystal structure of grandidierite was investigated by Stephenson and Moore [2]. Average distances AlVI –O 1.897 and 1.910, AlV –O 1.838, (Mg–Fe)V – O 2.042, SiIV –O 1.619, and BIII –O 1.358 Å were determined, and (Mg,Fe) ions occupy trigonal bipyranids. The Mössbauer spectra of grandidierite were analyzed, using the Lorentzian doublet method by Seifert and Olesch [3]. The spectrum of grandidierite at room temperature is characterized by a doublet δ ≈ 1.10 mm/s and  ≈ 1.70 mm/s cased by Fe2+ in the five-coordinated sites and a doublet δ ≈ 0.33 mm/s and  ≈ 1.20 mm/s cased by Fe3+ , and the conclusion on fivefold coordination of Fe2+ derived from the Mössbauer spectrum is consistent with that from the crystal structure determination. Qui et al. [4] analyzed the Mössbauer spectra of grandidierite from China at room temperature. The spectrum was fitted to three doublets: δ = 1.08 mm/s and  = 1.74 mm/s, δ = 1.09 mm/s and  = 2.76 mm/s, and δ = 0.28 mm/s and  = 0.39 mm/s assigned to Fe2+ in the five-coordinated sites, the octahedral sites and Fe3+ in the octahedral sites, respectively. Kornerupine, (
,Mg,Fe)(Al,Mg,Fe)9 (Si,Al,B)5 O21 (OH,F), is also a relatively uncommon Mg–Fe borosilicate reported from around 50 localities. The crystal

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structure of kornerupine was investigated by several authors [5–8], and the chemical crystallography of kornerupine was discussed in detail by Moore et al. [9]. In addition, the Mössbauer spectroscopic study of kornerupine was carried out by Grew et al. [8]. The spectrum of kornerupine was fitted to three Fe2+ doublets and one Fe3+ doublet using the Lorentzian doublet method, and the Fe2+ doublets were assigned to Fe2+ in the octahedral M1 and M2 sites and an irregular, eightfold-coordinated X site, respectively. The Mössbauer spectra of grandidierite and kornerupine at 298 K and 90 K were measured in this work, and the quadrupole splitting distributions from the Mössbauer spectra were obtained by using the Voigt-based method. Site occupancies of iron in two minerals above were obtained.

2. Experimental The samples of grandidierite and kornerupine investigated here are from the Larsemann Hills, East Antarctica. Ren and Zhao [10] found grandidierite, kornerupine and tourmaline in Antarctica for the first time, and it has been shown that the grandidierite, kornerupine, and tourmaline occur in high-grade pelitic gneisses, and three minerals were formed in the intensive boronization period after peak metamorphosis. The X-ray diffraction method was used to check purity of the samples, and no impurity was found. The electron microprobe analyses for two samples were made using a CAMECA SX 51 electron microprobe with the standards. The analytical conditions were as follows: acceleration voltage 15 kV, beam current 20 nA, electron beam diameter 2 µm, counting time 10 s. The program PAP was used for matrix corrections. The Mössbauer spectra of grandidierite and kornerupine were recorded on an M-500 spectrometer in conjunction with a CANBERRA 35 1024 multichannel analyzer. A source of about 10 mCi 57 Co in Pd matrix was used with a xenon (methane) proportional counter as a gamma-ray detector. The spectrometer velocity was regularly calibrated with a thin high-purity α-Fe foil, and the values of the isomer shift are given relative to the α-Fe standard. The spectra at 90 K were obtained with an OXFORD instrument MD 306 cryostat. This model is capable of changing the temperature in the range of 77–300 K, using nitrogen with a variation of 0.5 K. The absorbers were made with a thickness of about 5 mg Fe/cm2 . A Voigt-based QSD method for arbitrary shape QSDs developed by Rancourt and Ping [11] and Ping et al. [12] was used to fit the spectra of grandidierite and kornerupine. The method assumes a certain number m of generalized sites each having their own continuous QSD. Each normalized site-specific QSD is composed of a certain number (ni for site i) of Gaussian components resulting in the sum of Voigt lines in the fit. Two site-specific parameters (δ0 and δ1 ) describe distribution components of each site. The center shifts δ are considered to be linearly correlated

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with the quadrupole splitting values  according to δ = δ0 + δ1 , where δ0 is the value of δ when the distribution parameter has a value of zero, and δ1 is the coupling of δ to a distributed hyperfine parameter. In addition, three component-specific parameters (, σ and h) are required to describe a Gaussian QSD component, where  and σ are the center and σ width of the Gaussian QSD component, respectively, and h is the height of one line in the symmetric elemental Lorentzian doublet. In the absorption experiment using a thin absorber, the width of Lorentzian line has a precise physical meaning, and it is not an adjustable parameter and takes to be 0.194 mm/s.

