Characterization of Synthetic Hedenbergite (Cafesi2o6)–Petedunnite (Caznsi2o6) Solid Solution Series by X-Ray Single Crystal Diffraction

Phys Chem Minerals (2005) 32: 552–563 DOI 10.1007/s00269-005-0025-2

ORIGINAL PAPER

Matthias Heuer Æ Alexandra L. Huber Geoﬀrey D. Bromiley Æ Karl Thomas Fehr Æ Klaus Bente

Characterization of synthetic hedenbergite (CaFeSi2O6)–petedunnite (CaZnSi2O6) solid solution series by X-ray single crystal diffraction

Received: 6 January 2005 / Accepted: 12 July 2005 / Published online: 11 November 2005 Springer-Verlag 2005

Abstract Clinopyroxenes of the solid solution series he- Introduction denbergite (CaFeSi2O6)–petedunnite (CaZnSi2O6) were synthesized at temperatures of 825–1200C and pres- Hedenbergite (CaFeSi O ) and petedunnite (Ca- sures of 0.5–2.5 GPa. Compositions were determined by 2 6 ZnSi O ) are chain silicates belonging to the group of electron microprobe analysis. Selected crystals were 2 6 clinopyroxenes crystallizing in the monoclinic space investigated by means of single crystal diffraction and group C2/c. Ca occupies the distorted eightfold-coordi- structure refinement and the structural distortion was nated M2 polyhedra, whereas Fe2+ and Zn2+ occupy studied depending on the substitution of iron by zinc on the sixfold-coordinated M1 octahedra in hedenbergite the octahedral M1 site. It is shown that the coordination and petedunnite, respectively. The structures of end of the M1 site has the most significant effect on M–O member hedenbergite and petedunnite were refined by bond lengths, with changes on the other sites accom- Clark et al. (1969) and Ohashi et al. (1996), respectively. modating this distortion. The mean quadratic elonga- Hydrothermal synthesis of hedenbergite was per- tion and the octahedral angle variance as quantitative formed by Nolan (1969), Rutstein and Yund (1969), measures of the distortion of the coordination polyhe- 57 Turnock et al. (1973), Gustafson (1974), Kinrade et al. dron were correlated with former results of Fe Mo¨ ss- (1975), Burton et al. (1982), Haselton et al. (1987), bauer spectroscopy at 298 K. The results presented now Moecher and Chou (1990), Raudsepp et al. (1990), complete an earlier work on synthetic, crystalline pow- Perkins and Vielzeuf (1992), Kawasaki and Ito (1994), ders of the same material and deliver exact structural Zhang et al. (1997) and Redhammer et al. (2000). The data that were not possible to obtain by Rietveld stability of hedenbergite at 0.2 GPa as a function of refinements on powder data. temperature and oxygen fugacity was determined by Gustafson (1974) and Burton et al. (1982). Keywords Petedunnite Æ Hedenbergite Æ Solid Naturally occurring petedunnite was first described solution Æ Synthesis Æ Crystal chemistry Æ Single crystal by Essene and Peacor (1987) from Zn skarns in Frank- diffraction Æ Clinopyroxene lin, New Jersey. Petedunnite occurs as a major component in quaternary solid solution with hedenbergite, johannsenite (CaMnSi2O6) and diopside (CaMgSi2O6) (Huber et al. 2000). Pure CaZnSi2O6 has not been observed in nature but was synthesized at 900C, 2 GPa by Essene and Peacor (1987), at 900, 970 and 1,000C/ M. Heuer (&) Æ K. Bente Institut fu¨ r Mineralogie, Kristallographie und 2 GPa by Huber et al. (2004a, b) and at 1350C/2.5 GPa Materialwissenschaft, Scharnhorststraße 20, by Redhammer and Roth (2005). The stability field of 04275 Leipzig, Germany end-member petedunnite is restricted to pressures E-mail: [email protected] greater then 0.8 GPa, as shown experimentally by Huber A. L. Huber Æ K. T. Fehr et al. (2004b). Department of Earth- and Environmental Sciences, First results on the synthesis of hedenbergite–pete- Ludwig-Maximilians University Munich, Theresienstr.41, dunnite solid solutions upto 30 mol% petedunnite at 80333 Munich, Germany 0.5 GPa have been reported by Fehr and Hobelsberger (1997). The complete hedenbergite–petedunnite solid G. D. Bromiley Department of Earth Sciences, University of Cambridge, solution series was synthesized over a wide temperature Downing Street, CB2 3EQ Cambridge, UK and pressure range by Huber et al. (2004a). Preliminary 553 studies on the characterisation of the solid solution CaCO3 (99.999%), Fe2O3 (99.99%), Fe (99.999%), FeO series hedenbergite–petedunnite were conducted by (99.9%) and ZnO (99.99%). All oxides, except FeO, Heuer et al. (2002a, b), Huber and Bromiley (2001), were annealed at high temperatures. Three different Huber and Fehr (2002, 2003a, b), Huber et al. (2004a). mixtures were prepared by sintering oxides in appro- In nature, hedenbergitic clinopyroxenes and sulfides, priate portions according to the hedenbergite–petedun- such as sphalerite, are common constituents of skarns in nite solid solution’s bulk compositions as described in phase assemblages with garnet, ilvaite and epidote (e.g., Huber et al. (2004a). Nakano et al. 1994; Capitani and Mellini 2000). An in- The initial material for pure petedunnite was pre- tercrystalline exchange of Fe and Zn occurs between pared like oxide mix (I) but without Fe and Fe2O3. coexisting hedenbergite and sphalerite, resulting in A hydrous experiment (hd8b4_1a) at 825C and chemical inhomogeneities within the rims of coexisting 0.5 GPa was conducted using an internally heated gas phases (Fehr and Heuss–Assbichler, 1994; Huber et al. media apparatus (Yoder 1950; Huckenholz et al. 1975) 2004b). The corresponding intercrystalline exchange and a conventional cold-seal pressure vessel (Luth and reaction can be described by the model reaction: Tuttle 1963). Experiments at higher pressures were performed ZnS þ CaFeSi2O6ðhedenbergiteÞ using a piston-cylinder solid media apparatus. Most ¼ FeS þ CaZnSi2O6ðpetedunniteÞ intermediate solid solutions (hd3gb31, hd4gb31, hd5gb21, hd7gb21; see Table 1) were synthesized at the Zinc contents in hedenbergite and coexisting sphalerite Bayerisches Geoinstitut using an end-loaded piston- upto 600 and 9000 ppm, respectively, were observed by cylinder type apparatus. Run conditions for all synthesis Nakano et al. (1994) and Fehr and Heuss–Assbichler experiments are given in Table 1 and all experimental (1994). In order to describe the equilibrium conditions details are given in Huber et al. (2004a). and kinetics of the intercrystalline Zn–Fe exchange For the data collection on a conventional four-circle equilibrium between zincian hedenbergite and ferroan diffractometer (P4, Bruker), operating with monochro- sphalerite, the thermodynamic mixing properties of the matic Mo Ka radiation (tube power 50 kV/30 mA), 1–3 solid solution series hedenbergite–petedunnite have to be crystals of each sample were checked for reflection known. Experimental determinations of thermodynamic intensity, reflection profile shape and twinning to select mixing properties and diffusion constants require the ones assuring the highest data quality. If available, homogeneous material with defined crystal-chemical crystals with well-developed faces were used to realize a properties. Therefore, the aim of this study was to syn- face indexed absorption correction, which was carried thesize intermediate members of the solid solution series out with the program XPREP (Bruker 1994). Otherwise hedenbergite–petedunnite at defined oxygen fugacities preferably isometrical crystal fragments were measured and to determine their structure by X-ray diffraction and to correct the absorption empirically using w-scans. The composition by electron microprobe analysis (EMPA). structural refinements were carried out using SHELXL- Furthermore, these data should be correlated with pre- 97 (Sheldrick 1997) providing full-matrix least-squares vious results of 57Fe Mo¨ ssbauer spectroscopy creating a on F2 . Further experimental details for the individual cross reference of two independent methods, which can hkl measurements and refinements are listed in Table 2. give information on the M1-site. The results presented After the experiments, the composition of the selected here now complete an earlier study of synthetic, crystal- crystals was determined using an electron microprobe line powders of the same material and delivers exact (Camebax SX100) operated at 20 keV acceleration structural data which were not possible to obtain by Ri- voltage and 20 nA beam current. Synthetic wollastonite etveld refinements on powder data (Huber et al. 2004a). (Ca, Si), sphalerite (Zn) and hematite (Fe) were used as Experimental standards and matrix correction was performed by PAP procedure (Pouchou and Pichoir 1984). The reproduc- Syntheses were conducted using pure crystalline phases ibility of standard analyses was less then 1% for each element routinely analyzed. prepared from sources of reagent grade SiO2 (99.995%),