3. Results and Discussion According to the electron microprobe analyses the chemical compositions of grandidierite and kornerupine are listed in Table I. The chemical formulas of two samples were calculated, based on the chemical compositions listed in Table I: Grandidierite: (K0.01 Mg0.70 Fe0.24 )Al2.98 Si1.04 BO9 , Kornerupine: (K0.01 Ca0.01 Mn0.01 Mg2.59 Fe1.10 Al5.55 Ti0.03 )(Al0.16 Si3.84 B)O21(OH). The Mössbauer spectra of grandidierite and kornerupine at 298 K and 90 K are shown in Figures 1 and 2, respectively. Table II summarized the calculated Mössbauer parameters for the spectra of both minerals. The solid line joining the data points of a given spectrum is the fit result, and other solid lines represent separate contributions from Fe2+ and Fe3+ in the polyhedral sites. The ratios of ferric to total iron for grandidierite and kornerupine were presented in Table II. There is a difference in the Mössbauer fraction between Fe3+ and Fe2+ , and the Mössbauer fraction f for various ferrous- and/or ferric-containing minerals was evaluated by De Grave and Van Alboom [13]. According to their investigation, averaged values of f (Fe3+ )/f (Fe2+ ) for some silicates at 298 K and 90 K are 1.21 and 1.06, respectively. The ratios of ferric to total iron for grandidierite and kornerupine were calculated, basing on the relative absorption areas and the value of f (Fe3+ )/f (Fe2+ ). It is obvious that the ratios of ferric to total iron at 298 K and 90 K for both minerals are close to each other, respectively. Table I. The chemical compositions of grandidierite and kornerupine. Minerals

SiO2

Al2 O3

Grandidierite 20.80 50.40 Kornerupine 30.37 38.35

B 2 O3

MgO

FeO

MnO TiO2

11.56 4.59

9.37 5.82 13.75 10.36 0.11

0.27

CaO K2 O H2 O Total 0.04 0.07

0.03 0.02

1.19

98.02 99.08

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Figure 1. Mössbauer spectra of grandidierite (a) 298 K and (b) 90 K.

3.1. GRANDIDIERITE Grandidierite at 298 K and 90 K gave very similar Mössbauer spectra, characterized by intense absorptions on ∼2.0 mm/s and ∼0.1 mm/s and weak absorptions on ∼0.8 mm/s and ∼−0.2 mm/s. The spectrum of grandidierite is modeled by two Fe2+ QSDs (denoted [2+]-1) having different Gaussian components and one Fe3+ QSDs (denoted [3+]-1) having a single Gaussian component. The QSDs are assigned to Fe2+ in the five-coordinated sites and to Fe2+ and Fe3+ in the octahedral sites. The QSDs of Fe2+ in the five-coordinated sites and Fe2+ in the octahedral sites obtained from fitting the spectra of grandidierite at 298 K and 90 K are shown in Figures 3 and 4, respectively. Grandidierite is orthorhombic, space group Pbnm. The crystal structure of gradidierite consists of four kinds of oxygen polyhedra: boron-centered triangular groups, silicon-centered tetrahedra, magnesium (iron)-centered and aluminumcentered distorted trigonal bipyramids, and aluminum-centered octahedra [2]. By comparison with the crystal structure of grandidierite, QSD with δ=1.082 mm/s and

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Figure 2. Mössbauer spectra of kornerupine (a) 298 K and (b) 90 K.