Table 1 Experimental conditions for syntheses Sample Initiala T (C) Pressure (GPa) Time (h) Buﬀer

hd10hk1a III 900 1.2 22 No buffer hd8b41a I 825 0.5 153 fb hd7gb21 II 1,000 1.0 72 C hd5gb21 II 850 1.8 65 C a hd4gb31 II 970 2.0 72 C The initial oxide mixes are hd3gb31 II 850 1.8 64 C described in the text hd2dg21 II 1,200 2.5 72 No buffer fb furnace buffer, C graphite pd91b I 1,000 1.9 72 fb capsule Table 2 Individual measurement conditions and general refinement parameters; measurement conditions and the refinement parameters of the samples hd2dg21 and hd5gb21 are 554 already published elsewhere (Heuer et al. 2002a, b)

hd10hk1a hd8b41a hd7gb21 hd5gb21 hd4gb31 hd3gb31 hd2dg21 pd91b

Measured/ Ca1.01(2) Fe0.99(2) Ca1.02(4) Fe0.69(4) Ca0.98(1) Fe0.86(7) Ca0.98(2) Fe0.59(3) Ca1.01(1) Ca0.99(1) Fe0.27(9) Ca1.00(1) Fe0.21(2) Ca1.00(2) Zn0.99(3) refined Si1.98(1) O6/ Zn0.27(6) Si2.02(5) O6/ Zn0.16(8) Si2.00(2) O6/ Zn0.46(3) Si1.98(2) O6/ Fe0.40(8) Zn0.60(7) Zn0.75(9) Si1.98(2) O6/ Zn0.85(3) Si1.97(1) O6/ Si2.01(1) O6/ formula CaFeSi2O6 CaFe0.79 Zn0.21 Si2O6 CaFe0.83 Zn0.17 Si2O6 CaFe0.52 Zn0.48 Si2O6 Si2.00(2) O6/ CaFe0.42 Zn0.58 Si2O6 CaFe0.21 Zn0.85 Si2O6 CaZnSi2O6 CaFe0.5 Zn0.5 Si2O6 Formula 248.11 250.01 250.97 253.92 251.19 255.25 258.71 257.63 weight T [K] 293(2) 293(2) 293(2) 293(2) 293(2) 293(2) 293(2) 293(2) Wavelength [A˚ ] 0.70932 0.70932 0.70932 0.70932 0.70932 0.70932 0.70932 0.70932 Crystal syst., monoclinic, monoclinic, monoclinic, C 2/c monoclinic, monoclinic, monoclinic, monoclinic, monoclinic, space group C 2/c C 2/c C 2/c C 2/c C 2/c C 2/c C 2/c a[A˚ ] 9.8672(14) 9.8605(19) 9.8502(16) 9.8206(8) 9.8447(16) 9.8369(16) 9.8306(14) 9.8243(17) b[A˚ ] 9.0469(12) 9.0304(17) 9.0294(16) 8.9966(8) 9.0175(15) 9.0043(13) 9.0018(12) 8.9939(15) c[A˚ ] 5.2584(7) 5.2690(9) 5.2584(9) 5.2487(4) 5.2614(9) 5.2605(9) 5.2604(8) 5.2608(8) b [] 104.794(9) 105.138(10) 105.052(9) 105.34(1) 105.342(8) 105.435(10) 105.685(11) 105.794(10) Volume [A˚ 3 ] 453.84(11) 452.89(14) 451.64(14) 447.2(14) 450.43(13) 449.14(12) 448.17(11) 447.29(13) 3 Z, qcalc [g/cm ] 4, 3.631 4, 3.667 4, 3.691 4, 3.743 4, 3.716 4, 3.775 4, 3.834 4, 3.826 l [mm1 ] 4.93 5.36 5.58 6.06 6.23 6.46 6.970 7.12 F(000) 488 491 493 498 496 500 502 504 Crystal size 0.2·0.2· 0.14·0.15· 0.08·0.08· 0.05·0.21· 0.13·0.12· 0.1·0.1·0.05 mm 0.16X0.19X 0.16·0.15· 0.3 mm 0.2 mm 0.05 mm 0.21 mm 0.06 mm 0.29 mm 0.16 mm H range 3 to 40 3to40 3to40 3to40 3to40 3to40 3to40 3to40 Limiting indices 1 £ h £ 17, 1 £ h £ 17, 1 £ h £ 17, 1 £ h £ 17, 1 £ h £ 16, 1 £ h £ 17, 1 £ h £ 17, 1 £ h £ 17, 1 £ k £ 16, 1 £ k £ 16, 1 £ k £ 16, 1 £ k £ 16, 1 £ k £ 16, 1 £ k £ 16, 1 £ k £ 16, 1 £ k £ 16, 9 £ l £ 9 9 £ l £ 9 9 £ l £ 9 9 £ l £ 9 9 £ l £ 9 9 £ l £ 9 9 £ l £ 9 9 £ l £ 9 Reflections 1723/1402 1725/1403 1722/1401 1718/1396 1681/1366 1712/1394 1706/1389 1705/1387 collected / unique [R(int)=0.0230] [R(int)=0.0214] [R(int)=0.0333] [R(int) = 0.0222] [R(int)=0.0300] [R(int)=0.0313] [R(int) = 0.0153] [R(int)=0.0325] Completeness to 100.0% 100.0% 99.9% 100.0% 97.8% 99.9% 99.9% 100.0% theta = 40 Data/restraints/ 1402/0/48 1403/0/49 1401/0/49 1396/0/49 1366/0/49 1394/0/48 1389/0/49 1387/0/48 parameters GooF on F2 1.408 1.473 1.177 1.410 1.292 1.255 1.806 1.312 Final R R1 = 0.0289, R1 = 0.0290, R1 = 0.0366, R1 = 0.0295, R1 = 0.0322, R1 = 0.0338, R1 = 0.0248, R1 = 0.0321, [I>2sigma(I)] wR2 = 0.0718 wR2 = 0.0694 wR2 = 0.0701 wR2 = 0.0650 wR2 = 0.0716 wR2 = 0.0703 wR2 = 0.0608 wR2 = 0.0742 R (all data) R1 = 0.0365, R1 = 0.0341, R1 = 0.0569, R1 = 0.0356, R1 = 0.0429, R1 = 0.0450, R1 = 0.0270, R1 = 0.0436, wR2 = 0.0744 wR2 = 0.0710 wR2 = 0.0758 wR2 = 0.0667 wR2 = 0.0745 wR2 = 0.0736 wR2 = 0.0614 wR2 = 0.0774 Extinction par. 0.0116(7) 0.0193(8) 0.0011(4) 0.0038(4) 0.0053(5) 0.0120(6) 0.0100(6) 0.0180(8) Largest diff. peak 0.872 and 0.7110.848 and 0.630 1.383 and 0.816 1.381 and 0.940 0.954 and 0.841 0.936 and 0.802 1.151 and 0.685 0.818 and 0.928 and hole [e /A˚ 3] 555

Table 3 Reﬁned atomic coordinates, site occupancies and anisotropic thermal displacement parameters for selected samples of the hedenbergite–petedunnite solid solution series;measurement conditions and the reﬁnement parameters of the samples hd2dg21 and hd5gb21 are already published elsewhere (Heuer et al. 2002a, b)

hd10hk1a hd8b41a hd7gb21 hd5gb21 hd4gb31 hd3gb31 hd2dg21 pd9_1b

M2 x 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.0000 0.00000 y 0.30034(5) 0.30041(4) 0.30011(6) 0.30019(4) 0.30028(5) 0.30010(5) 0.30017(4) 0.30002(6) z 0.25000 0.25000 0.25000 0.25000 0.25000 0.25000 0.2500 0.25000 sofCa 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000 u11 0.01223(15) 0.01256(15) 0.01081(21) 0.0140(20) 0.01205(20) 0.01122(18) 0.0156(1) 0.01122(20) u22 0.01026(14) 0.00984(14) 0.00853(19) 0.0098(10) 0.00861(16) 0.00797(15) 0.0128(1) 0.00946(17) u33 0.00927(13) 0.00939(14) 0.00734(18) 0.0098(10) 0.00856(16) 0.00753(16) 0.0120(1) 0.00867(17) u23 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.0000 0.00000 u12 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.0000 0.00000 u13 0.00011(11) 0.00040(11) 0.00030(15) 0.0011(10) 0.00059(13) 0.00041(13) 0.0015(1) 0.00002(14) M1 x 0.00000 0.00000 0.00000 0.0000 0.00000 0.00000 0.0000 0.00000 y 0.90742(3) 0.90678(3) 0.90676(4) 0.90635(3) 0.90626(3) 0.90608(3) 0.90590(2) 0.90578(3) z 0.25000 0.25000 0.25000 0.2500 0.25000 0.25000 0.2500 0.25000 sofZn 0 0.10537(392) 0.08259(524) 0.483(9) 0.24805(490) 0.29339(516) 0.810(1) 0.50000 SofFe 0.50000 0.39463(392) 0.41741(524) 0.517(9) 0.25195(490) 0.20661(516) 0.190(1) 0 u11 0.00847(11) 0.00829(11) 0.00639(13) 0.0101(1) 0.00813(13) 0.00730(11) 0.0123(1) 0.00806(12) u22 0.00832(12) 0.00837(11) 0.00583(13) 0.0086(1) 0.00739(12) 0.00733(11) 0.0119(1) 0.00874(12) u33 0.00774(11) 0.00765(10) 0.00560(13) 0.0083(1) 0.00706(11) 0.00576(10) 0.0106(1) 0.00762(11) u23 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.0000 0.00000 u12 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.0000 0.00000 u13 0.00122(8) 0.00148(8) 0.00091(9) 0.00229(8) 0.00185(8) 0.00151(8) 0.00289(7) 0.00132(8) Si x 0.28782(4) 0.28740(4) 0.28753(5) 0.28709(4) 0.28698(5) 0.28691(5) 0.28672(4) 0.28641(5) y 0.09250(4) 0.09254(4) 0.09231(5) 0.09252(4) 0.09254(5) 0.09250(5) 0.09259(3) 0.09253(5) z 0.23271(7) 0.23154(7) 0.23216(9) 0.23072(7) 0.23096(8) 0.23055(8) 0.22966(7) 0.22926(9) sof 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 u11 0.00685(15) 0.00657(15) 0.00491(18) 0.0084(2) 0.00656(19) 0.00538(16) 0.0101(2) 0.00549(18) u22 0.00779(15) 0.00760(15) 0.00557(19) 0.0075(2) 0.00648(17) 0.00571(16) 0.0104(2) 0.00702(18) u33 0.00650(14) 0.00657(14) 0.00458(18) 0.0074(2) 0.00619(17) 0.00495(16) 0.0097(1) 0.00656(17) u23 0.00033(10) 0.00036(9) 0.00025(14) 0.00025(9) 0.00020(12) 0.00012(12) 0.00025(8) 0.00019(13) u12 0.00032(11) 0.00015(10) 0.00008(16) 0.0003(1) 0.00009(13) 0.00023(13) 0.00022(8) 0.00003(14) u13 0.00137(11) 0.00162(11) 0.00112(14) 0.0023(1) 0.00202(13) 0.00159(12) 0.0030(1) 0.00125(14) O1 x 0.11941(11) 0.11852(11) 0.11884(14) 0.1178(1) 0.11790(13) 0.11724(12) 0.1169(1) 0.11631(14) y 0.09020(11) 0.08959(10) 0.08931(14) 0.0894(1) 0.08924(12) 0.08901(12) 0.08914(9) 0.08909(13) z 0.15227(20) 0.14970(19) 0.15016(24) 0.1479(2) 0.14787(23) 0.14690(23) 0.1455(2) 0.14432(24) sof 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 u11 0.00705(35) 0.00735(34) 0.00525(42) 0.0083(4) 0.00669(43) 0.00572(38) 0.0106(3) 0.00532(43) u22 0.01168(40) 0.01107(37) 0.00945(48) 0.0103(4) 0.00933(42) 0.00965(42) 0.0134(3) 0.00993(45) u33 0.00877(35) 0.00897(35) 0.00728(44) 0.0101(4) 0.00838(40) 0.00709(40) 0.0118(3) 0.00717(40) u23 0.00003(28) 0.00039(25) 0.00025(40) 0.0004(3) 0.00045(34) 0.00054(33) 0.0003(2) 0.00105(35) u12 0.00003(29) 0.00040(27) 0.00004(42) 0.0002(3) 0.00003(34) 0.00013(34) 0.0005(2) 0.00041(37) u13 0.00115(29) 0.00174(28) 0.00105(35) 0.0023(3) 0.00173(33) 0.00170(32) 0.0028(3) 0.00029(34) O2 x 0.36288(12) 0.36186(11) 0.36196(15) 0.3615(1) 0.36135(13) 0.36128(13) 0.3607(1) 0.36023(14) y 0.24625(12) 0.24688(11) 0.24713(15) 0.2473(1) 0.24721(13) 0.24775(13) 0.2480(1) 0.24824(14) z 0.32396(20) 0.32321(19) 0.32272(25) 0.3223(2) 0.32224(23) 0.32200(23) 0.3218(2) 0.32158(23) sof 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 u11 0.01347(41) 0.01315(38) 0.01248(55) 0.0141(4) 0.01223(48) 0.01158(46) 0.0152(3) 0.01013(51) u22 0.00860(37) 0.00954(37) 0.00605(45) 0.0088(4) 0.00699(42) 0.00780(42) 0.0118(3) 0.00828(44) u33 0.01159(34) 0.01101(32) 0.00941(49) 0.0120(3) 0.01064(42) 0.00866(42) 0.0137(3) 0.01002(43) u23 0.00104(30) 0.00104(26) 0.00102(39) 0.0008(3) 0.00072(34) 0.00102(32) 0.0006(3) 0.00069(36) u12 0.00281(34) 0.00279(30) 0.00279(44) 0.0030(3) 0.00297(37) 0.00230(37) 0.0025(3) 0.00251(40) u13 0.00259(31) 0.00283(30) 0.00220(44) 0.0035(3) 0.00273(37) 0.00245(36) 0.0037(3) 0.00135(39) 556