 = 1.723 mm/s is assigned to Fe2+ in fivefold coordination in this study. Seifert and Olesch [3] measured the Mössbauer spectra of grandidierite, and the spectra at 298 K were analyzed, using two Lorentzian doublets with δ = 1.099–1.106 mm/s,  = 1.681–1.724 mm/s and δ = 0.333–0.365 mm/s,  = 1.133–1.252 mm/s. The former was attributed to Fe2+ in the fivefold-coordinated sites, while the latter was assigned to Fe3+ , but no specific sites were proposed. It is apparent that our assignment for QSD with δ = 1.082 mm/s and  = 1.723 mm/s is consistent with that obtained by Seifert and Olesch [3]. The correlation between the coordination number of Fe3+ and the isomer shift was discussed by several authors [14–20]. It has been found that at room temperature the isomer shifts of Fe3+ in octahedral and tetrahedral sites for oxygen coordination of iron in silicate and oxide minerals are in the range of 0.34–0.50 mm/s and 0.12–0.30 mm/s, respectively. It is predicted that the isomer shift of Fe3+ in fivefold-coordinated sites is between that in the octahedral sites and that in the tetrahedral sites. As a result, QSD with δ = 0.311 mm/s and  = 1.223 mm/s is assigned to Fe3+ in the fivefold-coordinated sites. In

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Table II. The Mössbauer parameters for folded spectra Minerals

T (K)

Grandidierite 298

90

Kornerupine 298

90

Site [2+]-1 [2+]-1 [3+]-1 [2+]-1 [2+]-1 [3+]-1 [2+]-1 [2+]-1 [2+]-1 [2+]-1 [3+]-1 [2+]-1 [2+]-1 [2+]-1 [2+]-1 [3+]-1

δ (mm/s)  (mm/s) σ (mm/s) A (%) Assignment 1.082 1.073 0.311 1.213 1.119 0.409 1.143 1.144 1.145 1.147 0.352 1.268 1.275 1.280 1.293 0.463

1.723 2.335 1.223 1.882 2.456 1.303 2.696 2.269 1.685 0.921 1.759 3.274 2.767 2.411 1.522 1.817

0.080 0.813 0.382 0.198 0.417 0.377 0.666 0.185 0.381 0.202 0.373 0.550 0.384 0.393 0.393 0.466

61 26 13 58 31 11 11 20 35 8 26 8 13 41 11 27

Fe3+ /Fe2+ + Fe3+ χ 2

Fe2+ (five fold) Fe2+ (six fold) Fe3+ (five fold) Fe2+ (five fold) Fe2+ (six fold) Fe3+ (five fold) Fe2+ (X) Fe2+ (M2) Fe2+ (M1) Fe2+ (M1) Fe3+ (M4) Fe2+ (X) Fe2+ (M2) Fe2+ (M1) Fe2+ (M1) Fe3+ (M4)

Figure 3. Fe2+ QSDs from Mössbauer spectra of grandidierite at 298 K.

0.15

1.35

0.12

0.96

0.29

1.02

0.28

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Figure 4. Fe2+ QSDs from Mössbauer spectra of grandidierite at 90 K.

addition to two aforementioned QSDs a third one with δ = 1.073 mm/s and  = 2.335 mm/s was observed in the spectrum of grandidierite investigated here. The average bond lengths AlVI –O 1.897 and 1.910, AlV –O 1.838 Å were determined by Stephenson and Moore [2], and the value for AlVI –O is larger than that for AlV –O. Considering ionic radii of Fe2+ , it is reasonable to assign QSD with δ = 1.073 mm/s and  = 2.335 mm/s to Fe2+ in the sixfold-coordinated sites with large average bond length. The assignment for the spectrum of grandidierite at 90 K is given in Table I, based on that at 298 K.

3.2. KORNERUPINE The spectrum of kornerupine at 298 K is characterized by two dominant more or less asymmetrically broadened absorption peaks centered on ∼0 mm/s and ∼2.2 mm/s and two weak absorption peaks centered on ∼−0.3 mm/s and ∼1.2 mm/s, and at 90 K absorption peaks on ∼0 mm/s and ∼−0.3 mm/s are merged into an absorption on ∼0 mm/s. The spectrum of kornerupine is refined using four Fe2+ QSDs (denoted [2+]-1) with different Gaussian components and one Fe3+ QSD (denoted [3+]-1) with a single Gaussian component. The QSDs are assigned to Fe2+ in the X sites and to Fe2+ and Fe3+ in the octahedral sites. QSDs

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Figure 5. Fe2+ QSDs from Mössbauer spectra of kornerupine at 298 K.