Table 3 (Contd.)

hd10hk1a hd8b41a hd7gb21 hd5gb21 hd4gb31 hd3gb31 hd2dg21 pd9_1b

O3 x 0.35027(10) 0.35024(10) 0.34997(14) 0.3502(1) 0.35023(12) 0.35015(12) 0.35019(8) 0.34991(14) y 0.01981(12) 0.01947(11) 0.01949(15) 0.0190(1) 0.01935(13) 0.01897(13) 0.0190(1) 0.01895(14) z 0.99298(18) 0.99333(17) 0.99382(23) 0.9932(2) 0.99344(21) 0.99320(21) 0.9939(2) 0.99359(23) sof 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 u11 0.00967(38) 0.00877(35) 0.00723(46) 0.0101(4) 0.00865(46) 0.00789(42) 0.0123(3) 0.00762(46) u22 0.01276(40) 0.01272(37) 0.01045(48) 0.0121(4) 0.01046(43) 0.01024(42) 0.0144(3) 0.01077(45) u33 0.00794(35) 0.00868(34) 0.00649(46) 0.0091(3) 0.00805(42) 0.00663(40) 0.0112(3) 0.00798(42) u23 0.00260(29) 0.00315(27) 0.00356(39) 0.0025(3) 0.00263(35) 0.00253(33) 0.0026(2) 0.00215(37) u12 0.00055(31) 0.00057(28) 0.00076(43) 0.0002(3) 0.00060(36) 0.00008(35) 0.0002(2) 0.00052(39) u13 0.00247(29) 0.00221(27) 0.00271(38) 0.0029(3) 0.00340(35) 0.00306(34) 0.0038(3) 0.00173(37)

The starting model for all refinements was the he- Results denbergite structure published by Cameron et al. (1973). This model was modified concerning lattice parameters, Clinopyroxene single crystals along the join hedenberg- mixed occupancy of the M1 site and appropriate con- ite–petedunnite were synthesized with sizes upto straints and then refined using the measured data. In the 200 · 200 · 300 lm from highly unstable initial oxide end of each refinement the thermal displacement factors mixtures at temperatures of 825–1,200C and pressures were processed anisotropically. All refined parameters of 0.5–2.5 GPa. All members of the hedenbergite–pete- are listed in Table 3. dunnite solid solution series investigated here show C2/c symmetry at room temperature. Their chemical compositions are listed in Table 2 as a structural sum for- The octahedral M1 site mula in comparison with the refined formula. Microprobe analyses prove that crystals are homoge- Within the solid solution series hedenbergite–petedun- neous and do not show any chemical zonation with nite, the octahedral M1 site exhibits the strongest 2+ exception of hd7gb21, which had a deviating composi- structural changes, because the substitution of Fe by 2+ tion of Ca Zn Fe Si O and a small Zn is restricted to this site. This restriction is valid, 0.98(1) 0.16(8) 0.86(7) 2.00(2) 6 2+ inclusion of Ca Zn Fe Si O . Sample because compositional data implies that Ca fully 0.99(1) 0.31(7) 0.70(7) 2.00(2) 6 4+ hd7gb21 was synthesized under conditions close to the occupies the M2 site and Si fully occupies the T-site. border of the stability field of petedunnite, what might Within the substitution all M1–O bond lengths decrease explain the decomposition into two different clinopy- with increasing Zn-content as shown in Fig. 1 and Ta- roxenes (Huber and Bromiley 2001; Huber et al. 2004b]. ble 4. Starting with a more regular FeO6-octahedron in Since the inclusion had a volume fraction of only 0.03 of hedenbergite, which has two short [2.0920(11) A˚ ], two the measured crystal (estimated from BSE SEM images) medium [2.1425(11) A˚ ] and two long [2.1669(10) A˚ ] Fe– the corresponding refinement results may have higher O bonds, the site changes continuously into the more uncertainties, but are considered to be still significant for distorted ZnO6- octahedron of petedunnite with four short [2.0785(14) A˚ and 2.0788(13) A˚ ] and two long Ca0.98(1)Zn0.16(8)Fe0.86(7)Si2.00(2)O6. Refinement con- straints on chemistry and site occupancy were based on [2.1636(13)A˚ ] Zn–O bonds. Similar distortions are re- the results of the microprobe analysis with the assump- ported for pure petedunnite by Ohashi et al. (1996) and tion that Fe2+ and Zn2+ share the M1 site, Ca2+ fully Redhammer and Roth (2005) and as a very distinctive occupies the M2 site and that Si4+ fully occupies the feature of the M2 and the M1 site in monoclinic T-site. and orthorhombic ZnSiO3 by Morimoto et al. (1975).

Table 4 M1–O bond lengths of selected hedenbergite– M1–O2(1)D, M1–O1(2)A, M1–O1(1)A, petedunnite solid solution M1–O2(1)C (A˚ ) M1–O1(2)B (A˚ ) M1-O1(1)B (A˚ ) members pd91b 2.0785(14) 2.0788(13) 2.1636(13) hd2dg21 2.0778(9) 2.0877(10) 2.1641(9) hd3gb31 2.0767(12) 2.0999(12) 2.1611(12) hd4gb31 2.0831(12) 2.1084(12) 2.1653(12) hd5gb21 2.0818(11) 2.1096(11) 2.1649(10) hd7gb21 2.0839(14) 2.1260(13) 2.1638(13) hd8b41a 2.0889(11) 2.1253(10) 2.1664(10) hd10hk1a 2.0920(11) 2.1425(11) 2.1669(11) 557

Fig. 1 M1–O bond lengths along the join hedenbergite– petedunnite. Data are given in Table 4

Fig. 2 M2–O bond lengths along the join hedenbergite– petedunnite. Data are given in Table 5

2+ Furthermore in a large number of structures, Zn (Ca2ZnSi2O7; Warren and Trautz 1930) gahnite (ZnA- prefers a tetrahedral coordination, for example, in wil- l2O4; Saalfeld 1964) and synthetic zinc-feldspar Ca- lemite (Zn2SiO4; Simonov et al. 1977), hardystonite ZnSi3O8 (Heuer et al. 1998). 558