of Fe2+ in the X sites and Fe2+ in the octahedral sites obtained from fitting the spectra of kornerupine at 298 K and 90 K are shown in Figures 5 and 6. Kornerupine is orthorhombic, space group Cmcm. According to the investigation of the crystal structure of kornerupine, the cations occupy sites [X] with a distorted cubic coordination, five octahedral sites [M1–M5] and three tetrahedral sites [T(1)–T(3)]. The average bond lengths M1–O 2.115 Å, M2–O 2.080 Å, M3–O 1.926 Å, M4–O 1.976 Å, M5–O 1.909 Å were determined [9]. Considering ionic radii of Fe2+ , Fe2+ ions favor to occupy M1 and M2 sites. According to Robinson et al. [21], a convenient and realistic way to quantify the distortion from Oh symmetry for those octahedra that show variations in both bond length and bond angle is the variance σ 2 of the octahedral bond angles θi . The calculation on the basis of the crystal structure data shows that σ 2 for the M1 and M2 sites are 214.2 and 153.9, respectively. As demonstrated by Robinson et al. [21], this distortion parameter σ 2 linearly correlates with the mean octahedral quadratic elongation λ, so either the parameter σ 2 or λ could be used to measure the site-distortion. Li and De Grave [19] investigated the correlation of quadrupole splitting with the site-distortion parameters in chain silicates, and it has been found that the quadrupole splitting  initially increases very steeply with increasing site-distortion parameters, and subsequently shows a moderate lowering. Ingalls [22] related the magnitude of (Fe2+ ) to the strength and symmetry of the crystalline field acting on the probe nuclei. His calculations predicted that

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Figure 6. Fe2+ QSDs from Mössbauer spectra of kornerupine at 90 K.

for moderate deviations from cubic symmetry, |(Fe2+ )| increased with increasing crystal-field splitting of the T2g orbital ground level until reaching the maximum for a certain value of this splitting. With a further increase of the deformation, the magnitude (Fe2+ ) lowers as a consequence of the lattice contribution increasing more rapidly than the dominant valence contribution, the two contributions having the opposite sign. This latter effect has been suggested to explain the observed negative correlation between the (Fe2+ ) value and the distortion of the octahedral coordination in chain silicates. Compared with the site-distortion in silicate minerals, it can be seen that M1 and M2 site-distortions in kornerupine are similar to the M4 ones in gedrite and cummigtonite [23]. This indicates that the M1 and M2 sites in kornerupine are the most distorted ones among the different octahedral sites. As a consequence, the correlation between the (Fe2+ ) value and the distortion of the octahedral coordination in kornerupine falls in the part with a negative slope. As compared with the M2 site, the M1 sites are more distorted, therefore, QSDs with δ = 1.144 mm/s and  = 2.269 mm/s are assigned to Fe2+ in the M2 sites, and the QSDs with δ = 1.145 mm/s,  = 1.168 mm/s and δ = 1.147 mm/s and  = 0.921 mm/s are attributed to Fe2+ in the M1 sites. Since the B-bearing tetrahedron shares a corner with the M1 octahedron, the substitution of Al and Si for B would change the geometry of the M1 octahedra, giving rise to multiple QSDs with different quadrupole splittings [8]. In other words, splitting of the QSD in the M1 sites into two QSDs is due to the next-nearest-neighbor effects.