The general trend of decreasing M1–O bond lengths All these bonds remain constant over the whole heden- is in accordance with the effective ionic radii of Zn2+ bergite–petedunnite solid solution series (see Fig. 3 and ˚ 2+ ˚ ˚ (0.74A) and Fe (0.92 A, HS/0.75 A, LS) in octahedral Table 6) and so the SiO4 tetrahedron is the most stable coordination (Shannon 1976). part of the structure, which is a typical behavior for silicates. Nevertheless the whole tetrahedra undergo changes as an they are tilted as an unit corresponding to The M2 polyhedron changes of the M1 site. Thompson (1970) noted that one can define an S- and Since Ca2+ fully occupies the M2 site in all measured an O-rotation, which are rotations with the same rota- crystals, changes in M2–O bond lengths within the he- tion axis and opposite sense. Thus, the triangular face of denbergite–petedunnite solid solution series are much a tetrahedron comes into the (S)ame orientation as a lower, but not negligible. With increasing Zn-content, parallel triangular face of the next octahedron when it is the M2–O3(1)D,C bonds decrease from 2.6328(11) to S-rotated and does the (O)pposite for an O-rotation (see 2.6060(14) A˚ , whereas the M2–O3(2)D,C bonds increase Fig. 4). from 2.7252(11) to 2.7366(14) A˚ and the other M2–O Like most clinopyroxenes, hedenbergite and pete- bond lengths [in average 2.3416(12) and 2.3618(12) A˚ ] dunnite as well as intermediate solid solutions show an do not show any significant changes (see Fig. 2 and O-rotation, which can be illustrated by the O3(1)D- Table 5). These changes reflect a compensation of the O3(2)D-O3(1)D angle between those edges of the tetra- structure deformation due to Zn2+ substitution onto the hedra forming the connecting line of the chains (Red- M1 site. This is supported by the observation that the hammer and Roth 2004). This angle is 180 when the longer and weaker M2–O3 can be distorted more easily chain is completely stretched and changes from than the shorter and stronger M2–O2 and M2–O1 164.48(4) for hedenbergite to 165.17(4) for petedun- bonds. nite. Furthermore these triangular faces of the tetrahedra are not in one plane, but show a small tilt, which can The tetrahedral site be visualized by the O2(2)D-O3(2)D-O2(1)D angle (see Fig. 4) which is 160.39(4) for hedenbergite and The T-site, which is fully occupied by Si4+ has four 161.25(4) for petedunnite. Both angles increase with an different bond lengths with the average values T– increasing Zn-content of the solid solution, implying O2(1)A=1.5906(12) A˚ , T–O1(1)A=1.6070(12) A˚ ,T– that the tetrahedral chains become increasingly stretched O3(1)A=1.6714(11) A˚ and T–O3(2)A= 1.6899(11) A˚ . (Table 7 and Fig. 5).

Fig. 3 T–O bond lengths along the join hedenbergite– petedunnite. Data are given in Table 6 559

Table 5 M2–O bond lengths of selected hedenbergite– M2–O2(2)D, M2–O1(1)A, M2–O3(1)D, M2–O3(2)D, petedunnite solid solution M2–O2(2)C (A˚ ) M2–O1(1)B (A˚ ) M2–O3(1)C (A˚ ) M2–O3(2)C (A˚ ) members pd91b 2.3394(13) 2.3589(14) 2.6060(14) 2.7366(14) hd2dg21 2.3384(10) 2.3605(10) 2.6058(10) 2.7362(10) hd3gb31 2.3413(13) 2.3601(12) 2.6118(13) 2.7326(12) hd4gb31 2.3422(12) 2.3638(12) 2.6164(13) 2.7312(12) hd5gb21 2.3430(11) 2.3610(11) 2.6148(12) 2.7332(11) hd7gb21 2.3436(13) 2.3638(14) 2.6246(14) 2.7322(14) hd8b41a 2.3441(11) 2.3647(11) 2.6229(11) 2.7312(11) hd10hk1a 2.3408(11) 2.3614(11) 2.6328(11) 2.7252(11)

Table 6 T–O bond lengths of selected hedenbergite– T–O2(1)A (A˚ ) T–O1(1)A (A˚ ) T–O3(1)A (A˚ ) T–O3(2)A (A˚ ) petedunnite solid solution members pd91b 1.5893(14) 1.6067(15) 1.6695(14) 1.6909(13) hd2dg21 1.5908(9) 1.6080(10) 1.6692(9) 1.6908(9) hd3gb31 1.5912(13) 1.6091(13) 1.6726(12) 1.6875(12) hd4gb31 1.5890(12) 1.6054(13) 1.6730(12) 1.6902(12) hd5gb21 1.5901(11) 1.6073(12) 1.6735(10) 1.6886(11) hd7gb21 1.5925(14) 1.6049(14) 1.6675(13) 1.6891(13) hd8b41a 1.5906(11) 1.6077(11) 1.6732(10) 1.6924(10) hd10hk1a 1.5909(11) 1.6069(11) 1.6726(10) 1.6898(10)

Fig. 4 Part of the petedunnite structure showing an ‘‘O’’- rotation of the SiO4 tetrahedral and the bridge angles of the T- chain

cates occupies an octahedral coordination only in high- Discussion pressure phases like petedunnite (Ohashi et al. 1996), hedenbergite–petedunnite solid solution (this study) and Data on phase stability and the results of structural ZnSiO3 (Morimoto et al. 1975). Furthermore this is investigation support the conclusion that Zn2+ in sili- 560

Fig. 5 T-bridge angles along the join hedenbergite– petedunnite. Data are given in Table 7

Fig. 6 Mean quadratic elongation and octahedral angle variance along the join hedenbergite-petedunnite

Table 7 Bridge angles of the T-chain of selected hedenbergite– petedunnite solid solution members supported by phase equilibrium studies revealing a wide O3(1)D-O3(2) O2(2)D-O3(2) P–T range, where hedenbergite is stable but a stability D-O3(1)D () D-O2(1)D () ﬁeld for petedunnite limited to higher pressures (Huber et al. 2004b). In the mentioned structures the M1-octa- pd91b 165.17(4) 161.25(4) hedron shows an increasing distortion with increasing hd2dg21 165.21(4) 161.25(4) Zn-content. As stated above, there is a large number of hd3gb31 165.20(4) 161.06(4) 2+ hd4gb31 164.89(4) 160.96(4) structures conﬁrming that Zn prefers a tetrahedral hd5gb21 165.19(4) 160.98(4) coordination, for example, in willemite (Zn2SiO4; Si- hd7gb21 164.75(4) 160.90(4) monov et al. 1977), hardystonite (Ca2ZnSi2O7; Warren hd8b41a 164.80(4) 160.70(4) and Trautz 1930) gahnite (ZnAl O ; Saalfeld 1964) and hd10hk1a 164.48(4) 160.39(4) 2 4 CaZnSi3O8 (Heuer et al. 1998). 561

Fig. 7 Quadrupole splitting of ferrous iron on octahedral M1 site at room temperature in synthetic hedenbergite– petedunnite solid solutions as function of mean quadratic elongation and octahedral angle variance

Correlation of structural changes with results versus the increasing Zn content of the solid solution. If of 57Fe Mo¨ ßbauer spectroscopy one uses an interpolation of the development of the quadrupole splitting, DE, published in Huber et al. The structural changes within the solid solution series (2004a), the values can be matched to the composition of hedenbergite–petedunnite, which are dominated by the the measured single crystals. The result is shown in changing distortion of the M1 site are in good agreement Fig. 7 and confirms the decrease of DE, which is already with results of 57Fe Mo¨ ssbauer spectroscopy published reported in Huber et al. (2004a) with additional data. in an earlier work dealing with the same material but The change of the quadrupole splittings across the crystalline powders (Huber et al. 2004a). According to join hedenbergite–petedunnite reflects a variation of the their data, the character of the chemical bonding does electric field gradient at the nucleus that can be attrib- not change by substituting Zn in hedenbergite, as dem- uted to an increasing distortion of the M1 site with onstrated by a constant isomer shift. In turn the quad- increasing petedunnite component. The present case is rupole splitting of ferrous iron on the M1 site is strongly another example where the quadrupole splitting of Fe2+ affected by composition along the binary joins heden- on an octahedral site decreases with increasing site dis- bergite–petedunnite and decreases with increasing pete- tortion as described by Ingalls (1964). However, it dunnite component. should be noted that structural refinements on single- The mean quadratic elongation, koct (Robinson et al. crystal diffraction data result in averaged structures and 1971), serves as a quantitative measure of the distortion it is not necessarily valid that the averaged octahedral of the coordination polyhedra due to different bond site is representative of individual sites occupied by iron. lengths and is defined by: The 57Fe Mo¨ ßbauer spectroscopy is sensitive to the local environment of all sites solely occupied by iron, which X6 . 2 may differ from the averaged octahedron. hik ¼ ðÞl =l 6; oct i o Comparable results are reported for the hedenberg- i¼1 ite–diopside solid solution (Dollase and Gustafson 2+ where lo is the center-to-vertex distance for a regular 1982), where the quadrupole splitting of Fe on M1 octahedron whose volume is equal to that of the strained also decreases with increasing distortion and increasing 2+ or distorted octahedron with bond lengths li. Mg content of this site. Since the mean quadratic elongation only contains the contributions of the different bond lengths, one additionally has to consider the octahedral angle vari- Summary 2 ance, rhðoctÞ (Robinson et al. 1971), measuring the deviation of the angles between the bonds in a distorted Clinopyroxene single crystals along the join hedenberg- octahedron, hi, from the ideal value of 90 in an undis- ite–petedunnite were synthesized with sizes upto torted octahedron. The octahedral angle variance is gi- 200 · 200 · 300 lm from highly unstable initial oxide ven by mixtures at temperatures of 825–1200C and pressures of 0.5–2.5 GPa. X12 . 2 2 Their chemical compositions were determined by r ¼ ðÞh 90 11: hðoctÞ i electron microprobe analysis, which confirms that Zn2+ i¼1 exclusively substitutes for Fe2+, whereas the Ca- and Si- Figure 6 shows the increasing mean quadratic elon- contents were not significantly below one and two for- gation and octahedral angle variance of the M1 site mula units, respectively. 562

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