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The single-crystal structure refinement of kornerupine shows that Fe2+ occupies not only the octahedral M1 and M2 sites, but also the strongly distorted X site. δ ∼ 1.2 mm/s and  ∼ 3.5 mm/s for a more typical eightfold-coordinated site in pyrope were obtained [24]. The definition of the distortion parameter for the octahedral site was given by Robinson et al. [21], but not for an eightfold-coordinated site. The bond lengths of the eightfold-coordinated site are 2.197 Å (×4), 2.343 Å (×4) in pyrope [25], while the bond lengths are 2.071 Å (×2), 2.286 Å (×2), and 2.628 Å (×4) in kornerupine [9]. It is apparent from the bond lengths that the eightfold-coordinated sites in kornerupine are more distorted as compared with that in pyrope. Since the eightfold-coordinated sites in both pyrope and kornerupine are strongly distorted, the quadrupole splitting (Fe2+ ) is negatively correlated with the polyhedral distortion. As a consequence, a QSD with a large splitting  = 2.696 mm/s at 298 K is assigned to Fe2+ in the X site. It should be pointed out that the isomer shift of Fe2+ in the dodecahedral sites in pyrope is approximately 1.2–1.3 mm/s [24]. In fact the value of the isomer shift correlates with the average bond lengths, and it has been found that a nearly linear relationship exists between the isomer shift and the average bond length in silicates [19, 20]. Since the four bond lengths (2.628 Å (×4)) are much larger than the other four ones (2.071 Å (×2), 2.286 Å (×2)) in kornerupine, the bond strengths and interactions between the former cations and the corresponding oxygen atoms are much smaller and could be neglected as compared with the latter, so the eightfold coordinated sites in kornerupine could approximately be regarded as ‘tetrahedra’ when the correlation between the bond length and isomer shift is used to estimate the value of the isomer shift. In this case, the mean bond length of ‘the tetrahedra’ is equal to 2.178 Å, this value is smaller than the mean bond length 2.27 Å of the dodecahedral sites in pyrope, but very close to that of octahedral in silicates [19]. Therefore, the isomer shift of Fe2+ in the dedocahedral sites in kornerupine is smaller than that in pyrope and close to that in the octahedra in silicates. Considering the ion radius of Fe3+ and the bond lengths of the M3, M4, and M5 sites, it can be predicted that Fe3+ may occupy the M3, M4, and M5 sites in the crystal structure of kornerupine. As mentioned above, Fe3+ QSD with δ = 0.352 mm/s and  = 1.759 mm/s was observed in the spectrum of kornerupine at 298 K, and the quadrupole splitting of Fe3+ in the spectrum of kornerupine was large. The quadrupole splitting of Fe3+ in the octahedral sites in most silicates and oxides is in the range of 0.3–1.2 mm/s [26]. Ingalls [22] demonstrated that the quadrupole splitting of Fe3+ increased with the increasing distortion. The highest value of the quadrupole splitting of Fe3+ in the M3 sites in the crystal structure of epidote was obtained [27]. The variance σ 2 of the octahedral bond angles of the M3 sites in epidote is 74.8 [23]. As compared with the sites in most minerals, the M3 sites in epidote are more distorted, therefore the quadrupole splitting of Fe3+ in the M3 sites in the crystal structure of epidote is large. The variances σ 2 of the octahedral bond angles of M3, M4, and M5 are 34.5, 85.08, and 24.31. M4 is most distorted of the octahedral sites among the M3, M4, and M5 sites.

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As a consequence, it is reasonable to assign QSDs with δ = 0.352 mm/s and  = 1.759 mm/s to Fe3+ in the M4 sites in kornerupine. Based on their crystal chemistry study, Moore and Araki [6] suggest that Fe3+ occurs only in the M4 sites, and our assignment for Fe3+ is consistent with that obtained by Moore and Araki [6]. The assignment for the spectrum of kornerupine at 90 K is given in Table I, based on that at 298 K. 4. Conclusions The following conclusions could be drawn on the basis of the results and discussion above: (1) The Fe2+ and Fe3+ contributions in the spectra of grandidierite at 298 K and 90 K are refined with two Fe2+ sites and one Fe3+ site, one Fe2+ QSD being assigned to the fivefold-coordinated sites, and a second Fe2+ QSD to the octahedral sites, and an Fe3+ QSD to the octahedral sites. According to the ratios of ferric to total iron at 298 K listed in Table II, the chemical formula of 3+ grandidierite could be rewritten as (K0.01 Mg0.70 Fe2+ 0.20 Fe0.04 ) Al2.98 Si1.04 BO9 ; (2) The spectra of kornerupine at 298 K and 90 K are modeled by four Fe2+ QSDs being assigned to Fe2+ in the X sites and the M2 and M1 sites, and an Fe3+ QSD to Fe3+ in the M4 sites. According to the ratios of ferric to total iron at 298 K listed in Table II, the chemical formula of kornerupine could be rewrit2+ 3+ ten as (K0.01 Ca0.01 Mg0.16 Fe2+ 0.12 )(Al5.55 Ti0.03 Mn0.01 Mg2.43 Fe0.66 Fe0.32 )(Al0.16 Si3.84 B)O21 (OH). Acknowledgements The authors wish to thank Prof. D. N. Ye for helpful discussions. This work has been supported by the National Science Foundation of China (NSFC) (Project No. 40072019). References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

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